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-        [大二寒假] 科学文章写作 | Writing in the Sciences
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-<a class="md-skip" href="#大一春夏-概率论与数理统计">
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-              [大一春夏] 概率论与数理统计
+              🔮 概率论与数理统计
             
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-        [大一秋冬] C小程 琐碎知识点整理
+        🔮 C小程 琐碎知识点整理
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-<a href="./">[大一春夏] 概率论与数理统计</a>
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+          🔮 概率论与数理统计
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-        [大一暑假] Deep Learning for Computer Vision | CS231N
+        🔮 Deep Learning for Computer Vision | CS231N
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-        [大一暑假] 计算机系统概论 | Introduction to Computing Systems
+        🔮 计算机系统概论 | Introduction to Computing Systems
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-<a href="../D2QD_DigitalDesign/">[大二秋冬] 数字逻辑设计 | Digital Design</a>
+<a href="../D2QD_DigitalDesign/">💎 数字逻辑设计 | Digital Design</a>
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+          💎 数字逻辑设计 | Digital Design
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-<a href="../D2QD_Intro2CV/">[大二秋冬] 计算机视觉导论 | I2CV</a>
+<a href="../D2QD_Intro2CV/">💎 计算机视觉导论 | I2CV</a>
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-          [大二秋冬] 计算机视觉导论 | I2CV
+          💎 计算机视觉导论 | I2CV
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 <a class="md-nav__link" href="../D2HJ_StanfordWriting/">
-        [大二寒假] 科学文章写作 | Writing in the Sciences
+        🔮 科学文章写作 | Writing in the Sciences
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-<a href="../D2CX_ComputerOrganization/">[大二春夏] 计算机组成 | Computer Organization</a>
+<a href="../D2CX_ComputerOrganization/">🔮 计算机组成 | Computer Organization</a>
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+          🔮 计算机组成 | Computer Organization
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-<a href="../D2CX_AdvancedDataStructure/">[大二春夏] 高级数据结构 | Advanced Data Structure</a>
+<a href="../D2CX_AdvancedDataStructure/">💎 高级数据结构 | Advanced Data Structure</a>
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-          [大二春夏] 高级数据结构 | Advanced Data Structure
+          💎 高级数据结构 | Advanced Data Structure
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-<a href="../D3QD_OperatingSystem/">[大三秋冬] 操作系统 | Operating System</a>
+<a href="../D3QD_OperatingSystem/">💎 操作系统 | Operating System</a>
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+          💎 操作系统 | Operating System
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-          [大三秋冬] 计算理论 | Theorem of Computing
+          🔮 计算理论 | Theorem of Computing
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+          🔮 计算理论 | Theorem of Computing
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+<h1 id="-概率论与数理统计">🔮 概率论与数理统计<a class="headerlink" href="#-概率论与数理统计" title="Permanent link">¶</a></h1>
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 <div class="admonition info">
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@@ -1121,7 +1121,7 @@ <h1 id="大一春夏-概率论与数理统计">[大一春夏] 概率论与数理
 <small>
     
       最后更新:
-      <span class="git-revision-date-localized-plugin git-revision-date-localized-plugin-datetime">2023年6月28日 00:12:38</span>
+      <span class="git-revision-date-localized-plugin git-revision-date-localized-plugin-datetime">2023年11月22日 11:17:54</span>
 <br/>
         创建日期:
         <span class="git-revision-date-localized-plugin git-revision-date-localized-plugin-datetime">2022年12月12日 16:29:19</span>
diff --git a/cour_note/D1QD_CXiaoCheng/index.html b/cour_note/D1QD_CXiaoCheng/index.html
index 65832ed1..c2153d39 100644
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+++ b/cour_note/D1QD_CXiaoCheng/index.html
@@ -11,7 +11,7 @@
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-<a class="md-skip" href="#大一秋冬-c小程-琐碎知识点整理">
+<a class="md-skip" href="#-c小程-琐碎知识点整理">
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-              [大一秋冬] C小程 琐碎知识点整理
+              🔮 C小程 琐碎知识点整理
             
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+          🔮 C小程 琐碎知识点整理
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+        🔮 C小程 琐碎知识点整理
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-<a href="../D1CX_ProbabilityAndStatistics/">[大一春夏] 概率论与数理统计</a>
+<a href="../D1CX_ProbabilityAndStatistics/">🔮 概率论与数理统计</a>
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-        [大一暑假] Deep Learning for Computer Vision | CS231N
+        🔮 Deep Learning for Computer Vision | CS231N
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-        [大一暑假] 计算机系统概论 | Introduction to Computing Systems
+        🔮 计算机系统概论 | Introduction to Computing Systems
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-<a href="../D2QD_DigitalDesign/">[大二秋冬] 数字逻辑设计 | Digital Design</a>
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+          💎 数字逻辑设计 | Digital Design
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-<a href="../D2QD_Intro2CV/">[大二秋冬] 计算机视觉导论 | I2CV</a>
+<a href="../D2QD_Intro2CV/">💎 计算机视觉导论 | I2CV</a>
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-        [大二寒假] 科学文章写作 | Writing in the Sciences
+        🔮 科学文章写作 | Writing in the Sciences
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-<a href="../D2CX_ComputerOrganization/">[大二春夏] 计算机组成 | Computer Organization</a>
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+          🔮 计算机组成 | Computer Organization
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-          [大二春夏] 高级数据结构 | Advanced Data Structure
+          💎 高级数据结构 | Advanced Data Structure
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@@ -912,7 +912,7 @@
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-<a href="../D3QD_OperatingSystem/">[大三秋冬] 操作系统 | Operating System</a>
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-          [大三秋冬] 操作系统 | Operating System
+          💎 操作系统 | Operating System
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-          [大三秋冬] 计算理论 | Theorem of Computing
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-          [大三秋冬] 计算理论 | Theorem of Computing
+          🔮 计算理论 | Theorem of Computing
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@@ -1269,9 +1269,9 @@
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-<h1 id="大一秋冬-c小程-琐碎知识点整理">[大一秋冬] C小程 琐碎知识点整理<a class="headerlink" href="#大一秋冬-c小程-琐碎知识点整理" title="Permanent link">¶</a></h1>
+<h1 id="-c小程-琐碎知识点整理">🔮 C小程 琐碎知识点整理<a class="headerlink" href="#-c小程-琐碎知识点整理" title="Permanent link">¶</a></h1>
 <div style="margin-top: -30px; font-size: 0.75em; opacity: 0.7;">
-<p><span class="twemoji"><svg viewbox="0 0 24 24" xmlns="http://www.w3.org/2000/svg"><path d="M12 2A10 10 0 0 0 2 12a10 10 0 0 0 10 10 10 10 0 0 0 10-10h-2a8 8 0 0 1-8 8 8 8 0 0 1-8-8 8 8 0 0 1 8-8V2m6.78 1a.69.69 0 0 0-.48.2l-1.22 1.21 2.5 2.5L20.8 5.7c.26-.26.26-.7 0-.95L19.25 3.2c-.13-.13-.3-.2-.47-.2m-2.41 2.12L9 12.5V15h2.5l7.37-7.38-2.5-2.5Z"></path></svg></span> 约 4830 个字 <span class="twemoji"><svg viewbox="0 0 640 512" xmlns="http://www.w3.org/2000/svg"><!--! Font Awesome Free 6.2.1 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2022 Fonticons, Inc.--><path d="M392.8 1.2c-17-4.9-34.7 5-39.6 22l-128 448c-4.9 17 5 34.7 22 39.6s34.7-5 39.6-22l128-448c4.9-17-5-34.7-22-39.6zm80.6 120.1c-12.5 12.5-12.5 32.8 0 45.3l89.3 89.4-89.4 89.4c-12.5 12.5-12.5 32.8 0 45.3s32.8 12.5 45.3 0l112-112c12.5-12.5 12.5-32.8 0-45.3l-112-112c-12.5-12.5-32.8-12.5-45.3 0zm-306.7 0c-12.5-12.5-32.8-12.5-45.3 0l-112 112c-12.5 12.5-12.5 32.8 0 45.3l112 112c12.5 12.5 32.8 12.5 45.3 0s12.5-32.8 0-45.3L77.3 256l89.4-89.4c12.5-12.5 12.5-32.8 0-45.3z"></path></svg></span> 53 行代码 <span class="twemoji"><svg viewbox="0 0 24 24" xmlns="http://www.w3.org/2000/svg"><path d="M12 20c4.42 0 8-3.58 8-8s-3.58-8-8-8-8 3.58-8 8 3.58 8 8 8m0-18c5.5 0 10 4.5 10 10s-4.5 10-10 10C6.47 22 2 17.5 2 12S6.5 2 12 2m.5 11H11V7h1.5v4.26l3.7-2.13.75 1.3L12.5 13Z"></path></svg></span> 预计阅读时间 17 分钟</p>
+<p><span class="twemoji"><svg viewbox="0 0 24 24" xmlns="http://www.w3.org/2000/svg"><path d="M12 2A10 10 0 0 0 2 12a10 10 0 0 0 10 10 10 10 0 0 0 10-10h-2a8 8 0 0 1-8 8 8 8 0 0 1-8-8 8 8 0 0 1 8-8V2m6.78 1a.69.69 0 0 0-.48.2l-1.22 1.21 2.5 2.5L20.8 5.7c.26-.26.26-.7 0-.95L19.25 3.2c-.13-.13-.3-.2-.47-.2m-2.41 2.12L9 12.5V15h2.5l7.37-7.38-2.5-2.5Z"></path></svg></span> 约 4826 个字 <span class="twemoji"><svg viewbox="0 0 640 512" xmlns="http://www.w3.org/2000/svg"><!--! Font Awesome Free 6.2.1 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2022 Fonticons, Inc.--><path d="M392.8 1.2c-17-4.9-34.7 5-39.6 22l-128 448c-4.9 17 5 34.7 22 39.6s34.7-5 39.6-22l128-448c4.9-17-5-34.7-22-39.6zm80.6 120.1c-12.5 12.5-12.5 32.8 0 45.3l89.3 89.4-89.4 89.4c-12.5 12.5-12.5 32.8 0 45.3s32.8 12.5 45.3 0l112-112c12.5-12.5 12.5-32.8 0-45.3l-112-112c-12.5-12.5-32.8-12.5-45.3 0zm-306.7 0c-12.5-12.5-32.8-12.5-45.3 0l-112 112c-12.5 12.5-12.5 32.8 0 45.3l112 112c12.5 12.5 32.8 12.5 45.3 0s12.5-32.8 0-45.3L77.3 256l89.4-89.4c12.5-12.5 12.5-32.8 0-45.3z"></path></svg></span> 53 行代码 <span class="twemoji"><svg viewbox="0 0 24 24" xmlns="http://www.w3.org/2000/svg"><path d="M12 20c4.42 0 8-3.58 8-8s-3.58-8-8-8-8 3.58-8 8 3.58 8 8 8m0-18c5.5 0 10 4.5 10 10s-4.5 10-10 10C6.47 22 2 17.5 2 12S6.5 2 12 2m.5 11H11V7h1.5v4.26l3.7-2.13.75 1.3L12.5 13Z"></path></svg></span> 预计阅读时间 17 分钟</p>
 </div>
 <blockquote>
 <p>用来整理C小程的一些细碎知识点。
@@ -2473,7 +2473,7 @@ <h2 id="其他">其他<a class="headerlink" href="#其他" title="Permanent link
 <small>
     
       最后更新:
-      <span class="git-revision-date-localized-plugin git-revision-date-localized-plugin-datetime">2023年11月7日 11:54:07</span>
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 <br/>
         创建日期:
         <span class="git-revision-date-localized-plugin git-revision-date-localized-plugin-datetime">2022年10月31日 14:53:50</span>
diff --git a/cour_note/D1SJ_Intro2CS/index.html b/cour_note/D1SJ_Intro2CS/index.html
index 2808156f..4f487615 100644
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-        [大一秋冬] C小程 琐碎知识点整理
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+          💎 数字逻辑设计 | Digital Design
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-          [大二秋冬] 计算机视觉导论 | I2CV
+          💎 计算机视觉导论 | I2CV
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-        [大二寒假] 科学文章写作 | Writing in the Sciences
+        🔮 科学文章写作 | Writing in the Sciences
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-<a href="../D2CX_ComputerOrganization/">[大二春夏] 计算机组成 | Computer Organization</a>
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+<h1 id="-计算机系统概论--introduction-to-computing-systems">🔮 计算机系统概论 | Introduction to Computing Systems<a class="headerlink" href="#-计算机系统概论--introduction-to-computing-systems" title="Permanent link">¶</a></h1>
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+<p><span class="twemoji"><svg viewbox="0 0 24 24" xmlns="http://www.w3.org/2000/svg"><path d="M12 2A10 10 0 0 0 2 12a10 10 0 0 0 10 10 10 10 0 0 0 10-10h-2a8 8 0 0 1-8 8 8 8 0 0 1-8-8 8 8 0 0 1 8-8V2m6.78 1a.69.69 0 0 0-.48.2l-1.22 1.21 2.5 2.5L20.8 5.7c.26-.26.26-.7 0-.95L19.25 3.2c-.13-.13-.3-.2-.47-.2m-2.41 2.12L9 12.5V15h2.5l7.37-7.38-2.5-2.5Z"></path></svg></span> 约 12 个字 </p>
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 <ul>
 <li><a href="https://www.yuque.com/isshikixiu/codes/ics">https://www.yuque.com/isshikixiu/codes/ics</a></li>
@@ -1103,7 +1103,7 @@ <h1 id="大一暑假-计算机系统概论--introduction-to-computing-systems">[
 <small>
     
       最后更新:
-      <span class="git-revision-date-localized-plugin git-revision-date-localized-plugin-datetime">2023年1月12日 10:56:39</span>
+      <span class="git-revision-date-localized-plugin git-revision-date-localized-plugin-datetime">2023年11月22日 11:17:54</span>
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         创建日期:
         <span class="git-revision-date-localized-plugin git-revision-date-localized-plugin-datetime">2023年1月12日 10:56:39</span>
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-<title>[大一暑假] Deep Learning for Computer Vision | CS231N - Isshiki修's Notebook</title>
+<title>🔮 Deep Learning for Computer Vision | CS231N - Isshiki修's Notebook</title>
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-<a class="md-skip" href="#大一暑假-deep-learning-for-computer-vision--cs231n">
+<a class="md-skip" href="#-deep-learning-for-computer-vision--cs231n">
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+        🔮 C小程 琐碎知识点整理
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-<a href="../D1CX_ProbabilityAndStatistics/">[大一春夏] 概率论与数理统计</a>
+<a href="../D1CX_ProbabilityAndStatistics/">🔮 概率论与数理统计</a>
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-<a href="../D2QD_DigitalDesign/">[大二秋冬] 数字逻辑设计 | Digital Design</a>
+<a href="../D2QD_DigitalDesign/">💎 数字逻辑设计 | Digital Design</a>
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-        [大二寒假] 科学文章写作 | Writing in the Sciences
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-              [大二春夏] 高级数据结构 | Advanced Data Structure
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-        [大二寒假] 科学文章写作 | Writing in the Sciences
+        🔮 科学文章写作 | Writing in the Sciences
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-<a href="../D2CX_ComputerOrganization/">[大二春夏] 计算机组成 | Computer Organization</a>
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+          🔮 计算机组成 | Computer Organization
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-<a href="../D3QD_OperatingSystem/">[大三秋冬] 操作系统 | Operating System</a>
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+          💎 操作系统 | Operating System
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+<h1 id="-高级数据结构--advanced-data-structure">💎 高级数据结构 | Advanced Data Structure<a class="headerlink" href="#-高级数据结构--advanced-data-structure" title="Permanent link">¶</a></h1>
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 <div class="admonition info">
 <p class="admonition-title">课程信息</p>
@@ -1144,7 +1144,7 @@ <h1 id="大二春夏-高级数据结构--advanced-data-structure">[大二春夏]
 <small>
     
       最后更新:
-      <span class="git-revision-date-localized-plugin git-revision-date-localized-plugin-datetime">2023年6月30日 09:22:55</span>
+      <span class="git-revision-date-localized-plugin git-revision-date-localized-plugin-datetime">2023年11月22日 11:17:54</span>
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         创建日期:
         <span class="git-revision-date-localized-plugin git-revision-date-localized-plugin-datetime">2023年2月27日 20:16:13</span>
diff --git a/cour_note/D2CX_ComputerOrganization/index.html b/cour_note/D2CX_ComputerOrganization/index.html
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-<title>[大二春夏] 计算机组成 | Computer Organization - Isshiki修's Notebook</title>
+<title>🔮 计算机组成 | Computer Organization - Isshiki修's Notebook</title>
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@@ -42,7 +42,7 @@
 <input autocomplete="off" class="md-toggle" data-md-toggle="search" id="__search" type="checkbox"/>
 <label class="md-overlay" for="__drawer"></label>
 <div data-md-component="skip">
-<a class="md-skip" href="#大二春夏-计算机组成--computer-organization">
+<a class="md-skip" href="#-计算机组成--computer-organization">
           跳转至
         </a>
 </div>
@@ -66,7 +66,7 @@
 <div class="md-header__topic" data-md-component="header-topic">
 <span class="md-ellipsis">
             
-              [大二春夏] 计算机组成 | Computer Organization
+              🔮 计算机组成 | Computer Organization
             
           </span>
 </div>
@@ -496,13 +496,13 @@
 <ul class="md-nav__list" data-md-scrollfix="">
 <li class="md-nav__item">
 <a class="md-nav__link" href="../D1QD_CXiaoCheng/">
-        [大一秋冬] C小程 琐碎知识点整理
+        🔮 C小程 琐碎知识点整理
       </a>
 </li>
 <li class="md-nav__item md-nav__item--nested">
 <input class="md-nav__toggle md-toggle" id="__nav_3_3" type="checkbox"/>
 <div class="md-nav__link md-nav__link--index">
-<a href="../D1CX_ProbabilityAndStatistics/">[大一春夏] 概率论与数理统计</a>
+<a href="../D1CX_ProbabilityAndStatistics/">🔮 概率论与数理统计</a>
 <label for="__nav_3_3">
 <span class="md-nav__icon md-icon"></span>
 </label>
@@ -510,7 +510,7 @@
 <nav aria-expanded="false" aria-labelledby="__nav_3_3_label" class="md-nav" data-md-level="2">
 <label class="md-nav__title" for="__nav_3_3">
 <span class="md-nav__icon md-icon"></span>
-          [大一春夏] 概率论与数理统计
+          🔮 概率论与数理统计
         </label>
 <ul class="md-nav__list" data-md-scrollfix="">
 <li class="md-nav__item">
@@ -558,18 +558,18 @@
 </li>
 <li class="md-nav__item">
 <a class="md-nav__link" href="../D1SJ_StanfordCS231n/">
-        [大一暑假] Deep Learning for Computer Vision | CS231N
+        🔮 Deep Learning for Computer Vision | CS231N
       </a>
 </li>
 <li class="md-nav__item">
 <a class="md-nav__link" href="../D1SJ_Intro2CS/">
-        [大一暑假] 计算机系统概论 | Introduction to Computing Systems
+        🔮 计算机系统概论 | Introduction to Computing Systems
       </a>
 </li>
 <li class="md-nav__item md-nav__item--nested">
 <input class="md-nav__toggle md-toggle" id="__nav_3_6" type="checkbox"/>
 <div class="md-nav__link md-nav__link--index">
-<a href="../D2QD_DigitalDesign/">[大二秋冬] 数字逻辑设计 | Digital Design</a>
+<a href="../D2QD_DigitalDesign/">💎 数字逻辑设计 | Digital Design</a>
 <label for="__nav_3_6">
 <span class="md-nav__icon md-icon"></span>
 </label>
@@ -577,7 +577,7 @@
 <nav aria-expanded="false" aria-labelledby="__nav_3_6_label" class="md-nav" data-md-level="2">
 <label class="md-nav__title" for="__nav_3_6">
 <span class="md-nav__icon md-icon"></span>
-          [大二秋冬] 数字逻辑设计 | Digital Design
+          💎 数字逻辑设计 | Digital Design
         </label>
 <ul class="md-nav__list" data-md-scrollfix="">
 <li class="md-nav__item">
@@ -621,7 +621,7 @@
 <li class="md-nav__item md-nav__item--nested">
 <input class="md-nav__toggle md-toggle" id="__nav_3_7" type="checkbox"/>
 <div class="md-nav__link md-nav__link--index">
-<a href="../D2QD_Intro2CV/">[大二秋冬] 计算机视觉导论 | I2CV</a>
+<a href="../D2QD_Intro2CV/">💎 计算机视觉导论 | I2CV</a>
 <label for="__nav_3_7">
 <span class="md-nav__icon md-icon"></span>
 </label>
@@ -629,7 +629,7 @@
 <nav aria-expanded="false" aria-labelledby="__nav_3_7_label" class="md-nav" data-md-level="2">
 <label class="md-nav__title" for="__nav_3_7">
 <span class="md-nav__icon md-icon"></span>
-          [大二秋冬] 计算机视觉导论 | I2CV
+          💎 计算机视觉导论 | I2CV
         </label>
 <ul class="md-nav__list" data-md-scrollfix="">
 <li class="md-nav__item">
@@ -702,18 +702,18 @@
 </li>
 <li class="md-nav__item">
 <a class="md-nav__link" href="../D2HJ_StanfordWriting/">
-        [大二寒假] 科学文章写作 | Writing in the Sciences
+        🔮 科学文章写作 | Writing in the Sciences
       </a>
 </li>
 <li class="md-nav__item md-nav__item--active md-nav__item--nested">
 <input checked="" class="md-nav__toggle md-toggle" id="__nav_3_9" type="checkbox"/>
 <div class="md-nav__link md-nav__link--index md-nav__link--active">
-<a href="./">[大二春夏] 计算机组成 | Computer Organization</a>
+<a href="./">🔮 计算机组成 | Computer Organization</a>
 </div>
 <nav aria-expanded="true" aria-labelledby="__nav_3_9_label" class="md-nav" data-md-level="2">
 <label class="md-nav__title" for="__nav_3_9">
 <span class="md-nav__icon md-icon"></span>
-          [大二春夏] 计算机组成 | Computer Organization
+          🔮 计算机组成 | Computer Organization
         </label>
 <ul class="md-nav__list" data-md-scrollfix="">
 </ul>
@@ -722,7 +722,7 @@
 <li class="md-nav__item md-nav__item--nested">
 <input class="md-nav__toggle md-toggle" id="__nav_3_10" type="checkbox"/>
 <div class="md-nav__link md-nav__link--index">
-<a href="../D2CX_AdvancedDataStructure/">[大二春夏] 高级数据结构 | Advanced Data Structure</a>
+<a href="../D2CX_AdvancedDataStructure/">💎 高级数据结构 | Advanced Data Structure</a>
 <label for="__nav_3_10">
 <span class="md-nav__icon md-icon"></span>
 </label>
@@ -730,7 +730,7 @@
 <nav aria-expanded="false" aria-labelledby="__nav_3_10_label" class="md-nav" data-md-level="2">
 <label class="md-nav__title" for="__nav_3_10">
 <span class="md-nav__icon md-icon"></span>
-          [大二春夏] 高级数据结构 | Advanced Data Structure
+          💎 高级数据结构 | Advanced Data Structure
         </label>
 <ul class="md-nav__list" data-md-scrollfix="">
 <li class="md-nav__item">
@@ -819,7 +819,7 @@
 <li class="md-nav__item md-nav__item--nested">
 <input class="md-nav__toggle md-toggle" id="__nav_3_11" type="checkbox"/>
 <div class="md-nav__link md-nav__link--index">
-<a href="../D3QD_OperatingSystem/">[大三秋冬] 操作系统 | Operating System</a>
+<a href="../D3QD_OperatingSystem/">💎 操作系统 | Operating System</a>
 <label for="__nav_3_11">
 <span class="md-nav__icon md-icon"></span>
 </label>
@@ -827,7 +827,7 @@
 <nav aria-expanded="false" aria-labelledby="__nav_3_11_label" class="md-nav" data-md-level="2">
 <label class="md-nav__title" for="__nav_3_11">
 <span class="md-nav__icon md-icon"></span>
-          [大三秋冬] 操作系统 | Operating System
+          💎 操作系统 | Operating System
         </label>
 <ul class="md-nav__list" data-md-scrollfix="">
 <li class="md-nav__item">
@@ -911,13 +911,13 @@
 <li class="md-nav__item md-nav__item--nested">
 <input class="md-nav__toggle md-toggle" id="__nav_3_12" type="checkbox"/>
 <label class="md-nav__link" for="__nav_3_12" id="__nav_3_12_label" tabindex="0">
-          [大三秋冬] 计算理论 | Theorem of Computing
+          🔮 计算理论 | Theorem of Computing
           <span class="md-nav__icon md-icon"></span>
 </label>
 <nav aria-expanded="false" aria-labelledby="__nav_3_12_label" class="md-nav" data-md-level="2">
 <label class="md-nav__title" for="__nav_3_12">
 <span class="md-nav__icon md-icon"></span>
-          [大三秋冬] 计算理论 | Theorem of Computing
+          🔮 计算理论 | Theorem of Computing
         </label>
 <ul class="md-nav__list" data-md-scrollfix="">
 <li class="md-nav__item">
@@ -1090,9 +1090,9 @@
 </div>
 <div class="md-content" data-md-component="content">
 <article class="md-content__inner md-typeset">
-<h1 id="大二春夏-计算机组成--computer-organization">[大二春夏] 计算机组成 | Computer Organization<a class="headerlink" href="#大二春夏-计算机组成--computer-organization" title="Permanent link">¶</a></h1>
+<h1 id="-计算机组成--computer-organization">🔮 计算机组成 | Computer Organization<a class="headerlink" href="#-计算机组成--computer-organization" title="Permanent link">¶</a></h1>
 <div style="margin-top: -30px; font-size: 0.75em; opacity: 0.7;">
-<p><span class="twemoji"><svg viewbox="0 0 24 24" xmlns="http://www.w3.org/2000/svg"><path d="M12 2A10 10 0 0 0 2 12a10 10 0 0 0 10 10 10 10 0 0 0 10-10h-2a8 8 0 0 1-8 8 8 8 0 0 1-8-8 8 8 0 0 1 8-8V2m6.78 1a.69.69 0 0 0-.48.2l-1.22 1.21 2.5 2.5L20.8 5.7c.26-.26.26-.7 0-.95L19.25 3.2c-.13-.13-.3-.2-.47-.2m-2.41 2.12L9 12.5V15h2.5l7.37-7.38-2.5-2.5Z"></path></svg></span> 约 61 个字 </p>
+<p><span class="twemoji"><svg viewbox="0 0 24 24" xmlns="http://www.w3.org/2000/svg"><path d="M12 2A10 10 0 0 0 2 12a10 10 0 0 0 10 10 10 10 0 0 0 10-10h-2a8 8 0 0 1-8 8 8 8 0 0 1-8-8 8 8 0 0 1 8-8V2m6.78 1a.69.69 0 0 0-.48.2l-1.22 1.21 2.5 2.5L20.8 5.7c.26-.26.26-.7 0-.95L19.25 3.2c-.13-.13-.3-.2-.47-.2m-2.41 2.12L9 12.5V15h2.5l7.37-7.38-2.5-2.5Z"></path></svg></span> 约 57 个字 </p>
 </div>
 <p>由于笔记太浪费时间了，我学习计组使用的是 xxjj 的笔记：</p>
 <p><a href="https://xuan-insr.github.io/computer_organization/1_prelude/">https://xuan-insr.github.io/computer_organization/1_prelude/</a></p>
@@ -1102,7 +1102,7 @@ <h1 id="大二春夏-计算机组成--computer-organization">[大二春夏] 计
 <small>
     
       最后更新:
-      <span class="git-revision-date-localized-plugin git-revision-date-localized-plugin-datetime">2023年5月4日 09:00:39</span>
+      <span class="git-revision-date-localized-plugin git-revision-date-localized-plugin-datetime">2023年11月22日 11:17:54</span>
 <br/>
         创建日期:
         <span class="git-revision-date-localized-plugin git-revision-date-localized-plugin-datetime">2023年1月12日 10:56:39</span>
diff --git a/cour_note/D2HJ_StanfordWriting/index.html b/cour_note/D2HJ_StanfordWriting/index.html
index 5d9ee291..0a720b7b 100644
--- a/cour_note/D2HJ_StanfordWriting/index.html
+++ b/cour_note/D2HJ_StanfordWriting/index.html
@@ -11,7 +11,7 @@
 <link href="../D2CX_ComputerOrganization/" rel="next"/>
 <link href="../../_assets/iro/IroPatch_Brown.ico" rel="icon"/>
 <meta content="mkdocs-1.4.2, mkdocs-material-9.0.12" name="generator"/>
-<title>[大二寒假] 科学文章写作 | Writing in the Sciences - Isshiki修's Notebook</title>
+<title>🔮 科学文章写作 | Writing in the Sciences - Isshiki修's Notebook</title>
 <link href="../../assets/stylesheets/main.0d440cfe.min.css" rel="stylesheet"/>
 <link href="../../assets/stylesheets/palette.2505c338.min.css" rel="stylesheet"/>
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+<a class="md-skip" href="#-科学文章写作--writing-in-the-sciences">
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-              [大二寒假] 科学文章写作 | Writing in the Sciences
+              🔮 科学文章写作 | Writing in the Sciences
             
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-        [大一秋冬] C小程 琐碎知识点整理
+        🔮 C小程 琐碎知识点整理
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-<a href="../D1CX_ProbabilityAndStatistics/">[大一春夏] 概率论与数理统计</a>
+<a href="../D1CX_ProbabilityAndStatistics/">🔮 概率论与数理统计</a>
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-          [大一春夏] 概率论与数理统计
+          🔮 概率论与数理统计
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-        [大一暑假] Deep Learning for Computer Vision | CS231N
+        🔮 Deep Learning for Computer Vision | CS231N
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 <a class="md-nav__link" href="../D1SJ_Intro2CS/">
-        [大一暑假] 计算机系统概论 | Introduction to Computing Systems
+        🔮 计算机系统概论 | Introduction to Computing Systems
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-<a href="../D2QD_DigitalDesign/">[大二秋冬] 数字逻辑设计 | Digital Design</a>
+<a href="../D2QD_DigitalDesign/">💎 数字逻辑设计 | Digital Design</a>
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-          [大二秋冬] 数字逻辑设计 | Digital Design
+          💎 数字逻辑设计 | Digital Design
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-<a href="../D2QD_Intro2CV/">[大二秋冬] 计算机视觉导论 | I2CV</a>
+<a href="../D2QD_Intro2CV/">💎 计算机视觉导论 | I2CV</a>
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-          [大二秋冬] 计算机视觉导论 | I2CV
+          💎 计算机视觉导论 | I2CV
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-        [大二寒假] 科学文章写作 | Writing in the Sciences
+        🔮 科学文章写作 | Writing in the Sciences
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-<a href="../D2CX_ComputerOrganization/">[大二春夏] 计算机组成 | Computer Organization</a>
+<a href="../D2CX_ComputerOrganization/">🔮 计算机组成 | Computer Organization</a>
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-          [大二春夏] 计算机组成 | Computer Organization
+          🔮 计算机组成 | Computer Organization
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-<a href="../D2CX_AdvancedDataStructure/">[大二春夏] 高级数据结构 | Advanced Data Structure</a>
+<a href="../D2CX_AdvancedDataStructure/">💎 高级数据结构 | Advanced Data Structure</a>
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-          [大二春夏] 高级数据结构 | Advanced Data Structure
+          💎 高级数据结构 | Advanced Data Structure
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-<a href="../D3QD_OperatingSystem/">[大三秋冬] 操作系统 | Operating System</a>
+<a href="../D3QD_OperatingSystem/">💎 操作系统 | Operating System</a>
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-          [大三秋冬] 操作系统 | Operating System
+          💎 操作系统 | Operating System
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-          [大三秋冬] 计算理论 | Theorem of Computing
+          🔮 计算理论 | Theorem of Computing
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+          🔮 计算理论 | Theorem of Computing
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+<h1 id="-科学文章写作--writing-in-the-sciences">🔮 科学文章写作 | Writing in the Sciences<a class="headerlink" href="#-科学文章写作--writing-in-the-sciences" title="Permanent link">¶</a></h1>
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-        [大一暑假] 计算机系统概论 | Introduction to Computing Systems
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-        [大二寒假] 科学文章写作 | Writing in the Sciences
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-          [大三秋冬] 计算理论 | Theorem of Computing
+          🔮 计算理论 | Theorem of Computing
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diff --git a/cour_note/D2QD_DigitalDesign/index.html b/cour_note/D2QD_DigitalDesign/index.html
index e017313e..9b156c3b 100644
--- a/cour_note/D2QD_DigitalDesign/index.html
+++ b/cour_note/D2QD_DigitalDesign/index.html
@@ -11,7 +11,7 @@
 <link href="Chap01/" rel="next"/>
 <link href="../../_assets/iro/IroPatch_Brown.ico" rel="icon"/>
 <meta content="mkdocs-1.4.2, mkdocs-material-9.0.12" name="generator"/>
-<title>[大二秋冬] 数字逻辑设计 | Digital Design - Isshiki修's Notebook</title>
+<title>🔮 数字逻辑设计 | Digital Design - Isshiki修's Notebook</title>
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-<a class="md-skip" href="#大二秋冬-数字逻辑设计--digital-design">
+<a class="md-skip" href="#-数字逻辑设计--digital-design">
           跳转至
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@@ -66,7 +66,7 @@
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-              [大二秋冬] 数字逻辑设计 | Digital Design
+              🔮 数字逻辑设计 | Digital Design
             
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-        [大一秋冬] C小程 琐碎知识点整理
+        🔮 C小程 琐碎知识点整理
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-<a href="../D1CX_ProbabilityAndStatistics/">[大一春夏] 概率论与数理统计</a>
+<a href="../D1CX_ProbabilityAndStatistics/">🔮 概率论与数理统计</a>
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-          [大一春夏] 概率论与数理统计
+          🔮 概率论与数理统计
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-        [大一暑假] Deep Learning for Computer Vision | CS231N
+        🔮 Deep Learning for Computer Vision | CS231N
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 <a class="md-nav__link" href="../D1SJ_Intro2CS/">
-        [大一暑假] 计算机系统概论 | Introduction to Computing Systems
+        🔮 计算机系统概论 | Introduction to Computing Systems
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-<a href="./">[大二秋冬] 数字逻辑设计 | Digital Design</a>
+<a href="./">💎 数字逻辑设计 | Digital Design</a>
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-          [大二秋冬] 数字逻辑设计 | Digital Design
+          💎 数字逻辑设计 | Digital Design
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-<a href="../D2QD_Intro2CV/">[大二秋冬] 计算机视觉导论 | I2CV</a>
+<a href="../D2QD_Intro2CV/">💎 计算机视觉导论 | I2CV</a>
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-          [大二秋冬] 计算机视觉导论 | I2CV
+          💎 计算机视觉导论 | I2CV
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-        [大二寒假] 科学文章写作 | Writing in the Sciences
+        🔮 科学文章写作 | Writing in the Sciences
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-<a href="../D2CX_ComputerOrganization/">[大二春夏] 计算机组成 | Computer Organization</a>
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+<h1 id="-数字逻辑设计--digital-design">🔮 数字逻辑设计 | Digital Design<a class="headerlink" href="#-数字逻辑设计--digital-design" title="Permanent link">¶</a></h1>
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       最后更新:
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+      <span class="git-revision-date-localized-plugin git-revision-date-localized-plugin-datetime">2023年11月22日 11:17:54</span>
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-        [大一暑假] 计算机系统概论 | Introduction to Computing Systems
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-<a class="md-skip" href="#大二学年-计算机视觉导论--introduction-to-computer-vision">
+<a class="md-skip" href="#-计算机视觉导论--introduction-to-computer-vision">
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-              [大二学年] 计算机视觉导论 | Introduction to Computer Vision
+              💎 计算机视觉导论 | Introduction to Computer Vision
             
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-        [大一秋冬] C小程 琐碎知识点整理
+        🔮 C小程 琐碎知识点整理
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-<a href="../D1CX_ProbabilityAndStatistics/">[大一春夏] 概率论与数理统计</a>
+<a href="../D1CX_ProbabilityAndStatistics/">🔮 概率论与数理统计</a>
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-          [大一春夏] 概率论与数理统计
+          🔮 概率论与数理统计
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-        [大一暑假] Deep Learning for Computer Vision | CS231N
+        🔮 Deep Learning for Computer Vision | CS231N
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-        [大一暑假] 计算机系统概论 | Introduction to Computing Systems
+        🔮 计算机系统概论 | Introduction to Computing Systems
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+          💎 数字逻辑设计 | Digital Design
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+<a href="./">💎 计算机视觉导论 | I2CV</a>
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-        [大二寒假] 科学文章写作 | Writing in the Sciences
+        🔮 科学文章写作 | Writing in the Sciences
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-<a href="../D2CX_ComputerOrganization/">[大二春夏] 计算机组成 | Computer Organization</a>
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-<a href="../D2CX_AdvancedDataStructure/">[大二春夏] 高级数据结构 | Advanced Data Structure</a>
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-        [大一暑假] 计算机系统概论 | Introduction to Computing Systems
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-        [大二寒假] 科学文章写作 | Writing in the Sciences
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-<a class="md-skip" href="#大三秋冬-操作系统--operating-system">
+<a class="md-skip" href="#-操作系统--operating-system">
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@@ -66,7 +66,7 @@
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-              [大三秋冬] 操作系统 | Operating System
+              💎 操作系统 | Operating System
             
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-        [大一秋冬] C小程 琐碎知识点整理
+        🔮 C小程 琐碎知识点整理
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-<a href="../D1CX_ProbabilityAndStatistics/">[大一春夏] 概率论与数理统计</a>
+<a href="../D1CX_ProbabilityAndStatistics/">🔮 概率论与数理统计</a>
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-          [大一春夏] 概率论与数理统计
+          🔮 概率论与数理统计
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-        [大一暑假] Deep Learning for Computer Vision | CS231N
+        🔮 Deep Learning for Computer Vision | CS231N
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 <a class="md-nav__link" href="../D1SJ_Intro2CS/">
-        [大一暑假] 计算机系统概论 | Introduction to Computing Systems
+        🔮 计算机系统概论 | Introduction to Computing Systems
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-<a href="../D2QD_DigitalDesign/">[大二秋冬] 数字逻辑设计 | Digital Design</a>
+<a href="../D2QD_DigitalDesign/">💎 数字逻辑设计 | Digital Design</a>
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-          [大二秋冬] 数字逻辑设计 | Digital Design
+          💎 数字逻辑设计 | Digital Design
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-<a href="../D2QD_Intro2CV/">[大二秋冬] 计算机视觉导论 | I2CV</a>
+<a href="../D2QD_Intro2CV/">💎 计算机视觉导论 | I2CV</a>
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-          [大二秋冬] 计算机视觉导论 | I2CV
+          💎 计算机视觉导论 | I2CV
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-        [大二寒假] 科学文章写作 | Writing in the Sciences
+        🔮 科学文章写作 | Writing in the Sciences
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-<a href="../D2CX_ComputerOrganization/">[大二春夏] 计算机组成 | Computer Organization</a>
+<a href="../D2CX_ComputerOrganization/">🔮 计算机组成 | Computer Organization</a>
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+          🔮 计算机组成 | Computer Organization
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-<a href="../D2CX_AdvancedDataStructure/">[大二春夏] 高级数据结构 | Advanced Data Structure</a>
+<a href="../D2CX_AdvancedDataStructure/">💎 高级数据结构 | Advanced Data Structure</a>
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-          [大二春夏] 高级数据结构 | Advanced Data Structure
+          💎 高级数据结构 | Advanced Data Structure
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-<a href="./">[大三秋冬] 操作系统 | Operating System</a>
+<a href="./">💎 操作系统 | Operating System</a>
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+<h1 id="-操作系统--operating-system">💎 操作系统 | Operating System<a class="headerlink" href="#-操作系统--operating-system" title="Permanent link">¶</a></h1>
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 <small>
     
       最后更新:
-      <span class="git-revision-date-localized-plugin git-revision-date-localized-plugin-datetime">2023年11月22日 11:09:32</span>
+      <span class="git-revision-date-localized-plugin git-revision-date-localized-plugin-datetime">2023年11月22日 11:17:54</span>
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-        [大一暑假] 计算机系统概论 | Introduction to Computing Systems
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-        [大二寒假] 科学文章写作 | Writing in the Sciences
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-        [大二寒假] 科学文章写作 | Writing in the Sciences
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-        [大二寒假] 科学文章写作 | Writing in the Sciences
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 <label class="md-nav__title" for="__nav_3_10">
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-          [大二春夏] 高级数据结构 | Advanced Data Structure
+          💎 高级数据结构 | Advanced Data Structure
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@@ -819,7 +819,7 @@
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 <div class="md-nav__link md-nav__link--index">
-<a href="../cour_note/D3QD_OperatingSystem/">[大三秋冬] 操作系统 | Operating System</a>
+<a href="../cour_note/D3QD_OperatingSystem/">💎 操作系统 | Operating System</a>
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@@ -827,7 +827,7 @@
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-          [大三秋冬] 操作系统 | Operating System
+          💎 操作系统 | Operating System
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@@ -911,13 +911,13 @@
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-          [大三秋冬] 计算理论 | Theorem of Computing
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-          [大三秋冬] 计算理论 | Theorem of Computing
+          🔮 计算理论 | Theorem of Computing
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diff --git a/search/search_index.json b/search/search_index.json
index 01942786..70549b22 100644
--- a/search/search_index.json
+++ b/search/search_index.json
@@ -1 +1 @@
-{"config":{"lang":["en"],"separator":"[\\s\\-\\.]+","pipeline":["stemmer"]},"docs":[{"location":"","title":"\u6b22\u8fce\uff01","text":"<p> \u7ea6 108 \u4e2a\u5b57 </p> <p> \u300e\u305d\u306e\u6642\u3092\u5f85\u3064\u3088\u300f      \u6211\u4eec\u767b\u4e0a\u9ad8\u5854\uff0c\u770b\u5230\u7684\u5374\u53ea\u6709\u9ed1\u591c\u3002  \u2014\u2014\u5b89\u5fb7\u70c8\u00b7\u7eaa\u5fb7\u300a\u5730\u7cae\u300b  </p> <p> \ud83e\udd7a \u5982\u679c\u975e\u8981\u652f\u6301\u4e00\u4e0b\u7684\u8bdd\u2026\u2026\u8fd9\u4e2a\u4e8c\u7ef4\u7801\u4e5f\u4e0d\u662f\u4e0d\u53ef\u4ee5\u626b\uff01 </p> <p>\u63a8\u8350\u9605\u8bfb</p> <ul> <li>\ud83d\udcc4 \u4f7f\u7528 reveal-md \u6765\u5199 Slides</li> <li>\ud83d\uddc2\ufe0f Git Something</li> <li>\ud83d\uddc2\ufe0f \u6570\u5b57\u903b\u8f91\u8bbe\u8ba1 | Digital Design</li> <li>\ud83d\uddc2\ufe0f \u9ad8\u7ea7\u6570\u636e\u7ed3\u6784 | Advanced Data Structure</li> <li>\ud83d\uddc2\ufe0f \u64cd\u4f5c\u7cfb\u7edf | Operating System\uff08\u66f4\u65b0\u4e2d\uff09</li> </ul> <p>\u7ad9\u70b9\u7edf\u8ba1</p> <p> \u672c\u7ad9\u76ee\u524d\u5171 96 \u9875\uff0c\u7d2f\u8ba1 194601 \u5b57\uff01 </p>"},{"location":"coming/","title":"\u5185\u5bb9\u6b63\u5728\u7f16\u8f91\u4e2d\u2026\u2026","text":"<p> \u7ea6 47 \u4e2a\u5b57 </p> <p>Missing</p> <p>\u672c\u90e8\u5206\u7684\u5185\u5bb9\u6b63\u5728\u7f16\u8f91\u4e2d\uff0c\u5c1a\u672a\u4e0a\u4f20\uff01</p> \u81ea\u5b9a\u4e49 admonition <p>definition</p> <p>proof</p> <p>property</p> <p>extra</p> <p>section</p> <p>key-point</p> <p>advice</p> <p>not-advice</p> <p>eg</p>"},{"location":"link/","title":"\u4f60\u597d\uff01","text":"<p> \u7ea6 177 \u4e2a\u5b57  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 1 \u5206\u949f</p> <p>\ud83d\udcdc \u4ecb\u7ecd</p> <p>\u4f60\u597d\uff01\u6211\u60f3\u4e3a\u8fd9\u4e2a\u5c0f\u7f51\u7ad9\u8d4b\u4e88\u4e00\u4e9b\u793e\u4ea4\u4ef7\u503c\uff0c\u60f3\u8ba4\u8bc6\u66f4\u591a\u5389\u5bb3\u7684\u4eba\uff01\u6b22\u8fce\u5927\u5bb6\u5728\u8fd9\u91cc\u804a\u5929\uff0c\u6216\u662f\u7559\u4e0b\u53cb\u94fe\u4ea4\u6362\uff01</p> <p>\ud83d\udd17 \u53cb\u94fe</p> <p> \u9889\u65f6\u4eba\u5f71 \u8fd9\u662f\u6211\u7684\u535a\u5ba2\uff01\u65f6\u4e0d\u65f6\u66f4\u65b0\u4e00\u4e9b\u548c\u6280\u672f\u6ca1\u5173\u7cfb\u7684\u6587\u7ae0\u3002 </p> <p> \u54b8\u9c7c\u6684 \u7684 \u4ee3\u7801\u7a7a\u95f4 \u81ed\u5149\u5934\uff0c\u66b4\u63cdxyx\uff01 </p> <p> \u9e64\u7fd4\u4e07\u91cc \u7684 \u7b14\u8bb0\u672c  \ud83e\udd24 xg \u6559\u6b7b\u6211\uff01 </p> <p> Zicx \u7684 \u7b14\u8bb0\u672c  \ud83e\udd24 \u662f\u8d85\u5f3a\u65ed\u5b9d\uff01 </p> <p> sakuratsuyu \u7684 \u7b14\u8bb0\u672c  \ud83e\udd24 \u65e0\u654c\u9ea6\u54e5\u5e26\u5e26\u6211\uff01 </p> <p> Bowling \u7684 \u7b14\u8bb0\u672c  \u88ab\u795e\u4ed9\u5b66\u5f1f\u8584\u7eb1 orz  </p> <p> MinJoker \u7684 \u7b14\u8bb0\u672c  \u88ab\u795e\u4ed9\u5b66\u5f1f\u8584\u7eb1 orz  </p> <p> Zizheng's Blog  \u4f6c\uff01  </p> \ud83d\udd17 \u6709\u610f\u601d\u7684\u94fe\u63a5 <p>\u5728\u8fd9\u91cc\u6536\u96c6\u4e00\u4e9b\u6709\u610f\u601d\u7684\u94fe\u63a5\uff01</p> <ul> <li>https://quickref.me/</li> </ul>"},{"location":"cour_note/","title":"\u6249\u9875","text":"<p> \u7ea6 20 \u4e2a\u5b57 </p> <p> \u300e\u305d\u306e\u6642\u3092\u5f85\u3064\u3088\u300f      \u4e00\u5207\u5b89\u4e50\uff0c\u65e0\u4e0d\u6765\u81ea\u56f0\u82e6\u3002  \u2014\u2014\u590f\u76ee\u6f31\u77f3\u300a\u5fc3\u300b  </p>"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/","title":"[\u5927\u4e00\u6625\u590f] \u6982\u7387\u8bba\u4e0e\u6570\u7406\u7edf\u8ba1","text":"<p> \u7ea6 168 \u4e2a\u5b57  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 1 \u5206\u949f</p> <p>\u8bfe\u7a0b\u4fe1\u606f</p> <ul> <li>\u667a\u4e91\u94fe\u63a5\uff1a\ud83d\udd17</li> <li>\u6388\u8bfe\uff1a\u5434\u56fd\u6862</li> <li>\u6559\u6750\uff1a\u300a\u6982\u7387\u8bba\u4e0e\u6570\u7406\u7edf\u8ba1\u300b\uff0c\u5f20\u5e3c\u594b\uff0c\u9ad8\u7b49\u6559\u80b2\u51fa\u7248\u793e</li> <li>\u8f85\u52a9\u6559\u6750\uff1a\u300a\u6982\u7387\u8bba\u4e0e\u6570\u7406\u7edf\u8ba1\u6559\u7a0b \u7b2c\u4e09\u7248\u300b\uff0c\u8306\u8bd7\u677e\uff0c\u9ad8\u7b49\u6559\u80b2\u51fa\u7248\u793e\uff08\u540e\u7b80\u79f0\u6a59\u4e66\uff09</li> </ul> <p>Notes</p> <ul> <li> [1.x] \u6982\u7387\u8bba\u7684\u57fa\u672c\u6982\u5ff5</li> <li> [2.x] \u968f\u673a\u53d8\u91cf\u53ca\u5176\u6982\u7387\u5206\u5e03</li> <li> [3.x] \u591a\u5143\u968f\u673a\u53d8\u91cf\u53ca\u5176\u5206\u5e03</li> <li> [4.x] \u968f\u673a\u53d8\u91cf\u7684\u6570\u5b57\u7279\u5f81</li> <li> [5.x] \u5927\u6570\u5b9a\u5f8b\u53ca\u4e2d\u5fc3\u6781\u9650\u5b9a\u7406</li> <li> [6.x] \u7edf\u8ba1\u91cf\u4e0e\u62bd\u6837\u5206\u5e03</li> <li> [7.x] \u53c2\u6570\u4f30\u8ba1</li> <li> [8.x] \u5047\u8bbe\u68c0\u9a8c</li> </ul>"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap01/","title":"[1.x] \u6982\u7387\u8bba\u7684\u57fa\u672c\u6982\u5ff5","text":"<p> \u7ea6 1144 \u4e2a\u5b57  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 4 \u5206\u949f</p>"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap01/#\u6837\u672c\u7a7a\u95f4\u4e0e\u968f\u673a\u4e8b\u4ef6","title":"\u6837\u672c\u7a7a\u95f4\u4e0e\u968f\u673a\u4e8b\u4ef6","text":"<p>\u968f\u673a\u8bd5\u9a8c(random experiment)\u7684\u7279\u70b9\uff1a</p> <ol> <li>\u53ef\u4ee5\u590d\u73b0\uff1b</li> <li>\u6bcf\u6b21\u8bd5\u9a8c\u7684\u7ed3\u679c\u4e0d\u5b9a\uff0c\u4f46\u4e8b\u5148\u53ef\u4ee5\u77e5\u9053\u8bd5\u9a8c\u7684\u6240\u6709\u53ef\u80fd\u7ed3\u679c\uff1b</li> </ol> <p>\u800c\u968f\u673a\u8bd5\u9a8c\u7684\u6240\u6709\u53ef\u80fd\u7ed3\u679c\u6784\u6210\u7684\u96c6\u5408\u4e3a\u6837\u672c\u7a7a\u95f4(sample space)\uff0c\u8bb0\u4e3a \\(S\\)\uff0c\u5176\u4e2d\u7684\u6bcf\u4e00\u4e2a\u5143\u7d20\u4e3a\u6837\u672c\u70b9(sample point)\u3002\u800c\u6837\u672c\u7a7a\u95f4\u7684\u4efb\u4e00\u5b50\u96c6\u6210\u4e3a\u968f\u673a\u4e8b\u4ef6(random event)\uff0c\u7b80\u79f0\u4e8b\u4ef6\u3002</p> <ul> <li>\u7279\u522b\u7684\uff0c\u53ea\u542b\u6709\u4e00\u4e2a\u6837\u672c\u7684\u5b50\u96c6\u79f0\u4e3a\u57fa\u672c\u4e8b\u4ef6\u3002</li> </ul> <p>\u4e8b\u4ef6\u7684\u76f8\u4e92\u5173\u7cfb</p> <p> \u4ece\u5de6\u5230\u53f3\u5206\u522b\uff1a\u5305\u542b | \u548c\u4e8b\u4ef6 | \u79ef\u4e8b\u4ef6 | \u9006\u4e8b\u4ef6 | \u5dee\u4e8b\u4ef6</p> <ul> <li>\u4e24\u4e92\u9006\u4e8b\u4ef6\u53c8\u79f0\u5bf9\u7acb\u4e8b\u4ef6\u3002</li> <li>\u82e5 \\(AB=\\varnothing\\)\uff0c\u5219\u79f0\u4e24\u4e8b\u4ef6\u4e0d\u76f8\u5bb9\uff08\u6216\u4e92\u65a5\uff09</li> <li>\u82e5 \\(A\\subset B \\;and\\;B\\subset A\\)\uff0c\u5219\u79f0\u4e24\u4e8b\u4ef6\u76f8\u7b49</li> </ul> <p>\u5176\u4e2d\uff0c\u548c\u3001\u4ea4\u3001\u9006\u4e8b\u4ef6\u6709\u5982\u4e0b\u8fd0\u7b97\u89c4\u5f8b\uff1a</p> <ul> <li>\u4ea4\u6362\u5f8b\uff1a\\(A\\cup B=B\\cup A\\;,\\;A\\cap B=B\\cap A\\)\uff1b</li> <li>\u7ed3\u5408\u5f8b\uff1a\\(A\\cup(B\\cup C)=(A\\cup B)\\cup C\\;,\\;A(BC)=(AB)C\\)\uff1b</li> <li>\u5206\u914d\u5f8b\uff1a\\(A(B\\cup C)=(AB)\\cup(AC)\\;,\\;(AB)\\cup C=(A\\cup C)(B\\cup C)\\)\uff1b</li> <li>\u5bf9\u5076\u5f8b / \u5fb7\u6469\u6839\u5b9a\u5f8b(De Morgan's law)\uff1a\\(\\overline{\\bigcup\\limits^n_{j=1}A_j}=\\bigcap\\limits^n_{j=1}\\overline{A_j}\\;,\\;\\overline{\\bigcap\\limits^n_{j=1}A_j}=\\bigcup\\limits^n_{j=1}\\overline{A_j}\\)\uff1b</li> </ul> <p>\u4e32\u8054\u7cfb\u7edf\u4e0e\u5e76\u8054\u7cfb\u7edf\uff1a</p> <ul> <li>\u4e32\u8054\u7cfb\u7edf\uff1a\\(A=\\bigcap\\limits_{i=1}^nA_i\\)</li> <li>\u5e76\u8054\u7cfb\u7edf\uff1a\\(A=\\bigcup\\limits_{i=1}^nA_i\\)</li> </ul>"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap01/#\u9891\u7387\u4e0e\u6982\u7387","title":"\u9891\u7387\u4e0e\u6982\u7387","text":"<p>\u9891\u7387 = \u9891\u6570 / \u8bd5\u9a8c\u603b\u6b21\u6570</p> <p>\u82e5\u6837\u672c\u7a7a\u95f4 \\(S\\) \u4e2d\u7684\u4efb\u4e00\u4e8b\u4ef6 \\(A\\)\uff0c\u5b9a\u4e49\u6982\u7387 \\(P(A)\\) \u6ee1\u8db3\u4ee5\u4e0b\u4e09\u6761\u516c\u7406\uff1a</p> <ol> <li>\u975e\u8d1f\u6027 \\(P(A)\\geq0\\)\uff1b</li> <li>\u89c4\u8303\u6027 / \u6b63\u5219\u6027 \\(P(S)=1\\)\uff1b</li> <li>\u53ef\u5217\u53ef\u52a0\u6027\uff1a\u5bf9\u4e8e \\(S\\) \u4e2d\u4e0d\u76f8\u5bb9\u7684\u4e8b\u4ef6 \\(A_i\\)\uff0c\u6709 \\(P(\\bigcup\\limits^{+\\infty}_{j=1}A_j)=\\sum\\limits_{j=1}^{+\\infty}P(A_j)\\)\uff1b</li> </ol> <p>\u7531\u6b64\u5f97\u5230\u5982\u4e0b\u51e0\u6761\u6982\u7387\u7684\u6027\u8d28\uff1a</p> <ol> <li>\u5bf9\u4e8e\u6709\u9650\u4e2a\u4e24\u4e24\u4e0d\u76f8\u5bb9\u7684\u4e8b\u4ef6\u7684\u548c\u4e8b\u4ef6\uff0c\u6709 \\(P(\\bigcup\\limits^n_{j=1}A_j)=\\sum\\limits_{j=1}^nP(A_j)\\)\uff1b</li> <li>\\(P(A)=1-P(\\overline A)\\)\uff1b\u7279\u522b\u7684\uff0c\u53ef\u4ee5\u5f97\u5230 \\(P(\\varnothing)=0\\)\uff1b</li> <li>\u5f53 \\(A\\supset B\\) \u65f6\uff0c\\(P(A-B) = P(A)-P(B)\\) \u4e14 \\(P(A)\\geq P(B)\\)\uff1b</li> <li>\u6982\u7387\u7684\u52a0\u6cd5\u516c\u5f0f\uff1a\\(P(A\\cup B)=P(A)+P(B)-P(AB)\\)\uff1b\u63a8\u5e7f\u5373\u5bb9\u65a5\u539f\u7406\uff1b</li> <li>\u52a0\u6cd5\u516c\u5f0f\u7684\u63a8\u8bba\uff1a\\(P(A\\cup B)\\leq P(A)+P(B)\\)\uff1b</li> </ol>"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap01/#\u7b49\u53ef\u80fd\u6982\u578b","title":"\u7b49\u53ef\u80fd\u6982\u578b","text":"<p>\u5982\u679c\u968f\u673a\u4e8b\u4ef6\u6ee1\u8db3\uff1a</p> <ol> <li>\\(S\\) \u4e2d\u6837\u672c\u70b9\u6570\u6709\u9650\uff1b</li> <li>\\(\\forall i,j \\in\\{1,2,...,n\\},\\;P(e_i) = P(e_j)\\)\uff0c\u5373\u7b49\u53ef\u80fd\uff1b</li> </ol> <p>\u5219\u8be5\u8bd5\u9a8c\u95ee\u9898\u4e3a\u7b49\u53ef\u80fd\u6982\u578b\uff08\u53e4\u5178\u6982\u578b\uff09\u6709\u5982\u4e0b\u6027\u8d28\uff1a\u82e5\u603b\u4e8b\u4ef6\u4e2a\u6570\u4e3a \\(N\\)\uff0c\\(A\\) \u4e3a \\(n\\) \u4e2a\u57fa\u672c\u4e8b\u4ef6\u7684\u548c\u4e8b\u4ef6\uff0c\u5219 \\(P(A)=\\frac{n}{N}\\)\u3002</p>"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap01/#\u6761\u4ef6\u6982\u7387","title":"\u6761\u4ef6\u6982\u7387","text":"<p>\u5982\u679c \\(P(B)&gt;0\\)\uff0c\u90a3\u4e48\u5b9a\u4e49\u5728 \\(B\\) \u53d1\u751f\u7684\u6761\u4ef6\u4e0b \\(A\\) \u53d1\u751f\u7684\u6761\u4ef6\u6982\u7387(contidional probability)\u4e3a\uff1a\\(P(A|B)=\\frac{P(AB)}{P(B)}\\)</p> <p>\u6761\u4ef6\u6982\u7387\u662f\u5728\u65b0\u7684\u6837\u672c\u7a7a\u95f4\u4e0b\u7684\u6982\u7387\u5ea6\u91cf\uff0c\u5b83\u6ee1\u8db3\u6982\u7387\u7684\u5b9a\u4e49\u548c\u6027\u8d28\u3002</p> <p>\u5b9a\u4e49\u5b8c\u5907\u4e8b\u4ef6\u7ec4\u4e3a \\(S\\) \u7684\u4e00\u4e2a\u5212\u5206 \\(B_1,B_2,...,B_n\\)\uff0c\u5b83\u6ee1\u8db3\u5982\u4e0b\u6027\u8d28\uff1a</p> <ol> <li>\\(B_iB_j=\\varnothing,i,j,...,n,i\\not=j\\)\uff1b</li> <li>\\(\\bigcup\\limits^n_{i=1}B_i=S\\)\uff1b</li> </ol> <p>\u8bbe \\(S\\) \u4e3a\u4e00\u6837\u672c\u7a7a\u95f4\uff0c\\(A\\) \u4e3a\u8be5\u8bd5\u9a8c\u7684\u4e8b\u4ef6\uff0c\\(\\{B_i\\}\\) \u4e3a \\(S\\) \u7684\u4e00\u4e2a\u5212\u5206\uff0c\u5219\u6709\uff1a</p> <ul> <li>\u82e5 \\(A_1,...,A_n,...\\) \u4e92\u4e0d\u76f8\u5bb9\uff0c\u5219 \\(P(\\cup_{n=1}^{\\infty}A_n|B)=\\sum\\limits_{n=1}^{\\infty}P(A_n|B)\\)\uff1b</li> <li>\u4e58\u6cd5\u516c\u5f0f\uff1a\u5f53 \\(P(A)\\not=0\\;\\,\\;P(B)\\not=0\\) \u65f6\uff0c\u6709 \\(P(AB)=P(A)*P(B|A)=P(B)*P(A|B)\\)\uff1b</li> <li>\u5168\u6982\u7387\u516c\u5f0f\uff1a\\(P(A)=\\sum\\limits_{j=1}^nP(B_j)P(A|B_j)\\)\uff1b</li> <li>\u8d1d\u53f6\u65af\u516c\u5f0f\uff1a\\(P(B_k|A)=\\frac{P(B_kA)}{P(A)}=\\frac{P(B_k)P(A|B_k)}{\\sum\\limits_{j=1}^nP(B_j)P(A|B_j)}\\)\uff1b</li> <li>\u5176\u4e2d\uff0c\u6211\u4eec\u79f0 \\(P(B_j)\\) \u8fd9\u79cd\u4e8b\u5148\u77e5\u9053\u7684\u6982\u7387\u4e3a\u5148\u9a8c\u6982\u7387\uff1b\u800c \\(P(B_j|A)\\) \u8fd9\u79cd\uff0c\u5f53\u4e8b\u4ef6 \\(A\\) \u53d1\u751f\u540e\u9700\u8981\u4fee\u6b63 \\(B_j\\) \u7684\u6982\u7387\u6210\u4e3a\u540e\u9a8c\u6982\u7387\u3002</li> </ul>"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap01/#\u4e8b\u4ef6\u72ec\u7acb\u6027\u4e0e\u72ec\u7acb\u8bd5\u9a8c","title":"\u4e8b\u4ef6\u72ec\u7acb\u6027\u4e0e\u72ec\u7acb\u8bd5\u9a8c","text":"<p>\u8bbe \\(A,B\\) \u4e3a\u4e24\u4e2a\u968f\u673a\u4e8b\u4ef6\uff0c\u82e5\u6709 \\(P(AB)=P(A)*P(B)\\)\uff0c\u5219 \\(A,B\\) \u76f8\u4e92\u72ec\u7acb(independent)\u5176\u5b9e\u9645\u610f\u4e49\u662f\uff0c\u4e8b\u4ef6 \\(A\\) \u7684\u53d1\u751f\u4e0e\u4e8b\u4ef6 \\(B\\) \u7684\u53d1\u751f\u4e92\u4e0d\u5f71\u54cd\u3002\u90a3\u4e48\u5c31\u6709\u7ed3\u8bba\uff1a\\(while\\;\\;P(AB)=P(A)*P(B)\\;\\;,\\;\\;P(A|B)=P(A)\\)\uff1b</p> <p>\u5f53\u51fa\u73b0\u4e24\u4e2a\u4ee5\u4e0a\u7684\u968f\u673a\u4e8b\u4ef6\u65f6\uff0c\u5982\u4e09\u4e2a\u968f\u673a\u4e8b\u4ef6 \\(A,B,C\\)\uff0c\u5f53\uff1a\\(P(AB)=P(A)*P(B)\\;,\\;P(AC)=P(A)*P(C)\\;,\\;P(BC)=P(B)*P(C)\\) \u90fd\u6210\u7acb\uff0c\u5219\u79f0\u4e8b\u4ef6 \\(A,B,C\\) \u4e24\u4e24\u72ec\u7acb\uff1b\u5982\u679c\u540c\u65f6\u8fd8\u6ee1\u8db3\uff1a\\(P(ABC)=P(A)P(B)P(C)\\) \u5219\u79f0\u4e8b\u4ef6 \\(A,B,C\\) \u76f8\u4e92\u72ec\u7acb\u3002</p> <ul> <li>\u663e\u7136\u6709\uff1a\u76f8\u4e92\u72ec\u7acb \\(\\Rightarrow\\) \u4e24\u4e24\u72ec\u7acb</li> </ul> <p>\u66f4\u666e\u904d\u7684\uff1a\u5b9a\u4e49 \\(\\{A_i\\}\\) \u76f8\u4e92\u72ec\u7acb\u5f53\u4e14\u4ec5\u5f53 \\(\\forall{i_j},\\;P(\\prod_{j=1}^k A_{i_j})=\\prod_{j=1}^kP(A_{i_j})\\)</p> <p>\u72ec\u7acb\u8bd5\u9a8c\u4e0e\u91cd\u590d\u8bd5\u9a8c\uff1a</p> <ul> <li>\u72ec\u7acb\u8bd5\u9a8c\u5404\u4e2a\u8bd5\u9a8c\u7ed3\u679c\u4e92\u4e0d\u5f71\u54cd\uff1b</li> <li>\u91cd\u590d\u8bd5\u9a8c\u7684\u6bcf\u4e00\u6b21\u5b50\u8bd5\u9a8c\u90fd\u5728\u76f8\u540c\u60c5\u51b5\u4e0b\u8fdb\u884c\uff1b</li> </ul>"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap02/","title":"[2.x] \u968f\u673a\u53d8\u91cf\u53ca\u5176\u6982\u7387\u5206\u5e03","text":"<p> \u7ea6 1166 \u4e2a\u5b57  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 4 \u5206\u949f</p> <p>\u968f\u673a\u53d8\u91cf\u662f\u5b9a\u4e49\u5728\u6837\u672c\u7a7a\u95f4 \\(S\\) \u4e0a\u7684\u5b9e\u503c\u5355\u503c\u51fd\u6570\u3002\u5e38\u7528\u5927\u5199\u5b57\u6bcd \\(X,Y,Z\\) \u6765\u8868\u793a\u968f\u673a\u53d8\u91cf\uff0c\u7528\u5c0f\u5199\u5b57\u6bcd \\(x,y,z\\) \u8868\u793a\u5176\u53d6\u503c\u3002</p>"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap02/#\u79bb\u6563\u578b\u968f\u673a\u53d8\u91cf","title":"\u79bb\u6563\u578b\u968f\u673a\u53d8\u91cf","text":"<p>\u79bb\u6563\u578b\u968f\u673a\u53d8\u91cf(discrete random variable)\u5982\u679c\u968f\u673a\u53d8\u91cf\u53d6\u6709\u9650\u4e2a\u6216\u53ef\u5217\u4e2a\u503c\uff0c\u5219\u6b64\u968f\u673a\u53d8\u91cf\u4e3a\u79bb\u6563\u578b\u968f\u673a\u53d8\u91cf\uff0c\u800c\u82e5\u5176\u53ef\u80fd\u53d6\u503c\u4e3a \\(\\{x_i\\}\\)\uff0c\u5219\u79f0 \\(P\\{X=x_k\\}=p_k\\;,\\;k=1,2,...\\) \u4e3a \\(X\\) \u7684\u6982\u7387\u5206\u5e03\u5f8b(probability mass function)\uff0c\u4e5f\u53ef\u4ee5\u7528\u5217\u8868\u7684\u65b9\u5f0f\u8868\u8fbe\u3002\u56e0\u4e3a\u6837\u672c\u7a7a\u95f4 \\(S=\\{X=x_1,X=x_2,\\,...\\,,X=x_n\\,...\\,\\}\\) \u4e2d\u5404\u6837\u672c\u70b9\u4e24\u4e24\u4e0d\u76f8\u5bb9\uff0c\u6240\u4ee5\uff1a\\(1=P(S)=\\sum\\limits_{i=1}^{+\\infty}P(X=x_i)=\\sum\\limits_{i=1}^{+\\infty}{p_i}\\)</p>"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap02/#\u4e24\u70b9\u5206\u5e03","title":"\u4e24\u70b9\u5206\u5e03","text":"<p>\u5982\u679c\u968f\u673a\u53d8\u91cf \\(X\\) \u7684\u6982\u7387\u5206\u5e03\u5f8b\u4e3a\uff1a</p> <p> x 0 1 P 1-p p </p> \\[ P\\{X=k\\}=p^k(1-p)^{1-k}\\;,\\;\\;\\;k=0\\;or\\;1 \\] <p>\u5219\u79f0 \\(X\\) \u4e3a\u670d\u4ece\u53c2\u6570\u4e3a \\(p\\) \u7684 \\(0-1\\) \u5206\u5e03\uff0c\u4e5f\u79f0\u4e3a\u4e24\u70b9\u5206\u5e03\uff0c\u5e76\u8bb0\u4e3a \\(X\\sim B(1,p)\\) \u6216\u8005 \\(X\\sim 0-1(p)\\)</p> <p>\u5b9a\u4e49\u4f2f\u52aa\u5229(Bernoulli)\u8bd5\u9a8c\u4e3a\uff1a\u5728 \\(n\\) \u6b21\u72ec\u7acb\u91cd\u590d\u8bd5\u9a8c\u4e2d\uff0c\u6bcf\u6b21\u53ea\u6709 \\(A\\) \u548c \\(\\overline A\\) \u4e24\u79cd\u7ed3\u679c\uff0c\u4e14\u6982\u7387\u4e0d\u53d8\uff0c\u5219\u8fd9\u4e00\u7cfb\u5217\u8bd5\u9a8c\u4e3a\u4f2f\u52aa\u5229\u8bd5\u9a8c\u3002</p>"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap02/#\u4e8c\u9879\u5206\u5e03","title":"\u4e8c\u9879\u5206\u5e03","text":"<p>\u82e5\u968f\u673a\u53d8\u91cf \\(X\\) \u8868\u793a \\(n\\) \u91cd\u8d1d\u52aa\u529b\u5b9e\u9a8c\u4e2d\u4e8b\u4ef6A\u53d1\u751f\u7684\u6b21\u6570\uff0c\u5176\u6982\u7387\u5206\u5e03\u5f8b\u4e3a\uff1a</p> \\[ P\\{X=k\\}={\\rm C}_n^kp^k(1-p)^{n-k}\\;,\\;\\;k=0,1,2,...,n \\] <p>\u5219\u79f0 \\(X\\) \u4e3a\u670d\u4ece\u53c2\u6570\u4e3a \\((n,p)\\) \u7684\u4e8c\u9879\u5206\u5e03(binomial distribution)\uff0c\u5e76\u8bb0\u4e3a \\(X\\sim B(n,p)\\)</p> <p>\u6839\u636e\u4e8c\u9879\u5f0f\u5b9a\u7406\uff0c\u4e8c\u9879\u5206\u5e03\u6709\u5982\u4e0b\u6027\u8d28\uff1a</p> \\[ \\sum\\limits_{k=0}^n{\\rm C}_n^kp^k(1-p)^{n-k}=1 \\] <ul> <li>\u5982\u679c\u9047\u5230\u6765\u81ea\u4e8e\u4e24\u70b9\u5206\u5e03\u7684\u603b\u4f53\u7684\uff0c\u5bb9\u91cf\u4e3a \\(n\\) \u7684\u6837\u672c\u7684\u5747\u503c \\(\\overline X\\)\uff0c\u5219\u6709 \\(n\u00b7\\overline X=\\sum\\limits_{i=1}^n X_i \\sim B(n,p)\\)</li> </ul>"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap02/#\u6cca\u677e\u5206\u5e03","title":"\u6cca\u677e\u5206\u5e03","text":"<p>\u5982\u679c\u968f\u673a\u53d8\u91cf \\(X\\) \u7684\u6982\u7387\u5206\u5e03\u5f8b\u4e3a\uff1a</p> \\[ P(X=k)=\\frac{e^{-\\lambda}\\lambda^k}{k!}\\;,\\;\\;\\;k=0,1,2,... \\] <p>\u5176\u4e2d \\(\\lambda &gt; 0\\)\uff0c\u5219\u79f0 \\(X\\) \u670d\u4ece\u53c2\u6570\u4e3a \\(\\lambda\\) \u7684\u6cca\u677e\u5206\u5e03(Poisson distribution)\uff0c\u8bb0\u505a \\(X \\sim P(\\lambda)\\)</p> <p>\u5f53 \\(n\\) \u8db3\u591f\u5927\uff0c\\(p\\) \u5145\u5206\u5c0f(\u4e00\u822c\u8981\u6c42 \\(p&lt;0.1\\))\uff0c\u4e14 \\(np\\) \u4fdd\u6301\u9002\u5f53\u5927\u5c0f\u65f6\uff0c\u53c2\u6570\u4e3a \\((n,p)\\) \u7684\u4e8c\u9879\u5206\u5e03\u53ef\u4ee5\u7528\u6cca\u677e\u5206\u5e03\u8fd1\u4f3c\u63cf\u8ff0\uff0c\u5176\u4e2d \\(\\lambda = np\\)\uff0c\u5373\uff1a</p> \\[ {\\rm C}_n^kp^k(1-p)^{n-k} \\sim \\frac{e^{-\\lambda}\\lambda^k}{k!}\\;\\;\\;\\;\\;(n\\rightarrow\\infty,p&lt;\\varepsilon,\\lambda=np) \\]"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap02/#\u8d85\u51e0\u4f55\u5206\u5e03","title":"\u8d85\u51e0\u4f55\u5206\u5e03","text":"<p>\u5982\u679c\u968f\u673a\u53d8\u91cf \\(X\\) \u7684\u6982\u7387\u5206\u5e03\u5f8b\u4e3a\uff1a</p> \\[ P\\{X=k\\}=\\frac{{\\rm C}_a^k{\\rm C}_b^{n-k}}{{\\rm C}_{a+b}^n}\\;,\\;\\;\\;k=l_1,l_1+1,...,l_2 \\] <p>\u5219\u79f0 \\(X\\) \u4e3a\u670d\u4ece\u8d85\u51e0\u4f55\u5206\u5e03(hypergeometric distribution)\uff0c\u5e76\u8bb0\u4e3a \\(X\\sim H(n,a,p)\\)</p> <ul> <li>\u5176\u610f\u4e49\u4e3a\uff0c\u5982\uff1a\\(a\\) \u767d\u7403\uff0c\\(b\\) \u7ea2\u7403\uff0c\u53d6 \\(n\\) \u6b21\u5f97\u5230 \\(X\\) \u4e2a\u767d\u7403</li> </ul> <p>\u5982\u679c\u968f\u673a\u53d8\u91cf \\(X\\) \u7684\u6982\u7387\u5206\u5e03\u5f8b\u4e3a\uff1a</p> \\[ P\\{X=k\\}=p(1-p)^{k-1}\\;,\\;\\;\\;k=1,2,... \\] <p>\u5219\u79f0 \\(X\\) \u4e3a\u670d\u4ece\u53c2\u6570\u4e3a \\(p\\) \u7684\u51e0\u4f55\u5206\u5e03(geometric distribution)\u3002</p>"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap02/#\u8fde\u7eed\u578b\u968f\u673a\u53d8\u91cf","title":"\u8fde\u7eed\u578b\u968f\u673a\u53d8\u91cf","text":"<p>\u5b9a\u4e49\uff1a\u8bbe \\(X\\) \u4e3a\u968f\u673a\u53d8\u91cf\uff0c\\(x\\) \u4e3a\u4efb\u610f\u5b9e\u6570\uff0c\u51fd\u6570 \\(F(x)=P\\{X\\leq x\\}\\) \u4e3a\u968f\u673a\u53d8\u91cf \\(X\\) \u7684\u6982\u7387\u5206\u5e03\u51fd\u6570\uff0c\u7b80\u79f0\u4e3a\u5206\u5e03\u51fd\u6570(distribution function)\u3002\uff08\u79bb\u6563\u968f\u673a\u53d8\u91cf\u540c\u6837\u53ef\u4ee5\u6709\u5206\u5e03\u51fd\u6570\uff09</p> <p>\u5219\u6709\u4ee5\u4e0b\u7ed3\u8bba\uff1a</p> \\[ P\\{x_1&lt;X\\leq x_2\\}=P\\{X\\leq x_2\\}-P\\{X\\leq x_1\\}=F(x_2)-F(x_1) \\] <p>\u5f53 \\(X\\) \u4e3a\u79bb\u6563\u578b\u968f\u673a\u53d8\u91cf\u65f6\uff0c\u8bbe \\(X\\) \u7684\u6982\u7387\u5206\u5e03\u5f8b\u4e3a \\(P\\{X=x_i\\}=p_i\\;,\\;\\;i=1,2,...\\)\uff0c\u5219 \\(X\\) \u7684\u5206\u5e03\u51fd\u6570\u4e3a\uff1a</p> \\[ F(x) = P\\{X\\leq x\\}=\\sum\\limits_{x_i\\leq x}P\\{X=x_i\\} \\] <p>\u5173\u4e8e \\(F(x)\\) \u6709\u4ee5\u4e0b\u7ed3\u8bba\uff1a</p> <ol> <li>\\(F(x)\\) \u5355\u8c03\u4e0d\u51cf\uff1b</li> <li>\\(0\\leq F(x) \\leq 1\\) \u4e14 \\(F(-\\infty)=0\\)\uff0c\\(F(+\\infty)=1\\)\uff1b</li> <li>\\(F(x)\\) \u53f3\u8fde\u7eed\uff0c\u5373 \\(F(x+0)=F(x)\\)\uff1b</li> <li>\\(P(a&lt;X\\leq b)=F(b)-F(a)\\)\uff1b</li> </ol> <p>\u5982\u679c\u5bf9\u4e8e\u968f\u673a\u53d8\u91cf \\(X\\)\uff0c\u5176\u5206\u5e03\u51fd\u6570\u4e3a \\(F(x)\\)\uff0c\u82e5\u5b58\u5728\u4e00\u4e2a\u975e\u8d1f\u7684\u5b9e\u51fd\u6570 \\(f(x)\\)\uff0c\u4f7f\u5bf9\u4e8e\u4efb\u610f\u5b9e\u6570 \\(x\\)\uff0c\u6709\uff1a</p> \\[ F(x) = \\int_{-\\infty}^{x}f(t)dt \\] <p>\u5219\u79f0 \\(X\\) \u4e3a\u8fde\u7eed\u578b\u968f\u673a\u53d8\u91cf\uff0c\u5e76\u4e14\u79f0 \\(f(x)\\) \u4e3a \\(X\\) \u7684\u6982\u7387\u5bc6\u5ea6\u51fd\u6570(probability density function)\uff0c\u7b80\u79f0\u4e3a\u5bc6\u5ea6\u51fd\u6570\u3002</p> <p>\u5173\u4e8e \\(f(x)\\) \u6709\u4ee5\u4e0b\u7ed3\u8bba\uff1a</p> <ol> <li>\\(f(x) \\geq 0\\)\uff1b</li> <li>\\(\\int_{-\\infty}^{\\infty}f(x)dx=1\\)\uff1b</li> <li>\\(\\forall x_1,x_2\\in \\mathbf{R}\\;\\;(x_1&lt;x_2)\\;,\\;\\;P\\{x_1&lt;X\\leq x_2\\}=F(x_2)-F(x_1)=\\int^{x_2}_{x_1}f(t)dt\\)\uff1b</li> <li>\u5728\\(f(x)\\) \u7684\u8fde\u7eed\u70b9 \\(x\\) \u5904\uff0c\\(F'(x)=f(x)\\)</li> <li>\\(P\\{X=a\\} = 0\\)\uff0c\u5373\u8fde\u7eed\u578b\u968f\u673a\u53d8\u91cf\u4efb\u53d6\u4e00\u4e2a\u5b9a\u503c\u7684\u6982\u7387\u4e3a\u96f6\uff0c\u56e0\u6b64\u8fde\u7eed\u578b\u968f\u673a\u53d8\u91cf\u843d\u5728\u5f00\u533a\u95f4\u4e0e\u76f8\u5e94\u95ed\u533a\u95f4\u4e0a\u7684\u6982\u7387\u76f8\u7b49\uff1b</li> </ol>"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap02/#\u5747\u5300\u5206\u5e03","title":"\u5747\u5300\u5206\u5e03","text":"<p>\u8bbe\u968f\u673a\u53d8\u91cf \\(X\\) \u5c31\u6709\u5bc6\u5ea6\u51fd\u6570\uff1a</p> \\[ f(x)=\\begin{cases} \\frac{1}{b-a}, &amp; x\\in(a,b) \\\\[1ex] 0, &amp; \\text{else} \\end{cases} \\] <p>\u5219\u79f0 \\(X\\) \u670d\u4ece\u533a\u95f4 \\((a,b)\\) \u4e0a\u7684\u5747\u5300\u5206\u5e03\uff0c\u5e76\u8bb0\u4e3a \\(X\\sim U(a,b)\\)</p> <p>\u800c\u5f97\u5230\u5bf9\u5e94\u7684\u5206\u5e03\u51fd\u6570\u4e3a\uff1a</p> \\[ F(x)=\\begin{cases} 0, &amp; x&lt;a \\\\[1ex] \\frac{x-a}{b-a}, &amp; a\\leq x&lt;b \\\\[1ex] 1, &amp; x\\geq b \\end{cases} \\] <p></p>"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap02/#\u6307\u6570\u5206\u5e03","title":"\u6307\u6570\u5206\u5e03","text":"<p>\u82e5\u968f\u673a\u53d8\u91cf \\(X\\) \u5177\u6709\u5bc6\u5ea6\u51fd\u6570\uff1a</p> \\[ f(x)=\\begin{cases} \\lambda e^{-\\lambda x}, &amp; x&gt;0 \\\\[1ex] 0\uff0c&amp; x\\leq0  \\end{cases} \\] <p>\u4e5f\u6709\u5730\u65b9\u5199\u6210\u8fd9\u6837\uff1a</p> \\[ f(x)=\\begin{cases} \\frac{1}{\\theta} e^{-\\frac{1}{\\theta} x}, &amp; x&gt;0 \\\\[1ex] 0\uff0c&amp; x\\leq0 \\end{cases} \\] <p>\u5176\u4e2d \\(\\lambda &gt; 0\\)\uff0c\u5219\u79f0 \\(X\\) \u670d\u4ece\u53c2\u6570\u4e3a \\(\\lambda\\) \u7684\u6307\u6570\u5206\u5e03(exponential distribution)\uff0c\u8bb0\u4e3a \\(X\\sim E(\\lambda)\\)</p> <p>\u6307\u6570\u5206\u5e03\u5bf9\u5e94\u7684\u5206\u5e03\u51fd\u6570\u4e3a\uff1a</p> \\[ F(x)=\\int_{-\\infty}^{x}f(t)\\mathrm{d}t= \\begin{cases} 1-e^{-\\lambda x}, &amp; x&gt;0 \\\\[1ex] 0\uff0c&amp; x\\leq0 \\end{cases} \\] <p>\u6307\u6570\u5206\u5e03\u5177\u6709\u65e0\u8bb0\u5fc6\u6027\uff0c\u5373 \\(P(X&gt;s | X&gt;t_0)=P(X&gt;s-t_0)\\)\u3002</p>"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap02/#\u6b63\u6001\u5206\u5e03","title":"\u6b63\u6001\u5206\u5e03","text":"<p>\u5982\u679c\u968f\u673a\u53d8\u91cf \\(X\\) \u5177\u6709\u5bc6\u5ea6\u51fd\u6570\uff1a</p> \\[ f(x)=\\frac{1}{\\sqrt{2\\pi}\\sigma}e^{-\\frac{(x-\\mu)^2}{2\\sigma^2}}\\;, \\;\\;\\; |x|&lt;+\\infty \\] <p>\u5176\u4e2d \\(\\sigma&gt;0\\;,\\;|\\mu|&lt;+\\infty\\) \u4e3a\u5e38\u6570\uff0c\u5219\u79f0 \\(X\\) \u670d\u4ece\u53c2\u6570\u4e3a \\((\\mu,\\sigma)\\) \u7684\u6b63\u6001\u5206\u5e03(normal distribution / Gauss distribution)\uff0c\u6216\u8005\u79f0 \\(X\\) \u4e3a\u6b63\u6001\u53d8\u91cf\uff0c\u8bb0\u4e3a \\(X\\sim N(\\mu,\\sigma^2)\\)\u3002</p> <p>\u5176\u5bf9\u5e94\u7684\u5206\u5e03\u51fd\u6570\u4e3a\uff1a</p> \\[ F(x)=\\int_{-\\infty}^{x}\\frac{1}{\\sqrt{2\\pi}\\sigma}e^{-\\frac{(t-\\mu)^2}{2\\sigma^2}}dt \\] <p>\u5728\u4e0a\u9762\u51fa\u73b0\u7684\u5f0f\u5b50\u4e2d\uff0c\\(\\mu\\) \u4e3a\u4f4d\u7f6e\u53c2\u6570\uff0c\u51b3\u5b9a\u4e86\u5206\u5e03\u56fe\u50cf\u7684\u5bf9\u79f0\u8f74\u4f4d\u7f6e\uff1b\\(\\sigma\\) \u4e3a\u5c3a\u5ea6\u53c2\u6570\uff0c\u51b3\u5b9a\u4e86\u5f62\u72b6\uff0c\\(\\sigma\\) \u8d8a\u5c0f\uff0c\u56fe\u50cf\u8d8a\u96c6\u4e2d\u3002</p> <p>\u7279\u522b\u7684\uff0c\u5f53 \\(\\mu=0\\;,\\;\\sigma=1\\) \u65f6\uff0c\u5982\u679c\u8bb0\u8fd9\u65f6\u7684\u6b63\u592a\u53d8\u91cf\u4e3a \\(Z\\)\uff0c\u5373 \\(Z\\sim N(0,1)\\) \u5219\u5b83\u670d\u4ece\u6807\u51c6\u6b63\u6001\u5206\u5e03(standard normal distribution)\u3002\u5219\u5176\u5bc6\u5ea6\u51fd\u6570\u4e3a\uff1a</p> \\[ \\varphi(x)=\\frac{1}{\\sqrt{2\\pi}}e^{-\\frac{x^2}{2}}\\;, \\;\\;\\;|x|&lt;+\\infty \\] <p>\u5219\u5bf9\u5e94\u7684\u5206\u5e03\u51fd\u6570\u4e3a\uff1a</p> \\[ \\Phi(x) = \\int_{-\\infty}^{x}\\frac{1}{\\sqrt{2\\pi}}e^{-\\frac{t^2}{2}}dt \\] <ul> <li>\u5219\u663e\u7136\u6709 \\(\\Phi(x)+\\Phi(-x)=1\\)</li> <li>\u7136\u800c\u7531\u4e8e\u5176\u65e0\u6cd5\u8ba1\u7b97\uff0c\u6240\u4ee5\u6211\u4eec\u9700\u8981\u67e5\u8868\u83b7\u5f97\u5177\u4f53\u503c\uff0c\u4ee5\u4e0b\u4e3a\u6807\u51c6\u6b63\u6001\u5206\u5e03\u8868\uff1a<ul> <li>https://www.shuxuele.com/data/standard-normal-distribution-table.html</li> <li>https://www.chip1stop.com/sp/knowledge/019_normal-distribution-table_zh</li> </ul> </li> </ul> <p>\u800c\u5bf9\u4e8e\u4e0d\u662f\u6807\u51c6\u6b63\u6001\u5206\u5e03\u7684\u6b63\u6001\u5206\u5e03\uff0c\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u7ebf\u6027\u53d8\u6362\uff08\u6807\u51c6\u5316\uff09\u6765\u8f6c\u6362\u4e3a\u6807\u51c6\u6b63\u6001\u5206\u5e03\uff1a</p> <ul> <li>\u82e5 \\(X\\sim N(\\mu,\\sigma^2)\\)\uff0c\u5219 \\(P\\{a&lt;X&lt;b\\}= P\\{\\frac{a-\\mu}{\\sigma}&lt; \\frac{X-\\mu}{\\sigma} &lt; \\frac{b-\\mu}{\\sigma} \\}=\\Phi(\\frac{b-\\mu}{\\sigma})-\\Phi(\\frac{a-\\mu}{\\sigma})\\)</li> <li>\u7279\u522b\u7684\uff1a\u82e5 \\(X\\sim N(\\mu,\\sigma^2)\\)\uff0c\u5219 \\(P\\{|X-\\mu|&lt;k\\sigma\\} = \\Phi(k)-\\Phi(-k)=2\\Phi(k)-1\\)</li> <li>\\(3\\sigma\\) \u6cd5\u5219</li> </ul>"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap02/#\u968f\u673a\u53d8\u91cf\u51fd\u6570\u7684\u5206\u5e03","title":"\u968f\u673a\u53d8\u91cf\u51fd\u6570\u7684\u5206\u5e03","text":"<p>\u5982\u679c\uff1a</p> <ul> <li>\\(X\\) \u4e3a\u8fde\u7eed\u578b\u968f\u673a\u53d8\u91cf\uff0c\u4e14\u5176\u5bc6\u5ea6\u51fd\u6570\u4e3a \\(f_X(x)\\)\uff1b</li> <li>\u968f\u673a\u53d8\u91cf \\(Y=g(X)\\)\uff1b</li> <li>\u51fd\u6570 \\(y=g(x)\\) \u4e3a\u4e00\u4e25\u683c\u5355\u8c03\uff08\u589e/\u51cf\uff09\u51fd\u6570\uff0c\u5e76\u4e14\u53ef\u5fae\uff1b</li> </ul> <p>\u5219\u8bb0 \\(y=g(x)\\) \u7684\u53cd\u51fd\u6570\u4e3a \\(x=h(y)\\)\uff0c\u5f97\u5230 \\(Y\\) \u7684\u5bc6\u5ea6\u51fd\u6570\u4e3a\uff1a</p> \\[ f_Y(y)=\\begin{cases} f_X(h(y))\u00b7|h'(y)|\\;, &amp; y\\in D,\\\\[1ex] 0, &amp; y\\not\\in D \\end{cases} \\] <ul> <li>\u5176\u4e2d \\(D\\) \u4e3a \\(y=g(x)\\) \u7684\u503c\u57df\u3002</li> </ul> <p>\u6709\u5173\u6b63\u6001\u5206\u5e03\u7684\u91cd\u8981\u7ed3\u8bba\uff1a</p> <p>\u82e5 \\(X\\sim N(\\mu,\\sigma^2)\\)\uff0c\u5219 \\(Y=aX+b \\sim N(a\\mu+b,a^2\\sigma^2)\\)</p> <ul> <li>\u6807\u51c6\u5316\uff1a\u7279\u522b\u7684\uff0c\u82e5 \\(X\\sim N(\\mu,\\sigma^2)\\)\uff0c\u5219 \\(\\frac{X-\\mu}{\\sigma}\\sim N(0,1)\\)\uff1b</li> <li>\u5373\u6b63\u6001\u5206\u5e03\u7684\u968f\u673a\u53d8\u91cf\u7ebf\u6027\u53d8\u6362\u540e\u6b63\u6001\u6027\u4e0d\u53d8\uff1b</li> </ul>"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap03/","title":"[3.x] \u591a\u5143\u968f\u673a\u53d8\u91cf\u53ca\u5176\u5206\u5e03","text":"<p> \u7ea6 406 \u4e2a\u5b57  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 1 \u5206\u949f</p>"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap03/#\u4e8c\u7ef4\u79bb\u6563\u578b\u968f\u673a\u53d8\u91cf","title":"\u4e8c\u7ef4\u79bb\u6563\u578b\u968f\u673a\u53d8\u91cf","text":""},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap03/#\u8054\u5408\u5206\u5e03\u5f8b","title":"\u8054\u5408\u5206\u5e03\u5f8b","text":"<ul> <li>\u8054\u5408\u5206\u5e03\u5f8b\uff08Joint Mass Function\uff09 \\(P(X=x_i,Y=y_j)=p_{ij}, \\; i,j=1,2,\\dots\\)\uff1b</li> </ul>"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap03/#\u8fb9\u9645\u5206\u5e03\u5f8b","title":"\u8fb9\u9645\u5206\u5e03\u5f8b","text":"<ul> <li>\u8fb9\u9645\u5206\u5e03\u5f8b\uff08Marginal Mass Function\uff09\u662f\u8054\u5408\u5206\u5e03\u5f8b\u7684\u884c/\u5217\u6c42\u548c\uff1b</li> <li>\\(P(X=x_i)=P(X=x_1,\\bigcup_{j=1}^{\\infty}(Y=y_j))=\\sum_{j=1}^{\\infty}p_{ij}:=p_{i\u00b7}\\)\uff1b</li> <li>\\(P(Y=y_j)=P(\\bigcup_{j=1}^{\\infty}(X=x_i),Y=y_j)=\\sum_{i=1}^{\\infty}p_{ij}:=p_{\u00b7j}\\)\uff1b</li> </ul>"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap03/#\u6761\u4ef6\u5206\u5e03\u5f8b","title":"\u6761\u4ef6\u5206\u5e03\u5f8b","text":"<ul> <li>\u6761\u4ef6\u5206\u5e03\u5f8b\uff08Conditional Mass Function\uff09 \\(P\\{X=x_i|Y=y_j\\}=\\frac{P(X=x_i,Y=y_j)}{P(Y=y_j)}=\\frac{p_{ij}}{p_{\u00b7j}}\\;\\;i,j=1,2,...\\)\uff1b</li> <li>\\(P\\{X&lt;x|Y&lt;y\\}=\\frac{P\\{X&lt;x,Y&lt;y\\}}{P\\{Y&lt;y\\}}\\)\uff0c\u7136\u540e\u6839\u636e\u8054\u5408\u5206\u5e03\u5f8b\u548c\u8fb9\u9645\u5206\u5e03\u5f8b\u8bfb\u8868\u8ba1\u7b97\uff1b</li> </ul>"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap03/#\u4e8c\u7ef4\u968f\u673a\u53d8\u91cf\u7684\u5206\u5e03\u51fd\u6570","title":"\u4e8c\u7ef4\u968f\u673a\u53d8\u91cf\u7684\u5206\u5e03\u51fd\u6570","text":""},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap03/#\u8054\u5408\u5206\u5e03\u51fd\u6570","title":"\u8054\u5408\u5206\u5e03\u51fd\u6570","text":"<p>\\(F(x,y)=P\\{X\\leq x,Y\\leq y\\}\\) \u4e3a \\((X,Y)\\) \u7684\u8054\u5408\u6982\u7387\u5206\u5e03\u51fd\u6570\uff0c\u7b80\u79f0\u8054\u5408\u5206\u5e03\u51fd\u6570\uff08Joint Distribution Function\uff09\uff0c\u5176\u5177\u6709\u5982\u4e0b\u6027\u8d28\uff1a</p> <ol> <li>\u56fa\u5b9a\u5176\u4e2d\u4e00\u4e2a\u53d8\u91cf\uff0c\u5219\u8be5\u4e8c\u5143\u51fd\u6570\u5173\u4e8e\u53e6\u5916\u4e00\u4e2a\u53d8\u91cf\u5355\u8c03\u4e0d\u51cf\uff1b</li> <li>\\(0\\leq F(x,y)\\leq 1\\)\uff0c\u4e14 \\(F(x,-\\infty)=F(-\\infty,y)=F(-\\infty,-\\infty)=0\\;,\\;F(+\\infty,+\\infty)=1\\)\uff1b</li> <li>\\(F(x,y)\\) \u5173\u4e8e \\(x\\) \u548c \\(y\\) \u5206\u522b\u53f3\u8fde\u7eed\uff08\u79bb\u6563\uff09\uff1b</li> <li>\\(x_1&lt;x_2\\;,\\;y_1&lt;y_2\\) \u65f6\uff0c\u6709\uff1a \\(P\\{x_1&lt;X\\leq x_2\\;,\\;y_1&lt;Y\\leq y_2\\}=F(x_2,y_2)-F(x_1,y_2)-F(x_2,y_1)+F(x_1,y_1)\\geq 0\\)</li> </ol> <ul> <li>Tips\uff1a\u8003\u8651\u51e0\u4f55\u610f\u4e49\uff01</li> </ul>"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap03/#\u8fb9\u9645\u5206\u5e03\u51fd\u6570","title":"\u8fb9\u9645\u5206\u5e03\u51fd\u6570","text":"<p>\\(F_X(x)=P\\{X\\leq x\\}=P\\{X\\leq x ,Y&lt;+\\infty\\}=F(x,+\\infty)=\\int_{-\\infty}^{+\\infty}f(x,y)dy\\) \u4e3a \\(X\\) \u5173\u4e8e\u8054\u5408\u5206\u5e03\u51fd\u6570 \\(F(x,y)\\) \u7684\u8fb9\u9645\u5206\u5e03\u51fd\u6570\uff08Marginal Distribution Function\uff09\u3002</p> <ul> <li>\u5bf9 \\(y\\) \u6765\u8bf4\u540c\u7406\u3002</li> </ul>"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap03/#\u6761\u4ef6\u5206\u5e03\u51fd\u6570","title":"\u6761\u4ef6\u5206\u5e03\u51fd\u6570","text":"<p>\\(F_{Y|X}(y|x)=P\\{Y\\leq y | X = x\\}=\\frac{P\\{Y\\leq y,X=x\\}}{P\\{X=x\\}}\\) \u4e3a \\(\\{ X=x \\}\\) \u6761\u4ef6\u4e0b \\(Y\\) \u7684\u6761\u4ef6\u5206\u5e03\u51fd\u6570\uff08Conditional Distribution Function\uff09\u3002</p> <p>\u8fdb\u4e00\u6b65\u63a8\u5e7f\uff0c\u82e5 \\(P(X=x)=0\\)\uff0c\u4f46\u5bf9\u4efb\u610f\u7ed9\u5b9a\u7684 \\(\\epsilon\\)\uff0c\\(P(x&lt;X\\leq x+\\epsilon)&gt;0\\)\uff0c\u5219\u5728 \\(\\{ X=x \\}\\) \u6761\u4ef6\u4e0b\uff0c\\(Y\\) \u7684\u6761\u4ef6\u5206\u5e03\u51fd\u6570\u4e3a \\(F_{Y|X}(y|x)=\\lim_{\\epsilon \\rarr 0^+}P\\{Y\\leq y|x&lt;X\\leq x+\\epsilon \\}\\)\uff0c\u4ecd\u8bb0\u4e3a \\(P\\{Y\\leq y | X = x\\}\\)\u3002</p>"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap03/#\u4e8c\u7ef4\u8fde\u7eed\u578b\u968f\u673a\u53d8\u91cf","title":"\u4e8c\u7ef4\u8fde\u7eed\u578b\u968f\u673a\u53d8\u91cf","text":""},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap03/#\u8054\u5408\u5bc6\u5ea6\u51fd\u6570","title":"\u8054\u5408\u5bc6\u5ea6\u51fd\u6570","text":"<p>\u8bbe\u4e8c\u5143\u968f\u673a\u53d8\u91cf \\((X,Y)\\) \u7684\u8054\u5408\u5206\u5e03\u51fd\u6570\u4e3a \\(F(x,y)\\)\uff0c\u82e5\u5b58\u5728\u4e8c\u5143\u51fd\u6570 \\(f(x,y)\\geq 0\\)\uff0c\u5219\u5bf9\u4e8e\u4efb\u610f\u7684\u5b9e\u6570 \\(x\\)\uff0c\\(y\\) \u6709 \\(F(x,y)=\\int_{-\\infty}^x\\int_{-\\infty}^yf(u,v)\\mathrm{d}u\\mathrm{d}v\\)\uff0c\u5219\u79f0 \\((X,Y)\\) \u4e3a\u4e8c\u7ef4\u8fde\u7eed\u578b\u968f\u673a\u53d8\u91cf\uff08Bivariate Continuous Random Variable\uff09\uff0c\u79f0 \\(f(x,y)\\) \u4e3a \\((X,Y)\\) \u7684\u8054\u5408\u6982\u7387\u5bc6\u5ea6\u51fd\u6570\uff08Joint Probability Density Function\uff09\uff0c\u7b80\u79f0\u4e3a\u8054\u5408\u5bc6\u5ea6\u51fd\u6570\u3002 \u5176\u5177\u6709\u4ee5\u4e0b\u6027\u8d28\uff1a</p> <ol> <li>\\(f(x,y)\\geq 0\\)\uff1b</li> <li>\\(F(+\\infty,+\\infty)=\\int_{-\\infty}^{+\\infty}\\int_{-\\infty}^{+\\infty}f(u,v)\\mathrm{d}u\\mathrm{d}v=1\\)\uff1b</li> <li>\u5728 \\(f(x,y)\\) \u7684\u8fde\u7eed\u70b9 \\((x,y)\\) \u4e0a\u6709 \\(\\frac{\\partial^2F(x,y)}{\\partial x\\partial y}=f(x,y)\\)\uff1b</li> <li>\\((X,Y)\\) \u843d\u5165 \\(xOy\\) \u5e73\u9762\u4efb\u610f\u533a\u57df \\(D\\) \u7684\u6982\u7387\u4e3a\uff1a\\(P\\{(X,Y)\\in D\\}=\\iint \\limits_{D} f(x,y)\\mathrm{d}x\\mathrm{d}y\\)\uff1b</li> <li>\u7531\u4e8e\u5176\u51e0\u4f55\u610f\u4e49\u4e3a\u843d\u5728\u4ee5 \\(D\\) \u4e3a\u5e95\uff0c\u4ee5\u66f2\u9762 \\(z=f(x,y)\\) \u4e3a\u9876\u9762\u7684\u67f1\u4f53\u4f53\u79ef\uff0c\u6240\u4ee5\u5f53 \\(D\\) \u9762\u79ef\u4e3a \\(0\\) \u65f6\u6982\u7387\u4e3a \\(0\\)\uff1b</li> <li><code>eg</code>\uff1a\\(P(X=1,Y=1)=0\\)\uff0c\\(P(X+Y=1)=0\\)\uff0c\\(P(X^2+Y^2=1)\\not =0\\)\uff1b</li> </ol>"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap03/#\u8fb9\u9645\u5bc6\u5ea6\u51fd\u6570","title":"\u8fb9\u9645\u5bc6\u5ea6\u51fd\u6570","text":"<p>\\(f_X(x)=\\int_{-\\infty}^{+\\infty}f(x,y)dy\\) \u4e3a\u8fb9\u9645\u6982\u7387\u5bc6\u5ea6\u51fd\u6570\uff08Marginal Probability Density Function\uff09\uff0c\u7b80\u79f0\u8fb9\u9645\u5bc6\u5ea6\u51fd\u6570\u3002</p>"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap03/#\u6761\u4ef6\u5bc6\u5ea6\u51fd\u6570","title":"\u6761\u4ef6\u5bc6\u5ea6\u51fd\u6570","text":"<p>\u5728\u7ed9\u5b9a \\(\\{X=x\\}\\) \u7684\u6761\u4ef6\u4e0b\uff0c\\(Y\\) \u7684\u6761\u4ef6\u6982\u7387\u5bc6\u5ea6\u51fd\u6570\uff08Conditional Prob-ability Density Function\uff09\u4e3a \\(f_{Y|X}(y|x)=\\frac{\\int^y_{-\\infty}f(x,v)\\mathrm{d}v}{f_X(x)}=\\frac{f(x,y)}{f_X(x)}\\;,\\;\\;f_X(x)\\not= 0\\)\uff0c\u7b80\u79f0\u6761\u4ef6\u5bc6\u5ea6\u51fd\u6570\u3002</p> <ul> <li>\u5bf9 \\(Y\\) \u6765\u8bf4\u540c\u7406\u3002</li> </ul>"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap03/#\u4e8c\u7ef4\u5747\u5300\u5206\u5e03\u4e0e\u4e8c\u7ef4\u6b63\u6001\u5206\u5e03","title":"\u4e8c\u7ef4\u5747\u5300\u5206\u5e03\u4e0e\u4e8c\u7ef4\u6b63\u6001\u5206\u5e03","text":"<p>\u5747\u5300\u5206\u5e03</p> <p>\u5982\u679c\u4e8c\u5143\u968f\u673a\u53d8\u91cf \\((X,Y)\\) \u5728\u4e8c\u7ef4\u6709\u754c\u533a\u95f4 \\(D\\) \u4e0a\u53d6\u503c\uff0c\u4e14\u5177\u6709\u8054\u5408\u5bc6\u5ea6\u51fd\u6570\uff1a</p> \\[ f(x,y)= \\begin{cases} \\frac{1}{\\text{Area of } D},&amp;(x,y)\\in D\\\\[1ex] 0,&amp;\\text{else} \\end{cases} \\] <p>\u5219\u79f0 \\((X,Y)\\) \u670d\u4ece \\(D\\) \u4e0a\u7684\u5747\u5300\u5206\u5e03\u3002\u5f97\u5230\uff1a</p> \\[ P\\{(X,Y)\\in D\\}=\\frac{\\text{Area of }D_1}{\\text{Area of }D}\\;,\\;\\;\\text{while }D_1\\subset D \\] <p>\u6b63\u6001\u5206\u5e03</p> <p>\u5982\u679c\u4e8c\u5143\u968f\u673a\u53d8\u91cf \\((X,Y)\\) \u5177\u6709\u8054\u5408\u5bc6\u5ea6\u51fd\u6570\uff1a</p> \\[ f(x,y)= \\frac{1}{ 2 \\pi \\sigma_1 \\sigma_2 \\sqrt{1-\\rho^2} } \\exp \\{   \\frac{-1}{ 2(1-\\rho^2) }   [     \\frac{ (x-\\mu)^2 }{ \\sigma_1^2 } - 2\\rho\\frac{ (x-\\mu_1)(y-\\mu_2) }{ \\sigma_1\\sigma_2 } + \\frac{ (y-\\mu_2)^2 }{ \\sigma_2^2 }   ] \\} \\] <p>\u4e14\u6709 \\(|\\mu_1|&lt;+\\infty\\)\uff0c\\(|\\mu_2|&lt;+\\infty\\)\uff0c\\(\\sigma_1&gt;0\\)\uff0c\\(\\sigma_2&gt;0\\)\uff0c\\(|\\rho|&lt;1\\)</p> <p>\u5219\u79f0 \\((X,Y)\\) \u670d\u4ece\u53c2\u6570\u4e3a \\((\\mu_1,\\mu_2,\\sigma_1^2,\\sigma_2^2,\\rho)\\) \u7684\u4e8c\u5143\u6b63\u6001\u5206\u5e03\uff08Bivariate Normal Distribution\uff09\uff0c\u8bb0\u505a \\((X,Y)\\sim N(\\mu_1,\\mu_2,\\sigma_1^2,\\sigma_2^2,\\rho)\\)\u3002</p> <ul> <li>\u4e8c\u7ef4\u6b63\u6001\u5206\u5e03\u7684\u4e24\u4e2a\u8fb9\u9645\u5206\u5e03\u90fd\u662f\u5bf9\u5e94\u53c2\u6570\u7684\u4e00\u7ef4\u6b63\u6001\u5206\u5e03\uff0c\u4e0e \\(\\rho\\) \u65e0\u5173\u3002</li> </ul>"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap03/#\u968f\u673a\u53d8\u91cf\u7684\u72ec\u7acb\u6027","title":"\u968f\u673a\u53d8\u91cf\u7684\u72ec\u7acb\u6027","text":"<p>\u5982\u679c\u5bf9\u4e8e\u4efb\u610f\u7684\u4e24\u4e2a\u5b9e\u6570\u96c6\u5408\\(D_1,D_2\\)\uff0c\u6709\\(P\\{X\\in D_1,Y\\in D_2\\}=P\\{X\\in D_1\\}\u00b7P\\{Y\\in D_2\\}\\)\uff0c\u5219\u79f0\u968f\u673a\u53d8\u91cf\\(X,Y\\)\u76f8\u4e92\u72ec\u7acb\uff0c\u5373\\(X,Y\\)\u72ec\u7acb\u3002\u5373\u540c\u65f6\u6709\\(P\\{X\\leq x,Y\\leq y\\}=P\\{X\\leq x\\}\u00b7P\\{Y\\leq y\\}\\)\uff0c\u5373\\(F(x,y)=F_X(x)\u00b7F_Y(y)\\)\u65f6\uff0c\\(X,Y\\)\u72ec\u7acb\u3002</p>"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap03/#\u5377\u79ef\u516c\u5f0f","title":"\u5377\u79ef\u516c\u5f0f","text":"<p>\u5f53 \\(X\\) \u548c \\(Y\\) \u76f8\u4e92\u72ec\u7acb\u65f6\uff0c\\(Z=X+Y\\) \u7684\u6761\u4ef6\u4e0b\uff1a</p> <ol> <li> <p>\\(F_Z(z) = \\iint \\limits_{x+y\\leq z}f(x,y)\\mathrm{d}x\\mathrm{d}y=\\int_{-\\infty}^{+\\infty}[\\int_{-\\infty}^{z-x}f(x,u-x)\\mathrm{d}y]\\mathrm{d}x = \\int_{-\\infty}^{+\\infty}[\\int_{-\\infty}^{z}f(x,u-x)\\mathrm{d}u]\\mathrm{d}x=\\int_{-\\infty}^{z}[\\int_{-\\infty}^{+\\infty}f(x,u-x)\\mathrm{d}x]\\mathrm{d}u =\\int_{-\\infty}^{z}f_Z(u)\\mathrm{d}y\\)\uff1b</p> </li> <li> <p>\u5176\u5bc6\u5ea6\u51fd\u6570\u516c\u5f0f\u79f0\u4e3a\u5377\u79ef\u516c\u5f0f\uff1a\\(f_X*f_Y=\\int_{-\\infty}^{+\\infty}f_X(x)f_Y(z-x)\\mathrm{d}x=\\int_{-\\infty}^{+\\infty}f_X(z-y)f_Y(y)\\mathrm{d}y\\)\uff1b</p> </li> </ol> <p>\\(M=max(X,Y)\\;\\;and\\;\\;N=min(X,Y)\\) \u7684\u5206\u5e03\uff1a</p> <ul> <li>\\(F_{max}(z)=P(M\\leq z)=P(X\\leq z,Y\\leq z)\\xlongequal{\\text{X,Y independent}}P(X\\leq z)P(Y\\leq z)=F_X(z)F_Y(z)\\)\uff1b</li> <li>\\(F_{min}(z)=P(N\\leq z)=1-P(N&gt;z)=1-P(X&gt;z,Y&gt;z)\\xlongequal{\\text{X,Y independent}}1-P(X&gt;z)P(Y&gt;z)=1-(1-F_X(z))(1-F_Y(z))\\)\uff1b</li> </ul>"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap04/","title":"[4.x] \u968f\u673a\u53d8\u91cf\u7684\u6570\u5b57\u7279\u5f81","text":"<p> \u7ea6 1668 \u4e2a\u5b57  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 6 \u5206\u949f</p> <p>\u8bbe\u79bb\u6563\u968f\u673a\u53d8\u91cf\\(X\\)\u7684\u6982\u7387\u5206\u5e03\u7387\u4e3a\\(P\\{X=x_i\\}=p_i,\\;\\;i=1,2,...\\)\uff0c\u82e5\u7ea7\u6570\\(\\sum_{i=1}^{+\\infty}=|x_i|p_i&lt;+\\infty\\)\uff08\u7edd\u5bf9\u6536\u655b\uff09\uff0c\u5219\u79f0\u7ea7\u6570\\(\\sum_{i=1}^{+\\infty}x_ip_i\\)\u4e3a\\(X\\)\u7684\u6570\u5b66\u671f\u671b\uff08Mathematical Expectation\uff09\u6216\u5747\u503c\uff08Mean\uff09\uff0c\u7b80\u79f0\u4e3a\u671f\u671b\uff0c\u8bb0\\(E(X)=\\sum_{i=1}^{+\\infty}x_ip_i\\)\u3002\u5982\u679c\\(\\sum_{i=1}^{+\\infty}=|x_i|p_i=+\\infty\\)\u5219\u79f0\u968f\u673a\u53d8\u91cf\\(X\\)\u7684\u6570\u5b66\u671f\u671b\u4e0d\u5b58\u5728\u3002</p> <p>\u8bbe\u8fde\u7eed\u968f\u673a\u53d8\u91cf\\(X\\)\u7684\u5bc6\u5ea6\u51fd\u6570\u4e3a\\(f(x)\\)\uff0c\u82e5\\(\\int^{+\\infty}_{-\\infty}|x|f(x)\\mathrm{d} x&lt;+\\infty\\)\uff0c\u5219\u79f0\u79ef\u5206\\(\\int^{+\\infty}_{-\\infty}xf(x)\\mathrm{d} x\\)\u4e3a\\(X\\)\u7684\u6570\u5b66\u671f\u671b\u6216\u5747\u503c\uff0c\u7b80\u79f0\u4e3a\u671f\u671b\uff0c\u8bb0\\(E(X)=\\int^{+\\infty}_{-\\infty}xf(x)\\mathrm{d} x\\)\u3002\u5982\u679c\\(\\int^{+\\infty}_{-\\infty}|x|f(x)\\mathrm{d} x=+\\infty\\)\u5219\u79f0\u968f\u673a\u53d8\u91cf\\(X\\)\u7684\u6570\u5b66\u671f\u671b\u4e0d\u5b58\u5728\u3002</p> <p>\u6cca\u677e\u5206\u5e03\u7684\u6570\u5b66\u671f\u671b\u8bbe\u968f\u673a\u53d8\u91cf\\(X\\)\u670d\u4ece\u6cca\u677e\u5206\u5e03\\(P(\\lambda)\\;(\\lambda&gt;0)\\)\uff0c\u5219\uff1a\\(E(X)=\\sum_{k=0}^{+\\infty}k\u30fb P\\{X=k\\}=\\sum_{k=0}^{+\\infty}k\u30fb\\frac{\\lambda^{k}}{k!}e^{-\\lambda}=\\lambda\\sum_{k=1}^{+\\infty}\\frac{\\lambda^{k-1}}{(k-1)!}e^{-\\lambda}=\\lambda\\) \u7531\u6b64\u5f0f\u53ef\u77e5\uff0c\u5df2\u77e5\u6cca\u677e\u5206\u5e03\u7684\u6570\u5b66\u671f\u671b\u53ef\u4ee5\u786e\u5b9a\u6cca\u677e\u5206\u5e03\u3002</p> <p>\u6307\u6570\u5206\u5e03\u7684\u6570\u5b66\u671f\u671b\u8bbe\u968f\u673a\u53d8\u91cf\\(X\\)\u670d\u4ece\u6307\u6570\u5206\u5e03\\(E(\\lambda)\\;(\\lambda&gt;0)\\)\uff0c\u5219\uff1a\\(E(X)=\\int_{-\\infty}^{+\\infty}xf(x)\\mathrm{d}x=\\int_{0}^{+\\infty}x\\lambda e^{-\\lambda x}\\mathrm{d}x=-\\int_{0}^{+\\infty}x\\mathrm{d}e^{-\\lambda x}\\\\=-(xe^{-\\lambda x})\\big|_{0}^{+\\infty}+\\int_{0}^{+\\infty}e^{-\\lambda x}\\mathrm{d}x=\\frac{1}{\\lambda}\\) \u7531\u6b64\u5f0f\u53ef\u77e5\uff0c\u5df2\u77e5\u6307\u6570\u5206\u5e03\u7684\u6570\u5b66\u671f\u671b\u53ef\u4ee5\u786e\u5b9a\u6307\u6570\u5206\u5e03\u3002</p> <p>\u6807\u51c6\u6b63\u6001\u5206\u5e03\u7684\u6570\u5b66\u671f\u671b\u8bbe\u968f\u673a\u53d8\u91cf\\(X\\)\u670d\u4ece\u6807\u51c6\u6b63\u6001\u5206\u5e03\\(N(0,1)\\)\uff0c\u6ce8\u610f\u5230\u5176\u7684\u5bc6\u5ea6\u51fd\u6570\uff1a\\(\\varphi(x)=\\frac{1}{\\sqrt{2\\pi}}e^{-x^2/2},\\;x\\in \\R\\)\u4e3a\u5076\u51fd\u6570\uff0c\u90a3\u4e48\\(x\\varphi(x)\\)\u662f\u5947\u51fd\u6570\uff0c\u6240\u4ee5\\(E(x)=0\\)</p> <p>\u5bf9\u4e8e\u968f\u673a\u53d8\u91cf\u51fd\u6570\uff0c\u53ea\u9700\u8981\u5c06\u5b9a\u4e49\u4e2d\\(x_i\\)\u6362\u4e3a\\(g(x_i)\\)\u5373\u53ef\uff0c\u5f53\u7136\u9700\u8981\u4fdd\u8bc1\u671f\u671b\u5b58\u5728\u3002\u800c\u9664\u4e86\u5b9a\u4e49\u8ba1\u7b97\uff0c\u4e5f\u6709\u4e00\u4e9b\u6027\u8d28\u53ef\u4ee5\u7b80\u5316\u8ba1\u7b97\u3002</p> <p>\u6570\u5b66\u671f\u671b\u7684\u6027\u8d28\uff1a</p> <ol> <li>\u82e5\\(C\\)\u662f\u5e38\u6570\uff0c\u5219\\(E(C) = C\\)\uff1b</li> <li>\u8bbe\\(X\\)\u662f\u968f\u673a\u53d8\u91cf\uff0c\\(C\\)\u662f\u5e38\u6570\uff0c\u5219\\(E(C\u30fbX)=C\u30fbE(X)\\)\uff1b</li> <li>\u8bbe\\(X,Y\\)\u662f\u4e24\u4e2a\u968f\u673a\u53d8\u91cf\uff0c\u5219\\(E(X+Y)=E(X)+E(Y)\\)\uff1b</li> <li>\u8fd9\u4e00\u6027\u8d28\u53ef\u4ee5\u63a8\u5e7f\u5230\u4efb\u610f\u6709\u9650\u4e2a\u968f\u673a\u53d8\u91cf\u7ebf\u6027\u7ec4\u5408\u7684\u60c5\u51b5\uff1a\\(E(\\sum^n_i{c_i\u30fbX_i})=\\sum^n_i c_i\u30fbE(X_i)\\)\uff1b</li> <li>\u4e0a\u8ff0\u4e09\u6761\u5408\u5e76\u8d77\u6765\u5c31\u662f\\(E(aX+bY+c)=aE(X)+bE(Y)+c\\)\uff1b</li> <li>\u8bbe\\(X,Y\\)\u662f\u76f8\u4e92\u72ec\u7acb\u7684\u968f\u673a\u53d8\u91cf\uff0c\u5219\\(E(X\u30fbY)=E(X)\u30fbE(Y)\\)\uff0c\u4f46\u9006\u547d\u9898\u4e0d\u6210\u7acb\uff1b</li> <li>\u8fd9\u4e00\u6027\u8d28\u53ef\u4ee5\u63a8\u5e7f\u5230\u4efb\u610f\u6709\u9650\u4e2a\u968f\u673a\u53d8\u91cf\uff1a\\(E(\\prod_i^nX_i)=\\prod_i^nE(X_i)\\)\uff1b</li> </ol> <p>\u8bbe\\(X\\)\u4e3a\u968f\u673a\u53d8\u91cf\uff0c\u82e5\\(E\\{[X-E(X)]^2\\}\\)\u5b58\u5728\uff0c\u5219\u79f0\u5176\u4e3a\\(X\\)\u7684\u65b9\u5dee\uff0c\u8bb0\u4f5c\\(Var(X)\\)\u6216\\(D(X)\\)\uff0c\u5373\\(Var(X)=E\\{[X-E(X)]^2\\}\\)\u3002\u8bb0\\(\\delta(X)=\\sqrt{(Var(X))}\\)\u4e3a\\(X\\)\u7684\u6807\u51c6\u5dee\u6216\u5747\u65b9\u5dee\u3002</p> <p>\u6570\u5b66\u671f\u671b\u5b58\u5728\u662f\u65b9\u5dee\u5b58\u5728\u7684\u5fc5\u8981\u4f46\u4e0d\u5145\u5206\u5b58\u5728\u3002</p> <p>\u65b9\u5dee\u523b\u753b\u4e86\\(X\\)\u53d6\u503c\u7684\u5206\u6563\u7a0b\u5ea6\uff1a</p> <ul> <li>\u82e5\\(X\\)\u53d6\u503c\u96c6\u4e2d\uff0c\u5219\\(Var(X)\\)\u8f83\u5c0f\uff1b</li> <li>\u82e5\\(X\\)\u53d6\u503c\u5206\u6563\uff0c\u5219\\(Var(X)\\)\u8f83\u5927\uff1b</li> </ul> <p>\u800c\u5176\u8ba1\u7b97\u65b9\u6cd5\u53ef\u4ee5\u5229\u7528\u671f\u671b\u7684\u6027\u8d28\uff0c\u8bb0\\(g(X)=(X-E(X))^2\\)\uff0c\u7136\u540e\u8ba1\u7b97\\(E(g(X))\\)\u3002\u5177\u4f53\u7684\uff1a</p> <ul> <li>\u79bb\u6563\u578b\uff1a\\(Var(X)=E\\{[X-E(X)]^2\\}=\\sum_{i=1}^{+\\infty}[x_i-E(X)]^2p_i\\)\uff1b</li> <li>\u8fde\u7eed\u578b\uff1a\\(Var(X)=E\\{[X-E(X)]^2\\}=\\int_{-\\infty}^{+\\infty}[x-E(X)]^2f(x)\\mathrm dx\\)\uff1b</li> <li>\u800c\u5229\u7528\u671f\u671b\u7684\u6027\u8d28\uff0c\u53ef\u4ee5\u5f97\u5230\\(Var(X)=E(X^2)-E^2(X)\\)\uff1b</li> </ul> <p>\u6cca\u677e\u5206\u5e03\u7684\u65b9\u5dee\\(\\because E(X^2)=E(X(X-1)+X)=E(X(X-1))+E(X)=\\sum_{k=0}^{\\infty}k(k-1)\\frac{\\lambda^ke^{-\\lambda}}{k!}+\\lambda=\\lambda^2+\\lambda\\\\ \\therefore Var(X)=E(X^2)+E^2(X)=\\lambda\\)</p> <p>\u6307\u6570\u5206\u5e03\u7684\u65b9\u5dee\\(\\because E(X^2)=\\int_{-\\infty}^{+\\infty}x^2f(x)\\mathrm dx=\\int_0^{+\\infty}x^2\\lambda e^{-\\lambda x}\\mathrm d x=-x^2e^{-\\lambda x}\\big|^{+\\infty}_0+\\int^{+\\infty}_{0}2xe^{-\\lambda x}\\mathrm dx=\\frac{2}{\\lambda^2}\\\\ \\therefore Var(X)=E(X^2)-E^2(X)=\\frac{1}{\\lambda^2}\\)</p> <p>\u65b9\u5dee\u7684\u6027\u8d28\uff1a</p> <ol> <li>\u82e5\\(C\\)\u662f\u5e38\u6570\uff0c\u5219\\(Var(C) = 0\\)\uff1b</li> <li>\u8bbe\\(X\\)\u662f\u968f\u673a\u53d8\u91cf\uff0c\\(C\\)\u662f\u5e38\u6570\uff0c\u5219\\(Var(C\u30fbX)=C^2\u30fbVar(X)\\)\uff1b</li> <li>\u8bbe\\(X,Y\\)\u662f\u4e24\u4e2a\u968f\u673a\u53d8\u91cf\uff0c\u5219\\(Var(X\\pm Y)=Var(X)+Var(Y)\\pm2E\\{[X-E(X)][Y-E(Y)]\\}\\\\=Var(X)+Var(Y)\\pm 2Cov(X,Y)\\)\uff1b</li> <li>\u7279\u522b\u7684\uff0c\u5982\u679c\\(X,Y\\)\u76f8\u4e92\u72ec\u7acb\uff0c\u5219\\(Var(X\\pm Y)=Var(X)+Var(Y)\\)\uff1b</li> <li>\u8fdb\u4e00\u6b65\u7684\uff0c\u5982\u679c\\(X_i\\;(i=1,2,...,n)\\)\u5f7c\u6b64\u72ec\u7acb\uff0c\u5219\\(Var(c_1X_1\\pm c_2X_2\\pm...\\pm c_nX_n)=c_1^2Var(X_1)+c_2^2Var(X_2)+...+c_n^2Var(X_n)\\)</li> <li>\u4e0a\u8ff0\u4e09\u6761\u5408\u5e76\u8d77\u6765\u5c31\u662f\\(Var(aX+bY+c)=a^2Var(X)+b^2Var(Y)\\)\uff1b</li> <li>\\(Var(X)\\leq E((X-c)^2)\\)\uff0c\u5e76\u4e14\u5f53\u4e14\u4ec5\u5f53\\(E(X)=c\\)\u65f6\u7b49\u53f7\u6210\u7acb\uff1b</li> <li>\\(Var(X)=0 \\;\\;\\;\\;\\;\\Leftrightarrow \\;\\;\\;\\;\\;P(X=c)=1 \\;\\;\\;and\\;\\;\\;c=E(X)\\)\uff1b</li> </ol> <p>\u53d8\u5f02\u7cfb\u6570\u53c8\u53eb\u201c\u6807\u51c6\u5dee\u7387\u201d\uff0c\u662f\u8861\u91cf\u8d44\u6599\u4e2d\u5404\u89c2\u6d4b\u503c\u53d8\u5f02\u7a0b\u5ea6\u7684\u53e6\u5916\u4e00\u4e2a\u6570\u5b57\u7279\u5f81\u3002\u53d8\u5f02\u7cfb\u6570\\(Cv(X)=\\frac{\\sqrt{Var(X)}}{E(X)}\\)\u540c\u6837\u63cf\u8ff0\u79bb\u6563\u7a0b\u5ea6\uff0c\u5b83\u53ef\u4ee5\u6d88\u9664\u5355\u4f4d\u6216\u5e73\u5747\u6570\u4e0d\u540c\u5bf9\u4e24\u4e2a\u6216\u591a\u4e2a\u8d44\u6599\u53d8\u5f02\u7a0b\u5ea6\u6bd4\u8f83\u7684\u5f71\u54cd\u3002</p> <p>\u968f\u673a\u53d8\u91cf\\(X,Y\\)\u7684\u534f\u65b9\u5dee\\(Cov(X,Y)=E\\{[X-E(X)][Y-E(Y)]\\}=E(XY)-E(X)E(Y)\\)</p> <p>\u968f\u673a\u53d8\u91cf\\(X,Y\\)\u7684\u76f8\u5173\u7cfb\u6570\\(\\rho _{_{XY}}=\\frac{Cov(X,Y)}{\\sqrt{Var(X)Var(Y)}}\\)</p> <p>\u534f\u65b9\u5dee\u7684\u6027\u8d28\uff1a</p> <ol> <li>\\(Cov(X,Y)=Cov(Y,X)\\)\uff1b</li> <li>\\(Cov(X,Y)=E(XY)-E(X)E(Y)\\)\uff1b</li> <li>\\(Cov(aX,bY)=abCov(X,Y)\\;,\\;\\;a,b\\in\\R\\)\uff1b</li> <li>\\(Cov(X+Y,Z)=Cov(X,Z)+Cov(Y,Z)\\)\uff1b</li> <li>\\(Cov(X,X)=Var(X)\\)\uff1b</li> <li>\\(Cov(c,Y)=E(cY)-E(c)E(Y)=0\\;,\\;\\;c\\in\\R\\)\uff1b</li> <li>\\(Cov(X+Y,X-Y)=Cov(X,X)-Cov(Y,Y)=Var(X)-Var(Y)\\)\uff1b</li> <li>\\(Cov(X^*,Y^*)=Cov(\\frac{X-E(X)}{\\sqrt{Var(X)}},\\frac{Y-E(Y)}{\\sqrt{Var(Y)}})=\\frac{Cov(X,Y)}{\\sqrt{Var(X)}\\sqrt{Var(Y)}}=\\rho_{_{XY}}\\)\uff1b</li> <li>\\(Cov(aX+bY,cX+dY)=acVar(X)+bdVar(Y)+(ad+bc)Cov(X,Y)\\)\uff1b</li> <li>\\(D(aX+bY)=a^2Var(X)+b^2Var(Y)+2abCov(X,Y)\\)\uff1b</li> </ol> <p>\u76f8\u5173\u7cfb\u6570\u7684\u6027\u8d28</p> <ol> <li>\\(|\\rho_{_{XY}}|\\leq 1\\)\uff1b</li> <li>\\(|\\rho_{_{XY}}|=1 \\;\\;\\; \\Leftrightarrow \\;\\;\\; \\exists a,b\\in \\R,\\;s.t.\\;P(Y=a+bX)=1|\\)\uff1b</li> <li>\\(\\rho_{_{XY}}=1\\)\u65f6\uff0c\\(b&gt;0\\)\uff1b</li> <li>\\(\\rho_{_{XY}}=-1\\)\u65f6\uff0c\\(b&lt;0\\)\uff1b</li> </ol> <p>\u76f8\u5173\u7cfb\u6570\\(\\rho_{_{XY}}\\)\u662f\u7528\u6765\u8868\u5f81\\(X,Y\\)\u4e4b\u95f4\u7ebf\u6027\u5173\u7cfb\u7d27\u5bc6\u7a0b\u5ea6\u7684\u91cf\uff1a</p> <ul> <li>\\(|\\rho_{_{XY}}|\\)\u6bd4\u8f83\u5927\u65f6\uff0c\u8bef\u5dee\u8f83\u5c0f\uff0c\u8868\u793a\\(X,Y\\)\u7ebf\u6027\u5173\u7cfb\u7684\u7a0b\u5ea6\u597d\uff1b</li> <li>\\(|\\rho_{_{XY}}|=1\\)\u65f6\uff0c\u8bef\u5dee\u4e3a\\(0\\)\uff0c\u8868\u793a\\(X,Y\\)\u4e4b\u95f4\u4ee5\u6982\u7387\\(1\\)\u5b58\u5728\u7ebf\u6027\u5173\u7cfb\uff1b</li> <li>\\(|\\rho_{_{XY}}|\\)\u6bd4\u8f83\u5c0f\u65f6\uff0c\u8bef\u5dee\u8f83\u5927\uff0c\u8868\u660e\\(X,Y\\)\u7ebf\u6027\u5173\u7cfb\u7684\u7a0b\u5ea6\u5dee\uff1b</li> <li>\\(\\rho_{_{XY}}&gt;0\\)\u65f6\uff0c\\(X,Y\\)\u6b63\u76f8\u5173\uff1b</li> <li>\\(\\rho_{_{XY}}&lt;0\\)\u65f6\uff0c\\(X,Y\\)\u8d1f\u76f8\u5173\uff1b</li> <li>\\(\\rho_{_{XY}}=0\\)\u65f6\uff0c\u79f0\\(X,Y\\)\u4e0d\u76f8\u5173\u6216\u96f6\u76f8\u5173\uff08\u4ec5\u4ec5\u5bf9\u4e8e\u7ebf\u6027\u5173\u7cfb\u6765\u8bf4\uff0c\u4e0e\u72ec\u7acb\u7684\u542b\u4e49\u4e0d\u540c\uff09\uff1b</li> <li>\u6b64\u65f6\u6709\uff1a</li> <li>\\(Cov(X,Y)=0\\)\uff1b</li> <li>\\(E(XY)=E(X)E(Y)\\)\uff1b</li> <li>\\(Var(X\\pm Y)=Var(X)+Var(Y)\\)\uff1b</li> <li>\u4e8e\u662f\u6709\u7ed3\u8bba\uff1a</li> </ul> <p>\\(X,Y\\text{\u4e92\u76f8\u72ec\u7acb} \\;\\; \\Rightarrow \\;\\; X,Y\\text{\u4e0d\u76f8\u5173}\\\\ X,Y\\text{\u4e0d\u72ec\u7acb}\\;\\;\\Leftarrow \\;\\;X,Y\\text{\u76f8\u5173}\\)</p> <p>\u591a\u5143\u968f\u673a\u53d8\u91cf\u7684\u6570\u5b57\u7279\u5f81\u8bbe\\(n\\)\u5143\u968f\u673a\u53d8\u91cf\\(X=(X_1,X_2,...,X_n)^T\\)\uff0c\u82e5\u6bcf\u4e00\u4e2a\u5206\u91cf\u7684\u6570\u5b66\u671f\u671b\u90fd\u5b58\u5728\uff0c\u5219\u79f0\\(E(X)=(E(X_1),E(X_2),...,E(X_n))^T\\)\u4e3a\\(n\\)\u5143\u968f\u673a\u53d8\u91cf\\(X\\)\u7684\u6570\u5b66\u671f\u671b\uff08\u5411\u91cf\uff09\u3002</p> <p>\u8bbe\\(n\\)\u7ef4\u968f\u673a\u53d8\u91cf\\(\\vec{X}=(X_1,X_2,...,X_n)^T\\)\uff0c\\(Cov(X_i,X_j)\\;\\;(i,j=1,2,...,n)\\)\u90fd\u5b58\u5728\uff0c\u5219\uff1a\\(\\begin{bmatrix}  Var(X_1) &amp; Cov(X_1,X_2) &amp; ... &amp; Cov(X_1,X_n)\\\\  Cov(X_2,X_1) &amp; Var(X_2) &amp; ... &amp; Cov(X_2,X_n)\\\\ ... &amp; ... &amp; ...  &amp; ... \\\\ Cov(X_n,X_1) &amp; Cov(X_n,X_2) &amp; ... &amp; Var(X_n) \\end{bmatrix}\\) \u79f0\u4e4b\u4e3a\\(\\vec{X}\\)\u7684\u534f\u65b9\u5dee\u77e9\u9635\u3002\u5b83\u662f\u4e00\u4e2a\u5bf9\u79f0\u7684\u975e\u8d1f\u5b9a\u77e9\u9635\u3002</p> <p>\\(n\\)\u7ef4\u6b63\u6001\u53d8\u91cf\u91cd\u8981\u6027\u8d28</p> <ol> <li>\\(n\\)\u7ef4\u6b63\u6001\u53d8\u91cf\\((X_1,X_2,...,X_n)\\)\u7684\u6bcf\u4e00\u4e2a\u5206\u91cf\\(X_i\\)\u90fd\u662f\u6b63\u6001\u53d8\u91cf\uff1b</li> <li>\u53cd\u4e4b\uff0c\u5982\u679c\\(X_i\\)\u90fd\u662f\u6b63\u6001\u53d8\u91cf\uff0c\u4e14\u76f8\u4e92\u72ec\u7acb\uff0c\u5219\\((X_1,X_2,...,X_n)\\)\u662f\\(n\\)\u7ef4\u6b63\u6001\u53d8\u91cf\uff1b</li> <li>\\(n\\)\u7ef4\u968f\u673a\u53d8\u91cf\\((X_1,X_2,...,X_n)\\)\u670d\u4ece\\(n\\)\u7ef4\u6b63\u6001\u5206\u5e03\u7684\u5145\u8981\u6761\u4ef6\u8bbe\u4e0d\u5168\u4e3a\\(0\\)\u7684\\(l_i\\)\u5e38\u6570\uff0c\u5747\u6709\\(\\sum_i^n l_iX_i\\)\u670d\u4ece\u4e00\u7ef4\u6b63\u6001\u5206\u5e03\uff1b</li> <li>\u82e5\\((X_1,X_2,...,X_n)\\)\u670d\u4ece\\(n\\)\u7ef4\u6b63\u6001\u5206\u5e03\uff0c\u8bbe\\(Y_1,Y_2,...,Y_k\\)\u662f\\(X_i\\)\u7684\u7ebf\u578b\u51fd\u6570\uff0c\u5219\\((Y_1,Y_2,...,Y_k)\\)\u4e5f\u670d\u4ece\u591a\u7ef4\u6b63\u6001\u5206\u5e03\uff1b</li> <li>\u82e5\\((X_1,X_2,...,X_n)\\)\u670d\u4ece\\(n\\)\u7ef4\u6b63\u6001\u5206\u5e03\uff0c\u5219\\(X_i\\)\u4e92\u76f8\u72ec\u7acb\u7684\u5145\u8981\u6761\u4ef6\u662f\\(X_i\\)\u4e24\u4e24\u4e0d\u76f8\u5173\uff1b</li> </ol>"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap05/","title":"[5.x] \u5927\u6570\u5b9a\u5f8b\u53ca\u4e2d\u5fc3\u6781\u9650\u5b9a\u7406","text":"<p> \u7ea6 1172 \u4e2a\u5b57  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 4 \u5206\u949f</p>"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap05/#\u4f9d\u6982\u7387\u6536\u655b","title":"\u4f9d\u6982\u7387\u6536\u655b","text":"<p>\u4f9d\u6982\u7387\u6536\u655b\u8bbe\\(\\{Y_n,n\\geq1\\}\\)\u4e3a\u4e00\u968f\u673a\u53d8\u91cf\u5e8f\u5217\uff0c\\(c\\)\u4e3a\u4e00\u5e38\u6570\u3002\u82e5\\(\\forall\\varepsilon&gt;0\\;\\;\\;s.t. \\;\\;\\lim_{n\\to+\\infty}P\\{|Y_n-c|\\geq\\varepsilon\\}=0\\)\uff0c\u5219\u79f0\\(\\{Y_n,n\\geq1\\}\\)\u4f9d\u6982\u7387\u6536\u655b(Convergence in Probability)\u4e8e\\(c\\)\uff0c\u8bb0\u505a\\(Y_n\\xrightarrow{P} c\\;,\\;\\;n\\to+\\infty\\)\u3002\u7b49\u4ef7\u7684\uff0c\u4e5f\u53ef\u4ee5\u5c06\u6761\u4ef6\u5199\u6210\\(\\forall\\varepsilon&gt;0\\;\\;\\;s.t. \\;\\;\\lim_{n\\to+\\infty}P\\{|Y_n-c|&lt;\\varepsilon\\}=1\\)\u3002</p> <ul> <li>\u8fd9\u79cd\u6536\u655b\u4e0d\u662f\u6570\u5b66\u610f\u4e49\u4e0a\u7684\u4e00\u822c\u6536\u655b\uff0c\u800c\u662f\u6982\u7387\u610f\u4e49\u4e0b\u7684\u4e00\u79cd\u6536\u655b</li> <li>\u5176\u542b\u4e49\u662f\uff1a\\(Y_n\\)\u5bf9\\(c\\)\u7684\u7edd\u5bf9\u504f\u5dee\u4e0d\u5c0f\u4e8e\u4efb\u4f55\u4e00\u4e2a\u7ed9\u5b9a\u91cf\u7684\u53ef\u80fd\u6027\u968f\\(n\\)\u7684\u589e\u5927\u800c\u8d8a\u6765\u8d8a\u5c0f\uff1b\u6216\u8005\u7edd\u5bf9\u504f\u5dee\\(|Y_n-c|\\)\u5c0f\u4e8e\u4efb\u4f55\u4e00\u4e2a\u7ed9\u5b9a\u91cf\u7684\u53ef\u80fd\u6027\u968f\\(n\\)\u7684\u589e\u5927\u65f6\u800c\u8d8a\u6765\u8d8a\u63a5\u8fd1\u4e8e\\(1\\)</li> </ul> <p>\u4f9d\u6982\u7387\u6536\u655b\u6709\u5982\u4e0b\u91cd\u8981\u6027\u8d28\uff1a\u82e5\uff1a</p> <ol> <li>\\(\\left\\{ \\begin{aligned} X_n\\xrightarrow{P} a\\\\ Y_n\\xrightarrow{P} b \\end{aligned} \\right. \\;\\;,\\;\\;n\\to+\\infty\\;\\;,\\;\\;a,b\\in\\mathbf{R}\\)\uff1b</li> <li>\u4e8c\u5143\u51fd\u6570\\(g(x,y)\\)\u5728\u70b9\\((a,b)\\)\u8fde\u7eed\uff08\u4f8b\u5982\u56db\u5219\u8fd0\u7b97\uff09\uff1b</li> </ol> <p>\u5219\u6709\uff1a</p> <ul> <li>\\(g(X_n,Y_n)\\xrightarrow{P}g(a,b)\\)\u3002</li> </ul> <p>\u8be5\u6027\u8d28\u5373\u4f9d\u6982\u7387\u6536\u655b\u53ef\u4ee5\u5728\u53cc\u76ee\u8fd0\u7b97\u7b26\u4e2d\u8fdb\u884c\u4e0b\u653e\u3002</p> <p>\u9a6c\u5c14\u53ef\u592b(Markov)\u4e0d\u7b49\u5f0f\u82e5\u968f\u673a\u53d8\u91cf\\(Y\\)\u7684\\(k\\)\u9636\uff08\u539f\u70b9\uff09\u77e9\u5b58\u5728\uff08\\(k\\geq1\\)\uff09\uff0c\u5219\\(\\forall \\varepsilon &gt; 0\\)\uff0c\u6709\uff1a\\(P \\{ |Y| \\geq \\varepsilon \\}\\leq \\frac{E(|Y|^k)}{\\varepsilon^k}\\;\\; or \\;\\; P\\{|Y| &lt; \\varepsilon \\} \\geq 1 - \\frac{E(|Y|^k)}{\\varepsilon^k}\\) \u7279\u522b\u5730\uff0c\u5f53\\(Y\\)\u53d6\u975e\u8d1f\u503c\u7684\u968f\u673a\u53d8\u91cf\u4e14\u5b83\u7684\\(k\\)\u9636\u77e9\u5b58\u5728\u65f6\uff0c\u6709\uff1a\\(P\\{Y\\geq \\varepsilon\\} \\leq \\frac{E(Y^k)}{\\varepsilon^k}\\)</p> <p>\u5207\u6bd4\u96ea\u592b(Chebyshev)\u4e0d\u7b49\u5f0f\u662f\u9a6c\u5c14\u53ef\u592b\u4e0d\u7b49\u5f0f\u7684\u63a8\u8bba\u82e5\u968f\u673a\u53d8\u91cf\\(X\\)\u7684\u6570\u5b66\u671f\u671b\u548c\u65b9\u5dee\u5b58\u5728\uff0c\u5206\u522b\u8bb0\\(E(X)=\\mu\\;,\\; Var(X) = \\sigma^2\\)\uff0c\u5219\\(\\forall \\varepsilon &gt; 0\\)\uff0c\u6709\uff1a\\(P\\{ |X-\\mu|\\geq \\varepsilon \\} \\leq \\frac{\\sigma^2}{\\varepsilon^2}\\;\\;or\\;\\;P\\{ |X-\\mu|&lt; \\varepsilon \\} \\geq1- \\frac{\\sigma^2}{\\varepsilon^2}\\) \u53ef\u4ee5\u8bb0\u5fc6\u4e3a\\(P\\{ \\sigma^2\\geq \\varepsilon^2 \\} \\leq \\frac{\\sigma^2}{\\varepsilon^2}\\;\\;or\\;\\;P\\{ \\sigma^2&lt; \\varepsilon^2 \\} \\geq1- \\frac{\\sigma^2}{\\varepsilon^2}\\) </p>"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap05/#\u5927\u6570\u5b9a\u7406","title":"\u5927\u6570\u5b9a\u7406","text":"<ul> <li>\u4e3b\u8981\u8ba8\u8bba\u4ec0\u4e48\u6761\u4ef6\u4e0b\uff0c\u968f\u673a\u53d8\u91cf\u5e8f\u5217\u7684\u7b97\u672f\u5e73\u5747\u4f9d\u6982\u7387\u6536\u655b\u5230\u5176\u5747\u503c\u7684\u7b97\u672f\u5e73\u5747\u3002</li> </ul> <p>\u5927\u6570\u5b9a\u7406\uff08\u4e00\u822c\u5f62\u5f0f\uff09\u8bbe\\(\\{Y_i,i\\geq1\\}\\)\u4e3a\u4e00\u968f\u673a\u53d8\u91cf\u5e8f\u5217\uff0c\u82e5\u5b58\u5728\u5e38\u6570\u5e8f\u5217\\({c_n,n\\geq 1}\\)\uff0c\u4f7f\\(\\forall \\varepsilon &gt; 0\\)\uff0c\u6709;\\(\\lim_{n\\to+\\infty}P\\{|\\frac{1}{n}\\sum_{i=1}^{n}Y_i-c_n|\\geq \\varepsilon\\}=0 \\;\\; or \\;\\; \\lim_{n\\to+\\infty}P\\{|\\frac{1}{n}\\sum_{i=1}^{n}Y_i-c_n|&lt; \\varepsilon\\}=1\\) \u5373\uff1a\\((\\frac{1}{n}\\sum_{i=1}^{n}Y_i-c_n)\\xrightarrow{P}0\\;\\;,\\;\\;n\\to+\\infty\\)\uff0c\u5219\u79f0\u968f\u673a\u53d8\u91cf\u5e8f\u5217\\(\\{Y_i,i\\geq1\\}\\)\u670d\u4ece\u5f31\u5927\u6570\u5b9a\u7406(Weak Law of Large Numbers)\uff0c\u7b80\u79f0\u670d\u4ece\u5927\u6570\u5b9a\u5f8b\u3002\u89c2\u5bdf\u5230\u5982\u679c\u4ee4\\(Z_n=\\frac{1}{n}\\sum_{i=1}^{n}Y_i\\)\uff0c\u5219\u8868\u8fbe\u5f0f\u7684\u542b\u4e49\u4e3a\\(Z_n\\xrightarrow{P}c\\;\\;,\\;\\;n\\to+\\infty\\)\uff0c\u5373\u5927\u6570\u5b9a\u5f8b\u4e5f\u53ef\u4ee5\u8868\u8ff0\u4e3a\uff1a</p> <ul> <li>\u968f\u673a\u53d8\u91cf\u5e8f\u5217\u524d\\(n\\)\u4e2a\u53d8\u91cf\u7684\u7b97\u672f\u5e73\u5747\u4f9d\u6982\u7387\u6536\u655b\u4e8e\\(c\\)\uff0c \u5219\u8fd9\u4e2a\u968f\u673a\u53d8\u91cf\u5e8f\u5217\u670d\u4ece\u5927\u6570\u5b9a\u5f8b\u3002</li> </ul> <p>\u6a59\u4e66\u7ed9\u51fa\u7684\u5b9a\u4e49\u5f0f\u662f\uff1a\\(\\lim_{n\\to \\infty}P\\big(\\big|   \\frac{1}{n}\\sum_{i=1}^{n}X_i-\\frac{1}{n}\\sum_{i=1}^{n}E(X_i)  \\big|&lt;\\varepsilon\\big)=1\\)</p> <ul> <li>\u63a5\u4e0b\u6765\u7ed9\u51fa\u7684\u5927\u6570\u5b9a\u5f8b\u7684\u533a\u522b\u4f53\u73b0\u5728\u6761\u4ef6\u4e0a\uff1a\u6709\u4e9b\u662f\u76f8\u4e92\u72ec\u7acb\u7684\u968f\u673a\u53d8\u91cf\uff0c\u6709\u4e9b\u662f\u76f8\u4f9d\u7684\u968f\u673a\u53d8\u91cf\uff0c\u6709\u4e9b\u662f\u540c\u5206\u5e03\u7684\u968f\u673a\u53d8\u91cf\uff0c\u6709\u4e9b\u662f\u4e0d\u540c\u5206\u5e03\u7684\u968f\u673a\u53d8\u91cf\u3002</li> </ul> <p>\u4f2f\u52aa\u5229(Bernoulli)\u5927\u6570\u5b9a\u5f8b\u8bbe\\(n_A\\)\u8868\u793a\\(n\\)\u91cd\u8d1d\u52aa\u529b\u5b9e\u9a8c\u4e2d\u4e8b\u4ef6\\(A\\)\u53d1\u751f\u7684\u6b21\u6570\uff0c\u5e76\u8bb0\\(P(A)=p\\)\uff0c\u5219\\(\\forall \\varepsilon &gt; 0\\)\uff0c\u6709\uff1a\\(\\lim_{n\\to+\\infty}P\\{|\\frac{n_A}{n}-p|\\geq \\varepsilon\\}=0\\)</p> <p>\u8f9b\u94a6(Khinchin)\u5927\u6570\u5b9a\u5f8b*\u5373\u4f7f\u968f\u673a\u53d8\u91cf\u7684\u65b9\u5dee\u4e0d\u5b58\u5728\uff0c\u671f\u671b\u5b58\u5728\u5373\u53ef\u8bbe\\(\\{X_i,i\\geq 1\\}\\)\u4e3a\u72ec\u7acb\u540c\u5206\u5e03\u7684\u968f\u673a\u53d8\u91cf\u5e8f\u5217\uff0c\u4e14\u6570\u5b66\u671f\u671b\u4e3a\\(\\mu\\)\uff0c\u5219\\(\\forall\\varepsilon&gt;0\\)\uff0c\u6709\uff1a\\(\\lim_{n\\to+\\infty}P\\{|\\frac{1}{n}\\sum_{i=1}^{n}X_i-\\mu|\\geq \\varepsilon\\}=0\\;\\;\\;or\\;\\;\\;\\frac{1}{n}\\sum_{i=1}^{n}X_i\\xrightarrow{P}\\mu\\;\\;,\\;\\;n\\to+\\infty\\)</p> <p>\u8f9b\u94a6\u5927\u6570\u5b9a\u5f8b\u6709\u5982\u4e0b\u63a8\u8bba\uff1a\u8bbe\\(\\{X_i,i\\geq 1\\}\\)\u4e3a\u72ec\u7acb\u540c\u5206\u5e03\u7684\u968f\u673a\u53d8\u91cf\u5e8f\u5217\uff0c\u82e5\\(h(x)\\)\u4e3a\u8fde\u7eed\u51fd\u6570\uff0c\u4e14\\(E(|h(X_1)|)&lt;+\\infty\\)\uff0c\u5219\\(\\forall\\varepsilon&gt;0\\)\uff0c\u6709\uff1a\\(\\lim_{n\\to+\\infty}P\\{|\\frac{1}{n}\\sum^{n}_{i=1}h(X_i)-a|\\geq\\varepsilon\\}=0\\;\\;\\;or\\;\\;\\;\\frac{1}{n}\\sum_{i=1}^{n}h(X_i)\\xrightarrow{P}a\\;\\;,\\;\\;n\\to+\\infty \\\\ where\\;\\;\\;a=E(|h(X_1)|)\\)</p>"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap05/#\u4e2d\u5fc3\u6781\u9650\u5b9a\u7406","title":"\u4e2d\u5fc3\u6781\u9650\u5b9a\u7406","text":"<ul> <li>\u8ba8\u8bba\u4ec0\u4e48\u6761\u4ef6\u4e0b\uff0c\u72ec\u7acb\u968f\u673a\u53d8\u91cf\u548c\u7684\u5206\u5e03\u51fd\u6570\\(Y=\\sum X_i\\)\u7684\u5206\u5e03\u51fd\u6570\u4f1a\u6536\u655b\u4e8e\u6b63\u6001\u5206\u5e03\u3002</li> </ul>"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap05/#\u72ec\u7acb\u540c\u5206\u5e03\u65f6","title":"\u72ec\u7acb\u540c\u5206\u5e03\u65f6","text":"<p>\u6797\u5fb7\u4f2f\u683c-\u83b1\u7ef4\u4e2d\u5fc3\u6781\u9650\u5b9a\u7406\u8bbe\\(\\{X_i,i\\geq 1\\}\\)\u4e3a\u72ec\u7acb\u540c\u5206\u5e03\u7684\u968f\u673a\u53d8\u91cf\u5e8f\u5217\uff0c\u4e14\\(E(X_i)=\\mu\\;\\;,\\;\\;Var(X_i)=\\sigma^2\\;\\;(\\sigma&gt;0)\\)\uff0c\u5219\\(\\forall x\\in \\mathbf{R}\\)\uff0c\u6709\uff1a</p> \\[ \\begin{aligned} \\lim_{n\\to+\\infty}P\\left\\{ \\frac{ \\begin{aligned}     \\sum_{i=1}^{n}X_i-E(\\sum_{i=1}^{n}X_i) \\end{aligned} }{\\begin{aligned}     \\sqrt{\\mathrm{Var}(\\sum_{i=1}^{n}X_i)} \\end{aligned}}\\leq x\\right\\}&amp;= \\lim_{n\\to+\\infty}P\\left\\{ \\frac{ \\begin{aligned}     \\sum_{i=1}^{n}X_i-n\\mu \\end{aligned} }{\\begin{aligned}     \\sigma\\sqrt{n} \\end{aligned}}\\leq x\\right\\} \\\\ &amp;=\\frac{1}{\\sqrt{2\\pi}}\\int_{-\\infty}^{x}e^{-\\frac{t^2}{2}}\\mathrm{d}t \\\\ &amp;=\\Phi(x) \\end{aligned} \\] <p>\u6362\u53e5\u8bdd\u6765\u8bf4\uff0c\\(E(X_i)=\\mu\\;\\;,\\;\\;Var(X_i)=\\sigma^2\\;\\;(\\sigma&gt;0)\\)\u7684\u72ec\u7acb\u540c\u5206\u5e03\u7684\u968f\u673a\u53d8\u91cf\u5e8f\u5217\u7684\u90e8\u5206\u548c\\(\\sum_{i=1}^{n}X_i\\)\u7684\u6807\u51c6\u5316\u91cf</p> \\[ \\frac{ \\begin{aligned}     \\sum_{i=1}^{n}X_i-n\\mu \\end{aligned} }{\\begin{aligned}     \\sigma\\sqrt{n} \\end{aligned}} \\overset{\\text{approximately}}{\\sim} N(0,1)\\;\\;,\\;\\;\\text{where }n\\text{ is big enough} \\] <p>\uff0c\u5f53\u7136\u4e5f\u53ef\u4ee5\u5199\u6210\uff1a</p> \\[ \\frac{ \\begin{aligned}     \\frac{1}{n}\\sum_{i=1}^{n}X_i-\\mu \\end{aligned} }{\\begin{aligned}     \\frac{\\sigma}{\\sqrt{n}} \\end{aligned}} \\overset{\\text{approximately}}{\\sim} N(0,1)\\;\\;,\\;\\;\\text{where }n\\text{ is big enough} \\]"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap05/#\u4e8c\u9879\u5206\u5e03\u7684\u6b63\u6001\u8fd1\u4f3c","title":"\u4e8c\u9879\u5206\u5e03\u7684\u6b63\u6001\u8fd1\u4f3c","text":"<p>\u6797\u5fb7\u4f2f\u683c-\u83b1\u7ef4\u4e2d\u5fc3\u6781\u9650\u5b9a\u7406\u6709\u5982\u4e0b\u63a8\u8bba\uff1a\u68e3\u83ab\u5f17-\u62c9\u666e\u62c9\u65af\u4e2d\u5fc3\u6781\u9650\u5b9a\u7406\u8bbe\\(n_A\\)\u8868\u793a\\(n\\)\u91cd\u8d1d\u52aa\u529b\u5b9e\u9a8c\u4e2d\u4e8b\u4ef6\\(A\\)\u53d1\u751f\u7684\u6b21\u6570\uff0c\u5e76\u8bb0\\(P(A)=p\\)\uff0c\u5219</p> \\[ \\forall x\\in\\mathbf{R}$\uff0c\u6709\uff1a&lt;br /&gt;$\\lim_{n\\to+\\infty}P\\{\\frac{n_A-np}{\\sqrt{np(1-p)}}\\leq x\\}=\\frac{1}{\\sqrt{2\\pi}}\\int_{-\\infty}^{x}e^{-\\frac{t^2}{2}}\\mathrm{d}t=\\Phi(x) \\]"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap05/#\u72ec\u7acb\u4e0d\u540c\u5206\u5e03\u65f6\u4e0d\u8981\u6c42","title":"\u72ec\u7acb\u4e0d\u540c\u5206\u5e03\u65f6(\u4e0d\u8981\u6c42)","text":"<p>\u674e\u96c5\u666e\u8bfa\u592b\u4e2d\u5fc3\u6781\u9650\u5b9a\u7406\u8bbe\\(\\{X_i,i\\geq 1\\}\\)\u4e3a\u76f8\u4e92\u72ec\u7acb\u7684\u968f\u673a\u53d8\u91cf\u5e8f\u5217\uff0c\u4e14\\(E(X_i)=\\mu_i\\;\\;,\\;\\;Var(X_i)=\\sigma_i^2\\;\\;(\\sigma&gt;0)\\)\uff0c\u82e5\\(\\exists\\varepsilon&gt;0\\)\u4f7f\u5f97\uff1a\\(\\lim_{+\\infty}\\frac{1}{B_n^{2+\\varepsilon}}\\sum_{i=1}^{n}E|X_i-\\mu_i|^{2+\\varepsilon}=0\\;\\;\\;where\\;\\;\\;B_n^{2}=\\sum_{i=1}^{n}\\sigma_i^2\\) \u5219\uff1a </p>"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap06/","title":"[6.x] \u7edf\u8ba1\u91cf\u4e0e\u62bd\u6837\u5206\u5e03","text":"<p> \u7ea6 1586 \u4e2a\u5b57  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 5 \u5206\u949f</p>"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap06/#\u6982\u5ff5","title":"\u6982\u5ff5","text":"<p>\u603b\u4f53(Population)\u4e2a\u4f53(Individual)\u603b\u4f53\u5bb9\u91cf\u6709\u9650\u603b\u4f53(Finite Population)\u65e0\u9650\u603b\u4f53(Infinite Population)\u6837\u672c(Sample)</p> <ul> <li>\u6709\u4ee3\u8868\u6027</li> <li>\u6709\u72ec\u7acb\u6027</li> </ul> <p>\u6837\u672c\u5bb9\u91cf\u968f\u673a\u6837\u672c(Random Sample)\u7b80\u5355\u968f\u673a\u6837\u672c(Simple Random Sample)\u6837\u672c\u503c / \u89c2\u5bdf\u503c\u6837\u672c\u7684\u8054\u5408\u5206\u5e03\u51fd\u6570\uff1a\\(F(x_1,x_2,...,x_n)=\\prod_{i=1}^{n} F(x_i).\\)</p> <p>\u5b9a\u4e49\u8bbe\u603b\u4f53\\(X\\)\u662f\u5177\u6709\u5206\u5e03\u51fd\u6570\\(F(\u00b7)\\)\u7684\u968f\u673a\u53d8\u91cf\uff0c\\(X_1,X_2,...,X_n\\)\u662f\u6765\u81ea\u603b\u4f53\\(X\\)\u7684\u968f\u673a\u6837\u672c\uff0c\u82e5\u6ee1\u8db3\uff1a</p> <ol> <li>\\(X_1,X_2,...,X_n\\)\u662f\u662f\u76f8\u4e92\u72ec\u7acb\u7684\u968f\u673a\u53d8\u91cf\uff1b</li> <li>\u6bcf\u4e00\u4e2a\\(X_i\\)\u4e0e\\(X\\)\u6709\u76f8\u540c\u7684\u5206\u5e03\u51fd\u6570\uff1b</li> </ol> <p>\u5219\u79f0\\(X_1,X_2,...,X_n\\)\u4e3a\u53d6\u81ea\u603b\u4f53\\(X\\)\u7684\u7b80\u5355\u968f\u673a\u6837\u672c\u3002</p>"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap06/#\u7edf\u8ba1\u91cf\u53ca\u5176\u5206\u5e03","title":"\u7edf\u8ba1\u91cf\u53ca\u5176\u5206\u5e03","text":"<p>\u7edf\u8ba1\u91cf(Statistic)\u8bbe\\(X_1,X_2,...,X_n\\)\u662f\u6765\u81ea\u603b\u4f53\\(X\\)\u7684\u4e00\u4e2a\u6837\u672c\uff0c\\(g(X_1,X_2,...,X_n)\\)\u662f\u6837\u672c\\(X_1,X_2,...,X_n\\)\u7684\u51fd\u6570\uff0c\u82e5\\(g\\)\u4e2d\u4e0d\u542b\u672a\u77e5\u53c2\u6570\uff0c\u5219\u79f0\\(g(X_1,X_2,...,X_n)\\)\u662f\u4e00\u7edf\u8ba1\u91cf\u3002</p> <ul> <li>\u5c3d\u7ba1\u7edf\u8ba1\u91cf\u4e0d\u4f9d\u8d56\u4e8e\u672a\u77e5\u53c2\u6570\uff0c\u4f46\u662f\u4ed6\u4eec\u7684\u5206\u5e03\u4f9d\u8d56\u4e8e\u672a\u77e5\u53c2\u6570\u3002</li> </ul> <p>\u5982\u4e0b\u4e3a\u51e0\u79cd\u5e38\u89c1\u7684\u91cd\u8981\u7edf\u8ba1\u91cf\uff1a</p> <ol> <li>\u6837\u672c\u5747\u503c\uff08\u5e38\u4f5c\u4e3a\u603b\u4f53\u503c\\(\\mu\\)\u7684\u4f30\u8ba1\uff09</li> </ol> <p>\\(\\overline{X}=\\frac{1}{n}\\sum_{i=1}^{n}X_i\\) \\(E(\\overline x)=\\mu\\;\\;,\\;\\;Var(\\overline x)=\\sigma^2/n\\)</p> <ul> <li>\u6027\u8d28\uff1a<ol> <li>\\(\\sum_{i=1}^{n}(x_i-\\overline{x})=0\\)\uff1b</li> <li>\u6570\u636e\u89c2\u6d4b\u503c\u4e0e\u6837\u672c\u5747\u503c\u7684\u504f\u5dee\u5e73\u65b9\u548c\u6700\u5c0f\uff0c\u5373\u5728\u5f62\u5982\\(\\sum(x_i-c)^2\\)\u7684\u51fd\u6570\u4e2d\uff0c\\(\\sum(x_i-\\overline x)^2\\)\u6700\u5c0f\uff1b</li> <li>\u82e5\u603b\u4f53\u670d\u4ece\\(N(\\mu,\\sigma^2)\\)\uff0c\u5219\\(\\overline x\\)\u7684\u7cbe\u786e\u5206\u5e03\u4e3a\\(N(\\mu,\\sigma^2/n)\\)\uff1b </li> <li>\u82e5\u603b\u4f53\u5206\u5e03\u672a\u77e5\u6216\u4e0d\u662f\u6b63\u6001\u5206\u5e03\uff0c\u5219\u5f53\\(n\\)\u8f83\u5927\u65f6\uff0c\\(\\overline x\\)\u8fd1\u4f3c\u670d\u4ece\\(N(\\mu,\\sigma^2/n)\\)\uff1b</li> </ol> </li> <li>\u6837\u672c\u65b9\u5dee\uff08\u5e38\u4f5c\u4e3a\u603b\u4f53\u65b9\u5dee\\(\\sigma^2\\)\u7684\u65e0\u504f\u4f30\u8ba1\uff09</li> </ul> \\[ S^2=\\frac{1}{n-1}\\sum_{i=1}^{n}(X_i-\\overline{X})^2=\\frac{1}{n-1}(\\sum_{i=1}^{n}X_i^2-n\\overline{X}^2) \\] \\[ E(S^2)=\\sigma^2 \\] <ul> <li>\u5bf9\u4e8e\u6837\u672c\u504f\u5dee\u5e73\u65b9\u548c\u6709\u4e09\u4e2a\u5e38\u7528\u7684\u8868\u8fbe\u5f0f\uff1a</li> </ul> <p>\\(\\sum(x_i-\\overline x)^2=\\sum x_i^2-\\frac{(\\sum x_i)^2}{n}=\\sum x_i^2-n\\overline x^2\\)</p> <ol> <li>\u6837\u672c\u6807\u51c6\u5dee</li> </ol> <p>\\(S=\\sqrt{S^2}=\\sqrt{\\frac{1}{n-1}\\sum_{i=1}^{n}(X_i-\\overline{X})^2}\\)</p> <ol> <li>\u6837\u672c\\(k\\)\u9636\uff08\u539f\u70b9\uff09\u77e9\uff08\u5e38\u4f5c\u4e3a\u603b\u4f53\u539f\u70b9\u77e9\\(\\mu_k\\)\u7684\u4f30\u8ba1\uff09</li> </ol> <p>\\(A_k=\\frac{1}{n}\\sum_{i=1}^{n}X_i^k,\\;\\;k=1,2,...\\)</p> <ol> <li>\u6837\u672c\\(k\\)\u9636\u4e2d\u5fc3\u8ddd\uff08\u5e38\u4f5c\u4e3a\u603b\u4f53\u4e2d\u5fc3\u77e9\\(\\nu_k\\)\u7684\u4f30\u8ba1\uff09\uff08\\(B_2\\)\u53ef\u4f5c\u4e3a\u603b\u4f53\u65b9\u5dee\\(\\sigma^2\\)\u7684\u6709\u504f\u4f30\u8ba1\uff09</li> </ol> <p>\\(B_k=\\frac{1}{n}\\sum_{i=1}^{n}(X_i-\\overline{X})^k,\\;\\;k=2,3,...\\)</p> <ul> <li>\u603b\u4f53\u7684\u4efb\u610f\u4e00\u4e2a\u672a\u77e5\u53c2\u6570\u53ef\u4ee5\u6709\u591a\u4e2a\u4e0d\u540c\u7684\u4f30\u8ba1\uff0c\u56e0\u6b64\u53c2\u6570\u4f30\u8ba1\u4e0d\u552f\u4e00\uff1b</li> <li>\u5047\u8bbe\\(X_1,X_2,...,X_n\\)\u662f\\(X\\)\u4e2d\u62bd\u53d6\u7684\u7b80\u5355\u968f\u673a\u6837\u672c\uff0c\\(\\mu_k=E(X^k)\\)\u5b58\u5728\uff0c\u7531\u8f9b\u94a6\u5927\u6570\u5b9a\u5f8b\u53ef\u77e5\uff1a</li> </ul> <p>\\(A_k=\\frac{1}{n}\\sum_{i=1}^{n}X_i^k\\xrightarrow{P}\\mu_k,\\;\\;k=1,2,...\\)</p>"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap06/#\u4e09\u5927\u62bd\u6837\u5206\u5e03","title":"\u4e09\u5927\u62bd\u6837\u5206\u5e03","text":"<p>\u7edf\u8ba1\u91cf\u7684\u5206\u5e03\u6210\u4e3a\u62bd\u6837\u5206\u5e03(Sampling Distribution)\uff0c\u5728\u4f7f\u7528\u7edf\u8ba1\u91cf\u8fdb\u884c\u63a8\u65ad\u65f6\u9700\u8981\u77e5\u9053\u62bd\u6837\u5206\u5e03\u3002</p>"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap06/#\u03c7\u00b2\u5206\u5e03--\u5361\u65b9\u5206\u5e03","title":"\u03c7\u00b2\u5206\u5e03 / \u5361\u65b9\u5206\u5e03","text":"<p>\\(\\chi^2\\)\u5206\u5e03 / \u5361\u65b9\u5206\u5e03\u8bbe\\(X_1,X_2,...,X_n\\)\u4e3a\u72ec\u7acb\u540c\u5206\u5e03\u670d\u4ece\\(N(0,1)\\)\u3002\u8bb0\\(Y=X_1^2+X_2^2+...+X_n^2\\)\uff0c\u5219\u79f0\\(Y\\)\u670d\u4ece\u81ea\u7531\u5ea6\u4e3a\\(n\\)\u7684\\(\\chi^2\\)\u5206\u5e03\uff0c\u8bb0\\(Y\\sim \\chi^2(n)\\)\u3002\\(\\chi^2\\)\u5206\u5e03\u7684\u5bc6\u5ea6\u51fd\u6570\u4e3a\uff1a</p> \\[ f_{\\chi^2}(x)= \\left\\{ \\begin{aligned} &amp;\\frac{1}{2^\\frac{n}{2}\\Gamma(\\frac{n}{2})}x^{\\frac{n}{2}-1}e^{-\\frac{x}{2}},&amp;x&gt;0, \\\\ &amp;0,&amp;other, \\end{aligned} \\right. \\] <p>\\(\\chi^2\\)\u5206\u5e03\u6709\u5982\u4e0b\u6027\u8d28\uff1a</p> <ol> <li>\\(\\chi^2\\)\u5206\u5e03\u53ef\u52a0\uff1a\u8bbe\\(Y_1 \\sim \\chi^2(m),\\;Y_2\\sim\\chi^2(n)\\)\uff0c\u4e14\u4e24\u8005\u4e92\u76f8\u72ec\u7acb\uff0c\u5219\\(Y_1+Y_2\\sim \\chi^2(m+n)\\)\uff1b</li> <li>\\(\\chi^2\\)\u5206\u5e03\u7684\u6570\u5b66\u671f\u671b\u4e0e\u65b9\u5dee\uff1a\\(E(\\chi^2(n))=n,\\;Var(\\chi^2(n))=2n\\)\uff1b</li> <li>\\(\\chi^2\\)\u5206\u5e03\u5206\u4f4d\u6570\uff1a\u5bf9\u4e8e\u7ed9\u5b9a\u7684\u6b63\u6570\\(\\alpha,\\;0&lt;\\alpha&lt;1\\)\uff0c\u79f0\u6ee1\u8db3\u6761\u4ef6\\(P\\{\\chi^2&gt;\\chi^2_\\alpha(n)\\}=\\int^{+\\infty}_{\\chi^2_\\alpha(n)}f_{\\chi^2}(x)\\mathrm{d}x=\\alpha\\)\u7684\u70b9\\(\\chi^2_{\\alpha}(n)\\)\u4e3a\\(\\chi^2(n)\\)*\u4fa7\uff09\\(\\alpha\\)\u5206\u4f4d\u6570*\u3002</li> </ol> <p></p> <ol> <li>\u8bbe\\(X_1,X_2,...,X_n\\)\u4e3a\u6765\u81ea\u6b63\u6001\u603b\u4f53\\(N(\\mu,\\sigma^2)\\)\u7684\u7b80\u5355\u968f\u673a\u6837\u672c\uff0c\\(\\overline{X}\\)\u662f\u6837\u672c\u5747\u503c\uff0c\\(S^2\\)\u662f\u6837\u672c\u65b9\u5dee\uff0c\u5219\u6709\uff1a</li> <li>\\(\\overline X\\)\u4e0e\\(S^2\\)\u76f8\u4e92\u72ec\u7acb\uff1b</li> <li>\\(\\overline X\\sim  N(\\mu,\\sigma^2/n)\\)\uff1b</li> <li>\\(\\frac{\\sum_{i=1}^n(X_i-\\overline X)^2}{\\sigma^2}=\\frac{(n-1)S^2}{\\sigma^2}\\sim \\chi^2(n-1)\\)\uff1b</li> </ol>"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap06/#t-\u5206\u5e03--\u5b66\u751f\u6c0f\u5206\u5e03","title":"t \u5206\u5e03 / \u5b66\u751f\u6c0f\u5206\u5e03","text":"<p>\\(t\\)\u5206\u5e03 / \u5b66\u751f\u6c0f(Student)\u5206\u5e03\u8bbe\\(X\\sim N(0,1),Y\\sim\\chi^2(n)\\)\uff0c\u4e14\\(X,Y\\)\u76f8\u4e92\u72ec\u7acb\uff0c\u5219\u79f0\u968f\u673a\u53d8\u91cf\\(t=\\frac{X}{\\sqrt{Y/n}}\\)\u670d\u4ece\u81ea\u7531\u5ea6\u4e3a\\(n\\)\u7684\\(t\\)\u5206\u5e03\uff0c\u8bb0\u505a\\(t\\sim t(n)\\)\uff0c\u5176\u5bc6\u5ea6\u51fd\u6570\u4e3a\uff1a</p> \\[ f_t(x)=\\frac{\\Gamma[(n+1)/2]}{\\sqrt{\\pi n}\\Gamma(\\frac{n}{2})}(1+\\frac{x^2}{n})^{-\\frac{n+1}{2}},\\;\\;-\\infty&lt;x&lt;+\\infty \\] <p>\u5176\u4e2d\\(\\Gamma(\\alpha)=\\int_0^{+\\infty}t^{\\alpha-1}e^{-t}\\mathrm{d}t\\)\uff0c\\(\\Gamma(\\alpha+1)=\\alpha\\Gamma(\\alpha)=\\alpha!(if\\;\\alpha\\in\\Z)\\)\uff0c\\(\\Gamma(0.5)=\\sqrt{\\pi}\\) \\(t\\)\u5206\u5e03\u6709\u5982\u4e0b\u6027\u8d28\uff1a</p> <ol> <li>\\(t\\)\u5206\u5e03\u7684\u5bc6\u5ea6\u51fd\u6570\\(f_t(x)\\)\u662f\u5076\u51fd\u6570\uff0c\u5173\u4e8e\\(y\\)\u8f74\u5bf9\u79f0\uff1b</li> <li>\u7531\\(t\\)\u5206\u5e03\u7684\u5bc6\u5ea6\u51fd\u6570\u53ef\u4ee5\u5f97\u5230\uff1a\\(\\lim_{n\\to+\\infty}f_t(x)=\\frac{1}{\\sqrt{2\\pi}}e^{-{x^2}/{2}}\\)\uff1b</li> <li>\u5f53\\(n\\)\u8db3\u591f\u5927\u65f6\uff0c\\(t\\)\u5206\u5e03\u8fd1\u4f3c\u4e8e\u6807\u51c6\u6b63\u6001\u5206\u5e03\\(N(0,1)\\)\uff1b</li> <li>\\(t\\)\u5206\u5e03\u5206\u4f4d\u6570\uff0c\u5bf9\u4e8e\u7ed9\u5b9a\u7684\u6b63\u6570\\(\\alpha,\\;\\;0&lt;\\alpha&lt;1\\)\uff0c\u79f0\u6ee1\u8db3\u6761\u4ef6\\(P\\{t&gt;t_\\alpha(n)\\}=\\int_{t_\\alpha(n)}^{+\\infty}f_t(x)\\mathrm{d}x=\\alpha\\)\u7684\u70b9\\(t_\\alpha(n)\\)\u4e3a\\(t(n)\\)\u5206\u5e03\u7684\u4e0a\uff08\u4fa7\uff09\\(\\alpha\\)\u5206\u4f4d\u6570\uff1b</li> </ol> <p></p> <ol> <li>\\(t^2\\sim F(1,n)\\)\uff1b</li> <li>\u81ea\u7531\u5ea6\u4e3a\\(1\\)\u7684\\(t\\)\u5206\u5e03\u5c31\u662f\u6807\u51c6\u67ef\u897f\u5206\u5e03\uff0c\u5176\u5747\u503c\u4e0d\u5b58\u5728\uff1b</li> <li>\\(n&gt;1\\)\u65f6\\(t\\)\u5206\u5e03\u7684\u6570\u5b66\u671f\u671b\u5b58\u5728\u4e14\u4e3a\\(0\\)\uff1b</li> <li>\\(n&gt;2\\)\u65f6\\(t\\)\u5206\u5e03\u7684\u65b9\u5dee\u5b58\u5728\u4e14\u4e3a\\(\\frac{n}{n-2}\\)\uff1b</li> <li>\u5f53\u81ea\u7531\u5ea6\u6bd4\u8f83\u5927\u65f6\uff0c\\(t\\)\u5206\u5e03\u53ef\u4ee5\u7528\\(N(0,1)\\)\u5206\u5e03\u8fd1\u4f3c\uff1b</li> </ol> <p>\u63a8\u8bba\uff1a</p> <ul> <li>\u8bbe\\(x_1,x_2,x_3,..,x_n\\)\u662f\u6765\u81ea\u6b63\u6001\u5206\u5e03\\(N(\\mu,\\sigma^2)\\)\u7684\u4e00\u4e2a\u6837\u672c\uff0c\\(\\overline x\\)\u548c\\(S^2\\)\u5206\u522b\u662f\u8be5\u6837\u672c\u7684\u6837\u672c\u5747\u503c\u4e0e\u6837\u672c\u65b9\u5dee\uff0c\u5219\u6709\\(t=\\frac{\\overline x-\\mu}{S/\\sqrt n}\\sim t(n-1)\\)\uff1b</li> </ul>"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap06/#f-\u5206\u5e03","title":"F \u5206\u5e03","text":"<p>\\(F\\)\u5206\u5e03\u8bbe\\(U\\sim\\chi^2(n_1)\\)\uff0c\\(V\\sim \\chi^2(n_2)\\)\uff0c\u4e14\\(U\\)\u548c\\(V\\)\u76f8\u4e92\u72ec\u7acb\uff0c\u5219\u79f0\u968f\u673a\u53d8\u91cf\\(F=\\frac{U/n_1}{V/n_2}\\)\u670d\u4ece\u81ea\u7531\u5ea6\u4e3a\\((n_1,n_2)\\)\u7684\\(F\\)\u5206\u5e03\uff0c\u8bb0\\(F\\sim F(n_1,n_2)\\)\u3002\u5176\u5bc6\u5ea6\u51fd\u6570\u4e3a  \\(F\\)\u5206\u5e03\u6709\u5982\u4e0b\u6027\u8d28\uff1a</p> <ol> <li>\u5982\u679c\\(F\\sim F(n_1,n_2)\\)\uff0c\u5219\\(\\frac{1}{F}\\sim F(n_2,n_1)\\)\uff1b</li> <li>\u5982\u679c\\(X\\sim t(n)\\)\uff0c\u5219\\(X^2\\sim F(1,n)\\)\uff1b</li> </ol> <p></p> <p>\u8bbe\\(X_1,X_2,...,X_n\\)\u4e3a\u6765\u81ea\u6b63\u6001\u603b\u4f53\\(N(\\mu,\\sigma^2)\\)\u7684\u7b80\u5355\u968f\u673a\u6837\u672c\uff0c\\(\\overline{X}\\)\u662f\u6837\u672c\u5747\u503c\uff0c\\(S^2\\)\u662f\u6837\u672c\u65b9\u5dee\uff0c\u5219\u6709\uff1a</p> <ol> <li>\\(\\frac{(n-1)S^2}{\\sigma^2}\\sim \\chi^2(n-1)\\)\uff1b</li> <li>\\(\\overline{X}\\)\u4e0e\\(S^2\\)\u76f8\u4e92\u72ec\u7acb\uff1b</li> <li>\\(\\frac{\\overline X - \\mu}{S/\\sqrt n}\\sim t(n-1)\\)\uff1b</li> </ol> <p>\u8bbe\\(X_1,X_2,...,X_n\\)\u548c\\(Y_1,Y_2,...,Y_n\\)\u4e3a\u6765\u81ea\u6b63\u6001\u603b\u4f53\\(N(\\mu_1,\\sigma_1^2)\\)\u548c\\(N(\\mu_2,\\sigma_2^2)\\)\u7684\u4e24\u4e2a\u76f8\u4e92\u72ec\u7acb\u7684\u7b80\u5355\u968f\u673a\u6837\u672c\uff0c\\(\\overline{X},\\overline Y\\)\u662f\u6837\u672c\u5747\u503c\uff0c\\(S_1^2,S_2^2\\)\u662f\u6837\u672c\u65b9\u5dee\uff0c\u5219\u6709\uff1a</p> <ol> <li>\\(\\frac{S_1^2/\\sigma_1^2}{S_2^2/\\sigma^2_2}\\sim F(n_1-1,n_2-2)\\)\uff1b</li> <li>\u5f53\\(\\sigma_1^2=\\sigma_2^2=\\sigma^2\\)\u65f6\uff1a</li> </ol> <p>\\(\\frac{ (\\overline X - \\overline Y) - (\\mu_1-\\mu_2) }{ S_\\omega\\sqrt{\\frac{1}{n_1}+\\frac{1}{n_2}} }\\sim t(n_1+n_2-2)\\) \u5176\u4e2d\\(S^2_\\omega=\\frac{(n_1-1)S_1^2+(n_2-n_1)S^2_2}{n_1+n_2-2}\\)</p>"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap07/","title":"[7.x] \u53c2\u6570\u4f30\u8ba1","text":"<p> \u7ea6 1368 \u4e2a\u5b57  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 5 \u5206\u949f</p>"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap07/#\u70b9\u4f30\u8ba1","title":"\u70b9\u4f30\u8ba1","text":"<p>\u8bbe\u603b\u4f53\\(X\\)\u7684\u5206\u5e03\u51fd\u6570\u4e3a\\(F(x;\\theta)\\)\uff0c\\(\\theta\\)\u662f\u5f85\u4f30\u53c2\u6570\uff0c\\(X_1,X_2,...,X_n\\)\u662f\\(X\\)\u7684\u4e00\u4e2a\u6837\u672c\u3002\u70b9\u4f30\u8ba1\u5c31\u662f\u8981\u6784\u9020\u4e00\u4e2a\u9002\u5f53\u7684\u7edf\u8ba1\u91cf\\(\\hat{\\theta}(X_1,X_2,...,X_n)\\)\uff0c\u7528\u6765\u4f30\u8ba1\u672a\u77e5\u53c2\u6570\\(\\theta\\)\uff0c\u6211\u4eec\u79f0\\(\\hat{\\theta}(X_1,X_2,...,X_n)\\)\u4e3a\\(\\theta\\)\u7684\u4f30\u8ba1\u91cf\u3002\u5982\u679c\u628a\u5176\u4e2d\u7684\u6837\u672c\u503c\u7528\\(x_1,x_2,...,x_n\\)\u4ee3\u66ff\uff0c\u5219\u79f0\\(\\hat\\theta(x_1,x_2,...,x_n)\\)\u4e3a\\(\\theta\\)\u7684\u4e00\u4e2a\u4f30\u8ba1\u503c\u3002\u5728\u4e0d\u5bfc\u81f4\u6df7\u6dc6\u7684\u60c5\u51b5\u4e0b\uff0c\u4e24\u8005\u90fd\u53ef\u4ee5\u88ab\u79f0\u4e3a\u201c\u4f30\u8ba1\u201d\uff0c\u5e76\u90fd\u53ef\u4ee5\u7b80\u8bb0\u4e3a\\(\\hat\\theta\\)\u3002</p>"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap07/#\u77e9\u6cd5","title":"\u77e9\u6cd5","text":"<p>\u505a\u9898\u6b65\u9aa4\uff1a</p> <ol> <li>\u5047\u8bbe\u6709\\(k\\)\u4e2a\u5f85\u6c42\u672a\u77e5\u53c2\u6570\uff1b</li> <li>\u5217\u5173\u4e8e\\(\\mu_1,\\mu_2,...,\\mu_k\\)\u7684\u65b9\u7a0b\u7ec4\uff1b</li> <li>\u4ece\u65b9\u7a0b\u7ec4\u4e2d\u89e3\u51fa\u8fd9\\(k\\)\u4e2a\u53c2\u6570\uff1b</li> <li>\u5982\u679c\u65b9\u7a0b\u4e2d\u5b58\u5728\u6052\u7b49\u5f0f\uff0c\u5219\u53ef\u4ee5\u987a\u5ef6\u6c42\\(\\mu_{k+1}\\)\uff1b</li> <li>\u7406\u8bba\u4e0a\u4efb\u610f\\(k\\)\u4e2a\u5173\u4e8e\\(\\mu_i\\)\u7684\u65b9\u7a0b\u7ec4\u90fd\u53ef\u4ee5\uff0c\u4f46\u8003\u8bd5\u8981\u6c42\u524d\\(k\\)\u4e2a\u624d\u7b97\u5bf9\uff1b</li> </ol>"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap07/#\u6781\u5927\u4f3c\u7136\u6cd5","title":"\u6781\u5927\u4f3c\u7136\u6cd5","text":"<p>\u505a\u9898\u6b65\u9aa4\uff1a</p> <ol> <li>\u6784\u9020\u5bf9\u6570\u4f3c\u7136\u51fd\u6570(Likelihood Function)\\(L(\\theta)=\\ln p(x_1,...,x_n,\\theta)\\)\uff1b</li> <li>\u6c42\\(\\hat\\theta\\;\\;s.t.\\;\\;L(\\hat\\theta;x_1,x_2,...,x_n)=\\max_{\\theta\\in\\Theta}L(\\theta;x_1,x_2,...,x_n)\\)\uff1b</li> <li>\u89e3\u5bf9\u6570\u4f3c\u7136\u65b9\u7a0b(Log-likelihood Equation)\\(\\frac{\\mathrm{d}L(\\theta)}{\\mathrm{d}\\theta}=0\\)\uff0c\u68c0\u9a8c\u6781\u5927\u503c\u70b9\uff1b</li> <li>\u68c0\u9a8c\u7aef\u70b9\uff1b</li> <li>\u6c42\u6700\u5927\u503c\u70b9\uff1b</li> </ol> <p>\u6027\u8d28\uff1a</p> <ul> <li>\u6781\u5927\u4f3c\u7136\u4f30\u8ba1\u7684\u4e0d\u53d8\u6027</li> <li>\u8bbe\u53c2\u6570\\(\\theta\\)\u7684\u6781\u5927\u4f3c\u7136\u4f30\u8ba1\u4e3a\\(\\hat\\theta\\)\uff0c\\(\\theta^*=g(\\theta)\\)\u662f\\(\\theta\\)\u7684\u8fde\u7eed\u51fd\u6570\uff0c\u5219\u53c2\u6570\\(\\theta^*\\)\u7684\u6781\u5927\u4f3c\u7136\u4f30\u8ba1\u4e3a\\(\\hat\\theta^*=g(\\hat\\theta)\\)\uff1b</li> </ul>"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap07/#\u4f30\u8ba1\u91cf\u7684\u8bc4\u4ef7\u51c6\u8005","title":"\u4f30\u8ba1\u91cf\u7684\u8bc4\u4ef7\u51c6\u8005","text":""},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap07/#\u65e0\u504f\u6027\u51c6\u5219","title":"\u65e0\u504f\u6027\u51c6\u5219","text":"<p>\u8bbe\\(\\theta\\)\u662f\u603b\u4f53\\(X\\)\u7684\u5f85\u4f30\u53c2\u6570\uff0c\\(X_1,X_2,...,X_n\\) \u662f\u6765\u81ea\u603b\u4f53\\(X\\)\u7684\u6837\u672c\uff0c\u82e5\u4f30\u8ba1\u91cf\\(\\hat\\theta=\\hat\\theta(X_1,X_2,...,X_n)\\)\u7684\u6570\u5b66\u671f\u671b\u5b58\u5728\uff0c\u6ee1\u8db3\\(E(\\hat\\theta)=\\theta,\\;\\;\\forall\\theta\\in\\Theta\\)\uff0c\u5219\u79f0\\(\\hat\\theta\\)\u662f\\(\\theta\\)\u7684\u65e0\u504f\u4f30\u8ba1\u91cf\u6216\u65e0\u504f\u4f30\u8ba1(Unbiased Estimation)\u3002</p> <ul> <li>\u82e5\\(E(\\hat\\theta)\\not=\\theta\\)\uff0c\u5219\u79f0\\(E(\\hat\\theta)-\\theta\\)\u4e3a\u4f30\u8ba1\u91cf\\(\\hat\\theta\\)\u7684\u504f\u5dee\uff1b</li> <li>\u82e5\\(E(\\hat\\theta)\\not=\\theta\\)\uff0c\u4f46\u82e5\u6ee1\u8db3\\(\\lim_{x\\to+\\infty}E(\\hat\\theta)=0\\)\uff0c\u5219\u79f0\\(\\hat\\theta\\)\u662f\\(\\theta\\)\u7684\u6e10\u8fdb\u65e0\u504f\u4f30\u8ba1(Asymptotic Unbiased Estimation)\uff1b</li> </ul>"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap07/#\u6709\u6548\u6027\u51c6\u5219","title":"\u6709\u6548\u6027\u51c6\u5219","text":"<p>\u8bbe\\(\\theta_1\\)\u548c\\(\\theta_2\\) \u662f\u53c2\u6570\\(\\theta\\)\u7684\u65e0\u504f\u4f30\u8ba1\uff0c\u82e5\\(\\forall \\theta\\in\\Theta\\)\uff0c\\(Var_\\theta(\\hat\\theta_1)\\leq Var_\\theta(\\hat\\theta_2)\\)\uff0c\u4e14\u4e0d\u6052\u53d6\u201c=\u201d\uff0c\u5219\u79f0\\(\\hat\\theta_1\\)\u6bd4\\(\\hat\\theta_2\\)\u6709\u6548\u3002</p>"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap07/#\u5747\u65b9\u8bef\u5dee\u51c6\u5219","title":"\u5747\u65b9\u8bef\u5dee\u51c6\u5219","text":"<p>\\(E[(\\hat\\theta-\\theta)^2] =Var(\\hat\\theta)+(E(\\hat\\theta)-\\theta)^2\\)\u662f\u4f30\u8ba1\u91cf\\(\\hat\\theta\\)\u7684\u5747\u65b9\u8bef\u5dee(Mean Square Error)\uff0c\u8bb0\u4e3a\\(Mse(\\hat\\theta)\\)\u3002\u82e5\\(Mse(\\hat\\theta_1)\\leq Mse(\\hat\\theta_2)\\)\u4e14\u4e0d\u6052\u53d6\u201c=\u201d\uff0c\u5219\u79f0\\(\\hat\\theta_1\\)\u4f18\u4e8e\\(\\hat\\theta_2\\)\u3002</p> <ul> <li>\u82e5\\(\\hat\\theta\\)\u662f\u53c2\u6570\\(\\theta\\)\u7684\u65e0\u504f\u4f30\u8ba1\u91cf\uff0c\u5219\u6709\\(Mse(\\hat\\theta)=Var(\\hat\\theta)\\)\uff1b</li> <li>\u56e0\u800c\u5747\u65b9\u8bef\u5dee\u51c6\u5219\u5e38\u7528\u4e8e\u6709\u504f\u4f30\u8ba1\u91cf\u4e4b\u95f4\uff0c\u6216\u6709\u504f\u4f30\u8ba1\u91cf\u4e0e\u65e0\u504f\u4f30\u8ba1\u91cf\u4e4b\u95f4\u7684\u6bd4\u8f83\uff1b</li> </ul>"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap07/#\u76f8\u5408\u6027\u51c6\u5219","title":"\u76f8\u5408\u6027\u51c6\u5219","text":"<p>\u82e5\\(\\lim_{n\\to+\\infty}P\\{|\\hat\\theta_n-\\theta|&lt;\\varepsilon\\}=1\\)\uff0c\u5373\\(\\hat\\theta _n \\xrightarrow{P}\\theta\\)\uff0c\u5219\u79f0\\(\\hat\\theta_n\\)\u662f\\(\\theta\\)\u7684\u76f8\u5408\u4f30\u8ba1\u91cf(Consistent Estimation)\u3002\u6709\u5982\u4e0b\u5b9a\u7406\uff1a</p> <ul> <li>\u8bbe\\(\\hat\\theta_n=\\hat\\theta_n(x_1,x_2,...,x_n)\\)\u662f\\(\\theta\\)\u7684\u4e00\u4e2a\u4f30\u8ba1\u91cf\uff0c\u82e5\\(\\lim_{n\\to \\infty}E(\\hat\\theta)=\\theta,\\;\\;\\;\\lim_{n\\to\\infty}Var(\\hat\\theta_n)=0,\\)\u5219\\(\\hat\\theta_n\\)\u662f\\(\\theta\\)\u7684\u76f8\u5408\u4f30\u8ba1\u3002</li> </ul>"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap07/#\u533a\u95f4\u4f30\u8ba1","title":"\u533a\u95f4\u4f30\u8ba1","text":"<ul> <li>\u6a59\u4e66 P300</li> <li>\u7eff\u4e66 P190</li> <li>\u8fd9\u91cc\u53ea\u7ed9\u51fa\u7279\u5b9a\u4f30\u8ba1\u7684\u8868\u8fbe\u5f0f</li> </ul>"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap07/#\u5355\u4e2a\u6b63\u6001\u603b\u4f53\u53c2\u6570\u7684\u7f6e\u4fe1\u533a\u95f4","title":"\u5355\u4e2a\u6b63\u6001\u603b\u4f53\u53c2\u6570\u7684\u7f6e\u4fe1\u533a\u95f4","text":"<p>\u91c7\u7528\u4e0a\u4fa7\u5206\u4f4d\u6570\\(X\\sim N(\\mu,\\sigma^2)\\)</p> <p>\\(\\sigma\\)\u5df2\u77e5\u65f6\\(\\mu\\)\u7684\u7f6e\u4fe1\u533a\u95f4\\(\\overline x \\sim N(\\mu,\\sigma^2/n)\\;\\;\\rightarrow\\;\\; \\frac{\\overline x-\\mu}{\\sigma/\\sqrt{n}}\\sim N(0,1)\\) \\([\\hat\\theta_L,\\hat\\theta_U]=[\\;\\;\\overline x-\\frac{z_{\\alpha/2}\u00b7\\sigma}{\\sqrt{n}}\\;\\;,\\;\\;\\overline x + \\frac{z_{\\alpha/2}\u00b7\\sigma}{\\sqrt{n}}\\;\\;]\\) \\(\\sigma\\)\u672a\u77e5\u65f6\\(\\mu\\)\u7684\u7f6e\u4fe1\u533a\u95f4\\(\\frac{\\sqrt{n}(\\overline x - \\mu)}{\\sqrt{s^2} }\\sim t(n-1)\\) \\([\\hat\\theta_L,\\hat\\theta_U]=\\left[\\;\\; \\overline x - \\frac{t_{\\alpha/2}(n-1)s}{\\sqrt{n}} \\;\\;,\\;\\; \\overline x + \\frac{t_{\\alpha/2}(n-1)s}{\\sqrt{n}} \\;\\;\\right]\\) \\(\\sigma^2\\)\u7684\u7f6e\u4fe1\u533a\u95f4\uff08\u5f53\u4f5c\\(\\mu\\)\u672a\u77e5\uff09\\(\\frac{(n-1)s^2}{\\sigma^2}\\sim \\chi^2(n-1)\\) \\([\\hat\\theta_L,\\hat\\theta_U]=\\left[\\;\\; \\frac{(n-1)s^2}{\\chi^2_{\\alpha/2}(n-1)} \\;\\;,\\;\\; \\frac{(n-1)s^2}{\\chi^2_{1-\\alpha/2}(n-1)} \\;\\;\\right]\\)</p>"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap07/#\u4e24\u4e2a\u6b63\u6001\u603b\u4f53\u4e0b\u7684\u7f6e\u4fe1\u533a\u95f4","title":"\u4e24\u4e2a\u6b63\u6001\u603b\u4f53\u4e0b\u7684\u7f6e\u4fe1\u533a\u95f4","text":"<p>\\(\\sigma_1^2,\\sigma_2^2\\)\u5df2\u77e5\u65f6\\(\\mu_1-\\mu_2\\)\u7684\u7f6e\u4fe1\u533a\u95f4\\(\\overline x - \\overline y \\sim N(\\mu_1-\\mu_2,\\frac{\\sigma_1^2}{n_1},\\frac{\\sigma_2^2}{n_2})\\) \\([\\hat\\theta_L,\\hat\\theta_U]=\\left[\\;\\;\\overline x - \\overline y+ z_{\\alpha/2}\\sqrt{\\frac{\\sigma_1^2}{n_1}+\\frac{\\sigma_2^2}{n_2}}\\;\\;,\\;\\;\\overline x - \\overline y- z_{\\alpha/2}\\sqrt{\\frac{\\sigma_1^2}{n_1}+\\frac{\\sigma_2^2}{n_2}}\\;\\;\\right]\\) \\(\\sigma_1^2,\\sigma_2^2\\)\u672a\u77e5\u4f46\u76f8\u540c(\\(\\sigma_1^2=\\sigma_2^2=\\sigma^2\\))\u65f6\\(\\mu_1-\\mu_2\\)\u7684\u7f6e\u4fe1\u533a\u95f4\u53d6\\(\\sigma^2\\)\u7684\u65e0\u504f\u4f30\u8ba1\u91cf\\(S^2_w=\\frac{(n_1-1)S_1^2+(n_2-1)S_2^2}{n_1+n_2-2}\\) \\(\\frac{(\\overline x -\\overline y)-(\\mu_1-\\mu_2)}{S_w\\sqrt{\\frac{1}{n_1}+\\frac{1}{n_2}}}\\sim t  (n_1+n_2-2)\\) \\([\\hat\\theta_L,\\hat\\theta_U]=\\left[\\;\\; \\overline x - \\overline y\\pm t_{\\alpha/2}(n_1+n_2-2)S_w\\sqrt{\\frac{1}{n_1}+\\frac{1}{n_2}} \\;\\;\\right]\\) \\(\\sigma_1^2,\\sigma_2^2\\)\u672a\u77e5\u4e14\u4e0d\u540c(\\(\\sigma_1^2\\not=\\sigma_2^2\\))\u65f6\\(\\mu_1-\\mu_2\\)\u7684\u7f6e\u4fe1\u533a\u95f4</p> <ul> <li>\u5f53\u6837\u672c\u5bb9\u91cf\\(n_1,n_2\\)\u8db3\u591f\u5927\u65f6\uff0c\u6709\\(\\frac{(\\overline x -\\overline y)-(\\mu_1 - \\mu_2)}{\\sqrt{\\frac{S_1^2}{n_1}+\\frac{S_2^2}{n_2}}}\\sim N(0,1)\\)</li> <li>\\([\\hat\\theta_L,\\hat\\theta_U]=\\left[\\;\\; \\overline x - \\overline y\\pm z_{\\alpha/2}\\sqrt{\\frac{S_1^2}{n_1}+\\frac{S_2^2}{n_2}} \\;\\;\\right]\\)</li> <li>\u800c\u5bf9\u4e8e\u5bb9\u91cf\u4e0d\u5927\u7684\u5c0f\u6837\u672c\uff0c\u6709\u5982\u4e0b\u7ed3\u8bba\uff1a</li> <li>\\(\\frac{(\\overline X-\\overline Y)-(\\mu_1-\\mu_2)}{\\sqrt{\\frac{S_1^2}{n_1}+\\frac{S_2^2}{n_2}}}\\sim t(k)\\;\\;where \\;\\; k=\\frac{(\\frac{S_1^2}{n_1}+\\frac{S_2^2}{n_2})^2}{\\frac{(S_1^2)^2}{n_1^2(n_1-1)}+\\frac{(S_2^2)^2}{n_2^2(n_2-1)}}\\)\uff1b</li> <li>\\([\\hat\\theta_L,\\hat\\theta_U]=\\left[\\;\\; \\overline x - \\overline y\\pm t_{\\alpha/2}(k)\\sqrt{\\frac{S_1^2}{n_1}+\\frac{S_2^2}{n_2}} \\;\\;\\right]\\)</li> </ul> <p>\\(\\frac{\\sigma^2_1}{\\sigma_2^2}\\)\u7684\u533a\u95f4\u4f30\u8ba1\\(\\frac{S_1^2/S_2^2}{\\sigma^2_1/\\sigma_2^2}\\sim F(n_1-1,n_2-1)\\)</p> \\[ [\\hat\\theta_L,\\hat\\theta_U]=\\left[\\;\\; \\frac{S_1^2/S_2^2}{F_{\\alpha/2}(n_1-1,n_2-1)} \\;\\;,\\;\\; \\frac{S_1^2/S_2^2}{F_{1-\\alpha/2}(n_1-1,n_2-1)} \\;\\;\\right] \\]"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap08/","title":"[8.x] \u5047\u8bbe\u68c0\u9a8c","text":"<p> \u7ea6 133 \u4e2a\u5b57 </p> <ul> <li>\u6a59\u4e66 P314</li> <li>\u7eff\u4e66 P211</li> </ul>"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap08/#\u5904\u7406\u5047\u8bbe\u68c0\u9a8c\u95ee\u9898\u7684\u57fa\u672c\u6b65\u9aa4","title":"\u5904\u7406\u5047\u8bbe\u68c0\u9a8c\u95ee\u9898\u7684\u57fa\u672c\u6b65\u9aa4","text":"<ol> <li>\u63d0\u51fa\u539f\u5047\u8bbe\u548c\u5907\u62e9\u5047\u8bbe\uff1b</li> <li>\u9009\u62e9\u68c0\u9a8c\u540c\u8ba1\u91cf\uff0c\u7ed9\u51fa\u62d2\u7edd\u57df\u5f62\u5f0f\uff1b</li> <li>\u9009\u62e9\u663e\u8457\u6027\u6c34\u5e73\uff0c\u6c42\u62d2\u7edd\u57df\u4e2d\u7684\u4e34\u754c\u503c\uff08\u7ed9\u51fa\u62d2\u7edd\u57df\uff09\uff1b</li> <li>\u6839\u636e\u5b9e\u9645\u6837\u672c\u4f5c\u51fa\u5224\u65ad\uff1b</li> </ol> <p>\u6216\u8005</p> <ol> <li>\u63d0\u51fa\u539f\u5047\u8bbe\u548c\u5907\u62e9\u5047\u8bbe\uff1b</li> <li>\u9009\u62e9\u68c0\u9a8c\u540c\u8ba1\u91cf\uff0c\u7ed9\u51fa\u62d2\u7edd\u57df\u5f62\u5f0f\uff1b</li> <li>\u8ba1\u7b97\u68c0\u9a8c\u7edf\u8ba1\u91cf\u7684\u89c2\u5bdf\u503c\u548c\\(P\\_\\)\u503c\uff1b</li> <li>\u6839\u636e\u7ed9\u5b9a\u7684\u663e\u8457\u6c34\u5e73\\(\\alpha\\)\u4f5c\u51fa\u5224\u65ad\uff1b</li> </ol> <p></p>"},{"location":"cour_note/D1QD_CXiaoCheng/","title":"[\u5927\u4e00\u79cb\u51ac] C\u5c0f\u7a0b \u7410\u788e\u77e5\u8bc6\u70b9\u6574\u7406","text":"<p> \u7ea6 4830 \u4e2a\u5b57  53 \u884c\u4ee3\u7801  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 17 \u5206\u949f</p> <p>\u7528\u6765\u6574\u7406C\u5c0f\u7a0b\u7684\u4e00\u4e9b\u7ec6\u788e\u77e5\u8bc6\u70b9\u3002 \u6392\u7248\u6ca1\u6709\u903b\u8f91\uff0c\u5185\u5bb9\u4e5f\u4e0d\u5b8c\u6574\u3002 \u8be5\u6587\u6863\u9488\u5bf9\u6211\u4e2a\u4eba\u3002 \u6709\u4e00\u4e9b\u4e0d\u5728\u8003\u8bd5\u8303\u56f4\u5185\u7684\u4e1c\u897f\uff0c\u6211\u89c9\u5f97\u6709\u610f\u601d\u4e5f\u4e22\u4e0a\u53bb\u4e86\u3002</p>"},{"location":"cour_note/D1QD_CXiaoCheng/#\u60f3\u4e0d\u51fa\u6807\u9898\u7684\u90fd\u653e\u8fd9","title":"\u60f3\u4e0d\u51fa\u6807\u9898\u7684\u90fd\u653e\u8fd9","text":"<ul> <li>\u51af\u00b7\u8bfa\u4f9d\u66fc\u7ed3\u6784\uff1a\u4e00\u79cd\u5c06\u7a0b\u5e8f\u6307\u4ee4\u5b58\u50a8\u5668\u548c\u6570\u636e\u5b58\u50a8\u5668\u5408\u5e76\u5728\u4e00\u8d77\u7684\u7535\u8111\u8bbe\u8ba1\u6982\u5ff5\u7ed3\u6784\u3002   </li> <li>\u95ee\u4f60\u4e00\u4e2a<code>char</code>\u578b\u53d8\u91cf\u7684\u503c\u662f\u591a\u5c11\uff0c\u8981\u4e48\u8bb0\u5f97 \u5f15\u53f7\uff0c\u8981\u4e48\u8bb0\u5f97\u7528 ASCII </li> <li>C\u8bed\u8a00\u7a0b\u5e8f \u6613\u4e8e\u79fb\u690d <ul> <li>\u4e0e\u786c\u4ef6\u6709\u5173\u7684\u56e0\u7d20\u88ab\u4ece\u8bed\u8a00\u4e3b\u4f53\u4e2d\u5206\u79bb\u51fa\u6765   </li> </ul> </li> <li>C\u8bed\u8a00\u6570\u636e\u7c7b\u578b\u68c0\u67e5\u4e0d\u4e25\u683c    </li> <li>C\u8bed\u8a00\u8868\u8fbe\u5f0f\u51fa\u73b0\u4e8c\u4e49\u6027    </li> <li>C\u8bed\u8a00\u4e0d\u80fd\u81ea\u52a8\u68c0\u67e5\u6570\u636e\u8d8a\u754c   </li> <li>\u6570\u636e\u6587\u4ef6\u53ef\u5206\u4e3a \u6587\u672c\u6587\u4ef6 \u548c \u4e8c\u8fdb\u5236\u6587\u4ef6 </li> <li>\u6587\u4ef6\u7684\u6570\u636e\u6d41\u53c8\u5206\u4e3a \u5b57\u7b26\u6d41 \u548c \u4e8c\u8fdb\u5236\u6d41 </li> <li>\u4e0b\u9762\u8fd9\u4e9b\u8bf4\u6cd5\u90fd\u6ca1\u9519\uff0c\u4f46\u662f\u6211\u60f3\u5230\u4e86\u66f4\u597d\u7684\u8bf4\u6cd5\u6240\u4ee5\u5212\u4e86\u4ed6\u4eec    </li> <li><code>typedef</code>\u6570\u7ec4\u7684\u683c\u5f0f\u5982\u4e0b\uff1a<ul> <li><code>typedef int array[10];</code></li> </ul> </li> <li>\u5219\u4e0b\u9762\u4e24\u4e2a\u7b49\u6548\uff1a<ul> <li>int a[10];</li> <li>array a;</li> </ul> </li> <li>\u4f46\u7cfb\u7edf\u5bf9\u4ed6\u4eec\u7684\u7c7b\u578b\u8ba4\u5b9a\u4e0d\u540c\uff0c<code>array</code>\u4f5c\u4e3a\u4e00\u4e2a\u65b0\u7684<code>~~type~~</code>\u5b58\u5728 </li> <li><code>typedef</code>\u7684\u5b9a\u4e49 \u7c7b\u4f3c \u4e8e\u53d8\u91cf\u7684\u5b9a\u4e49\uff1a<ul> <li>\u300ceg\u300d\u4e8c\u7ea7\u6307\u9488\u6570\u7ec4\uff1a<code>typedef int **P[10];</code> \u4e4b\u540e\u4f60\u53ef\u4ee5\u7528<code>P</code>\u4ee3\u8868\u4e00\u4e2a \u6307\u5411 \u4e00\u4e2a\u6307\u5411\u6574\u578b\u7684\u6307\u9488 \u7684\u6307\u9488 \u7684 10\u7ef4\u6570\u7ec4 \u7684 \u7c7b\u578b\uff0810\u4e2a\u4e8c\u7ea7\u6307\u9488\uff09</li> <li>\u300ceg\u300d\u4e00\u7ea7\u6570\u7ec4\u6307\u9488\uff1a<code>typedef int (*P)[10];</code> \u4e4b\u540e\u4f60\u53ef\u4ee5\u7528<code>P</code>\u4ee3\u8868\u4e00\u4e2a \u6307\u5411 10\u7ef4\u6570\u7ec4 \u7684\u6307\u9488 \u7684 \u7c7b\u578b(1\u4e2a\u4e00\u7ea7\u6307\u9488)</li> <li>\u76f8\u5173\u5185\u5bb9\uff1a\u8fd9\u91cc</li> </ul> </li> <li><code>typedef</code>\u7684\u5185\u5bb9 \u4e00\u822c \u7528 \u5927\u5199\u5355\u8bcd(\u6bd4\u5982FILE)\u8868\u793a\u8fd9\u662f\u4e00\u4e2a\u81ea\u5b9a\u4e49\u7c7b\u578b\uff0c\u4f46\u4e0d\u7528\u5927\u5199\u4e5f\u4e0d\u4f1a\u51fa\u9519    </li> <li><code>break;</code>\u53ef\u4ee5\u51fa\u73b0\u5728 loop \u6216\u8005 switch \u5185    </li> <li>\u8981\u5c0f\u5fc3\u85cf\u5728\u53c2\u6570\u8868\u91cc\u7684\u7c7b\u578b\u8f6c\u6362    </li> </ul> \u9898\u9762\u7b54\u6848 <ul> <li>\u5982\u4e0b\u7a0b\u5e8f\u7684\u8f93\u51fa\u4e3a___\u3002</li> </ul> <pre><code>#include &lt;stdio.h&gt;\n\ndouble myFunction(int x){\nreturn x;\n}\n\nint main(){\nprintf(\"%lf\",myFunction(3.14));\n}\n</code></pre> <ul> <li>3</li> <li>\u56e0\u4e3a 3.14 \u5728\u4f20\u5165 <code>myFunction(int)</code> \u65f6\u53d1\u751f\u4e86\u7c7b\u578b\u8f6c\u6362\u3002   </li> </ul> <ul> <li>\u5b57\u7b26\u4e32\u6570\u7ec4\u4ee5<code>\\0</code>\u4e3a\u7ed3\u675f\u7b26</li> <li> <p>\u53ef\u4ee5\u76f4\u63a5\u7528<code>[]</code>\u8bbf\u95ee\u5b57\u7b26\u4e32\u5e38\u91cf\u7684\u67d0\u4e2a\u5b57\u7b26</p> <ul> <li>\u5982<code>\"ABC\"[1] = 'B'</code> </li> </ul> </li> <li> <p>\u5c0f\u5fc3 \u9690\u85cf \u7684\u201c0\u201d\uff1a</p> </li> <li><code>int a[3][4] = {{1,2,3},{1,2,3}}</code>\u5b9e\u9645\u4e0a\u7b49\u6548\u4e8e<code>int a[3][4] = {{1,2,3,0},{1,2,3,0},{0,0,0,0}}</code></li> <li><code>EOF</code>\u5b9e\u9645\u4e0a\u5c31\u662f<code>-1</code> </li> <li><code>NULL</code>\u5b9e\u9645\u4e0a\u5c31\u662f<code>0LL</code> </li> <li>\u5b9a\u4e49\u51fd\u6570\u65f6\u7701\u7565\u51fd\u6570\u7684\u8fd4\u56de\u7c7b\u578b\uff0c\u5219\u5b9e\u9645\u8fd4\u56de\u7c7b\u578b\u662f<code>int</code></li> <li><code>puts()</code>\u53ea\u80fd\u8f93\u51fa\u5b57\u7b26\u4e32(\u8f93\u51fa\u7684\u4e1c\u897f\u5fc5\u987b\u6709<code>\\0</code>\u5426\u5219\u4f1a\u6302\uff0c\u610f\u601d\u662f\u8bf4 \u6570\u5b57\u3001\u5b57\u7b26 \u90fd\u4e0d\u53ef\u4ee5)    </li> </ul> <p> </p> <ul> <li> <p>\u8fd9\u4e2a\u62a5\u9519 <pre><code>#include&lt;stdio.h&gt;\n\n{}\n\nint main(){\n}\n</code></pre></p> </li> <li> <p>\u8fd9\u4e2a\u4e0d\u62a5\u9519 <pre><code>#include&lt;stdio.h&gt;\n\nint main(){\n{}\n}\n</code></pre></p> </li> </ul>"},{"location":"cour_note/D1QD_CXiaoCheng/#\u6570\u636e\u7c7b\u578b\u4e0e\u5b57\u8282\u5206\u914d","title":"\u6570\u636e\u7c7b\u578b\u4e0e\u5b57\u8282\u5206\u914d","text":"\u6570\u636e\u7c7b\u578b \u5b57\u8282\u6570 \u8bf4\u660e char 1 int 4 short 2 long 4 long long 8 unsigned 8 float 4 \u6709\u6548\u4f4d\u6570\u4e00\u822c\u57287~8\u4f4d double 8 \u6709\u6548\u4f4d\u7f6e\u4e00\u822c\u572815~16\u4f4d \u6240\u6709 \u6307\u9488(64x/32x) 8/4 struct\u3001\u6570\u7ec4 - \u5185\u5b58\u4e3a\u6240\u6709\u6210\u5458\u53d8\u91cf\u7684\u5185\u5b58\u548c\uff08\u4f46\u662f\u9700\u8981\u8003\u8651\u5bf9\u9f50\uff09 <ul> <li>\u5bf9\u4e8e\u5e38\u6570\uff1a<ul> <li><code>sizeof(1) = 4</code></li> <li><code>sizeof(1ll) = 8</code></li> <li><code>sizeof(1.0) = 8</code></li> <li><code>sizeof(1.0f) = 4</code></li> </ul> </li> <li><code>sizeof()</code>\u662f\u4e00\u4e2a\u8fd0\u7b97\u7b26\uff0c\u4e0d\u662f\u51fd\u6570\uff0c\u800c\u4e14\u5728\u7f16\u8bd1\u9636\u6bb5\u5c31\u5b8c\u6210\u66ff\u6362\u3002<ul> <li>\u5982\u679c<code>k</code>\u7684\u7c7b\u578b\u53608B\u5185\u5b58\uff0c\u5219<code>sizeof(++k)</code>\u5728\u7f16\u8bd1\u9636\u6bb5\u88ab\u66ff\u6362\u4e3a8\uff0c\u800c<code>k</code>\u7684 \u503c\u4e0d\u4f1a\u6539\u53d8</li> </ul> </li> </ul>"},{"location":"cour_note/D1QD_CXiaoCheng/#\u7f16\u8bd1\u7f16\u8bd1\u9884\u5904\u7406","title":"\u7f16\u8bd1\u3001\u7f16\u8bd1\u9884\u5904\u7406","text":"<ul> <li>\u7f16\u8bd1\u9884\u5904\u7406<ul> <li>\u7f16\u8bd1\u9884\u5904\u7406\u662f C \u8bed\u8a00\u7f16\u8bd1\u7a0b\u5e8f\u7684\u7ec4\u6210\u90e8\u5206\uff0c\u7528\u4e8e\u89e3\u91ca\u5904\u7406 C \u8bed\u8a00\u7a0b\u5e8f\u4e2d\u7684\u9884\u5904\u7406\u6307\u4ee4\uff08\u7279\u5f81\u662f\u4ee5<code>#</code>\u5f00\u5934\uff0c\u5b83\u4eec\u4e0d\u662f\u771f\u6b63\u7684 C \u8bed\u53e5\uff09</li> <li>\u7f16\u8bd1\u9884\u5904\u7406\u5728\u6b63\u5f0f\u7f16\u8bd1\u4e4b\u524d</li> </ul> </li> <li><code>#include</code><ul> <li>\u5982\u679c\u540e\u9762\u662f<code>&lt;xxx&gt;</code>\uff0c\u5219\u5c06\u4f7f\u7528 C \u8bed\u8a00\u7684 \u6807\u51c6\u5934\u6587\u4ef6</li> <li>\u5982\u679c\u540e\u9762\u662f<code>\"xxx\"</code>\uff0c\u5c06\u5148\u5230\u5f53\u524d\u5de5\u4f5c\u76ee\u5f55\u5bfb\u627e\u88ab\u5305\u542b\u7684\u6587\u4ef6\uff0c\u627e\u4e0d\u5230\u5219\u53bb\u7cfb\u7edf<code>include</code>\u76ee\u5f55\u5bfb\u627e</li> </ul> </li> <li>\u5b8f<ul> <li>\u57fa\u672c\u683c\u5f0f <code>#define \u5b8f\u540d(\u5b8f\u53c2) \u5b8f\u5b9a\u4e49\u5b57\u7b26\u4e32</code></li> <li>\u5b8f\u53ea\u662f\u7eaf\u7cb9\u7684\u5bf9\u4ee3\u7801\u7684\u5b57\u7b26\u4e32\u66ff\u6362\uff01</li> </ul> </li> <li> <p>\u6761\u4ef6\u7f16\u8bd1   <pre><code>#define FLAG 1\n#if FLAG\n//\u7a0b\u5e8f\u6bb51\n#else\n//\u7a0b\u5e8f\u6bb52\n#endif\n</code></pre></p> </li> <li> <p>\u7531\u4e8e\u8fd9\u4e9b\u90fd\u5728\u9884\u7f16\u8bd1\u4e2d\u5904\u7406\uff1a</p> <ul> <li><code>#if</code>\u540e\u9762\u7684\u6761\u4ef6\u53ea\u80fd\u662f\u5b8f\u540d</li> <li>\u4e0d\u5728\u6761\u4ef6\u9009\u62e9\u8303\u56f4\u5185\u7684\u4ee3\u7801\u4e0d\u4f1a\u88ab\u7f16\u8bd1   </li> </ul> </li> <li> <p>\u7f16\u8bd1\u7a0b\u5e8f \u9996\u5148\u8981\u5bf9 \u6e90\u7a0b\u5e8f \u8fdb\u884c \u8bcd\u6cd5\u5206\u6790\uff0c\u7136\u540e\u8fdb\u884c \u8bed\u6cd5\u5206\u6790 \u548c \u8bed\u4e49\u5206\u6790</p> </li> <li>\u7f16\u5199\u7a0b\u5e8f  -&gt;  \u7f16\u8bd1\u751f\u6210\u4e8c\u8fdb\u5236obj\u76ee\u6807\u7a0b\u5e8f\u6587\u4ef6  -&gt; \u4e0e\u5e93\u51fd\u6570\u8fdb\u884c\u8fde\u63a5\uff0c\u5f62\u6210exe\u53ef\u6267\u884c\u6587\u4ef6</li> </ul>"},{"location":"cour_note/D1QD_CXiaoCheng/#\u8f93\u5165\u8f93\u51fa\u4e2d\u7684\u683c\u5f0f\u63a7\u5236\u7b26","title":"\u8f93\u5165\u8f93\u51fa\u4e2d\u7684\u683c\u5f0f\u63a7\u5236\u7b26","text":"\u63a7\u5236\u7b26 \u8bf4\u660e <code>%d</code> \u5341\u8fdb\u5236\u6574\u578b <code>%ld</code> \u5341\u8fdb\u5236\u957f\u6574\u578b <code>%md</code> \uff08\\(m \\in \\text{R}\\)\uff0c\u5982<code>%2d</code>\uff09 m \u4e3a\u6307\u5b9a\u7684\u8f93\u51fa\u5b57\u6bb5\u7684\u5bbd\u5ea6\u3002\u5982\u679c\u6570\u636e\u7684\u4f4d\u6570\u5c0f\u4e8e m\uff0c\u5219\u5de6\u7aef\u8865\u4ee5\u7a7a\u683c\uff0c\u82e5\u5927\u4e8e m\uff0c\u5219\u6309\u5b9e\u9645\u4f4d\u6570\u8f93\u51fa\u3002\u5982\u679c\u52a0<code>-</code>\u8868\u793a\u5de6\u5bf9\u9f50\uff1b\u5982\u679c\u52a0<code>+</code>\u6216\u4e0d\u52a0\u8868\u793a\u53f3\u5bf9\u9f50\u3002 \u5982<code>%-2d</code>\uff0c<code>%+3d</code> <code>%u</code> \u5341\u8fdb\u5236\u65e0\u7b26\u53f7\u6574\u578b <code>%lu</code> \u5341\u8fdb\u5236\u65e0\u7b26\u53f7\u957f\u6574\u578b <code>%c</code> \u5b57\u7b26 <code>%f</code> <code>%e</code> \u5bf9\u4e8e<code>scanf</code>\u4ec5\u8868\u793a\u5355\u7cbe\u5ea6\u6d6e\u70b9\u6570\u5bf9\u4e8e<code>printf</code>\u4e0e<code>%lf</code>\u7b49\u4ef7\u3002\u4e0d\u6307\u5b9a\u5b57\u6bb5\u5bbd\u5ea6\uff0c\u7531\u7cfb\u7edf\u81ea\u52a8\u6307\u5b9a\uff0c\u6574\u6570\u90e8\u5206\u5168\u90e8\u8f93\u51fa\uff0c\u5c0f\u6570\u90e8\u5206\u8f93\u51fa 6 \u4f4d\uff0c\u8d85\u8fc7 6 \u4f4d\u7684 \u56db\u820d\u4e94\u5165 <code>%.mf</code>\uff08\uff0c\u5982<code>%.6f</code>\uff09 \u8f93\u51fa\u5b9e\u6570\u65f6 \u5c0f\u6570\u70b9\u540e \u4fdd\u7559 m \u4f4d <code>%lf</code> <code>%le</code> \u5bf9\u4e8e<code>scanf</code>\u4ec5\u8868\u793a\u53cc\u7cbe\u5ea6\u6d6e\u70b9\u6570\u5bf9\u4e8e<code>printf</code>\u4e0e<code>%f</code>\u7b49\u4ef7\u3002\u4e0d\u6307\u5b9a\u5b57\u6bb5\u5bbd\u5ea6\uff0c\u7531\u7cfb\u7edf\u81ea\u52a8\u6307\u5b9a\uff0c\u6574\u6570\u90e8\u5206\u5168\u90e8\u8f93\u51fa\uff0c\u5c0f\u6570\u90e8\u5206\u8f93\u51fa 6 \u4f4d\uff0c\u8d85\u8fc7 6 \u4f4d\u7684 \u56db\u820d\u4e94\u5165 <code>%.mlf</code>\uff08\uff0c\u5982<code>%.6lf</code>\uff09 \u8f93\u51fa\u5b9e\u6570\u65f6 \u5c0f\u6570\u70b9\u540e \u4fdd\u7559 m \u4f4d <code>%p</code> \u5730\u5740 <code>%s</code> \u5b57\u7b26\u4e32 <code>%o</code> \u516b\u8fdb\u5236\u6574\u578b <code>%lo</code> \u516b\u8fdb\u5236\u957f\u6574\u578b <code>%x</code> <code>%X</code> <code>%#x</code> <code>%#X</code> \u5341\u516d\u8fdb\u5236\u6574\u578b <code>%lx</code> <code>%lX</code> \u5341\u516d\u8fdb\u5236\u957f\u6574\u578b"},{"location":"cour_note/D1QD_CXiaoCheng/#\u5e38\u89c1\u8f6c\u4e49\u5b57\u7b26","title":"\u5e38\u89c1\u8f6c\u4e49\u5b57\u7b26","text":"\u8f6c\u4e49\u5b57\u7b26 \u610f\u4e49 ASCII\uff08Dec\uff09 ASCII\uff08Hex\uff09 <code>\\b</code> \u9000\u683c(BS) \uff0c\u5c06\u5f53\u524d\u4f4d\u7f6e\u79fb\u5230\u524d\u4e00\u5217 008 0x08 <code>\\n</code> \u6362\u884c(LF) \uff0c\u5c06\u5f53\u524d\u4f4d\u7f6e\u79fb\u5230\u4e0b\u4e00\u884c\u5f00\u5934 010 0x10 <code>\\r</code> \u56de\u8f66(CR) \uff0c\u5c06\u5f53\u524d\u4f4d\u7f6e\u79fb\u5230\u672c\u884c\u5f00\u5934 013 0x13 <code>\\t</code> \u6c34\u5e73\u5236\u8868(HT) 009 0x09 <code>\\'</code> \u5355\u5f15\u53f7 039 0x27 <code>\\\"</code> \u53cc\u5f15\u53f7 034 0x22 <code>\\\\</code> \u53cd\u659c\u6760 092 0x5C <code>\\ddd</code> 1~3\u4f4d\u7684\u516b\u8fdb\u5236\u6574\u6570\u6240\u4ee3\u8868\u7684ASCII\u7b26\u6bd4\u5982<code>\\041</code>\u6216\u8005<code>\\41</code>\u8868\u793a<code>!</code> - - <code>\\xhh</code> 1~2\u4f4d\u7684\u5341\u516d\u8fdb\u5236\u6574\u6570\u6240\u8868\u793a\u7684ASCII\u7b26\u6bd4\u5982<code>\\x21</code>\u8868\u793a<code>!</code> - -"},{"location":"cour_note/D1QD_CXiaoCheng/#\u5e38\u7528\u6570\u5b66\u51fd\u6570","title":"\u5e38\u7528\u6570\u5b66\u51fd\u6570","text":"<ul> <li><code>sqrt(x)</code> \\(\\sqrt x\\)\uff0c\u8fd4\u56de<code>double</code>\u7c7b\u578b</li> <li><code>pow(x,n)</code> \\(x^n\\)\uff0c\u8fd4\u56de<code>double</code>\u7c7b\u578b</li> <li><code>exp(x)</code> \\(e^x\\)\uff0c\u8fd4\u56de<code>double</code>\u7c7b\u578b</li> <li><code>fabs(x)</code> \\(|x|\\)\uff0c\u8fd4\u56de<code>double</code>\u7c7b\u578b</li> <li><code>log(x)</code> \\(\\ln{x}\\)\uff0c\u8fd4\u56de<code>double</code>\u7c7b\u578b</li> </ul>"},{"location":"cour_note/D1QD_CXiaoCheng/#\u5faa\u73af\u8bed\u53e5","title":"\u5faa\u73af\u8bed\u53e5","text":"<p>\u5982\u4e0b\u7684\u5faa\u73af\u8bed\u53e5\uff1a <pre><code>for(\u8868\u8fbe\u5f0f1;\u8868\u8fbe\u5f0f2;\u8868\u8fbe\u5f0f3){\n\u8bed\u53e5\n}\n</code></pre> \u5176\u6d41\u7a0b\u5e94\u5f53\u5982\u4e0b\uff1a</p> <pre><code>graph LR\n    A[\u8868\u8fbe\u5f0f1] --&gt; B{\u8868\u8fbe\u5f0f2};\n    B --&gt;|Yes| C[\u8bed\u53e5];\n    C --&gt; D[\u8868\u8fbe\u5f0f3];\n    D --&gt; B;\n    B ----&gt;|No| E[\u7ed3\u675f\u5faa\u73af];</code></pre>"},{"location":"cour_note/D1QD_CXiaoCheng/#\u5206\u652f\u8bed\u53e5","title":"\u5206\u652f\u8bed\u53e5","text":"<ul> <li>\u5206\u652f\u8bed\u53e5\u6d4b\u8bd5\u6570\u636e\u81f3\u5c11\u9700\u8981\u51e0\u7ec4\u95ee\u9898\uff1a\u8981\u6ce8\u610f\u6570\u636e\u8fb9\u754c\u4e5f\u8981\u7b97\u4e00\u7ec4:<ul> <li>\u5982\u4e0b\u5206\u652f\u8bed\u53e5\u9700\u8981\u8bbe\u8ba1\u81f3\u5c11___\u7ec4\u6d4b\u8bd5\u6570\u636e\uff1f</li> </ul> </li> </ul> \u9898\u9762\u7b54\u6848 <pre><code>if(x &lt; 60){\n//\u8bed\u53e5\n}\n</code></pre> <ul> <li>\u7b54\u6848\uff1a3</li> <li>\u89e3\u6790\uff1a<code>x &lt; 60</code> <code>x = 60</code> <code>x &gt; 60</code></li> </ul> <ul> <li><code>switch()</code>\u8bed\u53e5<ul> <li>\u9664\u4e86\u5e26\u5f15\u53f7\u7684\u5b57\u7b26\uff0c<code>case</code>\u540e\u9762\u8981\u6253\u7a7a\u683c\uff0c\u4e0d\u6253\u7a7a\u683c\u53ef\u80fd\u80fd\u8fc7\u7f16\u8bd1\u4f46\u662f\u65e0\u6cd5\u6b63\u5e38\u5224\u65ad</li> <li><code>case 'a'</code> \u6709\u6548</li> <li><code>case'a'</code> \u6709\u6548</li> <li><code>casea</code> \u65e0\u6548</li> <li><code>case1</code> \u65e0\u6548</li> <li><code>case</code>\u540e\u8ddf\u7684\u5fc5\u987b\u662f\u4e0d\u91cd\u590d\u7684\u5e38\u91cf\u8868\u8fbe\u5f0f\uff0c\u4e0d\u53ef\u4ee5\u662f\u53d8\u91cf\u53c2\u4e0e\u7684\u8868\u8fbe\u5f0f</li> <li>\u4e0d\u6253<code>break</code>\u4f1a\u4ece\u7b26\u5408\u6761\u4ef6\u7684<code>case</code>\u5f00\u59cb\u4e00\u76f4\u5f80\u4e0b\u5230\u5e95\u6216\u8005\u4e4b\u540e\u7b2c\u4e00\u4e2a<code>break</code></li> </ul> </li> <li> <p>\u6240\u4ee5<code>break;</code>\u4e0d\u4e00\u5b9a\u53ea\u80fd\u51fa\u73b0\u5728\u5faa\u73af\u91cc   </p> </li> <li> <p>C\u8bed\u8a00\u7684\u903b\u8f91\u8fd0\u7b97\u5177\u6709\u7701\u7565\u7279\u6027\uff1a\u5f53\u524d\u4e00\u4e2a\u8868\u8fbe\u5f0f\u5df2\u7ecf\u80fd\u591f\u51b3\u5b9a\u6574\u4e2a\u8868\u8fbe\u5f0f\u7684\u503c\u7684\u65f6\u5019\uff0c\u4e0d\u8ba1\u7b97\u540e\u9762\u90a3\u4e2a\u8868\u8fbe\u5f0f</p> </li> </ul> \u9898\u9762\u7b54\u6848 <ul> <li>\u4e0b\u5217\u7a0b\u5e8f\u6bb5\u7ed3\u675f\u540e<code>x</code>\u548c<code>y</code>\u7684\u503c\u5206\u522b\u4e3a___ \uff0c ___\u3002</li> </ul> <pre><code>int x = 0 , y = 0;\nif((++x) || (++y)){\n//\u8bed\u53e5\n}\n</code></pre> <ul> <li>\u7b54\u6848\uff1a1\uff0c0</li> </ul>"},{"location":"cour_note/D1QD_CXiaoCheng/#\u53d8\u91cf\u7684\u751f\u547d\u5468\u671f\u4f5c\u7528\u57df","title":"\u53d8\u91cf\u7684\u751f\u547d\u5468\u671f&amp;\u4f5c\u7528\u57df","text":"\u9759\u6001\u53d8\u91cf \u81ea\u52a8\u53d8\u91cf \u8fd9\u4e00\u7ec4\u5173\u7cfb\u7684\u7740\u91cd\u70b9\u5728\u5185\u5b58 \u5b58\u50a8\u4f4d\u7f6e \u548c \u751f\u547d\u5468\u671f \u7684\u95ee\u9898 \u5168\u5c40\u53d8\u91cf \u5c40\u90e8\u53d8\u91cf \u8fd9\u4e00\u7ec4\u5173\u7cfb\u7684\u7740\u91cd\u70b9\u5728 \u4f5c\u7528\u57df <ul> <li>\u5c40\u90e8\u53d8\u91cf \u7684\u6709\u6548\u4f7f\u7528\u8303\u56f4\u6700\u5927\u7a0b\u5ea6\u4fdd\u8bc1\u4e86\u5404\u90e8\u5206\u4e4b\u95f4\u7684\u72ec\u7acb\u6027\uff0c\u964d\u4f4e\u4e86\u5404\u4e2a\u6a21\u5757\u4e4b\u95f4\u7684\u8026\u5408\u5ea6</li> <li> <p>\u5168\u5c40\u53d8\u91cf \u7684 \u4f5c\u7528\u57df \u662f\u4ece \u5b9a\u4e49\u5f00\u59cb\u5230\u6587\u4ef6\u7ed3\u675f</p> </li> <li> <p>\u4e00\u65e6\u5728\u7a0b\u5e8f\u4e2d\u5b9a\u4e49\u4e86\u53d8\u91cf\uff0c\u8ba1\u7b97\u673a\u5728\u6267\u884c\u8fc7\u7a0b\u4e2d\u4f1a\u6839\u636e\u53d8\u91cf\u7684\u7c7b\u578b\u5206\u914d\u76f8\u5e94\u7684\u5185\u5b58\u5355\u5143\u4f9b\u53d8\u91cf\u4fdd\u5b58\u6570\u636e</p> </li> <li>\u81ea\u52a8\u53d8\u91cf\u7684\u5b9a\u4e49\u4e3a\uff1a<code>auto \u7c7b\u578b \u53d8\u91cf\u8868;</code> \u4e00\u822c\u60c5\u51b5\u4e0b<code>auto</code>\u53ef\u4ee5\u7701\u7565</li> <li>\u81ea\u52a8\u53d8\u91cf\u4f1a \u81ea\u52a8\u5206\u914d\u56de\u6536\u5185\u5b58</li> </ul> \u7cfb\u7edf\u5b58\u50a8\u533a \u7528\u6237\u5b58\u50a8\u533a \u7a0b\u5e8f\u533a\uff08\u4ee3\u7801\u5185\u5bb9\uff09 \u6570\u636e\u533a \u9759\u6001\u5b58\u50a8\u533a \u5168\u5c40\u53d8\u91cf \u9759\u6001\u5c40\u90e8\u53d8\u91cf \u52a8\u6001\u5b58\u50a8\u533a \u5404\u4e2a\u6a21\u5757\u4e0b\u7684\u52a8\u6001\u5c40\u90e8\u53d8\u91cf \u5404\u4e2a\u6a21\u5757\u4e0b\u7684\u52a8\u6001\u5c40\u90e8\u53d8\u91cf ... <ul> <li>\u9759\u6001\u5c40\u90e8\u53d8\u91cf\u7684\u5185\u5b58\u5b58\u50a8\u5728 \u9759\u6001\u5b58\u50a8\u533a \u4e2d\uff0c\u751f\u547d\u5468\u671f\u6301\u7eed\u5230\u7a0b\u5e8f\u7ed3\u675f\uff0c\u4e0d\u4f1a\u5728\u9000\u51fa\u51fd\u6570\u7684\u65f6\u5019\u88ab\u56de\u6536\uff0c\u4e0b\u4e00\u6b21\u4f7f\u7528\u540e\u4f1a\u88ab\u91cd\u65b0\u6fc0\u6d3b</li> <li>\u4e0e\u52a8\u6001\u5168\u5c40\u53d8\u91cf\u76f8\u6bd4\uff0c\u9759\u6001\u5168\u5c40\u53d8\u91cf\u7684\u4f5c\u7528\u57df\u5728\u5f53\u524d\u6587\u4ef6\u5185\uff0c\u52a8\u6001\u5168\u5c40\u53d8\u91cf\u5728\u591a\u6587\u4ef6\u9879\u76ee\u4e2d\u5728\u6bcf\u4e00\u4e2a\u6587\u4ef6\u90fd\u53ef\u4ee5\u7528</li> <li>\u9759\u6001\u53d8\u91cf\u7684\u5b9a\u4e49\u4e3a\uff1a<code>static \u7c7b\u578b \u53d8\u91cf\u8868;</code></li> <li>\u9759\u6001\u53d8\u91cf\u521d\u503c\u9ed8\u8ba4\u4e3a <code>0</code></li> </ul>"},{"location":"cour_note/D1QD_CXiaoCheng/#\u8865\u7801","title":"\u8865\u7801","text":"<ul> <li>\u4e3a\u4e86\u65b9\u4fbf\u8ba1\u7b97\u673a\u5185\u7684\u8fd0\u7b97\uff0c\u4e00\u822c\u7528 \u8865\u7801 \u8868\u793a\u6570\u503c</li> <li>\u8865\u7801 \u7684\u8ba1\u7b97\uff1a\u8d1f\u6570 \u9664\u4e86\u7b26\u53f7\u4f4d \u53d6\u53cd\u52a0\u4e00<ul> <li>\u300ceg\u300d\u4e24\u4e2a\u5b57\u8282\u5b58\u50a8-17\uff1a</li> <li>\u539f\u7801\uff1a<code>1000``0000</code> <code>0001``0001</code></li> <li>\u53cd\u7801\uff1a<code>1111``1111</code> <code>1110``1110</code></li> <li>\u8865\u7801\uff1a<code>1111``1111</code> <code>1110``1111</code></li> </ul> </li> <li>\u4f7f\u7528 \u8865\u7801 \u65b9\u4fbf\u7684\u539f\u56e0\u662f\uff1a\u5904\u7406\u8d1f\u6570\u548c\u6574\u6570\u76f8\u52a0\uff0c\u5b9e\u9645\u4e0a\u662f\u505a\u540c\u4f59\u8fd0\u7b97\uff1a<ul> <li>\\(-3\\) = \\((1101)_{\u8865\u7801}\\)</li> <li>\\(6\\) = \\((0110)_{\u8865\u7801}\\)</li> <li>\\(-3 + 6\\) = \\((1101)_{\u8865\u7801} + (0110)_{\u8865\u7801}\\) =  \\((0011)_{\u8865\u7801}\\) =  \\(3\\)</li> <li>\u4f46\u662f\u5982\u679c\u628a\u8865\u7801\u90fd\u5f53\u505a\u662f\u67d0\u4e2a\u6570\u7684\u539f\u7801\u5462\uff1f</li> <li>\\((1101)_{\u539f\u7801}\\) = \\(13\\)</li> <li>\\((0110)_{\u539f\u7801}\\) = \\(6\\) </li> <li>\\((0110)_{\u539f\u7801}\\) + \\((1101)_{\u539f\u7801}\\) = \\(13+6\\) = \\(19\\) = \\((0011)_{\u539f\u7801} + (10000)_{\u539f\u7801}\\)</li> <li>\u663e\u7136\uff0c\u8fd9\u91cc\u7684<code>10000</code>\u6ea2\u51fa\u4e86\uff0c\u662f\u4e0d\u662f\u5f88\u50cf\u53d6\u6a21\uff1f</li> <li>\\(19 \\equiv 3 \\mod 16\\)</li> <li>\u800c\u8fd9\u4e2a<code>16</code>\u5c31\u662f\\(2^4\\)\uff0c\u8fd9\u4e2a<code>4</code>\u662f\u4ec0\u4e48\u663e\u800c\u6613\u89c1</li> <li>\u6240\u4ee5\u5b9e\u9645\u4e0a\u7684\u903b\u8f91\u5c31\u662f\uff1a</li> <li>\u5229\u7528\u7b26\u53f7\u4f4d\u628a<code>x</code>\u4e2a\u5b57\u8282\u7684\u50a8\u5b58\u5b57\u8282\u5206\u6210\u4e24\u90e8\u5206\uff0c\u5176\u4e2d\\(0 \\;\\;\\sim\\;\\; (2^{8x-1}-1)\\)\u8868\u793a\u975e\u8d1f\u6570\u7684\u5b58\u50a8\u8303\u56f4\uff0c \\(2^{8x-1} \\;\\;\\sim\\;\\; (2^{8x}-1)\\)\u8868\u793a\u8d1f\u6570\u7684\u5b58\u50a8\u8303\u56f4\uff0c\u5e76\u901a\u8fc7\u4e0a\u9762\u63d0\u5230\u7684\u8f6c\u6362\u65b9\u5f0f\u5bf9\u8d1f\u6570\u8fdb\u884c\u987a\u5e8f\u6620\u5c04</li> <li>\u8fdb\u884c\u8fd0\u7b97\u65f6\uff0c\u7b97\u4e0a\u7b26\u53f7\u4f4d\u53c2\u4e0e\u8fd0\u7b97\uff0c\u7b97\u51fa\u6765\u7684\u4e1c\u897f\u6574\u4e2a\u518d\u4f5c\u4e3a\u7b54\u6848\u7684\u8865\u7801</li> <li>\u4e00\u8a00\u4ee5\u853d\u4e4b\uff0c\u5728\u5bf916\u53d6\u4f59\u2014\u2014\u4ea6\u5373\u8d85\u8fc74Bits\u90fd\u5c06\u6ea2\u51fa \u7684\u60c5\u51b5\u4e0b\uff0c\u201c+13\u201d\u4e0e\u201c-3\u201d\u662f\u7b49\u4ef7\u7684\uff0c\u8fd9\u5c31\u662f\u4ece\u53d6\u6a21\u89d2\u5ea6\u6765\u7406\u89e3\u201c\u8865\u7801\u201d\u3002</li> </ul> </li> <li> <p>\u800c\u65e0\u7b26\u53f7\u6574\u6570\u5c31\u662f\u5c06\u539f\u6765\u5b58\u50a8\u8d1f\u6570\u7684\u8fd9\u90e8\u5206\u4f5c\u4e3a\u6574\u6570\u7684\u5ef6\u7eed\u90e8\u5206</p> </li> <li> <p>\u5bf9\u4e8e\u5404\u7c7b\u578b\u6574\u578b\u6570\u636e\u7684\u957f\u5ea6\u4ec5\u6709\u5df2\u4e0b\u8981\u6c42\uff1a</p> <ul> <li>\\(sizeof(\\text{short}) \\leq sizeof(\\text{int}) \\leq sizeof(\\text{long})\\) </li> </ul> </li> <li> <p>\u6574\u578b\u5e38\u91cf\u7684\u89c4\u5219\uff1a</p> <ul> <li>\u524d\u7f00\uff1a</li> <li>\u5341\u8fdb\u5236 \u9996\u4f4d\u6570\u5b57\u5fc5\u987b\u975e0   \u300ceg\u300d\uff1a<code>114514</code></li> <li>\u516b\u8fdb\u5236 \u9996\u4f4d\u6570\u5b57\u5fc5\u987b\u662f0   \u300ceg\u300d\uff1a<code>01616210</code></li> <li>\u5341\u516d\u8fdb\u5236 \u5f00\u5934\u5fc5\u987b\u662f0x\u62160X   \u300ceg\u300d\uff1a<code>0xfff</code></li> <li>\u540e\u7f00\uff1a\uff08\u5927\u5c0f\u5199\u4e0d\u654f\u611f\uff09</li> <li>L \u8868\u793a\u957f\u6574\u578b   \u300ceg\u300d\uff1a<code>123456L</code></li> <li>LL \u8868\u793a\u957f\u957f\u6574\u578b   \u300ceg\u300d\uff1a<code>123456LL</code></li> <li>U \u8868\u793a\u65e0\u7b26\u53f7\u6574\u578b   \u300ceg\u300d\uff1a<code>123456U</code></li> <li>U\u548cL\u53ef\u4ee5\u6df7\u5408\u4f7f\u7528\uff0c\u4e0d\u654f\u611f\u987a\u5e8f</li> </ul> </li> </ul>"},{"location":"cour_note/D1QD_CXiaoCheng/#\u8fd0\u7b97","title":"\u8fd0\u7b97","text":"<ul> <li>\u7b97\u6570\u8fd0\u7b97\u7b26\u7684\u51e0\u4e2a\u89c4\u5219\uff1a<ul> <li>\u6574\u6570\u9664\u6cd5\u5f97\u5230\u6574\u6570 (\u5206\u5b50\u6216\u5206\u6bcd\u4efb\u610f\u4e00\u4e2a\u4e3a\u6d6e\u70b9\u6570\u5373\u53ef\u81ea\u52a8\u7c7b\u578b\u8f6c\u6362\u540e\u505a\u6d6e\u70b9\u8fd0\u7b97)</li> <li>\u53d6\u4f59 \u8fd0\u7b97\u4ec5\u5bf9 \u6574\u578b \u6570\u636e\u4f7f\u7528</li> <li><code>+</code> <code>-</code>\u53ef\u505a\u5355\u76ee\u8fd0\u7b97\u7b26\u8868\u793a\u6b63\u8d1f</li> <li>\u53cc\u76ee\u8fd0\u7b97\u7b26\u4f1a\u4fdd\u8bc1\u4e24\u4fa7\u7684\u6570\u636e \u7c7b\u578b\u76f8\u540c(\u5bf9\u4e8e\u4e0d\u540c\u7684\u8f93\u5165\u6570\u636e\u4f1a\u8fdb\u884c\u81ea\u52a8\u7c7b\u578b\u8f6c\u6362)</li> <li>\u81ea\u52a8\u7c7b\u578b\u8f6c\u6362\uff1a<ul> <li>\u975e\u8d4b\u503c\u8fd0\u7b97\uff1a\u603b\u662f\u7531\u4f4e\u5411\u9ad8\u8f6c\u6362  </li> <li>\u8d4b\u503c\u8fd0\u7b97\uff1a\u8f6c\u6362\u4e3a\u88ab\u8d4b\u503c\u7684\u53d8\u91cf\u7c7b\u578b</li> </ul> </li> </ul> </li> </ul>"},{"location":"cour_note/D1QD_CXiaoCheng/#\u8fd0\u7b97\u7b26\u4f18\u5148\u7ea7\u540c\u7ea7\u9075\u5faa\u7ed3\u5408\u65b9\u5411\u89c4\u5f8b","title":"\u8fd0\u7b97\u7b26\u4f18\u5148\u7ea7(\u540c\u7ea7\u9075\u5faa\u7ed3\u5408\u65b9\u5411\u89c4\u5f8b)","text":"<p>\u5982\u6709\u51b2\u7a81\uff0c\u8bf7\u4f18\u5148\u53c2\u8003 \u8fd9\u91cc\u3002</p> \u4f18\u5148\u7ea7 \u8fd0\u7b97\u7b26 \u540d\u79f0\u6216\u542b\u4e49 \u4f7f\u7528\u5f62\u5f0f \u7ed3\u5408\u65b9\u5411 1 [] \u6570\u7ec4\u4e0b\u6807 \u6570\u7ec4\u540d[\u5e38\u91cf\u8868\u8fbe\u5f0f] \u5de6\u5230\u53f3 () \u5706\u62ec\u53f7 \uff08\u8868\u8fbe\u5f0f\uff09/\u51fd\u6570\u540d(\u5f62\u53c2\u8868) . \u6210\u5458\u9009\u62e9\uff08\u5bf9\u8c61\uff09 \u5bf9\u8c61.\u6210\u5458\u540d -&gt; \u6210\u5458\u9009\u62e9\uff08\u6307\u9488\uff09 \u5bf9\u8c61\u6307\u9488-&gt;\u6210\u5458\u540d ++ \u540e\u7f6e\u81ea\u589e\u8fd0\u7b97\u7b26 \u53d8\u91cf\u540d++ -- \u540e\u7f6e\u81ea\u51cf\u8fd0\u7b97\u7b26 \u53d8\u91cf\u540d-- 2 - \u8d1f\u53f7\u8fd0\u7b97\u7b26 -\u8868\u8fbe\u5f0f \u53f3\u5230\u5de6 (\u7c7b\u578b) \u5f3a\u5236\u7c7b\u578b\u8f6c\u6362 (\u6570\u636e\u7c7b\u578b)\u8868\u8fbe\u5f0f ++ \u524d\u7f6e\u81ea\u589e\u8fd0\u7b97\u7b26 ++\u53d8\u91cf\u540d -- \u524d\u7f6e\u81ea\u51cf\u8fd0\u7b97\u7b26 --\u53d8\u91cf\u540d * \u53d6\u503c\u8fd0\u7b97\u7b26 *\u6307\u9488\u53d8\u91cf &amp; \u53d6\u5730\u5740\u8fd0\u7b97\u7b26 &amp;\u53d8\u91cf\u540d ! \u903b\u8f91\u975e\u8fd0\u7b97\u7b26 !\u8868\u8fbe\u5f0f ~ \u6309\u4f4d\u53d6\u53cd\u8fd0\u7b97\u7b26 ~\u8868\u8fbe\u5f0f sizeof() \u957f\u5ea6\u8fd0\u7b97\u7b26 sizeof(\u8868\u8fbe\u5f0f) 3 / \u9664 \u8868\u8fbe\u5f0f/\u8868\u8fbe\u5f0f \u5de6\u5230\u53f3 * \u4e58 \u8868\u8fbe\u5f0f*\u8868\u8fbe\u5f0f % \u4f59\u6570\uff08\u53d6\u6a21\uff09 \u6574\u578b\u8868\u8fbe\u5f0f/\u6574\u578b\u8868\u8fbe\u5f0f 4 + \u52a0 \u8868\u8fbe\u5f0f+\u8868\u8fbe\u5f0f \u5de6\u5230\u53f3 - \u51cf \u8868\u8fbe\u5f0f-\u8868\u8fbe\u5f0f 5 &lt;&lt; \u5de6\u79fb \u53d8\u91cf&lt;&lt;\u8868\u8fbe\u5f0f \u5de6\u5230\u53f3 &gt;&gt; \u53f3\u79fb \u53d8\u91cf&gt;&gt;\u8868\u8fbe\u5f0f 6 &gt; \u5927\u4e8e \u8868\u8fbe\u5f0f&gt;\u8868\u8fbe\u5f0f \u5de6\u5230\u53f3 &gt;= \u5927\u4e8e\u7b49\u4e8e \u8868\u8fbe\u5f0f&gt;=\u8868\u8fbe\u5f0f &lt; \u5c0f\u4e8e \u8868\u8fbe\u5f0f&lt;\u8868\u8fbe\u5f0f &lt;= \u5c0f\u4e8e\u7b49\u4e8e \u8868\u8fbe\u5f0f&lt;=\u8868\u8fbe\u5f0f 7 == \u7b49\u4e8e \u8868\u8fbe\u5f0f==\u8868\u8fbe\u5f0f \u5de6\u5230\u53f3 != \u4e0d\u7b49\u4e8e \u8868\u8fbe\u5f0f!= \u8868\u8fbe\u5f0f 8 &amp; \u6309\u4f4d\u4e0e \u8868\u8fbe\u5f0f&amp;\u8868\u8fbe\u5f0f \u5de6\u5230\u53f3 9 ^ \u6309\u4f4d\u5f02\u6216 \u8868\u8fbe\u5f0f^\u8868\u8fbe\u5f0f \u5de6\u5230\u53f3 10 | \u6309\u4f4d\u6216 \u8868\u8fbe\u5f0f|\u8868\u8fbe\u5f0f \u5de6\u5230\u53f3 11 &amp;&amp; \u903b\u8f91\u4e0e \u8868\u8fbe\u5f0f&amp;&amp;\u8868\u8fbe\u5f0f \u5de6\u5230\u53f3 12 || \u903b\u8f91\u6216 \u8868\u8fbe\u5f0f||\u8868\u8fbe\u5f0f \u5de6\u5230\u53f3 13 ?: \u6761\u4ef6\u8fd0\u7b97\u7b26 \u8868\u8fbe\u5f0f1? \u8868\u8fbe\u5f0f2: \u8868\u8fbe\u5f0f3 \u53f3\u5230\u5de6 14 = \u8d4b\u503c\u8fd0\u7b97\u7b26 \u53d8\u91cf=\u8868\u8fbe\u5f0f \u53f3\u5230\u5de6 /= \u9664\u540e\u8d4b\u503c \u53d8\u91cf/=\u8868\u8fbe\u5f0f *= \u4e58\u540e\u8d4b\u503c \u53d8\u91cf*=\u8868\u8fbe\u5f0f %= \u53d6\u6a21\u540e\u8d4b\u503c \u53d8\u91cf%=\u8868\u8fbe\u5f0f += \u52a0\u540e\u8d4b\u503c \u53d8\u91cf+=\u8868\u8fbe\u5f0f -= \u51cf\u540e\u8d4b\u503c \u53d8\u91cf-=\u8868\u8fbe\u5f0f &lt;&lt;= \u5de6\u79fb\u540e\u8d4b\u503c \u53d8\u91cf&lt;&lt;=\u8868\u8fbe\u5f0f &gt;&gt;= \u53f3\u79fb\u540e\u8d4b\u503c \u53d8\u91cf&gt;&gt;=\u8868\u8fbe\u5f0f &amp;= \u6309\u4f4d\u4e0e\u540e\u8d4b\u503c \u53d8\u91cf&amp;=\u8868\u8fbe\u5f0f ^= \u6309\u4f4d\u5f02\u6216\u540e\u8d4b\u503c \u53d8\u91cf^=\u8868\u8fbe\u5f0f |= \u6309\u4f4d\u6216\u540e\u8d4b\u503c \u53d8\u91cf|=\u8868\u8fbe\u5f0f 15 , \u9017\u53f7\u8fd0\u7b97\u7b26 \u8868\u8fbe\u5f0f,\u8868\u8fbe\u5f0f,\u2026 \u5de6\u5230\u53f3"},{"location":"cour_note/D1QD_CXiaoCheng/#\u6307\u9488\u76f8\u5173","title":"\u6307\u9488\u76f8\u5173","text":"<ul> <li>C\u8bed\u8a00\u89c4\u5b9a\uff0c\u6570\u7ec4\u540d\u8868\u793a\u8be5\u6570\u7ec4\u6240\u5206\u914d\u8fde\u7eed\u5185\u5b58\u7a7a\u95f4\u4e2d\u7b2c\u4e00\u4e2a\u5355\u5143\u7684\u5730\u5740\uff0c\u5373 \u9996\u5730\u5740</li> <li>\u4e8c\u7ef4\u6570\u7ec4\u7684\u5185\u5b58\u5b58\u653e\u4ecd\u7136\u91c7\u53d6\u987a\u5e8f\u5b58\u653e\uff0c\u5373\u6570\u7ec4<code>a[3][2]</code>\u4e2d<code>a[1][1]</code>\u7684\u5730\u5740\u4e0e<code>a[2][0]</code>\u76f8\u90bb</li> <li>\u4e8c\u7ef4\u6570\u7ec4\u7533\u8bf7\u65f6\u5982\u679c\u521d\u59cb\u5316\u53ef\u4ee5\u7701\u7565\u884c\u957f\u5ea6\uff0c\u5982<code>a[][3] = {1,2,3,4,5,6,7}</code></li> <li>\u5bf9\u4e8e\u4e8c\u7ef4\u6570\u7ec4<code>a[x][y]</code>\uff1a\uff08x,y\u662f\u4e24\u4e2a\u5e38\u6570\uff09<ul> <li><code>&amp;a</code>\u8868\u793a\u6570\u7ec4\u5730\u5740\uff0c<code>&amp;a+1</code>\u8868\u793a\u7684\u6570\u7ec4\u672b\u5c3e\u540e\u7684\u5730\u5740    <ul> <li>\u5373\uff1a<code>&amp;a+1</code> = (<code>&amp;a</code>) + \\(1\\times x\\times y\\times sizeof(\\text{element})\\)</li> </ul> </li> <li><code>a</code>\u6216\u8005<code>&amp;a[0]</code>\u8868\u793a\u6570\u7ec4\u9996\u884c\u5730\u5740\uff0c<code>a+1</code>\u8868\u793a\u6570\u7ec4\u4e0b\u4e00\u884c\u5730\u5740<ul> <li>\u5373\uff1a<code>a+1</code> =  (<code>a</code>) + \\(1\\times y\\times sizeof(\\text{element})\\) <code>a</code>\u5b9e\u9645\u4e0a\u662f\u4e00\u4e2a<code>x</code>\u7ef4 \u6570\u7ec4\u7684\u6307\u9488\uff0c\u8be5\u6570\u7ec4\u7684 \u5143\u7d20 \u4e3a\u82e5\u5e72<code>y</code> \u7ef4\u6570\u7ec4</li> </ul> </li> <li><code>&amp;a[0][0]</code>\u6216\u8005<code>a[0]</code>\u8868\u793a\u6570\u7ec4\u9996\u5143\u7d20\u5730\u5740\uff0c\u4e5f\u53eb\u5217\u5730\u5740\uff0c<code>&amp;a[0][0]+1</code>\u8868\u793a\u6570\u7ec4\u4e0b\u4e00\u5143\u7d20\u5730\u5740<ul> <li>\u5373\uff1a<code>&amp;a[0][0]+1</code> =  (<code>&amp;a[0][0]</code>) + \\(sizeof(\\text{element})\\)</li> </ul> </li> <li>\u4f46\u4e0a\u9762\u51e0\u4e2a\u6307\u9488\u7684 \u503c \u90fd\u4e00\u6837</li> <li><code>a[i][j]</code>\u7b49\u6548\u4e8e<code>*( *(a+i) + j )</code></li> </ul> </li> <li><code>int *p[5]</code>\u5b9a\u4e49\u4e86\u4e00\u4e2asize\u4e3a5\u7684\u6574\u578b \u6307\u9488\u7684\u6570\u7ec4 (\u8fd9\u91cc\u6709\u4e94\u4e2a\u6307\u9488)</li> <li> <p><code>int (*p)[5]</code>\u5b9a\u4e49\u4e86\u4e00\u4e2asize\u4e3a5\u7684 \u6570\u7ec4\u7684\u6307\u9488 (\u8fd9\u91cc\u53ea\u6709\u4e00\u4e2a\u6307\u9488)</p> </li> <li> <p>\u7ed9\u6307\u9488\u8d4b\u503c\u7684\u529e\u6cd5\uff1a</p> <ul> <li><code>p = &amp;x;</code></li> <li><code>p = 0;</code></li> <li><code>p = NULL;</code></li> <li><code>p = (int *)1732;</code></li> </ul> </li> <li> <p>\u6307\u9488\u8fd0\u7b97\uff1a</p> <ul> <li><code>*p+1;</code> <code>++*p;</code>\u7684\u64cd\u4f5c\u5bf9\u8c61\u90fd\u662f<code>p</code>\u6307\u5411\u7684 \u5143\u7d20\u503c</li> <li><code>*p++;</code>\u7684\u64cd\u4f5c\u5bf9\u8c61\u5219\u662f \u6307\u9488\u672c\u8eab\uff0c\u542b\u4e49\u662f\u6307\u5411\u4e0b\u4e00\u4e2a\u5730\u5740</li> <li>\u5f53\u51fa\u73b0\u4e0a\u8ff0\u8bed\u53e5\u53c2\u4e0e\u590d\u6742\u8868\u8fbe\u5f0f\u65f6\uff0c<code>*p++</code>\u4f1a\u5728\u8f93\u51fa<code>*p</code>\u540e\u518d\u6307\u5411\u4e0b\u4e00\u4e2a\u5730\u5740</li> </ul> </li> <li> <p>\u53ef\u4ee5\u901a\u8fc7\u5c06\u4e00\u4e2a \u5b57\u7b26\u4e32\u5e38\u91cf \u8d4b\u503c\u7ed9\u4e00\u4e2a\u6307\u9488\u7684\u65b9\u5f0f\u6765\u7ed9\u8be5\u5b57\u7b26\u4e32\u5206\u914d\u5730\u5740</p> <ul> <li>\u5373\u4f8b\u5982<code>char *p;   p = \"awa\";</code>\u662f\u5408\u7406\u7684</li> </ul> </li> <li><code>*strcpy(char *to,char *from)</code>\u51fd\u6570\u7684\u4f5c\u7528\u662f\uff0c\u628a \u5b57\u7b26\u6570\u7ec4 <code>from[]</code>\u590d\u5236\u5230<code>to[]</code>\u4e2d\u5e76\u8fd4\u56de<code>to[]</code></li> <li><code>*strcat(char *to,char *from)</code>\u51fd\u6570\u7684\u4f5c\u7528\u662f\uff0c\u628a \u5b57\u7b26\u6570\u7ec4 <code>from[]</code>\u6dfb\u52a0\u5230<code>to[]</code>\u672b\u5c3e\u5e76\u8fd4\u56de<code>to[]</code><ul> <li>\u8865\u5145\uff1a\u6240\u8c13\u7684\u6dfb\u52a0\uff0c\u5c31\u662f\u7528<code>from[]</code>\u53bb\u66ff\u6362<code>to[]</code>\u7b2c\u4e00\u4e2a<code>\\0</code>\u4e4b\u540e\u7684\u5143\u7d20</li> </ul> </li> <li><code>strcmp(char *a,char *b)</code>\u51fd\u6570\u7684\u4f5c\u7528\u662f\uff0c\u6bd4\u8f83 \u5b57\u7b26\u6570\u7ec4 <code>a[]</code>\u548c<code>b[]</code>\u5728<code>\\0</code>\u524d\u7684\u5185\u5bb9\u662f\u5426\u7b49\u4ef7<ul> <li>\u5982\u679c\u7b49\u4ef7 \u8fd4\u56de0</li> <li>\u5982\u679ca&lt;b \u8fd4\u56de-1</li> <li>\u5982\u679ca&gt;b \u8fd4\u56de1</li> </ul> </li> <li> <p><code>strlen(char *s)</code>\u51fd\u6570\u7684\u4f5c\u7528\u662f\uff0c\u8fd4\u56de \u5b57\u7b26\u6570\u7ec4 <code>s[]</code>\u5728<code>\\0</code>\u524d\u7684\u5143\u7d20\u4e2a\u6570</p> </li> <li> <p>\u5173\u4e8e\u6307\u9488\u548c\u7ed3\u6784\u4f53\u7684\u5173\u7cfb\uff0c\u53ea\u9700\u8981\u8bb0\u4f4f \u53d6\u503c\u7b26<code>*</code> \u7684\u4f18\u5148\u7ea7 \u4f4e\u4e8e \u6210\u5458\u8bbf\u95ee\u7b26<code>.</code> \u7684\u4f18\u5148\u7ea7</p> </li> <li> <p><code>void *malloc(size_t size)</code>\u7533\u8bf7<code>size</code>\u5927\u5c0f\u7684\u5185\u5b58\uff0c\u4ee5\u5b57\u8282\u4e3a\u5355\u4f4d\uff0c\u8fd4\u56de\u4e00\u4e2a\u6307\u5411\u8fd9\u4e2a\u5185\u5b58\u7684\u6307\u9488</p> </li> <li> <p><code>void free(void *ptr)</code>\u91ca\u653e\u6307\u9488<code>ptr</code>\u6240\u6307\u7684\u5185\u5b58</p> </li> <li> <p>\u5bf9\u4e8e\u8fd4\u56de\u6307\u9488\u7684\u51fd\u6570\uff0c\u4e0d\u80fd\u8fd4\u56de\u5728\u51fd\u6570\u5185\u5b9a\u4e49\u7684 \u5c40\u90e8\u53d8\u91cf \u7684\u6307\u9488</p> </li> <li> <p>\u51fd\u6570\u6307\u9488\u7684\u5b9a\u4e49\uff1a<code>\u7c7b\u578b\u540d(*\u53d8\u91cf\u540d)(\u53c2\u6570\u7c7b\u578b\u8868)</code></p> <ul> <li>\u300ceg\u300d<code>int(*fun)(int,int)</code></li> </ul> </li> </ul> <p>\u4e22\u4e00\u4e2axxjj\u7684\u6587\u7ae0\u5728\u8fd9\u91cc\u00a0\u00a0\u70b9\u51fb\u8df3\u8f6c</p> <ul> <li><code>FILE *fp;</code>\u7533\u8bf7\u4e86\u4e00\u4e2a\u6587\u4ef6\u6307\u9488</li> </ul>"},{"location":"cour_note/D1QD_CXiaoCheng/#\u547d\u4ee4\u884c\u53c2\u6570","title":"\u547d\u4ee4\u884c\u53c2\u6570","text":"<ul> <li><code>main()</code>\u53ef\u4ee5\u6709\u4e24\u4e2a\u53c2\u6570\uff1a<ul> <li><code>main(int argc,char *argv[])</code></li> <li><code>argc</code>\u8868\u793a\u547d\u4ee4\u884c\u53c2\u6570\u6570\u91cf</li> <li><code>argv[]</code>\u6307\u5411\u5404\u4e2a\u547d\u4ee4\u884c\u53c2\u6570</li> <li><code>argv[0]</code>\u6307\u5411\u547d\u4ee4</li> <li><code>argv[1,]</code>\u6307\u5411\u53c2\u6570 </li> <li>\u300ceg\u300d\u547d\u4ee4\u884c\u8f93\u5165<code>./code.exe hello world</code></li> <li>\u5728\u7a0b\u5e8f\u4e2d\uff1a</li> <li><code>argc = 3</code></li> <li><code>*argv[] = {\"./code.exe\\0\",\"hello\\0\",\"world\\0\"}</code></li> </ul> </li> </ul>"},{"location":"cour_note/D1QD_CXiaoCheng/#\u6587\u4ef6\u64cd\u4f5c","title":"\u6587\u4ef6\u64cd\u4f5c","text":"<ul> <li><code>FILE *fp;</code>\u7533\u8bf7\u4e00\u4e2a\u6587\u4ef6\u6307\u9488</li> <li><code>fp = fopen(\"\u6587\u4ef6\u540d\",\"\u4f7f\u7528\u65b9\u5f0f\");</code>\u94fe\u63a5\u6307\u9488<code>fp</code>\u5230\u6587\u4ef6\u5e76\u6307\u5b9a\u6a21\u5f0f</li> </ul> \u6587\u672c\u6587\u4ef6 \u4e8c\u8fdb\u5236\u6587\u4ef6 \u4f7f\u7528\u65b9\u5f0f \u542b\u4e49 \u4f7f\u7528\u65b9\u5f0f \u542b\u4e49 \"r\" \u6253\u5f00 &amp; \u53ea\u8bfb \"rb\" \u6253\u5f00 &amp; \u53ea\u8bfb \"w\" \u65b0\u5efa(\u6e05\u7a7a) &amp; \u53ea\u5199 \"wb\" \u65b0\u5efa &amp; \u53ea\u5199 \"a\" \u6253\u5f00 &amp; \u8ffd\u52a0 \"ab\" \u6253\u5f00 &amp; \u8ffd\u52a0 \"r+\" \u6253\u5f00 &amp; \u8bfb\u5199 \"rb+\" \u6253\u5f00 &amp; \u8bfb\u5199 \"w+\" \u65b0\u5efa(\u6e05\u7a7a) &amp; \u8bfb\u5199 \"wb+\" \u65b0\u5efa &amp; \u8bfb\u5199 \"a+\" \u6253\u5f00 &amp; \u8bfb &amp; \u8ffd\u52a0 \"ab+\" \u6253\u5f00 &amp; \u8bfb &amp; \u8ffd\u52a0 \u8bf4\u660e \u4f7f\u7528<code>\"w\"</code>/<code>\"w+\"</code>\u65f6\uff0c\u6587\u4ef6\u5185\u5bb9\u4f1a\u88ab\u8986\u76d6\uff08\u56e0\u4e3a\u6e05\u7a7a\u540e\u518d\u5199\u5165\uff09 \u4f7f\u7528<code>\"a\"</code>/<code>\"a+\"</code>\u65f6\uff0c\u8f93\u5165\u5185\u5bb9\u4f1a\u5199\u5728\u6587\u4ef6\u5185\u5bb9\u540e\u9762 <ul> <li>\u8f93\u5165\u6587\u4ef6\u540d\u65f6\u53ef\u4ee5\u5199\u8def\u5f84\uff0c\u8def\u5f84\u4e2d\u8981\u4f7f\u7528<code>\\\\</code>\u6765\u533a\u5206\u5c42\u7ea7</li> <li><code>fprintf(fp,\"\u683c\u5f0f\u5b57\u7b26\u4e32\",\u53d8\u91cf\u8868);</code>\u5199\u5165\u6570\u636e\u5230<code>fp</code>\u6307\u5411\u7684\u6587\u4ef6\uff0c\u540e\u4e24\u4e2a\u53c2\u6570\u7684\u683c\u5f0f\u548c<code>printf()</code>\u4e00\u6837</li> <li><code>fclose()</code>\u5173\u95ed\u6587\u4ef6\u5e76\u5237\u65b0\u7f13\u5b58\u533a<ul> <li>\u987a\u5229\u6267\u884c\u4e86\u6587\u4ef6\u5173\u95ed\u64cd\u4f5c\u65f6\uff0c<code>fclose()</code>\u51fd\u6570\u7684\u8fd4\u56de\u503c\u662f<code>0</code>\uff0c\u5426\u5219\u8fd4\u56de<code>EOF</code></li> </ul> </li> <li><code>rewind(fp)</code>\u8ba9<code>fp</code>\u8fd4\u56de<code>fp</code>\u6240\u6307\u7684\u6587\u4ef6\u7684\u5f00\u5934\u5730\u5740</li> <li><code>rtell(fp)</code>\u8ba9<code>fp</code>\u8fd4\u56de<code>fp</code>\u7684\u5f53\u524d\u4f4d\u7f6e(<code>long int</code>\u7c7b\u578b\uff0c\u4ece<code>0</code>~<code>len</code>)\uff0c\u6210\u529f\u8fd4\u56de\u5f53\u524d\u503c(\u4e00\u5f00\u59cb\u662f0\uff0c\u6bcf\u5411\u540e\u79fb\u52a8\u4e00\u6b21+1)\uff0c\u5426\u5219\u8fd4\u56de<code>-1L</code></li> <li><code>fseek(FILE *fp,\"\u504f\u79fb\u91cf\",\"\u8d77\u59cb\u4f4d\u7f6e\")</code>\u5c06<code>fp</code>\u4ece<code>\"\u8d77\u59cb\u4f4d\u7f6e\"</code>\u5f00\u59cb\u5411\u540e\u79fb\u52a8<code>\"\u504f\u79fb\u91cf\"</code><ul> <li>\u53ef\u9009\u7684<code>\"\u8d77\u59cb\u4f4d\u7f6e\"</code>\uff1a</li> <li><code>SEEK_SET</code>\u6587\u4ef6\u5f00\u5934</li> <li><code>SEEK_CUR</code>\u5f53\u524d\u4f4d\u7f6e</li> <li><code>SEEK_END</code>\u6587\u4ef6\u672b\u5c3e</li> <li>\u300ceg\u300d\u79fb\u52a8\u6307\u9488<code>fp</code>\u5230\u6587\u4ef6\u672b\u5c3e\uff1a<code>fseek(fp,0L,SEEK_END);</code></li> </ul> </li> <li><code>feof(fp)</code>\u5982\u679c<code>fp</code>\u5230\u8fbe\u4e86<code>EOF</code>\uff0c\u8fd4\u56de\u975e\u96f6\u503c\uff0c\u5426\u5219\u8fd4\u56de<code>0</code></li> <li><code>fflush(fp)</code>\u5237\u65b0<code>fp</code>\u7684\u7f13\u51b2\u533a\uff0c\u6210\u529f\u8fd4\u56de<code>0</code>\uff0c\u5426\u5219\u8fd4\u56de<code>EOF</code></li> <li><code>fgets((char*)str,limt,fp)</code>\u4ece<code>fp</code>\u8bfb\u5165\u4e00\u884c\u7684<code>limit-1</code>\u4e2a\u5b57\u7b26\u5e76\u5b58\u5165<code>str</code>\u4e2d\uff0c\u5e76\u5728\u672b\u5c3e\u52a0<code>\\0</code>\uff0c\u7136\u540e\u8fd4\u56de\u8bfb\u5165\u7684\u5185\u5bb9(\u5982\u679c\u6ca1\u8bfb\u5b8c<code>limit-1</code>\u4e2a\u5b57\u7b26\u5c31\u9047\u5230\u4e86\u884c\u672b\u5c31\u5230\u6b64\u4e3a\u6b62)</li> <li><code>fputc(ch,fp)</code>\u5728<code>fp</code>\u4e2d\u5199\u5165\u5355\u4e2a\u5b57\u7b26<code>ch</code>\uff0c\u6210\u529f\u8fd4\u56de<code>ch</code>\uff0c\u5426\u5219\u8fd4\u56de<code>EOF</code></li> <li> <p><code>fgetc(fp)</code>\u83b7\u53d6\u4e0b\u4e00\u4e2a\u5b57\u7b26(\u5982\u679c\u5230\u8fbe<code>EOF</code>\u5c31\u8bfb\u5165\u4e86<code>-1</code>\uff0c\u53c2\u8003\u8fd9\u91cc)</p> </li> <li> <p>C\u7a0b\u5e8f\u5bf9\u6587\u4ef6\u5f85\u5904\u7406\u91c7\u7528\u5185\u5b58\u7f13\u51b2\u6587\u4ef6\u7cfb\u7edf\u7684\u65b9\u5f0f\u8fdb\u884c</p> </li> <li>\u4f7f\u7528\u7f13\u51b2\u6587\u4ef6\u7cfb\u7edf\u53ef\u4ee5\u5927\u5927\u63d0\u9ad8\u6587\u4ef6\u64cd\u4f5c\u901f\u5ea6</li> <li>\u6587\u4ef6\u4fdd\u5b58\u5728\u78c1\u76d8\u4e0a\uff0c\u78c1\u76d8\u6570\u636e\u7684\u7ec4\u7ec7\u65b9\u5f0f\u6309\u6247\u533a\u8fdb\u884c\uff0c\u89c4\u5b9a \u6bcf\u4e2a\u6247\u533a\u5927\u5c0f\u4e3a512B</li> <li>\u4e00\u822c\u5fae\u578b\u8ba1\u7b97\u673a\u4e2d\u7684C\u8bed\u8a00\u7cfb\u7edf\u4e5f\u5c06\u7f13\u51b2\u533a\u5927\u5c0f\u5b9a\u4e3a512B</li> <li>\u8fdb\u884c\u6570\u636e\u5199\u5165\u5de5\u4f5c\u65f6:<ul> <li>\u628a\u6570\u636e\u5199\u5165\u6587\u4ef6\u7f13\u51b2\u533a</li> <li>\u5199\u6ee1512B\u4ee5\u540e\uff0cOS\u81ea\u52a8\u628a\u6570\u636e\u5199\u5165\u78c1\u76d8\u7684\u4e00\u4e2a\u6247\u533a\uff0c\u7136\u540e\u6e05\u7a7a\u6587\u4ef6\u7f13\u51b2\u533a</li> <li>\u91cd\u590d\u4e0a\u8ff0\u884c\u4e3a</li> </ul> </li> <li>\u6587\u4ef6\u6253\u5f00\u7684\u5b9e\u8d28\u662f\u628a\u78c1\u76d8\u6587\u4ef6\u548c\u6587\u4ef6\u7f13\u51b2\u533a\u5bf9\u5e94\u8d77\u6765\uff0c\u5177\u4f53\u6d41\u7a0b\u5982\u4e0b;</li> <li>\u5728\u78c1\u76d8\u4e2d\u627e\u5230\u6307\u5b9a\u6587\u4ef6</li> <li>\u5728\u5185\u5b58\u4e2d\u5206\u914d\u4fdd\u5b58\u4e00\u4e2aFILE\u7c7b\u578b\u7ed3\u6784\u7684\u5355\u5143\uff0816B\uff09</li> <li>\u5728\u5185\u5b58\u4e2d\u5206\u914d\u6587\u4ef6\u7f13\u51b2\u533a\u5355\u5143\uff08512B\uff09</li> <li> <p>\u8fd4\u56deFILE\u7684\u7ed3\u6784\u5730\u5740</p> </li> <li> <p><code>FILE</code>\u672c\u8d28\u4e0a\u662f\u4e00\u4e2a\u7ed3\u6784\u4f53\u7c7b\u578b\uff0c\u5b9a\u4e49\u5982\u4e0b\uff1a <pre><code>typedef struct{\nshort            level;       /*\u7f13\u51b2\u533a\u4f7f\u7528\u91cf*/\nunsigned         flags;       /*\u6587\u4ef6\u72b6\u6001\u6807\u5fd7*/\nchar             fd;          /*\u6587\u4ef6\u63cf\u8ff0\u7b26*/\nshort            bsize;       /*\u7f13\u51b2\u533a\u5927\u5c0f*/\nunsigned char    *buffer;     /*\u6587\u4ef6\u7f13\u51b2\u533a\u9996\u5730\u5740*/\nunsigned char    *curp;       /*\u6307\u5411\u6587\u4ef6\u7f13\u51b2\u533a\u7684\u5de5\u4f5c\u6307\u9488*/\nunsigned char    hold;        /*\u5176\u4ed6\u4fe1\u606f*/\nunsigned         istemp;\nshort            token;\n} FILE;\n</code></pre></p> </li> </ul>"},{"location":"cour_note/D1QD_CXiaoCheng/#\u5176\u4ed6","title":"\u5176\u4ed6","text":"<p>\u8d34\u4e00\u4e9b\u5176\u4ed6\u5b66\u957f\u7684\u6587\u7ae0\uff1a</p> <ul> <li>https://blog.zhanghai.me/c-exam-notes/</li> <li>https://blog.yzsun.me/c-traps-and-pitfalls/</li> </ul>"},{"location":"cour_note/D1SJ_Intro2CS/","title":"[\u5927\u4e00\u6691\u5047] \u8ba1\u7b97\u673a\u7cfb\u7edf\u6982\u8bba | Introduction to Computing Systems","text":"<p> \u7ea6 16 \u4e2a\u5b57 </p> <ul> <li>https://www.yuque.com/isshikixiu/codes/ics</li> </ul>"},{"location":"cour_note/D1SJ_StanfordCS231n/","title":"[\u5927\u4e00\u6691\u5047] Deep Learning for Computer Vision | CS231N","text":"<p> \u7ea6 3447 \u4e2a\u5b57  17 \u884c\u4ee3\u7801  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 12 \u5206\u949f</p> \u8bfe\u7a0b\u4ecb\u7ecd <ul> <li>\u56e0\u4e3a\u6211\u53ea\u80fd\u627e\u5230 17 \u5e74\u7684\u89c6\u9891\uff0c\u6240\u4ee5\u662f\u8ddf\u7740 17 \u5e74\u7684\u7248\u672c\u5b66\u3002</li> </ul> <p>Course Website: \ud83d\udd17</p> <p>Course Video: \ud83d\udd17</p> <p>Course Description</p> <ul> <li>Computer Vision has become ubiquitous in our society, with applications in search, image understanding, apps, mapping, medicine, drones, and self-driving cars. Core to many of these applications are visual recognition tasks such as image classification, localization and detection. Recent developments in neural network (aka \u201cdeep learning\u201d) approaches have greatly advanced the performance of these state-of-the-art visual recognition systems. This course is a deep dive into the details of deep learning architectures with a focus on learning end-to-end models for these tasks, particularly image classification. During the 10-week course, students will learn to implement and train their own neural networks and gain a detailed understanding of cutting-edge research in computer vision. Additionally, the final assignment will give them the opportunity to train and apply multi-million parameter networks on real-world vision problems of their choice. Through multiple hands-on assignments and the final course project, students will acquire the toolset for setting up deep learning tasks and practical engineering tricks for training and fine-tuning deep neural networks.</li> </ul> <p>Assignments</p> <ul> <li>Assignment 1: \ud83d\udd17</li> <li>Assignment 2: \ud83d\udd17</li> <li>Assignment 3: \ud83d\udd17</li> </ul> \u53c2\u8003\u8d44\u6599 <ul> <li>\u5b66\u957f\u7b14\u8bb0\uff1a\ud83d\udd17</li> </ul>"},{"location":"cour_note/D1SJ_StanfordCS231n/#lecture-1-introduction-to-convolutional-neural-networks-for-visual-recognition","title":"Lecture 1: Introduction to Convolutional Neural Networks for Visual Recognition","text":"<ul> <li>Video: \ud83d\udd17 </li> <li>Slides: \ud83d\udd17 </li> </ul> <ul> <li>\u4e00\u4e9b\u65e9\u671f\u7684\u5173\u4e8e CV \u7684\u601d\u8003</li> </ul> <ul> <li>\u65e9\u671f\u5bf9\u5982\u4f55\u8868\u793a\u7269\u4f53\uff0c\u8d85\u8d8a\u300cBlock World\u300d\u7684\u8868\u793a\u65b9\u6cd5</li> </ul> <p> \u5176\u6838\u5fc3\u601d\u60f3\u662f\u5c06\u590d\u6742\u7684\u89c6\u89c9\u4fe1\u606f\u7b80\u5316\u4e3a\u7b80\u5355\u5bf9\u8c61\u7684\u7ec4\u5408\u3002</p> <p>\u4eba\u4eec\u610f\u8bc6\u5230\u76f4\u63a5\u8bc6\u522b\u7269\u4f53\u6bd4\u8f83\u56f0\u96be\uff0c\u4e8e\u662f\u60f3\u5230\u4e86 \u5206\u5272\u56fe\u5f62(image segmentation) \u2014\u2014\u5373\u5148\u505a\u5c06\u50cf\u7d20\u5206\u7ec4\uff1a</p> <p></p> <ul> <li>\u542f\u53d1\uff1a\u89c6\u89c9\u8bc6\u522b\u7684\u91cd\u70b9\u53ef\u4ee5\u4ece\u8bc6\u522b\u5bf9\u8c61\u7684\u4e00\u4e9b\u5177\u6709\u8bc6\u522b\u529b\u548c\u4e0d\u6613\u53d8\u5316\u7684\u90e8\u5206\u5f00\u59cb</li> </ul> <p></p> <p>\u6709\u7aef\u8054\u60f3 FDS \u7684 Voting Tree</p> <ul> <li>\u603b\u7684\u800c\u8a00 \u5bf9\u8c61\u8bc6\u522b \u662f CV \u9886\u57df\u7684\u4e00\u4e2a\u91cd\u8981\u8bdd\u9898</li> <li>\u8be5\u8bfe\u7a0b\u91cd\u70b9\u4e3a \u5377\u79ef\u795e\u7ecf\u7f51\u7edc(Convolutional Neural Network / CNN)</li> <li>\u5177\u4f53\u7740\u773c\u70b9\u4e3a \u56fe\u50cf\u5206\u7c7b\u95ee\u9898(image classification)</li> <li>\u4e5f\u5c06\u6d89\u53ca \u5bf9\u8c61\u68c0\u6d4b(object detection)\u3001\u56fe\u50cf\u5b57\u5e55(image captioning) \u7b49\u95ee\u9898</li> </ul>"},{"location":"cour_note/D1SJ_StanfordCS231n/#lecture-2-image-classification-pipeline","title":"Lecture 2: Image Classification Pipeline","text":"<ul> <li>Video: \ud83d\udd17 </li> <li>Slides: \ud83d\udd17 </li> <li>CIFAR-10 &amp; CIFAR-100: \ud83d\udd17 </li> <li>\u524d\u7f6e\uff1aPython Numpy Tutorial: \ud83d\udd17</li> </ul> <ul> <li>\u8bed\u4e49\u9e3f\u6c9f(semantic gap)</li> </ul>"},{"location":"cour_note/D1SJ_StanfordCS231n/#data-driven-approach","title":"Data-Driven Approach","text":"<ol> <li>Collect a dataset of images and labels;</li> <li>Use Machine Learning to train a classifier;</li> <li>Evaluate the classifier on new images;</li> <li>\u5f97\u5230\u7684\u6a21\u578b\u6709\u4e24\u4e2a\u6838\u5fc3 API\uff1a\u4e00\u4e2a\u7528\u4e8e \u8bad\u7ec3(train)\uff0c\u4e00\u4e2a\u7528\u4e8e \u9884\u6d4b(predict)\u3002</li> <li>\u4e00\u822c\u60c5\u51b5\u4e0b\uff0c\u6211\u4eec\u4e0d\u4ecb\u610f\u8bad\u7ec3\u65f6\u95f4\u957f\uff0c\u4f46\u5e0c\u671b\u9884\u6d4b\u6548\u7387\u9ad8\u3002</li> </ol> <p>CIFAR-10 &amp; CIFAR-100: \ud83d\udd17 </p> <p>Distance Metric to compare images</p> <p></p> <p>\u6211\u4eec\u5c06\u5206\u7c7b\u95ee\u9898\u770b\u4f5c\u5728\u201c\u7a7a\u95f4\u201d\u4e2d\u7684\u67d3\u8272\u95ee\u9898\uff0c\u70b9\u8868\u793a\u8bad\u7ec3\u6570\u636e\uff0c\u5176\u989c\u8272\u8868\u793a\u5176\u88ab\u6807\u8bb0\u7684\u5206\u7c7b\uff1b\u800c\u753b\u677f\u4e2d\u5176\u4ed6\u90e8\u5206\u7684\u989c\u8272\u5219\u8868\u793a\u5f53\u70b9\u843d\u5728\u8fd9\u4e2a\u4f4d\u7f6e\u65f6\u5019\u4f1a\u88ab\u5206\u7c7b\u4e3a\u54ea\u4e00\u79cd\u3002</p> <p></p> <p>\u4e2d\u95f4\u201c\u9ec4\u8272\u90e8\u5206\u201d\u8fd9\u79cd\u5b64\u7acb\u7684\u5c0f\u5c9b\u5728\u5b9e\u9645\u5bf9\u6570\u636e\u8fdb\u884c\u9884\u6d4b\u5de5\u4f5c\u65f6\u53ef\u80fd\u4e0d\u662f\u5f88\u597d\u3002</p> <p></p> <p>\u8fd9\u4e9b\u90e8\u5206\u53ef\u80fd\u6709\u566a\u58f0\u6216\u662f\u865a\u5047\u7684\u3002             </p> L1 (Manhattan) distance:  (stupid in most cases)L2 (Euclidean ) distance:  (better by comparison) <ul> <li>\\(d_1(I_1,I_2)=\\sum_{p}|I_1^{p}-I_2^{p}|\\)</li> </ul> <p> </p> <ul> <li>\u5982\u679c\u56fe\u50cf\u65cb\u8f6c\uff0c\u9884\u6d4b\u7ed3\u679c\u4f1a\u53d1\u751f\u6539\u53d8\u3002</li> </ul> <ul> <li>\\(d_2(I_1,I_2)=\\sum_{p}\\sqrt{(I_1^p-I_2^p)^2}\\)</li> </ul> <p> </p> <p>K-Nearest Neighbors: \ud83d\udd17</p> <p>Interactive Demo: \ud83d\udd17</p> <p>Instead of copying label from nearest neighbor, take majority vote from K closest points.</p> <p></p> <p>\u4f8b\u5982\uff0cK=1 \u65f6\u4e2d\u95f4\u7684\u9ec4\u8272\u533a\u57df\u7531\u4e8e\u9644\u8fd1\u90fd\u662f\u7eff\u70b9\uff0c\u6240\u4ee5\u5728 K \u589e\u957f\u7684\u65f6\u5019\u7eff\u8272\u5728\u8ba1\u7b97\u4e2d\u7684\u6743\u91cd\u53d8\u5927\uff0c\u6240\u4ee5\u6700\u540e\u88ab\u6807\u8bb0\u4e3a\u7eff\u8272\u3002s</p> <ul> <li>\u5f53\u7136\uff0c\u8fd9\u79cd\u901a\u8fc7\u6bd4\u8f83\u201c\u8ddd\u79bb\u201d\u7684\u5206\u7c7b\u65b9\u6848\u5e76\u4e0d\u4ec5\u9650\u4e8e\u56fe\u7247\u7b49\uff0c\u5bf9\u4e8e\u4efb\u4f55\u9700\u8981\u5206\u7c7b\u7684\u6570\u636e\uff0c\u4f8b\u5982\u6587\u672c\uff0c\u53ea\u8981\u80fd\u5b9a\u4e49\u80fd\u591f\u91cf\u5316\u7684\u201c\u8ddd\u79bb\u201d\u4ee5\u53ca\u4e00\u7cfb\u5217\u76f8\u5e94\u7684\u89c4\u5219\uff0c\u5c31\u80fd\u4f7f\u7528\u8fd9\u79cd\u65b9\u6cd5\u6765\u8fdb\u884c\u5206\u7c7b\u3002</li> <li>\u7136\u800c\uff0cK-\u4e34\u8fd1\u7b97\u6cd5 \u5728\u56fe\u50cf\u5206\u7c7b\u4e0a\u51e0\u4e4e\u4e0d\u600e\u4e48\u4f7f\u7528\uff0c\u4e3b\u8981\u662f\u56e0\u4e3a\u5b83\u5b9e\u9645\u4f7f\u7528\u8d77\u6765\uff0c\u9884\u6d4b\u6548\u7387\u8f83\u4f4e\uff1b\u4e14\u201c\u8ddd\u79bb\u5ea6\u91cf\u201d\u5e76\u4e0d\u975e\u5e38\u9002\u5408\u56fe\u50cf\u5904\u7406\uff08\u5b83\u65e0\u6cd5\u5b8c\u6574\u63cf\u8ff0\u56fe\u50cf\u4e0a\u7684\u8ddd\u79bb\u4fe1\u606f\u6216\u56fe\u50cf\u4e4b\u95f4\u7684\u5dee\u5f02\uff09\uff1b\u6b64\u5916\u5b83\u8fd8\u6709\u4e00\u4e2a\u6bd4\u8f83\u4e25\u91cd\u7684\u95ee\u9898\uff1a\u7ef4\u6570\u707e\u96be(curse of dimensionality) \ud83d\udd17 \uff08\u56e0\u4e3a\u53ea\u6709\u8bad\u7ec3\u6837\u672c\u8db3\u591f\u5bc6\u96c6\uff0cK-\u4e34\u8fd1\u7b97\u6cd5\u624d\u80fd\u6b63\u5e38\u8fd0\u884c\uff09\u3002</li> </ul>"},{"location":"cour_note/D1SJ_StanfordCS231n/#hyperparameters","title":"Hyperparameters","text":"<ul> <li> <p>Choices about the algorithm that we set rather than learn.</p> </li> <li> <p>eg: best k to use; best distance to use (L1/L2);</p> </li> </ul> <p>Setting Hyperparameters (\u8c03\u53c2)</p> <p></p> <p>\u5373\uff0c\u6211\u4eec\u9700\u8981\u786e\u4fdd\u8db3\u591f\u7684\u8bad\u7ec3\u96c6\uff0c\u5e76\u901a\u8fc7\u9a8c\u8bc1\u96c6\u8fdb\u884c\u8c03\u53c2\uff0c\u5e76\u5728\u4e00\u5207\u90fd\u5b8c\u6210\u4ee5\u540e\u624d\u4f7f\u7528\u6d4b\u8bd5\u96c6\u6765\u9a8c\u8bc1\u6a21\u578b\u7684\u51c6\u786e\u5ea6\u3002</p> <p></p>"},{"location":"cour_note/D1SJ_StanfordCS231n/#linear-classification","title":"Linear Classification","text":"<p>Parametric Approach</p> \\[ f(x,W)=Wx+b \\] <p></p> <p>\u8fd9\u91cc\u7684 10 numbers \u8868\u793a\u7684\u662f CIFAR-10 \u4e2d\u7684 10 \u4e2a\u7c7b\u522b\u5bf9\u5e94\u7684\u5f97\u5206\u3002</p> <ul> <li>\u5373\uff0c\u6211\u4eec\u6784\u9020\u4e00\u4e2a\u51fd\u6570\uff0c\u8f93\u5165\u5305\u542b\u56fe\u50cf\u6570\u636e \\(x\\) \u548c\u6743\u91cd\u53c2\u6570 \\(W\\)\uff0c\u6ee1\u8db3\u5176\u8ba1\u7b97\u7ed3\u679c\u4e3a\u5404\u4e2a\u7c7b\u522b\u7684\u9884\u6d4b\u5f97\u5206</li> <li>\u6700\u7ec8\u5f97\u5230\u4e00\u4e2a\u6a21\u7248\uff0c\u5b83\u5c06\u5c1d\u8bd5\u6027\u5730\u9002\u5e94\u8be5\u7c7b\u91cc\u5c3d\u53ef\u80fd\u591a\u7684\u6837\u672c</li> </ul> <p></p> <p></p> <p>\u5982\u679c\u5c06\u9ad8\u7ef4\u7a7a\u95f4\u7684\u60c5\u51b5\u6620\u5c04\u5230\u5e73\u9762\u7684\u51e0\u4f55\u89d2\u5ea6\u6765\u7406\u89e3\uff0c\u5c31\u597d\u50cf\u5728\u5212\u4e00\u9053\u9053\u76f4\u7ebf\u6765\u8fdb\u884c\u5212\u5206\u3002</p> <ul> <li>\u4ece\u8fd9\u79cd\u89d2\u5ea6\u6765\u7406\u89e3\u5c31\u5f88\u5bb9\u6613\u53d1\u73b0\uff0c\u5355\u4e00\u7684\u7ebf\u6027\u5206\u7c7b\u5177\u6709\u5c40\u9650\u6027\uff0c\u4f8b\u5982\u5bf9\u4e8e\u591a\u6a21\u6001\u7684\u6570\u636e\uff0c\u4f7f\u7528\u5355\u4e00\u7684\u7ebf\u6027\u5206\u7c7b\u53ef\u80fd\u4f1a\u6bd4\u8f83\u5403\u529b\u3002</li> </ul>"},{"location":"cour_note/D1SJ_StanfordCS231n/#lecture-3-loss-functions-and-optimization","title":"Lecture 3: Loss Functions and Optimization","text":"<ul> <li>Video: \ud83d\udd17 </li> <li>Slides: \ud83d\udd17 </li> </ul> <ul> <li>Linear classifier is an example of parametric classifier.</li> <li> <p>\u6211\u4eec\u53ef\u4ee5\u8fd9\u6837\u7406\u89e3 Linear Classifation \u4e2d\u7684 \\(W\\)\uff1a\u77e9\u9635\u4e2d\u7684\u6bcf\u4e00\u4e2a\u53c2\u6570\u8868\u793a\u4e86\u6bcf\u4e00\u4e2a\u50cf\u7d20\u70b9(\u5355\u4e2a\u989c\u8272\u901a\u9053)\u5bf9\u4e8e\u8bc6\u522b\u67d0\u4e2a\u7c7b\u7684\u8d21\u732e\u6743\u91cd\u3002</p> </li> <li> <p>A loss function that quantifies our unhappiness with the scores across the training data, tells how good our current classifier is. </p> </li> <li>Given a dataset of examples \\(\\{(x_1,y_i)\\}_{i=1}^N\\), where \\(x_i\\) is image and \\(y_i\\) is label. And loss over the dataset is a sum of loss over examples: \\(L = \\frac{1}{N}\\sum L_i(f(xi,W),y_i)\\).</li> <li>Loss function \u662f\u7528\u6765\u5ea6\u91cf \\(W\\) \u7684\u5408\u9002\u7a0b\u5ea6\u7684\uff0c\u6211\u4eec\u901a\u8fc7\u5bfb\u627e\u5728 \\(W\\) \u7a7a\u95f4\u4e2d\u635f\u5931\u51fd\u6570\u53d6\u6700\u503c\u65f6\u7684 \\(W\\) \u6765\u627e\u5230\u6211\u4eec\u8ba4\u4e3a\u6700\u5408\u9002\u7684 \\(W\\)\u3002</li> </ul>"},{"location":"cour_note/D1SJ_StanfordCS231n/#multi-class-svm-loss","title":"Multi-class SVM Loss","text":"<p>\u5982\u4f55\u7406\u89e3\u90a3\u5f20\u56fe\uff1f(hinge loss?)</p> <p>Let \\(s = f(x_i,W)\\), then SVM loss is:</p> \\[ L_i = \\sum_{j \\not = y_i } \\left\\{     \\begin{align*}         &amp;0              &amp;\\text{if } s_{y_i} \\geq s_j + 1\\\\         &amp;s_j-s_{y_i}+1  &amp;\\text{otherwise}     \\end{align*} \\right. = \\sum_{j \\not = y_i } \\text{max}(0,s_j-s_{y_i}+1) \\] <ul> <li>\u4e5f\u5c31\u662f\u8bf4\uff0c\u5bf9\u4e8e\u67d0\u4e00\u4e2a\u6837\u672c\uff0c\u5b83\u5b9e\u9645\u7c7b\u522b\u5bf9\u5e94\u7684\u5f97\u5206\u5982\u679c\u8fdc\u5927\u4e8e\uff08\u6211\u4eec\u9700\u8981\u4e00\u4e2a\u8fb9\u754c \uff0c\u5c31\u662f\u4e0a\u56fe\u4e2d\u7684\\(+1\\)\uff09\u67d0\u4e2a\u5176\u4ed6\u7c7b\u522b\u7684\u5f97\u5206\uff0c\u90a3\u4e48\u8be5\u201c\u5176\u4ed6\u7c7b\u522b\u201d\u5bf9\u635f\u5931\u51fd\u6570\u7684\u8d21\u732e\u5373\u4e3a\\(0\\)\uff1b\u53cd\u4e4b\uff0c\u5982\u679c\u5e76\u6ca1\u6709\u8fdc\u5927\u4e8e\u5176\u4ed6\u67d0\u4e2a\u7c7b\u522b\u7684\u5f97\u5206\uff0c\u5219\u9700\u8981\u5c06\u8fd9\u4e2a\u504f\u5dee\u4f5c\u4e3a\u5bf9\u635f\u5931\u51fd\u6570\u7684\u8d21\u732e\u3002</li> </ul> <p> </p> <pre><code>def L_i_Vectorized(x, y, W):\n    scores = W.dot(x)\n    margins = np.maximum(0, scores - scores[y] + 1)\n    margins[y] = 0\n    loss_i = np.sum(margins)\n    return loss_i\n</code></pre> <ul> <li>Overview</li> </ul> \\[ f(x,W) = Wx\\\\ L = \\frac{1}{N}\\sum_{i=1}^{n}\\sum_{j\\not = y_i}\\text{max}(0,f(x;W)_j-f(x_i;W)_{y_i}+1) \\] <p></p> <ul> <li>However, for that we only calculate a loss in terms of the data, some strange things like overfitting will happen.</li> </ul> <p></p> <ul> <li>\u84dd\u70b9\u4e3a\u6a21\u578b\u8bad\u7ec3\u6570\u636e\uff0c\u7eff\u8272\u7684\u4e3a\u9a8c\u8bc1\u6216\u8005\u5b9e\u9645\u6570\u636e\u7b49\u3002</li> <li>\u84dd\u8272\u7684\u4e3a\u8fc7\u62df\u5408\u540e\u6a21\u578b\u8bad\u7ec3\u51fa\u6765\u7684\u9884\u6d4b\u8d8b\u52bf\uff0c\u4ed6\u4eec\u5b8c\u5168\u7b26\u5408\u8bad\u7ec3\u6a21\u578b\u7684\u6570\u636e\uff0c\u4f46\u662f\u53ef\u4ee5\u53d1\u73b0\uff0c\u7eff\u8272\u7684\u7ebf\u6761\u624d\u662f\u5b9e\u9645\u7684\u6211\u4eec\u5e0c\u671b\u5f97\u5230\u7684\u8d8b\u52bf\u3002</li> <li>\u8fd9\u79cd\u9884\u6d4b\u7ed3\u679c\u8fc7\u5ea6\u62df\u5408\u4e86\u8bad\u7ec3\u6570\u636e\u7684\u884c\u4e3a\u53ca\u4e3a\u8fc7\u62df\u5408\u3002</li> </ul> <p>To solve it, we use regularization.</p> <p></p> <p>The regularization term.</p> <p></p> <p>Occam's Razor</p> <ul> <li>The regularization term encourages the model to somehow pick a simpler \\(W\\) depending on the dask and the model.</li> </ul> <p>So your standard loss function usually has two terms, a data loss and a regularization loss, and there's a hyperparameter(mentioned already in L2) here, lambda, which trades off between the two.</p>"},{"location":"cour_note/D1SJ_StanfordCS231n/#regularization","title":"Regularization","text":"<p>There are many regularizations used in practice, and the most common one is probably L2 regularization or weight decay. </p> <p>In common use:</p> <ul> <li>L2 regularization: \\(R(W) = \\sum_{k}\\sum_lW_{k,l}^2\\);</li> <li>L1 regularization: \\(R(W) = \\sum_k\\sum_l |W_{k,l}|\\);</li> <li>Elastic net (L1+L2): \\(R(W) = \\sum_k\\sum_l (\\beta W_{k,l}^2+|W_{k,l}|)\\);</li> <li>Max norm regularization</li> <li>Dropout</li> <li>Fancier: Batch normalization, stochastic depth...</li> </ul> <p>The whole idea of regularization is just any thing that you do to your model, that sort of penalizes somehow the complexity of the model, rather than explicitly trying to fit the training data. Each regularization has its own feature, you should choose them depends on the problems.</p>"},{"location":"cour_note/D1SJ_StanfordCS231n/#softmax-classifier-multinomial-logistic-regression","title":"Softmax Classifier (Multinomial Logistic Regression)","text":"<ul> <li>It normalizes the scores to a probability distribution.</li> <li>Then we just want the probablity of the true class is high and as close to one.</li> <li>scores = unnormalized log probabilities of the classes</li> <li>\\(P(Y=k|X=x_i)=\\frac{e^{s_k}}{\\sum_j e^{s_j}}\\;,\\;\\;where\\;s=f(x_i;W)\\);</li> <li>That is \\(L_i=-\\log P(Y=y_i|X=x_i)=-\\log(\\frac{e^{s_k}}{\\sum_j e^{s_j}})\\);</li> </ul> <p>eg for Softmax Classifier.</p> <p></p> <p>Compare the two.</p> <ul> <li>\u5728\u5b9e\u9645\u4f7f\u7528\u4e2d\uff0cSVM \u5728\u4fdd\u8bc1\u771f\u5b9e\u6807\u7b7e\u5bf9\u5e94\u7684\u5f97\u5206\u9ad8\u4e8e\u5176\u4ed6\u5f97\u5206\u4e00\u5b9a\u91cf\u540e\u5c31\u63a5\u53d7\u4e86\uff0c\u5373\u5b58\u5728\u4e00\u4e2a\u660e\u786e\u7684\u7a81\u53d8\u6807\u51c6\uff1b\u800c\u5bf9\u4e8e Softmax \u6765\u8bf4\uff0c\u5b83\u4f1a\u5728\u8fd9\u4e2a\u8fc7\u7a0b\u4e2d\u4e0d\u65ad\u5c06\u6b63\u786e\u6807\u7b7e\u5bf9\u5e94\u7684\u6982\u7387\u5411\\(1\\)\u903c\u8fd1\uff0c\u4e0d\u65ad\u4f18\u5316\u81ea\u5df1\u3002</li> </ul> <p></p>"},{"location":"cour_note/D1SJ_StanfordCS231n/#optimization","title":"Optimization","text":"<ul> <li>Strategy #1: A first _very bad _idea solution: Random search</li> <li>Strategy #2: Gradient Descent / Follow the slope(gradient\\(\\nabla\\))</li> <li>Always use analytic gradient, but check implementation with numerical gradient. This is called a gradient check.</li> </ul> <p><pre><code>## Vanilla Gradient Descent\n\nwhile True:\n    weights_grad = evaluate_gradient(loss_fun, data, weight)\n    weights += - step_size * weights_grad ## perform parameter update\n</code></pre> <code>step_size</code> is a hyperparameter here, it's also called a learning rate sometimes. Stochastic Gradient Descent (SGD) - The basic Gradient Descent will be messy when \\(N\\) is large! - So we need to start with approximate sum using a minibatch of examples.    - 32 / 64 / 128 common</p> <pre><code>## Vanilla Gradient Descent\n\nwhile True:\n    data_batch = sample_training_data(data, 256) ## sample 256 examples\n    weights_grad = evaluate_gradient(loss_fun, data_batch, weight)\n    weights += - step_size * weights_grad ## perform parameter update\n</code></pre> <ul> <li>Online Demo: \ud83d\udd17</li> </ul>"},{"location":"cour_note/D1SJ_StanfordCS231n/#aside-image-features","title":"Aside: Image Features","text":""},{"location":"cour_note/D1SJ_StanfordCS231n/#lecture-4-introduction-to-neural-networks","title":"Lecture 4: Introduction to Neural Networks","text":"<ul> <li>Video: \ud83d\udd17 </li> <li>Slides: \ud83d\udd17 </li> </ul>"},{"location":"cour_note/D1SJ_StanfordCS231n/#computational-graphs","title":"Computational graphs","text":"<p>eg. for the linear classifier.</p>"},{"location":"cour_note/D1SJ_StanfordCS231n/#backpropagation","title":"Backpropagation","text":"<p>\u901a\u8fc7\u5c06\u7b97\u5f0f\u5199\u6210\u8fd9\u79cd\u201c\u8282\u70b9\u56fe\u201d\u7684\u5f62\u5f0f\uff0c\u53ef\u4ee5\u8fdb\u4e00\u6b65\u8ba9\u6211\u4eec\u770b\u6e05\u8ba1\u7b97\u8fc7\u7a0b\u5e76\u65b9\u4fbf\u6211\u4eec\u8ba1\u7b97\u68af\u5ea6\u3002\u5177\u4f53\u6765\u8bf4\uff0c\u4f8b\u5982 \\(f(x,y,z)=(x+y)z\\)\uff0c\u5c06\u5176\u5199\u6210\u8282\u70b9\u56fe\u5982\u4e0b\uff0c\u5e76\u8ba1\u7b97\u6240\u9700\u8981\u7684\u53c2\u6570\u3002</p> <p> </p> <p>\u7136\u540e\u6211\u4eec\u4ece\u56fe\u7684\u672b\u7aef\u5f00\u59cb\u8ba1\u7b97\uff0c\u5f97\u5230\u8fd9\u4e9b\u8282\u70b9\u6570\u636e\uff1a</p> <p>\\(\\left\\{ \\begin{aligned} &amp;\\frac{\\partial{f}}{\\partial{f}}=1,\\\\ &amp;\\frac{\\partial{f}}{\\partial{z}}=q=3,\\\\ &amp;\\frac{\\partial{f}}{\\partial{q}}=z=-4,\\\\ &amp;\\frac{\\partial{f}}{\\partial{x}}=\\frac{\\partial{f}}{\\partial{q}}\\frac{\\partial{q}}{\\partial{x}}=-4,\\\\ &amp;\\frac{\\partial{f}}{\\partial{y}}=\\frac{\\partial{f}}{\\partial{q}}\\frac{\\partial{q}}{\\partial{y}}=-4 \\end{aligned} \\right.\\)</p> <p></p> <p></p> <p>backprop (red lines)</p> <p>\u53ef\u4ee5\u53d1\u73b0\uff0c\u6211\u4eec\u5728\u8ba1\u7b97\u8fc7\u7a0b\u4e2d\u53ea\u9700\u8981\u5c06\u201c\u76f8\u90bb\u201d\u68af\u5ea6\u4e58\u4ee5\"local gradient\"\u5373\u53ef\u8ba1\u7b97\u51fa\u6240\u9700\u8981\u7684\u65b0\u7684\"local gradient\"\u3002\u800c\u53ea\u9700\u8981\u518d\u6cbf\u7740\u8def\u5f84\u518d\u5c06\u6240\u6709\u7684\"local gradient\"\u7d2f\u4e58\u8d77\u6765\uff0c\u5c31\u80fd\u5f97\u5230\u6bcf\u4e00\u4e2a\u53d8\u91cf\u5173\u4e8e\u8868\u8fbe\u5f0f\u7684\u68af\u5ea6\u3002</p> <p></p> <p>\u7279\u522b\u7684\uff0c\u7531\u4e8e\u8282\u70b9\u662f\u6211\u4eec\u8ba4\u4e3a\u5b9a\u4e49\u7684\uff0c\u800c\u4e14\u8be5\u65b9\u6cd5\u6240\u4f9d\u8d56\u201c\u94fe\u5f0f\u6cd5\u5219\u201d\u4e5f\u5141\u8bb8\u51fd\u6570\u7684\u81ea\u7531\u7ec4\u5408\uff0c\u6240\u4ee5\u6211\u4eec\u53ef\u4ee5\u4eba\u4e3a\u201c\u5408\u5e76/\u5206\u5272\u201d\u4e00\u4e9b\u8282\u70b9\uff0c\u4f8b\u5982\u5728\u4e0a\u9762\u90a3\u4e2a\u4f8b\u5b50\u4e2d\uff0c\u6211\u4eec\u53ef\u4ee5\u5c06\u6700\u540e\u56db\u4e2a\u8282\u70b9\u5408\u5e76\u4e3a\u4e00\u4e2a\"sigmoid function\"(i.e. \\(\\frac{1}{1+e^{-x}}\\))\u3002</p> <p></p>"},{"location":"cour_note/D1SJ_StanfordCS231n/#patterns-in-backward-flow","title":"Patterns in backward flow","text":"<p>\u53e6\u5916\u4e00\u79cd\u7406\u89e3\u7b97\u7b26\u5728\u8ba1\u7b97\u56fe\u4e2d\u7684\u4f5c\u7528\u7684\u601d\u8def\u3002</p> <p>\u53ef\u4ee5\u53d1\u73b0\uff0c<code>max()</code> \u8fd0\u7b97\u5728\u68af\u5ea6\u4f20\u9012\u8fc7\u7a0b\u4e2d\u53ea\u8d77\u5230\u8def\u7531\u5668\u7684\u4f5c\u7528\uff0c\u4e5f\u5c31\u662f\u8bf4\u5c06\u5176\u4f20\u9012\u5230\u8f83\u5927\u7684\u90a3\u4e2a\u53d8\u91cf\u90a3\u4e00\u4fa7\uff0c\u4f46\u4e0d\u6539\u53d8\u68af\u5ea6\u7684\u503c\uff1b\u800c\u5bf9\u4e8e\u8f83\u5c0f\u7684\u90a3\u4e2a\u53d8\u91cf\uff0c\u68af\u5ea6\u4f20\u9012\u88ab\u963b\u65ad\uff0c\u76ee\u6807\u53d8\u91cf\u7684\u68af\u5ea6\u4e3a \\(0\\)\u3002</p> <p>\u5c06\u8fd9\u4e2a\u6d41\u7a0b\u8fc1\u79fb\u5230\u795e\u7ecf\u7f51\u7edc\u4e0a\uff0c\u6211\u4eec\u53ea\u9700\u8981\u5c06\u8fd9\u4e9b\u6570\u5b57\u53d8\u4e3a Jacobian matrix \u5373\u53ef\u3002</p> <p></p> <ul> <li>Always check: The gradient with respect to a variable should have the same shape as the variable.</li> <li>Because each element of your gradient is quantifying how much that element is contributing to your final output.</li> </ul> <p>\u5728\u5177\u4f53\u5b9e\u73b0\u4e2d\uff0c\u6211\u4eec\u4e00\u822c\u4f1a\u5b9e\u73b0\u4e00\u4e2a <code>forward()</code> \u7528\u4e8e\u8ba1\u7b97\u51fd\u6570\u7684\u8f93\u51fa\uff0c\u4ee5\u53ca\u4e00\u4e2a <code>backward()</code> \u7528\u4e8e\u6309\u7167\u4e0a\u9762\u63d0\u5230\u7684\u65b9\u6cd5\u8ba1\u7b97\u68af\u5ea6\u3002</p> <p></p> <p>Summary</p> <ul> <li>Neural nets will be very large: impractical to write down gradient formula by hand for all parameters.</li> <li>Backpropagation = recursive application of the chain rule along a computational graph to compute the gradients of all inputs/parameters/intermediates.</li> <li>Implementations maintain a graph structure, where the nodes implement the <code>forward()</code> / <code>backward()</code> API.</li> <li>Forward: compute result of an operation and save any intermediates needed for gradient computation in memory.</li> <li>Backward: apply the chain rule to compute the *gradient *of the loss function with respect to the inputs.</li> </ul>"},{"location":"cour_note/D1SJ_StanfordCS231n/#neural-networks","title":"Neural Networks","text":"<p>\u901a\u8fc7\u51fd\u6570\u53e0\u52a0\u7684\u65b9\u5f0f\u6765\u5b9e\u73b0\u795e\u7ecf\u7f51\u7edc\u3002</p> <p></p> <p>\u4e0e\u751f\u7269\u795e\u7ecf\u7684\u4e00\u4e2a\u7c7b\u6bd4</p> <p></p> <p></p> <p>Summary</p> <ul> <li>We arrange neurons into fully-connected layers.</li> <li>The abstraction of a layer has the nice property that it allows us to use efficient vectorized code (e.g. matrix multiplies).</li> <li>Neural networks are not really neural.</li> </ul>"},{"location":"cour_note/D1SJ_StanfordCS231n/#lecture-5-convolutional-neural-networks","title":"Lecture 5: Convolutional Neural Networks","text":"<ul> <li>Video: \ud83d\udd17</li> <li>Slides: \ud83d\udd17</li> </ul>"},{"location":"cour_note/D1SJ_StanfordCS231n/#convolutional-neural-networks","title":"Convolutional Neural Networks","text":"<p>\u4e4b\u524d\u63d0\u5230\u8fc7\u7684 Fully Connected Layer \u4f1a\u5c06\u591a\u7ef4\u7684\u6570\u636e\u62c9\u4f38\u4e3a\u5411\u91cf\u7684\u5f62\u5f0f\uff0c\u76f8\u6bd4\u4e4b\u4e0b\uff0c Convolution Layer \u5219\u4f1a\u4fdd\u7559\u8f93\u5165\u6570\u636e\u7684\u5f62\u72b6 \u7279\u5f81\uff0c\u4e00\u822c\u6765\u8bf4\uff0cfilter \u4f1a\u4e0e\u6570\u636e\u5177\u6709\u76f8\u540c\u7684\u6df1\u5ea6\uff08\u4f8b\u5982 input \u662f 32x32x3\uff0c\u90a3\u4e48 filter \u53ef\u4ee5\u4e3a 5x5x3\uff09\u3002\u901a\u8fc7\u5c06 filter \u4e0e input \u7684\u67d0\u4e00\u4e2a\u540c\u5f62\u72b6\u7684\u5b50\u533a\u57df\u505a\u70b9\u79ef\uff0c\u6211\u4eec\u5c31\u53ef\u4ee5\u5f97\u5230\u4e00\u4e2a\u6570\u5b57\u3002</p> <ul> <li>Convolve the filter with the image. (i.e. \"slide over the image spatially, computing dot products\")</li> </ul> <p></p> <p>\u5728\u67d0\u4e2a\u4f4d\u7f6e\u83b7\u5f97\u70b9\u79ef\uff0c\u5373 filter \u5982\u4f55\u4f5c\u7528\u4e8e input</p> <p></p> <p>\u91c7\u7528\u591a\u4e2a filters \u5e76\u5c06\u7ed3\u679c\u53e0\u52a0\uff0c\u6211\u4eec\u5c31\u53ef\u4ee5\u5f97\u5230\u591a\u4e2a\u6fc0\u6d3b\u56fe(activation maps)\uff0c\u4f5c\u4e3a\u4e00\u4e2a\u5904\u7406\u540e\u7684\u6570\u636e\u3002 - ConvNet is a sequence of Convolution Layers, interspersed with activation functions.</p> <p></p> <p>\u5173\u4e8e\u8f93\u51fa\u7684\u6fc0\u6d3b\u56fe\u7684\u5927\u5c0f\uff0c\u6709\u5982\u4e0a\u516c\u5f0f\u3002</p> <p>\u901a\u8fc7\u9009\u62e9\u6b65\u957f\uff0c\u6211\u4eec\u53ef\u4ee5\u63a7\u5236\u6ed1\u52a8\u7684\u901f\u7387\u3002\u4ece\u67d0\u79cd\u610f\u4e49\u4e0a\u6765\u8bb2\u8fd9\u4e5f\u662f\u5728\u63a7\u5236\u6ed1\u52a8\u7ed3\u679c\u7684\u5206\u8fa8\u7387\uff0c\u4e5f\u662f\u6c60\u5316\u64cd\u4f5c\u80cc\u540e\u7684\u601d\u60f3\u4e4b\u4e00\u3002\u800c\u5177\u4f53\u9009\u62e9\u5927\u6b65\u957f\u8fd8\u662f\u5c0f\u6b65\u957f\u662f\u4f60\u9700\u8981\u5bf9\u5404\u79cd\u56e0\u7d20\u8fdb\u884c\u8003\u91cf\u51b3\u5b9a\u7684\u3002</p> <p>\u53ef\u4ee5\u53d1\u73b0\uff0c\u6b65\u957f\u4e3a 3 \u65f6\u65e0\u6cd5\u5339\u914d\u3002\u800c\u5728\u5b9e\u8df5\u8fc7\u7a0b\u4e2d\uff0c\u6211\u4eec\u6709\u4e00\u4e9b\u624b\u6bb5\u6765\u89e3\u51b3\u8fd9\u79cd\u65e0\u6cd5\u5339\u914d\u7684\u60c5\u51b5\uff0c\u5982\"zero pad to borders\"\u4ee5\u4f7f\u5927\u5c0f\u7b26\u5408\u6b65\u957f\u3002</p> <ul> <li>The zero padding does add some sort of extraneous features at the corners, and we're doing our best to get some value and do, like process that region of the image. And so zero padding is kind of one way to do this. There's also other ways to do this that, you know, you can try and like, mirror the values here or extend them, and so it doesn't have to be zero padding, but in practice this is one thing that works reasonably.</li> </ul> <p></p> <p>\u6ce8\u610f\uff0c\u91c7\u7528\u96f6\u6269\u5c55\u4ee5\u540e\u4e0a\u4e00\u5f20\u56fe\u7684\u516c\u5f0f\u5c31\u65e0\u6cd5\u4f7f\u7528\u4e86\u3002\u8fd9\u4e5f\u6b63\u662f\u96f6\u6269\u5c55\u7684\u4e00\u4e2a\u7279\u70b9\uff0c\u5b83\u53ef\u4ee5\u8ba9\u56fe\u50cf\u7684\u5f62\u72b6\u4e0d\u5fc5\u7f29\u5c0f\u3002</p> <p>\u4e00\u9053\u6d4b\u8bd5\u9898\uff1a</p> \u9898\u9762\u7b54\u6848 <p></p> <p>\u8ba1\u7b97\u8fd9\u6837\u4e00\u5c42\u4e2d\u6709\u591a\u5c11\u53c2\u6570\u3002</p> <p>Ans</p> <ul> <li>Each filter has \\(5\\times5\\times3_{\\text{(depth)}} + 1_{\\text{(for bias)}} = 76\\) params.</li> <li>So the total number is \\(76\\times 10 = 760\\).</li> </ul>"},{"location":"cour_note/D1SJ_StanfordCS231n/#pooling-layer","title":"Pooling layer","text":"<ul> <li>makes the representations smaller and more manageable</li> <li>operates over each activation map independently:</li> </ul> <p>just downsample</p> <p>A common way to do this is max pooling:</p> <p></p> <p>just take the max value</p> <p>\u5bf9\u4e8e\u6c60\u5316\u5c42\uff0c\u5728\u8fdb\u884c\u6ed1\u52a8\u7a97\u53e3\u65f6\u6211\u4eec\u66f4\u5e0c\u671b\u6b65\u957f\u7684\u8bbe\u7f6e\u80fd\u4f7f filter \u6ca1\u6709\u91cd\u53e0\uff0c\u4ee5\u6ee1\u8db3\u5c0f\u8282\u5f00\u5934\u63d0\u5230\u7684\"independently\"\u3002</p>"},{"location":"cour_note/D1SJ_StanfordCS231n/#fully-connected-layer-fc-layer","title":"Fully Connected Layer (FC layer)","text":"<ul> <li>Contains neurons that connect to the entire input volume, as in ordinary Neural Networks.</li> </ul>"},{"location":"cour_note/D2CX_AdvancedDataStructure/","title":"[\u5927\u4e8c\u6625\u590f] \u9ad8\u7ea7\u6570\u636e\u7ed3\u6784 | Advanced Data Structure","text":"<p> \u7ea6 152 \u4e2a\u5b57  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 1 \u5206\u949f</p> <p>\u8bfe\u7a0b\u4fe1\u606f</p> <p>\u7ffb\u8f6c\u8bfe\u5802*</p> <p>\u5206\u6570\u6784\u6210\uff1a</p> <ul> <li>5% = HW</li> <li>5% = Quiz\uff08\u5212\u5206\u5230\u54ea\u91cc\u8fd8\u4e0d\u77e5\u9053\uff09</li> <li>10% = Discussions</li> <li>30% = Research Project &amp; Peer Review</li> <li>10% = max(\u671f\u4e2d\uff0c\u671f\u672b)</li> <li>40% = \u671f\u672b</li> </ul> <p>\u7b14\u8bb0\u76f8\u5173</p> <p>\u53c2\u8003\u7b14\u8bb0\uff1a</p> <ul> <li>https://www.yuque.com/xianyuxuan/saltfish_shop/course_res_index#cIhfl</li> </ul> <p>List</p> <ul> <li> Lecture 1 | AVL Trees &amp; Splay Trees &amp; Amortized Analysis</li> <li> Lecture 2 | Red Black Tree &amp; B+ Tree</li> <li> Lecture 3 | Inverted File Index</li> <li> Lecture 4 | Leftist Heaps &amp; Skew Heaps</li> <li> Lecture 5 | Binominal Trees</li> <li> Lecture 6 | Backtracing</li> <li> Lecture 7 | Divide &amp; Conquer</li> <li> Lecture 8 | Dynamic Programming</li> <li> Lecture 9 | Greedy Algorithms</li> <li> Lecture 10 | NP Completeness</li> <li> Lecture 11 | Approximation</li> <li> Lecture 12 | Local Search</li> <li> Lecture 13 | Randomized Algorithms</li> <li> Lecture 14 | Parallel</li> <li> <p> Lecture 15 | External Sorting</p> </li> <li> <p> Topic 1 | Amortized Analysis</p> </li> </ul>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Ex01/","title":"Topic 1 | Amortized Analysis","text":"<p> \u7ea6 1041 \u4e2a\u5b57  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 3 \u5206\u949f</p> <p>\u8bf4\u660e</p> <p>\u8ba1\u5212\u5728\u4e00\u6bb5\u65f6\u95f4\u5185\u91cd\u5199\u8fd9\u4e00\u90e8\u5206\u7684\u5185\u5bb9\uff0c\u73b0\u5728\u7684\u5185\u5bb9\u662f\u4ece\u539f\u6765\u7684 Lec01 \u91cc\u76f4\u63a5\u8fc1\u79fb\u8fc7\u6765\u7684\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Ex01/#\u644a\u8fd8\u5206\u6790","title":"\u644a\u8fd8\u5206\u6790","text":"<p>link</p> <p>Wikipedia: https://zh.wikipedia.org/wiki/%E5%B9%B3%E6%91%8A%E5%88%86%E6%9E%90</p> <p>\u4e0d\u597d\u610f\u601d</p> <p>\u6211\u5b9e\u5728\u4e0d\u77e5\u9053\u600e\u4e48\u6e05\u6670\u5730\u8bb2\u660e\u767d\u201c\u644a\u8fd8\u201d\u662f\u4ec0\u4e48\uff0c\u611f\u89c9\u8bb2\u4e0d\u592a\u6e05\u695a\uff0c\u6240\u4ee5\u5c31\u6bd4\u8f83\u7b80\u5355\u7684\u4ecb\u7ecd\u4e86\uff0c\u4f46\u662f\u6211\u4ecd\u7136\u4f1a\u6307\u51fa\u6211\u5b66\u4e60\u8fc7\u7a0b\u4e2d\u8ba4\u4e3a\u5bf9\u6211\u542f\u53d1\u6027\u6bd4\u8f83\u5927\u7684\u5730\u65b9\u3002</p> <p>\u6240\u8c13\u7684\u644a\u8fd8\u5206\u6790\uff0c\u5206\u6790\u7684\u662f\u644a\u8fd8\u8fb9\u754c\uff0c\u6216\u8005\u8bf4\u644a\u8fd8\u65f6\u95f4\u590d\u6742\u5ea6\u3002\u5e73\u5e38\u6211\u4eec\u5206\u6790\u65f6\u95f4\u590d\u6742\u5ea6\u65f6\uff0c\u9488\u5bf9\u7684\u5f80\u5f80\u662f\u67d0\u4e2a\u5177\u4f53\u7684\u64cd\u4f5c\u3002\u800c\u644a\u8fd8\u5206\u6790\u7684\u5bf9\u8c61\u5219\u662f\u4e00\u4e2a\u6570\u636e\u7ed3\u6784\u7684\u4e00\u7cfb\u5217\u64cd\u4f5c\uff0c\u800c\u8fd9\u4e00\u7cfb\u5217\u64cd\u4f5c\u4e2d\u6709\u6210\u672c\u8f83\u4f4e\u7684\uff0c\u4e5f\u6709\u6210\u672c\u8f83\u9ad8\u7684\uff0c\u800c\u4e14\u64cd\u4f5c\u4e4b\u95f4\u4e5f\u53ef\u80fd\u6709\u4e92\u76f8\u5f71\u54cd\u3002</p> <p>\u800c\u644a\u8fd8\u5206\u6790\u5219\u662f\u4ee5\u4e00\u4e2a\u66f4\u5168\u5c40\u7684\u89d2\u5ea6\u6765\u8ba1\u7b97\u201c\u5e73\u5747\u201d\u7684\u64cd\u4f5c\u4ee3\u4ef7\uff0c\u5b83\u8ba1\u7b97\u7684\u662f\u4ece\u521d\u59cb\u72b6\u6001\u5f00\u59cb\uff0c\u8fde\u7eed\u7684 M \u6b21\u4efb\u610f\u64cd\u4f5c\u6700\u591a\u6709 \u7684\u4ee3\u4ef7\u3002\u9700\u8981\u6ce8\u610f\u7684\u662f\uff0c\u5b83\u4e0d\u540c\u4e8e\u5e73\u5747\u65f6\u95f4\u5206\u6790\uff08\u6240\u6709\u53ef\u80fd\u7684\u64cd\u4f5c\u51fa\u73b0\u6982\u7387\u5e73\u5747\uff0c\u4e5f\u5c31\u662f\u76f4\u63a5\u6c42\u5e73\u5747\uff09\u548c\u6982\u7387\u7b97\u6cd5\u7684\u6982\u7387\u5206\u6790\uff08\u5e73\u5747\u8bdd\u6240\u6709\u53ef\u80fd\u7684\u968f\u673a\u9009\u62e9\uff0c\u4e5f\u5c31\u662f\u52a0\u6743\u6c42\u5e73\u5747\uff09\u4e0d\u540c\uff0c\u644a\u8fd8\u5206\u6790\u548c\u6982\u7387\u5b8c\u5168\u65e0\u5173\u3002</p> <p>\u5bb9\u6613\u5f97\u5230\u5982\u4e0b\u7b49\u5f0f\uff1a</p> \\[ \\text{worst-case bound} \\geq \\text{amortized bound} \\geq \\text{average-case bound} \\] <p>\u6211\u4eec\u77e5\u9053\uff0c\u7531\u4e8e amortized bound \u9650\u5236\u4e86\u6240\u6709\u7684 M \u6b21\u64cd\u4f5c\uff0c\u6240\u4ee5\u5176\u4e0a\u754c\u5c31\u7b49\u4e8e\u6700\u5dee\u7684\u60c5\u51b5\u53d1\u751f M \u6b21\uff08\u5f53\u7136\uff0c\u5f88\u591a\u60c5\u51b5\u4e0b\u4e0d\u4e00\u5b9a\u80fd\u53d6\u5230\u5168\u90fd\u662f\u6700\u5dee\u60c5\u51b5\uff09\uff1b\u540c\u6837\u7684\uff0c\u7531\u4e8e\u9700\u8981\u5bf9\u4efb\u610f\u7ec4\u5408\u90fd\u6210\u7acb\uff0c\u6240\u4ee5\u4e00\u5b9a\u4e0d\u4f1a\u5c0f\u4e8e\u7edf\u8ba1\u5b66\u610f\u4e49\u4e0a\u7684\u5e73\u5747\u60c5\u51b5\u3002</p> <p>\u521a\u5f00\u59cb\u5b66\u5230\u644a\u8fd8\u5206\u6790\u7684\u65f6\u5019\uff0c\u770b\u7740\u8fd9\u4e9b\u5185\u5bb9\u6709\u4e00\u79cd\u83ab\u540d\u5176\u5999\u7684\u611f\u89c9\uff0c\u4e0d\u77e5\u9053\u5b83\u5728\u5e72\u561b\uff0c\u540e\u6765\u6211\u624d\u53d1\u73b0\u6211\u8bef\u89e3\u4e86\u644a\u8fd8\u5206\u6790\u7684\u76ee\u7684\u3002\u6240\u4ee5\u6211\u611f\u89c9\u8fd8\u662f\u9700\u8981\u5c31\u6b64\u7ed9\u51fa\u6211\u81ea\u5df1\u7684\u7406\u89e3\u3002</p> <p>\u644a\u8fd8\u5206\u6790</p> <p>\u5728\u6211\u7406\u89e3\u4e2d\uff0c\u644a\u8fd8\u5206\u6790\u5b9e\u9645\u4e0a\u662f\u4e00\u7cfb\u5217\u8bc1\u660e\u65b9\u6cd5\uff0c\u66f4\u8fdb\u4e00\u6b65\u7684\u8bf4\uff0c\u5728\u6211\u4eec\u4e4b\u540e\u4f1a\u8bb2\u5230\u7684\u4e09\u4e2a\u5206\u6790\u65b9\u6cd5\u4e2d\uff0c\u6709\u4e00\u4e9b\u53ef\u80fd\u96be\u4ee5\u76f4\u63a5\u5f97\u5230\u644a\u8fd8\u590d\u6742\u5ea6\u3002\u4f46\u662f\u5b9e\u9645\u4e0a\uff0c\u4ed6\u4eec\u7684\u8fc7\u7a0b\u66f4\u50cf\u662f\u5df2\u77e5\u4e00\u4e2a\u644a\u8fd8\u8fb9\u754c\uff0c\u5e76\u8bc1\u660e\u5b83\u786e\u5b9e\u662f\u8fb9\u754c\u3002</p> <p>\u5e38\u89c1\u7684\u644a\u8fd8\u5206\u6790\u6709\u4e09\u79cd\uff1a\u805a\u5408(aggregate)\u6cd5\u3001\u6838(accounting)\u6cd5\u3001\u52bf\u80fd(potential)\u6cd5\uff0c\u63a5\u4e0b\u6765\u4e00\u4e00\u4ecb\u7ecd\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Ex01/#\u805a\u5408\u6cd5","title":"\u805a\u5408\u6cd5","text":"<p>\u805a\u5408\u6cd5\u76f8\u5bf9\u7b80\u5355\uff0c\u5c31\u662f\u76f4\u63a5\u7d2f\u79ef\u8fde\u7eed M \u6b21\u64cd\u4f5c\u7684\u4ee3\u4ef7\uff0c\u518d\u9664\u4ee5 M\u3002</p> \\[ T_{amortized} = \\frac{\\sum_i{T_i}}{n} \\]"},{"location":"cour_note/D2CX_AdvancedDataStructure/Ex01/#\u6838\u6cd5","title":"\u6838\u6cd5","text":"<p>link</p> <p>\u5173\u4e8e Accounting Analysis \u53ef\u4ee5\u53c2\u8003\u8fd9\u7bc7\u6587\u7ae0\uff1ahttps://www.baeldung.com/cs/amortized-analysis</p> <p>\u505a\u4e00\u4e2a\u6bd4\u55bb\u7684\u8bdd\uff0c\u53ef\u4ee5\u8fd9\u4e48\u7406\u89e3\uff1a</p> <p>\u4f60\u53bb\u5403\u5348\u996d\uff0c\u5403\u7d20\u83dc\u8981 \u00a51\uff08\u5bf9\u6807\u6d88\u8017\u8f83\u5c0f\u7684\u64cd\u4f5c\uff09\uff0c\u5403\u8364\u83dc\u8981 \u00a54\uff08\u5bf9\u6807\u6d88\u8017\u8f83\u5927\u7684\u64cd\u4f5c\uff09\uff0c\u73b0\u5728\u4f60\u77e5\u9053\u4f60\u6bcf\u5929\u5403\u5348\u996d\u7684\u644a\u8fd8\u5f00\u9500\u4e3a \u00a52\uff08\u4ece\u8bc1\u660e\u7684\u89d2\u5ea6\u6765\u7406\u89e3\uff09\uff0c\u5e76\u4e14\u6211\u65e0\u8111\u7684\u8ba4\u4e3a\u6bcf\u4e2a\u64cd\u4f5c\u7684\u644a\u8fd8\u4ee3\u4ef7\u90fd\u662f \u00a52\uff08\u5728\u6838\u6cd5\u4e2d\uff0c\u6574\u4f53\u7684\u644a\u8fd8\u5f00\u9500\u548c\u5355\u4e2a\u64cd\u4f5c\u7684\u644a\u8fd8\u5f00\u9500\u662f\u4e0d\u4e00\u6837\u7684\uff0c\u5355\u4e2a\u64cd\u4f5c\u7684\u644a\u8fd8\u5f00\u9500\u662f\u53ef\u80fd\u4e92\u4e0d\u4e00\u6837\u7684\uff0cM \u4e2a\u64cd\u4f5c\u6c42\u548c\u53d6\u5e73\u5747\u4ee5\u540e\u624d\u662f\u6574\u4f53\u7684\u644a\u8fd8\u4ee3\u4ef7\uff09\u3002\u90a3\u4e48\u4f60\u4eca\u5929\u5403\u7d20\u83dc\uff0c\u8d26\u6237\u5165\u8d26 \u00a51\uff082 - 1 = 1\uff09\uff1b\u660e\u5929\u4f60\u4e5f\u5403\u7d20\u83dc\uff0c\u8d26\u6237\u4e5f\u5165\u8d26 \u00a51\uff1b\u540e\u5929\u4f60\u5403\u8364\u83dc\u4e86\uff0c\u90a3\u4e48\u8d26\u6237\u5c31\u51fa\u8d26 \u00a52\uff082 - 4 = -2\uff09\u2026\u2026</p> <p>\u6838\u6cd5\u5927\u6982\u5c31\u662f\u6309\u7167\u8fd9\u4e48\u4e00\u4e2a\u601d\u8def\u6765\u8bc1\u660e\uff0c\u4e0d\u8fc7\u5177\u4f53\u7ec6\u8282\u548c\u4e0a\u9762\u8fd9\u4e2a\u6848\u4f8b\u8fd8\u662f\u6709\u533a\u522b\u7684\uff0c\u53ef\u4ee5\u8be6\u7ec6\u53c2\u8003\u4e0a\u9762\u90a3\u7247\u6587\u7ae0\uff0c\u6211\u89c9\u5f97\u914d\u56fe\u548c\u8bf4\u660e\u90fd\u5f88\u8be6\u7ec6\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Ex01/#\u52bf\u80fd\u6cd5","title":"\u52bf\u80fd\u6cd5","text":"<p>link</p> <p>\u5173\u4e8e Potential Analysis \u53ef\u4ee5\u53c2\u8003\u8fd9\u7bc7\u6587\u7ae0\uff1ahttps://en.wikipedia.org/wiki/Potential_method \u4ee5\u53ca ltgg \u7684\u8fd9\u671f\u5468\u62a5\u8bb2\u7684\u4e5f\u5f88\u597d\uff1ahttps://www.yuque.com/xianyuxuan/saltfish_shop/weekly002_amortized_analysis#KmnY6</p> <p>\u52bf\u80fd\u6cd5\u5f3a\u63a8 ltgg \u7684\u8fd9\u7bc7\u6587\u7ae0\uff0c\u8bb2\u7684\u975e\u5e38\u597d\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec01/","title":"Lecture 1 | AVL Trees &amp; Splay Trees","text":"<p> \u7ea6 7119 \u4e2a\u5b57  385 \u884c\u4ee3\u7801  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 29 \u5206\u949f</p> <p>\u8bf4\u660e</p> <p>\u539f\u5148\u5b89\u6392\u5728\u8fd9\u4e00\u7ae0\u8282\u7684\u644a\u8fd8\u5206\u6790\u73b0\u5728\u88ab\u8fc1\u79fb\u5230\u4e86\u8fd9\u4e2a\u5730\u65b9\uff1aTopic 1 | Amortized Analysis\u3002</p> <p>\u9605\u8bfb\u6280\u5de7</p> <p>\u56e0\u4e3a\u6ca1\u6cd5\u5728\u8fd9\u91cc\u7528\u4ee3\u7801\u5199\u52a8\u753b\uff0c\u6240\u4ee5\u6211\u7528 Tab \u6a21\u62df\u4e86\u4e00\u4e0b\u52a8\u753b\u5e27\uff0c\u53ef\u4ee5\u624b\u52a8\u5207\u6362\u8fd9\u4e9b\u6807\u7b7e\u6765\u52a8\u6001\u89c2\u5bdf\u3002\u4e00\u822c\u8fd9\u79cd\u5185\u5bb9\u7684 Tab \u6807\u9898\u90fd\u4f1a\u662f <code>Frame {}</code>\u3002</p> Frame 1Frame 2Frame 3 <p>Like</p> <p>Like this</p> <p>Like this!</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec01/#avl-\u6811","title":"AVL \u6811","text":""},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec01/#\u6982\u5ff5","title":"\u6982\u5ff5","text":"<p>link</p> <p>OI Wiki: https://oi-wiki.org/ds/avl/</p> <p>\u6211\u4eec\u77e5\u9053\uff0c\u5bf9\u4e8e\u4e00\u68f5\u4e8c\u53c9\u641c\u7d22\u6811\uff0c\u5176\u5bf9\u70b9\u7684\u64cd\u4f5c\u4ee3\u4ef7\u4e3a \\(O(\\log n)\\)\u3002\u7136\u800c\u5728\u6700\u574f\u60c5\u51b5\u4e0b\uff0c\u5b83\u4f1a\u9000\u5316\u6210 \\(O(n)\\)\uff0c\u4f8b\u5982\u8fd9\u662f\u4e00\u68f5\u53ea\u6709\u5de6\u5b69\u5b50\u6811\u7684\u94fe\u578b\u4e8c\u53c9\u6811\uff0c\u90a3\u4e48\u64cd\u4f5c\u8fd9\u91cc\u552f\u4e00\u7684\u53f6\u5b69\u5b50\u8282\u70b9\u5c31\u662f \\(O(n)\\)\u3002</p> <p>\u6362\u53e5\u8bdd\u6765\u8bf4\uff0c\u4e00\u68f5\u4e8c\u53c9\u6811\u7684\u7ef4\u62a4\u6210\u672c\u57fa\u672c\u4e0a\u4e0e\u5176\u9ad8\u5ea6\u6b63\u76f8\u5173\u3002\u56e0\u800c\u4e00\u4e2a\u5f88\u81ea\u7136\u7684\u60f3\u6cd5\u662f\uff0c\u5982\u679c\u6211\u4eec\u60f3\u8ba9\u4e00\u68f5\u4e8c\u53c9\u6811\u597d\u7ef4\u62a4\uff0c\u90a3\u4e48\u5c31\u5e0c\u671b\u5b83\u7684\u9ad8\u5ea6\u5c3d\u53ef\u80fd\u4f4e\uff0c\u800c\u5728\u70b9\u6570\u56fa\u5b9a\u7684\u60c5\u51b5\u4e0b\uff0c\u4e00\u79cd\u6734\u7d20\u7684\u601d\u60f3\u662f\u8ba9\u8282\u70b9\u5c3d\u53ef\u80fd\u201c\u5747\u5300\u201d\u5730\u5206\u5e03\u5728\u6811\u4e0a\u3002</p> <p>height of a tree</p> <p>\u6811\u7684\u9ad8\u5ea6(Height of Tree)\u7b49\u4e8e\u5176\u6839\u8282\u70b9\u5230\u53f6\u5b69\u5b50\u8282\u70b9\u7684\u82e5\u5e72\u8def\u5f84\u4e2d\uff0c\u6700\u5927\u7684\u8ddd\u79bb\uff08\u5373\u8fb9\u7684\u6570\u91cf\uff09\uff0c\u4e5f\u5c31\u662f\u6df1\u5ea6\u6700\u6df1\u7684\u8282\u70b9\u5230\u6839\u8282\u70b9\u5230\u8ddd\u79bb\u3002</p> <p>\u7279\u522b\u7684\uff0c\u4e00\u68f5\u7a7a\u6811\u7684\u9ad8\u5ea6\u4e3a -1\u3002</p> <p>\u8bf4\u7684\u901a\u4fd7\u4e00\u4e9b\uff0c\u5c31\u662f\u6811\u7684\u5c42\u6570\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec01/#avl-\u6811_1","title":"AVL \u6811","text":"<p>\u800c AVL Tree \u662f\u4e00\u79cd\u5e73\u8861(balanced)\u7684\u4e8c\u53c9\u641c\u7d22\u6811\uff0c\u901a\u8fc7\u300c\u9ad8\u5ea6\u300d\u8fd9\u4e2a\u91cf\uff0c\u5b9a\u4e49\u4e86\u300c\u5e73\u8861\u300d\u8fd9\u4ef6\u4e8b\u3002</p> <p>AVL Tree</p> <ol> <li>\u4e00\u4e2a\u7a7a\u4e8c\u53c9\u6811\u662f\u4e00\u4e2a AVL \u6811\uff1b</li> <li>\u5982\u679c\u4e8c\u53c9\u6811 \\(T\\) \u662f\u4e00\u4e2a AVL \u6811\uff0c\u5219\u5176\u5de6\u53f3\u5b69\u5b50\u6811 \\(T_l\\) \u548c \\(T_r\\) \u4e5f\u90fd\u5e94\u8be5\u662f AVL \u6811\uff0c\u4e14\u6709 \\(|h(T_l) - h(T_r)| \\leq 1\\)\uff1b</li> </ol> <p>Balance Factor</p> <p>\u4e00\u4e2a\u8282\u70b9\u7684\u5e73\u8861\u56e0\u5b50(Balance Factor, BF)\u7528\u6765\u63cf\u8ff0\u4e00\u4e2a\u8282\u70b9\u7684\u5e73\u8861\u72b6\u6001\uff0c\u5bf9\u4e8e\u8282\u70b9 \\(T_p\\)\uff0c\u5b83\u7684\u5de6\u5b69\u5b50\u6811\u4e3a \\(T_l\\)\uff0c\u53f3\u5b69\u5b50\u6811\u4e3a \\(T_r\\)\uff0c\u5219\uff1a</p> \\[ BF(T_p) = h(T_l) - h(T_r) \\] <p>\u6240\u4ee5\u4e0a\u9762\u7684\u7b2c 2 \u6761\u53c8\u53ef\u4ee5\u5199\u6210\uff1a</p> <ul> <li>\u5982\u679c\u4e8c\u53c9\u6811 \\(T\\) \u662f\u4e00\u4e2a AVL \u6811\uff0c\u5219\u5176\u5de6\u53f3\u5b69\u5b50\u6811 \\(T_l\\) \u548c \\(T_r\\) \u4e5f\u90fd\u5e94\u8be5\u662f AVL \u6811\uff0c\u4e14\u6709 \\(BF(T_p) \\in \\{0, \\pm 1\\}\\)\uff1b</li> </ul> <p>\u8bf4\u7684\u901a\u4fd7\u4e00\u4e9b\u5c31\u662f\uff0cAVL \u6811\u7684\u6bcf\u4e00\u4e2a\u70b9\u90fd\u5e73\u8861\uff0c\u800c\u5e73\u8861\u4e0e\u5426\u53d6\u51b3\u4e8e\u8282\u70b9\u7684\u4e24\u4e2a\u5b69\u5b50\u6811\u5c42\u6570\u4e4b\u5dee\u662f\u5426\u8d85\u8fc7 1\u3002</p> <p>\u5728\u8fd9\u79cd\u5b9a\u4e49\u4e0b\uff0cAVL \u6811\u7684\u9ad8\u5ea6\u53ef\u4ee5\u8bc1\u660e\u4e3a \\(O(\\log N)\\)\uff0c\u8bc1\u660e\u5982\u4e0b\uff1a</p> <p>Height of AVL Trees</p> <pre><code>graph TD;\nA((\"Root\"))\nB[/\"Left Subtree\"\\]\nC[/\"Right Subtree\"\\]\nA === B\nA === C</code></pre> <p>\u6211\u4eec\u8bb0 \\(n_h\\) \u662f\u9ad8\u5ea6\u4e3a \\(h\\) \u7684 AVL \u6811\u6240\u5305\u542b\u7684\u6700\u5c11\u8282\u70b9\u6570\uff0c\u5219\u6709\u5982\u4e0b\u9012\u63a8\u5173\u7cfb\uff1a</p> \\[ n_h = \\left\\{     \\begin{array}{l}         1                       &amp; (h = 0) \\\\         2                       &amp; (h = 1) \\\\         n_{h-1} + n_{h-2} + 1   &amp; (h &gt; 1)     \\end{array} \\right. \\] <p>\u53d1\u73b0 \\(n_h + 1\\) \u7b26\u5408 Fibonacci \u6570\u5217\u7684\u9012\u63a8\u516c\u5f0f\uff08\u4f46\u662f\u521d\u59cb\u6761\u4ef6\u4e0d\u4e00\u6837\uff09\uff0c\u6240\u4ee5\u6211\u4eec\u53ef\u4ee5\u7528 Fibonacci \u5bf9\u5176\u8fdb\u884c\u4e00\u4e2a\u4f30\u8ba1\u3002</p> <p>\u800c\u5bf9\u4e8e\u5982\u4e0b Fibonacci \u6570\u5217\uff1a</p> \\[ F_i = \\left\\{     \\begin{array}{l}         1                   &amp; (i = 1) \\\\         1                   &amp; (i = 2) \\\\         F_{i-1} + F_{i-2}   &amp; (i &gt; 2)     \\end{array} \\right. \\] <p>\u5176\u901a\u9879\u4e3a\uff1a</p> \\[ \\begin{aligned}     F_n &amp;= \\frac{1}{\\sqrt{5}} \\left( \\left( \\frac{1 + \\sqrt{5}}{2} \\right)^n - \\left( \\frac{1 - \\sqrt{5}}{2} \\right)^n \\right) \\\\         &amp;\\approx \\frac{1}{\\sqrt{5}} \\left( \\frac{1 + \\sqrt{5}}{2} \\right)^n \\\\     \\log{(F_n)} &amp;\\approx n \\end{aligned} \\] <p>\u800c \\(n_h + 1 \\approx F_{h+2}\\)\uff0c\u6240\u4ee5 \\(h \\approx \\log{(n_h)}\\)\uff0c\u4e5f\u5c31\u662f\u8bf4 \\(h \\approx \\log{N}\\)\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec01/#\u89c6\u89d2","title":"\u89c6\u89d2","text":"<p>\u800c\u6211\u4eec\u8c08\u8bba AVL \u6811\u65f6\uff0c\u6211\u4eec\u5e0c\u671b\u4ee5\u4e00\u4e2a\u52a8\u6001\u7684\u89c6\u89d2\u6765\u8c08\u8bba AVL \u6811\uff0c\u5373\u8ba8\u8bba\uff1a\u67d0\u4e00\u68f5\u6811\u662f\u5426\u662f AVL \u6811\uff1b\u5728\u67d0\u4e2a\u64cd\u4f5c\u540e\uff0c\u5b83\u662f\u5426\u4ecd\u7136\u662f AVL \u6811\uff1b\u82e5\u539f\u5148\u662f\uff0c\u800c\u7ecf\u8fc7\u64cd\u4f5c\u540e\u4e0d\u518d\u662f\uff0c\u90a3\u8981\u5982\u4f55\u5c06\u5b83\u91cd\u65b0\u53d8\u4e3a AVL \u6811\u3002</p> <p>\u4ee5\u4e0a\u4e09\u4e2a\u6b65\u9aa4\u662f\u7b80\u5316\u540e\u7684\u5efa\u6a21\uff0c\u5b83\u6210\u4e3a\u6211\u4eec\u89e3\u51b3\u5176\u4ed6\u95ee\u9898\u7684\u6700\u5c0f\u5355\u5143\u548c\u57fa\u7840\u3002</p> <p>\u6240\u4ee5\u5728\u8fd9\u79cd\u6a21\u578b\u4e0b\uff0c\u6211\u4eec\u9700\u8981\u5b9a\u4e49\u4e24\u4e2a\u4e1c\u897f\uff1a</p> <p>Trouble Maker &amp; Trouble Finder</p> <p>\u4ee5 \ud83c\udf30 \u6765\u8bf4\u660e\u3002</p> Frame 1Frame 2 <p>\u4e0b\u56fe\u4e3a\u4e00\u4e2a AVL \u6811\uff1a</p> <pre><code>graph TD;\nA((\"8, BF=1\"))\nB((\"4, BF=0\"))\nC((\"9, BF=0\"))\nD((\"2, BF=0\"))\nE((\"6, BF=0\"))\nA === B\nA === C\nB === D\nB === E</code></pre> <p>\u73b0\u5728\u6211\u4eec\u63d2\u5165 <code>5</code>\uff1a</p> <pre><code>graph TD;\nA((\"8, BF=2\"))\nB((\"4, BF=-1\"))\nC((\"9, BF=0\"))\nD((\"2, BF=0\"))\nE((\"6, BF=1\"))\nF((\"5, BF=0\"))\nA === B\nA === C\nB === D\nB === E\nE === F\nE === NULL</code></pre> <p>\u6211\u4eec\u53d1\u73b0\uff0c\u6b64\u65f6 <code>8</code> \u7684\u300c\u5e73\u8861\u56e0\u5b50\u300d\u53d8\u6210\u4e862\uff0c\u4e0d\u518d\u7b26\u5408 AVL \u6811\u7684\u8981\u6c42\uff0c\u800c\u8fd9\u4e00\u5207\u90fd\u662f <code>5</code> \u7684\u63d2\u5165\u5bfc\u81f4\u7684\u2014\u2014\u4e8e\u662f\u6211\u4eec\u79f0\u50cf\u8fd9\u91cc\u7684 <code>8</code> \u4e00\u6837\uff0c\u7531\u4e8e\u67d0\u4e2a\u70b9\u7684\u63d2\u5165\uff0c\u5176\u300c\u5e73\u8861\u56e0\u5b50\u300d\u4e0d\u518d\u7b26\u5408\u8981\u6c42\u7684\u70b9\uff0c\u4e3a Trouble Finder\uff1b\u800c\u50cf\u8fd9\u91cc\u7684 <code>5</code> \u4e00\u6837\uff0c\u5bfc\u81f4 Trouble Finder \u51fa\u73b0\u7684\u70b9\uff0c\u88ab\u79f0\u4e4b\u4e3a Trouble Maker\u3002</p> <p>\u5f62\u8c61\u5730\u63cf\u8ff0\u8fd9\u4ef6\u4e8b\u5c31\u662f\uff0c\u5728\u52a8\u6001\u63d2\u5165 <code>5</code> \u8fd9\u4e2a\u8fc7\u7a0b\u4e2d\uff0c\u51fa\u73b0\u4e86\u4e00\u4e2a \"Trouble\"\uff0c\u5bfc\u81f4\u8fd9\u4e2a\u6811\u4e0d\u518d\u662f AVL \u6811\uff0c\u800c <code>5</code> \u662f\u8fd9\u4e2a \"Trouble\" \u7684 \"Maker\"\uff0c<code>8</code> \u662f \"Finder\"\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec01/#\u64cd\u4f5c","title":"\u64cd\u4f5c","text":"<p>\u672c\u5c0f\u8282\u6240\u9700\u8981\u8bb2\u7684\u5185\u5bb9\u5c31\u662f#\u89c6\u89d2\u4e2d\u63d0\u5230\u7684\u201c\u91cd\u65b0\u53d8\u4e3a AVL \u6811\u201d\u8fd9\u4e00\u89c6\u89d2\uff0c\u4e5f\u5c31\u662f AVL \u6811\u7684\u7ef4\u62a4\u3002</p> <p>\u9996\u5148\uff0c \u6211\u4eec\u9700\u8981\u5bf9 AVL \u6811\u7684\u7834\u574f\u60c5\u51b5\u8fdb\u884c\u5206\u7c7b\uff0c\u6839\u636e \"Trouble Finder\"\u3001\"Related Trouble Finder's Child\"\u3001\"Trouble Maker\"\u8fd9\u4e09\u4e2a\u70b9\u7684\u76f8\u5bf9\u5173\u7cfb\uff0c\u5206\u4e3a <code>LL</code>\u3001<code>RR</code>\u3001<code>LR</code>\u3001<code>RL</code> \u56db\u79cd\uff1a</p> <p>\u540c\u5fc3\u5706\u8868\u793a\u8fd9\u4e2a\u70b9\u662f\u9700\u8981\u6211\u4eec\u5728\u540e\u7eed\u64cd\u4f5c\u4e2d\u5173\u6ce8\u7684\u3002</p> <p>\u6b64\u5916\uff0c\u867d\u7136\u5b9e\u9645\u60c5\u51b5\u4e0b\u53ef\u80fd\u51fa\u73b0\u591a\u4e2a Trouble Finder\uff0c\u4f46\u662f\u6211\u4eec\u53ea\u5173\u6ce8\u4ee5\u300c\u8ddd\u79bb\u6848\u53d1\u73b0\u573a\u6700\u8fd1\u7684 Trouble Finder\u300d\u4e3a\u6839\u7684\u5b69\u5b50\u6811\uff08\u8fd9\u53e5\u8bdd\u975e\u5e38\u91cd\u8981\uff09\u3002</p> LLRRLRRL <pre><code>flowchart TD\n    A(((\"Trouble\\nFinder\")))\n    B(((\"Left\\nChild\")))\n    C((\"Right\\nChild\"))\n    D((\"L Left\\nChild\"))\n    DA[/\"Left and Right Subtrees\"\\]\n    E((\"L Right\\nChild\"))\n    EA[/\"Left and Right Subtrees\"\\]\n    F((\"R Left\\nChild\"))\n    FA[/\"Left and Right Subtrees\"\\]\n    G((\"R Right\\nChild\"))\n    GA[/\"Left and Right Subtrees\"\\]\n    H((\"Trouble\\nMaker\"))\n    A === B\n    A === C\n    B === D === DA === H\n    B === E === EA\n    C === F === FA\n    C === G === GA</code></pre> <pre><code>flowchart TD\n    A(((\"Trouble\\nFinder\")))\n    B((\"Left\\nChild\"))\n    C(((\"Right\\nChild\")))\n    D((\"L Left\\nChild\"))\n    DA[/\"Left and Right Subtrees\"\\]\n    E((\"L Right\\nChild\"))\n    EA[/\"Left and Right Subtrees\"\\]\n    F((\"R Left\\nChild\"))\n    FA[/\"Left and Right Subtrees\"\\]\n    G((\"R Right\\nChild\"))\n    GA[/\"Left and Right Subtrees\"\\]\n    H((\"Trouble\\nMaker\"))\n    A === B\n    A === C\n    B === D === DA\n    B === E === EA\n    C === F === FA\n    C === G === GA === H</code></pre> <pre><code>flowchart TD\n    A(((\"Trouble\\nFinder\")))\n    B(((\"Left\\nChild\")))\n    C((\"Right\\nChild\"))\n    D((\"L Left\\nChild\"))\n    DA[/\"Left and Right Subtrees\"\\]\n    E(((\"L Right\\nChild\")))\n    EA[/\"Left and Right Subtrees\"\\]\n    F((\"R Left\\nChild\"))\n    FA[/\"Left and Right Subtrees\"\\]\n    G((\"R Right\\nChild\"))\n    GA[/\"Left and Right Subtrees\"\\]\n    H((\"Trouble\\nMaker\"))\n    A === B\n    A === C\n    B === D === DA\n    B === E === EA === H\n    C === F === FA\n    C === G === GA</code></pre> <pre><code>flowchart TD\n    A(((\"Trouble\\nFinder\")))\n    B((\"Left\\nChild\"))\n    C(((\"Right\\nChild\")))\n    D((\"L Left\\nChild\"))\n    DA[/\"Left and Right Subtrees\"\\]\n    E((\"L Right\\nChild\"))\n    EA[/\"Left and Right Subtrees\"\\]\n    F(((\"R Left\\nChild\")))\n    FA[/\"Left and Right Subtrees\"\\]\n    G((\"R Right\\nChild\"))\n    GA[/\"Left and Right Subtrees\"\\]\n    H((\"Trouble\\nMaker\"))\n    A === B\n    A === C\n    B === D === DA\n    B === E === EA\n    C === F === FA === H\n    C === G === GA</code></pre> <p>\u7a0d\u4f5c\u89e3\u91ca\uff0c\u4f8b\u5982 <code>LR</code>\uff0c\u8868\u793a\u7684\u662f Trouble Maker \u5728 Trouble Finder \u7684 L \u5b69\u5b50\u8282\u70b9\u7684 R \u5b69\u5b50\u6811\u4e2d\u3002</p> <p>\u53e6\u5916\uff0c\u5bf9\u4e8e\u6211\u53ea\u5728 <code>LR</code> \u548c <code>RL</code> \u4e2d\u7740\u91cd\u4e8c\u7ea7\u5b69\u5b50\u8282\u70b9\uff0c\u5e76\u4e0d\u662f\u7b14\u8bef\u3002\u4e4b\u540e\u4f1a\u8be6\u7ec6\u4ecb\u7ecd\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec01/#ll--rr","title":"LL &amp; RR","text":"<p>\u5e9f\u8bdd</p> <p>\u5927\u90e8\u5206\u6559\u6750\u90fd\u503e\u5411\u4e8e\u7ee7\u7eed\u7528\u201c\u65cb\u8f6c\u201d\u6765\u6982\u62ec\u8fd9\u4e9b\u65b9\u6cd5\uff0c\u786e\u5b9e\u5176\u5b9e\u4ece\u62bd\u8c61\u89d2\u5ea6\u6765\u8bb2\u81f3\u5c11 <code>LL</code> \u548c <code>RR</code> \u90e8\u5206\u4e5f\u8fd8\u662f\u50cf\u7684\uff0c\u4f46\u662f\u6211\u89c9\u5f97\u8fd9\u5e76\u4e0d\u5229\u4e8e\u8bb0\u5fc6\u548c\u7406\u89e3\u8fd9\u4e2a\u8fc7\u7a0b\uff0c\u5c24\u5176\u662f\u5bf9\u4e8e <code>LR</code> \u548c <code>RL</code> \u7684\u90e8\u5206\u3002</p> <p>\u6240\u4ee5\u5728 <code>LL</code> \u548c <code>RR</code> \u90e8\u5206\uff0c\u6211\u8fd8\u662f\u4f1a\u5148\u4ecb\u7ecd\u4e00\u4e0b\u6bd4\u8f83\u4f20\u7edf\u7684\uff0c\u7528\u201c\u65cb\u8f6c\u201d\u7684\u65b9\u5f0f\u6765\u7406\u89e3\uff0c\u4e4b\u540e\u6211\u5c06\u5c1d\u8bd5\u7740\u7528\u6211\u81ea\u5df1\u7684\u601d\u8def\u6765\u8bb2\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec01/#\u65cb\u8f6c\u89c6\u89d2","title":"\u201c\u65cb\u8f6c\u201d\u89c6\u89d2","text":"<p><code>LL</code> \u548c <code>RR</code> \u8fd9\u4e24\u79cd\u60c5\u51b5\u76f8\u5bf9\u76f4\u89c2\u3002\u7531\u4e8e\u5b83\u4eec\u7684\u64cd\u4f5c\u662f\u5bf9\u79f0\u7684\uff0c\u6240\u4ee5\u6211\u8fd9\u91cc\u4ee5 <code>LL</code> \u4e3a\u4f8b\u3002</p> <pre><code>    flowchart TD\n        A(((\"Trouble\\nFinder\")))\n        C[/\"Right Subtree\"\\]\n\n        subgraph SA[\"New Left Subtree\"]\n\n            subgraph SB[\"New L Left Subtree\"]\n                D[/\"L Left Subtree\"\\]\n                H((\"Trouble\\nMaker\"))\n            end\n\n            B(((\"Left\\nChild\")))\n            E[/\"L Right Subtree\"\\]\n        end\n\n        A === B\n        A === C\n        B === D === H\n        B === E</code></pre> <p>\u6839\u636e\u76f8\u5173\u6027\u8d28\uff0c\u6211\u4eec\u5f97\u5230\u8fd9\u4e2a\u6a21\u578b\u6709\u5982\u4e0b\u6027\u8d28\uff1a</p> <p>\u4e00\u4e9b\u6027\u8d28</p> <ol> <li>\\(BF(\\text{Trouble Finder}) = h(\\text{New Left Subtree}) - h(\\text{Right Subtree}) = 2\\)\uff1b</li> <li>\\(h(\\text{New L Left Subtree}) - h(\\text{L Right Subtree}) = 1\\)\uff1b<ul> <li>\u5982\u679c\u6b64\u5dee\u4e3a 0\uff0c\u5219\u4e0d\u5e94\u5f53\u6210\u4e3a Trouble Maker\uff0c\u82e5\u6b64\u5dee\u4e3a 2\uff0c\u5219 Left Child \u5e94\u5f53\u4e3a Trouble Finder\uff1b</li> </ul> </li> </ol> <p>\u73b0\u5728\u6211\u4eec\u5e0c\u671b\u5728\u4fdd\u7559\u4e8c\u53c9\u641c\u7d22\u6811\u7684\u6027\u8d28\u4e0b\uff0c\u8981\u8ba9 \\(|BF(\\text{Trouble Finder})|\\) \u53d8\u5c0f\uff0c\u4e00\u4e2a\u5f88\u81ea\u7136\u7684\u60f3\u6cd5\u5c31\u662f\u8ba9 \\(h(\\text{New Left Subtree})\\) \u53bb -1\uff0c\u8ba9 \\(h(\\text{Right Subtree})\\) \u53bb +1\u3002</p> <p>\u4e8e\u662f\u6211\u4eec\u53d1\u73b0\uff0c\u8fd9\u6837\u7684\u64cd\u4f5c\u521a\u597d\uff1a</p> <p>LL Single Rotation</p> <p>\u5728 Frame 2 \u548c Frame 3 \u4e4b\u95f4\u6dfb\u52a0\u7684\u7ec6\u7ebf\u662f\u4e3a\u4e86\u8868\u793a\u8fd9\u91cc L Right Subtree \u7684\u8f6c\u79fb\u65b9\u6cd5\uff0c\u8ba9 2 ~ 3 \u5e27\u7684\u201c\u65cb\u8f6c\u201d\u8fc7\u7a0b\u4e2d\u66f4\u52a0\u6e05\u6670\u3002</p> <p>\u6b64\u5916\uff0c\u8fd9\u91cc\u8981\u7d20\u7684\u547d\u540d\u90fd\u662f\u57fa\u4e8e Frame 1 \u7684\uff0c\u5bf9\u4e8e Frame 4 \u6765\u8bf4 L Right Subtree \u663e\u7136\u5df2\u7ecf\u4e0d\u662f L Right Subtree \u4e86\u3002</p> Frame 1Frame 2Frame 3Frame 4 <pre><code>    flowchart TD\n        A(((\"Trouble\\nFinder\")))\n        B(((\"Left\\nChild\")))\n        C[/\"Right Subtree\"\\]\n        D[/\"L Left Subtree\"\\]\n        H((\"Trouble\\nMaker\"))\n        E[/\"L Right Subtree\"\\]\n\n        A === B\n        A === C\n        B === D === H\n        B === E</code></pre> <pre><code>    flowchart TD\n        A(((\"Trouble\\nFinder\")))\n        B(((\"Left\\nChild\")))\n        C[/\"Right Subtree\"\\]\n        D[/\"L Left Subtree\"\\]\n        E[/\"L Right Subtree\"\\]\n        H((\"Trouble\\nMaker\"))\n\n        A === B\n        A --- E\n        A === C\n        B === D === H\n        B === E</code></pre> <pre><code>    flowchart TD\n        A(((\"Trouble\\nFinder\")))\n        B(((\"Left\\nChild\")))\n        C[/\"Right Subtree\"\\]\n        D[/\"L Left Subtree\"\\]\n        E[/\"L Right Subtree\"\\]\n        H((\"Trouble\\nMaker\"))\n\n        B === D === H\n        B --- E\n        B === A\n        A === E\n        A === C\n</code></pre> <pre><code>    flowchart TD\n        A(((\"Trouble\\nFinder\")))\n        B(((\"Left\\nChild\")))\n        C[/\"Right Subtree\"\\]\n        D[/\"L Left Subtree\"\\]\n        E[/\"L Right Subtree\"\\]\n        H((\"Trouble\\nMaker\"))\n\n        B === D === H\n        B === A\n        A === E\n        A === C\n</code></pre> <p>\u4f60\u751a\u81f3\u80fd\u4ece\u6574\u4e2a\u6846\u5728 2 ~ 3 \u5e27\u7684\u53d8\u77ed\u611f\u53d7\u5230\u8fd9\u4e2a\u6811\u7684\u9ad8\u5ea6\u51cf\u5c11\u4e86x\uff08\u9003\uff09</p> <p>\u90a3\u4e48\u8fd8\u6709\u4e00\u4e2a\u95ee\u9898\u662f\uff0c\u5982\u4f55\u8bc1\u660e\u8fd9\u6837\u53d8\u6362\u80fd\u591f\u4fdd\u6301 AVL \u7684\u6027\u8d28\u5462\uff1f</p> <p>\u6211\u4e2a\u4eba\u8ba4\u4e3a\u4e3b\u8981\u6709\u4e24\u4e2a\u7ef4\u5ea6\uff0c\u4e00\u662f\u4fdd\u6301\u4e8c\u53c9\u641c\u7d22\u6811\u7684\u6027\u8d28\uff0c\u4e8c\u662f\u4fdd\u6301\u5e73\u8861\u7684\u6027\u8d28\uff0c\u6211\u7684\u8bc1\u660e\u5185\u5bb9\u6298\u53e0\u8d77\u6765\u4e86\uff0c\u5efa\u8bae\u8bfb\u8005\u53ef\u4ee5\u5148\u81ea\u5df1\u601d\u8003\u4e00\u4e0b\u518d\u5c55\u5f00\u770b\u770b\u6211\u7684\u60f3\u6cd5\u3002</p> \u4e8c\u53c9\u641c\u7d22\u6811\u6027\u8d28\u7684\u4fdd\u6301 <p></p> <p>\u4e0d\u77e5\u9053\u8bfb\u8005\u662f\u5426\u53d1\u73b0\uff0c\u5bf9\u4e8e\u4e00\u4e2a\u6392\u5217\u5f97\u5f53\u7684\u4e8c\u53c9\u641c\u7d22\u6811\uff0c\u5982\u679c\u6211\u4ece\u5de6\u5230\u53f3\uff0c\u4f7f\u7528\u4e00\u6761\u7ad6\u76f4\u7684\u626b\u63cf\u7ebf\u626b\u63cf\u6574\u4e2a\u6811\uff0c\u5c06\u4f1a\u5f97\u5230\u4e00\u4e2a\u5355\u8c03\u5e8f\u5217\uff0c\u8fd9\u4e5f\u6b63\u5bf9\u5e94\u7740\u8fd9\u4e2a\u4e8c\u53c9\u641c\u7d22\u6811\u6240\u7ef4\u62a4\u7684\u6709\u5e8f\u6570\u5217\u3002</p> <p>\u57fa\u4e8e\u8fd9\u79cd\u8bba\u8c03\uff0c\u518d\u56de\u5934\u770b\u4e0a\u9762\u90a3\u4e2a\u52a8\u6001\u7684\u8fc7\u7a0b\uff0c\u751a\u81f3\u662f\u89c2\u5bdf\u6211\u5728 2 ~ 3 \u5e27\u753b\u51fa\u6765\u7684\u8fd9\u4e2a\u4e09\u89d2\u5f62\u7684\u65cb\u8f6c\uff0c\u5c31\u4f1a\u53d1\u73b0\u8fd9\u79cd\u65cb\u8f6c\u5b9e\u9645\u4e0a\u53ea\u662f\u5728\u5c06\u8282\u70b9\u4e0a\u4e0b\u79fb\u52a8\uff0c\u6240\u4ee5\u4e0d\u6539\u53d8\u4e8c\u53c9\u641c\u7d22\u6811\u7684\u6027\u8d28\u3002</p> \u5e73\u8861\u7684\u4fdd\u6301 <p>\u8ba9\u6211\u4eec\u5148\u56de\u987e\u4e00\u4e0b\u5728\u4e0a\u9762\u7ed9\u51fa\u7684\u4e00\u4e9b\u6027\u8d28\u4e2d\u7684\u7b2c 2 \u6761\uff1a \\(h(\\text{New L Left Subtree}) - h(\\text{L Right Subtree}) = 1\\)\u3002</p> <p>\u5728\u4ed4\u7ec6\u601d\u8003\u6574\u4e2a\u65cb\u8f6c\u8fc7\u7a0b\u4e2d\u6bcf\u4e00\u4e2a Subtree \u7684\u9ad8\u5ea6\u7684\u53d8\u5316\uff0c\u5373\u53ef\u5f97\u5230\u8bc1\u660e\u3002    </p> <p>\u800c RR Single Rotation \u5b8c\u5168\u5bf9\u79f0\uff0c\u6240\u4ee5\u4e0d\u518d\u8d58\u8ff0\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec01/#\u6362\u6839\u89c6\u89d2","title":"\u201c\u6362\u6839\u201d\u89c6\u89d2","text":"<p>\u73b0\u5728\u6211\u60f3\u5c1d\u8bd5\u7740\u7528\u6211\u81ea\u5df1\u7684\u65b9\u5f0f\u6765\u7406\u89e3\u8fd9\u4e2a\u95ee\u9898\u3002</p> <p>\u9996\u5148\u8ba9\u6211\u4eec\u4eba\u529b\u52a8\u753b\u4e00\u4e0b\u8fd9\u4e2a\u8fc7\u7a0b\uff08\u5212\u6389\uff09\uff1a</p> <p>LL Single Rotation</p> <p>\u6b64\u5916\uff0c\u8fd9\u91cc\u8981\u7d20\u7684\u547d\u540d\u90fd\u662f\u57fa\u4e8e Frame 1 \u7684\uff0c\u5bf9\u4e8e Frame 4 \u6765\u8bf4 L Right Subtree \u663e\u7136\u5df2\u7ecf\u4e0d\u662f L Right Subtree \u4e86\u3002</p> Frame 1Frame 2Frame 3Frame 4Frame 5 <pre><code>    flowchart TD\n        A(((\"Trouble\\nFinder\")))\n        B(((\"Left\\nChild\")))\n        C[/\"Right Subtree\"\\]\n        D[/\"L Left Subtree\"\\]\n        H((\"Trouble\\nMaker\"))\n        E[/\"L Right Subtree\"\\]\n\n        A === B\n        A === C\n        B === D === H\n        B === E</code></pre> <pre><code>    flowchart TD\n        A(((\"Trouble\\nFinder\")))\n        B(((\"Left\\nChild\")))\n        C[/\"Right Subtree\"\\]\n        D[/\"L Left Subtree\"\\]\n        H((\"Trouble\\nMaker\"))\n        E[/\"L Right Subtree\"\\]\n\n        A --- B\n        A === C\n        B === D === H\n        B === E</code></pre> <pre><code>    flowchart TD\n        B(((\"Left\\nChild\")))\n        D[/\"L Left Subtree\"\\]\n        E[/\"L Right Subtree\"\\]\n        H((\"Trouble\\nMaker\"))\n        A(((\"Trouble\\nFinder\")))\n        C[/\"Right Subtree\"\\]\n\n        A === C\n        B === D === H\n        B === E</code></pre> <pre><code>    flowchart TD\n        B(((\"Left\\nChild\")))\n        D[/\"L Left Subtree\"\\]\n        E[/\"L Right Subtree\"\\]\n        H((\"Trouble\\nMaker\"))\n        A(((\"Trouble\\nFinder\")))\n        C[/\"Right Subtree\"\\]\n\n        A === C\n        B === D === H\n        A === E</code></pre> <pre><code>    flowchart TD\n        A(((\"Trouble\\nFinder\")))\n        B(((\"Left\\nChild\")))\n        C[/\"Right Subtree\"\\]\n        D[/\"L Left Subtree\"\\]\n        E[/\"L Right Subtree\"\\]\n        H((\"Trouble\\nMaker\"))\n\n        B === D === H\n        B === A\n        A === E\n        A === C\n</code></pre> <p>\u9996\u5148\uff0c\u6211\u4eec\u9047\u5230\u7684\u95ee\u9898\u662f\u4ec0\u4e48\uff1f\u662f Trouble Maker \u8fdb\u6765\u4ee5\u540e\uff0cTrouble Finder \u53d1\u73b0 \\(h(T_l) - h(T_r) = 2\\)\u4e86\uff0c\u7528\u901a\u4fd7\u7684\u8bdd\u6765\u8bf4\u5c31\u662f\u5de6\u5b69\u5b50\u6811\u592a\u9ad8\u4e86\uff0c\u7136\u800c\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u5de6\u5b69\u5b50\u6811\u4f9d\u7136\u8fd8\u7ad9\u5728\u4e00\u4e2a\u53f0\u5b50\uff08Trouble Finder\uff09\u4e0a\u548c Trouble Finder \u6bd4\u8eab\u9ad8\uff0c\u6240\u4ee5\u6211\u4eec\u9700\u8981\u5c06\u5b83\u4ece\u53f0\u5b50\u4e0a\u8bf7\u4e0b\u6765\u3002\u4e5f\u5c31\u662f\u8bf4\uff0c\u65e2\u7136\u5de6\u5b69\u5b50\u6811\u592a\u9ad8\u4e86\uff0c\u90a3\u4e48\u6211\u4eec\u5c31\u4e0d\u5e0c\u671b\u8ba9\u5b83\u518d\u6210\u4e3a\u8c01\u7684\u5b69\u5b50\u6811\uff0c\u56e0\u4e3a\u6210\u4e3a\u8c01\u7684\u5b69\u5b50\u6811\u5fc5\u7136\u610f\u5473\u7740\u8fd9\u6761\u8def\u5f84\u4f1a\u66f4\u957f\u3002</p> <p>\u90a3\u4e48\u73b0\u5728\u6211\u4eec\u628a\u5b83\u4ece\u53f0\u5b50\u4e0a\u8bf7\u4e0b\u6765\uff0c\u4e5f\u5c31\u662f\u8bf4\u5272\u88c2\u5b83\u548c Trouble Finder \u7684\u4eb2\u5b50\u5173\u7cfb\uff08\u5bf9\u5e94 Frame 2\uff09\u8ba9\u5b83\u4eec\u540c\u53f0\u201c\u5bf9\u6297\u201d\uff08\u8fd9\u4e00\u6b65\u5728 <code>LL</code> \u548c <code>RR</code> \u53ef\u80fd\u663e\u5f97\u6bd4\u8f83\u591a\u4f59\uff0c\u4f46\u662f\u5728 <code>LR</code> \u548c <code>RL</code> \u5c31\u4f1a\u8ba9\u95ee\u9898\u6e05\u6670\u5f88\u591a\uff09\u3002</p> <p>\u7136\u800c\u6211\u4eec\u4ecd\u7136\u9700\u8981\u8ba9\u8fd9\u4e2a\u68ee\u6797\u91cd\u65b0\u53d8\u56de\u4e00\u4e2a\u6811\uff0c\u6240\u4ee5\u5c31\u9700\u8981\u91cd\u65b0\u4ece\u91cc\u9762\u627e\u5230\u6839\u8282\u70b9\uff0c\u663e\u7136\uff0c\u53ea\u80fd\u9009\u62e9 Trouble Finder \u65c1\u8fb9 \u7684 Left Child\u3002\u4f46\u662f\u4e3a\u4e86\u7ee7\u7eed\u7ef4\u62a4\u4e8c\u53c9\u641c\u7d22\u6811\u7684\u6027\u8d28\uff0c\u6240\u4ee5\u6211\u4eec\u9700\u8981\u5c06 L Right Subtree \u79fb\u690d\u5230 Trouble Finder \u5fc5\u5b9a\u7a7a\u7f3a\uff08\u56e0\u4e3a\u8fd9\u91cc\u539f\u5148\u662f Left Child\uff09\u7684\u5de6\u6307\u9488\u4e0a\u3002</p> <p>OK\uff0c\u4f60\u53ef\u80fd\u89c9\u5f97\u8fd9\u4e2a\u89e3\u91ca\u5bf9\u4e8e LL Single Rotation \u6765\u8bf4\u663e\u5f97\u5341\u5206\u591a\u6b64\u4e00\u4e3e\uff0c\u4f46\u662f\u8fd9\u90fd\u662f\u4e3a\u4e86\u7ed9\u540e\u9762\u505a\u7684\u94fa\u57ab\uff0c\u867d\u7136\u8fd9\u4e2a\u65b9\u6cd5\u770b\u8d77\u6765\u7e41\u7410\u5197\u4f59\uff0c\u4f46\u662f\u5df2\u7ecf\u8db3\u4ee5\u89e3\u91ca\u539f\u5148\u7684 Single Rotation \u65e0\u6cd5\u89e3\u91ca\u7684 LR &amp; RL \u64cd\u4f5c\u65b9\u6cd5\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec01/#lr--rl","title":"LR &amp; RL","text":"<p>\u9996\u5148\u6211\u4eec\u9700\u8981\u77e5\u9053\u4e3a\u4ec0\u4e48\u4e4b\u524d\u7684\u65b9\u6cd5\u4e0d\u884c\uff0c\u4e5f\u662f\u6211\u89c9\u5f97\u201c\u65cb\u8f6c\u201d\u8fd9\u4e2a\u505a\u6cd5\u5728\u8fd9\u4e2a\u63a8\u8fdb\u8fc7\u7a0b\u4e2d\u6bd4\u8f83\u5272\u88c2\u7684\u5730\u65b9\uff1a\uff08\u5bf9\u7167 #\u65cb\u8f6c\u89c6\u89d2 \u7684\u5185\u5bb9\u9605\u8bfb\uff09\u6211\u4eec\u53d1\u73b0\uff0c\u7531\u4e8e LL \u4e2d\u7684 Trouble Maker \u5728\u5de6\u4fa7\u5b69\u5b50\u6811\u4e0a\uff0c\u6240\u4ee5\u5728\u65cb\u8f6c\u8fc7\u7a0b\u4e2d\uff0c\u76f8\u5f53\u4e8e\u628a\u5b83\u201c\u62fd\u201d\u4e0a\u6765\u4e86\u3002\u7136\u800c\u5bf9\u4e8e L Right Subtree\uff0c\u65e0\u8bba\u662f\u65cb\u8f6c\u524d\u8fd8\u662f\u65cb\u8f6c\u540e\uff0c\u4e3a\u4e86\u7ef4\u62a4\u4e8c\u53c9\u641c\u7d22\u6811\u7684\u6027\u8d28\uff0c\u5b83\u90fd\u88ab\u63a5\u5728\u4e86\u6df1\u5ea6\u4e3a 1 \u7684\u8282\u70b9\u4e0a\uff0c\u6362\u53e5\u8bdd\u6765\u8bf4 L Right Subtree \u8d21\u732e\u7684\u9ad8\u5ea6\u5e76\u6ca1\u6709\u6539\u53d8\u3002\u5bf9\u4e8e RL \u7684\u60c5\u51b5\u4e5f\u662f\u540c\u7406\u7684\u3002\u6240\u4ee5\u6211\u4eec\u5e76\u4e0d\u80fd\u4f7f\u7528 LL Single Rotation \u7684\u65b9\u6cd5\u6765\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\u3002</p> <p>\u5173\u4e8e\u65cb\u8f6c\u89c6\u89d2</p> <p>\u5982\u679c\u4ece\u65cb\u8f6c\u89c6\u89d2\u6765\u8003\u8651\uff0c\u786e\u5b9e\u4e5f\u80fd\u8003\u8651\u8fd9\u4e2a\u8fc7\u7a0b\uff0c\u4f46\u4e00\u65b9\u9762\u8fc7\u4e8e\u590d\u6742\uff0c\u4e00\u65b9\u9762\u5b9e\u9645\u5b9e\u73b0\u8fc7\u7a0b\u4e2d\u4e5f\u5b8c\u5168\u53ef\u4ee5\u88ab\u4f18\u5316\uff0c\u6240\u4ee5\u6211\u5e0c\u671b\u4f7f\u7528\u6362\u6839\u7684\u89c6\u89d2\u6765\u7406\u89e3\u8fd9\u4e2a\u95ee\u9898\u3002</p> <p>\u90a3\u4e48\u6211\u4eec\u6362\u4e00\u4e2a\u601d\u8def\uff0c\u7528\u201c\u6362\u6839\u201d\u89c6\u89d2\u6765\u770b\u5f85\u8fd9\u4e2a\u95ee\u9898\uff1a</p> <p>LR Rotation</p> <p>\u8fd9\u91cc\u4e24\u4e2a Subtree \u63a5\u5230\u540c\u4e00\u4e2a Trouble Maker \u7684\u610f\u601d\u662f Trouble Maker \u53ef\u4ee5\u51fa\u73b0\u5728\u4e24\u8005\u4efb\u4e00\u4e2d\u3002</p> Frame 1Frame 2Frame 3Frame 4Frame 5 <pre><code>    flowchart TD\n        A(((\"Trouble\\nFinder\")))\n        B(((\"Left\\nChild\")))\n        C[/\"Right Subtree\"\\]\n        D((\"L Left\\nChild\"))\n        DA[/\"L Left Subtree\"\\]\n        H((\"Trouble\\nMaker\"))\n        E(((\"L Right\\nChild\")))\n        EA[/\"L Left Subtree\"\\]\n        EB[/\"L Right Subtree\"\\]\n\n        A === B\n        A === C\n        B === D === DA\n        B === E === EA --- H\n        E === EB --- H</code></pre> <pre><code>    flowchart TD\n        A(((\"Trouble\\nFinder\")))\n        B(((\"Left\\nChild\")))\n        C[/\"Right Subtree\"\\]\n        D((\"L Left\\nChild\"))\n        DA[/\"L Left Subtree\"\\]\n        H((\"Trouble\\nMaker\"))\n        E(((\"L Right\\nChild\")))\n        EA[/\"L Left Subtree\"\\]\n        EB[/\"L Right Subtree\"\\]\n\n        A --- B\n        A === C\n        B === D === DA\n        B --- E === EA --- H\n        E === EB --- H</code></pre> <pre><code>    flowchart TD\n\n        B(((\"Left\\nChild\")))\n        D((\"L Left\\nChild\"))\n        DA[/\"L Left Subtree\"\\]\n        H((\"Trouble\\nMaker\"))\n        E(((\"L Right\\nChild\")))\n        EA[/\"L Left Subtree\"\\]\n        EB[/\"L Right Subtree\"\\]\n        A(((\"Trouble\\nFinder\")))\n        C[/\"Right Subtree\"\\]\n\n        A === C\n        B === D === DA\n        E === EA --- H\n        E === EB --- H</code></pre> <pre><code>    flowchart TD\n\n        B(((\"Left\\nChild\")))\n        D((\"L Left\\nChild\"))\n        DA[/\"L Left Subtree\"\\]\n        H((\"Trouble\\nMaker\"))\n        E(((\"L Right\\nChild\")))\n        EA[/\"L Left Subtree\"\\]\n        EB[/\"L Right Subtree\"\\]\n        A(((\"Trouble\\nFinder\")))\n        C[/\"Right Subtree\"\\]\n\n        A === C\n        B === D === DA\n        E --- EA --- H\n        E --- EB --- H</code></pre> <pre><code>    flowchart TD\n\n        D((\"L Left\\nChild\"))\n        B(((\"Left\\nChild\")))\n        DA[/\"L Left Subtree\"\\]\n        E(((\"L Right\\nChild\")))\n        EA[/\"L Left Subtree\"\\]\n        EB[/\"L Right Subtree\"\\]\n        H((\"Trouble\\nMaker\"))\n        A(((\"Trouble\\nFinder\")))\n        C[/\"Right Subtree\"\\]\n\n        E === B\n        E === A\n        B === D === DA\n        B === EA --- H\n        A === EB --- H\n        A === C</code></pre> \u5173\u4e8e\u8bb0\u5fc6 <p>\u8bb0\u5fc6\u8fd9\u4e2a\u64cd\u4f5c\u5982\u4f55\u505a\u7684\u8bdd\uff0c\u6211\u7684\u8bb0\u5fc6\u65b9\u6cd5\u662f\u8fd9\u6837\u7684\uff1a</p> Frame 1Frame 2Frame 3Frame 4 <pre><code>    flowchart TD\n        A(((\"Trouble\\nFinder\")))\n        B(((\"Left\\nChild\")))\n        C[/\"Right Subtree\"\\]\n        D((\"L Left\\nChild\"))\n        DA[/\"L Left Subtree\"\\]\n        H((\"Trouble\\nMaker\"))\n        E(((\"L Right\\nChild\")))\n        EA[/\"L Left Subtree\"\\]\n        EB[/\"L Right Subtree\"\\]\n\n        A === B\n        A === C\n        B === D === DA\n        B === E === EA --- H\n        E === EB --- H</code></pre> <pre><code>    flowchart TD\n        A(((\"Trouble\\nFinder\")))\n        B(((\"Left\\nChild\")))\n        C[/\"Right Subtree\"\\]\n        D((\"L Left\\nChild\"))\n        DA[/\"L Left Subtree\"\\]\n        H((\"Trouble\\nMaker\"))\n        E(((\"L Right\\nChild\")))\n        EA[/\"L Left Subtree\"\\]\n        EB[/\"L Right Subtree\"\\]\n\n        A --- B\n        A --- E\n        A === C\n        B === D === DA\n        B --- E === EA --- H\n        E === EB --- H</code></pre> <pre><code>    flowchart TD\n        A(((\"Trouble\\nFinder\")))\n        B(((\"Left\\nChild\")))\n        D((\"L Left\\nChild\"))\n        DA[/\"L Left Subtree\"\\]\n        H((\"Trouble\\nMaker\"))\n        E(((\"L Right\\nChild\")))\n        EA[/\"L Left Subtree\"\\]\n        EB[/\"L Right Subtree\"\\]\n        C[/\"Right Subtree\"\\]\n\n        A --- B\n        E --- B \n        E --- A\n        B === D === DA\n        B --- EA --- H\n        A --- EB --- H\n        A === C</code></pre> <pre><code>    flowchart TD\n        A(((\"Trouble\\nFinder\")))\n        B(((\"Left\\nChild\")))\n        D((\"L Left\\nChild\"))\n        DA[/\"L Left Subtree\"\\]\n        H((\"Trouble\\nMaker\"))\n        E(((\"L Right\\nChild\")))\n        EA[/\"L Left Subtree\"\\]\n        EB[/\"L Right Subtree\"\\]\n        C[/\"Right Subtree\"\\]\n\n        E --- B \n        E --- A\n        B === D === DA\n        B --- EA --- H\n        A --- EB --- H\n        A === C</code></pre> <p>\u7528\u8bed\u8a00\u6982\u62ec\u5c31\u662f\uff0c\u627e\u5230\u5173\u952e\u7684\u90a3\u4e09\u4e2a\u70b9\uff0c\u7136\u540e\u628a\u6700\u4e0b\u9762\u7684\u9876\u5230\u4e0a\u9762\u53bb\uff0c\u5269\u4e0b\u4e24\u4e2a\u4f5c\u4e3a\u5de6\u53f3\u5b69\u5b50\u6811\uff0c\u539f\u5148\u7684\u90a3\u4e2a\u70b9\u7684\u5de6\u53f3\u5b69\u5b50\u6811\u5219\u5bf9\u5e94\u5730\uff0c\u5de6\u5b69\u5b50\u6811\u63a5\u5230\u5de6\u8fb9\u7a7a\u7f3a\u7684\u53f3\u5b69\u5b50\u6811\u4e0a\uff0c\u53f3\u5b69\u5b50\u6811\u63a5\u5230\u53f3\u8fb9\u7a7a\u7f3a\u7684\u5de6\u5b69\u5b50\u6811\u4e0a\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec01/#\u5176\u4ed6\u95ee\u9898","title":"\u5176\u4ed6\u95ee\u9898","text":"<p>\u5982\u679c\u4e00\u4e2a Trouble \u4ea7\u751f\u540e\uff0c\u51fa\u73b0\u4e86\u591a\u4e2a Trouble Finder\uff0c\u8be5\u5982\u4f55\u5904\u7406\uff1f</p> <p>\u9996\u5148\uff0c\u8bf7\u56de\u987e\u4e00\u4e0b #\u64cd\u4f5c \u4e2d\u88ab\u52a0\u7c97\u7684\u8fd9\u4e00\u53e5\u8bdd\uff0c\u300c\u4ee5\u300e\u8ddd\u79bb\u6848\u53d1\u73b0\u573a\u6700\u8fd1\u7684 Trouble Finder\u300f\u4e3a\u6839\u7684\u5b69\u5b50\u6811\u300d\u3002\u4e5f\u5c31\u662f\u8bf4\uff0c\u6211\u4eec\u73b0\u5728\u5df2\u7ecf\u6709\u4e86\u89e3\u51b3\u6700\u8fd1\u7684 Trouble Finder \u7684\u65b9\u6848\u3002</p> <p>\u611f\u6027\u7684\u601d\u8003\uff0cAVL \u7684\u201c\u5e73\u8861\u201d\u53ef\u4ee5\u7531\u9012\u5f52\u5f62\u5f0f\u5b9a\u4e49\uff0c\u5177\u4f53\u6765\u8bf4\u8861\u91cf\u7684\u662f\u5de6\u53f3\u5b69\u5b50\u6811\u7684\u201c\u9ad8\u5ea6\u201d\u5dee\u3002\u5f53\u6211\u4eec\u89e3\u51b3\u4e86\u4e00\u4e2a Trouble Finder\uff0c\u610f\u5473\u7740\u6211\u4eec\u8ba9 Trouble Finder \u7684\u6700\u9ad8\u7684\u90a3\u4e2a\u5b69\u5b50\u6811\u9ad8\u5ea6 -1\uff0c\u8fd9\u4e5f\u610f\u5473\u7740\u4ee5 Trouble Finder \u4e3a\u6839\u7684\u90a3\u4e2a\u5b69\u5b50\u6811\u9ad8\u5ea6 -1\uff0c\u8fd9\u4e5f\u610f\u5473\u7740\u5176\u6240\u6709\u7236\u8282\u70b9\u7684\u5e73\u8861\u56e0\u5b50\u90fd\u4f1a\u76f8\u5e94\u5730\u53d8\u5316\u3002</p> <p>\u4e00\u4e2a Trouble \u5f53\u4e14\u4ec5\u6709\u4e00\u4e2a Trouble Maker\uff0c\u800c\u4e14\u5b83\u5fc5\u5b9a\u662f Trouble Finder \u6240\u5173\u6ce8\u7684\u90a3\u4e2a\u201c\u6700\u957f\u8def\u5f84\u201d\u7684\u7aef\u70b9\uff0c\u8fd9\u4e5f\u610f\u5473\u7740\u6240\u6709\u7684\u5b50 Trouble Finder \u90fd\u5728\u5bf9\u5e94\u7684\u7236 Trouble Finder \u7684\u201c\u6700\u957f\u8def\u5f84\u201d\u4e0a\u3002\u800c\u73b0\u5728\u6211\u4eec\u8ba9\u5b50 Trouble Finder \u552f\u4e00\uff08\u5982\u679c\u4e0d\u552f\u4e00\uff0c\u90a3\u5728\u8fd9\u4e2a Trouble Maker \u5230\u6765\u4e4b\u524d\u5c31\u5df2\u7ecf\u5b58\u5728 Trouble \u4e86\uff09\u7684\u6700\u957f\u8def\u5f84\u4e5f\u5e94\u5f53\u4f1a -1\u3002\u800c\u8fd9\u5fc5\u5c06\u5bfc\u81f4\u5176\u5e73\u8861\u56e0\u5b50\u7684\u7edd\u5bf9\u503c -1\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec01/#splay-\u6811","title":"Splay \u6811","text":"<p>link</p> <p>OI Wiki: https://oi-wiki.org/ds/splay/</p> <p>Splay \u6811\uff0c\u5373\u4f38\u5c55\u6811\uff0c\u60f3\u8981\u89e3\u51b3\u7684\u95ee\u9898\u548c AVL \u6811\u7c7b\u4f3c\uff0c\u53ea\u4e0d\u8fc7 Splay \u6811\u5e0c\u671b\u8fbe\u5230\u7684\u76ee\u6807\u662f\u5728\u644a\u8fd8(Amortized)\u590d\u6742\u5ea6\\(O(\\log N)\\)\u7684\u60c5\u51b5\u4e0b\u5b8c\u6210\u5927\u90e8\u5206\u5bf9\u70b9\u64cd\u4f5c\u3002</p> <p>\u6211\u4eec\u77e5\u9053\uff0c\u4e3a\u4f7f AVL \u4fdd\u6301\u5e73\u8861\uff0c\u6211\u4eec\u9700\u8981\u7ef4\u62a4\u4ece\u6839\u8282\u70b9\u5230 Trouble Maker \u8fd9\u6761\u8def\u5f84\u4e0a\u6240\u6709\u70b9\u7684\u5e73\u8861\u56e0\u5b50\u3002\u800c Splay \u5219\u4e0d\u518d\u7ef4\u62a4\u8fd9\u4e9b\u4fe1\u606f\uff0c\u8fd9\u610f\u5473\u7740\u6211\u4eec\u65e0\u6cd5\u4fdd\u8bc1 Splay \u6811\u7684\u72b6\u6001\u90fd\u662f\u5e73\u8861\u7684\uff0c\u4f46\u662f\u6211\u4eec\u5e0c\u671b\u5b83\u5c3d\u53ef\u80fd\u5e73\u8861\u3002\u5177\u4f53\u6765\u8bf4\u5c31\u662f\u5bf9\u4e8e \\(M\\) \u6b21\u4efb\u610f\u64cd\u4f5c\uff0c\u5176\u65f6\u95f4\u590d\u6742\u5ea6\u90fd\u4e3a \\(O(M\\log N)\\)\uff0c\u5747\u644a\u4e0b\u6765\u8fd9 \\(M\\) \u4e2a\u64cd\u4f5c\u6bcf\u4e00\u4e2a\u90fd\u9700\u8981 \\(O(\\log N)\\)\u3002</p> <p>\u5bf9\u4e8e\u4e00\u4e2a\u6811\uff0c\u6211\u4eec\u5bf9\u5176\u8282\u70b9\u8fdb\u884c\u7684\u64cd\u4f5c\u53ef\u80fd\u662f\uff1a\u589e\u70b9\u3001\u5220\u70b9\u3001\u6539\u70b9\u3001\u67e5\u70b9\u7b49\u7b49\uff0c\u800c\u4e0d\u540c\u7c7b\u578b\u7684\u64cd\u4f5c\u5f00\u9500\u53ef\u80fd\u4e0d\u5c3d\u76f8\u540c\u3002\u7b80\u5355\u7684\u8ba1\u7b97\u5176\u5e73\u5747\u503c\u5219\u5ffd\u7565\u4e86\u8fd9\u4e9b\u64cd\u4f5c\u4e4b\u95f4\u4e92\u76f8\u7684\u5f71\u54cd\u6216\u8005\u662f\u64cd\u4f5c\u9891\u7387\u7684\u95ee\u9898\uff0c\u6240\u4ee5\u6211\u4eec\u8fd9\u91cc\u4f7f\u7528\u644a\u8fd8\u590d\u6742\u5ea6\u6765\u63cf\u8ff0\u5176\u6548\u7387\u3002</p> <p>\u5173\u4e8e\u644a\u8fd8\u7684\u95ee\u9898\u6211\u4eec\u8fd8\u4f1a\u5728\u4e4b\u540e\u8fdb\u4e00\u6b65\u6df1\u5165\u3002</p> <p>\u90a3\u4e48\u8bf4\u4e86\u8fd9\u4e48\u591a\uff0cSplay \u662f\u600e\u4e48\u5b9e\u73b0\u8fd9\u4e00\u76ee\u6807\u7684\u5462\uff1f</p> <p>Splay \u7684\u6838\u5fc3\u601d\u60f3\u5c31\u662f\uff0c\u6bcf\u5f53\u6211\u4eec\u8bbf\u95ee\u4e00\u4e2a\u8282\u70b9\uff08\u6bd4\u5982\u67e5\u8be2\u67d0\u4e2a\u70b9\u3001\u63d2\u5165\u67d0\u4e2a\u70b9\uff0c\u751a\u81f3\u662f\u5220\u9664\u67d0\u4e2a\u70b9\uff09\uff0c\u6211\u4eec\u5c31\u901a\u8fc7\u4e00\u7cfb\u5217\u64cd\u4f5c\u5c06\u76ee\u6807\u70b9\u8f6c\u79fb\u5230\u6839\u90e8\uff0c\u5f62\u8c61\u4e0a\u7406\u89e3\u5c31\u662f\u4e0d\u65ad\u65cb\u8f6c\u6574\u4e2a\u6811\u7684\u6784\u9020\uff0c\u77e5\u9053\u628a\u70b9\u8f6c\u5230\u6839\u90e8\u3002</p> <p>\u4f8b\u5982\u6211\u4eec\u67e5\u8be2\u70b9 \\(k_1\\)\uff0c\u5219\u4f1a\u901a\u8fc7\u65cb\u8f6c\u5c06\u5b83\u8f6c\u5230\u6839\u3002</p> Frame 1Frame 2Frame 3 <p></p> <p></p> <p></p> <p>\u53ef\u4ee5\u53d1\u73b0\uff0cFrame 1 ~ 2 \u5c31\u662f\u6211\u4eec\u524d\u9762\u63d0\u5230\u8fc7\u7684 LR Rotation\uff0c\u800c Frame 2 ~ 3 \u5c31\u662f\u7ecf\u8fc7\u4e86\u4e24\u6b21 LL Rotation\u3002\u5f53\u7136\uff0c\u5728 Splay \u91cc\u8fd9\u4e9b\u64cd\u4f5c\u90fd\u6709\u4e86\u65b0\u7684\u540d\u5b57\u3002</p> <p>\u8fd9\u4e2a\u4f8b\u5b50\u53ea\u662f\u4e3a\u4e86\u7ed9\u8bfb\u8005\u4e00\u4e2a\u521d\u59cb\u5370\u8c61\uff0c\u4e4b\u540e\u6211\u4eec\u5c06\u66f4\u8be6\u7ec6\u3001\u51c6\u786e\u7684\u4ecb\u7ecd\u64cd\u4f5c\u3002</p> <p>\uff08\u6ca1\u73a9\u8fc7\u53ef\u80fd\u542c\u4e0d\u592a\u61c2\uff09\u4e0d\u77e5\u9053\u5927\u5bb6\u6709\u6ca1\u6709\u73a9\u8fc7\u90a3\u79cd\u7535\u5b50\u6e38\u620f\uff0c\u5c31\u662f\u6709\u597d\u591a\u8f6c\u76d8\uff0c\u76f8\u90bb\u8f6c\u76d8\u4e4b\u95f4\u6709\u4ea4\u754c\u5904\uff0c\u8fd9\u4e9b\u4ea4\u754c\u70b9\u4e0a\u90fd\u4f1a\u6709\u5706\u7403\uff0c\u5f53\u4e00\u4e2a\u8f6c\u76d8\u65cb\u8f6c\u7684\u65f6\u5019\uff0c\u5176\u5706\u5468\u4e0a\u7684\u7403\u4f53\u90fd\u4f1a\u8ddf\u7740\u8fd9\u4e2a\u5706\u5468\u8f6c\u52a8\u3002\u901a\u8fc7\u4e0d\u505c\u8f6c\u52a8\u76f8\u90bb\u7684\u5706\u76d8\uff0c\u6211\u4eec\u53ef\u4ee5\u5b9e\u73b0\u628a\u67d0\u4e2a\u4f4d\u7f6e\u7684\u5706\u7403\u8f6c\u79fb\u5230\u53e6\u5916\u4e00\u4e2a\u4f4d\u7f6e\u3002\u800c Splay \u5dee\u4e0d\u591a\u662f\u8fd9\u4e48\u4e2a\u611f\u89c9\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec01/#\u57fa\u672c\u64cd\u4f5c","title":"\u57fa\u672c\u64cd\u4f5c","text":"<p>\u9996\u5148\u6211\u4eec\u505a\u4e00\u4e2a\u7ea6\u5b9a\uff0c\u5bf9\u4e8e\u4efb\u610f\u4e00\u4e2a\u8282\u70b9 X\uff0c\u6211\u4eec\u8bb0\u5176\u7236\u8282\u70b9\u4e3a P(Parent)\uff0c\u5176\u7236\u8282\u70b9\u7684\u7236\u8282\u70b9\u4e3a G(Grandparent)\u3002</p> <ul> <li>\u5f53\u6211\u4eec\u8bbf\u95ee\u5230\u67d0\u4e2a\u70b9 X \u65f6\uff1a<ul> <li>\u5982\u679c P \u662f\u6839\u8282\u70b9\uff0c\u5219\u76f4\u63a5\u8fdb\u884c\u4e00\u6b21 Single Rotation\uff0c\u5c06 X \u8f6c\u5230\u6839\u8282\u70b9\uff1b</li> <li>\u5982\u679c P \u4e0d\u662f\u6839\u8282\u70b9\uff1a<ul> <li>\u5f53\u60c5\u51b5\u4e3a LR / RL \u65f6\uff0c\u8fdb\u884c\u4e00\u6b21 LR Rotation \u6216 RL Rotation\uff0c\u6211\u4eec\u79f0\u4e4b\u4e3a zig-zag\uff1b</li> <li>\u5f53\u60c5\u51b5\u4e3a LL / RR \u65f6\uff0c\u8fdb\u884c\u4e24\u6b21 Single Rotation\uff0c\u4f7f\u5f97 X\u3001P\u3001G \u7684\u987a\u5e8f\u9006\u8f6c\uff0c\u50cf\u8df7\u8df7\u677f\u4e00\u6837\uff0c\u6211\u4eec\u79f0\u4e4b\u4e3a zig-zig\uff1b</li> </ul> </li> <li>\u4e0d\u65ad\u5bf9 X \u8fdb\u884c Splay \u64cd\u4f5c\uff0c\u76f4\u5230 X \u6210\u4e3a\u6839\u8282\u70b9\uff1b</li> </ul> </li> </ul> <p></p> <p>\u53ef\u4ee5\u53d1\u73b0\uff0c\u5176\u5177\u4f53\u64cd\u4f5c\u57fa\u672c\u5c31\u548c AVL \u6811\u7684\u76f8\u5173\u64cd\u4f5c\u6709\u5f88\u5927\u91cd\u5408\u3002</p> <p>\u6548\u679c</p> <p>Splaying not only moves the accessed node to the root, but also roughly halves the depth of most nodes on the path.</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec01/#\u5bf9\u70b9\u64cd\u4f5c","title":"\u5bf9\u70b9\u64cd\u4f5c","text":"<p>\u7531\u4e8e Splay Tree \u9664\u4e86\u5728\u5b8c\u6210\u6240\u6709\u64cd\u4f5c\u4ee5\u540e\u90fd\u9700\u8981\u8fdb\u884c\u4e00\u6b21 Splay \u64cd\u4f5c\uff0c\u5176\u4ed6\u90e8\u5206\u90fd\u548c BST \u4e00\u6837\uff0c\u6240\u4ee5\u8fd9\u91cc\u53ea\u7b80\u5355\u4ecb\u7ecd\u4e00\u4e0b Splay \u7684\u90e8\u5206\u3002</p> <p>Find X</p> <p>\u6839\u636e BST \u7684\u6027\u8d28\uff0c\u53ef\u4ee5\u5728 \\(O(\\log N)\\) \u7684\u65f6\u95f4\u91cc\u627e\u5230 \\(X\\)\uff0c\u63a5\u4e0b\u6765\u901a\u8fc7\u65cb\u8f6c\u64cd\u4f5c\uff0c\u5c06 \\(X\\) \u4e0d\u65ad\u65cb\u8f6c\u81f3\u6839\uff0c\u6700\u7ec8\u76f4\u63a5\u53d6\u51fa Root \u5373\u4e3a\u7ed3\u679c\u3002   </p> <p>Remove X</p> <p>\u6839\u636e BST \u7684\u6027\u8d28\uff0c\u53ef\u4ee5\u5728 \\(O(\\log N)\\) \u7684\u65f6\u95f4\u91cc\u627e\u5230 \\(X\\)\uff0c\u63a5\u4e0b\u6765\u901a\u8fc7\u65cb\u8f6c\u64cd\u4f5c\uff0c\u5c06 \\(X\\) \u4e0d\u65ad\u65cb\u8f6c\u81f3\u6839\uff0c\u63a5\u4e0b\u6765\u5220\u9664 Root \u8282\u70b9\uff0c\u5e76\u5728\u7ef4\u62a4 BST \u6027\u8d28\u7684\u60c5\u51b5\u4e0b\u9012\u5f52\u5730\u5408\u5e76\u5de6\u53f3\u5b69\u5b50\u6811\u5373\u53ef\u3002</p> <p>Find Max</p> <p>\u6839\u636e BST \u7684\u6027\u8d28\uff0c\u53ef\u4ee5\u5728 \\(O(\\log N)\\) \u7684\u65f6\u95f4\u91cc\u627e\u5230\u6700\u5927\u503c\uff0c\u5c06\u5b83\u65cb\u8f6c\u5230\u6839\u90e8\u4ee5\u540e\uff0c\u53ef\u4ee5\u53d1\u73b0\u5b83\u6ca1\u6709\u53f3\u5b69\u5b50\u6811\uff0c\u76f4\u63a5\u5220\u6389\u5c31\u884c\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec01/#\u644a\u8fd8\u5206\u6790","title":"\u644a\u8fd8\u5206\u6790","text":"<p>\u524d\u7f6e\u9605\u8bfb</p> <p>\u5173\u4e8e\u644a\u8fd8\u5206\u6790\u7684\u57fa\u672c\u77e5\u8bc6\uff0c\u8bf7\u67e5\u770b Topic 1 | Amortized Analysis\u3002</p> <p>\u6b64\u5904\uff0c\u6211\u4eec\u5c06\u4f7f\u7528\u52bf\u80fd\u6cd5\u6765\u5206\u6790 Splay \u7684\u644a\u8fd8\u590d\u6742\u5ea6\uff0c\u7531\u4e8e\u8bfe\u4ef6\u7701\u7565\u4e86\u5f88\u591a\u7ec6\u8282\u4e0a\u7684\u89e3\u91ca\uff0c\u6240\u4ee5\u6211\u8fd9\u91cc\u4f1a\u8865\u5145\u975e\u5e38\u591a\u5185\u5bb9\u3002</p> <p>reference</p> <p>http://www2.hawaii.edu/~nodari/teaching/f19/scribes/notes06.pdf</p> <p>\u5f00\u59cb\u5206\u6790\u4e4b\u524d\uff0c\u6211\u4eec\u9996\u5148\u9700\u8981\u660e\u786e\u5206\u6790\u7684\u76ee\u6807\uff1a</p> <p>\u5bf9\u4e8e Splay\uff0c\u5b83\u4e0d\u50cf\u6211\u4eec\u5728 Topic 1 | Amortized Analysis \u63d0\u5230\u7684\u90a3\u4e9b\u6848\u4f8b\u4e00\u6837\uff0c\u5b58\u5728\u660e\u663e\u7684\u51cf\u52bf\u548c\u589e\u52bf\u884c\u4e3a\u3002\u5bf9\u4e8e Splay \u6765\u8bf4\uff0c\u6240\u6709\u6211\u4eec\u63d0\u5230\u7684\u64cd\u4f5c\u90fd\u4f9d\u8d56\u4e8e\u5c06\u76ee\u6807\u70b9\u65cb\u8f6c\u5230\u6839\u6765\u5b9e\u73b0\uff0c\u800c\u8fd9\u4e5f\u6210\u4e3a\u5176\u4e3b\u8981\u5f00\u9500\uff08\u90e8\u5206\u5e38\u6570\u64cd\u4f5c\u663e\u7136\u88ab\u8986\u76d6\uff0c\u63d2\u5165\u4e4b\u7c7b\u7684\u64cd\u4f5c\u4e4b\u6240\u4ee5\u80fd\u88ab\u5ffd\u7565\u7684\u539f\u56e0\uff0c\u53ef\u4ee5\u53c2\u8003 ltgg \u7684\u8fd9\u7bc7\u6587\u7ae0\uff09\u3002\u5176\u4e2d\u6211\u4eec\u4f1a\u7528\u5230\u82e5\u5e72\u6b21 <code>zig</code>\u3001<code>zig-zag</code>\u3001<code>zig-zig</code> \u7684\u64cd\u4f5c\u3002</p> <p>\u56e0\u6b64\u6211\u4eec\u53ef\u4ee5\u8ba4\u4e3a\uff0c\u6211\u4eec\u8981\u5206\u6790\u7684\u76ee\u6807\u4e3a\uff1a</p> \\[ T_{\\text{rotate }x\\text{ to root}} = T_{\\text{zig}} + \\sum{ {T_{\\text{zig-zag}}}_i } + \\sum{ {T_{\\text{zig-zig}}}_i } \\] <p>\u4e0a\u9762\u4e09\u4e2a\u90e8\u5206\u6bcf\u4e00\u4e2a\u90fd\u6709\u53ef\u80fd\u662f \\(0\\)\uff0c\u800c <code>zig</code> \u6700\u591a\u53ea\u4f1a\u53d1\u751f\u4e00\u6b21\uff01</p> <p>\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u9700\u8981\u8bbe\u8ba1\u4e00\u4e2a\u52bf\u80fd\u51fd\u6570 \\(\\Phi(x)\\)\uff0c\u5e76\u4e14\u6839\u636e\u6211\u4eec\u63d0\u5230\u8fc7\u7684\u52bf\u80fd\u5206\u6790\u6cd5\u7684\u7279\u6027\uff0c\\(\\Phi(x)\\) \u5e94\u8be5\u5177\u6709\u8fd9\u4e48\u51e0\u4e2a\u7279\u5f81\uff1a</p> <ul> <li>\u5f00\u9500\u5927\u7684\u64cd\u4f5c\u5e94\u5f53\u503e\u5411\u8ba9\u52bf\u80fd\u964d\uff0c\u5f00\u9500\u5c0f\u7684\u64cd\u4f5c\u5e94\u5f53\u503e\u5411\u8ba9\u52bf\u80fd\u5347\uff1b</li> <li>\u52bf\u80fd\u9ad8\u503e\u5411\u4e8e\u8ba9\u67d0\u4e9b\u64cd\u4f5c\u5f00\u9500\u5927\uff0c\u52bf\u80fd\u4f4e\u503e\u5411\u4e8e\u8ba9\u67d0\u4e9b\u64cd\u4f5c\u5f00\u9500\u5c0f\uff1b</li> <li>\\(\\Phi(final) &gt; \\Phi(initial)\\)\uff1b</li> </ul> <p>\u4e8e\u662f\u8fd9\u91cc\u6211\u4eec\u8bbe\u8ba1\u7684\u52bf\u80fd\u51fd\u6570\u4e3a\uff1a</p> \\[ \\Phi(T) = \\sum_{des \\in T} \\log Size(des) = \\sum_{des \\in T} Rank(des)\\\\ \\begin{aligned}     &amp;\\text{Where } des \\text{ means the descendant of } T \\text{,}\\\\     &amp;\\text{and } Size(des) \\text{ means the number of the nodes of } des \\text{.} \\\\     &amp;\\text{And we note } Rank(des) = \\log Size(des) \\approx Height(des) \\text{.} \\end{aligned} \\] <p>\u7528\u8bed\u8a00\u63cf\u8ff0\u4e00\u4e0b\u5c31\u662f\uff0c\u5bf9\u4e8e\u67d0\u4e2a\u5b69\u5b50\u6811 \\(T\\)\uff0c\u5176\u52bf\u80fd\u51fd\u6570 \\(\\Phi(T)\\) \u7b49\u4e8e\u4ee5\u6240\u6709\u5b83\u7684\u540e\u4ee3\u4e3a\u6839\u7684\u5b69\u5b50\u6811\u7684\u5927\u5c0f\u53d6\u5bf9\u6570\u4ee5\u540e\u6c42\u548c\u3002</p> <p>Rank v.s. Height</p> <p>\u8fd9\u91cc\u9700\u8981\u6ce8\u610f\u7684\u4e00\u4e2a\u70b9\u662f\uff0c\u867d\u7136 \\(Rank(des) \\approx Height(des)\\)\uff0c\u4f46\u662f\u6211\u4eec\u4e0d\u5e94\u8be5\u7528 \\(Height()\\) \u6765\u4ee3\u66ff \\(Rank()\\)\uff0c\u4e3b\u8981\u539f\u56e0\u662f\u5728\u65cb\u8f6c\u8fc7\u7a0b\u4e2d\uff0c\\(Rank()\\) \u4e0d\u4f1a\u53d8\u5316\uff08\u56e0\u4e3a \\(Size()\\) \u4e0d\u4f1a\u53d8\u5316\uff09\uff0c\u4f46\u662f \\(Height()\\) \u53ef\u80fd\u53d8\u5316\u3002\u6362\u53e5\u8bdd\u6765\u8bf4\uff0c\u5982\u679c\u9009\u7528 \\(Height()\\) \u4f5c\u4e3a\u52bf\u80fd\u51fd\u6570\uff0c\u6211\u4eec\u5c31\u4e0d\u5f97\u5df2\u8003\u8651\u6574\u68f5\u6811\uff0c\u800c\u975e\u53ea\u9700\u8981\u8003\u8651\u5f53\u524d\u65cb\u8f6c\u6d89\u53ca\u7684\u5b69\u5b50\u6811\u3002</p> <p>\u5173\u4e8e\u6b63\u786e\u6027\u7684\u8bf4\u660e\uff0c\u6211\u4f1a\u653e\u5728\u4e4b\u540e\u7684\u8fc7\u7a0b\u4e2d\u4e00\u4e2a\u4e2a\u63d2\u5165\uff0c\u5b83\u4eec\u4f1a\u88ab\u5305\u88f9\u5728 <code>key-point</code> \u6587\u5b57\u6846\u4e2d\uff0c\u8bf7\u6ce8\u610f\u8fd9\u4e9b\u5185\u5bb9\u3002\u63a5\u4e0b\u6765\u6211\u4eec\u5c31\u53ef\u4ee5\u5f00\u59cb\u5206\u6790\u4e86\uff0c\u6839\u636e\u6211\u4eec\u7ed9\u5b9a\u7684\u76ee\u6807\uff1a</p> \\[ T_{\\text{rotate }x\\text{ to root}} = T_{\\text{zig}} + \\sum{ {T_{\\text{zig-zag}}}_i } + \\sum{ {T_{\\text{zig-zig}}}_i } \\] <p>\u6211\u4eec\u5229\u7528\u5747\u644a\u5206\u6790\uff0c\u9700\u8981\u5f97\u5230\u4e00\u4e2a\u5e73\u6ed1\u4e0a\u754c\uff1a</p> \\[ \\hat{c}_{\\text{rotate }x\\text{ to root}} = \\hat{c}_{\\text{zig}} + \\sum{ {\\hat{c}_{\\text{zig-zag}}}_i } + \\sum{ {\\hat{c}_{\\text{zig-zig}}}_i } \\] <p>\u800c\u6211\u4eec\u9700\u8981\u8bc1\u660e \\(\\hat{c}_{\\text{rotate }x\\text{ to root}} = O(\\log{N})\\)\uff0c\u73b0\u5728\u6211\u4eec\u9700\u8981\u5206\u522b\u5206\u6790 <code>zig</code>\u3001<code>zig-zag</code>\u3001<code>zig-zig</code>\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec01/#zig","title":"zig","text":"<p>Amortized Analysis for Zig</p> <p></p> \\[ \\begin{aligned}     {\\hat{c}_{\\text{zig}}}_i     &amp;= {c_{\\text{zig}}}_i + \\Phi_{i}(X) - \\Phi_{i-1}(P) \\\\     &amp;= 1 + Rank_{i}(X) - Rank_{i-1}(X) +  Rank_{i}(P) - Rank_{i-1}(P) \\end{aligned} \\] <p>\u89c2\u5bdf\u914d\u56fe\uff0c\\(X\\) \u591a\u4e86 \\(P\\) \u548c \\(C\\) \u4f5c\u4e3a\u5b50\u55e3\uff0c\u800c \\(P\\) \u60b2\u60e8\u5730\u5931\u53bb\u4e86 \\(X\\) \u4e00\u65cf\uff0c\u751a\u81f3\u6210\u4e86 \\(X\\) \u7684\u540e\u4ee3\uff0c\u5373 \\(X\\) \u76db \\(P\\) \u8870\uff0c\u56e0\u6b64\u5c31\u6709\u4e0d\u7b49\u5f0f\uff1a</p> \\[ \\left\\{     \\begin{aligned}         &amp; Rank_{i}(X) - Rank_{i-1}(X) \\geq 0\\\\         &amp; Rank_{i}(P) - Rank_{i-1}(P) \\leq 0     \\end{aligned}     \\right. \\] <p>\u6240\u4ee5\u6211\u4eec\u53ef\u4ee5\u505a\u7b80\u5355\u7684\u7f29\u653e\uff1a</p> \\[ \\begin{aligned}     {\\hat{c}_{\\text{zig}}}_i     &amp;= 1 + \\underbrace{Rank_{i}(X) - Rank_{i-1}(X)}_{\\geq 0} + \\underbrace{Rank_{i}(P) - Rank_{i-1}(P)}_{\\leq 0} \\\\     &amp;\\leq 1 + Rank_{i}(X) - Rank_{i-1}(X) \\end{aligned} \\] <p>\u4e3a\u4ec0\u4e48\u4e0d\u662f\u53e6\u5916\u4e00\u79cd\u9009\u62e9 / \u4e3a\u4f55\u8fd9\u6837\u7f29\u653e\uff1f</p> <p>\u8fd9\u4e00\u90e8\u5206\u5728 cy \u7684 PPT \u91cc\u5e76\u6ca1\u6709\u8be6\u7ec6\u8bf4\u660e\uff0c\u4f46\u662f\u6211\u8ba4\u4e3a\u8fd9\u662f\u8fd9\u4e2a\u5206\u6790\u65b9\u6cd5\u6210\u7acb\u4e00\u4e2a\u975e\u5e38\u91cd\u8981\u7684\u56e0\u7d20\uff01</p> <p>\u4e5f\u8bb8\u4f60\u5df2\u7ecf\u6ce8\u610f\u5230\u4e86\uff0c\u53c8\u6216\u8005\u4f60\u4e86\u89e3\u4e86\u4e4b\u540e\u4e24\u79cd\u5206\u6790\uff0c\u53c8\u56de\u8fc7\u5934\u6765\u601d\u8003\u53d1\u73b0\uff0c\u8fd9\u91cc\u5176\u5b9e\u5b58\u5728\u53e6\u5916\u4e00\u79cd\u66f4\u7d27\u51d1\u7684\u7f29\u653e\u65b9\u6cd5\uff08\u751a\u81f3\u4e0d\u80fd\u8bf4\u201c\u7f29\u653e\u201d\uff09\uff0c\u89c2\u5bdf\u5230 \\(Size_{i}(X) =Size_{i-1}(P)\\)\uff0c\u6240\u4ee5\uff1a</p> \\[ \\begin{aligned}     {\\hat{c}_{\\text{zig}}}_i     &amp;= 1 + Rank_{i}(P) - Rank_{i-1}(X) + \\underbrace{Rank_{i}(X) - Rank_{i-1}(P)}_{= 0} \\\\     &amp;= 1 + Rank_{i}(P) - Rank_{i-1}(X) \\end{aligned} \\] <p>\u4f46\u662f\u8fd9\u4e0d\u4fbf\u4e8e\u6211\u4eec\u4e4b\u540e\u7684\u4f20\u9012\u3002\u8fd8\u8bb0\u5f97\u6211\u4eec\u8981\u6c42\u7684\u76ee\u6807\u5417\uff1f</p> \\[ \\hat{c}_{\\text{rotate }x\\text{ to root}} = \\hat{c}_{\\text{zig}} + \\sum{ {\\hat{c}_{\\text{zig-zag}}}_i } + \\sum{ {\\hat{c}_{\\text{zig-zig}}}_i } \\] <p>\u6211\u4eec\u4e4b\u540e\u9700\u8981\u5bf9\u5404\u79cd \\(\\hat{c}\\) \u8fdb\u884c\u6c42\u548c\uff0c\u800c\u6bcf\u4e00\u6b21\u7684 \\(X,\\;P,\\;G\\) \u90fd\u662f\u4e0d\u540c\u7684\uff0c\u4e3a\u4e86\u5728\u6c42\u548c\u7684\u65f6\u5019\u5b9e\u73b0\u9519\u4f4d\u76f8\u51cf\uff0c\u6211\u4eec\u5fc5\u987b\u4fdd\u8bc1\u7f29\u653e\u5f97\u5230\u7684\u7ed3\u679c\u5177\u6709\u4e00\u5b9a\u7684\u4f20\u9012\u6027\u8d28\uff0c\u6216\u8005\u8bf4\u5728\u6c42\u548c\u8fc7\u7a0b\u4e2d\u80fd\u591f\u8fbe\u5230\u88c2\u9879\u76f8\u6d88\u7684\u6548\u679c\u3002</p> <p>\u800c\u5bf9\u4e8e Splay \u6765\u8bf4\uff0c\u6211\u4eec\u7684\u64cd\u4f5c\u4f20\u9012\uff0c\u6b63\u662f\u901a\u8fc7\u4e0d\u65ad\u5c06\u6211\u4eec\u5173\u6ce8\u7684 \\(X\\) \u70b9\u9012\u5f52\u5730\u5411\u4e0a\u65cb\u8f6c\u5b9e\u73b0\u7684\u3002\u6362\u53e5\u8bdd\u6765\u8bf4\uff0c\\(\\Phi_{i}(X)\\) \u4e2d\u7684 \\(X\\)\uff0c\u5c31\u662f \\(\\Phi_{i-1}(X)\\) \u4e2d\u7684 \\(X\\)\uff0c\u5982\u6b64\u6211\u4eec\u6700\u7ec8\u53ef\u4ee5\u5f97\u5230 \\(\\Phi_{n}(X) - \\Phi_{0}(X)\\)\uff0c\u800c\u5176\u4e2d\u4e00\u4e2a\u662f\u6839\uff0c\u4e00\u4e2a\u662f\u6211\u4eec\u4e00\u5f00\u59cb\u6253\u7b97\u64cd\u4f5c\u7684\u90a3\u4e2a\u70b9\u3002</p> <p>\u4e8e\u662f\u6211\u4eec\u7406\u60f3\u7684\u7f29\u653e\u76ee\u6807\u5c31\u662f \\(k(Rank_{i}(X) - Rank_{i-1}(X)) \\;\\; \\text{where } k \\text{ is fixed for all the terms}\\)\u3002</p> <p>\u4e0d\u8fc7\u4f60\u53ef\u80fd\u53c8\u8981\u63d0\u95ee\u4e86\uff0c<code>zig</code> \u5206\u6790\u7684\u7ed3\u679c\u91cc\u4e0d\u662f\u6709\u4e2a \\({c_{\\text{zig}}}_i = 1\\) \u5417\uff1f</p> <p>\u8fd9\u662f\u56e0\u4e3a <code>zig</code> \u6700\u591a\u53ea\u53d1\u751f\u4e00\u6b21\uff0c\u6240\u4ee5\u8fd9\u4e2a\u5e38\u6570\u662f\u6ca1\u6709\u5f71\u54cd\u7684\u3002</p> <p>\u771f\u7684\u9700\u8981\u90fd\u7f29\u653e\u5230\u76f8\u540c\u7684 k \u5417</p> <p>\u968f\u4e4b\u800c\u6765\u7684\uff0c\u4e00\u4e2a\u9700\u8981\u8ba8\u8bba\u7684\u95ee\u9898\u662f\u300c\\(\\text{where } k \\text{ is fixed for all the terms}\\)\u300d\u771f\u7684\u91cd\u8981\u5417\uff0c\u6362\u53e5\u8bdd\u6765\u8bf4\uff0c\u6211\u4eec\u5fc5\u987b\u4fdd\u8bc1\u4e09\u4e2a\u90e8\u5206\u7f29\u653e\u51fa\u6765\u90fd\u5177\u6709\u76f8\u540c\u7684 \\(k\\) \u5417\uff1f</p> <p>\u9996\u5148\uff0c\u91cd\u8981\u80af\u5b9a\u662f\u91cd\u8981\u7684\uff0c\u53ea\u4e0d\u8fc7\u5728\u8fd9\u4e2a\u95ee\u9898\u4e2d\uff0c\u7531\u4e8e\u6211\u4eec\u65cb\u8f6c\u7684\u65b9\u5411\u90fd\u662f\u5411\u4e0a\uff0c\u6240\u4ee5 \\(Rank_{i}(X) \\geq Rank_{i-1}(X)\\)\uff0c\u56e0\u6b64\u6211\u4eec\u53ea\u9700\u8981\u6700\u540e\u5c06\u5b83\u4eec\u4e00\u8d77\u90fd\u7f29\u653e\u5230 \\(k_{overall} = \\max\\{k_\\text{zig}, k_\\text{zig-zag}, k_\\text{zig-zig} \\}\\) \u5c31\u53ef\u4ee5\u4e86\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec01/#zig-zag","title":"zig-zag","text":"<p>Amortized Analysis for Zig-Zag</p> <p></p> \\[ \\begin{aligned}     {\\hat{c}_{\\text{zig-zag}}}_i      &amp;= {c_{\\text{zig-zag}}}_i + \\Phi_{i}(X)- \\Phi_{i-1}(G) \\\\     &amp;= 2 + Rank_{i}(X) - Rank_{i-1}(X) + Rank_{i}(P) - Rank_{i-1}(P) + Rank_{i}(G) - Rank_{i-1}(G) \\end{aligned} \\] <p>\u89c2\u5bdf\u914d\u56fe\uff0c\\(X\\) \u53c8\u4e00\u6b21\u7edd\u5730\u53cd\u51fb\uff0c\u6210\u4e3a\u5b83\u5bb6\u957f\u548c\u5b83\u5bb6\u957f\u7684\u5bb6\u957f\u5171\u540c\u7684\u5bb6\u957f\uff1b\\(G\\) \u635f\u5931\u6700\u60e8\u91cd\uff0c\u4e22\u6389\u4e86 \\(A,\\;B\\) \u4e24\u65cf\u5b50\u55e3\u3002</p> <p>\u5728\u8fd9\u6b21\u7684\u7f29\u653e\u4e2d\uff0c\u6839\u636e\u6211\u4eec\u4e4b\u524d\u5728 <code>key-point</code> \u91cc\u63d0\u5230\u7684\uff0c\u6211\u4eec\u9700\u8981\u5c06\u5b83\u7f29\u653e\u5230 \\(k(Rank_{i}(X) - Rank_{i-1}(X))\\) \u7684\u5f62\u5f0f\uff0c\u5e76\u4e14\u7531\u4e8e <code>zig-zig</code> \u4f1a\u591a\u6b21\u53d1\u751f\uff0c\u6240\u4ee5\u6211\u4eec\u4e5f\u5f97\u60f3\u529e\u6cd5\u641e\u6389\u8fd9\u91cc\u7684 \\({c_{\\text{zig-zag}}}_i = 2\\)\uff0c\u5426\u5219\u6700\u540e\u5c31\u4f1a\u51fa\u73b0\u4e00\u4e2a \\(2p(n)\\) \u7684 term\uff0c\u800c\u6211\u4eec\u7684\u8bc1\u660e\u76ee\u6807\u662f \\(\\log{N}\\)\uff0c\u6240\u4ee5\u6211\u4eec\u5fc5\u987b\u5c06\u8fd9\u4e2a \\(2\\) \u6d88\u6389\u3002\u800c\u4e3a\u4e86\u6d88\u9664\u8fd9\u4e2a \\(2\\)\uff0c\u6211\u4eec\u9700\u8981\u5148\u5f15\u5165\u4e00\u4e2a\u5f15\u7406\uff1a</p> <p>Lemma 1</p> <p>\u7531\u4e8e \\(y = \\log{x}\\) \u662f\u5355\u8c03\u7684\u51f8\u51fd\u6570\uff0c\u6240\u4ee5\u6709 \\(\\frac{\\log{x} + \\log{b}}{2} \\leq \\log {\\frac{a+b}{2}}\\)\u3002</p> <p>\u800c\u5728 Splay \u7684\u5747\u644a\u590d\u6742\u5ea6\u5206\u6790\u8fc7\u7a0b\u4e2d\uff0c\u6211\u4eec\u7684 \\(\\log{x}\\) \u6307\u7684\u662f \\(\\log_2{x}\\)\uff0c\u56e0\u6b64\u6709\uff1a</p> \\[ \\begin{aligned}     \\log{a} + \\log{b}      &amp;= 2\\left( \\frac{\\log{a} + \\log{b}}{2} \\right) \\\\     &amp;\\leq 2\\left( \\log{\\frac{a+b}{2}} \\right) \\\\     &amp;= 2\\left( \\log{(a+b)} - \\log{2} \\right) \\\\     &amp;= 2 \\log{(a+b)} - 2 \\\\ \\end{aligned} \\] <p>\u770b\u5230\u8fd9\u91cc\u51fa\u73b0\u4e86\u4e00\u4e2a \\(-2\\) \u6211\u4eec\u5c31\u80fd\u957f\u8212\u4e00\u53e3\u6c14\u4e86\uff0c\u8fd9\u4e0b \\({c_{\\text{zig-zag}}}_i = 2\\) \u6b7b\u5230\u4e34\u5934\u54af\uff01\u5bf9\u7167\u914d\u56fe\u770b\uff0c\u6211\u4eec\u53ef\u4ee5\u5f97\u5230\uff1a</p> \\[ \\begin{aligned}     Rank_{i}(P) + Rank_{i}(G)   &amp;= \\log{Size_{i}(P)} + \\log{Size_{i}(G)} \\\\                                 &amp;\\leq 2\\log{\\left(Size_{i}(P)+Size_{i}(G)\\right)} - 2 &amp; \\text{(Lemma 1)}\\\\                                 &amp;\\leq 2\\log{\\left(Size_{i}(P)+Size_{i}(G)+1\\right)} - 2 \\\\                                 &amp;\\leq 2\\log{Size_{i}(X)} - 2 \\\\                                 &amp;\\leq 2Rank_{i}(X) - 2 \\\\ \\end{aligned} \\] <p>\u56e0\u6b64\uff0c\u6211\u4eec\u80fd\u591f\u5f97\u5230\u8fd9\u4e9b\u76f8\u7b49\u6216\u4e0d\u7b49\u5173\u7cfb\uff1a</p> \\[ \\left\\{     \\begin{aligned}         Rank_{i}(X) &amp;= Rank_{i-1}(G) \\\\         Rank_{i}(P) + Rank_{i}(G) &amp;\\leq 2Rank_{i}(X) - 2 \\\\         Rank_{i-1}(P) + Rank_{i-1}(X) &amp;\\geq 2Rank_{i-1}(X)     \\end{aligned} \\right. \\] <p>\u4e8e\u662f\u6211\u4eec\u53ef\u4ee5\u5b9e\u73b0\u7f29\u653e\uff1a</p> \\[ \\begin{aligned}     {\\hat{c}_{\\text{zig-zag}}}_i      &amp;= 2 + Rank_{i}(X) - Rank_{i-1}(X) + Rank_{i}(P) - Rank_{i-1}(P) + Rank_{i}(G) - Rank_{i-1}(G) \\\\     &amp;= 2 + \\left( Rank_{i}(X) - Rank_{i-1}(G)\\right )           + \\left( Rank_{i}(P) + Rank_{i}(G) \\right)          - \\left( Rank_{i-1}(P) + Rank_{i-1}(X) \\right) \\\\     &amp;\\leq 2 + 0 + 2Rank_{i}(X) - 2 + 2Rank_{i-1}(X) \\\\     &amp;= 2\\left(Rank_{i}(X) - Rank_{i-1}(X)\\right) \\end{aligned} \\] <p>\u7686\u5927\u6b22\u559c\uff01</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec01/#zig-zig","title":"zig-zig","text":"<p>Amortized Analysis for Zig-Zig</p> <p></p> \\[ \\begin{aligned}     {\\hat{c}_{\\text{zig-zig}}}_i      &amp;= {c_{\\text{zig-zig}}}_i + \\Phi_{i}(X)- \\Phi_{i-1}(G) \\\\     &amp;= 2 + Rank_{i}(X) - Rank_{i-1}(X) + Rank_{i}(P) - Rank_{i-1}(P) + Rank_{i}(G) - Rank_{i-1}(G) \\end{aligned} \\] <p>\u4e3a\u4e86\u5b9e\u73b0 <code>zig-zig</code> \u7684\u7f29\u653e\uff0c\u6211\u4eec\u8fd8\u9700\u8981\u5bf9 Lemma 1 \u8fdb\u884c\u4e00\u4e2a\u6d3b\u7528\u3002\u5bf9\u7167\u914d\u56fe\uff0c\u5f97\u5230\uff1a</p> \\[ \\begin{aligned}     Rank_{i}(G) + Rank_{i-1}(X)          &amp;\\leq 2\\log{\\left(              \\underbrace{Size_{i}(G)}_{\\mathbf{C}+\\mathbf{D}+G}           + \\underbrace{Size_{i-1}(X)}_{\\mathbf{A}+\\mathbf{B}+X}         \\right)} - 2 &amp; \\text{(Lemma 1)} \\\\         &amp;\\leq 2\\log{\\left( Size_{i}(G) + Size_{i-1}(X) + 1 \\right)} - 2 &amp; \\\\         &amp;= 2\\log{\\left( Size_{i}(X) \\right)} - 2 \\\\         &amp;= 2Rank_{i}(X) - 2 \\\\     Rank_{i}(G)          &amp;\\leq 2Rank_{i}(X) - Rank_{i-1}(X) - 2 \\end{aligned} \\] <p>\u8fd9\u4e00\u6b65\u5f88\u96be\u60f3\uff0c\u4f46\u662f\u4e5f\u975e\u5e38\u5173\u952e\u3002</p> <p>\u4e8e\u662f\uff0c\u6211\u4eec\u6709\u5982\u4e0b\u8fd9\u4e9b\u4e0d\u7b49\u5f0f\uff1a</p> \\[ \\left\\{     \\begin{aligned}         Rank_{i}(X) &amp;= Rank_{i-1}(G) \\\\         Rank_{i}(G) &amp;\\leq 2Rank_{i}(X) - Rank_{i-1}(X) - 2 \\\\         Rank_{i}(P) &amp;\\leq Rank_{i}(X) \\\\         Rank_{i-1}(P) &amp;\\geq Rank_{i-1}(X)     \\end{aligned} \\right. \\] <p>\u4e8e\u662f\u6211\u4eec\u5c31\u53ef\u4ee5\u5bf9\u5176\u8fdb\u884c\u8be1\u5f02\u7684\u7f29\u653e\uff1a</p> \\[ \\begin{aligned}     {\\hat{c}_{\\text{zig-zig}}}_i      &amp;= 2 + Rank_{i}(X) - Rank_{i-1}(X) + Rank_{i}(P) - Rank_{i-1}(P) + Rank_{i}(G) - Rank_{i-1}(G) \\\\     &amp;= 2 + \\left( Rank_{i}(X) - Rank_{i-1}(G) \\right)          + Rank_{i}(G)          + Rank_{i}(P)          - Rank_{i-1}(P)          - Rank_{i-1}(X) \\\\     &amp;\\leq 2 + 0              + \\left( 2Rank_{i}(X) - Rank_{i-1}(X) - 2 \\right)              + Rank_{i}(X)             - Rank_{i-1}(X)             - Rank_{i-1}(X) \\\\     &amp;= 3\\left( Rank_{i}(X) - Rank_{i-1}(X) \\right) \\end{aligned} \\] <p>\ud83d\ude29 \u81f3\u6b64\uff0c\u6211\u4eec\u603b\u7b97\u662f\u628a\u725b\u9b3c\u86c7\u795e\u7684 <code>zig-zig</code> \u7684\u8bc1\u660e\u4e5f\u7ed9\u641e\u5b9a\u4e86\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec01/#\u7ed3\u8bba","title":"\u7ed3\u8bba","text":"<p>Amortized Analysis for Splay</p> <p>\u81f3\u6b64\uff0c\u5bf9\u4e8e\u4e09\u79cd\u64cd\u4f5c\uff0c\u6211\u4eec\u90fd\u5f97\u5230\u4e86\u5b83\u4eec\u7684\u5747\u644a\u4e0a\u754c\uff1a</p> \\[ \\begin{aligned}     {\\hat{c}_{\\text{zig}}}_i &amp;\\leq 1 + Rank_{i}(X) - Rank_{i-1}(X) \\\\     {\\hat{c}_{\\text{zig-zag}}}_i &amp;\\leq 2\\left(Rank_{i}(X) - Rank_{i-1}(X)\\right) \\\\     {\\hat{c}_{\\text{zig-zig}}}_i &amp;\\leq 3\\left(Rank_{i}(X) - Rank_{i-1}(X)\\right) \\end{aligned} \\] <p>\u6839\u636e\u6211\u4eec\u5728 <code>key-point</code> \u6846\u300c\u771f\u7684\u9700\u8981\u90fd\u7f29\u653e\u5230\u76f8\u540c\u7684 k \u5417\u300d\u4e2d\u7684\u5185\u5bb9\uff0c\u6211\u4eec\u63a5\u4e0b\u6765\u53ef\u4ee5\u5c06\u5b83\u4eec\u7684 \\(k\\) \u90fd\u7f29\u653e\u4e3a \\(3\\)\uff1a</p> \\[ \\begin{aligned}     {\\hat{c}_{\\text{zig}}}_i &amp;\\leq 1 + 3\\left( Rank_{i}(X) - Rank_{i-1}(X) \\right) \\\\     {\\hat{c}_{\\text{zig-zag}}}_i &amp;\\leq 3\\left( Rank_{i}(X) - Rank_{i-1}(X) \\right) \\\\     {\\hat{c}_{\\text{zig-zig}}}_i &amp;\\leq 3\\left( Rank_{i}(X) - Rank_{i-1}(X) \\right) \\end{aligned} \\] <p>\u4e8e\u662f\uff0c\u6211\u4eec\u5c31\u53ef\u4ee5\u5f97\u5230\u6700\u7ec8\u7684\u5747\u644a\u4e0a\u754c\uff1a</p> \\[ \\begin{aligned}     \\hat{c}_{\\text{rotate }x\\text{ to root}}          &amp;= \\hat{c}_{\\text{zig}} + \\sum{ {\\hat{c}_{\\text{zig-zag}}}_i } + \\sum{ {\\hat{c}_{\\text{zig-zig}}}_i } \\\\         &amp;= O(1) + 3\\left( Rank_{N}(X) - Rank_{0}(X) \\right) \\\\         &amp;= O(\\log{N}) \\end{aligned} \\] <p>\u53ef\u4ee5\u4ed4\u7ec6\u60f3\u60f3\u6c42\u548c\u5f0f\u662f\u5982\u4f55\u201c\u76f8\u6d88\u201d\u5f97\u5230\u6700\u540e\u7684\u5f0f\u5b50\u7684\uff0c\u8fd9\u91cc\u7684 \\(\\sum {\\hat{c}_\\text{...}}_i\\) \u7684 \\(i\\) \u5e76\u4e0d\u662f\u5728\u6c42\u548c\u5f0f\u4e2d\u5404\u81ea\u8fde\u7eed\u7684\uff0c\u4f46\u662f\u4e09\u4e2a term \u653e\u5728\u4e00\u8d77\uff0c\u5219\u53ef\u4ee5\u56ca\u62ec \\(i\\in\\{1,2,...,N\\}\\)</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec02/","title":"Lecture 2 | Red Black Tree &amp; B+ Tree","text":"<p> \u7ea6 4971 \u4e2a\u5b57  43 \u884c\u4ee3\u7801  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 17 \u5206\u949f</p> <p>\u8bf4\u660e</p> <p>\u800c\u4e3a\u4e86\u63d0\u9ad8\u7b14\u8bb0\u6574\u7406\u6548\u7387\uff0c\u53ef\u80fd\u4f1a\u8003\u8651\u7528\u66f4\u591a\u7684\u5f15\u7528\u548c\u66f4\u7b80\u5355\u7684\u8bed\u8a00\u3002\u5982\u679c\u60a8\u89c9\u5f97\u6709\u54ea\u91cc\u8bf4\u7684\u4e0d\u591f\u6e05\u695a\uff0c\u8bf7\u76f4\u63a5\u5728\u8bc4\u8bba\u533a\u72e0\u72e0 blame \u6211\uff01</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec02/#\u7ea2\u9ed1\u6811","title":"\u7ea2\u9ed1\u6811","text":"<p>link</p> <p>OI Wiki: https://oi-wiki.org/ds/rbtree/</p> <p>Wikipedia: https://en.wikipedia.org/wiki/Red%E2%80%93black_tree</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec02/#\u6982\u5ff5","title":"\u6982\u5ff5","text":"<p>\u987e\u540d\u601d\u4e49\uff0c\u7ea2\u9ed1\u6811(Red Black Tree)\u5c31\u662f\u4e00\u79cd\u8282\u70b9\u5206\u7c7b\u4e3a\u7ea2\u9ed1\u4e24\u8272\u7684\uff0c\u6bd4\u8f83\u5e73\u8861\u7684\u4e8c\u53c9\u641c\u7d22\u6811\u3002\u53ea\u4e0d\u8fc7\u4e0d\u540c\u4e8e AVL \u6811\uff0c\u7ea2\u9ed1\u6811\u7684\u201c\u5e73\u8861\u201d\u6027\u8d28\u662f\u901a\u8fc7\u9ed1\u9ad8(black height)\u6765\u5b9a\u4e49\u7684\u3002\u63a5\u4e0b\u6765\u4f9d\u6b21\u7ed9\u51fa\u7ea2\u9ed1\u6811\u7684\u5b9a\u4e49\u548c\u9ed1\u9ad8\u7684\u5b9a\u4e49\u3002</p> <p>Red Black Tree</p> <p> </p> <p>\u7ea2\u9ed1\u6811\u662f\u6ee1\u8db3\u5982\u4e0b\u6027\u8d28\u7684\u4e00\u79cd\u4e8c\u53c9\u641c\u7d22\u6811\uff1a</p> <p>Properties of RBTree</p> <p>@cy's PPT</p> <ol> <li>Every node is either red or black.</li> <li>The root is black.</li> <li>Every leaf (<code>NIL</code>) is black.</li> <li>if a node is red, then both its children are black.</li> <li>For each node, all simple paths from the node to descendant leaves contain the same number of black nodes.</li> </ol> <p>ch \u8001\u5e08\u8bf4\uff0c\u5e0c\u671b\u6211\u4eec\u80fd\u628a\u8fd9\u4e94\u6761\u6027\u8d28\u719f\u7ec3\u8bb0\u4f4f\uff0c\u600e\u4e48\u53ef\u80fd\uff08\u9003\uff09\u3002</p> <p>\u8bf4\u660e</p> <p>\u7531\u4e8e\u8fd9\u91cc\u7684\u201c\u53f6\u5b50\u7ed3\u70b9\u201d\u88ab\u91cd\u65b0\u5b9a\u4e49\u4e86\uff0c\u4e3a\u4e86\u63cf\u8ff0\u65b9\u4fbf\uff0c\u6211\u73b0\u5728\u79f0\u6240\u6709\u4e24\u4e2a\u5b50\u7ed3\u70b9\u90fd\u662f <code>NIL</code> \u7684\u7ed3\u70b9\u4e3a\u672b\u7aef\u7ed3\u70b9\uff08\u4e5f\u5c31\u662f\u901a\u4fd7\u610f\u4e49\u4e0a\u7684\u53f6\u5b50\u7ed3\u70b9\uff09\u3002\u800c\u8fd9\u4e2a\u5b9a\u4e49\u53ea\u662f\u6211\u81ea\u5df1\u8bf4\u8bf4\u7684\uff01</p> @Wiki <ol> <li>Every node is either red or black.</li> <li>All <code>NIL</code> nodes (figure above) are considered black.</li> <li>A red node does not have a red child.</li> <li>Every path from a given node to any of its descendant <code>NIL</code> nodes goes through the same number of black nodes.</li> </ol> @OI Wiki <ol> <li>\u6bcf\u4e00\u4e2a\u8282\u70b9\u8981\u4e48\u662f\u7ea2\u8272\uff0c\u8981\u4e48\u662f\u9ed1\u8272\uff1b</li> <li><code>NIL</code> \u8282\u70b9\uff08\u7a7a\u53f6\u5b50\u8282\u70b9\uff09\u4e3a\u9ed1\u8272\uff1b</li> <li>\u7ea2\u8272\u8282\u70b9\u7684\u5b50\u8282\u70b9\u5fc5\u987b\u4e3a\u9ed1\u8272\uff1b</li> <li>\u4ece\u6839\u8282\u70b9\u5230 <code>NIL</code> \u8282\u70b9\u7684\u6bcf\u6761\u8def\u5f84\u4e0a\u7684\u9ed1\u8272\u8282\u70b9\u6570\u91cf\u76f8\u540c\uff1b</li> </ol> <p>black height, bh</p> <p>\u7279\u5b9a\u8282\u70b9\u7684\u9ed1\u9ad8\uff0c\u7b49\u4e8e\u8be5\u8282\u70b9\u5230\u53f6\u7ed3\u70b9\u5230\u7b80\u5355\u8def\u5f84\u4e2d\uff08\u4e0d\u5305\u62ec\u81ea\u8eab\uff09\uff0c\u9ed1\u8272\u8282\u70b9\u7684\u6570\u91cf\u3002</p> <p>\u63a5\u4e0b\u6765\u4e3a\u4e86\u52a0\u6df1\u7406\u89e3\uff0c\u6709\u4e00\u4e9b\u8fa8\u6790\u53ef\u4ee5\u505a\uff1a</p> T1T2 \u9898\u9762\u7b54\u6848 <p>\u4e0b\u56fe\u7684\u7ea2\u9ed1\u6811\u662f\u5426\u5408\u6cd5\uff1f</p> <p></p> <p>\u4e0d\u5408\u6cd5\u3002</p> <p><code>16</code> \u53f7\u8282\u70b9\u7684\u53f3\u513f\u5b50\u662f\u4e00\u4e2a\u9ed1\u53f6\u5b50\uff0c\u800c\u8fd9\u4e2a\u53f6\u5b50\u5230\u6839\u7684\u8def\u5f84\u4e0a\u53ea\u6709 3 \u4e2a\u9ed1\u8282\u70b9\uff0c\u800c\u5176\u4ed6\u53f6\u5b50\u5230\u6839\u90fd\u6709 4 \u4e2a\u9ed1\u8282\u70b9\u3002</p> <p>\u6240\u4ee5\u6211\u4eec\u9700\u8981\u8b66\u60d5\u53ea\u6709\u4e00\u4e2a\u975e\u53f6\u513f\u5b50\u7684\u7ea2\u8272\u8282\u70b9\u3002</p> \u9898\u9762\u7b54\u6848 <p>\u4e0b\u56fe\u7684\u7ea2\u9ed1\u6811\u662f\u5426\u5408\u6cd5\uff1f</p> <p></p> <p>\u5408\u6cd5\u3002</p> <p>\u6839\u636e T1 \u7684\u89e3\u6790\uff0c\u6211\u4eec\u5f97\u5230\u8fd9\u6837\u4e00\u4e2a\u7ed3\u8bba\uff1a</p> <p>\u5408\u6cd5\u7ea2\u9ed1\u6811\u4e0d\u5b58\u5728\u53ea\u6709\u4e00\u4e2a\u975e\u53f6\u5b50\u8282\u70b9\u7684\u7ea2\u8272\u8282\u70b9\uff01</p> <p>or</p> <p>\u5408\u6cd5\u7ea2\u9ed1\u6811\u7684\u7ea2\u8272\u8282\u70b9\u7684\u4e24\u4e2a\u5b50\u8282\u70b9\u4e00\u5b9a\u90fd\u662f\u53f6\u5b50\u6216\u90fd\u4e0d\u662f\u53f6\u5b50\uff01</p> <p>\u6b64\u5916\uff0c\u5173\u4e8e\u7ea2\u9ed1\u6811\u7684\u9ad8\uff0c\u6211\u4eec\u6709\u5982\u4e0b\u6027\u8d28\uff1a</p> <p>property about height of RBTree</p> <p>\u4e00\u4e2a\u6709 \\(N\\) \u4e2a\u5185\u90e8\u8282\u70b9\uff08\u4e0d\u5305\u62ec\u53f6\u5b50\u7ed3\u70b9\uff09\u7684\u7ea2\u9ed1\u6811\uff0c\u5176\u9ad8\u5ea6\u6700\u5927\u4e3a \\(2\\log_2 (N+1)\\)\u3002</p> the proof of the property <p>\u5173\u4e8e\u9ed1\u9ad8\u548c\u70b9\u6570\u7684\u5173\u7cfb\u3002</p> <ol> <li>\u9996\u5148\u6211\u4eec\u6709 \\(N \\geq 2^{bh}-1\\)\uff0c\u4e5f\u5c31\u662f \\(bh \\leq \\log_2 (N+1)\\)\uff1b</li> <li>\u7136\u540e\u663e\u7136\u6709 \\(2 bh(Tree) &gt;= h(Tree)\\)</li> </ol>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec02/#\u64cd\u4f5c","title":"\u64cd\u4f5c","text":"<p>\u63d0\u9192</p> <p>\u6211\u4eec\u8fd9\u91cc\u4ecb\u7ecd\u7684\u90fd\u662f bottom-up \u7684\u601d\u8def\uff0c\u4e0d\u540c\u4e8e AVL \u6811\uff0c\u7ea2\u9ed1\u6811\u662f\u5b58\u5728 top-down \u7684\u64cd\u4f5c\u65b9\u6cd5\u7684\uff0c\u800c\u8fd9\u4e5f\u662f\u7ea2\u9ed1\u6811\u4e00\u4e2a\u975e\u5e38\u5f3a\u5927\u7684\u4f18\u52bf\uff0c\u5b58\u5728 top-down \u7684\u5904\u7406\u65b9\u6cd5\u610f\u5473\u7740\u6211\u4eec\u53ef\u4ee5\u8fdb\u884c\u66f4\u5feb\u7684\u5e76\u884c\u64cd\u4f5c\u3002\u4f46\u662f\u6211\u4eec\u4e0d\u5728\u8fd9\u91cc\u8be6\u7ec6\u5c55\u5f00\u3002</p> <p>\u540c AVL \u6811\u7684\u8c03\u6574\u64cd\u4f5c\u7c7b\u4f3c\uff0c\u7ea2\u9ed1\u6811\u7684\u8c03\u6574\u64cd\u4f5c\u4e5f\u662f\u5de6\u53f3\u5bf9\u79f0\u7684\uff0c\u6240\u4ee5\u6211\u4eec\u4e5f\u4ecd\u7136\u53ea\u8ba8\u8bba\u4e00\u4fa7\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec02/#\u63d2\u5165","title":"\u63d2\u5165","text":"<p>\u6211\u4eec\u77e5\u9053\uff0c\u5bf9\u9ed1\u9ad8\u6709\u8d21\u732e\u7684\u53ea\u6709\u9ed1\u8272\u8282\u70b9\uff0c\u56e0\u6b64 <code>NIL</code> \u8282\u70b9\u88ab\u4e00\u4e2a\u7ea2\u8272\u8282\u70b9\u7f6e\u6362\u5e76\u4e0d\u4f1a\u6539\u53d8\u4e00\u9897\u7ea2\u9ed1\u6811\u7684\u9ed1\u9ad8\uff0c\u56e0\u4e3a\u7ea2\u8272\u8282\u70b9\u8fd8\u4f1a\u6709\u4e00\u5c42 <code>NIL</code> \u5b50\u8282\u70b9\uff1b\u7136\u800c\u5bf9\u4e8e\u7ea2\u8272\u8282\u70b9\uff0c\u5374\u6709\u7740\u7ea2\u8272\u7ed3\u70b9\u4e92\u4e0d\u76f8\u90bb\u7684\u9650\u5236\u3002</p> <p>\u56e0\u6b64\uff0c\u201c\u63d2\u5165\u201d\u64cd\u4f5c\u7684\u4e3b\u8981\u601d\u8def\u5c31\u662f\uff0c\u5148\u5c06\u6574\u4e2a\u7ea2\u9ed1\u6811\u5f53\u4f5c\u4e00\u4e2a\u666e\u901a\u7684\u4e8c\u53c9\u641c\u7d22\u6811\uff0c\u5c06\u76ee\u6807\u6570\u636e\u63d2\u5165\u5230\u6811\u7684\u672b\u7aef\uff08\u4e5f\u5c31\u662f\u7f6e\u6362\u4e00\u4e2a <code>NIL</code> \u8282\u70b9\uff09\uff0c\u5e76\u5c06\u5b83\u67d3\u4e3a\u7ea2\u8272\uff0c\u518d\u8c03\u6574\u4f7f\u4e4b\u5728\u4fdd\u8bc1\u9ed1\u9ad8\u4e0d\u53d8\u7684\u60c5\u51b5\u4e0b\uff0c\u6ee1\u8db3\u7ea2\u8272\u8282\u70b9\u4e0d\u80fd\u76f8\u90bb\u7684\u8981\u6c42\u3002</p> <p>\u73b0\u5728\uff0c\u6211\u4eec\u8bb0\u8fd9\u4e2a\u88ab\u63d2\u5165\u7684\u8282\u70b9\u4e3a <code>x</code>\uff0c\u4efb\u610f\u4e00\u4e2a\u8282\u70b9 <code>node</code> \u7684\u5bb6\u957f\u8282\u70b9\u4e3a <code>node.p</code>\uff0c\u5219\uff1a</p> <ol> <li>\u5982\u679c <code>x.p</code> \u662f\u9ed1\u8272\u7684\uff0c\u90a3\u4e48\u6211\u4eec\u4e0d\u9700\u8981\u505a\u4efb\u4f55\u8c03\u6574\uff1b</li> <li>\u5982\u679c <code>x.p</code> \u662f\u7ea2\u8272\u7684\uff0c\u90a3\u4e48\u6211\u4eec\u9700\u8981\u8fdb\u884c\u8c03\u6574\uff1b<ul> <li>\u6b64\u65f6\u56e0\u4e3a\u539f\u6765\u7684\u6811\u7b26\u5408\u7ea2\u9ed1\u6027\u8d28\uff0c<code>x.p.p</code> \u5fc5\u5b9a\u5b58\u5728\uff08\u7ea2 <code>x.p</code> \u4e0d\u80fd\u662f\u6839\uff09\u4e14\u5fc5\u5b9a\u662f\u9ed1\u8272\u7684\uff1b</li> </ul> </li> </ol> <p>\u6839\u636e\u8fd9\u4e9b\u8ba8\u8bba\uff0c\u6211\u4eec\u5c31\u80fd\u5217\u4e3e\u51fa\u6765\u4e00\u4e2a\u7ea2\u8272\u7684\u70b9\u88ab\u63d2\u5165\u540e\uff0c\u5728 <code>2.</code> \u7684\u60c5\u51b5\u4e0b\u6240\u6709\u7684\u521d\u59cb\u60c5\u51b5\uff0c\u5373\u4e0b\u9762\u7b2c\u4e00\u5f20\u56fe\u3002</p> <p></p> <p>\u7531\u4e8e\u7ea2\u9ed1\u6811\u7684\u64cd\u4f5c\u4e2d\uff0c\u6709\u4e00\u90e8\u5206\u9700\u8981\u8fdb\u884c\u9012\u5f52\u8f6c\u79fb\uff0c\u800c\u5176\u4e2d\u4e2d\u95f4\u6b65\u9aa4\u51fa\u73b0\u4e86\u5f88\u591a\u540c\u6784\u7684\u7ed3\u6784\uff0c\u6240\u4ee5\u4e3a\u4e86\u7b80\u5316\u8bf4\u660e\uff0c\u6211\u4eec\u5bf9\u5176\u8fdb\u884c\u7edf\u4e00\uff0c\u6240\u6709\u60c5\u51b5\u90fd\u88ab\u5f52\u7eb3\u4e3a\u4e0a\u9762\u7b2c\u4e8c\u5f20\u56fe\u3002</p> <p>\u800c\u7b2c\u4e8c\u5f20\u56fe\u4e2d\u63d0\u5230\u7684\u6a59\u8272\u7ed3\u70b9\uff0c\u4e5f\u5c31\u662f\u6807\u4e3a\u201c\u88ab\u63d2\u5165\u7684\u7ea2\u8272\u8282\u70b9\u201d\u7684\u7ed3\u70b9\uff0c\u5b9e\u9645\u8fc7\u7a0b\u4e2d\u5e76\u4e0d\u4e00\u5b9a\u6307\u7684\u662f\u88ab\u300c\u63d2\u5165\u300d\u7684\u90a3\u4e2a\u70b9\uff0c\u4e5f\u53ef\u80fd\u662f\u5728 case 1 \u5411\u4e0a\u9012\u5f52\u65f6\uff0c\u7b80\u5316\u7684\u539f\u6765\u90a3\u9897\u5b50\u6811\u3002\u6362\u53e5\u8bdd\u6765\u8bf4\uff0c\u8fd9\u91cc\u7684\u201c\u88ab\u63d2\u5165\u7684\u7ea2\u8272\u8282\u70b9\u53ca\u5176\u5b50\u6811\u201d\uff0c\u5b9e\u9645\u4e0a\u53ef\u80fd\u662f\u6307\u300c\u5bfc\u81f4\u7ea2\u9ed1\u6027\u8d28\u88ab\u7834\u574f\u7684\u7ea2\u6839\u5b50\u6811\u300d\u3002</p> <p>\u63a5\u4e0b\u6765\u6211\u4eec\u6765\u8ba8\u8bba\u5404\u79cd\u60c5\u51b5\u8981\u600e\u4e48\u5904\u7406\u3002</p> <p>\u8bf4\u660e</p> <p>\u8fd9\u91cc case 1 ~ case 3 \u7684\u7f16\u53f7\u4e3b\u8981\u662f\u4e3a\u4e86\u548c\u8bfe\u7a0b ppt \u5bf9\u6807\uff0c\u4f46\u662f\u63a5\u4e0b\u6765\u4f60\u4f1a\u53d1\u73b0\u6211\u662f\u6309\u7167 case 3 -&gt; case 1 \u6765\u4ecb\u7ecd\u64cd\u4f5c\u7684\uff0c\u8fd9\u662f\u56e0\u4e3a\u6211\u89c9\u5f97\u8fd9\u6837\u5b89\u6392\u66f4\u5408\u7406\uff0c\u800c\u975e\u6392\u7248\u6df7\u4e71\u3002</p> Insertion / case 3 <p>\u5bf9\u4e8e case 3\uff0c \u6211\u4eec\u9ad8\u5174\u5730\u53d1\u73b0\uff0c\u8fd9\u6837\u7684\u4e00\u6b21\u67d3\u8272\u548c\u4e00\u6b21\u65cb\u8f6c\u521a\u597d\u80fd\u8ba9\u8fd9\u68f5\u5b50\u6811\u5b8c\u6210\u8c03\u6574\uff01</p> <p></p> Insertion / case 2 <p>\u5bf9\u4e8e case 2\uff0c\u6211\u4eec\u53ef\u4ee5\u76f4\u63a5\u8fdb\u884c\u4e00\u4e2a Rotation \u64cd\u4f5c\u5c06\u5b83\u8f6c\u5316\u4e3a case 3\u3002</p> <p>\u4f46\u662f\u5b9e\u9645\u4e0a\uff0c\u7ec6\u5fc3\u7684\u5c0f\u670b\u53cb\u5df2\u7ecf\u53d1\u73b0\u4e86\uff0c\u4ece case 2 -&gt; case 3 -&gt; done \u7684\u8fc7\u7a0b \u5b9e\u9645\u4e0a\u5c31\u662f\u4e00\u4e2a LR Rotation\uff01</p> <p></p> Insertion / case 1 <p>\u5bf9\u4e8e case 1\uff0c\u56fe\u4e2d\u7684\u4e24\u79cd\u60c5\u51b5\u662f\u7b49\u4ef7\u7684\u3002\u6240\u4ee5\u6211\u4eec\u53ea\u5c55\u793a\u5176\u4e2d\u4e00\u79cd\u3002</p> <p>\u6211\u4eec\u53ea\u9700\u8981\u5c06\u56fe\u4e2d\u7684\u6839\u8282\u70b9\u67d3\u7ea2\uff0c\u5c06\u6839\u7684\u4e24\u4e2a\u5b50\u8282\u70b9\u67d3\u9ed1\uff0c\u7c7b\u4f3c\u4e8e\u5c06\u9ed1\u8282\u70b9\u201c\u4e0b\u653e\u201d\u3002</p> <p></p> <p>\u901a\u8fc7\u7b2c\u4e00\u6b65\u64cd\u4f5c\uff0c\u6211\u4eec\u53ef\u4ee5\u4fdd\u8bc1\u8fd9\u6574\u4e2a\u5b50\u6811\u5fc5\u5b9a\u5e73\u8861\u3001\u4e0d\u5f71\u54cd\u5bb6\u957f\u8282\u70b9\u7684\u9ed1\u9ad8\uff08\u9664\u4e86\u5bb6\u957f\u662f\u6839\u7684\u60c5\u51b5\uff09\u4e14\u7ea2\u70b9\u4e0d\u90bb\u7684\u3002</p> <p>\u7136\u800c\u6211\u4eec\u5e76\u4e0d\u77e5\u9053\u8fd9\u4e2a\u6839\u7684\u5bb6\u957f\u8282\u70b9\u662f\u5426\u662f\u7ea2\u8272\u8282\u70b9\uff0c\u56e0\u6b64\u505a\u5206\u7c7b\u8ba8\u8bba\u3002\u5018\u82e5\u5176\u6839\u7684\u5bb6\u957f\u8282\u70b9\u662f\u7ea2\u8272\u8282\u70b9\uff0c\u90a3\u4e48\u6211\u4eec\u8fd8\u9700\u8981\u5411\u4e0a\u9012\u5f52\uff0c\u7ee7\u7eed\u8c03\u6574\uff0c\u6839\u636e\u5b9e\u9645\u60c5\u51b5\u8f6c\u5316\u4e3a\u5176\u4ed6 case\uff1b\u82e5\u8fd9\u5b50\u6811\u7684\u6839\u6ca1\u6709\u5bb6\u957f\u8282\u70b9\uff0c\u5219\u76f4\u63a5\u67d3\u9ed1\u7ea2\u6839\u5373\u53ef\uff1b\u800c\u5018\u82e5\u5b50\u6811\u6839\u8282\u70b9\u7684\u5bb6\u957f\u8282\u70b9\u662f\u9ed1\u8282\u70b9\uff0c\u90a3\u4e48\u6211\u4eec\u5c31\u8c03\u6574\u5b8c\u6bd5\u4e86\u3002</p> <p>\u5728\u8fd9\u4e09\u4e2a\u8fc7\u7a0b\u4e2d\uff0c\u6211\u4eec\u89c2\u5bdf\u5230\uff0c\u53ea\u6709 case 1 \u7684\u8f6c\u5316\u4f1a\u5bfc\u81f4\u6211\u4eec\u9012\u5f52\u5411\u4e0a\uff0c\u800c case 2 \u5411 case 3 \u7684\u8f6c\u5316\u5e76\u4e0d\u4f1a\u5bfc\u81f4\u6211\u4eec\u6539\u53d8\u5173\u6ce8\u7684\u5b50\u6811\u7684\u8303\u56f4\u3002</p> <p>\u4e3a\u4e86\u66f4\u6e05\u6670\u5730\u770b\u51fa\u5404\u4e2a\u65b9\u6cd5\u4e4b\u95f4\u7684\u8f6c\u5316\u5173\u7cfb\uff0c\u4e8e\u662f\u6211\u4eec\u53ef\u4ee5\u753b\u4e00\u4e2a\u72b6\u6001\u673a\uff1a</p> <pre><code>graph LR;\nA[\"case 1\"]\nB[\"case 2\"]\nC[\"case 3\"]\nD([\"finish\"])\n\nA ===&gt;|\"C\"| B ---&gt;|\"R\"| C\nA ===&gt;|\"C\"| A ---&gt;|\"C\"| D\nA ===&gt;|\"C\"| C ---&gt;|\"C&amp;R\"| D</code></pre> <p>\u6ce8\u610f\uff0c\u72b6\u6001\u673a\u4e2d\u7684\u7c97\u7ebf\u8868\u793a\u8f6c\u6362\u8fc7\u7a0b\u4e2d\uff0c\u6211\u4eec\u5173\u6ce8\u7684\u201c\u5b50\u6811\u201d\u5411\u4e0a\u6500\u5347\u4e86\u4e00\u7ea7\uff1b\u800c\u7ec6\u7ebf\u8868\u793a\u6211\u4eec\u5173\u6ce8\u7684\u5b50\u6811\u4ecd\u7136\u662f\u8fd9\u4e00\u5c42\u7684\u90a3\u4e00\u68f5\u3002\u4ee5\u53ca\uff0c<code>C</code> \u8868\u793a\u67d3\u8272\u64cd\u4f5c\uff0c<code>R</code> \u8868\u793a\u65cb\u8f6c\u64cd\u4f5c\u3002</p> <p>\u5176\u4e2d\uff0c\u4efb\u4f55\u4e00\u4e2a\u60c5\u51b5\u90fd\u53ef\u4ee5\u4f5c\u4e3a\u4e00\u4e2a\u521d\u59cb\u60c5\u51b5\u3002\u6240\u4ee5\u53ef\u4ee5\u6570\u51fa\uff0c\u5230\u8fbe finish \u7684\u8def\u5f84\u4e2d\uff0c\u6700\u591a\u51fa\u73b0 2 \u6b21 Rotation\uff08case 2 -&gt; case 3 -&gt; finish\uff09\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec02/#\u5220\u9664","title":"\u5220\u9664","text":"<p>\u5173\u4e8e\u5220\u9664\u64cd\u4f5c\uff0c\u4e0b\u9762\u8fd9\u4e2a\u89c6\u9891\u8bb2\u7684\u5f88\u6e05\u6670\uff01\u53ea\u4e0d\u8fc7 case 1 \u53ef\u80fd\u8fd8\u6709\u4e9b\u7ec6\u8282\u9700\u8981\u6ce8\u610f\u3002</p> <p>\ud83d\udc49 \u7ea2\u9ed1\u6811\u5feb\u901f\u5165\u95e8 - 04\u5220\u9664</p> <p>\u8981\u5220\u9664\u67d0\u4e2a\u8282\u70b9 x\uff0c\u6211\u4eec\u9996\u5148\u8981\u627e\u5230\u5b83\uff0c\u5728 BST \u4e2d\u627e\u5230\u67d0\u4e2a x \u7684\u5f00\u9500\u4e3a \\(O(\\log N)\\)\u3002\u63a5\u4e0b\u6765\u6211\u4eec\u8981\u5220\u9664\u8fd9\u4e2a\u4efb\u610f\u4f4d\u7f6e\u7684\u8282\u70b9\uff0c\u8fd9\u52bf\u5fc5\u8ba9\u7ea2\u9ed1\u6811\u7684\u7ed3\u6784\u53d1\u751f\u53d8\u5316\u3002\u6b64\u5916\uff0c\u7ea2\u9ed1\u6027\u8d28\u7684\u7ef4\u62a4\u4e5f\u662f\u4e00\u4e2a\u8ba9\u4eba\u5934\u75bc\u7684\u95ee\u9898\uff0c\u56e0\u6b64\uff0c\u6211\u4eec\u5bf9\u8fd9\u4e9b\u60c5\u51b5\u505a\u5206\u7c7b\u8ba8\u8bba\uff1a</p> \u6ca1\u6709\u975e<code>NIL</code>\u5b50\u8282\u70b9 \u6709\u4e00\u4e2a\u975e<code>NIL</code>\u5b50\u8282\u70b9 \u6709\u4e24\u4e2a\u975e<code>NIL</code>\u5b50\u8282\u70b9 \u76f4\u63a5\u7528<code>NIL</code>\u66ff\u4ee3 \u76f4\u63a5\u5220\u9664\uff0c\u7528\u5b50\u8282\u70b9\u66ff\u4ee3\u5b83 \u5c06\u503c\u4e0e\u5de6\u5b50\u6811\u6700\u5927\u503c\u6216\u53f3\u5b50\u6811\u6700\u5c0f\u503c\u4ea4\u6362\uff0c\u989c\u8272\u4e0d\u6362\uff0c\u7136\u540e\u5220\u9664\u76ee\u6807\u70b9 <p>\u5176\u4e2d\uff0c\u6bcf\u4e00\u9879\u64cd\u4f5c\u90fd\u4f1a\u5bfc\u81f4\u4e00\u4e2a\u70b9\u7684\u6d88\u5931\uff08\u6bd5\u7adf\u662f\u5220\u9664\uff09\uff0c\u800c\u5982\u679c\u6d88\u5931\u7684\u662f\u7ea2\u8272\u8282\u70b9\uff0c\u90a3\u4e48\u5c06\u4e0d\u4f1a\u5f71\u54cd\u9ed1\u9ad8\uff1b\u800c\u5982\u679c\u6d88\u5931\u7684\u662f\u9ed1\u8272\u8282\u70b9\uff0c\u90a3\u4e48\u5c06\u4f1a\u5bfc\u81f4\u9ed1\u9ad8\u51cf\u5c11\u4e00\uff0c\u6b64\u65f6\u6211\u4eec\u9700\u8981\u505a\u8fdb\u4e00\u6b65\u64cd\u4f5c\u3002</p> <ul> <li> TODO: \u8fd9\u91cc\u9700\u8981\u914d\u56fe\u8bb2\u6e05\u695a\u8282\u70b9\u7684\u5177\u4f53\u53d8\u6362\u5230\u5e95\u662f\u600e\u4e48\u6837\u7684\uff0c\u5c24\u5176\u662f\u8282\u70b9\u989c\u8272\u53d8\u5316\u5230\u5e95\u662f\u600e\u4e48\u4e00\u56de\u4e8b\uff0c\u4e4b\u540e\u5927\u6982\u9700\u8981\u91cd\u5199</li> </ul> <p>\u8bf4\u660e</p> <p>\u867d\u7136\u6211\u60f3\u5c3d\u53ef\u80fd\u62df\u5408 cy \u7684 ppt\uff0c\u4f46\u662f\u6211\u7b2c\u4e00\u904d\u5b9e\u5728\u6ca1\u770b\u61c2\uff0c\u6240\u4ee5 case \u7684\u7f16\u53f7\u6211\u5c31\u6309\u7167\u4e0a\u9762\u90a3\u4e2a\u89c6\u9891\u6765\u4e86\u3002</p> <p>\u8fd9\u662f case \u5e8f\u53f7\u7684\u5bf9\u5e94\u5173\u7cfb\uff1a</p> my cy's my cy's case 1 case 2 case 2 case 4 case 3 case 3 case 4 case 1 <p>\u6211\u4eec\u6839\u636e\u60c5\u51b5\uff0c\u5c06\u60c5\u51b5\u5206\u4e3a\u56db\u79cd\uff1a</p> <p></p> <p>\u9700\u8981\u505a\u4e00\u4e0b\u7b80\u5355\u8bf4\u660e\uff0c\u7c7b\u6bd4\u6211\u4eec\u5728#\u63d2\u5165\uff0c\u5728\u5220\u9664\u8fc7\u7a0b\u4e2d\u4e5f\u5b58\u5728\u9700\u8981\u5411\u4e0a\u9012\u5f52\u7684\u60c5\u51b5\u3002\u4e0e\u300c\u88ab\u63d2\u5165\u7684\u7ea2\u8272\u8282\u70b9\u300d\u7c7b\u4f3c\u7684\uff0c\u6211\u4eec\u8fd9\u91cc\u7684\u300c\u9700\u8981\u88ab\u5220\u9664\u7684\u76ee\u6807\u70b9\u300d\uff0c\u4e5f\u5e94\u5f53\u88ab\u770b\u4f5c\u300c\u5bfc\u81f4\u8c03\u6574\u51fa\u73b0\u7684\u5b50\u6811\u300d\uff0c\u66f4\u8fdb\u4e00\u6b65\u7684\uff0c\u53ef\u4ee5\u5b9a\u4e49\u6210\u300c\u7531\u4e8e\u5220\u9664\u4e86\u67d0\u4e2a\u7ed3\u70b9\uff0c\u9ed1\u9ad8 -1 \u7684\u5b50\u6811\u300d\uff0c\u8bf7\u8bb0\u4f4f\u8fd9\u4e2a\u5b9a\u4e49\uff0c\u8fd9\u4f1a\u8ba9\u4e4b\u540e\u7684\u9012\u5f52\u64cd\u4f5c\u53d8\u5f97\u81ea\u7136\u3002</p> <p>\u4f55\u65f6\u5220\u9664\u90a3\u4e2a\u7ed3\u70b9\uff1f</p> <p>\u867d\u7136\u6211\u4eec\u5bf9\u300c\u9700\u8981\u88ab\u5220\u9664\u7684\u76ee\u6807\u70b9\u300d\u8fdb\u884c\u4e86\u9012\u5f52\u7684\u6269\u5c55\u5b9a\u4e49\uff0c\u4f46\u662f\u5728\u7b2c\u4e00\u5c42\u6211\u4eec\u5c31\u53ef\u4ee5\u76f4\u63a5\u5c06\u5b83\u5220\u6389\u4e86\u3002\u800c\u8fd9\u4e2a\u70b9\u88ab\u5220\u9664\u9020\u6210\u7684\u5f71\u54cd\uff0c\u5df2\u7ecf\u7531\u300c\u7531\u4e8e\u5220\u9664\u7ed3\u70b9\uff0c\u9ed1\u9ad8 -1 \u7684\u5b50\u6811\u300d\u7ee7\u627f\u4e86\u3002</p> <p>\u5728\u4e4b\u540e\u7684\u914d\u56fe\u4e2d\uff0c\u6211\u4eec\u90fd\u4e0d\u4f1a\u5c55\u793a x \u662f\u5982\u4f55\u88ab\u5220\u6389\u7684\uff0c\u800c\u662f\u5728\u7ed3\u679c\u56fe\u4e2d\u4fdd\u7559 x\u3002\u5982\u679c\u8bf4 x \u5c31\u662f\u6211\u4eec\u4e00\u5f00\u59cb\u8981\u5220\u9664\u7684\u90a3\u4e2a\u70b9\uff0c\u90a3\u4e48\u6211\u4eec\u5e94\u5f53\u5220\u6389 x\uff0c\u76f4\u63a5\u6362\u6210 <code>NIL</code>\uff1b\u5982\u679c x \u662f\u5728\u4f20\u9012\u8fc7\u7a0b\u4e2d\uff0c\u8868\u793a\u300c\u9ed1\u9ad8 -1 \u7684\u5b50\u6811\u300d\u7684\u6839\uff0c\u90a3\u4e48\u4e0d\u7528\u505a\u989d\u5916\u5904\u7406\u3002</p> <p>\u7c7b\u4f3c\u4e8e\u6211\u4eec\u5728\u300cInsertion / case 3\u300d\u91cc\u63d0\u5230\u7684\u201c\u4e0b\u653e\u201d\u9ed1\u8282\u70b9\uff0c\u5220\u9664\u64cd\u4f5c\u7684\u601d\u8def\u57fa\u672c\u4e0a\u662f\u201c\u4e0a\u653e\u201d\u9ed1\u8282\u70b9\uff0c\u6216\u8005\u8bf4\u201c\u5438\u7eb3\u201d\u9ed1\u8282\u70b9\u3002\u8fd9\u4e2a\u201c\u5438\u7eb3\u201d\u7684\u884c\u4e3a\uff0c\u6307\u7684\u662f\u4e00\u4e2a\u9ed1\u70b9\uff0c\u539f\u6765\u53ea\u4e3a\u53f3\u5b50\u6811\u4e2d\u7684\u6240\u6709\u8def\u5f84\u63d0\u4f9b\u4e86\u9ed1\u9ad8\uff0c\u73b0\u5728\u7531\u4e8e\u5b83\u7684 sibling \u5b50\u6811\u4e2d\u5c11\u4e86\u4e00\u4e2a\u9ed1\u8272\u8282\u70b9\uff0c\u6211\u4eec\u5c06\u8fd9\u4e2a\u9ed1\u8272\u8282\u70b9\u8f6c\u79fb\u5230\u5b83\u4eec\u7684\u5bb6\u957f\u8282\u70b9\u8282\u70b9\uff0c\u4e8e\u662f\u8fd9\u4e2a\u8282\u70b9\u540c\u65f6\u4e3a\u5de6\u53f3\u5b50\u6811\u7684\u6240\u6709\u8def\u5f84\u90fd\u8d21\u732e\u4e86\u9ed1\u9ad8\u3002</p> <p>\u63a5\u4e0b\u6765\u6211\u4eec\u9010\u4e2a\u5206\u6790\u53d8\u5316\uff1a</p> <p>Deletion / case 1</p> <p>\u867d\u7136\u5927\u90e8\u5206\u6559\u7a0b\u90fd\u628a case 1 \u5f53\u4f5c\u4e00\u4e2a case\uff0c\u4f46\u662f\u6211\u89c9\u5f97\u5b8c\u5168\u53ef\u4ee5\u628a\u5b83\u6309\u7167 a \u8282\u70b9\u7684\u7ea2\u9ed1\uff0c\u5206\u4e3a\u4e24\u79cd\u60c5\u51b5\u3002</p> <p></p> <p>Deletion / case 1.1</p> <p>\u5f53 a \u4e3a\u7ea2\u6839\u65f6\uff0c\u7531\u4e8e x \u8d21\u732e\u4e86\uff08\u76f8\u5bf9\u4e8e\u539f\u7ea2\u9ed1\u6811\uff09-1 \u7684\u9ed1\u9ad8\uff0c\u4e3a\u4e86\u4fdd\u8bc1\u6574\u4e2a\u5b50\u6811\u8d21\u732e\u7684\u9ed1\u9ad8\u4e0d\u53d8\uff0c\u6211\u4eec\u8003\u8651\u628a w \u7684\u9ed1\u9ad8\u201c\u4e0a\u653e\u201d\u5230 a \u4e0a\uff0c\u4e5f\u5c31\u662f\u4ece\u4e0b\u9762\u201c\u5438\u7eb3\u201d\u4e0a\u6765\u3002</p> <p></p> <p>Deletion / case 1.2</p> <p>\u5f53 a \u4e3a\u9ed1\u6839\u65f6\uff0c\u6211\u4eec\u6ca1\u6709\u7a7a\u4f59\u7684\u4f4d\u7f6e\u6765\u201c\u5438\u7eb3\u201d w \u7684\u9ed1\u9ad8\uff0c\u4f46\u662f\u5de6\u5b50\u6811\u548c\u53f3\u5b50\u6811\u7684\u4e0d\u5e73\u8861\u662f\u5fc5\u987b\u89e3\u51b3\u7684\uff0c\u800c\u6211\u4eec\u7edd\u4e0d\u80fd\u5bc4\u5e0c\u671b\u4e8e\u201c\u5728\u4e0d\u77e5\u9053\u6709\u6ca1\u6709\u7ea2\u8272\u8282\u70b9\u7684 b \u548c c \u7684\u5b50\u6811\u4e2d\u53bb\u5bfb\u627e\u7ea2\u8272\u8282\u70b9\u201d\u8fd9\u4e2a\u60f3\u6cd5\u3002</p> <p>\u6240\u4ee5\u6211\u4eec\u53ef\u4ee5\u4eff\u7167\u300cInsertion / case 3\u300d\uff0c\u5c06\u6574\u4e2a\u6811\u6807\u8bb0\u4e3a\u7070\u8272\u2014\u2014\u300c\u7531\u4e8e\u5220\u9664\u7ed3\u70b9\uff0c\u9ed1\u9ad8 -1 \u7684\u5b50\u6811\u300d\uff0c\u7136\u540e\u8fdb\u4e00\u6b65\u6839\u636e\u5176\u5bb6\u957f\u8282\u70b9\u7684\u60c5\u51b5\u9012\u5f52\u5230\u5176\u4ed6 case\u3002\u5176\u4e2d\uff0c\u5f53\u6211\u4eec\u9012\u5f52\u5230 a \u662f\u6574\u4e2a\u6811\u7684\u6839\u65f6\u53ef\u4ee5\u9000\u51fa\uff0c\u56e0\u4e3a\u8fd9\u76f8\u5f53\u4e8e\u6574\u4e2a\u6811\u7684\u9ed1\u9ad8 -1\uff0c\u4e0d\u5f71\u54cd\u7ea2\u9ed1\u6027\u8d28\u3002</p> <p></p> <p>Deletion / case 2</p> <p>\u753b\u4e0d\u52a8\u56fe\u4e86\uff0c\u5148\u8bed\u8a00\u63cf\u8ff0\u4e00\u4e0b\u3002</p> <ol> <li>\u5c06 w \u67d3\u4e3a a \u7684\u989c\u8272\uff0c\u518d\u5c06 a \u548c c \u67d3\u6210\u9ed1\u8272\uff1b</li> <li>\u5c06 a \u5de6\u65cb\uff0c\u4f7f w \u6210\u4e3a\u8fd9\u4e2a\u5b50\u6811\u65b0\u7684\u6839\uff0ca \u6210\u4e3a w \u7684\u5de6\u513f\u5b50\uff0cb \u6210\u4e3a a \u7684\u53f3\u513f\u5b50\uff1b</li> <li>\u8c03\u6574\u7ed3\u675f\uff1b</li> </ol> <p>Deletion / case 3</p> <p>\u753b\u4e0d\u52a8\u56fe\u4e86\uff0c\u5148\u8bed\u8a00\u63cf\u8ff0\u4e00\u4e0b\u3002</p> <ol> <li>\u4ea4\u6362 b \u548c w \u7684\u989c\u8272\uff1b</li> <li>\u5c06 w \u53f3\u65cb\uff0c\u4f7f b \u6210\u4e3a a \u7684\u53f3\u513f\u5b50\uff0cw \u6210\u4e3a b \u7684\u53f3\u513f\u5b50\uff0cb \u7684\u53f3\u513f\u5b50\u6210\u4e3a w \u7684\u5de6\u513f\u5b50\uff1b</li> <li>\u6b64\u65f6\u60c5\u51b5\u8f6c\u5316\u4e3a case 2\uff1b</li> </ol> <p>Deletion / case 4</p> <p>\u753b\u4e0d\u52a8\u56fe\u4e86\uff0c\u5148\u8bed\u8a00\u63cf\u8ff0\u4e00\u4e0b\u3002</p> <ol> <li>\u4ea4\u6362 a \u548c w \u7684\u989c\u8272\uff1b</li> <li>\u5c06 a \u5de6\u65cb\uff0c\u4f7f w \u6210\u4e3a\u8fd9\u4e2a\u5b50\u6811\u65b0\u7684\u6839\uff0ca \u6210\u4e3a w \u7684\u5de6\u513f\u5b50\uff0cb \u6210\u4e3a a \u7684\u53f3\u513f\u5b50\uff1b</li> <li>\u6b64\u65f6\u6839\u636e\u5b50\u6811 a \u7684\u60c5\u51b5\uff0c\u8f6c\u5316\u4e3a case 1.1 / case 2 / case 3\uff1b</li> </ol> \u533a\u5206 case 1.1 \u548c case 1.2\u4e0d\u533a\u5206 case 1.1 \u548c case 1.2 <pre><code>graph LR;\nA1[\"case 1.1\"]\nA2[\"case 1.2\"]\nB[\"case 2\"]\nC[\"case 3\"]\nD[\"case 4\"]\nE[\"finish\"]\n\nA1 ---&gt;|\"C\"| E\nA2 ===&gt;|\"C\"| A1\nA2 ===&gt;|\"C\"| A2\nA2 ===&gt;|\"C\"| B\nA2 ===&gt;|\"C\"| C\nA2 ===&gt;|\"C\"| D\nC ---&gt;|\"C&amp;R\"| B ---&gt;|\"C&amp;R\"| E\nD ===&gt;|\"C&amp;R\"| A1\nD ===&gt;|\"C&amp;R\"| B\nD ===&gt;|\"C&amp;R\"| C</code></pre> <pre><code>graph LR;\nA[\"case 1\"]\nB[\"case 2\"]\nC[\"case 3\"]\nD[\"case 4\"]\nE[\"finish\"]\n\nA ---&gt;|\"C\\nfrom case 1.1\"| E\nA ===&gt;|\"C\\nfrom case 1.2\"| A\nA ===&gt;|\"C\\nfrom case 1.2\"| B\nA ===&gt;|\"C\\nfrom case 1.2\"| C\nA ===&gt;|\"C\\nfrom case 1.2\"| D\nC ---&gt;|\"C&amp;R\"| B ---&gt;|\"C&amp;R\"| E\nD ===&gt;|\"C&amp;R\\nto case 1.1 \"| A\nD ===&gt;|\"C&amp;R\"| B\nD ===&gt;|\"C&amp;R\"| C</code></pre> <p>\u6ce8\u610f\uff0c\u72b6\u6001\u673a\u4e2d\u7684\u7c97\u7ebf\u8868\u793a\u8f6c\u6362\u8fc7\u7a0b\u4e2d\uff0c\u6211\u4eec\u5173\u6ce8\u7684\u201c\u5b50\u6811\u201d\u5411\u4e0a\u6216\u5411\u4e0b\u8f6c\u79fb\u4e86\u4e00\u7ea7\uff08\u7531 case 4 \u51fa\u53d1\u65f6\u4e0b\u964d\uff0c\u7531 case 1.2 \u51fa\u53d1\u65f6\u4e0a\u5347\uff09\uff1b\u800c\u7ec6\u7ebf\u8868\u793a\u6211\u4eec\u5173\u6ce8\u7684\u5b50\u6811\u4ecd\u7136\u662f\u8fd9\u4e00\u5c42\u7684\u90a3\u4e00\u68f5\u3002\u4ee5\u53ca\uff0c<code>C</code> \u8868\u793a\u67d3\u8272\u64cd\u4f5c\uff0c<code>R</code> \u8868\u793a\u65cb\u8f6c\u64cd\u4f5c\u3002</p> <p>\u5176\u4e2d\uff0c\u4efb\u4f55\u4e00\u4e2a\u60c5\u51b5\u90fd\u53ef\u4ee5\u4f5c\u4e3a\u4e00\u4e2a\u521d\u59cb\u60c5\u51b5\u3002\u6240\u4ee5\u53ef\u4ee5\u6570\u51fa\uff0c\u5230\u8fbe finish \u7684\u8def\u5f84\u4e2d\uff0c\u6700\u591a\u51fa\u73b0 3 \u6b21 Rotation\uff08case 4 -&gt; case 3 -&gt; case 2 -&gt; finish\uff09\u3002</p> <p>\u6839\u636e\u524d\u9762\u72b6\u6001\u673a\u7684\u76f8\u5173\u5185\u5bb9\uff0c\u6211\u4eec\u4e0d\u96be\u5f97\u5230\u8fd9\u5f20\u8868\u683c\uff0c\u5b83\u7edf\u8ba1\u7684\u662f Rotation \u5728\u4e0d\u540c\u6570\u636e\u7ed3\u6784\u3001\u4e0d\u540c\u64cd\u4f5c\u4e2d\u51fa\u73b0\u7684\u6570\u91cf\uff1a</p> Option AVL Tree RB Tree Insertion \\(\\leq 2\\) \\(\\leq 2\\) Deletion \\(O(\\log N)\\) \\(\\leq 3\\)"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec02/#b-tree","title":"B+ Tree","text":"<p>link</p> <p>OI Wiki: https://oi-wiki.org/ds/bplus-tree/</p> <p>Wiki: https://en.wikipedia.org/wiki/B%2B_tree</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec02/#\u6982\u5ff5_1","title":"\u6982\u5ff5","text":"<p>B+ \u6811\u662f\u4e00\u79cd\u7528\u6811\u72b6\u5f62\u5f0f\u7ef4\u62a4\u6709\u5e8f\u6570\u5217\u6bd4\u8f83\u4fe1\u606f\u7684\u6570\u636e\u7ed3\u6784\uff0c\u5176\u589e\u6539\u64cd\u4f5c\u62e5\u76f8\u5bf9\u4e8e\u4e8c\u53c9\u6811\u7ed3\u6784\u66f4\u52a0\u7a33\u5b9a\u7684\u5bf9\u6570\u65f6\u95f4\u590d\u6742\u5ea6\uff0c\u901a\u5e38\u7528\u4e8e\u6570\u636e\u5e93\u548c\u64cd\u4f5c\u7cfb\u7edf\u7684\u6587\u4ef6\u7cfb\u7edf\u4e2d\u3002</p> <p>B+ Tree</p> <p>\u5982\u4e0b\u56fe\u5c31\u662f\u4e00\u9897 \\(M=4\\) \u7684 B+ \u6811\uff0c\u53ef\u4ee5\u5bf9\u7167\u7740\u8fd9\u4e2a\u4f8b\u5b50\u6765\u7406\u89e3\u6027\u8d28\u3002</p> <p></p> <p>\u66f4\u4e00\u822c\u5730\u6765\u8bf4\uff0cB+ \u6811\u6ee1\u8db3\u5982\u4e0b\u6027\u8d28\uff1a</p> <p>property of B+ Tree</p> <p>@cy's PPT</p> <ol> <li>The root is either a leaf or has between \\(2\\) and \\(M\\) children.</li> <li>All nonleaf nodes (except the root) have between \\(\\lceil M/2 \\rceil\\) and M children.</li> <li>All leaves are at the same depth.</li> </ol> <p>Assume each nonroot leaf also has between \\(\\lceil M/2 \\rceil\\) and \\(M\\) children.</p> <p>\u6240\u6709\u771f\u5b9e\u7684\u6570\u636e\u90fd\u88ab\u5b58\u50a8\u5728\u53f6\u5b50\u7ed3\u70b9\u4e2d\uff0c\u5f62\u6210\u4e00\u4e2a\u6709\u5e8f\u7684\u6570\u5217\u3002\u800c\u975e\u53f6\u5b50\u7ed3\u70b9\u4e2d\u7b2c <code>i</code> \u4e2a\u952e\u503c\u7b49\u4e8e\u5176\u7b2c <code>i+1</code> \u68f5\u5b50\u6811\u7684\u6700\u5c0f\u503c\uff08\u5728\u4e0a\u56fe\u4e2d\u8868\u73b0\u4e3a\u989c\u8272\u76f8\u540c\u7684\u4e00\u5bf9\u4e0a\u4e0b\u7ed3\u70b9\uff09\uff0c\u56e0\u6b64\u975e\u53f6\u7ed3\u70b9\u6700\u591a\u5b58 \\(M-1\\) \u4e2a\u503c\u3002</p> \u53d1\u73b0 <p>\u4e8e\u662f\u6211\u4eec\u53d1\u73b0\u8fd9\u6837\u4e00\u4e2a\u6027\u8d28\uff1a\u5728\u5b58\u50a8\u6570\u503c\u4e0d\u91cd\u590d\u7684\u60c5\u51b5\u4e0b\uff0c\u975e\u53f6\u7ed3\u70b9\u5b58\u50a8\u7684\u952e\u503c\u90fd\u4e0d\u76f8\u540c\u3002</p> <p>\u8bc1\u660e\u5f88\u7b80\u5355\uff0c\u5bf9\u4e8e\u4efb\u610f\u4e00\u4e2a\u975e\u53f6\u5b50\u7ed3\u70b9\uff0c\u5b83\u5b58\u50a8\u7684\u503c\u5fc5\u5b9a\u4e0d\u4f1a\u88ab\u5b83\u7684\u5b50\u8282\u70b9\u5b58\u50a8\uff08\u5982\u679c\u5b83\u7684\u5b50\u8282\u70b9\u4e0d\u662f\u53f6\u5b50\uff09\uff0c\u56e0\u4e3a\u5b83\u5b58\u7684\u662f\u5b83\u7684\u5b50\u8282\u70b9\u7684\u7b2c\u4e00\u4e2a\u5b50\u6811\u7684\u6700\u5c0f\u503c\uff0c\u800c\u5b83\u7684\u5b50\u8282\u70b9\u5b58\u7684\u662f\u7b2c\u4e8c\u4e2a\u5b50\u6811\u5f00\u59cb\u7684\u6700\u5c0f\u503c\u3002</p> <p>\u6211\u4eec\u79f0\u8fd9\u6837\u7684\u6811\u4e3a\u4e00\u4e2a \\(M\\) \u9636(order) B+ \u6811\u3002\u5bf9\u4e8e\u5e38\u89c1\u7684 \\(M\\)\uff0c\u6bd4\u5982\u4e00\u68f5 \\(4\\) \u9636 B+ \u6811\uff0c\u6211\u4eec\u4e5f\u79f0\u4e4b\u4e3a\u4e00\u68f5 2-3-4 \u6811\uff0c\u4e00\u822c \\(M\\) \u7684\u9009\u62e9\u4e3a 3 \u6216 4\u3002</p> <p>\u7279\u522b\u8bf4\u660e\uff0c\u5bf9\u4e8e B+ \u6811\uff0c\u5c06\u5b83\u7684\u53f6\u5b50\u7ed3\u70b9\u62fc\u63a5\u8d77\u6765\uff0c\u5b9e\u9645\u4e0a\u5c31\u662f\u4e00\u4e2a\u6709\u5e8f\u6570\u5217\u3002</p> <p>\u62bd\u8c61\u5730\u6765\u8bf4\u5c31\u662f\uff0c\u6211\u4eec\u628a\u4e00\u4e2a\u6570\u5217\u76f8\u5bf9\u5747\u5300\u7684\u5206\u4e3a \\(m\\) \u5757\uff0c\u7136\u540e\u628a\u5206\u754c\u7684\u6570\u62ff\u51fa\u6765\u3002\u5f53\u6211\u4eec\u53bb\u67e5\u627e\u6216\u63d2\u5165\u65f6\uff0c\u53ea\u9700\u8981\u548c\u8fd9\u4e9b\u8fb9\u754c\u6570\u8fdb\u884c\u6bd4\u8f83\uff0c\u5c31\u77e5\u9053\u5b83\u5e94\u8be5\u653e\u5728\u54ea\u4e00\u5757\u91cc\u3002\u518d\u4e0d\u65ad\u7ec6\u5316\u7c92\u5ea6\uff0c\u7528\u7c7b\u4f3c\u4e8e\u201c\\(m\\) \u5206\u201d\u7684\u601d\u60f3\u6765\u627e\u5230\u76ee\u6807\u4f4d\u7f6e\u3002</p> <p>\u5728\u6211\u770b\u6765\u8fd9\u4e2a\u5b9a\u4e49\u975e\u5e38\u6e05\u6670\uff0c\u5c31\u662f\u5c06\u6574\u4e2a\u5e8f\u5217\u6309\u7167\u4e0d\u540c\u7c92\u5ea6\u5212\u5206\uff0c\u7136\u540e\u7531\u5927\u5230\u5c0f\u8fdb\u884c\u903c\u8fd1\u3002</p> <p>depth of B+ Tree</p> <p>\u7531\u4e8e\u5b83\u5728\u7a7a\u95f4\u6700\u6d6a\u8d39\u7684\u60c5\u51b5\u4e0b\u662f\u4e00\u68f5 \\(\\lceil M/2 \\rceil\\) \u53c9\u6811\uff0c\u6240\u4ee5 B+ \u6811\u7684\u6df1\u5ea6\u662f \\(O(\\lceil \\log_{\\lceil M/2 \\rceil} N \\rceil)\\)\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec02/#\u64cd\u4f5c_1","title":"\u64cd\u4f5c","text":"<p>\u7531\u4e8e B+ \u6811\u7684\u6027\u8d28\u5341\u5206\u81ea\u7136\uff0c\u6240\u4ee5\u5b83\u7684\u64cd\u4f5c\u4ece\u601d\u60f3\u5c42\u9762\u4e0a\u6765\u8bf4\u4e5f\u975e\u5e38\u7b80\u5355\u3002\u5176\u66f4\u591a\u7684\u96be\u5ea6\u5728\u4e8e\u5b9e\u73b0\u4e0a\u3002</p> <p>\u5173\u4e8e\u5b9e\u73b0\u7684\u5efa\u8bae</p> <p>\u7531\u4e8e B+ \u6811\u5173\u4e8e\u5185\u90e8\u8282\u70b9\u548c\u53f6\u5b50\u7684\u5b9a\u4e49\u5341\u5206\u5272\u88c2\uff08\u867d\u7136\u7ea2\u9ed1\u6811\u53f6\u4e5f\u5f88\u5272\u88c2\uff0c\u4f46\u662f\u6bd5\u7adf\u7ea2\u9ed1\u6811\u7684\u53f6\u5b50\u4e0d\u9700\u8981\u4ec0\u4e48\u64cd\u4f5c\uff0c\u4f46\u662f B+ \u6811\u9700\u8981\uff09\uff0c\u6240\u4ee5\u5728\u5b9e\u73b0\u8fc7\u7a0b\u4e2d\u4f1a\u9047\u5230\u4e00\u4e9b\u9ebb\u70e6\u3002</p> <p>\u6211\u4e2a\u4eba\u5efa\u8bae\uff0c\u5982\u679c\u4f60\u5341\u5206\u719f\u6089 oop\uff0c\u90a3\u4e48\u53ef\u4ee5\u5c1d\u8bd5\u7528\u591a\u6001\u6765\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\u3002\u53cd\u6b63\u6211\u5b9e\u73b0 B+ \u6811\u7684\u65f6\u5019\u5bf9 cpp \u7684 oop \u6211\u8bf4\u4e0d\u4e0a\u5341\u5206\u719f\u7ec3\uff0c\u6240\u4ee5\u6211\u76f4\u63a5\u65e0\u8111\u4f7f\u7528 <code>struct</code> with tag \u5b9e\u73b0\u4e86\u3002</p> <p>\u800c\u5728\u5f00\u59cb\u5199\u4ee3\u7801\u4e4b\u524d\uff0c\u6211\u5f3a\u70c8\u5efa\u8bae\u5927\u5bb6\u6309\u7167\u6211\u4e0b\u9762\u505a\u56fe\u7684\u683c\u5f0f\uff0c\u6a21\u62df\u4e00\u904d\u5404\u4e2a\u64cd\u4f5c\uff01\u5e76\u5728\u6a21\u62df\u8fc7\u7a0b\u4e2d\uff0c\u89c2\u5bdf\u6570\u636e\u7684\u6d41\u52a8\u4ee5\u53ca\u8282\u70b9\u7684\u7ed3\u6784\u53d8\u5316\u3002</p> <p>\u6b64\u5916\uff0c\u5728\u8ba8\u8bba\u8fd9\u4e9b\u64cd\u4f5c\u65f6\uff0c\u5148\u8ba9\u6211\u4eec\u5ffd\u7565\u5982\u4f55\u4ece\u7a7a\u5efa\u7acb\u8d77\u4e00\u4e2a B+ \u6811\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec02/#\u67e5\u627e","title":"\u67e5\u627e","text":"<p>\u548c\u4e8c\u53c9\u6811\u7684\u67e5\u627e\u5341\u5206\u76f8\u4f3c\uff0c\u6240\u4ee5\u8fd9\u91cc\u53ea\u6a21\u62df\u4e00\u4e0b\u4e3e\u4e2a\u4f8b\u5b50\u3002</p> <p></p> <p>\u4f8b\u5982\uff0c\u6211\u4eec\u5728\u4e0a\u9762\u8fd9\u68f5\u6811\u4e2d\u627e <code>43</code> \u8fd9\u4e2a\u503c\uff0c\u6a59\u8272\u90e8\u5206\u8868\u793a\u6211\u4eec\u7684\u7126\u70b9\u3002</p> <p>Find(43)</p> Frame 1Frame 2Frame 3 <p></p> <p>\u6211\u4eec\u53d1\u73b0\u6709 \\(21 \\leq 43 &lt; 48\\)\uff0c\u6240\u4ee5\u987a\u7740\u6807\u8bc6\u7684\u6a59\u8272\u6307\u9488\u5411\u4e0b\u3002</p> <p></p> <p>\u6211\u4eec\u53d1\u73b0\u6709 \\(41 \\leq 43\\)\uff0c\u6240\u4ee5\u987a\u7740\u6807\u8bc6\u7684\u6a59\u8272\u6307\u9488\u5411\u4e0b\u3002</p> <p></p> <p>\u5df2\u7ecf\u8d70\u5230\u53f6\u5b50\u7ed3\u70b9\uff0c\u6700\u540e\u53d1\u73b0\u6211\u4eec\u8981\u627e\u7684 <code>43</code>\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec02/#\u63d2\u5165_1","title":"\u63d2\u5165","text":"<p>\u63d2\u5165\u7684\u65b9\u6cd5\u4e5f\u76f8\u5bf9\u6734\u7d20\u7b80\u5355\uff0c\u5c31\u662f\u627e\u5230\u8be5\u63d2\u5165\u7684\u5730\u65b9\u4ee5\u540e\u63d2\u5165\u5373\u53ef\u3002</p> <p>\u53ea\u4e0d\u8fc7\u9700\u8981\u6ce8\u610f\u4e00\u4ef6\u4e8b\uff0c\u5f53\u8fd9\u4e2a\u63d2\u5165\uff0c\u5bfc\u81f4\u4e86 B+ \u6811\u7684\u6027\u8d28\u4e0d\u518d\u6210\u7acb\u65f6\uff0c\u5373\u5bfc\u81f4\u5176\u5bb6\u957f\u8282\u70b9\u7684\u5b50\u8282\u70b9\u6570\u91cf\u4e3a \\(M+1\\) \u65f6\uff0c\u6211\u4eec\u9700\u8981\u5c06\u8fd9\u4e2a\u7ed3\u70b9\u5e73\u5747\u5206\u88c2\u6210\u4e24\u4e2a\uff0c\u6b64\u65f6\u663e\u7136\u6709\u4e24\u4e2a\u5b50\u6811\u7684\u8282\u70b9\u6570\u91cf\u90fd\u4e0d\u5c0f\u4e8e \\(\\lceil M+1 \\rceil\\)\u3002\u4f46\u8fd9\u8fd8\u4e0d\u591f\uff0c\u5206\u88c2\u5bfc\u81f4\u5bb6\u957f\u8282\u70b9\u7684\u5bb6\u957f\u8282\u70b9\u7684\u5b50\u8282\u70b9\u53d8\u591a\uff0c\u6240\u4ee5\u6211\u4eec\u8fd8\u5f97\u5411\u4e0a\u9012\u5f52\u3002</p> <p>\u4f9d\u7136\u662f\u8fdb\u884c\u4e00\u4e2a\u6a21\u62df\uff0c\u6211\u4eec\u6a21\u62df\u63d2\u5165 <code>46</code> \u548c <code>44</code>\u3002</p> <p>Insert(46), no split</p> Frame 1Frame 2Frame 3 <p></p> <p>\u540c\u67e5\u627e\uff0c\u7565\u3002</p> <p></p> <p>\u540c\u67e5\u627e\uff0c\u7565\u3002</p> <p></p> <p>\u627e\u5230\u8981\u585e\u7684\u4f4d\u7f6e\u4e86\uff0c\u53d1\u73b0\u8981\u585e\u7684\u5730\u65b9\u662f <code>45</code> \u7684\u540e\u9762\uff0c\u63d2\u5165\u4ee5\u540e\u53d1\u73b0\u4e00\u5171 4 \u4e2a\u6570\uff0c\u800c \\(M=4\\)\uff0c\u4e0d\u9700\u8981\u5206\u88c2\u3002</p> <p>Insert(44), split</p> Frame 1Frame 2Frame 3Frame 4Frame 5Frame 6 <p></p> <p>\u540c\u67e5\u627e\uff0c\u7565\u3002</p> <p></p> <p>\u540c\u67e5\u627e\uff0c\u7565\u3002</p> <p></p> <p>\u627e\u5230\u8981\u585e\u7684\u4f4d\u7f6e\u4e86\uff0c\u53d1\u73b0\u8981\u585e\u7684\u5730\u65b9\u662f <code>45</code> \u7684\u524d\u9762\uff0c\u63d2\u5165\u4ee5\u540e\u53d1\u73b0\u4e00\u5171 5 \u4e2a\u6570\uff0c\u800c \\(M=4\\)\uff0c\u9700\u8981\u5206\u88c2\uff01</p> <p></p> <p>\u5411\u4e0a\u9012\u5f52\uff0c\u6211\u4eec\u60b2\u75db\u5730\u53d1\u73b0\uff0c\u8fd9\u4e2a\u8282\u70b9\u5728\u5206\u88c2\u540e\u6709\u4e86 <code>5</code> \u4e2a\u5b50\u8282\u70b9\uff0c\u4e0d\u5f97\u4e0d\u518d\u6b21\u5206\u88c2\u3002</p> <p></p> <p>\u5411\u4e0a\u9012\u5f52\uff0c\u6211\u7684\u8001\u5929\u7237\u5440\uff0c\u600e\u4e48\u8fd8\u6ca1\u5230\u5934\uff01\u8fd9\u4e0b\u6211\u4eec\u8981\u5206\u88c2\u6839\u90e8\u4e86\uff01</p> <p></p> <p>\u7531\u4e8e\u6839\u90e8\u88ab\u88c2\u5f00\u4e86\uff0c\u6240\u4ee5\u6211\u4eec\u9700\u8981\u6dfb\u52a0\u4e00\u4e2a\u65b0\u7684\u6839\uff0c\u8fd9\u4e5f\u610f\u5473\u7740\u6811\u7684\u5c42\u6570\u589e\u9ad8\u4e86\u3002</p> <p>\u73b0\u5728\uff0c\u6211\u4eec\u7ec8\u4e8e\u5b8c\u6210\u4e86\u63d2\u5165\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec03/","title":"Lecture 3 | Inverted File Index","text":"<p> \u7ea6 1461 \u4e2a\u5b57  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 5 \u5206\u949f</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec03/#\u5012\u6392\u7d22\u5f15","title":"\u5012\u6392\u7d22\u5f15","text":"<p>\u5012\u6392\u7d22\u5f15\uff08inverted file index\uff09\u662f\u4e00\u79cd\u5e38\u89c1\u7684\u6587\u672c\u68c0\u7d22\u6280\u672f\uff0c\u7528\u4e8e\u5feb\u901f\u67e5\u627e\u5305\u542b\u7279\u5b9a\u5355\u8bcd\u6216\u77ed\u8bed\u7684\u6587\u6863\u3002\u5b83\u901a\u8fc7\u5c06\u5355\u8bcd\u6216\u77ed\u8bed\u4f5c\u4e3a\u5173\u952e\u5b57\uff0c\u5e76\u5c06\u5b83\u4eec\u51fa\u73b0\u5728\u6587\u6863\u4e2d\u7684\u4f4d\u7f6e\u8bb0\u5f55\u5728\u4e00\u4e2a\u7d22\u5f15\u4e2d\uff0c\u4ece\u800c\u652f\u6301\u5feb\u901f\u7684\u6587\u672c\u68c0\u7d22\u3002\u5728\u641c\u7d22\u8fc7\u7a0b\u4e2d\uff0c\u7cfb\u7edf\u53ef\u4ee5\u5feb\u901f\u5730\u5b9a\u4f4d\u5305\u542b\u6307\u5b9a\u5355\u8bcd\u6216\u77ed\u8bed\u7684\u6587\u6863\uff0c\u5e76\u8fd4\u56de\u5b83\u4eec\u7684\u76f8\u5173\u4fe1\u606f\u3002\u5012\u6392\u7d22\u5f15\u5e7f\u6cdb\u5e94\u7528\u4e8e\u641c\u7d22\u5f15\u64ce\u3001\u6570\u636e\u5e93\u7cfb\u7edf\u548c\u4fe1\u606f\u68c0\u7d22\u7b49\u9886\u57df\u3002</p> <p>\u2014\u2014 ChatGPT</p> <p>Info</p> <p>Wiki: https://en.wikipedia.org/wiki/Inverted_index</p> <p>\u6240\u8c13\u7684\u5012\u6392\u7d22\u5f15\uff0c\u6240\u6709\u7684\u601d\u60f3\u90fd\u51dd\u7ed3\u5728\u4e86\u201c\u5012\u201d\uff0c\u4e5f\u5c31\u662f inverted\u3002\u5982\u679c\u53ef\u4ee5\uff0c\u6211\u89c9\u5f97\u7528\u201c\u9006\u201d\u66f4\u5408\u9002\u3002\u8fd9\u91cc\u7684\u7d22\u5f15\u5bf9\u8c61\u6307\u7684\u662f\u201c\u6587\u6863\u201d\u548c\u201c\u5355\u8bcd\u201d\u4e4b\u95f4\u7684\u5173\u7cfb\uff0c\u800c\u5012\u6392\u7d22\u5f15\u7684\u610f\u601d\u662f\uff0c\u5bf9\u4e8e\u6bcf\u4e00\u4e2a\u5355\u8bcd\uff0c\u6211\u4eec\u8bb0\u5f55\u5b83\u51fa\u73b0\u5728\u54ea\u4e9b\u6587\u6863\u4e2d\uff0c\u4ee5\u53ca\u8bb0\u5f55\u4ed6\u4eec\u51fa\u73b0\u7684\u6b21\u6570\uff08\u9891\u7387\uff09\u3002</p> <p>\u641c\u7d22\u5f15\u64ce\u662f\u4e00\u4e2a\u975e\u5e38\u5e38\u89c1\u7684\uff0c\u5012\u6392\u7d22\u5f15\u7684\u5e94\u7528\u6848\u4f8b\uff0c\u6211\u4eec\u901a\u8fc7\u8f93\u5165\u6211\u4eec\u5173\u6ce8\u7684\u8bcd\u8bed\uff0c\u6765\u7d22\u5f15\u5305\u542b\u8fd9\u4e2a\u8bcd\u7684\u6240\u6709\u6587\u6863\u3002 \u5f53\u7136\uff0c\u5728\u8fd9\u91cc\u6211\u4eec\u8003\u8651\u7684\u662f\u82f1\u6587\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec03/#\u5012\u6392\u7d22\u5f15\u7684\u5b9e\u73b0","title":"\u5012\u6392\u7d22\u5f15\u7684\u5b9e\u73b0","text":"<p>\u77e5\u9053\u4e86\u5012\u6392\u7d22\u5f15\u7684\u601d\u60f3\u4e4b\u540e\uff0c\u5176\u5b9e\u73b0\u5c31\u53d8\u5f97\u975e\u5e38\u76f4\u89c2\u4e86\u3002\u6211\u4eec\u53ef\u4ee5\u7528\u4e00\u4e2a\u5b57\u5178\u6765\u63cf\u8ff0\u4e00\u7c7b\u5173\u7cfb\uff0c\u5176\u4e3b\u952e\u4e3a\u5355\u8bcd\uff0c\u952e\u503c\u4e3a\u8fd9\u4e2a\u5355\u8bcd\u51fa\u73b0\u7684\u6240\u6709\u4f4d\u7f6e\u3002</p> <p>\u6700\u6734\u7d20\u7684\u7248\u672c\u5c31\u662f\u8ba9\u952e\u503c\u4e3a\u5355\u8bcd\u51fa\u73b0\u8fc7\u7684\u6587\u6863\u7684\u5e8f\u53f7\u5e8f\u5217\uff0c\u800c\u5982\u679c\u6211\u4eec\u8fd8\u9700\u8981\u77e5\u9053\u8bcd\u6c47\u51fa\u73b0\u7684\u4f4d\u7f6e\uff0c\u5219\u53ef\u4ee5\u8ba9\u952e\u503c\u662f\u4e00\u4e2a\u4e8c\u5143\u7ec4\u7684\u5e8f\u5217\uff0c\u5176\u4e2d\u7b2c\u4e00\u4e2a\u5143\u7d20\u662f\u6587\u6863\u7684\u5e8f\u53f7\uff0c\u7b2c\u4e8c\u4e2a\u5143\u7d20\u662f\u5355\u8bcd\u5728\u6587\u6863\u4e2d\u51fa\u73b0\u7684\u4f4d\u7f6e\u3002</p> <p>\u4e00\u4e2a \ud83c\udf30</p> <p>\u4f8b\u5982\u6211\u4eec\u6709\u5982\u4e0b\u6587\u4ef6\u96c6\uff1a</p> <p>\u6587\u6863\u96c6</p> Doc Text 1 Gold silver truck 2 Shipment of gold damaged in a fire 3 Delivery of silver arrived in a silver truck 4 Shipment of gold arrived in a truck <p>\u90a3\u4e48\u6211\u4eec\u53ef\u4ee5\u5f97\u5230\u5982\u4e0b\u7684\u5012\u6392\u7d22\u5f15\uff1a</p> <p>\u5012\u6392\u7d22\u5f15</p> No. Term Times; (Doc ID: Places) 1 a {3; (2;6),(3;6),(4;6)} 2 arrived {2; (3;4),(4;4)} 3 damaged {1; (2;4)} 4 delivery {1; (3;1)} 5 fire {1; (2;7)} 6 gold {3; (1;1),(2;3),(4;3)} 7 of {3; (2;2),(3;2),(4;2)} 8 in {3; (2;5),(3;5),(4;5)} 9 shipment {2; (2;1),(4;1)} 10 silver {2; (1;2),(3;3,7)} 11 truck {3; (1;3),(3;8),(4;7)} <p>\u6240\u4ee5\u5b9e\u9645\u4e0a\u975e\u5e38\u7b80\u5355\uff0c\u6211\u4eec\u53ea\u9700\u8981\u626b\u63cf\u6587\u6863\uff0c\u7136\u540e\u5b58\u4e0b\u6bcf\u4e00\u4e2a\u6587\u4ef6\u5728\u54ea\u91cc\u51fa\u73b0\u8fc7\u5373\u53ef\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec03/#\u6539\u8fdb","title":"\u6539\u8fdb","text":"<p>\u90a3\u4e48\u5230\u6b64\u4e3a\u6b62\u4e86\u5417\uff1f\u975e\u4e5f\u3002\u5018\u82e5\u6beb\u65e0\u8282\u5236\u7684\u5c06\u6240\u6709\u8bcd\u90fd\u5b58\u5230\u5012\u6392\u7d22\u5f15\u4e2d\uff0c\u90a3\u4e48\u6211\u4eec\u7684\u5012\u6392\u7d22\u5f15\u5c31\u4f1a\u53d8\u5f97\u975e\u5e38\u5927\uff0c\u5176\u4e2d\u5fc5\u7136\u6709\u5f88\u591a\u5197\u4f59\u4fe1\u606f\u5b58\u5728\uff0c\u6240\u4ee5\u6211\u4eec\u9700\u8981\u5bf9\u5012\u6392\u7d22\u5f15\u8fdb\u884c\u4e00\u4e9b\u6539\u8fdb\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec03/#\u505c\u7528\u8bcd","title":"\u505c\u7528\u8bcd","text":"<p>\u6211\u4eec\u89c2\u5bdf\u5230\uff0c\u6211\u4eec\u5b58\u4e0b\u6765\u7684\u8fd9\u4e9b\u5185\u5bb9\u4e2d\uff0c\u6709\u4e00\u4e9b\u4e1c\u897f\u9891\u7e41\u5730\u51fa\u73b0\u5728\u6240\u6709\u6587\u6863\u4e2d\uff0c\u5728\u7279\u5b9a\u60c5\u51b5\u4e0b\uff0c\u8fd9\u4e9b\u8bcd\u53ef\u80fd\u5e76\u4e0d\u4f1a\u6210\u4e3a\u4e00\u4e2a\u7d22\u5f15\uff0c\u4f8b\u5982\u6b63\u5e38\u7684\u82f1\u6587\u6587\u7ae0\u4e2d\u7684 <code>a</code>\uff0c<code>the</code> \u7b49\u3002\u6240\u4ee5\uff0c\u5bf9\u4e8e\u8fd9\u4e00\u7c7b\u8bcd\u2014\u2014\u6211\u4eec\u79f0\u4e4b\u4e3a\u505c\u7528\u8bcd(stop words)\uff0c\u5bf9\u4e8e\u505c\u7528\u8bcd\uff0c\u6211\u4eec\u5c31\u4e0d\u9700\u8981\u5c06\u4ed6\u4eec\u5b58\u4e0b\u4e86\u3002</p> <p>\u54ea\u4e9b\u8bcd\u4f1a\u6210\u4e3a\u505c\u7528\u8bcd\uff1f</p> <p>\u4e00\u822c\u4e00\u4e2a\u8bcd\u6210\u4e3a\u505c\u7528\u8bcd\uff0c\u662f\u56e0\u4e3a\u5b83\u65e0\u6cd5\u6210\u4e3a\u4e00\u4e2a\u6709\u6548\u7684\u68c0\u7d22\u5173\u952e\u5b57\uff0c\u5b83\u53ef\u80fd\u662f\u5728\u5927\u91cf\u8d44\u6599\u4e2d\u5927\u91cf\u51fa\u73b0\uff0c\u5bfc\u81f4\u6211\u4eec\u65e0\u6cd5\u5229\u7528\u5b83\u627e\u51fa\u6211\u4eec\u60f3\u8981\u7684\u8d44\u6599\u3002\u6362\u53e5\u8bdd\u6765\u8bf4\uff0c\u4e00\u4e2a\u5171\u901a\u70b9\u662f\u5b83\u4eec\u901a\u5e38\u90fd\u6709\u7740\u76f8\u5f53\u9ad8\u7684\u51fa\u73b0\u9891\u7387\u3002</p> <p>\u4f46\u662f\u6211\u4eec\u4e5f\u4e0d\u80fd\u76f2\u76ee\u5730\u5c06\u6240\u6709\u7684\u8bcd\u90fd\u4f5c\u4e3a\u505c\u7528\u8bcd\uff0c\u56e0\u4e3a\u6709\u4e9b\u8bcd\u5b83\u5728\u67d0\u4e9b\u542b\u4e49\u4e0b\u9002\u5408\u4f5c\u4e3a\u4e00\u79cd\u505c\u7528\u8bcd\uff0c\u4f46\u662f\u5728\u53e6\u4e00\u4e9b\u542b\u4e49\u4e0b\uff0c\u5b83\u5c31\u4e0d\u9002\u5408\u4f5c\u4e3a\u505c\u7528\u8bcd\u4e86\uff0c\u4e0d\u8fc7\u8fd9\u4e2a\u95ee\u9898\u5c31\u53d8\u5f97\u6bd4\u8f83\u590d\u6742\u4e86\uff0c\u6240\u4ee5\u8fd9\u91cc\u5e76\u4e0d\u5c55\u5f00\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec03/#\u8bcd\u5e72\u5206\u6790","title":"\u8bcd\u5e72\u5206\u6790","text":"<p>\u8bcd\u5e72\u5206\u6790(word stemming)\u662f\u4e00\u79cd\u5c06\u5355\u8bcd\u8f6c\u6362\u4e3a\u5176\u8bcd\u5e72\u7684\u6280\u672f\u3002\u4f8b\u5982\uff0c\u8bcd\u5e72\u5206\u6790\u53ef\u4ee5\u5c06\u5355\u8bcd <code>trouble</code>\uff0c<code>troubled</code>\uff0c<code>troubles</code>\uff0c<code>troubling</code> \u90fd\u8f6c\u6362\u4e3a <code>trouble</code>\uff08\u751a\u81f3\u662f <code>troubl</code>\uff0c\u6838\u5fc3\u76ee\u7684\u662f\u8ba9\u5b83\u4eec\u53d8\u6210\u540c\u4e00\u4e2a\u5355\u8bcd\uff09\u3002\u76f8\u540c\u8bcd\u5e72\u7684\u8bcd\u6709\u7740\u7c7b\u4f3c\u7684\u542b\u4e49\uff0c\u5728\u68c0\u7d22 <code>troubled</code> \u7684\u65f6\u5019\uff0c\u5f53\u7136\u4e5f\u53ef\u80fd\u60f3\u627e\u5230\u5305\u542b <code>trouble</code> \u7684\u6587\u6863\u3002\u8fd9\u79cd\u6280\u672f\u4e5f\u53ef\u4ee5\u8ba9\u591a\u4e2a\u5355\u8bcd\u5171\u4eab\u540c\u4e00\u6761\u7d22\u5f15\u8bb0\u5f55\uff0c\u5728\u5b58\u548c\u627e\u7684\u8fc7\u7a0b\u4e2d\u90fd\u80fd\u4f18\u5316\u6548\u679c\u3002</p> <p>\u4e0d\u8fc7\u5728\u5177\u4f53\u64cd\u4f5c\u65b9\u9762\uff0c\u8fd9\u4e2a\u4e1c\u897f\u5c31\u663e\u5f97\u6bd4\u8f83\u7e41\u6742\u548c\u66b4\u529b\u4e86\uff0c\u6211\u4eec\u53ea\u80fd\u6839\u636e\u8bed\u6cd5\u89c4\u8303\u8fdb\u884c\u66b4\u529b\u5339\u914d\u548c\u5224\u65ad\uff0c\u8fd9\u91cc\u6211\u4eec\u5c31\u4e0d\u5c55\u5f00\u4e86\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec03/#\u5206\u5e03\u5f0f","title":"\u5206\u5e03\u5f0f","text":"<p>\u53ef\u60f3\u800c\u77e5\uff0c\u5bf9\u4e8e\u4e00\u4e2a\u641c\u7d22\u5f15\u64ce\u6765\u8bf4\uff0c\u5b83\u6240\u9700\u8981\u7d22\u5f15\u7684\u6587\u6599\u662f\u975e\u5e38\u5e9e\u5927\u7684\uff0c\u6240\u4ee5\u6211\u4eec\u901a\u5e38\u9700\u8981\u5c06\u5176\u5206\u5e03\u5f0f\u5730\u5b58\u50a8\u548c\u7d22\u5f15\u3002</p> <p>\u800c\u8fd9\u91cc\u6709\u4e24\u79cd\u5206\u5e03\u5f0f\u7684\u7b56\u7565\uff0c\u5176\u4e00\u662f\u6839\u636e\u5355\u8bcd\u7684\u5b57\u5178\u5e8f\u8fdb\u884c\u5206\u5e03\u5f0f\uff0c\u5176\u4e8c\u662f\u6839\u636e\u6587\u6863\u8fdb\u884c\u5206\u5e03\u5f0f\u3002</p> <p>\u663e\u7136\u6839\u636e\u5355\u8bcd\u7684\u5185\u5bb9\u8fdb\u884c\u5206\u5e03\u5f0f\uff0c\u80fd\u591f\u63d0\u9ad8\u7d22\u5f15\u6548\u7387\uff0c\u4f46\u662f\u8fd9\u6837\u7684\u8bdd\uff0c\u6211\u4eec\u5c31\u9700\u8981\u5c06\u6240\u6709\u5f62\u5f0f\u63a5\u8fd1\u7684\u5355\u8bcd\u90fd\u5b58\u50a8\u5728\u4e00\u4e2a\u5730\u65b9\uff0c\u8fd9\u6837\u5c31\u4f1a\u9020\u6210\u5355\u70b9\u6545\u969c\uff0c\u5bb9\u707e\u80fd\u529b\u5f88\u5dee\uff0c\u6240\u4ee5\u8fd9\u79cd\u65b9\u5f0f\u5e76\u4e0d\u662f\u5f88\u597d\u3002</p> <p>\u800c\u7b2c\u4e8c\u79cd\u529e\u6cd5\u5219\u6709\u8f83\u5f3a\u7684\u5bb9\u707e\u6027\u80fd\u3002\u5373\u4f7f\u4e00\u53f0\u673a\u5668\u65e0\u6cd5\u5de5\u4f5c\uff0c\u4e5f\u4e0d\u4f1a\u5267\u70c8\u5f71\u54cd\u5230\u6574\u4e2a\u7cfb\u7edf\u7684\u5de5\u4f5c\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec03/#\u6027\u80fd\u8bc4\u4f30","title":"\u6027\u80fd\u8bc4\u4f30","text":"<p>\u548c\u7edf\u8ba1\u5b66\u7684\u5047\u8bbe\u68c0\u9a8c\u7c7b\u4f3c\uff0c\u4e5f\u548c\u673a\u5668\u5b66\u4e60\u9886\u57df\u7684 Average Precision \u7c7b\u4f3c\u3002</p> <p>\u8fd9\u4e9b\u5185\u5bb9\u53ef\u4ee5\u5f88\u597d\u7684\u7c7b\u6bd4\uff0c\u6682\u65f6\u4e0d\u518d\u5c55\u5f00\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec04/","title":"Lecture 4 | Leftist Heap &amp; Skew Heap","text":"<p> \u7ea6 4406 \u4e2a\u5b57  97 \u884c\u4ee3\u7801  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 16 \u5206\u949f</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec04/#leftist-heap","title":"Leftist Heap","text":"<p>link</p> <p>OI Wiki: https://oi-wiki.org/ds/leftist-tree/</p> <p>Wikipedia: https://en.wikipedia.org/wiki/Leftist_tree</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec04/#\u6982\u5ff5","title":"\u6982\u5ff5","text":"<p>\u5de6\u504f\u5806\uff0c\u6216\u8005\u8bf4\u5de6\u504f\u5806(Leftist Heap)\uff0c\u5b83\u76f8\u6bd4\u4e8e\u666e\u901a\u7684\u5806\uff0c\u66f4\u597d\u7684\u4e00\u70b9\u5728\u4e8e\u5b83\u652f\u6301\u5feb\u901f\u7684\u5806\u5408\u5e76\u64cd\u4f5c\u3002\u201c\u5de6\u504f\u201d\uff0c\u5e76\u4e0d\u65ad\u5c06\u65b0\u7684\u4e1c\u897f\u5f80\u53f3\u4fa7\u5408\u5e76\uff0c\u6765\u5b9e\u73b0\u6bcf\u6b21\u90fd\u662f\u5f80\u76f8\u5bf9\u5c0f\u7684\u90a3\u4e00\u4fa7\u585e\u8fdb\u4e1c\u897f\uff0c\u8fdb\u800c\u4fdd\u76f8\u5bf9\u8bc1\u4e86\u8fd9\u4e2a</p> <p>\u7531\u4e8e\u5de6\u504f\u5806\u4e0d\u518d\u662f\u4e00\u4e2a\u5b8c\u5168\u4e8c\u53c9\u6811\uff0c\u6240\u4ee5\u6211\u4eec\u4e0d\u80fd\u518d\u50cf\u7ef4\u62a4\u5927\u6839\u5806\u5c0f\u8ddf\u5806\u90a3\u6837\u7528\u6570\u7ec4\u6765\u7ef4\u62a4\u5b83\u4e86\u3002</p> <p>\u4e00\u4e2a\u5de6\u504f\u5806\u7684\u7ed3\u70b9\u7ef4\u62a4\u4e86\u5de6\u53f3\u5b50\u5806\u7684\u5730\u5740\u3001\u81ea\u8eab\u7684\u952e\u503c\u3001\u548c\u4e00\u4e2a\u201c\u8ddd\u79bb(dist)\u201d\u3002</p> <pre><code>struct LeftistHeapNode {\nElementType val;\nint dist;\nLeftistHeapNode * ls, * rs;\n};\n</code></pre> <p>'dist' in leftist heap</p> <ol> <li>\u5982\u679c\u4e00\u4e2a\u7ed3\u70b9\u7684\u5de6\u5b69\u5b50\u6216\u53f3\u5b69\u5b50\u4e3a\u7a7a\u7ed3\u70b9\uff0c\u5219\u8be5\u7ed3\u70b9\u7684 dist \u4e3a \\(0\\)\uff0c\u8fd9\u79cd\u7ed3\u70b9\u88ab\u79f0\u4e3a\u5916\u7ed3\u70b9\uff1b</li> <li>\u5982\u679c\u4e00\u4e2a\u7ed3\u70b9\u7684\u5de6\u5b69\u5b50\u548c\u53f3\u5b69\u5b50\u90fd\u4e0d\u4e3a\u7a7a\uff0c\u5219\u8be5\u7ed3\u70b9\u7684 dist \u4e3a \\(\\min{(dist_\\text{left child}, dist_\\text{right child})} + 1\\)\uff1b</li> </ol> <p>eg</p> <p> </p> <p>\u800c\u5de6\u504f\u5806\u5c31\u5efa\u7acb\u5728\u8fd9\u4e9b\u6027\u8d28\u4e0a\uff1a</p> <p>Leftist Heap</p> <p>\u5de6\u504f\u5806\u662f\u7ed3\u70b9\u7684\u952e\u503c\u5e94\u5f53\u4e0d\u5927\u4e8e\uff08\u4e0d\u5c0f\u4e8e\uff09\u5176\u5b69\u5b50\u7ed3\u70b9\u7684\u952e\u503c\u7684\u4e8c\u53c9\u6811\uff08\u5373\u5806\u7684\u6027\u8d28\uff09\uff0c\u4e14\u6ee1\u8db3\u300c\u5de6\u504f\u300d\u6027\u8d28\u2014\u2014\u7ed3\u70b9\u7684\u5de6\u5b69\u5b50\u7684 dist \u4e0d\u5c0f\u4e8e\u53f3\u5b69\u5b50\u7684 dist\u3002</p> <p>\u56e0\u6b64\uff0c\u56de\u987e dist \u7684\u5b9a\u4e49\uff0c\u6211\u4eec\u53ef\u4ee5\u5f97\u5230\u6269\u5c55\u6027\u8d28\uff1a</p> <p>properties</p> <ol> <li>\u7ed3\u70b9\u7684 dist \u7b49\u4e8e \\(dist_\\text{right child} + 1\\)\uff08\u5047\u8bbe \\(dist_\\text{NULL} = -1\\)\uff09\uff1b</li> <li>\u5982\u679c \\(dist_i = N\\)\uff0c\u5219\u4ee5 \\(i\\) \u4e3a\u6839\u7684\u5b50\u6811\u81f3\u5c11\u662f\u4e00\u4e2a \\(N+1\\) \u5c42\u7684\u5b8c\u7f8e\u4e8c\u53c9\u6811\uff0c\u81f3\u5c11\u6709 \\(2^{N+1}-1\\) \u4e2a\u7ed3\u70b9\uff1b</li> </ol> <p> </p> <p>\u6ce8\u610f\uff0c\u5728\u793a\u610f\u56fe\u4e2d\u6211\u4eec\u7701\u7565\u4e86\u7ed3\u70b9\u81ea\u8eab\u952e\u503c\u7684\u6807\u8bb0\uff0c\u4f46\u65e2\u7136\u4f5c\u4e3a\u4e00\u4e2a\u5806\uff0c\u5b83\u5c31\u9700\u8981\u6ee1\u8db3\u5806\u7684\u6027\u8d28\uff0c\u5373\u7ed3\u70b9\u7684\u952e\u503c\u4e0d\u5927\u4e8e\uff08\u4e0d\u5c0f\u4e8e\uff09\u5176\u5b69\u5b50\u7ed3\u70b9\u7684\u952e\u503c\u3002\u5728\u5b9e\u9645\u4f7f\u7528\u8fc7\u7a0b\u4e2d\uff0c\u952e\u503c\u5f88\u53ef\u80fd\u4e0d\u518d\u662f\u5355\u7eaf\u7684\u6570\uff0c\u5927\u5c0f\u5173\u7cfb\u53ef\u80fd\u8f6c\u5316\u4e3a\u504f\u5e8f\u5173\u7cfb\u3002</p> <p>\u7b80\u5355\u601d\u8003\u4e00\u4e0b\uff0c\u4e3a\u4ec0\u4e48\u5de6\u504f\u5806\u4f1a\u8fd9\u4e48\u8bbe\u8ba1\u5462\uff1f\u5b9e\u9645\u4e0a\uff0c\u5408\u5e76\u5806\u9700\u8981\u8003\u8651\u7684\u975e\u5e38\u91cd\u8981\u7684\u4e00\u4e2a\u70b9\u5c31\u662f\u8981\u80fd\u5728\u4e4b\u540e\u7684\u64cd\u4f5c\u4e2d\u5c3d\u53ef\u80fd\u5730\u7ef4\u62a4\u5806\u7684\u201c\u5e73\u8861\u201d\uff0c\u5426\u5219\u6211\u4eec\u628a\u5806\u7ef4\u62a4\u6210\u4e86\u4e00\u4e2a\u94fe\uff0c\u90a3\u663e\u7136\u662f\u975e\u5e38\u7cdf\u7cd5\u7684\u3002</p> <p>\u800c\u5de6\u504f\u5806\u901a\u8fc7\u7ef4\u62a4\u6574\u4e2a\u5806\u201c\u5de6\u504f\u201d\uff0c\u5e76\u4e0d\u65ad\u5f80\u53f3\u4fa7\u5408\u5e76\uff0c\u6765\u5b9e\u73b0\u6bcf\u6b21\u90fd\u662f\u5f80 dist \u76f8\u5bf9\u5c0f\u7684\u90a3\u4e00\u4fa7\u585e\u8fdb\u4e1c\u897f\uff0c\u8fdb\u800c\u4fdd\u8bc1\u4e86\u8fd9\u4e2a\u5806\u7684\u76f8\u5bf9\u5e73\u8861\u6027\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec04/#\u64cd\u4f5c","title":"\u64cd\u4f5c","text":"<p>\u5de6\u504f\u5806\u7684\u6838\u5fc3\u64cd\u4f5c\u5c31\u662f\u5408\u5e76\u3002\u800c\u5176\u5b83\u64cd\u4f5c\u90fd\u53ef\u4ee5\u770b\u4f5c\u662f\u5408\u5e76\u7684\u7279\u6b8a\u60c5\u51b5\u3002\u56e0\u6b64\u6211\u4eec\u9996\u5148\u8ba8\u8bba\u4efb\u610f\u4e24\u4e2a\u5de6\u504f\u5806\u7684\u5408\u5e76\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec04/#\u5408\u5e76","title":"\u5408\u5e76","text":"<p>\u4f5c\u4e3a\u5de6\u504f\u5806\u7684\u6838\u5fc3\u64cd\u4f5c\uff0c\u5408\u5e76\u64cd\u4f5c\u81ea\u7136\u5c31\u662f\u8981\u5728\u6ee1\u8db3\u6027\u8d28\u7684\u6761\u4ef6\u4e0b\uff0c\u5408\u5e76\u4e24\u4e2a\u5de6\u504f\u5806\u3002\u5927\u81f4\u601d\u8def\u5c31\u662f\u5148\u7ef4\u62a4\u5806\u7684\u6027\u8d28\uff0c\u5728\u56de\u6eaf\u65f6\u7ef4\u62a4\u5de6\u504f\u6027\u8d28\uff0c\u6240\u4ee5\u5b9e\u9645\u4e0a\u5b83\u662f\u4e00\u4e2a\u5148\u81ea\u4e0a\u800c\u4e0b\u518d\u81ea\u4e0b\u800c\u4e0a\u7684\u8fc7\u7a0b\u3002</p> <p>\u6309\u7167\u5b9e\u73b0\u65b9\u6cd5\uff0c\u5de6\u504f\u5806\u7684\u5408\u5e76\u53ef\u4ee5\u5206\u4e3a\u9012\u5f52\u5f0f\u548c\u8fed\u4ee3\u5f0f\u4e24\u79cd\u3002\u5176\u4e2d\u524d\u8005\u53ef\u80fd\u66f4\u4e3a\u76f4\u89c9\uff0c\u800c\u540e\u8005\u53ef\u89c6\u5316\u540e\u5219\u66f4\u4e3a\u76f4\u89c2\u3002</p> <p>\u4e3a\u4e86\u65b9\u4fbf\u540e\u7eed\u7684\u4ee3\u7801\u63cf\u8ff0\uff0c\u6211\u4eec\u9996\u5148\u7ed9\u51fa\u5de6\u504f\u5806\u7ed3\u70b9\u5728\u672c\u6587\u4e2d\u7684\u5b9a\u4e49\uff1a</p> <pre><code>struct LeftistHeapNode {\nElementType val;\nint dist;\nLeftistHeapNode * ls, * rs;\n};\n</code></pre>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec04/#\u9012\u5f52\u5f0f","title":"\u9012\u5f52\u5f0f","text":"<p>\u9012\u5f52\u5f0f\u5148\u6bd4\u8f83\u5f53\u524d\u4e24\u4e2a\u5f85\u5408\u5e76\u5b50\u6811\u7684\u6839\u7ed3\u70b9\u7684\u952e\u503c\uff0c\u9009\u62e9\u8f83\u5c0f\uff08\u8f83\u5927\uff09\u7684\u90a3\u4e2a\u4f5c\u4e3a\u6839\u7ed3\u70b9\uff0c\u5176\u5de6\u5b50\u6811\u4f9d\u7136\u4e3a\u5de6\u5b50\u6811\uff0c\u53f3\u5b50\u6811\u66f4\u65b0\u4e3a\u300c\u53f3\u5b50\u6811\u548c\u53e6\u4e00\u4e2a\u5f85\u5408\u5e76\u5b50\u6811\u7684\u5408\u5e76\u7ed3\u679c\u300d\u3002</p> <p>\u5f53\u7136\uff0c\u5728\u9012\u5f52\u5730\u66f4\u65b0\u5b8c\u540e\uff0c\u6211\u4eec\u9700\u8981\u68c0\u67e5\u5de6\u5b50\u6811\u548c\u53f3\u5b50\u6811\u662f\u5426\u6ee1\u8db3 \\(dist_\\text{left child} \\geq dist_\\text{right child}\\) \u7684\u6027\u8d28\uff0c\u5982\u679c\u4e0d\u6ee1\u8db3\uff0c\u6211\u4eec\u5219\u9700\u8981\u4ea4\u6362\u5de6\u53f3\u5b50\u6811\u6765\u7ef4\u6301\u6027\u8d28\u3002</p> <pre><code>LeftistHeapNode * merge(LeftistHeapNode * x, LeftistHeapNode * y) {\n// Recursive exit. If any is NULL, return the other as the new root of subtree.\nif (x == NULL) return y;\nif (y == NULL) return x;\n\n// If `x`'s val is smaller than `y`'s, swap them, which means we always operates on `x`.\nif (x-&gt;val &gt; y-&gt;val) {\nswap(x, y);\n}\n\n// Merge `x`'s right subtree and `y`, and set `x`'s right subtree to the result.\nx-&gt;rs = merge(x-&gt;rs, y);\n\n// If `x`'s left subtree's dist is smaller than `x`'s right subtree's dist, swap them.\nif (x-&gt;ls-&gt;dist == NULL || x-&gt;ls-&gt;dist &lt; x-&gt;rs-&gt;dist) {\nswap(x-&gt;ls, x-&gt;rs);\n}\n\n// Update x's dist.\nx-&gt;dist = x-&gt;rs-&gt;dist + 1;\n\n// Return x as the new root of subtree.\nreturn x;\n}\n</code></pre> <p>\ud83c\udf30</p> <p>\u73b0\u5728\u6211\u4eec\u6a21\u62df\u4e00\u4e0b\u8fd9\u4e2a\u8fc7\u7a0b\uff0c\u73b0\u5728\u6211\u4eec\u6709\u4e0b\u9762\u4e24\u4e2a\u5de6\u504f\u5806\uff0c\u5c1d\u8bd5\u5408\u5e76\u5b83\u4eec\u3002</p> Frame 0Frame 1Frame 2Frame 3Frame 4Frame 5 <p></p> <p></p> <p>\u6211\u4eec\u53d1\u73b0\uff0c\u7ecf\u8fc7\u6bd4\u8f83\uff0c\u2776 \u66f4\u5c0f\uff0c\u6240\u4ee5\u6211\u4eec\u5c06 \u2776 \u4f5c\u4e3a\u5408\u5e76\u540e\u7684\u6839\u7ed3\u70b9\uff0c\u5de6\u5b50\u6811\u4e0d\u53d8\uff0c\u53f3\u5b50\u6811\u66f4\u65b0\u4e3a\u300c\u7eff\u6811\u53f3\u5b50\u6811\u548c\u84dd\u6811\u7684\u5408\u5e76\u7ed3\u679c\u300d\u3002</p> <p></p> <p>\u7ecf\u8fc7\u6bd4\u8f83\uff0c\u2777 \u66f4\u5c0f\uff0c\u6240\u4ee5\u6211\u4eec\u5c06 \u2777 \u4f5c\u4e3a\u5408\u5e76\u540e\u7684\u6839\u7ed3\u70b9\uff0c\u5de6\u5b50\u6811\u4e0d\u53d8\uff0c\u53f3\u5b50\u6811\u66f4\u65b0\u4e3a\u300c\u84dd\u6811\u53f3\u5b50\u6811\u548c\u7eff\u6811\u7684\u5408\u5e76\u7ed3\u679c\u300d\u3002</p> <p></p> <p>\u6700\u540e\u8fd8\u5269\u4e0b\u4e24\u4e2a\u7ed3\u70b9\u5566\uff01\u5b9e\u9645\u4e0a\u8fd9\u91cc\u76f4\u63a5\u6a21\u62df\u4e86\u4e24\u4e2a\u6b65\u9aa4\uff0c\u9996\u5148\u662f\u6bd4\u8f83 \u277a \u548c \u277b\uff0c\u5e76\u9009\u62e9\u4e86 \u277a \u4f5c\u4e3a\u65b0\u6839\uff1b\u63a5\u4e0b\u6765\u5728\u9012\u5f52\u7684\u8fc7\u7a0b\u4e2d\u53d1\u73b0\u9700\u8981\u5408\u5e76 <code>NULL</code> \u548c \u277b\uff0c\u6240\u4ee5\u76f4\u63a5\u8fd4\u56de\u4e86 \u277b\u3002</p> <p>\u7136\u800c\u8fd8\u6ca1\u6709\u7ed3\u675f\uff0c\u6211\u4eec\u8fd8\u9700\u8981\u5904\u7406\u5de6\u53f3\u5b50\u6811 dist \u5927\u5c0f\u5173\u7cfb\u95ee\u9898\u3002</p> <p></p> <p>\u6211\u4eec\u53d1\u73b0 \u277a \u7684\u5de6\u5b69\u5b50\u4e3a <code>NULL</code>\uff0c\u6211\u4eec\u8bb0 \\(dist_\\text{NULL} = -1\\)\uff0c\u53f3\u5b69\u5b50 \u277b \u6709 \\(dist_\\text{right child}=0\\)\uff0c\u6240\u4ee5\u9700\u8981\u4ea4\u6362\u4e24\u4e2a\u5b69\u5b50\u3002</p> <p></p> <p>\u8fd9\u91cc\u4e5f\u8df3\u8fc7\u4e86\u4e24\u4e2a\u6b65\u9aa4\uff1a</p> <p>\u5f80\u56de\u8d70\uff0c\u53d1\u73b0 \u277a \u7684 dist \u5c0f\u4e8e \u2779 \u7684 dist\uff0c\u6ee1\u8db3\u6027\u8d28\uff0c\u4e0d\u9700\u8981\u6539\u53d8\u3002</p> <p>\u7ee7\u7eed\u5f80\u56de\u8d70\uff0c\u53d1\u73b0 \u2777 \u548c \u2778 \u7684 dist \u76f8\u540c\uff0c\u6ee1\u8db3\u6027\u8d28\uff0c\u4e5f\u4e0d\u9700\u8981\u6539\u53d8\u3002</p> <p>\u4ece\u8fd9\u91cc\u4e5f\u53ef\u4ee5\u770b\u51fa\u6765\uff0c\u5e76\u4e0d\u662f\u770b\u4e0a\u53bb\u66f4\u5927\u7684\u5b50\u6811\u4e00\u5b9a\u5728\u5de6\u4fa7\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec04/#\u8fed\u4ee3\u5f0f","title":"\u8fed\u4ee3\u5f0f","text":"<p>\u8fed\u4ee3\u5f0f\u662f\u6839\u636e\u5b83\u7684\u5b9e\u73b0\u65b9\u6cd5\u6765\u547d\u540d\u7684\uff0c\u4f46\u662f\u6211\u8ba4\u4e3a\u4ece\u53ef\u89c6\u5316\u7684\u89d2\u5ea6\u6765\u7406\u89e3\u8fed\u4ee3\u5f0f\u53ef\u80fd\u66f4\u6709\u610f\u601d\u3002\u4e8b\u5b9e\u4e0a\u5728\u5f88\u591a\u9898\u76ee\u4e2d\u6211\u89c9\u5f97\u8fd9\u4e2a\u65b9\u6cd5\u505a\u9898\u66f4\u52a0\u65b9\u4fbf\u3002</p> <p>\u8fed\u4ee3\u5f0f\u7ef4\u62a4\u4e24\u4e2a\u989d\u5916\u7684\u6307\u9488\uff0c\u5206\u522b\u6307\u5411\u4e24\u68f5\u6811\u8fd8\u6ca1\u88ab\u5408\u5e76\u7684\u5b50\u6811\u7684\u6839\uff0c\u5e76\u4e0d\u65ad\u9009\u62e9\u8f83\u5c0f\u7684\u90a3\u4e2a\u5408\u5e76\u8fdb\u53bb\uff0c\u76f4\u5230\u4e24\u4e2a\u6307\u9488\u90fd\u4e3a\u7a7a\u3002\u53ef\u4ee5\u53d1\u73b0\uff0c\u8fd9\u4e2a\u8fc7\u7a0b\u548c\u5f52\u5e76\u6392\u5e8f\u7684\u540e\u534a\u90e8\u5206\u975e\u5e38\u76f8\u4f3c\uff0c\u5b9e\u9645\u4e0a\u5f53\u6211\u4eec\u4ece\u53ef\u89c6\u5316\u7684\u89d2\u5ea6\u53bb\u770b\u8fd9\u4ef6\u4e8b\u4ee5\u540e\uff0c\u4f1a\u53d1\u73b0\u8fd9\u91cc\u505a\u7684\u5c31\u662f\u4e00\u4e2a\u5f52\u5e76\u3002</p> <pre><code>LeftistHeapNode * merge(LeftistHeapNode * x, LeftistHeapNode * y) {\n// `tx` &amp; `ty` are the pointers to the roots of the subtrees that haven't been merged.\nLeftistHeapNode * tx = x, * ty = y;\n// `res` is the root of the merged final tree, while `cur` is the latest node that has been merged.\nLeftistHeapNode * res = NULL, * cur = NULL;\n\n// Begin merging.\nwhie (tx != NULL &amp;&amp; ty != NULL) {\n// If `tx`'s val is smaller than `ty`'s, swap them, which means we always operates on `tx`.\nif (tx-&gt;val &gt; ty-&gt;val) {\nswap(tx, ty);\n}\n\n// Specially mark the root on the first merge.\nif (res == NULL) {\nres = tx;\ncur = tx;\n} else {\ncur-&gt;rs = tx;\ncur = cur-&gt;rs;\n}\n\n// Go on.\ntx = tx-&gt;rs;\n}\n\n// Merge the rest of the tree.\nwhile (ty != NULL) {\n// Specially mark the root on the first merge. (rarely happens but not impossible)\nif (res == NULL) {\nres = ty;\ncur = ty;\n} else {\ncur-&gt;rs = ty;\ncur = cur-&gt;rs;\n}\n\n// Go on.\nty = ty-&gt;rs;\n}\n\n// Adjust the left and right subtrees of all the nodes according to the properties of `dist`. \n// It does the same work as the adjust part in the recursive version. I ignore it here.\nres = adjust(res);\n\nreturn res;\n}\n</code></pre> <p>\u4f9d\u65e7\u662f\u4ee5\u4e0a\u9762\u8fdb\u884c\u6a21\u62df\u7684\u90a3\u4e2a\u5408\u5e76\u4e3a \ud83c\udf30 \u8fdb\u884c\u6a21\u62df\u3002</p> <p>\ud83c\udf30</p> <p>\u9996\u5148\uff0c\u6211\u4eec\u5bf9\u56fe\u7247\u7684\u6392\u7248\u7a0d\u5fae\u505a\u4e00\u4e9b\u6539\u53d8\uff0c\u6211\u4eec\u4e0d\u518d\u6309\u7167\u4e4b\u524d\u753b\u5806\u7684\u65b9\u5f0f\u53bb\u753b\uff0c\u800c\u662f\u201c\u5de6\u504f\u201d\u5730\u53bb\u753b\uff1a</p> <p></p> <p>\u53ef\u4ee5\u53d1\u73b0\uff0c\u5728\u8c03\u6574\u4e4b\u524d</p> Frame 0Frame 1Frame 2Frame 3Frame 4Frame 5 <p></p> <p>\u7eff\u8272\u548c\u84dd\u8272\u7684\u7bad\u5934\u5206\u522b\u8868\u793a\u4e24\u4e2a\u5f85\u5408\u5e76\u5b50\u6811\u5c1a\u672a\u5408\u5e76\u7684\u5b50\u6811\u7684\u6839\uff0c\u7d2b\u8272\u7bad\u5934\u8868\u793a\u6700\u8fd1\u7684\u5408\u5e76\u53d1\u751f\u7684\u4f4d\u7f6e\u3002</p> <p></p> <p>\u6bd4\u8f83 \u2776 \u548c \u2777\uff0c\u53d1\u73b0 \u2776 \u66f4\u5c0f\uff0c\u6240\u4ee5\u6211\u4eec\u5c06 \u2776 \u4f5c\u4e3a\u5408\u5e76\u540e\u7684\u6839\u7ed3\u70b9\uff0c\u5de6\u5b50\u6811\u968f\u4e4b\u5408\u5e76\u8fdb\u53bb\uff0c\u540c\u65f6\u66f4\u65b0\u7eff\u8272\u7bad\u5934\u6307\u5411\u5c1a\u672a\u5408\u5e76\u8fdb\u53bb\u7684 \u277a\u3002</p> <p></p> <p>\u548c\u4e0a\u4e00\u6b65\u7c7b\u4f3c\u7684\uff0c\u6bd4\u8f83 \u277a \u548c \u2777\uff0c\u53d1\u73b0 \u2777 \u66f4\u5c0f\uff0c\u6240\u4ee5\u6211\u4eec\u5c06 \u2777 \u4f5c\u4e3a\u5408\u5e76\u540e\u7684\u6839\u7ed3\u70b9\uff0c\u5de6\u5b50\u6811\u968f\u4e4b\u5408\u5e76\u8fdb\u53bb\uff0c\u540c\u65f6\u66f4\u65b0\u84dd\u8272\u7bad\u5934\u6307\u5411\u5c1a\u672a\u5408\u5e76\u8fdb\u53bb\u7684 \u277b\u3002</p> <p></p> <p>\u4f9d\u7136\u7c7b\u4f3c\u5730\uff0c\u6bd4\u8f83 \u277a \u548c \u277b\uff0c\u53d1\u73b0 \u277a \u66f4\u5c0f\uff0c\u6240\u4ee5\u6211\u4eec\u5c06 \u277a \u4f5c\u4e3a\u5408\u5e76\u540e\u7684\u6839\u7ed3\u70b9\uff0c\u5de6\u5b50\u6811\u968f\u4e4b\u5408\u5e76\u8fdb\u53bb\uff0c\u540c\u65f6\u66f4\u65b0\u7eff\u8272\u7bad\u5934\u6307\u5411 <code>NULL</code>\u3002</p> <p></p> <p>\u8fd9\u65f6\u5019\u6211\u4eec\u53d1\u73b0\u5df2\u7ecf\u6709\u4e00\u4e2a\u6307\u9488\u7a7a\u4e86\uff0c\u4e5f\u5c31\u662f\u7eff\u8272\u6307\u9488\u5df2\u7ecf\u6307\u5411\u4e86 <code>NULL</code>\uff0c\u8fd9\u4e2a\u65f6\u5019\u6211\u4eec\u53ea\u9700\u8981\u6309\u987a\u5e8f\u628a\u84dd\u8272\u6307\u9488\u6307\u5411\u7684\u5185\u5bb9\u90fd\u63a8\u8fdb\u53bb\u5373\u53ef\u3002</p> <p></p> <p>\u63a5\u4e0b\u6765\u6211\u4eec\u8fd8\u9700\u8981\u7ef4\u62a4 dist \u4fe1\u606f\u5e76\u6839\u636e\u6027\u8d28\u4ea4\u6362\u5de6\u53f3\u5b50\u6811\u3002\u8fd9\u4e00\u90e8\u5206\u548c\u4e4b\u524d\u4e00\u6837\uff0c\u5c31\u4e0d\u518d\u8d58\u8ff0\u4e86\u3002</p> <p>\ud83c\udf30/\ud83d\udd25</p> <p>\u5f53\u7136\uff0c\u8fd9\u4e48\u6765\u770b\u53ef\u80fd\u8fd8\u662f\u5f88\u4e71\uff0c\u8054\u60f3\u6211\u4eec\u4e4b\u524d\u53d1\u73b0\u5b83\u548c\u5f52\u5e76\u6392\u5e8f\u5f88\u50cf\uff0c\u6211\u4eec\u8fd8\u53ef\u4ee5\u7528\u4e00\u4e2a\u66f4\u52a0\u76f4\u89c2\u7684\u65b9\u5f0f\u6765\u770b\u8fd9\u4e2a\u8fc7\u7a0b\uff1a</p> Frame 0Frame 1Frame 2 <p></p> <p>\u540c\u6837\u4ece\u8fd9\u5f20\u56fe\u5f00\u59cb\uff0c\u7531\u4e8e\u6211\u4eec\u4e4b\u524d\u63d0\u5230\u7684\uff0c\u5b83\u7c7b\u4f3c\u4e8e\u4e00\u4e2a\u9012\u5f52\u6392\u5e8f\u7684\u540e\u534a\u90e8\u5206\uff0c\u5177\u4f53\u6765\u8bf4\u662f\u6307\u5408\u5e76\u4e24\u4e2a\u6709\u5e8f\u6570\u5217\u7684\u8fc7\u7a0b\u3002</p> <p>\u4e5f\u5c31\u662f\u8bf4\uff0c\u6211\u4eec\u53ef\u4ee5\u5c06\u8fd9\u4e24\u4e2a\u5de6\u504f\u5806\u6539\u5199\u6210\u4e24\u4e2a\u6709\u5e8f\u6570\u5217\uff01</p> <p></p> <p>\u7531\u4e8e\u6211\u4eec\u5728\u5408\u5e76\u8fc7\u7a0b\u4e2d\u603b\u662f\u627e\u53f3\u5b69\u5b50\uff0c\u6240\u4ee5\u6211\u4eec\u5c31\u6cbf\u7740\u6700\u53f3\u6cbf\u8def\u5f84\u628a\u6ca1\u4e2a\u5de6\u504f\u5806\u62c6\u6210\u8fd9\u79cd\u201c\u60ac\u540a\u201d\u7684\u5e26\u72b6\u5f62\u5f0f\uff0c\u6bcf\u4e00\u201c\u6761\u201d\u7684\u503c\u53d6\u51b3\u4e8e\u6839\u7684\u952e\u503c\uff0c\u4e5f\u5c31\u662f\u8fd9\u4e00\u201c\u6761\u201d\u7684\u6700\u9876\u90e8\u3002</p> <p>\u5728\u8fd9\u5f20\u56fe\u4e2d\uff0c\u6211\u4eec\u5f97\u5230\u7684\u4e24\u4e2a\u6709\u5e8f\u6570\u7ec4\u5206\u522b\u662f [1, 5] \u548c [2, 6]\uff0c\u63a5\u4e0b\u6765\u6211\u4eec\u5c06\u5b83\u4eec\u8fdb\u884c\u6392\u5e8f\u3002</p> <p> </p> <p>\u7ecf\u8fc7\u6392\u5e8f\uff0c\u5c31\u4f1a\u53d1\u73b0\u5b83\u4eec\u521a\u597d\u7b26\u5408\u6211\u4eec\u5728\u4e0a\u9762\u6b65\u9aa4\u5f97\u5230\u7684\u7ed3\u679c\uff08\u53ef\u4ee5\u5bf9\u6bd4\u7740\u4e0a\u9762\u7684 Frame 4 \u770b\uff09\u3002\u5b9e\u9645\u4e0a\uff0c\u53ea\u8981\u4f60\u56de\u987e\u4e00\u4e0b\u5f52\u5e76\u6392\u5e8f\u7684\u8fc7\u7a0b\uff0c\u518d\u5bf9\u6bd4\u7740\u770b\u4e0a\u9762\u7684\u8fc7\u7a0b\uff0c\u5c31\u4f1a\u53d1\u73b0\u4e00\u6a21\u4e00\u6837\u3002</p> <p>\u518d\u6b21\u63d0\u9192\uff0c\u8fd9\u4e00\u5c0f\u8282\u8bb2\u7684\u90e8\u5206\u90fd\u5ffd\u7565\u4e86\u4e4b\u540e\u8c03\u6574\u5b50\u6811\u5de6\u504f\u6027\u8d28\u7684\u8fc7\u7a0b\uff0c\u5b9e\u9645\u4e0a\u8fd9\u4e5f\u5c31\u5355\u7eaf\u662f\u4e00\u4e2a\u7ef4\u62a4\u5806\u6027\u8d28\u7684\u8fc7\u7a0b\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec04/#\u5355\u70b9\u63d2\u5165","title":"\u5355\u70b9\u63d2\u5165","text":"<p>\u63d2\u5165\u7ed3\u70b9\u53ef\u4ee5\u770b\u4f5c\u5408\u5e76\u4e00\u4e2a\u53ea\u6709\u4e00\u4e2a\u7ed3\u70b9\u7684\u5de6\u504f\u5806\uff0c\u6240\u4ee5\u6211\u4eec\u53ef\u4ee5\u76f4\u63a5\u590d\u7528\u5408\u5e76\u8fc7\u7a0b\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec04/#\u5355\u70b9\u5220\u9664","title":"\u5355\u70b9\u5220\u9664","text":"<p>\u8ba9\u6211\u4eec\u4e00\u822c\u6027\u5730\u8003\u8651\u4e00\u4e2a\u7ed3\u70b9\uff0c\u4e0e\u5b83\u76f8\u5173\u7684\u4e3b\u8981\u6709\u4e09\u4e2a\u65b9\u5411\uff1a\u7236\u7ed3\u70b9\u548c\u4e24\u4e2a\u5b69\u5b50\u7ed3\u70b9\u3002</p> <p>\u800c\u5355\u70b9\u5220\u9664\u7684\u64cd\u4f5c\u4e5f\u5f88\u7b80\u5355\uff0c\u53ea\u9700\u8981\u5408\u5e76\u9700\u8981\u88ab\u5220\u9664\u7684\u7ed3\u70b9\u7684\u4e24\u4e2a\u5b50\u7ed3\u70b9\uff0c\u7136\u540e\u5c06\u8fd9\u4e2a\u65b0\u7684\u6811\u7684\u6839\u4ee3\u66ff\u88ab\u5220\u9664\u7684\u7ed3\u70b9\uff0c\u518d\u5728\u56de\u6eaf\u7684\u8fc7\u7a0b\u4e2d bottom-up \u5730\u66f4\u65b0 dist \u5373\u53ef\u3002</p> <pre><code>LeftistHeapNode * del(LeftistHeapNode * cur, ElementType x) {\nif (cur-&gt;val == x) {\n// Just return the merge of the children.\nreturn merge(cur-&gt;l, cur-&gt;r);\n} else {\n// Not this subtree.\nif (cur-&gt;val &gt; x) return cur;\n\n// Otherwise, search the `x`.\nif (cur-&gt;l != NULL) del(cur-&gt;l, x);\nif (cur-&gt;r != NULL) del(cur-&gt;r, x);\n\n// Adjust the dist bottom-up.\nadjust(cur);\n}\n}\n</code></pre>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec04/#skew-heap","title":"Skew Heap","text":"<p>link</p> <p>Wikipedia: https://en.wikipedia.org/wiki/Skew_heap</p> <p>\u659c\u5806(Skew Hea)\u662f\u6bd4\u5de6\u504f\u5806\u66f4\u4e3a\u4e00\u822c\u7684\u6570\u636e\u7ed3\u6784\uff0c\u5b83\u540c\u6837\u6709\u7740\u80fd\u591f\u5feb\u901f\u5408\u5e76\u7684\u6027\u8d28\u3002</p> <p>\u5934\u8111\u98ce\u66b4</p> <p>\u8ba9\u6211\u4eec\u56de\u987e\u4e00\u4e0b\u5de6\u504f\u5806\uff0c\u7531\u4e8e\u9700\u8981\u81ea\u4e0b\u800c\u4e0a\u5730\u7ef4\u62a4 dist\uff0c\u6240\u4ee5\u6211\u4eec\u65e0\u6cd5\u8fdb\u884c\u5e76\u53d1\u64cd\u4f5c\u3002\u56de\u987e AVL \u6811\uff0c\u540c\u6837\u4e3a\u4e86\u7ef4\u62a4\u5b83\u6bd4\u8f83\u4e25\u683c\u7684\u5e73\u8861\u6027\u8d28\uff0c\u6211\u4eec\u4e5f\u65e0\u6cd5\u8fdb\u884c\u5e76\u53d1\u64cd\u4f5c\uff0c\u800c\u7ea2\u9ed1\u6811\u5219\u901a\u8fc7\u4e00\u4e2a\u80fd\u591f\u4ec5\u4ec5\u901a\u8fc7\u53d8\u8272\u5c31\u80fd\u8c03\u6574\u7684\u9ed1\u9ad8\u6765\u89c4\u907f\u4e86\u5fc5\u987b\u81ea\u4e0b\u800c\u4e0a\u7ef4\u62a4\u7684\u95ee\u9898\uff0c\u5b9e\u73b0\u4e86\u5e76\u53d1\u3002</p> <p>\u6362\u53e5\u8bdd\u6765\u8bf4\uff0c\u8981\u60f3\u5c06\u5de6\u504f\u5806\u6539\u53d8\u5730\u80fd\u591f\u8fdb\u884c\u81ea\u4e0a\u800c\u4e0b\u7ef4\u62a4\uff0c\u5c31\u9700\u8981\u6539\u53d8\u751a\u81f3\u653e\u5f03\u5b83\u7684\u5de6\u504f\u6027\u8d28\u7684\u4e25\u683c\u6027\u2014\u2014\u800c\u8fd9\u5c31\u662f\u659c\u5806\u7684\u7531\u6765\u3002</p> <p>\u659c\u5806\u4e5f\u9700\u8981\u6ee1\u8db3\u5927\u6839\u5806\uff08\u5c0f\u6839\u5806\uff09\u7684\u6027\u8d28\uff0c\u800c\u5b83\u7684\u5408\u5e76\u548c\u5de6\u504f\u5806\u7684\u5408\u5e76\u4e5f\u5341\u5206\u7c7b\u4f3c\uff0c\u53ea\u4e0d\u8fc7\u6211\u4eec\u8fd9\u6b21\u65e0\u6761\u4ef6\u7684\u4ea4\u6362\u5de6\u53f3\u5b50\u6811\uff0c\u6362\u53e5\u8bdd\u6765\u8bf4\uff0c\u4e0d\u7ba1\u5de6\u504f\u6027\u8d28\u5982\u4f55\u53d8\u5316\uff0c\u6211\u4eec\u90fd\u4f1a\u9009\u62e9\u4ea4\u6362\u53c2\u4e0e\u5408\u5e76\u7684\u5de6\u53f3\u5b50\u6811\uff0c\u8fd9\u6837\u6211\u4eec\u5c31\u4e0d\u9700\u8981\u5728\u56de\u6eaf\u7684\u65f6\u5019\u624d\u8fdb\u884c\u5de6\u53f3\u5b50\u6811\u7684\u4ea4\u6362\uff0c\u4e8e\u662f\u5c31\u5b9e\u73b0\u4e86\u5b8c\u5168\u7684\u81ea\u4e0a\u800c\u4e0b\u3002</p> <p>\u8ba9\u6211\u4eec\u6765\u770b\u770b wiki \u91cc\u7ed9\u51fa\u7684 \ud83c\udf30\uff1a</p> <p>\ud83c\udf30 from wikipedia</p> Frame 0Frame 1 <p></p> <p>\u8fd9\u662f\u6211\u4eec\u9700\u8981\u5408\u5e76\u7684\u4e24\u4e2a\u5806\u3002</p> <p></p> <p>\u7701\u7565\u4e86\u4e2d\u95f4\u7684\u6b65\u9aa4\uff0c\u53ef\u4ee5\u5c1d\u8bd5\u6a21\u62df\u4e00\u4e0b\uff0c\u6bcf\u4e00\u6b21\u5408\u5e76\u64cd\u4f5c\u7ed3\u675f\u4e4b\u540e\u90fd\u4ea4\u6362\u5de6\u53f3\u5b50\u6811\u3002</p> <p>\u6211\u4eec\u603b\u662f\u5148\u5f80\u53f3\u4fa7\u5b50\u6811\u9012\u5f52\u4e0b\u53bb\u5730\u5408\u5e76\uff0c\u6ca1\u5b8c\u6210\u4e00\u6b21\u5408\u5e76\u5c31\u4ea4\u6362\u8fd9\u4e2a\u5b50\u6811\u548c\u5b83\u7684\u5144\u5f1f\u59d0\u59b9\uff0c\u800c\u5b83\u7684\u5144\u5f1f\u59d0\u59b9\u5728\u8fd9\u6b21\u4ea4\u6362\u5b8c\u4ee5\u540e\u5c31\u4e0d\u4f1a\u518d\u53d1\u751f\u6539\u53d8\uff0c\u800c\u8fd9\u4e2a\u5b50\u6811\u5219\u4f1a\u7ee7\u7eed\u8fdb\u884c\u4e0b\u4e00\u6b21\u5408\u5e76\u3002</p> <p>\u7701\u7565\u4e0a\u9762\u7684\u7ed8\u56fe\u663e\u7136\u662f\u6211\u61d2\u5f97\u753b\u4e86\uff0c\u76f8\u4fe1\u5927\u5bb6\u5728\u4e86\u89e3\u5de6\u504f\u5806\u7684\u5408\u5e76\u4ee5\u540e\u4e5f\u80fd\u5f88\u5feb\u611f\u53d7\u5230\u659c\u5806\u662f\u5982\u4f55\u5408\u5e76\u7684\u3002</p> <p>\u5f53\u7136\uff0c\u5b83\u4e5f\u662f\u652f\u6301\u8fed\u4ee3\u7684\u5199\u6cd5\u7684\uff0c\u548c\u662f\u548c\u4e4b\u524d\u7684\u505a\u6cd5\u7c7b\u4f3c\uff0c\u6211\u4eec\u53ef\u4ee5\u6392\u5e8f\u6bcf\u4e00\u201c\u6761\u201d\uff0c\u7136\u540e\u518d\u5408\u5e76\u3002Wikipedia \u4e0a\u63d0\u4f9b\u4e86\u4e00\u7cfb\u5217\u7684\u8fc7\u7a0b\u56fe\uff0c\u4f46\u662f\u90a3\u4e2a\u8fc7\u7a0b\u56fe\u6709\u70b9\u81ea\u4e0b\u800c\u4e0a\u7684\u610f\u601d\uff0c\u4f46\u662f\u5b9e\u9645\u4e0a\u81ea\u4e0a\u800c\u4e0b\u505a\u4e5f\u662f\u4e00\u6837\u7684\u3002\u5982\u679c\u6709\u5174\u8da3\u53ef\u4ee5\u53bb\u770b\u770b Wiki \u4e0a\u7684\u8fc7\u7a0b\uff1a\ud83d\udd17\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec04/#\u5408\u7406\u6027\u5206\u6790","title":"\u5408\u7406\u6027\u5206\u6790","text":"<p>\u7136\u800c\uff0c\u968f\u4e4b\u51fa\u73b0\u7684\u4e00\u4e2a\u95ee\u9898\u4e0a\uff0c\u6211\u4eec\u7528\u4e86\u8fd9\u79cd\u770b\u8d77\u6765\u6709\u70b9\u4e0d\u7ba1\u4e09\u4e03\u4e8c\u5341\u4e00\u7684\u505a\u6cd5\uff0c\u90a3\u5b83\u7684\u6b63\u786e\u6027\u5982\u4f55\u4fdd\u8bc1\u5462\uff1f</p> <p>\u9996\u5148\u8fdb\u884c\u611f\u6027\u7684\u7406\u89e3\u3002\u6211\u4eec\u6bcf\u5408\u5e76\u4e24\u4e2a\u5806\u90fd\u662f\u6cbf\u7740\u6700\u53f3\u4fa7\u8def\u5f84\u5408\u5e76\uff08\u867d\u7136\u4e2d\u95f4\u4f1a\u88ab\u4e0d\u505c\u8f6c\u5230\u5de6\u8fb9\uff09\uff0c\u5373\u6bcf\u6b21\u4f1a\u88ab\u6539\u53d8\u7684\u5b50\u6811\u5de6\u53f3\u987a\u5e8f\u7684\u8282\u70b9\u90fd\u662f\u6700\u53f3\u4fa7\u7684\u8282\u70b9\uff0c\u800c\u518d\u5408\u5e76\u8fc7\u7a0b\u4e2d\u5982\u679c\u6bcf\u6b21\u5408\u5e76\u90fd\u5c06\u53d1\u751f\u7684\u53d8\u5316\u8f6c\u5230\u5de6\u4fa7\uff0c\u4ee5\u6b64\u6765\u51cf\u5c0f\u5408\u5e76\u64cd\u4f5c\u5e26\u6765\u7684\u9ad8\u5ea6\u201c\u7d2f\u79ef\u201d\u3002</p> <p>\u8fdb\u4e00\u6b65\u89e3\u91ca</p> <p>\u4ee5\u6bcf\u6b21\u53ea\u63d2\u5165\u4e00\u4e2a\u70b9\u4e3a\u4f8b\u5b50\u8bf4\u660e\u95ee\u9898\u3002</p> <p>\u8fdb\u4e00\u6b65\u5bf9\u9012\u5f52\u65cb\u8f6c\u5230\u5de6\u4fa7\u505a\u89e3\u91ca\uff0c\u9012\u5f52\u6027\u5730\u8f6c\u5230\u5de6\u4fa7\uff0c\u4f7f\u5f97\u672c\u6765\u6700\u53f3\u4fa7\u7684\u8def\u5f84\u53d8\u5230\u6700\u5de6\u4fa7\uff0c\u5373\u4f7f\u4e4b\u540e\u4ea4\u6362\u4f1a\u91cd\u65b0\u8bbf\u95ee\u5230\u8fd9\u4e2a\u5b50\u6811\uff0c\u4f46\u6b64\u65f6\u9664\u4e86\u6839\uff0c\u5176\u4ed6\u90e8\u5206\u4f9d\u7136\u662f\u6700\u5de6\u4fa7\u7684\u8def\u5f84\uff0c\u4e5f\u4e0d\u4f1a\u518d\u8f7b\u6613\u5730\u8bbf\u95ee\u5230\u8fd9\u6b21\u8def\u5f84\u3002</p> <p>\u7528\u56fe\u6765\u505a\u89e3\u91ca\u7684\u8bdd\uff0c\u5c31\u662f\u8fd9\u6837\uff1a</p> <p></p> <p>\u6211\u4eec\u53ea\u5173\u6ce8\u4e00\u5f00\u59cb\u4f5c\u4e3a\u6700\u53f3\u4fa7\u7684\u8fd9\u4e09\u4e2a\u7ea2\u70b9\uff0c\u53ef\u4ee5\u53d1\u73b0\uff0c\u5728\u4e24\u6b21\u64cd\u4f5c\u540e\uff0c\u9664\u4e86\u76f4\u63a5\u4f5c\u4e3a\u6839\u7684\u5b50\u6811\u7684\u90a3\u4e2a\u8282\u70b9\u88ab\u8f6c\u4e86\u8fc7\u6765\uff0c\u5176\u4ed6\u7684\u4e4b\u540e\u7684\u8282\u70b9\u90fd\u662f\u4f5c\u4e3a\u201c\u6700\u5de6\u4fa7\u201d\u7684\u8282\u70b9\u51fa\u73b0\u7684\uff0c\u867d\u7136\u56fe\u4e2d\u53ea\u6709\u8fd9\u4e00\u4e2a\uff0c\u4f46\u662f\u5f53\u6811\u7684\u89c4\u6a21\u53d8\u5927\u540e\uff0c\u8fd9\u4e2a\u4f18\u52bf\u4f1a\u66f4\u52a0\u660e\u663e\u3002</p> <p>\u6839\u636e\u8fd9\u4e2a\u7279\u70b9\uff0c\u6211\u4eec\u53ef\u4ee5\u975e\u5e38\u7b80\u5355\u5730\u7406\u89e3\u4e0b\u9762\u8fd9\u9053\u9898\uff1a</p> \u9898\u9762\u7b54\u6848 &amp; \u89e3\u91ca <p>The result of inserting keys \\(1\\) to \\(2^k\u22121\\) for any \\(k&gt;4\\) in order into an initially empty skew heap is always a full binary tree. (T/F)</p> <p>\u5373\u5bf9\u4e8e\u4efb\u610f\u7684 \\(k&gt;4\\) \u7684\u60c5\u51b5\uff0c\u6309\u987a\u5e8f\u5f80\u4e00\u4e2a\u659c\u5806\u91cc\u63d2\u5165 \\(1\\sim2^k-1\\) \u8fd9\u4e9b\u6570\uff0c\u5f97\u5230\u7684\u7ed3\u679c\u90fd\u4f1a\u662f\u4e00\u4e2a\u6ee1\u4e8c\u53c9\u6811\u3002\uff08\u5bf9/\u9519\uff09</p> <p>\u7b54\u6848\u662f T\u3002</p> <p>\u9996\u5148\uff0c\u4ece\u63d2\u5165\u7684\u5143\u7d20\u7684\u6570\u91cf\u6765\u770b\uff0c\u662f\u6ee1\u8db3\u6ee1\u4e8c\u53c9\u6811\u7684\u5fc5\u8981\u6761\u4ef6\u7684\u3002</p> <p>\u800c\u6839\u636e\u6211\u4eec\u4e0a\u9762\u63cf\u8ff0\u7684\uff0c\u8df3\u8fc7\u80af\u5b9a\u6210\u7acb\u7684\u521d\u59cb\u60c5\u51b5\uff0c\u6211\u4eec\u53ef\u4ee5\u505a\u4e00\u4e2a\u7b80\u5355\u7684\u5f52\u7eb3\uff0c\u8fc7\u7a0b\u5e76\u4e0d\u5b8c\u6574\u4e0e\u4e25\u8c28\uff0c\u4f46\u662f\u5927\u6982\u5c31\u662f\u8fd9\u4e48\u4e2a\u610f\u601d\u3002</p> <p>\u5bf9\u4e8e\u4e00\u4e2a\u6ee1\u4e8c\u53c9\u6811\uff0c\u6211\u4eec\u73b0\u5728\u8981\u63d2\u5165\u4e00\u4e2a\u6570\uff0c\u663e\u7136\u8fd9\u4e2a\u6570\u6bd4\u6811\u91cc\u4efb\u4f55\u4e00\u4e2a\u90fd\u8981\u5927\u3002\u800c\u5f53\u8fd9\u4e2a\u6570\u88ab\u63d2\u5165\u540e\uff0c\u5b83\u6210\u4e3a\u6574\u4e2a\u5806\uff0c\u6216\u8005\u8bf4\u6574\u4e2a\u6811\u6700\u5de6\u4fa7\u7684\u4e00\u6761\u3002\u800c\u5728\u63a5\u4e0b\u6765\u7684\u4ea4\u6362\u8fc7\u7a0b\u4e2d\uff0c\u5b83\u4f1a\u4e0d\u65ad\u88ab\u7529\u6765\u7529\u53bb\uff0c\u6700\u7ec8\u7ecf\u8fc7 2^k \u6b21\u540e\u88ab\u7529\u5230\u6700\u53f3\u8fb9\uff0c\u4e5f\u5c31\u662f\u8fce\u63a5\u5b83\u7684\u7b2c\u4e00\u4e2a\u5b69\u5b50\u3002\u663e\u7136\uff0c\u5bf9\u4e8e\u8be5\u5c42\u7684\u6240\u6709\u8282\u70b9\u6765\u8bf4\u90fd\u9700\u8981 2^k \u6b21\u624d\u4f1a\u8fdb\u5165\u5230\u6700\u53f3\u4fa7\u8def\u5f84\u3002</p> <p>\uff08\u8fd9\u4e2a\u8fc7\u7a0b\u53ef\u4ee5\u7c7b\u6bd4\u4e8c\u8fdb\u5236\u6570\u7684\u81ea\u589e\uff0c\u4f60\u53ef\u4ee5\u6839\u636e\u8fd9\u4e2a\u8282\u70b9\u7684\u6bcf\u4e2a\u524d\u9a71\u5206\u522b\u662f\u5de6\u5b69\u5b50\u8fd8\u662f\u53f3\u5b69\u5b50\u6765\u5206\u914d\u5bf9\u5e94\u7684\u4f4d\u5b50\u662f <code>0</code> \u8fd8\u662f <code>1</code>\u3002\uff09</p> <p>\u5f53\u7136\uff0c\u5982\u4e0a\u7684\u6027\u8d28\u53ea\u80fd\u5e2e\u52a9\u6211\u4eec\u611f\u6027\u7684\u7406\u89e3\u8fd9\u4e2a\u6b63\u786e\u6027\u3002\u63a5\u4e0b\u6765\u6211\u4eec\u4ece\u644a\u8fd8\u5206\u6790\u7684\u89d2\u5ea6\u6765\u5206\u6790\u5176\u6b63\u786e\u6027\uff0c\u5373\u5176\u5747\u644a\u590d\u6742\u5ea6\u4e3a \\(O(\\log N)\\)\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec04/#\u644a\u8fd8\u5206\u6790","title":"\u644a\u8fd8\u5206\u6790","text":"<ul> <li>\u524d\u60c5\u63d0\u8981\uff1aTopic 1 | \u644a\u8fd8\u5206\u6790</li> </ul> <p>\u8fd9\u91cc\u6211\u4eec\u91c7\u7528\u52bf\u80fd\u6cd5\u8fdb\u884c\u5206\u6790\u3002</p> <p>\u5206\u6790 skew heap \u7684\u5747\u644a\u590d\u6742\u5ea6\uff0c\u4e3b\u8981\u5c31\u662f\u5206\u6790\u5408\u5e76\u64cd\u4f5c\u7684\u590d\u6742\u5ea6\uff0c\u56e0\u4e3a\u5176\u4ed6\u64cd\u4f5c\u90fd\u53ef\u4ee5\u8f6c\u5316\u4e3a\u5408\u5e76\u64cd\u4f5c\u3002</p> <p>\u63a5\u4e0b\u6765\u6211\u4eec\u9700\u8981\u5b9a\u4e49\u52bf\u80fd\u51fd\u6570\uff1a</p> <p>\u52bf\u80fd\u51fd\u6570</p> <p>\u6211\u4eec\u5b9a\u4e49 \\(\\Phi(Heap) = \\text{number of heavy node in } Heap\\)\u3002</p> <p>\u5176\u4e2d\uff0c\u989d\u5916\u9700\u8981\u5b9a\u4e49 heavy node \u548c light node\uff1a</p> <p>heavy node &amp; light node</p> <p>\u5bf9\u4e8e\u4e00\u4e2a\u5b50\u5806 \\(H\\)\uff0c\u5982\u679c \\(size(H.\\text{right\\_descendant}) \\geq \\frac{1}{2}size(H)\\)\uff0c\u5219 \\(H\\) \u662f heavy node\uff0c\u5426\u5219\u662f light node\u3002 </p> @ cy'ppt <p>A node p is heavy if the number of descendants of p\u2019s right subtree is at least half of the number of descendants of p, and light otherwise.  Note that the number of descendants of a node includes the node itself.</p> <p>\u663e\u7136\uff0c\u5bf9\u4e8e heavy node \u548c light node\uff0c\u4ee5\u53ca\u5408\u5e76\u64cd\u4f5c\uff0c\u6709\u8fd9\u4e48\u4e00\u4e9b\u6027\u8d28\uff1a</p> <p>properties</p> <ol> <li>\u5982\u679c\u4e00\u4e2a\u8282\u70b9\u662f heavy node\uff0c\u5e76\u4e14\u5728\u5176\u53f3\u5b50\u6811\u53d1\u751f\u4e86\u5408\u5e76\uff08\u5305\u62ec\u7ffb\u8f6c\uff09\uff0c\u90a3\u4e48\u5b83\u4e00\u5b9a\u53d8\u4e3a\u4e00\u4e2a light node\uff1b</li> <li>\u5982\u679c\u4e00\u4e2a\u8282\u70b9\u662f light node\uff0c\u5e76\u4e14\u5728\u5176\u53f3\u5b50\u6811\u53d1\u751f\u4e86\u5408\u5e76\uff08\u5305\u62ec\u7ffb\u8f6c\uff09\uff0c\u90a3\u4e48\u5b83\u53ef\u80fd\u53d8\u4e3a\u4e00\u4e2a heavy node\uff1b</li> <li>\u5408\u5e76\u8fc7\u7a0b\u4e2d\uff0c\u5982\u679c\u4e00\u4e2a\u8282\u70b9\u7684 heavy/light \u53d1\u751f\u53d8\u5316\uff0c\u90a3\u4e48\u5b83\u539f\u5148\u4e00\u5b9a\u5728\u5806\u7684\u6700\u53f3\u4fa7\u8def\u5f84\u4e0a\uff1b</li> </ol> <p>\u5217\u51fa\u516c\u5f0f\uff1a</p> \\[ \\hat{c} = c + \\Phi(H_{merged}) - \\Phi(H_x) - \\Phi(H_y) \\] <p>\u5176\u4e2d\uff0c\\(c\\) \u4e3a\u5408\u5e76\u64cd\u4f5c\u7684\uff08\u6700\u574f\uff09\u590d\u6742\u5ea6\uff0c\\(H_{merged}\\) \u4e3a\u5408\u5e76\u540e\u7684\u5806\u7684\u52bf\u80fd\uff0c\\(H_x\\) \u548c \\(H_y\\) \u5206\u522b\u4e3a\u5408\u5e76\u524d\u7684\u4e24\u4e2a\u5806\u7684\u52bf\u80fd\u3002</p> <p>\u6839\u636e property 3\uff0c\u5728\u5408\u5e76\u8fc7\u7a0b\u4e2d\u5e76\u975e\u6240\u6709\u8282\u70b9\u90fd\u6536\u5230\u5f71\u54cd\u3002\u6211\u4eec\u53ef\u4ee5\u5355\u72ec\u8bb0\u5f55 \\(l_{x}\\) \u4e3a \\(H_x\\) \u6700\u53f3\u4fa7\u8def\u5f84\u4e0a\u7684 light node \u6570\u91cf\uff0c\\(h_{x}\\) \u4e3a \\(H_x\\) \u6700\u53f3\u4fa7\u8def\u5f84\u4e0a\u7684 heavy node \u6570\u91cf\uff0c\\(h^0_{x}\\) \u4e3a \\(H_x\\) \u6240\u6709\u4e0d\u5728\u6700\u53f3\u4fa7\u8def\u5f84\u4e0a\u7684 heavy node \u6570\u91cf\uff08\u5373 \\(\\text{count of heavy nodes of } H_x = H_x + H^0_x\\)\uff09\u3002</p> <p>\u4e8e\u662f\uff0c\u6211\u4eec\u53ef\u4ee5\u5c06\u4e0a\u5f0f\u5199\u5f00\uff1a</p> \\[ \\left\\{     \\begin{aligned}         c &amp;= l_x + h_x + l_y + h_y &amp;(1)\\\\         \\Phi(H_{merged}) &amp;\\leq l_x + h^0_x + l_y + h^0_y &amp;(2)\\\\         \\Phi(H_x) &amp;= h_x + h^0_{x} &amp;(3)\\\\         \\Phi(H_y) &amp;= h_y + h^0_{y} &amp;(4)     \\end{aligned} \\right. \\] <p>\u5176\u4e2d\u7a0d\u5fae\u505a\u4e00\u4e9b\u89e3\u91ca\uff1a</p> <ol> <li>\\((1)\\)\uff1a\\(c\\) \u4e3a\u5408\u5e76\u64cd\u4f5c\u7684\uff08\u6700\u574f\uff09\u590d\u6742\u5ea6\uff0c\u5373\u6211\u4eec\u7684\u679a\u4e3e\u6d89\u53ca\u4e86\u4e24\u4e2a\u5806\u6240\u6709\u7684\u53f3\u4fa7\u8def\u5f84\uff1b</li> <li>\\((2)\\)\uff1a\u5728\u5408\u5e76\u64cd\u4f5c\u4ee5\u540e\uff0c\u6839\u636e property 1 \u548c property 2\uff0c\u53ef\u4ee5\u5f97\u5230\u8fd9\u4e2a\u4e0d\u7b49\u5f0f\uff1b</li> <li>\\((3)\\) \u548c \\((4)\\)\uff1a\u6839\u636e\u52bf\u80fd\u51fd\u6570\u7684\u5b9a\u4e49\u5f97\u5230\uff1b</li> </ol> <p>\u4e8e\u662f\uff0c\u5c06\u5b83\u4eec\u4ee3\u5165\u5f97\u5230\u7ed3\u679c\uff1a</p> \\[ \\begin{aligned} \\hat{c}      &amp;= c + \\Phi(H_{merged}) - \\Phi(H_x) - \\Phi(H_y) \\\\     &amp;\\leq (l_x + h_x + l_y + h_y)     + (l_x + h^0_x + l_y + h^0_y)     - (h_x + h^0_{x})     - (h_y + h^0_{y}) \\\\     &amp;\\leq 2(l_x + l_y) \\\\ \\hat{c}     &amp;= O(\\log{N}) \\end{aligned} \\]"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec05/","title":"Lecture 5 | Binomial Queue","text":"<p> \u7ea6 2196 \u4e2a\u5b57  12 \u884c\u4ee3\u7801  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 7 \u5206\u949f</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec05/#binomial-queue","title":"Binomial Queue","text":"<p>\u5806\u7684\u5176\u4e2d\u4e00\u4e2a\u5e94\u7528\u5c31\u662f\u4f18\u5148\u961f\u5217\u3002\u672c\u8282\u8981\u4ecb\u7ecd\u7684\u4e8c\u9879\u961f\u5217(Binomial Queue)\u4e5f\u662f\u4f18\u5148\u961f\u5217\u7684\u4e00\u79cd\u5b9e\u73b0\uff0c\u53ea\u4e0d\u8fc7\u4e0d\u540c\u4e8e\u4e4b\u524d\u6211\u4eec\u7528\u4e00\u4e2a\u5806\u7ef4\u62a4\u4f18\u5148\u961f\u5217\uff0c\u4e8c\u9879\u961f\u5217\u540c\u65f6\u7ef4\u62a4\u4e86\u5177\u6709\u4e0d\u540c\u7279\u5f81\u7684\u82e5\u5e72\u961f\u5217\u3002</p> <p>link</p> <p>Wikipedia: https://en.wikipedia.org/wiki/Binomial_heap</p> <p>YouTube: https://www.youtube.com/watch?v=6JxvKfSV9Ns \uff08\u867d\u7136\u8fd9\u4e2a\u89c6\u9891\u662f\u8bb2\u89e3\u6590\u6ce2\u90a3\u5951\u5806\u7684\uff0c\u4f46\u662f\u4e2d\u95f4\u5148\u8bb2\u4e86\u4e8c\u9879\u5806\u3002\uff09</p> <p>\u5b66\u4e60\u5efa\u8bae</p> <p>\u5728\u6b63\u5f0f\u5f00\u59cb\u672c\u8282\u5185\u5bb9\u4e4b\u524d\uff0c\u8bf7\u5e26\u7740\u8fd9\u6837\u4e00\u4e2a\u5ff5\u5934\uff1a\u5c3d\u529b\u601d\u8003\u4e8c\u9879\u961f\u5217\u4e0e\u4e8c\u8fdb\u5236\u7684\u5173\u7cfb\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec05/#\u6982\u5ff5","title":"\u6982\u5ff5","text":"<p>\u4e8c\u9879\u961f\u5217(Binomial Queue)\u672c\u8d28\u4e0a\u662f\u4e00\u7cfb\u5217\u4e8c\u9879\u6811(Binomial Tree)\u7684\u96c6\u5408\u3002\u6240\u4ee5\u6211\u4eec\u9996\u5148\u7ed9\u5b9a\u4e8c\u9879\u6811(Binomial Tree)\u7684\u5b9a\u4e49\uff1a</p> <p>Binomial Tree</p> <p>\u4e8c\u9879\u6811\u6ee1\u8db3\u5806\u7684\u6027\u8d28\uff0c\u5373 parent \u8282\u70b9\u7684\u503c\u5c0f\u4e8e\uff08\u5927\u4e8e\uff09 child \u8282\u70b9\u7684\u503c\u3002</p> <p>\u4e00\u4e2a\u975e\u5e38\u5173\u952e\u7684\u6027\u8d28\u662f\uff0c\\(k\\) \u9636\u4e8c\u9879\u6811\u90fd\u662f\u540c\u6784\u7684\uff0c\u4e14 \\(k\\) \u9636\u4e8c\u9879\u6811\u662f\u4e24\u4e2a \\(k-1\\) \u9636\u4e8c\u9879\u6811\u5408\u5e76\u5f97\u5230\u7684\u3002\u800c\u5176\u5408\u5e76\u65b9\u5f0f\u662f\u76f4\u63a5\u4ee4\u5176\u4e2d\u4e00\u68f5\u6210\u4e3a\u53e6\u5916\u4e00\u68f5\u7684\u6839\u7684\u65b0 child\uff0c\u8fd9\u4e5f\u51b3\u5b9a\u4e86\u4e8c\u9879\u6811\u7684\u6839\u6bcf\u4e00\u4e2a child \u672c\u8eab\u4e5f\u90fd\u662f\u4e00\u4e2a\u4e8c\u9879\u6811\u3002</p> <p> </p> <p>\u663e\u7136\u80fd\u591f\u5f97\u5230\uff0c\u4e8c\u9879\u6811\u5e76\u975e\u4e8c\u53c9\u6811\uff1b\u66f4\u8fdb\u4e00\u6b65\u7684\uff0c\\(k\\) \u9636\u4e8c\u9879\u6811 \\(B_k\\) \u7684\u6839\u6709 \\(k\\) \u4e2a child\uff0c\\(2^k\\) \u4e2a\u8282\u70b9\uff1b\u518d\u8fdb\u4e00\u6b65\u7684\uff0c\\(B_k\\) \u7684\u7b2c \\(d\\) \u5c42\u4e00\u5171\u6709 \\(C_k^d = \\binom{k}{d}\\) \u4e2a\u8282\u70b9\uff0c\u6709\u8da3\u7684\u662f\uff0c\u6240\u6709\u5c42\u7684\u8282\u70b9\u52a0\u8d77\u6765\u521a\u597d\u7b26\u5408\u4e8c\u9879\u5f0f\u5b9a\u7406\uff0c\u6b64\u6761\u5b9a\u7406\u53ef\u4ee5\u7531\u6570\u5b66\u5f52\u7eb3\u6cd5\u5f88\u5bb9\u6613\u5730\u8bc1\u660e\uff0c\u4e0d\u518d\u8d58\u8ff0\u3002</p> <p>\u5173\u4e8e\u5b9e\u73b0</p> <p>\u53ef\u4ee5\u53d1\u73b0\uff0c\u4e8c\u9879\u6811\u662f\u4e00\u4e2a \\(N\\) \u53c9\u6811\uff0c\u6240\u4ee5\u901a\u5e38\u6211\u4eec\u4f7f\u7528\u94fe\u8868 sibling \u7684\u5f62\u5f0f\u6765\u8868\u793a\u4e00\u4e2a\u8282\u70b9\u7684 children\u3002</p> <p>\u518d\u5bf9\u4e8c\u9879\u6811\u505a\u4e00\u4e2a\u7b80\u5355\u7684\u603b\u7ed3\uff0c\\(k\\) \u9636\u4e8c\u9879\u6811\u7ed3\u6784\u552f\u4e00\u786e\u5b9a\uff0c\u4e24\u4e2a \\(k\\) \u9636\u4e8c\u9879\u6811\u5408\u5e76\u540e\u5f97\u5230\u4e00\u4e2a \\(k+1\\) \u9636\u4e8c\u9879\u6811\uff0c\u800c\u4e8c\u9879\u6811\u672c\u8eab\u4e5f\u5177\u6709\u5806\u7684\u6027\u8d28\u3002</p> <p>\u4f46\u662f\uff0c\u867d\u7136\u4e8c\u9879\u6811\u5177\u6709\u5806\u7684\u6027\u8d28\uff0c\u770b\u4f3c\u80fd\u72ec\u7acb\u5b8c\u6210\u4f18\u5148\u961f\u5217\u7684\u529f\u80fd\uff0c\u4f46\u662f\u4e8c\u9879\u6811\u5bf9\u70b9\u7684\u6570\u91cf\u5177\u6709\u6bd4\u8f83\u4e25\u683c\u7684\u8981\u6c42\uff0c\u53ea\u6709\u70b9\u7684\u6570\u91cf\u7b26\u5408 \\(2^k\\) \u65f6\uff0c\u624d\u80fd\u4f7f\u7528\u4e8c\u9879\u6811\u8868\u793a\u3002\u56e0\u6b64\uff0c\u89c2\u5bdf\u4e00\u4e2a\u4e8c\u9879\u6811\u80fd\u627f\u8f7d\u7684\u70b9\u7684\u6570\u91cf\u7279\u5f81\uff0c\u6211\u4eec\u8054\u60f3\u5230\u4e8c\u8fdb\u5236\u5bf9\u6570\u7684\u8868\u793a\u2014\u2014\u6211\u4eec\u53ef\u4ee5\u7528\u4e00\u7cfb\u5217\u4e8c\u9879\u6811\u6765\u7ef4\u62a4 \\(N\\) \u4e2a\u8282\u70b9\u7684\u4f18\u5148\u961f\u5217\uff0c\u800c\u5177\u4f53\u7528\u51e0\u9636\u4e8c\u9879\u6811\uff0c\u5219\u53d6\u51b3\u4e8e \\(N\\) \u7684\u4e8c\u8fdb\u5236\u8868\u8fbe\u4e2d\uff0c\u4e3a <code>1</code> \u7684\u662f\u54ea\u51e0\u4f4d\u3002</p> <p>Binomial Queue</p> <p>\u4e8c\u9879\u961f\u5217(Binomial Queue)\u662f\u4e00\u7cfb\u5217\u4e8c\u9879\u6811(Binomial Tree)\u7684\u96c6\u5408\uff0c\u5176\u4e2d\u6bcf\u4e2a\u4e8c\u9879\u6811\u7684\u9636\u6570 \\(k\\) \u90fd\u662f\u4e0d\u540c\u7684\uff0c\u53cd\u8fc7\u6765\u8bb2\u8fd9\u53e5\u8bdd\uff0c\u96c6\u5408\u4e2d \\(k\\) \u9636\u7684\u4e8c\u9879\u6811\u8981\u4e48\u53ea\u6709\u4e00\u4e2a\uff0c\u8981\u4e48\u6ca1\u6709\u3002</p> <p>\ud83c\udf30</p> <p> </p> <p>\u9898\u76ee\u5b9e\u73b0\u7684\u4e8c\u9879\u961f\u5217\u4e0d\u4e00\u5b9a\u6709 min \u6307\u9488\uff01\u6ce8\u610f\u9762\u5411\u9898\u9762\u548c\u9009\u9879\u5224\u65ad\u5b9e\u73b0\u3002</p> <p>\u800c\u4e3a\u4f55\u8981\u8fd9\u4e48\u8bbe\u8ba1\u4e8c\u9879\u961f\u5217\u7684\u7ed3\u6784\uff0c\u5177\u4f53\u4f53\u73b0\u5728\u64cd\u4f5c\u7684\u8bbe\u8ba1\u4e2d\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec05/#\u64cd\u4f5c","title":"\u64cd\u4f5c","text":"<p>\u5728\u4e8c\u9879\u961f\u5217\u4e2d\uff0c\u5408\u5e76\u662f\u4e00\u4e2a\u975e\u5e38\u57fa\u7840\u7684\u64cd\u4f5c\uff0c\u4e5f\u662f\u7cbe\u9ad3\u6240\u5728\u3002</p> <p>\u800c\u4e3a\u4e86\u611f\u53d7\u8fd9\u4e9b\u64cd\u4f5c\u7684\u7cbe\u9ad3\uff0c\u5728\u7406\u89e3\u4e8c\u9879\u961f\u5217\u8fc7\u7a0b\u4e2d\uff0c\u53ef\u4ee5\u8bd5\u56fe\u4ece\u4e24\u4e2a\u7eac\u5ea6\u540c\u65f6\u7406\u89e3\u8fd9\u4e9b\u64cd\u4f5c\uff1a</p> <ol> <li>\u6811/\u5806\u7684\u7eac\u5ea6\uff0c\u5177\u4f53\u89c2\u5bdf\u6570\u636e\u7684\u8f6c\u79fb\u4e0e\u53d8\u5316\u8fc7\u7a0b\uff1b</li> <li>\u4e8c\u8fdb\u5236\u7684\u7eac\u5ea6\uff0c\u5c06 \\(k\\) \u9636\u4e8c\u9879\u6811\u62bd\u8c61\u4e3a bit vector \u7b2c \\(k\\) \u4f4d\u7684 <code>1</code>\uff0c\u4ece\u4e8c\u8fdb\u5236\u52a0\u6cd5\u7684\u89d2\u5ea6\u7406\u89e3\uff1b</li> </ol> <p>\u4e3a\u4e86\u65b9\u4fbf\u540e\u9762\u9610\u8ff0\uff0c\u6211\u4eec\u7b80\u5355\u505a\u4e00\u4e0b\u8bf4\u660e\uff1a</p> <p>\u7279\u5f81\u6bd4\u7279\u5411\u91cf</p> <p>\u5bf9\u4e8e\u4e00\u4e2a\u4e8c\u9879\u961f\u5217\uff0c\u5b9a\u4e49\u5b83\u7684\u7279\u5f81\u6bd4\u7279\u5411\u91cf\uff08\u6211\u81ea\u5df1\u53e3\u80e1\u7684\u4e1c\u897f\uff0c\u4e0d\u662f\u672f\u8bed\uff09\u662f\u5b83\u7684\u5143\u7d20\u6570\u91cf\u7684\u4e8c\u8fdb\u5236\u8868\u793a\uff08\u53cd\u8fc7\u6765\u8bf4\uff0c\u7279\u5f81\u6bd4\u7279\u5411\u91cf\u7684\u771f\u503c\u8868\u793a\u961f\u5217\u4e2d\u7684\u5143\u7d20\u6570\u91cf\uff09\u3002</p> <p>\ud83c\udf30</p> <p>\u4f8b\u5982\u4e0b\u56fe\u7684\u4f8b\u5b50\uff0c\u4e00\u5171\u6709 11 \u4e2a\u8282\u70b9\uff0c\u5176\u7279\u5f81\u6bd4\u7279\u5411\u91cf\u4e3a <code>1011</code>\uff0c\u521a\u597d\u5bf9\u5e94 \\(B_3\\) \\(B_1\\) \\(B_0\\)\u3002</p> <p> </p> <p>\u4e5f\u5c31\u662f\u8bf4\uff0c\u7279\u5f81\u6bd4\u7279\u5411\u91cf\u8c61\u5f81\u4e86\u4e8c\u9879\u961f\u5217\u7684\u96c6\u5408\u4e2d\u6709\u54ea\u51e0\u9636\u7684\u4e8c\u9879\u6811\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec05/#\u961f\u5217\u5408\u5e76","title":"\u961f\u5217\u5408\u5e76","text":"<p>\u5408\u5e76\u4e24\u4e2a\u4e8c\u9879\u961f\u5217\uff0c\u5b9e\u9645\u4e0a\u5c31\u662f\u5408\u5e76\u4e24\u4e2a\u96c6\u5408\uff0c\u5408\u5e76\u8fc7\u7a0b\u4e2d\uff0c\u6211\u4eec\u5206\u522b\u5408\u5e76\u6bcf\u4e00\u4e2a \\(k\\) \u9636\u4e8c\u9879\u6811\uff0c\u5f53\u4e24\u4e2a\u4e8c\u9879\u961f\u5217\u90fd\u5b58\u5728 \\(k\\) \u9636\u4e8c\u9879\u6811\u65f6\uff0c\u5b83\u4eec\u5408\u5e76\u4e3a\u4e00\u68f5 \\(k+1\\) \u9636\u4e8c\u9879\u6811\u3002\u53ef\u4ee5\u8054\u60f3\uff0c\u8fd9\u9879\u64cd\u4f5c\u201c\u5bf9\u5e94\u201d\u7740\u7279\u5f81\u6bd4\u7279\u5411\u91cf\u7684\u76f8\u52a0\uff0c\u800c\u5408\u5e76\u64cd\u4f5c\u5219\u7c7b\u4f3c\u4e8e\u8fdb\u4f4d\u3002</p> <p>\u56e0\u6b64\uff0c\u5b83\u5c31\u7c7b\u4f3c\u4e8e\u4e00\u4e2a 1bit \u7684\u5168\u52a0\u5668\u3002</p> <pre><code>graph LR;\nA([\"T1.B[k]\"])\nB([\"T2.B[k]\"])\nC([\"T.carry[k-1]\"])\nD([\"T.result[k]\"])\nE([\"T.carry[k]\"])\nADD[\"Adder\"]\nA ---&gt; ADD\nB ---&gt; ADD\nC ---&gt; ADD\nADD ---&gt; D\nADD ---&gt; E</code></pre> <p>\u4e8e\u662f\uff0c\u6839\u636e\u4e00\u4e2a carry \u4f4d\u3001\u4e00\u4e2a\u88ab\u5408\u5e76\u6811\u548c\u4e00\u4e2a\u5408\u5e76\u6811\u7684\u60c5\u51b5\uff0c\u6709\u4e00\u5171 \\(2^3=8\\) \u79cd\u53ef\u80fd\u3002</p> <p>\ud83c\udf30</p> <p>\u5047\u8bbe\u6211\u4eec\u73b0\u5728\u6709\u8fd9\u6837\u4e24\u4e2a\u4e8c\u9879\u961f\u5217\u9700\u8981\u5408\u5e76\uff1a</p> <p> </p> <p>\u5219\u5176\u5408\u5e76\u7684\u64cd\u4f5c\u53ef\u4ee5\u8fd9\u6837\u63cf\u8ff0\u3002</p> \u7279\u5f81\u6bd4\u7279\u5411\u91cf\u89c6\u89d2\u5177\u4f53\u89c6\u89d2 <p>\u7eff\u8272\u4e8c\u9879\u961f\u5217\u7684\u7279\u5f81\u6bd4\u7279\u5411\u91cf\u4e3a <code>1011</code>\uff0c\u84dd\u8272\u7684\u4e3a <code>1001</code>\uff0c\u4e24\u8005\u76f8\u52a0\u5f97\u5230 <code>10100</code>\u3002</p> Frame 1Frame 2Frame 3Frame 4Frame 5Frame 6 <p> </p> <p>\\(B_0\\) \u5408\u5e76\uff0c\u7531\u4e8e \\(T_{green}.B_0\\) \u548c \\(T_{blue}.B_0\\) \u90fd\u5b58\u5728\uff0c\u6240\u4ee5\u5408\u5e76\u4ea7\u751f\u4e3a \\(T.C_0\\)\uff0c\\(T.R_0\\) \u4e3a\u7a7a\u3002</p> <p> </p> <p>\\(B_1\\) \u5408\u5e76\uff0c\u7531\u4e8e \\(T_{green}.B_1\\) \u548c \\(T.C_0\\) \u5b58\u5728\uff0c\u6240\u4ee5\u5408\u5e76\u4ea7\u751f\u4e3a \\(T.C_1\\)\uff0c\\(T.R_1\\) \u4e3a\u7a7a\u3002</p> <p> </p> <p>\\(B_2\\) \u5408\u5e76\uff0c\u7531\u4e8e\u53ea\u6709 \\(T.C_1\\) \u5b58\u5728\uff0c\u6240\u4ee5\u76f4\u63a5\u4ee4 \\(T.R_2 = T.C_1\\)\uff0c\\(T.C_2\\) \u4e3a\u7a7a\u3002</p> <p> </p> <p>\\(B_3\\) \u5408\u5e76\uff0c\u7531\u4e8e \\(T_{green}.B_1\\)\uff0c\\(T_{blue}.B_1\\) \u548c \\(T.C_2\\) \u90fd\u4e0d\u5b58\u5728\uff0c\u6240\u4ee5 \\(T.R_3\\) \u4e3a\u7a7a\uff0c\\(T.C_1\\) \u4e3a\u7a7a\u3002</p> <p> </p> <p>\\(B_4\\) \u5408\u5e76\uff0c\u7531\u4e8e \\(T_{green}.B_4\\) \u548c \\(T.C_3\\) \u90fd\u5b58\u5728\uff0c\u6240\u4ee5\u5408\u5e76\u4ea7\u751f\u4e3a \\(T.C_4\\)\uff0c\\(T.R_4\\) \u4e3a\u7a7a\u3002</p> <p> </p> <p>\\(B_5\\) \u5408\u5e76\uff0c\u7531\u4e8e\u53ea\u6709 \\(T.C_4\\) \u5b58\u5728\uff0c\u6240\u4ee5\u76f4\u63a5\u4ee4 \\(T.R_5 = T.C_4\\)\uff0c\\(T.C_5\\) \u4e3a\u7a7a\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec05/#\u5355\u70b9\u63d2\u5165","title":"\u5355\u70b9\u63d2\u5165","text":"<p>\u63d2\u5165\u7ed3\u70b9\u53ef\u4ee5\u770b\u4f5c\u5408\u5e76\u4e00\u4e2a\u53ea\u6709\u4e00\u4e2a\u7ed3\u70b9\u7684\u5de6\u504f\u5806\uff0c\u6240\u4ee5\u6211\u4eec\u53ef\u4ee5\u76f4\u63a5\u590d\u7528\u5408\u5e76\u8fc7\u7a0b\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec05/#\u67e5\u8be2\u961f\u9996","title":"\u67e5\u8be2\u961f\u9996","text":"<p>\u4e8c\u9879\u961f\u5217\u7684\u961f\u9996\uff0c\u4e5f\u5c31\u662f\u6574\u4e2a\u961f\u5217\u7684\u6700\u5c0f\u503c\uff08\u6700\u5927\u503c\uff09\uff0c\u5c31\u662f\u8fd9\u82e5\u5e72\u4e2a\uff08\\(O(\\log N)\\) \u4e2a\uff09\u4e8c\u9879\u6811\u7684\u6839\u4e2d\u6700\u5c0f\uff08\u6700\u5927\uff09\u7684\u90a3\u4e2a\u3002\u6240\u4ee5\u5176\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a \\(O(\\log N)\\)\u3002</p> <p>\u4e0d\u8fc7\u6709\u65f6\u5019\u6211\u4eec\u4e5f\u4f1a\u989d\u5916\u7ef4\u62a4\u4e00\u4e2a\u6307\u9488\uff0c\u6307\u5411\u5f53\u524d\u6700\u5c0f\u7684\u90a3\u4e2a\u6839\uff0c\u6b64\u65f6\u5176\u590d\u6742\u5ea6\u4e3a \\(O(1)\\)\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec05/#\u961f\u9996\u51fa\u961f","title":"\u961f\u9996\u51fa\u961f","text":"<p>\u961f\u9996\u51fa\u961f\u9996\u5148\u8981\u627e\u5230\u961f\u9996\uff0c\u8fd9\u4ef6\u4e8b\u6211\u4eec\u5728#\u67e5\u8be2\u961f\u9996\u5df2\u7ecf\u8ba8\u8bba\u8fc7\u4e86\u3002</p> <p>\u627e\u5230\u961f\u9996\u540e\uff0c\u6211\u4eec\u5c06\u5176\u4ece\u4e8c\u9879\u961f\u5217\u4e2d\u79fb\u9664\uff0c\u6211\u4eec\u77e5\u9053\uff0c\u961f\u9996\u5fc5\u7136\u662f\u67d0\u4e2a\u4e8c\u9879\u6811\u7684\u6839\uff0c\u6240\u4ee5\u5220\u6389\u8fd9\u4e2a\u961f\u9996\u4ee5\u540e\uff0c\u5c31\u4f1a\u4ea7\u751f \\(k\\) \u4e2a\u65b0\u7684\u5b50\u6811\u3002</p> <p>\u800c\u8ba9\u6211\u4eec\u56de\u987e\u4e8c\u9879\u6811\u7684\u5408\u5e76\u8fc7\u7a0b\uff0c\u53ef\u4ee5\u53d1\u73b0\uff0c\u6839\u7684\u6240\u6709\u513f\u5b50\u90fd\u662f\u4e00\u4e2a\u5b8c\u6574\u7684 \\(k\\) \u9636\u4e8c\u9879\u6811\u5408\u5e76\u8fc7\u6765\u7684\uff0c\u6240\u4ee5\u5f53\u6211\u4eec\u5220\u6389\u8fd9\u4e2a\u6839\uff0c\u4ea7\u751f\u7684\u6240\u6709\u5b50\u6811\u90fd\u662f\u4e8c\u9879\u6811\u3002</p> <p>\u56e0\u6b64\u6211\u4eec\u8054\u60f3\u5230\uff0c\u5c06\u961f\u9996\u51fa\u961f\u95ee\u9898\u8f6c\u5316\u4e3a\u5408\u5e76\u4e8c\u9879\u961f\u5217\u7684\u95ee\u9898\u2014\u2014\u5047\u8bbe \\(T\\) \u7684\u961f\u9996\u662f \\(B_k\\) \u7684\u6839\uff0c\u5219\u961f\u9996\u51fa\u961f\u53ef\u4ee5\u8f6c\u5316\u4e3a\u6c42\u89e3 \\(merge(T-B_k, B_k.root.children)\\) \u7684\u95ee\u9898\u3002</p> <p>\ud83c\udf30</p> <p>\u5047\u8bbe\u6211\u4eec\u6709\u5982\u4e0b\u7684\u4e8c\u9879\u961f\u5217\uff0c\u73b0\u5728\u8fdb\u884c\u5f39\u51fa\u961f\u9996\u7684\u64cd\u4f5c\u3002</p> <p> </p> \u7279\u5f81\u6bd4\u7279\u89c6\u89d2\u5177\u4f53\u89c6\u89d2 <p>\u5982\u4e0a\u961f\u5217\uff0c\u5176\u7279\u5f81\u6bd4\u7279\u5411\u91cf\u4e3a <code>10100</code>\uff0c\u5171 20 \u4e2a\u8282\u70b9\u3002\u73b0\u5728\u5220\u6389\u4e00\u4e2a\uff0c\u5e94\u5f53\u6709 19 \u4e2a\u8282\u70b9\u3002</p> <p>\u66f4\u5177\u4f53\u7684\uff0c<code>10100</code> = <code>10000</code> + <code>100</code>\uff0c\u5206\u522b\u4ee3\u8868\u4e24\u4e2a\u4e8c\u9879\u6811\uff0c\u800c\u6211\u4eec\u7684\u6700\u5c0f\u503c\u662f\u4ece <code>10000</code> \u6240\u4ee3\u8868\u7684\u6811\u91cc\u5220\u9664\u7684\uff0c\u6240\u4ee5\u65b0\u7684\u7279\u5f81\u6bd4\u7279\u5411\u91cf\u4e3a\uff1a(<code>10000</code> - 1) + <code>100</code> = <code>1111</code> + <code>100</code> = <code>10011</code>\uff0c\u5373 19 \u4e2a\u3002</p> <p>\u6ce8\u610f\u89c2\u5bdf\u8fd9\u91cc <code>10000</code> - 1 = <code>1111</code> \u7684\u53d8\u5316\uff0c\u5bfb\u627e\u5b83\u4e0e\u5177\u4f53\u89c6\u89d2\u4e2d\u7684\u5173\u7cfb\u3002</p> Frame 1Frame 2Frame 3Frame 4 <p> </p> <p>\u9996\u5148\u627e\u5230\u961f\u9996\uff0c\u5373\u6b64\u65f6 min \u6307\u9488\u6307\u5411\u7684\u5730\u65b9\u3002\u89c2\u5bdf\u5b83\u7684\u7ed3\u6784\uff0c\u6211\u4eec\u53d1\u73b0\u5b83\u5177\u6709\u56db\u4e2a\u5b50\u6811\uff0c\u5206\u522b\u662f \\(B_0 \\sim B_3\\)\uff0c\u5bf9\u5e94\u4e86\u6211\u4eec\u4e4b\u524d\u63d0\u5230\u7684\u300c\u6839\u7684\u6240\u6709\u513f\u5b50\u90fd\u662f\u4e00\u4e2a\u5b8c\u6574\u7684 \\(k\\) \u9636\u4e8c\u9879\u6811\u5408\u5e76\u8fc7\u6765\u7684\u300d\u3002</p> <p> </p> <p>\u4e8e\u662f\u6211\u4eec\u5c06\u8fd9\u4e2a\u5b50\u6811\u63d0\u53d6\u51fa\u6765\uff0c\u5c06\u539f\u672c\u7684\u4e8c\u9879\u961f\u5217\u62c6\u6210\u4e3a\u4e24\u4e2a\u4e8c\u9879\u961f\u5217\u3002</p> <p> </p> <p>\u73b0\u5728\u6211\u4eec\u5220\u9664\u201c\u961f\u9996\u201d\uff0c\u53d1\u73b0\u90a3\u68f5\u6811\u5206\u88c2\u6210\u4e86\u56db\u4e2a\u8fde\u7eed\u7684\u4e8c\u9879\u6811\uff08<code>10000</code> - 1 = <code>1111</code>\uff09\u3002</p> <p> </p> <p>\u73b0\u5728\u95ee\u9898\u5c31\u8f6c\u5316\u4e3a\u4e86\u4e24\u4e2a\u4e8c\u9879\u961f\u5217\u5408\u5e76\u7684\u95ee\u9898\u3002\u5728\u6b64\u7701\u7565\u3002</p> <p>\u6ce8\u610f\u89c2\u5bdf\u5b8c\u6210\u7684\u4e8c\u9879\u961f\u5217\u7684\u7279\u5f81\u6bd4\u7279\u5411\u91cf\u548c\u4e0a\u9762\u7684\u7279\u5f81\u6bd4\u7279\u5411\u91cf\u89c6\u89d2\u7684\u7ed3\u679c\u3002</p> <p>\u63d0\u793a</p> <p>\u652f\u6301\u7740\u961f\u9996\u51fa\u961f\u53ef\u4ee5\u8fd9\u6837\u8fdb\u884c\u7684\u6027\u8d28\u5c31\u662f\uff0c\u6bcf\u4e00\u4e2a\u4e8c\u9879\u6811\u7684\u6839\u7684 children \u672c\u8eab\u4e5f\u90fd\u662f\u4e8c\u9879\u6811\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec05/#\u644a\u8fd8\u5206\u6790","title":"\u644a\u8fd8\u5206\u6790","text":""},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec05/#project-fibonacci-queue","title":"Project: Fibonacci Queue","text":"<p>Link</p> <p>YouTube: https://www.youtube.com/watch?v=6JxvKfSV9Ns</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec06/","title":"Lecture 6 | Backtracing","text":"<p> \u7ea6 459 \u4e2a\u5b57  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 2 \u5206\u949f</p> <p>link</p> <p>OI Wiki: https://oi-wiki.org/search/backtracking/</p> <p>Wikipedia: https://en.wikipedia.org/wiki/Backtracking</p> <p>\u8fd9\u4e00\u8282\u7684\u5185\u5bb9\u6bd4\u8f83\u6563\uff0c\u56e0\u4e3a\u56de\u6eaf\u662f\u4e00\u4e2a\u5f88\u57fa\u7840\u800c\u4e14\u5f88\u6cdb\u7528\u7684\u4e1c\u897f\uff0c\u6240\u4ee5\u611f\u89c9\u600e\u4e48\u8bb2\u90fd\u4e0d\u592a\u5408\u9002\u3002\u66f4\u591a\u7684\u662f\u9700\u8981\u5728\u5177\u4f53\u95ee\u9898\u3001\u5177\u4f53\u6a21\u578b\u4e2d\u53bb\u4f53\u4f1a\u3002</p> <p>\u52a0\u4e0a\u5982\u679c\u6bcf\u4e00\u4e2a\u5185\u5bb9\u90fd\u8981\u5f80\u6b7b\u91cc\u53bb\u53d9\u8ff0\u7684\u8bdd\u5b9e\u5728\u592a\u7d2f\u4e86\uff0c\u6240\u4ee5\u56de\u6eaf\u8fd9\u4e00\u7ae0\u60f3\u5077\u4e2a\u61d2\uff0c\u5c31\u7b80\u5355\u8bb0\u5f55\u4e00\u4e0b\u8bfe\u4e0a\u63d0\u5230\u8fc7\u7684\u4e00\u4e9b\u6a21\u578b\u5427\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec06/#\u516b\u7687\u540e","title":"\u516b\u7687\u540e","text":"<p>\u975e\u5e38\u7ecf\u5178\u7684\u95ee\u9898\uff0c\u76f8\u4fe1\u63a5\u89e6\u8fc7\u7b97\u6cd5\u7684\u540c\u5b66\u57fa\u672c\u4e0a\u90fd\u7ed5\u4e0d\u5f00\u8fd9\u4e2a\u4e1c\u897f\u3002</p> <p>link</p> <p>Wikipedia: https://en.wikipedia.org/wiki/Eight_queens_puzzle</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec06/#\u6848\u4f8b-the-turnpike-reconstruction-problem","title":"[\u6848\u4f8b] The Turnpike Reconstruction Problem","text":"<p>\u6536\u8d39\u7ad9\u91cd\u5efa\u95ee\u9898(The Turnpike Reconstruction Problem)\u63cf\u8ff0\u7684\u662f\u4e00\u6761\u88ab\u62bd\u8c61\u4e3a\u76f4\u7ebf\u7684\u516c\u8def\u4e0a\uff0c\u6709 \\(N\\) \u4e2a\u6536\u8d39\u7ad9\uff08\\(x_1, x_2, ..., x_N\\)\uff09\u3002\u73b0\u5728\u7ed9\u51fa\u4efb\u610f\u4e24\u4e2a\u6536\u8d39\u7ad9\u4e4b\u95f4\u7684\u8ddd\u79bb\u7684\u53ef\u91cd\u96c6\u5408 \\(D\\)\uff0c\uff08\u53ef\u60f3\u800c\u77e5\uff0c\u4e00\u5171\u6709 \\(\\frac{N(N-1)}{2}\\) \u4e2a\u5143\u7d20\uff09\uff0c\u6c42\u6536\u8d39\u7ad9\u7684\u4f4d\u7f6e\uff0c\u5373\u7ed9\u5b9a\u4efb\u610f\u4e24\u70b9\u7684\u8ddd\u79bb\u96c6\u5408\uff0c\u6c42\u51fa\u8fd9\u4e9b\u70b9\u7684\u5750\u6807\u3002</p> <p>solution</p> <p>\u5927\u6982\u601d\u8def\u5c31\u662f\uff0c\u9996\u5148\u5047\u8bbe \\(x_1 = 0\\)\uff0c\u90a3\u4e48\u5f88\u663e\u7136 \\(x_N = \\mathop{max} \\{D\\}\\)\u3002\u540c\u65f6\u6211\u4eec\u4e5f\u5f97\u5230\u8fd9\u6761\u7ebf\u6bb5\u7684\u957f\u5ea6\u4e3a \\(\\mathop{max} \\{D\\}\\)\u3002\u63a5\u4e0b\u6765 \\(D\\) \u4e2d\u4ece\u5927\u5230\u5c0f\u53d6\u51fa\u5143\u7d20\uff0c\u5219\u5fc5\u5b9a\u8ffd\u52a0\u5728 \\(x_1\\) \u53f3\u4fa7\u6216 \\(x_N\\) \u5de6\u4fa7\uff0c\u4ee5\u6b64\u7c7b\u63a8\u3002\uff08\u53cd\u8bc1\u6cd5\u53ef\u4ee5\u8bc1\u660e\u5728\u5b8c\u5168\u5b89\u6392\u597d\u4e4b\u524d\u90fd\u662f\u8ffd\u52a0\u5728\u5de6\u4fa7\u6216\u8005\u53f3\u4fa7\u7684\u65e2\u5b9a\u8fb9\u754c\u4e4b\u95f4\u7684\uff09\u3002\u800c\u6bcf\u4e00\u6b21\u8ffd\u52a0\u7684\u9009\u62e9\u90fd\u4ee3\u8868\u51b3\u7b56\u6811\u4e2d\u7684\u4e00\u4e2a\u5206\u652f\uff0c\u53ef\u4ee5\u5229\u7528\u5176\u5b83\u6761\u4ef6\u8fdb\u884c\u526a\u679d\uff08\u4f8b\u5982 \\(D\\) \u4e2d\u6709 \\(x_p - x_0\\) \u5c31\u4e00\u5b9a\u6709 \\(x_N - x_p\\)\uff09\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec06/#\u0251-\u03b2-\u526a\u679d","title":"\u0251-\u03b2 \u526a\u679d","text":"<p>link</p> <p>Wikipedia: https://en.wikipedia.org/wiki/Alpha%E2%80%93beta_pruning</p> <ul> <li>\u5b9e\u9645\u4e0a\u5c31\u7c7b\u4f3c\u4e8e\u6c42\u89e3\u4e0d\u80fd\u8fde\u7eed\u5411\u53f3\u7684\uff0c\u4ece\u6839\u5230\u53f6\u5b50\u7684\u8def\u5f84\u3002</li> </ul>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec07/","title":"Lecture 7 | Divide &amp; Conquer","text":"<p> \u7ea6 3626 \u4e2a\u5b57  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 12 \u5206\u949f</p> <p>\u611f\u89c9\u8fd9\u51e0\u8282\u8bfe\u4e0a\u7684\u5185\u5bb9\u90fd\u633a\u5bbd\u6cdb\u7684\u554ax</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec07/#\u6982\u8ff0","title":"\u6982\u8ff0","text":"<p>link</p> <p>Wikipedia: https://en.wikipedia.org/wiki/Divide-and-conquer_algorithm</p> <p>\u5957\u7528 Wiki \u4e0a\u7684\u8bf4\u6cd5\uff0c\u5206\u6cbb\u6cd5(Divide-and-conquer algorithm)\u5c5e\u4e8e\u4e00\u79cd\u7b97\u6cd5\u8303\u578b\uff0c\u5b83\u7684\u57fa\u672c\u601d\u60f3\u662f\u5c06\u4e00\u4e2a\u95ee\u9898\u5206\u89e3\u4e3a\u82e5\u5e72\u4e2a\u89c4\u6a21\u8f83\u5c0f\u7684\u76f8\u540c\u95ee\u9898\uff0c\u7136\u540e\u9012\u5f52\u5730\u89e3\u51b3\u8fd9\u4e9b\u5b50\u95ee\u9898\uff0c\u6700\u540e\u5c06\u8fd9\u4e9b\u5b50\u95ee\u9898\u7684\u89e3\u5408\u5e76\u5f97\u5230\u539f\u95ee\u9898\u7684\u89e3\uff0c\u4e00\u4e2a\u6bd4\u8f83\u7ecf\u5178\u7684\u6848\u4f8b\u5c31\u662f\u5f52\u5e76\u6392\u5e8f\u3002</p> <p>\u672c\u8282\u7684\u91cd\u70b9\u5b9e\u9645\u4e0a\u4e5f\u5e76\u4e0d\u662f\u805a\u7126\u4e8e\u5206\u6cbb\u672c\u8eab\uff0c\u800c\u662f\u5176\u590d\u6742\u5ea6\u5206\u6790\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec07/#\u6848\u4f8b-closet-points-problem","title":"[\u6848\u4f8b] Closet Points Problem","text":"<p>\u4e8c\u7ef4\u6700\u8fd1\u70b9\u95ee\u9898(Closet Points Problem)\uff0c\u6307\u7684\u662f\u7ed9\u5b9a\u5e73\u9762\u4e0a\u7684 n \u4e2a\u70b9\uff0c\u627e\u51fa\u5176\u4e2d\u8ddd\u79bb\u6700\u8fd1\u7684\u4e24\u4e2a\u70b9\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec07/#\u6734\u7d20\u65b9\u6cd5","title":"\u6734\u7d20\u65b9\u6cd5","text":"<p>\u6700\u6734\u7d20\u7684\u505a\u6cd5\u5f53\u7136\u662f\u679a\u4e3e\u6240\u6709\u7684\u70b9\u5bf9\uff0c\u4e00\u5171\u9700\u8981 \\(C_{N}^{2} = {{N}\\choose{2}} = \\frac{N(N-1)}{2}\\) \u5373\u590d\u6742\u5ea6\u4e3a \\(O(N^2)\\)\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec07/#\u5206\u6cbb\u65b9\u6cd5","title":"\u5206\u6cbb\u65b9\u6cd5","text":"<p>\u73b0\u5728\u6211\u4eec\u7c7b\u6bd4\u6700\u5927\u5b50\u5e8f\u5217\u548c\u95ee\u9898\u7684\u5206\u6cbb\u505a\u6cd5\u3002</p> \u6700\u5927\u5b50\u5e8f\u5217\u548c\u7684\u5206\u6cbb\u505a\u6cd5 <ol> <li>\u5c06\u5e8f\u5217\u5206\u4e3a\u5de6\u53f3\u4e24\u90e8\u5206\uff0c\u5206\u522b\u6c42\u89e3\u6700\u5927\u5b50\u5e8f\u5217\u548c\uff1b</li> <li>\u6c42\u89e3\u8de8\u8d8a\u4e2d\u70b9\u7684\u6700\u5927\u5b50\u5e8f\u5217\u548c\uff1b</li> <li>\u6bd4\u8f83\u4e09\u8005\u7684\u5927\u5c0f\uff0c\u53d6\u6700\u5927\u503c\uff1b</li> </ol> <p>\u6211\u4eec\u53ef\u4ee5\u5c06\u6574\u4e2a\u5e73\u9762\u5206\u4e3a\u4e24\u4e2a\u90e8\u5206\uff0c\u5373\u5982\u56fe\u4e2d\u7eff\u8272\u7ebf\u5c06\u70b9\u5bf9\u5212\u5206\u4e3a\u4e24\u4e2a\u90e8\u5206\u3002</p> <p> </p> <p>\u63a5\u4e0b\u6765\u6211\u4eec\u540c\u6837\u5206\u4e3a\u8fd9\u4e48\u4e09\u6b65\uff1a</p> <ol> <li>\u5c06\u70b9\u5bf9\u5206\u4e3a\u5de6\u53f3\u4e24\u90e8\u5206\uff0c\u5206\u522b\u6c42\u89e3\u6700\u8fd1\u70b9\u5bf9\uff1b</li> <li>\u5bfb\u627e\u8de8\u8d8a\u5206\u754c\u7ebf\u7684\u70b9\u5bf9\uff0c\u4ece\u4e2d\u5bfb\u627e\u6700\u8fd1\u70b9\u5bf9\uff1b</li> <li>\u6bd4\u8f83\u4e09\u8005\u7684\u5927\u5c0f\uff0c\u53d6\u6700\u5c0f\u503c\uff1b</li> </ol> <p>\u663e\u7136\uff0c\u6211\u4eec\u73b0\u5728\u9700\u8981\u89e3\u51b3\u7684\u5c31\u662f\u8981\u5982\u4f55\u8bbe\u8ba1\u7b2c\u4e8c\u6b65\u7684\u5b9e\u73b0\uff0c\u4ee5\u6c42\u66f4\u4f18\u7684\u590d\u6742\u5ea6\u3002</p> <p>\u9996\u5148\u6211\u4eec\u5047\u8bbe\u5728\u7b2c\u4e00\u6b65\u4e2d\uff0c\u6211\u4eec\u6c42\u5f97\u4e24\u8fb9\u6c42\u5f97\u7684\u6700\u5c0f\u8ddd\u79bb\u4e2d\u8f83\u5c0f\u7684\u90a3\u4e2a\u4e3a \\(\\delta\\)\uff0c\u6362\u53e5\u8bdd\u6765\u8bf4\uff0c\u5982\u679c\u7b54\u6848\u5728\u7b2c\u4e8c\u6b65\u4e2d\u88ab\u66f4\u65b0\uff0c\u90a3\u4e48\u5b83\u7684\u8ddd\u79bb\u9700\u8981\u5c0f\u4e8e \\(\\delta\\)\u3002\u800c\u6211\u4eec\u77e5\u9053\uff0c\u5728\u7b2c\u4e8c\u6b65\u4e2d\u88ab\u62ff\u51fa\u6765\u7684\u70b9\u5bf9\uff0c\u4e00\u5b9a\u662f\u4e00\u4e2a\u5728\u5206\u754c\u7ebf\u5de6\u4fa7\u4e00\u4e2a\u5728\u5206\u754c\u7ebf \\(L\\) \u53f3\u4fa7\u3002\u6734\u7d20\u7684\u6765\u60f3\uff0c\u5728\u8ddd\u79bb\u5206\u754c\u7ebf \\(\\delta\\) \u4ee5\u5916\u7684\u70b9\u5bf9\u4e2d\uff0c\u6211\u4eec\u662f\u4e0d\u9700\u8981\u8003\u8651\u7684\u3002\u800c\u5728\u8ddd\u79bb\u5206\u754c\u7ebf \\(\\delta\\) \u4ee5\u5185\u7684\u70b9\uff0c\u90fd\u5b58\u5728\u6210\u4e3a\u7b54\u6848\u70b9\u5bf9\u70b9\u53ef\u80fd\u3002</p> <p> </p> <p>\u5982\u56fe\uff0c\u73b0\u5728\u6211\u4eec\u77e5\u9053\uff0c\u53ea\u6709\u843d\u5728\u4e24\u6761\u6df1\u7eff\u8272\u4e4b\u95f4\u7684\u70b9\u624d\u53ef\u80fd\u4f1a\u66f4\u65b0\u7b54\u6848\u3002</p> <p>\u73b0\u5728\u6211\u4eec\u9700\u8981\u505a\u7684\u662f\uff0c\u4ece\u5206\u754c\u7ebf\u5de6\u4fa7\u7684\u533a\u57df\u91cc\u62ff\u4e00\u4e2a\u70b9\uff0c\u548c\u5206\u754c\u7ebf\u53f3\u8fb9\u7684\u4e00\u4e2a\u70b9\u505a\u5339\u914d\uff0c\u7136\u540e\u53d6\u6240\u6709\u7ed3\u679c\u4e2d\u7684\u6700\u5c0f\u70b9\u3002\u4e0d\u8fc7\u8fd9\u4ef6\u4e8b\u4ecd\u7136\u53ef\u4ee5\u4f18\u5316\u2014\u2014\u5728\u4e8c\u7ef4\u7684\u6570\u636e\u4e2d\uff0c\u4ec5\u5bf9\u4e00\u4e2a\u7eac\u5ea6\u505a\u7ea6\u675f\u5f80\u5f80\u4f1a\u5bfc\u81f4\u4e8b\u60c5\u53d8\u5f97\u4e0d\u90a3\u4e48\u7a33\u5b9a\uff0c\u6240\u4ee5\u6211\u4eec\u540c\u6837\u8003\u8651\u5728\u53e6\u5916\u4e00\u4e2a\u65b9\u5411\u505a\u7ea6\u675f\u3002</p> <p>\u4e5f\u662f\u57fa\u4e8e\u8303\u56f4\u7ea6\u675f\u7684\u8003\u8651\u3002\u5047\u8bbe\u6211\u4eec\u4ee5\u5de6\u4fa7\u7684\u70b9\u4e3a\u57fa\u51c6\uff0c\u4ece\u4e0a\u5f80\u4e0b\u505a\u904d\u5386\u8fd9\u4e9b\u70b9\uff0c\u90a3\u4e48\u5bf9\u4e8e\u70b9 \\(p_{l_i}\\)\uff0c\u5177\u6709\u80fd\u591f\u66f4\u65b0\u7b54\u6848\u7684\uff0c \\(\\mathop{dis} (p_{l_i}, p_{r_j}) \\leq \\delta\\) \u7684 \\(p_{r_j}\\)\uff0c\u4e00\u5b9a\u6709 \\(\\mathop{dis_{\\parallel bound}}(p_{l_i}, p_{r_j}) \\leq \\delta\\)\uff08\u76f4\u89d2\u4e09\u89d2\u5f62\u659c\u8fb9\u6700\u957f\uff09\u3002</p> <p>\u56e0\u6b64\uff0c\u5bf9\u4e8e\u9009\u5b9a\u70b9 \\(p_{l_i}\\)\uff0c\u5176\u6240\u6709\u53ef\u80fd\u5bfc\u81f4\u7b54\u6848\u66f4\u65b0\u7684\u70b9\u90fd\u88ab\u6846\u5b9a\u5728\u4e00\u4e2a \\(2\\delta \\times \\delta\\) \u7684\u77e9\u5f62\u4e2d\u3002</p> <p>\u800c\u66f4\u5947\u5999\u7684\u662f\uff0c\u8fd9\u4e2a\u7531\u53c2\u6570 \\(\\delta\\) \u6307\u5b9a\u7684\u77e9\u5f62\uff0c\u5de7\u5999\u5730\u7ea6\u675f\u4e86\u843d\u5728\u77e9\u5f62\u4e2d\u7684\u70b9\u7684\u6700\u5927\u6570\u91cf\u3002</p> <p> </p> <p>\u5728\u8fd9\u6837\u4e00\u4e2a\u533a\u57df\u4e2d\uff0c\u6211\u4eec\u9700\u8981\u7ea6\u675f\u6240\u6709\u843d\u5728 \\(\\delta \\times \\delta\\) \u7684 L \u533a\u57df\u4e2d\u7684\u70b9\uff0c\u4e92\u76f8\u7684\u8ddd\u79bb\u90fd\u5927\u4e8e\u7b49\u4e8e \\(\\delta\\)\uff0c\u5bf9 R \u533a\u57df\u4e2d\u7684\u70b9\u4e5f\u6709\u76f8\u540c\u7684\u7ea6\u675f\u3002\u4e0d\u96be\u53d1\u73b0\uff0c\u5728\u6700\u7406\u60f3\u6700\u7406\u60f3\u7684\u60c5\u51b5\u4e0b\u2014\u2014\u95ed\u533a\u95f4\u3001\u5141\u8bb8\u70b9\u91cd\u5408\u7684\u60c5\u51b5\u4e0b\uff0c\u8fd9\u4e2a\u77e9\u5f62\u6700\u591a\u4e5f\u53ea\u80fd\u653e\u516b\u4e2a\u70b9\uff08\u4e24\u8fb9\u5404\u56db\u4e2a\uff09\uff1a</p> <p> </p> <p>\u800c\u66f4\u4e00\u822c\u7684\u60c5\u51b5\u4e0b\uff0c\u6700\u591a\u4e5f\u53ea\u80fd\u653e\u516d\u4e2a\u70b9\uff08\u4e24\u8fb9\u5404\u4e09\u4e2a\uff09\u3002</p> <p>\u65e0\u8bba\u5982\u4f55\uff0c\u6211\u4eec\u53ef\u4ee5\u5f97\u5230\u7ed3\u8bba\uff0c\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u5bf9\u4e8e\u6bcf\u4e00\u4e2a\u9009\u5b9a\u7684 \\(p_{l_i}\\)\uff0c\u5bfb\u627e\u5176\u53ef\u80fd\u5bfc\u81f4\u7b54\u6848\u66f4\u65b0\u7684\u70b9\u7684\u590d\u6742\u5ea6\u90fd\u662f\u5e38\u6570\u7ea7\u7684\u3002</p> <p>\u800c\u679a\u4e3e\u8fd9\u4e9b\u201c\u9009\u5b9a\u70b9\u201d\uff0c\u4e5f\u5c31\u662f\u679a\u4e3e \\(p_{l_i}\\)\uff0c\u5176\u590d\u6742\u5ea6\uff08\u6491\u6b7b\uff09\u662f \\(O(N)\\)\u3002</p> <p>\u4e8e\u662f\u6211\u4eec\u80fd\u5f97\u5230\u8fd9\u4e2a\u5206\u6cbb\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u8ba1\u7b97\u9012\u63a8\u516c\u5f0f\uff1a</p> \\[ T(N) = \\underbrace{2\\; T(\\frac{N}{2})}_{\\text{Step 1. divide}} + \\underbrace{O(N)}_{\\text{Step 2. across}} = O(N\\log N) \\] <p>\u800c\u6211\u4eec\u63a5\u4e0b\u6765\u8981\u89e3\u51b3\u7684\u5c31\u662f\uff0c\u5982\u4f55\u901a\u8fc7\u8fd9\u4e2a\u9012\u63a8\u5f0f\u5f97\u5230\u7ed3\u679c\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec07/#\u590d\u6742\u5ea6\u5206\u6790","title":"\u590d\u6742\u5ea6\u5206\u6790","text":"<p>\u5728\u5f00\u59cb\u63a5\u4e0b\u6765\u7684\u5185\u5bb9\u4e4b\u524d\uff0c\u6211\u4eec\u9700\u8981\u7ed9\u51fa\u66f4\u4e00\u822c\u7684\uff0c\u6211\u4eec\u60f3\u8981\u89e3\u51b3\u7684\u95ee\u9898\uff0c\u5373\u6c42\u89e3\u65f6\u95f4\u590d\u6742\u5ea6\u9012\u63a8\u516c\u5f0f\u5f62\u5982\u4e0b\u5f0f\u7684\u7b97\u6cd5\u7684\u65f6\u95f4\u590d\u6742\u5ea6\uff1a</p> \\[ T(N) = aT(\\frac{N}{b}) + f(N) \\;\\;\\;\\; a,b \\in Z^+ \\] <p>\u4f8b\u5982\uff0c\u4e0a\u9762\u7684\u6700\u8fd1\u70b9\u5bf9\u95ee\u9898\uff0c\u5c31\u662f \\(a = 2,\\; b = 2,\\; f(N) = O(N)\\) \u7684\u60c5\u51b5\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec07/#\u4ee3\u6362\u6cd5","title":"\u4ee3\u6362\u6cd5","text":"<p>\u4ee3\u6362\u6cd5(substitution method)\u7684\u601d\u8def\u975e\u5e38\u76f4\u767d\uff0c\u9996\u5148\u6211\u4eec\u901a\u8fc7\u67d0\u4e9b\u624b\u6bb5\uff08\u6bd4\u5982\u5927\u773c\u89c2\u5bdf\u6cd5\ud83d\udc40\uff09\u6765\u5f97\u5230\u4e00\u4e2a\u9884\u8bbe\u7684\u7ed3\u679c\uff0c\u63a5\u4e0b\u6765\u901a\u8fc7\u4ee3\u5165\u3001\u5f52\u7eb3\u7684\u65b9\u6cd5\u6765\u8bc1\u660e\u8fd9\u4e2a\u7ed3\u679c\u3002</p> <p>\u5927\u80c6\u731c\u6d4b\uff0c\u5c0f\u5fc3\u6c42\u8bc1\uff01</p> <p>\ud83c\udf30</p> \u9898\u9762\u89e3\u7b54 <p>\u6c42\u89e3\u590d\u6742\u5ea6\uff1a</p> \\[ T(N) = 2\\; T(\\frac{N}{2}) + N \\] <p>\u9884\u8bbe\uff1a</p> \\[ T(N) = O(N\\log N) \\] <p>\u4ee3\u5165\uff1a</p> <ul> <li>\u5bf9\u4e8e\u8db3\u591f\u5c0f\u7684 \\(m &lt; N\\)\uff0c\u6709\uff1a</li> </ul> \\[ T(\\frac{m}{2}) = O(\\frac{m}{2}\\log \\frac{m}{2}) \\leq c \\frac{m}{2}\\log \\frac{m}{2} \\] <ul> <li>\u5c06\u4e0a\u5f0f\u4ee3\u5165\uff1a</li> </ul> \\[ T(m) = 2\\; T(\\frac{m}{2}) + m \\] <ul> <li>\u5f97\uff1a</li> </ul> \\[ T(m) \\leq 2\\; c \\frac{m}{2}\\log \\frac{m}{2} + m \\leq c m \\log m \\text{ for } c \\geq 1 \\] <p>\u5bf9\u4e8e\u8db3\u591f\u5c0f\u7684 \\(m = 2\\) \u5f0f\u5b50\u5c31\u53ef\u4ee5\u6210\u7acb\uff0c\u7531\u5f52\u7eb3\u6cd5\u5f97\u7ed3\u8bba\u6210\u7acb\u3002</p> <p>\u4e0d\u8fc7\u5f88\u663e\u7136\uff0c\u5728\u67d0\u4e9b\u60c5\u51b5\u4e0b\u6211\u4eec\u6c42\u8bc1\u4e86\u4e00\u4e2a\u590d\u6742\u5ea6\u7684\u5047\u8bbe\u6210\u7acb\uff0c\u4f46\u5b83\u5e76\u4e0d\u4e00\u5b9a\u8db3\u591f\u7d27\uff0c\u8fd9\u662f\u731c\u89e3\u6cd5\u7684\u901a\u75c5\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec07/#\u9012\u5f52\u6811\u6cd5","title":"\u9012\u5f52\u6811\u6cd5","text":"<p>\u9012\u5f52\u6811\u6cd5(recursion-tree method)\u7684\u601d\u8def\u662f\uff0c\u6211\u4eec\u901a\u8fc7\u753b\u51fa\u9012\u5f52\u6811\u6765\u5206\u6790\u7b97\u6cd5\u7684\u65f6\u95f4\u590d\u6742\u5ea6\uff0c\u5b9e\u9645\u4e0a\u548c\u76f4\u63a5\u6570\u5b66\u63a8\u7406\u7684\u533a\u522b\u4e0d\u662f\u5f88\u5927\uff0c\u4e3b\u8981\u5c31\u662f\u901a\u8fc7\u89c2\u5bdf\u9012\u5f52\u8fc7\u7a0b\u4e2d\u6570\u636e\u589e\u957f\u7684\u6a21\u5f0f\u6765\u8fdb\u884c\u5206\u6790\u3002</p> some mathematical tools \\[ a^{\\log_b N} = \\exp^{\\frac{\\ln N}{\\ln b} \\ln a} = \\exp^{\\frac{\\ln a}{\\ln b} \\ln N} = N^{\\log_b a} \\] <p>\u5c31\u7c7b\u4f3c\u4e8e\u76f4\u63a5\u5c55\u5f00\u5f0f\u5b50\uff0c\u53ea\u4e0d\u8fc7\u901a\u8fc7\u6811\u72b6\u56fe\u7684\u5f62\u5f0f\u6216\u8bb8\u66f4\u52a0\u76f4\u89c2\u3002</p> <p>\u5bf9\u4e8e\u4e00\u4e2a\u9012\u63a8\u5f0f\uff0c\u6211\u4eec\u5c06\u5b83\u4e0d\u65ad\u5c55\u5f00\u4ee5\u540e\uff0c\u5176\u5f62\u5f0f\u5927\u6982\u4f1a\u662f\u8fd9\u6837\uff1a</p> \\[ T(N) = ... =  \\underbrace{\\sum_{leaf_i}^{leaves}T(N_{leaf_i})}_{conquer} +  \\underbrace{\\sum_{node_i}^{non-leaf-nodes}f(N_{node_i})}_{combine} \\] <p>\u5176\u4e2d\uff0c\u7531\u4e8e\u672b\u7aef\u5b50\u95ee\u9898\u7684\u89c4\u6a21\u4e00\u822c\u90fd\u8db3\u591f\u5c0f\uff0c\u53ef\u4ee5\u8ba4\u4e3a \\(T(N_{leaf_i})\\) \u90fd\u662f\u5e38\u6570\uff0c\u4e8e\u662f\u4e0a\u5f0f\u53c8\u53ef\u4ee5\u53d8\u5316\u4e3a\uff1a</p> \\[ T(N) = ... =  \\underbrace{c\\; N_{leaves}}_{conquer} +  \\underbrace{\\sum_{node_i}^{non-leaf-nodes}f(N_{node_i})}_{combine} \\] <p>\u5177\u4f53\u6765\u8bf4\u89e3\u91ca\u5176\u542b\u4e49\uff0ccombine \u90e8\u5206\u5c31\u662f\u5728\u6bcf\u4e00\u6b21\u201c\u5206\u6cbb\u201d\u7684\u5904\u7406\u65f6\u95f4\uff0c\u5982\u5408\u5e76\u5f53\u524d\u7684\u5b50\u95ee\u9898\u5206\u6cbb\u540e\u7684\u7ed3\u679c\uff0c\u4f53\u73b0\u5728\u9012\u63a8\u5f0f\u7684 \\(f(N)\\) \u90e8\u5206\uff1b\u800c conquer \u90e8\u5206\u6307\u7684\u662f\u5f53\u201c\u5206\u6cbb\u201d\u7684\u201c\u6cbb\u201d\u5728\u201c\u5206\u201d\u7684\u672b\u7aef\u7684\u4f53\u73b0\uff0c\u5373\u5bf9\u4e8e\u8db3\u591f\u5c0f\u7684\u89c4\u6a21\u7684\u95ee\u9898\uff0c\u4e0d\u518d\u9700\u8981\u7ee7\u7eed\u201c\u5206\u201d\u7684\u65f6\u5019\uff0c\u5bf9\u5176\u5904\u7406\u7684\u5f00\u9500\u3002</p> <p>\u5b9e\u9645\u4e0a\u5728\u4ee3\u7801\u5c42\u9762\u8fd9\u4e24\u90e8\u5206\u53ef\u80fd\u533a\u522b\u4e0d\u5927\uff08\u53ef\u80fd\u5c31\u662f\u4e00\u4e2a\u5206\u652f\u7684\u4e8b\u60c5\uff09\uff0c\u4e0d\u8fc7\u5728\u6570\u5b66\u610f\u4e49\u4e0a\uff0c\u5bf9\u4e8e\u4e00\u4e2a\u9012\u63a8\u5f0f\u5b50\u6c42\u89e3\u6211\u4eec\u4e00\u822c\u662f\u9700\u8981\u201c\u9996\u9879\u201d\u7684\uff0c\u6216\u8005\u8bf4\u662f\u201c\u6700\u5e95\u5c42\u201d\u7684\uff0c\u800c\u8fd9\u4e2a\u201c\u6700\u5e95\u5c42\u201d\u7684\u90e8\u5206\u5c31\u662f conquer \u90e8\u5206\u3002</p> <p>\u63a5\u4e0b\u6765\u7ed3\u5408 \ud83c\udf30 \u6765\u5206\u6790\u4e00\u4e0b\uff1a</p> <p>\ud83c\udf30</p> <p></p> <p>From cy's ppt.</p> <p><code>\\underbrace</code> \u4e0b\u9762\u90a3\u4e2a\u7b49\u5f0f\u7684\u8bc1\u660e\u5728\u4e0a\u9762\u7684 \"some mathematical tools\"\u3002</p> <p>\u53ef\u4ee5\u53d1\u73b0\uff0c\u6b64\u60c5\u51b5\u4e0b \\(a = 3,\\; b = 4,\\; f(N) = \\Theta(N^2)\\)\uff0c\u4e5f\u5c31\u662f\u8bf4\u6bcf\u6b21\u5206\u4e3a \\(3\\) \u4e2a\u5b50\u95ee\u9898\uff0c\u5b50\u95ee\u9898\u7684\u89c4\u6a21\u662f \\(\\frac{N}{4}\\)\uff0c\u800c\u5408\u5e76\u5f00\u9500\u4e3a \\(\\Theta(N^2)\\)\u3002</p> <p>\u6b64\u65f6\u7531\u4e8e\u5206\u6cbb\u7684\u7b56\u7565\u662f\u76f8\u5bf9\u5747\u5300\u7684\uff0c\u6240\u4ee5\u6211\u4eec\u53ef\u4ee5\u8ba4\u4e3a\u5f97\u5230\u7684\u662f\u4e00\u4e2a\u5b8c\u7f8e\u4e09\u53c9\u6811\u3002</p> <p>\u663e\u7136\uff0c\u6811\u9ad8\u4e3a \\(\\log_4 N\\)\uff0c\u6839\u8bb0\u4e3a \\(0\\)\uff0c\u6bcf\u4e2a\u5206\u6cbb\u8282\u70b9\u7684 combine \u5f00\u9500\u5df2\u7ecf\u6807\u6ce8\u5728\u56fe\u7684\u8282\u70b9\u4f4d\u7f6e\uff0c\u6a2a\u5411\u7bad\u5934\u6807\u8bb0\u7684\u662f\u5bf9\u8be5\u5c42\u6240\u6709\u8282\u70b9\u7684\u5f00\u9500\u7684\u6c42\u548c\u3002\u7279\u522b\u7684\uff0c\u5bf9\u4e8e\u6700\u5e95\u5c42\uff0c\u5373\u53f6\u5b50\u5c42\uff0c\u5b83\u8868\u793a\u7684\u662f conquer \u90e8\u5206\u7684\u5f00\u9500\uff08\u867d\u7136\u6211\u4e2a\u4eba\u89c9\u5f97\u6ca1\u5fc5\u8981\u533a\u5206\u8fd9\u4fe9\uff09\u3002</p> <p>\u4e8e\u662f\u6211\u4eec\u53ef\u4ee5\u6839\u636e\u4e0b\u5f0f\u7684\u5f62\u5f0f\uff0c\u5bf9\u5176\u8fdb\u884c\u6c42\u548c\uff0c\u5f97\u5230\u56fe\u7247\u4e2d\u4e0b\u65b9\u7684\u5f0f\u5b50\u3002</p> \\[ T(N) = ... =  \\underbrace{c\\; N_{leaves}}_{conquer} +  \\underbrace{\\sum_{node_i}^{non-leaf-nodes}f(N_{node_i})}_{combine} \\]"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec07/#\u4e3b\u65b9\u6cd5","title":"\u4e3b\u65b9\u6cd5","text":"<p>link</p> <p>OI Wiki: https://oi-wiki.org/basic/complexity/#\u4e3b\u5b9a\u7406-master-theorem</p> <p>Wikipedia: https://en.wikipedia.org/wiki/Master_theorem_(analysis_of_algorithms)</p> <p>\u4e3b\u65b9\u6cd5(master method)\u4e4b\u6240\u4ee5\u53eb\u201c\u4e3b\u201d\uff0c\u662f\u56e0\u4e3a\u5b83\u5206\u6790\u7684\u662f combine \u548c conquer \u90e8\u5206\u5b70\u4e3a\u4e3b\u5bfc\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec07/#\u5f62\u5f0f\u4e00","title":"\u5f62\u5f0f\u4e00","text":"<p>Form 1</p> <p>\u5bf9\u4e8e\u5f62\u5982 \\(T(N)=aT(N/b)+f(N)\\) \u7684\u9012\u63a8\u5f0f\uff1a</p> <ol> <li>\u82e5 \\(f(N)=O(N^{(\\log_b{a})-\\varepsilon}), \\text{ for }\\varepsilon&gt;0\\)\uff0c\u90a3\u4e48 \\(T(N)=\\Theta(N^{\\log_b{a}})\\)\uff1b</li> <li>\u82e5 \\(f(N)=\\Theta(N^{\\log_b{a}})\\)\uff0c\u90a3\u4e48 \\(T(N)=\\Theta(N^{\\log_b{a}}\\log{N})\\)\uff1b</li> <li>\u82e5 \\(f(N)=\\Omega(N^{(\\log_b{a})+\\varepsilon}), \\text{ for }\\varepsilon&gt;0\\) \u4e14 \\(af(\\frac{N}{b})&lt;cf(N), \\text{ for } c&lt;1 \\text{ and } \\forall N &gt; N_0\\)\uff0c\u90a3\u4e48 \\(T(N)=\\Theta(f(N))\\)\uff1b</li> </ol> <p>\u60c5\u51b5\u4e09\u7684\u540e\u9762\u90a3\u4e2a\u6761\u4ef6\u53c8\u53eb regularity condition\u3002</p> <p>\u56de\u987e\u6211\u4eec\u5728\u524d\u9762\u8bf4\u7684\u90a3\u53e5\u8bdd\uff0c\u300c\u4e3b\u65b9\u6cd5(master method)\u4e4b\u6240\u4ee5\u53eb\u201c\u4e3b\u201d\uff0c\u662f\u56e0\u4e3a\u5b83\u5206\u6790\u7684\u662f combine \u548c conquer \u90e8\u5206\u5b70\u4e3a\u4e3b\u5bfc\u300d\uff0c\u89c2\u5bdf\u4e09\u79cd\u60c5\u51b5\u7684\u533a\u5206\u6761\u4ef6\u90fd\u662f\u6bd4\u8f83 \\(f(N)\\)\uff08\u6bcf\u4e00\u6b21\u7684 combine \u5f00\u9500\uff09 \u548c \\(N^{\\log_b{a}}\\)\uff08\u5373\u6c42\u548c\u5f0f\u4e2d\u7684 conquer \u7684\u5f00\u9500\uff09\uff0c\u5f53 \\(f(N)\\) \u8db3\u591f\u5c0f\u65f6\uff0c\u4ee5 conquer \u5f00\u9500\u4e3a\u4e3b\uff08i.e. case 1\uff09\uff1b\u5f53\u8db3\u591f\u5927\u65f6\uff0c\u4ee5 combine \u4e3a\u4e3b\uff08i.e. case 3\uff09\uff1b\u800c\u5176\u4e2d\u8fd8\u6709\u4e00\u4e2a\u4e2d\u95f4\u72b6\u6001\uff08i.e. case 2\uff09\u3002</p> examples for form 1 <ul> <li>\u3010eg1\u3011\\(a = b = 2,\\; f(N) = N\\)\uff1b<ul> <li>\\(f(N) = N = \\Theta(N^{\\log_2{2}})\\)\uff0c\u9002\u7528\u4e8e\u60c5\u51b5 2\uff1b</li> <li>\u56e0\u6b64\u5f97\u5230\u7ed3\u679c \\(T(N) = \\Theta(N \\log N)\\)\uff1b</li> </ul> </li> <li>\u3010eg2\u3011\\(a = b = 2,\\; f(N) = N \\log N\\)\uff1b<ul> <li>\\(f(N) = N \\log N\\)\uff0c\u867d\u7136 \\(N \\log N = \\Omega(N^{\\log_2{2}})\\)\uff0c\u4f46\u662f \\(N \\log N \\neq \\Omega(N^{(\\log_2{2}) - \\varepsilon})\\)\uff0c\u6240\u4ee5\u4e0d\u9002\u7528\u4e8e\u60c5\u51b5 3\uff1b<ul> <li>\u5177\u4f53\u6765\u8bf4\uff0c\\(\\lim \\limits_{N\\to \\infty} \\frac{N \\log N}{N^{1+\\varepsilon}}=\\lim \\limits_{N\\to \\infty} \\frac{\\log N}{N^{\\varepsilon}} = 0 \\text{ for fixed } \\varepsilon &gt; 0\\)\uff1b</li> <li>\u8fd9\u4e2a\u4f8b\u5b50\u4f53\u73b0\u51fa\u4e86 \\(\\varepsilon\\) \u7684\u4e00\u5b9a\u4f5c\u7528\uff1b</li> </ul> </li> </ul> </li> </ul>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec07/#\u8bc1\u660e","title":"\u8bc1\u660e","text":"<p>proof for form 1</p> <p>\u5bf9\u4e8e\u5f62\u5982 \\(T(N)=aT(N/b)+f(N)\\) \u7684\u9012\u63a8\u5f0f\uff0c\u6211\u4eec\u9700\u8981\u4f9d\u6b21\u8bc1\u660e\uff0c\u6b64\u5904\u6211\u4eec\u4f7f\u7528\u9012\u5f52\u6811\u6cd5\u8fdb\u884c\u8bc1\u660e\u3002</p> \u60c5\u51b5\u4e00 <p>\ud83c\udfaf \u76ee\u6807\uff1a\u82e5 \\(f(N)=O(N^{(\\log_b{a})-\\varepsilon}), \\text{ for }\\varepsilon&gt;0\\)\uff0c\u90a3\u4e48 \\(T(N)=\\Theta(N^{\\log_b{a}})\\)\uff1b</p> <p>\ud83e\udea7 \u8bc1\u660e\uff1a\u6211\u4eec\u9996\u5148\u9700\u8981\u7ed8\u5236\u51fa\u5bf9\u5e94\u7684\u9012\u5f52\u6811\uff0c\u6216\u8005\u641e\u6e05\u695a\u5c55\u5f00\u540e\u7684\u60c5\u51b5\uff0c\u56e0\u4e3a\u61d2\u5f97\u753b\u56fe\u6240\u4ee5\u6211\u8fd9\u91cc\u91c7\u7528\u6587\u5b57\u53d9\u8ff0\u3002</p> <p>\u6811\u9ad8 \\(\\log_b{N}\\)\uff0c\u5171 \\(\\log_b{N} + 1\\) \u5c42\uff0c\u5219\u6709\uff1a</p> <ul> <li>\u7b2c \\(0\\) \u5c42\uff08\u6839\uff09\u4e00\u5171 \\(1\\) \u9879\uff0ccombine \u7684\u5f00\u9500\u4e3a \\(f(N)\\)\uff1b</li> <li>\u7b2c \\(1\\) \u5c42\u4e00\u5171 \\(a\\) \u9879\uff0ccombine \u7684\u5f00\u9500\u4e3a \\(a\\times f(\\frac{N}{b})\\)\uff1b</li> <li>\u7b2c \\(2\\) \u5c42\u4e00\u5171 \\(a^2\\) \u9879\uff0ccombine \u7684\u5f00\u9500\u4e3a \\(a^2 \\times f(\\frac{N}{b^2})\\)\uff1b</li> <li>......</li> <li>\u7b2c \\(j\\) \u5c42\u4e00\u5171 \\(a^j\\) \u9879\uff0ccombine \u7684\u5f00\u9500\u4e3a \\(a^j \\times f(\\frac{N}{b^j})\\)\uff1b</li> <li>......</li> <li>\u7b2c \\((\\log_b{N}) - 1\\) \u5c42\u4e00\u5171 \\(a^{(\\log_b{N}) - 1}\\) \u9879\uff0ccombine \u7684\u5f00\u9500\u4e3a \\(a^{(\\log_b{N}) - 1} \\times f(\\frac{N}{b^{(\\log_b{N}) - 1}})\\)\uff1b</li> <li>\u7b2c \\(\\log_b{N}\\) \u5c42\uff0c\u5373\u4e3a\u53f6\u5b50\u5c42\uff0c\u4e00\u5171 \\(a^{\\log_b{N}} = N^{\\log_b{a}}\\) \u9879\uff0cconquer \u7684\u5f00\u9500\u4e3a \\(N^{\\log_b{a}} \\times \\Theta(1) = \\Theta(N^{\\log_b{a}})\\)\uff1b</li> </ul> <p>\u5f97\u5230\u6c42\u548c\u5f0f\uff1a</p> \\[ T(N) = \\Theta(N^{\\log_b{a}}) + \\sum_{j = 0}^{(\\log_b{N})-1} a^j f(\\frac{N}{b^j}) \\] <p>\u800c\u6211\u4eec\u6709\u6761\u4ef6 \\(f(N)=O(N^{(\\log_b{a})-\\varepsilon}), \\text{ for }\\varepsilon&gt;0\\)\uff0c\u5c06\u5b83\u4ee3\u5165\u5230\u4e0a\u5f0f\u4e2d\u5f97\u5230\uff1a</p> \\[ \\begin{aligned} T(N)  &amp;= \\Theta(N^{\\log_b{a}}) + \\sum_{j = 0}^{(\\log_b{N})-1} a^j O\\left(\\left(\\frac{N}{b^j}\\right)^{(\\log_b{a})-\\varepsilon}\\right)\\\\ &amp;= \\Theta(N^{\\log_b{a}}) + O\\left(     N^{(\\log_b{a}) - \\varepsilon}     \\times     \\sum_{j = 0}^{(\\log_b{N})-1} \\left(\\frac{a}{b^{(\\log_b{a})-\\varepsilon}}\\right)^j \\right) \\\\ &amp;= \\Theta(N^{\\log_b{a}}) + O\\left(     N^{(\\log_b{a}) - \\varepsilon}     \\times     \\sum_{j = 0}^{(\\log_b{N})-1} (b^{\\varepsilon})^j \\right) \\\\ &amp;= \\Theta(N^{\\log_b{a}}) + O\\left(     N^{(\\log_b{a}) - \\varepsilon}     \\times     \\frac{1\\times(1-(b^\\varepsilon)^{\\log_b{N}})}{1-b^\\varepsilon} \\right) \\\\ &amp;= \\Theta(N^{\\log_b{a}}) + O\\left(     N^{(\\log_b{a}) - \\varepsilon}     \\times     \\frac{N^\\varepsilon-1}{b^\\varepsilon-1} \\right) \\\\ &amp;= \\Theta(N^{\\log_b{a}}) + O\\left(     N^{(\\log_b{a}) - \\varepsilon}     \\times     N^\\varepsilon \\right) \\\\ &amp;= \\Theta(N^{\\log_b{a}}) + O\\left(     N^{\\log_b{a}} \\right) \\\\ &amp;= \\Theta(N^{\\log_b{a}}) \\end{aligned} \\] <p>\u81f3\u6b64\uff0c\u60c5\u51b5\u4e00\u8bc1\u660e\u5b8c\u6bd5\u3002</p> \u60c5\u51b5\u4e8c <p>\ud83c\udfaf \u76ee\u6807\uff1a\u82e5 \\(f(N)=\\Theta(N^{\\log_b{a}})\\)\uff0c\u90a3\u4e48 \\(T(N)=\\Theta(N^{\\log_b{a}}\\log{N})\\)\uff1b</p> <p>\ud83e\udea7 \u8bc1\u660e\uff1a\u524d\u9762\u7684\u90e8\u5206\u548c\u60c5\u51b5\u4e00\u7684\u7c7b\u4f3c\uff0c\u6211\u4eec\u901a\u8fc7\u76f8\u540c\u7684\u6b65\u9aa4\u5f97\u5230\u76f8\u540c\u7684\u6c42\u548c\u5f0f\uff1a</p> \\[ T(N) = \\Theta(N^{\\log_b{a}}) + \\sum_{j = 0}^{(\\log_b{N})-1} a^j f(\\frac{N}{b^j}) \\] <p>\u800c\u6211\u4eec\u6709\u6761\u4ef6 \\(f(N)=\\Theta(N^{\\log_b{a}})\\)\uff0c\u5c06\u5b83\u4ee3\u5165\u5230\u4e0a\u5f0f\u4e2d\u5f97\u5230\uff1a</p> \\[\\begin{aligned} T(N) &amp;= \\Theta(N^{\\log_b{a}}) + \\sum_{j=0}^{(\\log_b{N})-1}a^j\\Theta\\left(\\left(\\frac{N}{b^j}\\right)^{\\log_b{a}}\\right) \\\\ &amp;= \\Theta(N^{\\log_b{a}}) + \\Theta\\left(     N^{\\log_b{a}} \\times     \\sum_{j=0}^{(\\log_b{N})-1}\\left(\\frac{a}{b^{\\log_b{a}}}\\right)^j \\right) \\\\ &amp;= \\Theta(N^{\\log_b{a}}) + \\Theta\\left(     N^{\\log_b{a}} \\times     \\log_b{N} \\right) \\\\ &amp;= \\Theta(N^{\\log_b{a}}\\log{N}) \\end{aligned}\\] <p>\u81f3\u6b64\uff0c\u60c5\u51b5\u4e8c\u8bc1\u660e\u5b8c\u6bd5\u3002</p> \u60c5\u51b5\u4e09 <p>\ud83c\udfaf \u76ee\u6807\uff1a\u82e5 \\(f(N)=\\Omega(N^{(\\log_b{a})+\\varepsilon}), \\text{ for }\\varepsilon&gt;0\\) \u4e14 \\(af(\\frac{N}{b})&lt;cf(N), \\text{ for } c&lt;1 \\text{ and } \\forall N &gt; N_0\\)\uff0c\u90a3\u4e48 \\(T(N)=\\Theta(f(N))\\)\uff1b</p> <p>\ud83e\udea7 \u8bc1\u660e\uff1a\u60c5\u51b5\u4e09\u7684\u8bc1\u660e\uff0c\u4ece\u6761\u4ef6\u7684\u53d8\u5316\u5c31\u53ef\u4ee5\u770b\u51fa\u6765\u548c\u524d\u9762\u7a0d\u8bb8\u6709\u4e9b\u4e0d\u540c\u4e86\u3002\u4e0d\u8fc7\u6c42\u548c\u5f0f\u7684\u5f97\u5230\u8fd8\u662f\u4e00\u6837\uff0c\u901a\u8fc7\u548c\u4e4b\u524d\u4e00\u6837\u7684\u65b9\u6cd5\uff0c\u6211\u4eec\u9996\u5148\u5f97\u5230\u6c42\u548c\u5f0f\uff1a</p> \\[ T(N) = \\Theta(N^{\\log_b{a}}) + \\sum_{j = 0}^{(\\log_b{N})-1} a^j f(\\frac{N}{b^j}) \\] <p>\u63a5\u4e0b\u6765\u7684\u6b65\u9aa4\u548c\u4e4b\u524d\u4e0d\u540c\u3002\u5728\u7ee7\u7eed\u4e4b\u524d\uff0c\u6211\u4eec\u9996\u5148\u89c2\u5bdf\u4e0d\u7b49\u5f0f \\(af(\\frac{N}{b})&lt;cf(N)\\)\uff0c\u5728\u6211\u4eec\u7684\u6c42\u548c\u5f0f\u4e2d\uff0c\u6211\u4eec\u89c2\u5bdf\u5230\u6211\u4eec\u6709\u5927\u91cf\u7684\u5f62\u5982 \\(a^jf(\\frac{N}{b^j})\\) \u7684\u9879\uff0c\u800c\u8fd9\u4e9b\u9879\u90fd\u53ef\u4ee5\u901a\u8fc7\u8fed\u4ee3\u4e0a\u9762\u90a3\u4e2a\u4e0d\u7b49\u5f0f\u6765\u5b9e\u73b0\uff0c\u5373\uff1a</p> \\[ a^jf(\\frac{N}{b^j}) &lt; c\\times a^{j-1}f(\\frac{N}{b^{j-1}}) &lt; ... &lt; c^j f(N) \\] <p>\u5c06\u8fd9\u4e2a\u4e0d\u7b49\u5f0f\u5e94\u7528\u4e8e\u6c42\u548c\u5f0f\u4e2d\uff0c\u6211\u4eec\u80fd\u591f\u5f97\u5230\uff1a</p> \\[ \\begin{aligned}     T(N)      &amp;&lt; \\Theta(N^{\\log_b{a}}) + \\sum_{j=0}^{(\\log_b{N})-1}c^j f(N) \\\\     &amp;= \\Theta(N^{\\log_b{a}}) + f(N) \\sum_{j=0}^{(\\log_b{N})-1}c^j \\\\     &amp;= \\Theta(N^{\\log_b{a}}) + f(N) \\times \\frac{c^{1-\\log_b{N}}}{1-c} \\\\     &amp;= \\Theta(N^{\\log_b{a}}) + f(N) \\times \\frac{1-N^{\\log_b{c}}}{1-c} \\end{aligned}         \\] <p>\u800c\u7531\u4e8e \\(c&lt;1\\)\uff0c\u6240\u4ee5 \\(\\log_b{c} &lt; 0\\)\uff1b\u800c \\(N &gt; 0\\)\uff0c\u800c\u4e14\u4e00\u822c\u975e\u5e38\u5927\uff0c\u6240\u4ee5 \\(N^{\\log_b{c}} \\in (0,1)\\)\u3002\u56e0\u6b64\uff0c\u5bf9\u4e8e\u786e\u5b9a\u7684\u5e38\u6570 \\(c\\)\uff0c\u6211\u4eec\u6709 \\(\\frac{1-N^{\\log_b{c}}}{1-c} \\in \\left(0, \\frac{1}{1-c}\\right)\\)\uff1b</p> <p>\u56e0\u6b64\uff0c\u4e0a\u5f0f\u4fbf\u80fd\u6539\u53d8\u4e3a\uff1a</p> \\[ \\begin{aligned}     T(N)      &amp;&lt; \\Theta(N^{\\log_b{a}}) + f(N) \\times \\frac{1-N^{\\log_b{c}}}{1-c} \\\\     &amp;&lt; \\Theta(N^{\\log_b{a}}) + f(N) \\times \\frac{1}{1-c} \\end{aligned} \\] <p>\u5e76\u4e14\uff0c\u7531\u4e8e \\(f(N)=\\Omega(N^{(\\log_b{a})+\\varepsilon}), \\text{ for }\\varepsilon&gt;0\\)\uff0c\u6240\u4ee5\u6839\u636e\u7b26\u53f7\u5b9a\u4e49\u53ef\u4ee5\u5f97\u5230 \\(T(N) = O(f(N))\\)\u3002</p> <p>\u800c\u6211\u4eec\u77e5\u9053\uff0c\u8981\u8bc1\u660e \\(T(N) = \\Theta(f(N))\\) \u8fd8\u9700\u8981\u8bc1\u660e \\(T(N) = \\Omega(f(N))\\)\uff1a</p> \\[ \\begin{aligned} T(N) &amp;= \\Theta(N^{\\log_b{a}}) + \\sum_{j = 0}^{(\\log_b{N})-1} a^j f(\\frac{N}{b^j}) &amp;\\geq \\sum_{j = 0}^{(\\log_b{N})-1} a^j f(\\frac{N}{b^j}) &amp;\\geq f(N) \\end{aligned} \\] <p>\u7531\u6b64\u5f97\u5230 \\(T(N) = \\Omega(f(N))\\)\uff0c\u6700\u7ec8\u8bc1\u5f97 \\(T(N) = \\Theta(f(N))\\)\uff0c\u81f3\u6b64\uff0c\u60c5\u51b5\u4e09\u8bc1\u660e\u5b8c\u6bd5\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec07/#\u5f62\u5f0f\u4e8c","title":"\u5f62\u5f0f\u4e8c","text":"<p>Form 2</p> <p>\u5bf9\u4e8e\u5f62\u5982 \\(T(N) = aT(\\frac{N}{b}) + f(N)\\) \u7684\u9012\u63a8\u5f0f\uff1a</p> <ol> <li>\u82e5 \\(af(\\frac{N}{b}) = \\kappa f(N) \\text{ for fixed } \\kappa &lt; 1\\)\uff0c\u90a3\u4e48 \\(T(N) = \\Theta(f(N))\\)\uff1b</li> <li>\u82e5 \\(af(\\frac{N}{b}) = \\Kappa f(N) \\text{ for fixed } \\Kappa &gt; 1\\)\uff0c\u90a3\u4e48 \\(T(N) = \\Theta(N^{\\log_b{a}}) = \\Theta(a^{\\log_b{N}})\\)\uff08\u4e2a\u4eba\u611f\u89c9\u540e\u9762\u90a3\u4e2a\u5f0f\u5b50\u66f4\u65b9\u4fbf\u76f4\u89c2\u8bb0\u5fc6\uff09\uff1b</li> <li>\u82e5 \\(af(\\frac{N}{b}) = f(N)\\)\uff0c\u90a3\u4e48 \\(T(N) = \\Theta(f(N) \\log_b N)\\)\uff1b</li> </ol>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec07/#\u8bc1\u660e_1","title":"\u8bc1\u660e","text":"<p>proof for form 2</p> <p>\u5bf9\u4e8e\u5f62\u5982 \\(T(N)=aT(N/b)+f(N)\\) \u7684\u9012\u63a8\u5f0f\uff0c\u57fa\u4e8e\u7ebf\u6027\u5173\u7cfb\u7684\u5f62\u5f0f\u4e8c\u7684\u8bc1\u660e\u5b9e\u9645\u4e0a\u548c\u5f62\u5f0f\u4e00\u7684\u7b2c\u4e09\u79cd\u60c5\u51b5\u7684\u8bc1\u660e\u975e\u5e38\u76f8\u50cf\u3002</p> <p>\u5047\u8bbe\u6211\u4eec\u6709 \\(af(\\frac{N}{b}) = c f(N)\\)\uff0c\u53ea\u9700\u8981\u8ba8\u8bba \\(c\\) \u7684\u53d6\u503c\u8303\u56f4\u5bf9\u7ed3\u679c\u7684\u5f71\u54cd\uff0c\u5c31\u53ef\u4ee5\u4e00\u6b21\u6027\u5f97\u5230\u7ed3\u679c\u3002</p> <p>\u7c7b\u4f3c\u4e8e\u5f62\u5f0f\u4e00\u7684\u7b2c\u4e09\u79cd\u60c5\u51b5\u7684\u8bc1\u660e\uff0c\u6211\u4eec\u8fed\u4ee3\u8be5\u5173\u7cfb\u5f0f\uff0c\u5f97\u5230\u5173\u7cfb\uff1a</p> \\[ a^j f(\\frac{N}{b^j}) = c^j f(N) \\] <p>\u4e8e\u662f\uff0c\u6211\u4eec\u6709\uff1a</p> \\[ \\begin{aligned}     T(N)     &amp;= \\Theta(N^{\\log_b{a}}) + \\sum_{j = 0}^{(\\log_b{N})-1} a^j f(\\frac{N}{b^j}) \\\\     &amp;= \\Theta(N^{\\log_b{a}}) + \\sum_{j = 0}^{(\\log_b{N})-1} c^j f(N) \\\\     &amp;= \\Theta(N^{\\log_b{a}}) + f(N) \\sum_{j = 0}^{(\\log_b{N})-1} c^j \\\\     &amp;= \\Theta(N^{\\log_b{a}}) + f(N) \\times \\frac{1-N^{\\log_b{c}}}{1-c} \\\\ \\end{aligned} \\] <p>\u5929\u5450\uff0c\u8fd9\u4e0d\u5c31\u662f\u5f62\u5f0f\u4e00\u91cc\u7b2c\u4e09\u79cd\u60c5\u51b5\u7684\u5f0f\u5b50\u5417\uff1f\u7136\u800c\u5f53\u6211\u4eec\u6ee1\u5fc3\u6b22\u559c\u5730\u6253\u7b97\u7167\u7740\u5b83\u8bc1\u660e\u5f62\u5f0f\u4e8c\u7684\u60c5\u51b5\u4e00\u65f6\u4f1a\u53d1\u73b0\uff0c\u6761\u4ef6\u597d\u50cf\u4e0d\u591f\u3002\u6211\u4eec\u73b0\u5728\u5e76\u6ca1\u6709\u663e\u5f0f\u7684 \\(f(N) = \\Omega(N^{\\log_b {a}} + \\epsilon)\\) \u7684\u6761\u4ef6\uff0c\u800c\u8fd9\u4e2a\u6761\u4ef6\u6700\u7ec8\u51b3\u5b9a conquer \u90e8\u5206\u548c combine \u90e8\u5206\u8c01\u5360\u4e3b\u5bfc\u5730\u4f4d\u3002\u4f46\u662f\uff0c\u6211\u4eec\u5b9e\u9645\u4e0a\u53ea\u9700\u8981\u5f97\u5230 \\(f(N)\\) = \\(\\Omega(N^{\\log_b {a}})\\) \u5c31\u591f\u4e86\u3002\u5176\u5b9e \\(af(\\frac{N}{b}) \\sim c f(N)\\) \u8fd9\u4ef6\u4e8b\u672c\u8eab\u5c31\u6697\u542b\u4e86\u5b83\u4e0e \\(N^{\\log_b {a}}\\) \u7684\u5173\u7cfb\uff1a</p> <p>\u4e3a\u4e86\u91cd\u590d\u5229\u7528\u8fc7\u7a0b\uff0c\u6211\u76f4\u63a5\u7528 \\(\\sim\\) \u6765\u4ee3\u66ff \\(&lt;,&gt;,=\\) \u4e86\uff0c\u8fc7\u7a0b\u4e2d\u4fdd\u6301\u4f20\u9012\u6027\u3002</p> \\[ c f(N) \\sim a f(\\frac{N}{b}) \\sim ... \\sim a^L f(\\frac{N}{b^L}) \\] <p>\u53ef\u4ee5\u53d1\u73b0\uff0c\u8fd9\u4e00\u6b65\u8fd8\u662f\u548c\u5f62\u5f0f\u4e00\u7684\u7b2c\u4e09\u79cd\u60c5\u51b5\u7684\u8bc1\u660e\u8fc7\u7a0b\u9ad8\u5ea6\u76f8\u4f3c\u3002\u53ea\u4e0d\u8fc7\u73b0\u5728\u6211\u4eec\u8981\u66f4\u8fdb\u4e00\u6b65\u5730\u770b\u8fd9\u4e2a\u5f0f\u5b50\u3002</p> <p>\u5f53 \\(c &lt; 1\\) \u65f6\uff0c\u5b9e\u9645\u4e0a\u6709 \\(f(N) &gt; af(\\frac{N}{b})\\)\uff1b\u5f53 \\(c = 1\\) \u65f6\uff0c\u5b9e\u9645\u4e0a\u6709 \\(f(N) = af(\\frac{N}{b})\\)\uff1b \\(c &gt; 1\\) \u65f6\uff0c\u5b9e\u9645\u4e0a\u6709 \\(f(N) &lt; af(\\frac{N}{b})\\)\uff1b</p> <p>\u6211\u4eec\u5047\u8bbe \\(\\frac{N}{b^L}\\) \u8db3\u591f\u5c0f\uff08\u5373\u9012\u5f52\u5230\u6700\u672b\u7aef\uff0c\u53ea\u9700\u8981\u8fdb\u884c conquer \u7684\u65f6\u5019\uff09\uff0c\u5373 \\(\\frac{N}{b^L} = \\Theta(1)\\)\uff0c\u90a3\u4e48\u5c31\u6709 \\(L = \\Theta(\\log_b{N})\\)\u3002\u4e8e\u662f\uff0c\u6211\u4eec\u6709\uff1a</p> \\[ f(N) \\sim \\Theta(a^{\\log_b{N}}) = \\Theta(N^{\\log_b{a}}) \\] <p>\u7686\u5927\u6b22\u559c\uff01\u4e09\u4e2a\u613f\u671b\uff0c\u4e00\u6b21\u6ee1\u8db3\uff01</p> <p>\u5269\u4e0b\u7684\u8bc1\u660e\u8fc7\u7a0b\u6211\u5c31\u4e0d\u518d\u8d58\u8ff0\u4e86\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec07/#\u5f62\u5f0f\u4e09","title":"\u5f62\u5f0f\u4e09","text":"<p>Form 3</p> <p>\u7b2c\u4e09\u79cd\u5f62\u5f0f\u662f\u5bf9\u4e8e \\((N)\\) \u7684\u7279\u522b\u5f62\u5f0f\uff0c\u5f53\u9012\u63a8\u5173\u7cfb\u6ee1\u8db3\uff1a</p> \\[ \\begin{aligned} &amp; T(N) = a T(\\frac{n}{b}) + \\Theta(N^k \\log^p{N}) &amp; \\text{Where } a \\geq 1,\\; b &gt; 1,\\; p \\geq 0 \\end{aligned} \\] <p>\u5176\u590d\u6742\u5ea6\u6709\u7ed3\u8bba\uff1a</p> \\[ T(N) = \\left\\{     \\begin{aligned}         &amp; O(N^{\\log_b{a}}) &amp; \\text{if } a &gt; b^{k} \\\\         &amp; O(N^k \\log^{p+1}{N}) &amp; \\text{if } a = b^{k} \\\\         &amp; O(N^k \\log^{p}{N}) &amp; \\text{if } a &lt; b^{k}     \\end{aligned} \\right. \\] <p>\u5b9e\u9645\u4e0a\u8fd9\u4e2a\u5f0f\u5b50\u4e5f\u975e\u5e38\u597d\u8ba4\uff0c\u5c5e\u4e8e\u5f62\u5f0f\u4e8c\u7684\u4e00\u79cd\u7279\u6b8a\u5f62\u5f0f\u3002\u53ef\u4ee5\u5bf9\u7167\u7740\u770b\uff0c\u975e\u5e38\u5bb9\u6613\u770b\u51fa\u5173\u7cfb\u3002</p> <p>\u53ea\u4e0d\u8fc7\u5bf9\u4e8e\u7279\u6b8a\u60c5\u51b5\uff0c\u8fd9\u4e2a\u5f62\u5f0f\u7684\u7ea6\u675f\u66f4\u52a0\u7cbe\u786e\uff0c\u8bc1\u660e\u8fc7\u7a0b\u6709\u7f18\u518d\u8865\u5427x</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec08/","title":"Lecture 8 | Dynamic Programming","text":"<p> \u7ea6 4 \u4e2a\u5b57 </p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec09/","title":"Lecture 9 | Greedy Algorithms","text":"<p> \u7ea6 895 \u4e2a\u5b57  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 3 \u5206\u949f</p> <p>\u679c\u7136\u8d8a\u6765\u8d8a\u5bbd\u6cdb\u4e86</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec09/#\u6982\u5ff5","title":"\u6982\u5ff5","text":"<p>\u8d2a\u5fc3\u7b97\u6cd5(Greedy Algorithms)\u662f\u4e00\u79cd\u5728\u6c42\u89e3\u4f18\u5316\u95ee\u9898\u65f6\u91c7\u7528\u7684\u7b56\u7565\uff0c\u5b83\u5728\u6bcf\u4e2a\u51b3\u7b56\u9636\u6bb5\u90fd\u9009\u62e9\u5f53\u524d\u770b\u8d77\u6765\u6700\u4f18\u7684\u89e3\u51b3\u65b9\u6848\uff0c\u4ece\u800c\u5e0c\u671b\u80fd\u591f\u8fbe\u5230\u5168\u5c40\u6700\u4f18\u89e3\u3002\u8d2a\u5fc3\u7b97\u6cd5\u7684\u6838\u5fc3\u601d\u60f3\u662f\u5c40\u90e8\u6700\u4f18\u9009\u62e9\uff0c\u901a\u8fc7\u4e00\u7cfb\u5217\u5c40\u90e8\u6700\u4f18\u7684\u9009\u62e9\uff0c\u6765\u8fbe\u5230\u5168\u5c40\u6700\u4f18\u7684\u76ee\u6807\u3002\u8d2a\u5fc3\u7b97\u6cd5\u6613\u4e8e\u5b9e\u73b0\uff0c\u4f46\u5e76\u4e0d\u603b\u662f\u80fd\u591f\u5f97\u5230\u5168\u5c40\u6700\u4f18\u89e3\uff0c\u56e0\u6b64\u5728\u4f7f\u7528\u8d2a\u5fc3\u7b97\u6cd5\u65f6\u9700\u8981\u5206\u6790\u95ee\u9898\u7684\u7279\u6027\u4ee5\u786e\u4fdd\u5176\u9002\u7528\u6027\u3002</p> <p>\u2014\u2014ChatGPT</p> <p>\u8d2a\u5fc3\u601d\u60f3\u548c\u5b83\u7684\u540d\u5b57\u4e00\u6837\u7b80\u5355\u66b4\u529b\uff0c\u5c31\u662f\u5728\u6bcf\u4e00\u4e2a\u6b65\u9aa4\u4e2d\u90fd\u91c7\u53d6\u5c40\u90e8\u6700\u4f18\u89e3\uff0c\u6700\u7ec8\u6c42\u5f97\u6700\u4f18\u89e3\u3002\u4f46\u662f\u663e\u7136\u8fd9\u4e2a\u65b9\u6cd5\u5e76\u4e0d\u603b\u80fd\u201c\u6700\u7ec8\u6c42\u5f97\u6700\u4f18\u89e3\u201d\u3002\u56e0\u6b64\u867d\u7136\u8fd9\u4e2a\u65b9\u6cd5\u770b\u8d77\u6765\u76f4\u63a5\u66b4\u529b\uff0c\u4f46\u662f\u5982\u4f55\u627e\u5230\u7528\u300c\u8d2a\u5fc3\u300d\u89e3\u51b3\u95ee\u9898\u7684\u8def\u5f84\uff0c\u5f80\u5f80\u662f\u9700\u8981\u52a8\u52a8\u8111\u5b50\u7684\u3002</p> <p>\u548c dp \u4e00\u6837\uff0c\u8d2a\u5fc3\u662f\u4e00\u4e2a\u6bd4\u8f83\u601d\u60f3\u6027\u8d28\u7684\u4e1c\u897f\uff0c\u6240\u4ee5\u6211\u4eec\u9700\u8981\u501f\u52a9\u8bb8\u591a\u6848\u4f8b\u6765\u8fdb\u884c\u5206\u6790\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec09/#\u6848\u4f8b-activity-selection-problem","title":"[\u6848\u4f8b] Activity Selection Problem","text":"<p>\u5728\u8bfe\u4ef6\u4e0a\uff0c\u6d3b\u52a8\u9009\u62e9\u95ee\u9898(Activity Selection Problem)\u7684\u9648\u8ff0\u5982\u4e0b\uff1a</p> <p>Activity Selection Problem</p> <p>Given a set of activities \\(S = { a_1, a_2, ..., a_n }\\) that wish to use a resource (e.g. a classroom).  Each \\(a_i\\) takes place during a time interval \\([s_i, f_i)\\).</p> <p>Activities \\(a_i\\) and \\(a_j\\) are compatible if \\(s_i \\geq f_j\\) or \\(s_j \\geq f_i\\) (i.e. their time intervals do not overlap).</p> <p>Goal: Select a maximum-size subset of mutually compatible activities.</p> <ul> <li>Assume \\(f_1\\geq f_2 \\geq ... \\geq f_n\\).</li> </ul> <p>\u62bd\u8c61\u6765\u8bf4\u5c31\u662f\u4e00\u4e2a\u4e00\u7ef4\u7684\u5bc6\u94fa\u95ee\u9898\u3002\u7ed9\u5b9a\u65f6\u95f4\u7ebf\u4e0a\u7684\u82e5\u5e72\u533a\u95f4 \\([s_i, f_i)\\)\uff0c\u6c42\u51fa\u6700\u591a\u80fd\u4e0d\u91cd\u53e0\u5730\u5728\u8fd9\u4e2a\u65f6\u95f4\u7ebf\u4e0a\u653e\u7f6e\u591a\u5c11\u4e2a\u533a\u95f4\u3002\u9898\u76ee\u989d\u5916\u4fdd\u8bc1\u4e86\u8f93\u5165\u6570\u636e\u662f\u6839\u636e \\(f_i\\) \u6709\u5e8f\u7684\uff0c\u4e0d\u8fc7\u8fd9\u4e0d\u662f\u5f88\u91cd\u8981\u3002</p> <p>bad try 1</p> <p>\u4e00\u4e2a\u975e\u5e38 naive \u7684\u60f3\u6cd5\u5c31\u662f\uff0c\u54ea\u95e8\u8bfe\u5148\u5f00\u59cb\u6211\u5148\u9009\u54ea\u95e8\u8bfe\uff0c\u8fd9\u4e2a\u60f3\u6cd5\u975e\u5e38\u7684\u8282\u7701\u8111\u7ec6\u80de\uff0c\u4f46\u662f\u663e\u7136\u4e0d\u5bf9\u3002\u6211\u968f\u968f\u4fbf\u4fbf\u6765\u4e2a\u6700\u65e9\u5f00\u59cb\u6700\u665a\u7ed3\u675f\u7684\u8bfe\uff0c\u5c31\u80fd\u76f4\u63a5 hack \u6389\u8fd9\u4e2a\u65b9\u6cd5\u3002</p> <p>bad try 2</p> <p>\u518d\u6765\u4e00\u4e2a\u5929\u771f\u7684\u60f3\u6cd5\uff0c\u6211\u6bcf\u6b21\u90fd\u9009\u533a\u95f4\u957f\u5ea6\u6700\u5c11\u7684\uff0c\u867d\u7136\u770b\u8d77\u6765\u80fd\u8ba9\u5b83\u201c\u76f8\u5bf9\u6bd4\u8f83\u591a\u201d\uff0c\u4f46\u662f\u663e\u7136\u4e5f\u65e0\u6cd5\u4fdd\u8bc1\u7ed3\u679c\u7684\u6700\u4f18\u6027\uff0c\u4e5f\u975e\u5e38\u597d hack\u3002</p> <p>search</p> <p>\u800c\u53e6\u5916\u4e00\u4e2a\u66b4\u529b\u7684\u60f3\u6cd5\u5c31\u662f\uff0c\u6211\u53bb\u679a\u4e3e\u6bcf\u4e00\u79cd\u53ef\u80fd\uff0c\u4e5f\u5c31\u662f\u6211\u4eec\u4fd7\u79f0\u7684\u66b4\u641c\uff0c\u8fd8\u53ef\u4ee5\u7528\u4e0a\u526a\u679d\u7b49\u64cd\u4f5c\uff0c\u867d\u7136\u53ef\u4ee5\uff0c\u4f46\u662f\u592a\u4e0d\u4f18\u96c5\u4e86\uff0c\u800c\u4e14\u65f6\u95f4\u590d\u6742\u5ea6\u672a\u5fc5\u662f\u6211\u4eec\u80fd\u63a5\u53d7\u7684\u3002</p> <p>dp</p> <p>\u65e2\u7136\u66b4\u641c\u4e0d\u884c\uff0c\u90a3\u8bd5\u8bd5 dp \u5462\uff1f\u5728\u8fd9\u4e2a\u95ee\u9898\u4e2d\uff0c\u6211\u4eec\u53ef\u4ee5\u5199\u51fa\u5982\u4e0b\u8f6c\u79fb\u65b9\u7a0b\uff1a</p> \\[ dp_i = \\left\\{     \\begin{aligned}         &amp;1 &amp; i = 1 \\\\         &amp;\\max\\{             dp_{i-1},             dp_{f(i)} + 1         \\} &amp; i &gt; 1     \\end{aligned} \\right. \\] <p>\u5176\u4e2d\uff0c\\(dp_i\\) \u8868\u793a\u5230\u7b2c \\(i\\) \u4e2a\u533a\u95f4\u622a\u6b62\u7684\u65f6\u95f4\u4e3a\u6b62\uff0c\u6700\u591a\u6709\u591a\u5c11\u4e2a\u9879\u76ee\u53ef\u4ee5\u88ab\u5b89\u6392\uff1b\\(f(i)\\) \u662f\u6700\u5927\u7684\u6ee1\u8db3 \\(f_j \\leq s_i\\) \u7684\u533a\u95f4\u7684\u7f16\u53f7 \\(j\\)\uff0c\u4e5f\u5c31\u662f\u80fd\u591f\u4e0d\u91cd\u53e0\u653e\u4e0b\u7684\uff0c\u6700\u665a\u7684\u90a3\u4e2a\u6d3b\u52a8\u3002</p> <p>\u6211\u4eec\u53d1\u73b0\uff0c\u8fd9\u4e48\u505a\u662f\u53ef\u4ee5\u7684\u3002\u53ea\u4e0d\u8fc7\u8fd9\u6837\u505a\u7684\u8bdd\uff0c\u5176\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a \\(O(N^2)\\)\u3002</p> <p>greedy</p> <p>\u663e\u7136\uff0c\u8fd9\u4e2a\u6848\u4f8b\u653e\u5728\u8fd9\u4e2a\u5730\u65b9\u80af\u5b9a\u662f\u6709\u8d2a\u5fc3\u89e3\u7684\u3002\u800c\u4e14\u9898\u76ee\u7684 \u201cAssume\u201d \u63d0\u793a\u6027\u5df2\u7ecf\u5f88\u5f3a\u4e86\u3002\u6211\u4eec\u53ea\u9700\u8981\u6309\u7167\u7ed3\u675f\u65f6\u95f4\uff0c\u904d\u5386\u8fd9\u4e9b\u533a\u95f4\uff0c\u80fd\u585e\u4e0b\u5c31\u585e\uff0c\u5373\u53ef \\(O(N)\\) \u8d2a\u5fc3\u6c42\u89e3\u3002</p> <p>TODO:</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec10/","title":"Lecture 10 | NP Completeness","text":"<p> \u7ea6 3027 \u4e2a\u5b57  10 \u884c\u4ee3\u7801  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 10 \u5206\u949f</p> <p>\u5bfc\u8bfb</p> <p>\u7531\u4e8e\u672c\u8282\u6d89\u53ca\u8f83\u591a\u6982\u5ff5\uff0c\u5e76\u4e14\u77e5\u8bc6\u6811\u957f\u7684\u5f88\u84ec\u677e\uff0c\u6240\u4ee5\u6211\u51b3\u5b9a\u5c1d\u8bd5\u975e\u7ebf\u6027\u7ec4\u7ec7\u5185\u5bb9\uff0c\u56e0\u6b64\u672c\u6587\u7684\u9605\u8bfb\u987a\u5e8f\u53ef\u80fd\u4e5f\u5e76\u4e0d\u4f1a\u662f\u7ebf\u6027\u7684\u3002</p> <p>\u6240\u6709\u63d0\u5230\u7684\u3001\u5e76\u4e14\u672c\u6587\u4f1a\u4ecb\u7ecd\u7684\u76f8\u5173\u5185\u5bb9\uff0c\u90fd\u4f1a\u4ee5\u94fe\u63a5\u548c\u653e\u5927\u955c\ud83d\udd0d\u7684\u5f62\u5f0f\u51fa\u73b0\u3002\u63a8\u8350\u4f7f\u7528\u9f20\u6807\u4e2d\u952e\u7b49\u65b9\u5f0f\u6253\u5f00\u65b0\u6807\u7b7e\u9875\u67e5\u770b\uff0c\u65b9\u4fbf\u56de\u6eaf\u3002</p> <p>\u63a8\u8350\u7684\u9605\u8bfb\u987a\u5e8f\u662f\uff0c\u987a\u7740\u8bfb\u4e0b\u53bb\uff0c\u6bcf\u6b21\u51fa\u73b0 \ud83d\udd0d \u90fd\u8fdb\u884c\u6df1\u5ea6\u4f18\u5148\u641c\u7d22\u5f0f\u7684\u5b66\u4e60\uff0c\u76f4\u81f3\u770b\u5b8c\u5168\u6587\u3002</p> <p>\u5176\u4e2d\uff0c\u5728 \u76f8\u5173\u6982\u5ff5 \u4e4b\u540e\u7684\u90e8\u5206\uff0c\u6211\u4f1a\u4fdd\u8bc1\u5728\u524d\u9762\u90fd\u6709\u63d0\u53ca\uff0c\u800c\u5176\u4e4b\u524d\u7684\u5185\u5bb9\uff0c\u63a8\u8350\u90fd\u5728\u987a\u5e8f\u9605\u8bfb\u4e2d\u6d89\u53ca\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec10/#\u6982\u8ff0","title":"\u6982\u8ff0","text":"<p>Links</p> <p>OI Wiki: https://oi-wiki.org/misc/cc-basic/</p> <p>Wikipedia: https://en.wikipedia.org/wiki/P_versus_NP_problem</p> <p>Wikipedia: https://en.wikipedia.org/wiki/NP-completeness</p> <p>Wikipedia: https://en.wikipedia.org/wiki/NP-hardness</p> <p>\u6839\u636e\u95ee\u9898\u7684\u96be\u5ea6\uff0c\u7531\u4e0d\u540c\u7684\u5b9a\u4e49\u5212\u5206\uff0c\u95ee\u9898\u53ef\u4ee5\u5206\u4e3a\uff1a</p> <p>P \u95ee\u9898(polynomial time)\u3001NP \u95ee\u9898(nondeterministic polynomial time)\u3001NPC \u95ee\u9898(NP complete)\u3001NPH \u95ee\u9898(NP hard)\u3002\u9664\u6b64\u4e4b\u5916 \uff0c\u6211\u4eec\u8fd8\u9700\u8981\u989d\u5916\u4e86\u89e3\u4e0d\u53ef\u8ba1\u7b97\u95ee\u9898(undecidable)\u3002</p> <p>\u7531\u4e8e\u4e0d\u53ef\u8ba1\u7b97\u95ee\u9898\u6bd4\u8f83\u7279\u6b8a\uff0c\u6240\u4ee5\u6211\u5148\u653e\u5728\u524d\u9762\u4ecb\u7ecd\u3002</p> Undecidable Problem <p>Links</p> <p>Wikipedia: https://en.wikipedia.org/wiki/Undecidable_problem</p> <p>\u4e0d\u53ef\u5224\u5b9a\u95ee\u9898(undecidable problem)\u662f\u4e00\u7c7b\u7279\u6b8a\u7684\u51b3\u5b9a\u6027\u95ee\u9898\uff0c\u5b83\u7684\u7279\u70b9\u662f\u6211\u4eec\u65e0\u6cd5\u8bbe\u8ba1\u4e00\u4e2a\u7b97\u6cd5\u6765\u6c42\u89e3\u5b83\u7684\u7ed3\u679c\u3002</p> <p>\u5176\u4e2d\u4e00\u4e2a\u6bd4\u8f83\u5178\u578b\u7684\u4f8b\u5b50\u5c31\u662f\u505c\u673a\u95ee\u9898\ud83d\udd0d\u3002</p> <p>\u6211\u4eec\u53ef\u4ee5\u7528\u8fd9\u6837\u4e00\u5f20\u56fe\u6765\u8868\u793a\u5176\u4ed6\u51e0\u4e2a\u6982\u5ff5\u7684\u5173\u7cfb\uff1a</p> <p> </p> <p>Source: https://en.wikipedia.org/wiki/NP-hardness</p> <p>\u53ef\u4ee5\u7c97\u6d45\u7684\u6309\u7167\u56fe\u4e2d\u7684\u201cComplexity\u201d\u8f74\u6765\u7406\u89e3\u5176\u4e2d\u7684\u8f6c\u5316\u5173\u7cfb\uff0c\u63a5\u4e0b\u6765\u7ed9\u51fa\u5b83\u4eec\u7684\u8be6\u7ec6\u5b9a\u4e49\uff1a</p> <p>P</p> <p>P \u53d6\u81ea polynomial time\uff0c\u6307\u7684\u662f\u53ef\u4ee5\u7528\u786e\u5b9a\u578b\u56fe\u7075\u673a\ud83d\udd0d\u5728\u591a\u9879\u5f0f\u65f6\u95f4\u5185\u89e3\u51b3\u7684\u95ee\u9898\u3002</p> <p>\u4e5f\u5c31\u662f\u6211\u4eec\u901a\u5e38\u610f\u4e49\u4e0b\u6240\u8bf4\u7684\uff0c\u53ef\u4ee5\u5728\u591a\u9879\u5f0f\u65f6\u95f4\u5185\u89e3\u51b3\u7684\u95ee\u9898\u3002</p> <p>NP</p> <p>NP \u5373 nondeterministic polynomial time\uff0c\u6307\u7684\u662f\u53ef\u4ee5\u7528\u975e\u786e\u5b9a\u578b\u56fe\u7075\u673a\ud83d\udd0d\u5728\u591a\u9879\u5f0f\u65f6\u95f4\u5185\u89e3\u51b3\u7684\u95ee\u9898\u3002\u8fd9\u4e2a\u8bf4\u6cd5\u7b49\u4ef7\u4e8e\u53ef\u4ee5\u7528\u786e\u5b9a\u578b\u56fe\u7075\u673a\ud83d\udd0d\u5728\u591a\u9879\u5f0f\u65f6\u95f4\u5185\u9a8c\u8bc1\uff08\u5224\u65ad\u7b54\u6848\u662f\u5426\u6b63\u786e\uff09\u3002</p> <p>\u4e5f\u5c31\u662f\u6211\u4eec\u901a\u5e38\u610f\u4e49\u4e0b\u6240\u8bf4\u7684\uff0c\u53ef\u4ee5\u5728\u591a\u9879\u5f0f\u65f6\u95f4\u5185\u9a8c\u8bc1\u7684\u95ee\u9898\u3002</p> <p>NPC</p> <p>NPC \u5373 NP complete\uff0cNP \u5b8c\u5168\uff0c\u662f NP \u4e2d\u6700\u96be\u7684\u51b3\u5b9a\u6027\u95ee\u9898\uff08\u5e76\u4e0d\u662f\u65e0\u9650\u5b9a\u8bcd\u7684\u6700\u96be\u7684\u95ee\u9898\uff01\uff09\u3002\u800c\u6211\u4eec\u79f0\u6ee1\u8db3\u5982\u4e0b\u6761\u4ef6\u7684\u95ee\u9898\u4e3a NPC \u95ee\u9898\uff1a</p> <ol> <li>\u662f\u4e00\u4e2a NP \u95ee\u9898\uff1b</li> <li>\u6240\u6709 NP \u95ee\u9898\u90fd\u53ef\u4ee5\u591a\u9879\u5f0f\u65f6\u95f4\u5f52\u7ea6\ud83d\udd0d\u4e3a\u8be5\u95ee\u9898\uff1b</li> </ol> <p>\u7531 2 \u53ef\u4ee5\u6709\u7ed3\u8bba\uff0c\u6240\u6709\u7684 NPC \u95ee\u9898\u96be\u5ea6\u76f8\u540c\u2014\u2014\u4e00\u65e6\u6709\u4e00\u4e2a NPC \u95ee\u9898\u88ab\u89e3\u51b3\uff0c\u90a3\u4e48\u6240\u6709 NPC \u95ee\u9898\uff0c\u4e43\u81f3\u6240\u6709 NP \u95ee\u9898\u90fd\u80fd\u88ab\u89e3\u51b3\u3002</p> <p>\u5982\u679c\u6211\u4eec\u8bd5\u56fe\u8bc1\u660e\u4e00\u4e2a\u95ee\u9898\u662f NPC \u95ee\u9898\uff0c\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u8fd9\u79cd\u624b\u6bb5\uff1a</p> <ol> <li>\u5224\u5b9a\u8be5\u95ee\u9898\u662f\u4e00\u4e2a NP \u95ee\u9898\uff1b</li> <li>\u5224\u5b9a\u4e00\u4e2a\u5df2\u77e5\u7684 NPC \u95ee\u9898\u53ef\u4ee5\u591a\u9879\u5f0f\u65f6\u95f4\u5f52\u7ea6\ud83d\udd0d\u4e3a\u8be5\u95ee\u9898\uff0c\u6216\u5224\u5b9a\u8be5\u95ee\u9898\u662f NPH\uff08\u5728\u4e0b\u9762\uff09\u95ee\u9898\uff1b</li> </ol> <p>\u7b2c\u4e00\u4e2a\u88ab\u8bc1\u660e\u662f NPC \u7684\u95ee\u9898\u662f Circuit-SAT\ud83d\udd0d \u95ee\u9898\u3002</p> <p>P ?= NP &amp; NPC</p> <p>\u5173\u4e8e P \u548c NP \u7684\u5173\u7cfb\uff0c\u6211\u4eec\u4ecd\u7136\u4e0d\u77e5\u9053 P \u662f\u5426\u80fd\u7b49\u4e8e NP\uff0c\u5373\u6211\u4eec\u4ecd\u7136\u4e0d\u77e5\u9053\u662f\u5426\u5b58\u5728\u591a\u9879\u5f0f\u7b97\u6cd5\u53ef\u4ee5\u89e3\u51b3\u4e00\u5207 NP \u95ee\u9898\u3002</p> <p>\u800c\u5176\u4e2d\u7684\u5173\u952e\u5c31\u662f\uff0c\u5982\u679c\u6211\u4eec\u80fd\u627e\u5230 NPC \u95ee\u9898\u7684\u591a\u9879\u5f0f\u89e3\u6cd5\uff0c\u90a3\u4e48\u5c31\u53ef\u4ee5\u8bc1\u660e P = NP\u3002</p> <p>NPH</p> <p>NPH \u5373 NP hard\uff0cNP \u56f0\u96be\uff0c\u5b83\u4e0d\u4e00\u5b9a\u9700\u8981\u662f NP \u95ee\u9898\u3002\u800c\u6240\u6709 NP \u95ee\u9898\u90fd\u53ef\u4ee5\u591a\u9879\u5f0f\u65f6\u95f4\u5f52\u7ea6\ud83d\udd0d\u4e3a NPH \u95ee\u9898\u3002</p> <p>\u4e5f\u5c31\u662f\u8bf4 \\(NPC = NP \\cap NPH\\)\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec10/#\u8bfe\u5185\u6848\u4f8b","title":"\u8bfe\u5185\u6848\u4f8b","text":"<p>\u63a5\u4e0b\u6765\u7684\u5185\u5bb9\u90fd\u662f\u8bfe\u4ef6\u4e2d\u63d0\u5230\u7684\u4e00\u4e9b\u5177\u4f53\u95ee\u9898\u548c\u6848\u4f8b\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec10/#halting-problem","title":"Halting Problem","text":"<p>Links</p> <p>Wikipedia: https://en.wikipedia.org/wiki/Halting_problem</p> <p>\u505c\u673a\u95ee\u9898\u662f\u4e00\u4e2a\u5178\u578b\u7684\u4e0d\u53ef\u8ba1\u7b97\u95ee\u9898\uff0c\u5b83\u6307\u7684\u662f\uff0c\u5bf9\u4e8e\u4efb\u610f\u4e00\u4e2a\u7a0b\u5e8f\uff0c\u6211\u4eec\u65e0\u6cd5\u8bbe\u8ba1\u4e00\u4e2a\u7b97\u6cd5\u6765\u5224\u65ad\u5b83\u662f\u5426\u4f1a\u5728\u6709\u9650\u65f6\u95f4\u5185\u505c\u673a\uff08\u5373\u5224\u65ad\u7a0b\u5e8f\u662f\u5426\u4f1a\u6b7b\u5faa\u73af\uff09\u3002</p> <p>\u6211\u4eec\u901a\u8fc7\u53cd\u8bc1\u6cd5\u53ef\u4ee5\u8bc1\u660e\uff1a</p> <p>\u5047\u8bbe\u5b58\u5728\u51fd\u6570 <code>willHalt(func F)</code> \u53ef\u4ee5\u5224\u65ad\u51fd\u6570 F \u662f\u5426\u4f1a\u505c\u673a\uff0c\u5982\u679c\u4f1a\uff0c\u5219\u8fd4\u56de <code>true</code>\uff0c\u5426\u5219\u8fd4\u56de <code>false</code>\u3002\u90a3\u4e48\u6211\u4eec\u53ef\u4ee5\u6784\u9020\u4e00\u4e2a\u8fd9\u6837\u7684\u51fd\u6570 <code>foo()</code>\uff1a</p> <pre><code>void foo() {\nif ( willHalt(foo) ) {\nwhile (true) {} // Endless loop.\n}\nreturn;\n}\n</code></pre> <p>\u63a5\u4e0b\u6765\uff0c\u5982\u679c\u6211\u4eec\u60f3\u77e5\u9053 <code>foo()</code> \u662f\u5426\u4f1a\u505c\u673a\uff0c\u5c31\u4f1a\u6267\u884c <code>willHalt(foo)</code>\u3002\u7136\u800c\u5728 <code>foo()</code> \u5185\u90e8\u4e5f\u6709\u4e00\u4e2a <code>willHalt(foo)</code>\uff0c\u5982\u679c\u5b83\u8ba4\u4e3a <code>foo()</code> \u4f1a\u505c\u673a\uff0c\u5219\u6784\u9020\u4e00\u4e2a\u6b7b\u5faa\u73af\uff1b\u800c\u5982\u679c\u5b83\u8ba4\u4e3a <code>foo()</code> \u4e0d\u4f1a\u505c\u673a\uff0c\u5219\u9009\u62e9\u8ba9\u5b83\u7acb\u523b\u505c\u673a\uff0c\u4e8e\u662f\u8fd9\u91cc\u5c31\u4ea7\u751f\u4e86\u77db\u76fe\u3002</p> <p>\u7406\u89e3\u4e0a\u9762\u8fd9\u6bb5\u5185\u5bb9\u7684\u5173\u952e\u5c31\u662f\uff0c\u8fd9\u91cc\u867d\u7136\u4e0d\u5b58\u5728\u4e8b\u5b9e\u610f\u4e49\u4e0a\u7684\u201c\u6b7b\u5faa\u73af\u201d\uff0c\u4f46\u53ef\u4ee5\u7406\u89e3\u4e3a\u8fd9\u91cc\u5b58\u5728\u4e00\u4e2a\u903b\u8f91\u4e0a\u7684\u9012\u5f52\uff0c\u800c\u8fd9\u79cd\u201c\u903b\u8f91\u4e0a\u7684\u9012\u5f52\u201d\uff0c\u6b63\u662f\u5bfc\u81f4\u505c\u673a\u95ee\u9898\u6210\u4e3a\u4e00\u4e2a\u4e0d\u53ef\u8ba1\u7b97\u95ee\u9898\u7684\u539f\u56e0\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec10/#hamilton-cycle-problem","title":"Hamilton Cycle Problem","text":"<p>links</p> <p>Wikipedia: https://en.wikipedia.org/wiki/Hamiltonian_path_problem</p> <p>OI Wiki: https://oi-wiki.org/graph/hamilton</p> <p>\u54c8\u5bc6\u987f\u56de\u8def\u95ee\u9898</p> <p>\u7ed9\u5b9a\u4e00\u4e2a\u56fe\uff0c\u5224\u65ad\u662f\u5426\u5b58\u5728\u4e00\u6761\u8def\u5f84\uff0c\u4f7f\u5f97\u5b83\u7ecf\u8fc7\u56fe\u4e2d\u7684\u6bcf\u4e2a\u70b9\u6070\u597d\u4e00\u6b21\uff0c\u4e14\u6700\u540e\u56de\u5230\u8d77\u70b9\u3002</p> <p>\u54c8\u5bc6\u987f\u56de\u8def\u95ee\u9898\u662f\u4e00\u4e2a NPC \u95ee\u9898\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec10/#traveling-salesman-problem","title":"Traveling Salesman Problem","text":"<p>Links</p> <p>Wikipedia: https://en.wikipedia.org/wiki/Travelling_salesman_problem</p> <p>\u65c5\u884c\u5546\u95ee\u9898</p> <p>\u65c5\u884c\u5546\u95ee\u9898\u6709\u4e24\u79cd\u5b9a\u4e49\uff0c\u5176\u4e2d\u524d\u8005\u662f NPH\uff0c\u800c\u88ab\u79f0\u4e3a\u201c\u5224\u5b9a\u7248\u672c\u201d\u7684\u540e\u8005\u662f NPC\u3002</p> \u539f\u59cb\u5b9a\u4e49\u5224\u5b9a\u7248\u672c <p>\u7ed9\u5b9a\u4e00\u4e2a\u5b8c\u5168\u56fe\uff0c\u5224\u65ad\u662f\u5426\u5b58\u5728\u4e00\u6761\u8def\u5f84\uff0c\u4f7f\u5f97\u5b83\u7ecf\u8fc7\u56fe\u4e2d\u7684\u6bcf\u4e2a\u70b9\u6070\u597d\u4e00\u6b21\uff0c\u4e14\u6700\u540e\u56de\u5230\u8d77\u70b9\uff0c\u4e14\u8def\u5f84\u957f\u5ea6\u6700\u77ed\u3002</p> <p>\"Given a list of cities and the distances between each pair of cities, what is the shortest possible route that visits each city exactly once and returns to the origin city?\"</p> <p>From Wikipedia</p> <p>\u8be5\u7248\u672c\u7684 TSP \u95ee\u9898\u662f\u4e00\u4e2a NPH \u95ee\u9898\uff0c\u5e38\u5e38\u51fa\u73b0\u5728\u7ec4\u5408\u4f18\u5316\u7684\u8bed\u5883\u4e2d\u3002</p> <p>\u7ed9\u5b9a\u4e00\u4e2a\u5b8c\u5168\u56fe\uff0c\u5224\u65ad\u662f\u5426\u5b58\u5728\u4e00\u6761\u8def\u5f84\uff0c\u4f7f\u5f97\u5b83\u7ecf\u8fc7\u56fe\u4e2d\u7684\u6bcf\u4e2a\u70b9\u6070\u597d\u4e00\u6b21\uff0c\u4e14\u6700\u540e\u56de\u5230\u8d77\u70b9\uff0c\u4e14\u8def\u5f84\u957f\u5ea6\u4e0d\u8d85\u8fc7 \\(k\\)\u3002</p> <p>\u8be5\u7248\u672c\u7684 TSP \u95ee\u9898\u662f\u4e00\u4e2a NPC \u95ee\u9898\uff0c\u5e38\u5e38\u51fa\u73b0\u5728\u590d\u6742\u5ea6\u7406\u8bba\u7684\u8bed\u5883\u4e2d\u3002</p> <p>\u9700\u8981\u6ce8\u610f\uff0c\u63a5\u4e0b\u6765\u6211\u4eec\u8c08\u8bba\u7684\u90fd\u662f\u5224\u5b9a\u7248\u672c\u7684 TSP\uff01</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec10/#\u5224\u5b9a\u7248\u672c\u7684-npc-\u8bc1\u660e","title":"\u5224\u5b9a\u7248\u672c\u7684 NPC \u8bc1\u660e","text":"<p>\u73b0\u5728\uff0c\u5047\u8bbe\u6211\u4eec\u5df2\u77e5 Hamilton Cycle Problem \u95ee\u9898\u662f\u4e00\u4e2a NPC \u95ee\u9898\uff0c\u5c1d\u8bd5\u901a\u8fc7\u591a\u9879\u5f0f\u65f6\u95f4\u5f52\u7ea6\ud83d\udd0d\u7684\u65b9\u5f0f\u6765\u8bc1\u660e TSP \u4e5f\u662f\u4e00\u4e2a NPC \u95ee\u9898\u3002</p> <p>Recommended Reading</p> <p>https://opendsa-server.cs.vt.edu/ODSA/Books/Everything/html/hamiltonianCycle_to_TSP.html</p> <p>\u9996\u5148\u56de\u987e\u8bc1\u660e NPC \u7684\u6b65\u9aa4\uff1a</p> <ol> <li>\u5224\u5b9a\u8be5\u95ee\u9898\u662f\u4e00\u4e2a NP \u95ee\u9898\uff1b</li> <li>\u5224\u5b9a\u4e00\u4e2a\u5df2\u77e5\u7684 NPC \u95ee\u9898\u53ef\u4ee5\u591a\u9879\u5f0f\u65f6\u95f4\u5f52\u7ea6\ud83d\udd0d\u4e3a\u8be5\u95ee\u9898\uff0c\u6216\u8005\u8bf4\u5224\u5b9a\u8be5\u95ee\u9898\u662f NPH \u95ee\u9898\uff1b</li> </ol> <p>\u4ee3\u5165\u5230\u8fd9\u4e2a\u95ee\u9898\u4e2d\uff0c\u4e5f\u5c31\u662f\u6211\u4eec\u9700\u8981\u8bc1\u660e\uff1a</p> <ol> <li>TSP \u662f\u4e00\u4e2a NP \u95ee\u9898\uff1b</li> <li>Hamilton Cycle Problem \u53ef\u4ee5\u591a\u9879\u5f0f\u65f6\u95f4\u5f52\u7ea6\ud83d\udd0d\u4e3a TSP\uff1b</li> </ol> <p>TSP is NP</p> <p>\u8bc1\u660e TSP \u662f\u4e00\u4e2a NP \u95ee\u9898\u5373\u8bc1\u660e TSP \u7684\u89e3\u53ef\u4ee5\u5728\u591a\u9879\u5f0f\u65f6\u95f4\u5185\u88ab\u9a8c\u8bc1\u3002\u800c\u9a8c\u8bc1\u4e00\u4e2a\u89e3\u662f TSP \u95ee\u9898\u7684\u89e3\uff0c\u9700\u8981\u8bc1\u660e\u4e0b\u9762\u4e24\u4e2a\u70b9\uff1a</p> <ol> <li>\u8fd9\u6761\u8def\u5f84\u7ecf\u8fc7\u4e86\u6240\u6709\u8282\u70b9\u6070\u597d\u4e00\u6b21\uff1b</li> <li>\u8fd9\u6761\u8def\u5f84\u957f\u5ea6\u4e0d\u8d85\u8fc7\\(k\\)\uff1b</li> </ol> <p>\u663e\u7136\uff0c\u8fd9\u4e24\u6761\u90fd\u53ea\u9700\u8981 \\(O(N)\\) \u7684\u5f00\u9500\u5c31\u80fd\u9a8c\u8bc1\u3002</p> <p>\u4e8e\u662f\uff0c\u6211\u4eec\u5f97\u5230\u7ed3\u8bba\uff1a\\(\\text{TSP} \\in \\text{NP}\\)\u3002</p> <p>TSP is NPH</p> <p>\u8981\u8bc1\u660e TSP \u662f\u4e00\u4e2a NPH \u95ee\u9898\uff0c\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u8bc1\u660e Hamilton Cycle Problem(HCP) \u53ef\u4ee5\u591a\u9879\u5f0f\u65f6\u95f4\u5f52\u7ea6\ud83d\udd0d\u4e3a TSP\u3002</p> <p>\u4e3a\u6b64\uff0c\u6211\u4eec\u9700\u8981\u5bf9\u6bd4 HCP \u548c TSP \u7684\u5dee\u5f02\u3002</p> <p>\u4ee5 HCP \u4e3a\u57fa\u7840\u63cf\u8ff0 TSP\uff0c\u5b9e\u9645\u4e0a\u5c31\u662f\u5728\u4e00\u5f20\u5b8c\u5168\u56fe\u4e0a\u5bfb\u627e\u603b\u957f\u4e0d\u8d85\u8fc7 \\(k\\) \u7684\u54c8\u5bc6\u987f\u73af\u8def\uff0c\u5177\u4f53\u6765\u8bf4\uff1a</p> HCP TSP \u56fe \\(G(V,E)\\) \u5b8c\u5168\u56fe \\(G'(V',E')\\) \u65e0\u8fb9\u6743 \u6709\u8fb9\u6743 - \\(\\sum v_i \\leq k\\) <p>\u800c\u4e3a\u4e86\u8bc1\u660e \\(\\text{HCP} \\leq_p \\text{TCP}\\)\uff0c\u6211\u4eec\u8bbe\u8ba1\u4e00\u4e2a\u591a\u9879\u5f0f\u65f6\u95f4\u7684\u65b9\u6cd5 <code>f()</code> \u5b9e\u73b0 \\(G(V,E) \\to G'(V',E')\\)\uff0c\u5177\u4f53\u6765\u8bf4\uff0c\u5b83\u505a\u8fd9\u4e9b\u4e8b\uff1a</p> <ol> <li>\u8fde\u63a5 \\(G\\) \u4e2d\u6240\u6709\u6ca1\u8fde\u4e0a\u7684\u8fb9\uff0c\u4f7f \\(G\\) \u6210\u4e3a\u4e00\u5f20\u65e0\u6743\u5b8c\u5168\u56fe\uff1b</li> <li>\u5bf9\u4e8e\u65e0\u6743\u5b8c\u5168\u56fe\u4e2d\u7684\u6bcf\u4e00\u6761\u8fb9 \\(v^c_i\\)\uff0c\u5982\u679c\u5728 \\(G\\) \u4e2d\u4e5f\u6709\u8fd9\u6761\u8fb9\uff0c\u90a3\u4e48\u4ee4\u5b83\u8fb9\u6743\u4e3a 0\uff0c\u5426\u5219\u4ee4\u5b83\u8fb9\u6743\u4e3a 1\uff0c\u4e8e\u662f\u5f97\u5230\u6709\u6743\u5b8c\u5168\u56fe \\(G'(V',E')\\)\uff1b</li> </ol> <p> </p> <p>\u53f3\u56fe\u4e2d\u6240\u6709\u7684\u84dd\u8fb9\u8fb9\u6743\u90fd\u4e3a 0\uff0c\u7eff\u8fb9\u8fb9\u6743\u90fd\u4e3a 1\u3002</p> <p>\u7531\u4e8e\u5b8c\u5168\u56fe\u7684\u8fb9\u6570\u4e3a \\(\\frac{n(n-1)}{2}\\)\uff0c\u6240\u4ee5\u8fd9\u4e2a\u6b65\u9aa4\u663e\u7136\u662f\u591a\u9879\u5f0f\u65f6\u95f4\u7684\u3002</p> <p>\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u53d1\u73b0\uff0c\u539f\u95ee\u9898\u4e3a\u5728 \\(G\\) \u4e0a\u5bfb\u627e\u54c8\u5bc6\u987f\u73af\uff0c\u7b49\u4ef7\u4e8e\u5728 \\(G' = f(G)\\) \u4e0a\u505a \\(k = 0\\) \u7684 TSP\u3002\u7531\u6b64\u8bc1\u660e \\(\\text{HCP} \\leq_{p} \\text{TSP}\\)\uff0c\u5373 \\(\\text{TSP} \\in \\text{NPH}\\)\u3002</p> <p>\u7efc\u4e0a\u6240\u8ff0\uff0c\u7531\u4e8e \\(\\text{TSP} \\in \\text{NP}\\) \u4e14 \\(\\text{TSP} \\in \\text{NPH}\\)\uff0c\u6240\u4ee5 \\(\\text{TSP} \\in \\text{NPC}\\)\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec10/#circuit-sat","title":"Circuit-SAT","text":"<p>Links</p> <p>Wikipedia: https://en.wikipedia.org/wiki/Circuit_satisfiability_problem</p> <p>Circuit-SAT \u53c8\u53eb circuit satisfiability problem\uff0c\u5b83\u662f\u6700\u65e9\u88ab\u8bc1\u660e\u662f NPC \u7684\u95ee\u9898\uff0c\u5373\u901a\u8fc7 NPC \u95ee\u9898\u7684\u5b9a\u4e49\u8bc1\u660e\u3002</p> <p>\u5176\u5177\u4f53\u63cf\u8ff0\u5982\u4e0b\uff1a</p> <p>Circuit-SAT</p> <p>Circuit-SAT \u5373\u4e3a\u786e\u5b9a\u7ed9\u5b9a\u5e03\u5c14\u7535\u8def\u662f\u5426\u5177\u6709\u4f7f\u8f93\u51fa\u4e3a\u771f\u7684\u8f93\u5165\u5206\u914d\u7684\u51b3\u7b56\u7684\u95ee\u9898\u3002</p> <p></p> <p>Source: https://en.wikipedia.org/wiki/Circuit_satisfiability_problem</p> <p>\u4e0a\u56fe\u4e2d\uff0c\u5de6\u4fa7\u7535\u8def\u6ee1\u8db3\u6761\u4ef6\uff0c\u53f3\u4fa7\u7535\u8def\u4e0d\u6ee1\u8db3\u6761\u4ef6\u3002</p> <p>\u6216\u8005\uff0c\u66f4\u62bd\u8c61\u7684\u6765\u8bf4\uff0c\u662f\u5224\u65ad\u4e00\u4e2a\u5177\u6709 \\(n\\) \u4e2a\u5e03\u5c14\u53d8\u91cf\u7684\u5e03\u5c14\u8868\u8fbe\u5f0f\u662f\u5426\u5177\u6709\u7ed3\u679c\u4e3a True \u7684\u89e3\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec10/#3-sat","title":"3-SAT","text":"<p>Links</p> <p>Wikipedia: https://en.wikipedia.org/wiki/Boolean_satisfiability_problem#3-satisfiability</p> <p>3-SAT \u6307\u7684\u662f Circuit-SAT \u95ee\u9898\u7684\u4e00\u4e2a\u7279\u4f8b\uff0c\u5b83\u5bf9\u5e03\u5c14\u7535\u8def\uff0c\u6216\u8005\u8bf4\u5e03\u5c14\u8868\u8fbe\u5f0f\u7684\u5f62\u5f0f\u6709\u7279\u6b8a\u8981\u6c42\uff0c\u5177\u4f53\u6765\u8bf4\uff0c\u5b83\u8981\u6c42\u5e03\u5c14\u8868\u8fbe\u5f0f\u5f62\u5982\uff1a</p> \\[ (x_1 \\vee x_2 \\vee x_3) \\wedge (x_4 \\vee x_5 \\vee x_6) \\wedge \\cdots \\wedge (x_{n-2} \\vee x_{n-1} \\vee x_n) \\] <ul> <li>\u53d8\u91cf\u662f\u5426\u91cd\u590d\u3001\u662f\u5426\u53d6\u975e\u4e0d\u662f\u91cd\u70b9\uff0c\\(x_1\\) \u53ef\u4ee5\u548c \\(x_6\\) \u662f\u540c\u4e00\u4e2a\u53d8\u91cf\uff0c\u4e5f\u53ef\u4ee5\u662f\u67d0\u4e2a\u53d8\u91cf\u7684\u975e\uff0c\u91cd\u70b9\u662f\u8fd9\u91cc\u7684\u4e09\u4e2a\u4e00\u7ec4\u7684\u5f62\u5f0f\u3002</li> </ul>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec10/#a-formal-language-framework","title":"A formal-language Framework","text":"<ul> <li> TODO: Finish this part.</li> </ul>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec10/#\u76f8\u5173\u6982\u5ff5","title":"\u76f8\u5173\u6982\u5ff5","text":"<p>\u8bf4\u660e</p> <p>\u4ee5\u4e0b\u90e8\u5206\u7684\u5185\u5bb9\u662f\u4e3a\u4e86\u8fdb\u4e00\u6b65\u8bf4\u660e\u4e0a\u6587\u4e2d\u90e8\u5206\u5185\u5bb9\u800c\u4ecb\u7ecd\u7684\u6982\u5ff5\uff0c\u5e76\u4e0d\u5177\u6709\u7ec4\u7ec7\u7ed3\u6784\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec10/#\u56fe\u7075\u673a","title":"\u56fe\u7075\u673a","text":"<p>Links</p> <p>Wikipedia: https://en.wikipedia.org/wiki/Turing_machine</p> <p>Wikipedia: https://en.wikipedia.org/wiki/Nondeterministic_Turing_machine</p> <p>\u56fe\u7075\u673a\u6709\u4e00\u4e9b\u53d8\u4f53\uff0c\u800c\u6211\u4eec\u5728\u8fd9\u91cc\u5f15\u5165\u56fe\u7075\u673a\u662f\u4e3a\u4e86\u4ecb\u7ecd P/NP\uff0c\u53ea\u4ecb\u7ecd\u786e\u5b9a\u578b\u56fe\u7075\u673a\u548c\u975e\u786e\u5b9a\u578b\u56fe\u7075\u673a\u3002</p> <p>\u56fe\u7075\u673a\u7531\u4e00\u4e2a\u65e0\u9650\u957f\u7684\u7eb8\u5e26\u548c\u4e00\u4e2a\u8bfb\u5199\u5934\u7ec4\u6210\u3002\u7eb8\u5e26\u88ab\u5212\u5206\u4e3a\u4e00\u4e2a\u4e2a\u683c\u5b50\uff0c\u6bcf\u4e2a\u683c\u5b50\u4e0a\u6709\u4e00\u4e2a\u7b26\u53f7\uff0c\u8bfb\u5199\u5934\u53ef\u4ee5\u5728\u7eb8\u5e26\u4e0a\u79fb\u52a8\uff0c\u8bfb\u5199\u5934\u53ef\u4ee5\u8bfb\u53d6\u5f53\u524d\u683c\u5b50\u4e0a\u7684\u7b26\u53f7\uff0c\u4e5f\u53ef\u4ee5\u6539\u53d8\u5f53\u524d\u683c\u5b50\u4e0a\u7684\u7b26\u53f7\u3002\u56fe\u7075\u673a\u7684\u72b6\u6001\u662f\u4e00\u4e2a\u6709\u9650\u96c6\u5408\uff0c\u6bcf\u4e2a\u72b6\u6001\u90fd\u6709\u4e00\u4e2a\u8f6c\u79fb\u51fd\u6570\uff0c\u8f6c\u79fb\u51fd\u6570\u7684\u8f93\u5165\u662f\u5f53\u524d\u72b6\u6001\u548c\u5f53\u524d\u683c\u5b50\u4e0a\u7684\u7b26\u53f7\uff0c\u8f93\u51fa\u662f\u4e0b\u4e00\u4e2a\u72b6\u6001\u3001\u4e0b\u4e00\u4e2a\u683c\u5b50\u4e0a\u7684\u7b26\u53f7\u548c\u8bfb\u5199\u5934\u7684\u79fb\u52a8\u65b9\u5411\u3002</p> <p>\u66f4\u672c\u8d28\u7684\u6765\u8bf4\uff0c\u56fe\u7075\u673a\u662f\u4e00\u79cd\u8ba1\u7b97\u6a21\u578b\uff0c\u6211\u4eec\u53ef\u4ee5\u7528\u5b83\u6765\u8868\u793a\u4efb\u4f55\u6709\u9650\u903b\u8f91\u6570\u5b66\u8fc7\u7a0b\u3002\u786e\u5b9a\u578b\u56fe\u7075\u673a\u4e0e\u6211\u4eec\u5e38\u89c4\u7406\u89e3\u7684\u8ba1\u7b97\u673a\u903b\u8f91\u7c7b\u4f3c\uff0c\u5373\u4e0b\u4e00\u6b65\u8981\u505a\u4ec0\u4e48\u53ef\u4ee5\u6839\u636e\u5f53\u524d\u72b6\u6001\u786e\u5b9a\u3002\u800c\u975e\u786e\u5b9a\u578b\u56fe\u7075\u673a\u5219\u7c7b\u4f3c\u4e8e\u80fd\u591f\u8fdb\u884c\u65e0\u9650\u5e76\u884c\uff0c\u5e76\u4e14\u6700\u7ec8\u603b\u662f\u9009\u62e9\u901a\u5411\u6b63\u786e\u7b54\u6848\u7684\u65b9\u5411\u7684\u90a3\u6761\u8def\uff08\u6709\u70b9\u7c7b\u4f3c\u4e8e\u5b83\u80fd\u5f00\u5e73\u884c\u5b87\u5b99\uff0c\u5e76\u4e14\u603b\u662f\u8ba9\u4f60\u89c2\u6d4b\u5230\u6b63\u786e\u7684\u90a3\u4e00\u4e2a\u5e73\u884c\u5b87\u5b99\uff09\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec10/#\u591a\u9879\u5f0f\u65f6\u95f4\u5f52\u7ea6","title":"\u591a\u9879\u5f0f\u65f6\u95f4\u5f52\u7ea6","text":"<p>Links</p> <p>Wikipedia: https://en.wikipedia.org/wiki/Polynomial-time_reduction</p> <p>\u6211\u4eec\u5f15\u5165 P/NP \u7b49\u8fd9\u4e9b\u6982\u5ff5\uff0c\u662f\u4e3a\u4e86\u8861\u91cf\u95ee\u9898\u7684\u590d\u6742\u7a0b\u5ea6\uff0c\u800c\u5982\u4f55\u5728\u5177\u4f53\u7684\u201c\u95ee\u9898\u201d\u95f4\u4f20\u9012\u3001\u6bd4\u8f83\u8fd9\u79cd\u201c\u590d\u6742\u7a0b\u5ea6\u201d\uff0c\u5c31\u662f\u591a\u9879\u5f0f\u65f6\u95f4\u5f52\u7ea6(polynomial reduce)\u7684\u76ee\u7684\u3002</p> <pre><code>graph LR;\nA[\"\u95ee\u9898 A\"]\nB[\"\u95ee\u9898 B\"]\nA ===&gt;|\"\u591a\u9879\u5f0f\u65f6\u95f4\u8f6c\u5316\"| B</code></pre> <p>\u5982\u679c\u6211\u4eec\u80fd\u5728\u591a\u9879\u5f0f\u65f6\u95f4\u7684\u590d\u6742\u5ea6\u5185\uff0c\u5c06\u95ee\u9898 A \u8f6c\u5316\u4e3a\u95ee\u9898 B\uff0c\u5219\u79f0\u95ee\u9898 A \u53ef\u4ee5\u591a\u9879\u5f0f\u65f6\u95f4\u5f52\u7ea6(polynomial reduce)\u4e3a B\uff0c\u8bb0\u4e3a \\(A \\leq_{p} B\\)\uff0c\u8868\u793a A \u4e0d\u4f1a\u6bd4 B \u96be\u3002</p> <p>\u800c\u91c7\u53d6\u6570\u5b66\u8bed\u8a00\u6765\u63cf\u8ff0\uff0c\u5219\u662f\uff1a</p> \\[ \\begin{aligned} A \\leq_{p} B  \\;\\;\\Leftrightarrow\\;\\; &amp; \\exist f() \\text{ which runs in polynomial time}, \\\\ &amp; s.t.    \\;\\; \\forall x \\in A,\\; f(x) \\in B \\\\ &amp; \\text{and}\\; \\forall f(x) \\in B,\\; y \\in A \\end{aligned} \\]"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec11/","title":"Lecture 11 | Approximation","text":"<p> \u7ea6 5372 \u4e2a\u5b57  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 18 \u5206\u949f</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec11/#\u8fd1\u4f3c\u7b97\u6cd5","title":"\u8fd1\u4f3c\u7b97\u6cd5","text":"<p>links</p> <p>Wikipedia: https://en.wikipedia.org/wiki/Approximation_algorithm</p> <p>\u5728\u4e0a\u4e00\u7ae0\u4e2d\u6211\u4eec\u4ecb\u7ecd\u4e86 P/NP \u95ee\u9898\uff0c\u800c\u5927\u5bb6\u666e\u904d\u8ba4\u4e3a P \u2260 NP\uff0c\u8fd9\u5c31\u610f\u5473\u7740\u5bf9\u4e8e\u67d0\u4e9b\u95ee\u9898\uff0c\u6211\u4eec\u65e0\u6cd5\u4f7f\u7528\u591a\u9879\u5f0f\u65f6\u95f4\u89e3\u51b3\uff0c\u800c\u5728\u95ee\u9898\u89c4\u6a21\u53d8\u5927\u65f6\uff0c\u8d8a\u53d1\u4e0d\u53ef\u63a5\u53d7\u3002</p> <p>\u56e0\u6b64\uff0c\u6211\u4eec\u8003\u8651\u80fd\u5426\u9000\u800c\u6c42\u5176\u6b21\uff0c\u5728\u591a\u9879\u5f0f\u65f6\u95f4\u5185\u6c42\u4e00\u4e2a\u6bd4\u8f83\u4f18\u7684\u89e3\u3002\u66f4\u5177\u4f53\u7684\u6765\u8bf4\uff0c\u6211\u4eec\u5c1d\u8bd5\u5bfb\u627e\u4e00\u79cd\u591a\u9879\u5f0f\u7b97\u6cd5\uff0c\u4f7f\u5f97\u5176\u7ed3\u679c\u59cb\u7ec8\u5728\u5173\u4e8e\u51c6\u786e\u89e3\u7684\u53ef\u63a5\u53d7\u504f\u5dee\u8303\u56f4\u5185\uff0c\u5bf9\u4e8e\u8fd9\u79cd\u7b97\u6cd5\uff0c\u6211\u4eec\u79f0\u4e4b\u4e3a\u8fd1\u4f3c\u7b97\u6cd5(approximation algorithm)\u3002</p> <p>\u6211\u4eec\u8bbe \\(f(n, x)\\) \u662f\u5bf9\u8f93\u5165\u5927\u5c0f\u4e3a \\(n\\) \u7684\u60c5\u51b5\u4e0b\uff0c\u5bf9\u7ed3\u679c \\(x\\) \u7684\u6700\u574f\u60c5\u51b5\u7684\u4e00\u4e2a\u76f4\u89c2\u91cf\u5316\uff08\u4f8b\u5982 dist, weight...\uff09\uff0c\u82e5\u8bbe \\(x^*\\) \u4e3a\u51c6\u786e\u89e3\uff0c\\(x\\) \u4e3a\u7ed9\u5b9a\u7b97\u6cd5\u7ed3\u679c\uff0c\u5219\u6211\u4eec\u5b9a\u4e49\u8fd1\u4f3c\u6bd4(Approximation Ratio)\\(\\rho\\)\uff1a</p> \\[ \\forall n \\rho = \\max\\left\\{\\frac{f(n, x)}{f(n, x^*)}, \\frac{f(n, x^*)}{f(n, x)}\\right\\} \\] <p>\u5219\u79f0\u7ed9\u5b9a\u7b97\u6cd5\u4e3a \\(\\rho\\) \u8fd1\u4f3c\u7b97\u6cd5(\\(\\rho\\)-approximation algorithm)\u3002</p> <p>\u8fd1\u4f3c\u7b97\u6cd5 v.s. \u968f\u673a\u7b97\u6cd5</p> <p>\u5728\u770b\u5230\u8fd1\u4f3c\u7b97\u6cd5\u65f6\uff0c\u6211\u8111\u5b50\u91cc\u4e00\u4e0b\u5b50\u6d6e\u73b0\u51fa\u4e86\u968f\u673a\u7b97\u6cd5\u7684\u6982\u5ff5\uff0c\u540c\u6837\u662f\u6c42\u51c6\u786e\u89e3\u7684\u8fd1\u4f3c\u89e3\uff0c\u4e24\u8005\u6709\u4f55\u533a\u522b\u5462\uff1f</p> hint: \u6700\u574f\u60c5\u51b5 <p>\u8fd1\u4f3c\u7b97\u6cd5\u548c\u968f\u673a\u7b97\u6cd5\u6700\u5927\u7684\u533a\u522b\u5c31\u662f\uff0c\u5f53\u6211\u4eec\u8bbe\u8ba1\u3001\u5206\u6790\u3001\u8ba8\u8bba\u8fd1\u4f3c\u7b97\u6cd5\u7684\u65f6\u5019\uff0c\u6211\u4eec\u5173\u6ce8\u7684\u90fd\u662f\u5b83\u7684\u6700\u574f\u60c5\u51b5\u3002\u4e5f\u5c31\u662f\u8bf4\uff0c\u8fd1\u4f3c\u7b97\u6cd5\u662f\u5b8c\u5168\u53ef\u63a7\u7684\uff0c\u800c\u7eaf\u7cb9\u7684\u968f\u673a\u7b97\u6cd5\u5219\u662f\u901a\u8fc7\u6982\u7387\u6765\u51cf\u5c11\u574f\u60c5\u51b5\u51fa\u73b0\u7684\u53ef\u80fd\uff0c\u5e76\u6ca1\u6709\u4e25\u683c\u7684\u7ea6\u675f\u3002\u8fd1\u4f3c\u7b97\u6cd5\u6700\u574f\u4e5f\u5c31\u574f\u5230 \\(\\rho\\)\uff0c\u800c\u968f\u673a\u7b97\u6cd5\u6700\u574f\u53ef\u4ee5\u574f\u5230\u6d77\u62c9\u9c81\u5927\u9646\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec11/#\u8fd1\u4f3c\u8303\u5f0f","title":"\u8fd1\u4f3c\u8303\u5f0f","text":"<p>links</p> <p>Wikipedia: https://en.wikipedia.org/wiki/Polynomial-time_approximation_scheme</p> <p>\u8fd1\u4f3c\u8303\u5f0f(approximation scheme)\u6307\u7684\u662f\u5bf9\u4e8e\u67d0\u4e2a\u4f18\u5316\u95ee\u9898\u7684\u4e00\u65cf\u76f8\u540c\u6a21\u5f0f\u7684\u7b97\u6cd5\uff0c\u5b83\u4eec\u6ee1\u8db3\u5bf9\u4e8e\u786e\u5b9a\u7684 \\(\\epsilon &gt; 0\\)\uff0c\u7b97\u6cd5\u7684\u8fd1\u4f3c\u6bd4\u4e3a \\(1+\\epsilon\\)\u3002</p> <p>\u53ef\u4ee5\u7c97\u7cd9\u5730\u7406\u89e3\u4e3a\uff1a\u201c\u8303\u5f0f\u201d\u662f\u4e00\u4e2a\u8f93\u51fa\u4e3a\u7b97\u6cd5\u7684\u7279\u6b8a\u51fd\u6570\uff0c\u800c \\(\\epsilon\\) \u662f\u201c\u8303\u5f0f\u201d\u7684\u4e00\u4e2a\u53c2\u6570\uff0c\u5bf9\u4e8e\u7279\u5b9a\u7684 \\(\\epsilon\\)\uff0c\u201c\u8303\u5f0f\u201d\u8f93\u51fa\u4e00\u4e2a\u7279\u5b9a\u7684\u7b97\u6cd5\uff08\u8fd9\u4e9b\u7b97\u6cd5\u6709\u7740\u76f8\u540c\u7684\u6a21\u5f0f\uff09\uff0c\u800c\u8fd9\u4e9b\u201c\u8303\u5f0f\u201d\u8f93\u51fa\u7684\u7b97\u6cd5\uff0c\u90fd\u89e3\u51b3\u540c\u4e00\u4e2a\u95ee\u9898\uff0c\u5e76\u4e14\u5bf9\u4e8e\u4efb\u610f\u56fa\u5b9a\u7684 \\(\\epsilon\\) \u5176\u8fd1\u4f3c\u6bd4\u4e3a \\(1+\\epsilon\\)\u3002</p> <p>\u800c\u5173\u4e8e \\(\\epsilon &gt; 0\\) \u8fd9\u4e2a\u7ea6\u675f\uff0c\u662f\u56e0\u4e3a\u8fd1\u4f3c\u6bd4\u5fc5\u5b9a\u5927\u4e8e 1\u3002</p> <p>\u800c\u6b64\u65f6\uff0c\u8fd9\u4e00\u65cf\u7684\u7b97\u6cd5\u7684\u590d\u6742\u5ea6\u53ef\u4ee5\u8868\u793a\u4e3a \\(O(f(n, \\epsilon))\\)\uff0c\u5982 \\(O(n^{2/\\epsilon}), O((\\frac{1}{\\epsilon})^2n^3)\\)\u3002\u5f53 \\(f(n, \\epsilon)\\) \u5173\u4e8e \\(n\\) \u662f\u591a\u9879\u5f0f\u65f6\uff0c\u6211\u4eec\u79f0\u5176\u4e3a\u591a\u9879\u5f0f\u65f6\u95f4\u8fd1\u4f3c\u8303\u5f0f(polynomial-time approximation scheme, PTAS)\u3002\u5f53 \\(f(n, \\epsilon)\\) \u5173\u4e8e \\(n\\) \u548c \\(\\frac{1}{\\epsilon}\\) \u90fd\u662f\u591a\u9879\u5f0f\u65f6\uff0c\u6211\u4eec\u79f0\u5176\u4e3a\u5b8c\u5168\u591a\u9879\u5f0f\u65f6\u95f4\u8fd1\u4f3c\u8303\u5f0f(fully polynomial-time approximation scheme, FPTAS)\u3002</p> <p>\u4e3a\u4ec0\u4e48\u8981\u533a\u5206 PTAS \u548c FPTAS \u5462\uff1f\u6211\u4eec\u89c2\u5bdf \\(\\epsilon\\) \u5bf9\u7b97\u6cd5\u7684\u5f71\u54cd\uff1a\u968f\u7740 \\(\\epsilon\\) \u7684\u51cf\u5c0f\uff0c\u8fd1\u4f3c\u6bd4\u9010\u6e10\u53d8\u5c0f\uff0c\u5373\u51c6\u786e\u5ea6\u63d0\u9ad8\uff1b\u800c \\(\\frac{1}{\\epsilon}\\) \u53d8\u5927\uff0c\u800c\u901a\u5e38\u6765\u8bf4 \\(\\frac{1}{\\epsilon}\\) \u4e0e\u7b97\u6cd5\u590d\u6742\u5ea6\u90fd\u662f\u6b63\u76f8\u5173\u7684\uff0c\u56e0\u6b64\u4f1a\u5bfc\u81f4\u7b97\u6cd5\u590d\u6742\u5ea6\u5347\u9ad8\u3002\u5982\u679c\u8bf4\u8fd9\u4e2a\u8fd1\u4f3c\u8303\u5f0f\u662f FPTAS\uff0c\u90a3\u4e48\u4e3a\u4e86\u63d0\u9ad8\u51c6\u786e\u5ea6\u800c\u7f29\u5c0f \\(\\epsilon\\)\uff0c\u5bfc\u81f4\u7684\u590d\u6742\u5ea6\u53d8\u5316\u662f\u76f8\u5bf9\u53ef\u63a5\u53d7\u7684\uff08\u591a\u9879\u5f0f\u7ea7\u7684\u53d8\u5316\uff0c\u5982 \\((\\frac{1}{\\epsilon})^2n^3\\) \u5173\u4e8e \\(\\frac{1}{\\epsilon}\\) \u662f\u591a\u9879\u5f0f\u7ea7\u7684\uff09\uff1b\u7136\u800c\u5982\u679c\u5b83\u4e0d\u662f FPTAS\uff0c\u90a3\u4e48 \\(\\epsilon\\) \u7684\u7f29\u5c0f\u53ef\u80fd\u5e26\u6765\u6050\u6016\u7684\u590d\u6742\u5ea6\u589e\u52a0\uff08\u5982 \\(n^{2/\\epsilon}\\) \u5173\u4e8e \\(\\epsilon\\) \u662f\u6307\u6570\u7ea7\u7684\uff09\u3002</p> <p>\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u4ee5\u82e5\u5e72\u5177\u4f53\u4f8b\u5b50\u505a\u5206\u6790\uff0c\u4ee5\u4fbf\u66f4\u597d\u5730\u7406\u89e3\u8fd1\u4f3c\u7b97\u6cd5\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec11/#\u6848\u4f8b-approximate-bin-packing","title":"[\u6848\u4f8b] Approximate Bin Packing","text":"<p>links</p> <p>Wikipedia: https://en.wikipedia.org/wiki/Bin_packing</p> <p>\u88c5\u7bb1\u95ee\u9898\u6307\u7684\u662f\uff0c\u7ed9\u5b9a \\(N\\) \u4e2a item\uff0c\u7b2c \\(i\\in [1,N]\\) \u4e2a item \u7684 size \u4e3a \\(S_i \\in (0,1]\\)\uff0c\u4e00\u4e2a bin \u7684\u5927\u5c0f\u4e3a \\(1\\)\uff0c\u5c1d\u8bd5\u5bfb\u627e\u6700\u5c11\u7684\uff0c\u80fd\u591f\u88c5\u8f7d\u6240\u6709 item \u7684 bin \u7684\u6570\u91cf\u3002</p> \ud83c\udf30 \u4f8b\u5b50 <p>\u7ed9\u5b9a 7 \u4e2a item\uff0csize \u5206\u522b\u4e3a \\(0.2, 0.5, 0.4, 0.7, 0.1, 0.3, 0.8\\)\uff0c\u5219\u6700\u5c11\u9700\u8981 3 \u4e2a bin\uff08\u51c6\u786e\u89e3\uff09\uff1a</p> <ul> <li>bin 1: \\(0.2 + 0.8\\);</li> <li>bin 2: \\(0.7 + 0.3\\);</li> <li>bin 3: \\(0.4 + 0.1 + 0.5\\);</li> </ul> <p>\u8fd9\u662f\u4e00\u4e2a NP hard \u95ee\u9898\uff0c\u73b0\u5728\u6211\u4eec\u8003\u8651\u4e09\u79cd\u8fd1\u4f3c\u89e3\u6cd5\u3002\u9700\u8981\u6ce8\u610f\u7684\u662f\uff0c\u8fd9\u4e09\u79cd\u90fd\u662f\u5728\u7ebf(online)\u89e3\u6cd5\uff0c\u5373\u5904\u7406 \\(item_i\\) \u65f6\u6211\u4eec\u4e0d\u77e5\u9053 \\(item_{i+1}\\sim item_{N}\\) \u7684\u60c5\u51b5\u3002\u4e4b\u540e\u6211\u4eec\u4f1a\u518d\u8ba8\u8bba\u79bb\u7ebf(offline)\u505a\u6cd5\uff0c\u4e5f\u5c31\u662f\u6211\u4eec\u77e5\u9053\u6240\u6709 item \u7684\u60c5\u51b5\u4ee5\u540e\u518d\u7ed9\u51fa\u7b56\u7565\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec11/#online-next-fit-nf","title":"(online) Next Fit (NF)","text":"<p>links</p> <p>Wikipedia: https://en.wikipedia.org/wiki/Next-fit_bin_packing</p> <p>NF \u7b56\u7565\u603b\u662f\u9009\u62e9\u5f53\u524d\u6700\u540e\u4e00\u4e2a bin\uff0c\u82e5\u80fd\u591f\u5bb9\u7eb3\uff0c\u5219\u5c06\u5f53\u524d item \u653e\u5165\u5176\u4e2d\uff0c\u5426\u5219\u65b0\u5f00\u4e00\u4e2a bin\u3002</p> <p>NF \u7b56\u7565\u603b\u662f\u4f7f\u7528\u4e0d\u8d85\u8fc7 \\(2M-1\\) \u4e2a bin\uff0c\u5176\u4e2d \\(M\\) \u8868\u793a\u51c6\u786e\u89e3\u7684 \\(\\#bin\\)\u3002</p> proof for 2M-1 <p>\u6211\u4eec\u4ece NF \u7684\u7ed3\u679c\u51fa\u53d1\uff0c\u8bc1\u660e\u5f53 NF \u7684\u7ed3\u679c\u4e3a\u9700\u8981 \\(2M-1\\) \u6216 \\(2M\\) \u4e2a bin \u65f6\uff0c\u51c6\u786e\u89e3\u4e3a\u81f3\u5c11\u9700\u8981 \\(M\\) \u4e2a bin\u3002</p> <p>\u5047\u8bbe \\(S(B_i)\\) \u8868\u793a\u7b2c \\(i\\) \u4e2a bin \u7684 size\uff0c\u5219\u6839\u636e NF \u7684\u5b9a\u4e49\uff0c\u6709\uff1a\\(S(B_{i}) + S(B_{i+1}) &gt; 1\\)\uff08\u662f NF \u7684\u5fc5\u8981\u4e0d\u5145\u5206\u6761\u4ef6\uff09\u3002\u7a0d\u4f5c\u89e3\u91ca\uff0c\u4f7f\u7528\u53cd\u8bc1\u6cd5\uff0c\u5047\u8bbe \\(S(B_{i}) + S(B_{i+1}) \\leq 1\\)\uff0c\u8fd9\u8bf4\u660e\u65e0\u8bba \\(B_{i+1}\\) \u4e2d\u6709\u591a\u5c11 item\uff0c\u90fd\u4e00\u5b9a\u80fd\u653e\u8fdb \\(B_i\\)\uff0c\u800c\u8fd9\u4e0e NF \u201c\\(B_i\\) \u653e\u4e0d\u4e0b\u4e86\u624d\u5f00\u59cb\u653e \\(B_{i+1}\\)\u201d \u7684\u6027\u8d28\u76f8\u8fdd\u80cc\u3002\u4e8e\u662f\u6211\u4eec\u5c06\u6240\u6709\u6876\u4e24\u4e24\u914d\u5bf9\uff1a</p> <p>1.\u5f53 NF \u7684\u7ed3\u679c\u662f\u9700\u8981 \\(2M-1\\) \u4e2a bin \u65f6\uff1a</p> \\[ \\left\\{ \\begin{aligned}     S(B_1) + S(B_2) &amp;&gt; 1 \\\\     S(B_3) + S(B_4) &amp;&gt; 1 \\\\     \\vdots \\\\     S(B_{2M-3}) + S(B_{2M-2}) &amp;&gt; 1 \\\\     S(B_{2M-1}) &amp;\\leq 1 \\end{aligned} \\right. \\\\ \\begin{aligned}     &amp;\\therefore \\sum_{i=1}^{2M-1} &gt; \\sum_{i=1}^{2M-2} &gt; M-1 \\\\     &amp;\\therefore \\sum_{i=1}^{2M-1} \\geq M \\end{aligned} \\] <p>\u5373 item \u7684\u603b size \u81f3\u5c11\u4e3a M\uff0c\u5373\u81f3\u5c11\u9700\u8981 \\(M\\) \u4e2a bin\u3002</p> <p>2.\u800c\u5f53 NF \u7684\u7ed3\u679c\u662f\u9700\u8981 \\(2M\\) \u4e2a bin \u65f6\uff0c\u53ef\u4ee5\u8f6c\u5316\u4e3a \\(2M-1\\) \u7684\u60c5\u51b5\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec11/#online-first-fit-ff","title":"(online) First Fit (FF)","text":"<p>links</p> <p>Wikipedia: https://en.wikipedia.org/wiki/First-fit_bin_packing</p> <p>FF \u7b56\u7565\u603b\u662f\u9009\u62e9\u7b2c\u4e00\u4e2a\u80fd\u653e\u4e0b\u5f53\u524d item \u7684 bin\uff0c\u82e5\u6240\u6709 bin \u90fd\u65e0\u6cd5\u5bb9\u7eb3\u5f53\u524d item\uff0c\u5219\u65b0\u5f00\u4e00\u4e2a bin\u3002</p> <p>NF \u7b56\u7565\u603b\u662f\u4f7f\u7528\u4e0d\u8d85\u8fc7 \\(\\lfloor 1.7M \\rfloor\\) \u4e2a bin\uff0c\u5e76\u4e14\u5b58\u5728\u4e00\u65cf\u80fd\u5bf9\u8fb9\u754c\u53d6\u7b49\u7684\u8f93\u5165\uff0c\u5176\u4e2d \\(M\\) \u8868\u793a\u51c6\u786e\u89e3\u7684 \\(\\#bin\\)\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec11/#online-best-fit-bf","title":"(online) Best Fit (BF)","text":"<p>links</p> <p>Wikipedia: https://en.wikipedia.org/wiki/Best-fit_bin_packing</p> <p>BF \u7b56\u7565\u603b\u662f\u9009\u62e9\u80fd\u591f\u5bb9\u7eb3\u5f53\u524d item \u4e14\u5269\u4f59\u7a7a\u95f4\u6700\u5c0f\u7684 bin\uff08\u5373 tightest\uff09\uff0c\u82e5\u6240\u6709 bin \u90fd\u65e0\u6cd5\u5bb9\u7eb3\u5f53\u524d item\uff0c\u5219\u65b0\u5f00\u4e00\u4e2a bin\u3002</p> <p>NF \u7b56\u7565\u4e5f\u603b\u662f\u4f7f\u7528\u4e0d\u8d85\u8fc7 \\(\\lfloor 1.7M \\rfloor\\) \u4e2a bin\uff0c\u5e76\u4e14\u5b58\u5728\u4e00\u65cf\u80fd\u5bf9\u8fb9\u754c\u53d6\u7b49\u7684\u8f93\u5165\uff0c\u5176\u4e2d \\(M\\) \u8868\u793a\u51c6\u786e\u89e3\u7684 \\(\\#bin\\)\u3002</p> <p>\u867d\u7136\u5728\u7ebf\u505a\u6cd5\u7531\u4e8e\u5bf9\u4fe1\u606f\u628a\u63e1\u7684\u4e0d\u5168\u9762\uff0c\u5728\u4e0d\u7279\u6b8a\u6784\u9020\u8f93\u5165\u7684\u60c5\u51b5\u4e0b\u751a\u81f3\u51e0\u4e4e\u4e0d\u53ef\u80fd\u8fbe\u5230\u6700\u4f18\u89e3\uff0c\u4f46\u662f\u73b0\u5b9e\u4e16\u754c\u4e2d\u6709\u5f88\u591a\u80fd\u5efa\u6a21\u4e3a\u88c5\u7bb1\u95ee\u9898\u7684\u95ee\u9898\uff0c\u90fd\u8981\u6c42\u4f7f\u7528\u5728\u7ebf\u505a\u6cd5\u89e3\u51b3\u3002\u56e0\u6b64\uff0c\u7814\u7a76\u5728\u7ebf\u505a\u6cd5\u8fd8\u662f\u6709\u5176\u610f\u4e49\u7684\u3002</p> <p>\u6b64\u5916\uff0c\u5173\u4e8e\u5728\u7ebf\u505a\u6cd5\uff0c\u6709\u4e00\u4e2a\u7ed3\u8bba\uff1a</p> <p>theorem</p> <p>\u5bf9\u4e8e\u88c5\u7bb1\u95ee\u9898\uff0c\u5982\u679c\u9650\u5b9a\u4f7f\u7528\u5728\u7ebf\u505a\u6cd5\uff0c\u5219\u6700\u4f18\u7684\u8fd1\u4f3c\u89e3\u6cd5\uff0c\u5176\u6700\u574f\u60c5\u51b5\u7684\u7ed3\u679c\u4e5f\u81f3\u5c11\u9700\u8981\u51c6\u786e\u89e3\u7684 \\(\\frac{5}{3}\\)\u3002</p> <p>PPT \u4e0a\u7684\u539f\u8bdd\u662f\uff0c\u65e0\u8bba\u54ea\u79cd\u5728\u7ebf\u505a\u6cd5\u4e5f\u81f3\u5c11\u9700\u8981\u4f7f\u7528 \\(\\frac{5}{3}\\) \u7684\u51c6\u786e\u89e3\u7ed9\u51fa\u7684\u6570\u91cf\uff0c\u4f46\u662f\u663e\u7136\u8fd9\u4e2a \\(\\frac{5}{3}\\) \u662f\u9488\u5bf9\u6700\u574f\u89e3\u7684\u8ba8\u8bba\u3002\u56de\u987e\u300c\u8fd1\u4f3c\u7b97\u6cd5 v.s. \u968f\u673a\u7b97\u6cd5\u300d\u8fd9\u4e2a block \u91cc\u7684\u5185\u5bb9\uff0c\u6211\u4eec\u5206\u6790\u8fd1\u4f3c\u89e3\uff0c\u90fd\u662f\u9488\u5bf9\u5176\u6700\u574f\u60c5\u51b5\u6765\u8bf4\u7684\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec11/#offline-first-fit-decreasing-ffd","title":"(offline) First Fit Decreasing (FFD)","text":"<p>\u79bb\u7ebf\u505a\u6cd5\u7684\u4f18\u52bf\u5728\u4e8e\u5b83\u80fd\u591f\u83b7\u5f97\u6240\u6709 item \u7684\u4fe1\u606f\u4ee5\u6c42\u7edf\u7b79\u89c4\u5212\u3002\u8fd9\u91cc\u7ed9\u51fa\u7684\u8fd1\u4f3c\u505a\u6cd5\u662f\uff0c\u5c06 item \u6309\u7167 size \u964d\u5e8f\u6392\u5e8f\uff0c\u800c\u540e\u4f7f\u7528 FF\uff08\u6216 BF\uff0c\u7531\u4e8e\u5355\u8c03\u6027\uff0c\u4e24\u8005\u7b49\u4ef7\uff09\u3002</p> \ud83c\udf30 \u4f8b\u5b50 <p>\u7ed9\u5b9a 7 \u4e2a item\uff08\u540c\u4e4b\u524d\u7684 \ud83c\udf30\uff09\uff0c\u7ecf\u8fc7\u6392\u5e8f\u540e\uff0c\u5b83\u4eec\u7684 size \u5206\u522b\u4e3a $0.8, 0.7, 0.5, 0.4, 0.3, 0.2, 0.1\uff0c\u5219\u6700\u5c11\u9700\u8981 3 \u4e2a bin\uff08\u51c6\u786e\u89e3\uff09\uff1a</p> <ul> <li>bin 1: \\(0.8 + 0.2\\);</li> <li>bin 2: \\(0.7 + 0.3\\);</li> <li>bin 3: \\(0.5 + 0.4 + 0.1\\);</li> </ul> <p>FFD \u7b56\u7565\u603b\u662f\u4f7f\u7528\u4e0d\u8d85\u8fc7 \\(\\frac{11}{9}M + \\frac{6}{9}\\) \u4e2a bin\uff08\u4e3a\u5565\u5c31\u8fde wiki \u4e5f\u4e0d\u7ea6 6/9\uff09\uff0c\u5e76\u4e14\u5b58\u5728\u4e00\u65cf\u80fd\u5bf9\u8fb9\u754c\u53d6\u7b49\u7684\u8f93\u5165\uff0c\u5176\u4e2d \\(M\\) \u8868\u793a\u51c6\u786e\u89e3\u7684 \\(\\#bin\\)\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec11/#\u6848\u4f8b-knapsack-problem","title":"[\u6848\u4f8b] Knapsack Problem","text":"<p>link</p> <p>Wikipedia: https://en.wikipedia.org/wiki/Knapsack_problem</p> <p>\u4e00\u4e2a\u4e0e\u88c5\u7bb1\u95ee\u9898\u5f88\u50cf\u7684\u95ee\u9898\u662f\u80cc\u5305\u95ee\u9898\u3002\u5176\u5927\u81f4\u63cf\u8ff0\u5982\u4e0b\uff1a\u7ed9\u5b9a\u4e00\u4e2a\u5bb9\u91cf\u4e3a \\(M\\) \u7684\u80cc\u5305\uff0c\u4ee5\u53ca \\(N\\) \u4e2a item\uff0c\u7b2c \\(i\\) \u4e2a item \u7684\u91cd\u91cf\u4e3a \\(w_i\\)\uff0c\u5176\u5229\u6da6\u4e3a \\(p_i\\)\u3002\u8981\u6c42\u5728\u4e0d\u8d85\u8fc7\u80cc\u5305\u5bb9\u91cf\u7684\u524d\u63d0\u4e0b\uff0c\u4f7f\u5f97\u80cc\u5305\u4e2d\u7684\u5229\u6da6\u6700\u5927\u5316\u3002\uff08\u6211\u4e5f\u4e0d\u77e5\u9053\u4e3a\u4ec0\u4e48 PPT \u4e0a\u4f1a\u628a\u5bb9\u91cf\u548c\u91cd\u91cf\u5173\u8054\u8d77\u6765\uff0canyway\uff0c\u5bb9\u91cf\u9650\u5236\u4e86 item \u7684\u91cd\u91cf\u548c\u3002\uff09</p> <p>\u6ce8\u610f</p> <p>\u6216\u8bb8\u5728\u5b66\u4e60 dp \u7684\u65f6\u5019\u4f60\u5df2\u7ecf\u63a5\u89e6\u8fc7\u80cc\u5305\u95ee\u9898\u4e86\uff0c\u4f46\u662f\u8bf7\u6ce8\u610f\uff0c\u6211\u4eec\u8fd9\u91cc\u8ba8\u8bba\u7684\u80cc\u5305\u95ee\u9898\u6709\u4e00\u4e2a\u975e\u5e38\u91cd\u8981\u7684\u7279\u70b9\u5c31\u662f\uff0c\u5bb9\u91cf\u548c\u5229\u6da6\u90fd\u662f\u5b9e\u6570\uff0c\u66f4\u76f4\u767d\u7684\u6765\u8bf4\uff0c\u4f60\u6ca1\u529e\u6cd5\u901a\u8fc7\u5c06\u5bb9\u91cf\u6216\u5229\u6da6\u4f5c\u4e3a\u72b6\u6001\u6765 dp \u6c42\u51c6\u786e\u89e3\u3002</p> <p>\u800c\u6839\u636e\u6bcf\u4e00\u4e2a\u7269\u54c1\u80fd\u5426\u81ea\u7531\u62c6\u5206\uff0c\u80cc\u5305\u95ee\u9898\u5206\u4e3a fractional version \u548c 0-1 version \u4e24\u7c7b\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec11/#fractional-version","title":"Fractional Version","text":"<p>\u5982\u679c\u6211\u4eec\u8bb0 \\(x_i\\in[0,1]\\) \u4e3a\u7b2c \\(i\\) \u4e2a item \u7684\u9009\u4e2d\u91cf\uff08\u5373\u5047\u8bbe item \u90fd\u662f\u8fde\u7eed\u53ef\u5206\u7684\uff09\uff0c\u5219\u7ea6\u675f\u6761\u4ef6\u53ef\u4ee5\u8868\u8ff0\u4e3a \\(\\sum_{i}^N w_ix_i \\leq M\\)\uff0c\u73b0\u5728\u6c42 \\(\\sum_{i}^{N} p_ix_i\\) \u7684\u6700\u5927\u503c\u3002</p> \ud83c\udf30 \u4f8b\u5b50 <p>\u5047\u8bbe\u73b0\u5728 \\(M = 20.0\\)\uff0c\u5e76\u4e14 \\(N = 3\\)\uff0c\u5206\u522b\u662f\uff1a</p> <ul> <li>item 1: \\(w_1 = 18.0, p_1 = 25.0\\); </li> <li>item 2: \\(w_2 = 15.0, p_2 = 24.0\\);</li> <li>item 3: \\(w_3 = 10.0, p_3 = 15.0\\);</li> </ul> <p>\u5219\u6700\u4f18\u89e3\u4e3a \\(x_1 = 0, x_2 = 1, x_3 = \\frac{1}{2}\\)\uff0c\u6b64\u65f6 \\(\\sum_{i}^{N} p_ix_i = 31.5\\)\u3002</p> <p>\u7531\u4e8e \\(x_i\\in[0,1]\\)\uff0c\u7ed9\u4e86\u6211\u4eec\u6781\u5927\u7684\u9009\u62e9\u81ea\u7531\uff0c\u6211\u4eec\u53ef\u4ee5\u9009\u62e9\u4efb\u610f\u591a\u7684\u67d0\u4e2a\u7269\u54c1\u3002\u90a3\u4e48\u975e\u5e38\u6734\u7d20\u7684\u4e00\u4e2a\u60f3\u6cd5\u5c31\u662f\uff0c\u5c3d\u53ef\u80fd\u591a\u5730\u9009\u62e9\u201c\u6027\u4ef7\u6bd4\u201d\u9ad8\u7684\u7269\u54c1\u3002\u4e5f\u5c31\u662f\u8bf4\uff0c\u6211\u4eec\u53ef\u4ee5\u6309\u7167 \\(\\frac{p_i}{w_i}\\)\uff08PPT \u79f0\u4e4b\u4e3a profit density\uff09\u964d\u5e8f\u6392\u5e8f\uff0c\u800c\u540e\u4ece\u5927\u5230\u5c0f\u4f9d\u6b21\u9009\u62e9\u7269\u54c1\uff0c\u76f4\u5230\u80cc\u5305\u88c5\u6ee1\u4e3a\u6b62\u3002</p> <p>\u4e0d\u8fc7\u8be5\u505a\u6cd5\u5df2\u7ecf\u662f\u51c6\u786e\u89e3\u4e86\uff0c\u6240\u4ee5\u6211\u4eec\u4e0d\u5bf9\u5b83\u8fdb\u884c\u5173\u4e8e\u8fd1\u4f3c\u7b97\u6cd5\u7684\u8ba8\u8bba\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec11/#0-1-version","title":"0-1 Version","text":"<p>\u76f8\u8f83\u4e8e fractional version\uff0c0-1 version \u8981\u6c42 \\(x_i \\in \\{0,1\\}\\)\uff0c\u6362\u53e5\u8bdd\u8bf4\u6bcf\u4e00\u4e2a\u7269\u54c1\u8981\u4e48\u9009\u8981\u4e48\u4e0d\u9009\u3002\u8fd9\u662f\u4e00\u4e2a\u7ecf\u5178\u7684 NPC \u95ee\u9898\uff0c\u6211\u4eec\u5c1d\u8bd5\u4f7f\u7528\u8fd1\u4f3c\u7b97\u6cd5\u6765\u6c42\u8f83\u4f18\u89e3\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec11/#\u8d2a\u5fc3\u505a\u6cd5","title":"\u8d2a\u5fc3\u505a\u6cd5","text":"<p>\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528\u8d2a\u5fc3\u7b97\u6cd5\uff0c\u8d2a\u5fc3\u7b56\u7565\u53ef\u4ee5\u662f\u603b\u662f\u9009\u53ef\u4ee5\u653e\u5f97\u4e0b\u7684\u3001\u8fd8\u6ca1\u653e\u5165\u4e2d\u7684\uff0c\u5229\u6da6\u6700\u5927\u7684\u6216 \\(\\frac{p_i}{w_i}\\) \u6700\u5927\u7684\u3002\u8fd9\u4e9b\u505a\u6cd5\u7684\u8fd1\u4f3c\u6bd4\u90fd\u662f 2\u3002</p> proof for rho = 2 <p>\u6211\u4eec\u7528 \\(p_\\text{max}\\) \u8868\u793a\u6240\u6709 item \u4e2d\u6700\u5927\u7684\u5229\u6da6\uff0c\u7528 \\(P_\\text{optimal}\\) \u8868\u793a\u51c6\u786e\u89e3\uff0c\\(P_\\text{greedy}\\) \u8868\u793a\u6211\u4eec\u4f7f\u7528\u8d2a\u5fc3\u505a\u6cd5\u5f97\u5230\u7684\u7b54\u6848\u3002\u5728\u8be5\u95ee\u9898\u4e2d\uff0c\u8fd1\u4f3c\u6bd4\u7684\u8ba1\u7b97\u8868\u8fbe\u5f0f\u4e3a\uff1a</p> \\[ \\rho = \\max(     \\frac{P_\\text{optimal}}{P_\\text{greedy}},     \\frac{P_\\text{greedy}}{P_\\text{optimal}} ) \\] <p>\u4e0b\u9762\u662f\u8bc1\u660e\u8fc7\u7a0b\uff1a</p> \\[ \\left\\{ \\begin{aligned}     &amp; p_\\text{max} \\leq P_\\text{greedy} &amp; (1)\\\\     &amp; P_\\text{optimal} \\leq P_\\text{greedy} + p_\\text{max} &amp; (2) \\end{aligned} \\right. \\] <p>\u5c06 \\((1)\\) \u5f0f\u4e24\u4fa7\u540c\u9664\u4ee5 \\(P_\\text{greedy}\\) \u5f97\uff1a</p> \\[ \\frac{p_\\text{max}}{P_\\text{greedy}} \\leq 1 \\quad (3) \\] <p>\u5c06 \\((2)\\) \u5f0f\u4e24\u4fa7\u540c\u9664\u4ee5 \\(P_\\text{greedy}\\)\uff0c\u5e76\u4ee3\u5165 \\((3)\\) \u5f97\uff1a</p> \\[ \\frac{P_\\text{optimal}}{P_\\text{greedy}} \\leq 1 + \\frac{p_\\text{max}}{P_\\text{greedy}} \\leq 2 \\] <p>PPT \u7684\u8bc1\u660e\u8fc7\u7a0b\u4e2d\u8fd8\u6709\u4e00\u4e2a\u4e0d\u7b49\u5f0f\uff0c\u867d\u7136\u6210\u7acb\uff0c\u4f46\u662f\u597d\u50cf\u6ca1\u8d77\u5230\u4f5c\u7528\uff0c\u6211\u5c31\u6269\u5c55\u4e00\u4e0b\u5199\u5728\u8fd9\u91cc\u6c42\u4e2a\u773c\u719f\u4e86\uff1a</p> \\[ p_\\text{max} \\leq P_\\text{greedy} \\leq P_\\text{optimal} \\leq P_\\text{frac} \\] <p>\u5176\u4e2d \\(P_\\text{frac}\\) \u6307\u7684\u662f\u540c\u6837\u7684\u6570\u636e\u4e0b fractional version \u7684\u7b54\u6848\u3002</p> <p>\u8865\u5145\u7ed3\u8bba\uff1a\u80cc\u5305\u95ee\u9898\u5177\u6709 FPTAS\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec11/#\u52a8\u6001\u89c4\u5212\u505a\u6cd5","title":"\u52a8\u6001\u89c4\u5212\u505a\u6cd5","text":"<p>\uff08\u771f\u662f\u6df7\u4e71\uff09</p> \\[ W_{i,p} = \\text{the minimum weight of a collection from } \\{1, \u2026, i\\} \\text{ with total profit being  exactly } p \\\\ W_{i,p} = \\left\\{ \\begin{aligned}     &amp;\\infty &amp;&amp; i = 0 \\\\     &amp;W_{i-1, p} &amp;&amp; p_i &gt; p \\\\     &amp;\\min\\{W_{i-1, p}, w_i + W_{i-1, p-p_i}\\} &amp;&amp; otherwise         \\end{aligned} \\right.\\\\ i = 1, ..., n; p = 1, ..., n\\cdot p_\\text{max} \\\\ O(n^2p_\\text{max}) \\] <p>\u5982\u679c \\(p_\\text{max}\\) \u5f88\u5927\uff0c\u53ef\u4ee5\u8003\u8651\u5c06\u5b83\u4eec\u8fd1\u4f3c\u53d6\u6574\uff0c\u7c7b\u4f3c\u4e8e\u5c06\u6d6e\u70b9\u6570\u5411\u4e0a\u53d6\u6574\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec11/#\u6848\u4f8b-the-k-center-problem","title":"[\u6848\u4f8b] The K-center Problem","text":"<p>link</p> <p>Berkeley's: https://ugtcs.berkeley.edu/src/approx-sp19/scribe-notes-2.pdf</p> <p>\uff08\u4e8c\u7ef4\uff09K \u4e2d\u5fc3\u95ee\u9898\u6307\uff1a\u7ed9\u5b9a\u5e73\u9762\u4e0a\u7684\u4e00\u7cfb\u5217 site\uff08\u5373\u70b9\uff09\uff0c\u5728\u5e73\u9762\u4e2d\u627e\u51fa \\(k\\) \u4e2a\u4e0d\u540c\u7684 center\uff0c\u8bb0 \\(site_i\\) \u5230\u79bb\u5b83\u6700\u8fd1\u7684 center \u7684\u8ddd\u79bb\u4e3a \\(dis_i\\)\uff0c\u6c42 \\(\\max \\{dis_i\\}\\) \u7684\u6700\u5c0f\u503c\u3002</p> <p>\u6570\u5b66\u8bed\u8a00\u8868\u8fbe</p> <p>\u8bbe \\(C = \\{c_1, c_2, ..., c_k\\}\\) \u4e3a \\(k\\) \u4e2a center\uff0c\\(S = \\{s_1, s_2, ..., s_n\\}\\) \u4e3a \\(n\\) \u4e2a site\uff0c\u6211\u4eec\u5b9a\u4e49 site \u5230\u5173\u4e8e center \u7684\u96c6\u5408 \\(C\\) \u7684\u8ddd\u79bb\u4e3a\uff1a</p> \\[ dis(s_i, C) = \\min_{c_i\\in C} \\{ dis(s_i, c_i) \\} \\] <p>\u5373 \\(s_i\\) \u5230\u8ddd\u79bb\u5b83\u6700\u8fd1\u7684 center \u7684\u8ddd\u79bb\u3002</p> <p>\u5b9a\u4e49\u6700\u5927\u7684\u6700\u5c0f\u8986\u76d6\u534a\u5f84\u4e3a\uff1a</p> \\[ r(C) = \\max_{s_i\\in S} \\{ dis(s_i, C) \\} \\\\ \\] <p>\u73b0\u5728\u8981\u5bfb\u627e\u4e00\u4e2a \\(C\\) \u4f7f\u5f97 \\(r(C)\\) \u6700\u5c0f\uff08\\(|C| = k\\)\uff09\u3002</p> <p>\u5f88\u7ed5\uff0c\u975e\u5e38\u7ed5\u3002\u63a5\u4e0b\u6765\u5f00\u59cb\u8bf4\u4eba\u8bdd\u3002</p> <p>\u5e73\u9762\u7684\u95ee\u9898\u6211\u4eec\u5c31\u7528\u5e73\u9762\u7684\u601d\u8def\u6765\u770b\uff0c\u5c31\u662f\u4e00\u4e2a\u5e73\u9762\u4e0a\u6709\u4e00\u5806\u70b9\uff0c\u73b0\u5728\u6211\u8981\u5728\u4e0a\u9762\u627e \\(k\\) \u4e2a\u4e2d\u5fc3\u53bb\u753b\u5706\uff0c\u4f7f\u5f97\u8fd9 \\(k\\) \u4e2a\u5706\u80fd\u8986\u76d6\u6240\u6709\u7684\u70b9\u3002\u73b0\u5728\u8981\u6c42\u6700\u5927\u7684\u90a3\u4e2a\u5706\u7684\u534a\u5f84\u6700\u5c0f\u80fd\u591a\u5c0f\u3002</p> \u5173\u4e8e\u8ddd\u79bb <p>PPT \u4e0a\u5bf9\u8ddd\u79bb\u505a\u4e86\u66f4\u8fdb\u4e00\u6b65\u7684\u8bf4\u660e\uff0c\u4f46\u662f\u5176\u5b9e\u5e76\u4e0d\u662f\u8fd9\u4e2a\u95ee\u9898\u7684\u91cd\u70b9\uff0c\u4f46\u662f\u4e3a\u4e86\u4e25\u8c28\u6027\uff0c\u6211\u8fd8\u662f\u5728\u8fd9\u91cc\u653e\u4e0a\u4e09\u6761\u6027\u8d28\uff1a</p> <p>3 property of 'distance'</p> \\[ \\begin{aligned}     &amp; dis(x,x) = 0 &amp;&amp; \\text{(identity)} \\\\     &amp; dis(x,y) = dis(y,x) &amp;&amp; \\text{(symmetry)} \\\\     &amp; dis(x,y) \\leq dis(x,z) + dis(z,y) &amp;&amp; \\text{(triangle inequality)} \\end{aligned} \\] <p>\u788e\u788e\u5ff5</p> <p>\u8fd9\u4e2a\u4e1c\u897f\u548c\u805a\u7c7b\u6709\u70b9\u50cf\u3002\u4e3b\u8981\u96be\u70b9\u5c31\u5728\u4e8e\uff0c\u6211\u4eec\u4e0d\u77e5\u9053\u5e94\u8be5\u4ee5\u4f55\u79cd\u7b56\u7565\u53bb\u8986\u76d6\u8fd9\u4e9b\u70b9\uff0c\u8981\u662f\u628a\u4e24\u4e2a\u8ddd\u79bb\u5f88\u8fdc\u7684\u70b9\u5212\u5728\u540c\u4e00\u4e2a\u5706\u5185\uff0c\u90a3\u7b54\u6848\u80af\u5b9a\u5c0f\u4e0d\u4e86\u3002</p> <p>\u63a5\u4e0b\u6765\u6211\u4eec\u6765\u5c1d\u8bd5\u89e3\u51b3\u7684\u8fd9\u4e2a\u95ee\u9898\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec11/#naive-greedy","title":"Naive Greedy","text":"<p>\u4e00\u4e2a\u505a\u6cd5\u662f\uff0c\u6211\u4eec\u6bcf\u6b21\u90fd\u9009\u62e9\u6700\u53ef\u80fd\u6210\u4e3a\u4e2d\u5fc3\u7684\u90a3\u4e2a\u70b9\uff0c\u5177\u4f53\u6765\u8bf4\uff1a</p> <ol> <li>\u5982\u679c\u662f\u7b2c\u4e00\u4e2a\u70b9\uff0c\u5c31\u9009\u53d6\u6240\u6709\u70b9\u7684\u4e2d\u5fc3\uff1b</li> <li>\u5982\u679c\u4e0d\u662f\u7b2c\u4e00\u4e2a\u70b9\uff0c\u5c31\u9009\u53d6\u80fd\u4e00\u4e2a\u6700\u80fd\u8ba9 \\(r(C)\\) \u4e0b\u964d\u7684\uff1b</li> </ol> <p>\u8fd9\u4e2a\u505a\u6cd5\u7684 bug \u6bd4\u8f83\u5927\uff0c\u5047\u8bbe\u6211\u4eec\u7684\u70b9\u662f\u805a\u7c7b\u975e\u5e38\u660e\u663e\u7684\u4e24\u4e2a\u70b9\u4e91\uff0c\u90a3\u4e48\u7b2c\u4e00\u4e2a\u70b9\u5c31\u4f1a\u843d\u5728\u4e24\u4e2a\u70b9\u4e91\u4e4b\u95f4\uff0c\u8fd9\u5f88\u8822\uff0c\u6240\u4ee5\u6211\u4eec\u4e0d\u6d6a\u8d39\u8fc7\u591a\u65f6\u95f4\u5728\u8fd9\u4e2a\u65b9\u6cd5\u4e0a\u3002</p> <p>\u6ce8\u610f\uff0c\u968f\u7740 center \u7684\u589e\u52a0\uff0c\u539f\u6765\u4ee5 \\(c_i\\) \u4e3a center \u7684 site \u5f88\u53ef\u80fd\u4ee5\u6700\u65b0\u63d2\u5165\u7684 \\(c_j\\) \u4e3a center\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec11/#2r-greedy","title":"2r-Greedy","text":"<p>\u65e2\u7136\u6b63\u5411\u505a\u5f88\u56f0\u96be\uff0c\u90a3\u6211\u4eec\u80fd\u4e0d\u80fd\u53cd\u7740\u505a\u5462\uff1f\u6709\u4e00\u79cd\u5957\u8def\u53eb\u4e8c\u5206\u7b54\u6848\uff0c\u5373\u5148\u731c\u7b54\u6848\uff0c\u518d\u9a8c\u8bc1\u662f\u5426\u662f\u7b54\u6848\u3002\u5728\u8fd9\u4e2a\u95ee\u9898\u4e2d\u6211\u4eec\u53ef\u4ee5\u8fc1\u79fb\u8fd9\u4e2a\u601d\u60f3\uff0c\u5373\u5148\u731c\u4e00\u4e2a \\(r\\)\uff0c\u7136\u540e\u5c1d\u8bd5\u7528 \\(k\\) \u4e2a\u534a\u5f84\u4e3a \\(r\\) \u7684\u5706\u53bb\u8986\u76d6\u5269\u4e0b\u7684\u6240\u6709\u70b9\u3002</p> <p>\u66f4\u5177\u4f53\u7684\u6765\u8bf4\uff0c\u5047\u8bbe\u51c6\u786e\u89e3\u5bf9\u5e94\u7684\u4e00\u4e2a center \u96c6\u5408\u4e3a \\(C^*\\)\uff0c\u90a3\u4e48 \\(\\forall r(C_x) \\geq r(C^*)\\) \u7684 \\(C_x\\) \u90fd\u5fc5\u5b9a\u5b58\u5728\u8986\u76d6\u65b9\u6848\uff1b\u53cd\u8fc7\u6765\u8bf4\uff0c\u5982\u679c\u6211\u4eec\u80fd\u591f\u9a8c\u8bc1\u5bf9\u4e8e \\(C_x\\) \u80fd\u591f\u8986\u76d6\u6240\u6709\u7684\u70b9\uff0c\u90a3\u4e48\u5c31\u53ef\u4ee5\u7ea6\u675f\u51c6\u786e\u89e3 \\(r(C^*) \\leq r(C_x)\\)\u3002</p> <p>\u5982\u4f55\u201c\u9a8c\u8bc1\u201d</p> <p>\u53ef\u662f\uff0c\u4ed4\u7ec6\u4e00\u60f3\u6211\u4eec\u53d1\u73b0\uff0c\u4e8c\u5206\u7b54\u6848\u7684\u8fc7\u7a0b\u4e2d\uff0c\u201c\u9a8c\u8bc1\u5bf9\u4e8e \\(C_x\\) \u80fd\u591f\u8986\u76d6\u6240\u6709\u7684\u70b9\u201d\u8fd9\u4ef6\u4e8b\u4e5f\u4e0d\u597d\u505a\uff0c\u867d\u7136\u6211\u4eec\u6709\u534a\u5f84\uff0c\u4f46\u662f\u6211\u4eec\u4e5f\u5f88\u96be\u627e\u5230\u4e00\u4e2a\u6700\u597d\u7684\u65b9\u6848\u6765\u8986\u76d6\u6240\u6709\u7684\u70b9\u3002</p> hint: \u8fd1\u4f3c\u7b97\u6cd5 <p>\u4e8e\u662f\u6211\u4eec\u7684\u8fd1\u4f3c\u7b97\u6cd5\u5c31\u53ef\u4ee5\u5927\u5c55\u62f3\u811a\u4e86\u3002\u4f46\u662f\u9700\u8981\u6ce8\u610f\uff0c\u8fd9\u91cc\u6240\u8c13\u7684\u8fd1\u4f3c\u7b97\u6cd5\uff0c\u6307\u7684\u662f\u4f7f\u7528\u4e8c\u5206\u7b54\u6848\u6c42\u89e3 \\(r(C)\\) \u8fd9\u4e2a\u7b97\u6cd5\uff0c\u800c\u975e\u5224\u65ad \\(k\\) \u4e2a\u534a\u5f84\u4e3a \\(r\\) \u7684\u5706\u80fd\u5426\u8986\u76d6\u6240\u6709\u70b9\u7684\u7b97\u6cd5\u3002\u8fd9\u4e00\u70b9\u975e\u5e38\u91cd\u8981\uff01</p> <p>\u800c\u5173\u4e8e\u7b97\u6cd5\u5177\u4f53\u5982\u4f55\u64cd\u4f5c\uff0c\u8bf7\u63a5\u7740\u770b\u3002 </p> <p>\u9996\u5148\uff0c\u6211\u4eec\u518d\u6b21\u68b3\u7406\u4e00\u4e0b\u8fd9\u4e2a\u7b97\u6cd5\uff0c\u5b83\u5305\u542b\u5185\u5916\u4e24\u5c42\uff0c\u9996\u5148\u5916\u90e8\u901a\u8fc7\u5728\u7b54\u6848\u7684\u5019\u9009\u533a\u95f4\uff08\u5373 \\((0, r_\\text{max}]\\)\uff0c\\(r_\\text{max}\\) \u4e3a\u6700\u8fdc\u7684\u4e24\u4e2a\u70b9\u7684\u8ddd\u79bb\uff09\u4e8c\u5206\u5019\u9009\u503c\uff0c\u63a5\u7740\u901a\u8fc7\u5224\u5b9a\u7b97\u6cd5\u6765\u5224\u5b9a\u63a5\u4e0b\u6765\u7684\u4e8c\u5206\u65b9\u5411\u3002</p> <p>\u7136\u800c\uff0c\u7531\u4e8e\u6211\u4eec\u5f88\u96be\u5728\u591a\u9879\u5f0f\u65f6\u95f4\u5b9e\u73b0\u51c6\u786e\u7684\u201c\u5224\u5b9a\u201d\uff0c\u6240\u4ee5\u6211\u4eec\u91c7\u53d6\u8fd9\u6837\u4e00\u4e2a\u542f\u53d1\u5f0f\u7684\u7b56\u7565\u6765\u8fdb\u884c\u5bbd\u6cdb\u7684\u5fc5\u8981\u6761\u4ef6\u7b5b\u9009\uff1a</p> <p>\u6d41\u7a0b\u63cf\u8ff0</p> <p>\u8bbe \\(C_x\\) \u8868\u793a\u9009\u4e2d\u7684 center\uff0c\\(S_x\\) \u8868\u793a\u5c1a\u672a\u88ab\u4efb\u4f55\u5706\u8986\u76d6\u7684 site\uff0c\\(r_x\\) \u8868\u793a\u5f53\u524d\u4e8c\u5206\u51fa\u6765\u7684\uff0c\u8981\u6211\u4eec\u5224\u65ad\u7684\u534a\u5f84\uff0c\\(S\\) \u4f9d\u7136\u8868\u793a\u6240\u6709 site \u7684\u96c6\u5408\uff1a</p> <ol> <li>\u521d\u59cb\u5316 \\(C_x = \\emptyset\\)\uff1b</li> <li>\u5f53 \\(S_x \\not = \\emptyset\\) \u65f6\uff08\u5373\u8fd8\u6709\u70b9\u6ca1\u88ab\u8986\u76d6\u65f6\uff09\uff0c\u91cd\u590d\u8fd9\u4e9b\u64cd\u4f5c\uff1a<ol> <li>\u968f\u673a\u9009\u53d6\u4e00\u4e2a site \\(s_i \\in S_x\\)\uff0c\u5c06\u5176\u63d2\u5165 \\(C_x\\)\uff08\u5373\u5c06 \\(s_i\\) \u5f53\u4f5c\u4e00\u4e2a center\uff09\uff0c\u5e76\u4ece \\(S_x\\) \u4e2d\u5c06 \\(s_i\\) \u5220\u9664\uff08\u5373 \\(s_i\\) \u5fc5\u5b9a\u88ab\u8986\u76d6\uff09\uff1b</li> <li>\u5220\u9664 \\(S_x\\) \u4e2d\u6240\u6709\u8ddd\u79bb \\(s_i\\) \u4e0d\u8db3 \\(r_x\\) \u7684\u70b9\uff08\u5373\u5220\u9664\u6ee1\u8db3 \\(dis(s_i, s_j) \\leq r_x\\) \u7684\u6240\u6709 \\(s_k \\in S_x\\)\uff09\uff1b</li> </ol> </li> <li>\u5f53\u6240\u6709\u70b9\u90fd\u88ab\u8986\u76d6\u540e\uff1a<ol> <li>\u5982\u679c \\(|C_x| \\leq k\\)\uff0c\u5219\u8fd4\u56de yes\uff1b</li> <li>\u5426\u5219\u8fd4\u56de no\uff1b</li> </ol> </li> </ol> <p>\u5982\u679c\u8fd4\u56de yes\uff0c\u5219\u4e0b\u4e00\u4e2a \\(r_x\\) \u5e94\u5f53\u53d6\u66f4\u5c0f\u7684 \\(r_x\\)\uff1b\u5982\u679c\u8fd4\u56de no\uff0c\u4e0b\u4e00\u6b21\u5e94\u8be5\u53d6\u66f4\u5927\u7684 \\(r_x\\)\uff08\u7a0d\u5019\u4f1a\u89e3\u91ca\u4e3a\u4ec0\u4e48\uff09\u3002</p> <p>\u73b0\u5728\u5bf9\u5176\u505a\u8fdb\u4e00\u6b65\u89e3\u91ca\u3002\u8fd9\u662f\u4e00\u4e2a\u542f\u53d1\u5f0f\u7684\u505a\u6cd5\uff0c\u65e8\u5728\u6bcf\u6b21\u5bfb\u627e\u8fd8\u6ca1\u88ab\u8986\u76d6\u7684\u70b9\u4f5c\u4e3a\u65b0\u7684 center\uff0c\u7528\u4e00\u4e2a\u534a\u5f84\u4e3a \\(2r_x\\) \u7684\u5706\u53bb\u8986\u76d6\u5269\u4e0b\u7684\u70b9\u3002\u901a\u8fc7\u5224\u65ad\u8fd9\u6837\u6240\u9700\u8981\u7684 center \u6570\u91cf\u662f\u5426\u8d85\u8fc7 \\(k\\) \u6765\u5224\u65ad\u662f\u5426\u80fd\u591f\u8986\u76d6\u3002\u63a5\u4e0b\u6765\u5f88\u7ed5\uff0c\u8bf7\u4e00\u6b65\u4e00\u6b65\u7684\u770b\uff1a</p> <ol> <li>\u5f53\u8fd9\u4e2a\u542f\u53d1\u5f0f\u641c\u7d22\u6210\u529f\u65f6\uff0c\u8bf4\u660e \\(2r_x \\geq r(C^*)\\)\uff0c\u5373 \\(k\\) \u4e2a \\(2r_x\\) \u7684\u5706\u53ef\u4ee5\u8986\u76d6\u6240\u6709\u70b9\uff1b</li> <li>\u5f53\u8fd9\u4e2a\u542f\u53d1\u5f0f\u641c\u7d22\u5931\u8d25\u65f6\uff0c\u4e0d\u80fd\u8bf4\u660e \\(2r_x \\geq r(C^*)\\)\uff0c\u5373 \\(k\\) \u4e2a \\(2r_x\\) \u7684\u5706\u4e0d\u80fd\u8986\u76d6\u6240\u6709\u70b9\uff0c\u56e0\u4e3a\u542f\u53d1\u5f0f\u65b9\u6848\u5e76\u4e0d\u662f\u6700\u4f18\u65b9\u6848\uff1b\u4f46\u662f\u80fd\u8bf4\u660e\u5fc5\u5b9a\u4e0d\u5b58\u5728 \\(r_x\\) \u7684\u8986\u76d6\uff0c\u5373 \\(r_x \\leq r(C^*)\\)\uff08\u8bc1\u660e\u89c1\u4e0b\u65b9 lemma\uff09\uff1b</li> </ol> lemma <p>\u5047\u8bbe\u534a\u5f84\u4e3a \\(r\\)\uff0c\u4ee5 \\(c\\) \u4e3a\u5706\u5fc3\u7684\u5706 \\(C\\) \u8986\u76d6\u4e86 \\(S\\) \u4e2d\u7684\u6240\u6709\u70b9\u3002</p> <p>\u90a3\u4e48\uff0c\u5bf9\u4e8e\u56fa\u5b9a\u7684\u534a\u5f84 \\(r'\\)\uff0c\u8981\u60f3\u53d6\u4efb\u610f\u7684 \\(s_i \\in S\\) \u4e3a\u5706\u5fc3\uff0c\u5f62\u6210\u7684\u5706 \\(C_i\\)\uff0c\u603b\u662f\u80fd\u8986\u76d6 \\(S\\) \u4e2d\u7684\u6240\u6709\u70b9\uff0c\u5219 \\(r' \\geq 2r\\)\u3002</p> <p>lemma \u7684\u8bc1\u660e\u5c31\u4e0d\u5728\u8fd9\u91cc\u5c55\u5f00\u4e86\uff0c\u8bc1\u660e\u7684\u5173\u952e\u662f\u8003\u8651\u4e24\u70b9\u5206\u5e03\u5728\u76f4\u5f84\u4e24\u7aef\u7684\u60c5\u51b5\u3002</p> <p>\u8fd9\u4e2a\u5f15\u7406\u7684\u9644\u52a0\u7ed3\u8bba\u5c31\u662f\uff1a</p> \\[ \\forall i \\quad C \\subset C_i \\] <p>\u5373\u4ee5 \\(r\\) \u4e3a\u534a\u5f84\u7684\u6700\u4f18\u8986\u76d6\u5706\uff0c\u4e00\u5b9a\u80fd\u88ab\u4ee5\u4efb\u610f \\(s_i\\) \u4e3a\u5706\u5fc3\u3001\\(2r\\) \u4e3a\u534a\u5f84\u7684\u5706\u6240\u8986\u76d6\u3002</p> <p> </p> <p>\u5f53\u6211\u4eec\u53d1\u73b0\u6211\u4eec\u5904\u4e8e\u60c5\u51b5 <code>1.</code> \u65f6\uff0c\u6211\u4eec\u5f00\u5fc3\u7684\u53d1\u73b0\u6211\u4eec\u786e\u5b9e\u5f97\u5230\u4e86\u4e00\u4e2a\u8ddd\u79bb \\(r(C^*)\\) \u66f4\u8fd1\u7684\u4e0a\u754c \\(2r_x\\)\uff0c\u7531\u4e8e\u4e8c\u5206\u7684\u6027\u8d28\uff0c\u6211\u4eec\u6bcf\u6b21\u901a\u8fc7 <code>1.</code> \u786e\u5b9a\u7684\u4e0a\u754c\uff0c\u603b\u662f\u8d8a\u6765\u8d8a\u7d27\u7684\u3002</p> <p>\u5f53\u6211\u4eec\u5904\u4e8e\u60c5\u51b5 <code>2.</code> \u65f6\uff0c\u6211\u4eec\u4e0d\u77e5\u9053 \\(2r_x\\) \u548c \\(r(C^*)\\) \u7684\u5927\u5c0f\u5173\u7cfb\uff0c\u4f46\u662f\u77e5\u9053 \\(r_x\\) \u548c \\(r(C^*)\\) \u7684\u5173\u7cfb\uff0c\u7531\u4e8e\u4e8c\u5206\u7684\u6027\u8d28\uff0c\u6211\u4eec\u6bcf\u6b21\u901a\u8fc7 <code>2.</code> \u786e\u5b9a\u7684\u4e0b\u754c\uff0c\u4e5f\u603b\u662f\u8d8a\u6765\u8d8a\u7d27\u7684\u3002</p> <p>\u800c\u6700\u7ec8\uff0c\u6211\u4eec\u4f1a\u5f97\u5230\u4e00\u4e2a\u6700\u7ec8\u7684 \\(r_{x_0}\\)\uff0c\u6ee1\u8db3\uff1a\\(r_{x_0} \\leq r(C^*) \\leq 2r_{x_0}\\)\uff08\u5f0f\u4e2d\u54ea\u8fb9\u80fd\u53d6\u7b49\u53d6\u51b3\u4e8e\u6700\u540e\u843d\u5728 <code>1.</code> \u8fd8\u662f <code>2.</code>\uff09\u3002</p> <p>\u800c\u6211\u4eec\u6700\u7ec8\u7ed9\u51fa\u7684\u7b54\u6848\u662f \\(2r_{x_0}\\)\uff08\u56e0\u4e3a \\(r_{x_0}\\) \u4e0d\u6ee1\u8db3\u6761\u4ef6\uff0c\u4e0d\u662f\u89e3\uff0c\u66f4\u4e0d\u662f\u8fd1\u4f3c\u89e3\uff09\u3002</p> <p>\u73b0\u5728\uff0c\u6211\u4eec\u6765\u8ba1\u7b97\u8fd1\u4f3c\u6bd4\uff1a</p> \\[ \\begin{aligned}     &amp; \\begin{aligned}         \\because \\;\\;\\;         &amp; r_{x_0} \\leq r(C^*) \\leq 2r_{x_0} \\\\         &amp; \\frac{1}{2} \\leq \\frac{r(C^*)}{2r_{x_0}} \\leq 1 \\\\         &amp; 1 \\leq \\frac{2r_{x_0}}{r(C^*)} \\leq 2     \\end{aligned} \\\\     &amp; \\therefore \\; \\rho = \\max\\{             \\frac{ 2 r_{x_0} }{ r(C^*) },             \\frac{ r(C^*) }{ 2 r_{x_0} }         \\} = 2 \\end{aligned} \\]"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec11/#smarter-greedy","title":"Smarter Greedy","text":"<p>\u6211\u4eec\u5173\u6ce8\u5230\uff0c\u4e0a\u9762\u90a3\u4e2a\u505a\u6cd5\u603b\u662f\u968f\u673a\u7684\u9009\u53d6\u65b0\u7684 \\(c_i\\)\uff0c\u4f46\u662f\u5bf9\u4e8e center \u7684\u9009\u53d6\uff0c\u6211\u4eec\u5176\u5b9e\u53ef\u4ee5\u603b\u662f\u9009\u62e9\u8ddd\u79bb\u5df2\u6709\u7684 center \u6700\u8fdc\u7684\u70b9\uff0c\u6b64\u5916\uff0c\u5f53 \\(|C| &gt; k\\) \u65f6\uff0c\u6211\u4eec\u4e5f\u6ca1\u5fc5\u8981\u7ee7\u7eed\u505a\u4e86\u3002</p> <p>\u6d41\u7a0b\u63cf\u8ff0</p> <ol> <li>\u521d\u59cb\u5316 \\(C_x = \\emptyset\\)\uff0c\\(S_x = S\\)\uff1b</li> <li>\u968f\u673a\u9009\u53d6\u4e00\u4e2a site \\(s_i \\in S_x\\)\uff0c\u5c06\u5176\u63d2\u5165 \\(C_x\\)\uff0c\u5e76\u4ece \\(S_x\\) \u4e2d\u5c06 \\(s_i\\) \u5220\u9664\uff1b</li> <li>\u5f53 \\(|C_x| \\leq k\\) \u4e14 \\(S_x \\not = \\emptyset\\) \u65f6\uff0c\u91cd\u590d\u4ee5\u4e0b\u6b65\u9aa4\uff1a<ol> <li>\u9009\u53d6\u4e00\u4e2a site \\(s_i \\in S_x\\)\uff0c\u8fd9\u4e2a site \u6ee1\u8db3 \\(\\forall s_j \\in S_x \\quad dis(s_i, C_x) \\geq dis(s_j, C_x)\\)\uff08\u5373\u8fd9\u4e2a\u70b9\u662f\u8fd8\u6ca1\u88ab\u8986\u76d6\u7684\u70b9\u4e2d\u8ddd\u79bb \\(C_x\\) \u6700\u8fdc\u7684\u70b9\uff09\uff1b</li> <li>\u5c06 \\(s_i\\) \u63d2\u5165 \\(C_x\\)\uff0c\u5e76\u4ece \\(S_x\\) \u4e2d\u5c06 \\(s_i\\) \u5220\u9664\uff1b</li> </ol> </li> <li>\u5982\u679c \\(|C_x| \\leq k\\) \u4e14 \\(S_x = \\emptyset\\)\uff0c\u5219\u8fd4\u56de yes\uff1b\u5426\u5219\u8fd4\u56de no\u3002</li> </ol> <p>\u7531\u4e8e\u8fd9\u4e2a\u505a\u6cd5\u5b9e\u9645\u4e0a\u53ea\u662f\u4f18\u5316\u4e86\u4e00\u4e0b\u542f\u53d1\u5f0f\u7684\u7b56\u7565\uff0c\u5e76\u6ca1\u6709\u6539\u53d8\u5185\u6838\uff0c\u6240\u4ee5\u5176\u8fd1\u4f3c\u6bd4\u4ecd\u7136\u662f \\(2\\)\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec11/#\u603b\u7ed3","title":"\u603b\u7ed3","text":"<p>\u5173\u4e8e\u7b97\u6cd5\u7684\u8bbe\u8ba1\uff0c\u6211\u4eec\u8003\u8651\u8fd9\u4e09\u4e2a\u7ef4\u5ea6\uff1a</p> <ol> <li>\u6700\u4f18\u6027(optimality)\uff1a\u5373\u80fd\u6c42\u51c6\u786e\u89e3\uff1b</li> <li>\u9ad8\u6548\u6027(efficiency)\uff1a\u5373\u7b97\u6cd5\u662f\u5426\u9ad8\u6548\uff1b</li> <li>\u666e\u904d\u6027(all instances)\uff1a\u5373\u7b97\u6cd5\u662f\u5426\u666e\u904d\u9002\u7528\u4e8e\u6240\u6709\u7684\u60c5\u51b5\uff1b</li> </ol> <p>\u5018\u82e5\u4e00\u4e2a\u89e3\u6cd5\uff1a</p> <ol> <li>\u540c\u65f6\u6ee1\u8db3\u6700\u4f18\u6027\u548c\u9ad8\u6548\u6027\uff0c\u90a3\u4e48\u8fd9\u4e2a\u7b97\u6cd5\u5bf9\u7279\u6b8a\u60c5\u51b5\u80fd\u9ad8\u6548\u6c42\u51c6\u786e\u89e3\uff1b</li> <li>\u540c\u65f6\u6ee1\u8db3\u6700\u4f18\u6027\u548c\u666e\u904d\u6027\uff0c\u90a3\u4e48\u8fd9\u4e2a\u7b97\u6cd5\u5bf9\u6240\u6709\u60c5\u51b5\u90fd\u80fd\u6c42\u51c6\u786e\u89e3\uff1b</li> <li>\u540c\u65f6\u6ee1\u8db3\u9ad8\u6548\u6027\u548c\u666e\u904d\u6027\uff0c\u90a3\u4e48\u8fd9\u4e2a\u7b97\u6cd5\u53ef\u80fd\u662f\u4e2a\u8fd1\u4f3c\u7b97\u6cd5\uff1b</li> </ol> <p>\u5c31\u7b97 N=NP \u6210\u7acb\uff0c\u6211\u4eec\u4ecd\u7136\u65e0\u6cd5\u4fdd\u8bc1\u4e09\u4e2a\u613f\u671b\u4e00\u6b21\u6ee1\u8db3\u3002</p> <p>\u4e0d\u662f\u5f88\u660e\u767d\u6700\u540e\u4e00\u53e5\u8bdd\u5982\u4f55\u7406\u89e3\uff0c\u4f46\u662f\u8fd9\u4e00\u90e8\u5206\u5e94\u8be5\u5c31\u662f\u770b\u4e2a\u773c\u719f\uff0c\u4e0d\u662f\u5f88\u91cd\u8981\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec12/","title":"Lecture 12 | Local Search","text":"<p> \u7ea6 365 \u4e2a\u5b57  17 \u884c\u4ee3\u7801  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 1 \u5206\u949f</p> <p>\u65f6\u95f4\u5306\u5fd9\uff0c\u5185\u5bb9\u7b80\u7565</p> <ul> <li>local optimum is a best solution in a neighborhood</li> <li>start with a feasible solution and search a better one within the neighborhood</li> <li>a local optimum is achieved if no improvement is possible</li> </ul> <p>\u5373\u5148\u627e\u5230\u4e00\u4e2a\u53ef\u884c\u89e3\uff0c\u4ee5\u53ca\u91cf\u5316\u5176\u4f18\u7a0b\u5ea6\u7684\u76ee\u6807\u51fd\u6570\uff0c\u518d\u5728\u8fd9\u4e2a\u53ef\u884c\u89e3\u4e0a\u5bfb\u6c42\u4f18\u5316\uff0c\u76f4\u5230\u8fbe\u5230\u5c40\u90e8\u6700\u4f18\u89e3\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec12/#\u6848\u4f8b-the-vertex-cover-problem","title":"[\u6848\u4f8b] The Vertex Cover Problem","text":"<p>\u9876\u70b9\u8986\u76d6\u95ee\u9898(vertex cover problem)\u6307\u7ed9\u5b9a\u4e00\u4e2a\u65e0\u5411\u56fe \\(G=(V,E)\\)\uff0c\u627e\u5230\u4e00\u4e2a\u6700\u5c0f\u7684\u9876\u70b9\u96c6 \\(S\\subseteq V\\)\uff0c\u4f7f\u5f97\u6bcf\u6761\u8fb9 \\((u,v)\\) \u90fd\u81f3\u5c11\u6709\u4e00\u4e2a\u7aef\u70b9\u5728 \\(S\\) \u4e2d\uff08\u5373 \\(u\\in S \\lor v\\in S\\)\uff09\u3002</p> <p>\u8fd9\u4e2a\u95ee\u9898\u7684\u53ef\u884c\u89e3\u4e3a \\(S = V\\)\uff0c\u5373\u5b8c\u5168\u8986\u76d6\uff0c\u5176\u76ee\u6807\u51fd\u6570\u4e3a \\(cost(S) = |S|\\)\u3002\u5373\uff0c\u6211\u4eec\u5c1d\u8bd5\u4f7f\u7528 local search \u6765\u964d\u4f4e \\(|S|\\)\u3002</p> <p>\u7ed9\u51fa\u51e0\u79cd\u6848\u4f8b\u4ee5\u53ca\u53ef\u89c6\u5316\uff0c\u8bf4\u660e\u5c40\u90e8\u641c\u7d22\u5bb9\u6613\u5931\u6548\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec12/#\u6885\u7279\u7f57\u6ce2\u5229\u65af\u7b97\u6cd5","title":"\u6885\u7279\u7f57\u6ce2\u5229\u65af\u7b97\u6cd5","text":"<p>\u6885\u7279\u7f57\u6ce2\u5229\u65af\u7b97\u6cd5(the Metropolis algorithm)\u7684\u8fc7\u7a0b\uff1a</p> <p>\u51d1\u5408\u4e00\u4e0b\uff0c\u4e4b\u540e\u6709\u7a7a\u518d\u6539\u3002</p> <pre><code>SolutionType Metropolis() {   Define constants k and T;\nStart from a feasible solution S \\in FS ;\nMinCost = cost(S);\nwhile (1) {\nS\u2019 = Randomly chosen from N(S); CurrentCost = cost(S\u2019);\nif ( CurrentCost &lt; MinCost ) {\nMinCost = CurrentCost;    S = S\u2019;\n}\nelse {\nWith a probability e^{-\\Delta cost / (kT)}, let S = S\u2019;\nelse  break;\n}\n}\nreturn S;\n}\n</code></pre> <p>\u6ce8\uff1a\u5bf9\u4e8ecase 1\uff0c\u6709\u4e00\u5b9a\u6982\u7387\u53ef\u4ee5\u8df3\u51falocal optimum\u5f97\u5230\u6b63\u786e\u89e3\u3002\u4f46\u662f\u5bf9case 0\uff0c\u6709\u53ef\u80fd\u5728\u52a01\u548c\u51cf1\u4e4b\u95f4\u65e0\u9650\u9707\u8361\u2026\u2026 \u6ce8\uff1a\u5f53\uff08\u6e29\u5ea6\uff09T\u5f88\u9ad8\u65f6\uff0c\u4e0a\u5761\u7684\u6982\u7387\u51e0\u4e4e\u4e3a1\uff0c\u5bb9\u6613\u5f15\u8d77\u5e95\u90e8\u9707\u8361\uff1b\u5f53T\u63a5\u8fd10\u65f6\uff0c\u4e0a\u5761\u6982\u7387\u51e0\u4e4e\u4e3a0\uff0c\u63a5\u8fd1\u539f\u59cb\u7684\u68af\u5ea6\u4e0b\u964d\u6cd5\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec12/#\u6a21\u62df\u9000\u706b","title":"\u6a21\u62df\u9000\u706b","text":"<p>\u6a21\u62df\u9000\u706b(simulated annealing)</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec12/#\u6848\u4f8b-hopfield-neural-networks","title":"[\u6848\u4f8b] Hopfield Neural Networks","text":"<p>links</p> <p>Wikipedia: https://en.wikipedia.org/wiki/Hopfield_network</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec12/#\u6848\u4f8b-the-maximum-cut-problem","title":"[\u6848\u4f8b] The Maximum Cut Problem","text":"<p>links</p> <p>Wikipedia: https://en.wikipedia.org/wiki/Maximum_cut</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec13/","title":"Lecture 13 | Randomized Algorithms","text":"<p> \u7ea6 25 \u4e2a\u5b57 </p> <p>\u65f6\u95f4\u5306\u5fd9\uff0c\u5185\u5bb9\u7b80\u7565</p> <p>\u4e00\u4e9b\u6982\u5ff5\u8bf4\u660e</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec13/#the-hiring-problem","title":"The Hiring Problem","text":""},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec13/#modified-quick-sort","title":"Modified Quick Sort","text":""},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec14/","title":"Lecture 14 | Parallel","text":"<p> \u7ea6 3 \u4e2a\u5b57 </p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec15/","title":"Lecture 15 | External Sorting","text":"<p> \u7ea6 6424 \u4e2a\u5b57  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 21 \u5206\u949f</p> <p>link</p> <p>Wikipedia: https://en.wikipedia.org/wiki/External_sorting</p> <p>\u5916\u6392\u5e8f\u4e0e\u6570\u636e\u5e93\u7cfb\u7edf\u4e2d\u7684\u76f8\u5173\u5185\u5bb9\u6709\u4ea4\u53c9\u5173\u7cfb\uff0c\u5f53\u9700\u8981\u6392\u5e8f\u7684\u6570\u636e\u8fc7\u5927\uff0c\u800c\u65e0\u6cd5\u88ab\u5b8c\u5168\u653e\u5728\u5185\u5b58\u65f6\uff0c\u666e\u901a\u7684\u6392\u5e8f\u7b97\u6cd5\u65e0\u6cd5\u88ab\u5e94\u7528\u3002\u6b64\u65f6\u9700\u8981\u4f7f\u7528\u5916\u6392\u5e8f\uff0c\u7b80\u5355\u6765\u8bf4\u5c31\u662f\u5728\u66f4\u5927\u7684\u5c3a\u5ea6\u4e0a\u8fdb\u884c\u7c7b\u4f3c\u5f52\u5e76\u7684\u64cd\u4f5c\u3002</p> <p>\u800c\u6b63\u56e0\u4e3a\u6b64\uff0c\u5916\u90e8\u6392\u5e8f\u7684\u8fc7\u7a0b\u4e0e\u786c\u4ef6\u8bbe\u8ba1\u6709\u4e00\u5b9a\u5173\u7cfb\u3002</p> \u4e0e\u786c\u4ef6\u76f8\u5173\u7684\u4e00\u4e9b\u8bf4\u660e <p>\u5177\u4f53\u6765\u8bf4\uff0c\u666e\u901a\u7684\u6392\u5e8f\u7b97\u6cd5\u6392\u5e8f\u7684\u5bf9\u8c61\u90fd\u662f\u653e\u5728\u5185\u5b58\u91cc\u7684\u4e00\u4e9b\u6570\u636e\uff0c\u4f8b\u5982\u4e00\u4e2a <code>int</code> \u6570\u7ec4\u3002\u7136\u800c\u5916\u90e8\u6392\u5e8f\u6392\u5e8f\u7684\u5bf9\u8c61\uff0c\u6216\u8005\u8bf4\u8981\u6392\u5e8f\u7684\u90a3\u4e2a\u201c\u6570\u7ec4\u201d\uff0c\u6ca1\u6cd5\u88ab\u5b8c\u6574\u5730\u5b58\u5728\u5185\u5b58\u91cc\uff0c\u5b83\u4eec\u90fd\u88ab\u5b58\u50a8\u5728\u786c\u76d8\u4e4b\u7c7b\u7684\u975e\u6613\u5931\u4ecb\u8d28\u4e2d\uff0c\u800c\u4ece\u8fd9\u79cd\u4ecb\u8d28\u91cc\u8bfb\u53d6\u6570\u636e\u5f80\u5f80\u5177\u6709\u8f83\u5927\u7684\u5f00\u9500\uff0c\u6240\u4ee5\u6211\u4eec\u603b\u662f\u201c\u4e00\u5757\u4e00\u5757\u201d\u4ece\u91cc\u9762\u90a3\u6570\u636e\u3002</p> <p>\u6253\u4e2a\u6bd4\u65b9\uff0c\u4f60\u73b0\u5728\u9700\u8981\u5bf9\u4e00\u6574\u4e2a\u56fe\u4e66\u9986\uff08\u786c\u76d8\uff09\u7684\u4e66\u505a\u6392\u5e8f\uff0c\u4f46\u662f\u4f60\u7684\u684c\u5b50\uff08\u5185\u5b58\uff09\u4e0a\u6700\u591a\u653e\u4e0b\u4e09\u5341\u672c\u4e66\uff0c\u6362\u53e5\u8bdd\u6765\u8bf4\uff0c\u4f60\u4e00\u6b21\u6700\u591a\u5904\u7406\u4e09\u5341\u672c\u4e66\u3002\u800c\u4e3a\u4e86\u4ece\u56fe\u4e66\u9986\u4e2d\u83b7\u53d6\u9700\u8981\u6392\u7684\u4e66\uff0c\u4f60\u5f97\u5148\u627e\u5230\u8fd9\u4e9b\u4e66\u5728\u54ea\uff08seek\uff09\uff0c\u7136\u540e\u518d\u628a\u8fde\u7eed\u7684\u4e09\u5341\u672c\u4e66\u62ff\u51fa\u6765\uff08block transfer\uff09\uff0c\u653e\u5230\u4f60\u7684\u684c\u5b50\uff08\u5185\u5b58\uff09\u4e0a\u518d\u6392\u5e8f\uff0c\u800c\u4e3a\u4e86\u7ed9\u63a5\u4e0b\u6765\u4e09\u5341\u672c\u4e66\u817e\u4f4d\u7f6e\uff0c\u4f60\u8fd8\u5f97\u628a\u6392\u597d\u7684\u4e09\u5341\u672c\u4e66\u518d\u653e\u56de\u53bb\uff08\u5373\u8bb0\u5f55\u4e0b\u6392\u5e8f\u7ed3\u679c\uff0c\u540c\u6837\u4e5f\u662f\u4e00\u6b21 block transfer\uff09\u3002</p> <p>\u7efc\u4e0a\u6240\u8ff0\uff0c\u5916\u90e8\u6392\u5e8f\u4e3b\u8981\u89e3\u51b3\u7684\u5c31\u662f\uff0c\u6309\u7167\u600e\u6837\u7684\u7b56\u7565\u6765\u5bf9\u8fd9\u4e9b\u6570\u636e\u8fdb\u884c\u6392\u5e8f\u3002</p> <p>\u5bfc\u8bfb</p> <p>\u7531\u4e8e ADS \u4ecb\u7ecd\u7684\u5916\u6392\u5e8f\u548c\u540c\u65f6\u671f\u6570\u636e\u5e93\u7cfb\u7edf\u8fd9\u95e8\u8bfe\u4ecb\u7ecd\u7684\u5916\u6392\u5e8f\u6709\u540c\u6709\u5f02\uff0c\u6240\u4ee5\u6211\u6253\u7b97\u5148\u5728\u5927\u6982\u8bb2\u5916\u6392\u5e8f\u7684\u6838\u5fc3\u601d\u8def\uff0c\u518d\u5c55\u5f00 ADS \u8bfe\u7a0b\u4e2d\u7684\u5177\u4f53\u8fc7\u7a0b\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec15/#\u6982\u8ff0","title":"\u6982\u8ff0","text":"<p>\u5916\u6392\u5e8f\u7684\u57fa\u672c\u601d\u8def\u5c31\u662f\u5c06\u6570\u636e\u5206\u4e3a\u82e5\u5e72\u4e2a\u5c0f\u5757\uff0c\u7136\u540e\u5bf9\u6bcf\u4e2a\u5c0f\u5757\u8fdb\u884c\u6392\u5e8f\uff0c\u6700\u540e\u518d\u5c06\u8fd9\u4e9b\u5c0f\u5757\u5408\u5e76\u8d77\u6765\u3002\u800c\u6211\u4eec\u5e38\u8bf4\u7684\u5f52\u5e76\u6392\u5e8f\uff0c\u6307\u7684\u662f\u9012\u5f52\u5730\u5c06\u4e24\u5757\u5408\u6210\u4e00\u5757\uff0c\u800c\u6240\u8c13\u7684 \\(k\\) \u8def\uff08\\(k\\)-way\uff09\u5f52\u5e76\uff0c\u5c31\u662f\u5c06 \\(k\\) \u5757\u5408\u6210\u4e00\u5757\u3002</p> <p>\u90a3\u4e48\u5982\u4f55\u5f52\u5e76\u5462\uff1f\u6211\u5c06\u4ece\u4e24\u4e2a\u7ef4\u5ea6\u6765\u7b80\u5355\u9610\u8ff0\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec15/#\u903b\u8f91\u7ef4\u5ea6","title":"\u903b\u8f91\u7ef4\u5ea6","text":"<p>\u5916\u90e8\u6392\u5e8f\u6240\u4f7f\u7528\u7684\u5f52\u5e76\u6392\u5e8f\u4ece\u903b\u8f91\u4e0a\u6765\u8bb2\u548c\u666e\u901a\u7684\u5f52\u5e76\u6392\u5e8f\u4e00\u81f4\uff0c\u603b\u662f\u5c06 \\(k\\) \u4e2a\u6709\u5e8f\u5e8f\u5217\u5408\u5e76\u4e3a 1 \u4e2a\u6709\u5e8f\u5e8f\u5217\u3002</p> <p>\u800c\u8fd9\u91cc\u7684\u201c\u6709\u5e8f\u5e8f\u5217\u201d\uff0c\u5728\u5916\u6392\u5e8f\u4e2d\u88ab\u79f0\u4e3a\u201crun\u201d\uff0c\u5373\u6bcf\u6b21\u5f52\u5e76\u6211\u4eec\u53e6 \\(k\\) \u4e2a run \u53d8\u6210\u4e00\u4e2a run\u3002\u6b63\u7740\u8bf4\u5c31\u662f\uff1a</p> <p>run</p> <p>\u4e00\u4e2a run \u6307\u7684\u662f\u4e00\u6bb5\u8fc7\u7a0b\u4e2d\u7684\u6570\u636e\uff0c\u5728\u672c\u6587\u4e2d\u7279\u6307\u5f85\u5f52\u5e76\u7684\u6709\u5e8f\u7684\u5e8f\u5217\uff0c\u5728 \\(k\\)-way merge \u4e2d\uff0c\u6211\u4eec\u603b\u662f\u5c06 \\(k\\) \u4e2a run \u5408\u5e76\u4e3a 1 \u4e2a run\u3002</p> <p>\u8bf4\u660e</p> <p>\u8fd9\u91cc\u7684 run \u7684\u5b9a\u4e49\u662f\u6211\u81ea\u5df1\u8111\u8865\u51fa\u6765\u7684\uff0c\u5e76\u4e0d\u786e\u5b9a\u662f\u5426\u4e25\u683c\uff0c\u4f46\u662f\u53ef\u4ee5\u4fdd\u8bc1\u7684\u662f\uff1a \u4e00\u4e2a run \u5728\u53c2\u4e0e merge \u4e4b\u524d\u80af\u5b9a\u5df2\u7ecf\u6709\u5e8f\u4e86\uff0c\u53ef\u4ee5\u7406\u89e3\u4e3a \"have already run\"\uff0c\u800c\u4e3a\u4e86\u4e0d\u6405\u7cca\u8bfb\u8005\u7684\u8111\u5b50\uff0c\u6211\u8fd9\u91cc\u5c31\u4ee5\u8fd9\u4e2a\u5b9a\u4e49\u4e3a\u51c6\u3002</p> <p>\u4ece\u6267\u884c\u7684\u987a\u5e8f\u6765\u8bf4\uff0c\u5185\u6392\u5e8f\u4e2d\u7684\u5f52\u5e76\u6392\u5e8f\u662f\u4e00\u4e2a\u81ea\u4e0a\u800c\u4e0b\u4e0d\u65ad \\(\\frac{1}{k}\\) \u5730\u5212\u5206\uff0c\u518d\u81ea\u4e0b\u800c\u4e0a\u4e0d\u65ad\u5f52\u5e76\u7684\u8fc7\u7a0b\u3002\u76f8\u53cd\uff0c\u5916\u6392\u5e8f\u7531\u4e8e\u5176\u7279\u6027\u9650\u5236\uff0c\u5176\u201c\u5f52\u5e76\u6bb5\u201d\u5e76\u4e0d\u662f\u81ea\u4e0a\u800c\u4e0b \\(\\frac{1}{k}\\) \u5212\u5206\u51fa\u6765\u7684\uff0c\u800c\u662f\u6839\u636e\u786c\u4ef6\u5904\u7406\u80fd\u529b\uff0c\u76f4\u63a5\u5212\u5206\u597d\u6700\u5c0f\u7684\u5f52\u5e76\u6bb5\uff0c\u7136\u540e\u76f4\u63a5\u81ea\u4e0b\u800c\u4e0a\u5f52\u5e76\u3002</p> <p>\u800c\u8fd9\u6837\u4e00\u4e2a\u5c06 \\(k \\cdot c\\) \u4e2a run merge \u6210 \\(c\\) \u4e2a run \u7684\u8fc7\u7a0b\uff0c\u6211\u4eec\u79f0\u4e4b\u4e3a\u4e00\u4e2a <code>pass</code>\u3002\uff08\u5728\u5f52\u5e76\u6811\u4e0a\u4f53\u73b0\u4e3a\u4e00\u5c42\u3002\uff09</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec15/#\u7269\u7406\u7ef4\u5ea6","title":"\u7269\u7406\u7ef4\u5ea6","text":"<p>\u5173\u4e8e\u7269\u7406\u7ef4\u5ea6\uff0c\u6d89\u53ca\u5230\u4e00\u4e9b\u786c\u4ef6\u77e5\u8bc6\uff0c\u5728 ADS \u4e2d\u4e3a\u4e86\u65b9\u4fbf\u8bf4\u660e\u4f1a\u5c06\u5176\u7b80\u5316\uff0c\u6709\u5173 block \u7684\u6982\u5ff5\u5c06\u88ab\u62bd\u8c61\u5316\u4e3a\u201c\u6570\u636e\u5355\u4f4d\u201d\u3002</p> <p>\u6211\u4eec\u77e5\u9053\uff0c\u5185\u5b58\u7684\u5927\u5c0f\u662f\u6709\u9650\u7684\uff0c\u5212\u5206\u7ed9\u5f52\u5e76\u6570\u636e\u7684\u5185\u5b58\u4e5f\u5e94\u5f53\u662f\u6709\u9650\u7684\uff0c\u6211\u4eec\u7528 \\(M\\) \u6765\u8bb0\u5b83\uff0c\u5373\u5185\u5b58\u4e2d\u4e00\u6b21\u53ea\u80fd\u5904\u7406 \\(M\\) \u4e2a\u5355\u4f4d\u7684\u6570\u636e\u3002</p> <p>\u66f4\u7ec6\u8282\u7684\uff0c\u6211\u4eec\u5e94\u5f53\u66f4\u5177\u7269\u7406\u5927\u5c0f\u6765\u8ba1\u7b97 \\(M\\)\uff0c\u4f8b\u5982\u4e00\u6761\u6570\u636e\u7684\u5927\u5c0f\u662f \\(l \\text{Bytes}\\)\uff0c\u800c\u5185\u5b58\u7684\u5927\u5c0f\u662f \\(m \\text{Bytes}\\)\uff0c\u90a3\u4e48\u4e00\u4e2a\u5185\u5b58\u80fd\u591f\u5bb9\u7eb3\u7684\u6570\u636e\u6570\u91cf\u5e94\u5f53\u4e3a \\(\\lfloor \\frac{m}{l} \\rfloor\\)\u3002</p> <p>\u4f46\u662f\u65e2\u7136\u8981\u5f52\u5e76\uff0c\u6211\u4eec\u5c31\u9700\u8981\u5c06 \\(k\\) \u8def\u7684\u6570\u636e\u8bfb\u5165\u5230\u5185\u5b58\u4e2d\uff0c\u6700\u7406\u60f3\u7684\u60c5\u51b5\u4e0b\u6211\u4eec\u80af\u5b9a\u5e0c\u671b\u8fd9 \\(k\\) \u8def\u90fd\u80fd\u8bfb\u5165\u5230\u5185\u5b58\u4e2d\uff0c\u4f46\u662f\u663e\u7136\u8fd9\u662f\u4e0d\u5207\u5b9e\u9645\u7684\uff0c\u6211\u4eec\u6700\u591a\u516c\u5e73\u5730\u8bfb\u5165\u6bcf\u4e00\u8def\u7684\u524d \\(\\lfloor \\frac{M}{k} \\rfloor\\) \u4e2a\u6570\u636e\u2014\u2014\u4f46\u8fd9\u5df2\u7ecf\u8db3\u591f\u2014\u2014\u5bf9\u4e8e \\(k\\) \u4e2a\u6709\u5e8f\u5e8f\u5217\u7684\u5408\u5e76\u64cd\u4f5c\uff0c\u5176\u5408\u5e76\u8fc7\u7a0b\u4e2d\u4e5f\u6070\u597d\u53ea\u4e0e\u6700\u9760\u524d\u7684\u3001\u672a\u6392\u5e8f\u7684\u4e00\u90e8\u5206\u6570\u636e\u6709\u5173\u3002</p> <p>\u8bf4\u660e</p> <p>\u4e4b\u540e\u6240\u63d0\u5230\u7684\uff0c\u6709\u5173\u4e8e\u6392\u5e8f\u6570\u636e\u7684\u201c\u5185\u5b58\u201d\uff0c\u6307\u7684\u90fd\u662f\u5212\u5206\u7ed9\u7b97\u6cd5\uff0c\u7528\u6765\u5b58\u653e\u5f52\u5e76\u6570\u636e\u7684\u5185\u5b58\uff01</p> <p>example</p> <p>\u4e3e\u4f8b\u6765\u8bf4\uff0c\u5047\u8bbe\u73b0\u5728\u6709\u4e24\u4e2a run\uff0c\u5206\u522b\u4e3a\uff1a</p> <ol> <li><code>1</code> <code>3</code> <code>5</code> <code>7</code> <code>9</code></li> <li><code>0</code> <code>2</code> <code>4</code> <code>6</code> <code>8</code></li> </ol> <p>\u4f46\u662f\u5185\u5b58\u53ea\u80fd\u653e 4 \u4e2a\u5355\u4f4d\u6570\u636e\uff0c\u6240\u4ee5\u5bf9\u4e8e\u6bcf\u4e2a run \u603b\u662f\u53ea\u6709\u524d 2 \u4e2a\u6570\u636e\u662f\u53ef\u89c1\u7684\u3002\u4f46\u662f\u8fd9\u5e76\u4e0d\u5f71\u54cd\u6211\u4eec\u53ef\u4ee5\u786e\u5b9a\u8fd9\u4e24\u4e2a run \u5408\u5e76\u7684\u7ed3\u679c\u4e2d\uff0c\u524d\u4e00\u90e8\u5206\u662f <code>0</code> <code>1</code> <code>2</code>\uff0c\u800c\u81f3\u4e8e <code>2</code> \u540e\u9762\u6392\u4ec0\u4e48\uff0c\u5219\u8981\u4ece <code>run2</code> \u4e2d\u53d6\u51fa\u4e4b\u540e\u7684\u6570\u636e\uff0c\u518d\u4e0e <code>run1</code> \u4f59\u4e0b\u7684 <code>_</code> <code>3</code> \u5408\u5e76\u3002</p> <p>\u6613\u9519\u70b9</p> <p>\u6ce8\u610f\uff0c\u5f53\u5176\u4e2d\u4e00\u4e2a\u6bb5\u7684 buffer \u7a7a\u4e86\u4ee5\u540e\uff0c\u6211\u4eec\u4e0d\u80fd\u76f4\u63a5\u628a\u5176\u4ed6\u6bb5\u7684 buffer \u76f4\u63a5\u6392\u5e8f\u8fdb\u53bb\uff0c\u800c\u5fc5\u987b\u5148\u586b\u5145\u8fd9\u4e2a\u7a7a buffer \u7684\u5185\u5bb9\uff0c\u518d\u7ee7\u7eed\u6392\u5e8f\u3002</p> <p>\u60f3\u8c61\u8fd9\u6837\u4e00\u4e2a\u60c5\u51b5\uff0c\u7a7a buffer \u5c06\u8981\u8f7d\u5165\u7684\u4e0b\u4e00\u6bb5\u6570\u636e\u662f <code>3</code> <code>4</code> <code>5</code>\uff0c\u800c\u53e6\u5916\u4e00\u4e2a buffer \u5269\u4e0b\u7684\u6570\u636e\u662f <code>7</code>\uff0c\u90a3\u4e48\u663e\u7136\uff0c<code>3</code> <code>4</code> <code>5</code> \u5e94\u8be5\u5148\u4e8e <code>7</code> \u88ab\u6392\u5e8f\u3002</p> <p>\u800c\u8fd9\u4e2a\u8fc7\u7a0b\u4e5f\u6b63\u662f\u5916\u6392\u5e8f\u80fd\u591f\u8fdb\u884c\u7684\u4e00\u4e2a\u91cd\u8981\u57fa\u7840\u3002</p> <p>\u5176\u4e2d\u6bd4\u8f83\u7279\u522b\u7684\u6b65\u9aa4\u5c31\u662f\uff0c\u6700\u5f00\u59cb\u7684\u6392\u5e8f\uff0c\u5373\u7b2c\u4e00\u4e2a pass\u3002\u5148\u524d\u6211\u4eec\u5728#\u903b\u8f91\u7ef4\u5ea6\u91cc\u63d0\u5230\u4e86\uff0c\u5916\u6392\u5e8f\u7684\u7b2c\u4e00\u4e2a pass \u4f1a\u76f4\u63a5\u5212\u5206\u597d\u6700\u5c0f\u7684\u5f52\u5e76\u6bb5\uff0c\u800c\u8fd9\u4e2a\u201c\u6700\u5c0f\u5f52\u5e76\u6bb5\u201d\u7684\u5927\u5c0f\u5c31\u662f \\(M\\)\u3002\u7528\u8bed\u8a00\u63cf\u8ff0\uff0c\u5c31\u662f\u6700\u65e9\u7684 run \u7684\u5927\u5c0f\u5c31\u662f\u5e73\u5747\u6bcf\u4e00\u8def\u80fd\u591f\u5728\u5185\u5b58\u4e2d\u5904\u7406\u7684\u6700\u5927\u6570\u636e\u5355\u4f4d\u91cf\u3002</p> <p>\u7136\u800c\u95ee\u9898\u51fa\u73b0\u4e86\uff0c\u6839\u636e\u6211\u4e4b\u524d\u7ed9\u51fa\u7684\u5b9a\u4e49\uff0crun \u5e94\u5f53\u662f\u6709\u5e8f\u7684\uff0c\u4f46\u662f\u4ece\u539f\u59cb\u6570\u636e\u91cc\u8bfb\u51fa\u6765\u7684\u201c\u6700\u5c0f\u5f52\u5e76\u6bb5\u201d\u662f\u65e0\u5e8f\u7684\u3002\u4f46\u662f\u5bf9\u4e8e\u6700\u521d\u7684 run\uff0c\u5b83\u5fc5\u7136\u80fd\u591f\u6574\u6bb5\u653e\u5230\u5185\u5b58\u91cc\uff08\u66f4\u8fdb\u4e00\u6b65\u7684\uff0c\u4e5f\u53ea\u6709\u6700\u521d\u7684 run \u80fd\u591f\u5b8c\u6574\u5730\u653e\u5230\u5185\u5b58\u91cc\uff09\uff0c\u56e0\u6b64\u76f4\u63a5\u5bf9\u5176\u8fdb\u884c\u5185\u6392\u5e8f\u5373\u53ef\u3002</p> <p>\u903b\u8f91\u8054\u7cfb</p> <ul> <li>\u56e0\u4e3a\u5185\u6392\u5e8f\u5f88\u5feb\uff0c\u6240\u4ee5\u8981\u5c3d\u53ef\u80fd\u5229\u7528\u5185\u6392\u5e8f\uff1b</li> <li>\u6240\u4ee5\u4e00\u5f00\u59cb\u5c31\u8981\u5c06\u80fd\u5185\u6392\u5e8f\u505a\u7684\u4e8b\u60c5\u90fd\u7528\u5185\u6392\u5e8f\u89e3\u51b3\uff1b</li> <li>\u6240\u4ee5\u6700\u521d\u7684 run \u7684\u5927\u5c0f\u662f \\(M\\)\u3002</li> </ul> <p>\u4e2d\u7ee7</p> <p>\u4ee5\u4e0a\u5185\u5bb9\u662f\u5bf9\u5916\u6392\u5e8f\u6838\u5fc3\u601d\u60f3\u7684\u4e00\u4e2a\u7b80\u5355\u4ecb\u7ecd\uff0c\u63a5\u4e0b\u6765\u6211\u4eec\u5c06\u4ee5 ADS \u6240\u4ecb\u7ecd\u7684\u5916\u6392\u5e8f\u8303\u5f0f\uff0c\u6765\u4ecb\u7ecd\u4e00\u4e0b\u5177\u4f53\u7684\u8fc7\u7a0b\u548c\u4e00\u4e9b\u6539\u8fdb\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec15/#\u5177\u4f53\u5206\u6790","title":"\u5177\u4f53\u5206\u6790","text":"<p>ADS \u4e2d\u76f8\u6bd4\u4e0a\u9762\u4ecb\u7ecd\u7684\u90e8\u5206\uff0c\u53c8\u5f15\u5165\u4e86\u4e00\u4e2a\u53eb tape \u7684\u6982\u5ff5\uff0ctape \u7684\u4e2d\u6587\u662f\u78c1\u5e26\uff0c\u800c\u5728\u8fd9\u4e2a\u6846\u67b6\u4e2d\uff0c\u6211\u66f4\u503e\u5411\u4e8e\u628a\u5b83\u5f53\u4f5c\u4e00\u4e2a\u62bd\u8c61\u7684\u6982\u5ff5\u3002</p> <p>\u76f8\u5bf9\u5e94\u7684\uff0c\u5176\u5b9e\u9645\u8fc7\u7a0b\u4e0e\u4e0a\u9762\u63cf\u8ff0\u7684\u65b9\u6cd5\u53ef\u80fd\u6709\u4e00\u4e9b\u611f\u53d7\u4e0a\u7684\u5dee\u522b\uff0c\u5982\u679c\u53ea\u662f\u4e86\u89e3\u601d\u60f3\u7684\u8bdd\u4e0a\u534a\u90e8\u5206\u5df2\u7ecf\u8db3\u591f\uff08\u5f53\u7136\u540e\u9762\u8fd8\u6709\u4e00\u4e9b\u57fa\u4e8e\u5982\u4e0b\u6a21\u578b\u7684\u4f18\u5316\u8ba8\u8bba\uff09\uff0c\u4f46\u662f\u6bd5\u7adf\u8fd8\u662f\u9762\u5411\u8003\u8bd5\uff0c\u6240\u4ee5\u8fd8\u662f\u9700\u8981\u4ee5 ADS \u8bfe\u4ef6\u7684\u65b9\u6cd5\u518d\u4ecb\u7ecd\u4e00\u6b21\u3002</p> <p>\u8bf4\u660e</p> <p>\u6211\u4e4b\u540e\u4f1a\u4ee5 run \u4e3a\u5355\u4f4d\uff0c\u6765\u63cf\u8ff0\u5408\u5e76\u8fc7\u7a0b\u3002\u4f46\u662f\u5b9e\u9645\u53d1\u751f\u5728\u8ba1\u7b97\u673a\u91cc\u7684\u6b65\u9aa4\u66f4\u52a0\u590d\u6742\uff1a</p> <p>\u9700\u8981\u5148\u5c06\u6bcf\u4e00\u6761 tape \u7684\u4e00\u90e8\u5206\u6570\u636e\u8bfb\u5165\u5185\u5b58\u7684 buffer \u4e2d\uff0c\u7136\u540e\u5229\u7528\u8fd9\u4e9b buffer \u6765\u8fdb\u884c\u6392\u5e8f\uff1b\u5f53\u67d0\u4e2a buffer \u7a7a\u4e86\u4ee5\u540e\u8981\u7acb\u523b\u5c06\u5bf9\u5e94 tape \u7684\u4e0b\u4e00\u90e8\u5206\u6570\u636e\u8bfb\u5165\uff0c\u76f4\u5230\u6ca1\u6709\u6570\u636e\u53ef\u4ee5\u586b\u5145\u4e3a\u6b62\u3002</p> <p>\u4e5f\u6b63\u662f#\u7269\u7406\u7ef4\u5ea6\u6240\u8bf4\u7684\u90a3\u4e9b\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec15/#\u6734\u7d20\u8fc7\u7a0b\u5206\u6790","title":"\u6734\u7d20\u8fc7\u7a0b\u5206\u6790","text":"<p>\u6211\u4eec\u4ee5 2-way merge \u4e3a\u4f8b\uff0c\u7ed3\u5408 ADS \u8bfe\u4ef6\u4e2d\u7684\u914d\u56fe\u6765\u8bf4\u660e\u3002</p> \u51c6\u5907 <p> </p> <p>\u56fe\u4e2d \\(T_1\\) \u662f\u4e00\u6761 tape \u7684\u7f16\u53f7\uff0c\u6211\u4eec\u53ef\u4ee5\u7406\u89e3\u4e3a\u4e00\u4e2a\u5e8f\u5217\u7684\u7269\u7406\u5730\u5740\uff0c\u6216\u66f4\u901a\u4fd7\u7684\u6765\u8bf4\uff0c\u53ef\u4ee5\u5f53\u4f5c\u4e00\u4e2a\u6570\u7ec4\uff0c\u53ea\u4e0d\u8fc7\u5b83\u7684\u5b9e\u9645\u6570\u636e\u662f\u5728\u786c\u76d8\u4e2d\u3002\u6362\u53e5\u8bdd\u6765\u8bf4\uff0c\u8fd9\u91cc\u7684 tape \u8868\u793a\u7684\u90fd\u662f\u786c\u76d8\u4e2d\u7684\u6570\u636e\u3002</p> <p>\u8fd9\u6761 tape \u4e2d\u6709 13 \u4e2a\u5143\u7d20\uff0c\u6211\u4eec\u8bb0\u5176\u4e3a \\(N = 13\\)\u3002\u800c\u8fd9\u6761\u539f\u59cb\u7684 tape \u88ab\u5212\u5206\u4e3a\u4e86 5 \u6bb5\uff0c\u6bcf\u4e00\u6bb5\u90fd\u6709\u4e0d\u8d85\u8fc7 3 \u4e2a\u5143\u7d20\uff0c\u6b64\u65f6 \\(M = 3\\)\u3002\u5373\u6709 \\(\\lceil \\frac{N}{M} \\rceil = 5\\)\u3002</p> Pass 1 <p>\u73b0\u5728\u6211\u4eec\u8981\u5f00\u59cb merge \u4e86\u3002\u5bf9\u4e8e\u8fd9\u6bb5\u6570\u636e\u6765\u8bf4\uff0c\u8fd9\u662f\u610f\u4e49\u91cd\u5927\u7684\u201c\u4eba\u751f\u7b2c\u4e00\u6b21\u201d\uff0c\u76f8\u6bd4\u4e8e\u5176\u4ed6\u5f52\u5e76\u90fd\u662f\u4ece 2 \u4e2a tape \u5f00\u59cb\u7684 pass\uff0c\u8fd9\u4e00\u6b21\u663e\u5f97\u6709\u4e9b\u7279\u6b8a\u3002</p> <p>\u5728\u7b2c\u4e00\u8f6e\u4e2d\uff0c\u9762\u5bf9\u5168\u90e8\u90fd\u662f\u65e0\u5e8f\u7684\u6570\u636e\uff0c\u6211\u4eec\u5c06\u8fd9 \\(\\lceil \\frac{N}{M} \\rceil = 5\\) \u4e2a\u6bb5\u5747\u5206\u5230\u4e24\u6761 tape \u4e0a\uff082-way\uff09\uff0c\u8fd9\u91cc\u7ecf\u5386\u4e24\u4e2a\u6b65\u9aa4\uff1a</p> <ol> <li>\u4f9d\u6b21\u8bfb\u53d6 \\(T_1\\) \u4e2d\u6bcf\u4e00\u6bb5\u6570\u636e\uff08\u521a\u597d\u5360\u6ee1\u5185\u5b58\uff09\uff0c\u5e76\u5bf9\u5b83\u4eec\u8fdb\u884c\u5185\u6392\u5e8f\uff1b</li> <li>\u5c06\u6392\u5e8f\u5b8c\u7684\u6bb5\uff0c\u8ffd\u52a0\u5199\u5230 \\(T_2\\) \u6216 \\(T_3\\) \u4e2d\uff08\u5177\u4f53\u6bcf\u4e00\u4e2a tape \u5199\u51e0\u6761\uff0c\u4f1a\u6709\u4e13\u95e8\u7b56\u7565\u505a\u8c03\u6574\uff0c\u76ee\u524d\u5148\u5e73\u5206\u7740\u653e\uff09\uff1b</li> </ol> <p>\u4e8e\u662f\uff0c\\(T_1\\) \u4e2d\u7684\u6570\u636e\u4fbf\u88ab\u8f6c\u79fb\u5230\u4e86 \\(T_2\\) \u548c \\(T_3\\)\u3002\u4e3a\u4e86\u91cd\u590d\u5229\u7528 tape\uff0c\u6b64\u65f6\u7684 \\(T_1\\) \u88ab\u770b\u4f5c\u53ef\u4ee5\u7528\u7684\u7a7a\u78c1\u76d8\u4e86\u3002</p> <p> </p> <p>\u4e8e\u662f\uff0c\u5b8c\u6210\u4e86\u7b2c\u4e00\u4e2a pass\u3002</p> Pass 2 <p>\u4e4b\u540e\u7684 pass \u5219\u57fa\u672c\u9075\u5faa\u540c\u6837\u7684\u89c4\u5219\uff0c\u4e0d\u65ad\u53d6\u6bcf\u4e00\u8def\u7684\u7b2c\u4e00\u4e2a run \u5e76 merge\uff0c\u5e76\u4e14\u5c06\u7ed3\u679c\u5199\u5230\u4e24\u4e2a\uff08k \u4e2a\uff09\u95f2\u7f6e\u7684 tape \u4e0a\uff08\u548c\u524d\u9762\u8bf4\u8fc7\u7684\u4e00\u6837\uff0c\u8fd9\u91cc\u6682\u4e14\u5c06\u5206\u914d\u7b56\u7565\u5b9a\u4e3a\u5e73\u5206\u5230\u6bcf\u4e00\u4e2a tape \u4e0a\uff09\u3002</p> <p>\u4f8b\u5982\uff0c\u6211\u4eec\u8981\u53d6 \\(T_2\\) \u548c \\(T_3\\) \u7684\u7b2c\u4e00\u6bb5\uff0c\u6267\u884c\u5f52\u5e76\u64cd\u4f5c\uff0c\u5f97\u5230\u4e00\u4e2a\u65b0\u7684\uff0c\u6709 6 \u4e2a\u6570\u636e\u7684 run\uff0c\u5e76\u5199\u5230\u95f2\u7f6e\u7684 \\(T_1\\) \u4e0a\uff1b\u63a5\u4e0b\u6765\u53d6 \\(T_2\\) \u548c \\(T_3\\) \u7684\u7b2c\u4e8c\u6bb5\uff0c\u5f52\u5e76\u5f97\u5230\u65b0\u7684 run\uff0c\u6b64\u65f6\u6211\u4eec\u53d1\u73b0\uff0c\\(T_1\\)\u3001\\(T_2\\)\u3001\\(T_3\\) \u90fd\u4e0d\u662f\u95f2\u7f6e\u7684\uff0c\u6240\u4ee5\u6211\u4eec\u9700\u8981\u4e00\u4e2a\u65b0\u7684 tape\uff0c\u5199\u5230 \\(T_4\\) \u4e0a\u3002</p> <p> </p> <p>\u4e8e\u662f\uff0c\u5b8c\u6210\u4e86\u7b2c\u4e8c\u4e2a pass\u3002</p> Pass 3 <p>pass 3 \u548c pass 2 \u7684\u8fc7\u7a0b\u57fa\u672c\u4e00\u81f4\u3002\u73b0\u5728\u7684 tape \u72b6\u6001\u662f \\(\\{T_2, T_3\\}\\) \u95f2\u7f6e\uff0c\u6211\u4eec\u53d6 \\(T_1\\) \u548c \\(T_4\\) \u7684\u7b2c\u4e00\u6bb5\uff0c\u5f97\u5230\u4e00\u4e2a\u65b0\u7684 run\uff0c\u5305\u542b 12 \u4e2a\u5143\u7d20\uff1b\u53d6 \\(T_1\\) \u548c \\(T_4\\) \u7684\u7b2c\u4e8c\u6bb5\uff0c\u5f97\u5230\u4e00\u4e2a\u65b0\u7684 run\uff0c\u5305\u542b 1 \u4e2a\u5143\u7d20\u3002\u8fd9\u4e24\u6bb5\u88ab\u5206\u914d\u5230\u4e24\u6761\u7a7a\u95f2 tape \u4e0a\uff0c\u5373 \\(T_2\\) \u548c \\(T_3\\)\u3002</p> <p> </p> <p>\u4e8e\u662f\uff0c\u5b8c\u6210\u4e86\u7b2c\u4e09\u4e2a pass\u3002</p> Pass 4 <p>\u540c\u6837\uff0cpass 4 \u548c\u524d\u9762\u4e24\u4e2a pass \u7684\u8fc7\u7a0b\u4e5f\u662f\u4e00\u81f4\u6027\u7684\uff0c\u4e0d\u505a\u8fc7\u591a\u89e3\u91ca\uff0c\u5bf9\u4e8e\u89c4\u6a21\u66f4\u5927\u7684\u6570\u636e\u4e5f\u662f\u4e00\u6837\uff0c\u9664\u4e86\u7b2c\u4e00\u4e2a pass \u6bd4\u8f83\u7279\u6b8a\uff0c\u5176\u5b83 pass \u90fd\u662f\u4e00\u6837\u7684\u3002\u6700\u7ec8\u5f97\u5230\u53ea\u5269\u4e0b\u4e00\u4e2a tape \u4e2d\u5305\u542b\u552f\u4e00\u7684 run \u65f6\uff0c\u6392\u5e8f\u5c31\u7ed3\u675f\u4e86\u3002</p> <p> </p> <p>\u81f3\u6b64\uff0c\u6392\u5e8f\u7ed3\u675f\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec15/#\u4f18\u5316\u7a7a\u95f4","title":"\u4f18\u5316\u7a7a\u95f4","text":"<p>\u53ef\u4ee5\u4f18\u5316\u7684\u90e8\u5206\u4e3b\u8981\u6709\u8fd9\u4e48\u51e0\u4e2a\uff1a</p> <ul> <li>\u4e00\u4e2a pass \u610f\u5473\u7740\u82e5\u5e72\u6b21 seek\uff0c\u6240\u4ee5\u51cf\u5c11 pass \u53ef\u4ee5\u662f\u4e00\u4e2a\u65b9\u5411\uff1b<ul> <li>#pass-\u6570\u91cf\u5206\u6790\u4e0e\u4f18\u5316</li> </ul> </li> <li>merge \u7684\u8fc7\u7a0b\u4e2d\u4f1a\u591a\u6b21\u8bfb\u53d6 tape \u4e2d\u7684\u6570\u636e\uff0c\u800c\u5bf9\u4e8e\u8ba1\u7b97\u673a\u6765\u8bf4\u5355\u6b21\u5927\u91cf\u8bfb\u53d6\u6bd4\u591a\u6b21\u5c0f\u91cf\u8bfb\u53d6\u66f4\u9ad8\u6548\uff0c\u5982\u4f55\u4f18\u5316\u6570\u636e\u8bfb\u53d6\u4e5f\u662f\u4e00\u4e2a\u65b9\u5411\uff1b<ul> <li>#tape-\u6570\u91cf\u5206\u6790\u4e0e\u4f18\u5316</li> </ul> </li> <li>\u5982\u4f55\u66f4\u9ad8\u6548\u7684\u5728 \\(k\\)-way merge \u8fc7\u7a0b\u4e2d\uff0c\u5f52\u5e76 M \u4e2a\u5206\u522b\u6765\u81ea k \u4e2a\u5e8f\u5217\u7684\u6570\u636e\uff0c\u5373\u5185\u6392\u5e8f\u7684\u7b56\u7565\uff0c\u4e5f\u4e0a\u4f18\u5316\u7684\u4e00\u4e2a\u65b9\u5411\uff1b<ul> <li>#k-\u8def\u5185\u6392\u5e8f\u4f18\u5316</li> </ul> </li> <li>\u8bfb\u5165\u3001\u5185\u6392\u5e8f\u3001\u8f93\u51fa\uff0c\u8fd9\u4e09\u4e2a\u4e8b\u52a1\u76ee\u524d\u662f\u505c\u673a\u4e32\u884c\u7684\uff0c\u8003\u8651\u5c06\u5176\u5e76\u884c\u5316\u4e5f\u662f\u4e00\u4e2a\u65b9\u5411\uff1b<ul> <li> TODO</li> </ul> </li> </ul>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec15/#pass-\u6570\u91cf\u5206\u6790\u4e0e\u4f18\u5316","title":"pass \u6570\u91cf\u5206\u6790\u4e0e\u4f18\u5316","text":"<p>\u4f8b\u5b50\u4e2d\u4e00\u5171\u7ecf\u8fc7\u4e86 4 \u6b21 pass\u3002\u5982\u679c\u6211\u4eec\u8bb0 \\(max(\\#run)\\) \u4e3a \\(\\#run\\) \u6700\u591a\u7684 tape \u7684 \\(\\#run\\)\uff0c\u5219\u6bcf\u4e00\u6b21 pass \u4f1a\u4ee4 \\(max(\\#run)\\) \u7f29\u5c0f\u4e00\u534a\uff0c\u76f4\u5230 \\(max(\\#run)\\) \u53d8\u4e3a 1\uff0c\u4e14\u53ea\u6709\u5b83\u4e00\u6761 tape \u8fd8\u6709\u6570\u636e\uff0c\u6807\u5fd7\u7740\u6392\u5e8f\u7ed3\u675f\u3002</p> <p>\u5982\u679c\u4e13\u6ce8\u4e8e \\(\\#run\\) \u7684\u53d8\u5316\uff0c\u90a3\u4e48\u4e0a\u9762\u7684\u6a21\u62df\u6b65\u9aa4\u5927\u81f4\u662f\u8fd9\u4e48\u4e00\u4e2a\u8fc7\u7a0b\uff1a</p> <p>Pass 1</p> <p>\u539f\u5148 \\(T_1\\) \u4e0a \\(\\#run = 5\\)\uff0c\u73b0\u5c06\u5b83\u5206\u914d\u5230\u4e24\u6761 tape \u4e0a\uff0c\u4e8e\u662f\u6709\uff1a</p> <ul> <li>\\(T_2\\) \u4e0a \\(\\#run = 3\\)\uff1b</li> <li>\\(T_3\\) \u4e0a \\(\\#run = 2\\)\uff1b</li> </ul> <p>Pass 2</p> <p>\u4f9d\u6b21\u53d6 \\(T_2\\) \u548c \\(T_3\\) \u7684\u7b2c\u4e00\u6bb5\uff0c\u5f52\u5e76\u5f97\u5230\u65b0\u7684 run\uff0c\u5747\u5206\u5230\u53e6\u5916\u4e24\u6761 tape \u4e0a\uff08\u672a\u4f18\u5316\u7684\u505a\u6cd5\uff0c\u4f18\u5316\u505a\u6cd5\u53c2\u8003#tape-\u4f18\u5316\uff09\uff0c\u4e8e\u662f\u6709\uff1a</p> <ul> <li>\\(T_2\\) \u4e0a \\(\\#run = 3-1 = 2\\)\uff1b</li> <li>\\(T_3\\) \u4e0a \\(\\#run = 2-1 = 1\\)\uff1b</li> <li>\\(T_1\\) \u4e0a \\(\\#run = 0+1 = 1\\)\uff1b</li> <li>\\(T_4\\) \u4e0a \\(\\#run = 0\\)\uff1b</li> </ul> <p>\u7ee7\u7eed\u53d6\uff0c\u5373\uff1a</p> <ul> <li>\\(T_2\\) \u4e0a \\(\\#run = 2-1 = 1\\)\uff1b</li> <li>\\(T_3\\) \u4e0a \\(\\#run = 1-1 = 0\\)\uff1b</li> <li>\\(T_1\\) \u4e0a \\(\\#run = 1\\)\uff1b</li> <li>\\(T_4\\) \u4e0a \\(\\#run = 0+1 = 1\\)\uff1b</li> </ul> <p>\\(T_3\\) \u4e0a\u5df2\u7ecf\u6ca1\u6709\u4e86\uff0c\u4f46\u662f \\(T_2\\) \u8fd8\u6ca1\u53d6\u5b8c\uff0c\u6240\u4ee5\u53ea\u4ece \\(T_2\\) \u62ff\uff1a</p> <ul> <li>\\(T_2\\) \u4e0a \\(\\#run = 1-1 = 0\\)\uff1b</li> <li>\\(T_3\\) \u4e0a \\(\\#run = 0\\)\uff1b</li> <li>\\(T_1\\) \u4e0a \\(\\#run = 1+1 = 2\\)\uff1b</li> <li>\\(T_4\\) \u4e0a \\(\\#run = 1\\)\uff1b</li> </ul> <p>\u6a21\u62df\u5230\u4ece\u8fd9\u91cc\u5176\u5b9e\u5df2\u7ecf\u53ef\u4ee5\u770b\u51fa\u6765\u4e86\uff0c\u5bf9\u4e8e 2-way merge \u6765\u8bf4\uff0c\u6392\u9664\u672b\u6bb5\u60c5\u51b5\uff0c\u4ece\u7b2c\u4e8c\u4e2a pass \u5f00\u59cb\uff0c\u57fa\u672c\u4e0a\u6bcf\u6b21\u90fd\u662f\u4ece 2 \u8def\u4e2d\u5404\u53d6 1 \u4e2a run\uff0c\u5e76\u5408\u5e76\u4e3a 1 \u4e2a run\u3002\u6362\u53e5\u8bdd\u6765\u8bf4\uff0c\u6bcf\u4e00\u4e2a pass \u4f1a\u8ba9 \\(total(\\#run)\\) \u7f29\u5c0f\u4e3a\u539f\u6765\u7684 \\(\\frac{1}{2}\\)\u3002</p> <p>\u90a3\u4e48\uff0c\u5bf9\u4e8e \\(k\\)-way merge \u6765\u8bf4\uff0c\u5c31\u662f\u4ece\u7b2c\u4e8c\u4e2a pass \u5f00\u59cb\uff0c\u6bcf\u6b21\u4ece \\(k\\) \u8def\u4e2d\u5404\u53d6 1 \u4e2a run\uff0c\u5e76\u5408\u5e76\u4e3a 1 \u4e2a run\uff0c\u6bcf\u4e00\u4e2a pass \u4f1a\u8ba9 \\(total(\\#run)\\) \u7f29\u5c0f\u4e3a\u539f\u6765\u7684 \\(\\frac{1}{k}\\)\u3002</p> <p>\u56e0\u6b64\uff0c\u6211\u4eec\u53ef\u4ee5\u5f52\u7eb3\u5f97\u5230\u5982\u4e0b\u8ba1\u7b97\u5f0f\uff1a</p> \\[ \\begin{aligned} \\#pass &amp;= \\underbrace{         1     }_{\\text{pass 1}}     +      \\underbrace{         \\lceil \\log_{k}{(\\#run)}\\rceil     }_{\\text{rest passes}} \\\\     &amp;= \\underbrace{         1     }_{\\text{pass 1}}     +      \\underbrace{         \\lceil \\log_{k}{             \\lceil \\frac{N}{M} \\rceil         }\\rceil     }_{\\text{rest passes}}  \\end{aligned} \\] <p>\u5176\u4e2d\uff0c\\(k\\) \u8868\u793a\u5f52\u5e76\u8def\u6570\uff0c\\(N\\) \u8868\u793a\u6570\u636e\u91cf\uff0c\\(M\\) \u8868\u793a\u5185\u5b58\u4e00\u6b21\u80fd\u5904\u7406\u7684\u6570\u636e\u91cf\u3002</p> <p>\u90a3\u4e48\uff0c\u51cf\u5c11 pass \u7684\u65b9\u6cd5\u4e5f\u5f88\u76f4\u89c2\u4e86\uff0c\u53ea\u9700\u8981\u589e\u52a0 \\(k\\) \u5373\u53ef\uff0c\u5373\u91c7\u53d6\u66f4\u591a\u8def\u7684\u5f52\u5e76\uff0c\u5c31\u80fd\u51cf\u5c11 pass\u3002</p> <p>\u7136\u800c\uff0c\u5176\u4e2d\u5fc5\u7136\u5b58\u5728\u4e00\u4e2a trade-off \u7684\u5173\u7cfb\uff0c\u867d\u7136 \\(k\\) \u589e\u52a0\u53ef\u4ee5\u51cf\u5c11 \\(\\#pass\\)\uff0c\u4f46\u662f\u5728\u63a5\u4e0b\u6765\u4e00\u8282\u4e2d\u6211\u4eec\u4f1a\u77e5\u9053\uff0c\\(k\\) \u8fc7\u5927\u4f1a\u5bfc\u81f4 tape \u9700\u6c42\u91cf\u589e\u52a0\uff0c\u6b64\u5916\uff0c\\(k\\) \u7684\u589e\u52a0\u4e5f\u4f1a\u5bfc\u81f4\u5185\u6392\u5e8f\u7684\u590d\u6742\u5ea6\u589e\u52a0\uff0c\u4e5f\u4f1a\u589e\u52a0 pass \u5185\u7684 seek \u6b21\u6570\u3002</p> <p>\u5f53\u7136\uff0c\u9664\u4e86\u66b4\u529b\u7684\u589e\u52a0 \\(k\\) \u4ee5\u5916\uff0c\u6211\u4eec\u8fd8\u53ef\u4ee5\u901a\u8fc7\u4f7f\u7528\u66ff\u6362\u9009\u62e9(Replacement Selection)\u7b97\u6cd5\uff0c\u6765\u751f\u6210\u6bd4 \\(M\\) \u5927\u7684\u521d\u59cb run\uff0c\u4ee5\u76f8\u5bf9\u51cf\u5c11 pass \u6570\u91cf\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec15/#\u66ff\u6362\u9009\u62e9\u7b97\u6cd5","title":"\u66ff\u6362\u9009\u62e9\u7b97\u6cd5","text":"<p>\u66ff\u6362\u9009\u62e9(Replacement Selection) \u5728 hw15 \u4e2d\u88ab\u5e03\u7f6e\u4e3a\u7f16\u7a0b\u9898\uff0c\u6240\u4ee5\u5176\u5b9e\u73b0\u8fc7\u7a0b\u53ef\u4ee5\u7ed3\u5408\u90a3\u9053\u9898\u76ee\u6765\u5b66\u4e60\u3002</p> Replacement Selection @ PTA <p>When the input is much too large to fit into memory, we have to do external sorting instead of internal sorting. One of the key steps in external sorting is to generate sets of sorted records (also called runs) with limited internal memory. The simplest method is to read as many records as possible into the memory, and sort them internally, then write the resulting run back to some tape. The size of each run is the same as the capacity of the internal memory.</p> <p>Replacement Selection sorting algorithm was described in 1965 by Donald Knuth. Notice that as soon as the first record is written to an output tape, the memory it used becomes available for another record. Assume that we are sorting in ascending order, if the next record is not smaller than the record we have just output, then it can be included in the run.</p> <p>For example, suppose that we have a set of input { 81, 94, 11, 96, 12, 99, 35 }, and our memory can sort 3 records only. By the simplest method we will obtain three runs: { 11, 81, 94 }, { 12, 96, 99 } and { 35 }. According to the replacement selection algorithm, we would read and sort the first 3 records { 81, 94, 11 } and output 11 as the smallest one. Then one space is available so 96 is read in and will join the first run since it is larger than 11. Now we have { 81, 94, 96 }. After 81 is out, 12 comes in but it must belong to the next run since it is smaller than 81. Hence we have { 94, 96, 12 } where 12 will stay since it belongs to the next run. When 94 is out and 99 is in, since 99 is larger than 94, it must belong to the first run. Eventually we will obtain two runs: the first one contains { 11, 81, 94, 96, 99 } and the second one contains { 12, 35 }.</p> <p>Your job is to implement this replacement selection algorithm.</p> <p>\u5229\u7528\u66ff\u6362\u9009\u62e9\u7b56\u7565\u4ee5\u540e\uff0c\u6bcf\u4e00\u6b21\u751f\u6210\u7684 run \u4e00\u5b9a\u4e0d\u5c0f\u4e8e \\(M\\)\uff08\u672b\u7aef\u4f59\u6570\u9664\u5916\uff09\uff0c\u4e8e\u662f\u76f8\u5bf9\u6765\u8bf4 \\(\\#pass\\) \u5c31\u4f1a\u51cf\u5c11\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec15/#tape-\u6570\u91cf\u5206\u6790\u4e0e\u4f18\u5316","title":"tape \u6570\u91cf\u5206\u6790\u4e0e\u4f18\u5316","text":"<p>\u5982\u679c\u4f7f\u7528#\u6734\u7d20\u8fc7\u7a0b\u5206\u6790\u4e2d\u7684\u65b9\u6cd5\uff0c\u90a3\u4e48\u6211\u4eec\u4f7f\u7528 \\(k\\)-way merge \u81f3\u5c11\u9700\u8981 \\(2k\\) \u4e2a tape\u3002</p> <p>\u8fd9\u5176\u5b9e\u5f88\u597d\u7406\u89e3\uff0c\u6211\u4eec\u6bcf\u4e00\u4e2a pass \u9700\u8981 \\(k\\) \u4e2a tape \u6765\u5b58\u653e\u6bcf\u4e00\u8def\u7684\u5e8f\u5217\uff0c\u800c\u5176\u7ed3\u679c\u8981\u5e73\u5206\u653e\u590d\u5236\u5230\u4e0b\u4e00\u4e2a pass \u6240\u9700\u8981\u7684 \\(k\\) \u4e2a pass \u4e2d\uff0c\u6240\u4ee5\u81f3\u5c11\u9700\u8981 \\(2k\\) \u4e2a tape \u8f6e\u6362\u7740\u6765\u5b58\u50a8\u6570\u636e\u3002</p> <p>\u800c\u8fd9\u4e0d\u5229\u4e8e\u6211\u4eec\u901a\u8fc7\u589e\u52a0 \\(k\\) \u6765\u51cf\u5c11 \\(\\#pass\\)\uff0c\u56e0\u6b64\u6211\u4eec\u8003\u8651\u67d0\u79cd\u7b56\u7565\u6765\u4f18\u5316 tape \u7684\u4f7f\u7528\u3002</p> <p>\u5728#\u6734\u7d20\u8fc7\u7a0b\u5206\u6790\u4e2d\u6211\u591a\u6b21\u6697\u793a\uff0c\u4e4b\u540e\u4f1a\u5bf9\u300c\u5c06\u5f52\u5e76\u540e\u7684 run \u5e73\u5206\u5230\u5404 tape\u300d\u8fd9\u4ef6\u4e8b\u505a\u4f18\u5316\u3002</p> <p>\u6211\u4eec\u53ef\u4ee5\u8003\u8651\uff0c\u4e0d\u5e73\u5747\u7684\u5c06\u5f52\u5e76\u540e\u7684 run \u5206\u914d\u5230\u5404\u4e2a tape \u4e0a\uff0c\u5373\u603b\u6709\u4e00\u4e9b tape \u6bd4\u522b\u7684 tape \u591a\u4e00\u4e9b run\u3002\u867d\u7136\u5728\u5e73\u5206\u7684\u7b56\u7565\u4e2d\uff0c\u4e5f\u6709\u53ef\u80fd\u4f1a\u6709\u591a\u51fa\u6765\u7684 run\uff0c\u4f46\u662f\u53ea\u4f1a\u591a\u4e00\u4e2a\uff08\u4e5f\u5c31\u662f\u5c06 \\(x \\mod k\\) \u7684\u4f59\u6570\u5206\u914d\u5230\u5176\u4e2d\u51e0\u4e2a tape \u4e0a\uff09\u3002\u6b64\u65f6\u8fd9\u4e9b\u591a\u51fa\u6765\u7684 run \u53ef\u80fd\u5c31\u662f\u5355\u7eaf\u7684\u4ece\u4e00\u4e2a tape \u522b\u590d\u5236\u5230\u53e6\u5916\u4e00\u4e2a tape \u4e0a\uff0c\u770b\u8d77\u6765\u662f\u4e2a\u975e\u5e38\u6ca1\u5fc5\u8981\u7684\u64cd\u4f5c\uff0c\u4e3a\u4ec0\u4e48\u4e0d\u76f4\u63a5\u7559\u4e0b\u5b83\uff0c\u5c06\u5f53\u524d tape \u62ff\u5230\u4e0b\u4e00\u8f6e\u7528\u5462\uff1f</p> <p>\u4f46\u662f\u7531\u4e8e\u5e73\u5206\u7b56\u7565\u4e0b\uff0c\u8fd9\u4e2a\u60c5\u51b5\u7684\u51fa\u73b0\u5e76\u4e0d\u53ef\u63a7\uff0c\u800c\u4e14\u603b\u662f\u4f1a\u5f15\u8d77\u60ac\u6b8a\u7684 tape \u95f4\u7684\u6570\u91cf\u5dee\uff0c\u6240\u4ee5\u6211\u4eec\u8003\u8651\u80fd\u4e0d\u80fd\u4e3b\u52a8\u5229\u7528\u8fd9\u4e2a\u6027\u8d28\u3002</p> <p>\u5b9e\u5728\u60f3\u4e0d\u5230\u600e\u4e48\u8fc7\u5ea6\u4e86\uff0c\u800c\u4e14\u6025\u6025\u6025\uff0c\u6240\u4ee5\u76f4\u63a5\u4e0a\u7ed3\u8bba\u3002</p> <p>\u6211\u4eec\u6309\u7167 Fibonacci \u6570\u5217\u7684\u9879\u6765\u5206\u914d\u6bcf\u4e2a tape \u7684 \\(\\#run\\)\uff0c\u6b64\u65f6\u6bcf\u4e00\u4e2a pass \u53ea\u9700\u8981\u4e00\u4e2a\u6709\u4e00\u4e2a\u7a7a\u95f2\u7684 tape \u5373\u53ef\u3002</p> <p>example</p> \\[ \\text{Fibonacci}: {1,1,2,3,5,8,13,21,...} \\] <p>\u5047\u8bbe\u6211\u4eec\u73b0\u5728\u6709\u4e24\u4e2a tape\uff0c\u5206\u522b\u6709 23 \u4e2a run \u548c 13 \u4e2a run\uff0c\u5219\uff1a</p> \\(T_1\\) \\(T_2\\) \\(T_3\\) \u8bf4\u660e 21 13 - \u521d\u59cb\u60c5\u51b5 8 - 13 \\(T_1\\) \u7684\u524d 13 \u4e2a\u4e0e \\(T_2\\) \u5f52\u5e76\uff0c\u7ed3\u679c\u5199\u5165 \\(T_3\\) - 8 5 \\(T_3\\) \u7684\u524d 8 \u4e2a\u4e0e \\(T_1\\) \u5f52\u5e76\uff0c\u7ed3\u679c\u5199\u5165 \\(T_2\\) 5 3 - \u7565 2 - 3 \u7565 - 2 1 \u7565 1 1 - \u7565 0 - 1 \u7565 <p>\u4f7f\u7528 Fibonacci \u6211\u4eec\u603b\u53ef\u4ee5\u6eda\u52a8\u7740\u5c06 \\(\\#run\\) \u7684\u89c4\u6a21\u7f29\u5c0f\u3002</p> k-way merge with k-order Fibonacci Sequence <p>\u5bf9\u4e8e \\(k\\)-way merge\uff0c\u6211\u4eec\u53ea\u9700\u8981\u6784\u9020 k \u9636 Fibonacci \u6570\u5217\uff0c\u7136\u540e\u6309\u7167\u8fd9\u4e2a\u6570\u5217\u6765\u5206\u914d\u6bcf\u4e2a tape \u7684 \\(\\#run\\) \u5373\u53ef\u3002</p> <p>k-order Fibonacci Sequence</p> <p>\u7ed9\u51fa k \u9636 Fibonacci \u6570\u5217\uff08\u4e0e PPT \u7565\u6709\u4e0d\u540c\uff0c\u4e3b\u8981\u4f53\u73b0\u5728\u4e0b\u6807\u4ece\u8c01\u5f00\u59cb\uff0c\u65e0\u4f24\u5927\u96c5\uff09\uff1a</p> \\[ \\left\\{ \\begin{aligned}     F^k_1 &amp;= 1 \\\\     F^k_2 &amp;= 1 \\\\     &amp; \\vdots\\\\     F^k_n &amp;= F^k_{n-1} + F^k_{n-2} + \\cdots + F^k_{n-k} \\quad (n &gt; k) \\end{aligned} \\right. \\] <p>\u8fd9\u4e2a\u7ed3\u8bba\u770b\u8d77\u6765\u5f88\u81ea\u7136\uff0c\u4f46\u662f\u5b9e\u9645\u4e0a\u662f\u600e\u4e48\u64cd\u4f5c\u7684\u5462\uff1fPPT \u538b\u6839\u6ca1\u8bb2\uff0c\u56e0\u6b64\uff0c\u6211\u5728\u8be2\u95ee ch \u8001\u5e08\u4ee5\u540e\uff0c\u5199\u4e0b\u4e86\u8fd9\u4e2a\u90e8\u5206\uff0c\u65e8\u5728\u8865\u5145 \\(k\\)-way merge \u4f7f\u7528 k \u9636 Fibonacci \u4f18\u5316\u7684\u65b9\u6cd5\u3002</p> <p>\u9996\u5148\uff0c\u505a\u4e00\u4e9b\u5f3a\u8c03\uff1a</p> <ol> <li>\u8be5\u65b9\u6cd5\u9648\u8ff0\u8fc7\u7a0b\u4e2d\uff0ck \u8def\u59cb\u7ec8\u76f4\u63a5\u5408\u5e76\u6210\u4e00\u8def\uff08\u5343\u4e07\u4e0d\u8981\u7528\u201citerative\u201d\u7684\u601d\u8def\u6765\u8003\u8651\uff0c\u5c31\u7b97 iterative\uff0c\u8fed\u4ee3\u5b8c\u4e86\u4e5f\u8fd8\u662f k \u8def\u5f52\u4e3a 1 \u8def\uff09\uff1b</li> <li>\u6211\u4eec\u7684\u76ee\u7684\u662f\u4f18\u5316\u6bcf\u4e00\u4e2a pass \u4e2d\u6bcf\u4e2a tape \u7684 \\(\\#run\\) \u4e0d\u4e00\u6837\u5e26\u6765\u7684\u6027\u80fd\u95ee\u9898\uff08\u4f8b\u5982\u5c34\u5c2c\u7684 \\(n\\) \u548c \\(n+1\\) \u5f52\uff0c\u4e0b\u4e00\u4e2a pass \u5c31\u5f97 \\(1\\) \u548c  \\(n\\) \u5f52\u4e86\uff09\uff1b</li> </ol> <p>\u5bf9\u4e8e\u7b2c \\(i\\) \u4e2a pass\uff0c\u6709 \\(k\\) \u4e2a tape\uff0c\u6211\u4eec\u8bb0\u6bcf\u4e00\u4e2a tape \u7684 \\(\\#run\\) \u4e3a \\(r_i\\)\uff0c\u5219\u6709\uff1a</p> <ul> <li>\\(\\max\\{r_i\\} = F^k_j\\);</li> <li>\\(\\min\\{r_i\\} = F^k_{j-1}\\);</li> </ul> <p>\u4e5f\u5c31\u662f\u8bf4\uff0c\u6bcf\u4e2a pass \u6700\u5927\u548c\u6700\u5c0f\u7684 \\(\\#run\\) \u5206\u522b\u6709 k \u9636 Fibonacci \u4e2d\u76f8\u90bb\u7684\u4e24\u9879\u3002</p> <p>\u8fd9\u91cc\u5206\u5f00\u7528 i \u548c j \u662f\u60f3\u8868\u8fbe\u8fd9\u4e2a\u5339\u914d\u5173\u7cfb\u4e0d\u91cd\u8981\uff0c\u91cd\u8981\u7684\u662f\u6700\u5927\u503c\u6700\u5c0f\u503c\u7531 Fibonacci \u76f8\u90bb\u9879\u6240\u786e\u5b9a\u3002</p> <p>\u90a3\u4e48\u5939\u5728\u6700\u5927\u548c\u6700\u5c0f\u7684\u4e2d\u95f4\u7684\u5176\u4ed6 \\(\\#run\\) \u8981\u5982\u4f55\u786e\u5b9a\u5462\uff1f\u9996\u5148\u6211\u4eec\u8fdb\u884c\u4e00\u6bb5\u63a8\u5bfc\uff1a</p> <p>\u5047\u8bbe \\(\\{r_i\\}\\) \u7ecf\u8fc7\u6392\u5e8f\uff0c\u5e76\u4e14\u521a\u597d\u80fd\u51d1\u4e0a\u6211\u4eec\u6240\u9700\u8981\u7684\u6570\u91cf\uff0c\u6709\uff1a</p> \\[ r_k &gt; r_{k-1} &gt; ... &gt; r_{2} &gt; r_{1} \\text{where } r_k = F^k_j \\text{ and } r_1 = F^k_{j-1} \\] <p>\u5728\u8fd9\u4e00\u4e2a pass \u4e2d\uff0c\u6211\u4eec\u5c06\u6240\u6709 tape \u7684\u524d \\(r1\\) \u4e2a run \u62ff\u51fa\u6765 merge\uff0c\u8fd9\u6837\uff0c\u9664\u4e86 \\(r_1\\) \u8fd9\u4e2a tape\uff0c\u5176\u4ed6 tape \u7684 \\(\\#run\\) \u90fd\u53d8\u4e3a \\(r_i-r_1\\)\u3002\u6b64\u65f6\u6709\u4e0d\u7b49\u5173\u7cfb\uff1a</p> \\[ r_1 &gt; r_k - r_1 &gt; r_{k-1} - r_1 &gt; ... &gt; r_{2} - r_1 \\] <p>\u8fd9\u91cc\u552f\u4e00\u9700\u8981\u8bf4\u660e\u7684\u5c31\u662f \\(r_1 &gt; r_k - r_1\\)\uff1a</p> proof of the relation \\[ \\begin{aligned}     &amp;\\begin{aligned}         \\because r_1          &amp;= F^k_{j-1} \\\\         &amp;= F^k_{j-2} + \\cdots + F^k_{j-k} + F^k_{j-k-1}     \\end{aligned}  &amp; (1)\\\\     &amp;\\begin{aligned}         \\text{and } r_k         &amp;= F^k_{j} \\\\         &amp;= F^k_{j-1} + F^k_{j-2} + \\cdots + F^k_{j-k}     \\end{aligned}  &amp; (2)\\\\     &amp;\\begin{aligned}         \\therefore r_k - r_1          &amp;= F^k_{j} - F^k_{j-1} \\quad \\text{ i.e. } (2) - (1)\\\\         &amp;= F^k_{j-2} + \\cdots + F^k_{j-k}     \\end{aligned}  &amp; (3)\\\\     &amp;\\begin{aligned}         \\therefore r_1 - (r_k - r_1)         &amp;= F^k_{j-k-1} &gt; 0 \\quad \\text{ i.e. } (1) - (3) \\\\     \\end{aligned} \\\\     &amp;\\begin{aligned}     \\therefore r_1 &gt; r_k - r_1     \\end{aligned} \\\\   \\end{aligned} \\] <p>\u5982\u679c\u6211\u4eec\u5c06\u73b0\u5728\u8fd9\u4e2a\u6392\u5e8f\u540e\u7684\u6570\u5217\u8bb0\u4e3a \\(\\{r_i'\\}\\)\uff0c\u5219\u6709\uff1a</p> \\[ \\left\\{ \\begin{aligned}     r_1' &amp;= r_2 - r_1 \\\\     r_2' &amp;= r_3 - r_1 \\\\     \\vdots \\\\     r_{k-1}' &amp;= r_k - r_1 \\\\     r_k' &amp;= r_1 \\end{aligned} \\right. \\] <p>\u6b64\u65f6\u6839\u636e\u6211\u4eec\u5173\u4e8e\u6700\u5927\u6700\u5c0f\u503c\u7684\u9648\u8ff0\uff0c\u53c8\u6709\uff1a</p> \\[ \\left\\{ \\begin{aligned}     r_1' &amp;= F^k_{j-2} \\\\     r_k' &amp;= F^k_{j-1} \\end{aligned} \\right. \\] <p>\u4e8e\u662f\u53ef\u4ee5\u63a8\u5f97\uff1a\\(r_2 = r_1 + F^k_{j-2} = F^k_{j-1} + F^k_{j-2}\\)\u3002\u5173\u4e8e \\(r_3, r_4\\)\uff0c\u4e5f\u662f\u4e00\u6837\u7684\u529e\u6cd5\uff0c\u5c06 \\(r_2\\) \u7684\u7ed3\u8bba\u8fc1\u79fb\u5230 \\(r_2'\\)\uff0c\u518d\u56de\u8fc7\u5934\u5f97\u5230 \\(r_3 = r_1 + r_2'= F^k_{j-1} + F^k_{j-2} + F^k_{j-3}\\)\uff0c\u4ee5\u6b64\u7c7b\u63a8\uff0c\u53ef\u4ee5\u5f97\u5230\u6700\u7ec8\u7ed3\u8bba\uff1a</p> \\[ \\left\\{ \\begin{aligned}     r_1 &amp;= F^k_{j-1} \\\\     r_2 &amp;= F^k_{j-1} + F^k_{j-2} \\\\     r_3 &amp;= F^k_{j-1} + F^k_{j-2} + F^k_{j-3} \\\\     \\vdots \\\\     r_k &amp;= F^k_{j-1} + F^k_{j-2} + ... + F^k_{j-k} = F^k_{j} \\end{aligned} \\right. \\] <p>\u601d\u8003\u9898</p> <p>\u53ef\u4ee5\u611f\u53d7\u601d\u8003\u4e00\u4e0b\u8fd9\u4e2a\u7279\u6027\uff08\u8003\u8651 2-way \u5373\u53ef\uff09\u4e0e\u9ec4\u91d1\u6bd4\u4f8b\u7684\u5173\u7cfb\uff01</p> <p>hint: \u5982\u4f55\u7406\u89e3 \\(\\frac{a_n}{a_{n-1}} \\approx \\frac{a_{n-1}}{a_n - a_{n-1}}\\) \u4e0e\u8fd9\u4e2a\u6027\u8d28\u7684\u5173\u7cfb\uff1f</p> <p>\u5f53\u7136\uff0c\u521a\u597d\u80fd\u51d1\u4e0a Fibonacci \u7684\u60c5\u51b5\u81ea\u7136\u662f\u5c11\u6570\uff0c\u5bf9\u4e8e\u65e0\u6cd5\u51d1\u4e0a Fibonacci \u7684\u60c5\u51b5\uff0c\u6211\u4eec\u53ef\u4ee5\u5c06\u591a\u4f59\u7684\u90e8\u5206\u5747\u5300\u7684\u5206\u5230\u8f83\u591a\u82e5\u5e72 tape \u4e0a\uff0c\u4ee5\u76f8\u5bf9\u7684\u5229\u7528 Fibonacci \u6570\u5217\u7684\u6027\u8d28\uff08\u8054\u7cfb\u601d\u8003\u9898\u7406\u89e3\uff09\u3002</p> <p>\u6ce8\u610f</p> <p>\u6216\u8bb8\u4f60\u5df2\u7ecf\u5f00\u59cb\u4ea7\u751f\u7591\u95ee\u4e86\uff0c\u5982\u679c\u8fd9\u6837\u6765\u505a\uff0c\u524d\u9762\u5bf9 \\(\\#pass\\) \u7684\u5206\u6790\u662f\u4e0d\u662f\u4e0d\u6210\u7acb\u4e86\u5462\uff1f</p> <p>\u6211\u60f3\u5e94\u8be5\u786e\u5b9e\u4e0d\u518d\u5b8c\u5168\u4e00\u6837\u4e86\uff0c\u4f46\u662f\u5e76\u4e0d\u5f71\u54cd\u6211\u4eec\u4e4b\u540e\u5229\u7528\u90a3\u4e2a\u7ed3\u8bba\u505a\u5b9a\u6027\u5206\u6790\uff0c\u6211\u4eec\u53ea\u9700\u8981\u77e5\u9053\uff0c\u91c7\u53d6 Fibonacci \u7b56\u7565\u6765\u4f18\u5316\u4f1a\u5bfc\u81f4 \\(\\#pass\\) \u589e\u591a\u5373\u53ef\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec15/#k-\u8def\u5185\u6392\u5e8f\u4f18\u5316","title":"k \u8def\u5185\u6392\u5e8f\u4f18\u5316","text":"<p>\u968f\u7740 \\(k\\) \u7684\u589e\u52a0\uff0c\u6211\u4eec\u4e0d\u80fd\u518d\u50cf\u4e24\u8def\u5f52\u5e76\u90a3\u6837\u76f4\u63a5\u8f93\u51fa\u8f83\u5c0f\u7684\u90a3\u4e2a\uff0c\u800c\u662f\u9700\u8981\u7ef4\u62a4\u6570\u636e\u7ed3\u6784\u6765\u603b\u662f\u8f93\u51fa k \u4e2a\u4e2d\u6700\u5c0f\u7684\u90a3\u4e2a\u2014\u2014\u6211\u4eec\u7528\u5806\u6765\u7ef4\u62a4\u6bcf\u4e00\u4e2a run \u5728\u5185\u5b58\u4e2d\u7684\u6570\u636e\u7684\u961f\u9996\u5143\u7d20\uff08\u540c\u65f6\u4e5f\u662f\u6700\u5c0f\u5143\u7d20\uff09\uff0c\u6bcf\u5f53\u5806\u9876\u5143\u7d20\u88ab\u8f93\u51fa\uff0c\u5c31\u9700\u8981\u4ece\u5bf9\u5e94\u7684 run \u4e2d\u8bfb\u5165\u4e0b\u4e00\u4e2a\u5143\u7d20\u3002</p> <p>\u6ce8\u610f</p> <p>\u9700\u8981\u6ce8\u610f\uff0c\u8fd9\u91cc\u7684\u5806\u662f\u989d\u5916\u7ef4\u62a4\u7684\uff0c\u800c\u6bcf\u6b21\u63a8\u5165\u5806\u4e2d\u7684\u5143\u7d20\u90fd\u662f\u4ece\u5bf9\u5e94\u7684 run \u7684 buffer \u4e2d\u62ff\u7684\uff0c\u800c\u4e0d\u662f\u6bcf\u6b21\u90fd\u4ece\u786c\u76d8\u4e2d\u62ff\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec15/#\u970d\u592b\u66fc\u6811\u4f18\u5316","title":"\u970d\u592b\u66fc\u6811\u4f18\u5316","text":"<p>\u5f53\u7136\uff0c\u6211\u4eec\u4e5f\u53ef\u4ee5\u4e0d\u4f7f\u7528\u76f4\u63a5 \\(k\\) \u8def\u5408\u5e76\uff0c\u800c\u662f\u91c7\u7528\u4e24\u4e24\u5f52\u5e76\u7684\u65b9\u6cd5\uff0c\u4e5f\u5c31\u662f wiki \u4e2d\u63d0\u5230\u7684\u8fed\u4ee3\u5f52\u5e76\uff08\u6ce8\u610f\uff0c\u8be5\u6761\u76ee\u4e2d\u63d0\u5230\u7684\u5f52\u5e76\u5e76\u6ca1\u6709\u8bf4\u660e\u662f\u5916\u6392\u5e8f\u80cc\u666f\uff0c\u4f46\u662f\u53ef\u4ee5\u8fc1\u79fb\uff09\u3002 </p> <p>\u5047\u8bbe\u6211\u4eec\u73b0\u5728\u6709\u82e5\u5e72\u4e2a run\uff0c\u5e76\u4e14\u6211\u4eec\u5c06\u8981\u8fdb\u884c\u4e24\u4e24\u5f52\u5e76\uff0c\u90a3\u4e48\u6211\u4eec\u53ef\u4ee5\u6839\u636e\u6bcf\u4e00\u4e2a run \u7684\u5927\u5c0f\uff0c\u6839\u636e\u970d\u592b\u66fc\u6811\u7684\u89c4\u5f8b\u6765\u8fdb\u884c\u5f52\u5e76\uff0c\u5373\u603b\u662f\u9009\u6700\u5c0f\u7684\u4e24\u4e2a\u8fdb\u884c\u5f52\u5e76\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec15/#\u5e76\u884c\u4f18\u5316","title":"\u5e76\u884c\u4f18\u5316","text":"<p>\u8fd9\u91cc\u5e76\u884c\u7684\u76ee\u6807\u4e3b\u8981\u662f\u4f7f\u7b97\u6cd5\u652f\u6301\u6570\u636e\u7684\u8bfb-\u7528-\u5199\u7684\u6d41\u6c34\u7ebf\uff0c\u4e5f\u5c31\u662f\u8bf4\u6211\u4eec\u8981\u60f3\u529e\u6cd5\u8ba9\u8bfb\u4e0d\u963b\u585e\u7528\uff0c\u7528\u4e0d\u963b\u585e\u5199\u3002</p> <p>\u5148\u524d\u6211\u4eec\u9700\u8981\u5148\u8bfb\u5165\u6570\u636e\uff0c\u7136\u540e\u8fdb\u884c\u6392\u5e8f\uff0c\u6392\u5e8f\u5b8c\u4e86\u518d\u5199\u5165\u78c1\u76d8\uff0c\u817e\u51fa\u5185\u5b58\u7a7a\u95f4\u4ee5\u4f9b\u4e0b\u4e00\u6b21\u8bfb\u5165\u3002\u90a3\u4e3a\u4ec0\u4e48\u4f1a\u963b\u585e\u5462\uff1f\u56e0\u4e3a\u6211\u4eec\u6ca1\u6cd5\u8bfb\u4e00\u4e2a\u6b63\u5728\u5199\u7684\u6570\u636e\u5757\uff0c\u6240\u4ee5\u6211\u4eec\u53ea\u9700\u8981\u5728\u4e0d\u540c\u7684\u6570\u636e\u5757\u8bfb\u548c\u5199\u5c31\u884c\u4e86\u3002\u5bf9\u4e8e \\(k\\)-way \u4e2d\u7684\u6bcf\u4e00\u8def\uff0c\u6211\u4eec\u90fd\u63d0\u4f9b\u4e24\u4e2a input buffer\uff0c\u4e00\u4e2a\u7528\u4e8e\u5199\uff0c\u4e00\u4e2a\u7528\u4e8e\u6392\u5e8f\u3002\u5f53\u6392\u5e8f buffer \u7a7a\u4e86\u7684\u65f6\u5019\uff0c\u5c31\u548c\u8bfb\u6ee1\u4e86\u7684 input buffer \u4ea4\u6362\uff0c\u65e0\u7f1d\u8854\u63a5\u7ee7\u7eed\u8f93\u51fa\u3002\u4e8e\u6b64\u540c\u65f6\uff0c\u521a\u521a\u88ab\u4ea4\u6362\u8fc7\u53bb\u7684 buffer \u5219\u53ef\u7528\u4e8e\u7ee7\u7eed\u8bfb\u5165\u3002</p> <p>\u56e0\u6b64\uff0c\u5982\u679c\u6211\u4eec\u6267\u884c direct \\(k\\)-way merge\uff0c\u5c31\u9700\u8981 \\(2k\\) \u4e2a input buffer\uff08\u8fd9\u91cc\u5f3a\u8c03 direct \u662f\u56e0\u4e3a\uff0c\u5982\u679c\u4f7f\u7528 iterative \u7684\u8bdd\uff0cinput buffer \u53ea\u9700\u8981 4 \u4e2a\uff09\u3002</p> <p>\u800c\u5bf9\u4e8e\u8f93\u51fa\uff0c\u6211\u4eec\u53ea\u9700\u8981 2 \u4e2a output buffer \u4ea4\u66ff\u4f7f\u7528\u5373\u53ef\uff0c\u4e00\u4e2a\u7528\u6765\u63a5\u6536\u6765\u81ea\u6392\u5e8f\u7b97\u6cd5\u7684\u8f93\u51fa\uff0c\u4e00\u4e2a\u7528\u6765\u5c06\u6570\u636e\u5199\u5165\u78c1\u76d8\u3002</p> <p>\u4f46\u662f\uff0c\u5e76\u884c\u4f18\u5316\u7684\u7f3a\u70b9\u5c31\u662f\u5360\u636e\u4e86\u66f4\u591a\u7684\u5185\u5b58\u7a7a\u95f4\u2014\u2014\u539f\u5148 \\(k + 1\\) \u4e2a buffer \u5e73\u5206\u7684\u7528\u4e8e\u5904\u7406\u6570\u636e\u7684\u5185\u5b58\uff0c\u73b0\u5728\u9700\u8981\u88ab \\(2k + 2\\) \u4e2a buffer \u5e73\u5206\uff0c\u6240\u4ee5\u6bcf\u4e00\u4e2a buffer \u7684\u5927\u5c0f\u4f1a\u53d8\u5c0f\u3002\u8fdb\u800c\u5bfc\u81f4\u6bcf\u4e00\u6b21\u4ece disk \u4e2d\u8bfb\u53d6\u7684\u6570\u636e\u53d8\u5c11\uff0c\u6240\u4ee5\u8981\u8bfb\u5b8c\u6570\u636e\u6240\u9700\u8981\u7684\u8bfb\u53d6\u6b21\u6570\u5c31\u589e\u52a0\uff0c\u5373 seek \u6b21\u6570\u589e\u52a0\u3002</p>"},{"location":"cour_note/D2CX_ComputerOrganization/","title":"[\u5927\u4e8c\u6625\u590f] \u8ba1\u7b97\u673a\u7ec4\u6210 | Computer Organization","text":"<p> \u7ea6 61 \u4e2a\u5b57 </p> <p>\u7531\u4e8e\u7b14\u8bb0\u592a\u6d6a\u8d39\u65f6\u95f4\u4e86\uff0c\u6211\u5b66\u4e60\u8ba1\u7ec4\u4f7f\u7528\u7684\u662f xxjj \u7684\u7b14\u8bb0\uff1a</p> <p>https://xuan-insr.github.io/computer_organization/1_prelude/</p> <p>\u987a\u4fbf\u61d2\u5f97\u81ea\u5df1\u91cd\u65b0\u8c03\u6574\uff0c\u76f4\u63a5\u5728\u4ed6\u7684\u7b14\u8bb0\u4e0a\u4fee\u6539\u7136\u540e PR \u4e86\u3002</p>"},{"location":"cour_note/D2HJ_StanfordWriting/","title":"[\u5927\u4e8c\u5bd2\u5047] \u79d1\u5b66\u6587\u7ae0\u5199\u4f5c | Writing in the Sciences","text":"<p> \u7ea6 1335 \u4e2a\u5b57  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 4 \u5206\u949f</p> <ul> <li>\u5b98\u65b9\u7f51\u7ad9\uff1a\ud83d\udd17</li> <li>\u89c6\u9891\u94fe\u63a5\uff1a\ud83d\udd17</li> <li>\u53c2\u8003\u7b14\u8bb0\uff1a\ud83d\udd17</li> </ul> <p>\u5410\u69fd</p> <p>\u4e0d\u662f\u6211\u8bf4\uff0c\u6211\u611f\u89c9\u8fd9\u8bfe\u7684\u7ec4\u7ec7\u6ca1\u6709\u5f88\u6e05\u6670\u7684\u903b\u8f91\uff0c\u6216\u8005\u8bf4\u5b9e\u9645\u4e0a\u5b83\u5e76\u4e0d\u5c5e\u4e8e\u80fd\u591f\u7528\u6846\u67b6\u6027\u7684\u5185\u5bb9\u6982\u62ec\u7684\uff0c\u800c\u662f\u4e0d\u65ad\u7684\u628a\u7ec6\u8282\u5185\u5bb9\u4e22\u51fa\u6765\u5e76\u5728\u6848\u4f8b\u4e2d\u5206\u6790\uff0c\u6240\u4ee5\u611f\u89c9\u7b14\u8bb0\u5f88\u96be\u505a\u554a\uff0c\u7136\u540e\u611f\u89c9\u7b2c\u4e00\u5355\u5143\u7684\u5185\u5bb9\u662f\u5bf9\u6574\u4e2a\u8bfe\u7a0b\u7684\u5927\u81f4\u6897\u6982\uff0c\u6240\u4ee5\u8fd9\u91cc\u653e\u7684\u4e3b\u8981\u662f\u7b2c\u4e00\u7ae0\u7684\u5185\u5bb9\uff0c\u540e\u9762\u5982\u679c\u6709\u9047\u5230\u6211\u89c9\u5f97\u6709\u5fc5\u8981\u4e14\u65b9\u4fbf\u8bb0\u4e0b\u6765\u7684\u4e1c\u897f\u4f1a\u5fd8\u91cc\u9762\u4e22\uff0c\u4f46\u662f\u6211\u4e2a\u4eba\u611f\u89c9\u8fd9\u4efd\u7b14\u8bb0\u7684\u8d28\u91cf\u4e0d\u662f\u5f88\u9ad8\uff0c\u6548\u679c\u4e5f\u4e0d\u662f\u5f88\u597d\u2014\u2014\u5bf9\u4e8e\u66ff\u4ee3\u8fd9\u95e8\u8bfe\u6765\u8bf4\u3002</p> <p>\u6897\u6982</p> <p>\u79d1\u5b66\u6587\u732e\u662f\u4e3a\u4e86\u89c2\u70b9\u4ea4\u6d41\u5b58\u5728\u7684\uff0c\u800c\u201c\u6587\u7ae0\u201d\u53ea\u662f\u89c2\u70b9\u4ea4\u6d41\u8fc7\u7a0b\u4e2d\u7684\u4e00\u79cd\u627f\u8f7d\u5f62\u5f0f\u3002\u6211\u4eec\u8981\u7740\u91cd\u4e8e\u8ba9\u8bfb\u8005\u80fd\u4ee5\u66f4\u5c0f\u7684\u8d1f\u62c5\u7406\u89e3\u6587\u7ae0\u7684\u5185\u6db5\uff0c\u5373\u7528\u7b80\u660e\u627c\u8981\u7684\u3001\u8109\u7edc\u6e05\u6670\u7684\u6587\u5b57\uff0c\u8868\u8fbe\uff08\u6709\u53ef\u80fd\u6bd4\u8f83\u590d\u6742\u7684\uff09\u89c2\u70b9\u548c\u903b\u8f91\u3002</p> <p>\u6b64\u5916\uff0c\u6211\u4eec\u8fd8\u9700\u8981\u201c\u4e3a\u8bfb\u8005\u670d\u52a1\u201d\uff0c\u8003\u8651\u5230\u6587\u7ae0\u7684\u9605\u8bfb\u8282\u594f\uff0c\u5c3d\u53ef\u80fd\u8ba9\u6587\u7ae0\u80fd\u591f\u88ab\u884c\u4e91\u6d41\u6c34\u5730\u9605\u8bfb\u4e0b\u6765\uff0c\u800c\u975e\u78d5\u78d5\u7eca\u7eca\u6216\u53cd\u53cd\u590d\u590d\u3002</p> <p>\u4e00\u7bc7\u79d1\u5b66\u6587\u7ae0\u662f\u4e3a\u4e86\u4ea4\u6d41\u89c2\u70b9\u800c\u5b58\u5728\u7684\uff0c\u6240\u4ee5\u5b83\u5e94\u5f53\u80fd\u591f\u8ba9\u4eba \u9ad8\u6548 \u5730\u83b7\u53d6\u6838\u5fc3\u5185\u5bb9\uff0c\u6e05\u6670 \u5730\u641e\u6e05\u695a\u6587\u7ae0\u8bf4\u4e86\u4ec0\u4e48\uff0c\u5c24\u5176\u5728\u64b0\u5199\u6587\u7ae0\u521d\u7a3f\u7684\u65f6\u5019\uff0c\u8981\u5c24\u5176\u6ce8\u91cd\u8fd9\u4e9b\uff1b\u5728\u6b64\u57fa\u7840\u4e0a \u4f18\u96c5 \u7684\u6587\u98ce\u80fd\u8ba9\u6587\u7ae0\u66f4\u4e0a\u4e00\u5c42\u697c\uff0c\u800c\u8fd9\u4e9b\u901a\u5e38\u662f\u5728\u4fee\u6539\u4e0e\u6da6\u8272\u4e2d\u4f53\u73b0\u51fa\u6765\u7684\u3002</p> <p>\u800c\u4e3a\u4e86\u5b9e\u73b0\u300c\u9ad8\u6548\u300d\u548c\u300c\u6e05\u6670\u300d\uff0c\u4f60\u9996\u5148\u5fc5\u987b\u6e05\u695a\u81ea\u5df1\u5c06\u8981\u8868\u8fbe\u4ec0\u4e48\uff08Have something to say.\uff09\uff0c\u5e76\u4e14\u68b3\u7406\u6e05\u8fd9\u4e9b\u5185\u5bb9\u7684\u8109\u7edc\u548c\u903b\u8f91\u5173\u7cfb\uff08Logical thinking.\uff09\uff0c\u6b64\u5916\uff0c\u4e3a\u4e86\u8f85\u52a9\u6784\u5efa\u8d77\u4e00\u7bc7\u6587\u7ae0\uff0c\u4f60\u8fd8\u9700\u8981\u4e00\u4e9b\u5199\u4f5c\u5957\u8def\uff08A few simple, learnable rules of style.\uff09\u3002</p> <p>\u8fd9\u91cc\u6709\u4e00\u4e9b\u5176\u5b83\u4e60\u60ef\u80fd\u591f\u5e2e\u52a9\u4f60\u66f4\u597d\u5730\u5199\u4f5c\uff1a</p> <ol> <li>\u65e5\u5e38\u591a\u8bfb\u591a\u5199\u591a\u6a21\u4eff\uff0c\u4e0d\u4e00\u5b9a\u8981\u548c\u79d1\u5b66\u6587\u7ae0\u6709\u5173\uff1b</li> <li>\u6539\u6b63\u4e00\u4e9b\u5b66\u4e60\u8fc7\u7a0b\u4e2d\u517b\u6210\u7684\u574f\u7684\u201c\u5b66\u672f\u201d\u5199\u4f5c\u4e60\u60ef\uff0c\u8bb2\u8005\u79f0\u4e4b\u4e3a deprogramming step\uff1b</li> <li>\u52a8\u7b14\u4e4b\u524d\u5148\u5c1d\u8bd5\u7740\u7528\u8bed\u8a00\u6765\u8bb2\u8ff0\u6587\u7ae0\u5185\u5bb9\uff0c\u6bd4\u5982\u548c\u4f60\u7684\u670b\u53cb\u8c08\u8c08\uff1b</li> <li>\u5c1d\u8bd5\u8ba9\u6587\u7ae0\u53d8\u5f97\u6709\u5438\u5f15\u529b\uff1b</li> <li>\u8ba4\u8bc6\u5230\u5199\u4f5c\u4e0d\u9700\u8981\u7075\u611f\uff0c\u4e0d\u8981\u628a\u7075\u611f\u5f53\u4f5c\u501f\u53e3\uff1b</li> <li>\u8ba4\u8bc6\u5230\u5199\u4f5c\u672c\u8eab\u662f\u56f0\u96be\u7684\uff0c\u800c\u5927\u5bb6\u90fd\u4e00\u6837\uff1b</li> <li>\u575a\u6301\u53cd\u590d\u4fee\u6539\uff0c\u751a\u81f3\u662f\u5728\u5199\u521d\u7a3f\u7684\u65f6\u5019\uff0c\u4f18\u5148\u628a\u6587\u7ae0\u6210\u54c1\u5199\u51fa\u6765\uff0c\u518d\u4e0d\u538c\u5176\u70e6\u5730\u4fee\u7f2e\uff1b</li> <li>\u6740\u4f10\u679c\u65ad\uff0c\u4e0d\u8981\u6267\u7740\u4e8e\u5df2\u7ecf\u5199\u51fa\u6765\u7684\u4f46\u662f\u5b9e\u9645\u4e0a\u4e0d\u9700\u8981\u7684\u6587\u5b57\uff1b</li> <li>\u627e\u4e00\u4e2a\u597d\u7f16\u8f91\uff0cta \u4eec\u53ef\u80fd\u4f1a\u7ed9\u4f60\u597d\u7684\u610f\u89c1\u548c\u5efa\u8bae\uff1b</li> <li>\u53bb\u5192\u9669\uff0c\u52c7\u6562\u5730\u53bb\u7a81\u7834\u684e\u688f\uff1b</li> </ol> <p>\u5177\u4f53\u5230\u5199\u4f5c\u65f6\uff0c\u6211\u4eec\u8981\u5207\u5fcc\u53e5\u5b50\u6666\u6da9\u96be\u61c2\uff0c\u5728\u5199\u4f5c\u8fc7\u7a0b\u4e2d\u6211\u4eec\u53ef\u80fd\u65e0\u610f\u8bc6\u5730\u7528\u6666\u6da9\u590d\u6742\u7684\u8bed\u53e5\u63a9\u76d6\u6211\u4eec\u60f3\u8981\u8868\u8fbe\u7684\u5185\u5bb9\uff0c\u5176\u4e2d\u53ef\u80fd\u7684\u539f\u56e0\u6709\uff1a</p> <p>\u5c06\u8bb8\u591a\u52a8\u8bcd\u8f6c\u5316\u4e3a\u540d\u8bcd\u4f7f\u7528</p> <p>Verbs drive sentences along and nouns slow them down.</p> <p>bad eg</p> <p>Adoptive cell transfer (ACT) immunotherapy is based on the ex vivo selection of tumor-reactive lymphocytes, and their activation and numerical expression before reinfusion to the autologous tumor-bearing host.</p> <p>\u4f7f\u7528\u6a21\u7cca\u5bbd\u6cdb\u7684\u8bcd</p> <p>\u6a21\u7cca\u5bbd\u6cdb\u7684\u3001\u4e0d\u591f\u5177\u4f53\u7684\u3001\u4e0d\u80fd\u8ba9\u8bfb\u8005\u8111\u4e2d\u4ea7\u751f\u76f4\u63a5\u5370\u8c61\u7684\u8bcd\u4f1a\u8ba9\u8bfb\u8005\u611f\u5230\u56f0\u60d1\u3002</p> <p>\u4f7f\u7528\u4e0d\u5fc5\u8981\u7684\u7f29\u5199\u6216\u672f\u8bed</p> <p>\u9664\u975e\u662f\u4e00\u4e9b\u5e7f\u4e3a\u4eba\u77e5\u7684\u7f29\u5199\uff0c\u5426\u5219\u5f88\u53ef\u80fd\u4e3a\u8bfb\u8005\u5e26\u6765\u56f0\u6270\u3002\u5373\u4f7f\u4f60\u5728\u524d\u6587\u4e2d\u5df2\u7ecf\u4ecb\u7ecd\uff0c\u5b83\u4eec\u5f88\u53ef\u80fd\u9700\u8981\u56de\u8fc7\u5934\u6765\u67e5\u9605\u624d\u80fd\u201c\u8bb0\u8d77\u201d\u8fd9\u4e2a\u7f29\u5199\u7684\u542b\u4e49\u3002</p> <p>\u4f7f\u7528\u88ab\u52a8\u8bed\u6001</p> <p>\u8fdd\u53cd\u4e86\u60c5\u7eea\u4e0a\u7684 \u4e3b-\u8c13-\u5bbe \u7684\u987a\u5e8f\u3002\u5f53\u7136\u8981\u6309\u7167\u5b9e\u9645\u60c5\u51b5\u6765\u8bf4\uff0c\u5173\u952e\u662f\u8981\u907f\u514d\u4e0d\u5fc5\u8981\u7684\u8bed\u6cd5\u53d8\u5316\u3002</p> <p>\u4e3b\u8bed\u548c\u52a8\u8bcd\u592a\u9065\u8fdc</p> <p>\u8bfb\u8005\u603b\u662f\u5728\u671f\u5f85\u627e\u5230\u4e00\u53e5\u8bdd\u91cc\u7684\u201c\u52a8\u8bcd\u201d\uff0c\u800c\u5982\u679c\u8fd9\u4e2a\u201c\u52a8\u8bcd\u201d\u592a\u96be\u627e\uff0c\u5c06\u4f1a\u5f71\u54cd\u6574\u53e5\u8bdd\u7684\u9605\u8bfb\u6548\u7387\u3002</p> <p>\u6362\u53e5\u8bdd\u6765\u8bf4\uff0c\u4e0d\u7ba1\u4f60\u7684\u5185\u5bb9\u662f\u5426\u590d\u6742\uff0c\u627f\u8f7d\u8fd9\u4e9b\u5185\u5bb9\u7684\u8bed\u53e5\u90fd\u4e0d\u5e94\u5f53\u662f\u590d\u6742\u7684\u3002</p> <p>\u603b\u7684\u6765\u8bf4\uff0c\u6709\u8fd9\u4e48\u4e9b\u539f\u5219\uff1a</p> <ol> <li>\u5220\u51cf\u4e0d\u5fc5\u8981\u7684\u8bcd\u6c47\uff0c\u5bf9\u6b64\u4fdd\u6301 \u654f\u611f \u548c \u65e0\u60c5\uff0c\u4e0d\u8981\u6297\u62d2\u91cd\u6784\u5b57\u53e5\uff1b<ul> <li>\u4e0d\u5fc5\u8981\u7684\u8bcd\u6c47\uff0c\u6bd4\u5982\uff1a\u6ca1\u6709\u5b9e\u9645\u542b\u4e49\u7684\u8bcd\uff0c\u4e00\u4e9b\u53ea\u6709\u8bed\u6c14\u4f5c\u7528\u7684\u8bcd\u7b49\uff1b</li> <li>\u4e0d\u5fc5\u8981\u7684\u8bcd\u6c47\uff0c\u6bd4\u5982\uff1a\u6ca1\u6709\u610f\u4e49\u7684\u7f29\u5199\u548c\u672f\u8bed\uff1b</li> <li>\u4e0d\u5fc5\u8981\u7684\u8bcd\u6c47\uff0c\u6bd4\u5982\uff1a\u524d\u540e\u8bed\u4e49\u91cd\u590d\u7684\u8bcd\uff1b</li> <li>\u4e0d\u5fc5\u8981\u7684\u8bcd\u6c47\uff0c\u6bd4\u5982\uff1aadv. \u4eec\uff1b</li> </ul> </li> <li>\u66f4\u591a\u5730\u4f7f\u7528\u4e3b\u52a8\u8bed\u6001\uff08\u4e3b\u8c13\u5bbe\uff09\u800c\u975e\u88ab\u52a8\u8bed\u6001\uff1b</li> <li>\u56f4\u7ed5 \u52a8\u8bcd \u5199\u4f5c\uff1a\u4f7f\u7528\u5f3a\u52a8\u8bcd\uff0c\u907f\u514d\u5c06\u52a8\u8bcd\u53d8\u6210\u540d\u8bcd\uff0c\u5e76\u5c06\u52a8\u8bcd\u653e\u5728\u9192\u76ee\u7684\u4f4d\u7f6e\uff1b</li> <li>\u9ad8\u8003\u82f1\u8bed\u4f5c\u6587\u600e\u4e48\u5199\uff0c\u79d1\u5b66\u6587\u732e\u5c31\u4e0d\u8981\u600e\u4e48\u5199\uff1b</li> </ol> <p>\u51cf\u5c11\u6587\u7ae0\u4e2d\u7684\u6df7\u4e71\u6709\u5982\u4e0b\u65b9\u6cd5\uff1a</p> <p>\u8f6c\u5426\u5b9a\u4e3a\u80af\u5b9a</p> from to not honest dishonest not harmful safe not important unimportant do not have lack do not remember forget do not pay attention to ignore do not succeed fail <p>\u5220\u53bb\u8fc7\u5269\u7684 \"there are\" / \"there is\"</p> <p>\u5220\u53bb\u4e0d\u5fc5\u8981\u7684\u4ecb\u8bcd</p>"},{"location":"cour_note/D2QD_DigitalDesign/","title":"[\u5927\u4e8c\u79cb\u51ac] \u6570\u5b57\u903b\u8f91\u8bbe\u8ba1 | Digital Design","text":"<p> \u7ea6 389 \u4e2a\u5b57  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 1 \u5206\u949f</p> <p>\u6ce8\u610f\uff01</p> <p>\u672c\u7ad9\u90e8\u7f72\u5728 GitHub pages \u4e0a\uff0c\u6240\u4ee5\u53ef\u80fd\u4f1a\u51fa\u73b0\u5361\u987f\u60c5\u51b5\uff0c\u4f7f\u7528\u4ee3\u7406\u53ef\u4ee5\u6781\u5927\u4f18\u5316\u9605\u8bfb\u4f53\u9a8c\u3002</p> <p>\u8bfe\u7a0b\u4fe1\u606f</p> <ul> <li>\u6388\u8bfe\uff1a\u8521\u94ed</li> <li>\u667a\u4e91\u8bfe\u5802\u94fe\u63a5\uff1a\ud83d\udd17</li> <li>\u6559\u6750\uff1aLogic and Computer Design Fundamentals, Fifth Edition</li> <li>\u672c\u6587\u4e3b\u8981\u6765\u81ea\u4e8e\u6211\u5543\u6559\u6750\u65f6\u7684\u7b14\u8bb0\uff0c\u4f46\u5c0f\u7ed3\u5b89\u6392\u4e0d\u5b8c\u5168\u662f\u6309\u7167\u8bfe\u672c\u6765</li> <li>\u56e0\u4e3a\u6211\u7684\u5f3a\u8feb\u75c7\uff0c\u6211\u5f88\u7ea0\u7ed3\u5982\u4f55\u628a\u8bdd\u8bf4\u901a\u987a\u548c\u628a\u4e0a\u4e0b\u903b\u8f91\u5199\u51fa\u6765\uff0c\u6240\u4ee5\u6709\u4e9b\u53ef\u80fd\u4e00\u773c\u5c31\u770b\u51fa\u6765\u7684\u4e1c\u897f\u6211\u8fd8\u662f\u8981\u89e3\u91ca\u4e00\u5927\u5806\uff0c\u6240\u4ee5\u53ef\u80fd\u4f1a\u6bd4\u8f83\u5570\u55e6\u545c\u545c\u545c\uff0c\u5e0c\u671b\u5927\u5bb6\u6709\u4efb\u4f55\u610f\u89c1\u6216\u8005\u5efa\u8bae\u90fd\u5199\u5728\u8bc4\u8bba\u533a\u91cc\u8ba9\u6211\u77e5\u9053\uff01\u5e0c\u671b\u8fd9\u4efd\u8d44\u6599\u53ef\u4ee5\u7ed9\u4f60\u5e26\u6765\u5e2e\u52a9\uff01</li> </ul> <p>\u5f88\u663e\u7136\uff0c\u6211\u70c2\u5c3e\u4e86\uff0c\u7b2c\u4e94\u7ae0\u5185\u5bb9\u5f88\u7b80\u964b\uff0c\u7b2c\u4e03\u7ae0\u57fa\u672c\u6ca1\u5199\uff0c\u5b9e\u5728\u662f\u8003\u524d\u6765\u4e0d\u53ca\u5199\u5b8c\u4e86\u3002\u4f46\u662f\u6211\u53ef\u4ee5\u4fdd\u8bc1\u9664\u6b64\u4e4b\u5916\u7684\u5185\u5bb9\u6211\u90fd\u662f\u4ed4\u7ec6\u63a8\u6572\u540e\u624d\u5199\u51fa\u6765\u7684orz\u3002</p> <p>\u6b64\u5916\uff0c\u5bf9\u4e8e\u6211\u5df2\u7ecf\u5199\u4e86\u7684\u5185\u5bb9\u6709\u7591\u4e49\uff0c\u6216\u662f\u5e0c\u671b\u80fd\u8865\u5145\u6211\u6ca1\u5199\u7684\u5185\u5bb9\uff0c\u6b22\u8fce\u63d0\u4ea4 PR\uff01</p> <p>List</p> <p>\u8865\u5929\u65f6\u5019\u7684\u4e00\u70b9\u60f3\u6cd5\uff0c\u56e0\u4e3a\u8bfe\u672c\u6bcf\u4e00\u7ae0\u90fd\u6709\u4e00\u4e2a summary\uff0c\u6240\u4ee5\u5982\u679c\u8981\u770b\u4e66\u7684\u8bdd\u6216\u8bb8\u53ef\u4ee5\u5148\u770b\u90a3\u4e2a summary \u518d\u770b\u5177\u4f53\u7684\u3002</p> <ul> <li> Chap 1 Digital Systems and Information</li> <li> Chap 2 Combinational Logic Circuits</li> <li> Chap 3 Combinational Logic Design</li> <li> Chap 4 Sequential Circuits</li> <li> Chap 5 Digital Hardware Implementation \uff08\u7565\u7b80\u7565\uff09</li> <li> Chap 6 Registers &amp; Register Transfers</li> <li> Chap 7 Memory Basics \uff08\u6ca1\u5199\uff09</li> <li> Glossary</li> </ul>"},{"location":"cour_note/D2QD_DigitalDesign/Chap01/","title":"Chap 1 Digital Systems and Information","text":"<p> \u7ea6 2053 \u4e2a\u5b57  9 \u884c\u4ee3\u7801  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 7 \u5206\u949f</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap01/#\u4fe1\u606f\u8868\u8fbe--information-representation","title":"\u4fe1\u606f\u8868\u8fbe | Information Representation","text":"<p>\u73b0\u5b9e\u4e16\u754c\u4e2d\u7684\u4fe1\u606f\u5f80\u5f80\u662f \u8fde\u7eed(continuous) \u7684\uff0c\u4f46\u5728\u4eba\u9020\u7269\u7684\u4e16\u754c\u4e2d\uff0c\u5927\u90e8\u5206\u4fe1\u606f\u90fd\u662f \u79bb\u6563(discrete) \u7684\u3002</p> <p>\u5728\u7535\u5b50\u4fe1\u606f\u7cfb\u7edf\u4e2d\uff0c\u4fe1\u53f7\u5206\u4e3a \u6a21\u62df\u4fe1\u53f7(analog signal) \u548c \u6570\u5b57\u4fe1\u53f7(digital signal) \u4e24\u79cd\u3002\u5176\u4e2d\uff0c\u5728 \u6570\u5b57\u4fe1\u53f7(digital signal) \u4e2d\u53c8\u6709\u591a\u79cd\u8868\u793a\u65b9\u6cd5\uff0c\u5982\u4eca\u6211\u4eec\u6700\u5e38\u7528\u7684\u662f \u4e8c\u8fdb\u5236(binary)\u3002\u5bf9\u5e94\u5230\u7535\u8def\u5c42\u9762\uff0c\u6211\u4eec\u5e38\u5e38\u7528 \u9ad8\u7535\u4f4d(HIGH) \u548c \u4f4e\u7535\u4f4d(LOW) \u6765\u8868\u5f81 <code>1</code> \u548c <code>0</code>\u3002</p> <p></p> <p>\u503c\u5f97\u6ce8\u610f\u7684\u662f\uff0c\u5728\u8f93\u5165\u548c\u8f93\u51fa\u4e2d\uff0c\u9ad8\u4f4e\u7535\u4f4d\u7684\u63a5\u53d7\u8303\u56f4\u662f\u4e0d\u540c\u7684\u3002\u53ef\u4ee5\u53d1\u73b0\uff0c\u8f93\u5165\u7684\u5224\u5b9a\u8303\u56f4\u6bd4\u8f93\u51fa\u7684\u5224\u5b9a\u8303\u56f4\u5927\uff0c\u5373 \u5bbd\u8fdb\u4e25\u51fa\u3002\u5176\u76ee\u7684\u662f\u4e3a\u4e86\u8fdb\u4e00\u6b65\u63d0\u9ad8\u7535\u8def\u5728\u566a\u97f3\u7b49\u5f02\u5e38\u5f71\u54cd\u4e0b\u4e5f\u80fd\u6b63\u5e38\u8868\u73b0\u7684\u80fd\u529b\u3002</p> HIGH input LOW input HIGH output LOW output 0.6 ~ 1.1 -0.1 ~ 0.4 0.9 ~ 1.1 -0.1 ~ 0.1 <p>\u6216\u8bb8\u4f60\u4e5f\u5df2\u7ecf\u6ce8\u610f\u5230\u4e86\uff0c\u5728\u56fe\u4e2d\uff0cHIGH \u7684\u63a5\u53d7\u8303\u56f4\u548c LOW \u7684\u63a5\u53d7\u8303\u56f4\u4e4b\u95f4\u8fd8\u5b58\u5728\u4e00\u6bb5\u533a\u57df\u3002\u843d\u5728\u8fd9\u4e00\u90e8\u5206\u7684\u7535\u5e73\u662f \u672a\u5b9a\u4e49(undefined) \u7684\uff0c\u4e5f\u88ab\u79f0\u4e3a\u662f \u6d6e\u52a8(floating) \u7684\u3002\u5982\u679c\u8f93\u51fa\u7684\u7535\u5e73\u662f\u5728\u6d6e\u52a8\u533a\u95f4\u7684\uff0c\u90a3\u4e48\u5176\u8ba4\u5b9a\u503c\u5c06\u662f\u968f\u673a\u7684\u3002</p> <p>\u4e8b\u5b9e\u4e0a\uff0c\u5728\u4fe1\u606f\u7684\u5bf9\u5e94\u4e0a\uff0c\u867d\u7136\u5c06\u9ad8\u4f4e\u7535\u5e73\u540c HIGH/LOW \u8054\u7cfb\u662f\u5f88\u81ea\u7136\u7684\uff0c\u4f46\u662f\u5c06\u4ed6\u4eec\u540c true/false \u6216\u8005 1/0 \u8054\u7cfb\u5176\u5b9e\u5e76\u4e0d\u552f\u4e00\u3002\u4f46\u662f\u5728\u4e00\u822c\u60c5\u51b5\u4e0b\uff08\u6211\u4eec\u79f0\u4e4b\u4e3a positive logic\uff09\uff0c\u6211\u4eec\u90fd\u8ba4\u4e3a HIGH ~ true ~ 1\uff0c LOW ~ false ~ 0\u3002</p> <p>\u53ef\u4ee5\u53d1\u73b0\uff0c(b) \u56fe\u4e2d\u7684\u6a21\u62df\u4fe1\u53f7\u5728\u7ecf\u8fc7\u6211\u4eec\u7684\u5668\u4ef6\u540e\uff0c\u4f1a\u88ab\u8ba4\u4e3a\u662f (c) \u56fe\u6240\u793a\u7684\u4fe1\u53f7\u3002\u800c\u8fd9\u4e9b\u64cd\u4f5c\u5728\u786c\u4ef6\u5c42\u9762\uff0c\u6211\u4eec\u901a\u8fc7 \u6676\u4f53\u7ba1(transistors) \u6765\u5b9e\u73b0\u3002</p> <p>\u8fd9\u4e5f\u7275\u626f\u5230\u6211\u4eec\u4e3a\u4ec0\u4e48\u6700\u7ec8\u4f7f\u7528\u4e8c\u8fdb\u5236\u6765\u8868\u793a\u4fe1\u606f\u3002\u4e00\u65b9\u9762\u662f\u56e0\u4e3a\u4e8c\u503c\u5668\u4ef6\u6bd4\u8f83\u5e38\u89c1\uff0c\u4ea6\u5373\u8fd9\u91cc\u63d0\u5230\u7684\u6676\u4f53\u7ba1\uff1b\u53e6\u5916\u4e00\u65b9\u9762\u662f\u4f7f\u7528\u4e8c\u8fdb\u5236\u53ef\u4ee5\u964d\u4f4e\u7535\u8def\u6210\u672c\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap01/#\u8ba1\u7b97\u673a\u7cfb\u7edf\u8bbe\u8ba1\u4e2d\u7684\u62bd\u8c61\u5c42--abstraction-layers-in-computer-systems-design","title":"\u8ba1\u7b97\u673a\u7cfb\u7edf\u8bbe\u8ba1\u4e2d\u7684\u62bd\u8c61\u5c42 | Abstraction Layers in Computer Systems Design","text":"\u8d8a\u4e0a\u5c42\u62bd\u8c61\u7a0b\u5ea6\u8d8a\u9ad8 Algorithms Programing Languages Operating Systems Instruction Set Architecture Microarchitecture Register Transfers Logic Gates Transistor Circuits"},{"location":"cour_note/D2QD_DigitalDesign/Chap01/#\u6570\u5b57\u7cfb\u7edf--number-systems","title":"\u6570\u5b57\u7cfb\u7edf | Number Systems","text":"<p>\u9996\u5148\u9700\u8981\u6d89\u53ca\u7684\u95ee\u9898\u662f\u8fdb\u5236\u8f6c\u6362\u3002</p> <p>\u5bf9\u4e8e\u4e00\u4e2a \\(r\\) \u8fdb\u5236\u6570\uff0c\u5b83\u4e00\u822c\u88ab\u5199\u6210\u8fd9\u6837\uff1a</p> \\[ (A_{n-1}A_{n-2}...A_1A_0A_{-1}...A_{-(m-1)}A_{-m})_{r} \\] <p>\u800c\u5b83\u5bf9\u5e94\u7684\u5341\u8fdb\u5236\u771f\u503c\u4e3a\uff1a</p> \\[ \\begin{aligned} \\sum_{i=-m}^{n-1} A_ir^i\\;\\; =&amp;A_{n-1}r^{n-1}+A_{n-2}r^{n-2}+...\\\\ +&amp;A_{1}r^{1}+A_0r^0+A_{-1}r^{-1}+...\\\\ +&amp;A_{-(m-1)}r^{m-1}+A_{-m}r^{-m} \\end{aligned} \\] <p>\u8ba1\u7b97\u673a\u9886\u57df\u5e38\u89c1\u7684\u8fdb\u5236\u4e3b\u8981\u662f \u4e8c\u8fdb\u5236(binary)\uff0c\u516b\u8fdb\u5236(octal)\uff0c\u5341\u8fdb\u5236(decimal) \u548c \u5341\u516d\u8fdb\u5236(hexadecimal)\u3002</p> <p>\u5176\u4e2d\u4e8c\u3001\u516b\u3001\u5341\u516d\u8fdb\u5236\u4e4b\u95f4\u7684\u8f6c\u6362\u975e\u5e38\u7b80\u5355\uff0c\u5b58\u5728\u591a\u4f4d\u5230\u4e00\u4f4d\u4e4b\u95f4\u7684\u65e0\u540e\u6548\u6027\u6620\u5c04\uff0c\u4f8b\u5982\u4e8c\u8fdb\u5236\u8f6c\u6362\u5230\u5341\u516d\u8fdb\u5236\u53ea\u9700\u8981\u5c06\u4ece\u4f4e\u5230\u9ad8\u6bcf\u56db\u4f4d\u8f6c\u5316\u6210\u5341\u516d\u8fdb\u5236\u4e2d\u7684\u4e00\u4f4d\u5373\u53ef\u3002</p> <p>\u9700\u8981\u6ce8\u610f\uff0c\u7531\u4e8e\u4e8c\u8fdb\u5236\u548c\u5341\u8fdb\u5236\u5728\u96f6\u4f4d\u4e0a\u7684\u6743\u91cd\u76f8\u540c\uff0c\u8fd9\u610f\u5473\u7740\u5728\u6574\u6570\u90e8\u5206\uff0c\u4e8c\u8fdb\u5236\u548c\u5341\u8fdb\u5236\u662f\u53ef\u4ee5\u76f8\u4e92\u7cbe\u51c6\u8f6c\u5316\u7684\uff08\u5373\u6700\u5c0f\u7cbe\u5ea6\u662f\u4e00\u81f4\u7684\uff0c\u90fd\u662f 1\uff09\uff1b\u7136\u800c\u8be5\u6027\u8d28\u5728\u5c0f\u6570\u90e8\u5206\u5e76\u4e0d\u6210\u7acb\uff08\u56e0\u4e3a\u5c0f\u6570\u90e8\u5206\u4e0d\u5b58\u5728\u201c\u6700\u5c0f\u7cbe\u5ea6\u201d\u4e00\u8bf4\uff09\uff0c\u5373\u5341\u8fdb\u5236\u65e0\u6cd5\u7cbe\u51c6\u8f6c\u5316\u4e3a\u4e8c\u8fdb\u5236\uff0c\u4f46\u4e8c\u8fdb\u5236\u53ef\u4ee5\u8f6c\u5316\u4e3a\u5341\u8fdb\u5236\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap01/#\u7b97\u672f\u8fd0\u7b97--arithmetic-operations","title":"\u7b97\u672f\u8fd0\u7b97 | Arithmetic Operations","text":"<p>\u8fd9\u91cc\u6d89\u53ca\u7684\u4e3b\u8981\u662f \u52a0\u6cd5(Addition)\u3001\u51cf\u6cd5(Subtraction)\u3001\u4e58\u6cd5(Multiplication)\u3002</p> <p>\u6574\u4f53\u6d41\u7a0b\u548c\u5c0f\u5b66\u7ad6\u5f0f\u52a0\u6cd5\u662f\u4e00\u81f4\u7684\u3002</p> \u4e8c\u8fdb\u5236\u8fd0\u7b97 <p> </p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap01/#\u7f16\u7801--codes","title":"\u7f16\u7801 | Codes","text":"<p>\u4e8c\u8fdb\u5236\u7f16\u7801\u4e3b\u8981\u5206\u4e3a\u8fd9\u4e48\u51e0\u79cd\uff1a</p> <ul> <li>Numeric<ul> <li>\u5fc5\u987b\u8868\u8fbe\u4e00\u5b9a\u8303\u56f4\u5185\u7684\u6570\u5b57\uff1b</li> <li>\u80fd\u591f\u652f\u6301\u7b80\u5355\u4e14\u666e\u904d\u7684\u8ba1\u7b97\uff1b</li> <li>\u548c\u4e8c\u8fdb\u5236\u6570\u503c\u672c\u8eab\u6709\u8f83\u5927\u5173\u8054\uff1b</li> </ul> </li> <li>Non-numeric<ul> <li>\u76f8\u5bf9\u7075\u6d3b\uff0c\u56e0\u4e3a\u4e0d\u9700\u8981\u9002\u914d\u666e\u904d\u7684\u8fd0\u7b97\u6cd5\u5219\uff1b<ul> <li>\u7075\u6d3b\u6027\u6307\uff0c\u4fdd\u8bc1\u7f16\u7801\u6620\u5c04\u5173\u7cfb\u662f\u552f\u4e00\u7684\u7684\u60c5\u51b5\u4e0b\u90fd\u53ef\u4ee5\u79f0\u4e3a\u5408\u6cd5\u7f16\u7801\uff1b</li> </ul> </li> <li>\u548c\u4e8c\u8fdb\u5236\u6570\u503c\u672c\u8eab\u672a\u5fc5\u6709\u5173\u7cfb\uff1b</li> </ul> </li> </ul>"},{"location":"cour_note/D2QD_DigitalDesign/Chap01/#\u72ec\u70ed\u7801--\u72ec\u51b7\u7801","title":"\u72ec\u70ed\u7801 &amp; \u72ec\u51b7\u7801","text":"<p>\u72ec\u70ed\u7801(one-hot) \u8981\u6c42\u6bd4\u7279\u5411\u91cf\u4e2d\u53ea\u6709\u4e00\u4f4d\u662f <code>1</code>\uff1b\u5bf9\u5e94\u7684\u8fd8\u6709 \u72ec\u51b7\u7801(one-cold)\u3002</p> <p>\u4f7f\u7528\u8fd9\u79cd\u7f16\u7801\u7684\u597d\u5904\u662f\uff0c\u51b3\u5b9a\u6216\u6539\u53d8\u72b6\u6001\u673a\u76ee\u524d\u7684\u72b6\u6001\u7684\u6210\u672c\u76f8\u5bf9\u8f83\u4f4e\uff0c\u5bb9\u6613\u8bbe\u8ba1\u4e5f\u5bb9\u6613\u68c0\u6d4b\u975e\u6cd5\u884c\u4e3a\u7b49\u3002</p> <p>\u4f46\u662f\u76f8\u5bf9\u5e94\u7684\uff0c\u7f3a\u70b9\u662f\u4fe1\u606f\u8868\u793a\u7387\u8f83\u4f4e\uff0c\u975e\u6cd5\u72b6\u6001\u975e\u5e38\u591a\u800c\u6709\u6548\u72b6\u6001\u5f88\u5c11\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap01/#bcd-\u7801","title":"BCD \u7801","text":"<p>\u7531\u4e8e\u771f\u5b9e\u4e16\u754c\u4e2d\u5927\u90e8\u5206\u6570\u636e\u8868\u8ff0\u90fd\u662f\u4ee5\u5341\u8fdb\u5236\u5b9e\u73b0\u7684\uff0c\u6240\u4ee5\u6211\u4eec\u9700\u8981\u7814\u7a76\u5982\u4f55\u7528\u4e8c\u8fdb\u5236\u6765\u8868\u793a\u5341\u8fdb\u5236\u3002</p> <p>\u9996\u5148\uff0c\u4e00\u4f4d\u4e8c\u8fdb\u5236\u6570\u80fd\u5305\u542b\u7684\u4fe1\u606f\u662f 1bit\uff0c\u4e5f\u5c31\u662f\u4e00\u4e2a\u201c\u771f\u201d\u6216\u8005\u4e00\u4e2a\u201c\u5047\u201d\u3002\u6211\u4eec\u79f0\u4e00\u4e2a\u62e5\u6709 n \u4e2a\u5143\u7d20\u7684\u4e8c\u8fdb\u5236\u5411\u91cf\u4e3a\u4e00\u4e2a n\u4f4d\u4e8c\u8fdb\u5236\u7f16\u7801(n-bit binary code)\u3002\u4e00\u4e2a n \u4f4d\u4e8c\u8fdb\u5236\u6570\u62e5\u6709 \\(2^{n}\\) \u79cd\u53ef\u80fd\u7684\u7ec4\u5408\uff0c\u56e0\u800c\u53ef\u4ee5\u8868\u793a \\(2^n\\) \u79cd\u4fe1\u606f\u3002</p> <p>\u800c\u6211\u4eec\u9700\u8981\u8bbe\u8ba1\u7684\u7f16\u7801\u7cfb\u7edf\uff0c\u5c31\u662f\u5c06\u6211\u4eec\u9700\u8981\u7684\u4fe1\u606f\u6620\u5c04\u5230\u8fd9 \\(2^n\\) \u4e2a\u201c\u7a7a\u4f4d\u201d\u4e2d\u3002\u5f53\u7136\uff0c\u5f53\u6211\u4eec\u9700\u8981\u8868\u793a\u7684\u4fe1\u606f\u6570\u91cf\u5e76\u4e0d\u662f 2 \u7684\u5e42\u6b21\u65f6\u5019\uff0c\u4f1a\u51fa\u73b0\u4e00\u4e9b \u672a\u5206\u914d(unassigned) \u7684\u6bd4\u7279\u7ec4\u5408\u3002</p> <p>\u800c\u5728\u8fd9\u79cd\u7f16\u7801\u4e2d\uff0c\u6700\u5e38\u7528\u7684\u5c31\u662f BCD\u7801(binary-coded demical)\u3002\u5176\u6838\u5fc3\u601d\u8def\u5c31\u662f\uff0c\u5c06\u5341\u8fdb\u5236\u7684\u6bcf\u4e00\u4f4d \u5206\u522b \u7528 \u771f\u503c\u76f8\u7b49\u7684 4 \u4f4d\u4e8c\u8fdb\u5236 \u8868\u793a\uff0c\u5373 <code>0</code> ~ <code>9</code> \u5206\u522b\u7528 <code>0000</code> ~ <code>1001</code> \u8868\u793a\u3002</p> DecimalSymbol BCDDigit <code>0</code> <code>0000</code> <code>1</code> <code>0001</code> <code>2</code> <code>0010</code> <code>3</code> <code>0011</code> <code>4</code> <code>0100</code> <code>5</code> <code>0101</code> <code>6</code> <code>0110</code> <code>7</code> <code>0111</code> <code>8</code> <code>1000</code> <code>9</code> <code>1001</code> <p>eg</p> \\[ \\mathrm{ (185)_{10}\\;=\\;(0001\\;1000\\;0101)_{BCD}\\;=\\;(10111001)_2 } \\]"},{"location":"cour_note/D2QD_DigitalDesign/Chap01/#\u4f59\u4e09\u7801","title":"\u4f59\u4e09\u7801","text":"<p>\u4e00\u79cd BCD\u7801 \u7684\u6539\u8fdb\u662f \u4f59\u4e09\u7801(Excess3)\u3002\u5176\u6838\u5fc3\u601d\u8def\u662f\u5728 BCD\u7801\u7684\u57fa\u7840\u4e0a\uff0c\u589e\u52a0\u4e00\u4e2a\u5927\u5c0f\u4e3a 3 \u7684\u504f\u79fb\u91cf\u3002</p> DecimalSymbol Excess3Digit <code>0</code> <code>0011</code> <code>1</code> <code>0100</code> <code>2</code> <code>0101</code> <code>3</code> <code>0110</code> <code>4</code> <code>0111</code> <code>5</code> <code>1000</code> <code>6</code> <code>1001</code> <code>7</code> <code>1010</code> <code>8</code> <code>1011</code> <code>9</code> <code>1100</code> <p>\u4e3a\u4ec0\u4e48\u662f 3 \u5462\uff1f\u9996\u5148\u8fd9\u4e2a 3 \u6765\u81ea\u4e8e \\(\\frac{16-10}{2}\\)\uff0c\u4e5f\u5c31\u662f 8421 \u7801\u7684\u5bb9\u91cf\u51cf\u53bb\u6211\u4eec\u9700\u8981\u8868\u793a\u7684\u6570\u5b57\u6570\u91cf\uff0c\u518d\u9664\u4ee5\u4e8c\u3002\u8fd9\u6837\u7684\u597d\u5904\u662f\uff0c\u5341\u8fdb\u5236\u4e0b\u80fd\u8fdb\u4f4d\u7684\u4e24\u4e2a\u6570\uff0c\u5728\u4f59\u4e09\u7801\u4e0b\u76f8\u52a0\u4e5f\u521a\u597d\u8fdb\u4f4d\u3002</p> <p>\u4f46\u662f\u9700\u8981\u5f3a\u8c03\u7684\u4e00\u70b9\u662f\uff0c\u7f16\u7801\u548c\u6570\u503c\u662f\u5b58\u5728\u533a\u522b\u7684\uff0c\u867d\u7136\u6211\u4eec\u63d0\u5230\u4e86\u4f59\u4e09\u7801\u76f8\u52a0\uff0c\u4f46\u662f\u7f16\u7801\u505a\u8fd0\u7b97\u591a\u6570\u60c5\u51b5\u4e0b\u662f\u6ca1\u6709\u610f\u4e49\u7684\u3002\u201c\u8fd0\u7b97\u201d\u7684\u4e3b\u4f53\u66f4\u591a\u662f\u6570\u503c\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap01/#\u683c\u96f7\u7801","title":"\u683c\u96f7\u7801","text":"<p>\u6b64\u5916\uff0c\u8fd9\u91cc\u4e0d\u5f97\u4e0d\u63d0\u7684\u53e6\u5916\u4e00\u4e2a\u7f16\u7801\u662f \u683c\u96f7\u7801(Gray Codes)\u3002\u683c\u96f7\u7801\u7684\u7279\u5f81\uff0c\u4e5f\u662f\u4ed6\u7684\u4f18\u70b9\uff0c\u5c31\u662f\u76f8\u90bb\u7684\u4e24\u4e2a\u6570\u5728\u4e8c\u8fdb\u5236\u4e0b\u7684\u8868\u793a\u53ea\u5dee\u4e00\u4f4d\uff08\u5f53\u5728\u5360\u6ee1\u65f6\uff0c\u5bf9\u4e8e\u6574\u4e2a\u7f16\u7801\u5e8f\u5217\uff0c\u73af\u72b6\u6ee1\u8db3\u8be5\u6761\u4ef6\uff09\u3002</p> <p>\u6bd4\u5982\u6709\u5982\u4e0b\u5e94\u7528\uff1a</p> <p></p> <p>\u4ee5\u53ca\u5728\u8bb8\u591a\u72b6\u6001\u63a7\u5236\u4e2d\u90fd\u6709\u7740\u5e7f\u6cdb\u7684\u5e94\u7528\u3002</p> <p>\u4ece\u7b14\u8bd5\u505a\u9898\u89d2\u5ea6\u6765\u8bf4\uff0c\u683c\u96f7\u7801\u6700\u9ebb\u70e6\u7684\u5176\u5b9e\u662f\u4e0e\u5341\u8fdb\u5236\u6570\u7684\u8f6c\u6362\u3002\uff08\u6b64\u5904 @CSP-S2019-Day1-T1\uff09</p> <p>\u4e2a\u4eba\u8ba4\u4e3a\u6700\u597d\u505a\u7684\u505a\u6cd5\u5c31\u662f\uff0c\u5047\u8bbe\u6211\u4eec\u8981\u627e\u7684\u662f\u7b2c k \u4e2a\u683c\u96f7\u7801\uff0c\u5219\u5bf9\u5e94\u7684\u683c\u96f7\u7801\u4e3a\uff1a</p> \\[ k \\;\\;\\mathrm{XOR}\\;\\; (k&gt;&gt;1) \\]"},{"location":"cour_note/D2QD_DigitalDesign/Chap01/#ascii-\u7801","title":"ASCII \u7801","text":"<p>\u5b57\u7b26\u7f16\u7801\u6240\u4f7f\u7528\u7684\u4e00\u822c\u662f ASCII \u7f16\u7801\uff0c\u7531\u4e8e ASCII \u5df2\u7ecf\u662f\u8001\u751f\u5e38\u8c08\u4e86\uff0c\u6240\u4ee5\u8fd9\u91cc\u4e0d\u518d\u5c55\u5f00\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap01/#\u5947\u5076\u6821\u9a8c\u4f4d","title":"\u5947\u5076\u6821\u9a8c\u4f4d","text":"<p>\u4fe1\u9053\u7f16\u7801\u4e0e\u4fe1\u6e90\u7f16\u7801\uff1a</p> <p></p> <p>\u5728\u4fe1\u53f7\u4f20\u8f93\u8fc7\u7a0b\u4e2d\uff0c\u53ef\u80fd\u7531\u4e8e\u73af\u5883\u5e72\u6270\u7b49\u539f\u56e0\uff0c\u51fa\u73b0\u5404\u79cd\u4fe1\u53f7\u6296\u52a8\uff0c\u6240\u4ee5\u4e3a\u4e86\u4fdd\u8bc1\u6570\u636e\u7684\u53ef\u4fe1\u5ea6\uff0c\u6211\u4eec\u9700\u8981\u4e00\u4e2a\u9519\u8bef\u68c0\u6d4b\u673a\u5236\u3002</p> <p>\u4e00\u79cd\u5e38\u89c1\u7684\u65b9\u6cd5\u662f \u5197\u4f59(Redundancy)\uff0c\u5373\u52a0\u5165\u4e00\u4e9b\u989d\u5916\u7684\u4fe1\u606f\u7528\u4ee5\u6821\u9a8c\u3002</p> <pre><code>graph TD\nA[Error Detection Techniques]\nB[Single Parity Check]\nC[Cyclic Redundancy Check]\nD[Check Sum]\n\nA--&gt;B\nA--&gt;C\nA--&gt;D</code></pre> <p>\u5176\u4e2d\u4e00\u79cd\u505a\u6cd5\u662f\u5f15\u5165 \u5947\u5076\u6821\u9a8c\u4f4d(Parity Bit)\u3002\u5b83\u5206\u4e3a \u5947\u6821\u9a8c(Odd Parity) \u548c \u5076\u6821\u9a8c(Even Parity)\u3002\u5206\u522b\u901a\u8fc7\u5f15\u5165\u989d\u5916\u7684\u4e00\u4f4d\uff0c\u6765\u4fdd\u8bc1\u6574\u4e2a\u4fe1\u606f\u4e32\u4e2d <code>1</code> \u7684\u6570\u91cf\u662f\u5947\u6570/\u5076\u6570\u3002</p> <ul> <li>\u6bd4\u5982\uff0c\u5982\u679c\u6211\u4eec\u91c7\u7528\u5076\u6821\u9a8c\uff0c\u539f\u59cb\u4fe1\u606f\u4e3a <code>1101</code>\uff0c\u5176\u4e2d\u6709 3 \u4e2a <code>1</code>\uff0c\u8fd9\u65f6\u6211\u4eec\u5728\u540e\u9762\u518d\u52a0\u4e0a\u4e00\u4e2a <code>1</code>\uff0c\u4fdd\u8bc1\u4e86\u6574\u4e2a\u4fe1\u606f\u4e32\u4e2d\u6709\u5076\u6570\u4e2a <code>1</code>\uff1b\u6216\u8005\u5982\u679c\u539f\u59cb\u4fe1\u606f\u4e3a <code>1001</code>\uff0c\u5176\u4e2d\u6709 2 \u4e2a <code>1</code>\uff0c\u8fd9\u65f6\u6211\u4eec\u5219\u5728\u540e\u9762\u52a0\u4e00\u4e2a <code>0</code>\u3002\u6b64\u65f6\uff0c\u5982\u679c\u4f20\u8f93\u8fc7\u7a0b\u4e2d\u51fa\u73b0\u4e86\u95ee\u9898\uff0c\u90a3\u4e48 <code>1</code> \u7684\u6570\u91cf\u5f88\u53ef\u80fd\u53d8\u6210\u4e86\u4e00\u4e2a\u5947\u6570\uff0c\u6b64\u65f6\u6211\u4eec\u5c31\u77e5\u9053\uff0c\u8fd9\u4e2a\u4fe1\u606f\u662f\u4e0d\u5bf9\u7684\u3002</li> </ul>"},{"location":"cour_note/D2QD_DigitalDesign/Chap02/","title":"Chap 2 Combinational Logic Circuits","text":"<p> \u7ea6 8091 \u4e2a\u5b57  25 \u884c\u4ee3\u7801  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 27 \u5206\u949f</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap02/#\u903b\u8f91\u8fd0\u7b97","title":"\u903b\u8f91\u8fd0\u7b97","text":"<p>\u903b\u8f91\u8fd0\u7b97\u7684\u5bf9\u8c61\u662f\u5e03\u5c14\u53d8\u91cf\uff0c\u4e5f\u5c31\u662f 0/1 \u4e8c\u503c\u3002</p> <p>\u4e3b\u8981\u7684\u8fd0\u7b97\u5c31\u662f \u4e0e(AND)\uff0c\u6216(OR)\uff0c\u975e(NOT)\uff0c\u5f02\u6216(XOR)\uff0c\u4ee5\u53ca \u4e0e\u975e(NAND)\uff0c\u6216\u975e(NOR)\uff0c\u540c\u6216(XNOR)\u3002</p> <p>\u9ad8\u7ef4</p> <p>\u591a\u8f93\u5165\u7684\u5f02\u6216\u548c\u540c\u6216\u88ab\u79f0\u4e3a\u5947\u51fd\u6570\u548c\u5076\u51fd\u6570\u3002</p> <p>\u53ef\u4ee5\u7528\u5b83\u4eec\u6765\u5b9e\u73b0\u5947\u6821\u9a8c\u548c\u5076\u6821\u9a8c\u3002</p> <p>\u800c\u4e14\u89c2\u5bdf\u5176\u5361\u8bfa\u56fe\u7684\u5f62\u72b6\uff08\u68cb\u76d8\u5f62\uff09\uff0c\u53ef\u4ee5\u53d1\u73b0\uff0c\u5b83\u4eec\u662f\u5929\u7136\u4f18\u5316\u7684\uff0c\u5373\u4e0d\u53ef\u4f18\u5316\u7684\u3002</p> <p>\u8fd0\u7b97\u89c4\u5219\u633a\u7b80\u5355\u7684\uff0c\u5728\u6b64\u7565\u53bb\u3002</p> <p>\u6bd4\u8f83\u57fa\u7840\u7684\uff0c\u9700\u8981\u4e86\u89e3\u4e0e\u6216\u975e\u7684\u7b26\u53f7\u8868\u793a\u3002</p> <ul> <li><code>A</code> <code>AND</code> <code>B</code> \u53ef\u5199\u4f5c \\(A\\cdot B\\) \u6216\u8005 \\(AB\\)\uff1b</li> <li><code>A</code> <code>OR</code> <code>B</code> \u53ef\u5199\u4f5c \\(A+B\\)\uff1b</li> <li><code>NOT A</code> \u53ef\u5199\u4f5c \\(\\overline{A}\\)\uff1b</li> </ul> <p>\u7531\u6b64\u53ef\u4ee5\u8fdb\u884c\u4e00\u4e9b\u7ec4\u5408\uff0c\u4f8b\u5982\uff1a</p> <ul> <li><code>A</code> <code>NOR</code> <code>B</code> \u53ef\u5199\u4f5c \\(\\overline{A+B}\\)\uff1b</li> <li><code>A</code> <code>NAND</code> <code>B</code> \u53ef\u5199\u4f5c \\(\\overline{A\\cdot B}\\)\uff1b</li> </ul> <p>\u518d\u6b21\u8fd8\u9700\u8981\u63d0\u5230\u7684\u662f \u5fb7\u00b7\u6469\u6839\u5b9a\u5f8b(De Morgan's Laws)\uff0c\u5176\u8868\u8ff0\u4e3a\uff1a</p> <ul> <li>\\(\\overline{A+B} = \\overline{A}\\cdot\\overline{B}\\)\uff1b</li> <li>\\(\\overline{A\\cdot B} = \\overline{A}+\\overline{B}\\)\uff1b</li> </ul>"},{"location":"cour_note/D2QD_DigitalDesign/Chap02/#\u903b\u8f91\u95e8","title":"\u903b\u8f91\u95e8","text":"<p>\u903b\u8f91\u95e8\u662f\u5728\u786c\u4ef6\u5c42\u9762\u4e0a\u5b9e\u73b0\u5e03\u5c14\u4ee3\u6570\u7684\u903b\u8f91\u5355\u5143\u3002\u5176\u64cd\u4f5c\u5bf9\u8c61\u4e3a\u9ad8\u4f4e\u7535\u5e73\u3002</p> <p></p> <p>\u5982\u56fe\uff0c(a)\u4e2d\u7ed8\u5236\u4e86\u4e09\u4e2a\u5e38\u7528\u903b\u8f91\u95e8\u7684\u7b26\u53f7\uff1b(b)\u4e2d\u5219\u63cf\u8ff0\u4e86\u8fd9\u4e9b\u8fd0\u7b97\u5728 \u65f6\u5e8f\u56fe(timing diagram) \u4e2d\u7684\u72b6\u6001\uff1b(c)\u5219\u63cf\u8ff0\u4e86\u5728\u5ef6\u65f6\uff08\u89c1\u4e0b\uff09\u6548\u5e94\u4e0b\u7684\u65f6\u5e8f\u56fe\u3002</p> <p>\u8fd8\u6709\u4e00\u4e2a\u6ce8\u610f\u70b9\u662f\uff0c\u975e\u95e8\u5176\u5b9e\u66f4\u591a\u7684\u88ab\u79f0\u4e3a inverter\uff0c\u800c\u975e NOT\u3002</p> <p>\u4f46\u662f\u7531\u4e8e\u662f\u7269\u7406\u5c42\u9762\u7684\u5b9e\u73b0\uff0c\u6240\u4ee5\u4f1a\u6709\u4e00\u4e9b\u903b\u8f91\u8fd0\u7b97\u5c42\u9762\u4e0d\u4f1a\u51fa\u73b0\u7684\u95ee\u9898\uff0c\u6bd4\u5982 \u5ef6\u65f6(delay)\u3002</p> <p></p> <p>Source: https://en.wikipedia.org/wiki/Signal_propagation_delay#Electronics</p> <p>\u5ef6\u65f6\u7684\u957f\u77ed\u4e0e\u5f88\u591a\u56e0\u7d20\u6709\u5173\uff0c\u53d6\u51b3\u4e8e\u903b\u8f91\u95e8\u7684\u5b9e\u73b0\u6280\u672f\u3002\u800c\u4e14\u901a\u5e38\u6765\u8bf4\uff0c\u5bf9\u4e8e\u4e0d\u540c\u8fd0\u7b97\u53c2\u6570\uff0c\u5176\u5ef6\u65f6\u4e5f\u4f1a\u6709\u4e0d\u540c\u3002</p> <p>\u6b64\u5916\uff0c\u4e0e\u95e8\u548c\u6216\u95e8\u53ef\u80fd\u6709\u66f4\u591a\u7684\u8f93\u5165\u5f15\u811a\uff0c\u5982\u4e0b\uff1a</p> <p></p> <p>\u81f3\u6b64\uff0c\u7ed9\u51fa\u4e86 AND, OR, NOT \u4e09\u4e2a\u95e8\u7684\u7b26\u53f7\u8868\u793a\uff0c\u7c7b\u4f3c\u4e0a\u4e00\u5c0f\u8282\u63d0\u5230\u7684\u90a3\u6837\uff0c\u6211\u4eec\u4e5f\u53ef\u4ee5\u5229\u7528\u8fd9\u4e09\u4e2a\u57fa\u7840\u7684\u95e8\u7535\u8def\u6765\u6784\u6210\u5176\u4ed6\u7684\u95e8\u7535\u8def\uff08\u867d\u7136\u901a\u5e38\u6765\u8bf4\uff0c\u6211\u4eec\u53ef\u80fd\u662f\u901a\u8fc7 NAND + NOT \u6765\u5b9e\u73b0 AND \u7684\uff09\u3002</p> <p>\u4e8e\u662f\u53c8\u5f15\u7533\u51fa\u4e00\u4e2a\u6982\u5ff5\u2014\u2014\u901a\u7528\u95e8(Universal Gate)\u3002\u4e00\u4e2a\u529f\u80fd\u5b8c\u5168\u7684\uff0c\u80fd\u591f\u8868\u793a\u5176\u4ed6\u6240\u6709\u95e8\u7684\u903b\u8f91\u95e8\u88ab\u79f0\u4e3a\u901a\u7528\u95e8\uff0c\u5728\u6211\u4eec\u5b66\u8fc7\u7684\u903b\u8f91\u95e8\u4e2d\uff0cNAND \u548c NOR \u90fd\u662f\u901a\u7528\u95e8\u3002</p> <p>\u63a8\u8350\u9605\u8bfb</p> <ul> <li>Title: Universal Logic Gates</li> <li>URL: https://www.electronics-tutorials.ws/logic/universal-gates.html</li> </ul> <p>Universal Logic gates can be used to produce any other logic or Boolean function with the NAND and NOR gates being minimal</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap02/#\u5e03\u5c14\u4ee3\u6570","title":"\u5e03\u5c14\u4ee3\u6570","text":"<p>literal ~ \u5b57\u9762\u91cf\uff0c\u4e5f\u5c31\u662f\u201c\u53d8\u91cf\u201d\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap02/#\u8fd0\u7b97\u5f8b","title":"\u8fd0\u7b97\u5f8b","text":"<p>\u8fd9\u5f20\u56fe\u7247\u603b\u7ed3\u4e86\u5e03\u5c14\u8fd0\u7b97\u4e2d\u7684\u8fd0\u7b97\u5f8b\uff0c\u4e2a\u4eba\u611f\u89c9\u6700\u9700\u8981\u5f3a\u5316\u8bb0\u5fc6\u7684\u662f 15 \u6761\uff0c\u56e0\u4e3a\u5e03\u5c14\u4ee3\u6570\u501f\u7528\u4e86\u666e\u901a\u4ee3\u6570\u7684\u7b26\u53f7\uff0c\u4f46\u7b2c 15 \u6761\u5728\u666e\u901a\u4ee3\u6570\u4e2d\u5e76\u4e0d\u6210\u7acb\uff0c\u6240\u4ee5\u5bf9\u4e8e\u4e60\u60ef\u8fd9\u5957\u7b26\u53f7\u7684\u4eba\u6765\u8bf4\u53ef\u80fd\u4e0d\u592a straightfoward\u3002</p> <p>\u5728\u8bb0\u5fc6\u8fd9\u5957\u8fd0\u7b97\u89c4\u5f8b\u7684\u65f6\u5019\uff0c\u6211\u4e2a\u4eba\u7684\u4e00\u4e2a\u60f3\u6cd5\u662f\uff0c\u4e00\u5b9a\u8981\u5efa\u7acb \u4e0e \u548c \u6216 \u662f\u5bf9\u7b49\u7684\u89c2\u5ff5\u3002\u6211\u4eec\u4e60\u60ef\u7528\u201c\u771f\u201d\u53bb\u7406\u89e3\u8fd9\u4e24\u4e2a\u8fd0\u7b97\uff0c\u4f46\u662f\u5b9e\u9645\u4e0a\u5982\u679c\u4f60\u4ee5\u201c\u5047\u201d\u4e3a\u4e3b\u4f53\u53bb\u5206\u6790\u8fd9\u4e24\u4e2a\u8fd0\u7b97\uff0c\u4f1a\u53d1\u73b0\u548c\u201c\u771f\u201d\u662f\u5b8c\u5168\u5bf9\u79f0\u7684\u3002\u6362\u8a00\u4e4b\uff0c \u4e0e \u548c \u6216 \u662f\u5b8c\u5168\u5bf9\u79f0\u7684\u8fd0\u7b97\uff0c\u800c\u975e\u50cf\u4ed6\u4eec\u501f\u7528\u7684\u7b26\u53f7 \\(\\times\\) \u548c \\(+\\) \u90a3\u6837\u5b58\u5728\u975e\u5bf9\u79f0\u5173\u7cfb\u3002</p> <p>\u4f46\u662f\u8ba9\u8fd9\u4ef6\u4e8b\u53d8\u5f97\u53c8\u6ca1\u90a3\u4e48\u7b80\u5355\u7684\u4e8b\u60c5\u662f\uff0c\u867d\u7136 \u4e0e \u548c \u6216 \u662f\u5bf9\u7b49\u7684\uff0c\u4f46\u662f\u6211\u4eec\u5728\u501f\u7528\u666e\u901a\u4ee3\u6570\u7b26\u53f7\u4f53\u7cfb\u7684\u540c\u65f6\uff0c\u53c8\u4eba\u4e3a\u5730\u7ed9\u4ed6\u4eec\u6dfb\u52a0\u4e86\u4f18\u5148\u7ea7\uff08\u4f46\u662f\u8fd9\u4e5f\u662f\u5fc5\u8981\u7684\uff0c\u5426\u5219\u8868\u8fbe\u5f0f\u5c31\u4f1a\u5145\u6ee1\u62ec\u53f7\uff09\u3002</p> <p>\u4f18\u5148\u7ea7\u4ece\u9ad8\u5230\u4f4e\u4f9d\u6b21\u4e3a\uff1a</p> <ol> <li>\u62ec\u53f7 / ()\uff1b</li> <li>\u975e / NOT / \\(\\overline A\\)\uff1b</li> <li>\u4e0e / AND / \\(\\cdot\\)\uff1b</li> <li>\u6216 / OR / \\(+\\)\uff1b</li> </ol> <p>\u4e2a\u4eba\u611f\u89c9\uff0c\u8fd9\u4e00\u79cd\u601d\u8def\u5e76\u4e0d\u76f4\u89c9\uff0c\u5c24\u5176\u662f\u501f\u7528\u666e\u901a\u4ee3\u6570\u7684\u7b26\u53f7\u4f53\u7cfb\u4ee5\u540e\u66f4\u52a0\u6df7\u6dc6\uff0c\u6240\u4ee5\u53ef\u80fd\u9700\u8981\u4e00\u4e9b\u7ec3\u4e60\u6765\u6446\u8131\u8fd9\u4e9b\u201c\u523b\u677f\u5370\u8c61\u201d\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap02/#\u8fd0\u7b97\u5f8b\u63a8\u5e7f","title":"\u8fd0\u7b97\u5f8b\u63a8\u5e7f","text":"<p>\u9664\u6b64\u4e4b\u5916\uff0c\u4ece\u4e0a\u9762\u63d0\u5230\u7684\u8fd0\u7b97\u5f8b\u4e2d\u8fd8\u80fd\u63a8\u5e7f\u51fa\u5982\u4e0b\u51e0\u4e2a\u6a21\u578b\uff1a</p> <p></p> <p>\u5bf9\u6bd4\u524d\u4e09\u4e2a\u548c\u540e\u4e09\u4e2a\uff0c\u6211\u4eec\u518d\u6b21\u53d1\u73b0\uff0c\u4e0e \u548c \u6216 \u5728\u903b\u8f91\u4e0a\u662f\u5bf9\u79f0\u7684\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap02/#\u5bf9\u5076\u6cd5\u5219","title":"\u5bf9\u5076\u6cd5\u5219","text":"<p>\u5bf9\u5076\u6cd5\u5219(Duality Rule)\uff1a\u4e00\u4e2a\u8868\u8fbe\u5f0f\u7684 \u5bf9\u5076(dual) \u4e3a\uff0c\u5c06\u6240\u6709\u7684 \u4e0e \u548c \u6216 \u5bf9\u8c03\u5f97\u5230\u7684\u5f0f\u5b50\uff08\u6ce8\u610f\uff01\u9700\u8981\u4fdd\u8bc1\u53c2\u4e0e\u8fd0\u7b97\u7684\u7ed3\u6784\u4e0d\u80fd\u53d8\uff08\u662f\u201c\u5e26\u62ec\u53f7\u201d\u7684\u5b8f\u5c55\u5f00\uff09\uff0c\u6bd4\u5982 \u4e00\u822c\u60c5\u51b5\u4e0b \\(A\\cdot B\\) \u4f1a\u88ab\u5bf9\u5076\u4e3a \\((A+B)\\) \u4ee5\u4fdd\u8bc1\u8fd0\u7b97\u987a\u5e8f\uff09\u3002</p> <p>eg</p> <ul> <li>\\(X+XY\\) \u548c \\(X(X+Y)\\) \u5bf9\u5076\uff1b</li> <li>\\(X(Y+Z)\\) \u548c \\(X+YZ\\) \u5bf9\u5076\uff1b</li> </ul> <p>\u800c\u4e00\u822c\u60c5\u51b5\u4e0b\uff0c\u9664\u975e\u67d0\u4e2a\u8868\u8fbe\u5f0f\u662f \u81ea\u5bf9\u5076(self-dual) \u7684\uff0c\u90a3\u4e48\u5b83\u7684\u8868\u73b0\u90fd\u4e0e\u539f\u8868\u8fbe\u5f0f\u4e0d\u540c\u3002</p> <p>\u5bf9\u5076\u8868\u8fbe\u5f0f\u5177\u6709\u5982\u4e0b\u6027\u8d28\uff1a</p> <ul> <li>\u5982\u679c F \u7684\u5bf9\u5076\u662f G\uff0c\u90a3\u4e48 F \u4e5f\u662f G \u7684\u5bf9\u5076\uff0c\u5373\u5bf9\u5076\u5173\u7cfb\u662f\u5bf9\u6210\u7684\uff1b</li> <li>\u5982\u679c\u8868\u8fbe\u5f0f F \u548c G \u7b49\u4ef7\uff0c\u90a3\u4e48\u4ed6\u4eec\u7684\u5bf9\u5076\u4e5f\u7b49\u4ef7\uff1b</li> </ul>"},{"location":"cour_note/D2QD_DigitalDesign/Chap02/#\u4e92\u8865\u51fd\u6570","title":"\u4e92\u8865\u51fd\u6570","text":"<p>\u4e00\u4e2a \u51fd\u6570\u7684\u4e92\u8865(Complement of a Function) \u6307\u7684\u662f\uff0c\u5c06\u5b83\u7684 \u5bf9\u5076\u51fd\u6570 \u4e2d\u6bcf\u4e00\u4e2a \u53d8\u91cf \u90fd\u53d6\u53cd\u5f97\u5230\u7684\u51fd\u6570\uff0c\u800c\u8be5\u51fd\u6570\u6b63\u597d\u7b49\u4e8e\u539f\u51fd\u6570\u7684 \u975e\u3002</p> <p>eg</p> <ul> <li>\u539f\u51fd\u6570\uff1a\\(F=\\overline{A}B+C\\overline{B}\\)\uff1b</li> <li>\u5176\u5bf9\u5076\u51fd\u6570\uff1a\\(F=(\\overline{A}+B)(C+\\overline{B})\\)\uff1b</li> <li>\u5176\u4e92\u8865\u51fd\u6570\uff1a\\(\\overline{F}=(A+\\overline{B})(\\overline{C}+D)\\)\uff1b</li> </ul>"},{"location":"cour_note/D2QD_DigitalDesign/Chap02/#\u66ff\u4ee3\u6cd5\u5219","title":"\u66ff\u4ee3\u6cd5\u5219","text":"<p>\u66ff\u4ee3\u6cd5\u5219(Substitution Rules): \u5982\u679c\u5c06\u4e00\u4e2a\u7b49\u5f0f\u4e2d \u6240\u6709\u7684 \u67d0\u4e2a\u53d8\u91cf \u90fd\u66ff\u6362\u4e3a\u540c\u4e00\u4e2a\u8868\u8fbe\u5f0f\uff0c\u5219\u7b49\u5f0f\u4f9d\u7136\u6210\u7acb\u3002</p> <p>eg</p> <ul> <li>\u539f\u7b49\u5f0f\uff1a\\(X(Y+Z)=XY+XZ\\)\uff1b</li> <li>\u5982\u679c\u4f7f\u7528 \\(X+YZ\\) \u66ff\u6362\u6240\u6709\u7684 \\(X\\)\uff0c\u5219\uff1a</li> <li>\u4fee\u6539\u540e\u7684\u7b49\u5f0f \\((X+YZ)(Y+Z)=(X+YZ)Y+(X+YZ)Z\\) \u4f9d\u7136\u6210\u7acb\uff1b</li> </ul>"},{"location":"cour_note/D2QD_DigitalDesign/Chap02/#\u4e00\u81f4\u6027\u5b9a\u7406","title":"\u4e00\u81f4\u6027\u5b9a\u7406","text":"<p>\u5728\u7b80\u5316\u903b\u8f91\u8868\u8fbe\u5f0f\u7684\u65f6\u5019\uff0c\u4e00\u81f4\u6027\u5b9a\u7406(Consensus Theorem) \u4e5f\u5f88\u6709\u7528\uff1a</p> \\[ XY+\\overline{X}Z+YZ=XY+\\overline{X}Z \\] <p>\u5176\u8bc1\u660e\u7684\u7b2c\u4e00\u6b65\u662f\u8fd9\u6837\u7684\uff1a \\(XY+\\overline{X}Z+YZ=XY+\\overline{X}Z+(X+\\overline{X})YZ\\)\uff0c\u90a3\u540e\u9762\u5c31\u5f88\u7b80\u5355\u4e86\u3002\u672c\u8d28\u4e0a\u8fd9\u4e2a\u7b49\u5f0f\u662f\u5229\u7528\u4e86\u88c2\u9879\uff0c\u9700\u8981\u5c06\u5176\u4e2d\u6700\u672c\u8d28\u7684\u90e8\u5206\uff0c\u6700\u5c0f\u7684\u7c92\u5ea6\u7ed9\u88c2\u5f00\u6765\uff0c\u7136\u540e\u518d\u6162\u6162\u6d88\u6389\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap02/#\u6807\u51c6\u5f62\u5f0f\u4e0e\u89c4\u8303\u5f62\u5f0f","title":"\u6807\u51c6\u5f62\u5f0f\u4e0e\u89c4\u8303\u5f62\u5f0f","text":"<p>\u7531\u4e8e\u672c\u8d28\u4e0a\u76f8\u7b49\u7684\u5e03\u5c14\u8868\u8fbe\u5f0f\u5b9e\u9645\u4e0a\u6709\u5f88\u591a\u79cd\u5199\u6cd5\uff0c\u800c\u4e14\u968f\u7740\u53d8\u91cf\u8d8a\u6765\u8d8a\u590d\u6742\uff0c\u4ed6\u4eec\u4e4b\u95f4\u7684\u6bd4\u8f83\u4f1a\u5f88\u56f0\u96be\u3002\u6240\u4ee5\u6211\u4eec\u9700\u8981\u5b9a\u4e49\u4e00\u79cd\u5f62\u5f0f\uff0c\u4f7f\u5f97\u6240\u6709\u76f8\u540c\u7684\u8868\u8fbe\u5f0f\u90fd\u80fd\u6bd4\u8f83\u65b9\u4fbf\u7684\u201c\u5316\u7b80\u201d\u4e3a\u540c\u4e00\u4e2a\u5f62\u5f0f\uff0c\u540c\u65f6\u4e5f\u80fd\u8fa8\u522b\u51fa\u4e24\u4e2a\u8868\u8fbe\u5f0f\u662f\u4e0d\u540c\u7684\u3002\u8fd9\u5c31\u5f15\u5165\u4e86 \u6807\u51c6\u5f62\u5f0f(Standard Forms)\uff0c\u5305\u62ec SOP \u548c POS\uff1b\u4ee5\u53ca \u89c4\u8303\u5f62\u5f0f(Canonical Forms)\uff0c\u5206\u522b\u4e3a \u6700\u5c0f\u9879\u4e4b\u548c(Sum of Minterms, SOM) \u548c \u6700\u5927\u9879\u4e4b\u79ef(Product of Maxterms, POM)\u3002</p> <p>\u4e3a\u4e86\u65b9\u4fbf\u63cf\u8ff0\uff0c\u5728\u7ee7\u7eed\u4e4b\u524d\uff0c\u6211\u4eec\u5148\u7ed9\u51fa\u8fd9\u6837\u4e00\u5f20 \ud83c\udf30 \u771f\u503c\u8868\u3002</p> \ud83c\udf30 Index X Y Z Output 0 / <code>000</code> <code>0</code> <code>0</code> <code>0</code> <code>0</code> 1 / <code>001</code> <code>0</code> <code>0</code> <code>1</code> <code>0</code> 2 / <code>010</code> <code>0</code> <code>1</code> <code>0</code> <code>1</code> 3 / <code>011</code> <code>0</code> <code>1</code> <code>1</code> <code>0</code> 4 / <code>100</code> <code>1</code> <code>0</code> <code>0</code> <code>1</code> 5 / <code>101</code> <code>1</code> <code>0</code> <code>1</code> <code>1</code> 6 / <code>110</code> <code>1</code> <code>1</code> <code>0</code> <code>0</code> 7 / <code>111</code> <code>1</code> <code>1</code> <code>1</code> <code>1</code> <p>\u6570\u503c\u662f\u968f\u4fbf\u6413\u7684\uff0c\u8bf7\u7559\u610f\u4e3a\u4ec0\u4e48\u4e3a\u8981\u5728 Index \u7279\u5730\u5199\u51fa\u4e8c\u8fdb\u5236\u7684\u8868\u8ff0\u3002</p> <p>\u5728\u5f00\u59cb\u4e4b\u524d\uff0c\u6211\u9700\u8981\u5f3a\u8c03\uff0c\u6211\u4eec\u5f15\u5165 SOM \u548c POM \u7684\u76ee\u7684\u662f\u5bfb\u627e\u4e00\u79cd\u6bd4\u8f83\u5178\u578b\u7684 \u8868\u8fbe\uff0c\u4f7f\u5f97\u4ed6\u4eec\u80fd\u591f \u786e\u5b9a \u4e00\u5f20\u771f\u503c\u8868\u3002\u5373\uff0c\u77e5\u9053\u8fd9\u79cd \u8868\u8fbe \u6211\u4eec\u5c31\u8db3\u591f\u5199\u51fa\u8fd9\u5f20\u771f\u503c\u8868\uff0c\u53cd\u4e4b\u4ea6\u7136\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap02/#\u6700\u5c0f\u9879\u4e4b\u548c-som","title":"\u6700\u5c0f\u9879\u4e4b\u548c SOM","text":"<p>\u8bfe\u672c\u4e2d\u5bf9\u6700\u5c0f\u9879\u7684\u63cf\u8ff0\u662f\uff1a</p> <p>A product term in which all the variables appear exactly once, either complemented or uncomplemented, is called minterm. </p> <p>Its characteristic property is that it represents exactly one combination of binary variable values in the truth table.</p> <p>\u7528\u6211\u7684\u8bdd\u6765\u8bf4\uff0c\u6700\u5c0f\u9879\u4e4b\u548c\u5c31\u662f\u6311\u51fa\u771f\u503c\u8868\u4e2d\u6240\u6709\u7ed3\u679c\u662f <code>1</code> \u7684\u6700\u5c0f\u9879\uff08\u6bd4\u8f83\u6a21\u7cca\u4f46\u76f4\u89c2\uff0c\u6240\u4ee5\u8bf7\u5148\u56eb\u56f5\u541e\u67a3\uff0c\u6211\u5728\u201c\u8ffd\u52a0\u8bf4\u660e\u201d\u4f1a\u8fdb\u4e00\u6b65\u8bf4\u660e\uff09\u7136\u540e <code>OR</code> \u8d77\u6765\u3002\u663e\u7136\uff0c\u6700\u5c0f\u9879\u4e4b\u548c\u7684\u542b\u4e49\u5c31\u662f\uff0c\u4e00\u65e6\u5b57\u9762\u91cf\u53d6\u503c\u7684\u7ec4\u5408\u5339\u914d\u4e86\u8fd9\u51e0\u4e2a\u201c\u6700\u5c0f\u9879\u201d\u7684\u5176\u4e2d\u4e00\u9879\uff0c\u90a3\u4e48\u7ed3\u679c\u5c31\u662f <code>1</code>\uff0c\u7b26\u5408\u4e86 <code>OR</code> \u7684\u201c\u67091\u5f971\u201d\u7684\u89c4\u5219\u3002</p> <p>\u6211\u4eec\u4f7f\u7528\u7b26\u53f7 \\(m_{idx}\\) \u6765\u8868\u793a\u53d8\u91cf\u7ec4\u5408 \\(idx\\) \u662f\u4e00\u4e2a\u6700\u5c0f\u9879\uff0c\u5176\u4e2d \\(idx\\) \u8868\u793a\u63cf\u8ff0\u7684\u90a3\u4e00\u9879\u5728\u771f\u503c\u8868\u7684\u5e8f\u53f7\uff0c\u540c\u65f6\u8fd9\u4e2a\u4e0b\u6807\u7684\u4e8c\u8fdb\u5236\u4e5f\u80fd\u53cd\u6620\u51fa\u5b57\u9762\u91cf\u7684\u7ec4\u5408\u3002</p> <p>\u4f8b\u5982\uff0c\u5728 \ud83c\udf30 \u4e2d\uff0coutput \u4e3a <code>1</code> \u7684\u9879\u6709\uff1a<code>010</code> <code>100</code> <code>101</code> <code>111</code> \u8fd9\u56db\u9879\uff0c\u90a3\u4e48\u6211\u4eec\u9700\u8981\u6311\u51fa\u6765\u7684\u6700\u5c0f\u9879\u8868\u8fbe\u5c31\u5206\u522b\u662f \\(m_{2}=\\overline{X}Y\\overline{Z}, \\; m_{4}=X\\overline{Y}\\overline{Z}, \\; m_{5}=X\\overline{Y}Z, \\; m_{7}=XYZ\\)\uff0c\u8fd9\u4e9b\u53d8\u91cf\u8868\u8fbe\u5f0f\u90fd\u662f\u5f53\u4e14\u4ec5\u5f53\u53d8\u91cf\u7ec4\u5408\u4e3a\u5bf9\u5e94\u9879\u65f6\u624d\u4f1a\u53d6 <code>1</code> \u7684\u8868\u8fbe\u5f0f\uff0c\u53ef\u4ee5\u8ba4\u4e3a\uff0c\u8fd9\u5199\u8868\u8fbe\u5f0f\u552f\u4e00\u8868\u8fbe\u4e86\u8fd9\u4e9b\u771f\u503c\u8868\u4e2d\u7684 <code>1</code>\u3002</p> \u8ffd\u52a0\u8bf4\u660e\uff08\u7b80\u5355\uff0c\u4f46\u662f\u5efa\u8bae\u770b\u4e00\u770b\uff09 <p>\u6216\u8bb8\u60a8\u89c9\u5f97\u6700\u5c0f\u9879\u7684\u5f97\u5230\u975e\u5e38\u7684\u81ea\u7136\u4e14\u7b80\u5355\uff0c\u6211\u5efa\u8bae\u60a8\u4e5f\u5c1d\u8bd5\u7740\u770b\u4e00\u770b\u8ffd\u52a0\u8bf4\u660e\uff0c\u56e0\u4e3a\u8fd9\u5bf9\u7406\u89e3\u6700\u5927\u9879\u633a\u6709\u5e2e\u52a9\u7684\u3002</p> <p>\u90a3\u4e48\u4ec0\u4e48\u662f\u201c\u5217\u4e3e\u201d\u5462\uff1f\u8ba9\u6211\u4eec\u518d\u770b\u4e00\u773c\u4e0a\u9762\u5bf9\u6700\u5c0f\u9879\u4e4b\u548c\u7684\u63cf\u8ff0\uff1a\u201c\u4e00\u65e6\u5b57\u9762\u91cf\u53d6\u503c\u7684\u7ec4\u5408\u5339\u914d\u8fd9\u51e0\u4e2a\u2018\u6700\u5c0f\u9879\u2019\u7684\u5176\u4e2d\u4e00\u9879\uff0c\u90a3\u4e48\u7ed3\u679c\u5c31\u662f\u771f\u201d\uff0c\u8ffd\u672c\u6eaf\u6e90\uff0c\u5728\u6700\u5c0f\u9879\u4e2d\uff0c\u6211\u4eec\u5c31\u9700\u8981\u505a\u5230\u53ea\u6709\u5f53\u4e00\u4e2a\u7535\u8def\u7684\u72b6\u6001\u662f\u7279\u5b9a\u7ec4\u5408\u65f6\uff0c\u5176\u8fd4\u56de\u503c\u4e3a <code>1</code>\u3002</p> <p>\u5177\u4f53\u6765\u8bf4\uff0c\u6bd4\u5982\uff0c\u5bf9\u4e8e \ud83c\udf30 \u4e2d\u7684 \\(m_{5}=X\\overline{Y}Z\\)\uff0c\u4e5f\u53ef\u4ee5\u901a\u8fc7\u8fd9\u6837\u4e00\u79cd\u66f4\u5570\u55e6\u7684\u65b9\u5f0f\u8868\u8fbe\u51fa\u6765\u662f\u8fd9\u6837\u7684\uff1a</p> <pre><code>if(X == 1 &amp;&amp; Y == 0 &amp;&amp; Z == 1) {\nOutput = 1;\n} else {\nOutput = 0;\n}\n</code></pre> <p>\uff08\u5faa\u5e8f\u6e10\u8fdb\uff09\u6211\u4eec\u53ef\u4ee5\u5c06\u5b83\u53d8\u5316\u4e3a\u8fd9\u6837\uff1a</p> <pre><code>if(X == 1 &amp;&amp; (!Y) == 1 &amp;&amp; Z == 1) {\nOutput = 1;\n} else {\nOutput = 0;\n}\n</code></pre> <p>\u5982\u679c\u4f60\u719f\u6089\u201c\u538b\u884c\u201d\u6280\u5de7\uff0c\u90a3\u4e48\u8fd9\u4e00\u6bb5\u90fd\u53ef\u4ee5\u5199\u6210\uff1a</p> <pre><code>Output = (X == 1 &amp;&amp; (!Y) == 1 &amp;&amp; Z == 1);\n</code></pre> <p>\u800c\u8fd9\u4e2a\u903b\u8f91\u8868\u8fbe\u5f0f\uff0c\u5b9e\u9645\u4e0a\u5df2\u7ecf\u548c \\(m_5=X\\overline{Y}Z\\) \u4e00\u6a21\u4e00\u6837\u4e86\u3002</p> <p>\u5728\u8fd9\u91cc\u7ed9\u51fa\u4e00\u4e2a\u603b\u7ed3\u6027\u7684\u8868\u8ff0\uff1a\u6240\u8c13\u7684\u201c\u6311\u51fa\u201d\uff0c\u5c31\u662f\u5bf9\u4e8e\u9009\u5b9a\u7684\u4e00\u4e2a\u5b57\u9762\u91cf\u53d6\u503c\u7684\u7ec4\u5408\uff0c\u7ed9\u51fa\u4e00\u4e2a\u7279\u5b9a\u7684\u8868\u8fbe\u5f0f\uff0c\u4f7f\u5f97\u53ea\u6709\u8fd9\u79cd\u7ec4\u5408\u7684\u7ed3\u679c\u662f \\(f\\)\uff0c\u800c\u5bf9\u4e8e\u4efb\u4f55\u5176\u4ed6\u53d6\u503c\u7684\u7ec4\u5408\uff0c\u8be5\u8868\u8fbe\u5f0f\u7684\u7ed3\u679c\u90fd\u662f \\(\\overline{f}\\)\uff0c\u5373\u5b9e\u73b0\u4e86\u8be5\u8868\u8fbe\u5f0f\u80fd \u552f\u4e00\u8868\u8fbe \u8fd9\u4e2a\u53d6\u503c\u7ec4\u5408\u3002\uff08\u8fd9\u91cc\u4e4b\u6240\u4ee5\u5199\u7684\u662f \\(f\\) \u800c\u4e0d\u662f <code>1</code>\uff0c\u662f\u4e3a\u4e86\u7ed9\u4e4b\u540e\u5206\u6790 POM \u505a\u94fa\u57ab\uff0c\u5bf9\u4e8e POM\uff0c<code>0</code> \u624d\u662f\u552f\u4e00\u8868\u8fbe\u7684\u7279\u5f81\u7ed3\u679c\u3002\uff09</p> <p>\u81f3\u6b64\uff0c\u6211\u4eec\u5f97\u5230\u4e86 \ud83c\udf30 \u6240\u5bf9\u5e94\u7684 SOM\uff1a</p> \\[ \\begin{array}{l}     F(X,Y,Z)     &amp; = \\sum m(2,4,5,7) \\\\     &amp; = m_2+m_4+m_5+m_7 \\\\     &amp; = \\overline{X}Y\\overline{Z}+X\\overline{Y}\\,\\overline{Z}+X\\overline{Y}Z+XYZ \\end{array} \\] <p>\u518d\u6b21\u5f52\u7eb3\uff0c\u4f7f\u7528\u901a\u4fd7\u7684\u8bdd\u6765\u8bf4\uff0c\u6700\u5c0f\u9879\u4e4b\u548c\u66f4\u50cf\u662f\u201c\u679a\u4e3e\u4e86\u6240\u6709 <code>1</code> \u7684\u53ef\u80fd\u201d\uff0c\u53ea\u8981\u5339\u914d\u4e86\u8fd9\u4e2a\u201c\u548c\u201d\u4e2d\u7684\u67d0\u4e00\u9879\uff08\u4e8b\u5b9e\u4e0a\u4e0d\u505a\u5316\u7b80\u7684\u8bdd\u4f60\u4e5f\u53ea\u80fd\u6ee1\u8db3\u4e00\u9879\u7684\u503c\u53d6\u5230 <code>1</code>\uff09\uff0c\u8868\u8fbe\u5f0f\u7684\u503c\u5c31\u4f1a\u53d8\u6210 <code>1</code>\uff1b\u800c\u4e00\u4e2a\u90fd\u4e0d\u5339\u914d\u7684\uff0c\u81ea\u7136\u5c31\u53ea\u80fd\u5f97\u5230 <code>0</code>\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap02/#\u6700\u5927\u9879\u4e4b\u79ef-pom","title":"\u6700\u5927\u9879\u4e4b\u79ef POM","text":"<p>\u5c31\u50cf\u6211\u4e4b\u524d\u4e0d\u65ad\u4e0d\u65ad\u4e0d\u65ad\u5f3a\u8c03\u7684\uff0c\u6240\u8c13\u7684 <code>1</code> \u548c <code>0</code> \u90fd\u53ea\u662f\u4eba\u4e3a\u5b9a\u4e49\u7684\uff0c\u6446\u8131\u6f5c\u610f\u8bc6\u91cc\u5bf9\u8fd9\u4e24\u8005\u4e4b\u4e00\u7684\u503e\u5411\uff08\u4f8b\u5982\u6211\u672c\u4eba\u5c31\u4e00\u76f4\u5f88\u503e\u5411\u4e8e\u4ee5 <code>1</code> \u4e3a\u4e3b\u4f53\u7814\u7a76\u95ee\u9898\uff09\u4f1a\u5bf9\u7406\u89e3\u6700\u5927\u9879\u4e4b\u79ef\u548c\u903b\u8f91\u8868\u8fbe\u5f0f\u5316\u7b80\u5f88\u6709\u5e2e\u52a9\u3002</p> <p>\u800c\u6700\u5927\u9879\u4e4b\u79ef\u2014\u2014\u4ee5\u6211\u4e2a\u4eba\u7684\u611a\u89c1\u2014\u2014\u5c31\u662f\u4ee5 <code>0</code> \u4e3a\u4e3b\u4f53\u6765\u7814\u7a76\u771f\u503c\u8868\u7684\u7279\u5f81\u7684\u3002</p> <p>\u8bfe\u672c\u4e2d\u5bf9\u6700\u5927\u9879\u7684\u63cf\u8ff0\u662f\uff1a</p> <p>A sum term that contains all the variables in complemented or uncomplemented form is called a maxterm.</p> <p>\u4e0e\u6700\u5c0f\u9879\u5bf9\u6bd4\uff0c\u65e0\u975e\u662f\u628a \"product term\" \u6362\u6210\u4e86 \"sum term\"\uff0c\u4e5f\u5c31\u662f\u628a AND \u6362\u6210\u4e86 OR\u3002</p> <p>\u800c\u6700\u5927\u9879\u4e4b\u79ef\uff0c\u5c31\u662f\u6311\u51fa\u6240\u6709\u7ed3\u679c\u4e3a <code>0</code> \u7684\u6700\u5927\u9879\uff08\u201c\u6311\u51fa\u201d\u7684\u5b9a\u4e49\u6211\u5df2\u7ecf\u5728 SOM \u7684\u8ffd\u52a0\u8bf4\u660e\u4e2d\u7ed9\u51fa\uff0c\u5728 POM \u7684\u8ffd\u52a0\u8bf4\u660e\u4e2d\u6211\u8fd8\u4f1a\u518d\u4e00\u6b21\u63d0\u53ca\uff09\uff0c\u518d\u505a AND\u3002\u4ee5 <code>1</code> \u4e3a\u4e3b\u4f53\u63cf\u8ff0 AND \u662f\u201c\u90fd1\u51fa1\u201d\uff0c\u800c\u4ee5 <code>0</code> \u4e3a\u4e3b\u4f53\u63cf\u8ff0 AND \u5219\u662f\u201c\u67090\u51fa0\u201d\uff0c\u8fd9\u4e0e OR \u7684\u201c\u67091\u51fa1\u201d\u4e5f\u662f\u9ad8\u5ea6\u5bf9\u79f0\u7684\uff08\u53cd\u4e4b\u4ea6\u7136\uff09\u3002\u4e5f\u5c31\u662f\u8bf4\uff0c\u6700\u5927\u9879\u4e4b\u79ef\u7684\u542b\u4e49\u662f\uff0c\u5728\u6700\u5927\u9879\u4e4b\u79ef\u4e2d\uff0c\u53ea\u8981\u5b57\u9762\u91cf\u53d6\u503c\u7684\u7ec4\u5408\u5339\u914d\u8fd9\u51e0\u4e2a\u201c\u6700\u5927\u9879\u201d\u7684\u5176\u4e2d\u4e00\u9879\uff0c\u6574\u4e2a\u8868\u8fbe\u5f0f\u7684\u7ed3\u679c\u5c31\u4f1a\u53d8\u6210 <code>0</code>\u3002</p> <p>\u7c7b\u4f3c\u7684\uff0c\u6211\u4eec\u4f7f\u7528\u7b26\u53f7 \\(M_{idx}\\) \u6765\u8868\u793a\u53d8\u91cf\u7ec4\u5408 \\(idx\\) \u662f\u4e00\u4e2a\u6700\u5927\u9879\uff0c\u5176\u4e2d \\(idx\\) \u8868\u793a\u63cf\u8ff0\u7684\u90a3\u4e00\u9879\u5728\u771f\u503c\u8868\u7684\u5e8f\u53f7\uff0c\u540c\u65f6\u8fd9\u4e2a\u4e0b\u6807\u7684\u4e8c\u8fdb\u5236\u4e5f\u80fd\u53cd\u6620\u51fa\u5b57\u9762\u91cf\u7684\u7ec4\u5408\u3002</p> <p>\u4f8b\u5982\uff0c\u5728 \ud83c\udf30 \u4e2d\uff0coutput \u4e3a <code>0</code> \u7684\u9879\u6709\uff1a<code>000</code> <code>001</code> <code>011</code> <code>110</code> \u8fd9\u56db\u9879\uff0c\u90a3\u4e48\u6211\u4eec\u9700\u8981\u6311\u51fa\u6765\u7684\u6700\u5c0f\u9879\u8868\u8fbe\u5c31\u5206\u522b\u662f \\(M_{0}=X+Y+Z, \\; M_{1}=X+Y+\\overline{Z}, \\; M_{3}=X+\\overline{Y}+\\overline{Z}, \\; M_{6}=\\overline{X}+\\overline{Y}+Z\\)\u3002\u53ef\u4ee5\u68c0\u9a8c\uff0c\u53ea\u6709\u4ee3\u5165\u4ed6\u4eec\u5bf9\u5e94\u7684\u90a3\u4e00\u884c\u771f\u503c\u8868\u7ec4\u5408\u65f6\uff0c\u4ed6\u4eec\u624d\u4f1a\u5f97\u5230 <code>0</code>\u3002</p> \u8ffd\u52a0\u8bf4\u660e <p>\u540c\u6837\u7684\uff0c\u56de\u987e\u6700\u5927\u9879\u4e4b\u79ef\u7684\u63cf\u8ff0\uff1a\u201c\u5728\u6700\u5927\u9879\u4e4b\u79ef\u4e2d\uff0c\u53ea\u8981\u5b57\u9762\u91cf\u53d6\u503c\u7684\u7ec4\u5408\u5339\u914d\u8fd9\u51e0\u4e2a\u2018\u6700\u5927\u9879\u2019\u7684\u5176\u4e2d\u4e00\u9879\uff0c\u6574\u4e2a\u8868\u8fbe\u5f0f\u7684\u7ed3\u679c\u5c31\u4f1a\u53d8\u6210 <code>0</code>\u201d\u3002</p> <p>\u5177\u4f53\u6765\u8bf4\uff0c\u6bd4\u5982\uff0c\u5bf9\u4e8e \ud83c\udf30 \u4e2d\u7684 \\(M_6=\\overline{X}+\\overline{Y}+Z\\)\uff0c\u6211\u4eec\u53ef\u4ee5\u5982\u4e0b\u63cf\u8ff0\uff1a</p> <pre><code>if(X == 1 &amp;&amp; Y == 1 &amp;&amp; Z == 0){\nOutput = 0;\n} else {\nOutput = 1;\n}\n</code></pre> <p>\u56de\u987e\u6700\u5927\u9879\u7684\u76ee\u7684\u662f\u6ee1\u8db3\u8fd9\u4e2a\u5206\u652f\u6761\u4ef6\u7684\u60c5\u51b5\u4e0b\u8f93\u51fa <code>0</code>\uff0c\u4e5f\u5c31\u662f\u8bf4\u6211\u4eec\u9700\u8981\u8868\u8fbe <code>(X == 1 &amp;&amp; Y == 1 &amp;&amp; Z == 0)</code> \u8fd9\u4e2a\u903b\u8f91\u6761\u4ef6\u3002\u4f46\u7531\u4e8e\u6700\u5927\u9879\u7684\u5b9e\u73b0\u5f62\u5f0f\u662f <code>OR</code>\uff0c\u6240\u4ee5\u6211\u4eec\u9700\u8981\u5c06 <code>&amp;&amp;</code> \u7684\u5f0f\u5b50\u4ee5 <code>||</code> \u7684\u5f62\u5f0f\u8868\u8fbe\u3002</p> <p>\u5f53\u7136\uff0c\u4f60\u53ef\u4ee5\u9009\u62e9\u4f7f\u7528\u5404\u79cd\u8fd0\u7b97\u5f8b\u6765\u5316\u7b80\uff0c\u4f46\u662f\u4e0d\u59a8\u60f3\u4e00\u60f3 <code>AND</code> \u548c <code>OR</code> \u7684\u8fd0\u7b97\u7279\u5f81\uff0c\u524d\u8005\u662f\u201c\u67090\u51fa0\u201d\uff0c\u540e\u8005\u662f\u201c\u67091\u51fa1\u201d\u3002\u800c\u5bf9\u4e8e <code>AND</code> \u6765\u8bf4\uff0c\u60f3\u8981\u505a\u5230\u6761\u4ef6\u7b5b\u9009\uff0c\u5c31\u9700\u8981\u6bcf\u4e00\u4e2a\u6761\u4ef6\u90fd\u662f <code>1</code>\uff0c\u6700\u540e\u5982\u679c\u7b5b\u9009\u6210\u529f\u7ed3\u679c\u5c31\u662f <code>1</code>\uff1b\u5bf9\u4e8e <code>OR</code> \u6765\u8bf4\uff0c\u5c31\u662f\u6bcf\u4e00\u4e2a\u6761\u4ef6\u90fd\u662f <code>0</code>\uff0c\u5982\u679c \u7b5b\u9009\u6210\u529f \u7684\u7ed3\u679c\u5c31\u662f <code>0</code>\u3002\u4e5f\u5c31\u662f\u8bf4\u5bf9\u4e8e\u6216\uff0c\u6211\u4eec\u53ef\u4ee5\u8fd9\u6837\u8868\u793a\uff1a</p> <pre><code>if((X == 0 || Y == 0 || (!Z) == 0) == 0){\nOutput = 0;\n} else {\nOutput = 1;\n}\n</code></pre> <p>\u540c\u6837\u8fdb\u884c\u4e00\u4e0b\u538b\u884c\uff1a</p> <pre><code>// It might be too complex.\nOutput = !((X == 0 || Y == 0 || (!Z) == 0) == 0);\n// So we can simplify it.\nOutput = (X == 0 || Y == 0 || (!Z) == 0);\n</code></pre> <p>\u8fd9\u4e5f\u6b63\u5bf9\u5e94\u4e86 \\(M_6=\\overline{X}+\\overline{Y}+Z\\)\u3002</p> <p>\u518d\u6b21\u7ed9\u51fa\u8fd9\u4e2a\u603b\u7ed3\u6027\u7684\u8868\u8ff0\uff1a\u6240\u8c13\u7684\u201c\u6311\u51fa\u201d\uff0c\u5c31\u662f\u5bf9\u4e8e\u9009\u5b9a\u7684\u4e00\u4e2a\u5b57\u9762\u91cf\u53d6\u503c\u7684\u7ec4\u5408\uff0c\u7ed9\u51fa\u4e00\u4e2a\u7279\u5b9a\u7684\u8868\u8fbe\u5f0f\uff0c\u4f7f\u5f97\u53ea\u6709\u8fd9\u79cd\u7ec4\u5408\u7684\u7ed3\u679c\u662f \\(f\\)\uff0c\u800c\u5bf9\u4e8e\u4efb\u4f55\u5176\u4ed6\u53d6\u503c\u7684\u7ec4\u5408\uff0c\u8be5\u8868\u8fbe\u5f0f\u7684\u7ed3\u679c\u90fd\u662f \\(\\overline{f}\\)\uff0c\u5373\u5b9e\u73b0\u4e86\u8be5\u8868\u8fbe\u5f0f\u80fd \u552f\u4e00\u8868\u8fbe \u8fd9\u4e2a\u53d6\u503c\u7ec4\u5408\u3002</p> <p>\u81f3\u6b64\uff0c\u6211\u4eec\u5f97\u5230\u4e86 \ud83c\udf30 \u6240\u5bf9\u5e94\u7684 POM\uff1a</p> \\[     \\begin{aligned}     F(X,Y,Z)     &amp; = \\prod M(0,1,3,6) \\\\     &amp; = M_0M_1M_3M_6 \\\\     &amp; = (X+Y+Z)(X+Y+\\overline{Z})(X+\\overline{Y}+\\overline{Z})(\\overline{X}+\\overline{Y}+Z) \\end{aligned} \\] <p>\u540c\u6837\u518d\u6b21\u5f52\u7eb3\uff0c\u4f7f\u7528\u901a\u4fd7\u7684\u8bdd\u6765\u8bf4\uff0c\u6700\u5927\u9879\u4e4b\u79ef\u66f4\u50cf\u662f\u201c\u679a\u4e3e\u4e86\u6240\u6709 <code>0</code> \u7684\u53ef\u80fd\u201d\uff0c\u53ea\u8981\u5339\u914d\u4e86\u8fd9\u4e2a\u201c\u79ef\u201d\u4e2d\u7684\u67d0\u4e00\u9879\uff0c\u8868\u8fbe\u5f0f\u7684\u503c\u5c31\u4f1a\u53d8\u6210 <code>0</code>\uff1b\u800c\u4e00\u4e2a\u90fd\u4e0d\u5339\u914d\u7684\uff0c\u81ea\u7136\u5c31\u53ea\u80fd\u5f97\u5230 <code>1</code>\u3002</p> <p>\u4e0e\u6700\u5c0f\u9879\u76f8\u6bd4\uff0c\u4e00\u4e2a\u679a\u4e3e\u4e86\u6240\u6709\u7684 <code>1</code> \u7684\u53ef\u80fd\uff0c\u4e00\u4e2a\u679a\u4e3e\u4e86\u6240\u6709\u662f <code>0</code> \u7684\u53ef\u80fd\uff0c\u5bf9\u4e8e\u4e00\u4e2a\u4e8c\u503c\u8868\u8fbe\u5f0f\u6765\u8bf4\uff0c\u4e24\u79cd \u8868\u8fbe \u90fd\u662f\u5145\u8981\u7684\u3002</p> <p>\u6b64\u65f6\uff0c\u6211\u4eec\u8fd8\u80fd\u53d1\u73b0\uff1a</p> <p>\u4f8b\u5982\uff1a\\(M_5 = \\overline{X} + Y + \\overline{Z} = \\overline{ X\\overline{Y}Z } = \\overline{m}_5\\)</p> <p>\u5173\u4e8e\u8fd9\u4e2a\u53d1\u73b0\u7684\u66f4\u591a\u7684\u4f8b\u5b50\u548c\u8bf4\u660e\uff0c\u53ef\u4ee5\u770b\u4e0b\u9762\u7684\u7b2c\u4e00\u4e2a\u7ec3\u4e60\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap02/#\u7ec3\u4e60","title":"\u7ec3\u4e60","text":"<p>\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u5c06\u901a\u8fc7\u4e00\u4e9b\u4f8b\u5b50\u6765\u8fdb\u4e00\u6b65\u5f3a\u5316\u8fd9\u4e9b\u7406\u89e3\uff0c\u5e76\u4e14\u6316\u6398\u4e00\u4e9b\u795e\u5947\u7684\u7279\u6027\u3002</p> \u9898\u9762\u7b54\u6848 <p>\u8bf7\u5206\u522b\u5199\u51fa\u5982\u4e0b\u771f\u503c\u8868\u4e2d \\(F\\) \u548c \\(\\overline{F}\\) \u7684 SOM \u548c POM\u3002 </p> <p>\u7b54\u6848\uff1a   \\begin{array}{l}     \\overline{F}(X,Y,Z)     &amp; = \\sum m(1,3,4,6) \\\\     &amp; = \\overline{X}\\,\\overline{Y}Z + \\overline{X}YZ + X\\overline{Y}\\,\\overline{Z} + XY\\overline{Z} \\\\     &amp; = \\prod M(0,2,5,7) \\\\     &amp; = (X+Y+Z)(X+\\overline{Y}+Z)(\\overline{X}+Y+\\overline{Z})(\\overline{X}+\\overline{Y}+\\overline{Z}) \\end{array}  \u4e8e\u662f\u6211\u4eec\u53d1\u73b0\u4e00\u4ef6\u5f88\u6709\u610f\u601d\u7684\u4e8b\u60c5\uff0c\\(F\\) \u7684 SOM \u7684\u4e0b\u6807\u4e0e \\(\\overline{F}\\) \u7684 POM \u7684\u4e0b\u6807\u662f\u4e00\u6837\u7684\uff1b\u5f53\u7136\u5bf9\u4e8e \\(F\\) \u7684 POM \u548c \\(\\overline{F}\\) \u7684 SOM \u4e5f\u662f\u4e00\u6837\u7684\u3002\u8fd9\u53c8\u5370\u8bc1\u4e86\u5bf9\u79f0\u6027\u3002</p> <p>\u4e4b\u540e\u7684\u7ec3\u4e60\u7b49\u6211\u505a\u4e86\u518d\u6dfb\u52a0x \u5982\u679c\u505a\u4e86\u7684\u8bddx \ud83d\ude0b</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap02/#\u7535\u8def\u5b9e\u73b0\u4e0e\u4f18\u5316","title":"\u7535\u8def\u5b9e\u73b0\u4e0e\u4f18\u5316","text":"<p>\u5f15\u5165</p> <p>\u6211\u4eec\u5f53\u7136\u53ef\u4ee5\u76f4\u63a5\u901a\u8fc7\u6807\u51c6\u5f62\u5f0f\u6765\u5f97\u5230\u5bf9\u5e94\u7684\u7535\u8def\uff0c\u4f46\u662f\u5728\u5b9e\u9645\u60c5\u51b5\u4e2d\uff0c\u8fd9\u6837\u505a\u4f1a\u5bfc\u81f4\u6210\u672c\u8fc7\u9ad8\u4ee5\u53ca\u7535\u8def\u590d\u6742\uff08\u56e0\u4e3a\u95e8\u592a\u591a\u4e86\uff09\uff0c\u6240\u4ee5\u6211\u4eec\u9700\u8981\u5bf9\u7535\u8def\u8fdb\u884c\u4f18\u5316\u3002\u5728\u8fd9\u91cc\uff0c\u6211\u4eec\u4ecb\u7ecd\u901a\u8fc7 \u5361\u8bfa\u56fe(Karnaugh map) \u6765\u4f18\u5316\u903b\u8f91\u7535\u8def\u7684\u65b9\u6cd5\u3002</p> <p>\u4e0d\u8fc7\u518d\u5f00\u59cb\u201c\u4f18\u5316\u201d\u7684\u8bdd\u9898\u4e4b\u524d\uff0c\u6211\u4eec\u9700\u8981\u5b9a\u4e49\u4ec0\u4e48\u662f\u201c\u4f18\u201d\uff0c\u4e5f\u5c31\u662f\u7ed9\u51fa\u4e00\u4e2a\u7535\u8def\u6210\u672c\u7684\u8861\u91cf\u4f9d\u636e\uff0c\u5373 \u6210\u672c\u6807\u51c6(cost criteria)\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap02/#\u6210\u672c\u6807\u51c6","title":"\u6210\u672c\u6807\u51c6","text":"<p>\u5728\u6210\u672c\u6807\u51c6\u4e2d\uff0c\u6211\u4eec\u9700\u8981\u4ecb\u7ecd\u7684\u4e3b\u8981\u6709\u4e09\u79cd\u6807\u51c6\uff0c\u5206\u522b\u662f\uff1a</p> <ul> <li>\u6309\u7167\u5b57\u9762\u91cf\u5b57\u9762\u91cf\u8ba1(literal cost)\uff1a\\(L\\)</li> <li>\u6309\u95e8\u8f93\u5165\u8ba1\uff0c\u4e0d\u8ba1\u975e\u95e8(gate-input cost)\uff1a\\(G\\)</li> <li>\u6309\u95e8\u8f93\u5165\u8ba1\uff0c\u8ba1\u975e\u95e8(gate-input cost with NOTs)\uff1a\\(GN\\)</li> </ul>"},{"location":"cour_note/D2QD_DigitalDesign/Chap02/#\u6309\u7167\u5b57\u9762\u91cf\u5b57\u9762\u91cf\u8ba1","title":"\u6309\u7167\u5b57\u9762\u91cf\u5b57\u9762\u91cf\u8ba1","text":"<p>\u5f88\u76f4\u767d\uff0c\u5c31\u662f\u6309\u7167\u8868\u8fbe\u5f0f\u4e2d\u6709\u591a\u5c11\u5b57\u9762\u91cf\u6765\u8ba1\u7b97\uff0c\u4f8b\u5982\uff1a</p> <ul> <li>\\(F = BD + A\\overline{B}C + A\\overline{C}\\,\\overline{D}\\) \u4e2d \\(L = 8\\)\uff1b</li> <li>\\(F = ABC+\\overline{A}\\,\\overline{B}\\,\\overline{C}\\) \u4e2d \\(L = 6\\)\uff1b</li> <li>\\(F = (A+B+C)(\\overline{A}+\\overline{B} + \\overline{C})\\) \u4e2d \\(L = 6\\)\uff1b</li> </ul> <p>\u53ef\u4ee5\u60f3\u8c61\uff0c\u867d\u7136\u8fd9\u79cd\u8ba1\u7b97\u65b9\u6cd5\u975e\u5e38\u7684\u7b80\u5355\uff0c\u4f46\u662f\u611f\u89c9\u4e0d\u592a\u9760\u8c31\u3002\u6bd4\u5982\uff0c\u540e\u9762\u4e24\u4e2a\u4f8b\u5b50\uff0c\u867d\u7136\u4ed6\u4eec\u7684 literal cost \u662f\u4e00\u6837\u7684\uff0c\u4f46\u662f\u663e\u7136\u5f00\u9500\u4e0d\u592a\u4e00\u6837\uff08\u56e0\u4e3a\u4e00\u4e2a\u662f 3+3 \u4e00\u4e2a\u662f 2+2+2\uff09\u3002\u6240\u4ee5\u6211\u4eec\u9700\u8981\u4e00\u4e2a\u66f4\u5408\u9002\u7684\u8ba1\u7b97\u65b9\u6cd5\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap02/#\u6309\u95e8\u8f93\u5165\u8ba1","title":"\u6309\u95e8\u8f93\u5165\u8ba1","text":"<p>\u6309\u7167\u95e8\u8f93\u5165\u8ba1\u5c31\u662f\u6309\u7167\u903b\u8f91\u95e8\u8f93\u5165\u5f15\u811a\u7684\u603b\u4e2a\u6570\u6765\u8ba1\u7b97\uff0c\u8fd9\u91cc\u7684\u8f93\u5165\u5e76\u4e0d\u4ec5\u4ec5\u662f\u76f4\u63a5\u6765\u81ea\u4e8e\u5b57\u9762\u91cf\u8f93\u5165\u7684\u90a3\u4e9b\u5f15\u811a\uff0c\u4e5f\u5305\u62ec\u5b57\u9762\u91cf\u505a\u8fd0\u7b97\u540e\u5f97\u5230\u7684\u7ed3\u679c\u4f5c\u4e3a\u8f93\u5165\u4f20\u5165\u4e0b\u4e00\u7ea7\u903b\u8f91\u95e8\u7684\u5f15\u811a\u3002</p> <p>\u6ce8\u610f</p> <p>\u867d\u7136\u975e\u95e8\u4e5f\u662f\u95e8\uff0c\u4f46\u662f\u6211\u4eec\u901a\u5e38\u4e0d\u628a\u975e\u95e8\u76f4\u63a5\u8ba1\u5165 gate-input cost\uff0c\u6240\u4ee5\u63a5\u4e0b\u6765\u63d0\u5230\u7684\u201c\u8f93\u5165\u5f15\u811a\u201d\u9ed8\u8ba4\u662f\u4e0d\u5305\u542b\u975e\u95e8\u7684\u8f93\u5165\u5f15\u811a\u7684\u3002</p> <p></p> <p>\u4f8b\u5982\u8fd9\u5f20\u5bf9\u5e94\u8868\u8fbe\u5f0f \\(F = A+BC+\\overline{B}\\,\\overline{C}\\) \u7684\u56fe\u4e2d\uff1a</p> <ul> <li>\u7eff\u8272\u539f\u70b9\u8868\u793a\u4e00\u7ea7\u8f93\u5165\u5f15\u811a\uff1b</li> <li>\u84dd\u8272\u65b9\u70b9\u8868\u793a\u4e8c\u7ea7\u8f93\u5165\u5f15\u811a\uff1b</li> <li>\u9ed1\u8272\u4e09\u89d2\u8868\u793a\u975e\u95e8\u7684\u8f93\u5165\u5f15\u811a\uff1b</li> </ul> <p>\u4e5f\u5c31\u662f\u8bf4\uff0c\u8fd9\u91cc\u4e00\u5171\u6709 5 + 2 = 7 \u4e2a\u8f93\u5165\u5f15\u811a\uff0c\u4ee5\u53ca 2 \u4e2a\u975e\u95e8\u8f93\u5165\u5f15\u811a\u3002</p> <p>\u4ece\u8868\u8fbe\u5f0f\u6765\u770b\uff0c\u5b83\u53ef\u4ee5\u770b\u4f5c\u662f\u6bcf\u4e00\u5c42\u8fd0\u7b97\u7684\u53c2\u6570\u6570\u91cf\u6c42\u548c\uff0c\u4e0d\u8fc7\u6211\u4eec\u5ffd\u7565\u975e\u95e8\u3002</p> <p>\u4f8b\u5982\uff0c\u5f0f\u5b50 \\(F=AB+\\overline{B}C+C\\overline{D}\\) \u4e2d\uff0c\u6700\u9876\u5c42\u7684\u8fd0\u7b97\u662f\u4e00\u4e2a\u4e09\u8f93\u5165\u6216\u8fd0\u7b97\uff0c\u6240\u4ee5\u6709 3 \u4e2a\u8f93\u5165\uff1b\u63a5\u4e0b\u6765\u6709\u4e09\u4e2a\u4e8c\u8f93\u5165\u4e0e\u8fd0\u7b97\uff0c\u6240\u4ee5\u5404\u8ba1 2 \u4e2a\u8f93\u5165\uff0c\u4e00\u5171 2 * 3 = 6 \u4e2a\u8f93\u5165\uff0c\u4e00\u5171\u662f 9 \u4e2a\u8f93\u5165\u3002</p> <p>\u5f53\u7136\uff0c\u5b9e\u9645\u4e0a\u4ece\u5e95\u5c42\u5f80\u4e0a\u6570\u66f4\u65b9\u4fbf\uff1a</p> <ul> <li>A \u548c B \u5404\u81ea\u7b97\u4e00\u4e2a\uff0cAB \u6574\u4f53\u7b97\u4e00\u4e2a\uff0c\u4e00\u5171 3 \u4e2a\uff1b</li> <li>\u4e00\u5171\u6709\u4e09\u7ec4\u7c7b\u4f3c AB \u7684\u7ed3\u6784\uff0c\u6240\u4ee5\u4e00\u5171\u662f 3 * 3 = 9 \u4e2a\uff1b</li> <li>\u5373 \\(G=9\\)\uff1b</li> </ul> <p>\u603b\u4e4b\uff0c\u5c31\u662f\u7c7b\u4f3c\u4e8e\u5728\u505a\u7b97\u5f0f\u5316\u7b80\uff0c\u6bcf\u505a\u4e00\u6b21\u5316\u7b80\u90fd\u9700\u8981\u8ba1\u5165\u4e00\u6b21\u64cd\u4f5c\u6570\u7684\u6570\u91cf\u3002</p> <p>\u800c\u5bf9\u4e8e gate-input cost with NOTs\uff0c\u53ea\u8981\u518d\u989d\u5916\u8ba1\u5165\u975e\u95e8\u7684\u8f93\u5165\u5373\u53ef\u3002\u4f8b\u5982\u4e0a\u9762\u90a3\u4e2a\u5f0f\u5b50\uff1a</p> <ul> <li>\u53d1\u73b0\u6709\u4e24\u4e2a\u88ab\u975e\u4e86\u7684\u5b57\u9762\u91cf\uff0c\u6240\u4ee5\u8981\u989d\u5916\u8ba1 2 \u4e2a\uff0c\u4e00\u5171\u662f 11 \u4e2a\uff1b</li> <li>\u5373 \\(GN=11\\)\uff1b</li> </ul> <p>\u6ce8\u610f</p> <p>\u5982\u679c\u51fa\u73b0\u4e86\u6bd4\u5982 \\(F=\\overline{A}B+\\overline{A}C\\) \u7684\u60c5\u51b5\uff0c\u975e\u95e8\u53ea\u9700\u8981\u8ba1 1 \u4e2a\uff0c\u56e0\u4e3a\u6211\u4eec\u5b9e\u9645\u4e0a\u662f\u628a\u975e\u4e86\u4ee5\u540e\u7684\u4e1c\u897f\u5f53\u4f5c\u4e86\u4e00\u4e2a\u5b57\u9762\u91cf\u518d\u7528\u7684\uff0c\u5728\u5b9e\u9645\u7535\u8def\u4e2d\uff0c\u6211\u4eec\u53ea\u9700\u8981\u975e\u4e00\u6b21\uff0c\u4e4b\u540e\u53ea\u9700\u8981\u628a\u8fd9\u4e2a\u8f93\u51fa\u503c\u62ff\u8d70\u53bb\u7528\u5c31\u884c\u3002</p> <p>\u63a5\u4e0b\u6765\u653e\u51e0\u9053\u4f8b\u9898\u3002</p> \u9898\u9762\u7b54\u6848 <p>\u8ba1\u7b97 \\(F=ABC+\\overline{A}\\,\\overline{B}\\,\\overline{C}\\) \u7684 \\(L\\)\u3001\\(G\\)\u3001\\(GN\\)\u3002</p> <ul> <li>\\(L = 6\\)\uff1b</li> <li>\\(G = 8\\)\uff1b</li> <li>\\(GN = 11\\)\uff1b</li> </ul> \u9898\u9762\u7b54\u6848 <p>\u8ba1\u7b97 \\(F=(A+\\overline{C})(\\overline{B}+C)(\\overline{A}+B)\\) \u7684 \\(L\\)\u3001\\(G\\)\u3001\\(GN\\)\u3002</p> <ul> <li>\\(L = 6\\)\uff1b</li> <li>\\(G = 9\\)\uff1b</li> <li>\\(GN = 12\\)\uff1b</li> </ul> \u9898\u9762\u7b54\u6848 <p>\u8ba1\u7b97 \\(F=(A+\\overline{B})(A+D)(B+C+\\overline{D})(\\overline{B}+\\overline{C}+D)\\) \u7684 \\(L\\)\u3001\\(G\\)\u3001\\(GN\\)\u3002</p> <ul> <li>\\(L = 10\\)\uff1b</li> <li>\\(G = 14\\)\uff1b</li> <li>\\(GN = 17\\)\uff1b</li> </ul> <p>\u8fd9\u91cc\u9700\u8981\u6ce8\u610f\uff0c\u51fa\u73b0\u4e86\u91cd\u590d\u7684\u88ab\u975e\u4e86\u7684\u5b57\u9762\u91cf\uff0c\u4e0d\u8981\u91cd\u590d\u8ba1\u7b97\uff01</p> \u9898\u9762\u7b54\u6848 <p>\u8ba1\u7b97 \\(F=BD+A\\overline{B}C+A\\overline{B}\\,\\overline{D}+AB\\overline{C}\\) \u7684 \\(L\\)\u3001\\(G\\)\u3001\\(GN\\)\u3002</p> <ul> <li>\\(L = 11\\)\uff1b</li> <li>\\(G = 15\\)\uff1b</li> <li>\\(GN = 18\\)\uff1b</li> </ul> <p>\u8fd9\u91cc\u540c\u6837\u9700\u8981\u6ce8\u610f\uff0c\u51fa\u73b0\u4e86\u91cd\u590d\u7684\u88ab\u975e\u4e86\u7684\u5b57\u9762\u91cf\uff0c\u4e0d\u8981\u91cd\u590d\u8ba1\u7b97\uff01</p> \u9898\u9762\u7b54\u6848 <p>\u8ba1\u7b97 \\(F=\\overline{A}\\,\\overline{C}(B+\\overline{D})+AC(B+\\overline{D})\\) \u7684 \\(L\\)\u3001\\(G\\)\u3001\\(GN\\)\u3002</p> <ul> <li>\\(L = 8\\)\uff1b</li> <li>\\(G = 12\\)\uff1b</li> <li>\\(GN = 15\\)\uff1b</li> </ul> <p>\u8fd9\u91cc\u540c\u6837\u9700\u8981\u6ce8\u610f\uff0c\u51fa\u73b0\u4e86\u6bd4\u8f83\u590d\u6742\u7684\u903b\u8f91\u8fd0\u7b97\uff0c\u4ee5 \\(\\overline{A}\\,\\overline{C}(B+\\overline{D})\\) \u4e3a\u4f8b\uff0c\u81ea\u9876\u5411\u4e0b\u662f\uff1a\u24f5\u4e09\u8f93\u5165\u4e0e\u95e8\uff0c\u24f6\u4e8c\u8f93\u5165\u6216\u95e8\uff1b\u6240\u4ee5\u5e94\u8be5\u662f \\(1^{\\overline{A}} + 1^{\\overline{C}} + 1^{B} + 1^{\\overline{D}} + 1^{B+\\overline{D}} + 1^{\\overline{A}\\,\\overline{C}(B+\\overline{D})}\\)\uff0c\u5373 6\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap02/#\u5361\u8bfa\u56fe","title":"\u5361\u8bfa\u56fe","text":""},{"location":"cour_note/D2QD_DigitalDesign/Chap02/#\u5361\u8bfa\u56fe\u7684\u601d\u60f3","title":"\u5361\u8bfa\u56fe\u7684\u601d\u60f3","text":"<p>\u4f18\u5316\u903b\u8f91\u8868\u8fbe\u5f0f\u6700\u76f4\u767d\u7684\u601d\u60f3\u5c31\u662f\u51cf\u5c11\u95e8\u7535\u8def\uff0c\u4e5f\u5c31\u662f\u53bb\u51cf\u5c11 gate-input cost\u3002\u90a3\u4e48\u8981\u5982\u4f55\u505a\u5462\uff1f</p> <p>\u6211\u4eec\u8003\u8651\u5230\u903b\u8f91\u8fd0\u7b97\u5f8b\u4e2d\u7684\u8fd9\u4e2a\u63a8\u5e7f\uff1a\\(XY+X\\overline{Y}=X(Y+\\overline{Y})=X\\)\uff0c\u4e5f\u5c31\u662f\u8bf4\uff0c\u5982\u679c\u4e24\u4e2a\u6700\u5c0f\u9879\u53ea\u5dee\u4e00\u4e2a\u5b57\u9762\u91cf\u7684\u975e\uff0c\u90a3\u4e48\u4ed6\u4eec\u662f\u53ef\u4ee5\u5408\u5e76\u7684\uff1b\u5f53\u7136\uff0c\u5bf9\u79f0\u7684\uff0c\u6839\u636e\\((X+\\overline{Y})(X+Y)=X+Y\\overline{Y}=X\\)\uff0c\u6211\u4eec\u4e5f\u53ef\u4ee5\u5f97\u5230\u8fd9\u4e2a\u7ed3\u8bba\u5bf9\u6700\u5927\u9879\u4e5f\u6210\u7acb\u3002</p> <p>\u662f\u4e0d\u662f\u89c9\u5f97\u201c\u53ea\u5dee\u4e00\u4e2a\u201d\u5f88\u8033\u719f\uff1f\u662f\u7684\uff01\u6211\u4eec\u60f3\u5230\u4e86\u683c\u96f7\u7801\uff01\u5047\u8bbe\u6211\u4eec\u5c06 n \u4e2a\u5b57\u9762\u91cf\u6392\u5217\u6210\u4e00\u4e2a n bits \u7684\u5411\u91cf\uff0c\u90a3\u4e48\u53ea\u9700\u8981\u6309\u7167\u683c\u96f7\u7801\u6392\u5e8f\uff0c\u4e00\u65e6\u53d1\u73b0\u6709\u76f8\u90bb\u7684\u6700\u5c0f\u9879\uff0c\u6211\u4eec\u5c31\u53ef\u4ee5\u5408\u5e76\u4ed6\u4eec\u3002</p> <p>\u4f46\u8fd9\u8fd8\u4e0d\u591f\u5145\u5206\uff0c\u4f8b\u5982\u5728\u4e00\u4e2a\u6709\u4e09\u4e2a\u5b57\u9762\u91cf\u7684\u903b\u8f91\u8868\u8fbe\u5f0f\u4e2d\uff0c\u201c\u4e0e\u4e00\u4e2a\u8868\u8fbe\u5f0f\u76f8\u90bb\u201d\u7684\u8868\u8fbe\u5f0f\u5176\u5b9e\u6709\u4e09\u4e2a\uff0c\u4f46\u662f\u7528\u7ebf\u6027\u7684\u8868\u793a\u65b9\u6cd5\u53c8\u6ca1\u6cd5\u5f88\u597d\u7684\u8868\u793a\u8fd9\u4e00\u70b9\uff0c\u6240\u4ee5\u6211\u4eec\u60f3\u5230\u5c06\u5b83\u5199\u6210\u4e00\u5f20\u4e8c\u7ef4\u7684\u8868\uff0c\u5373\u5c06\u5b57\u9762\u91cf\u62c6\u6210\u4e24\u7ec4 bit \u5411\u91cf\uff0c\u5404\u81ea\u6309\u7167\u683c\u96f7\u7801\u6392\u5217\uff0c\u5f62\u6210\u4e00\u5f20\u4e8c\u7ef4\u8868\uff0c\u8fd9\u5c31\u662f \u5361\u8bfa\u56fe(Karnaugh Map)\uff0c\u4e5f\u53eb K-map\u3002</p> <p></p> <p>\u53ef\u4ee5\u53d1\u73b0\uff0c\u4efb\u610f\u4e24\u4e2a\u76f8\u90bb\u7684\u683c\u5b50\u90fd\u53ea\u5dee\u4e00\u4e2a\u5b57\u9762\u91cf\u7684\u975e\uff0c\u800c\u4e14\u662f\u5145\u8981\u7684\uff0c\u5373\u6240\u6709\u201c\u76f8\u90bb\u201d\u90fd\u53ef\u4ee5\u5728\u8fd9\u5f20\u56fe\u8868\u73b0\u51fa\u6765\u3002</p> <p>\u8bf4\u660e</p> <p>\u7531\u4e8e\u683c\u96f7\u7801\u7684\u6027\u8d28\u662f\u4e00\u4e2a\u5728\u201c\u6ee1\u201d\u72b6\u6001\u4e0b \u73af\u72b6\u6210\u7acb \u7684\u6027\u8d28\uff0c\u6240\u4ee5\u5361\u8bfa\u56fe\u4e5f\u9700\u8981\u7528\u201c\u73af\u72b6\u201d\u7684\u601d\u8def\u53bb\u770b\uff0c\u8fd9\u91cc\u53ef\u4ee5\u8054\u60f3\u4e00\u4e0b\u884c\u5217\u5f0f\u7684\u5f62\u8c61\u5316\u8ba1\u7b97\u65b9\u6cd5\uff0c\u5c06\u8fd9\u5f20\u8868\u5f53\u4f5c\u4e00\u4e2a\u65e0\u9650\u6269\u5c55\u7684\u8868\u683c\u3002</p> <p>\u601d\u8003\u9898</p> <p>\u5728\u8fd9\u91cc\uff0c\u4e5f\u53ef\u4ee5\u5c1d\u8bd5\u7740\u611f\u53d7\u4e00\u4e0b\u4e24\u4e2a\u5b57\u9762\u91cf\u7684\u60c5\u51b5\u4e0b\uff0c\u5373\u5b9e\u9645\u4e0a\u201c\u76f8\u90bb\u4e5f\u53ea\u67092\u4e2a\u201d\u7684\u60c5\u51b5\u4e0b\uff0c\u4e5f\u53ef\u4ee5\u4f7f\u7528\u201c4\u4e2a\u76f8\u90bb\u201d\u7684\u5361\u8bfa\u56fe\u3002\u4e8b\u5b9e\u4e0a\uff0c\u4e09\u4e2a\u5b57\u9762\u91cf\u4e5f\u53ea\u6709\u201c3\u4e2a\u76f8\u90bb\u201d\uff0c\u4f46\u662f\u4e3a\u4ec0\u4e48\u53ef\u4ee5\u7528\u660e\u660e\u6709\u201c4\u4e2a\u76f8\u90bb\u201d\u7684\u5361\u8bfa\u56fe\u6765\u5b9e\u73b0\u5462\uff1f</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap02/#\u5361\u8bfa\u56fe\u7684\u5c40\u9650\u6027","title":"\u5361\u8bfa\u56fe\u7684\u5c40\u9650\u6027","text":"<p>\u7136\u800c\uff0c\u4e0a\u9762\u7684\u8bf4\u6cd5\u5176\u5b9e\u5f88\u7275\u5f3a\u3002\u56e0\u4e3a\u4e00\u5f20\u4e8c\u7ef4\u8868\u4e2d\uff0c\u80fd\u4e0e\u4e00\u4e2a\u5143\u7d20\u76f8\u90bb\u7684\u5143\u7d20\u6700\u591a\u53ea\u6709\u56db\u4e2a\uff0c\u4e5f\u5c31\u662f\u8bf4\u6211\u4eec\u6491\u6b7b\u4e5f\u53ea\u80fd\u7528\u5361\u8bfa\u56fe\u8868\u793a 4 \u4e2a\u5b57\u9762\u91cf\u7684\u60c5\u51b5\uff08\u5f53\u7136\u66f4\u591a\u7684\u53d8\u91cf\u4e5f\u6709\u5904\u7406\u7684\u65b9\u6cd5\uff0c\u4f46\u662f\u591a\u5c11\u6709\u70b9\u9ebb\u70e6\u4e86\uff09\u3002\u56e0\u6b64\uff0c\u5b9e\u9645\u4e0a\u5361\u8bfa\u56fe\u53ea\u80fd\u7528\u4e8e\u5316\u7b80\u975e\u5e38\u7b80\u5355\u7684\u903b\u8f91\u8868\u8fbe\u5f0f\u3002</p> <p>cm \u8001\u5e08\u5982\u662f\u8bf4</p> <p>\u66f4\u591a\u60c5\u51b5\u4e0b\uff0c\u5361\u8bfa\u56fe\u5b9e\u9645\u4e0a\u53ea\u9002\u5408\u6211\u4eec\u505a\u9898\u3002\u4f46\u662f\u5176\u601d\u8def\u662f\u975e\u5e38\u6709\u610f\u601d\u7684\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap02/#\u5361\u8bfa\u56fe\u7684\u7ed3\u6784","title":"\u5361\u8bfa\u56fe\u7684\u7ed3\u6784","text":"<p>\u8fd9\u91cc\u6211\u4eec\u4ee5 3 \u5143\u7684\u903b\u8f91\u8868\u8fbe\u5f0f\u4e3a\u4f8b\uff0c2 \u5143\u548c 4 \u5143\u7684\u601d\u8def\u662f\u4e00\u6837\u7684\u3002</p> <p>\u540c\u6837\uff0c\u4e3e\u4e00\u4e2a \ud83c\udf30 \uff1a\\(F(X,Y,Z) = \\sum m(2,3,4,5)\\)</p> <p>\u9996\u5148\u6211\u4eec\u6309\u7167\u6bd4\u7279\u5411\u91cf\u7684\u5f62\u5f0f\u628a\u6700\u5c0f\u9879\u5199\u51fa\u6765\uff1a</p> \u503c X Y Z 2 0 1 0 3 0 1 1 4 1 0 0 5 1 0 1 <p>\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u6765\u7ed8\u5236\u5361\u8bfa\u56fe\uff0c\u6211\u4eec\u5c06 bit \u5411\u91cf <code>[x, y, z]</code> \u62c6\u6210 <code>[x]</code> \u548c <code>[y, z]</code> \u505a\u5982\u4e0b\u8868\u683c\uff1a</p> <code>yz</code> = <code>00</code> <code>yz</code> = <code>01</code> <code>yz</code> = <code>11</code> <code>yz</code> = <code>10</code> <code>x</code> = <code>0</code> 0 0 1 1 <code>x</code> = <code>1</code> 1 1 0 0 <p>\u53e6\u5916\u4e00\u79cd\u6807\u6ce8\u8868\u683c\u7684\u65b9\u5f0f\u662f\u8fd9\u6837\uff0c\u5b83\u53ef\u80fd\u66f4\u6e05\u6670\uff1a</p> <p></p> <p>\u4f46\u662f\u4ed6\u4eec\u7684\u672c\u8d28\u90fd\u662f\u683c\u96f7\u7801\u3002</p> <p>4 \u5143\u5b57\u9762\u91cf\u7684\u5361\u8bfa\u56fe\u5219\u957f\u8fd9\u4e2a\u6837\u5b50\uff1a</p> <p></p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap02/#\u4f7f\u7528\u5361\u8bfa\u56fe\u4f18\u5316","title":"\u4f7f\u7528\u5361\u8bfa\u56fe\u4f18\u5316","text":"<p>\u5df2\u7ecf\u8bb2\u4e86\u601d\u60f3\u548c\u5361\u8bfa\u56fe\u7684\u7ed3\u6784\uff0c\u90a3\u4e48\u5230\u5e95\u8981\u5982\u4f55\u5229\u7528\u5361\u8bfa\u56fe\u8fdb\u884c\u4f18\u5316\u5462\uff1f</p> <p>\u8ba9\u6211\u4eec\u56de\u987e\u4f18\u5316\u7684\u65b9\u6cd5\uff0c\u5373\u5408\u5e76\u76f8\u90bb\u4e24\u9879\uff0c\u4e5f\u5c31\u662f\u627e\u5230\u5361\u8bfa\u56fe\u4e2d\u76f8\u90bb\u7684\u90e8\u5206\u3002\u4f46\u662f\u8fd9\u4e0d\u591f\uff0c\u6211\u4eec\u8fd8\u8981\u601d\u8003\u662f\u4e0d\u662f\u80fd\u5408\u5e76\u5df2\u7ecf\u76f8\u90bb\u7684\u90e8\u5206\uff0c\u6bd4\u5982\uff1a</p> <p>\u6211\u4eec\u901a\u8fc7\u5361\u8bfa\u56fe\uff0c\u9996\u5148\u5408\u5e76\u4e86 \\(WXYZ\\) \u548c \\(WXY\\overline{Z}\\)\uff0c\\(WX\\overline{Y}Z\\) \u548c \\(WX\\overline{Y}\\,\\overline{Z}\\)\uff0c\u5206\u522b\u5f97\u5230\u4e86 \\(WXY\\) \u548c \\(WX\\overline{Y}\\)\uff0c\u663e\u7136\u8fd9\u4e24\u4e2a\u4e1c\u897f\u4e5f\u662f\u53ef\u4ee5\u5408\u5e76\u7684\uff1b\u800c\u5728\u5361\u8bfa\u56fe\u4e0a\uff0c\u8fd9\u8868\u73b0\u4e3a\u4e24\u4e2a\u76f8\u90bb\u7684 <code>1*2</code> \u7684\u77e9\u5f62\u3002</p> <p>\u603b\u800c\u8a00\u4e4b\uff0c\u8fd9\u79cd\u8fed\u4ee3\u5408\u5e76\u7684\u884c\u4e3a\u6700\u7ec8\u53ef\u4ee5\u5212\u5f52\u4e3a\u8fd9\u6837\u4e00\u4e2a\u884c\u4e3a\uff1a</p> <p>\u6211\u4eec\u5728\u5361\u8bfa\u56fe\u4e2d\u5bfb\u627e\u82e5\u5e72 \u6781\u5927 \u7684 2 \u5e42\u77e9\u5f62\uff0c\u5373\u5143\u7d20\u4e2a\u6570\u4e3a 2 \u7684\u5e42\u6b21\uff08\u81ea\u7136\u8fb9\u957f\u4e5f\u90fd\u4e3a 2 \u7684\u5e42\u6b21\uff09\u7684\u77e9\u5f62\uff0c\u800c\u6bcf\u4e00\u4e2a\u77e9\u5f62\u6240\u8986\u76d6\u7684\u5143\u7d20\u90fd\u5e94\u8be5\u662f \u6700\u5c0f\u9879/\u6700\u5927\u9879\uff08\u4e00\u822c\u90fd\u662f\u505a\u6700\u5c0f\u9879\uff09\u3002\u9700\u8981\u6ce8\u610f\uff0c\u201c\u5faa\u73af\u201d\u7684\u6027\u8d28\u4ecd\u7136\u6ee1\u8db3\uff0c\u5373\u7b2c\u4e00\u5217\u548c\u6700\u540e\u4e00\u5217\uff0c\u7b2c\u4e00\u884c\u548c\u6700\u540e\u4e00\u884c\u4e5f\u53ef\u4ee5\u8ba4\u4e3a\u662f\u76f8\u90bb\u7684\u3002</p> <p></p> <p></p> <p>\u4f8b\u5982\uff1a</p> <p></p> <p>\u4f8b\u5982\uff1a</p> <p></p> <p>\u518d\u4f8b\u5982\uff1a</p> <p></p> <p>\u90fd\u662f\u5408\u7406\u7684\u5361\u8bfa\u56fe\u5212\u5206\u3002</p> <p>\u5728\u5f97\u5230\u8fd9\u4e9b\u5212\u5206\u540e\uff0c\u6211\u4eec\u5c31\u53ef\u4ee5\u5f88\u65b9\u4fbf\u5730\u5c06\u8fd9\u4e9b\u9879\u62ce\u51fa\u6765\uff0c\u5199\u51fa\u5b83\u4eec\u7684\u8868\u8fbe\u5f0f\u3002</p> <p>\u800c\u81f3\u4e8e\u5982\u4f55\u62ce\u51fa\u6765\u2014\u2014\u4e0d\u96be\u53d1\u73b0\uff0c\u5982\u679c\u4e00\u4e2a\u65b9\u6846\u4e2d\uff0c\u67d0\u4e00\u4e2a\u5b57\u9762\u91cf\u7684\u503c\u65e2\u53ef\u4ee5\u662f <code>0</code>\uff0c\u53c8\u53ef\u4ee5\u662f <code>1</code> \u65f6\uff08\u8fd9\u91cc\u6307\u7684\u662f\u8f93\u5165\u7684\u503c\uff0c\u5e76\u975e\u8f93\u51fa\u7ed3\u679c\uff09\uff0c\u5728\u8fd9\u4e2a\u4f18\u5316\u9879\u7684\u7ed3\u679c\u4e2d\u5c31\u53ef\u4ee5\u4e0d\u7528\u5199\u51fa\u8fd9\u4e2a\u5b57\u9762\u91cf\uff1b\u53cd\u4e4b\uff0c\u5982\u679c\u8fd9\u4e2a\u5b57\u9762\u91cf \\(X\\) \u7684\u503c\u90fd\u662f <code>0</code>\uff0c\u5219\u7ed3\u679c\u4e2d\u4f1a\u5305\u542b \\(\\overline{X}\\)\uff0c\u5982\u679c\u90fd\u662f <code>1</code>\uff0c\u5219\u7ed3\u679c\u4e2d\u4f1a\u5305\u542b \\(X\\)\u3002</p> \u9898\u9762\u7b54\u6848 <p>\u5229\u7528\u5361\u8bfa\u56fe\u4f18\u5316 \\(F(X,Y,Z) = \\sum m(0,1,2,4,6,7)\\) \u7684\u7ed3\u679c\u3002</p> <p>\u753b\u51fa\u8fd9\u4e2a\u8868\u8fbe\u5f0f\u5bf9\u5e94\u7684\u5361\u8bfa\u56fe\uff1a</p> <p></p> <p>\u7136\u540e\u5212\u51fa\u5176\u4e2d\u7684\u6781\u5927\u6700\u5c0f\u9879\u4f18\u5316\u9879\uff1a</p> <p></p> <p>\u5199\u51fa\u6765\u662f\uff1a</p> <ul> <li>\u7eff\uff1a\\(x=0,\\;y=0,\\;z=0/1\\)<ul> <li>\u6240\u4ee5\u662f\uff1a\\(\\overline{X}\\,\\overline{Y}\\)\uff1b</li> </ul> </li> <li>\u84dd\uff1a\\(x=0/1,\\;y=0/1,\\;z=0\\)<ul> <li>\u6240\u4ee5\u662f\uff1a\\(\\overline{Z}\\)\uff1b</li> </ul> </li> <li>\u7ea2\uff1a\\(x=1,\\;y=1,\\;z=0/1\\)<ul> <li>\u6240\u4ee5\u662f\uff1a\\(XY\\)</li> </ul> </li> </ul> <p>\u7efc\u4e0a\u6240\u8ff0\uff0c\u4f18\u5316\u7ed3\u679c\u662f \\(F = \\overline{X}\\,\\overline{Y} + \\overline{Z} + XY\\)</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap02/#\u4e0d\u5b9a\u9879","title":"\u4e0d\u5b9a\u9879","text":"<p>\u63a8\u8350\u9605\u8bfb</p> <p>https://www.geeksforgeeks.org/dont-care-x-conditions-in-k-maps/</p> <p>\u4e0d\u5b9a\u9879(Don't Cares) \u6307\u7684\u662f\u9700\u8981\u5316\u7b80\u7684\u903b\u8f91\u51fd\u6570\u4e2d\uff0c\u6ca1\u6709\u7ed9\u51fa\u5b9a\u4e49\u7684\u51e0\u9879\uff0c\u5b83\u4eec\u53ef\u80fd\u662f\uff1a</p> <ul> <li>\u8f93\u5165\u7ec4\u5408\u4e0d\u4f1a\u51fa\u73b0\uff1b</li> <li>\u8f93\u5165\u7ec4\u5408\u7684\u8f93\u51fa\u4e0d\u88ab\u4f7f\u7528\uff1b</li> </ul> <p>\u5bf9\u4e8e\u8fd9\u79cd\u9879\uff0c\u5728\u5361\u8bfa\u56fe\u4e2d\u7528 X \u6765\u8868\u793a\uff0c\u5728\u6700\u5c0f\u9879\u4e4b\u548c\u4e2d\u7528 \\(\\sum d(...)\\) \u8868\u793a\u3002\u6211\u4eec\u53ef\u4ee5\u968f\u610f\u5b9a\u4e49\u5b83\u4eec\u7684\u8f93\u51fa\uff0c\u6b64\u65f6\u5c31\u53ef\u4ee5\u5229\u7528\u8fd9\u4e9b\u9879\u6765\u65b9\u4fbf\u6211\u4eec\u7684\u4f18\u5316\u2014\u2014\u5f53\u6211\u4eec\u753b\u51fa\u6765\u7684\u6781\u5927\u77e9\u9635\u8d8a\u5927\uff0c\u6210\u672c\u5c31\u8d8a\u4f4e\u3002</p> <p>\u4f8b\u5982\uff0c\u6211\u4eec\u5b9a\u4e49\u4e00\u4e2a\u51fd\u6570\uff0c\u5f53\u8f93\u5165\u7684 BCD \u7801\u8868\u793a\u7684\u6570\u5b57\u5927\u4e8e\u7b49\u4e8e 5 \u65f6\u8fd4\u56de <code>1</code>\uff0c\u5219\u5b83\u53ef\u4ee5\u901a\u8fc7\u8fd9\u6837\u7684\u5f62\u5f0f\u6765\u4f18\u5316\uff1a</p> <p></p> <p>\u6839\u636e\u7ed3\u679c\uff0c\u5199\u51fa\u4f18\u5316\u540e\u7684\u8868\u8fbe\u5f0f\u4e3a\uff1a\\(F(W,X,Y,Z) = W + XY + XZ\\)\u3002</p> <p>\u7531\u5361\u8bfa\u56fe\u5f97\u5230\u4e58\u79ef\u7ed3\u679c</p> <p>\u5c3d\u7ba1\u6211\u4eec\u4e0d\u505c\u5f3a\u8c03 \u4e0e \u548c \u6216 \u662f\u5bf9\u79f0\u7684\uff0c\u4f46\u662f\u4ecd\u7136\u6709\u5f88\u591a\u64cd\u4f5c\u662f\u9274\u4e8e\u6211\u4eec\u5bf9 <code>1</code> \u7684\u504f\u7231\u624d\u4f1a\u987a\u624b\u7684\uff08\u4f60\u4f1a\u53d1\u73b0\uff0c\u628a\u4e58\u9664\u6362\u6210\u6211\u4eec\u5b8c\u5168\u4e0d\u719f\u6089\u7684\u7b26\u53f7\uff0c\u4f60\u751a\u81f3\u53ef\u80fd\u65e0\u4ece\u4e0b\u624b\uff09\u3002</p> <p>\u6240\u4ee5\uff0c\u5728\u5361\u8bfa\u56fe\u7684\u95ee\u9898\u4e2d\uff0c\u5982\u679c\u8981\u5229\u7528\u5361\u8bfa\u56fe\u5f97\u5230 \\(F\\) \u4f18\u5316\u540e\u7684\u4e58\u79ef\u5f62\u5f0f\uff0c\u4e5f\u53ef\u4ee5\u5c06\u95ee\u9898\u8f6c\u5316\u4e3a\u6c42 \\(\\overline{F}\\) \u4f18\u5316\u540e\u7684\u548c\u5f62\u5f0f\uff0c\u7136\u540e\u518d\u5bf9\u5176\u53d6\u53cd\u8fc7\uff0c\u5229\u7528\u5fb7\u00b7\u6469\u6839\u5b9a\u5f8b\u6765\u5f97\u5230\u7ed3\u679c\u3002</p> <p>\u5177\u4f53\u6765\u8bf4\u5c31\u662f\u53cd\u8f6c K-map \u4e2d\u6240\u6709\u7684 <code>0</code> \u548c <code>1</code>\uff0c\u7136\u540e\u7740\u773c\u4e8e SOM \u8fdb\u884c\u4f18\u5316\uff0c\u6700\u540e\u518d\u5bf9\u7ed3\u679c\u53d6\u53cd\uff0c\u7528\u5fb7\u00b7\u6469\u6839\u5b9a\u5f8b\u6765\u5f97\u5230\u7ed3\u679c\u3002</p> eg <p></p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap02/#\u8574\u542b\u9879\u4e3b\u8574\u542b\u9879\u4e0e\u57fa\u672c\u4e3b\u8574\u542b\u9879","title":"\u8574\u542b\u9879\u3001\u4e3b\u8574\u542b\u9879\u4e0e\u57fa\u672c\u4e3b\u8574\u542b\u9879","text":"<p>\u8574\u542b\u9879(implicant) \u5206\u4e3a \u4e3b\u8574\u542b\u9879(prime implicant) \u548c \u57fa\u672c\u4e3b\u8574\u542b\u9879(essential prime implicant)\u3002</p> <ul> <li>\u5728\u5361\u8bfa\u56fe\u4e2d\uff0c\u4e00\u4e2a\u8574\u542b\u9879\u5c31\u662f\u4efb\u610f\u4e00\u4e2a\u5305\u542b \\(2^n\\) \u4e2a <code>1</code> \u7684\u5355\u5143\uff1b</li> <li>\u800c\u4e3b\u8574\u542b\u9879\u5219\u662f\u5728\u5361\u8bfa\u56fe\u4e2d\u7684 \u6781\u5927 \u8574\u542b\u9879\uff1b<ul> <li>\u5bf9\u4e8e\u5b58\u5728 Dont'cares \u7684 K-map\uff0c\u5982\u679c\u6211\u4eec\u5173\u6ce8\u7684\u662f <code>1</code>\uff0c\u90a3\u6211\u4eec\u79ef\u6781\u5730\u5c06\u4ed6\u4eec\u5f53\u4f5c <code>1</code> \u6765\u5904\u7406\uff0c\u53cd\u4e4b\u4ea6\u7136\uff1b</li> <li>\u4f46\u662f\u5355\u72ec\u7684 <code>X</code> \u4e0d\u4f1a\u88ab\u8ba4\u4e3a\u662f\u4e3b\u8574\u542b\u9879\uff1b</li> </ul> </li> <li>\u57fa\u672c\u4e3b\u8574\u542b\u9879\u662f\u5305\u542b \u53ea\u88ab\u5b83(\u57fa\u672c\u4e3b\u8574\u542b\u9879)\u8986\u76d6\u7684 <code>1</code> \u7684\u4e3b\u8574\u542b\u9879\uff1b</li> </ul> <p></p> <p>\u5982\u56fe\uff0c\u5de6\u4fa7\u7684\u4e24\u4e2a\u4e3b\u8574\u542b\u9879\u56e0\u4e3a\u5305\u62ec\u4e86 \u24f5 \u548c \u24f6 \u8fd9\u4e24\u4e2a\u552f\u4e00\u7684 <code>1</code>\uff0c\u6240\u4ee5\u662f\u57fa\u672c\u4e3b\u8574\u542b\u9879\uff1b</p> <p>\u800c\u53f3\u4fa7\u7684\u8574\u542b\u9879\u5219\u662f\u4e00\u4e2a\u5197\u4f59\u7684\u8574\u542b\u9879\uff1b</p> <p>\u6ce8\u610f</p> <p>\u5bf9\u4e8e\u4efb\u610f\u51fd\u6570\uff0c\u4e3b\u8574\u542b\u9879\u4e00\u5b9a\u5b58\u5728\uff0c\u4f46\u662f\u57fa\u672c\u4e3b\u8574\u542b\u9879\u4e0d\u4e00\u5b9a\u5b58\u5728\u3002</p> <p>\ud83e\udd14</p> <p>\u6b63\u56e0\u4e3a\u6709\u57fa\u672c\u4e3b\u8574\u542b\u9879\u7684\u5b58\u5728\uff0c\u5bf9\u4e8e\u4e00\u4e2a\u4efb\u610f\u51fd\u6570\uff0c\u4f18\u5316\u7684\u591a\u89e3\u7ed3\u679c\u603b\u6709\u4e00\u90e8\u5206\u662f\u4e0d\u53d8\u7684\uff08\u53ea\u4e0d\u8fc7\u6ca1\u6709\u57fa\u672c\u4e3b\u8574\u542b\u9879\u7684\u65f6\u5019\u8fd9\u90e8\u5206\u4e3a\u96f6\uff09\u3002</p> <p>\u9ea6\u514b\u62c9\u594e\u56e0\u7b97\u6cd5</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap02/#\u7ecf\u5178\u7ec4\u5408\u7535\u8def","title":"\u7ecf\u5178\u7ec4\u5408\u7535\u8def","text":"<p>\u5f15\u5165</p> <p>\u5728\u5b9e\u9645\u8bbe\u8ba1\u4e2d\uff0c\u6211\u4eec\u6709\u4e00\u4e9b\u73b0\u6210\u7684\u7ec4\u5408\u7535\u8def\u80fd\u591f\u4f7f\u7528\uff0c\u6765\u65b9\u4fbf\u6211\u4eec\u8bbe\u8ba1\u3002</p> <p>\u4e0d\u8fc7\u6211\u6ca1\u6709\u5168\u5199\u51fa\u6765\uff1b</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap02/#\u4e09\u6001\u95e8","title":"\u4e09\u6001\u95e8","text":"<p>\u4e09\u6001\u7f13\u51b2\u5668(3-State Buffer)</p> <p>\u9664\u4e86\u8f93\u5165\u548c\u8f93\u51fa\uff0c\u5b83\u8fd8\u6709\u4e00\u4e2a \u4f7f\u80fd\u7aef(enable) \u6765\u63a7\u5236\u8f93\u51fa\u3002</p> <p>\u6240\u8c13\u7684\u4e09\u6001\u6307\u7684\u662f\uff1a</p> <ul> <li>\u5f53\u4f7f\u80fd\u7aef\u4e3a <code>1</code>\uff0c\u4e14\u8f93\u5165\u4e3a <code>1</code> \u65f6\uff0c\u8f93\u51fa\u4e3a <code>1</code>\uff1b</li> <li>\u5f53\u4f7f\u80fd\u7aef\u4e3a <code>1</code>\uff0c\u4e14\u8f93\u5165\u4e3a <code>0</code> \u65f6\uff0c\u8f93\u51fa\u4e3a <code>0</code>\uff1b</li> <li>\u5f53\u4f7f\u80fd\u7aef\u4e3a <code>0</code>\uff0c\u8f93\u51fa\u4e3a <code>Hi-Z</code>/<code>Z</code>/<code>z</code>(\u6d6e\u52a8\uff0c\u9ad8\u963b\u6001)\uff1b</li> </ul> <p></p> <p>\u4f5c\u7528</p> <p>\u6211\u4eec\u53ef\u4ee5\u7528\u4e09\u6001\u95e8\u6765\u89e3\u51b3\u591a\u8def\u8f93\u51fa\u4e92\u8054\u7684\u95ee\u9898\u3002\u6b63\u5982\u5728 ICS \u7b14\u8bb0\u4e2d\u63d0\u5230\u7684\uff0c\u53ef\u4ee5\u8ba9\u591a\u4e2a\u8f93\u5165\u5728\u540c\u4e00\u65f6\u523b\u53ea\u6709\u4e00\u4e2a\u88ab\u8f93\u51fa\u5230\u603b\u7ebf\u4e2d\u2014\u2014\u5b9e\u73b0\u7684\u624b\u6bb5\u5c31\u662f\u901a\u8fc7\u7535\u8def\u6765\u4f7f\u540c\u4e00\u65f6\u523b\u53ea\u6709\u4e00\u4e2a\u4f7f\u80fd\u7aef\u4e3a <code>1</code>\u3002</p> <p>\u5728\u6570\u5b57\u903b\u8f91\u8bbe\u8ba1\u4e2d\uff0c\u4e09\u6001\u95e8\u5b9e\u73b0\u603b\u7ebf\u7684\u76f8\u5173\u77e5\u8bc6\u5c06\u5728 \u7b2c\u516d\u7ae0 \u63d0\u5230\u3002</p> <p>\u788e\u788e\u5ff5</p> <p>\u6240\u4ee5\u4ec0\u4e48\u662f\u300c\u9ad8\u963b\u6001\u300d\uff1f\u5b83\u8981\u5982\u4f55\u7406\u89e3\uff1f\u4ee5\u4e0b\u662f\u6211\u6839\u636e\u5b83\u7684\u5e94\u7528\u53cd\u63a8\u5f97\u5230\u7684\u7ed3\u8bba\uff1a</p> <p>\u9ad8\u963b\u6001\u540c\u5b83\u5b57\u9762\u610f\u601d\u76f8\u540c\uff0c\u6211\u4eec\u53ef\u4ee5\u5f53\u5b83\u6b64\u65f6\u662f\u65ad\u8def\uff0c\u800c\u9ad8\u963b\u6001\u91cd\u70b9\u8981\u4e0e\u4f4e\u7535\u5e73\u505a\u533a\u5206\uff1a\u5982\u679c\u73b0\u5728\u5b58\u5728\u4e00\u4e2a\u201c\u5bfc\u7ebf\u201d\uff0c\u5b83\u6709\u4e09\u4e2a\u7aef\uff0c\u5176\u4e2d\u6211\u4eec\u4eba\u4e3a\u5730\u8ba4\u4e3a\u5176\u4e2d\u4e24\u4e2a\u662f\u8f93\u5165\uff0c\u5206\u522b\u547d\u540d\u4e3a a \u548c b\uff0c\u53e6\u5916\u4e00\u4e2a\u8ba4\u4e3a\u662f\u8f93\u51fa\uff0c\u547d\u540d\u4e3a c\u3002</p> <p>\u6b64\u65f6\uff0c\u6211\u4eec\u662f\u4e0d\u5141\u8bb8 a \u548c b \u4e00\u4e2a\u4e3a\u9ad8\u7535\u5e73\uff0c\u4e00\u4e2a\u4e3a\u4f4e\u7535\u5e73\u7684\uff0c\u56e0\u4e3a\u6211\u4eec\u8fd9\u91cc\u4eba\u4e3a\u5b9a\u4e49\u7684\u8f93\u5165\u8f93\u51fa\u5e76\u4e0d\u5f71\u54cd\u7535\u6d41\u7684\u6d41\u52a8\u65b9\u5411\uff0c\u6240\u4ee5\u5f53 a \u4e3a <code>1</code>\uff0cb \u4e3a <code>0</code> \u65f6\uff0c\u7535\u6d41\u5f88\u53ef\u80fd\u4f1a\u53d8\u6210\u4ece a \u6d41\u5411 b\uff0c\u7535\u6e90\u53ef\u80fd\u76f4\u63a5\u63a5\u5730\uff0c\u8fd9\u662f\u6211\u4eec\u4e0d\u5e0c\u671b\u770b\u5230\u7684\uff0c\u8fd9\u4e5f\u662f\u4e3a\u4ec0\u4e48\u6211\u4eec\u9700\u8981\u4e00\u4e2a\u6216\u95e8\u6765\u5b9e\u73b0\u8fd9\u4e2a\u903b\u8f91\u884c\u4e3a\uff08\u6362\u8a00\u4e4b\uff0c\u8fd9\u79cd\u201c\u4e09\u7aef\u201d\u7535\u8def\u662f\u76f8\u5f53\u5371\u9669\u7684\uff0c\u4e0d\u8fc7\u5f53\u6211\u4eec\u4eba\u4e3a\u5b9a\u4e49\u591a\u4e2a\u8f93\u51fa\u65f6\uff0c\u4e00\u822c\u4f5c\u4e3a\u63a5\u6536\u7aef\u7684\u7535\u8def\u90fd\u6709\u4e8c\u6781\u7ba1\u9632\u6b62\u9006\u6d41\uff0c\u6240\u4ee5\u5355\u8f93\u5165\u591a\u8f93\u51fa\u662f\u5f88\u5e38\u89c1\u7684\uff09\u3002</p> <p>\u4ece\u66f4\u62bd\u8c61\u5730\u89d2\u5ea6\u6765\u7406\u89e3\uff0c\u4e00\u6839\u5bfc\u7ebf\u6700\u591a\u627f\u8f7d\u4e00\u4efd\u4fe1\u606f\uff0c\u7136\u800c\u6709\u4e24\u4e2a\u8f93\u5165\u4ecb\u5165\uff0c\u6b64\u65f6\u6211\u4eec\u53ea\u6709 <code>0</code>/<code>1</code> \u4e24\u6001\uff0c\u4e0d\u7ba1\u600e\u4e48\u6837\uff0c\u6211\u4eec\u90fd\u540c\u65f6\u62ff\u5230\u4e86\u6765\u81ea\u4e24\u4e2a\u8f93\u5165\u7684\u6570\u636e\uff0c\u800c\u5bf9\u4e8e\u53ea\u80fd\u627f\u8f7d\u4e00\u4efd\u4fe1\u606f\u7684\u5bfc\u7ebf\u6765\u8bf4\uff0c\u8fd9\u4e24\u4e2a\u4fe1\u606f\u51b2\u7a81\u4e86\u3002\u6240\u4ee5\u6211\u4eec\u9700\u8981 <code>MUX</code> \u6765\u9009\u62e9\u6211\u4eec\u9700\u8981\u7684\u5230\u5e95\u662f\u54ea\u4e2a\u4fe1\u606f\uff0c\u7136\u540e\u518d\u7ed9\u5bfc\u7ebf\u3002</p> <p>\u800c\u4e09\u6001\u95e8\uff0c\u5728\u9ad8\u4f4e\u7535\u5e73\u5916\u5f15\u5165\u4e86\u300c\u9ad8\u963b\u6001\u300d\uff0c\u5c31\u975e\u5e38\u5de7\u5999\u5730\u89e3\u51b3\u4e86\u8fd9\u4e2a\u300c\u591a\u8f93\u5165\u300d\u5371\u9669\u7684\u95ee\u9898\uff0c\u5f53\u6211\u4eec\u4e0d\u5e0c\u671b\u8fd9\u4e2a\u6570\u636e\u88ab\u8f93\u5165\u65f6\uff0c\u6211\u4eec\u76f4\u63a5\u628a\u5b83\u65ad\u5f00\uff0c\u7c7b\u4f3c\u4e8e\u76f4\u63a5\u628a\u5f00\u5173\u65ad\u5f00\uff0c\u53ea\u8981\u6211\u4eec\u8ba9\u5bfc\u7ebf\u7684\u82e5\u5e72\u8f93\u5165\u4e2d\u53ea\u6709\u4e00\u4e2a\u4e09\u6001\u95e8\u4e0d\u5728\u300c\u9ad8\u963b\u6001\u300d\uff0c\u5c31\u80fd\u591f\u4f18\u96c5\u5730\u5b9e\u73b0\u591a\u8def\u8f93\u51fa\u4e92\u8054\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap02/#\u590d\u6742\u95e8","title":"\u590d\u6742\u95e8","text":"<p>\u901a\u8fc7\u4e00\u4e9b\u57fa\u672c\u95e8\u7ec4\u5408\u51fa\u6765\u7684\u95e8\uff0c\u5b83\u4eec\u7684\u8868\u793a\u65b9\u6cd5\u5927\u81f4\u5982\u4e0b\uff1a</p> <p> </p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap03/","title":"Chap 3 Combinational Logic Design","text":"<p> \u7ea6 4261 \u4e2a\u5b57  7 \u884c\u4ee3\u7801  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 14 \u5206\u949f</p> <p>\u5f15\u5165</p> <p>\u6309\u7167\u529f\u80fd\uff0c\u903b\u8f91\u7535\u8def\u5206\u4e3a\u4e24\u7c7b\uff1a</p> <ul> <li>\u7ec4\u5408\u7535\u8def(Combinational Circuit)<ul> <li>\u62e5\u6709 m \u4e2a\u8f93\u5165\u548c n \u4e2a\u8f93\u51fa\uff0c\u5176\u4e2d\u5305\u542b\u4e86 \\(2^m\\) \u79cd\u8f93\u5165\u7ec4\u5408\uff0c\u4ee5\u53ca\u5bf9\u5e94\u7684 n \u4e2a\u4e0d\u540c\u7684\u51fd\u6570\uff1b</li> <li>\u6700\u5173\u952e\u7684\u662f\uff0c\u5b83\u7684 \u8f93\u51fa\u53ea\u4f9d\u8d56\u4e8e\u8fd9 m \u4e2a\u8f93\u5165\u7684\u7ec4\u5408\uff08\u4e0d\u5305\u542b\u56de\u8def\uff09\uff1b</li> </ul> </li> <li>\u65f6\u5e8f\u7535\u8def(Sequential Logic Cirtuit)<ul> <li>\u4e0e\u4e4b\u5bf9\u5e94\u7684\uff0c\u65f6\u5e8f\u7535\u8def\u5177\u6709\u8bb0\u5fc6\u529f\u80fd\uff0c\u5373\u5b83\u7684\u8f93\u51fa\u53ef\u80fd\u4f1a\u4f9d\u8d56\u4e4b\u524d\u7684\u7ed3\u679c\uff1b</li> </ul> </li> </ul> <p>\u800c\u672c\u7ae0\u5c06\u7740\u773c\u4e8e\u7ec4\u5408\u7535\u8def\u7684\u76f8\u5173\u5185\u5bb9\uff0c\u65f6\u5e8f\u7535\u8def\u7684\u76f8\u5173\u5185\u5bb9\u5c06\u5728 \u4e0b\u4e00\u7ae0 \u4ecb\u7ecd\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap03/#\u7ec4\u5408\u7535\u8def\u8bbe\u8ba1","title":"\u7ec4\u5408\u7535\u8def\u8bbe\u8ba1","text":"<p>\u8868\u793a\u903b\u8f91\u7684\u65b9\u6cd5</p> <ol> <li>\u771f\u503c\u8868(Truth Table)\uff1b</li> <li>\u5e03\u5c14\u51fd\u6570(Boolean Function)\uff1b</li> <li>\u5361\u8bfa\u56fe(Karnaugh Maps)\uff1b</li> <li>\u65f6\u5e8f\u56fe(Timing Diagram)\uff1b</li> <li>\u903b\u8f91\u7535\u8def\u56fe(Logic Circuit)\uff1b</li> </ol> <p>\u5176\u4e2d\uff0c\u4e0b\u5212\u7ebf\u7684\u65b9\u6cd5\u5728\u529f\u80fd\u786e\u5b9a\u7684\u60c5\u51b5\u4e0b\uff0c\u5176\u8868\u793a\u662f\u552f\u4e00\u7684\u3002</p> <p>\u800c\u6211\u4eec\u7684\u8bbe\u8ba1\uff0c\u5c31\u662f\u5728\u6ee1\u8db3\u529f\u80fd\u7684\u524d\u63d0\u4e0b\uff0c\u5c3d\u53ef\u80fd\u4f18\u5316\u548c\u627e\u5230\u6700\u597d\u7684\u8bbe\u8ba1\u3002</p> <p>\u800c\u4e3b\u8981\u7684\u8bbe\u8ba1\u8fc7\u7a0b\u5982\u4e0b\uff1a</p> <ol> <li>\u786e\u5b9a\u7cfb\u7edf\u7684\u884c\u4e3a\uff1b</li> <li>\u9610\u8ff0\u8f93\u5165\u548c\u8f93\u51fa\u4e4b\u95f4\u7684\u903b\u8f91\u5173\u7cfb\uff0c\u5e76\u7528\u771f\u503c\u8868\u6216\u903b\u8f91\u8868\u8fbe\u5f0f\u8868\u8fbe\u51fa\u6765\uff1b</li> <li>\u4f18\u5316\u903b\u8f91\u8868\u8fbe\u4ee5\u51cf\u5c11\u6210\u672c(\u6bd4\u5982\u4f7f\u7528\u5361\u8bfa\u56fe)\uff1b</li> <li>\u5c06\u4f18\u5316\u540e\u7684\u903b\u8f91\u8bbe\u8ba1\u5de5\u827a\u6620\u5c04\u5230\u786c\u4ef6\u5b9e\u73b0\u4e0a\uff1b</li> <li>\u9a8c\u8bc1\u6b63\u786e\u6027\uff08\u5728\u4eff\u771f\u73af\u5883\u4e2d\uff09\uff1b</li> </ol> <pre><code>graph LR;\n\nA[\"\u5b9e\u9645\u95ee\u9898\"] ===&gt; B[\"\u771f\u503c\u8868\"]\n\nB ==&gt;|\"\u5316\u7b80\"| C[\"\u6700\u7b80\u529f\u80fd\"] ===&gt;|\"\u5de5\u827a\u6620\u5c04\"| D[\"\u7f51\u8868\"]\n\nB ==&gt;|\"\u53d8\u6362\"| E[\"\u5408\u9002\u7684\u8868\u8fbe\u5f0f\"] ===&gt;|\"\u5de5\u827a\u6620\u5c04\"| D</code></pre>"},{"location":"cour_note/D2QD_DigitalDesign/Chap03/#\u5206\u5c42\u8bbe\u8ba1","title":"\u5206\u5c42\u8bbe\u8ba1","text":"<p>\u5206\u5c42\u8bbe\u8ba1\u5373\u5c06\u590d\u6742\u95ee\u9898\u6a21\u5757\u5316\u5206\u89e3\u4e3a\u82e5\u5e72\u5c42\u6b21\uff0c\u7136\u540e\u9010\u4e2a\u62bd\u8c61\u89e3\u51b3\u3002</p> <p>\u5176\u8bbe\u8ba1\u65b9\u6cd5\u5206\u4e3a \u81ea\u9876\u5411\u4e0b(Top-Down) \u548c \u81ea\u5e95\u5411\u4e0a(Bottom-Up)\u3002</p> <p>\u524d\u8005\u4ece\u9700\u6c42\u5f00\u59cb\uff0c\u81ea\u9876\u5411\u4e0b\u5206\u89e3\u529f\u80fd\u8bbe\u8ba1\uff1b\u540e\u8005\u6839\u636e\u73b0\u6709\u7684\u5143\u4ef6\u53bb\u7ec4\u5408\u6210\u76ee\u6807\u529f\u80fd\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap03/#\u96c6\u6210\u7535\u8def","title":"\u96c6\u6210\u7535\u8def","text":"<p>\u96c6\u6210\u7535\u8def(integrated circuits) \u53c8\u53eb \u82af\u7247(chip)\uff0c\u5206\u4e3a\u5982\u4e0b\u82e5\u5e72\u7b49\u7ea7\uff1a</p> <ul> <li>SSI(small-scale integrated) \u5185\u542b\u4e0d\u5230 10 \u4e2a gates\uff1b</li> <li>MSI(medium-scale integrated) \u5185\u542b 10 ~ 100 \u4e2a gates\uff1b</li> <li>LSI(large-scale integrated) \u5185\u542b \u6210\u767e\u4e0a\u5343 \u4e2a gates\uff1b</li> <li>VLSI(very large-scale integrated) \u5185\u542b \u6210\u5343\u4e0a\u4ebf \u4e2a gates\uff1b</li> </ul>"},{"location":"cour_note/D2QD_DigitalDesign/Chap03/#\u6280\u672f\u53c2\u6570","title":"\u6280\u672f\u53c2\u6570","text":"<p>\u95e8\u7684\u5b9e\u73b0\u4e3b\u8981\u901a\u8fc7\u8fd9\u4e9b\u53c2\u6570\u7279\u6027\u6765\u63cf\u8ff0\uff1a</p> Name Description Fan-in \u4e00\u4e2a\u95e8\u53ef\u7528\u7684\u8f93\u5165 Fan-out \u4e00\u4e2a\u6805\u6781\u8f93\u51fa\u9a71\u52a8\u7684\u6807\u51c6\u8d1f\u8f7d\u6570\u91cf Logic Levels \u88ab\u8ba4\u4e3a\u662f\u9ad8\u4f4e\u7535\u5e73\u7684\u8f93\u5165\u8f93\u51fa\u7535\u538b\u8303\u56f4 Noise Margin \u5bf9\u5916\u754c\u566a\u58f0\u7684\u5bb9\u5fcd\u80fd\u529b(\u5177\u4f53\u6765\u8bf4\u662f\u4e0d\u4f1a\u5bfc\u81f4\u884c\u4e3a\u5f02\u53d8\u7684\u6700\u5927\u566a\u58f0\u538b\u503c) Cost for a gate \u7ee7\u627f\u7535\u8def\u7684\u95e8\u6210\u672c Propagation Delay \u4fe1\u53f7\u6539\u53d8\u540e\u4ece\u8f93\u5165\u5230\u8f93\u51fa\u6240\u9700\u7684\u53d8\u5316\u65f6\u95f4 Power Dissipation \u7535\u6e90\u8f93\u51fa\u80fd\u8017\u548c\u95e8\u7684\u80fd\u8017"},{"location":"cour_note/D2QD_DigitalDesign/Chap03/#\u6247\u5165\u6247\u51fa","title":"\u6247\u5165\u6247\u51fa","text":"<p>\u6247\u5165\u63cf\u8ff0\u4e86\u4e00\u4e2a\u95e8\u80fd\u591f\u63a5\u53d7\u7684\u6700\u591a\u8f93\u5165\u91cf\uff0c\u5982\u4e00\u4e2a\u56db\u8f93\u5165\u4e0e\u975e\u95e8\u7684\u6247\u5165\u5c31\u662f 4\uff1b\u800c\u6247\u51fa\u63cf\u8ff0\u7684\u5219\u662f\u4e00\u4e2a\u95e8\u7684\u8f93\u51fa(\u6805\u6781\u8f93\u51fa)\u5728\u4e0d\u964d\u4f4e\u5de5\u4f5c\u6027\u80fd\u7684\u60c5\u51b5\u4e0b\u80fd\u591f\u8d1f\u8f7d\u591a\u5c11\u95e8\uff0c\u4f8b\u5982\u4e00\u4e2a\u975e\u95e8\u7684\u8f93\u51fa\u80fd\u591f\u540c\u65f6\u8d1f\u8f7d 4 \u4e2a\u975e\u95e8\u5e76\u4e14\u90fd\u80fd\u6b63\u5e38\u5de5\u4f5c\uff0c\u5219\u5176\u6247\u51fa\u4e3a 4\uff0c\u5176\u4e5f\u80fd\u901a\u8fc7\u6807\u51c6\u8d1f\u8f7d\u6765\u5b9a\u4e49\u3002</p> <p>\u6807\u51c6\u8d1f\u8f7d</p> <p>\u6240\u8c13\u7684\u6807\u51c6\u8d1f\u8f7d\uff0c\u662f\u8861\u91cf\u201c\u8d1f\u8f7d\u201d\u7684\u4e00\u4e2a\u201c\u5355\u4f4d\u781d\u7801\u201d\u3002\u5176\u5927\u5c0f\u7b49\u4e8e\u4e00\u4e2a\u975e\u95e8(\u9006\u53d8\u5668)\u8d21\u732e\u7684\u8d1f\u8f7d\u538b\u529b\u3002</p> <p>\u90a3\u4e48\u8981\u5982\u4f55\u8bc4\u4f30\u8d1f\u8f7d\u5462\uff1f\u9996\u5148\u6211\u4eec\u5f15\u5165 \u8fc7\u6e21\u65f6\u95f4(transition time)\uff1a</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap03/#\u8f6c\u6362\u65f6\u95f4","title":"\u8f6c\u6362\u65f6\u95f4","text":"<p>\u8f6c\u6362\u65f6\u95f4\u5206\u4e3a \\(\\mathrm{t_{LH}}\\)(rise time) \u548c \\(\\mathrm{t_{HL}}\\)(fall time) \u4e24\u4e2a\u90e8\u5206\u3002</p> <ul> <li>rise time \u7b49\u4e8e\u6805\u6781\u8f93\u51fa\u4ece \\(\\mathrm{V_{CC}}\\) \u7684 10% \u5347\u9ad8\u5230 90% \u6240\u9700\u8981\u7684\u65f6\u95f4\uff1b</li> <li>fall time \u7b49\u4e8e\u6805\u6781\u8f93\u51fa\u4ece \\(\\mathrm{V_{CC}}\\) \u7684 90% \u964d\u4f4e\u5230 10% \u6240\u9700\u8981\u7684\u65f6\u95f4\uff1b</li> </ul> <p>\u901a\u8fc7\u65f6\u5e8f\u56fe\u8868\u793a\u5c31\u662f\u8fd9\u6837\uff1a</p> <p></p> <p>\u968f\u7740\u8d1f\u8f7d\u589e\u52a0\uff0c\u8f6c\u6362\u65f6\u95f4\u4e5f\u4f1a\u589e\u52a0\uff08\u7ed9\u7535\u5bb9\u5145\u7535\u7684\u65f6\u95f4\u589e\u52a0\uff09\uff0c\u800c\u6247\u51fa\u5b9a\u4e49\u4e2d\u63d0\u5230\u7684\u201c\u6700\u5927\u8d1f\u8f7d\u201d\uff0c\u5c31\u662f\u6307\u5b83\u7684\u8f6c\u6362\u65f6\u95f4\u4e0d\u8d85\u8fc7\u5b83\u9884\u5b9a\u7684\u6700\u5927\u8f6c\u6362\u65f6\u95f4\u3002</p> <p></p> <p>\u4ece\u5de6\u5230\u53f3\u8868\u793a\u8d1f\u8f7d\u4e0d\u65ad\u589e\u52a0\u65f6\uff0crise time \u7684\u53d8\u5316\u8d8b\u52bf\u3002</p> <p>\u5b9e\u9645\u4e0a\uff0c\u7c7b\u4f3c\u7684\uff0c\u8d85\u51fa\u6247\u5165\u540e\uff0c\u95e8\u5bf9\u8f93\u5165\u7684\u53cd\u5e94\u5c31\u592a\u6162\u4e86\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap03/#\u4f20\u64ad\u5ef6\u8fdf","title":"\u4f20\u64ad\u5ef6\u8fdf","text":"<p>\u4f20\u64ad\u5ef6\u8fdf(propagation delay) \u8861\u91cf\u4e86\u95e8\u7684\u8f93\u5165\u53d8\u5316\u5bfc\u81f4\u8f93\u51fa\u53d8\u5316\u6240\u9700\u8981\u7684\u65f6\u95f4\u3002\u7531\u4e8e\u4ece\u4f4e\u7535\u5e73\u8f6c\u5316\u5230\u9ad8\u7535\u5e73\u548c\u9ad8\u7535\u5e73\u8f6c\u5316\u5230\u4f4e\u7535\u5e73\u6240\u9700\u8981\u7684\u65f6\u95f4\u4e0d\u4e00\u6837\uff0c\u6240\u4ee5\u4f20\u64ad\u5ef6\u8fdf\u540c\u6837\u6709\u4e24\u4e2a\u90e8\u5206\uff0c\u5206\u522b\u4f7f\u7528 \\(\\mathrm{t_{PHL}}\\) \u548c \\(\\mathrm{t_{PLH}} \u6765\u8868\u793a\\)\u3002</p> <p>\u66f4\u5177\u4f53\u7684\u6765\u8bf4\uff0c\u4f20\u64ad\u5ef6\u8fdf\u7684\u8ba1\u7b97\u65b9\u6cd5\u662f\u8f93\u5165\u548c\u8f93\u51fa\u7684\u53d8\u5316\u4e2d\u70b9\uff08\u5373\u53d8\u5316\u5230 \\(\\frac{1}{2}V_{CC}\\) \u65f6\uff09\u7684\u65f6\u95f4\u5dee\uff0c\u901a\u8fc7\u65f6\u5e8f\u56fe\u8868\u793a\u5c31\u662f\u8fd9\u6837\uff1a</p> <p></p> <p>\u6b64\u5916\uff0c\u6211\u4eec\u8fd8\u53ef\u4ee5\u5f15\u5165 \\(\\mathrm{ t_{pd} }\\) \u6765\u7edf\u4e00\u8868\u793a \\(\\mathrm{t_{PHL}}\\) \u548c \\(\\mathrm{t_{PLH}}\\)\u3002\u6570\u503c\u4e0a\uff0c\\(\\mathrm{ t_{pd} } = average(\\mathrm{t_{PHL}}, \\mathrm{t_{PLH}})\\) \u6216 \\(\\mathrm{ t_{pd} } = max(\\mathrm{t_{PHL}}, \\mathrm{t_{PLH}})\\)\u3002</p> \u9898\u9762\u7b54\u6848 <p>\u6839\u636e\u65f6\u5e8f\u56fe\uff0c\u5199\u51fa\u95e8\u7684\u4f20\u64ad\u5ef6\u8fdf\uff0c\u6b64\u5904 \\(\\mathrm{ t_{pd} } = average(\\mathrm{t_{PHL}}, \\mathrm{t_{PLH}})\\)\u3002</p> <p></p> <p></p> <p>Transition Time vs. Propagation Delay</p> <p>\u8f6c\u6362\u65f6\u95f4\u4e13\u6ce8\u4e8e\u8f93\u51fa\u7684\u53d8\u5316\uff0c\u800c\u4f20\u64ad\u5ef6\u8fdf\u5219\u5305\u542b\u4e86\u8f93\u5165\u7684\u53d8\u5316\u548c\u8f93\u51fa\u7684\u53d8\u5316\u6574\u4e2a\u8fc7\u7a0b\u3002</p> <p>\u4ece\u65f6\u5e8f\u56fe\u4e0a\u7684\u8868\u793a\u6765\u770b\uff0c\u8f6c\u6362\u65f6\u95f4\u53ea\u9700\u8981\u8f93\u51fa\u7684\u65f6\u5e8f\u56fe\u5373\u53ef\u8868\u793a\uff1b\u4f46\u4f20\u64ad\u5ef6\u8fdf\u5219\u662f\u901a\u8fc7\u6bd4\u8f83\u8f93\u5165\u548c\u8f93\u51fa\u7684\u504f\u5dee\u6765\u8868\u793a\u7684\u3002</p> <p></p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap03/#\u5ef6\u8fdf\u6a21\u578b","title":"\u5ef6\u8fdf\u6a21\u578b","text":"<p>\u4e3a\u4e86\u7814\u7a76\u4e3a\u4ec0\u4e48\u4f1a\u5b58\u5728\u95e8\u5ef6\u8fdf\uff0c\u523b\u753b\u95e8\u7684 \u56fa\u6709\u95e8\u5ef6\u8fdf(inherent gate delay)\uff0c\u6211\u4eec\u9700\u8981\u5bf9\u5176\u5efa\u6a21\uff0c\u5e38\u89c1\u7684 \u5ef6\u8fdf\u6a21\u578b(delay model) \u6709\u4ee5\u4e0b\u4e24\u79cd\uff1a</p> <ul> <li>\u4f20\u8f93\u5ef6\u8fdf(transport delay): \u8ba4\u4e3a\u8f93\u5165\u548c\u8f93\u51fa\u4e4b\u95f4\u7684\u5ef6\u8fdf\u662f\u4e00\u4e2a\u5b9a\u503c\u7684\uff1b</li> </ul> <p></p> <ul> <li>\u60ef\u6027\u5ef6\u8fdf(inertial delay): \u5f15\u5165\u4e86 \u62d2\u7edd\u65f6\u95f4(rejection time)\uff0c\u53ea\u6709\u5f53\u8f93\u5165\u8fbe\u5230\u4e00\u5b9a\u80fd\u91cf\u540e\uff0c\u624d\u4f1a\u51fa\u53d1\u6805\u6781\u8f93\u51fa\uff08\u5728\u8fd9\u79cd\u6a21\u578b\u4e0b\uff0c\u566a\u97f3\u7b49\u4f1a\u88ab\u8fc7\u6ee4\uff09\uff1b</li> </ul> <p></p> <p>\u5c06\u4e0d\u5b58\u5728\u5ef6\u8fdf\u7684\u6a21\u578b\u3001\u4f20\u8f93\u5ef6\u8fdf\u6a21\u578b\u548c\u60ef\u6027\u5ef6\u8fdf\u6a21\u578b\u505a\u6bd4\u8f83\u5730\u6765\u770b\uff0c\u5c31\u662f\u5982\u4e0b\u60c5\u51b5\uff1a</p> <p></p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap03/#\u5ef6\u8fdf\u4ee5\u53ca\u76f8\u5173\u95ee\u9898","title":"\u5ef6\u8fdf\u4ee5\u53ca\u76f8\u5173\u95ee\u9898","text":"<p>\u5f15\u5165</p> <p>\u7531\u4e8e\u5b9e\u9645\u7535\u8def\u4e2d\u5b9e\u73b0\u5ef6\u8fdf\uff0c\u6570\u5b66\u4e0a\u7684\u903b\u8f91\u8868\u8fbe\u5f0f\u4e0e\u5b9e\u9645\u7535\u8def\u60c5\u51b5\u4f1a\u5b58\u5728\u4e0d\u540c\u2014\u2014\u5373\u5b58\u5728\u82e5\u5e72\u6570\u5b66\u4e0a\u65e0\u6cd5\u76f4\u63a5\u89e3\u51b3\u7684\u95ee\u9898\u3002</p> <p>\u6240\u4ee5\u7814\u7a76\u5ef6\u8fdf\u662f\u975e\u5e38\u5fc5\u8981\u7684\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap03/#\u5ef6\u8fdf\u8ba1\u7b97","title":"\u5ef6\u8fdf\u8ba1\u7b97","text":"<p>\u8ba1\u7b97\u4e00\u4e2a\u7535\u8def\u7684\u5ef6\u8fdf\u65f6\uff0c\u6709\u4e24\u65b9\u9762\u9700\u8981\u8003\u8651\uff0c\u4e00\u65b9\u9762\u662f\u7535\u8def\u81ea\u8eab\u6240\u5bfc\u81f4\u7684\u4e00\u4e2a\u56fa\u5b9a\u5ef6\u8fdf\uff0c\u53e6\u5916\u4e00\u65b9\u9762\u5219\u662f\u7531\u4e8e\u4e0d\u540c\u7684\u8d1f\u8f7d\u5bfc\u81f4\u7684\u989d\u5916\u5ef6\u8fdf\u3002</p> <p></p> <p>\u5728\u8fd9\u4e2a\u4f8b\u5b50\u4e2d\uff0c0.07 \u4e3a\u56fa\u5b9a\u5ef6\u8fdf\uff0c0.021 \u4e3a\u4e00\u4e2a\u6807\u51c6\u8d1f\u8f7d\u5e26\u6765\u7684\u5ef6\u8fdf\u7cfb\u6570\uff0cSL(4.5 here) \u5219\u662f\u6807\u51c6\u5316\u7684\u8d1f\u8f7d\u91cf\u3002</p> <p>\u800c\u5177\u4f53\u7684\u8868\u8fbe\u5f0f\uff0c\u4f1a\u5728 Cell Library \u91cc\u5199\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap03/#\u5ef6\u8fdf\u5e26\u6765\u7684\u95ee\u9898","title":"\u5ef6\u8fdf\u5e26\u6765\u7684\u95ee\u9898","text":"<p>\u7531\u4e8e\u5b58\u5728\u5ef6\u8fdf\uff0c\u8bb8\u591a\u5728\u6570\u5b66\u610f\u4e49\u4e0a\u6ca1\u6709\u95ee\u9898\u7684\u903b\u8f91\u8868\u8fbe\u5f0f\u5728\u7535\u8def\u4e2d\u5c31\u5b58\u5728\u975e\u5e38\u5927\u7684\u95ee\u9898\u3002</p> <p>\u4f8b\u5982\uff0c\u4ece\u6570\u5b66\u89d2\u5ea6\u770b\uff0c\\(\\mathrm{Y=\\overline{A}A}\\) \u7684\u503c\u6052\u4e3a <code>0</code>\uff0c\u4f46\u662f\u5b9e\u9645\u4e0a\u7531\u4e8e\u5ef6\u8fdf\uff0c\u5176\u4eff\u771f\u6ce2\u5f62\u4e2d\u4f1a\u51fa\u73b0\u8fd9\u6837\u4e00\u4e2a \u6bdb\u523a(glitch)\uff0c\u800c\u8fd9\u5728\u5de5\u7a0b\u610f\u4e49\u4e0a\u6709\u5f88\u5927\u7684\u95ee\u9898\u3002</p> <p></p> \u66f4\u590d\u6742\u7684 \ud83c\udf30 <p>\u8ba9\u6211\u4eec\u5206\u6790\u4e0b\u9762\u8fd9\u4e2a\u4e8c\u8def\u9009\u62e9\u5668\uff0c\u5176\u529f\u80fd\u662f\u901a\u8fc7 S \u63a7\u5236\u8f93\u51fa\u8868\u8fbe\u7684\u662f A \u8fd8\u662f B\uff0c\u5728\u4f20\u8f93\u5ef6\u8fdf\u6a21\u578b\u4e0b\uff0c\u5176\u6ce2\u5f62\u5982\u4e0b\uff1a</p> <p></p> <p>\u53ef\u4ee5\u53d1\u73b0\uff0cY \u4e2d\u51fa\u73b0\u4e86\u610f\u6599\u4e4b\u5916\u7684\u6bdb\u523a\u3002</p> <p>\u800c\u8fd9\u4e2d\u6bdb\u523a\u53ef\u4ee5\u7528\u6dfb\u52a0\u5197\u4f59\u9879\u6765\u89e3\u51b3\uff1a</p> <p></p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap03/#\u6b63\u903b\u8f91\u548c\u8d1f\u903b\u8f91","title":"\u6b63\u903b\u8f91\u548c\u8d1f\u903b\u8f91","text":"<p>\u6b63\u903b\u8f91(positive logic) \u5c31\u662f <code>1</code> \u662f\u6709\u6548\u4fe1\u53f7\uff0c\u8d1f\u903b\u8f91(negative logic) \u5c31\u662f <code>0</code> \u662f\u6709\u6548\u4fe1\u53f7\u3002\u800c\u5728\u6b63\u903b\u8f91\u4e2d AND \u95e8\u7684\u4f5c\u7528\u5c31\u7b49\u6548\u4e8e\u8d1f\u903b\u8f91\u4e2d OR \u95e8\u7684\u4f5c\u7528\uff0c\u8fd9\u4e5f\u6b63\u662f\u6211\u5728\u524d\u9762\u51e0\u7ae0\u7684\u7b14\u8bb0\u4e2d\u63d0\u5230\u7684\u5bf9\u79f0\u3002</p> <p>\u800c\u6b63\u903b\u8f91\u7684\u7535\u8def\u7684\u7b26\u53f7\u4e00\u822c\u5c31\u662f\u6b63\u5e38\u7684\u903b\u8f91\u95e8\u7b26\u53f7\uff0c\u800c\u8d1f\u903b\u8f91\u7684\u903b\u8f91\u95e8\u7b26\u53f7\u5219\u53ef\u80fd\u6709\u5c0f\u4e09\u89d2\u6807\uff0c\u5373 \u6781\u6027\u6307\u793a\u5668(polarity indicator)\uff1a</p> <p></p> <p>\u5982\u56fe\uff0c\u5de6\u4fa7\u662f\u6b63\u903b\u8f91\u7535\u8def\u7684\u7b26\u53f7\uff0c\u53f3\u4fa7\u662f\u8d1f\u903b\u8f91\u7535\u8def\u7684\u7b26\u53f7\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap03/#\u5de5\u827a\u6620\u5c04","title":"\u5de5\u827a\u6620\u5c04","text":"<p>\u5de5\u827a\u6620\u5c04(technology mapping) \u662f\u6307\u5c06\u903b\u8f91\u56fe\u6216\u7f51\u8868\u8f6c\u5316\u4e3a\u53ef\u4ee5\u7528\u5de5\u827a\u5b9e\u73b0\u7684\u5fc3\u7684\u56fe\u6216\u7f51\u8868\u7684\u8fc7\u7a0b\u3002</p> <p>\u6709\u65f6\u6211\u4eec\u4f1a\u4f7f\u7528\u4e0e\u975e\u95e8\u548c\u975e\u95e8\u66ff\u6362\u4e0e\u95e8\u548c\u6216\u95e8(\u56e0\u4e3a\u7535\u8def\u5c42\u9762\uff0c\u4e0e\u95e8\u5b9e\u9645\u4e0a\u5c31\u662f\u901a\u8fc7\u4e0e\u975e\u95e8\u5b9e\u73b0\u7684)\uff0c\u7136\u540e\u4f1a\u53d1\u73b0\u6709\u4e00\u4e9b\u8fde\u7eed\u5bf9\u975e\u95e8\u53ef\u4ee5\u76f8\u4e92\u62b5\u6d88\uff0c\u4f8b\u5982\u4e0b\u9762\u7684\u60c5\u51b5\uff1a</p> <p></p> <p>\u84dd\u7eff\u8272\u5757\u4e2d\u5373\u4e3a\u88ab\u66ff\u6362\u540e\u7684\u5185\u5bb9\uff0c\u7136\u540e\u6211\u4eec\u53d1\u73b0\u51fa\u73b0\u4e86\u82e5\u5e72\u53ef\u4ee5\u62b5\u6d88\u7684\u975e\u95e8\u3002</p> <p>\u5f53\u7136\uff0c\u4e5f\u53ef\u4ee5\u901a\u8fc7\u6216\u975e\u95e8\u6765\u5b9e\u73b0\uff0c\u6bd4\u5982\u4e0b\u9762\u7684\u60c5\u51b5\uff1a</p> <p></p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap03/#\u9a8c\u8bc1\u6b63\u786e\u6027","title":"\u9a8c\u8bc1\u6b63\u786e\u6027","text":"<p>\u9a8c\u8bc1\u6b63\u786e\u6027(Verification)\u6307\u7684\u662f\u8bc1\u660e\u6700\u7ec8\u8bbe\u8ba1\u7684\u7535\u8def\u80fd\u591f\u5b9e\u73b0\u9884\u671f\u4ea7\u54c1\u89c4\u683c\uff08Specification\uff09\u3002 \u7b80\u5355\u7684\u4ea7\u54c1\u89c4\u683c\u53ef\u4ee5\u7528\u771f\u503c\u8868\u3001\u5e03\u5c14\u4ee3\u6570\u5f0f\u3001HDL \u4ee3\u7801\u7b49\u63cf\u8ff0\u3002</p> <p>\u6700\u57fa\u672c\u7684\u9a8c\u8bc1\u6b63\u786e\u6027\u65b9\u6cd5\u6709\uff1a</p> <ul> <li>\u4eba\u5de5\u903b\u8f91\u5206\u6790(Manual Logic Analysis)\uff1a<ul> <li>\u627e\u5230\u6700\u7ec8\u7535\u8def\u7684\u771f\u503c\u8868\u6216\u5e03\u5c14\u4ee3\u6570\u5f0f\uff0c\u5224\u65ad\u5176\u662f\u5426\u548c\u9884\u671f\u4ea7\u54c1\u89c4\u683c\u4e00\u81f4\uff1b</li> </ul> </li> <li>\u4eff\u771f(Simulation)\uff1a<ul> <li>\u5728\u4eff\u771f\u73af\u5883\u4e2d\uff0c\u4f7f\u7528\u5408\u9002\u7684\u6d4b\u8bd5\u8f93\u5165\uff08\u6fc0\u52b1\u4fe1\u53f7\uff09\u6765\u6d4b\u8bd5\u6700\u7ec8\u7535\u8def\uff08\u6216\u5176\u7f51\u8868\uff0c\u53ef\u80fd\u7f16\u5199\u4e3a HDL\uff09\uff0c\u901a\u8fc7\u89c2\u5bdf\u5176\u54cd\u5e94\u7ed3\u679c\u6765\u5224\u65ad\u662f\u5426\u5b9e\u73b0\u9884\u671f\u4ea7\u54c1\u89c4\u683c\uff1b</li> </ul> </li> </ul> <p>Why Simulate?</p> <p>\u6211\u4eec\u66fe\u5728\u6570\u903b\u5b9e\u9a8c\u4e2d\u9a8c\u8bc1\u8fc7\u4e8c\u8f93\u5165\u4e0e\u975e\u95e8\u7684\u6b63\u786e\u6027\uff0c\u90a3\u65f6\u6211\u4eec\u91c7\u7528\u4eba\u5de5\u903b\u8f91\u5206\u6790\uff0c\u901a\u8fc7\u6d4b\u8bd5\u786e\u5b9a\u4e86\u5f85\u6d4b\u95e8\u7684\u771f\u503c\u8868\uff0c\u5e76\u5c06\u5176\u4e0e\u6807\u51c6\u7684\u4e8c\u8f93\u5165\u4e0e\u975e\u95e8\u771f\u503c\u8868\u6bd4\u8f83\uff0c\u4ece\u800c\u5224\u65ad\u6211\u4eec\u7684\u4e8c\u8f93\u5165\u4e0e\u975e\u95e8\u662f\u5426\u6b63\u786e\u5b9e\u73b0\uff1b</p> <p>\u4f46\u5982\u679c\u6211\u4eec\u9700\u8981\u9a8c\u8bc1\u4e00\u4e2a\u4e00\u767e\u4e07\u8f93\u5165\u4e0e\u975e\u95e8\u7684\u6b63\u786e\u6027\u5462\uff1f\uff08\u4ec5\u7528\u4e8e\u4e3e\u4f8b\uff09</p> <p>\u6211\u4eec\u53d1\u73b0\uff0c\u5728\u73b0\u5b9e\u4e16\u754c\u4e2d\u4eba\u5de5\u6c42\u89e3\u8fd9\u4e2a\u7535\u8def\u7684\u771f\u503c\u8868\u6216\u5e03\u5c14\u4ee3\u6570\u5f0f\u662f\u4e0d\u53ef\u80fd\u7684\u3002\u8fd9\u65f6\u5019\u6211\u4eec\u53ef\u4ee5\u8bbe\u8ba1\u4e00\u7ec4\u5177\u6709\u4ee3\u8868\u6027\u7684\u8f93\u5165\uff08\u4ecd\u7136\u662f\u4e2a\u4e0d\u5c0f\u7684\u6570\u76ee\uff09\uff0c\u8ba9\u8ba1\u7b97\u673a\u5728\u4eff\u771f\u73af\u5883\u4e2d\u7528\u8fd9\u7ec4\u8f93\u5165\u53bb\u6d4b\u8bd5\u7535\u8def\uff0c\u5e76\u5c06\u6d4b\u8bd5\u7ed3\u679c\u4e0e\u9884\u671f\u7ed3\u679c\u8fdb\u884c\u5bf9\u6bd4\u3002\u6211\u4eec\u65e0\u6cd5\u786e\u4fdd\u9a8c\u8bc1\u662f\u5426\u5145\u5206\uff0c\u4f46\u81f3\u5c11\u8fd9\u662f\u5b9e\u8df5\u610f\u4e49\u4e0a\u8db3\u591f\u5145\u5206\u7684\u9a8c\u8bc1\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap03/#\u7ec4\u5408\u903b\u8f91","title":"\u7ec4\u5408\u903b\u8f91","text":""},{"location":"cour_note/D2QD_DigitalDesign/Chap03/#\u57fa\u672c\u903b\u8f91\u51fd\u6570","title":"\u57fa\u672c\u903b\u8f91\u51fd\u6570","text":"<ul> <li>\u5e38\u91cf\u51fd\u6570(Value-Fixing)\uff1a\\(F=0\\;\\;or\\;\\;F=1\\) | \u8f93\u51fa\u5b9a\u503c\uff1b</li> <li>\u4f20\u8f93\u51fd\u6570(Transferring)\uff1a\\(F=X\\) | \u76f4\u63a5\u8f93\u51fa\u8f93\u5165\u503c\uff1b</li> <li>\u9006\u53d8\u51fd\u6570(Inverting)\uff1a\\(F=\\overline{X}\\) | \u8f93\u51fa\u8f93\u5165\u7684\u76f8\u53cd\uff1b</li> <li>\u4f7f\u80fd\u51fd\u6570(Enabling)\uff1a\\(F=X\\cdot En \\;\\; or \\;\\; F = X + \\overline{En}\\) | \u901a\u8fc7\u4f7f\u80fd\u63a7\u5236\u8f93\u51fa\u662f\u5426\u53ef\u53d8\uff0c\u5206\u4e3a\u4e24\u79cd\uff0c\u6bd4\u5982\u4e0e\u7684\u5f62\u5f0f\u4e2d\uff0c\u53ea\u6709 \\(En\\) \u4e3a <code>1</code> \u65f6\uff0c\\(F\\) \u8868\u73b0\u4e3a \\(X\\) \u7684\u503c\uff1b\u53cd\u4e4b\u8f93\u51fa\u5fc5\u5b9a\u4e3a <code>0</code>\uff08\u6ce8\u610f\u533a\u5206\u5b83\u4e0e\u4e09\u6001\u95e8\u7684\u533a\u522b\uff0c\u9ad8\u963b\u6001 or \u5b9a\u503c\uff09\uff1b</li> </ul>"},{"location":"cour_note/D2QD_DigitalDesign/Chap03/#\u57fa\u672c\u529f\u80fd\u5757","title":"\u57fa\u672c\u529f\u80fd\u5757","text":"<ul> <li>\u8bd1\u7801\u5668(Decoder)</li> <li> <p>\u7f16\u7801\u5668(Encoder)</p> </li> <li> <p>\uff08\u4e09\u7aef\uff09\u591a\u8def\u590d\u7528\u5668(Multiplexer) <code>MUX</code></p> </li> <li>\uff08\u4e09\u7aef\uff09\u4fe1\u53f7\u5206\u914d\u5668(Demultiplexer) <code>DEMUX</code></li> </ul>"},{"location":"cour_note/D2QD_DigitalDesign/Chap03/#\u8bd1\u7801\u5668","title":"\u8bd1\u7801\u5668","text":"<p>\u7a77\u4e3e\u53ef\u80fd\u6027\uff0c\u7a20\u5bc6 -&gt; \u7a20\u5bc6/\u7a00\u758f</p> <p>\u4e3a\u4e86\u8282\u7701\u95e8\u8f93\u5165\u6210\u672c\uff0c\u6211\u4eec\u5e38\u5e38\u4f7f\u7528 \u5206\u7ea7 \u7684\u601d\u60f3\u6765\u6784\u9020\u591a\u8f93\u5165\u591a\u8bd1\u7801\u5668\u3002</p> <p>eg</p> <p></p> <p>\u7531\u4e8e\u5e95\u5c42\u7684\u7535\u8def\u80fd\u591f\u76f4\u63a5\u5b9e\u73b0\u7684\u8fd0\u7b97\u5341\u5206\u5c40\u9650\uff0c\u6240\u4ee5\u9700\u8981\u7528\u8bd1\u7801\u5668\u6765\u5b9e\u73b0\u4e00\u4e9b\u57fa\u7840\u8fd0\u7b97\uff0c\u4f8b\u5982\u52a0\u6cd5\u3002</p> <p>\u4e00\u4f4d\u52a0\u6cd5\u5668\u5c31\u53ef\u4ee5\u901a\u8fc7\u8bd1\u7801\u5668\u548c\u6216\u95e8\u5b9e\u73b0\uff0c\u6838\u5fc3\u5c31\u662f\u679a\u4e3e\u8f93\u5165\u7684\u5404\u79cd\u60c5\u51b5\uff0c\u7136\u540e\u7528\u6216\u95e8\u62fe\u53d6 sum \u548c carry \u7684\u6700\u5c0f\u9879\u3002</p> <p></p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap03/#\u7f16\u7801\u5668","title":"\u7f16\u7801\u5668","text":"<p>\u7a20\u5bc6/\u7a00\u758f -&gt; \u7a20\u5bc6</p> <p>\u5982\u4e0a\u5b9a\u4e49\u7684\u7f16\u7801\u5668\u6709\u4e00\u4e2a\u9650\u5236\uff0c\u5373\u4efb\u4f55\u65f6\u5019\u8f93\u5165\u53ea\u80fd\u6709\u4e00\u4e2a\u662f\u6d3b\u52a8\u7684\uff0c\u5373\u8f93\u5165\u662f one-hot \u7684\u3002</p> <p>\u4f18\u5148\u7f16\u7801\u5668</p> <p>\u4f18\u5148\u7f16\u7801\u5668\u80fd\u591f\u5b9e\u73b0\u4f18\u5148\u7ea7\u51fd\u6570\uff0c\u5b83\u4e0d\u8981\u6c42\u8f93\u5165\u662f one-hot \u7684\uff0c\u800c\u662f\u603b\u662f\u5173\u6ce8\u6709\u6548\u8f93\u5165\u4e2d\u4f18\u5148\u7ea7\u6700\u9ad8\u7684\u90a3\u4e00\u4e2a\u3002\u5373\u6bd4\u5982\u5f53\u4f18\u5148\u7ea7\u6700\u9ad8\u7684\u90a3\u4e00\u4f4d\u662f <code>1</code> \u65f6\uff0c\u5176\u5b83\u6240\u6709\u4f18\u5148\u7ea7\u4e0d\u5982\u5b83\u7684\u4f4d\u7f6e\u7684\u503c\u90fd\u662f\u6211\u4eec\u4e0d\u5173\u5fc3\u7684\u5185\u5bb9\u4e86\u3002</p> <p>\u4e2d\u65ad(interrupt)\u5224\u4f18\u5668</p> <p>\u4f18\u5148\u7f16\u7801\u5668\u7684\u4e00\u79cd\u5e94\u7528\u5c31\u662f\u4e2d\u65ad\u5224\u4f18\u5668\u3002</p> <p></p> <p>\u5176\u4e2d \\(V\\) \u8868\u793a\u8f93\u51fa\u662f\u5426\u6709\u6548\uff0c\u5728\u4e2d\u65ad\u5224\u4f18\u7cfb\u7edf\u4e2d\u5373\u8868\u793a\u662f\u5426\u6709\u4e2d\u65ad\u8bf7\u6c42\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap03/#\u591a\u8def\u590d\u7528\u5668","title":"\u591a\u8def\u590d\u7528\u5668","text":"<p>\u901a\u8fc7\u63a7\u5236\u7aef\u9009\u62e9\u8f93\u51fa\u7684\u662f\u82e5\u5e72\u8f93\u5165\u4e2d\u7684\u54ea\u4e00\u4e2a\u3002</p> <p>\u901a\u8fc7\u4e09\u6001\u95e8\u6765\u5b9e\u73b0 <code>MUX</code> \u80fd\u591f\u964d\u4f4e\u95e8\u8f93\u5165\u4ee3\u4ef7\u3002</p> eg <p></p> <p>\u5b8c\u5168\u4f7f\u7528\u4e09\u6001\u95e8\u6765\u5b9e\u73b0\u56db\u8f93\u5165 <code>MUX</code>\uff0c\u95e8\u8f93\u5165\u5927\u5927\u51cf\u5c11\u3002</p> <p><code>MUX</code> \u8fd8\u53ef\u4ee5 \u5b9e\u73b0\u4efb\u610f\u7684\u903b\u8f91\u51fd\u6570\uff1a</p> <ul> <li>\u5c06\u63a7\u5236\u7aef\u5f53\u4f5c\u8f93\u5165\uff0c\u539f\u6765\u7684\u8f93\u5165\u5f53\u4f5c\u7ed3\u679c\uff1b</li> <li>\u5373\u53ef\u4ee5\u5c06\u4e00\u4e2a\u56db\u8f93\u5165 <code>MUX</code> \u5f53\u4f5c\u4e00\u4e2a\u4e8c\u8f93\u5165\u7684\u51fd\u6570\uff1b</li> </ul> <p>\u6362\u53e5\u8bdd\u6765\u8bf4\uff0c\u5c31\u662f\u5c06\u539f\u6765\u7684\u63a7\u5236\u7aef\u5f53\u4f5c\u8f93\u5165\u7aef\uff0c\u5e76\u5728\u539f\u6765\u7684\u8f93\u5165\u7aef\u5199\u5165\u903b\u8f91\u51fd\u6570\u7684\u771f\u503c\u8868\uff0c\u4ee5\u5b9e\u73b0\u4efb\u610f\u903b\u8f91\u51fd\u6570\u3002</p> <p>\u6211\u4eec\u8fd8\u53ef\u4ee5\u901a\u8fc7\u628a\u4e00\u90e8\u5206\u7684\u8f93\u5165\u5f53\u4f5c\u5e38\u91cf\u7aef\u6765\u7b80\u5316\u5143\u4ef6\uff08\u964d\u7ef4\uff09\uff1a</p> <p></p> <p>\u89c2\u5bdf\u5176\u6700\u5c0f\u9879\uff0c\u4f7f\u5176\u8f93\u51fa\u6240\u6709\u6700\u5c0f\u9879\u3002\u4f46\u662f\u5728\u964d\u7ef4\u8fc7\u7a0b\u4e2d\u5e76\u4e0d\u9700\u8981\u5168\u90fd\u662f C\uff0c\u5982\u679c\u5361\u8bfa\u56fe\u4e2d\u5b58\u5728\u53cc <code>1</code> \u6216\u8005\u53cc <code>0</code>\uff0c\u4e5f\u53ef\u4ee5\u4ecd\u7136\u4f7f\u7528\u5e38\u91cf\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap03/#\u4fe1\u53f7\u5206\u914d\u5668","title":"\u4fe1\u53f7\u5206\u914d\u5668","text":"<p>\u7b80\u5199\u4e3a <code>DEMUX</code>\uff0c\u901a\u8fc7\u63a7\u5236\u7aef\u9009\u62e9\u8f93\u5165\u7ed9\u5230\u82e5\u5e72\u8f93\u51fa\u4e2d\u7684\u54ea\u4e00\u4e2a\u3002</p> <p></p> <p>\u540e\u7eed \ud83d\udc49 \u53ef\u91cd\u7f16\u7a0b\u6280\u672f</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap03/#\u7b97\u672f\u903b\u8f91\u7535\u8def","title":"\u7b97\u672f\u903b\u8f91\u7535\u8def","text":"<p>\u6211\u4eec\u4e3b\u8981\u8ba8\u8bba\u7684\u8ba1\u7b97\u4e3b\u8981\u5305\u62ec\u903b\u8f91\u8fd0\u7b97\u548c\u7b97\u672f\u8fd0\u7b97\uff0c\u524d\u8005\u7531\u4e8e\u53ef\u4ee5\u76f4\u63a5\u901a\u8fc7\u57fa\u672c\u95e8\u5f88\u65b9\u4fbf\u5b9e\u73b0\uff0c\u6240\u4ee5\u6211\u4eec\u4e0d\u8fc7\u591a\u8003\u8651\uff1b\u5728\u6b64\u4e3b\u8981\u4ecb\u7ecd\u7b97\u6570\u8fd0\u7b97\u3002\u5728\u8ba1\u7b97\u673a\u786c\u4ef6\u4e2d\uff0c\u627f\u62c5\u8ba1\u7b97\u5de5\u4f5c\u7684\u4e3b\u8981\u90e8\u4ef6\u4e3a <code>ALU</code>(Arithmetic Logical Unit)\u3002</p> <p>\u5f15\u5165</p> <p>\u5728\u4e4b\u524d #\u8bd1\u7801\u5668 \u548c #\u591a\u8def\u590d\u7528\u5668 \u7684\u90e8\u5206\u4e2d\u5df2\u7ecf\u4ecb\u7ecd\u8fc7\u4e00\u4e9b\u5b9e\u73b0 1 bit \u52a0\u6cd5\u5668\u7684\u65b9\u6cd5\uff0c\u63a5\u4e0b\u6765\u6211\u4eec\u5c31\u6765\u8be6\u7ec6\u770b\u770b\u52a0\u6cd5\u5668\u8fd9\u4e2a\u4e1c\u897f\u3002</p> <p>\u9996\u5148\u6211\u4eec\u9700\u8981\u4e86\u89e3\u52a0\u6cd5\u5668\u6700\u5e95\u5c42\u7684\u5355\u5143\uff0c\u5373\u5b9e\u73b0 1 bit \u8fd0\u7b97\u7684 \u534a\u52a0\u5668(half adder) \u548c \u5168\u52a0\u5668(full adder)\uff0c\u63a5\u4e0b\u6765\u9700\u8981\u5c06\u4ed6\u4eec\u7ec4\u5408\u5728\u4e00\u8d77\uff0c\u5b9e\u73b0 n bits \u7684\u52a0\u6cd5\u5668\uff0c\u5176\u4e2d\u4e3b\u8981\u4ecb\u7ecd \u884c\u6ce2\u52a0\u6cd5\u5668(binary ripple carry adder)\u3002\u6b64\u5916\uff0c\u57fa\u4e8e\u4e00\u4e9b\u7f16\u7801\u7684\u77e5\u8bc6\uff0c\u6211\u4eec\u8fd8\u53ef\u4ee5\u5c06\u5b83\u6539\u88c5\u6210\u52a0\u51cf\u6cd5\u5668\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap03/#\u534a\u52a0\u5668--\u5168\u52a0\u5668","title":"\u534a\u52a0\u5668 &amp; \u5168\u52a0\u5668","text":"<p>\u5bf9\u4e8e\u4e8c\u8fdb\u5236\u52a0\u6cd5\uff0c\u5176\u8f93\u51fa\u65e0\u7591\u6709\u5f53\u524d\u4f4d\u7684\u548c <code>S</code> \u548c\u8fdb\u4f4d <code>C</code>\uff0c\u800c\u8f93\u5165\u9664\u4e86\u4e24\u4e2a\u64cd\u4f5c\u6570 <code>X</code> \u548c <code>Y</code> \u4ee5\u5916\uff0c\u8fd8\u53ef\u80fd\u6709\u4e0a\u4e00\u4f4d\u7684\u8fdb\u4f4d <code>Z</code>(\u6216\u8005<code>C{n-1}</code>)\u3002\u800c\u5bf9\u4e8e\u4e00\u4e2a\u4e8c\u8fdb\u5236\u6570\u7684\u7b2c\u4e00\u4f4d\uff0c\u663e\u7136\u4e0d\u4f1a\u6709\u8fdb\u4f4d\uff0c\u6216\u8005\u8bf4 <code>Z=0</code>\uff0c\u6240\u4ee5\u6211\u4eec\u53ef\u4ee5\u5c06\u8fd9\u4e2a <code>Z</code> \u53bb\u6389\uff0c\u5373\u8f93\u5165\u53ea\u6709 <code>X</code> \u548c <code>Y</code>\uff0c\u8fd9\u5c31\u662f \u534a\u52a0\u5668(half adder)\uff1b\u663e\u7136\uff0c\u5bf9\u5e94\u7684\uff0c\u5982\u679c\u8f93\u5165\u4e2d\u6709\u4e0a\u4e00\u4f4d\u7684\u8fdb\u4f4d <code>Z</code>\uff0c\u5219\u79f0\u4e3a \u5168\u52a0\u5668(full adder)\u3002</p> \u534a\u52a0\u5668\u5168\u52a0\u5668 \u903b\u8f91\u8868\u8fbe\u5f0f\u771f\u503c\u8868\u7535\u8def\u56fe \\[ S=\\overline{X}Y+X\\overline{Y}=X\\oplus Y \\\\ C = XY \\] <p> </p> <p> </p> \u903b\u8f91\u8868\u8fbe\u5f0f\u771f\u503c\u8868\u5361\u8bfa\u56fe\u903b\u8f91\u8868\u8fbe\u5f0f with XOR \\[ S=\\overline{X}\\,\\overline{Y}Z + \\overline{X}Y\\overline{Z} + X\\overline{Y}\\,\\overline{Z} + XYZ \\\\ C = XY + XZ + YZ \\] <p> </p> <p> </p> \\[ S = (X\\oplus Y)\\oplus Z \\\\ C = XY + Z(X\\oplus Y) \\]"},{"location":"cour_note/D2QD_DigitalDesign/Chap03/#\u884c\u6ce2\u52a0\u6cd5\u5668","title":"\u884c\u6ce2\u52a0\u6cd5\u5668","text":"<p>\u884c\u6ce2\u52a0\u6cd5\u5668\u662f\u6734\u7d20\u7684 n bits \u52a0\u6cd5\u5668\u5b9e\u73b0\u3002\u5176\u6838\u5fc3\u601d\u60f3\u4e5f\u5c31\u662f\u6a21\u62df\u6211\u4eec\u4f7f\u7528\u201c\u7ad6\u5f0f\u201d\u6765\u8ba1\u7b97\u52a0\u6cd5\uff0c\u4ece\u4f4e\u4f4d\u5f00\u59cb\u9010\u4f4d\u8ba1\u7b97\uff0c\u5e76\u5c06\u8fdb\u4f4d\u7ed9\u5230\u4e0b\u4e00\u4f4d\u4f5c\u4e3a\u8f93\u5165\u3002</p> <p>\u5b9e\u9645\u4e0a\u65e0\u8bba\u662f\u53ea\u7528\u534a\u52a0\u5668\u6216\u662f\u53ea\u7528\u5168\u52a0\u5668\uff0c\u90fd\u53ef\u4ee5\u5b9e\u73b0\u884c\u6ce2\u52a0\u6cd5\u5668\uff0c\u4f46\u662f\u6b8a\u9014\u540c\u5f52\uff0c\u65e0\u975e\u662f\u901a\u8fc7\u5916\u90e8\u5668\u4ef6\u6765\u8fdb\u884c\u4e92\u76f8\u8f6c\u5316\u800c\u5df2\u3002\u5982\u679c\u53ea\u4f7f\u7528\u5168\u52a0\u5668\u6765\u5b9e\u73b0\uff0c\u5219\u4ee5 4 bits \u884c\u6ce2\u52a0\u6cd5\u5668\u4e3a\u4f8b\uff0c\u5176\u5927\u81f4\u903b\u8f91\u5982\u4e0b\uff1a</p> <p></p> <p>\u5176\u4e2d\uff0c\u5728\u52a0\u6cd5\u5668\u4e2d\uff0c\\(C_0\\) \u5fc5\u7136\u662f <code>0</code>\u3002</p> <p>\u52a0\u51cf\u6cd5\u5668\uff0c\u6216\u8005\u8bf4\u52a0\u6cd5\u5668\uff0c\u4e00\u822c\u60c5\u51b5\u4e0b\u5728 <code>ALU</code> \u4e2d\u662f\u6700\u5f71\u54cd\u6548\u7387\u7684\u90e8\u5206\uff0c\u800c\u4e14\u5982\u679c\u4f7f\u7528\u884c\u6ce2\u52a0\u6cd5\u5668\uff0c\u968f\u7740\u4f4d\u6570\u589e\u52a0\u6548\u7387\u4f1a\u8d8a\u6765\u8d8a\u6162\u3002</p> <p>\u6240\u4ee5\u4f1a\u6709\u7c7b\u4f3c\u4e8e\u8d85\u524d\u8fdb\u4f4d\u52a0\u6cd5\u5668\u4e4b\u7c7b\u7684\u4e1c\u897f\u6765\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\u3002</p> <p>\u66f4\u591a\u7684\u5185\u5bb9\u53ef\u4ee5\u770b xxjj \u7684\u8ba1\u7ec4\u7b14\u8bb0\u3002\uff08\u6570\u903b\u4e2d\u6700\u591a\u4e86\u89e3\u5230\u8d85\u524d\u8fdb\u4f4d\u52a0\u6cd5\u5668\u5373\u53ef\u3002\uff09</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap03/#\u4e8c\u8fdb\u5236\u51cf\u6cd5","title":"\u4e8c\u8fdb\u5236\u51cf\u6cd5","text":"<p>\u9996\u5148\uff0c\u5728\u5f00\u59cb\u4e8c\u8fdb\u5236\u51cf\u6cd5\u7684\u4ecb\u7ecd\u4e4b\u524d\uff0c\u4f60\u9700\u8981\u4e86\u89e3 \u8865\u7801(2's complement)\uff0c\u4e0d\u8fc7\u8fd9\u4e2a\u4e1c\u897f\u5b9e\u5728\u662f\u63d0\u8fc7\u592a\u591a\u6b21\u4e86\u6240\u4ee5\u6211\u4e0d\u6253\u7b97\u5728\u8fd9\u91cc\u518d\u5199\u4e00\u6b21\uff0c\u53ef\u4ee5\u67e5\u770b\u6211\u7684 C \u5c0f\u7b14\u8bb0\u7684\u8865\u7801\u5185\u5bb9\u3002</p> <p>\u7ed3\u5408\u8865\u7801\uff0c\u6211\u4eec\u518d\u6765\u89c2\u5bdf\u884c\u6ce2\u52a0\u6cd5\u5668\uff0c\u6211\u4eec\u9700\u8981\u5bf9\u51cf\u6570\u7684\u6bcf\u4e00\u4f4d\u53d6\u53cd\uff0c\u5e76\u5bf9\u6574\u4e2a\u6570\u52a0\u4e00\uff0c\u518d\u76f4\u63a5\u5c06\u5b83\u4eec\u76f8\u52a0\u5373\u53ef\uff0c\u5373\u5c06\u51cf\u6cd5\u8f6c\u5316\u4e3a\u8865\u7801\u4e0b\u7684\u52a0\u6cd5\u3002</p> <p></p> <p>\u5176\u4e2d\u52a0\u4e00\u8fd9\u4e00\u6b65\u6070\u597d\u53ef\u4ee5\u901a\u8fc7\u5728\u52a0\u6cd5\u5668\u4e2d\u5fc5\u5b9a\u4e3a <code>0</code> \u7684 \\(C_0\\) \u6765\u5b9e\u73b0\u3002\u6211\u4eec\u5728\u8f93\u5165\u4e2d\u6dfb\u52a0\u5f02\u6216\u95e8\u6765\u5b9e\u73b0\u53cd\u7801(1's complement)\uff0c\u518d\u7528 \\(C_0\\) \u5b9e\u73b0\u52a0\u4e00\uff0c\u4ece\u800c\u5f97\u5230\u8865\u7801(2's complement)\uff0c\u5c31\u6837\u5c31\u53ef\u4ee5\u5b9e\u73b0\u52a0\u51cf\u6cd5\u5668\u3002</p> <p></p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap03/#\u6709\u7b26\u53f7\u6570\u7684\u8868\u793a\u4e0e\u8ba1\u7b97","title":"\u6709\u7b26\u53f7\u6570\u7684\u8868\u793a\u4e0e\u8ba1\u7b97","text":"<ul> <li> TODO: \u8865\u5145\u8fd9\u91cc\u3002</li> </ul>"},{"location":"cour_note/D2QD_DigitalDesign/Chap04/","title":"Chap 4 Sequential Circuits","text":"<p> \u7ea6 5781 \u4e2a\u5b57  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 19 \u5206\u949f</p> <p>\u4e0a\u4e00\u7ae0\u8bb2\u7684\u662f\u7ec4\u5408\u7535\u8def\uff0c\u867d\u7136\u7ec4\u5408\u7535\u8def\u80fd\u591f\u5b9e\u73b0\u8bf8\u591a\u529f\u80fd\uff0c\u4f46\u662f\u5b83\u4f9d\u7136\u5b58\u5728\u4e00\u4e9b\u7684\u95ee\u9898\uff1a</p> <ol> <li>\u5bf9\u4e8e\u590d\u6742\u7684\u903b\u8f91\uff0c\u62bd\u8c61\u5c42\u7ea7\u591a\uff0c\u5bfc\u81f4\u786c\u4ef6\u5c42\u9762\u5f00\u9500\u5927\u3001\u8017\u65f6\u957f\uff0c\u4e00\u65b9\u9762\u63d0\u9ad8\u6210\u672c\uff0c\u4e00\u65b9\u9762\u964d\u4f4e\u6548\u7387\uff1b</li> <li>\u7ec4\u5408\u7535\u8def\u6ca1\u6cd5\u5b9e\u73b0\u4fe1\u606f\u7684\u5b58\u50a8\uff0c\u6240\u6709\u7684\u529f\u80fd\u6a21\u5757\u5bf9\u4e8e\u7279\u5b9a\u7684\u8f93\u5165\u7ed9\u51fa\u76f8\u540c\u7684\u8f93\u51fa\uff1b</li> </ol> <p>\u800c\u65f6\u5e8f\u7535\u8def\u5219\u62e5\u6709\u5b58\u50a8\u4fe1\u606f\u7684\u80fd\u529b\uff0c\u5bf9\u4e8e\u65f6\u5e8f\u7535\u8def\u6765\u8bf4\uff0c\u8f93\u51fa\u9664\u4e86\u4e0e\u8f93\u5165\u6709\u5173\uff08\u751a\u81f3\u53ef\u4ee5\u6ca1\u6709\u8f93\u5165\uff09\uff0c\u4e5f\u53ef\u4ee5\u4e0e\u81ea\u8eab \u72b6\u6001(state) \u6709\u5173\u3002</p> <p>\u65f6\u5e8f\u7535\u8def\u4e3b\u8981\u5206\u4e3a\u4e24\u7c7b\uff08\u4e3b\u8981\u5206\u7c7b\u4f9d\u636e\u662f\u8f93\u5165\u4fe1\u53f7\u7684\u65f6\u95f4\u548c\u5185\u90e8\u72b6\u6001\u6539\u53d8\u7684\u65f6\u95f4\uff09\uff1a\u540c\u6b65\u65f6\u5e8f\u7535\u8def(synchronous sequential circuit) \u548c \u5f02\u6b65\u65f6\u5e8f\u7535\u8def(asynchronous sequential circuit)\u3002</p> <p>The behavior of a synchronous sequential circuit can be defined from the knowledge of its signals at discrete instants of time. The behavior of an asynchronous sequential circuit depends upon the inputs at any instant of time and the order in continuous time in which the inputs change.</p> <p>\u4e00\u822c\u6765\u8bf4\uff0c\u5f02\u6b65\u7535\u8def\u7684\u8bbe\u8ba1\u76f8\u5bf9\u56f0\u96be\uff08\u884c\u4e3a\u4e0e\u95e8\u7684\u4f20\u64ad\u5ef6\u8fdf\u548c\u8f93\u5165\u4fe1\u53f7\u53d8\u5316\u7684\u65f6\u95f4\u5e8f\u5217\u5bc6\u5207\u76f8\u5173\uff09\uff0c\u4f46\u4ecd\u7136\u5341\u5206\u5fc5\u8981\uff0c\u6bd4\u5982\u89e6\u53d1\u5668\u5c31\u662f\u4ee5\u4e00\u90e8\u9501\u5b58\u5668\u4e3a\u6a21\u5757\u8bbe\u8ba1\u7684\uff1b\u800c\u540c\u6b65\u7535\u8def\u7684\u4f7f\u7528\u66f4\u52a0\u5e7f\u6cdb\uff0c\u901a\u5e38\u8fd9\u4e9b\u201c\u79bb\u6563\u7684\u65f6\u523b\u201d\u90fd\u662f\u7531 \u65f6\u949f\u53d1\u751f\u5668(clock generator) \u8fd9\u79cd\u65f6\u5e8f\u5668\u4ef6\u4ea7\u751f\u5468\u671f\u6027\u7684 \u65f6\u949f\u8109\u51b2(clock pulse) \u5e8f\u5217\u6765\u5b9e\u73b0\u7684\uff08\u8fd9\u79cd\u7535\u8def\u4e00\u822c\u88ab\u79f0\u4e3a \u949f\u63a7\u65f6\u5e8f\u7535\u8def(clocked sequential circuit)\uff0c\u7531\u4e8e\u8bbe\u8ba1\u76f8\u5bf9\u5bb9\u6613\uff0c\u9c81\u68d2\u6027\u5f3a\uff0c\u6240\u4ee5\u88ab\u5e7f\u6cdb\u5e94\u7528\uff09\u3002</p> <p>\u7f13\u51b2</p> <p>\u7f13\u51b2\u5668(buffer) \u4e00\u822c\u901a\u8fc7\u4e24\u4e2a\u975e\u95e8\u4e32\u8054\uff0c\u5e76\u5c06\u8f93\u5165\u8fde\u901a\u8f93\u51fa\u5b9e\u73b0\uff0c\u8fd9\u6837\u80fd\u591f\u5b9e\u73b0\u4fe1\u606f\u7684\u5b58\u50a8\uff0c\u7136\u800c\u65e0\u6cd5\u4fee\u6539\u3002\u800c\u9501\u5b58\u5668\u5c31\u662f\u5728\u7f13\u51b2\u5668\u7684\u57fa\u7840\u4e0a\uff0c\u5c06\u975e\u95e8\u66ff\u6362\u4e3a\u6216\u975e\u95e8\u6216\u4e0e\u975e\u95e8\u5b9e\u73b0\u7684\u3002</p> <p></p> <p>\u5176\u4e2d\uff0c\u4ece\u7ed9\u5b9a\u8f93\u5165\u5230\u66f4\u65b0\u8f93\u51fa\u6709\u4e00\u4e2a \\(t_G\\) \u7684\u5ef6\u65f6\u3002</p> <p>\u5f15\u5165</p> <p>\u663e\u7136\uff0c\u6839\u636e\u4e0a\u9762\u7684\u6982\u8ff0\uff0c\u65f6\u5e8f\u7535\u8def\u4e2d\u6700\u91cd\u8981\u7684\u5c31\u662f\u4fe1\u606f\u5b58\u50a8\u5143\u4ef6\u3002\u5f53\u8f93\u5165\u4fe1\u53f7\u4e0d\u53d1\u751f\u53d8\u5316\u65f6\uff08\u91cd\u70b9\u662f\u53d8\u5316\uff0c\u5373\u8f93\u5165\u548c\u5b58\u50a8\u4fe1\u606f\u672a\u5fc5\u5b58\u5728\u5bf9\u5e94\u5173\u7cfb\uff09\u5b58\u50a8\u5143\u4ef6\u5c31\u80fd\u591f\u4fdd\u6301\u5176\u5185\u90e8\u5b58\u50a8\u7684\u4e8c\u8fdb\u5236\u6570\u636e\u3002</p> <p>\u5b58\u50a8\u5143\u4ef6\u4e3b\u8981\u7531 \u9501\u5b58\u5668(latch) \u548c \u89e6\u53d1\u5668(flip-flop) \u4e24\u79cd\uff0c\u5176\u4e2d\u524d\u8005\u662f\u540e\u8005\u7684\u57fa\u7840\uff0c\u6216\u8005\u8bf4\u591a\u6570\u60c5\u51b5\u4e0b\u6211\u4eec\u4f7f\u7528\u540e\u8005\uff0c\u4f46\u540e\u8005\u7531\u524d\u8005\u6784\u6210\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap04/#\u9501\u5b58\u5668","title":"\u9501\u5b58\u5668","text":""},{"location":"cour_note/D2QD_DigitalDesign/Chap04/#sr--sr-\u9501\u5b58\u5668","title":"SR &amp; S'R' \u9501\u5b58\u5668","text":"<p>SR \u9501\u5b58\u5668\u548c S'R' \u9501\u5b58\u5668\u7684\u57fa\u672c\u539f\u7406\u662f\u4e00\u81f4\u7684\uff0c\u53ea\u4e0d\u8fc7\u524d\u8005\u7528\u7684\u662f\u6216\u975e\u95e8\uff0c\u540e\u8005\u7528\u7684\u662f\u4e0e\u975e\u95e8\u3002</p> <p>SR \u9501\u5b58\u5668\u548c S'R' \u9501\u5b58\u5668\u7684\u8f93\u5165\u90fd\u662f S(Set) \u548c R(Reset) \u4e24\u4e2a\u90e8\u5206\uff0c\u8f93\u51fa\u90fd\u662f Q \u548c Q' \u4e24\u4e2a\u90e8\u5206\u3002</p> <p>\u540d\u79f0\u4e0a \u7684\u5171\u540c\u70b9\u662f\uff0c\u5f53 S \u4e3a <code>1</code> \u65f6\uff0cQ \u90fd\u4f1a\u662f <code>1</code>\uff1b\u5bf9\u4e8e R \u548c Q' \u4e5f\u662f\u8fd9\u6837\uff0c\u53ea\u4e0d\u8fc7\u8981\u6ce8\u610f\uff0cS'R'\u9501\u5b58\u5668\u8f93\u5165\u7684\u5e76\u4e0d\u662f\u8fd9\u91cc\u6240\u8bf4\u7684 S\uff0c\u800c\u662f\u5c06 S' \u4f5c\u4e3a\u8f93\u5165\u3002</p> SR \u9501\u5b58\u5668S'R' \u9501\u5b58\u5668 <p> </p> <p> </p> <p>\u4e00\u4e2a\u8bb0\u5fc6\u65b9\u6cd5\u662f\uff0cSR \u7684\u95e8\u5143\u4ef6\u5bf9 <code>1</code> \u654f\u611f\uff0c\u6240\u4ee5\u662f \u6216\u975e\u95e8 \u7684\u5b9e\u73b0\uff1b\u800c S'R' \u7684\u95e8\u5143\u4ef6\u5bf9 <code>0</code> \u654f\u611f\uff0c\u6240\u4ee5\u662f \u4e0e\u975e\u95e8 \u7684\u5b9e\u73b0\u3002\u800c\u901a\u8fc7 \u300c\u5f53 S \u4e3a <code>1</code> \u65f6\uff0cQ \u90fd\u4f1a\u662f <code>1</code>\u300d\u53ef\u4ee5\u5f97\u5230 S\u3001R \u4e0e Q\u3001Q' \u7684\u4f4d\u7f6e\u3002</p> <p>\u4f46\u662f\u5b9e\u9645\u7684\u5b58\u50a8\u5143\u4ef6\u5e76\u4e0d\u662f\u5355\u7eaf\u7684 SR/S'R' Latches\uff0c\u6240\u4ee5\u5b83\u4eec\u5f53\u7136\u662f\u5b58\u5728\u95ee\u9898\u7684\u3002\u7531\u4e8e\u7535\u8def\u5b58\u5728\u5ef6\u65f6\uff0c\u6240\u4ee5 S \u548c R \u7684\u8f93\u5165\u5f88\u96be\u540c\u65f6\u5230\u8fbe\uff0c\u6240\u4ee5\u6211\u4eec\u53ef\u4ee5\u5728\u524d\u9762\u52a0\u4e00\u4e2a\u63a7\u5236\u7aef\uff0c\u5f53\u786e\u4fdd\u4e24\u4e2a\u8f93\u5165\u90fd\u5230\u4f4d\u7684\u65f6\u5019\u518d\u4f7f\u80fd\u3002</p> <p>\u4e8e\u662f\u6211\u4eec\u5f97\u5230\u4e86\uff0c\u5e26\u63a7\u5236\u8f93\u5165\u7684 SR \u9501\u5b58\u5668(SR Latch with Control Input)\uff08S'R'\u7565\uff09\uff1a</p> <p></p> <p>\u6ce8\u610f\uff01SR \u9501\u5b58\u5668\u901a\u8fc7 \u6216\u975e\u95e8 \u5b9e\u73b0\uff0c\u4f46\u5e26\u8f93\u5165\u63a7\u5236\u7684 SR \u9501\u5b58\u5668\u5219\u901a\u8fc7 \u4e0e\u975e\u95e8 \u5b9e\u73b0\uff01</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap04/#d-\u9501\u5b58\u5668","title":"D \u9501\u5b58\u5668","text":"<p>D \u9501\u5b58\u5668\u5b9e\u9645\u4e0a\u662f\u5e26\u63a7\u5236\u8f93\u5165\u7684 SR \u9501\u5b58\u5668\u7684\u6539\u8fdb\u3002\u5176\u4e2d\u6211\u4eec\u5173\u6ce8\u5230\uff0c\u867d\u7136 S \u548c R \u8d77\u4f5c\u7528\u7684\u6709\u4e09\u79cd\u72b6\u6001</p> <p>\u6211\u4eec\u5173\u6ce8\u5230\uff0c\u5373\u4f7f\u662f\u5e26\u63a7\u5236\u8f93\u5165\u7684 SR \u9501\u5b58\u5668\uff0c\u4e5f\u5b58\u5728\u4e00\u4e2a\u300cundefined\u300d\u72b6\u6001\uff0c\u800c\u8fd9\u662f\u6211\u4eec\u4e0d\u5e0c\u671b\u51fa\u73b0\u7684\uff0c\u4e8e\u662f\u6211\u4eec\u60f3\uff0c\u80fd\u4e0d\u80fd\u907f\u514d\u8fd9\u79cd\u60c5\u51b5\u7684\u53d1\u751f\u3002\u8fd9\u65f6\u5019\u6211\u4eec\u89c2\u5bdf\u5230\uff0c\u7531\u4e8e\u53ef\u4ee5\u901a\u8fc7 C \u6765\u63a7\u5236\u662f\u5426\u4fdd\u6301\uff0c\u6240\u4ee5\u53ef\u4ee5\u76f4\u63a5\u5f3a\u5236\u8981\u6c42 \\(S = \\overline R\\)\uff0c\u4e8e\u662f\u5c31\u907f\u514d\u4e86 undefined \u60c5\u51b5\u7684\u51fa\u73b0\uff0c\u8fd9\u5c31\u662f D \u9501\u5b58\u5668\u3002</p> <p></p> <p>\u53ea\u6709\u5f53 C \u4e3a <code>1</code> \u65f6\uff0cD \u9501\u5b58\u5668\u624d\u80fd\u5199\u5165\u6570\u636e\uff1b\u800c\u5f53 C \u4e3a <code>0</code> \u65f6\uff0cD \u9501\u5b58\u5668\u7684\u6570\u636e\u5c31\u4e0d\u4f1a\u53d8\u5316\u3002</p> <p>\u900f\u660e\u7684\u5371\u5bb3\uff1a\u7a7a\u7ffb</p> <p>\u5f53\u7136\uff0cD \u9501\u5b58\u5668\u4e5f\u5b58\u5728\u95ee\u9898\u3002\u5982\u679c\u6211\u95e8\u5c06 \\(\\overline Q\\) \u63a5\u5230 \\(D\\) \u4e0a\uff0c\u5c31\u4f1a\u53d1\u73b0 D \u9501\u5b58\u5668\u5c06\u4e0d\u505c\u7684\u53d8\u5316\u5176\u4e2d\u7684\u6570\u636e\uff0c\u51fa\u73b0 \u7a7a\u7ffb\uff0c\u5bfc\u81f4\u6211\u4eec\u65e0\u6cd5\u786e\u5b9a C \u7f6e <code>0</code> \u65f6 Q \u7684\u8f93\u51fa\u7a76\u7adf\u662f\u4ec0\u4e48\uff0c\u800c\u8fd9\u662f\u975e\u5e38\u5371\u9669\u7684\u3002</p> <p>\u8fd9\u4e3b\u8981\u662f\u56e0\u4e3a D \u9501\u5b58\u5668\u7684\u8f93\u5165\u548c\u8f93\u51fa\u90fd\u662f\u76f4\u63a5\u66b4\u9732\u51fa\u6765\u3001\u540c\u65f6\u5141\u8bb8\u53d8\u5316\u7684\uff08\u4e0d\u662f\u540c\u65f6\u53d8\u5316\uff0c\u662f\u6307\u5728 Input \u53ef\u4ee5\u53d8\u7684\u65f6\u5019 Output \u4e5f\u80fd\u53d8\uff09\uff0c\u5373 \u900f\u660e(transparent) \u7684\u3002\u8fd9\u5c31\u5bfc\u81f4\u4e86\u5728\u4e00\u4e2a\u65f6\u949f\u5468\u671f\u91cc\uff0c\u540c\u65f6\u5b58\u5728 \u53ef\u4ee5\u4e92\u76f8\u5f71\u54cd \u7684\u4e24\u4e2a\u4e1c\u897f\u3002\u8fd9\u4e5f\u662f\u89e6\u53d1\u5668\u6240\u89e3\u51b3\u7684\u95ee\u9898\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap04/#\u89e6\u53d1\u5668","title":"\u89e6\u53d1\u5668","text":"<p>\u4e3a\u4e86\u89e3\u51b3\u4e0a\u9762\u63d0\u5230\u7684\uff0c\u7531\u300c\u900f\u660e\u300d\u5f15\u53d1\u7684\u95ee\u9898\uff0c\u800c\u91c7\u7528\u89e6\u53d1\u5668\u7684\u8bbe\u8ba1\u3002\u901a\u8fc7\u7ec4\u5408\u4e24\u4e2a\u9501\u5b58\u5668\uff0c\u4e3b\u8981\u6709\u4e24\u79cd\u5b9e\u73b0\u65b9\u6cd5\uff1a</p> <ol> <li>\u5728\u6709\u8109\u51b2\uff08\u9ad8\u7535\u5e73\uff09\u65f6\uff0c\u4fee\u6539\u7b2c\u4e00\u4e2a\u9501\u5b58\u5668\u7684\u503c\uff0c\u4fdd\u6301\u7b2c\u4e8c\u4e2a\u9501\u5b58\u5668\u7684\u503c\uff1b\u5728\u6ca1\u6709\u8109\u51b2\uff08\u4f4e\u7535\u5e73\uff09\u65f6\u5019\u4fdd\u6301\u7b2c\u4e00\u4e2a\u9501\u5b58\u5668\u7684\u503c\uff0c\u4fee\u6539\u7b2c\u4e8c\u4e2a\u9501\u5b58\u5668\u7684\u503c\uff0c\u66f4\u65b0\u89e6\u53d1\u5668\u7684\u72b6\u6001\uff0c\u5373 \u4e3b\u4ece\u5f0f(master-slave)\u89e6\u53d1\u5668\uff1b</li> <li>\u4ec5\u5728\u65f6\u949f\u7684\u8fb9\u7f18\u89e6\u53d1\uff0c\u5373\u5728\u7279\u5b9a\u65f6\u523b\u4ec5\u63a5\u53d7\u4e00\u4e2a\u8f93\u5165\uff0c\u5373 \u8fb9\u6cbf\u89e6\u53d1\u5f0f(edge-triggered)\u89e6\u53d1\u5668\uff1b</li> </ol> <p>\u8fb9\u6cbf\u89e6\u53d1\u5f0f D \u89e6\u53d1\u5668\u662f\u76ee\u524d\u4f7f\u7528\u6700\u5e7f\u6cdb\u7684\u89e6\u53d1\u5668\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap04/#sr-\u4e3b\u4ece\u89e6\u53d1\u5668","title":"SR \u4e3b\u4ece\u89e6\u53d1\u5668","text":"<p>\u867d\u7136\u5b83\u53eb FF\uff0c\u4f46\u5b83\u5e76\u4e0d\u7b26\u5408 FF \u7684\u7279\u5f81\uff0c\u7136\u800c\u5206\u7c7b\u4e0a\u53c8\u5c5e\u4e8e pulse-triggered FF\u3002</p> <p>SR \u89e6\u53d1\u5668\u77e5\u6240\u4ee5\u662f\u6240\u8c13\u7684 pulse-triggered \u7684\uff0c\u662f\u56e0\u4e3a\u5728 S \u548c R \u8f93\u5165\u90fd\u4e3a <code>0</code> \u65f6\uff0c\u5982\u679c\u51fa\u73b0\u566a\u97f3\uff0c\u5c31\u4f1a\u5bfc\u81f4 Slave \u5199\u5165\u5f02\u5e38\u6570\u636e\u3002</p> <p>\u4f46\u662f\u6211\u4e2a\u4eba\u8ba4\u4e3a\u8fd9\u662f SR \u81ea\u8eab\u6709\u4e24\u4e2a\u4fdd\u6301\u6001\u5bfc\u81f4\u7684\u5f0a\u7aef\uff0c\u800c\u5728\u5b9e\u9645\u4f7f\u7528\u8fc7\u7a0b\u4e2d\u6211\u4eec\u5c31\u4e0d\u5e94\u8be5\u6709\u8f93\u5165\u4e3a S \u548c R \u90fd\u4e3a <code>0</code> \u7684\u60c5\u51b5\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap04/#\u8fb9\u6cbf\u89e6\u53d1\u5f0f\u89e6\u53d1\u5668","title":"\u8fb9\u6cbf\u89e6\u53d1\u5f0f\u89e6\u53d1\u5668","text":"<p>\u4e0a\u9762\u5df2\u7ecf\u8bf4\u8fc7\u4e86\uff0c\u8fb9\u6cbf\u89e6\u53d1\u5f0f\u89e6\u53d1\u5668\u4e3b\u8981\u5bf9\u8109\u51b2\u7684 \u4e0a\u5347\u6cbf \u6216 \u4e0b\u964d\u6cbf \u654f\u611f\u3002</p> <p>\u4e0b\u56fe\u4e3a\u6b63\u8fb9\u6cbf\u89e6\u53d1 D \u89e6\u53d1\u5668\u7684\u5927\u81f4\u539f\u7406\u56fe\u3002</p> <p></p> <p>\u5173\u6ce8\u4e0a\u5347\u6cbf\u524d\u540e\uff0c\u4e0a\u5347\u6cbf\u524d\u4e00\u523b\uff0c\u4e3b\u9501\u5b58\u5668\u53ef\u5199\uff0c\u4ece\u9501\u5b58\u5668\u53ea\u8bfb\uff1b\u4e0a\u5347\u6cbf\u540e\u4e00\u523b\uff0c\u4e3b\u9501\u5b58\u5668\u53ea\u8bfb\uff0c\u4ece\u9501\u5b58\u5668\u53ea\u5199\uff0c\u4e14\u5199\u5165\u7684\u662f\u4e3b\u9501\u5b58\u5668\u5b58\u50a8\u7684\u503c\u2014\u2014\u6362\u53e5\u8bdd\u6765\u8bf4\uff0c\u5b58\u7684\u662f\u4e0a\u5347\u6cbf\u524d\u4e00\u523b\u5199\u5165\u4e3b\u9501\u5b58\u5668\u7684\u5185\u5bb9\u3002</p> <p>\u9700\u8981\u6ce8\u610f\u7684\u4e00\u70b9\u662f\uff0cD \u89e6\u53d1\u5668\u6ca1\u6709\u300c\u4fdd\u6301\u300d\u6001\u3002\u5982\u679c\u8981\u4f7f D \u89e6\u53d1\u5668\u4fdd\u6301\uff0c\u53ef\u4ee5\u4f7f\u65f6\u949f\u8109\u51b2\u5931\u6548\u6216\u901a\u8fc7 <code>MUX</code> \u5c06\u8f93\u51fa\u63a5\u5230\u8f93\u5165\u5b9e\u73b0\u3002\u5176\u4e2d\u524d\u8005\u4e0d\u592a\u5e38\u7528\uff0c\u56e0\u4e3a\u53d7\u95e8\u63a7\u7684\u65f6\u949f\u8109\u51b2\u8fdb\u5165\u89e6\u53d1\u5668\u65f6\u6709\u5ef6\u8fdf\uff0c\u5373 \u65f6\u949f\u504f\u79fb(clock skew)</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap04/#\u6807\u51c6\u56fe\u5f62\u7b26\u53f7","title":"\u6807\u51c6\u56fe\u5f62\u7b26\u53f7","text":"<p>\u5e26\u5706\u5708\u8868\u793a\u8d1f\u903b\u8f91\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap04/#\u76f4\u63a5\u8f93\u5165","title":"\u76f4\u63a5\u8f93\u5165","text":"<p>\u8fd9\u4e9b\u76f4\u63a5\u8f93\u5165\u5f80\u5f80\u662f\u5f02\u6b65\u7684\uff0c\u4e00\u822c\u7528\u6765\u5f02\u6b65\u7f6e\u4f4d\uff08\u76f4\u63a5\u7f6e\u4f4d\u6216\u9884\u7f6e\uff09\u6216\u5f02\u6b65\u590d\u4f4d\uff08\u76f4\u63a5\u590d\u4f4d\u6216\u6e05\u96f6\uff09\u3002</p> <p>\u5bf9\u4e8e\u65f6\u5e8f\u7535\u8def\u6765\u8bf4\uff0c\u300c\u590d\u4f4d\u300d\u6216\u300c\u7f6e\u4f4d\u300d\u8fd9\u79cd\u8f93\u5165\u5e38\u5e38\u4f5c\u4e3a\u521d\u59cb\u5316\uff0c\u5373\u786e\u5b9a\u5404\u4e2a\u89e6\u53d1\u5668\u7684\u300c\u521d\u59cb\u72b6\u6001\u300d\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap04/#\u65f6\u5e8f\u7535\u8def\u5206\u6790","title":"\u65f6\u5e8f\u7535\u8def\u5206\u6790","text":"<p>\u4e3a\u4e86\u5206\u6790\u65f6\u5e8f\u7535\u8def\uff0c\u6211\u4eec\u9700\u8981\u4e00\u4e9b\u5de5\u5177\u6765\u8868\u793a\u65f6\u5e8f\u7535\u8def\u7684\u4e00\u4e9b\u7279\u5f81\u4e0e\u903b\u8f91\u3002\u89c2\u5bdf\u65f6\u5e8f\u7535\u8def\u548c\u7ec4\u5408\u7535\u8def\u7684\u533a\u522b\uff0c\u53d1\u73b0\u6700\u6838\u5fc3\u7684\u5c31\u662f\u903b\u8f91\u8fd0\u7b97\u8fc7\u7a0b\u4e2d\u51fa\u73b0\u4e86\u300c\u72b6\u6001\u300d\u53c2\u4e0e\u8fd0\u7b97\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u9700\u8981\u5728\u5404\u4e2a\u7ec4\u5408\u7535\u8def\u5206\u6790\u4e2d\u91c7\u7528\u7684\u8868\u793a\u65b9\u6cd5\u4e2d\uff0c\u6dfb\u52a0\u8868\u793a\u300c\u72b6\u6001\u300d\u7684\u4fe1\u606f\u3002</p> <p>\u9664\u6b64\u4e4b\u5916\uff0c\u5982\u679c\u53ea\u662f\u5355\u7eaf\u7684\u5c06\u300c\u72b6\u6001\u300d\u4f5c\u4e3a\u4e00\u4e2a\u65b0\u7684\u8f93\u5165\uff0c\u4f5c\u4e3a\u589e\u91cf\u6dfb\u52a0\u5230\u8868\u8fbe\u65b9\u5f0f\u4e2d\uff0c\u4f1a\u53d1\u73b0\u8fd9\u4e9b\u8868\u8ff0\u4f1a\u663e\u5f97\u5f88\u91cd\u3002\u6240\u4ee5\u6211\u4eec\u4e5f\u9700\u8981\u5bfb\u627e\u4e00\u79cd\u66f4\u597d\u7684\u529e\u6cd5\u6765\u8868\u8fbe\u65f6\u5e8f\u7535\u8def\u4e2d\u7684\u903b\u8f91\uff0c\u8fd9\u5c31\u662f\u300c\u72b6\u6001\u56fe\u300d\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap04/#\u89e6\u53d1\u5668\u7684\u8f93\u5165\u65b9\u7a0b","title":"\u89e6\u53d1\u5668\u7684\u8f93\u5165\u65b9\u7a0b","text":"<p>\u89e6\u53d1\u5668\u7684\u8f93\u5165\u65b9\u7a0b(flip-flop input equation) \u4e3b\u8981\u662f\u4e3a\u5176\u63d0\u4f9b\u4e00\u4e2a\u4ee3\u6570\u8868\u8fbe\u65b9\u5f0f\u3002\u5b83\u7684\u4e3b\u8981\u60f3\u6cd5\u662f\u24f5\u8868\u8fbe\u6bcf\u4e00\u4e2a\u89e6\u53d1\u5668\u7684\u8f93\u5165\u4e0e\u8f93\u51fa\u4e4b\u95f4\u7684\u5173\u7cfb\uff1b\u24f6\u8868\u8fbe\u6bcf\u4e00\u4e2a\u76f4\u63a5\u8f93\u51fa\u7684\u903b\u8f91\u8868\u8fbe\u5f0f\u3002\u5176\u4e2d\uff0c\u89e6\u53d1\u5668\u7684\u8f93\u51fa\u7b26\u53f7\u8868\u793a\u4e86\u5176\u7c7b\u578b\uff08\u5373\u7b26\u53f7\uff09\u4e0e\u8f93\u51fa\uff08\u5373\u4e0b\u6807\uff09\u3002</p> <p>\u5177\u4f53\u6765\u8bf4\uff0c\u4f8b\u5982\u4e0b\u9762\u8fd9\u4e2a\u7535\u8def\uff1a</p> <p></p> <p>\u53ef\u4ee5\u53d1\u73b0\uff0c\u5176\u4e2d\u5305\u542b\u4e24\u4e2a\u89e6\u53d1\u5668 \\(D_A\\) \u548c \\(D_B\\)\uff0c\u4ee5\u53ca\u4e00\u4e2a\u7ec4\u5408\u903b\u8f91\u8f93\u51fa \\(Y\\)\uff0c\u56e0\u800c\u53ef\u4ee5\u6839\u636e\u7535\u8def\u7684\u7279\u5f81\uff0c\u5f97\u5230\u4e0b\u9762\u8fd9\u51e0\u4e2a\u5f0f\u5b50\uff1a</p> \\[ \\begin{aligned}     D_A &amp; = AX + BX \\\\     D_B &amp; = \\overline{A}X \\\\     Y   &amp; = (A + B)\\overline{X} \\end{aligned} \\]"},{"location":"cour_note/D2QD_DigitalDesign/Chap04/#\u72b6\u6001\u8868","title":"\u72b6\u6001\u8868","text":"<p>\u5f53\u7136\uff0c\u65f6\u5e8f\u7535\u8def\u7684\u903b\u8f91\u6709\u65f6\u5019\u4e5f\u53ef\u4ee5\u901a\u8fc7\u72b6\u6001\u8868\u6765\u63cf\u8ff0\uff0c\u53ea\u4e0d\u8fc7\u4e0e\u7ec4\u5408\u7535\u8def\u7684 \u771f\u503c\u8868 \u4e0d\u540c\uff0c\u72b6\u6001\u8868(state table) \u6709\u56db\u680f\uff1a\u5f53\u524d\u72b6\u6001(present state)\u3001\u8f93\u5165(input)\u3001\u4e0b\u4e00\u72b6\u6001(next state)\u3001\u8f93\u51fa(output)\u3002\u5176\u542b\u4e49\u662f\u6bd4\u8f83\u663e\u7136\u7684\uff0c\u53ea\u4e0d\u8fc7\u9700\u8981\u901a\u8fc7\u7535\u8def\u56fe\u5f97\u5230\u72b6\u6001\u8868\uff0c\u9700\u8981\u9996\u5148\u5f97\u5230\u300c\u5f53\u524d\u72b6\u6001\u300d\u5411\u300c\u4e0b\u4e00\u72b6\u6001\u300d\u8f6c\u79fb\u7684\u65b9\u7a0b\uff0c\u5373\u5bf9\u4e8e\u67d0\u4e2a\u65f6\u523b \\(t\\) \u7684\u89e6\u53d1\u5668 \\(A\\) \u7684\u8f93\u51fa \\(A(t)\\)\uff0c\u9700\u8981\u5f97\u5230\u5b83\u4e0b\u4e00\u523b\u7684\u72b6\u6001 \\(A(t+1) = f(A(t), ...)\\)\u3002</p> <p>\u540c\u6837\u4ee5\u8fd9\u4e2a\u7535\u8def\u4e3a \ud83c\udf30\uff1a</p> <p></p> <p>\u9996\u5148\u6211\u4eec\u5bf9 \\(D_A\\) \u5f97\u5230\u8f6c\u79fb\u65b9\u7a0b\uff1a\\(A(t+1) = D_A = A(t)X + B(t)X\\)\uff0c\u53ef\u4ee5\u7b80\u5199\u4e3a \\(A(t+1) = D_A = AX+BX\\)\u3002\u7c7b\u4f3c\u5730\u4e5f\u80fd\u5f97\u5230 \\(B\\) \u7684\u8f6c\u79fb\u65b9\u7a0b\u3002</p> <p>\u4e8e\u662f\uff0c\u6839\u636e\u8fd9\u4e9b\u4fe1\u606f\uff0c\u6211\u4eec\u53ef\u4ee5\u5199\u51fa\u5b83\u7684\u72b6\u6001\u8868\uff1a</p> Present State<code>AB</code> Input<code>X</code> Next State<code>AB</code> Output<code>Y</code> <code>00</code> <code>0</code> <code>00</code> <code>0</code> <code>00</code> <code>1</code> <code>01</code> <code>0</code> <code>01</code> <code>0</code> <code>00</code> <code>1</code> <code>01</code> <code>1</code> <code>11</code> <code>0</code> <code>10</code> <code>0</code> <code>00</code> <code>1</code> <code>10</code> <code>1</code> <code>10</code> <code>0</code> <code>11</code> <code>0</code> <code>00</code> <code>1</code> <code>11</code> <code>1</code> <code>10</code> <code>0</code> <p>Mealy model circuit &amp; Moore model circuit</p> <p>\u5982\u679c\u8f93\u51fa\u65e2\u4f9d\u8d56\u4e8e\u5f53\u524d\u72b6\u6001\uff0c\u4e5f\u4f9d\u8d56\u4e8e\u8f93\u5165\u7684\u65f6\u5e8f\u7535\u8def\uff0c\u5219\u79f0\u4e3a \u7c73\u52d2\u578b\u7535\u8def(Mealy model circuit)\uff1b\u800c\u5982\u679c\u8f93\u51fa\u53ea\u4f9d\u8d56\u4e8e\u5f53\u524d\u72b6\u6001\uff0c\u5219\u79f0\u4e3a \u6469\u5c14\u578b\u7535\u8def(Moore model circuit)\u3002</p> <p>\u5728 \u72b6\u6001\u56fe \u4e2d\uff0c\u6211\u4eec\u8fd8\u5c06\u518d\u4e00\u6b21\u9047\u5230\u8fd9\u4e24\u4e2a\u4eba\u540d\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap04/#\u72b6\u6001\u56fe","title":"\u72b6\u6001\u56fe","text":"<p>\u53ef\u4ee5\u53d1\u73b0\uff0c\u72b6\u6001\u8868\u6bd4\u8f83\u6e05\u6670\u7684\u8868\u8fbe\u4e86\u4e0d\u540c\u7684\u72b6\u6001\u548c\u8f93\u5165\u5f97\u5230\u7684\u7ed3\u679c\uff0c\u4f46\u662f\u5bf9\u4e8e\u300c\u4e0d\u540c\u72b6\u6001\u4e4b\u95f4\u662f\u5982\u4f55\u8f6c\u6362\u7684\u300d\u8fd9\u4ef6\u4e8b\u7684\u63cf\u8ff0\u5e76\u4e0d\u6e05\u6670\u3002\u800c\u5bf9\u4e8e\u300c\u8054\u7cfb\u300d\u8fd9\u4ef6\u4e8b\uff0c\u6709\u5411\u56fe\u662f\u4e00\u4e2a\u975e\u5e38\u597d\u7684\u5f62\u5f0f\uff0c\u6240\u4ee5\u6211\u4eec\u5c06\u4ecb\u7ecd \u72b6\u6001\u56fe(state diagram)\u3002</p> <p>\u72b6\u6001\u56fe\u627f\u8f7d\u7684\u4fe1\u606f\u91cf\u548c\u72b6\u6001\u8868\u662f\u4e00\u6837\u7684\uff0c\u6240\u4ee5\u4e5f\u662f\u9700\u8981\u8868\u8fbe \u5f53\u524d\u72b6\u6001(present state)\u3001\u8f93\u5165(input)\u3001\u4e0b\u4e00\u72b6\u6001(next state)\u3001\u8f93\u51fa(output) \u8fd9\u56db\u4e2a\u4e1c\u897f\u3002\u53ea\u4e0d\u8fc7\u300c\u4e0b\u4e00\u72b6\u6001\u300d\u662f\u901a\u8fc7\u6709\u5411\u8fb9\u6765\u8868\u793a\u7684\u3002\u5f53\u524d\u72b6\u6001\u4f5c\u4e3a\u4e00\u4e2a node \u7684\u5c5e\u6027\uff1b\u800c\u8f93\u5165\u4f5c\u4e3a edge \u7684\u4e00\u4e2a\u5c5e\u6027\uff1b\u81f3\u4e8e\u8f93\u51fa\uff0c\u6839\u636e\u5b83\u662f\u653e\u5728 edge \u4e0a\u8fd8\u662f node \u4e0a\uff0c\u5206\u4e3a \u7c73\u52d2\u578b(Mealy) \u548c \u6469\u5c14\u578b(Moore) \u4e24\u79cd\u3002</p> <p>Mealy</p> <p>\u4f8b\u5982\uff0c\u8fd9\u662f\u4e00\u4e2a \u7c73\u52d2\u578b \u7684\u72b6\u6001\u56fe\uff0c\u4ee5\u53ca\u5bf9\u5e94\u7684\u72b6\u6001\u8868\u3002</p> <p></p> <p>\u56e0\u4e3a\u7c73\u52d2\u578b\u7535\u8def\u7684 \u8f93\u51fa\u4e0e\u5f53\u524d\u72b6\u6001\u548c\u8f93\u5165\u90fd\u6709\u5173\uff0c\u6240\u4ee5\u8f93\u51fa\u4f1a\u548c\u8f93\u5165\u653e\u5728\u4e00\u8d77\uff0c\u5373\u653e\u5728 edge \u91cc\u3002</p> <p>\u5bf9\u4e8e\u7c73\u52d2\u578b\uff0cnode \u5185\u7684\u4e8c\u8fdb\u5236\u4e3a present state \u4e2d\u7684 <code>AB</code>\uff1bedge \u4e0a\u5206\u522b\u4e3a input \u548c output\uff1a<code>X</code>/<code>Y</code>\uff1b\u6709\u5411\u8fb9\u8868\u8fbe\u4e86\u6bcf\u4e2a\u72b6\u6001\u5728\u7279\u5b9a\u8f93\u5165\u4e0b\u7684\u4e0b\u4e00\u4e2a\u72b6\u6001\u3002</p> <p>\u4f8b\u5982\uff0c\u5173\u6ce8 node <code>00</code>\uff0c\u5b83\u6709\u4e00\u6761\u81ea\u73af <code>0</code>/<code>0</code>\uff0c\u5bf9\u5e94 \u72b6\u6001\u8868 \u7684\u7b2c\u4e00\u884c\uff1b\u5b83\u6709\u4e00\u6761 edge <code>1</code>/<code>0</code> \u6307\u5411 node <code>01</code>\uff0c\u5bf9\u5e94 \u72b6\u6001\u8868\u7684\u7b2c\u4e8c\u884c\u3002</p> <p>\u5f53\u7136\uff0c\u7c73\u52d2\u578b\u662f\u6709 \u7f3a\u9677 \u7684\uff0c\u5728\u65f6\u5e8f\u7535\u8def\u8bbe\u8ba1\u4e4b\u540e\u7684\u6b65\u9aa4\u4e2d\uff0c\u6211\u4eec\u9700\u8981\u6839\u636e\u5b83\u6765\u5bf9\u6bcf\u4e00\u4e2a\u72b6\u6001\u8bbe\u8ba1\u8f93\u51fa\u65b9\u7a0b\u3002\u6b64\u65f6\u7531\u4e8e\u4e24\u4e2a\u8f93\u51fa\u5171\u4eab\u540c\u4e00\u4e2a\u76ee\u6807\u72b6\u6001\uff0c\u6240\u4ee5\u6211\u4eec\u9700\u8981\u5c06\u4e24\u4e2a\u8f93\u51fa\u7ed3\u5408\u5230\u540c\u4e00\u4e2a\u5f0f\u5b50\u4e2d\uff0c\u8fd9\u5c06\u63d0\u9ad8\u8bbe\u8ba1\u96be\u5ea6\u548c\u7ec4\u5408\u7535\u8def\u6210\u672c\u3002</p> <p>Moore</p> <p>\u800c\u4e0b\u9762\u662f\u4e00\u4e2a \u6469\u5c14\u578b \u7684\u72b6\u6001\u56fe\uff0c\u4ee5\u53ca\u5bf9\u5e94\u7684\u72b6\u6001\u8868\u3002</p> <p></p> <p>\u56e0\u4e3a\u6469\u5c14\u578b\u7535\u8def\u7684 \u8f93\u51fa\u53ea\u4e0e\u5f53\u524d\u72b6\u6001\u6709\u5173\uff0c\u6240\u4ee5\u8f93\u51fa\u4f1a\u548c\u5f53\u524d\u72b6\u6001\u653e\u5728\u4e00\u8d77\uff0c\u5373\u653e\u5728 node \u91cc\u3002</p> <p>\u5bf9\u4e8e\u6469\u5c14\u578b\uff0cnode \u5185\u7684\u4e8c\u8fdb\u5236\u8868\u793a present state \u548c output\uff1a<code>A</code>/<code>Z</code>\uff1bedge \u4e0a\u5217\u4e3e\u4e86\u8fd9\u79cd\u8f6c\u79fb\u53ef\u80fd\u7684 inputs\uff1a<code>XY</code>\u3002</p> <p>\u4f8b\u5982\uff0c\u5173\u6ce8 node <code>0</code>/<code>0</code>\uff0c\u5b83\u6709\u4e24\u6761\u81ea\u73af <code>00</code> \u548c <code>11</code>\uff0c\u5206\u522b\u5bf9\u5e94 \u72b6\u6001\u8868 \u7684\u7b2c\u4e00\u884c\u548c\u7b2c\u56db\u884c\uff1b\u5b83\u6709\u4e24\u6761 edge <code>01</code> \u548c <code>10</code> \u6307\u5411 node <code>1</code>/<code>1</code>\uff0c\u5bf9\u5e94 \u72b6\u6001\u8868 \u7684\u7b2c\u4e8c\u884c\u548c\u7b2c\u4e09\u884c\u3002</p> <p>\u6469\u5c14\u578b\u4e5f\u5b58\u5728 \u7f3a\u9677 \u7684\uff0c\u975e\u5e38\u663e\u7136\uff0c\u76f8\u6bd4\u4e8e\u7c73\u52d2\u578b\uff0c\u6469\u5c14\u578b\u9700\u8981\u66f4\u591a\u7684\u72b6\u6001\u3002</p> <p>\u6362\u53e5\u8bdd\u6765\u8bf4\uff0c\u7c73\u52d2\u578b\u503e\u5411\u4e8e\u8868\u8fbe\u300c\u5728\u7279\u5b9a\u72b6\u6001\u4e0b\uff0c\u7279\u5b9a\u8f93\u5165\u5c06\u5bfc\u81f4\u67d0\u79cd\u7ed3\u679c\uff0c\u4ee5\u53ca\u72b6\u6001\u8f6c\u79fb\u300d\uff1b\u800c\u6469\u5c14\u578b\u503e\u5411\u4e8e\u8868\u8fbe\u300c\u7279\u5b9a\u8f93\u5165\u5c06\u5bfc\u81f4\u67d0\u4e2a\u72b6\u6001\u5411\u53e6\u5916\u4e00\u4e2a\u72b6\u6001\u8f6c\u79fb\uff0c\u800c\u8f93\u51fa\u66f4\u50cf\u662f\u4e00\u79cd\u72b6\u6001\u7684\u7ed3\u679c\u300d\u3002</p> <p>\u72b6\u6001\u56fe\u8fd8\u6709\u8fdb\u9636\u5f62\u6001\uff0c\u4e4b\u540e\u4f1a\u63d0\u53ca\uff0c\u5c31\u662f \u72b6\u6001\u673a\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap04/#\u7b49\u4ef7\u72b6\u6001","title":"\u7b49\u4ef7\u72b6\u6001","text":"<p>\u6682\u7565</p> <p>\u5ef6\u65f6\u5206\u6790</p> <p>\u5ef6\u65f6\u5206\u6790\u662f\u4e00\u4e2a\u91cd\u96be\u70b9\uff0c\u5bf9\u4e8e\u65f6\u5e8f\u7535\u8def\u7684\u5ef6\u65f6\u5206\u6790\uff0c\u5c06\u5728\u4e4b\u540e\u5355\u72ec\u5f00\u4e00\u4e2a\u5c0f\u7ed3\u91cd\u70b9\u4ecb\u7ecd\u3002</p> <p>\u8bf7\u53c2\u8003 \u5ef6\u65f6\u5206\u6790\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap04/#\u65f6\u5e8f\u7535\u8def\u7684\u8bbe\u8ba1","title":"\u65f6\u5e8f\u7535\u8def\u7684\u8bbe\u8ba1","text":"<p>\u7c7b\u6bd4\u7ec4\u5408\u903b\u8f91\u7535\u8def\u901a\u8fc7\u771f\u503c\u8868\u8bbe\u8ba1\u7535\u8def\uff0c\uff08\u540c\u6b65\uff09\u65f6\u5e8f\u7535\u8def\u4e3b\u8981\u4f9d\u636e\u72b6\u6001\u8868\uff08\u6216\u7b49\u4ef7\u8868\u8fbe\uff0c\u5982\u72b6\u6001\u56fe\uff09\u6765\u8bbe\u8ba1\u7535\u8def\u3002\u5b9e\u9645\u8bbe\u8ba1\u4e2d\uff0c\u6211\u4eec\u9700\u8981\u8003\u8651\u89e6\u53d1\u5668\u4ee5\u53ca\u5176\u5b83\u7ec4\u5408\u7535\u8def\u7684\u9009\u62e9\u4e0e\u8bbe\u8ba1\uff1a</p> <ul> <li>\u89e6\u53d1\u5668\u7684\u6570\u91cf\u57fa\u672c\u53d6\u51b3\u4e8e\u6574\u4e2a\u9700\u6c42\u4e2d \u72b6\u6001 \u7684\u6570\u91cf\uff0c\\(n\\) \u4e2a\u89e6\u53d1\u5668\u80fd\u591f\u8868\u8fbe \\(2^n\\) \u4e2a\u4e8c\u8fdb\u5236\u72b6\u6001\uff1b</li> <li>\u7ec4\u5408\u7535\u8def\u7684\u4e3b\u8981\u8bbe\u8ba1\u56f4\u7ed5 \u89e6\u53d1\u5668 \u7684 \u8f93\u5165 \u548c \u8f93\u51fa \u5c55\u5f00\uff1b</li> </ul> <p>\u800c\u4e3b\u8981\u7684\u8bbe\u8ba1\u8fc7\u7a0b\u548c\u7ec4\u5408\u903b\u8f91\u7535\u8def\u7684\u8bbe\u8ba1\u662f\u7c7b\u4f3c\u7684\uff0c\u5982\u4e0b\uff1a</p> <ol> <li>\u786e\u5b9a\u7cfb\u7edf\u7684\u884c\u4e3a\uff1b<ol> <li>\u63cf\u8ff0\u7cfb\u7edf\u884c\u4e3a\u8fc7\u7a0b\u4e2d\uff0c\u8981\u6ce8\u610f\u72b6\u6001\u7684\u590d\u7528\uff08\u4e0d\u8fc7\u5e76\u975e\u72b6\u6001\u8d8a\u5c11\u6210\u672c\u5c31\u8d8a\u5c0f\uff0c\u8fd9\u91cc\u6709\u89e6\u53d1\u5668\u6570\u91cf\u548c\u7ec4\u5408\u903b\u8f91\u7535\u8def\u7684 trade-off\uff09\uff1b</li> <li>\u786e\u5b9a\u7535\u8def\u7684\u521d\u59cb\u72b6\u6001\uff08\u590d\u4f4d\u72b6\u6001(reset state)\uff0c\u901a\u8fc7\u7ed9\u5b9a\u590d\u4f4d(reset)\u4fe1\u53f7\u5b9e\u73b0\uff09\uff1b<ul> <li>\u590d\u4f4d\u4e00\u822c\u53ef\u4ee5\u662f\u5f02\u6b65\u7684\uff1b</li> </ul> </li> </ol> </li> <li>\u9610\u8ff0\u8f93\u5165\u548c\u8f93\u51fa\u4e4b\u95f4\u7684\u903b\u8f91\u5173\u7cfb\uff0c\u5e76\u7528\u771f\u503c\u8868\u6216\u903b\u8f91\u8868\u8fbe\u5f0f\u8868\u8fbe\u51fa\u6765\uff1b</li> <li>\u7ed9\u8bbe\u8ba1\u597d\u7684\u72b6\u6001\u7f16\u7801\u8d4b\u503c\uff0c\u5f97\u5230\u5177\u4f53\u7684\u72b6\u6001\u8868\uff1b<ol> <li>\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528 \u6309\u8ba1\u6570\u987a\u5e8f\u3001 \u6309\u683c\u96f7\u7801\u3001\u7528\u72ec\u70ed\u7801 \u6765\u7ed9\u72b6\u6001\u8d4b\u503c\uff0c\u66f4\u7cfb\u7edf\u7684\u65b9\u6cd5\u6bd4\u8f83\u590d\u6742\uff0c\u4e0d\u505a\u8ba8\u8bba\uff1b</li> <li>\u5176\u4e2d\u8fd8\u6709\u4e00\u79cd\u60c5\u51b5\u662f\u6240\u9700\u8981\u7684\u72b6\u6001\u4e0d\u80fd\u5b8c\u6574\u586b\u5145 \\(2^n\\) \u79cd\u60c5\u51b5\uff0c\u9700\u8981\u8bbe\u8ba1\u65e0\u6548\u72b6\u6001\uff0c\u8fd9\u79cd\u65f6\u5019\u53ef\u4ee5\u4e0d\u8003\u8651\u5b83\u4eec\uff1b</li> </ol> </li> <li>\u6839\u636e\u72b6\u6001\u8868\u786e\u5b9a\u4f7f\u7528\u7684\u89e6\u53d1\u5668\u53ca\u5176\u8f93\u5165\u65b9\u7a0b\uff1b</li> <li>\u6839\u636e\u72b6\u6001\u8868\u786e\u5b9a\u8f93\u51fa\u65b9\u7a0b\uff1b</li> <li>\u4f18\u5316\u8f93\u5165\u65b9\u7a0b\u548c\u8f93\u51fa\u65b9\u7a0b\uff1b</li> <li>\u5c06\u4f18\u5316\u540e\u7684\u903b\u8f91\u8bbe\u8ba1\u5de5\u827a\u6620\u5c04\u5230\u786c\u4ef6\u5b9e\u73b0\u4e0a\uff1b</li> <li>\u9a8c\u8bc1\u6b63\u786e\u6027\uff08\u5728\u4eff\u771f\u73af\u5883\u4e2d\uff09\uff1b<ul> <li>\u4e3b\u8981\u5c31\u662f\u770b\u80fd\u4e0d\u80fd\u590d\u73b0\u72b6\u6001\u56fe\uff1b</li> </ul> </li> </ol>"},{"location":"cour_note/D2QD_DigitalDesign/Chap04/#\u72b6\u6001\u673a","title":"\u72b6\u6001\u673a","text":"<p>\u5c3d\u7ba1\u5728\u5c0f\u89c4\u6a21\u7684\u8bbe\u8ba1\u4e2d\uff0c\u72b6\u6001\u56fe\u8868\u73b0\u826f\u597d\uff0c\u4f46\u662f\u968f\u7740\u8bbe\u8ba1\u7684\u7cfb\u7edf\u89c4\u6a21\u53d8\u5927\uff0c\u6211\u4eec\u9700\u8981\u4e00\u4e2a\u66f4\u52a0\u6cdb\u7528\u7684\u65b9\u5f0f\u6765\u8868\u8fbe\u7c7b\u4f3c\u7684\u65f6\u5e8f\u903b\u8f91\u3002</p> <p>\u4e8e\u662f\uff0c\u6211\u4eec\u5728\u72b6\u6001\u56fe\u7684\u57fa\u7840\u4e0a\u8fdb\u884c\u4fee\u6539\uff0c\u8bbe\u8ba1\u4e86 \u72b6\u6001\u673a(State-Machine Diagram) \u6765\u505a\u8fd9\u4ef6\u4e8b\u3002</p> <p>\u72b6\u6001\u673a\u6df7\u7528\u4e86\u7c73\u52d2\u578b\u548c\u6469\u5c14\u578b\u7684\u8f93\u51fa\u683c\u5f0f\uff0c\u4f18\u52a3\u5728 \u72b6\u6001\u56fe \u4e2d\u6709\u6240\u63d0\u53ca\u3002\u5e76\u4e14\uff0c\u6709\u9650\u56fe\u5c06\u72b6\u6001\u8f6c\u79fb\u65b9\u7a0b\u4e5f\u5199\u5165\uff0c\u603b\u4f53\u4e0a\u5bf9\u7535\u8def\u8bbe\u8ba1\u66f4\u53cb\u597d\u3002\u4e0b\u56fe\u662f\u72b6\u6001\u673a\u7684\u4e00\u4e2a\u201c\u8303\u5f0f\u201d\u3002</p> <p>Generic State Diagram Template</p> <p></p> <p>\u9996\u5148\u89e3\u91ca\u4e00\u4e0b\u8fd9\u4e2a\u201c\u8303\u5f0f\u201d\uff1a</p> <p>\u5177\u4f53\u89e3\u91ca\u72b6\u6001\u673a\u6709\u54ea\u4e9b\u5185\u5bb9\uff0c\u4ee5\u53ca\u5404\u4e2a\u90e8\u5206\u4e4b\u95f4\u7684\u903b\u8f91\u3002\u5173\u4e8e\u5404\u4e2a\u90e8\u5206\u51fa\u73b0\u7684\u4f4d\u7f6e\uff0c\u8bf7\u53c2\u8003 Template\u3002</p> <p>\u53e6\u5916\uff0c\u4e3a\u4e86\u7b80\u5316\u8bed\u53e5\uff0c\u4e0b\u9762\u7684\u8bf4\u6cd5\u7701\u7565\u4e86\u65f6\u949f\uff0c\u8bf7\u8bb0\u5f97\u8003\u8651\u3002</p> <p>\u72b6\u6001\u673a\u6a21\u578b\u4e3b\u8981\u6709\u4e09\u8981\u7d20\uff1a\u8f93\u5165\u6761\u4ef6(Input Conditions)\u3001\u72b6\u6001\u8f6c\u79fb(Transitions) \u548c \u8f93\u51fa\u884c\u4e3a(Output Actions)\u3002\u603b\u4f53\u6765\u8bf4\uff0c\u8f93\u5165\u6761\u4ef6\u544a\u8bc9\u6211\u4eec\u6574\u4e2a\u72b6\u6001\u673a\u8981\u5982\u4f55\u53d8\u5316\uff1b\u72b6\u6001\u8f6c\u79fb\u63cf\u8ff0\u4e86\u72b6\u6001\u673a\u7684\u5185\u90e8\u8f6c\u79fb\u884c\u4e3a\uff0c\u5373\u56fe\u8bba\u4e0a\u7684\u6709\u5411\u8054\u901a\u5173\u7cfb\uff1b\u8f93\u51fa\u884c\u4e3a\u63cf\u8ff0\u52a8\u6001\u53d8\u5316\u8fc7\u7a0b\u4e2d\u72b6\u6001\u673a\u7684\u5bf9\u5916\u8868\u8fbe\u3002\u5176\u4e2d\uff0c\u72b6\u6001\u8f6c\u79fb\u548c\u8f93\u51fa\u884c\u4e3a\u662f\u6211\u4eec\u9700\u8981\u5173\u6ce8\u7684\u72b6\u6001\u673a\u7684\u4e24\u4e2a\u7ef4\u5ea6\uff0c\u8f93\u5165\u6761\u4ef6\u662f\u6211\u4eec\u7528\u6765\u505a\u5b9e\u65f6\u5224\u65ad\u7684\u5916\u90e8\u4f9d\u636e\u3002</p> <p>\u300c\u8f93\u5165\u6761\u4ef6\u300d\u662f\u7531\u8f93\u5165\u53d8\u91cf\u5f62\u6210\u7684\u4e00\u4e2a\u5e03\u5c14\u65b9\u7a0b\uff0c\u5728\u6574\u4e2a\u72b6\u6001\u673a\u4e2d\uff0c\u8f93\u5165\u662f\u53d8\u5316\u7684\u201c\u56e0\u53d8\u91cf\u201d\uff0c\u6362\u53e5\u8bdd\u6765\u8bf4\uff0c\u65e0\u8bba\u662f\u72b6\u6001\u8f6c\u79fb\u8fd8\u662f\u8f93\u51fa\uff0c\u90fd\u53d6\u51b3\u4e8e\u8f93\u5165\u6761\u4ef6\u3002\u800c\u5bfc\u81f4\u7279\u5b9a\u884c\u4e3a\u7684\u8f93\u5165\u6761\u4ef6\u5219\u88ab\u5206\u7c7b\u4e3a \u8f6c\u79fb\u6761\u4ef6(Transition Condition, TC) \u548c \u8f93\u51fa\u6761\u4ef6(Output Condition, OC)\u3002</p> <p>\u300c\u72b6\u6001\u8f6c\u79fb\u300d\u5728\u56fe\u4e2d\u8868\u73b0\u4e3a\u6709\u5411\u8fb9\uff0c\u5f53 TC \u6210\u7acb\u65f6\uff0c\u72b6\u6001\u8f6c\u79fb\u53d1\u751f\uff1b\u6216\u8005\u5bf9\u4e8e\u65e0\u6761\u4ef6\u8f6c\u79fb\uff0c\u53ea\u8981\u5f97\u5230\u65f6\u949f\u8109\u51b2\u5c31\u4f1a\u8f6c\u79fb\u5230\u4e0b\u4e00\u4e2a\u72b6\u6001\u3002</p> <p>\u300c\u8f93\u51fa\u884c\u4e3a\u300d\u5728\u72b6\u6001\u673a\u4e2d\u6709\u56db\u79cd\u89e6\u53d1\u65b9\u6cd5\uff08\u5373\u56db\u79cd OC\uff09\uff1aMoore\u3001\u4e0d\u4f9d\u8d56\u8f6c\u79fb(Transition-condition Independent, TCI) Mealy\u3001\u4f9d\u8d56\u8f6c\u79fb(Transition-condition Dependent, TCD) Mealy \u548c \u4f9d\u8d56\u8f6c\u79fb\u548c\u8f93\u51fa\u6761\u4ef6(Transition and Output-condition Dependent, TOCD) Mealy\u3002\u6839\u636e\u5b57\u9762\u610f\u601d\u6765\u770b\uff1a</p> <ul> <li>Moore \u53ea\u4e0e\u72b6\u6001\u6709\u5173\uff0c\u6240\u4ee5\u5728\u56fe\u4e2d\u4ece\u72b6\u6001\u8282\u70b9\u5f15\u51fa\uff1b</li> <li>TCI Mealy \u4e0e\u72b6\u6001\u548c\u8f93\u51fa\u6761\u4ef6\u6709\u5173\uff0c\u6240\u4ee5\u5728\u56fe\u4e2d\u4ece\u72b6\u6001\u8282\u70b9\u5f15\u51fa\u5199\u5728 OC \u540e\u9762\uff08<code>OC</code>/<code>TCI OA</code>\uff09\uff1b</li> <li>TCD Mealy \u4e0e\u8f6c\u79fb\u6761\u4ef6\u6709\u5173\uff0c\u5f53\u8f6c\u79fb\u6210\u7acb\u7684\u65f6\u5019\u53d1\u751f Output Action\uff0c\u6240\u4ee5\u76f4\u63a5\u5199\u5728 TC \u540e\u9762\uff08<code>TC</code>/<code>TCD OA</code>\uff09\uff1b</li> <li>TOCD Mealy \u5728\u8f6c\u79fb\u53d1\u751f\u65f6\u5019\u624d\u53ef\u80fd\u6761\u4ef6\u6210\u7acb\uff0c\u5373\u5f53 TC \u548c OC \u90fd\u6210\u7acb\u65f6\u624d\u53d1\u751f Output Action\uff0c\u6240\u4ee5\u9700\u8981\u4ece TC \u5f15\u51fa OC\uff0c\u5e76\u8ddf\u5728 OC \u540e\u9762\uff08<code>TC</code>\u2014\u2014<code>OC</code>/<code>TOCD OA</code>\uff09\uff1b         - \u5982\u679c\u51fa\u73b0\u590d\u6570\u7684 TOCD OA\uff0c\u5219\u4f7f\u7528 <code>,</code> \u5206\u9694\uff1b</li> </ul> <p>In a given state, an output action occurs if: (a) it is unconditional (Moore), (b)  TCI and its output condition OC = 1, (c) TCD and its transition condition TD = 1, and (d) TOCD and its transition condition TC and output condition OC are both equal to 1, i.e, TC\u00b7OC = 1. Note that Moore and TCI output actions attached to a state, apply to all transitions from the state as well.</p> <p>\u56de\u5230\u8f93\u51fa\u884c\u4e3a\u672c\u8eab\uff0c\u5f53 OC \u6210\u7acb\u65f6\u8f93\u51fa\u884c\u4e3a\u53d1\u751f\uff0c\u4e00\u822c\u4f1a\u5c06\u8f93\u51fa\u53d8\u91cf\u6807\u51fa\uff0c\u5982\u679c\u5199\u7684\u662f NOT X\uff0c\u8868\u793a OC \u6210\u7acb\u65f6 X \u5e94\u4e3a <code>0</code>\uff1b\u5982\u679c\u5199\u7684\u662f X\uff0c\u5219\u8868\u793a OC \u6210\u7acb\u65f6 X \u4e3a <code>1</code>\u3002</p> <p>\u6ce8\u610f\u70b9</p> <p>\u6b64\u5916\uff0c\u8fd8\u6709\u4e00\u4e2a\u70b9\u9700\u8981\u8fa8\u6790\uff0c\u7531\u4e8e\u300cTransition\u300d\u8868\u793a\u7684\u662f\u201c\u4e0b\u4e00\u4e2a\u201d\u72b6\u6001\uff0c\u6240\u4ee5\u5bf9\u4e8e\u5f53\u524d\u65f6\u523b\uff0c\u5f53\u524d\u8282\u70b9\u7684\u8f93\u51fa\u548c\u51fa\u5ea6\u7684\u8f93\u51fa\u4e0d\u80fd\u51b2\u7a81\u3002\u4f8b\u5982\uff0c\u4e0b\u56fe\u56e0\u4e3a Moore \u8f93\u51fa\u884c\u4e3a\u7684 Z \u548c TC=AB \u90a3\u6761\u8fb9\u7684 Z' \u51b2\u7a81\uff0c\u6240\u4ee5\u975e\u6cd5\u3002</p> <p></p> <p>\u5f53\u7136\uff0c\u975e\u6cd5\u72b6\u6001\u673a\u5e76\u4e0d\u53ea\u6709\u8fd9\u4e00\u4e2a\u5224\u636e\u3002\u4e0d\u8fc7\u6838\u5fc3\u601d\u60f3\u5c31\u662f \u4e0d\u80fd\u6709\u6b67\u4e49\u6216\u51b2\u7a81\u4e14\u9700\u8981\u5145\u5206\uff0c\u66f4\u6570\u5b66\u7684\u8868\u8fbe\u662f\uff0c\u5fc5\u987b\u6ee1\u8db3\u5982\u4e0b\u4e24\u4e2a\u6761\u4ef6\uff1a</p> <p>1.\u975e\u4ea4\uff1a\u5bf9\u4e8e\u6bcf\u4e00\u4e2a\u72b6\u6001 \\(S_i\\)\uff0c\u5b83\u7684\u4efb\u610f\u4e24\u4e2a\u51fa\u5ea6 \\((T_{ij},T_{jk})\\) \u90fd\u4e0d\u80fd\u540c\u65f6\u6210\u7acb\uff0c\u5373\u5e94\u6709\uff1a</p> \\[ \\forall (T_{ij},T_{ik})\\;,\\;\\;T_{ij}\\cdot T_{ik} = 0 \\] <p>2.\u5145\u5206\uff1a\u5bf9\u4e8e\u6bcf\u4e00\u4e2a\u72b6\u6001 \\(S_i\\)\uff0c\u5b83\u7684\u6240\u6709\u51fa\u5ea6\u6761\u4ef6\u5e94\u8be5\u6db5\u76d6\u6240\u6709\u53ef\u80fd\uff0c\u5373\u5e94\u6709\uff1a</p> \\[ \\sum_{j}T_{ij} = 1 \\] <p>Tips: \u4e0a\u9762\u662f\u5bf9 Transition Condition \u7684\u7ea6\u675f\uff0c\u5c06 TC \u6362\u6210 OC \u4e5f\u9700\u8981\u6210\u7acb\u3002</p> \u7f29\u5199\u5bf9\u7167\u8868 \u7f29\u5199 \u542b\u4e49 \u6ce8\u91ca TC Transition Condition \u8f6c\u79fb\u6761\u4ef6\uff1a\u5bfc\u81f4 Transition \u7684 Input Condition OC Output Condition \u8f93\u51fa\u6761\u4ef6\uff1a\u5bfc\u81f4 Output Actions \u7684 Input Condition TCI Transition-condition Independent \u4e0d\u4f9d\u8d56\u8f6c\u79fb\uff1a\u53ea\u4e0e State \u6709\u5173\u7684 Output Actions TCD Transition-condition Dependent \u4f9d\u8d56\u8f6c\u79fb\uff1aTransition Condition \u6210\u7acb\u624d\u6709 Output Actions TOCD Transition and Output-condition Dependent \u4f9d\u8d56\u8f6c\u79fb\u548c\u8f93\u51fa\u65b9\u7a0b\uff1aTransition Condition \u548c Output Condition \u90fd\u6210\u7acb\u624d\u6709 Output Actions State Machine Diagram \ud83c\udf30 <p></p> <p>\u6ce8\u610f\uff0c\u56fe\u4e2d\u6709\u4e00\u4e2a\u9519\u8bef\uff08\u5927\u6982\uff09\uff0c\u53f3\u4fa7 \\(S_1\\) \u7684 OC \u5e94\u4e3a \\((\\overline{A}\\cdot\\overline{B})\\)\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap04/#\u5ef6\u65f6\u5206\u6790","title":"\u5ef6\u65f6\u5206\u6790","text":"<p>\u9996\u5148\uff0c\u81ea\u4e0a\u800c\u4e0b\u7684\u7ed9\u51fa\u89c2\u5ff5\uff0c\u65f6\u5e8f\u7535\u8def\u7684\u5ef6\u65f6\u5206\u6790\u6709\u4e24\u4e2a\u4e3b\u8981\u90e8\u5206\u548c\u4e00\u4e2a\u6b21\u8981\u90e8\u5206\uff1a</p> <ol> <li>\u7ec4\u5408\u7535\u8def\u5bfc\u81f4\u7684\u5ef6\u65f6\uff1b</li> <li>\u89e6\u53d1\u5668\u5bfc\u81f4\u7684\u5ef6\u65f6\uff1b</li> <li>\u7535\u8def\u7684\u677e\u5f1b\u65f6\u95f4\uff1b</li> </ol> <p>\u5e76\u4e14\u5f80\u5f80\u662f\u6839\u636e\u89e6\u53d1\u5668\u7684\u7c7b\u578b\uff0c\u8ba1\u7b97\u4e00\u4e2a\u65f6\u949f\u5468\u671f\u7684\u65f6\u95f4\u3002\u6700\u6838\u5fc3\u7684\u95ee\u9898\u5c31\u662f\u8ba1\u7b97\u7535\u8def\u80fd\u591f\u6b63\u5e38\u5de5\u4f5c\u7684\u6700\u77ed\u65f6\u949f\u5468\u671f\u3002\u63a5\u4e0b\u6765\uff0c\u81ea\u4e0b\u800c\u4e0a\u7684\u8fdb\u884c\u7ec6\u8282\u8865\u5145\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap04/#\u7ec4\u5408\u7535\u8def\u5ef6\u65f6","title":"\u7ec4\u5408\u7535\u8def\u5ef6\u65f6","text":"<p>\u8fd9\u4e00\u90e8\u5206\u7684\u8be6\u7ec6\u5185\u5bb9\u5df2\u7ecf\u5728 \u4e0a\u4e00\u7ae0 \u4ecb\u7ecd\u8fc7\u4e86\uff0c\u5728\u8fd9\u91cc\uff0c\u4e3a\u4e86\u7b80\u5316\u8ba1\u7b97\u8fc7\u7a0b\uff0c\u6211\u4eec\u5168\u90e8\u91c7\u7528 \\(t_{pd}\\)\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap04/#\u89e6\u53d1\u5668\u5ef6\u65f6","title":"\u89e6\u53d1\u5668\u5ef6\u65f6","text":"<p>\u89e6\u53d1\u5668\u5ef6\u65f6\u76f8\u6bd4\u7ec4\u5408\u7535\u8def\u5ef6\u65f6\u590d\u6742\u5f88\u591a\uff0c\u4e3b\u8981\u76ee\u7684\u662f\u4e3a\u4e86\u4fdd\u8bc1\u91c7\u6837\u3002\u4e5f\u5c31\u662f\u8bf4\u5b83\u7684\u201c\u5ef6\u65f6\u201d\u5e76\u4e0d\u4ec5\u4ec5\u662f\u56e0\u4e3a\u7535\u4fe1\u53f7\u4f20\u64ad\u7684\u5ef6\u8fdf\uff0c\u8fd8\u6709\u4e3a\u4e86\u4fdd\u8bc1\u4fe1\u53f7\u7a33\u5b9a\u8bbe\u8ba1\u7684\u4e00\u4e9b\u5185\u5bb9\u3002</p> <p>\u5927\u81f4\u6765\u8bf4\u6709\u4e09\u4e2a\u90e8\u5206\uff1a</p> <ul> <li>Setup Time\uff1a\u91c7\u6837\u8fb9\u7f18\u524d\u8f93\u5165\u4fe1\u53f7\u9700\u8981\u4fdd\u6301\u7a33\u5b9a\u7684\u65f6\u95f4\uff1b</li> <li>Hold Time\uff1a\u91c7\u6837\u8fb9\u7f18\u540e\u8f93\u5165\u4fe1\u53f7\u9700\u8981\u4fdd\u6301\u7a33\u5b9a\u7684\u65f6\u95f4\uff1b</li> <li>Propagation Time\uff1a\u89e6\u53d1\u5668\u7684\u91c7\u6837\u8fb9\u7f18\u5230\u8f93\u51fa\u7a33\u5b9a\u7684\u65f6\u95f4\uff08\u4f20\u64ad\u65f6\u95f4\uff09\uff1b</li> </ul> <p>\u4e00\u7bc7\u4ecb\u7ecd Setup Time \u548c Hold Time \u7684 \u6587\u7ae0\u3002</p> <p>\u6839\u636e\u89e6\u53d1\u5668\u7684\u7c7b\u578b\u4e0d\u540c\uff0c\u4e3b\u8981\u7684 Setup Time \u4e5f\u4e0d\u540c\uff1a</p> <p></p> <p>\u5176\u4e2d\u6bd4\u8f83\u91cd\u8981\u7684\u4e00\u4e9b\u70b9\u662f\uff1a</p> <ol> <li>\u8fd9\u51e0\u4e2a\u65f6\u95f4\u70b9\u8d77\u70b9/\u7ec8\u70b9\u90fd\u662f\u89e6\u53d1\u8fb9\u7f18\uff1b</li> <li>Propagation Time \u4e00\u5b9a\u957f\u4e8e Hold Time\uff0c\u56e0\u6b64\u5728\u8ba1\u7b97\u7535\u8def\u5ef6\u8fdf\u65f6\u53ea\u8003\u8651 Propagation Time\uff1b</li> <li>Pulse-trigger \u548c Edge-trigger \u5728\u8868\u73b0\u4e0a\u7684\u533a\u522b\u5728\u4e8e Setup Time\uff0c\u524d\u8005\u9700\u8981\u8986\u76d6\u6574\u4e2a pulse(<code>pos</code> or <code>neg</code>)\uff1b</li> </ol>"},{"location":"cour_note/D2QD_DigitalDesign/Chap04/#\u677e\u5f1b\u65f6\u95f4","title":"\u677e\u5f1b\u65f6\u95f4","text":"<p>\u5b9e\u9645\u4e0a\u8fd9\u5c31\u662f\u7ed9\u6574\u4e2a\u7535\u8def\u7684\u4e00\u4e2a\u201c\u5bb9\u5dee\u201d\u65f6\u95f4\uff0c\u7ed9\u5b9a\u4e00\u4e2a\u8bef\u5dee\uff0c\u4f46\u662f\u7531\u4e8e\u901a\u8fc7\u524d\u4e24\u8005\u8ba1\u7b97\u51fa\u6765\u7684\u662f\u6700\u77ed\u65f6\u95f4\uff0c\u6240\u4ee5\u677e\u5f1b\u65f6\u95f4\u5fc5\u5b9a\u975e\u8d1f\u3002\uff08\u4e0d\u80fd\u5012\u6263\uff01\uff09</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap04/#\u65f6\u5e8f\u7535\u8def\u5ef6\u65f6","title":"\u65f6\u5e8f\u7535\u8def\u5ef6\u65f6","text":"<p>\u65f6\u5e8f\u7535\u8def\u7684\u5ef6\u65f6\u8ba1\u7b97\u5b9e\u9645\u4e0a\u662f\u4e3a\u4e86\u8ba1\u7b97\u65f6\u5e8f\u7535\u8def\u8fd0\u4f5c\u7684\u6700\u5927\u9891\u7387\u4ee5\u8bbe\u8ba1\u65f6\u949f\u9891\u7387\u3002\u6240\u4ee5\u6211\u4eec\u9700\u8981\u7b97\u51fa\u7535\u8def\u80fd\u591f\u7a33\u5b9a\u5de5\u4f5c\u7684\u6700\u5c0f\u65f6\u949f\u671f\u3002</p> <p>\u5176\u8ba1\u7b97\u9075\u5faa\u4e00\u5b9a\u65b9\u6cd5\uff1a</p> <p></p> <p>\u56fe\u4e2d \\(t_{pd,FF}\\) \u6307\u89e6\u53d1\u5668\u7684 propagation time\uff0c\\(t_{COMB}\\) \u6307\u7ec4\u5408\u7535\u8def\u7684\u603b\u4f20\u64ad\u65f6\u95f4\uff08\u4e00\u822c\u60c5\u51b5\u4e0b \\(t_{COMB} = \\max{\\sum_i t_{pd,gate_i}}\\)\uff09\uff0c\\(t_{s}\\) \u6307\u89e6\u53d1\u5668\u7684 setup time\uff0c\\(t_{slack}\\) \u8868\u793a\u7535\u8def\u7684\u677e\u5f1b\u65f6\u95f4\u3002</p> <p>\uff08\u5047\uff09\u7ecf\u9a8c\u4e4b\u8c08</p> <p>\u4e00\u822c\u4ece\u4e00\u4e2a FF \u7684\u8f93\u51fa\u51fa\u53d1\u5230 FF \u7684\u8f93\u5165\u7ed3\u675f\u3002</p> <ul> <li> \u6211\u89c9\u5f97\u8fd9\u91cc\u5e94\u8be5\u662f\u9700\u8981\u6709\u4f8b\u9898\u7684\uff0c\u4f46\u662f\u6211\u73b0\u5728\u8fd8\u6ca1\u505a\u9898\uff0c\u6240\u4ee5\u505a\u4e86\u518d\u5199\u3002</li> </ul>"},{"location":"cour_note/D2QD_DigitalDesign/Chap05/","title":"Chap 5 Digital Hardware Implementation","text":"<p> \u7ea6 1303 \u4e2a\u5b57  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 4 \u5206\u949f</p> <p>\u6ce8\u610f</p> <p>\u672c\u7ae0\u8282\u5728\u8865\u5929\u4e2d\u5b8c\u6210\uff0c\u5185\u5bb9\u53ef\u80fd\u6bd4\u8f83\u7b80\u7565\u3002</p> <ul> <li> TODO: Finish this.</li> </ul>"},{"location":"cour_note/D2QD_DigitalDesign/Chap05/#\u53ef\u91cd\u7f16\u7a0b\u6280\u672f","title":"\u53ef\u91cd\u7f16\u7a0b\u6280\u672f","text":"<p>\u53ef\u91cd\u7f16\u7a0b\u6280\u672f(programmable implementation technologies)</p> <p>\u76f4\u63a5\u66f4\u6539\u7535\u8def\u6765\u4fee\u6539\u7535\u8def\u529f\u80fd\u88ab\u79f0\u4e3a\u786c\u7f16\u7a0b\uff0c\u800c\u53ef\u91cd\u53d8\u6210\u6280\u672f\u8ba9\u6211\u4eec\u80fd\u591f\u4e0d\u66f4\u6539\u786c\u4ef6\u5e03\u7ebf\u7684\u60c5\u51b5\u4e0b\uff0c\u5b9e\u73b0\u903b\u8f91\u529f\u80fd\u7684\u91cd\u65b0\u7f16\u8f91\u3002</p> <p>FPGA</p> <p>\u73b0\u573a\u53ef\u7f16\u7a0b\u903b\u8f91\u95e8\u9635\u5217(Field Programmable Gate Array, FPGA) - \u67e5\u627e\u8868(lookup table, LUT)</p> <p>\u7f16\u7a0b\u6280\u672f(programming technologies) \u5728\u786c\u4ef6\u5c42\u9762\u6709\u4e09\u79cd\u5b9e\u73b0\u624b\u6bb5\uff1a</p> <ul> <li>\u63a7\u5236\u8fde\u63a5\u6765\u5b9e\u73b0\uff08\u4e0d\u662f\u53ef\u91cd\u7f16\u7a0b\uff09\uff1b<ul> <li>Mask programing</li> <li>Fuse</li> <li>Anti-fuse</li> </ul> </li> <li>\u63a7\u5236\u95e8\u7ea7\u7535\u8def\u7535\u538b\uff1b<ul> <li>Single-bit storage element</li> <li>Stored charge on a floating gate<ul> <li>Erasable</li> <li>Electrically erasable</li> <li>Flash (as in Flash Memory) </li> </ul> </li> </ul> </li> <li>\u4f7f\u7528\u67e5\u627e\u8868(LUT)\uff1b<ul> <li>Storage elements for the function<ul> <li>\u6bd4\u5982\u4f7f\u7528\u4e00\u4e2a <code>MUX</code>\uff0c\u5e76\u5c06\u8f93\u5165\u7aef\u63a5\u5185\u5b58\uff0c\u901a\u8fc7\u4fee\u6539\u5185\u5b58\u7684\u503c\u6765\u4fee\u6539 <code>MUX</code> \u7684\u884c\u4e3a\uff0c\u8fdb\u800c\u5b9e\u73b0\u51fd\u6570\u91cd\u7f16\u7a0b</li> </ul> </li> </ul> </li> </ul> <p>\u8bfe\u7a0b\u4e2d\u4ecb\u7ecd\u7684\u53ef\u91cd\u7f16\u7a0b\u7684\u5668\u4ef6\u4e3b\u8981\u6709\u5982\u4e0b\u56db\u79cd\uff1a</p> <ul> <li>\u53ea\u8bfb\u5185\u5b58 Read Only Memory (ROM) </li> <li>\u53ef\u7f16\u7a0b\u9635\u5217\u903b\u8f91 Programmable Array Logic (PAL\u24c7)</li> <li>\u53ef\u7f16\u7a0b\u903b\u8f91\u9635\u5217 Programmable Logic Array (PLA)</li> <li>Complex Programmable Logic Device (CPLD) or Field-Programmable Gate Array(FPGA)</li> </ul> <p>\u524d\u4e09\u8005\u90fd\u53ea\u80fd\u91cd\u5199\u4e00\u6b21\uff0c\u5982\u4e0b\u662f\u5b83\u4eec\u7684\u91cd\u5199\u5185\u5bb9\uff1a</p> <p></p> <p>\u5f15\u5165</p> <p>\u7531\u4e8e\u4e4b\u540e\u51fa\u73b0\u7684\u7535\u8def\u56fe\u4f1a\u975e\u5e38\u5e9e\u5927\uff0c\u6240\u4ee5\u9700\u8981\u5f15\u5165\u4e00\u4e9b\u903b\u8f91\u7b26\u53f7\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap05/#\u903b\u8f91\u7b26\u53f7\u4ecb\u7ecd","title":"\u903b\u8f91\u7b26\u53f7\u4ecb\u7ecd","text":"<p>Buffer</p> <p></p> <p>\u7b80\u5316\u8868\u793a\u4e00\u4e2a\u53d8\u91cf\u7684\u81ea\u8eab\u548c\u5176\u975e\uff1b</p> <p>Wire connecting</p> <p>\u5728\u53ef\u7f16\u7a0b\u903b\u8f91\u7535\u8def\u4e2d\uff0c\u7ebf\u7684\u8fde\u63a5\u4e0d\u518d\u53ea\u6709\u5355\u7eaf\u7684\u8fde\u901a\u548c\u4e0d\u8fde\u901a\u7684\u5173\u7cfb\uff1a</p> <p>\u5bf9\u4e8e\u4e24\u6761\u76f8\u4ea4\u5bfc\u7ebf\uff1a</p> <ul> <li>\u5982\u679c\u6ca1\u6709\u7279\u6b8a\u7b26\u53f7\uff0c\u5219\u8868\u793a\u8fd9\u4e2a\u4ea4\u53c9\u70b9 is not connected \uff1b</li> </ul> <p></p> <ul> <li>\u5982\u679c\u6709\u4e00\u4e2a \u274c\uff0c\u5219\u8868\u793a\u8fd9\u4e2a\u4ea4\u53c9\u70b9 programmable\uff1b</li> </ul> <p></p> <ul> <li>\u5982\u679c\u53ea\u6709\u4e00\u4e2a\u52a0\u7c97\u7684\u70b9\uff0c\u5219\u8868\u793a\u8fd9\u4e2a\u4ea4\u53c9\u70b9 not programmable\uff1b</li> </ul> <p></p> <p>\u7279\u522b\u7684\uff0c\u5982\u679c\u4e00\u4e2a\u5143\u5668\u4ef6\u7684\u6240\u6709\u8f93\u5165\u90fd\u662f programmable\uff0c\u6211\u4eec\u4e5f\u53ef\u4ee5\u9009\u62e9\u628a\u8fd9\u4e2a \u274c \u753b\u5230\u903b\u8f91\u95e8\u4e0a\uff08\u5982\u4e0b\u56fe e \u548c f\uff09\u3002</p> <p></p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap05/#rom","title":"ROM","text":"<p>ROM \u7684\u57fa\u672c\u7ed3\u6784\u5982\u4e0b\uff1a</p> <p></p> <p>\u800c ROM \u7684\u5927\u5c0f\u5982\u4e0b\u8ba1\u7b97\uff08\u4ee5\u4e0a\u56fe\u4e3a\u4f8b\uff09\uff1a</p> \\[ \\begin{aligned}     ROM\\;\\;size\\;\\;&amp;=\\;\\;address\\;\\;width\\;\\;\\times\\;\\;word\\;\\;width&amp;\\\\                    &amp;=\\;\\;2^2\\;\\;\\times\\;\\;4\\;\\;=\\;\\;16\\;\\;bit&amp; \\end{aligned} \\] eg <p>\u66f4\u6e05\u6670\u7684\u8868\u793a\u5176\u5185\u90e8\u903b\u8f91\u7684\uff0c\u53ef\u4ee5\u5c06 ROM \u5199\u6210\u8fd9\u6837\uff1a</p> <p></p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap05/#pal","title":"PAL","text":"<p>\u53ef\u91cd\u7f16\u7a0b\u8f93\u5165\u7ec4\u5408\u6765\u5f97\u5230\u56fa\u5b9a\u8f93\u51fa\u3002</p> <p>\u5176\u5177\u6709\u4e00\u4e2a\u7f3a\u9677\u662f\uff0c\u56e0\u4e3a\u8868\u8fbe\u51fd\u6570\u7684\u65b9\u6cd5\u4e0d\u662f\u901a\u8fc7 SOM \u6216\u8005 POM \u7684\u5f62\u5f0f\uff0c\u6240\u4ee5\u4e0d\u4e00\u5b9a\u80fd\u591f\u5b8c\u5907\u8868\u8fbe\u51fd\u6570\u3002</p> <p>\u5728\u6b64\u57fa\u7840\u4e0a\u7684\u4e00\u4e2a\u6539\u8fdb\u662f\uff0c\u901a\u8fc7\u5c06\u4e00\u4e2a\u65e2\u6709\u7684 PAL \u8f93\u51fa\u5f53\u4f5c\u8f93\u5165\uff0c\u8f93\u5165\u5230\u53e6\u5916\u4e00\u4e2a\u51fd\u6570\u4e2d\uff0c\u6765\u5f25\u8865\u9879\u4e0d\u8db3\u7684\u95ee\u9898\u3002</p> eg <p></p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap05/#pla","title":"PLA","text":"<p>\u4e0e PAL \u7684\u533a\u522b\u5728\u4e8e\uff0c\u5728\u8f93\u51fa\u7684\u65f6\u5019\u4e5f\u80fd\u5bf9\u8f93\u51fa\u7ec4\u5408\u8fdb\u884c\u91cd\u7f16\u7a0b\u3002</p> <p>\u5176\u540c PAL \u4e00\u6837\u5177\u6709\u4e00\u4e2a\u7f3a\u9677\u662f\uff0c\u56e0\u4e3a\u8868\u8fbe\u51fd\u6570\u7684\u65b9\u6cd5\u4e0d\u662f\u901a\u8fc7 SOM \u6216\u8005 POM \u7684\u5f62\u5f0f\uff0c\u6240\u4ee5\u4e0d\u4e00\u5b9a\u80fd\u591f\u5b8c\u5907\u8868\u8fbe\u51fd\u6570\u3002</p> <p>\u5728\u57fa\u7840\u4e0a\u4e00\u4e2a\u6539\u8fdb\u662f\u5728\u8f93\u51fa\u7684\u65f6\u5019\u518d\u505a\u4e00\u6b21\u5f02\u6216\uff08\u4e0d\u7528\u975e\u95e8\u4f53\u73b0\u4e86\u53ef\u91cd\u7f16\u7a0b\u7684\u601d\u60f3\uff09\uff0c\u4ee5\u4ea7\u751f\u65b0\u7684\u9879\uff0c\u6765\u5f25\u8865\u9879\u4e0d\u8db3\u7684\u95ee\u9898\u3002</p> <p></p> <p>\u53ef\u4ee5\u53d1\u73b0\uff0c\u51fa\u73b0\u4e86\u65b0\u7684\u9879\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap05/#lookup-tables","title":"Lookup Tables","text":"<p>\u901a\u8fc7\u8ba9\u6570\u636e\u6e90\u63a5\u5185\u5b58\uff0c\u5e76\u901a\u8fc7\u4fee\u6539\u771f\u503c\u8868\u5185\u7684\u503c\uff0c\u5373\u4fee\u6539\u5185\u5b58\u91cc\u7684\u503c\uff0c\u6765\u5b9e\u73b0\u6570\u636e\u6e90\u7684\u53d8\u5316\uff0c\u6765\u6539\u53d8 <code>MUX</code> \u7684\u884c\u4e3a\u3002</p> <p>\u4f46\u662f\u5b9e\u9645\u5e94\u7528\u4e2d\uff0c\u51fd\u6570\u8f93\u5165\u7684\u6570\u91cf\u4f1a\u53d8\u5316\uff0c\u56e0\u6b64\u6211\u4eec\u9700\u8981\u901a\u8fc7\u7075\u6d3b\u7ec4\u5408\u7684\u65b9\u6cd5\uff08\u6bd4\u5982\u901a\u8fc7\u56db\u9009\u4e8c\u9009\u4e00\u7684\u65b9\u5f0f\uff0c\u7528\u4e09\u4e2a\u4e8c\u9009\u4e00\u7684 <code>MUX</code> \u6765\u5b9e\u73b0\u56db\u9009\u4e00\uff09\u6765\u5b9e\u73b0\u591a\u8f93\u5165\u3002</p> <p>\u5e38\u89c1\u7684 <code>LUT</code> \u5927\u5c0f\u4ee5 16bits \u6216 64bits \u7684 4 \u8f93\u5165\u6216 6 \u8f93\u5165\u4e3a\u4e3b\u3002</p> <p>\u7531\u4e8e <code>LUT</code> \u5b58\u7684\u672c\u8d28\u4e0a\u662f\u771f\u503c\u8868\uff0c\u6240\u4ee5\u5b83\u53ef\u4ee5\u5b9e\u73b0\u4efb\u610f\u8f93\u5165\u7b26\u5408\u8981\u6c42\u7684\u903b\u8f91\u51fd\u6570\u3002</p> <p>\u6240\u4ee5\uff0c\u95ee\u9898\u5c31\u53d8\u5316\u4e3a\u5982\u4f55\u7528\u8f83\u5c0f\u7684 <code>LUT</code> \u6765\u7ec4\u5408\u5b9e\u73b0\u590d\u6742\u7684\u903b\u8f91\u51fd\u6570\u3002</p> <p><code>LUT</code> \u7684\u57fa\u672c\u7ed3\u6784\u5982\u4e0b\uff1a</p> <p></p> <p><code>FPGA</code> \u7684\u57fa\u672c\u7ed3\u6784\u5982\u4e0b\uff1a</p> <p></p> <p>\u5176\u4e3b\u8981\u5206\u4e3a\u4e09\u4e2a\u7ec4\u6210\u90e8\u5206\uff1a</p> <ul> <li>CLB(Configurable Logic Block)<ul> <li>\u5927\u91cf\u5b58\u50a8 <code>LUT</code></li> </ul> </li> <li>SM(Switch Matrix)<ul> <li>\u53ef\u7f16\u7a0b\u7684\u4ea4\u6362\u77e9\u9635</li> </ul> </li> <li>IOB(Input &amp; Output Block)<ul> <li>\u53ef\u7f16\u7a0b\u7684\u8f93\u5165\u8f93\u51fa\u5355\u5143</li> </ul> </li> </ul>"},{"location":"cour_note/D2QD_DigitalDesign/Chap05/#clb","title":"CLB","text":"<p>CLB \u662f <code>FPGA</code> \u4e2d\u7684\u57fa\u7840\u903b\u8f91\u5355\u5143\u3002</p> <p></p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap05/#sm","title":"SM","text":"<p>\u901a\u8fc7\u76f8\u5f53\u590d\u6742\u7684\u7b97\u6cd5\uff0c <code>SM</code> \u4f1a\u6839\u636e\u76ee\u6807\u903b\u8f91\uff0c\u9009\u62e9\u94fe\u63a5\u4e0d\u540c\u7684 <code>CLB</code> \u4ee5\u5b9e\u73b0\u590d\u6742\u903b\u8f91\u3002</p> <p>\u5b83\u5177\u6709\u8fd9\u4e9b\u57fa\u672c\u5c5e\u6027\uff1a</p> <ol> <li>Flexibility: \u8bc4\u4f30\u4e00\u6761\u7ebf\u53ef\u4ee5\u8fde\u63a5\u5230\u591a\u5c11\u7ebf\uff1b</li> <li>Topology: \u54ea\u4e9b\u7ebf\u53ef\u4ee5\u88ab\u8fde\u63a5\u5230\uff1b</li> <li>Routability: \u6709\u591a\u5c11\u56de\u8def\u53ef\u4ee5\u88ab\u8def\u7531\uff1b</li> </ol> <p></p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap05/#iob","title":"IOB","text":"<p><code>IOB</code> \u7528\u6765\u5bf9\u5916\u90e8\u8bbe\u5907\u8fdb\u884c\u8fde\u63a5\uff0c\u7528\u6765\u63a7\u5236\u8f93\u5165\u548c\u8f93\u51fa\u3002</p> <p></p> eg for <code>FPGA</code> <p>\u901a\u8fc7 <code>FPGA</code> \u5b9e\u73b0 \\(f=x_1x_2+\\overline{x_2x_3}\\)\uff1a</p> <p>\u5206\u89e3\u95ee\u9898\uff1a\\(f_1 = x_1x_2,\\;\\;f_2=\\overline{x_2x_3},\\;\\;f=f_1+f_2\\)\u3002</p> <p></p> <p>\u5728\u8f6f\u4ef6\u5c42\u9762\u7f16\u7a0b\u5b8c\u540e\uff0c\u4f1a\u751f\u6210\u4f4d\u6d41\u6587\u4ef6(<code>bitfile</code>)\uff0c\u4e0b\u8f7d\u5230\u677f\u65f6\u4f1a\u66f4\u65b0 <code>FPGA</code> \u4e2d\u7684\u5185\u5bb9\u3002</p> <p>\u7ec4\u5408\u51fd\u6570\u7684\u5b9e\u73b0\u65b9\u6cd5</p> <p>\u5230\u76ee\u524d\u4e3a\u6b62\uff0c\u4e0d\u7ba1\u662f\u53ef\u91cd\u7f16\u7a0b\u8fd8\u662f\u4e0d\u53ef\u91cd\u7f16\u7a0b\uff0c\u90fd\u5df2\u7ecf\u4ecb\u7ecd\u4e86\u5f88\u591a\u65b9\u6cd5\uff0c\u8fd9\u91cc\u8fdb\u884c\u4e00\u6b21\u5c0f\u7ed3\uff1a</p> <ol> <li><code>Decoder</code>s &amp; <code>OR</code> gates<ul> <li>\u5c06\u8bd1\u7801\u51fa\u6765\u7684\u9700\u8981\u7684\u76ee\u6807\u7ec4\u5408\u90fd <code>OR</code> \u5728\u4e00\u8d77\uff1b</li> </ul> </li> <li><code>MUX</code>s<ul> <li>\u901a\u8fc7\u591a\u8def\u9009\u62e9\u5668\u5b9e\u73b0\u4efb\u610f\u903b\u8f91\u51fd\u6570\uff1b </li> </ul> </li> <li><code>ROM</code>s</li> <li><code>PAL</code>s</li> <li><code>PLA</code>s</li> <li><code>LUT</code>s</li> </ol>"},{"location":"cour_note/D2QD_DigitalDesign/Chap06/","title":"Chap 6 Registers &amp; Register Transfers","text":"<p> \u7ea6 6700 \u4e2a\u5b57  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 22 \u5206\u949f</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap06/#\u5bc4\u5b58\u5668","title":"\u5bc4\u5b58\u5668","text":"<p>\u5bc4\u5b58\u5668(registers)\u7c97\u7565\u7684\u6765\u8bf4\u5c31\u662f\u4e00\u5806\u89e6\u53d1\u5668\u4ee5\u53ca\u5bf9\u5e94\u7684\u72b6\u6001\u63a7\u5236\u7535\u8def\uff0c\u7528\u6765\u5b9e\u73b0\u591a\u4f4d\u6570\u636e\u7684\u5b58\u50a8\u7b49\u64cd\u4f5c\u3002</p> <p>\u5176\u4e2d\u6709\u4e00\u79cd\u7279\u6b8a\u7684\u5bc4\u5b58\u5668\u53eb\u8ba1\u6570\u5668(counter)\uff0c\u975e\u5e38\u76f4\u767d\u7684\uff0c\u5b83\u7684\u884c\u4e3a\u5c31\u662f\u968f\u7740\u65f6\u949f\u5468\u671f\u4e0d\u65ad\u5728\u56fa\u5b9a\u7684\u72b6\u6001\u5e8f\u5217\u4e2d\u5faa\u73af\u3002\u66f4\u5f62\u8c61\u7684\uff0c\u4e00\u822c\u662f\u5b9e\u73b0\u81ea\u52a8\u7684\u8ba1\u6570\u529f\u80fd\uff0c\u50cf\u7535\u5b50\u65f6\u949f\u90a3\u6837\u3002</p> <p>Registers are useful for storing and manipulating information; counters are employed in circuits that sequence and control operations in a digital system.</p> <p>\u5b9e\u73b0\u5bc4\u5b58\u5668\u4e00\u4e2a\u6700\u76f4\u767d\u7684\u60f3\u6cd5\u5c31\u662f\u516c\u7528\u63a7\u5236\u7ebf\u8def\u548c\u5206\u5217\u6570\u636e\u7ebf\u8def\u6765\u63a7\u5236\u591a\u4e2a\u89e6\u53d1\u5668\uff0c\u5982\u4e0b\u56fe\u662f\u4f7f\u7528 D <code>FF</code> \u5b9e\u73b0\u7684\u4e00\u4e2a 4-bit register\uff1a</p> <p></p> <p>\u6211\u4eec\u79f0\u65b0\u6570\u636e\u88ab\u5199\u5165\u5bc4\u5b58\u5668\u7684\u64cd\u4f5c\u4e3a\u8f7d\u5165(load)\uff0c\u800c\u5982\u679c\u8f7d\u5165\u64cd\u4f5c\u5728\u540c\u4e00\u4e2a\u65f6\u949f\u8109\u51b2\u4e2d\u5b8c\u6210\uff0c\u6211\u4eec\u79f0\u4e4b\u662f\u5e76\u884c(parallel)\u7684\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap06/#\u4fdd\u6301","title":"\u4fdd\u6301","text":"<p>\u4f46\u662f\u6211\u4eec\u53d1\u73b0\uff0c\u5982\u56fe\u7684\u5bc4\u5b58\u5668\u5728\u6bcf\u4e2a\u65f6\u949f\u90fd\u5141\u8bb8\u8f7d\u5165\uff0c\u6362\u53e5\u8bdd\u6765\u8bf4\u6bcf\u4e2a\u65f6\u949f\u5468\u671f\u90fd\u4f1a\u6539\u53d8\u4e3a\u8f93\u5165\u3002\u4f46\u662f\u6211\u4eec\u5e0c\u671b\u5373\u4f7f\u6211\u4eec\u4e0d\u7ba1\u5b83\u5b83\u4e5f\u80fd\u4fdd\u6301\u4e4b\u524d\u7684\u503c\uff0c\u4e3b\u8981\u6709\u4e24\u4e2a\u65b9\u6848\u3002</p> <p>\u65b9\u6848 A</p> <p>\u5176\u4e2d\u4e00\u4e2a\u505a\u6cd5\u662f\u9700\u8981\u9009\u62e9\u6027\u7684\u8ba9\u5b83\u8ddf\u968f\u65f6\u949f\u8109\u51b2\u5207\u6362\u72b6\u6001\u3002\u505a\u6cd5\u5c31\u662f\u5c06 Control \u4fe1\u53f7\u4fee\u6539\u4e3a \\(C = \\overline{Load} + Clock\\)\uff0c\u5982\u6b64\u800c\u6765\uff0c\u5f53 \\(Load = 0\\) \u65f6\uff0c\u59cb\u7ec8\u6709 \\(C = 0\\)\uff0c\u8109\u51b2\u6d88\u5931\uff0c\u5bc4\u5b58\u5668\u65e0\u6cd5\u88ab\u8f7d\u5165\u3002\u5982\u4e0b\u56fe\uff0c\u8fd9\u79cd\u6280\u672f\u53eb\u95e8\u63a7\u65f6\u949f(clock gating)\u3002</p> <p></p> <p>clock skew</p> <p>\u7136\u800c\uff0c\u5728\u95e8\u63a7\u65f6\u949f\u6280\u672f\u4e2d\uff0c\u7531\u4e8e\u6dfb\u52a0\u4e86\u4e00\u4e2a\u989d\u5916\u7684\u903b\u8f91\u95e8\uff0c\u65f6\u949f\u8109\u51b2\u5230\u8fbe Control \u7684\u65f6\u5019\u4f1a\u51fa\u73b0\u989d\u5916\u7684\u4f20\u64ad\u5ef6\u65f6\uff0c\u5373\u65f6\u949f\u504f\u79fb(clock skew)\u3002\u800c\u8fd9\u5fae\u5c0f\u7684\u5ef6\u65f6\u4f1a\u5bfc\u81f4\u5728\u6574\u4e2a\u540c\u6b65\u7cfb\u7edf\u4e2d\uff0c\u4e0d\u540c\u7ec4\u4ef6\u5f97\u5230\u7684\u65f6\u949f\u8109\u51b2\u6709\u504f\u5dee\uff0c\u800c\u8fd9\u662f\u6211\u4eec\u6240\u4e0d\u5e0c\u671b\u770b\u5230\u7684\u3002\u6240\u4ee5\u5728\u5b9e\u9645\u8bbe\u8ba1\u4e2d\uff0c\u6211\u4eec\u5e94\u5f53\u907f\u514d\u6216\u5c3d\u53ef\u80fd\u7f29\u5c0f\u65f6\u949f\u504f\u79fb\u3002</p> <p>\u65b9\u6848 B</p> <p>\u53e6\u5916\u4e00\u4e2a\u505a\u6cd5\u662f\uff0c\u5728\u4e0d\u5e0c\u671b\u5b83\u4fee\u6539\u7684\u65f6\u5019\uff0c\u4e0d\u65ad\u5c06\u5b83\u7684\u8f93\u5165\u8f7d\u5165\uff0c\u4e5f\u5c31\u662f\u4fdd\u6301\u4e0d\u53d8\u3002\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u4e00\u4e2a <code>MUX</code> \u6765\u5b9e\u73b0\u8fd9\u4e2a\u529f\u80fd\uff0c\u7528 <code>EN</code> \u4f7f\u80fd\u7aef\u6765\u9009\u62e9\u662f\u8f7d\u5165\u65b0\u503c\u8fd8\u662f\u4fdd\u6301\u4e4b\u524d\u7684\u503c\uff0c\u5982\u4e0b\u56fe\u3002</p> <p></p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap06/#\u5bc4\u5b58\u5668\u5355\u5143","title":"\u5bc4\u5b58\u5668\u5355\u5143","text":"<p>\u5c0f\u8282\u5bfc\u8bfb</p> <p>\u672c\u5c0f\u8282\u5728\u4e66\u672c\u4e2d\u7684\u4f4d\u7f6e\u9760\u540e\uff0c\u4f46\u662f\u8003\u8651\u5230\u5185\u5bb9\u7684\u8fde\u7eed\u6027\u6211\u51b3\u5b9a\u63d0\u524d\uff0c\u672c\u8282\u5185\u5bb9\u4f1a\u6d89\u53ca\u4e00\u4e9b\u4e4b\u540e\u7684\u5185\u5bb9\uff0c\u5b9e\u9645\u4e0a\u7684\u7edd\u5bf9\u6027\u77e5\u8bc6\u8f83\u5c11\uff0c\u53ef\u4ee5\u7c97\u770b\u8fc7\u7559\u4e0b\u5370\u8c61\u5373\u53ef\uff0c\u5927\u90e8\u5206\u77e5\u8bc6\u9700\u8981\u901a\u8fc7\u6848\u4f8b\u5206\u6790\u548c\u5b9e\u8df5\u83b7\u5f97\uff0c\u662f\u7c7b\u4f3c\u4e8e\u8bbe\u8ba1\u6307\u5bfc\u601d\u60f3\u7684\u5185\u5bb9\u3002</p> <p>\u5bc4\u5b58\u5668\u5355\u5143(Register Cell)\u662f\u5bc4\u5b58\u5668\u7684\u4e2a\u4f53\u5355\u5143\uff0c\u4e3b\u8981\u5305\u62ec\u4e00\u4e2a <code>FF</code> \u53ca\u5b9e\u73b0\u5176\u7ec4\u5408\u903b\u8f91\u7684\u7ec4\u5408\u7535\u8def\u3002</p> <p>A single-bit cell of an iterative combinational circuit, connected to a flip-flop that provides the output, forms a two-state sequential circuit called a register cell</p> <p>\u5bf9\u4e8e n bits \u7684\u5bc4\u5b58\u5668\u5355\u5143\uff0c\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u5b9e\u73b0\u5176 1 bit \u7684\u5bc4\u5b58\u5668\u5355\u5143\uff0c\u5e76\u590d\u5236 n \u4efd\u5b9e\u73b0\u3002</p> <p>\u8bbe\u8ba1\u5bc4\u5b58\u5668\u5355\u5143\u65f6\uff0c\u6211\u4eec\u9700\u8981\u5bf9\u5bc4\u5b58\u5668\u5355\u5143\u8fdb\u884c\u5b9a\u4e49\u3002\u800c\u6307\u5b9a(Specify)\u4e00\u4e2a\u5bc4\u5b58\u5668\u5355\u5143\u7684\u529f\u80fd\u7684\u4e3b\u8981\u6709\u8fd9\u4e9b\u65b9\u9762\uff1a</p> <ul> <li>\u5bc4\u5b58\u5668\u7684\u529f\u80fd\u51fd\u6570\uff1b<ul> <li>\u4e00\u822c\u6307\u5bc4\u5b58\u5668\u4f20\u8f93\uff1b</li> </ul> </li> <li>\u63a7\u5236\u4fe1\u53f7\u6784\u6210\uff1b<ul> <li>\u6709\u54ea\u4e9b\u63a7\u5236\u4fe1\u53f7\u3001\u662f\u5426\u7f16\u7801\u3001\u5982\u4f55\u51b3\u5b9a\u662f\u5426 Load \u7b49\uff1b</li> </ul> </li> <li>\u5bc4\u5b58\u5668\u7684\u8f93\u5165\u6570\u636e\uff1b<ul> <li>\u6709\u54ea\u4e9b\u8f93\u5165\u6570\u636e\u3001\u662f\u5426\u9700\u8981\u9884\u5148\u5904\u7406\u7b49\uff1b</li> </ul> </li> </ul> <p>\u5728\u5b9e\u9645\u5b9e\u73b0\u65f6\uff0c\u5206\u4e3a <code>MUX</code> \u5b9e\u73b0\u548c\u65f6\u5e8f\u903b\u8f91\u5b9e\u73b0\u4e24\u79cd\u65b9\u6cd5\u3002</p> <p>\u524d\u8005\u5c31\u662f#\u57fa\u4e8e Mux \u5b9e\u73b0\u4f20\u8f93\u4e2d\u5c06\u8981\u63d0\u5230\u7684\u90a3\u6837\uff0c\u5173\u4e8e\u4e0a\u9762\u54ea\u4e9b\u5185\u5bb9\u5728\u8be5\u5c0f\u8282\u4e2d\u7684\u4f53\u73b0\u5982\u4e0b\u56fe\uff1b</p> <p></p> <p>\u4e5f\u5c31\u662f\u901a\u8fc7\u5206\u522b\u5b9e\u73b0\u903b\u8f91\uff0c\u7136\u540e\u901a\u8fc7\u63a7\u5236\u4fe1\u53f7\u9009\u62e9\u6570\u636e\u8f93\u5165\u6765\u5b9e\u73b0\u3002</p> <p>\u800c\u540e\u8005\u6309\u7167\u65f6\u5e8f\u7535\u8def\u7684\u8bbe\u8ba1\u65b9\u6cd5\uff0c\u786e\u5b9a\u72b6\u6001\u56fe\u540e\u6839\u636e\u72b6\u6001\u53d8\u5316\u8bbe\u8ba1\u65f6\u5e8f\u7535\u8def\uff0c\u8bbe\u8ba1\u4f18\u5316\u51b3\u5b9a\u72b6\u6001\u8f6c\u79fb\u65b9\u7a0b\u5b9e\u73b0\uff0c\u5177\u4f53\u53ef\u4ee5\u53c2\u8003\u7b2c\u56db\u7ae0#\u65f6\u5e8f\u7535\u8def\u8bbe\u8ba1\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap06/#\u5bc4\u5b58\u5668\u4f20\u8f93","title":"\u5bc4\u5b58\u5668\u4f20\u8f93","text":"<p>\u8bf4\u660e</p> <p>\u628a transfer \u7ffb\u8bd1\u4e3a\u201c\u4f20\u8f93\u201d\u662f\u6211\u8111\u74dc\u4e00\u62cd\u7684\u884c\u4e3a\uff0c\u6211\u5e76\u4e0d\u77e5\u9053\u7ffb\u8bd1\u6210\u4ec0\u4e48\u6bd4\u8f83\u5408\u9002\uff0c\u5982\u679c\u8bfb\u8005\u6709\u66f4\u597d\u7684\u7ffb\u8bd1\uff0c\u8bf7\u544a\u8bc9\u6211\uff01</p> <p>\u4e00\u4e2a\u590d\u6742\u7cfb\u7edf\u9664\u4e86\u4fe1\u606f\u7684\u5b58\u50a8\u8fd8\u9700\u8981\u4fe1\u606f\u7684\u4f20\u8f93\u548c\u5904\u7406\uff0c\u6362\u53e5\u8bdd\u6765\u8bf4\uff0c\u4e3a\u4e86\u5b9e\u73b0\u7075\u6d3b\u3001\u590d\u6742\u7684\u8ba1\u7b97\uff0c\u6211\u4eec\u9700\u8981\u4fe1\u606f\u4e4b\u95f4\u80fd\u591f\u5e7f\u6cdb\u5730\u4ea4\u4e92\u3002\u5927\u90e8\u5206\u7535\u5b50\u7cfb\u7edf\u8bbe\u8ba1\u4e2d\uff0c\u90fd\u4f1a\u6709\u4e00\u4e2a\u63a7\u5236\u5355\u5143(Control Unit)\u6765\u8d1f\u8d23\u6307\u6325\uff08\u51b3\u5b9a\u6307\u4ee4\u7684\u5e8f\u5217\uff09\u6570\u636e\u901a\u8def(Datapath)\u8fdb\u884c\u6570\u636e\u5904\u7406\u3002</p> <p>Datapaths are defined by their registers and the operations performed on binary data stored in the registers.</p> <p>\u5bf9\u4e8e\u5bc4\u5b58\u5668\u81ea\u8eab\u800c\u8a00\uff0c\u5b83\u53ef\u80fd\u5b9e\u73b0 \u8f7d\u5165(load)\u3001\u6e05\u7a7a(clear)\u3001\u4f4d\u79fb(shift)\uff08\u5173\u4e8e\u8fd9\u91cc\u7684shift\u7684\u542b\u4e49\u6211\u5b58\u7591\uff09 \u548c \u8ba1\u6570(count) \u7b49\u3002\u6b64\u5916\uff0c\u5bf9\u4e8e\u90a3\u4e9b\u5bc4\u5b58\u5668\u4e2d\u7684\u6570\u636e\u8fdb\u884c\u79fb\u52a8\u4e86\u7684\u52a0\u5de5\uff0c\u88ab\u79f0\u4e3a\u5bc4\u5b58\u5668\u4f20\u8f93\u64cd\u4f5c(Register Transfer Operations)\uff0c\u5b83\u4eec\u4e3b\u8981\u5305\u542b\u8fd9\u4e09\u4e2a\u90e8\u5206\uff1a</p> <ol> <li>\u7cfb\u7edf\u4e2d\u7684\u5bc4\u5b58\u5668\u96c6\u5408\uff1b</li> <li>\u5bf9\u4e8e\u6570\u636e\u7684\u64cd\u4f5c\uff1b</li> <li>\u76d1\u7763\u64cd\u4f5c\u5e8f\u5217\u7684\u63a7\u5236\uff1b</li> </ol> <p>\u5176\u4e2d\uff0c\u6700\u57fa\u7840\u7684\u90a3\u90e8\u5206\u64cd\u4f5c\u88ab\u79f0\u4e3a\u5fae\u64cd\u4f5c(microoperation)\uff0c\u5b83\u4eec\u662f\u5b9e\u73b0\u590d\u6742\u64cd\u4f5c\u7684\u57fa\u7840\uff0c\u4f8b\u5982\u5c06 R1 \u7684\u6570\u636e\u8f7d\u5165 R2\uff0c\u5c06 R1 \u548c R2 \u76f8\u52a0\uff0c\u6216\u662f\u81ea\u589e R1 \u7b49\u3002\u5b83\u4eec\u901a\u5e38\u4ee5\u6bd4\u7279\u5411\u91cf\u4e3a\u8f7d\u4f53\u5e76\u884c\u5b9e\u73b0\u7684\u3002</p> <p>Note that:</p> <p>the term \u201cmicrooperation,\u201d as used here, does not refer to any particular way of producing the control signals: specifically, it does not imply that the control signals are generated by a control unit based on a technique called microprogramming.</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap06/#\u5bc4\u5b58\u5668\u4f20\u8f93\u64cd\u4f5c--\u5bc4\u5b58\u5668\u4f20\u8f93\u8bed\u8a00","title":"\u5bc4\u5b58\u5668\u4f20\u8f93\u64cd\u4f5c &amp; \u5bc4\u5b58\u5668\u4f20\u8f93\u8bed\u8a00","text":"<p>\u5bf9\u4e8e\u7b80\u5355\u7684\u65f6\u5e8f\u903b\u8f91\u7cfb\u7edf\uff0c\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528\u72b6\u6001\u673a\u7b49\u65b9\u5f0f\u6765\u63cf\u8ff0\u5b83\u4eec\u7684\u884c\u4e3a\uff0c\u4f46\u662f\u5bf9\u4e0e\u89c4\u6a21\u66f4\u5927\u7684\u7cfb\u7edf\u6765\u8bf4\uff0c\u8fd9\u662f\u4e00\u4ef6\u5f88\u75db\u82e6\u7684\u4e8b\u60c5\u3002\u6240\u4ee5\u6211\u4eec\u5f15\u5165\u4e86\u4e00\u79cd\u4e13\u6ce8\u4e8e\u884c\u4e3a\u903b\u8f91\u7684\u8bed\u8a00\u6765\u63cf\u8ff0\u5bc4\u5b58\u5668\u4f20\u8f93\u4e2d\u7684\u903b\u8f91\u884c\u4e3a\uff1a\u5bc4\u5b58\u5668\u4f20\u8f93\u8bed\u8a00(Register Transfer Language, RTL)\u3002</p> <p>\u901a\u5e38\u5177\u6709\u7279\u6b8a\u529f\u80fd\u7684\u5bc4\u5b58\u5668\u90fd\u4f1a\u7528\u5176\u540d\u79f0\u7f29\u5199\u5927\u5199\u8868\u793a\uff0c\u4f8b\u5982 AR(Address Register)\uff0cPC(Program Counter)\uff0cIR(Instruction Register) \u6216\u8005\u66f4\u666e\u901a\u7684 R2(Register 2)\u3002</p> <p>Little-endian &amp; Big-endian</p> <p>\u6211\u4eec\u6709\u65f6\u5019\u4e5f\u4f1a\u7528\u8fd9\u4e9b\u5f62\u5f0f\u6765\u56fe\u5f62\u5316\u7684\u8868\u793a\u5bc4\u5b58\u5668\uff1a</p> <p></p> <p>\u6b64\u5916\uff0c\u5e38\u89c1\u64cd\u4f5c\u7528 RTL \u8868\u793a\u65b9\u6cd5\u548c\u7b26\u53f7\u5982\u4e0b\uff1a</p> <p></p> <p></p> <p>\u9700\u8981\u989d\u5916\u8bf4\u660e\u7684\u662f\uff0c\u5982\u679c\u6211\u4eec\u60f3\u8868\u8fbe\u6761\u4ef6\u8bed\u53e5\uff0c\u4f8b\u5982\u6211\u4eec\u60f3\u8868\u8fbe\uff1a</p> \\[ if\\, (K_1 = 1) \\,then\\, (R2 \\leftarrow R1) \\] <p>\u5219\u53ef\u4ee5\u5199\u4e3a\uff1a</p> \\[ K_1 : R2 \\leftarrow R1 \\]"},{"location":"cour_note/D2QD_DigitalDesign/Chap06/#\u5bc4\u5b58\u5668\u4f20\u8f93\u7684\u5b9e\u73b0","title":"\u5bc4\u5b58\u5668\u4f20\u8f93\u7684\u5b9e\u73b0","text":"<p>\u5f15\u5165</p> <p>\u5982\u4f55\u5b9e\u73b0\u5bc4\u5b58\u5668\u6240\u5b58\u50a8\u7684\u6570\u636e\u4e4b\u95f4\u7684\u5904\u7406\u4e0e\u4ea4\u4e92\u662f\u672c\u7ae0\u8282\u7684\u6838\u5fc3\u547d\u9898\u3002\u5982\u679c\u8bf4\u5fae\u64cd\u4f5c\u5904\u7406\u7684\u662f\u6570\u636e\u4e4b\u95f4\u7684\u5904\u7406\uff0c\u90a3\u5bc4\u5b58\u5668\u4f20\u8f93\u5219\u7740\u773c\u4e8e\u6570\u636e\u4e4b\u95f4\u7684\u4ea4\u4e92\u3002</p> <p>\u6362\u53e5\u8bdd\u6765\u8bf4\uff0c\u5982\u4f55\u628a\u6570\u636e\u7ed9\u5230\u522b\u7684\u5bc4\u5b58\u5668\u3001\u5982\u4f55\u83b7\u53d6\u522b\u7684\u5bc4\u5b58\u5668\u7ed9\u5230\u7684\u6570\u636e\u3001\u5982\u4f55\u4f20\u8f93\u548c\u9009\u62e9\u8fd9\u4e9b\u6570\u636e\uff0c\u5c31\u662f\u672c\u5c0f\u8282\u8981\u89e3\u51b3\u7684\u95ee\u9898\u3002</p> <p>\u7279\u522b\u7684\uff0c\u5bc4\u5b58\u5668\u4f20\u8f93\u7684\u5b9e\u73b0\u53ef\u4ee5\u76f4\u63a5\u5b9e\u73b0\u8f6c\u79fb\u64cd\u4f5c\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap06/#\u57fa\u4e8e-mux-\u5b9e\u73b0\u4f20\u8f93","title":"\u57fa\u4e8e MUX \u5b9e\u73b0\u4f20\u8f93","text":"<p>\u5bf9\u4e8e\u4e00\u4e2a\u5355\u4e00\u5bc4\u5b58\u5668\uff0c\u5b83\u7684\u8f93\u5165\u53ef\u80fd\u6709\u591a\u79cd\u6765\u6e90\uff0c\u4f8b\u5982\u5176\u5b83\u5bc4\u5b58\u5668\uff0c\u53c8\u6216\u8005\u662f\u5176\u4ed6\u64cd\u4f5c\u7684\u7ed3\u679c\u3002\u603b\u800c\u8a00\u4e4b\uff0c\u5b83\u7684\u8f93\u5165\u5f88\u53ef\u80fd\u662f\u4e0d\u552f\u4e00\u7684\uff0c\u800c\u540c\u4e00\u65f6\u523b\u6211\u4eec\u53ea\u80fd\u63a5\u53d7\u4e00\u4e2a\u6765\u6e90\u7684\u8f93\u5165\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u9700\u8981\u4f7f\u7528 <code>MUX</code> \u6765\u5bf9\u8f93\u5165\u8fdb\u884c\u9009\u62e9\u3002</p> <p>\u4e00\u4e2a\u7b80\u5355 \ud83c\udf30 \u5982\u4e0b\uff1a</p> <p></p> <p>\u7528\u8bed\u8a00\u6765\u63cf\u8ff0\u8fd9\u4e2a\u603b\u4f53\u67b6\u6784\u5c31\u662f\uff0c\u6211\u4eec\u901a\u8fc7\u4e00\u7cfb\u5217 one-hot \u7f16\u7801\uff08\u4e0d\u786e\u5b9a\uff0c\u4e5f\u8bb8\u53ef\u80fd\u90fd\u4e3a\u96f6\uff1f\u6211\u611f\u89c9\u53d6\u51b3\u4e8e\u4fdd\u6301\u7684\u5b9e\u73b0\u3002\uff09\u6765\u8868\u793a\u9009\u62e9\u54ea\u4e2a\u8f93\u5165\u6e90\uff08\u4e0b\u56fe\u4e2d \\(K_0\\sim K_{n-1}\\)\uff09\uff0c\u518d\u901a\u8fc7 <code>Encoder</code> \u5c06\u5b83\u4eec\u7f16\u7801\u4f5c\u4e3a <code>MUX</code> \u7684\u8f93\u5165\u9009\u62e9\u4fe1\u53f7\uff08\u4e0b\u56fe\u4e2d \\(S_m \\sim S_0\\)\uff09\uff0c\u4ece\u591a\u4e2a\u8f93\u5165\u6e90\uff08\u4e0b\u56fe\u4e2d 0 \\sim k \\sim (n-1)$\uff09\u4e2d\u9009\u62e9\u5bf9\u5e94\u7684\u6e90\uff0c\u5e76\u8f93\u51fa\uff0c\u7ed9\u5230 R0\uff1b\u6b64\u5916\uff0c\u5c06\u9009\u62e9\u4fe1\u53f7\u90fd\u6216\u8d77\u6765\uff0c\u4f5c\u4e3a R0 \u7684 Load \u4fe1\u53f7\u8f93\u5165\u3002</p> <p></p> <p>\u5176\u4e2d <code>MUX</code> \u7684 \\(k \\sim (n-1)\\) \u5b9e\u73b0\u4e86\u8f6c\u79fb\u64cd\u4f5c\u3002</p> <p>\u5c0f\u7ed3</p> <p>\u6362\u53e5\u8bdd\u6765\u8bf4\uff0c<code>MUX</code> \u5b9e\u73b0\u4e3b\u8981\u7684\u5b9e\u73b0\u4e86\u591a\u5bf9\u4e00\u7684\u6570\u636e\u4f20\u8f93\u95ee\u9898\u3002\u5982\u679c\u6211\u4eec\u5355\u5355\u4f7f\u7528 <code>MUX</code> \u6765\u5b8c\u6210\u5bc4\u5b58\u5668\u4e4b\u95f4\u7684\u6570\u636e\u4ea4\u4e92\uff08\u5047\u8bbe\u6240\u6709\u5bc4\u5b58\u5668\u90fd\u80fd\u76f8\u4e92\u4f20\u8f93\u6570\u636e\uff09\uff0c\u90a3\u5c06\u8fd9\u4e2a\u6a21\u578b\uff08\u56fe\u4f8b\u5728\u4e0b\u4e00\u5c0f\u8282\uff09\u62bd\u8c61\u540e\uff0c\u6211\u4eec\u5f97\u5230\u7684\u5c06\u662f\u4e00\u5f20\u201c\u5b8c\u5168\u56fe\u201d\uff0c\u7136\u800c\u5b83\u8089\u773c\u53ef\u89c1\u7684\u5f00\u9500\u5927\u3002</p> <p>\u800c\u603b\u7ebf\u5219\u975e\u5e38\u5de7\u5999\u5730\u4f18\u5316\u4e86\u8fd9\u4e2a\u95ee\u9898\uff08\u5e76\u4e0d\u662f\u4e0a\u4f4d\u66ff\u4ee3\u5173\u7cfb\uff09\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap06/#\u57fa\u4e8e\u603b\u7ebf\u5b9e\u73b0\u4f20\u8f93","title":"\u57fa\u4e8e\u603b\u7ebf\u5b9e\u73b0\u4f20\u8f93","text":"<p>\u5728\u4e0a\u4e00\u5c0f\u8282\u7684\u5c0f\u7ed3\u4e2d\u6211\u4eec\u5df2\u7ecf\u63d0\u5230\u4e86 <code>MUX</code> \u5b9e\u73b0\u7684\u4f18\u52a3\uff0c\u4e5f\u63d0\u5230\u4e86\u603b\u7ebf(bus)\u4f20\u8f93\u7684\u4f18\u52bf\uff0c\u90a3\u4e48\u5b83\u5177\u4f53\u6765\u8bf4\u5176\u5b9e\u73b0\u65b9\u6cd5\u6709\u4e24\u79cd\u2014\u2014\u901a\u8fc7\u5171\u6709 <code>MUX</code> \u5b9e\u73b0\uff0c\u6216\u901a\u8fc7\u4e09\u6001\u95e8\u5b9e\u73b0\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap06/#\u5171\u6709-mux-\u5b9e\u73b0","title":"\u5171\u6709 MUX \u5b9e\u73b0","text":"<p>\u8ba9\u6211\u4eec\u4ee5\u4e09\u4e2a\u5bc4\u5b58\u5668\u7684\u6a21\u578b\u4e3a\u4f8b\uff0c\u5bf9\u6bd4\u901a\u8fc7\u4e13\u6709 <code>MUX</code> \u5b9e\u73b0\u548c\u901a\u8fc7\u5355\u4e00\u603b\u7ebf(single bus)\u5b9e\u73b0\u7684\u533a\u522b\uff1a</p> <p></p> <p>\u9996\u5148\u5bf9\u603b\u7ebf\u5b9e\u73b0\u8fdb\u884c\u8bf4\u660e\uff0c\u540c\u6837\u662f\u4f7f\u7528 <code>MUX</code>\uff0c\u4f46\u6b64\u65f6 <code>MUX</code> \u4e0d\u518d\u662f\u67d0\u4e2a\u5bc4\u5b58\u5668\u7684\u4e13\u6709\u903b\u8f91(dedicated logic)\uff0c\u800c\u662f\u4e09\u4e2a\u5bc4\u5b58\u5668\u5171\u540c\u4f7f\u7528\u7684\u5171\u6709\u903b\u8f91(shared logic)\u3002\u603b\u7ebf\u4e2d\u7684 <code>MUX</code> \u5728\u6240\u6709\u5bc4\u5b58\u5668\u7684\u8f93\u5165\u4e2d\u9009\u62e9\u5176\u4e2d\u4e00\u4e2a\uff0c\u5e76\u5c06\u5b83\u8f93\u51fa\uff0c\u7ed9\u5230\u6240\u6709\u5bc4\u5b58\u5668\uff1b\u800c\u603b\u7ebf\u901a\u8fc7\u63a7\u5236 Load \u4fe1\u53f7\u6765\u9009\u62e9\u8ba9\u54ea\u4e2a\uff08\u6216\u54ea\u4e9b\uff09\u5bc4\u5b58\u5668\u5f97\u5230\u8fd9\u4e2a\u4fe1\u53f7\u3002</p> <p>\u63a5\u4e0b\u6765\u8fdb\u884c\u5bf9\u6bd4\uff0c\u4ee5\u603b\u7ebf\u5b9e\u73b0\u4e3a\u4e3b\u4f53\uff0c\u4e0e <code>MUX</code> \u5b9e\u73b0\u5bf9\u6bd4\uff1a</p> <ul> <li>\u4f18\u52bf\uff1a<ul> <li>\u7535\u8def\u66f4\u7cbe\u7b80\uff0c\u6210\u672c\u66f4\u4f4e\uff0c\u968f\u7740\u5bc4\u5b58\u5668\u589e\u52a0\u8fd9\u4e2a\u7279\u70b9\u66f4\u52a0\u660e\u663e\uff1b</li> </ul> </li> <li>\u52a3\u52bf\uff1a<ul> <li>\u540c\u4e00\u65f6\u523b\u5185\u603b\u7ebf\u53ea\u80fd\u4f20\u8f93\u4e00\u4e2a\u6570\u636e\uff0c\u5373\u53ea\u6709\u4e00\u4e2a\u6570\u636e\u6e90(source)\uff1b<ul> <li>\u540c\u4e00\u65f6\u949f\u5468\u671f\u5185\u53ea\u6709\u4e00\u4e2a\u6570\u636e\u80fd\u4f20\u8f93\u5230\u522b\u7684\u5730\u65b9\uff0c\u4f8b\u5982\u4ea4\u6362\u64cd\u4f5c\u5c31\u9700\u8981\u81f3\u5c11\u4e24\u4e2a bus \u624d\u80fd\u5b9e\u73b0\uff1b</li> </ul> </li> </ul> </li> </ul> <p>\u800c\u56e0\u4e3a\u8fd9\u4e9b\u7279\u70b9\uff0c\u6211\u4eec\u9700\u8981\u8bc4\u4f30\u6211\u4eec\u7684\u9700\u6c42\uff0c\u9009\u62e9\u5408\u9002\u7684\u7ed3\u6784\u6765\u5b9e\u73b0\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap06/#\u4e09\u6001\u95e8\u5b9e\u73b0","title":"\u4e09\u6001\u95e8\u5b9e\u73b0","text":"<p>\u4e09\u6001\u95e8\u7684\u76f8\u5173\u5185\u5bb9\u5df2\u7ecf\u5728\u524d\u9762\u4ecb\u7ecd\uff0c\u4f20\u8f93\u95e8\u5728\u8fd9\u91cc\uff0c\u5173\u4e8e\u672c\u5c0f\u8282\u7684\u77e5\u8bc6\uff0c\u53ef\u4ee5\u91cd\u70b9\u5173\u6ce8#\u4e09\u6001\u95e8/\u788e\u788e\u5ff5\u3002</p> <p>\u800c\u5173\u4e8e\u603b\u7ebf\u7684\u5b9e\u73b0\uff0c\u5f15\u7528\u4e00\u53e5\u6211\u5728#\u4e09\u6001\u95e8/\u788e\u788e\u5ff5\u91cc\u5199\u7684\u8bdd\uff1a</p> <p>\u53ea\u8981\u6211\u4eec\u8ba9\u5bfc\u7ebf\u7684\u82e5\u5e72\u8f93\u5165\u4e2d\u53ea\u6709\u4e00\u4e2a\u4e09\u6001\u95e8\u4e0d\u5728\u300c\u9ad8\u963b\u6001\u300d\uff0c\u5c31\u80fd\u591f\u4f18\u96c5\u5730\u5b9e\u73b0\u591a\u8def\u8f93\u51fa\u4e92\u8054\u3002</p> <p>\u5b9e\u9645\u4e0a\uff0c\u6240\u8c13\u7684\u4e09\u6001\u95e8\u5b9e\u73b0\u539f\u7406\u4e0a\u548c <code>MUX</code> \u5b9e\u73b0\u65e0\u4e8c\uff0c\u53ea\u4e0d\u8fc7\u6211\u4eec\u662f\u901a\u8fc7\u4e09\u6001\u95e8\u6765\u5b9e\u73b0\u300c\u8def\u7531\u300d\u8fd9\u4e2a\u903b\u8f91\u800c\u5df2\uff0c\u4e5f\u5c31\u662f\u4e66\u4e0a\u6240\u8bf4\u7684\uff1a</p> <p>Three-state buffer outputs can be connected together to form a multiplexed output line.</p> <p>\u4e0e <code>MUX</code> \u5b9e\u73b0\u76f8\u5bf9\u6bd4\uff0c\u4e09\u6001\u95e8\u5b9e\u73b0\u65b9\u5f0f\u5982\u4e0b\uff1a</p> <p></p> <p>\u8fdb\u884c\u7b80\u5355\u8bf4\u660e\uff0c(c) \u4e2d\u5bf9\u4e09\u6001\u95e8\u7684\u8868\u793a\u8fdb\u884c\u4e86\u7b80\u5316\uff0c\u542b\u4e49\u53c2\u8003 (a)\u3002\u5b83\u60f3\u8868\u8fbe\u7684\u4e3b\u8981\u542b\u4e49\u662f\uff0c\u5f53 <code>EN</code> \u4e3a <code>1</code> \u65f6\uff0c\u8868\u793a\u8f93\u51fa\uff1b\u53cd\u4e4b\u8868\u793a\u8f93\u5165\uff08\u5f53\u7136\uff0c\u771f\u6b63\u51b3\u5b9a\u662f\u5426\u8bfb\u5165\u5bc4\u5b58\u5668\u7684\u8fd8\u662f <code>LD</code>\uff09\u3002</p> \u4e2a\u4eba\u7591\u60d1 <p>\u4e66\u4e2d\u7684\u8868\u8ff0\u662f\uff1a</p> <p>If the three-state buffers are enabled, then the lines are outputs; if the three-state buffers are disabled, then the lines can be inputs.</p> <p>\u4f46\u662f\u770b (a) \u7684\u8868\u8fbe\uff0c\u4e0d\u7ba1 <code>EN</code> \u662f\u4ec0\u4e48\uff0c\u5b83\u5e94\u5f53\u90fd\u6709\u8f93\u5165\u624d\u5bf9\uff0c\u771f\u6b63\u51b3\u5b9a\u662f\u5426\u8f93\u5165\u8fdb\u6765\u7684\u5e94\u8be5\u8fd8\u662f <code>LD</code>\uff1f</p> <p>\u5bf9\u6bd4\u6765\u770b\uff0c\u4e09\u6001\u95e8\u7684\u5b9e\u73b0\u5927\u5927\u964d\u4f4e\u4e86\u603b\u7ebf\u7684\u5b9e\u73b0\u6210\u672c\uff0c\u7cbe\u7b80\u4e86\u7535\u8def\u7684\u5b9e\u73b0\uff0c\u6240\u4ee5\u901a\u5e38\u6765\u8bf4\u66f4\u5e38\u7528\u3002</p> \u4e2a\u4eba\u60f3\u6cd5 <p>\u867d\u7136\u4e66\u4e2d\u8bf4\u4e09\u6001\u95e8\u7684\u63a5\u7ebf\u6bd4 <code>MUX</code> \u7684\u5c11\u4e86\u4e00\u534a\uff0c\u4f46\u6211\u89c9\u7684\u4e09\u6001\u95e8\u53ea\u662f\u628a\u7ebf\u5206\u5c94\u7684\u5730\u65b9\u79fb\u52a8\u5230\u4e86\u5bc4\u5b58\u5668\u9644\u8fd1\uff0c\u6362\u53e5\u8bdd\u6765\u8bf4\u4e0d\u5982\u8bf4\u662f\u8282\u7701\u4e86\u5bfc\u7ebf\u7684\u957f\u5ea6\u3002\u4f46\u662f\u968f\u7740\u8f93\u5165\u7684\u589e\u52a0\uff0c<code>MUX</code> \u7684\u7ed3\u6784\u4f1a\u8d8a\u6765\u8d8a\u590d\u6742\u4e14\u9700\u8981\u91cd\u65b0\u8bbe\u8ba1\uff0c\u4f46\u4e09\u6001\u95e8\u53ea\u9700\u8981\u91cf\u7684\u589e\u52a0\u5c31\u884c\u4e86\uff0c\u6240\u4ee5\u786e\u5b9e\u662f\u66f4\u52a0\u5438\u5f15\u4eba\u3002\uff08\u5f53\u7136\uff0c\u867d\u7136\u4e66\u4e2d\u6ca1\u8bf4\uff0c\u4f46\u662f\u6211\u89c9\u5f97 Enable \u5fc5\u987b at most one-hot\uff0c\u800c\u8fd9\u90e8\u5206\u7684\u903b\u8f91\u5bf9\u4e8e\u4e24\u4e2a\u5b9e\u73b0\u65b9\u6cd5\u6765\u8bf4\u662f\u4e00\u6837\u7684\uff09</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap06/#\u5fae\u64cd\u4f5c\u53ca\u5176\u5b9e\u73b0","title":"\u5fae\u64cd\u4f5c\u53ca\u5176\u5b9e\u73b0","text":"<p>A microoperation is an elementary operation performed on data stored in registers or in memory.</p> <p>\u5fae\u64cd\u4f5c\u4e00\u822c\u5206\u4e3a\u8fd9\u56db\u79cd\uff1a</p> <ol> <li>\u8f6c\u79fb\uff0ctransfer microoperations\uff0c\u5c06\u6570\u636e\u4ece\u4e00\u4e2a\u5bc4\u5b58\u5668\u8f6c\u79fb\u5230\u53e6\u5916\u4e00\u4e2a\u5bc4\u5b58\u5668\uff1b</li> <li>\u7b97\u672f\uff0carithmetic microoperations\uff0c\u5bf9\u6570\u636e\u7684\u7b97\u672f\u8fd0\u7b97\u64cd\u4f5c\uff1b</li> <li>\u903b\u8f91\uff0clogic microoperations\uff0c\u5bf9\u6570\u636e\u7684\u903b\u8f91\u8fd0\u7b97\u64cd\u4f5c\uff1b</li> <li>\u4f4d\u79fb\uff0cshift microoperations\uff0c\u5bf9\u6570\u636e\u7684\u4f4d\u79fb\u64cd\u4f5c\uff1b</li> </ol> <p>A given microoperation may be of more than one type. For example, a 1s complement operation is both an arithmetic microoperation and a logic microoperation.</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap06/#\u8f6c\u79fb","title":"\u8f6c\u79fb","text":"<p>\u4e0d\u6539\u53d8\u6570\u636e\u672c\u8eab\uff0c\u53ea\u662f\u4ece\u4e00\u4e2a\u5bc4\u5b58\u5668\u4e2d\u628a\u6570\u636e\u79fb\u52a8\u5230\u53e6\u5916\u4e00\u4e2a\u5bc4\u5b58\u5668\u3002</p> <p>\u5c06 R0 \u4e2d\u7684\u6570\u636e\u8f6c\u79fb\u5230 R1 \u4e2d\uff0c\u7528 RTL \u8868\u793a\u5c31\u662f \\(R0 \\leftarrow R1\\)\u3002</p> <p>\u8fd9\u4e00\u90e8\u5206\u7684\u5b9e\u73b0\u9014\u5f84\u5728\u5bc4\u5b58\u5668\u4f20\u8f93\u7684\u5b9e\u73b0\u5df2\u7ecf\u9610\u8ff0\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap06/#\u7b97\u672f","title":"\u7b97\u672f","text":"<p>Multiplication and division are not listed in Table 6-3. Multiplication can be represented by the symbol * and division by /. These two operations are not included in the basic set of arithmetic microoperations because they are assumed to be implemented by sequences of basic microoperations. However, multiplication can be considered as a microoperation if implemented by a combinational circuit. In such a case, the result is transferred into a destination register at the clock edge after all signals have propagated through the entire combinational circuit</p> <p>\u52a0\u51cf\u6cd5\u5668</p> <p>\u5c31\u50cf\u6211\u4eec\u4e4b\u524d\u5b66\u8fc7\u7684\uff0c\u7528\u52a0\u6cd5\u5668\u5b9e\u73b0\u52a0\u51cf\u6cd5\u5668\uff0c\u5728 RTL \u548c\u6a21\u5757\u903b\u8f91\u7535\u8def\u7684\u7ef4\u5ea6\u4e0b\uff0c\u53ef\u4ee5\u8fd9\u4e48\u8868\u793a\uff1a</p> \\[ \\begin{aligned}     &amp;\\overline{X}K_1:R_1\\leftarrow R_1 + R_2 \\\\     &amp;XK_1:R_1\\leftarrow R_1 + \\overline{R_2} + 1 \\end{aligned} \\] <p></p> <p>\u6ce8\u610f</p> <p>\u5bf9\u4e8e\u5982\u4e0a\u51fa\u73b0\u7684\u5f62\u5f0f\u5982\uff1a\\(condition: reg \\leftarrow options one regs\\) \u7684\u8868\u8fbe\u5f0f\uff0c<code>:</code> \u5de6\u4fa7\u51fa\u73b0\u7684 <code>+</code> \u8868\u793a\u6216\uff0c\u53f3\u4fa7\u7684\u5219\u8868\u793a\u52a0\uff08\u201c\u4e58\u201d\u4e5f\u662f\u8fd9\u6837\uff09\uff01</p> <p>\u76f8\u5bf9\u5e94\u7684\uff0c\u52a0\u51cf\u6cd5\u7684\u5b9e\u73b0\u53ef\u4ee5\u901a\u8fc7\u52a0\u51cf\u6cd5\u5668\u5b9e\u73b0\uff0c\u4e58\u6cd5\u53ef\u4ee5\u7528\u4f4d\u79fb\u64cd\u4f5c\u5b9e\u73b0\uff0c\u800c\u9664\u6cd5\u76f8\u5bf9\u590d\u6742\u3002</p> <p>\u4e58\u6cd5\u5b9e\u73b0\u7684\u5927\u81f4\u601d\u8def</p> <p>\u5047\u8bbe\u6211\u4eec\u9700\u8981\u8ba1\u7b97 \\(a \\cdot b\\)\uff0c\u4e14 \\(a\\)\uff0c\\(b\\) \u90fd\u662f\u6574\u6570\uff0c\u5219\u53ef\u4ee5\u5c06 \\(b\\) \u5199\u6210\u4e8c\u8fdb\u5236\u5f62\u5f0f \\((b_{n-1}b_{n-2}...b_1b_0)_2\\)\uff0c\u4e8e\u662f\uff1a</p> \\[ \\begin{aligned}     a \\cdot b &amp;= a \\cdot (b_{n-1}b_{n-2}...b_1b_0)_2 \\\\               &amp;= a \\cdot \\left[ (b_{n-1}0...00)_2 + \\cdot (0b_{n-2}...00)_2 + ... + \\cdot (00...b_10)_2 + \\cdot(00...0b_0)_2 \\right]\\\\               &amp;= a \\cdot \\sum_{i = 0} ^{n-1} b_i \\cdot 2^{i} \\\\               &amp;= \\left(a \\cdot \\sum_{i = 0} ^{n-1} b_i\\right) \\;\\mathrm{&lt;&lt;}\\; i \\;\\;\\; \\text{where \"&lt;&lt;\" means \"Shift Left\"} \\end{aligned} \\] <p>\u4e8e\u662f\u5c31\u53ef\u4ee5\u901a\u8fc7\u4f4d\u79fb\u7684\u76f8\u5173\u77e5\u8bc6\u6765\u5b9e\u73b0\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap06/#\u903b\u8f91","title":"\u903b\u8f91","text":"<p>\u903b\u8f91\u8fd0\u7b97\u7684\u5b9e\u73b0\u76f8\u6bd4\u7b97\u672f\u66f4\u52a0\u76f4\u63a5\uff0c\u56e0\u4e3a\u5927\u90e8\u5206\u903b\u8f91\u90fd\u53ef\u4ee5\u901a\u8fc7\u903b\u8f91\u95e8\u6765\u5b9e\u73b0\u3002</p> <p>\u800c\u627f\u62c5\u903b\u8f91\u548c\u7b97\u672f\u8fd0\u7b97\u7684\u786c\u4ef6\u6a21\u5757\uff0c\u4e00\u822c\u88ab\u79f0\u4e3aALU\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap06/#\u4f4d\u79fb","title":"\u4f4d\u79fb","text":"<p>\u4f4d\u79fb\u7684\u5b9e\u73b0\u901a\u8fc7\u4f4d\u79fb\u5bc4\u5b58\u5668(Shift Register, SHR)\u5b9e\u73b0\u3002</p> <p>\u5f15\u5165</p> <p>\u4f4d\u79fb\u64cd\u4f5c\u4ece\u672c\u8d28\u4e0a\u6765\u8bb2\uff0c\u662f\u901a\u8fc7\u89e6\u53d1\u5668\u968f\u7740\u65f6\u949f\u8109\u51b2\uff0c\u5c06\u4e32\u884c\u6570\u636e\u4e00\u4f4d\u4e00\u4f4d\u5730\u79fb\u52a8\u5b9e\u73b0\u7684\u3002\u4f46\u662f\u5982\u679c\u8bfb\u8005\u5c1a\u672a\u7406\u89e3\u5176\u5b9e\u73b0\u539f\u7406\uff0c\u9605\u8bfb\u4ee5\u4e0b\u5185\u5bb9\u521a\u5f00\u59cb\u53ef\u80fd\u4f1a\u89c9\u5f97\u6709\u4e9b\u83ab\u540d\u5176\u5999\uff0c\u4f46\u662f\u8bf7\u5148\u9605\u8bfb\u4e32\u884c\u5b9e\u73b0\u548c\u5e76\u884c\u5316\u7684\u5185\u5bb9\uff0c\u77e5\u9053\u5b83\u4eec\u7684\u884c\u4e3a\u540e\uff0c\u53ef\u4ee5\u5148\u6682\u65f6\u8df3\u8fc7\u53cc\u5411\u4f4d\u79fb\u5bc4\u5b58\u5668\uff0c\u518d\u6765\u770b\u672c\u8282\u672b\u5c3e\u7684\u603b\u7ed3\uff0c\u4e5f\u8bb8\u80fd\u591f\u8ba9\u60a8\u660e\u767d\u5b83\u7a76\u7adf\u662f\u600e\u4e48\u5b9e\u73b0\u7684\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap06/#\u4e32\u884c\u5b9e\u73b0","title":"\u4e32\u884c\u5b9e\u73b0","text":"<p>\u4f4d\u79fb\u64cd\u4f5c\u6700\u7b80\u5355\u7684\u5b9e\u73b0\u53ea\u9700\u8981\u4e0e\u8f93\u5165\u6570\u76f8\u540c\u4f4d\u6570\u7684\u89e6\u53d1\u5668\u5b9e\u73b0\u3002\u5b83\u7684\u57fa\u672c\u7ed3\u6784\u5982\u4e0b\uff1a</p> <p></p> <p>\u56db\u4e2a\u89e6\u53d1\u5668\u9996\u5c3e\u76f8\u8fde\uff0c\u6700\u524d\u9762\u4e32\u884c\u8f93\u5165(Serial Input, SI)\u6570\u636e\uff0c\u672b\u7aef\u5f97\u5230\u4e32\u884c\u8f93\u51fa(Serial Output, SO)\uff0c\u5728\u4e0d\u540c\u65f6\u949f\u5468\u671f\u7684\u504f\u5dee\u4e0b\uff0c\u8fde\u7eed\u8bfb\u5165\u7684 n bits \u5373\u4e3a\u4e0d\u540c\u4f4d\u6570\u4f4d\u79fb\u7684\u7ed3\u679c\u3002</p> <p>\u4e32\u884c\u4f4d\u79fb\u64cd\u4f5c\u5b9e\u73b0\u7684\u6a21\u62df\u89e3\u91ca</p> <p>\u5047\u8bbe\u73b0\u5728\u6211\u4eec\u6709 4 \u4e2a <code>FF</code> \u9996\u5c3e\u76f8\u8fde\uff0c\u73b0\u5728\u4e32\u884c\u8f93\u5165 <code>1001</code> \u8fd9 4bits \u7684\u6570\u636e\uff08\u5f53\u7136\uff0c\u5b8c\u5168\u8f93\u5165\u9700\u8981 4 \u4e2a\u65f6\u949f\u5468\u671f\uff09\u3002</p> <p>\u5047\u8bbe\u7b2c 1 \u4e2a\u5468\u671f\u7ed3\u675f\u540e\uff0c<code>1001</code> \u6700\u53f3\u4fa7\u7684 <code>1</code> \u88ab\u5b58\u5728\u4e86\u7b2c\u4e00\u4e2a FF\uff0c\u5219\uff1a</p> \u5468\u671f \u5f85\u8f93\u5165 FF1 FF2 FF3 FF4 SO 1 <code>100</code> <code>1</code> ? ? ? <code>1???</code> 2 <code>10</code> <code>0</code> <code>1</code> ? ? <code>01??</code> 3 <code>1</code> <code>0</code> <code>0</code> <code>1</code> ? <code>001?</code> 4 <code>1</code> <code>0</code> <code>0</code> <code>1</code> <code>1001</code> 5 ? <code>1</code> <code>0</code> <code>0</code> <code>?100</code> 6 ? ? <code>1</code> <code>0</code> <code>??10</code> 7 ? ? ? <code>1</code> <code>???1</code> <p>\u8fd9\u91cc\u7684 SO \u6307\u7684\u662f\u4ece\u5f53\u524d\u8f6e\u6b21\u5f00\u59cb\uff0c\u8bfb\u5165 4bits \u6570\u636e\u5f97\u5230\u7684\u4e32\u884c\u8f93\u51fa\u7ed3\u679c\uff0c\u8fd9\u91cc\u7684 4bits \u5f53\u7136\u662f\u5bf9\u5e94\u8f93\u5165\u7684 4bits\u3002</p> <p>\u53ef\u4ee5\u53d1\u73b0\uff0c\u5728\u7b2c\u56db\u8f6e\u524d\u540e\u7684\u7ed3\u679c\u5206\u522b\u662f\u5de6\u79fb\u548c\u53f3\u79fb\u7684\u7ed3\u679c\uff0c\u5f53\u7136\uff0c\u5982\u679c\u662f\u8981\u8003\u8651\u5177\u6709\u5b9e\u9645\u8ba1\u7b97\u4ef7\u503c\u7684\u4f4d\u79fb\uff0c\u6211\u4eec\u5f53\u7136\u9700\u8981\u586b\u5145 <code>?</code> \u7684\u503c\uff0c\u4e0d\u8fc7\u8fd9\u90fd\u662f\u5c0f\u4e8b\u60c5\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap06/#\u5e76\u884c\u5316","title":"\u5e76\u884c\u5316","text":"<p>\u5e76\u884c\u5316\u4e3b\u8981\u6709\u4e24\u4e2a\u65b9\u9762\uff0c\u5373\u5e76\u884c\u8f93\u51fa(parallel output)\u548c\u5e76\u884c\u8f7d\u5165(parallel load)\uff0c\u5206\u522b\u5bf9\u5e94\u7740 \u5728\u540c\u4e00\u4e2a\u65f6\u95f4\u5468\u671f\u5185\u5f97\u5230\u6bcf\u4e00\u4e2a <code>FF</code> \u7684\u7ed3\u679c\u548c\u5bf9\u6bcf\u4e00\u4e2a <code>FF</code> \u8f7d\u5165\u6570\u636e\u3002</p> <p>\u5e76\u884c\u8f93\u51fa\u7684\u5b9e\u73b0\u975e\u5e38\u7b80\u5355\uff0c\u53ea\u9700\u8981\u7ed9\u6bcf\u4e00\u4e2a <code>FF</code> \u7684\u8f93\u51fa\u5f15\u51fa\u4e00\u6761\u7ebf\u5c31\u884c\u4e86\uff0c\u5b83\u4e0e\u4e32\u884c\u8f93\u51fa\u53ef\u4ee5\u76f4\u63a5\u540c\u65f6\u5b58\u5728\uff1b\u800c\u5e76\u884c\u8f93\u5165\u5219\u4e0e\u4e32\u884c\u8f93\u5165\u51b2\u7a81\uff0c\u4e00\u6b21\u53ea\u80fd\u5b9e\u73b0\u5176\u4e2d\u4e00\u4e2a\uff0c\u6240\u4ee5\u9700\u8981\u4e00\u4e9b\u63a7\u5236\u7535\u8def\uff1a</p> <p></p> <p>\u770b\u8d77\u6765\u6709\u70b9\u590d\u6742\uff0c\u4f46\u662f\u5b9e\u9645\u4e0a\u903b\u8f91\u8fd8\u662f\u5f88\u6e05\u6670\u7684\u3002</p> <ul> <li>\u7eb5\u5411\u89c2\u5bdf\u53f3\u4fa7\u7684\u56db\u4e2a <code>FF</code>\uff0c\u53ef\u4ee5\u53d1\u73b0\u57fa\u672c\u4e0a\u5c31\u662f\u4e32\u884c\u4f4d\u79fb\u5b9e\u73b0\uff0c\u53ea\u4e0d\u8fc7\u5176\u8f93\u5165\u4e0d\u518d\u662f\u76f4\u63a5\u4ece\u4e0a\u4e00\u4e2a <code>FF</code> \u90a3\u8fb9\u62ff\u6765\u7684\uff1b</li> <li>\u56db\u4e2a <code>FF</code> \u7684\u8f93\u5165\u662f\u7c7b\u4f3c\u7684\uff0c\u6240\u4ee5\u6211\u4eec\u4ec5\u5173\u6ce8\u6700\u4e0a\u9762\u7684\u90a3\u4e09\u4e2a\u4e0e\u95e8\u548c\u4e00\u4e2a\u6216\u95e8\uff0c\u8868\u793a\u6570\u636e\u8f93\u5165\u6709\u4e09\u4e2a\u53ef\u80fd\u7684\u6765\u6e90\uff1b<ol> <li>\u7b2c\u4e00\u4e2a\u4e0e\u95e8\uff0c\\(F_i=Shift \\cdot SI\\)\uff08\u5bf9\u4e8e\u540e\u9762\u51e0\u4e2a <code>FF</code>\uff0c\u5219\u662f \\(F_i=Shift \\cdot FF_{i-1}\\)\uff09\uff0c\u53ef\u4ee5\u53d1\u73b0\uff0c\u6b64\u65f6\u7535\u8def\u7684\u884c\u4e3a\u4e0e\u4e32\u884c\u4f4d\u79fb\u5b9e\u73b0\u4e00\u81f4\uff1b<ul> <li>\u5373 \\(Shift\\) \u4e3a <code>1</code> \u65f6\uff0c<code>SHR</code> \u8868\u73b0\u4e3a\u300c\u6bcf\u4e2a\u5468\u671f\u6267\u884c\u4e00\u6b21\u4f4d\u79fb\u300d\uff1b</li> </ul> </li> <li>\u7b2c\u4e8c\u4e2a\u4e0e\u95e8\uff0c\\(F_i=\\overline{Shift} \\cdot Load \\cdot D_i\\)\uff0c\u6b64\u65f6\u7535\u8def\u7684\u884c\u4e3a\u662f\u4f7f\u7528\u6bd4\u7279\u5411\u91cf\u5bf9\u6bcf\u4e00\u4e2a <code>FF</code> \u8d4b\u503c\uff0c\u5373\u5e76\u884c\u8f7d\u5165\uff1b<ul> <li>\u5373 \\(\\overline{Shift} \\cdot Load\\) \u4e3a <code>1</code> \u65f6\uff0c<code>SHR</code> \u8868\u73b0\u4e3a\u300c\u5e76\u884c\u8f7d\u5165\u300d\uff1b</li> </ul> </li> <li>\u7b2c\u4e09\u4e2a\u4e0e\u95e8\uff0c\\(F_i=\\overline{Shift} \\cdot \\overline{Load} \\cdot Q_i\\)\uff0c\u6b64\u65f6\u7535\u8def\u7684\u884c\u4e3a\u662f\u4fdd\u6301\u4e0a\u4e00\u5468\u671f\u7684\u7ed3\u679c\uff1b<ul> <li>\u5373 \\(\\overline{Shift} \\cdot \\overline{Load}\\) \u4e3a <code>1</code> \u65f6\uff0c<code>SHR</code> \u8868\u73b0\u4e3a\u300c\u4fdd\u6301\u300d\uff1b</li> </ul> </li> </ol> </li> </ul> <p>\u603b\u548c\u6765\u8bf4\uff0c\u5c31\u662f\uff1a</p> \\[ \\begin{aligned}       Shift :&amp; Q\\leftarrow \\mathrm{sl}\\; Q \\\\          \\overline{Shift}\\cdot Load :&amp; Q\\leftarrow D \\\\          \\overline{Shift}\\cdot \\overline{Load} :&amp; Q\\leftarrow Q \\end{aligned} \\] <p></p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap06/#\u53cc\u5411\u4f4d\u79fb\u5bc4\u5b58\u5668","title":"\u53cc\u5411\u4f4d\u79fb\u5bc4\u5b58\u5668","text":"<p>\u4e0a\u9762\u4ecb\u7ecd\u7684\u4f4d\u79fb\u5bc4\u5b58\u5668\u968f\u7740\u65f6\u949f\u5468\u671f\u7684\u4f9b\u7ed9\uff0c\u53ea\u80fd\u4e0d\u53ef\u9006\u3001\u5355\u5411\u5730\u8fdb\u884c\u4f4d\u79fb\uff0c\u8fd9\u79cd\u4f4d\u79fb\u5bc4\u5b58\u5668\u79f0\u4e3a\u65e0\u5411\u4f4d\u79fb\u5bc4\u5b58\u5668(Unidirectional SHR)\uff1b\u5bf9\u5e94\u7684\uff0c\u5982\u679c\u80fd\u591f\u652f\u6301\u53ef\u63a7\u5236\u7684\u5de6\u79fb\u53f3\u79fb\uff0c\u5219\u88ab\u79f0\u4e3a\u53cc\u5411\u4f4d\u79fb\u5bc4\u5b58\u5668(Bidirectional SHR)\u3002</p> <p>\u5176\u884c\u4e3a\u5982\u4e0b\uff1a</p> \\[ \\begin{aligned}     \\overline{S_0} \\cdot \\overline{S_1} :&amp; Q \\leftarrow Q\\\\     S_0 \\cdot \\overline{S_1} :&amp; Q\\leftarrow\\mathrm{Sl}\\; Q \\\\     \\overline{S_0} \\cdot S_1 :&amp; Q\\leftarrow\\mathrm{Sr}\\; Q \\\\     S_0 \\cdot S_1:&amp; Q\\leftarrow D \\end{aligned} \\] <p>\u5176\u5355\u5143\u5b9e\u73b0\u5982\u4e0b\uff1a</p> <p></p> <p>\u5176\u672c\u8d28\u4e0a\u5c31\u662f\u6dfb\u52a0\u4e86\u4e00\u4e2a <code>MUX</code> \u6765\u9009\u62e9\u4e0b\u4e00\u4e2a\u65f6\u949f\u662f\u7ee7\u627f \\((i+1)\\)\u3001\\((i-1)\\)\u3001\\(D_i\\) \u8fd8\u662f \\(Q\\)\u3002</p> <p>\u7efc\u5408\u9610\u8ff0</p> <p>\u4ee3\u7801\u610f\u4e49\u4e0a\u7684\u4f4d\u79fb\u4e00\u822c\u6307\u7684\u662f\u4e00\u4e2a\u53cc\u76ee\u64cd\u4f5c\uff0c\u5373\u53ef\u4ee5\u6307\u5b9a\u4f4d\u79fb\u591a\u5c11\u4f4d\uff0c\u8fd9\u4e2a\u53c2\u6570\u88ab\u79f0\u4e3a\u4f4d\u79fb\u91cf(Shift Amount)\u3002</p> <p>\u4f46\u5728\u786c\u4ef6\u5c42\u9762\u7684\u5b9e\u73b0\u4e0a\uff0c\u8fd9\u4e2a\u591a\u5c11\u201c\u4f4d\u201d\u53ea\u80fd\u901a\u8fc7\u5faa\u73af\u548c\u5df2\u7ecf\u5b9e\u73b0\u7684\u3001\u6709\u9650\u79cd\u786e\u5b9a\u4f4d\u79fb\u91cf\u7684\u4f4d\u79fb\u5b9e\u73b0\uff0c\u5728\u6211\u4eec\u63d0\u5230\u7684\u5b9e\u73b0\u4e2d\uff0c\u6307\u7684\u5c31\u662f\u6211\u4eec\u786c\u4ef6\u53ea\u5b9e\u73b0\u300c\u4e00\u4f4d\u4f4d\u79fb\u300d\uff0c\u5e76\u901a\u8fc7\u5faa\u73af\u5b9e\u73b0\u300c\u4efb\u610f\u4f4d\u4f4d\u79fb\u300d\uff0c\u800c\u8fd9\u4e2a\u201c\u5faa\u73af\u201d\uff0c\u5c31\u662f\u5728\u65f6\u949f\u5468\u671f\u4e0b\uff0c<code>FF</code> \u4e0d\u65ad\u7ee7\u627f\u4e0a\u4e00\u4e2a <code>FF</code> \u7684\u503c\u6765\u5b9e\u73b0\u7684\u3002</p> <p>\u800c\u5e76\u884c\u4e0e\u4e32\u884c\u5b9e\u73b0\u65e0\u975e\u662f\u4f53\u73b0\u8fd9\u4e2a\u7279\u5f81\u7684\u4e24\u79cd\u5b9e\u73b0\u65b9\u6cd5\u800c\u5df2\u3002</p> \u5173\u4e8e\u5e76\u884c\u548c\u4e32\u884c <p>\u8fd9\u662f\u4e00\u4e2a\u9898\u5916\u8bdd\uff0c\u6211\u6682\u65f6\u4e0d\u77e5\u9053\u653e\u54ea\u91cc\uff0c\u521a\u597d\u8fd9\u91cc\u63d0\u5230\u4e86\u5c31\u5728\u8fd9\u91cc\u8bf4\u4e86\u3002</p> <p>\u5b9e\u9645\u4e0a\uff0c\u867d\u7136\u770b\u8d77\u6765\u5e76\u884c\u7684\u6548\u7387\u4f1a\u6bd4\u4e32\u884c\u9ad8\u5f88\u591a\uff0c\u4f46\u662f\u5b9e\u9645\u4e0a\u5f88\u591a\u9ad8\u901f\u4f20\u8f93\u8bbe\u5907\u6216\u534f\u8bae\u7528\u7684\u90fd\u662f\u4e32\u884c\u3002\u8fd9\u662f\u56e0\u4e3a\uff0c\u5e76\u884c\u5355\u6b21\u4f20\u8f93\u7ebf\u8def\u591a\uff0c\u7ebf\u8def\u4e4b\u95f4\u7684\u8ddd\u79bb\u5c0f\uff0c\u5e72\u6270\u5927\uff0c\u6240\u4ee5\u76f8\u5bf9\u6765\u8bf4\u6b63\u5e38\u5de5\u4f5c\u6240\u4e0b\u5bf9\u9891\u7387\u7684\u8981\u6c42\u66f4\u9ad8\uff1b\u800c\u4e32\u884c\u7531\u4e8e\u53ef\u4ee5\u4f7f\u7528\u66f4\u9ad8\u7684\u9891\u7387\u5de5\u4f5c\uff0c\u6240\u4ee5\u5728\u67d0\u4e9b\u60c5\u51b5\u4e0b\u6548\u7387\u66f4\u9ad8\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap06/#\u8ba1\u6570\u5668","title":"\u8ba1\u6570\u5668","text":"<p>\u8ba1\u6570\u5668(counter) \u662f\u4ec0\u4e48\uff0c\u5df2\u7ecf\u5728#\u5bc4\u5b58\u5668\u4e2d\u89e3\u91ca\u4e86\uff0c\u6839\u636e\u5b9e\u73b0\u539f\u7406\uff0c\u4e3b\u8981\u5206\u4e3a\u884c\u6ce2\u8ba1\u6570\u5668(Ripple Counter)\u548c\u540c\u6b65\u8ba1\u6570\u5668(Synchronous Counter)\u4e24\u79cd\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap06/#\u884c\u6ce2\u8ba1\u6570\u5668","title":"\u884c\u6ce2\u8ba1\u6570\u5668","text":"<p>\u884c\u6ce2\u8ba1\u6570\u5668\u7684\u4e3b\u8981\u601d\u60f3\u5c31\u662f\u5c06\u4e00\u4e2a\u4e0d\u65ad\u81ea\u53cd\u7684 <code>FF</code> \u7684\u8f93\u51fa\u76f4\u63a5\u6216\u95f4\u63a5\u4f5c\u4e3a\u4e0b\u4e00\u4e2a <code>FF</code> \u7684\u65f6\u949f\u8109\u51b2\u3002\u7531\u4e8e\u5f62\u6210\u4e00\u6b21\u8109\u51b2\u9700\u8981\u4e00\u5bf9 <code>0</code>&amp;<code>1</code>\uff0c\u6240\u4ee5\u524d\u4e00\u4e2a <code>FF</code> \u53d6\u53cd\u4e24\u6b21\u624d\u80fd\u5f15\u8d77\u4e0b\u4e00\u4e2a <code>FF</code> \u53d6\u53cd\u4e00\u6b21\uff0c\u5982\u679c\u4e0b\u4e00\u4e2a <code>FF</code> \u662f\u5728\u4e0a\u4e00\u4e2a <code>FF</code> \u7684\u8f93\u51fa\u4ece <code>1</code> \u53d8 <code>0</code> \u65f6\u89e6\u53d1\uff0c\u90a3\u4e24\u4e2a <code>FF</code> \u7684\u53d8\u5316\u521a\u597d\u5bf9\u5e94\u4e8e\u4e8c\u8fdb\u5236\u81ea\u589e\u7684\u8fdb\u4f4d\u89c4\u5f8b\uff1a<code>(0,0)</code>\uff0c<code>(0,1)</code>\uff0c<code>(1,0)</code>\uff0c<code>(1,1)</code>\uff0c<code>0,0</code>\uff0c...</p> <p>\u4e8e\u662f\uff0c\u4e00\u4e2a 4-Bit \u884c\u6ce2\u8ba1\u6570\u5668\u7684\u903b\u8f91\u56fe\u5c31\u5982\u4e0b\uff1a</p> <p></p> <ul> <li>\u4e0a\u56fe\u4e2d\uff0c\u4e0b\u4e00\u4e2a <code>FF</code> \u7684\u65f6\u949f\u6765\u81ea\u4e8e\u4e0a\u4e00\u4e2a <code>FF</code> \u7684\u8f93\u51fa\u53d6\u53cd\uff0c\u4e5f\u5c31\u662f\u5bf9\u4e8e\u4e0a\u5347\u6cbf\u89e6\u53d1\u7684 <code>FF</code> \u6765\u8bf4\uff0c\u4e0b\u4e00\u4e2a <code>FF</code> \u4f1a\u5728\u4e0a\u4e00\u4e2a <code>FF</code> \u7684\u8f93\u51fa\u4ece <code>1</code> \u5230 <code>0</code> \u65f6\u81ea\u53cd\uff0c\u6240\u4ee5\u662f\u6b63\u5411\u8ba1\u65f6(Upward Counting)\uff1b</li> <li>\u53cd\u4e4b\uff0c\u5982\u679c\u4e0b\u4e00\u4e2a <code>FF</code> \u7684\u65f6\u949f\u6765\u81ea\u4e8e\u4e0a\u4e00\u4e2a <code>FF</code> \u7684\u76f4\u63a5\u8f93\u51fa\uff0c\u4e5f\u5c31\u662f\u5bf9\u4e8e\u4e0a\u5347\u6cbf\u89e6\u53d1\u7684 <code>FF</code> \u6765\u8bf4\uff0c\u4e0b\u4e00\u4e2a <code>FF</code> \u4f1a\u5728\u4e0a\u4e00\u4e2a <code>FF</code> \u7684\u8f93\u51fa\u4ece <code>0</code> \u5230 <code>1</code> \u65f6\u81ea\u53cd\uff0c\u6240\u4ee5\u662f\u9006\u5411\u8f93\u51fa(Downward Counting)\uff1b</li> </ul> <p></p> <p>\u53ef\u4ee5\u53d1\u73b0\uff0c\u884c\u6ce2\u8ba1\u6570\u5668\u7684\u4f18\u70b9\u662f\u7535\u8def\u7b80\u5355\uff0c\u6210\u672c\u4f4e\uff1b\u4f46\u662f\u7f3a\u70b9\u4e5f\u5f88\u660e\u663e\uff0c\u65e2\u7136\u5b83\u4e0e\u540c\u6b65\u8ba1\u6570\u5668\u76f8\u533a\u5206\uff0c\u5c31\u8bf4\u660e\u5b83\u4e0d\u662f\u540c\u6b65\u7535\u8def\uff0c\u6bcf\u4e00\u4e2a <code>FF</code> \u90fd\u4f1a\u6709\u4f20\u64ad\u5ef6\u65f6\uff0c\u968f\u7740\u8ba1\u6570\u8303\u56f4\u589e\u5927\uff0c\u603b\u4f20\u64ad\u5ef6\u65f6\u4e5f\u4f1a\u589e\u52a0\uff0c\u800c\u4e3a\u4e86\u8ba9\u7535\u8def\u6b63\u5e38\u5de5\u4f5c\uff0c\u65f6\u949f\u9891\u7387\u4e5f\u8981\u56e0\u6b64\u4e0b\u964d\u3002</p> <p>\u7531\u4e8e\u8fd9\u4e9b\uff0c\u4e66\u4e0a\u5bf9\u884c\u6ce2\u8ba1\u6570\u5668\u7684\u8bc4\u4ef7\u662f\u591a\u6570\u60c5\u51b5\u4e0b\u884c\u6ce2\u52a0\u6cd5\u5668\u53ea\u4f1a\u5728\u4f4e\u529f\u8017\u7535\u8def\u4e2d\u88ab\u91c7\u7528\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap06/#\u540c\u6b65\u8ba1\u6570\u5668","title":"\u540c\u6b65\u8ba1\u6570\u5668","text":"<p>\u540c\u6b65\u8ba1\u6570\u5668\u4ece\u5b9e\u73b0\u81ea\u589e\u7684\u539f\u7406\u4e0a\u6765\u8bf4\uff0c\u548c\u884c\u6ce2\u8ba1\u6570\u5668\u4e5f\u662f\u7c7b\u4f3c\u7684\uff0c\u540c\u6837\u662f\u5728\u4e0a\u4e00\u4e2a <code>FF</code> \u5b8c\u6210\u4e00\u6b21\u7ffb\u8f6c\u7684\u65f6\u5019\u8ba9\u4e0b\u4e00\u4e2a <code>FF</code> \u53d8\u5316\u3002\u53ea\u4e0d\u8fc7\u540c\u6b65\u8ba1\u6570\u5668\u4e0d\u662f\u63a7\u5236\u65f6\u949f\uff0c\u800c\u662f\u63a7\u5236\u300c<code>FF</code> \u5185\u7684\u503c\u662f\u5426\u53d6\u53cd\u300d\u6765\u5b9e\u73b0\uff0c\u800c\u5b83\u662f\u901a\u8fc7\u5f02\u6216\u95e8\u6765\u5b9e\u73b0\u7684\u3002</p> <p>\u6211\u4eec\u77e5\u9053\uff0c\\(0 \\;\\mathrm{XOR}\\; X = X\\)\uff0c\u800c \\(1 \\;\\mathrm{XOR}\\; X = \\overline{X}\\)\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u53ef\u4ee5\u63a7\u5236 <code>XOR</code> \u7684\u67d0\u4e2a\u8f93\u5165\u662f <code>0</code> \u8fd8\u662f <code>1</code> \u6765\u5b9e\u73b0\u53d6\u53cd\u8fd8\u662f\u4fdd\u6301\u7684\u5207\u6362\u3002</p> <p>\u4e0d\u8fc7\u9700\u8981\u533a\u5206\u7684\u662f\uff0c\u884c\u6ce2\u8ba1\u6570\u5668\u662f\u5728\u4e0a\u4e00\u4e2a <code>FF</code> \u53d8\u5316\u5b8c\u624d\u5f71\u54cd\u4e0b\u4e00\u4e2a\u7684\uff0c\u6240\u4ee5\u662f <code>1</code> \u53d8 <code>0</code> \u65f6\u9700\u8981\u8fdb\u4f4d\uff1b\u800c\u540c\u6b65\u8ba1\u6570\u5668\u7684\u6240\u6709 <code>FF</code> \u662f\u4e00\u8d77\u53d8\u5316\u7684\uff0c\u6240\u4ee5\u53ea\u6709\u5728\u524d\u9762\u90fd\u662f <code>1</code> \u65f6\u5019\uff0c\u8868\u793a\u4e0b\u4e00\u523b\u5b83\u4eec\u90fd\u8981\u8fdb\u4f4d\u4e86\uff0c\u5f53\u524d <code>FF</code> \u624d\u8fdb\u4f4d\u3002</p> <p>\u4e5f\u5c31\u662f\u8bf4\uff0c\u884c\u6ce2\u8ba1\u6570\u5668\u662f\u5efa\u7acb\u5728\u524d\u4e00\u4e2a <code>FF</code> \u7684\u7ed3\u679c\u8fdb\u884c\u53d8\u5316\uff1b\u800c\u5e76\u884c\u52a0\u6cd5\u5668\u662f\u5efa\u7acb\u5728\u4e0a\u4e00\u523b\u6240\u6709\u5173\u8054 <code>FF</code> \u7684\u72b6\u6001\uff0c\u5bf9\u4e0b\u4e00\u72b6\u6001\u7684\u9884\u5224\u3002</p> <p>\u5728\u8fd9\u57fa\u7840\u4e0a\uff0c\u540c\u6b65\u8ba1\u6570\u5668\u7684\u81ea\u589e\u5668(incrementer)\u6709\u4e24\u79cd\u4e0d\u540c\u7684\u5b9e\u73b0\u65b9\u6cd5\uff1a</p> <p></p> <p>(b) \u7684\u84dd\u8272\u90e8\u5206\u66ff\u6362 (a) \u7684\u84dd\u6846\u90e8\u5206\u4e3a\u7b2c\u4e8c\u79cd\u3002\u4e24\u79cd\u5206\u522b\u4e3a \u95e8\u4e32\u884c\u5b9e\u73b0 \u548c \u95e8\u5e76\u884c\u5b9e\u73b0\u3002</p> <p>\u4e24\u79cd\u5b9e\u73b0\u5176\u5b9e\u539f\u7406\u90fd\u662f\u4e00\u6837\u7684\uff0c\u53ea\u4e0d\u8fc7\u95e8\u4e32\u884c\u727a\u7272\u67d0\u4e9b\u60c5\u51b5\u4e0b\u7684\u8fd0\u884c\u6548\u7387\uff0c\u8282\u7ea6\u4e86\u95e8\u6210\u672c\uff1b\u800c\u95e8\u5e76\u884c\u63d0\u9ad8x\u4e86\u95e8\u6210\u672c\uff0c\u51cf\u5c11\u4e86\u67d0\u4e9b\u60c5\u51b5\u4e0b\u7684\u95e8\u5ef6\u8fdf\u3002</p> <p>\u5f53\u7136\uff0c\u65e2\u7136\u4f7f\u7528\u7684\u662f\u81ea\u589e\u5668\uff0c\u90a3\u4e48\u5b9e\u73b0\u7684\u81ea\u7136\u5c31\u662f\u6b63\u5411\u8ba1\u6570\u5668\u3002\u4e3a\u4e86\u5b9e\u73b0\u9006\u5411\u8ba1\u6570\u5668\uff0c\u6211\u4eec\u5219\u9700\u8981\u5c06\u81ea\u589e\u5668\u6362\u4e3a\u81ea\u51cf\u5668\u3002\u505a\u6cd5\u53ea\u4e0d\u8fc7\u662f\u5c06\u5f02\u6216\u95e8\u7684\u63a7\u5236\u4fe1\u53f7\u53d6\u53cd\u3002</p> <p>\u5177\u4f53\u6765\u8bf4\uff0c\u8f93\u5165\u51fd\u6570\u53d8\u4e3a\uff1a</p> \\[ \\begin{aligned}     D_{A0} = &amp; Q_0 \\oplus EN \\\\     D_{A1} = &amp; Q_1 \\oplus \\left(         (Q_0 \\cdot \\overline{S} + \\overline{Q_0} \\cdot S) \\cdot EN     \\right) \\\\     D_{A2} = &amp; Q_2 \\oplus \\left(         (Q_0 \\cdot Q_1 \\cdot \\overline{S} + \\overline{Q_0} \\cdot \\overline{Q_1} \\cdot S) \\cdot EN     \\right) \\\\     D_{A3} = &amp; Q_3 \\oplus \\left(         (Q_0 \\cdot Q_1 \\cdot Q_2 \\cdot \\overline{S} + \\overline{Q_0} \\cdot \\overline{Q_1} \\cdot \\overline{Q_2} \\cdot S) \\cdot EN     \\right) \\end{aligned} \\] <p>\u4ece\u8fd9\u4e2a\u8868\u8fbe\u5f0f\u4e5f\u53ef\u4ee5\u7565\u5fae\u611f\u53d7\u5230\u95e8\u4e32\u884c\u548c\u95e8\u5e76\u884c\u7684\u533a\u522b\u7a76\u7adf\u5728\u54ea\u91cc\uff0c\u5b83\u4eec\u4f7f\u7528\u540c\u4e00\u4e2a\u8868\u8fbe\u5f0f\uff0c\u53ea\u4e0d\u8fc7\u7528\u4e0d\u540c\u7684\u65b9\u5f0f\u6765\u5b9e\u73b0\u591a\u4f4d <code>AND</code> \u8fd0\u7b97\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap06/#\u540c\u6b65\u8f7d\u5165","title":"\u540c\u6b65\u8f7d\u5165","text":"<p>\u8fd9\u91cc\u540c\u6b65\u8f7d\u5165\u7684\u542b\u4e49\u53ef\u4ee5\u540c\u4f4d\u79fb\u5bc4\u5b58\u5668\u7684\u5e76\u884c\u8f7d\u5165\u7c7b\u6bd4\uff0c\u5176\u4e3b\u8981\u76ee\u7684\u662f\u5c06\u8ba1\u6570\u5668\u7684\u5f53\u524d\u503c\u8bbe\u4e3a\u4e00\u4e2a\u6211\u4eec\u9700\u8981\u7684\u6570\u5b57\u3002</p> <p>\u4ee5\u95e8\u4e32\u884c\u5b9e\u73b0\u4e3a\u4f8b\uff0c\u6dfb\u52a0\u529f\u80fd\u63a7\u5236\u903b\u8f91\u540e\u7684\u8bbe\u8ba1\u5982\u4e0b\uff1a</p> <p></p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap06/#\u4efb\u610f\u8ba1\u6570\u5e8f\u5217","title":"\u4efb\u610f\u8ba1\u6570\u5e8f\u5217","text":"<p>\u73b0\u5728\u8ba9\u6211\u4eec\u56de\u5f52\u8ba1\u6570\u5668\u7684\u884c\u4e3a\uff1a\u968f\u7740\u65f6\u949f\u5468\u671f\u4e0d\u65ad\u5728\u56fa\u5b9a\u7684\u72b6\u6001\u5e8f\u5217\u4e2d\u5faa\u73af\u3002\u4e5f\u5c31\u662f\u8bf4\uff0c\u8fd9\u4e2a\u5e8f\u5217\u672a\u5fc5\u9700\u8981\u662f\u6574\u6570\u81ea\u589e\u81ea\u51cf\u5e8f\u5217\u3002\u800c\u5b9e\u73b0\u67d0\u4e00\u5e8f\u5217\u7684\u8ba1\u6570\u884c\u4e3a\uff0c\u5b9e\u9645\u4e0a\u53ea\u8981\u8bbe\u8ba1\u597d\u6709\u9650\u72b6\u6001\u548c\u72b6\u6001\u4e4b\u95f4\u7684\u8f6c\u79fb\u5373\u53ef\u3002</p> <p>\u5f53\u7136\uff0c\u8fd9\u4e2a\u8bdd\u9898\u592a\u8fc7\u5bbd\u6cdb\uff0c\u6211\u4eec\u5728\u8fd9\u91cc\u5177\u4f53\u8ba8\u8bba\u7684\u8fd8\u662f\u6574\u6570\u81ea\u589e\u5e8f\u5217\uff0c\u53ea\u4e0d\u8fc7\u9650\u5236\u4e86\u4e0a\u4e0b\u754c\u3002\u4e66\u4e0a\u63d0\u4f9b\u7684\u6848\u4f8b\u662f BCD \u7801\u7684\u5faa\u73af\u8ba1\u6570\uff0c\u90a3\u6211\u4eec\u4e5f\u8ddf\u7740\u8fd9\u4e2a\u6848\u4f8b\u6765\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap06/#bcd-\u7801\u5faa\u73af\u8ba1\u6570","title":"BCD \u7801\u5faa\u73af\u8ba1\u6570","text":"<p>\u9996\u5148\u6211\u4eec\u9700\u8981\u6839\u636e\u65f6\u5e8f\u7535\u8def\u7684\u8bbe\u8ba1\u89c4\u5219\uff0c\u641e\u6e05\u695a\u72b6\u6001\u5e8f\u5217\uff0c\u663e\u7136\uff0c\u6839\u636e BCD \u7801\u7684\u5b9a\u4e49\uff0c\u6211\u4eec\u53ef\u4ee5\u6bdb\u6bdb\u5730\u8ba4\u4e3a\u5b83\u662f\u4e0b\u786e\u754c\u4e3a <code>0</code>\uff0c\u4e0a\u786e\u754c\u4e3a <code>9</code> \u7684 4 \u6bd4\u7279\u6574\u6570\u5e8f\u5217\u3002\u6362\u53e5\u8bdd\u8bf4\uff0c\u6211\u4eec\u9700\u8981\u5b9e\u73b0\u4e00\u4e2a\u8ba1\u6570\u5230 <code>9</code> \u540e\u4e0b\u4e00\u4e2a\u72b6\u6001\u662f <code>0</code> \u7684 4 \u6bd4\u7279\u8ba1\u6570\u5668\u3002</p> <p>\u4e8e\u662f\u6211\u4eec\u53ef\u4ee5\u5f53\u8ba1\u6570\u5668\u7684\u8f93\u51fa\u4e3a <code>9</code> \u65f6\uff0c\u4e0b\u4e00\u5468\u671f\u8ba9\u8ba1\u6570\u5668\u8f7d\u5165 <code>0</code>\uff1a</p> <p></p> <p>\u6309\u7406\u6765\u8bf4\u8fd9\u91cc\u5e94\u8be5\u662f \\(Load = Q_0\\cdot\\overline{Q_1}\\cdot\\overline{Q_2}\\cdot Q_3\\)\uff0c\u4ee5\u5bf9\u5e94 <code>9D=1001B</code>\uff0c\u4f46\u662f\u7531\u4e8e\u81ea\u589e\u8fc7\u7a0b\u4e2d\uff0c<code>1001</code> \u662f\u7b2c\u4e00\u4e2a\u6ee1\u8db3 <code>1??1</code> \u7684\u7ec4\u5408\uff0c\u6240\u4ee5\u53ef\u4ee5\u76f4\u63a5\u7b80\u5316\u4e3a \\(Load = Q_0\\cdot Q_3\\)\u3002</p> <p>\u5982\u4e0a\u662f\u4fee\u6539\u4e0a\u786e\u754c\u7684\u65b9\u6cd5\uff0c\u800c\u4fee\u6539\u4e0b\u786e\u754c\u7684\u65b9\u6cd5\u5219\u662f\u4fee\u6539 \\(D_i\\) \u5e8f\u5217\uff0c\u4f8b\u5982\u4e0a\u56fe\u4e2d \\(D\\) \u63a5\u5730\uff0c\u6240\u4ee5\u4e0b\u786e\u754c\u662f <code>0000B</code>\u3002</p> <p>Mod N \u8ba1\u6570\u5668</p> <p>\u5b9e\u9645\u4e0a\uff0c\u6211\u4eec\u53ef\u4ee5\u628a BCD \u7801\u5faa\u73af\u8ba1\u6570\u5668\u770b\u4f5c\u662f\u7279\u6b8a\u7684 Mod N \u8ba1\u6570\u5668\uff0c\u5373 N = 10 \u7684 Mod N \u8ba1\u6570\u5668\u3002</p> <p>\u6216\u8bb8\u4f60\u4f1a\u60f3\uff0c\u5b9e\u73b0 Mod N \u8ba1\u6570\u5668\u80fd\u4e0d\u80fd\u5728\u6ee1\u8db3\u8f93\u51fa\u6761\u4ef6\u540e\u76f4\u63a5\u4f7f\u7528 <code>Clear</code> \u8f93\u5165\u3002\u4f46\u662f\u8bf7\u4e0d\u8981\u5fd8\u8bb0\u4e86\uff0c<code>Clear</code> \u4e5f\u597d\uff0c<code>Set</code> \u4e5f\u7f62\uff0c\u5b83\u4eec\u90fd\u662f\u5f02\u6b65\u64cd\u4f5c\u3002\u6211\u4eec\u6ca1\u6709\u5fc5\u8981\u4e5f\u4e0d\u5e94\u8be5\u4f7f\u7528\u5f02\u6b65\u64cd\u4f5c\uff0c\u6240\u4ee5\u6700\u597d\u7684\u505a\u6cd5\u8fd8\u662f\u4f7f\u7528 <code>Load</code>\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap06/#\u5bc4\u5b58\u5668\u4f20\u8f93\u7684\u63a7\u5236","title":"\u5bc4\u5b58\u5668\u4f20\u8f93\u7684\u63a7\u5236","text":"<p>\u672a\u5b8c\u6210</p> <p>Control Unit</p> <ul> <li>Programmable sys<ul> <li>instructions (usually stored in memory RAM/ROM)</li> <li>program counter</li> </ul> </li> <li> <p>Nonprogrammable sys</p> <ul> <li>focus on this</li> <li>State machine diagrams for Control Unit design.</li> </ul> </li> <li> <p>Write a detailed system specification.</p> </li> <li>Define all external data and control input signals, all external data, control, and status output signals, and the registers of the datapath and control unit.</li> <li>Find a state machine diagram for the system including the register transfers in the datapath and in the control unit.</li> <li>Define internal control and status signals. Use these signals to separate output conditions and actions, including register transfers, from the state diagram flow and represent them in tabular form.</li> <li>Draw a block diagram of the datapath including all control and status inputs and outputs. Draw a block diagram of the control unit if it includes register transfer hardware.</li> <li>Design any specialized register transfer logic in both the control and datapath.</li> <li>Design the control unit logic.</li> <li>Verify the correct operation of the combined datapath and control logic. If verification fails, debug the system and reverify it.</li> </ul> <p>\u91cd\u70b9\u770b\u4e66\u4e0a\u7684\u4f8b\u5b50\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap07/","title":"Chap 7 Memory Basics","text":"<p> \u7ea6 737 \u4e2a\u5b57  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 2 \u5206\u949f</p> <p>\u6846\u67b6</p> <ul> <li>Two types: RAM &amp; ROM<ul> <li>RAM ship consists of an array of RAM cells, decoders, write circuits, read circuits, output circuits</li> <li>RAM bit slice</li> <li>DRAM</li> <li>Error-detection and correction codes, often based on Hamming codes</li> </ul> </li> <li>R&amp;W operations have specific steps and associated timing parameters: access time &amp; write cycle time</li> <li>static(SRAM) or dynamic(DRAM), volatile or nonvolatile</li> </ul>"},{"location":"cour_note/D2QD_DigitalDesign/Chap07/#7-1-memory","title":"7-1 Memory","text":"<p>Two types of memories are used in various parts of a computer: random-access memory (RAM) and read-only memory (ROM). RAM accepts new information for storage to be available later for use. The process of storing new information in memory is referred to as a memory write operation. The process of transferring the stored information out of memory is referred to as a memory read operation. RAM can perform both the write and the read operations, whereas ROM, as introduced in Section 6-8, performs only read operations. RAM sizes may range from hundreds to billions of bits.</p> <p>Memory is a collection of binary storage cells together with associated circuits needed to transfer information into and out of the cells.</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap07/#7-2-ram","title":"7-2 RAM","text":"<p>Memory cells can be accessed to transfer information to or from any desired location, with the access taking the same time regardless of the location, hence the name random-access memory. In contrast,serial memory, such as is exhibited by a hard drive, takes different lengths of time to access information, depending on where the desired location is relative to the current physical position of the disk.</p> <p><code>word</code>: </p> <p>A word is an entity of bits that moves in and out of memory as a unit\u2014a group of 1s and 0s that represents a number, an instruction, one or more alphanumeric characters, or other binary-coded information.</p> <p>A group of eight bits is called a byte. </p> <p>Most computer memories use words that are multiples of eight bits in length. Thus, a 16-bit word contains two bytes, and a 32-bit word is made up of four bytes. The capacity of a memory unit is usually stated as the total number of bytes that it can store.</p> <p>Communication between a memory and its environment is achieved through data input and output lines, address selection lines, and control lines that specify the direction of transfer of information.</p> <p>Computer memory varies greatly in size. It is customary to refer to the number of words (or bytes) in memory with one of the letters K (kilo), M (mega), or G (giga). K is equal to 2^10, M to 2^20, and G to 2^30.</p> <p>A word in memory is selected by its binary address. When a word is read or written, the memory operates on all 16 bits as a single unit.</p> <p>The 1K * 16 memory of the figure has 10 bits in the address and 16 bits in each word. The number of address bits needed in memory is dependent on the total number of words that can be stored and is independent of the number of bits in each word. The number of bits in the address for a word is determined from the relationship 2^k &gt;= m, where m is the total number of words and k is the minimum number of address bits satisfying the relationship.</p> <p>The two operations that a random-access memory can perform are write and read. A write is a transfer into memory of a new word to be stored. A read is a transfer of a copy of a stored word out of memory.</p> <p>The steps that must be taken for a write are as follows:</p> <ol> <li>Apply the binary address of the desired word to the address lines.</li> <li>Apply the data bits that must be stored in memory to the data input lines.</li> <li>Activate the Write input.</li> </ol> <p>The memory unit will then take the bits from the data input lines and store them in the word specified by the address lines.The steps that must be taken for a read are as follows:</p> <ol> <li>Apply the binary address of the desired word to the address lines.</li> <li>Activate the Read input.</li> </ol> <p>The memory will then take the bits from the word that has been selected by the address and apply them to the data output lines. The contents of the selected word are not changed by reading them.</p> <p>...</p> <p>To avoid destroying data in other memory words, it is important that this change occur after the signals on the address lines have become fixed at the desired values. </p>"},{"location":"cour_note/D2QD_DigitalDesign/glossary/","title":"\u8bcd\u6c47\u8868","text":"<p> \u7ea6 1051 \u4e2a\u5b57  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 4 \u5206\u949f</p> <p>\ud83d\ude4f</p> <p>\u8bcd\u6c47\u8868\u662f cm \u8001\u5e08\u6574\u7406\u7684\uff0c\u8ba9\u6211\u4eec\u8bf4 \u8c22\u8c22 cm \uff01</p>"},{"location":"cour_note/D2QD_DigitalDesign/glossary/#1---ch11-7","title":"1)   Ch1.1-7","text":"<p>odometer\uff1a\u91cc\u7a0b\u8868\uff0c\u8ba1\u7a0b\u5668</p> <p>signal conditioning: \u4fe1\u53f7\u8c03\u7406\u3001\u4fe1\u53f7\u5904\u7406</p> <p>capacitor\uff1a\u7535\u5bb9\u5668\uff0ce.g., capacitor charge\uff0c\u7535\u5bb9\u5668\u5145\u7535</p> <p>radix\uff1a\u57fa\u6570(= base)</p> <p>radix point\uff1a\u5c0f\u6570\u70b9</p> <p>number = integer portion(\u6574\u6570\u90e8\u5206) + fraction portion(\u5c0f\u6570\u90e8\u5206)</p> <p>power series\uff1a\u5e42\u7ea7\u6570</p> <p>binary\uff1a\u4e8c\u8fdb\u5236\uff0coctal\uff1a\u516b\u8fdb\u5236\uff0cdecimal\uff1a\u5341\u8fdb\u5236\uff1bhexadecimal\uff1a\u5341\u516d\u8fdb\u5236</p> <p>augend\uff1a\u88ab\u52a0\u6570</p> <p>addend\uff1a\u52a0\u6570</p> <p>minuend: \u88ab\u51cf\u6570</p> <p>subtrahend\uff1a\u51cf\u6570</p> <p>padding\uff1a\u586b\u5145</p> <p>weighted code\uff1a\u6709\u6743\u7801</p> <p>arithmetic\uff1a\u7b97\u672f\u3001\u56db\u5219\u8fd0\u7b97</p> <p>significant digit\uff1a\u6709\u6548\u4f4d</p> <p>punched paper\uff1a\u6253\u5b54\u7eb8\u5e26</p> <p>parity\uff1a\u5947\u5076\u6821\u9a8c</p> <p>even\uff1a\u5076\u6570</p> <p>odd\uff1a\u5947\u6570</p> <p>source coding\uff1a\u4fe1\u6e90\u7f16\u7801</p> <p>channel coding\uff1a\u4fe1\u9053\u7f16\u7801</p> <p>optical Shaft Encoder\uff1a\u5149\u8f74\u7f16\u7801\u5668</p> <p>positional number system\uff1a\u6309\u4f4d\u8bb0\u6570\u5236</p>"},{"location":"cour_note/D2QD_DigitalDesign/glossary/#2---ch21-3","title":"2)   Ch2.1-3","text":"<p>notation: \u6807\u8bb0\u6cd5</p> <p>operator\uff1a\u8fd0\u7b97\u7b26\u3001\u7b97\u5b50\uff0ce.g., logical operator \u903b\u8f91\u8fd0\u7b97\u7b26</p> <p>operand\uff1a\u64cd\u4f5c\u6570</p> <p>identifier\uff1a\u6807\u8bc6\u7b26=designator\uff0ce.g., variable identifier\uff1a\u53d8\u91cf\u6807\u8bc6\u7b26</p> <p>overbar: ( \u00af )\u4e0a\u6a2a\u7ebf</p> <p>single quote mark (')\uff1a\u5355\u5f15\u53f7</p> <p>normally-closed switch\uff1a\u5e38\u95ed\u5f00\u5173,e.g. Normally-Open(NO), Normally-Closed(NC)</p> <p>magnetic field\uff1a\u78c1\u573a</p> <p>energizing coil\uff1a\u6fc0\u52b1\u7ebf\u5708</p> <p>relay\uff1a\u7ee7\u7535\u5668</p> <p>transistor: \u6676\u4f53\u7ba1\u3001\u4e09\u6781\u7ba1</p> <p>precedence\uff1a\u4f18\u5148\u6743\uff0ce.g., Boolean Operator Precedence</p> <p>parenthesis\uff1a\u62ec\u53f7\uff08\u5355\u6570\u5f62\u5f0fparenthesis\uff09</p> <p>leave out\uff1a\u9057\u6f0f, e.g., If the meaning is unambiguous, we leave out the symbol  \u201c\u00b7\u201d.</p> <p>idempotence: \u5e42\u7b49\u6027</p> <p>involution: \u4e58\u65b9</p> <p>dual\uff1a\u5bf9\u5076= duality\uff0ce.g., The dual of an algebraic expression is obtained by interchanging +  and \u00b7 and interchanging 0\u2019s and 1\u2019s.</p> <p>dual function\uff1a\u5bf9\u5076\u51fd\u6570</p> <p>complement function: \u8865\u51fd\u6570</p> <p>canonical form\uff1a\u89c4\u8303\u5f62\u5f0f</p> <p>standard form\uff1a\u6807\u51c6\u5f62\u5f0f</p> <p>designator\uff1a\u6807\u8bc6\u7b26= identifier\uff0ce.g., We drop the \u201cm\u201d designators\uff1a\u6211\u4eec\u5220\u9664\u4e86m\u53d8\u91cf\u6807\u8bc6\u7b26</p> <p>identity: \u540c\u4e00\u6027\uff1b\u4e00\u81f4\uff1b\u76f8\u7b49\uff1be.g., Prove the identity of each of the following Boolean  equations, using algebraic manipulation.</p> <p>indices\uff1aindex\u7684\u590d\u6570(=indexes) \u4e00\u822c\u5728\u6570\u5b66\uff0c\u91d1\u878d\u548c\u76f8\u5173\u9886\u57df\u4f7f\u7528</p> <p>subscript\uff1a\u4e0b\u6807</p>"},{"location":"cour_note/D2QD_DigitalDesign/glossary/#3---ch24-7","title":"3)   Ch2.4-7","text":"<p>Venn diagram\uff1a\u7ef4\u6069\u56fe</p> <p>Implicant\uff1a\u8574\u6db5\u9879\uff1b\u8574\u542b\u9879\uff1b\u9690\u542b\u6570</p> <p>Prime implicant: \u4e3b\u8574\u542b\u9879</p> <p>essential prime implicant\uff1a\u57fa\u672c\u7d20\u8574\u6db5; \u5b9e\u8d28\u672c\u539f\u8574\u6db5</p> <p>Don't cares: \u65e0\u5173\u6700\u5c0f\u9879</p> <p>degenerate: \u9000\u5316, e.g., A NAND gate with one input degenerates to an inverter.</p> <p>Hi-Impedance Outputs: \u9ad8\u963b\u6001\u8f93\u51fa</p>"},{"location":"cour_note/D2QD_DigitalDesign/glossary/#4---ch3-1-2","title":"4)   ch3. 1-2","text":"<p>rudimentary:\u57fa\u7840\u7684\uff1b\u57fa\u672c\u7684\uff1b\u672a\u5145\u5206\u53d1\u5c55\u7684\uff1b\u539f\u59cb\u7684</p> <p>die: \u88f8\u7247\u3001\u82af\u7247</p> <p>wafer\uff1a\u6676\u5706</p> <p>margin: \u8fb9\u7f18\u3001\u5dee\u989d\uff0ce.g., noise margin\uff0c\u566a\u58f0\u5bb9\u9650</p> <p>superimpose: v.\u4f7f\uff08\u7532\uff09\u53e0\u6620\u5728\uff08\u4e59\uff09\u4e0a\uff1b\u4f7f\u91cd\u53e0, e.g., Noise margin refers to the maximum external  noise voltage superimposed on a normal input value that will not cause an undesirable change  in the circuit output</p> <p>dissipation: n.\u6d88\u8017\uff1b\u653e\u8361\uff1b\u6d6a\u8d39\uff1be.g., power dissipation = power consumption</p> <p>propagation delay\uff1a\u4f20\u64ad\u5ef6\u8fdf</p> <p>transition time\uff1a\u8f6c\u6362\u65f6\u95f4</p> <p>transport delay\uff1a\u4f20\u8f93\u5ef6\u8fdf</p> <p>inertial delay\uff1a\u60ef\u6027\u5ef6\u8fdf</p> <p>full custom: \u5b8c\u5168\u5b9a\u5236</p> <p>fabrication: \u5236\u9020\u3001\u5236\u4f5c</p> <p>cell library\uff1a\u5143\u4ef6\u5e93</p> <p>schematic\uff1a\u539f\u7406\u56fe\uff0c\u7b80\u56fe</p>"},{"location":"cour_note/D2QD_DigitalDesign/glossary/#5---ch3-3-9","title":"5)   ch3. 3-9","text":"<p>decoder\uff1a\u8bd1\u7801\u5668</p> <p>encoder\uff1a\u7f16\u7801\u5668</p> <p>multiplexer\uff1a\u591a\u8def\u590d\u7528\u5668\uff0cMultiplexer means many into one.</p> <p>demultiplexer\uff1a\u4fe1\u53f7\u5206\u79bb\u5668\u3001\u591a\u8def\u5206\u914d\u5668\uff0cThe demultiplexer means one into many.</p> <p>anode: \u9633\u6781\uff0c\u6b63\u6781</p> <p>cathode: \u9634\u6781\uff0c\u8d1f\u6781</p>"},{"location":"cour_note/D2QD_DigitalDesign/glossary/#6---ch3-8-10","title":"6)   Ch3. 8-10","text":"<p>Iterative array\uff1a\u8fed\u4ee3\u9635\u5217</p> <p>Ripple Carry Adder\uff1a\u884c\u6ce2\u8fdb\u4f4d\u52a0\u6cd5\u5668</p> <p>Carry Look-ahead Adder: \u8d85\u524d\u8fdb\u4f4d\u52a0\u6cd5\u5668</p> <p>bit-wise: \u4ee5\u4f4d\u4e3a\u64cd\u4f5c\u5bf9\u8c61\u7684(wise\u662f\u65b9\u5f0f\u4e4b\u610f),\u5982bit-wise operators(\u4f4d\u8fd0\u7b97\u7b26), 2-input bit-wise  addition functional block</p>"},{"location":"cour_note/D2QD_DigitalDesign/glossary/#7---ch311-12","title":"7)   Ch3.11-12","text":"<p>1's Complement\uff1a\u53cd\u7801</p> <p>2's Complement\uff1a\u8865\u7801</p> <p>magnitude\uff1a\u6570\u503c</p> <p>Signed-Magnitude\uff1a\u7b26\u53f7\u2014\u6570\u503c\u8868\u793a\u6cd5</p> <p>Signed-Complement\uff1a\u7b26\u53f7\u2014\u8865\u7801\u8868\u793a\u6cd5</p> <p>contraction\uff1a(n.) \u6536\u7f29\u3001\u7d27\u7f29\uff1bcontract\uff1a(v.) \u6536\u7f29</p>"},{"location":"cour_note/D2QD_DigitalDesign/glossary/#8---ch5-2","title":"8)   Ch5. 2","text":"<p>fuse intact\uff1a\u7194\u4e1d\u4fdd\u7559</p> <p>fuse blown\uff1a\u7194\u4e1d\u7194\u65ad</p> <p>volatile\uff1a\u6613\u5931\u6027\u7684</p> <p>non-volatile\uff1a\u975e\u6613\u5931\u6027\u7684</p>"},{"location":"cour_note/D2QD_DigitalDesign/glossary/#9---ch4-1-4","title":"9)   Ch4. 1-4","text":"<p>tractable: (adj.) \u6613\u5904\u7406\u7684\uff1b\u6613\u9a7e\u9a6d\u7684</p> <p>oscillator: (n.) \u632f\u8361\u5668</p> <p>capacitors: (n.) \u7535\u5bb9\u5668</p> <p>inductor: (n.) \u7535\u611f\u5668</p> <p>latch\uff1a\u9501\u5b58\u5668</p> <p>flip-flop\uff1a\u89e6\u53d1\u5668</p> <p>metastable state\uff1a\u4e9a\u7a33\u6001</p> <p>alternating clock\uff1a\u4ea4\u66ff\u65f6\u949f</p> <p>disposable sampling = 1s catching\uff1a\u4e00\u6b21\u91c7\u6837</p> <p>setup time\uff1a\u5efa\u7acb\u65f6\u95f4</p> <p>hold time\uff1a\u4fdd\u6301\u65f6\u95f4</p> <p>pulse-triggering\uff1a\u8109\u51b2\u89e6\u53d1</p> <p>level triggering\uff1a\u7535\u5e73\u89e6\u53d1</p> <p>edge triggering\uff1a\u8fb9\u6cbf\u89e6\u53d1</p> <p>self-recovery capability\uff1a\u81ea\u6062\u590d\u80fd\u529b</p> <p>equivalent state\uff1a\u7b49\u4ef7\u72b6\u6001</p>"},{"location":"cour_note/D2QD_DigitalDesign/glossary/#10--ch6-1-5","title":"10)  Ch6. 1-5","text":"<p>register\uff1a\u5bc4\u5b58\u5668</p> <p>register transfer operation\uff1a\u5bc4\u5b58\u5668\u4f20\u8f93\u64cd\u4f5c</p> <p>microoperation\uff1a\u5fae\u64cd\u4f5c</p> <p>register transfer structure\uff1a\u5bc4\u5b58\u5668\u4f20\u8f93\u7ed3\u6784</p> <p>bus\uff1a\u603b\u7ebf</p> <p>lateral: (adj.) \u4fa7\u9762\u7684\uff1b\u6a2a\u5411\u7684\uff1b\u5411\u4fa7\u9762\u79fb\u52a8\u7684</p> <p>laterally: (adv.) \u4fa7\u9762\u5730\uff1b\u6a2a\u5411\u5730\uff1b\u5411\u4fa7\u9762\u79fb\u52a8\u5730</p> <p>serial gating\uff1a\u4e32\u884c\u95e8\u63a7</p> <p>parallel gating\uff1a\u5e76\u884c\u95e8\u63a7</p> <p>counter\uff1a\u8ba1\u6570\u5668</p> <p>data path\uff1a\u6570\u636e\u901a\u9053</p> <p>control unit\uff1a\u63a7\u5236\u5355\u5143</p>"},{"location":"cour_note/D2QD_DigitalDesign/glossary/#11--ch7-1-7","title":"11)  Ch7. 1-7","text":"<p>strobe\uff1a\u9009\u901a\uff1b\u9009\u901a\u8109\u51b2\uff1b\u95f8\u95e8</p> <p>SRAM\uff1a\u9759\u6001\u5185\u5b58</p> <p>DRAM\uff1a\u52a8\u6001\u5185\u5b58</p> <p>coincident selection\uff1a\u91cd\u5408\u9009\u62e9</p> <p>word extension\uff1a\u5b57\u6269\u5c55</p> <p>bit extension\uff1a\u4f4d\u6269\u5c55</p> <p>address multiplexing\uff1a\u5730\u5740\u590d\u7528\uff08\u6307DRAM\uff09</p> <p>refresh\uff1a\u5237\u65b0</p> <p>synchronous DRAM(SDRAM)\uff1a\u540c\u6b65DRAM</p> <p>burst read\uff1a\u7206\u53d1\u6a21\u5f0f\u8bfb\u53d6\u6570\u636e</p> <p>burst length\uff1a\u7206\u53d1\u6a21\u5f0f\u7684\u6570\u636e\u8bfb/\u5199\u957f\u5ea6</p> <p>memory bandwidth\uff1a\u5185\u5b58\u5e26\u5bbd</p>"},{"location":"cour_note/D2QD_Intro2CV/","title":"[\u5927\u4e8c\u5b66\u5e74] \u8ba1\u7b97\u673a\u89c6\u89c9\u5bfc\u8bba | Introduction to Computer Vision","text":"<p> \u7ea6 149 \u4e2a\u5b57 </p> <p>\u8bfe\u7a0b\u4fe1\u606f</p> <ul> <li>\u672c\u6587\u4e3a\u8bfe\u7a0b\u300a\u8ba1\u7b97\u673a\u89c6\u89c9\u5bfc\u8bba\u300b\u7684\u8bfe\u7a0b\u7b14\u8bb0\uff0c\u8bfe\u7a0b\u4e3b\u8981\u4ecb\u7ecd\u8ba1\u7b97\u673a\u89c6\u89c9\u7684\u57fa\u7840\u7406\u8bba\u548c\u57fa\u672c\u65b9\u6cd5\u3002</li> <li>\u667a\u4e91\u94fe\u63a5\uff1a\ud83d\udd17</li> <li>\u6388\u8bfe\uff1a\u5468\u6653\u5dcd</li> <li> <p>\u6559\u6750\uff1a\ud83d\udcd9 .</p> </li> <li> <p>\u63a8\u8350\u8d44\u6e90\uff1ahttps://paperswithcode.com/</p> </li> </ul> <p>List</p> <ul> <li> Lecture 1 | Introduction</li> <li> Lecture 2 | Image Formation</li> <li> Lecture 3 | Image Processing</li> <li> Lecture 4 | Model Fitting and Optimization</li> <li> Lecture 5 | Feature Matching and Motion Estimation</li> <li> Lecture 6 | Image Alignment and Stitching</li> <li> Lecture 7 | Structure From Motion</li> <li> Lecture 8 | Depth Estimation &amp; 3D Reconstruction</li> <li> Lecture 9 | Deep Learning</li> <li> Lecture 10 | Recognition</li> <li> Lecture 11 | 3D Deep Learning</li> <li> Lecture 12 | Computational Photography 1</li> <li> Lecture 13 | Computational Photography 2</li> </ul> <p>Lab</p> <ul> <li>Lab Code</li> </ul>"},{"location":"cour_note/D2QD_Intro2CV/Lec01/","title":"Lecture 1 | Introduction","text":"<p> \u7ea6 1737 \u4e2a\u5b57  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 6 \u5206\u949f</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec01/#cv-\u7684\u4e3b\u8981\u4efb\u52a1","title":"CV \u7684\u4e3b\u8981\u4efb\u52a1","text":"<ul> <li>\u4e09\u7ef4\u91cd\u5efa / Reconstruction</li> <li>\u56fe\u50cf\u7406\u89e3 / Understanding</li> <li>\u56fe\u50cf\u5408\u6210 / Synthesis</li> </ul>"},{"location":"cour_note/D2QD_Intro2CV/Lec01/#cv-\u7684\u5e94\u7528","title":"CV \u7684\u5e94\u7528","text":"Application Examples <ul> <li>Face Reconstruction and Recognition</li> <li>Face ID</li> <li>Vending Machine with Face Detection</li> <li>DeepFake</li> <li>Augmented reality</li> <li>Factory Automation</li> <li>Vision Inspection</li> <li>Optical Character Recognition(OCR)</li> <li>Video Surveillance</li> <li>Human Computer Interaction: Optical Mouse</li> <li>Human Computer Interaction: Motion Sensing Games</li> <li>Visual Effects (VFX)</li> <li>Digital Human</li> <li>VR Tour</li> <li>Visual Localization and Navigation</li> <li>Autonomous Navigation: Space Exploration</li> <li>Robot Perception</li> <li>Autonomous Driving</li> <li>Augmented Reality</li> <li>Free Viewpoint Video</li> <li>Medical Image Analysis</li> <li>......</li> </ul>"},{"location":"cour_note/D2QD_Intro2CV/Lec01/#\u5b66\u672f\u5708\u6982\u51b5","title":"\u5b66\u672f\u5708\u6982\u51b5","text":"<p>CV \u9886\u57df\u7684\u51e0\u4e2a\u9876\u4f1a</p> <ul> <li>CVPR (Computer Vision and Pattern Recognition)</li> <li>ICCV (International Conference on Computer Vision)</li> <li>ECCV (European Conference on Computer Vision)</li> </ul> <p>\u56fe\u5f62\u5b66\u76f8\u5173\u7684\u9876\u4f1a</p> <ul> <li>ACM SIGGRAPH</li> </ul>"},{"location":"cour_note/D2QD_Intro2CV/Lec01/#\u8bfe\u7a0b\u6982\u8ff0","title":"\u8bfe\u7a0b\u6982\u8ff0","text":"<ul> <li>\u8bfe\u7a0b\u76ee\u6807<ul> <li>\u5b66\u4e60\u8ba1\u7b97\u673a\u89c6\u89c9\u76f8\u5173\u7684\u77e5\u8bc6</li> <li>\u5b66\u4f1a\u300c\u7528\u6570\u5b66\u63cf\u8ff0\u4e0e\u89e3\u51b3\u95ee\u9898\u300d<ul> <li><code>Linear Algebra</code> / <code>Optimization</code> / <code>Geometry</code></li> </ul> </li> </ul> </li> <li> <p>\u8bfe\u7a0b\u8d44\u6e90</p> <ul> <li>\u6559\u6750\uff1ahttps://szeliski.org/Book/ </li> </ul> </li> <li> <p>\u8bfe\u7a0b\u8ba1\u5212</p> <ul> <li>Basics. (Lec.02 \u2013 Lec.04)</li> <li>Reconstruction. (Lec.05 \u2013 Lec.09) </li> <li>Understanding. (Lec.10 \u2013 Lec.12)</li> <li>Synthesis. (Lec. 13 \u2013 Lec.14)</li> </ul> </li> </ul> <p>Note</p> <ul> <li>\u4f5c\u4e3a\u540e\u7eed\u8bfe\u7a0b\u7684\u57fa\u7840\uff0c\u9700\u8981\u590d\u4e60\u7ebf\u6027\u4ee3\u6570\u7684\u76f8\u5173\u77e5\u8bc6\uff0c\u5b83\u5c06\u8d2f\u7a7f\u6574\u4e2a\u8bfe\u7a0b\uff1b</li> <li>\u9700\u8981\u719f\u6089\u6d89\u53ca\u7684\u8bcd\u6c47\uff0c\u4e4b\u540e\u4f1a\u82e5\u5e72\u6b21\u63d0\u5230\uff1b</li> </ul>"},{"location":"cour_note/D2QD_Intro2CV/Lec01/#\u7ebf\u4ee3\u590d\u4e60","title":"\u7ebf\u4ee3\u590d\u4e60","text":""},{"location":"cour_note/D2QD_Intro2CV/Lec01/#\u7ebf\u6027\u53d8\u6362","title":"\u7ebf\u6027\u53d8\u6362","text":"<p>\u9996\u5148\uff0c\u4e00\u4e2a\u77e9\u9635\u5de6\u4e58\u4e00\u4e2a\u5411\u91cf\uff1a</p> <ul> <li>\u4ee3\u6570\u4e0a\uff0c\u7ed3\u679c\u5411\u91cf\u7684\u6bcf\u4e00\u9879\u76f8\u5f53\u4e8e\u539f\u5411\u91cf\u7684\u4e00\u4e2a\u52a0\u6743\u6c42\u548c\uff1b</li> <li>\u51e0\u4f55\u4e0a\uff0c\u7ed3\u679c\u5411\u91cf\u76f8\u5f53\u4e8e\u539f\u5411\u91cf\u505a\u51e0\u4f55\u53d8\u6362\u5f97\u5230\u7684\u65b0\u5411\u91cf\uff1b</li> </ul> <p>\u5728\u8fd9\u79cd\u57fa\u7840\u4e0a\uff0c\u77e9\u9635\u4e58\u6cd5\u53ef\u4ee5\u8ba4\u4e3a\u662f\u4e00\u7cfb\u5217\u5411\u91cf\uff08\u53f3\u4fa7\u77e9\u9635\uff09\u7ecf\u8fc7\u540c\u4e00\u4e2a\u53d8\u6362\u5f97\u5230\u65b0\u7684\u4e00\u7cfb\u5217\u5411\u91cf\u3002</p> <ul> <li>\u90a3\u4e48\u53cd\u8fc7\u6765\u7684\uff0c\u6211\u4eec\u4e5f\u53ef\u4ee5\u901a\u8fc7\u89c2\u5bdf\u67d0\u4e9b\u70b9\u5728\u53d8\u6362\u540e\u7684\u4f4d\u7f6e\u6765\u611f\u53d7\u8fd9\u4e2a\u201c\u53d8\u6362\u201d\u7684\u5177\u4f53\u5185\u5bb9\uff1b</li> <li>\u66f4\u7279\u522b\u7684\uff0c\u6211\u4eec\u53ef\u4ee5\u53d1\u73b0\uff0c\u53d8\u6362\u77e9\u9635\uff08\u5de6\u4fa7\u77e9\u9635\uff09\u7684\u6bcf\u4e00\u5217\uff0c\u5c31\u76f8\u5f53\u4e8e\u5bf9\u5e94\u7684\u5355\u4f4d\u57fa\uff08\u4f8b\u5982\u7b2c \\(2\\) \u5217\u5bf9\u5e94 \\(\\vec{a}(0,1)\\) \u5411\u91cf\uff09\u7ecf\u8fc7\u8fd9\u4e2a\u53d8\u6362\uff08\u53f3\u4e58\u8fd9\u4e2a\u53d8\u6362\u77e9\u9635\uff09\u5f97\u5230\u7684\u7ed3\u679c\uff1b</li> </ul> <p>Tips</p> <p>\u5b9e\u9645\u4e0a\uff0c\u4ece\u5355\u4f4d\u77e9\u9635\u7684\u89d2\u5ea6\u4e5f\u53ef\u4ee5\u5f88\u597d\u7684\u7406\u89e3\u8fd9\u4ef6\u4e8b\uff1a</p> \\[ \\begin{bmatrix}     a &amp; b \\\\     c &amp; d \\end{bmatrix} \\begin{bmatrix}     1 &amp; 0 \\\\     0 &amp; 1 \\end{bmatrix} = \\begin{bmatrix}     a &amp; b \\\\     c &amp; d \\end{bmatrix} \\] <p>\u6211\u4eec\u6765\u8bd5\u7740\u8fd0\u7528\u4e0a\u9762\u7684\u6280\u5de7\u6c42\u4e00\u4e2a\u65cb\u8f6c\u53d8\u6362\u5bf9\u5e94\u7684\u53d8\u6362\u77e9\u9635\u3002</p> \u9898\u9762\u7b54\u6848 <p> \u5047\u8bbe\u8be5\u77e9\u9635\u8ba9\u76ee\u6807\u56fe\u5f62\u987a\u65f6\u9488\u65cb\u8f6c \\(\\theta\\) \uff0c\u5219\u5176\u8868\u8fbe\u5f0f\u4e3a\uff1f</p> <p></p> <p>\u6211\u4eec\u505a\u6b64\u5206\u6790\uff1a</p> <ul> <li>\u5bf9\u4e8e\u53c2\u8003\u70b9 \\((1,0)\\)\uff0c\u7ecf\u8fc7\u65cb\u8f6c\u540e\u4f4d\u7f6e\u53d8\u5316\u4e3a \\((\\cos\\theta,-\\sin\\theta)\\)\uff1b</li> <li>\u5bf9\u4e8e\u53c2\u8003\u70b9 \\((0,1)\\)\uff0c\u7ecf\u8fc7\u65cb\u8f6c\u540e\u4f4d\u7f6e\u53d8\u5316\u4e3a \\((\\sin\\theta,\\cos\\theta)\\)\uff1b</li> </ul> <p>\u56e0\u6b64\uff0c\u6839\u636e\u4e0a\u9762\u63d0\u5230\u7684\u6280\u5de7\uff0c\u65cb\u8f6c\u5bf9\u5e94\u7684\u53d8\u6362\u77e9\u9635\u4e3a\uff1a</p> \\[ R_{\\theta,clockwise} =  \\begin{bmatrix}     \\cos\\theta &amp; \\sin\\theta \\\\      -\\sin\\theta &amp; \\cos\\theta \\end{bmatrix} \\] <p>\u7279\u522b\u7684\uff0c\u5982\u679c\u662f\u9006\u65f6\u9488\uff0c\u7ed3\u679c\u5c31\u662f\uff1a</p> \\[ R_{\\theta,anti-clockwise} =  \\begin{bmatrix}     \\cos\\theta &amp; -\\sin\\theta \\\\      \\sin\\theta &amp; \\cos\\theta \\end{bmatrix} \\]"},{"location":"cour_note/D2QD_Intro2CV/Lec01/#\u4eff\u5c04\u53d8\u6362\u4e0e\u9f50\u6b21\u5750\u6807","title":"\u4eff\u5c04\u53d8\u6362\u4e0e\u9f50\u6b21\u5750\u6807","text":"<p>\u4eff\u5c04\u53d8\u6362(Affine Transformations) \u4e3b\u8981\u5305\u62ec\u4e24\u4e2a\u90e8\u5206\uff0c\u5373\u7ebf\u6027\u53d8\u6362\u548c\u5e73\u79fb\uff08\u6362\u8a00\u4e4b\uff0c\u4eff\u5c04\u53d8\u6362\u5e76\u4e0d\u662f\u7ebf\u6027\u53d8\u6362\uff09\uff0c\u5176\u6570\u5b66\u8868\u8ff0\u4e3a\uff1a</p> \\[ \\begin{bmatrix}      x' \\\\     y'  \\end{bmatrix} = \\begin{bmatrix}      a &amp; b \\\\      c &amp; d \\end{bmatrix}  \\begin{bmatrix}      x \\\\      y  \\end{bmatrix} + \\begin{bmatrix}      t_x \\\\      t_y  \\end{bmatrix} \\] <p>\u4e3a\u4e86\u8ba9\u4eff\u5c04\u53d8\u6362\u4e5f\u80fd\u5199\u6210 \\(a=Mb\\) \u7684\u5f62\u5f0f\u4ee5\u7b80\u5316\u8fd0\u7b97\uff0c\u6211\u4eec\u53ef\u4ee5\u7528 \\(n+1\\) \u7ef4\u5411\u91cf\u6765\u8868\u793a \\(n\\) \u7ef4\u70b9\uff0c\u5373\u4f7f\u7528\u9f50\u6b21\u5750\u6807(homogenous coordinates)\uff1a</p> \\[ \\begin{bmatrix}     x'\\\\     y'\\\\     1 \\end{bmatrix} \\cong \\begin{bmatrix}     a &amp; b &amp; t_x \\\\     c &amp; d &amp; t_y \\\\     0 &amp; 0 &amp; 1 \\end{bmatrix} \\begin{bmatrix}     x \\\\     y \\\\     1 \\end{bmatrix} \\] <p>\u4e3a\u4ec0\u4e48\u662f \u201c1\u201d</p> <p>\u8fd9\u91cc\u6211\u4eec\u4e0d\u7981\u629b\u51fa\u4e00\u4e2a\u7591\u95ee\uff0c\u4e3a\u4ec0\u4e48\u9f50\u6b21\u5750\u6807\u6dfb\u52a0\u7684\u7ef4\u5ea6\u4e2d\u8981\u586b\u5165 1 \u5462\uff1f\u5b83\u6709\u4ec0\u4e48\u542b\u4e49\u5417\uff1f\u5b83\u4e0d\u80fd\u662f 2 \u6216\u8005\u522b\u7684\u4ec0\u4e48\u4e1c\u897f\u5417\uff1f</p> <p>\u7b54\u6848\u662f\uff0c\u5b83\u53ef\u4ee5\u662f\u522b\u7684\u4e1c\u897f\uff0c\u6216\u8005\u8bf4\u6211\u4eec\u9700\u8981\u5bf9\u5b9a\u4e49\u8fdb\u884c\u4e00\u4e2a\u6269\u5c55\uff0c\u4ee5\u4f7f\u9f50\u6b21\u5750\u6807\u6709\u66f4\u5927\u7684\u7528\u5904\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec01/#\u9f50\u6b21\u5750\u6807\u7684\u6269\u5c55\u6027\u8d28","title":"\u9f50\u6b21\u5750\u6807\u7684\u6269\u5c55\u6027\u8d28","text":"<p>\u4f8b\u5982\uff0c\\((x,y)\\) \u5bf9\u5e94\u7684\u9f50\u6b21\u5750\u6807\u4e3a \\((x,y,1)\\)\uff0c\u5982\u679c\u4f60\u628a\u5b83\u60f3\u8c61\u6210\u4e09\u7ef4\u7a7a\u95f4\u4e2d\u7684\u70b9\uff0c\u4f1a\u53d1\u73b0\uff0c\u5982\u679c\u6539\u53d8 1 \u7684\u503c\uff0c\u5f97\u5230\u7684\u70b9\u7684\u8f68\u8ff9\u4f1a\u662f\u82e5\u5e72\u5f20\u5e73\u884c\u7684\u5e73\u9762\uff0c\u4e5f\u5c31\u662f\u8bf4\u4ed6\u4eec\u5728\u4e09\u7ef4\u7a7a\u95f4\u4e0b\u662f\u76f8\u4e92\u72ec\u7acb\u7684\u3002</p> <p>\u6b64\u65f6\uff0c\u6211\u4eec\u5c31\u53ef\u4ee5\u4eba\u4e3a\u7684\u5b9a\u4e49\u4e00\u4e2a\u6bcf\u4e00\u4e2a\u5e73\u9762\u5185\u7684\u70b9\u7684\u6620\u5c04\u5173\u7cfb\uff08\u6211\u4eec\u53ea\u8003\u8651\u7b2c\u4e00\u8c61\u9650\uff09\uff0c\u4ece\u539f\u70b9\u5f15\u4e00\u6761\u5c04\u7ebf\uff0c\u76f4\u7ebf\u4e0a\u4e0e\u6bcf\u4e00\u4e2a\u5e73\u9762\u7684\u4ea4\u70b9\u6211\u4eec\u90fd\u8ba4\u4e3a\u5bf9\u5e94\u7740\u4e8c\u7ef4\u5e73\u9762\u4e0a\u7684\u540c\u4e00\u70b9\u3002</p> <p></p> <p>\u6362\u53e5\u8bdd\u6765\u8bf4\uff0c\u6211\u4eec\u7528 \\(n+1\\) \u7ef4\u7a7a\u95f4\u4e2d \u4ece\u539f\u70b9\u53d1\u51fa\u7684\u4e00\u6761 \u5c04\u7ebf \u6765\u63cf\u8ff0 \\(n\\) \u7ef4\u7a7a\u95f4\u4e2d\u7684\u4e00\u4e2a\u70b9\u3002</p> <p>\u4e8e\u662f\u6211\u4eec\u53ef\u4ee5\u7528\u4e0b\u9762\u7684\u5f0f\u5b50\u6765\u6982\u62ec\u6269\u5c55\u5b9a\u4e49\uff1a</p> <ul> <li>\\(\\begin{bmatrix}x\\\\y\\\\k\\end{bmatrix}\\) \u7b49\u4ef7\u4e8e \\(\\begin{bmatrix}x/k\\\\y/k\\\\1\\end{bmatrix}\\)\uff0c\u5f53\u7136\uff0c\\(k\\not=0\\)\uff1b</li> </ul> <p>\u800c\u5f15\u5165\u8fd9\u79cd\u60f3\u6cd5\u540e\uff0c\u6211\u4eec\u5c31\u77e5\u9053\u4e3a\u4ec0\u4e48\u901a\u8fc7\u9f50\u6b21\u5750\u6807\u5316\u5c31\u80fd\u628a\u5e73\u79fb\u53d8\u6210\u7ebf\u6027\u53d8\u6362\u2014\u2014\u6211\u4eec\u53ef\u4ee5\u5c06 \\(n\\) \u7ef4\u70b9\u7684\u5e73\u79fb\u770b\u4f5c \\(n+1\\) \u7ef4\u5c04\u7ebf\u7684\u65cb\u8f6c\uff0c\u800c\u65cb\u8f6c\u663e\u7136\u662f\u4e00\u4e2a\u7ebf\u6027\u53d8\u6362\u3002</p> <p>\u800c\u5173\u4e8e\u8be5\u6027\u8d28\u7684\u5176\u4ed6\u5e94\u7528\uff0c\u53ef\u4ee5\u770b Lecture 2 \u7684\u7b2c\u4e8c\u5c0f\u8282\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec01/#\u9006\u53d8\u6362","title":"\u9006\u53d8\u6362","text":"<p>\u7ebf\u6027\u53d8\u6362 \\(T\\) \u7684\u9006\u53d8\u6362(Inverse Transform)\u5c31\u662f\u5176\u53d8\u6362\u77e9\u9635\u7684\u9006 \\(T^{-1}\\)\uff0c\u663e\u7136\uff0c\u5e76\u4e0d\u662f\u6240\u6709\u53d8\u6362\u90fd\u662f\u53ef\u9006\u7684\u3002</p> <p>\u5f62\u8c61\u5730\u7406\u89e3\uff0c\u4e00\u4e2a\u53d8\u6362\u77e9\u9635\u5982\u679c\u4e0d\u6ee1\u79e9\uff08\u4e0d\u53ef\u9006\uff09\uff0c\u90a3\u4e48\u5c31\u4f1a\u6709\u51e0\u4e2a\u57fa\u5728\u53d8\u6362\u4e2d\u5408\u5e76\uff0c\u6216\u8005\u8bf4\u591a\u4e2a\u70b9\u88ab\u6620\u5c04\u4e3a\u540c\u4e00\u4e2a\u70b9\uff0c\u5bfc\u81f4\u65e0\u6cd5\u8fd8\u539f\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec01/#\u884c\u5217\u5f0f\u7684\u51e0\u4f55\u542b\u4e49","title":"\u884c\u5217\u5f0f\u7684\u51e0\u4f55\u542b\u4e49","text":"<p>\u884c\u5217\u5f0f(Determinant) \u7684\u503c\u7b49\u4e8e\u8fd9\u4e2a\u65b9\u9635\u4e2d\u7684\u5411\u91cf\u5bf9\u5e94\u7684 \u5e73\u884c\u56fe\u5f62/\u51e0\u4f55\u4f53/... \u7684 \u9762\u79ef/\u4f53\u79ef/...</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec01/#\u7279\u5f81\u503c\u548c\u7279\u5f81\u5411\u91cf","title":"\u7279\u5f81\u503c\u548c\u7279\u5f81\u5411\u91cf","text":"<p>\u7279\u5f81\u5411\u91cf(eigenvector)\u548c\u7279\u5f81\u503c(eigenvalue)\u7684\u5b9a\u4e49\u5982\u4e0b\uff1a</p> <p>\u5bf9\u4e8e\u77e9\u9635 \\(A\\in R^{N\\times N}\\)\uff0c\u5982\u679c\u6709\u5411\u91cf \\(v\\in R^{N}\\) \u548c\u5b9e\u6570 \\(\\lambda \\not = 0\\)\uff0c\u6ee1\u8db3\uff1a</p> \\[ Av = \\lambda v \\] <p>\u5219\u79f0 \\(v\\) \u662f\u77e9\u9635 \\(A\\) \u7684\u7279\u5f81\u5411\u91cf\uff0c\u5bf9\u5e94\u7684\u7279\u5f81\u503c\u4e3a \\(\\lambda\\)\u3002</p> <p>\u4ece\u51e0\u4f55\u53d8\u6362\u7684\u89d2\u5ea6\u6765\u7406\u89e3\u8fd9\u4e2a\u5b9a\u4e49\u5f0f\uff0c\u53ef\u4ee5\u63cf\u8ff0\u4e3a\uff1a\u5411\u91cf \\(v\\) \u7ecf\u8fc7\u53d8\u6362 \\(A\\) \u5f97\u5230\u7684\u7ed3\u679c\uff0c\u7b49\u4e8e\u76f4\u63a5\u5bf9 \\(v\\) \u8fdb\u884c\u7f29\u653e\uff08\u800c\u6ca1\u6709\u6539\u53d8\u65b9\u5411\uff09\u3002</p> <p>\u5de5\u7a0b\u8ba1\u7b97\u65b9\u6cd5</p> <p>\u4ee4\u4eba\u60ca\u559c\u7684\u662f\uff0c\u6211\u4eec\u5728\u5b9e\u9645\u8fd0\u7528\u65f6\uff0c\u53ef\u4ee5\u76f4\u63a5\u4f7f\u7528\u6570\u5b66\u5e93\u4e2d\u7684\u7279\u5f81\u503c\u5206\u89e3(eigen decomposition)\u65b9\u6cd5\uff0c\u5176\u5927\u81f4\u4f1a\u505a\u8fd9\u6837\u4e00\u4ef6\u4e8b\uff1a</p> <p></p> <p>\u5c06\u77e9\u9635 \\(A\\) \u5206\u89e3\u4e3a \\(Q\\Lambda Q^{-1}\\)\uff0c\u5176\u4e2d \\(Q\\) \u4e2d\u7684\u6bcf\u4e00\u5217\u5373\u4e3a \\(A\\) \u7684\u7279\u5f81\u5411\u91cf\uff0c\u5bf9\u89d2\u9635 \\(\\Lambda\\) \u4e2d\u7684\u7b2c \\(i\\) \u9879\u5c31\u662f\u7b2c \\(i\\) \u4e2a\u7279\u5f81\u5411\u91cf\u7684\u7279\u5f81\u503c\u3002</p> <p>\u7279\u5f81\u503c\u4e0e\u7279\u5f81\u5411\u91cf\u7684\u5e94\u7528\uff1a\u4e3b\u6210\u5206\u5206\u6790(principal component analysis)</p> <p></p> <p>\u4e3b\u6210\u5206(principal component)\u7b49\u4e8e\u534f\u65b9\u5dee\u77e9\u9635\u7684 \u7279\u5f81\u503c\u6700\u5927\u7684 \u90a3\u4e2a\u7279\u5f81\u5411\u91cf\u3002</p> <ul> <li>\u5982\u56fe\uff0c\u6211\u4eec\u8981\u4ece\u56fe\u4e2d\u627e\u5230\u4e00\u4e2a\u65b9\u5411\uff0c\u4f7f\u5f97\u6240\u6709\u6570\u636e\u70b9\u5728\u8fd9\u4e2a\u65b9\u5411\u4e0a\u7684\u6295\u5f71\uff0c\u65b9\u5dee\u6700\u5927\uff08\u6362\u8a00\u4e4b\uff0c\u627e\u5230\u8fd9\u4e9b\u6570\u636e\u7684\u4e00\u4e2a\u201c\u65b9\u5411\u201d\uff09\uff1b</li> <li>\u8bb0\u6240\u6709\u6570\u636e\u70b9\u4e3a \\(A\\)\uff0c\u5219 \\(A^{T}A\\) \u4e3a\u534f\u65b9\u5dee\u77e9\u9635(covariance matrix)\uff0c\u5176\u7279\u5f81\u5411\u91cf\u4e2d\uff0c\u7279\u5f81\u503c\u6700\u5927\u7684\u90a3\u4e2a\uff0c\u5c31\u662f\u8fd9\u7ec4\u6570\u636e\u7684\u4e3b\u6210\u5206\uff1b</li> </ul>"},{"location":"cour_note/D2QD_Intro2CV/Lec02/","title":"Lecture 2 | Image Formation","text":"<p> \u7ea6 3769 \u4e2a\u5b57  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 13 \u5206\u949f</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec02/#\u76f8\u673a\u4e0e\u5149\u5b66\u539f\u7406","title":"\u76f8\u673a\u4e0e\u5149\u5b66\u539f\u7406","text":""},{"location":"cour_note/D2QD_Intro2CV/Lec02/#\u5c0f\u5b54\u6210\u50cf","title":"\u5c0f\u5b54\u6210\u50cf","text":"<p>\u5982\u679c\u6211\u4eec\u76f4\u63a5\u62ff\u4e00\u5757\u5e73\u9762\u6765\u8bb0\u5f55\u81ea\u7136\u754c\u7684\u5149\u4fe1\u606f\uff0c\u4e0d\u96be\u53d1\u73b0\uff0c\u7531\u4e8e\u5149\u7ebf\u662f\u5411\u56db\u9762\u516b\u65b9\u4f20\u64ad\u7684\uff0c\u6240\u4ee5\u63a5\u6536\u5230\u7684\u4fe1\u606f\u4e5f\u4e71\u4e03\u516b\u7cdf\uff0c\u6240\u4ee5\u6211\u4eec\u9700\u8981\u901a\u8fc7\u4e00\u4e2a\u5c0f\u5b54\uff0c\u4e5f\u5c31\u662f\u5982\u4eca\u7684\u5149\u5708(aperture)\u6765\u5bf9\u5149\u7ebf\u8fdb\u884c\u4e00\u4e2a\u8fc7\u6ee4\u3002\u8fd9\u5c31\u662f\u65e9\u671f\u9488\u5b54\u6444\u50cf\u673a(pinhole camera)\u7684\u539f\u7406\u3002</p> <p> </p> <p>\u8fd9\u4e5f\u5c31\u662f\u6211\u4eec\u5f88\u65e9\u5c31\u5b66\u8fc7\u7684\uff0c\u5c0f\u5b54\u6210\u50cf\u539f\u7406\u3002\u800c\u5149\u5708\u8d8a\u5c0f\uff0c\u6210\u50cf\u4e5f\u4f1a\u8d8a\u6765\u8d8a\u6e05\u695a\uff0c\u4f46\u4e5f\u4e0d\u80fd\u592a\u5c0f\uff0c\u5426\u5219\u4f1a\u5bfc\u81f4\u4eae\u5ea6\u4e0d\u8db3\u751a\u81f3\u884d\u5c04\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec02/#\u900f\u955c","title":"\u900f\u955c","text":"<p>\u51f8\u900f\u955c\u5177\u6709\u6c47\u805a\u5149\u7ebf\u7684\u4f5c\u7528\uff0c\u5728\u6ee1\u8db3\u7279\u5b9a\u5149\u5b66\u51e0\u4f55\u5173\u7cfb\u7684\u524d\u63d0\u4e0b\u5177\u6709\u548c\u5c0f\u5b54\u6210\u50cf\u7c7b\u4f3c\u7684\u6548\u679c\uff0c\u4f46\u662f\u80fd\u591f\u6c47\u805a\u66f4\u591a\u7684\u5149\u7ebf\u3002</p> <p></p> <p>Source: https://fpcv.cs.columbia.edu/</p> <p>\u5bf9\u4e8e\u8584\u51f8\u900f\u955c\uff0c\u6709\u9ad8\u65af\u6210\u50cf\u516c\u5f0f\uff1a</p> \\[ \\frac{1}{i} + \\frac{1}{o} = \\frac{1}{f} \\] <p>\u5176\u4e2d \\(i\\) \u4e3a\u50cf\u8ddd(img dis)\uff0c\\(o\\) \u4e3a\u7269\u8ddd(obj dis)\uff0c\\(f\\) \u4e3a\u7126\u8ddd(focal len)\u3002</p> <p>\u800c\u5bf9\u4e8e\u5e73\u884c\u5149\uff0c\u6216\u8005\u8bf4 \\(o\\to +\\infty\\) \u65f6\uff0c\u5c31\u4f1a\u6709 \\(i=f\\)\u3002\u901a\u8fc7\u8fd9\u79cd\u65b9\u6cd5\uff0c\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u6d4b\u91cf\u5e73\u884c\u5149\u900f\u8fc7\u51f8\u900f\u955c\u6c47\u805a\u7684\u4f4d\u7f6e\u6765\u6d4b\u91cf\u7126\u8ddd\u3002</p> <p>\u540c\u65f6\u518d\u5f15\u5165\u4e00\u4e2a\u653e\u5927\u7387(Magnification)\uff1a\\(m=\\frac{h_i}{h_o}=\\frac{i}{o}\\)\u3002</p> <p></p> <p>Source: https://fpcv.cs.columbia.edu/</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec02/#\u89c6\u91ce-fovfield-of-view","title":"\u89c6\u91ce FoV(field of view)","text":"<p>\u7126\u8ddd\u548c\u5e95\u7247\u7684\u7ebf\u5ea6\u5171\u540c\u51b3\u5b9a\u4e86 FoV \u7684\u5927\u5c0f\u3002</p> <p></p> <p>Source: https://snapsnapsnap.photos/</p> <p>\u53ef\u4ee5\u53d1\u73b0\uff0c\u7126\u8ddd\u7684\u5927\u5c0f\u4f1a\u5f71\u54cd\u89c6\u91ce\u7684\u5927\u5c0f\u548c\u653e\u5927\u7387\u7684\u5927\u5c0f\u3002</p> <p>50mm/46\u00b0 \u4e0e\u4eba\u7684\u89c6\u91ce\u76f8\u8fd1\uff0c\u56e0\u6b64\u5b83\u88ab\u79f0\u4e3a\u6807\u51c6\u955c\u5934(standard lens).</p> <p>\u6b64\u5916\uff0c\u5373\u4f7f\u5728\u753b\u9762\u4e2d\u4fdd\u8bc1\u4e00\u4e2a\u7269\u4f53\u7684\u5927\u5c0f\u4e0d\u53d8\uff0c\u9009\u7528\u4e0d\u540c\u7684\u7126\u8ddd\u4e5f\u4f1a\u5bfc\u81f4\u753b\u9762\u7684\u53d8\u5316\u2014\u2014\u80cc\u666f\u7684\u5927\u5c0f\uff0c\u901a\u8fc7\u4e0b\u9762\u8fd9\u5f20\u56fe\u7684\u4e09\u4e2a\u753b\u9762\u6211\u4eec\u53ef\u4ee5\u5f88\u6e05\u6670\u7684\u611f\u53d7\u5230\u8fd9\u4e00\u70b9\u3002</p> <p></p> <p>\u6b64\u5916\uff0c\u4f20\u611f\u5668\u7684\u5927\u5c0f\uff0c\u6216\u8005\u8bf4\u5e95\u7247\u7684\u5927\u5c0f\uff0c\u4e5f\u4f1a\u5f71\u54cd FoV\u3002\u800c\u4e14\u4e00\u822c\u6765\u8bf4\uff0c\u8d8a\u5927\u7684\u5e95\u7247\u80fd\u591f\u63d0\u4f9b\u66f4\u9ad8\u7684\u5206\u8fa8\u7387\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec02/#f-\u6570","title":"F \u6570","text":"<p>F \u6570(F-Number)\u7528\u6765\u63cf\u8ff0\u5149\u5708\u7684\u76f8\u5bf9\u5927\u5c0f\uff0c\u5176\u5b9a\u4e49\u5f0f\u4e3a \\(N=\\frac{f}{D}\\)\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec02/#\u5bf9\u7126","title":"\u5bf9\u7126","text":"<p>Source: https://fpcv.cs.columbia.edu/</p> <p>\u7531\u76f8\u4f3c\u4e09\u89d2\u5f62\uff0c\u6ca1\u6709\u5bf9\u4e0a\u7126\u800c\u5f62\u6210\u7684\u5149\u6591(Blur Circle)\u7684\u8ba1\u7b97\u516c\u5f0f\u4e3a\uff1a</p> \\[ \\begin{align}     &amp;\\because \\frac{b}{D}=frac{|i'-i|}{i'} \\\\     &amp;\\therefore b = \\frac{D}{i'}|i'-i|\\;,\\;\\;\\;b \\propto D \\propto \\frac{1}{N} \\end{align} \\] <p>\u800c\u5bf9\u7126\uff0c\u5c31\u662f\u5c06\u5931\u7126\u7684\u5185\u5bb9\u91cd\u65b0\u6c47\u805a\u5230\u5e95\u7247\u4e0a\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec02/#\u666f\u6df1-dof","title":"\u666f\u6df1 DoF","text":"<p>\u6839\u636e\u4e0a\u4e00\u5c0f\u8282\u5f97\u5230\u7684\u7ed3\u8bba\uff0c\u7406\u8bba\u4e0a\u6211\u4eec\u597d\u50cf\u53ea\u6709\u6e05\u6670\u6210\u50cf\u4e00\u4e2a\u7279\u5b9a\u5e73\u9762\u4e0a\u7684\u5185\u5bb9\uff0c\u4f46\u662f\u5b9e\u9645\u4e0a\u76f8\u673a\u4e0a\u4f1a\u6709\u4e00\u6bb5\u8ddd\u79bb\u4e0a\u7684\u5185\u5bb9\u90fd\u662f\u6e05\u6670\u7684\uff0c\u8fd9\u6bb5\u8ddd\u79bb\u5c31\u662f\u666f\u6df1 DoF(Depth of Field)\u3002\u800c\u4e4b\u6240\u4ee5\u6709\u666f\u6df1\uff0c\u662f\u56e0\u4e3a\u5e95\u7247\u7684\u611f\u5149\u5143\u4ef6\u662f\u6709\u6781\u9650\u7684\uff0c\u5f53\u5149\u6591\u5c0f\u96e8\u8fd9\u4e2a\u6781\u9650\u65f6\uff0c\u62cd\u6444\u51fa\u6765\u7684\u5c31\u4ecd\u7136\u662f\u6e05\u6670\u7684\u3002</p> <p>\u800c\u666f\u6df1\u7684\u5927\u5c0f\u53ef\u4ee5\u8fd9\u4e48\u8ba1\u7b97\uff1a</p> <p></p> <p>\u6211\u4eec\u53ef\u4ee5\u53d1\u73b0\uff0c\u666f\u6df1\u7684\u5927\u5c0f \u5927\u81f4\u4e0e \u5149\u5708\u5927\u5c0f\u3001\u7269\u50cf \u6b63\u76f8\u5173\uff0c\u4e0e \u7126\u8ddd \u8d1f\u76f8\u5173\u3002</p> <p>\u5f15\u8a00</p> <p>\u7531\u4e8e\u6211\u4eec\u8003\u8651\u7684\u662f\u6210\u50cf\u95ee\u9898\uff0c\u6240\u4ee5\u66f4\u591a\u7684\u662f\u5728\u63cf\u8ff0\u4e09\u7ef4\u771f\u5b9e\u4fe1\u606f\u4e0e\u4e8c\u7ef4\u5e73\u9762\u4fe1\u606f\u4e4b\u95f4\u7684\u4e92\u76f8\u8868\u8fbe\u3002</p> <p>\u800c\u8fd9\u79cd\u201c\u63cf\u8ff0\u201d\u9700\u8981\u57fa\u4e8e\u4e00\u4e2a\u6295\u5f71\u6a21\u578b\u3002\u6216\u8005\u8bf4\u8bf4\u4e00\u79cd\u6620\u5c04\u5173\u7cfb\uff0c\u7b80\u5355\u6765\u8bf4\u5c31\u597d\u50cf\u201c\u70b9\u5149\u6e90\u6295\u5f71\u201d\u548c\u201c\u5e73\u884c\u5149\u6e90\u6295\u5f71\u201d\u3002</p> <p>\u4f46\u662f\u9700\u8981\u6ce8\u610f\uff0c\u65e0\u8bba\u662f\u54ea\u4e00\u79cd\u6a21\u578b\uff0c\u7531\u4e8e\u6211\u4eec\u5c06\u4e09\u7ef4\u4fe1\u606f\u901a\u8fc7\u4e0d\u53ef\u9006\u7684\u7ebf\u6027\u53d8\u6362\u538b\u7f29\u5230\u4e86\u4e8c\u7ef4\u4fe1\u606f\uff0c\u6240\u4ee5\u4e00\u5b9a\u662f\u5b58\u5728\u4fe1\u606f\u7f3a\u5931\u7684\u3002\u901a\u5e38\u6765\u8bf4\uff0c\u6307\u7684\u662f\u6df1\u5ea6\u7f3a\u5931\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec02/#\u900f\u89c6\u6295\u5f71","title":"\u900f\u89c6\u6295\u5f71","text":"<p>\u5982\u56fe\u662f 3D \u5750\u6807\u901a\u8fc7\u900f\u89c6\u6295\u5f71\u5230 2D \u5750\u6807\u5230\u793a\u610f\u56fe\u3002\u5176\u4e2d \\(x,y,Z\\) \u7528\u6765\u63cf\u8ff0\u7a7a\u95f4\u5750\u6807\u4fe1\u606f\uff0c\u65b9\u4fbf\u8d77\u89c1\uff0c\u6211\u4eec\u7528\u4ed6\u4eec\u8868\u793a\u76f8\u5bf9\u4e8e\u76f8\u673a\u4e2d\u5fc3(camera center)\u7684\u6b63\u4ea4\u5750\u6807\uff0c\u5176\u4e2d \\(Z\\) \u548c\u5149\u8f74(optical axis)\u65b9\u5411\u76f8\u540c\uff0c\u6211\u4eec\u4e5f\u53ef\u4ee5\u79f0\u4e4b\u4e3a\u6df1\u5ea6\u3002</p> <p>\u540c\u65f6\uff0c\u5149\u8f74\u5e94\u5f53\u5782\u76f4\u4e8e\u6210\u50cf\u5e73\u9762\uff0c\u800c\u5149\u8f74\u4e0e\u6210\u50cf\u5e73\u9762\u7684\u4ea4\u70b9\u4e3a\u56fe\u50cf\u4e2d\u5fc3(img center)\u3002</p> <p>\u53ef\u4ee5\u53d1\u73b0\uff0c\\(P\\) \u4e0e \\(p\\) \u7684\u5173\u7cfb\u5982\u4e0b\uff1a</p> \\[ p =  \\begin{bmatrix}     u \\\\     v \\end{bmatrix} = \\begin{bmatrix}     \\frac{f}{Z}\\cdot x \\\\     \\frac{f}{Z}\\cdot y \\end{bmatrix} \\] <p>\u90a3\u6709\u6ca1\u6709\u529e\u6cd5\u5c06 \\(p\\) \u548c \\(P\\) \u901a\u8fc7\u7ebf\u6027\u53d8\u5316\u653e\u5728\u540c\u4e00\u4e2a\u7b49\u5f0f\u91cc\u5462\uff1f</p> <p>\u6362\u53e5\u8bdd\u6765\u8bf4\uff0c\u6709\u6ca1\u6709\u529e\u6cd5\u4f7f\u5f97\u5982\u4e0b\u7b49\u5f0f\u6210\u7acb\uff1f</p> \\[ A \\begin{bmatrix}     x \\\\     y \\\\     z \\end{bmatrix} \\overset{?}= \\begin{bmatrix}     \\frac{f}{Z}\\cdot x \\\\     \\frac{f}{Z}\\cdot y \\end{bmatrix} \\] <p>\u5f88\u53ef\u60dc\uff0c\u7531\u4e8e\u5f0f\u5b50\u4e2d\u51fa\u73b0\u4e86 \\(\\frac{1}{Z}\\)\uff0c\u5373\u9664\u6cd5\uff0c\u5b83\u5e76\u4e0d\u662f\u4e2a\u7ebf\u6027\u53d8\u6362\u3002\u6240\u4ee5\u5373\u4f7f\u6211\u4eec\u6269\u5c55 \\(p\\) \u548c \\(P\\) \u7684\u7ef4\u5ea6\u6211\u4eec\u6ca1\u6cd5\u76f4\u63a5\u5c06\u5b83\u53d8\u6210\u7ebf\u6027\u53d8\u6362\u3002</p> <p>\u4f46\u662f\u4f60\u4e5f\u770b\u5230\u4e86\uff0c\u6211\u7528\u7684\u8bcd\u662f\u201c\u76f4\u63a5\u201d\uff0c\u6240\u4ee5\u6211\u4eec\u63a5\u4e0b\u6765\u53ef\u4ee5\uff1a</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec02/#\u5e94\u7528\u9f50\u6b21\u5750\u6807","title":"\u5e94\u7528\u9f50\u6b21\u5750\u6807","text":"<p>\u8ba9\u6211\u4eec\u56de\u987e\u9f50\u6b21\u5750\u6807\u7684 \u6269\u5c55\u6027\u8d28\uff0c\u5c06\u5b83\u5e94\u7528\u4e8e\u6b64\u5f0f\uff1a</p> \\[ \\begin{bmatrix}     \\frac{f}{Z}\\cdot x \\\\     \\frac{f}{Z}\\cdot y \\\\     1 \\end{bmatrix} \\cong \\begin{bmatrix}     f \\cdot x \\\\     f \\cdot y \\\\     Z \\end{bmatrix} \\] <p>\u4e8e\u662f\u6211\u4eec\u53d1\u73b0\uff0c\u867d\u7136\u6211\u4eec\u6ca1\u6cd5\u627e\u5230 \\(A\\) \u4f7f\u5f97\uff1a</p> \\[ A \\begin{bmatrix}     x \\\\     y \\\\     Z \\\\     1 \\end{bmatrix} \\overset{?}= \\begin{bmatrix}     \\frac{f}{Z}\\cdot x \\\\     \\frac{f}{Z}\\cdot y \\\\     1 \\end{bmatrix} \\] <p>\u6210\u7acb\uff0c\u4f46\u662f\u6211\u4eec\u53ef\u4ee5\u627e\u5230 \\(A=\\begin{bmatrix}f &amp; 0 &amp; 0 &amp; 0 \\\\ 0 &amp; f &amp; 0 &amp; 0 \\\\ 0 &amp; 0 &amp; 1 &amp; 0\\end{bmatrix}\\) \u4f7f\u5f97\uff1a</p> \\[ \\begin{bmatrix}     f &amp; 0 &amp; 0 &amp; 0 \\\\      0 &amp; f &amp; 0 &amp; 0 \\\\      0 &amp; 0 &amp; 1 &amp; 0 \\end{bmatrix} \\begin{bmatrix}     x \\\\     y \\\\     Z \\\\     1 \\end{bmatrix} = \\begin{bmatrix}     f \\cdot x \\\\     f \\cdot y \\\\     Z \\end{bmatrix} \\cong \\begin{bmatrix}     \\frac{f}{Z}\\cdot x \\\\     \\frac{f}{Z}\\cdot y \\\\     1 \\end{bmatrix} \\] <p>\u4e8e\u662f\uff0c\u6211\u4eec\u5c31\u6210\u529f\u7684\u901a\u8fc7\u7ebf\u6027\u53d8\u6362\u5c06 \\(P\\) \u548c \\(p\\) \u7edf\u4e00\u4e86\u8d77\u6765\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec02/#\u53ef\u89c6\u5316\u8868\u793a","title":"\u53ef\u89c6\u5316\u8868\u793a","text":"<p>\u6211\u4eec\u53ef\u4ee5\u53d1\u73b0\uff0c\u5c0f\u5b54\u6210\u50cf\u7684\u6a21\u578b\u89c6\u56fe\u5176\u5b9e\u8fd8\u662f\u6bd4\u8f83\u9ebb\u70e6\u7684\u3002\u73b0\u5728\u6211\u4eec\u628a\u8fd9\u4e2a\u5b9a\u89d2\u76f8\u4f3c\u5bf9\u6298\uff0c\u53d8\u6210 A \u5b57\u578b\u76f8\u4f3c\u6765\u8868\u793a\u8fd9\u4e2a\u6a21\u578b\uff0c\u4ee5\u7b80\u5316\u4e0d\u5fc5\u8981\u7684\u4fe1\u606f\uff0c\u540c\u65f6\u4e5f\u80fd\u66f4\u6e05\u6670\u5730\u8868\u793a\u900f\u89c6\u5173\u7cfb\u3002</p> <p>\u89c4\u5b9a\u6211\u4eec\u8ba8\u8bba\u7684\u95ee\u9898\u4e2d\u7269\u8ddd\u603b\u662f\u5927\u4e8e\u50cf\u8ddd\uff0c\u5219\u53ef\u4ee5\u5c06\u50cf\u8868\u793a\u4e3a\u76f8\u673a\u4e2d\u5fc3\u5230\u7269\u4f53\u7684\u653e\u5c04\u8fde\u7ebf\u4e2d\u7684\u622a\u9762\u3002</p> <p>\u5b83\u6bd4\u8f83\u597d\u5730\u8868\u8fbe\u4e86\u900f\u89c6\u5173\u7cfb\uff0c\u5373 \u76f8\u673a\u4e2d\u5fc3 \u7269\u70b9B \u50cf\u70b9B' \u59cb\u7ec8\u5171\u7ebf\u3002\u8fd9\u4e5f\u662f\u5728\u4e4b\u540e\u7684\u5185\u5bb9\u4e2d\u66f4\u52a0\u5e38\u89c1\u7684\u53ef\u89c6\u5316\u8868\u73b0\u65b9\u6cd5\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec02/#\u4fe1\u606f\u7f3a\u5931","title":"\u4fe1\u606f\u7f3a\u5931","text":"<p>\u7531\u4e8e\u5728\u900f\u89c6\u6295\u5f71\u7cfb\u7edf\u4e2d\uff0c\u7269\u4f53\u7684\u771f\u5b9e\u7ebf\u5ea6\u5927\u5c0f\u4e0e\u56fe\u50cf\u7ebf\u5ea6\u5927\u5c0f\u7684\u6bd4\u4f8b\u7531\u6df1\u5ea6\u51b3\u5b9a\uff0c\u4f46\u6df1\u5ea6\u53c8\u4e0d\u80fd\u76f4\u63a5\u4ece\u56fe\u4e2d\u83b7\u53d6\uff0c\u6240\u4ee5\u6709\u65f6\u5019\u6211\u4eec\u65e0\u6cd5\u6bd4\u8f83\u56fe\u50cf\u4e2d\u4e24\u4e2a\u7269\u4f53\u7684\u771f\u5b9e\u7ebf\u5ea6\u5dee\u3002\u6362\u53e5\u8bdd\u6765\u8bf4\uff0c\u957f\u5ea6\u4fe1\u606f\u548c\u89d2\u5ea6\u4fe1\u606f\u662f\u4e22\u5931\u7684\u3002</p> <p>\uff08\u591a\u6570\u60c5\u51b5\u4e0b\uff0c\u6211\u4eec\u9700\u8981\u4ee5\u4e00\u4e9b\u4e1c\u897f\u6765\u505a\u53c2\u8003\u7cfb\uff0c\u5224\u65ad A \u548c B \u7684\u6df1\u5ea6\u4fe1\u606f\uff0c\u518d\u5206\u6790\u4ed6\u4eec\u7684\u5b9e\u9645\u7ebf\u5ea6\u5927\u5c0f\u5173\u7cfb\u3002\uff09</p> <p>\u7136\u800c\u4ecd\u7136\u6709\u4e9b\u6027\u8d28\u662f\u4fdd\u7559\u7684\uff0c\u4f8b\u5982\u76f4\u7ebf\u4ecd\u7136\u662f\u76f4\u7ebf\uff0c\u4f46\u662f\u5b9e\u9645\u4e0a\uff0c\u5982\u679c\u4f60\u80fd\u60f3\u8c61\u7684\u8bdd\uff0c\u867d\u7136\u76f4\u7ebf\u4ecd\u7136\u662f\u76f4\u7ebf\uff0c\u4f46\u662f\u5b83\u7684\u201c\u7ebf\u5bc6\u5ea6\u201d\u4e0d\u4e00\u6837\u4e86\u3002</p> <p>\u6240\u4ee5\uff0c\u5982\u679c\u662f\u66f2\u7ebf\uff0c\u5b83\u867d\u7136\u4e0d\u4f1a\u53d8\u6210\u6298\u7ebf\uff0c\u4f46\u662f\u7279\u5f81\u53ef\u80fd\u5df2\u7ecf\u53d8\u4e86\uff0c\u6bd4\u5982\u5706\u662f\u4f1a\u626d\u66f2\u7684\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec02/#\u706d\u70b9\u4e0e\u706d\u7ebf","title":"\u706d\u70b9\u4e0e\u706d\u7ebf","text":"<p>\u5728\u900f\u89c6\u4e2d\u4e00\u4e2a\u5f88\u6709\u610f\u601d\u7684\u73b0\u8c61\u662f\u706d\u70b9(vanishing point)\u548c\u706d\u7ebf(vanishing line)\u3002</p> <p></p> <p>\u53ef\u4ee5\u53d1\u73b0\uff0c\u5728\u56fe\u50cf\u4e2d\u4e00\u6761\u4e0d\u65ad\u884d\u751f\u7684\u76f4\u7ebf\uff0c\u5728\u50cf\u4e2d\u6700\u7ec8\u4f1a\u7ec8\u7ed3\u4e8e\u4e00\u4e2a\u70b9\uff0c\u8fd9\u4e2a\u70b9\u5c31\u662f\u201c\u706d\u70b9\u201d\u3002\u51e0\u4f55\u4e0a\uff0c\u706d\u70b9\u4e0e\u76f8\u673a\u4e2d\u5fc3\u7684\u8fde\u7ebf\u5e94\u5f53\u5e73\u884c\u4e8e\u8be5\u76f4\u7ebf\u3002</p> <p>\u800c\u73b0\u5b9e\u4e2d\u76f8\u4e92\u5e73\u884c\u7684\u4e24\u6761\u76f4\u7ebf\uff0c\u6700\u7ec8\u4f1a\u5728\u56fe\u50cf\u4e2d\u7ec8\u6b62\u4e8e\u540c\u4e00\u4e2a\u706d\u70b9\u3002</p> <p>\u706d\u70b9\u672a\u5fc5\u5728\u56fe\u50cf\u4e2d\uff0c\u751a\u81f3\u53ef\u80fd\u65e0\u9650\u8fdc\u3002</p> <p> </p> <p></p> <p>\u521a\u624d\u63d0\u5230\uff0c\u5e73\u884c\u7ebf\u5171\u4eab\u706d\u70b9\u8fd9\u610f\u5473\u7740\u6709\u591a\u5c11\u7ec4\u5e73\u884c\u7ebf\u5c31\u6709\u591a\u5c11\u706d\u70b9\u3002</p> <p>\u5982\u679c\u6211\u4eec\u5c06\u4e00\u4e2a\u5e73\u9762\u50cf\u68cb\u76d8\u90a3\u6837\uff0c\u5212\u51fa\u4e24\u7ec4\u5e73\u884c\u7ebf\uff0c\u90a3\u4e48\u5c31\u4f1a\u5f97\u5230\u4e24\u4e2a\u706d\u70b9\uff0c\u5982\u56fe\u4e2d\u7684 \\(v_1\\) \u548c \\(v_2\\)\u3002\u8fd9\u610f\u5473\u7740\uff0c\u5bf9\u4e8e\u4e00\u4e2a\u5e73\u9762\uff0c\u6211\u4eec\u53ef\u4ee5\u4ece\u4e2d\u53d6\u51fa\u65e0\u6570\u7ec4\u5e73\u884c\u7ebf\uff0c\u56e0\u800c\u65e0\u9650\u5927\u7684\u5e73\u9762\u4f1a\u4ea7\u751f\u65e0\u6570\u591a\u7684\u706d\u70b9\uff0c\u800c\u8fd9\u4e9b\u706d\u70b9\u8fde\u6210\u7ebf\u5c31\u6210\u4e86\u201c\u706d\u7ebf\u201d\u3002\u5e38\u89c1\u7684\u706d\u7ebf\u5c31\u6bd4\u5982\u7167\u7247\u4e0a\u7684\u6d77\u5929\u754c\u7ebf\u3002</p> <p>\u56e0\u6b64\uff0c\u5982\u679c\u8bf4\u706d\u70b9\u8c61\u5f81\u4e86\u4e00\u7ec4\u5e73\u884c\u7ebf\uff0c\u90a3\u706d\u7ebf\u5c31\u662f\u8c61\u5f81\u4e86\u4e00\u5757\u5e73\u9762\u3002\u800c\u6211\u4eec\u5c31\u53ef\u4ee5\u901a\u8fc7\u770b\u5e73\u9762\u4e0a\u7684\u5185\u5bb9\u51fa\u73b0\u5728\u706d\u7ebf\u4ee5\u4e0a\u8fd8\u662f\u706d\u7ebf\u4e00\u4e0b\uff0c\u6765\u5224\u65ad\u5e73\u9762\u5728\u6211\u4eec\u7684\u76f8\u673a\u4e2d\u5fc3\u4ee5\u4e0b\u8fd8\u662f\u4ee5\u4e0a\uff08\u53ef\u4ee5\u601d\u8003\u4e00\u4e0b\u4e3a\u4ec0\u4e48\uff09\u3002</p> <p>Interesting Try</p> \u9898\u9762\u7b54\u6848 <p>\u89c2\u5bdf\u5982\u4e0b\u56fe\u7247\uff0c\u5224\u65ad \ud83e\ude82(\u8df3\u4f1e\u8005) \u5728 \ud83d\udcf7 \u4ee5\u4e0a\u8fd8\u662f\u4ee5\u4e0b\uff0c\u5e76\u9610\u660e\u7406\u7531\u3002</p> <p></p> <p>\u663e\u7136\uff0c\ud83e\ude82(\u8df3\u4f1e\u8005) \u5728 \ud83d\udcf7 \u4ee5\u4e0b\uff08\u4f1e\u5728\u4ee5\u4e0a\uff09\uff0c\u4f9d\u636e\u662f \u4eba \u5728 \u5929\u9645\u7ebf \u4ee5\u4e0b\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec02/#\u900f\u89c6\u7578\u53d8","title":"\u900f\u89c6\u7578\u53d8","text":"<p>\u5728\u62cd\u6444\u8f83\u5927\u7684\u7269\u4f53\u65f6\uff0c\u6bd4\u5982\u5efa\u7b51\u7269\uff0c\u5982\u679c\u5efa\u7b51\u7269\u7684\u5899\u9762\u6ca1\u6709\u548c\u5e95\u7247\u5e73\u884c\uff0c\u5219\u4f1a\u51fa\u73b0\u900f\u89c6\u7578\u53d8\u3002</p> <p>\u5728\u5efa\u7b51\u62cd\u6444\u65b9\u9762\uff0c\u6211\u4eec\u7684\u89e3\u51b3\u529e\u6cd5\u662f\u4e0b\u79fb\u4f20\u611f\u5668\uff0c\u4f7f\u5e95\u7247\u4e2d\u5fc3\u5728\u5149\u8f74\u4ea4\u70b9\u4ee5\u4e0b\uff0c\u8fd9\u79cd\u955c\u5934\u79f0\u4e3a\u79fb\u8f74\u955c\u5934\u3002</p> <p>\u53e6\u5916\u4e00\u79cd\u900f\u89c6\u7578\u53d8\u4f53\u73b0\u5728\u66f2\u7ebf\u7684\u5f62\u53d8\u4e0a\uff0c\u4e5f\u5c31\u662f\u6211\u4eec\u5e38\u611f\u53d7\u5230\u7684\uff0c\u7ad9\u5728\u8fb9\u4e0a\u7684\u4eba\u8138\u603b\u662f\u66f4\u5927\u4e00\u70b9\u3002\u800c\u8fd9\u79cd\u7578\u53d8\u5728\u65ad\u955c\u5934\u4e0b\u66f4\u5e38\u89c1\uff0c\u6240\u4ee5\u4eba\u50cf\u66f4\u591a\u7528\u7684\u662f\u957f\u7126\u955c\u5934\uff08\u5176\u4e00\u539f\u56e0\uff0c\u5176\u4ed6\u7684\u8fd8\u6709 FoV \u5c0f\u6240\u4ee5\u80cc\u666f\u66f4\u5e72\u51c0\u7b49\uff09\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec02/#\u6795\u578b\u7578\u53d8\u548c\u6876\u578b\u7578\u53d8","title":"\u6795\u578b\u7578\u53d8\u548c\u6876\u578b\u7578\u53d8","text":"\\[ \\begin{align} r^2 &amp; = {x'}_n^2 + {y'}_n^2 \\\\ {x'}_d &amp; = {x'}_n(1 + \\kappa_1 r^2 + \\kappa_2 r^4) \\\\ {y'}_d &amp; = {y'}_n(1 + \\kappa_1 r^2 + \\kappa_2 r^4) \\\\ \\end{align} \\] <p>\u800c\u8fd9\u79cd\u7167\u7247\u7684\u7ea0\u6b63\u529e\u6cd5\u5c31\u662f\u5bfb\u627e\u7167\u7247\u4e2d\u7684\u683c\u70b9\uff0c\u7136\u540e\u901a\u8fc7\u6570\u5b66\u65b9\u6cd5\u6765\u8fd8\u539f\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec02/#\u6b63\u4ea4\u6295\u5f71","title":"\u6b63\u4ea4\u6295\u5f71","text":"<p>\u6b63\u4ea4\u6295\u5f71\u7684\u542b\u4e49\u5c31\u662f\uff0c\u76f4\u63a5\u62b9\u6389\u6df1\u5ea6\u4fe1\u606f\uff0c\u4e09\u7ef4\u70b9 \\(P\\) \u5230\u4e8c\u7ef4\u70b9 \\(p\\) \u7684\u6620\u5c04\u89c4\u5219\u5982\u4e0b\uff1a</p> \\[ \\begin{bmatrix}     1 &amp; 0 &amp; 0 \\\\     0 &amp; 1 &amp; 0  \\end{bmatrix} \\begin{bmatrix}     x \\\\     y \\\\     z \\end{bmatrix} = \\begin{bmatrix}     x \\\\     y  \\end{bmatrix} \\] <p>\u4e5f\u5c31\u662f\u5e73\u884c\u5149\u6e90\u6295\u5f71\u3002</p> <p>\u8fd9\u79cd\u6295\u5f71\u53ef\u80fd\u4e0d\u592a\u62df\u771f\uff0c\u4f46\u662f\u5728\u67d0\u4e9b\u4e0d\u8981\u6c42\u7cbe\u5ea6\u7684\u60c5\u51b5\u4e0b\u6211\u4eec\u603b\u662f\u4e50\u4e8e\u4f7f\u7528\u7684\u3002</p> <p>\u8fd9\u6837\u8bf4\u53ef\u80fd\u6bd4\u8f83\u62bd\u8c61\uff0c\u4f46\u662f\u5b83\u5176\u5b9e\u5f88\u5e38\u89c1\uff0c\u6bd4\u5982\u5728\u4e00\u4e9b\u4ee5\u201c\u4e0a\u5e1d\u89c6\u89d2\u201d\u5c55\u5f00\u7684\u6e38\u620f\u4e2d\uff0c\u4f8b\u5982\u201c\u5f00\u7f57\u6e38\u620f\u201d\u3001\u201c\u6a21\u62df\u90fd\u5e02\u201d\u8fd9\u79cd\uff0c\u91c7\u7528\u7684\u57fa\u672c\u90fd\u662f\u8fd9\u79cd\u6295\u5f71\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec02/#\u5feb\u95e8shutter","title":"\u5feb\u95e8(Shutter)","text":"<ul> <li>\u66dd\u5149\u65f6\u95f4(shutter speed)</li> <li>\u957f\u66dd\u5149\u65f6\u95f4\u62cd\u6444\u95ea\u7535\u7b49\uff1b</li> <li>\u6eda\u52a8\u5feb\u95e8\u6548\u5e94(rolling shutter effect)</li> <li>\u7528\u6eda\u52a8\u5feb\u95e8\u62cd\u6444\u4f8b\u5982\u98ce\u6247\u65f6\uff0c\u4f1a\u51fa\u73b0\u4e00\u4e9b\u56fe\u50cf\u53d8\u5f62\uff1b</li> </ul>"},{"location":"cour_note/D2QD_Intro2CV/Lec02/#\u5149\u5ea6\u56fe\u50cf\u751f\u6210\u4e0e\u7740\u8272","title":"\u5149\u5ea6\u56fe\u50cf\u751f\u6210\u4e0e\u7740\u8272","text":"<p>\u5149\u5ea6\u56fe\u50cf\u751f\u6210\u8003\u8651\u7684\u4e3b\u8981\u662f\u5149\u5f3a\u548c\u989c\u8272\u4e24\u4e2a\u65b9\u9762\u7684\u95ee\u9898\u3002</p> <p>\u786c\u4ef6\u4e0a\uff0c\u5b83\u4eec\u90fd\u901a\u8fc7\u56fe\u50cf\u4f20\u611f\u5668(img sensor)\u5b9e\u73b0\u3002</p> <ul> <li>\u4e3b\u8981\u5206\u4e3a CMOS(Complimentary Metal-Oxide Semiconductor) \u548c CCD(Charge Coupled Device) \u4e24\u79cd\uff0c\u533a\u522b\u5728\u4e8e Electron to Voltage Conversion \u662f\u5426\u516c\u7528\uff1b</li> </ul> <p>\u5f15\u5165</p> <p>\u7740\u8272(shading)\u4e2d\u6240\u8bf4\u7684\u5149\u5f3a\uff0c\u4e3b\u8981\u6709\u4e24\u4e2a\u65b9\u9762\uff1a\u4e00\u65b9\u9762\u4e0e\u8ddd\u79bb\u5149\u6e90\u7684\u8ddd\u79bb\u6709\u5173\uff0c\u7406\u60f3\u60c5\u51b5\u4e0b\u7b26\u5408\u5e73\u65b9\u53cd\u6bd4\u5b9a\u5f8b\uff0c\u8fd9\u79cd\u7279\u5f81\u6211\u4eec\u79f0\u4e4b\u4e3a Light Falloff\uff1b\u53e6\u4e00\u65b9\u9762\u5b9e\u9645\u4e0a\u662f\u9700\u8981\u6211\u4eec\u8ba1\u7b97\u5149\u7684\u53cd\u5c04\u884c\u4e3a\u3002</p> <p>\u7406\u8bba\u4e0a\uff0c\u6211\u4eec\u4f1a\u9700\u8981\u53cc\u5411\u53cd\u5c04\u5206\u5e03\u51fd\u6570 BRDF(Bidirectional Reflectance Distribution Function)\u6765\u8ba1\u7b97\uff0cBRDF \u7684\u8f93\u5165\u5927\u81f4\u53ef\u4ee5\u5206\u4e3a\u5982\u4e0b\u51e0\u4e2a\uff1a</p> <ul> <li>\u89c2\u6d4b\u89d2\u5ea6(viewer direction)\uff1a\\(\\vec v\\)</li> <li>\u8868\u9762\u6cd5\u5411\u91cf(surface normal)\uff1a\\(\\vec n\\)</li> <li>\u5165\u5c04\u5149\u65b9\u5411(light direction)\uff1a \\(\\vec l\\)</li> <li>\u663e\u7136\uff0c\u5bf9\u4e8e\u6bcf\u4e00\u6761\u5149\u7ebf\u90fd\u9700\u8981\u7ed9\u51fa\uff1b</li> <li>\u8868\u9762\u6750\u8d28(surface parameters)</li> </ul> <p>\u53ef\u4ee5\u53d1\u73b0\uff0c\u9700\u8981\u5efa\u7acb\u8fd9\u6837\u4e00\u4e2a\u6a21\u578b\u662f\u5f88\u56f0\u96be\u7684\uff0c\u4e14\u8fd9\u4e2a\u6a21\u578b\u4e0d\u5e38\u7528\uff0c\u800c\u4e14\u8ba1\u7b97\u8d77\u6765\u6bd4\u8f83\u9ebb\u70e6\u3002</p> <p>\u53cd\u5c04\u4e3b\u8981\u53ef\u4ee5\u5f52\u7eb3\u4e3a\u4e24\u79cd\u7b80\u5355\u6a21\u578b\u548c\u4e00\u79cd\u6df7\u5408\u6a21\u578b\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec02/#\u6f2b\u53cd\u5c04","title":"\u6f2b\u53cd\u5c04","text":"<p>\u6f2b\u53cd\u5c04(diffuse reflection) \u53c8\u53eb \u6717\u4f2f\u53cd\u5c04(Lambertian reflection)\uff0c\u662f\u8868\u73b0\u5728\u7c97\u7cd9\u8868\u9762\u4e0a\u7684\u53cd\u5c04\u7279\u5f81\uff0c\u56e0\u4e3a\u6211\u4eec\u9ed8\u8ba4\u5b83\u5411\u56db\u9762\u516b\u65b9\u53cd\u5c04\u7684\u5149\u5f3a\u90fd\u4e00\u6837\uff0c\u6240\u4ee5\u5b83\u7684\u8ba1\u7b97\u76f8\u5bf9\u6bd4\u8f83\u7b80\u5355\uff08Shading independent of view direction\uff09\uff1a</p> \\[ L_d = k_d \\cdot \\frac{I}{r^2} \\cdot \\max(0,n\\cdot l) \\] <p>\u5bf9\u6210\u5206\u505a\u89e3\u91ca\uff1a</p> <ul> <li>\\(L_d\\) \u4e3a\u6f2b\u53cd\u5c04\u5149\u5f3a(diffusely reflected light)\uff1b</li> <li>\\(k_d\\) \u4e3a\u6f2b\u53d1\u5c04\u7cfb\u6570(diffuse coefficient)\uff0c\u5982\u989c\u8272\uff1b</li> <li>\\(\\frac{I}{r^2}\\) \u4e3a \u5230\u8fbe\u7740\u8272\u70b9\u7684\u5149\u5f3a\uff1b</li> <li>\\(\\max(0,n \\cdot l)\\) \u4e3a \u7740\u8272\u70b9\u5438\u6536\u7684\u5149\u5f3a\uff1b</li> </ul> \u5982\u4f55\u7406\u89e3\u5149\u5f3a\u5ea6\u4e0e\u89d2\u5ea6\u7684\u5173\u7cfb <p>\u4e00\u5f00\u59cb\u6ca1\u4ed4\u7ec6\u60f3\u7684\u65f6\u5019\u8fd8\u89c9\u5f97\u5f88\u81ea\u7136\uff0c\u4f46\u662f\u4ed4\u7ec6\u4e00\u60f3\u4e3a\u4ec0\u4e48\u80fd\u8fd9\u6837\u8868\u8ff0\uff1f\u4e8e\u662f\u548c\u540c\u5b66\u63a2\u8ba8\u4e86\u4e00\u4e0b\uff0c\u611f\u89c9\u4e00\u4e2a\u53ef\u4ee5\u63a5\u53d7\u7684\u89e3\u91ca\u662f\u8fd9\u6837\u7684\uff1a</p> <p>\u9996\u5148\uff0c\u8fd9\u91cc\u4e0e\u5176\u8bf4\u4e0e\u89d2\u5ea6\u76f8\u5173\uff0c\u4e0d\u5982\u8bf4\u4e0e\u5355\u4f4d\u9762\u79ef\u53d7\u5230\u7684\u5149\u7167\u5f3a\u5ea6\u6709\u5173\u3002\u6362\u53e5\u8bdd\u6765\u8bf4\uff0c\u5bf9\u4e8e\u540c\u4e00\u675f\u5149\uff0c\u503e\u659c\u7684\u9762\u4e0a\u4f1a\u6709\u66f4\u5927\u7684\u9762\u79ef\u88ab\u7167\u5c04\u5230\uff0c\u5747\u644a\u4e0b\u6765\u5355\u4f4d\u9762\u79ef\u4e0a\u7684\u5149\u5f3a\u5ea6\u5c31\u5c0f\uff0c\u6216\u8bb8\u53ef\u4ee5\u5c06\u5b83\u7406\u89e3\u6210\u7c7b\u4f3c\u4e8e\u201c\u5bc6\u5ea6\u201d\u7684\u6982\u5ff5\u3002</p> <p>\u5e26\u7740\u8fd9\u6837\u7684\u60f3\u6cd5\uff0c\u518d\u6765\u770b\u8fd9\u5f20\u56fe\uff0c\u5c31\u6bd4\u8f83\u6e05\u6670\u4e86\u3002</p> <p></p> <p>Source: https://sites.cs.ucsb.edu/~lingqi/teaching/games101.html</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec02/#\u9ad8\u5149\u53cd\u5c04","title":"\u9ad8\u5149\u53cd\u5c04","text":"<p>\u9ad8\u5149\u53cd\u5c04(specular reflection) \u7c7b\u4f3c\u6211\u4eec\u8ba4\u77e5\u4e2d\u7684\u955c\u9762\u53cd\u5c04\uff0c\u5b83\u7684\u7279\u5f81\u662f\u57fa\u672c\u7b26\u5408\u955c\u53cd\u5c04\u7684\u89c4\u5f8b\u3002</p> <p>\u5728\u9ad8\u5149\u53cd\u5c04\u4e2d\uff0c\u6211\u4eec\u9700\u8981\u5b9a\u4e49\u534a\u7a0b\u5411\u91cf(half vec)\\(\\vec h = bisector(\\vec v,\\vec l) = \\frac{\\vec v + \\vec l}{||\\vec v + \\vec l||}\\) </p> <p>\u5f53 \\(\\vec h\\) \u4e0e \\(\\vec n\\) \u975e\u5e38\u63a5\u8fd1\u65f6\uff0c\u5373 \\(\\alpha = &lt;\\vec n, \\vec h&gt;\\) \u5f88\u5c0f\u65f6\uff0c\u6211\u4eec\u79f0\u4e4b\u7b26\u5408\u9ad8\u5149\u53cd\u5c04\u3002</p> <p>\u9ad8\u5149\u53cd\u5c04\u7684\u5f3a\u5ea6\u516c\u5f0f\u5927\u81f4\u5982\u4e0b\uff1a</p> \\[ L_s = k_s \\cdot \\frac{I}{r^2} \\cdot \\max(0, \\cos\\alpha)^p=k_s \\cdot \\frac{I}{r^2} \\cdot \\max(0, \\vec n \\cdot \\vec h)^p \\] <p>\u5bf9\u6210\u5206\u505a\u89e3\u91ca\uff1a</p> <ul> <li>\\(L_s\\) \u4e3a\u9ad8\u5149\u53cd\u5c04\u5149\u5f3a(specularly reflected light)\uff1b</li> <li>\\(k_s\\) \u4e3a\u9ad8\u5149\u53d1\u5c04\u7cfb\u6570(specular coefficient)\uff1b</li> </ul> <p>\u5206\u6790\u53ef\u5f97\uff0c\\(p\\) \u8d8a\u5927\uff0c\u9ad8\u5149\u8d8a\u96c6\u4e2d\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec02/#blinn-phong-\u53cd\u5c04","title":"Blinn-Phong \u53cd\u5c04","text":"<p>Blinn-Phong \u53cd\u5c04\u6a21\u578b(Blinn-Phong Reflection Model)\u53ef\u4ee5\u8bf4\u96c6\u5408\u4e86\u524d\u4e24\u8005\uff0c\u6b64\u5916\u8fd8\u5f15\u5165\u4e86\u73af\u5883\u5149(ambient part)\u3002</p> \\[ L_a=k_aI_a \\] <p>Blinn-Phong \u53cd\u5c04\u6a21\u578b\u7684\u5927\u81f4\u6210\u5206\u5982\u4e0b\uff1a</p> <p></p> \\[ \\begin{align} L &amp; = L_a + L_d + L_s \\\\ &amp; = k_aI_a + k_d \\cdot \\frac{I}{r^2} \\cdot \\max(0,n\\cdot l) + k_s \\cdot \\frac{I}{r^2} \\cdot \\max(0, \\vec n \\cdot \\vec h)^p \\end{align} \\]"},{"location":"cour_note/D2QD_Intro2CV/Lec02/#\u989c\u8272","title":"\u989c\u8272","text":"<p>\u4e3a\u4e86\u63cf\u8ff0\u989c\u8272\uff0c\u6211\u4eec\u9700\u8981\u5b9a\u4e49\u8272\u5f69\u7a7a\u95f4(color spaces)\uff0c\u5e38\u89c1\u7684\u6709 RGB \u548c HSV \u7b49\uff0c\u5bf9\u76f8\u673a\u6765\u8bf4\u6211\u4eec\u66f4\u5e38\u7528\u7684\u662f RGB\u3002</p> in py <p>\u5728\u7b97\u6cd5\u4e2d\uff0c\u6211\u4eec\u7528\u77e9\u9635\u6765\u5b58\u50a8\u56fe\u50cf\u4fe1\u606f\uff0c\u5176\u4e2d\u5de6\u4e0a\u89d2\u7684\u5143\u7d20\u5750\u6807\u4e3a <code>(0, 0, :)</code>\uff0c\u5176\u4e2d\u7b2c\u4e09\u7ef4\u7528\u6765\u6307\u5b9a\u989c\u8272\u901a\u9053(channel)\uff0c\u6240\u4ee5\u7b2c i \u884c j \u5217\u7684\u50cf\u7d20\u70b9\u8868\u793a\u4e3a <code>(i-1, j-1, :)</code>\uff1b</p> <p>\u5728\u786c\u4ef6\u4e0a\uff0c\u989c\u8272\u4f20\u611f\u4e3b\u8981\u901a\u8fc7\u62dc\u5c14\u6ee4\u955c(Bayer filter)\u5b9e\u73b0\u3002\u4e5f\u5c31\u662f\u901a\u8fc7\u5728\u4f20\u611f\u5668\u524d\u5b89\u88c5\u4e00\u4e2a\u5355\u8272\u6ee4\u955c\uff0c\u6765\u63a5\u6536\u5355\u4e00\u8272\u5149\u3002\u5e38\u89c1\u7684\u505a\u6cd5\u662f\u4ee5\u7530\u5b57\u683c\u7684\u56db\u4e2a\u4f20\u611f\u5668\u4e3a\u5355\u4f4d\uff0c\u5206\u914d <code>R*1</code> <code>G*2</code> <code>B*1</code> \u7684\u6ee4\u955c\u3002</p> <p></p> <p>Source: https://en.wikipedia.org/wiki/Bayer_filter</p> <p>\u53ef\u4ee5\u53d1\u73b0\uff0c\u7eff\u8272\u7684\u6ee4\u955c\u66f4\u591a\uff0c\u56e0\u4e3a\u592a\u9633\u5149\u4e2d\u7eff\u8272\u6ce2\u6bb5\u66f4\u591a\uff0c\u4e8e\u662f\u4eba\u773c\u5bf9\u7eff\u8272\u66f4\u654f\u611f\u3002</p> <p>\u663e\u7136\uff0c\u8fd9\u6837\u5f97\u5230\u7684\u56fe\u7247\u9700\u8981\u8fdb\u884c\u63d2\u503c\u624d\u80fd\u5f97\u5230\u6700\u7ec8\u56fe\u7247\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec03/","title":"Lecture 3 | Image Processing","text":"<p> \u7ea6 5940 \u4e2a\u5b57  3 \u884c\u4ee3\u7801  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 20 \u5206\u949f</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec03/#\u57fa\u672c\u64cd\u4f5c","title":"\u57fa\u672c\u64cd\u4f5c","text":"<p>\u5bf9\u56fe\u50cf\u7684\u57fa\u672c\u64cd\u4f5c\u5373\u5728\u56fe\u50cf\u7f16\u8f91\u8f6f\u4ef6\u4e2d\u5e38\u89c1\u7684\u90a3\u4e48\u51e0\u79cd\uff0c\u7a0d\u540e\u6211\u4eec\u5c06\u4f1a\u7b80\u5355\u4ecb\u7ecd\u8fd9\u51e0\u79cd\u64cd\u4f5c\u662f\u5982\u4f55\u5b9e\u73b0\u7684\u3002</p> <p>\u4e0d\u8fc7\u5728\u6b64\u4e4b\u524d\uff0c\u6211\u4eec\u9700\u8981\u5148\u4ecb\u7ecd\u4e00\u4e2a\u5de5\u5177\u2014\u2014\u5377\u79ef(convolution)\uff0c\u4e4b\u540e\u4e00\u4e9b\u64cd\u4f5c\u90fd\u4f9d\u8d56\u4e8e\u6b64\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec03/#\u5377\u79ef","title":"\u5377\u79ef","text":"<p>\u6570\u5b66\u4e0a\u5bf9\u5377\u79ef(convolution)\u7ed9\u51fa\u7684\u5b9a\u4e49\u662f\uff1a</p> \\[ (f*g)(x)=\\int_{-\\infty}^{\\infty} f(y)g(x-y)\\mathrm{d}y \\] <p>\u7b2c\u4e00\u6b21\u63a5\u89e6\u8fd9\u4e2a\u5f0f\u5b50\u7684\u65f6\u5019\u6211\u4e2a\u4eba\u611f\u89c9\u662f\u4e00\u5934\u96fe\u6c34\u7684\u3002\u4f46\u662f\uff0c\u63a5\u4e0b\u6765\u8ba9\u6211\u4eec\u4ece\u4e00\u4e2a\u66f4\u76f4\u89c2\u7684\u89d2\u5ea6\u6765\u7406\u89e3\u4e00\u4e0b\u8fd9\u4e2a\u5f0f\u5b50\uff1a</p> <p>\u4e00\u8a00\u4ee5\u853d\u4e4b\uff1a\\((f*g)(x)\\) \u662f \\(g(x)\\) \u5728\u6ee4\u6ce2\u89c4\u5219 \\(f(y)\\) \u4e0b\u7684\u52a0\u6743\u5747\u503c\u51fd\u6570\u3002</p> <ul> <li>\u6211\u4eec\u4e00\u822c\u79f0 \\(f(y)\\) \u4e3a\u6ee4\u6ce2\u5668(filter)\uff0c\u8fd9\u662f\u56e0\u4e3a\u6211\u4eec\u672c\u8d28\u4e0a\u662f\u5728\u6c42 \\(g(x)\\) \u5728\u8fd9\u4e2a\u6ee4\u6ce2\u89c4\u5219\u4e0b\u52a0\u6743\u6c42\u5747\u503c\u751f\u6210\u7684\u65b0\u51fd\u6570\u3002</li> <li>\u6240\u4ee5\uff0c\\(f(y)\\) \u4e00\u822c\u662f\u6839\u636e\u9700\u6c42\u800c\u51b3\u5b9a\u7684\u4e00\u4e9b\u7279\u6b8a\u51fd\u6570\uff0c\u6bd4\u5982\u9ad8\u65af\u51fd\u6570\u3001\u7279\u5b9a\u533a\u95f4\u5185\u7684\u5e38\u51fd\u6570\u7b49\u3002</li> </ul> <p>\u9996\u5148\uff0c\u6211\u4eec\u5148\u6765\u4ece\u4e00\u7ef4\u79bb\u6563\u7684\u89d2\u5ea6\u6765\u7406\u89e3\u5377\u79ef\uff0c\u5373\uff1a</p> \\[ (f*a)_i = \\sum_{j=-m}^{m} f_j * a_{i+j}  \\] <p>\u5f53\u7136\uff0c\u4e0a\u9762\u53ef\u80fd\u51fa\u73b0 \\(f_{-1}\\) \u8fd9\u79cd\u9b3c\u755c\u7684\u4e1c\u897f\uff0c\u4f46\u662f\u5b9e\u9645\u4e0a\u8fd9\u91cc\u7684 \\(f\\) \u6570\u5217\u786e\u5b9e\u662f\u5b9a\u4e49\u5728\u6574\u4e2a\u6574\u6570\u8f74\u4e0a\u7684\uff08\u5f53\u7136\u4e0b\u6807\u5565\u7684\u662f\u65e0\u6240\u8c13\u7684\uff0c\u7ec8\u70b9\u5173\u6ce8\u4e0b\u9762\u7684\u6a21\u62df\u8fc7\u7a0b\uff09</p> <p>\u6bd4\u5982\uff0c\u6211\u4eec\u6709\u539f\u59cb\u6570\u5217 \\(a_n\\) \u548c\u6ee4\u6ce2\u5668\u6570\u5217 \\(f_m\\) \u5982\u4e0b\uff1a</p> \\(a_n\\) 2 4 2 6 2 \\(f_m\\) 1 2 1 \\(f_m\\) \u7684\u201c\u4e2d\u5fc3\u201d \u2b06\ufe0f <p>\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u6765\u624b\u52a8\u6a21\u62df\u4e00\u4e0b\u5377\u79ef\u8fc7\u7a0b\uff1a</p> \u5377\u79ef\u8fc7\u7a0b \\(a_n\\) 2 4 2 6 2 \u6b63\u5728\u88ab\u5377\u7684\u6570 \u2b06\ufe0f \u2b06\ufe0f\u2b06\ufe0f \u2b06\ufe0f \\(f_m\\) 1 2 1 0 0 \\(f_m\\) \u7684\u201c\u4e2d\u5fc3\u201d \u2b06\ufe0f \u5377\u79ef\u7684\u8fc7\u7a0b \\(1\\times2+2\\times4+1\\times2\\) \u5377\u51fa\u6765\u7684\u7ed3\u679c - \\(12\\) \\(a_n\\) 2 4 2 6 2 \u6b63\u5728\u88ab\u5377\u7684\u6570 \u2b06\ufe0f \u2b06\ufe0f\u2b06\ufe0f \u2b06\ufe0f \\(f_m\\) 0 1 2 1 0 \\(f_m\\) \u7684\u201c\u4e2d\u5fc3\u201d \u2b06\ufe0f \u5377\u79ef\u7684\u8fc7\u7a0b \\(1\\times4+2\\times2+1\\times6\\) \u5377\u51fa\u6765\u7684\u7ed3\u679c - \\(12\\) \\(14\\) \\(a_n\\) 2 4 2 6 2 \u6b63\u5728\u88ab\u5377\u7684\u6570 \u2b06\ufe0f \u2b06\ufe0f\u2b06\ufe0f \u2b06\ufe0f \\(f_m\\) 0 0 1 2 1 \\(f_m\\) \u7684\u201c\u4e2d\u5fc3\u201d \u2b06\ufe0f \u5377\u79ef\u7684\u8fc7\u7a0b \\(1\\times2+2\\times6+1\\times2\\) \u5377\u51fa\u6765\u7684\u7ed3\u679c - \\(12\\) \\(14\\) \\(16\\) - <p>\u53ef\u4ee5\u53d1\u73b0\uff0c\u5982\u679c \\(f_m\\) \u6bcf\u4e00\u9879\u90fd\u9664\u4ee5 4\uff0c\u90a3\u5b9e\u9645\u4e0a\u8fd9\u4e2a\u8fc7\u7a0b\u5c31\u662f\u5728\u6c42\u6bcf\u4e00\u9879\u4e0e\u76f8\u90bb\u4e24\u9879\u7684\u52a0\u6743\u5e73\u5747\uff08\u4e2d\u5fc3\u6743\u91cd\u66f4\u5927\uff09\u3002</p> <p>\u73b0\u5728\uff0c\u4ece\u79bb\u6563\u4f1a\u5230\u8fde\u7eed\u7684\u60c5\u51b5\uff0c\u6211\u4eec\u4ecb\u7ecd\u6700\u7ecf\u5178\u7684\u4e00\u4e2a\u5377\u79ef\u5e94\u7528\u2014\u2014\"box function\"\uff0c\u5176\u4f5c\u4e3a\u6ee4\u6ce2\u5668\u65f6\u5b9a\u4e49\u5982\u4e0b\uff1a</p> <p></p> \\[ f(x) =  \\left\\{     \\begin{array}{}         1 &amp;|x| \\leq 0.5\\\\         0 &amp;otherwise     \\end{array} \\right. \\] <p>\u800c\u5c06\u5b83\u5e26\u5165\u5377\u79ef\u7684\u8868\u8fbe\u5f0f\uff0c\u5f97\u5230\u7684\u7ed3\u679c\u5c31\u662f\uff1a</p> \\[ (f*g)(x)=\\int_{-0.5}^{0.5}g(x-y)\\mathrm{d}y \\] <p>\u90a3\u5b9e\u9645\u4e0a\uff0c\u8fd9\u5c31\u662f\u5728\u6c42\u51fd\u6570\u5728\u5bbd\u5ea6\u4e3a 1 \u7684\u8303\u56f4\u5185\u7684\u5747\u503c\u3002</p> <p>\u73b0\u5728\uff0c\u6211\u4eec\u5c06\u5b83\u8fdb\u884c\u4e00\u70b9\u6269\u5c55\uff0c\u6765\u5230\u4e8c\u7ef4\uff0c\u5219\u53ef\u4ee5\u5c06\u79bb\u6563\u7684\u5377\u79ef\u8fc7\u7a0b\u7528\u8fd9\u6837\u4e00\u4e2a gif \u6765\u8868\u793a\uff1a</p> <p> </p> <ul> <li>Wiki \u4e2d\u6709\u66f4\u9177\u7684\u52a8\u56fe\uff1a\ud83d\udd17</li> </ul> <p>\u601d\u8003</p> <p>\u53ef\u4ee5\u53d1\u73b0\uff0c\u5728\u4e8c\u7ef4\u5377\u79ef\u7684\u8fc7\u7a0b\u4e2d\uff0c\u6211\u4eec\u5377\u51fa\u6765\u7684\u4e1c\u897f\u8981\u6bd4\u539f\u59cb\u56fe\u50cf\u5c0f\u3002\u800c\u5176\u4e2d\u4e00\u79cd\u89e3\u51b3\u7684\u65b9\u6cd5\u662f padding\u3002\u5728\u6b64\u4e0d\u505a\u8fc7\u591a\u4ecb\u7ecd\u3002</p> <p>\u5178\u578b\u6ee4\u6ce2\u5668</p> <p>\u5176\u4ed6\u5178\u578b\u7684\u6ee4\u6ce2\u5668\u53ef\u80fd\u5c06\u5728\u4e4b\u540e\u4ecb\u7ecd\uff0c\u8fd9\u91cc\u7b80\u5355\u63d0\u51e0\u4e2a\uff1a</p> <ul> <li>\u9ad8\u65af\u6ee4\u6ce2\u5668(\u4e2d\u5fc3\u6743\u91cd\u5927)</li> <li>\u9510\u5316\u6ee4\u6ce2\u5668</li> <li>\u8fb9\u7f18\u68c0\u6d4b\u6ee4\u6ce2\u5668</li> <li>\u53ef\u5206\u79bb\u6ee4\u6ce2\u5668</li> <li>\u53cc\u8fb9\u6ee4\u6ce2\u5668</li> <li>\u2026\u2026</li> </ul>"},{"location":"cour_note/D2QD_Intro2CV/Lec03/#\u589e\u52a0\u5bf9\u6bd4\u5ea6","title":"\u589e\u52a0\u5bf9\u6bd4\u5ea6","text":"<p>\u589e\u52a0\u5bf9\u6bd4\u5ea6(increase contrast)\u5373\u8ba9\u753b\u9762\u4e2d\u7684\u989c\u8272\u5411\u4e24\u4e2a\u6781\u7aef\u504f\u79fb\uff0c\u901a\u4fd7\u6765\u8bf4\u5c31\u662f\u9ed1\u7684\u66f4\u9ed1\uff0c\u767d\u7684\u66f4\u767d\u3002</p> <p>\u4f53\u611f\u4e0a\u8ba9\u4e00\u5f20\u96fe\u8499\u8499\u7684\u7167\u7247\u53d8\u5f97\u66f4\u52a0\u9ed1\u767d\u5206\u660e\u3002</p> <p>\u4e0a\u9762\u4e5f\u8bf4\u4e86\uff0c\u662f\u5c06\u8272\u5f69\u5411\u4e24\u4e2a\u6781\u7aef\u504f\u79fb\uff0c\u5b9e\u9645\u4e0a\u5c31\u662f\u8bb2\u539f\u6765\u7684\u989c\u8272\u8fdb\u884c\u4e00\u4e2a\u6620\u5c04\uff0c\u4ee4 \\(color'(x,y) = f[color(x,y)]\\)\u3002</p> <p>\u90a3\u4e48\u4e00\u822c\u6765\u8bf4\uff0c\u6211\u4eec\u91c7\u7528S \u66f2\u7ebf(S curve)\u6765\u8fdb\u884c\u8fd9\u4e2a\u6620\u5c04\uff0c\u4e5f\u5c31\u662f\u5c06\u539f\u672c\u5747\u5300\u5206\u5e03\u7684\u70b9\u6309\u7167 S \u66f2\u7ebf\u8fdb\u884c\u62c9\u4f38\u548c\u538b\u7f29\uff0c\u8fd9\u6837\uff0c\u767d\u7684\u4f1a\u66f4\u767d\uff0c\u9ed1\u7684\u5c31\u4f1a\u66f4\u9ed1\u3002</p> <p> </p> <p>\u56fe\u4e2d\u6a2a\u5750\u6807\u8868\u793a\u539f\u6765\u7684\u989c\u8272\uff0c\u7eb5\u5750\u6807\u8868\u793a\u6620\u5c04\u540e\u7684\u989c\u8272\uff0c\u53ef\u4ee5\u53d1\u73b0\u9ed1\u8272\u90e8\u5206\u7684\u989c\u8272\u90fd\u5411\u9ed1\u8272\u504f\u79fb\uff0c\u767d\u8272\u90e8\u5206\u4ea6\u7136\u3002</p> <p>\u800c\u5177\u4f53\u4f7f\u7528\u7684\u66f2\u7ebf\uff0c\u5219\u9700\u8981\u6839\u636e\u9700\u6c42\u8fdb\u884c\u8c03\u6574\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec03/#\u53cd\u8272","title":"\u53cd\u8272","text":"<p>\u987e\u540d\u601d\u4e49\uff0c\u56fe\u50cf\u53d6\u53cd\u8272(image invert)\u5c31\u662f\u5c06\u989c\u8272\u53d6\u53cd\uff0c\u9ed1\u53d8\u767d\uff0c\u767d\u53d8\u9ed1\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec03/#\u8fb9\u7f18\u63d0\u53d6","title":"\u8fb9\u7f18\u63d0\u53d6","text":"<p>\u8fb9\u7f18\u63d0\u53d6 Edge detection</p> <p>\u5f15\u5165</p> <p>\u6a21\u7cca(blur) \u548c \u9510\u5316(sharpen) \u662f\u4e24\u4e2a\u5bf9\u5e94\u7684\u6982\u5ff5\uff0c\u5b9e\u73b0\u7684\u624b\u6bb5\u4e5f\u975e\u5e38\u7c7b\u4f3c\u3002</p> <p>\u4f7f\u7528\u5bf9\u6bd4</p> <ul> <li>\u4ece\u5e94\u7528\u6765\u8bb2\uff0c\u6a21\u7cca\u53ef\u4ee5\u7528\u6765\u505a\u4e00\u4e9b\u964d\u566a\u7684\u5de5\u4f5c\uff0c\u4e5f\u53ef\u4ee5\u7ed9\u56fe\u7247\u8425\u9020\u51fa\u4e00\u79cd\u5149\u6ed1\u7684\u8d28\u611f\uff1b</li> <li>\u800c\u9510\u5316\u53ef\u4ee5\u4e00\u5b9a\u7a0b\u5ea6\u4e0a\u589e\u52a0\u56fe\u7247\u7684\u6e05\u6670\u5ea6\u3002</li> </ul>"},{"location":"cour_note/D2QD_Intro2CV/Lec03/#\u6a21\u7cca","title":"\u6a21\u7cca","text":"<p>\u6240\u8c13\u7684\u6a21\u7cca(blur)\uff0c\u50cf\u662f\u5c06\u67d0\u4e2a\u4f4d\u7f6e\u7684\u50cf\u7d20\u548c\u5468\u56f4\u6df7\u5408\u8d77\u6765\uff0c\u66f4\u6570\u5b66\u7684\u8868\u8ff0\u6765\u8bf4\uff0c\u9700\u8981\u4e0e\u5468\u56f4\u8fdb\u884c\u52a0\u6743\u6c42\u5e73\u5747\uff0c\u6ca1\u9519\uff0c\u6211\u4eec\u9700\u8981\u4f7f\u7528\u5377\u79ef\u6765\u5b9e\u73b0\u3002</p> <p></p> <p>Source: Stanford CS248, Winter 202</p> <p>\u4f8b\u5982\uff0c\u5047\u8bbe\u6211\u4eec\u7528\u8fd9\u6837\u4e00\u4e2a\u4e8c\u7ef4\u6ee4\u6ce2\u5668\u5bf9\u4e00\u5f20\u56fe\u50cf\u8fdb\u884c\u5377\u79ef\uff1a</p> \\[ \\begin{bmatrix}     \\frac{1}{9} &amp; \\frac{1}{9} &amp; \\frac{1}{9} \\\\     \\frac{1}{9} &amp; \\frac{1}{9} &amp; \\frac{1}{9} \\\\     \\frac{1}{9} &amp; \\frac{1}{9} &amp; \\frac{1}{9} \\end{bmatrix} \\] <p>\u90a3\u4e48\u65b0\u5f97\u5230\u7684\u56fe\u7247\u4e2d\u7684\u50cf\u7d20\u5c06\u4f1a\u7b49\u4e8e\u539f\u56fe\u7247\u8fd9\u4e2a\u50cf\u7d20\u5468\u56f4\u7684 8 \u4e2a\u50cf\u7d20\u548c\u5b83\u6c42\u5e73\u5747\u5f97\u5230\u7684\u989c\u8272\u3002</p> <p>\u518d\u6bd4\u5982\uff0c\u6ee4\u6ce2\u5668\u4f7f\u7528\u9ad8\u65af\u51fd\u6570\u7684\u9ad8\u65af\u6a21\u7cca\uff1a</p> \\[ f(i,j)=\\frac{1}{2\\pi \\sigma^2}e^{-\\frac{i^2+j^2}{2\\sigma^2}} \\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\; \\begin{bmatrix}     0.075 &amp; 0.124 &amp; 0.075 \\\\     0.124 &amp; 0.204 &amp; 0.124 \\\\     0.075 &amp; 0.124 &amp; 0.075 \\end{bmatrix} \\] <p>\u9ad8\u65af\u6a21\u7cca\u4f1a\u66f4\u52a0\u6ce8\u91cd\u4e2d\u5fc3\u7684\u6743\u91cd\uff0c\u6240\u4ee5\u6a21\u7cca\u8d77\u6765\u76f8\u5bf9\u6765\u8bf4\u66f4\u80fd\u4fdd\u6301\u56fe\u7247\u539f\u6765\u7684\u7279\u5f81\u4e00\u70b9\u3002</p> <p>\u66f4\u4f18\u79c0\u7684\u4e00\u79cd\u6a21\u7cca</p> <p>\u4e00\u79cd\u66f4\u6709\u7528\u7684\u6a21\u7cca\u662f\uff0c\u63d0\u53d6\u8fb9\u7f18\u540e\u7684\u6a21\u7cca\uff0c\u5373\u6a21\u7cca\u8fc7\u7a0b\u4e2d\u4e0d\u5f71\u54cd\u8fb9\u7f18\uff0c\u6bd4\u5982\u4eba\u8138\u8fb9\u7f18\u6a21\u7cca\uff0c\u53ea\u5f71\u54cd\u8138\u800c\u4e0d\u5f71\u54cd\u5176\u4ed6\u90e8\u5206\u3002</p> <p>\u5177\u4f53\u5b9e\u73b0\u6211\u4eec\u5c06\u5728 \u518d\u770b\u6ee4\u6ce2\u5668 \u4e2d\u7684 \u53cc\u8fb9\u6ee4\u6ce2\u5668\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec03/#\u9510\u5316","title":"\u9510\u5316","text":"<p>\u6211\u4eec\u6ce8\u610f\u5230\uff0c\u6a21\u7cca\u4e2d\u7684\u6ee4\u6ce2\u5668\u57fa\u672c\u4e0a\u6bcf\u4e00\u4e2a\u5143\u7d20\u90fd\u662f\u975e\u8d1f\u6570\uff0c\u610f\u601d\u662f\u5377\u79ef\u7ed3\u679c\u4e2d\u4f1a\u4fdd\u7559\u4e00\u90e8\u5206\u8fd9\u4e9b\u50cf\u7d20\u7684\u7279\u5f81\u3002</p> <p>\u90a3\u5982\u679c\u6211\u4eec\u628a\u5176\u4e2d\u4e00\u90e8\u5206\u6539\u6210\u8d1f\u6570\u5462\uff1f\u90a3\u5c31\u8bf4\u660e\u5377\u79ef\u7ed3\u679c\u4e2d\u4f1a\u51cf\u53bb\u8fd9\u90e8\u5206\u7684\u7279\u5f81\u3002\u4e5f\u5c31\u662f\u8bf4\uff0c\u5982\u679c\u6743\u503c\u4e3a\u8d1f\u6570\u7684\u50cf\u7d20\u548c\u6743\u503c\u4e3a\u6b63\u6570\u7684\u50cf\u7d20\u5f88\u50cf\uff0c\u90a3\u4e48\u8fd9\u4e2a\u7279\u5f81\u5c31\u4f1a\u88ab\u524a\u5f31\uff1b\u53cd\u8fc7\u6765\u8bf4\uff0c\u5982\u679c\u6743\u503c\u4e3a\u8d1f\u6570\u7684\u50cf\u7d20\u548c\u6743\u503c\u4e3a\u6b63\u6570\u7684\u50cf\u7d20\u51e0\u4e4e\u76f8\u53cd\uff0c\u90a3\u4e48\u6743\u503c\u4e3a\u6b63\u6570\u7684\u50cf\u7d20\u7684\u7279\u5f81\u5c31\u4f1a\u88ab\u52a0\u5f3a\u3002</p> <p>\u6211\u4eec\u8003\u8651\u8fd9\u6837\u4e00\u4e2a\u7279\u6b8a\u4f8b\u5b50\uff1a</p> \\[ \\begin{bmatrix}     0 &amp; -1 &amp; 0 \\\\     -1 &amp; 5 &amp; -1 \\\\     0 &amp; -1 &amp; 0 \\end{bmatrix} \\] <p>\u5982\u679c\u8fb9\u7f18\u7684\u70b9\u548c\u77e9\u9635\u4e2d\u5fc3\u7684\u70b9\u4e0d\u4e00\u6837\uff0c\u5219\u77e9\u9635\u4e2d\u5fc3\u7684\u70b9\u7684\u7279\u5f81\u4f1a\u88ab\u5f3a\u8c03\uff0c\u5373\u4f1a\u653e\u5927\u76f8\u90bb\u70b9\u7684\u533a\u522b\uff0c\u8fd9\u5c31\u662f\u9510\u5316(sharpen)\u7684\u539f\u7406\u3002</p> <p></p> <p>Source: Stanford CS248, Winter 202</p> <p>\u6a21\u7cca\u4e0e\u9510\u5316\u7684\u8054\u7cfb</p> <ul> <li>\u5982\u679c\u5b9a\u4e49\u539f\u672c\u7684\u56fe\u50cf\u4e3a \\(I\\)\uff0c\u6a21\u7cca\u540e\u7684\u56fe\u50cf\u4e3a \\(I_b\\)</li> <li>\u5b9a\u4e49\u56fe\u50cf\u4e2d\u7684\u9ad8\u9891(high frequencies)\u4e3a I_h = I - I_b\uff1b</li> <li>\u5219\u9510\u5316\u7684\u56fe\u50cf \\(I_s = I + I_h\\)\uff1b</li> <li>\u5373\u6709 \\(2I = I_s + I_h\\)\uff0c\u53ef\u4ee5\u53d1\u73b0\uff0c\u53c8\u4e00\u4e2a\u7c7b\u4f3c\u4e8e\u4e92\u8865\u7684\u5173\u7cfb\uff1b</li> <li>\u800c\u8fd9\u91cc\u7684\u9ad8\u9891\u53ef\u4ee5\u7406\u89e3\u4e3a\u56fe\u50cf\u4e2d\u53d8\u5316\u6bd4\u8f83\u660e\u663e\u7684\u5730\u65b9\uff1b</li> </ul> <p> </p> <p> </p>"},{"location":"cour_note/D2QD_Intro2CV/Lec03/#\u518d\u770b\u6ee4\u6ce2\u5668","title":"\u518d\u770b\u6ee4\u6ce2\u5668","text":"<p>\u4e0a\u9762\u6211\u4eec\u5df2\u7ecf\u63d0\u5230\u4e86\u7528\u4e8e\u6a21\u7cca\u7684\u6ee4\u6ce2\u5668\uff08\u6bd4\u5982\u9ad8\u65af\u6ee4\u6ce2\u5668\uff09\uff0c\u7528\u4e8e\u9510\u5316\u7684\u6ee4\u6ce2\u5668\uff0c\u63a5\u4e0b\u6765\u8ba9\u6211\u4eec\u770b\u770b\u5176\u4ed6\u7684\u6ee4\u6ce2\u5668\u7684\u76f8\u5173\u5185\u5bb9\uff1a</p> \u6c34\u5e73/\u5782\u76f4\u68af\u5ea6\u63d0\u53d6 <p></p> <ul> <li>Extracts horizontal gradients</li> </ul> \\[ \\begin{bmatrix}     -1 &amp; 0 &amp; 1 \\\\     -2 &amp; 0 &amp; 2 \\\\     -1 &amp; 0 &amp; 1 \\end{bmatrix} \\] <ul> <li>Extracts vertical gradients</li> </ul> \\[ \\begin{bmatrix}     -1 &amp; -2 &amp; -1 \\\\     0 &amp; 0 &amp; 0 \\\\     1 &amp; 2 &amp; 1 \\end{bmatrix} \\] \u53ef\u5206\u79bb\u6ee4\u6ce2\u5668 <ul> <li>Separable filter\uff0c\u53ef\u4ee5\u7528\u8fd9\u79cd\u65b9\u5f0f\u6765\u964d\u4f4e\u8ba1\u7b97\u91cf\uff1b  </li> <li>\u53ea\u8981\u8868\u8fbe\u5f0f\u53ef\u4ee5\u5199\u6210\u4e24\u4e2a\u51fd\u6570\u76f8\u4e58\uff0c\u90a3\u57fa\u672c\u662f separable \u7684;<ul> <li>\u6bd4\u5982\u9ad8\u65af\u77e9\u9635\u5c31\u53ef\u4ee5\u62c6\u6210\u8fd9\u6837\uff1a</li> <li>\\(f(i,j)=\\frac{1}{2\\pi \\sigma^2}e^{-\\frac{i^2+j^2}{2\\sigma^2}}=\\frac{1}{2\\pi \\sigma^2}e^{-\\frac{i^2}{2\\sigma^2}}\\cdot e^{-\\frac{j^2}{2\\sigma^2}}\\)</li> </ul> </li> </ul> \u53cc\u8fb9\u6ee4\u6ce2\u5668 <ul> <li> <p>\u53cc\u8fb9\u6ee4\u6ce2\u5668 Bilateral filter</p> <ul> <li>\u5728\u6ee4\u6ce2\u65f6\uff0c\u6bcf\u4e00\u4e2a\u70b9\u7684\u6743\u91cd\u4e0e \u76ee\u6807\u70b9 \u4e0e \u4e2d\u5fc3\u70b9\u7684\u76f8\u4f3c\u7a0b\u5ea6\u6709\u5173;</li> </ul> </li> <li> <p> TODO: \u66f4\u8be6\u7ec6\u5730\u8bb2\u8fd9\u91cc</p> </li> </ul> <p></p> <p>\u5f15\u5165</p> <p>\u56fe\u50cf\u91c7\u6837(sampling)\u5206\u4e3a\u5411\u4e0a\u91c7\u6837(up-sampling)\u548c\u5411\u4e0b\u91c7\u6837(down-sampling)\u4e24\u79cd\u3002</p> <p>\u66f4\u901a\u4fd7\u7684\u6765\u8bf4\uff0c\u5c31\u662f\u5728\u4fdd\u6301\u56fe\u50cf\u7279\u5f81\u7684\u60c5\u51b5\u4e0b\u5bf9\u56fe\u7247\u8fdb\u884c\u7f29\u653e\u3002\u663e\u7136\uff0c\u5728\u7f29\u653e\u56fe\u50cf\u65f6\uff0c\u4f1a\u51fa\u73b0\u50cf\u7d20\u6570\u91cf\u7684\u53d8\u5316\uff0c\u90a3\u8981\u5982\u4f55\u6dfb\u52a0\u50cf\u7d20\u3001\u5982\u4f55\u51cf\u5c11\u50cf\u7d20\uff0c\u5c31\u662f\u56fe\u50cf\u91c7\u6837\u8003\u8651\u7684\u4e8b\u60c5\u3002</p> <p>\u6b64\u5916\uff0c\u5c06\u4e24\u8005\u7ed3\u5408\uff0c\u8fd8\u4f1a\u6709\u4f8b\u5982\u6539\u53d8\u56fe\u7247\u957f\u5bbd\u6bd4\uff0c\u8fdb\u884c\u62c9\u4f38\u8fd9\u79cd\u95ee\u9898\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec03/#\u7f29\u5c0f\u56fe\u7247\u5411\u4e0b\u91c7\u6837","title":"\u7f29\u5c0f\u56fe\u7247\uff1a\u5411\u4e0b\u91c7\u6837","text":"<p>\u5411\u4e0b\u91c7\u6837\u4e5f\u5c31\u662f\u8ba9\u56fe\u7247\u53d8\u5c0f\uff0c\u8fd9\u91cc\u4e3b\u8981\u9700\u8981\u8003\u8651\u7684\u95ee\u9898\u662f\u5982\u4f55\u7f29\u5c0f\u56fe\u7247\uff0c\u5982\u4f55\u907f\u514d\u51fa\u73b0\u4fe1\u53f7\u8d70\u6837\u7684\u95ee\u9898\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec03/#\u4fe1\u53f7\u8d70\u6837","title":"\u4fe1\u53f7\u8d70\u6837","text":"<p>\u8bf4\u5230\u8ba9\u56fe\u50cf\u53d8\u5c0f\uff0c\u6700\u7b80\u5355\u7684\u4e00\u4e2a\u60f3\u6cd5\u5c31\u662f\u2014\u2014\u6bd4\u5982\uff0c\u8ba9\u56fe\u7247\u7684\u7ebf\u5ea6\u7f29\u5c0f\u4e00\u534a\uff0c\u53ef\u4ee5\u6bcf\u56db\u4e2a\u683c\u5b50\u5c31\u91c7\u4e00\u4e2a\u683c\u5b50\u7684\u6837\u672c\u3002</p> <p></p> <p>\u800c\u8fd9\u79cd\u7c97\u66b4\u7684\u505a\u6cd5\u5219\u6709\u53ef\u80fd\u5bfc\u81f4\uff1a</p> <p>-\u6469\u5c14\u7eb9(Moir\u00e9 Patterns)\u3002 -\u9a6c\u8f66\u8f6e\u9519\u89c9(Wagon Wheel Illusion) - ...</p> <p>\u800c\u8fd9\u4e9b\u7531\u91c7\u6837\u5bfc\u81f4\u7684\u95ee\u9898\uff0c\u6211\u4eec\u79f0\u4e4b\u4e3a\u4fe1\u53f7\u8d70\u6837(aliasing)\u3002</p> <p>\u4ece\u672c\u8d28\u4e0a\u6765\u8bf4\uff0c\u4fe1\u53f7\u8d70\u6837\u7684\u53d1\u751f\uff0c\u662f\u56e0\u4e3a\u91c7\u6837\u9891\u7387\u8ddf\u4e0d\u4e0a\u56fe\u50cf\u9891\u7387\u5bfc\u81f4\u7684\u3002</p> <p>Signals are changing too fast but sampled too slow.</p> <p>\u5982\u4f55\u7406\u89e3\u8fd9\u91cc\u7684\u201c\u9891\u7387\u201d</p> <p>\u5728\u4e4b\u540e\u7684\u90e8\u5206\u4e2d\uff0c\u6211\u4eec\u4f1a\u7ed9\u51fa\u8fd9\u91cc\u7684\u201c\u9891\u7387\u201d\u7684\u6765\u6e90\u3002</p> <p>\u4f46\u662f\u4e00\u4e2a\u66f4\u76f4\u89c2\uff0c\u66f4\u6a21\u7cca\u7684\u770b\u6cd5\u662f\uff1a\u5982\u679c\u4e00\u4e2a\u56fe\u50cf\u7684\u67d0\u4e2a\u90e8\u5206\u53d8\u5316\u8d8a\u5267\u70c8\uff0c\u4e00\u822c\u6765\u8bf4\u5176\u9891\u7387\u5c31\u4f1a\u8f83\u5927\u3002\u6bd4\u5982\u56fe\u50cf\u4e2d\u6709\u4e00\u4e2a\u975e\u5e38\u5206\u660e\u7684\u8fb9\u754c\uff0c\u90a3\u4e48\u5b83\u7684\u9891\u7387\u4e00\u822c\u4e0d\u4f1a\u4f4e\u3002</p> <p>\u800c\u8fd9\u91cc\u7684\u201c\u91c7\u6837\u9891\u7387\u201d\u8861\u91cf\u4e86\u4fe1\u53f7\u53d8\u5316\u7684\u9891\u7387\u3002</p> <p>\u6bd4\u5982\uff0c\u5982\u679c\u5bf9\u4e00\u4e2a\u6b63\u5f26\u6ce2\u8fdb\u884c\u91c7\u6837\uff0c\u5373\u4ece\u4e00\u4e2a\u8fde\u7eed\u7684\u6b63\u5f26\u6a21\u62df\u4fe1\u53f7\u4e2d\u9009\u53d6\u82e5\u5e72\u70b9\uff0c\u53ef\u4ee5\u53d1\u73b0\uff0c\u4e0d\u540c\u91c7\u6837\u9891\u7387\u548c\u4e0d\u540c\u7684\u56fe\u50cf\u9891\u7387\u7684\u9009\u53d6\u65b9\u6848\u4f1a\u4ea7\u751f\u4e0d\u540c\u7684\u7ed3\u679c\uff1a</p> <p></p> <p>\u53ef\u4ee5\u53d1\u73b0\uff0c\u5bf9\u4e8e\u4e0a\u9762\u7684\u51e0\u4e2a\u51fd\u6570\uff0c\u91c7\u6837\u9891\u7387\u548c\u539f\u51fd\u6570\u7684\u9891\u7387\u5339\u914d\u8f83\u597d\uff0c\u6240\u4ee5\u91c7\u6837\u5f97\u5230\u7684\u70b9\u57fa\u672c\u80fd\u53cd\u6620\u51fa\u539f\u6765\u56fe\u5f62\u7684\u7279\u5f81\uff1b\u4f46\u662f\u5bf9\u4e8e\u6bd4\u8f83\u4e0b\u9762\u7684\u51e0\u4e2a\u66f2\u7ebf\uff0c\u91c7\u6837\u5c31\u4e0d\u662f\u5f88\u7406\u60f3\u4e86\u3002</p> <p>\u6bd4\u8f83\u76f4\u89c2\u7684\u4e00\u4e2a\u60f3\u6cd5\u662f\uff0c\u8fc7\u6162\u70b9\u91c7\u6837\u9891\u7387\u4f1a\u5bfc\u81f4\u4fe1\u606f\u4e22\u5931\uff0c\u751a\u81f3\u662f\u8868\u73b0\u51fa\u5176\u5b83\u9891\u7387\u7684\u4fe1\u53f7\u7684\u7279\u5f81\uff0c\u8fd9\u4e9b\u4e0d\u6b63\u5e38\u7684\u884c\u4e3a\u5c31\u5bfc\u81f4\u4e86\u4fe1\u53f7\u8d70\u6837\u3002</p> <p>\u8fd9\u4e2a\u201c\u9891\u7387\u201d\u548c\u56fe\u50cf\u6709\u4ec0\u4e48\u5173\u7cfb\uff1f</p> <p>\u9996\u5148\u6211\u4eec\u77e5\u9053\uff0c\u8981\u5411\u6709\u201c\u9891\u7387\u201d\u8fd9\u4e2a\u5c5e\u6027\uff0c\u8868\u8fbe\u5f0f\u6216\u8005\u8bf4\u51fd\u6570\u9700\u8981\u662f\u5468\u671f\u6027\u7684\u3002\u7136\u800c\u201c\u5468\u671f\u6027\u201d\u5bf9\u4e8e\u4efb\u610f\u51fd\u6570\u6765\u8bf4\u53ef\u80fd\u662f\u4e00\u4e2a\u8f83\u4e3a\u82db\u523b\u7684\u6761\u4ef6\u3002</p> <p>\u6b64\u65f6\u5c31\u8f6e\u5230\u5085\u7acb\u53f6\u53d8\u6362\u767b\u573a\u4e86\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec03/#fourier-\u53d8\u6362","title":"Fourier \u53d8\u6362","text":"<p>\u6700\u7b80\u5355\u76f4\u767d\u5730\u7406\u89e3\u5085\u7acb\u53f6\u53d8\u6362(Fourier Transform)\uff0c\u5b9e\u9645\u4e0a\u5c31\u662f\u5c06\u4efb\u610f\u53ef\u4ee5\u8fdb\u884c\u5085\u7acb\u53f6\u53d8\u6362\u7684\u51fd\u6570\uff0c\u53d8\u5316\u4e3a\u4e00\u4e2a\u6b63\u5f26\u3001\u4f59\u5f26\u51fd\u6570\u7ea7\u6570\u7684\u5f62\u5f0f\u3002</p> <p>\u4f8b\u5982\u6700\u7ecf\u5178\u7684\uff0c\u4f7f\u7528\u4e0d\u540c\u9891\u7387\u7684\u6b63\u5f26\u6ce2\u6765\u62df\u5408\u4e00\u4e2a\u65b9\u6ce2\u3002</p> <p>\u8fd9\u91cc\u5f15\u6d41\u4e00\u4e2a xg \u7684\u89c6\u9891\uff1ahttps://www.bilibili.com/video/BV1Y7411W73U/</p> <p>\u6b64\u65f6\u4f60\u53ef\u80fd\u4f1a\u95ee\uff0c\u6b63\u4f59\u5f26\u51fd\u6570\u7684\u7ea7\u6570\u4e5f\u4e0d\u4fdd\u8bc1\u6709\u5468\u671f\u554a\uff0c\u4f46\u662f\u8bf7\u6ce8\u610f\uff0c\u6211\u4eec\u7684\u76ee\u7684\u5e76\u4e0d\u662f\u627e\u5230\u4e00\u4e2a\u5468\u671f\uff0c\u800c\u662f\u80fd\u591f\u4f7f\u7528\u9891\u7387\u6765\u8868\u8fbe\u8fd9\u4e2a\u51fd\u6570\u7684\u67d0\u4e9b\u7279\u5f81\u3002</p> <p>\u6211\u4eec\u77e5\u9053\uff0c\u6b63\u4f59\u5f26\u51fd\u6570\u662f\u5177\u6709\u5468\u671f\u6027\u7684\uff0c\u90a3\u4e48\u6211\u4eec\u5c31\u53ef\u4ee5\u7528\u8fd9\u4e2a\u7ea7\u6570\u4e2d\u7684\u6b63\u4f59\u5f26\u51fd\u6570\u7684\u9891\u7387\u6765\u8868\u8fbe\u8fd9\u4e2a\u51fd\u6570\u3002</p> <p></p> <p>\u4e0b\u9762\u8fd9\u5f20\u56fe\u7247\u5c31\u662f\u7f16\u7801\u540e\u7684\u9891\u8c31\u3002</p> <p>\u800c\u5728\u6b27\u62c9\u516c\u5f0f \\(e^{i\\theta} = \\cos\\theta + i\\sin\\theta\\) \u7684\u7edf\u4e00\u4e0b\uff0cFourier \u53d8\u6362\u53ef\u4ee5\u8868\u793a\u4e3a\uff1a</p> \\[ F(u) = \\int^{\\infty}_{-\\infty} f(x) e^{-i2\\pi ux} \\rm{d} x \\\\ f(x) = \\int^{\\infty}_{-\\infty} F(u) e^{i2\\pi ux} \\rm{d} u \\\\ \\text{ where 'x' refers to space, 'u' refers to frequency} \\] <p>\u901a\u8fc7\u8fd9\u79cd\u5f62\u5f0f\uff0c\u6211\u4eec\u5b9e\u73b0\u4e86 spatial domain \u548c frequency domain \u4e4b\u95f4\u7684\u7edf\u4e00\u3002</p> <pre><code>graph LR;\nA([\"spatial domain\"]) ==&gt;|\"Fourier transform\"| B([\"frequency domain\"])\nB ===&gt;|\"Inverse transform\"| A</code></pre> <p>\u5c1d\u8bd5\u4f7f\u7528\u5377\u79ef\u7684\u89d2\u5ea6\u6765\u770b\u5085\u7acb\u53f6\u53d8\u6362</p> <p>\u89c2\u5bdf\u5f0f\u5b50 \\(F(u) = \\int^{\\infty}_{-\\infty} f(x) e^{-i2\\pi ux} \\rm{d} x\\)\uff0c\u662f\u4e0d\u662f\u80fd\u5c06\u5b83\u770b\u4f5c\u4e00\u4e2a\u5377\u79ef\u5f0f\u5462\uff1f</p> <ul> <li> TODO: \u5177\u4f53\u89e3\u91ca\u6682\u65f6\u5495\u5495\u5495\u3002</li> </ul> <p>\u4e00\u4e2a\u6709\u610f\u601d\u7684\u6027\u8d28</p> <p>\u800c\u4f7f\u7528 Fourier \u7684\u53e6\u5916\u4e00\u4e2a\u597d\u5904\u662f\uff0c\u5b83\u4e3a\u6211\u4eec\u5e26\u6765\u4e86\u8fd9\u6837\u4e00\u4e2a\u6570\u5b66\u6027\u8d28\uff1a</p> Spatial Domain Frequency Domain \\(g(x) = f(x) * h(x)\\)  Convolution \\(\\leftrightarrow\\) \\(G(u) = F(u)H(u)\\)  Multiplication g(x)=f(x)h(x)  Multiplication \\(\\leftrightarrow\\) \\(G(u) = F(u) * H(u)\\)  Convolution <p>\u5177\u4f53\u6765\u8bf4\uff0c\u4f8b\u5982\uff1a</p> <p>\u6211\u4eec\u5bf9\u4e00\u4e2a\u56fe\u50cf\u8fdb\u884c\u6a21\u7cca\u5904\u7406\uff0c\u5373\u5c06\u56fe\u50cf\u4e0e Blur Kernel \u8fdb\u884c\u5377\u79ef\uff0c\u5c31\u7b49\u6548\u4e8e\u5c06\u8fd9\u4e24\u4e2a\u77e9\u9635\u5728\u9891\u7387\u57df\u4e2d\u76f8\u4e58\u3002</p> <p></p> <p>\u800c\u4f20\u7edf\u56fe\u50cf\u538b\u7f29\uff0c\u5bf9\u5e94\u5230\u9891\u7387\u57df\u4e0a\uff0c\u5c31\u662f\u5c06\u4ed6\u4eec\u7684\u4e8c\u7ef4\u9891\u8c31\u4e2d\u7684\u9ad8\u9891\u4e22\u6389\u3002</p> <p>\u90a3\u4e48\u5f97\u5230 Fourier \u53d8\u6362\u8fd9\u4e2a\u5de5\u5177\u4ee5\u540e\uff0c\u6211\u4eec\u5c31\u53ef\u4ee5\u5c06\u8f83\u96be\u5904\u7406\u7684\u50cf\u7d20\u4fe1\u606f\u8f6c\u5316\u4e3a\u9891\u7387\u4fe1\u606f\u3002</p> <p>\u5982\u4e0b\u56fe\uff0c\u5c06\u4e00\u5f20\u56fe\u7247\u4fe1\u606f\u7f16\u7801\u4e3a\u4e86\u9891\u8c31\u7684\u5f62\u5f0f\u3002\u7531\u4e8e\u8fd9\u91cc\u7684\u9891\u8c31\u662f\u4e8c\u7ef4\u7684\uff0c\u6240\u4ee5\u4f7f\u7528\u4e00\u5f20\u7070\u5ea6\u56fe\u8868\u73b0\u51fa\u6765\u3002</p> <p></p> <ul> <li> TODO: \u9700\u8981\u66f4\u8be6\u7ec6\u7684\u89e3\u91ca</li> </ul> <p>\u597d\uff0c\u6709\u4e86\u8fd9\u4e9b\u94fa\u57ab\uff0c\u6211\u4eec\u5728\u56de\u5934\u6765\u8bb2\u91c7\u6837\uff0c\u8fd9\u6b21\u6211\u4eec\u5c06\u5c1d\u8bd5\u7740\u540c\u65f6\u4ece Spatial domain \u548c Frequency domain \u7684\u89d2\u5ea6\u6765\u770b\u5f85\u95ee\u9898\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec03/#\u91c7\u6837","title":"\u91c7\u6837","text":"<p>\u9996\u5148\uff0c\u6211\u4eec\u4ece\u5b57\u9762\u610f\u601d\u4e0a\u548c\u76ee\u7684\u4e0a\u6765\u7406\u89e3\u4e00\u4e0b\u91c7\u6837\u3002</p> <p>wiki \u4e0a\u5bf9\u91c7\u6837\u7684\u5b9a\u4e49\u662f\u8fd9\u6837\u7684\uff1a</p> <p>\u5728\u4fe1\u53f7\u5904\u7406\u9886\u57df\uff0c\u91c7\u6837\u662f\u5c06\u4fe1\u53f7\u4ece\u8fde\u7eed\u65f6\u95f4\u57df\u4e0a\u7684\u6a21\u62df\u4fe1\u53f7\u8f6c\u6362\u5230\u79bb\u6563\u65f6\u95f4\u57df\u4e0a\u7684\u79bb\u6563\u4fe1\u53f7\u7684\u8fc7\u7a0b\u3002</p> <p>\u663e\u7136\uff0c\u6211\u4eec\u8fd9\u91cc\u91c7\u6837\u7684\u5b9a\u4e49\u548c\u8fd9\u91cc\u7684\u5b9a\u4e49\u5e76\u4e0d\u4e00\u6837\u3002\u4e0e\u4e4b\u4e0d\u540c\u7684\u662f\uff0c\u6211\u4eec\u9700\u8981\u4ece\u539f\u59cb\u7684\uff0c\u8fd1\u4f3c\u8fde\u7eed\u7684\u56fe\u7247\u4e2d\u63d0\u53d6\u51fa\u5177\u6709\u7279\u5f81\u7684\u4e00\u4e9b\u540c\u6837\u662f\u79bb\u6563\u7684\u7684\u4fe1\u606f\uff0c\u4ee5\u6b64\u6765\u5b9e\u73b0\u6211\u4eec\u5c06\u56fe\u7247\u8fdb\u884c\u653e\u5927\u7f29\u5c0f\u53d8\u6362\u7684\u76ee\u7684\u3002</p> <p>\u5173\u4e8e\u91c7\u6837\u66f4\u6570\u5b66\u7684\u5b9a\u4e49\uff0c\u5c31\u662f\u4f7f\u7528\uff08\u68b3\u5f62\uff09\u8109\u51b2\u51fd\u6570(Dirac comb function)\u53bb\u4e58\u88ab\u91c7\u6837\u7684\u51fd\u6570\u3002</p> <ul> <li>\u8109\u51b2\u51fd\u6570\u7ecf\u8fc7 Fourier \u53d8\u6362\u540e\u4ecd\u7136\u662f\u68b3\u5f62\u7684\u3002</li> </ul> <p></p> <ul> <li>\u901a\u8fc7\u8109\u51b2\u51fd\u6570\uff0c\u6211\u4eec\u5c06\u7279\u5b9a\u9891\u7387\u7684\u5185\u5bb9\u7ed9\u8fc7\u6ee4\u4e0b\u6765\uff0c\u5c06\u4e00\u4e2a\u201c\u8fde\u7eed\u201d\u7684\u5185\u5bb9\u91c7\u6837\u4e3a\u4e86\u4e00\u4e2a\u201c\u79bb\u6563\u201d\u7684\u5185\u5bb9\u3002</li> </ul> <p></p> <p>\u53d6\u51b3\u4e8e\u8109\u51b2\u51fd\u6570\u7684\u9891\u7387\uff0c\u91c7\u6837\u53c8\u88ab\u5206\u4e3a\u5bc6\u96c6\u91c7\u6837(Dense sampling)\u548c\u7a00\u758f\u91c7\u6837(Sparse sampling)\uff0c\u4e5f\u5c31\u5206\u522b\u5bf9\u5e94\u7740\u4e4b\u524d\u63d0\u5230\u7684\uff0c\u91c7\u6837\u9891\u7387\u8f83\u9ad8\u548c\u91c7\u6837\u9891\u7387\u8f83\u4f4e\u7684\u60c5\u51b5\u3002</p> <p>\u800c\u7a00\u758f\u91c7\u6837\u5bfc\u81f4\u7684\u4fe1\u53f7\u8d70\u6837\u95ee\u9898\uff0c\u5c31\u662f\u91c7\u6837\u7ed3\u679c\u518d\u9891\u7387\u57df\u4e2d\u51fa\u73b0\u4e86\u4ea4\u96c6\u3002</p> <ul> <li> TODO: \u7406\u89e3\u5e76\u89e3\u91ca\u8fd9\u4e00\u70b9\u3002</li> </ul>"},{"location":"cour_note/D2QD_Intro2CV/Lec03/#\u51cf\u5c11\u8d70\u6837","title":"\u51cf\u5c11\u8d70\u6837","text":"<p>\u65e2\u7136\u641e\u6e05\u695a\u4e86\u8d70\u6837\u662f\u5982\u4f55\u4ea7\u751f\u7684\uff0c\u90a3\u63a5\u4e0b\u6765\u6211\u4eec\u5c31\u9700\u8981\u8003\u8651\u5982\u4f55\u51cf\u5c11\u4fe1\u53f7\u8d70\u6837\u3002</p> <p>\u603b\u4f53\u6765\u8bf4\uff0c\u6709\u8fd9\u4e48\u4e24\u79cd\u9009\u62e9\uff1a</p> <ol> <li>\u63d0\u9ad8\u91c7\u6837\u9891\u7387\uff1b</li> <li>\u5148\u8fc7\u6ee4\u9ad8\u9891\u518d\u91c7\u6837\uff1b</li> </ol> <p>\u9996\u5148\u6211\u4eec\u56de\u987e\u77e5\u9053\uff0c\u8d70\u6837\u662f\u7531\u4e8e\u91c7\u6837\u9891\u7387\u4f4e\u4e8e\u56fe\u50cf\u9ad8\u9891\u5bfc\u81f4\u7684\uff0c\u90a3\u4e48\u6211\u4eec\u53ea\u9700\u8981\u63d0\u9ad8\u91c7\u6837\u9891\u7387\u5c31\u80fd\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\u4e86\u3002</p> <p>\u800c\u5177\u4f53\u9700\u8981\u63d0\u9ad8\u5230\u591a\u5c11\u5462\uff1f\u5c31\u9700\u8981\u5948\u594e\u65af\u91c7\u6837\u5b9a\u7406(Nyquies-Shannon Theorem)\u3002</p> <p>\u5948\u594e\u65af\u91c7\u6837\u5b9a\u7406</p> <p>\u5f53\u7136\uff0c\u4e3a\u4e86\u8de8\u8fc7\u4e00\u4e2a\u66f4\u9ad8\u7684\u95e8\u69db\u6211\u4eec\u4e5f\u4e0d\u4e00\u5b9a\u9700\u8981\u589e\u957f\u81ea\u5df1\u7684\u817f\u3002\u5728\u80fd\u591f\u63a5\u53d7\u7684\u60c5\u51b5\u4e0b\uff0c\u6211\u4eec\u4e5f\u53ef\u4ee5\u9009\u62e9\u964d\u4f4e\u95e8\u69db\u2014\u2014\u5373\uff0c\u5148\u5c06\u9ad8\u9891\u6ee4\u6ce2\uff0c\u518d\u8fdb\u884c\u91c7\u6837\u3002</p> <p>\u66f4\u5f62\u8c61\u5730\u6765\u8bf4\uff0c\u5728\u9891\u7387\u57df\u4e2d\u53bb\u6389\u4ea4\u96c6\u7684\u624b\u6bb5\u4e3a\uff1a</p> <p></p> <p>\u90a3\u4e48\u8981\u5982\u4f55\u5b9e\u73b0\u5462\uff1f</p> <p>\u56de\u987e\u6211\u4eec\u4e00\u5f00\u59cb\u7ed9\u51fa\u7684\uff0c\u5173\u4e8e\u9891\u7387\u7684\u4e00\u4e2a\u6a21\u7cca\u7684\u7406\u89e3\uff0c\u201c\u5982\u679c\u4e00\u4e2a\u56fe\u50cf\u7684\u67d0\u4e2a\u90e8\u5206\u53d8\u5316\u8d8a\u5267\u70c8\uff0c\u4e00\u822c\u6765\u8bf4\u5176\u9891\u7387\u5c31\u4f1a\u8f83\u5927\u201d\u3002\u6362\u53e5\u8bdd\u6765\u8bf4\uff0c\u8981\u6d88\u53bb\u8fd9\u4e2a\u9ad8\u9891\uff0c\u6211\u4eec\u5c31\u9700\u8981\u8ba9\u62b9\u53bb\u8fd9\u4e9b\u201c\u53d8\u5316\u5267\u70c8\u201d\u7684\u6210\u5206\u3002\u518d\u63a5\u5730\u6c14\u4e00\u70b9\uff0c\u5c31\u662f\u6211\u4eec\u9700\u8981\u5c06\u8fd9\u4e9b\u68f1\u89d2\u62b9\u5f00\u2014\u2014\u6240\u4ee5\u4e00\u79cd\u624b\u6bb5\u5c31\u662f\u8fdb\u884c\u6a21\u7cca\u3002</p> \u4e00\u4e2a\u76f4\u89c2\u7684 \ud83c\udf30 <p>\u6211\u4eec\u4ee5\u5bf9\u4e00\u4e2a\u4e09\u89d2\u5f62\u91c7\u6837\u4e3a\u4f8b\uff0c\u8bf4\u660e\u5982\u4f55\u6ee4\u9ad8\u9891\uff1a</p> <p></p> <p>\u53ef\u4ee5\u53d1\u73b0\uff0c\u76f4\u63a5\u91c7\u6837\u4f1a\u5bfc\u81f4\u7ed3\u679c\u4e0d\u592a\u7406\u60f3\u63a5\u4e0b\u6765\u6211\u4eec\u5728\u91c7\u6837\u4e4b\u524d\u8fdb\u884c\u4e00\u6b21\u6a21\u7cca\u64cd\u4f5c\uff1a</p> <p></p> <p>\u5b83\u5c06\u8d85\u8fc7\u5948\u594e\u65af\u9891\u7387\u7684\u90e8\u5206\u6ee4\u6ce2\u540e\uff0c\u660e\u663e\u53d1\u73b0\u91c7\u6837\u4fdd\u7559\u7684\u539f\u672c\u56fe\u50cf\u7684\u7279\u5f81\u66f4\u591a\u4e86\u3002</p> <p>\u800c\u8fd9\u91cc\u5c31\u4ea7\u751f\u4e86\u4e00\u4e2a\u6bd4\u8f83\u8d34\u8fd1\u65e5\u5e38\u751f\u6d3b\u7684\u8bcd\uff0c\u53eb\u6297\u952f\u9f7f(anti-aliasing)\uff0c\u6216\u8005\u8bf4\u53cd\u8d70\u6837\u3002</p> <p></p>"},{"location":"cour_note/D2QD_Intro2CV/Lec03/#\u5948\u594e\u65af\u91c7\u6837\u5b9a\u7406","title":"\u5948\u594e\u65af\u91c7\u6837\u5b9a\u7406","text":"<p>\u9996\u5148\u89c4\u5b9a\u9891\u5e26\u9650\u5236\u4fe1\u53f7(band-limited signal) \\(f_0\\) \u662f\u56fe\u50cf\u9891\u7387\u7684\u4e00\u4e2a\u4e0a\u754c\uff1b\u5219\u5948\u594e\u65af\u91c7\u6837\u5b9a\u7406\u6307\u51fa\uff0c\u5982\u679c\u91c7\u6837\u9891\u7387\u5927\u4e8e \\(2f_0\\)\uff0c\u5219\u8be5\u91c7\u6837\u5f97\u5230\u7684\u7ed3\u679c\u53ef\u4ee5\u5b8c\u7f8e\u8868\u5f81\u539f\u51fd\u6570\u7684\u7279\u5f81\uff0c\u5373 \"perfectly reconstruct\"\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec03/#\u653e\u5927\u56fe\u7247\u5411\u4e0a\u91c7\u6837--\u63d2\u503c","title":"\u653e\u5927\u56fe\u7247\uff1a\u5411\u4e0a\u91c7\u6837 / \u63d2\u503c","text":"<p>\u56fe\u50cf\u653e\u5927(image magnification)\u662f\u56fe\u50cf\u7f29\u5c0f\u7684\u9006\u53d8\u6362(\u5e9f\u8bdd)\uff0c\u4f46\u662f\u5b9e\u9645\u4e0a\u5e76\u4e0d\u80fd\u4e25\u683c\u5730\u8bf4\u662f\u9006\u53d8\u6362\uff0c\u56e0\u4e3a\u56fe\u50cf\u7f29\u5c0f\u4e0e\u56fe\u50cf\u653e\u5927\u90fd\u662f\u4e0d\u53ef\u9006\u7684\u2014\u2014\u5373\uff0c\u56fe\u7247\u7f29\u5c0f\u5fc5\u7136\u5e26\u5566\u50cf\u7d20\u635f\u5931\uff0c\u56fe\u50cf\u653e\u5927\u5fc5\u7136\u5e26\u6765\u4e00\u4e9b\u901a\u8fc7\u8ba1\u7b97\u5f97\u5230\u7684\u8fd1\u4f3c\u50cf\u7d20\uff0c\u800c\u8fd9\u4e9b\u50cf\u7d20\u5728\u53d8\u6362\u5f97\u5230\u7684\u7ed3\u679c\u56fe\u50cf\u4e2d\u4e0e\u539f\u672c\u50cf\u7d20\u662f\u65e0\u6cd5\u533a\u5206\u7684\u3002</p> <p>\u90a3\u4e48\uff0c\u5355\u5c31\u56fe\u50cf\u653e\u5927\u6765\u8bf4\uff0c\u6211\u4eec\u5c31\u9700\u8981\u6839\u636e\u5df2\u6709\u7684\u50cf\u7d20\uff0c\u8fdb\u884c\u4e00\u4e9b\u63d2\u503c(interpolation)\u64cd\u4f5c\uff0c\u4ee5\u751f\u6210\u90a3\u4e9b\u653e\u5927\u8fc7\u7a0b\u4e2d\u65b0\u51fa\u73b0\u7684\u50cf\u7d20\u3002</p> <p>\u6211\u4eec\u4ece\u5bf9\u4e00\u4e2a\u4e00\u5143\u4e00\u7ef4\u51fd\u6570\u63d2\u503c\u7684\u89d2\u5ea6\u6765\u770b\u8fd9\u4e2a\u95ee\u9898\uff0c\u5373\u628a\u8fd9\u4e2a\u95ee\u9898\u62bd\u8c61\u4e3a\u5728\u91c7\u6837\u5f53\u4e2d\u63d2\u5165\u70b9\u7684\u95ee\u9898\u3002\u4f8b\u5982\uff0c\u6211\u4eec\u73b0\u5728\u6709\u4e00\u4e2a\u6765\u81ea\u4e8e\u6b63\u5f26\u51fd\u6570\u7684\u91c7\u6837\uff0c\u73b0\u5728\u6211\u4eec\u5e0c\u671b\u5728 \\(x\\in(x_i,x_{i+1})\\) \u4e2d\u63d2\u5165\u4e00\u4e2a\u70b9 \\((x_{ip}, y_{ip})\\) \u4f7f\u5f97\u5b83\u5c3d\u53ef\u80fd\u7b26\u5408\u539f\u672c\u7684\u6b63\u5f26\u51fd\u6570\u2014\u2014\u53c8\u6216\u8005\u8bf4\uff0c\u4f7f\u5f97\u5b83\u770b\u8d77\u6765\u5c3d\u53ef\u80fd\u5408\u7406\u3002</p> <p>\u800c\u8fd9\u4e2a\u95ee\u9898\uff0c\u6211\u4eec\u518d\u8fdb\u4e00\u6b65\u5730\u601d\u8003\uff0c\u5b9e\u9645\u4e0a\u5c31\u662f\u5229\u7528\u73b0\u6709\u7684\u70b9\u53bb\u62df\u5408\u4e00\u4e2a\u65b0\u7684\u51fd\u6570\uff0c\u7136\u540e\u518d\u7528\u8fd9\u4e2a\u51fd\u6570\u4e0a\u53d6\u7684\u70b9\u4f5c\u4e3a\u63d2\u5165\u7684\u70b9\u3002</p> <p>\u90a3\u4e48\u6bd4\u8f83\u5e38\u89c1\u7684\u201c\u62df\u5408\u201d\u65b9\u6cd5\u6709\u8fd9\u4e48\u51e0\u79cd\uff1a</p> <p>1.\u6700\u8fd1\u63d2\u503c(nearest-neighbor interpolation)\uff1b 2.\u7ebf\u6027\u63d2\u503c(linear interpolation)\uff1b 3.(3\u6b21)\u591a\u9879\u5f0f\u63d2\u503c(cubic interpolation)\uff1b</p> <p>\u63a5\u4e0b\u6765\u6211\u4eec\u4e00\u4e00\u4ecb\u7ecd\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec03/#\u6700\u8fd1\u63d2\u503c","title":"\u6700\u8fd1\u63d2\u503c","text":"<p>\u6240\u8c13\u7684\u6700\u8fd1\u63d2\u503c(nearest-neighbor interpolation)\uff0c\u5b9e\u9645\u4e0a\u4e0e KNN \u7684 K=1 \u7684\u7279\u6b8a\u60c5\u51b5\u3002\u5373\uff0c\\(y(x) = y(x_{\\mathop{argmin}(|x-x_i|)})\\)\u3002\u8bf4\u4eba\u8bdd\u5c31\u662f\u6a2a\u5750\u6807\u79bb\u54ea\u4e2a\u8fd1\uff0c\u5c31\u548c\u54ea\u4e2a\u4e00\u6837\u3002</p> <p></p> <p>\u5176\u4e2d\u7ea2\u8272\u4e3a\u539f\u6709\u7684\u91c7\u6837\u70b9\uff0c\u84dd\u8272\u4e3a\u6211\u4eec\u7684\u6240\u6709\u63d2\u503c\u6784\u6210\u7684\u66f2\u7ebf\u3002</p> <p>\u89c2\u5bdf\u8fd9\u6761\u84dd\u8272\u66f2\u7ebf\uff0c\u4e0d\u96be\u53d1\u73b0\uff0c\u5b83\u5177\u6709\u8fd9\u51e0\u4e2a\u7279\u5f81\uff1a</p> <ul> <li>\u4e0d\u8fde\u7eed\uff08\u5177\u4f53\u6765\u8bf4\u5c31\u662f\u5728\u6bcf\u4e24\u4e2a\u91c7\u6837\u70b9\u7684\u4e2d\u95f4\uff0c\u4f1a\u51fa\u73b0\u65ad\u70b9\uff09\uff1b</li> <li>\u4e0d\u5149\u6ed1\uff08\u65ad\u70b9\u5904\u65e0\u6cd5\u6c42\u5bfc\uff09\uff1b</li> </ul> <p>\u800c\u4e14\u62cd\u8111\u74dc\u60f3\u60f3\u4e5f\u80fd\u611f\u53d7\u5230\uff0c\u8fd9\u79cd\u63d2\u503c\u7684\u65b9\u6cd5\u5e76\u4e0d\u4f18\u96c5\u2014\u2014\u4e00\u5f20\u56fe\u7247\u653e\u5927\u540e\u4e00\u4e2a\u50cf\u7d20\u7684\u989c\u8272\u53d6\u51b3\u4e8e\u6700\u8fd1\u7684\u91c7\u6837\u50cf\u7d20\u989c\u8272\u2014\u2014\u5728\u591a\u6570\u60c5\u51b5\u4e0b\uff0c\u6211\u4eec\u5e76\u4e0d\u5e0c\u671b\u6709\u8fd9\u6837\u7684\u7ed3\u679c\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec03/#\u7ebf\u6027\u63d2\u503c","title":"\u7ebf\u6027\u63d2\u503c","text":"<p>\u7ebf\u6027\u63d2\u503c(linear interpolation)\u5c31\u662f\u76f4\u63a5\u505a\u8fde\u7ebf\uff0c\u5c06\u76f8\u90bb\u7684\u70b9\u4e24\u4e24\u7528\u76f4\u7ebf\u8fde\u8d77\u6765\uff0c\u7ed8\u5236\u51fa\u4e00\u4e2a\u6298\u7ebf\u56fe\u3002</p> <p></p> <p>\u5176\u4e2d\u7ea2\u8272\u4e3a\u539f\u6709\u7684\u91c7\u6837\u70b9\uff0c\u84dd\u8272\u4e3a\u6211\u4eec\u7684\u6240\u6709\u63d2\u503c\u6784\u6210\u7684\u66f2\u7ebf\u3002</p> <p>\u53ef\u4ee5\u53d1\u73b0\uff0c\u76f8\u6bd4\u4e8e\u6700\u8fd1\u63d2\u503c\uff0c\u7ebf\u6027\u63d2\u503c\u5bf9\u539f\u51fd\u6570\u7684\u62df\u5408\u6027\u76f8\u5bf9\u6765\u8bf4\u597d\u4e86\u5f88\u591a\uff0c\u800c\u4e14\u53d8\u5f97\u8fde\u7eed\u4e86\uff0c\u89c2\u5bdf\u84dd\u8272\u66f2\u7ebf\uff0c\u53d1\u73b0\u6709\u8fd9\u4e48\u51e0\u4e2a\u7279\u5f81\uff1a</p> <ul> <li>\u8fde\u7eed\uff1b</li> <li>\u4e0d\u5149\u6ed1\uff08\u5728\u91c7\u6837\u70b9\u51fd\u6570\u4f1a\u51fa\u73b0\u7a81\u53d8\uff0c\u65e0\u6cd5\u6c42\u5bfc\uff09\uff1b</li> </ul> <p>\u4e8e\u662f\u6211\u4eec\u7ee7\u7eed\u6539\u8fdb\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec03/#3\u6b21\u591a\u9879\u5f0f\u63d2\u503c","title":"(3\u6b21)\u591a\u9879\u5f0f\u63d2\u503c","text":"<p>\u987e\u540d\u601d\u4e49\uff0c(3\u6b21)\u591a\u9879\u5f0f\u63d2\u503c(cubic interpolation)\u5c31\u662f\u4f7f\u7528\u591a\u9879\u5f0f\u51fd\u6570\u6bb5\u6765\u62df\u5408\u91c7\u6837\u533a\u95f4\u3002</p> <p>\u8fd9\u91cc\u9700\u8981\u505a\u4e00\u4e2a\u8fa8\u6790\uff1a\u5e76\u4e0d\u662f\u7528\u4e00\u4e2a\u591a\u9879\u5f0f\u6765\u62df\u5408\u6240\u6709\u7684\u91c7\u6837\u70b9\uff0c\u800c\u662f\u7528\u591a\u9879\u5f0f\u6765\u62df\u5408\u4e00\u5bf9\u91c7\u6837\u70b9\uff0c\u5373\u4e00\u4e2a interval\u3002</p> <p></p> <p>\u5176\u4e2d\u7ea2\u8272\u4e3a\u539f\u6709\u7684\u91c7\u6837\u70b9\uff0c\u84dd\u8272\u4e3a\u6211\u4eec\u7684\u6240\u6709\u63d2\u503c\u6784\u6210\u7684\u66f2\u7ebf\u3002</p> <p>\u5176\u4e2d\uff0c\u6bcf\u4e00\u6bb5 interval \u7684\u84dd\u8272\u7ebf\u6761\u90fd\u7b26\u5408 \\(f_i(x) = a_ix^3 + b_ix^2 + c_ix + d_i, x \\in [x_i, x_{i+1}]\\)\uff1b\u5e76\u4e14\u6211\u4eec\u4fdd\u8bc1\u5728\u91c7\u6837\u70b9\u5904\u5b83\u4eec\u90fd\u662f\u5149\u6ed1\u7684\uff0c\u5373\u4fdd\u8bc1 \\(\\forall i, \\frac{\\mathrm{d}f_i(x_{i+1})}{\\mathrm{d} x} = \\frac{\\mathrm{d}f_{i+1}(x_{i+1})}{\\mathrm{d} x}\\)</p> <p>\u4e8e\u662f\uff0c\u5b83\u81ea\u7136\u5c31\u5177\u6709\u4ee5\u4e0b\u6027\u8d28\uff1a</p> <ol> <li>\u8fde\u7eed\uff1b</li> <li>\u5149\u6ed1\uff1b</li> </ol> <p>\u66f4\u5177\u4f53\u7684</p> <p>\u521a\u624d\u8bb2\u7684\u90fd\u662f\u4ece\u4e00\u7ef4\u51fd\u6570\u7684\u89d2\u5ea6\u6765\u601d\u8003\u63d2\u503c\uff0c\u73b0\u5728\u6211\u4eec\u6765\u4ecb\u7ecd\u4e00\u4e9b\u5728\u4e8c\u7ef4\u5c42\u9762\u505a\u63d2\u503c\u7684\u6848\u4f8b\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec03/#\u53cc\u7ebf\u6027\u63d2\u503c","title":"\u53cc\u7ebf\u6027\u63d2\u503c","text":"<p>\u53cc\u7ebf\u6027\u63d2\u503c(bilinear interpolation)\u5c31\u662f\u5728\u4e8c\u7ef4\u5e73\u9762\u5185\u505a\u7ebf\u6027\u63d2\u503c\uff0c\u601d\u8def\u975e\u5e38\u7b80\u5355\u3002</p> <p></p> <p>\u5982\u56fe\uff0c\u6211\u4eec\u5e0c\u671b\u5728\u7ea2\u70b9\u5904\u8fdb\u884c\u63d2\u503c\uff0c\u90a3\u4e48\u6211\u4eec\u5c31\u4f1a\u9009\u53d6\u4e0e\u4e4b\u76f8\u90bb\u7684\u56db\u4e2a\u70b9\uff0c\\(u_{ij},\\;\\; i,j\\in \\{0,1\\}\\)\uff0c\u518d\u6839\u636e\u8fd9\u4e2a\u70b9\u5728\u8fd9\u4e2a\u77e9\u9635\u4e2d\u7684\u4f4d\u7f6e\u8fdb\u884c\u6c42\u503c\u3002</p> \u5177\u4f53\u8ba1\u7b97\u65b9\u6cd5 <p> </p>"},{"location":"cour_note/D2QD_Intro2CV/Lec03/#\u53cc3\u6b21\u591a\u9879\u5f0f\u63d2\u503c","title":"\u53cc(3\u6b21)\u591a\u9879\u5f0f\u63d2\u503c","text":"<p>wiki \ud83d\udd17</p> <p>\u53cc(3\u6b21)\u591a\u9879\u5f0f\u63d2\u503c(bicubic interpolation)\u5373\u5728\u4e8c\u7ef4\u5e73\u9762\u505a(3\u6b21)\u591a\u9879\u5f0f\u63d2\u503c\uff0c\u5b9e\u73b0\u601d\u8def\u4e0e\u53cc\u7ebf\u6027\u63d2\u503c\u662f\u7c7b\u4f3c\u7684\u3002</p> \\[ p(x,y) = \\sum_{i=0}^{3}\\sum_{j=0}^{3}a_{i,j}x^iy^j \\] <p>What's '4' means here?</p> <p>\u8d85\u5206\u8fa8\u7387</p> <p>\u5728\u5f97\u5230\u8fd9\u4e9b\u63d2\u503c\u7b56\u7565\u540e\uff0c\u6211\u4eec\u5c31\u53ef\u4ee5\u5f15\u51fa\u8d85\u5206\u8fa8\u7387(Super-Resolution)\u8fd9\u4e2a\u6982\u5ff5\uff0c\u5373\u901a\u8fc7\u63d2\u503c\uff0c\u6211\u4eec\u5c06\u4e00\u5f20\u56fe\u7247\u7684\u5206\u8fa8\u7387\u63d0\u9ad8\uff0c\u5f97\u5230\u8d85\u8fc7\u539f\u6709\u56fe\u7247\u5206\u8fa8\u7387\u7684\u4e00\u5f20\u56fe\u7247\u3002</p> <p>\u4f8b\u5982\uff0c\u901a\u8fc7\u4e0b\u9762\u8fd9\u4e2a\u5bf9\u6bd4\uff0c\u6211\u4eec\u4f1a\u53d1\u73b0\uff0c\u591a\u9879\u5f0f\u63d2\u503c\u7684\u8868\u73b0\u6bd4\u7ebf\u6027\u63d2\u503c\u7684\u8868\u73b0\u597d\u4e0d\u5c11\u3002</p> <p></p>"},{"location":"cour_note/D2QD_Intro2CV/Lec03/#\u6539\u53d8\u56fe\u50cf\u957f\u5bbd\u6bd4","title":"\u6539\u53d8\u56fe\u50cf\u957f\u5bbd\u6bd4","text":"<p>\u6539\u53d8\u56fe\u50cf\u957f\u5bbd\u6bd4(aspect ratio)\u8fd9\u4ef6\u4e8b\u8c8c\u4f3c\u53ef\u4ee5\u76f4\u63a5\u901a\u8fc7\u5355\u7ef4\u5ea6\u4e0a\u8fdb\u884c\u7f29\u653e\u6765\u5b9e\u73b0\uff08\u8fdb\u884c\u4e00\u7ef4\u63d2\u503cor\u91c7\u6837\uff09\uff0c\u4f46\u662f\u662f\u5426\u5b58\u5728\u522b\u7684\u65b9\u6cd5\uff0c\u4e0d\u5927\u5e45\u6539\u53d8\u6574\u4f53\u56fe\u50cf\u5f62\u72b6\u7684\u60c5\u51b5\u4e0b\uff0c\u5b9e\u73b0\u8be5\u5f7c\u5cb8\u957f\u5bbd\u6bd4\u5462\uff1f</p> <p>\u5b9e\u9645\u4e0a\uff0c\u6709\u4e00\u4e2a\u505a\u6cd5\u5c31\u662f\u5077\u5077\u5220\u6389\u51e0\u884c/\u51e0\u5217\u50cf\u7d20\uff0c\u5bf9\u4eba\u773c\u6765\u8bf4\u8fd9\u8c8c\u4f3c\u662f\u96be\u4ee5\u5bdf\u89c9\u7684\u3002</p> <p>\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u6765\u505a\u4e00\u4e9b\u6539\u8fdb\uff0c\u6211\u4eec\u8fd9\u6b21\u4e0d\u662f\u66b4\u529b\u7684\u5220\u9664\u4e00\u884c\u6216\u4e00\u5217\uff0c\u800c\u662f\u6709\u9009\u62e9\u6027\u7684\uff0c\u5728\u6bcf\u4e00\u884c\u91cc\u5220\u9664\u51e0\u4e2a\u50cf\u7d20\u3002\u4e3a\u4e86\u4fdd\u8bc1\u56fe\u50cf\u4e0d\u9519\u4f4d\uff0c\u6211\u4eec\u5e0c\u671b\u8fd9\u4e9b\u9009\u4e2d\u7684\u50cf\u7d20\u53ef\u4ee5\u88ab\u770b\u4f5c\u56fe\u50cf\u4e0a\u7684\u201c\u88c2\u7f1d\u201d\uff0c\u5373\u4e00\u6761\u5f2f\u5f2f\u66f2\u66f2\u7684\u66f2\u7ebf\u3002</p> <p></p> <p>\u8fd9\u79cd\u505a\u6cd5\u53ebseam carving\uff0c\u6211\u4eec\u9700\u8981\u627e\u5230\u6bd4\u8f83\u4e0d\u91cd\u8981\u7684\u4e00\u8fde\u4e32\u8fde\u7eed\u50cf\u7d20\u3002\u800c\u8fd9\u91cc\u7684\u201c\u4e0d\u91cd\u8981\u201d\uff0c\u6307\u7684\u5c31\u662f\u90a3\u4e9b\u53d8\u5316\u4e0d\u90a3\u4e48\u5267\u70c8\u7684\u50cf\u7d20\uff0c\u5373\u4e0e\u5468\u56f4\u5341\u5206\u76f8\u8fd1\u7684\u70b9\u3002</p> <p>\u66f4\u6570\u5b66\u7684\u8868\u8ff0\u662f\uff1a</p> <ul> <li>\u6211\u4eec\u5b9a\u4e49edge energy\\(E(I) = \\big|\\frac{\\partial I}{\\partial x}\\big| + \\big| \\frac{\\partial I}{\\partial y} \\big|\\)\uff1b</li> <li>\u627e\u5230\u4ece\u9876\u5230\u5e95\u7684\u4e00\u6761\u8054\u901a\uff08\u5c31\u662f\u4e0b\u4e00\u4e2a\u70b9\u80af\u5b9a\u4e0e\u4e0a\u4e00\u4e2a\u70b9\u76f8\u90bb\u6216\u8005\u5171\u540c\u9876\u70b9\uff09\u8def\u5f84\uff0c\u4f7f\u5f97 edge energy \u6700\u5c0f\uff1b</li> <li>\u7136\u540e\u5c06\u8fd9\u6761\u8def\u5f84\u4ece\u56fe\u7247\u4e2d\u5220\u9664\uff0c\u5c31\u597d\u50cf\u5c06\u8fd9\u4e2a\u88c2\u7f1d\u4e24\u8fb9\u62fc\u8d77\u6765\uff1b</li> </ul> <p>\u800c\u81f3\u4e8e\u5bfb\u627e\u6700\u77ed\u8def\u7684\u7b97\u6cd5\uff0c\u5219\u662f\u4e2a dp \u95ee\u9898\uff0c\u5728\u8fd9\u91cc\u5c31\u4e0d\u5c55\u5f00\u4e86\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec04/","title":"Lecture 4 | Model Fitting and Optimization","text":"<p> \u7ea6 4135 \u4e2a\u5b57  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 14 \u5206\u949f</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec04/#\u4f18\u5316","title":"\u4f18\u5316","text":"<p>\u9996\u5148\u6211\u4eec\u6765\u5b9a\u4e49\u4e00\u4e2a\u4f18\u5316(Optimization)\u95ee\u9898\u7684\u6a21\u578b\uff1a</p> <p>\u4f18\u5316\u95ee\u9898\u7684\u6a21\u578b</p> <p>\u8bbe\u76ee\u6807\u51fd\u6570\\(f_0(\\vec x)\\) \u6ee1\u8db3\u7ea6\u675f\u6761\u4ef6\uff1a</p> \\[ \\left\\{ \\begin{aligned}     f_i(\\vec x) &amp;\\leq 0,  &amp;i = 1,...,m &amp; \\text{inequality constraint functions} \\\\     g_i(\\vec x) &amp;= 0,  &amp;i = 1,...,p &amp; \\text{equality constraint functions}&amp; \\end{aligned} \\right. \\] <p>\u6c42 \\(\\vec x\\in \\mathrm{R}^n\\) \uff0c\u4f7f \\(f_0(\\vec{x})\\) \u6700\u5c0f\uff08\u5373\u6700\u4f18\uff09\u3002</p> <p>\u5f88\u663e\u7136\uff0c\u8fd9\u548c\u6211\u4eec\u9ad8\u4e2d\u63a5\u89e6\u7684\u7ebf\u6027\u89c4\u5212\u5f88\u50cf\uff0c\u5b9e\u9645\u4e0a\u7ebf\u6027\u89c4\u5212\u5c31\u662f\u5176\u4e2d\u4e00\u79cd\u4f18\u5316\u95ee\u9898\u3002</p> <p>\u800c\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u9700\u8981\u5c1d\u8bd5\u5c06\u4e00\u4e9b\u590d\u6742\u95ee\u9898\u8f6c\u5316\u4e3a\u4f18\u5316\u95ee\u9898\uff0c\u5373\u6839\u636e\u95ee\u9898\uff0c\u5199\u51fa\u76ee\u6807\u51fd\u6570\u548c\u7ea6\u675f\u6761\u4ef6\uff0c\u5e76\u901a\u8fc7\u4e00\u4e9b\u65b9\u6cd5\u6765\u5f97\u5230\u6211\u4eec\u9700\u8981\u7684 \\(\\vec x\\)\u3002</p> <p>\ud83c\udf30 \u56fe\u50cf\u53bb\u6a21\u7cca\u95ee\u9898</p> <p>\u5728\u8fd9\u4e2a \ud83c\udf30 \u4e2d\uff0c\u6211\u4eec\u5df2\u77e5\u6a21\u7cca\u56fe\u50cf \\(Y\\) \u548c\u6a21\u7cca\u6ee4\u6ce2\u5668(\u5377\u79ef\u6838) \\(F\\)\uff0c\u9700\u8981\u901a\u8fc7\u4f18\u5316\u7684\u65b9\u6cd5\u6765\u6c42\u5377\u79ef\u8fd0\u7b97\u4e4b\u524d\u7684\u6e05\u6670\u56fe\u50cf \\(X\\)\u3002</p> <p>\u8fdb\u4e00\u6b65\u6765\u8bf4\uff0c\u5c31\u662f\u627e\u5230\u6e05\u6670\u7684\u56fe\u50cf \\(X\\)\uff0c\u4f7f\u5f97\u5b83\u505a\u6a21\u7cca\u5904\u7406\u540e\u4e0e\u5df2\u77e5\u7684\u6a21\u7cca\u56fe\u50cf \\(Y\\) \u5dee\u522b\u5c3d\u53ef\u80fd\u5c0f\uff0c\u4e8e\u662f\u95ee\u9898\u8f6c\u5316\u4e3a\uff1a</p> <ul> <li>\u76ee\u6807\u51fd\u6570\u4e3a \\(\\min\\limits_{X} || Y - F * X ||^2_2\\) \u7684\u4f18\u5316\u95ee\u9898\u3002</li> </ul>"},{"location":"cour_note/D2QD_Intro2CV/Lec04/#\u6a21\u578b\u62df\u5408","title":"\u6a21\u578b\u62df\u5408","text":"<p>\u4e3a\u4e86\u7814\u7a76\u5206\u6790\u5b9e\u9645\u95ee\u9898\uff0c\u6211\u4eec\u9700\u8981\u5bf9\u95ee\u9898\u8fdb\u884c\u4e00\u4e2a\u5efa\u6a21\uff0c\u66f4\u5177\u4f53\u7684\u6765\u8bf4\u5c31\u662f\u6839\u636e\u5b9e\u9645\u60c5\u51b5\uff0c\u5bfb\u627e\u6570\u636e\u4e4b\u95f4\u7684\u5173\u7cfb\uff0c\u5e76\u5efa\u7acb\u6570\u5b66\u6a21\u578b\u3002</p> <p>\u4e00\u4e2a\u6570\u5b66\u6a21\u578b(model)\u63cf\u8ff0\u95ee\u9898\u4e2d\u8f93\u5165\u548c\u8f93\u51fa\u7684\u5173\u7cfb\uff0c\u4f8b\u5982\uff1a\u7ebf\u6027\u6a21\u578b(linear model) \\(b = a^T x\\) \u5c31\u63cf\u8ff0\u4e86\u8f93\u5165(input) \\(a\\) \u548c\u8f93\u51fa(output) \\(b\\) \u5173\u4e8e\u6a21\u578b\u53c2\u6570(model parameter) \\(x\\) \u7684\u5173\u7cfb\u3002</p> <p>\u800c\u5b9e\u9645\u7684\u7ed3\u679c\u5f88\u96be\u4e25\u683c\u6ee1\u8db3\u6570\u5b66\u6a21\u578b\uff0c\u8fd9\u662f\u7531\u591a\u65b9\u539f\u56e0\u5bfc\u81f4\u7684\uff0c\u6240\u4ee5\u6211\u4eec\u5f80\u5f80\u505a\u7684\u662f\u5bf9\u5b9e\u9645\u60c5\u51b5\u8fdb\u884c\u6a21\u578b\u62df\u5408(model fitting)\u3002</p> <p>\u66f4\u5177\u4f53\u7684\u6765\u8bf4\uff0c\u6211\u4eec\u53ef\u80fd\u5df2\u7ecf\u6709\u4e00\u4e2a\u5148\u9a8c\u7684\u5047\u8bbe\uff0c\u5373\u6570\u636e\u7b26\u5408\u54ea\u79cd\u6a21\u578b\uff0c\u63a5\u4e0b\u6765\u6839\u636e\u6570\u636e\u6765\u5206\u6790\u5f97\u5230\u5408\u9002\u7684 model parameters\uff0c\u800c\u8fd9\u4e2a\u6b65\u9aa4\u4e5f\u5e38\u5e38\u88ab\u79f0\u4e3a learning\u3002</p> <p>\u4e00\u79cd\u6bd4\u8f83\u7ecf\u5178\u7684\u903c\u8fd1\u65b9\u6cd5\uff08\u6700\u5c0f\u4e8c\u4e58\u6cd5\uff09\u662f\u6c42\u4f7f\u5747\u65b9\u8bef\u5dee(mean square error, MSE)\u6700\u5c0f\u7684 model parameters\uff1a</p> <p>\\(\\hat{x} = \\mathop{\\arg \\min\\limits_x} \\sum\\limits_i(b_i - a_i^Tx)^2\\)</p> <p>\u800c\u5982\u679c\u6211\u4eec\u5047\u8bbe\u6570\u636e\u4e2d\u7684\u566a\u58f0\u662f\u9ad8\u65af\u5206\u5e03\u7684\uff08\u5b9e\u9645\u4e0a\u5927\u90e8\u5206\u566a\u58f0\u5728\u57fa\u6570\u8db3\u591f\u5927\u7684\u60c5\u51b5\u4e0b\u90fd\u53ef\u4ee5\u770b\u4f5c\u4e3a\u9ad8\u65af\u5206\u5e03\u7684\uff09\uff0c\u90a3\u4e48\u53ef\u4ee5\u4e0e\u7edf\u8ba1\u5b66\u7684\u6781\u5927\u4f3c\u7136\u4f30\u8ba1(maximum likelihood estimation, MLE)\u76f8\u7edf\u4e00.</p> <p>MSE vs. MLE</p> <p>MSE vs MLE for linear regression</p> <p>\u5177\u4f53\u6765\u8bf4\uff0c\\(b_i = a_i^T x + n, \\;\\; n \\sim G(0,\\sigma)\\)\uff0c\u800c\u5bf9\u4e8e\u7ed9\u5b9a\u7684 \\(x\\)\uff0c\u5176\u4f3c\u7136(likehood)\\(P[(a_i,b_i)|x] = P[b_i-a_i^Tx] \\propto \\exp \\left( - \\frac{(b_i-a_i^Tx)^2}{2\\sigma^2} \\right)\\)\uff0c\u8868\u793a\u5728 model parameter \u4e3a \\(x\\) \u7684\u60c5\u51b5\u4e0b\uff0c\u6570\u636e\u7b26\u5408 \\((a_i,b_i)\\) \u7684\u53ef\u80fd\u6027\u3002</p> Maximum Likelihood Estimation <p> If the data points are independent,</p> \\[ \\begin{aligned} P[(a_1, b_1)(a_2, b_2)\\dots|x] &amp; = \\prod\\limits_iP[(a_i, b_i)|x] = \\prod\\limits_i P[b_i - a_i^T x] \\\\ &amp; \\propto \\exp\\left(-\\frac{\\sum_i(b_i - a_i^Tx)^2}{2\\sigma^2}\\right) = \\exp\\left(-\\frac{||Ax-b||^2_2}{2\\sigma^2}\\right) \\end{aligned} \\] <p>That is, maximize the likelihood to find the best \\(x\\).</p> \\[ \\begin{aligned} \\hat x &amp;= \\mathop{\\arg \\max\\limits_x} P[(a_1, b_1)(a_2, b_2)\\dots|x] \\\\ &amp;= \\mathop{\\arg \\max\\limits_x} \\exp\\left(-\\frac{||Ax-b||^2_2}{2\\sigma^2}\\right)  = \\mathop{\\arg \\min\\limits_x}||Ax - b||_2^2 \\end{aligned} \\] <p>MSE = MLE with Gaussian noise assumption</p> <p>\u9700\u8981\u8865\u6570\u5b66\u77e5\u8bc6\uff0c\u5b8c\u5584\u8fd9\u90e8\u5206\u5185\u5bb9</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec04/#\u6570\u503c\u65b9\u6cd5","title":"\u6570\u503c\u65b9\u6cd5","text":"<p>\u4e0a\u4e00\u5c0f\u8282\u4ecb\u7ecd\u4e86\u5982\u4f55\u5bf9\u5b9e\u9645\u95ee\u9898\u8fdb\u884c\u6570\u5b66\u5efa\u6a21\uff0c\u63a5\u4e0b\u6765\u9700\u8981\u4ecb\u7ecd\u7684\u662f\u5982\u4f55\u6c42\u89e3\u6570\u5b66\u6a21\u578b\u3002</p> <p>\u6211\u4eec\u77e5\u9053\uff0c\u5bf9\u4e8e\u4e00\u4e9b\u6bd4\u8f83\u7b80\u5355\u7684\u6a21\u578b\uff0c\u6211\u4eec\u53ef\u4ee5\u76f4\u63a5\u6c42\u5176\u89e3\u6790\u89e3(analytical solution)\uff0c\u6bd4\u5982\u4f7f\u7528\u6c42\u5bfc\u7b49\u65b9\u6cd5\u3002</p> <p>\ud83c\udf30</p> <p>\u4ee5\u521a\u624d\u7684\u7ebf\u6027 MSE \u4e3a\u4f8b\uff0c\\(\\hat{x} = \\mathop{\\arg \\min\\limits_x} \\sum\\limits_i(b_i - a_i^Tx)^2\\) \u7b49\u6548\u4e8e\u6c42\u89e3\u7b49\u5f0f \\(A^TAx=A^Tb\\)\u3002</p> <p>\u7136\u800c\uff0c\u5b9e\u9645\u60c5\u51b5\u662f\u5927\u90e8\u5206\u95ee\u9898\u8fc7\u4e8e\u590d\u6742\uff0c\u6211\u4eec\u6ca1\u6cd5\u76f4\u63a5\u6c42\u5176\u89e3\u6790\u89e3\uff0c\u6240\u4ee5\u6211\u4eec\u9700\u8981\u91c7\u7528\u4e00\u4e9b\u5373\u91c7\u7528\u4e00\u4e9b\u6570\u503c\u65b9\u6cd5(numerical methods)\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec04/#\u68af\u5ea6\u4e0b\u964d","title":"\u68af\u5ea6\u4e0b\u964d","text":"<p>\u7531\u4e8e\u76f8\u5173\u9886\u57df\u7684\u201c\u51fd\u6570\u201d\u7b49\u57fa\u672c\u4e0a\u90fd\u662f\u9ad8\u7ef4\u7684\uff0c\u6240\u4ee5\u6211\u4eec\u4e00\u822c\u4f7f\u7528\u4e8c\u7ef4\u51fd\u6570\u56fe\u50cf\u7684\u65b9\u6cd5\u6765\u5f62\u8c61\u8868\u793a\u51fd\u6570\uff0c\u5373\u4f7f\u7528\u201c\u7b49\u9ad8\u7ebf\u201d\u7684\u5f62\u5f0f\u6765\u53ef\u89c6\u5316\u51fd\u6570\u3002</p> <p>\u867d\u7136\u6ca1\u6cd5\u76f4\u63a5\u6c42\u89e3\u6790\u89e3\uff0c\u4f46\u662f\u4e00\u822c\u51fd\u6570\u90fd\u5177\u6709\u4e00\u4e9b\u5c40\u90e8\u6027\u8d28\uff0c\u4f8b\u5982\u6781\u503c\u70b9\u4e34\u57df\u7684\u68af\u5ea6\u90fd\u6307\u5411\u6781\u503c\u70b9\u3002\u6a21\u7cca\u5730\u6765\u8bf4\uff0c\u53ea\u8981\u6211\u4eec\u968f\u7740\u201c\u68af\u5ea6\u201d\u53bb\u201c\u4e0b\u964d\u201d\uff0c\u5c31\u6709\u53ef\u80fd\u627e\u5230\u6781\u503c\u70b9\uff0c\u8fd9\u5c31\u662f\u901a\u8fc7\u68af\u5ea6\u4e0b\u964d(gradient descent)\u7684\u65b9\u6cd5\u6765\u89e3\u51b3\u4f18\u5316\u95ee\u9898\u3002</p> <p>\u7b80\u5355\u63cf\u8ff0\u68af\u5ea6\u4e0b\u964d\u7684\u8fc7\u7a0b\uff1a</p> <ol> <li>\u521d\u59cb\u5316\u8d77\u70b9\u5750\u6807 x\uff1b</li> <li>\u76f4\u5230 x \u6536\u655b\u5230\u6211\u4eec\u6ee1\u610f\u7684\u7a0b\u5ea6\u4e4b\u524d\uff1a<ol> <li>\u8ba1\u7b97\u4e0b\u964d\u65b9\u5411 p\uff1b</li> <li>\u51b3\u5b9a\u4e0b\u964d\u6b65\u957f \u237a\uff1b</li> <li>\u66f4\u65b0 x = x + \u237ap\uff1b</li> </ol> </li> </ol> <p> </p> <p>Sourece: https://commons.wikimedia.org/w/index.php?curid=2283984</p> <p>\u5176\u4e2d\u6709\u4e09\u4ef6\u4e8b\u9700\u8981\u7279\u6b8a\u8bf4\u660e\uff1a</p> <ul> <li>\u5982\u4f55\u786e\u5b9a\u4e0b\u964d\u65b9\u5411 \\(\\vec p\\)</li> <li>\u5982\u4f55\u786e\u5b9a\u4e0b\u964d\u6b65\u957f</li> <li>\u5168\u5c40\u6700\u4f18\u548c\u5c40\u90e8\u6700\u4f18</li> </ul>"},{"location":"cour_note/D2QD_Intro2CV/Lec04/#\u786e\u5b9a\u4e0b\u964d\u65b9\u5411","title":"\u786e\u5b9a\u4e0b\u964d\u65b9\u5411","text":"<p>\u5bf9\u4e8e\u6211\u4eec\u4ee5\u524d\u63a5\u89e6\u8fc7\u7684\u51fd\u6570\uff0c\u5373\u5f62\u5f0f\u76f8\u5bf9\u7b80\u5355\u7684\u51fd\u6570\uff0c\u6211\u4eec\u5f53\u7136\u53ef\u4ee5\u76f4\u63a5\u6c42\u5176\u68af\u5ea6\u5f97\u5230\u4e0b\u964d\u65b9\u5411\u3002\u7136\u800c\u5b9e\u9645\u95ee\u9898\u4e2d\u7684\u51fd\u6570\u53ef\u80fd\u975e\u5e38\u590d\u6742\uff0c\u6216\u68af\u5ea6\u89e3\u6790\u5f0f\u5f88\u96be\u5f97\u5230\u3002\u8fd9\u65f6\u5019\u6211\u4eec\u5c31\u53ea\u80fd\u9000\u800c\u6c42\u5176\u6b21\uff0c\u6c42\u5176\u201c\u8fd1\u4f3c\u201d\u68af\u5ea6\u65b9\u5411\u3002\u6362\u53e5\u8bdd\u6765\u8bf4\uff0c\u6211\u4eec\u5e0c\u671b\u80fd\u591f\u627e\u5230\u4e00\u4e2a\u548c\u539f\u51fd\u6570\u5728\u5c40\u90e8\u548c\u8be5\u51fd\u6570\u5f88\u50cf\u7684\u62df\u5408\u51fd\u6570\uff0c\u5e76\u4e14\u7528\u8fd9\u4e2a\u62df\u5408\u51fd\u6570\u7684\u68af\u5ea6\u65b9\u5411\u6765\u51b3\u5b9a\u68af\u5ea6\u4e0b\u964d\u7684\u65b9\u5411\u3002</p> <p>\u4e8e\u662f\u6211\u4eec\u60f3\u5230\u6cf0\u52d2\u5c55\u5f00\uff0c\u5b83\u5c06\u51fd\u6570\u5c55\u5f00\u4e3a\u591a\u9879\u5f0f\uff0c\u800c\u591a\u9879\u5f0f\u7684\u68af\u5ea6\u662f\u76f8\u5bf9\u5bb9\u6613\u5f97\u5230\u7684\u3002</p> <p>\u5176\u4e2d\u6bd4\u8f83\u5e38\u7528\u7684\u662f\uff1a</p> <ul> <li>first-order approximation: \\(F(x_k + \\Delta x) \\approx F(x_k) + J_F \\Delta x\\)</li> <li>second-order approximation: \\(F(x_k + \\Delta x) \\approx F(x_k) + J_F\\Delta x + \\frac{1}{2}\\Delta x^T H_F \\Delta x\\)</li> </ul> <p>\u5176\u4e2d \\(J_F\\) \u662f\u96c5\u5404\u6bd4\u77e9\u9635\uff0c\u53ef\u4ee5\u7406\u89e3\u4e3a\u591a\u7ef4\u5411\u91cf\u51fd\u6570\u7684\u5bfc\u6570\uff1b\\(H_F\\) \u662f\u6d77\u68ee\u77e9\u9635\uff0c\u53ef\u4ee5\u7406\u89e3\u4e3a\u591a\u4f4d\u5411\u91cf\u51fd\u6570\u7684\u4e8c\u9636\u5bfc\u6570\u3002</p> <p>\u63a5\u4e0b\u6765\u4ee5 first-order approximation \u4e3a\u4f8b\u7ee7\u7eed\u5206\u6790\u3002</p> <p>\u89c2\u5bdf \\(F(x_k + \\Delta x) \\approx F(x_k) + J_F \\Delta x\\)\uff0c\u53d1\u73b0\u5f53 \\(J_F\\Delta x &lt; 0\\) \u65f6\uff0c \\(F(x_0 + \\Delta x)\\) \u5927\u6982\u7387\u6bd4 \\(F(x_0)\\) \u5c0f\uff0c\u5373\u201c\u4e0b\u964d\u201d\uff0c\u6240\u4ee5\u5728 first-order approximation \u7684\u60c5\u51b5\u4e0b\uff0c\u4e00\u822c\u9009\u62e9\u65b9\u5411 \\(\\vec p = -J_F^T\\)\uff0c\u4e8e\u662f\u4f4d\u79fb\u91cf \\(movement = -J_F \\cdot J_F^T \\cdot step\\)\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec04/#\u786e\u5b9a\u4e0b\u964d\u6b65\u957f","title":"\u786e\u5b9a\u4e0b\u964d\u6b65\u957f","text":"<p>\u5373\u4f7f\u4f46\u4ece\u4e0b\u964d\u901f\u7387\u6765\u8003\u8651\uff0c\u6b65\u957f\u592a\u957f\u6216\u592a\u5c0f\u4e5f\u90fd\u6709\u660e\u663e\u7684\u95ee\u9898\uff1a</p> <p> </p> <p>\u6240\u4ee5\u6b65\u957f\u7684\u9009\u62e9\u5bf9\u4e0b\u964d\u901f\u7387\u7684\u5341\u5206\u5173\u952e\u3002</p> <p>\u4e3a\u4e86\u4e13\u6ce8\u4e8e\u6b65\u957f\u7684\u9009\u62e9\uff0c\u6211\u4eec\u8bb0 \\(\\phi(\\alpha) = F(x+\\alpha h),\\;\\;\\text{where x and h fixed}, x\\geq 0\\)\u3002\u73b0\u5728\u6211\u4eec\u5e0c\u671b\u627e\u5230\u4e00\u4e2a\u80fd\u8ba9 \\(\\phi(\\alpha)\\) \u5c3d\u53ef\u80fd\u5c0f\u4e8e \\(\\phi(0)\\) \u7684 \\(\\alpha\\)\u3002\u63a5\u4e0b\u6765\u6211\u4eec\u4ecb\u7ecd Backtracking Algorithm\uff1a</p> <ol> <li>\u521d\u59cb\u5316 \\(\\alpha\\) \u4e3a\u4e00\u4e2a\u6bd4\u8f83\u5927\u7684\u503c\uff1b</li> <li>\u4e0d\u65ad\u51cf\u5c0f \\(\\alpha\\) \u76f4\u5230 \\(\\phi(\\alpha) \\leq \\phi(0) + \\gamma\\phi'(0)\\alpha\\)\uff1b<ul> <li>\u5176\u4e2d \\(\\gamma\\in(0,1)\\) \u662f\u4e00\u4e2a\u56fa\u5b9a\u7684\u53c2\u6570\uff1b</li> </ul> </li> </ol> <p> </p> <p>\u6362\u53e5\u8bdd\u8bf4\u5c31\u662f\uff0c\u7b26\u5408\u9884\u671f\u7684\u6700\u5927\u6b65\u957f\uff0c\u8fd9\u4e2a\u201c\u9884\u671f\u201d\uff0c\u5c31\u662f\u901a\u8fc7 \\(\\gamma\\) \u4f53\u73b0\u7684\u3002\u56fe\u4e2d\u7ea2\u8272\u865a\u7ebf\u548c\u9ed1\u8272\u7ec6\u7ebf\u5206\u522b\u662f \\(\\gamma\\) \u53d6\u8fb9\u754c\u503c\u65f6\u7684\u60c5\u51b5\uff0c\u800c\u7ea2\u8272\u5b9e\u7ebf\u5219\u8868\u793a\u6211\u4eec\u7684\u9884\u671f\u968f \\(\\alpha\\) \u7684\u53d8\u5316\u3002</p> <p>\u4e0a\u9762\u4f7f\u7528 first-order approximation \u4e3a\u4f8b\u4ecb\u7ecd\u7684\u8fd9\u5957\u65b9\u6cd5\u5c31\u662f\u6700\u901f\u68af\u5ea6\u4e0b\u964d\u6cd5(steepest descent method)\u3002</p> <p>\u6700\u901f\u68af\u5ea6\u4e0b\u964d\u6cd5</p> <p>\\(\\vec p = -J_F^T\\)\uff1b</p> <ul> <li>\u4f18\u70b9<ul> <li>\u5bb9\u6613\u5b9e\u73b0\uff1b</li> <li>\u5728\u8ddd\u79bb\u76ee\u6807\u70b9\u8f83\u8fdc\u65f6\u8868\u73b0\u826f\u597d\uff1b</li> </ul> </li> <li>\u7f3a\u70b9<ul> <li>\u5728\u76ee\u6807\u70b9\u9644\u8fd1\u6536\u655b\u6bd4\u8f83\u6162\uff1b</li> <li>\u6d6a\u8d39\u4e86\u5927\u91cf\u7b97\u529b\uff1b</li> </ul> </li> </ul> <p>\u8fd9\u662f\u56e0\u4e3a\uff0c\u6700\u901f\u68af\u5ea6\u4e0b\u964d\u6cd5\u4e3b\u8981\u91c7\u7528\u7684\u662f first-order approximation\uff0c\u6ca1\u6709\u4f53\u73b0\u66f2\u7387\u7279\u5f81\u3002</p> <p>\u56e0\u800c\u4e00\u79cd\u5f88\u81ea\u7136\u7684\u6539\u8fdb\u65b9\u6cd5\u5c31\u662f\u4f7f\u7528 second-order approximation\uff0c\u5373\u725b\u987f\u6cd5(Newton Method)\u3002</p> <p>\u725b\u987f\u6cd5</p> <p>\\(F(x_k + \\Delta x) \\approx F(x_k) + J_F\\Delta x + \\frac{1}{2}\\Delta x^T H_F \\Delta x\\)</p> <p>\u5bf9\u5b83\u6c42\u5bfc\u5f97\u5230 \\(\\frac{\\partial F}{\\partial \\Delta x} = J_F^T+H_F\\Delta x = 0\\)\u3002</p> <p>\u6240\u4ee5\u5f97\u5230\u65b9\u5411\u4e3a \\(\\vec p = \\Delta x =  -H_F^{-1}J_F^T\\)</p> <ul> <li>\u4f18\u70b9<ul> <li>\u5728\u76ee\u6807\u70b9\u9644\u8fd1\u4e0b\u964d\u901f\u5ea6\u76f8\u5bf9\u66f4\u5feb\uff1b</li> </ul> </li> <li>\u7f3a\u70b9<ul> <li>Hessian matrix \u7684\u8ba1\u7b97\u9700\u8981\u76f8\u5f53\u7b97\u529b\uff0c\u751a\u81f3\u6709\u65f6\u5019\u65e0\u6cd5\u8ba1\u7b97\uff1b</li> </ul> </li> </ul> <p>\u7531\u6b64\u53d1\u73b0\uff0c\u725b\u987f\u6cd5\u7684\u8868\u73b0\u4f1a\u597d\u5f88\u591a\uff0c\u5982\u679c\u80fd\u591f\u907f\u514d\u8ba1\u7b97\u9ed1\u585e\u77e9\u9635\uff0c\u5c31\u53ef\u4ee5\u8fdb\u4e00\u6b65\u63d0\u9ad8\u725b\u987f\u6cd5\u7684\u6548\u679c\uff0c\u4e8e\u662f\u5c31\u51fa\u73b0\u4e86\u9ad8\u65af\u725b\u987f\u6cd5(Gauss-Newton method)\u3002</p> <p>\u9ad8\u65af\u725b\u987f\u6cd5</p> <p>\u5bf9\u4e8e\u89e3\u51b3\u6700\u5c0f\u4e8c\u4e58\u6cd5 \\(\\hat x = \\mathop{\\arg \\min\\limits_x} ||R(x)||^2_2\\) \u7684\u95ee\u9898\u8868\u73b0\u975e\u5e38\u597d\u3002</p> <p>\u5bf9\u4e8e\u8fd9\u7c7b\u95ee\u9898\uff0c\u9ad8\u65af\u725b\u987f\u6cd5\u4f7f\u7528 \\(J_R^TJ_R\\) \u6765\u8fd1\u4f3c\u4ee3\u66ff \\(H_F\\)\uff0c\u5f97\u5230\u4e0b\u964d\u65b9\u5411\u4e3a \\(\\vec p = -(J_R^TJ_R)^{-1}J_R^T,\\;\\;\\text{where }J_R\\text{ is the Jacobian of }R(x)\\)\u3002</p> <ul> <li>\u4f18\u70b9<ul> <li>\u4e0d\u9700\u8981\u8ba1\u7b97 Hessian matrix\uff0c\u53ea\u9700\u8981\u8ba1\u7b97 Jacobian matrix\uff1b</li> </ul> </li> <li>\u7f3a\u70b9<ul> <li>\u7531\u4e8e \\(J_R^TJ_R\\) \u4e0d\u6b63\u5b9a\uff0c\u6240\u4ee5\u672a\u5fc5\u53ef\u9006\uff0c\u9ad8\u65af\u725b\u987f\u6cd5\u6210\u7acb\u7684\u524d\u63d0\u662f\u5176\u53ef\u9006\uff1b</li> <li>\u5f53\u7136\uff0c\u53ef\u4ee5\u4f7f\u7528 Levenberg-Marquardt \u7b97\u6cd5\uff08LM \u7b97\u6cd5\uff09\uff0c\u5373\u5c06 \\(J_R^TJ_R\\) \u4fee\u6b63\u4e3a \\(J_R^TJ_R + \\lambda I\\) \u4ee5\u4fdd\u8bc1\u6b63\u5b9a\uff1b</li> </ul> </li> </ul> Levenberg-Marquardt <p>Wiki: \ud83d\udd17</p> \\[ \\Delta x = -(J_R^TJ_R+\\lambda I)^{-1}J_R^TR(x_k) \\] <ul> <li>The effect of \\(\\lambda\\):<ul> <li>\\(\\lambda \\to \\infty\\): Gradient descent, and stepsize is small;</li> <li>\\(\\lambda \\to 0\\): Gauss-Newton step;</li> </ul> </li> <li>How to determine \\(\\lambda\\):<ul> <li>Update in every iteration;</li> <li>When decreases obviously, \\(\\lambda\\uparrow\\);</li> <li>When doesn't decrease obviously, \\(\\lambda\\downarrow\\);</li> </ul> </li> </ul> <p>\u7b80\u5355\u6765\u8bf4\uff0cLM \u5c31\u662f\u7efc\u5408\u4e86\u6700\u901f\u68af\u5ea6\u4e0b\u964d\u6cd5\u548c\u725b\u987f\u6cd5\u7684\u4f18\u70b9\uff0c\u5728\u8fdc\u79bb\u76ee\u6807\u70b9\u7684\u65f6\u5019\u4f7f\u7528\u6700\u901f\u68af\u5ea6\u4e0b\u964d\u6cd5\uff0c\u4fdd\u8bc1\u542f\u52a8\u901f\u5ea6\u5feb\uff1b\u5728\u9760\u8fd1\u76ee\u6807\u70b9\u7684\u65f6\u5019\u4f7f\u7528\u725b\u987f\u6cd5\uff0c\u4fdd\u8bc1\u6536\u655b\u901f\u5ea6\u8db3\u591f\u5feb\uff1b\u5e76\u4e14\u4fdd\u8bc1 \\(J_R^TJ_R+\\lambda I\\) \u6b63\u5b9a\uff0c\u6240\u4ee5\u59cb\u7ec8\u80fd\u591f\u4f7f\u725b\u987f\u6cd5\u6210\u7acb\u3002</p> <p>\u5e26\u7ea6\u675f\u7684\u4f18\u5316\u95ee\u9898</p> <p>\u5bf9\u4e8e\u5e26\u7ea6\u675f\u7684\u4f18\u5316\u95ee\u9898(constrained optimization)\uff0c\u5219\u9700\u8981\u6839\u636e\u5b9e\u9645\u95ee\u9898\u6c42\u89e3\u3002</p> <ul> <li>\u6211\u4eec\u53ef\u80fd\u53ef\u4ee5\u8f6c\u5316\u95ee\u9898\uff0c\u4f7f\u7528\u66f4\u7b80\u5355\u7684\u8868\u8fbe\u5f0f\u53bb\u62df\u5408\u539f\u6765\u7684\u8868\u8fbe\u5f0f\uff0c\u6765\u6c42\u89e3\uff1b</li> <li>\u5176\u4e2d\uff0c\uff08\u51f9\uff09\u51f8\u51fd\u6570\u662f\u4e00\u5b9a\u80fd\u627e\u5230\u6700\u4f18\u89e3\u7684\uff0c\u6211\u4eec\u79f0\u8fd9\u79cd\u95ee\u9898\u4e3a\u51f8\u4f18\u5316\u95ee\u9898(Convex optimization)</li> </ul> <p>\u63a8\u8350\u540c\u540d\u8bfb\u7269\uff1ahttps://web.stanford.edu/class/ee364a</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec04/#\u5168\u5c40\u6700\u4f18\u548c\u5c40\u90e8\u6700\u4f18","title":"\u5168\u5c40\u6700\u4f18\u548c\u5c40\u90e8\u6700\u4f18","text":"<p>\u5206\u591a\u4e2a batch \u6765\u5904\u7406\uff0c\u5927\u91cf\u6492\u70b9\uff0c\u7136\u540e\u6bd4\u8f83\u6bcf\u4e00\u4e2a batch \u7684\u7ed3\u679c\uff0c\u6700\u7ec8\u53d6\u6700\u597d\u7684\u4e00\u4e2a\u5373\u53ef\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec04/#\u9c81\u68d2\u4f30\u8ba1","title":"\u9c81\u68d2\u4f30\u8ba1","text":"<p>\u9c81\u68d2\u4f30\u8ba1(robust estimation)\u662f\u5bf9\u4ece\u5404\u79cd\u6982\u7387\u5206\u5e03\uff08\u5c24\u5176\u662f\u975e\u6b63\u6001\u5206\u5e03\uff09\u4e2d\u63d0\u53d6\u7684\u6570\u636e\u5177\u6709\u826f\u597d\u6027\u80fd\u7684\u7edf\u8ba1\u3002</p> <p>\u5728\u62df\u5408\u6a21\u578b\u4e2d\uff0c\u96be\u514d\u51fa\u73b0\u4e00\u4e9b\u4e0d\u7b26\u5408\u9884\u671f\u7684\u70b9\uff0c\u800c\u5b83\u4eec\u4f1a\u5bf9\u62df\u5408\u7ed3\u679c\u4ea7\u751f\u6216\u591a\u6216\u5c0f\u7684\u5f71\u54cd\uff0c\u800c\u5982\u4f55\u6743\u8861\u8fd9\u4e9b\u566a\u58f0\u4e0e\u771f\u6b63\u6709\u7528\u7684\u6570\u636e\u70b9\u4e4b\u95f4\u7684\u5173\u7cfb\uff0c\u5c31\u662f\u9c81\u68d2\u4f30\u8ba1\u7684\u8bfe\u9898\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec04/#\u5185\u70b9--\u5916\u70b9","title":"\u5185\u70b9 &amp; \u5916\u70b9","text":"<p>\u9996\u5148\u6211\u4eec\u5bf9\u6570\u636e\u70b9\u8fdb\u884c\u5206\u7c7b\uff1a</p> <ul> <li>\u5185\u70b9(inlier)\uff1a\u7b26\u5408\u6211\u4eec\u9884\u671f\u7684\u6a21\u578b\u62df\u5408\u7684\u70b9\uff1b</li> <li>\u5916\u70b9(outlier)\uff1a\u5b8c\u5168\u4e0d\u7b26\u5408\u6211\u4eec\u9884\u671f\u6a21\u578b\u7684\u70b9\uff0c\u53c8\u53eb\u79bb\u7fa4\uff1b</li> </ul> <p></p> <p>\u5916\u70b9\u7684\u5f71\u54cd</p> <p>\u7531\u4e8e\u5916\u70b9\u504f\u79bb\u5f88\u5927\uff0c\u800c\u6700\u5c0f\u4e8c\u4e58\u6cd5\u4e2d\u5b58\u5728\u5e73\u65b9\u64cd\u4f5c\uff0c\u6240\u4ee5\u6700\u5c0f\u4e8c\u4e58\u6cd5\u62df\u5408\u53d7\u8fd9\u4e9b\u5916\u70b9\u5f71\u54cd\u5f88\u5927\uff1a</p> <p></p>"},{"location":"cour_note/D2QD_Intro2CV/Lec04/#\u4e0d\u540c\u7684\u635f\u5931\u51fd\u6570","title":"\u4e0d\u540c\u7684\u635f\u5931\u51fd\u6570","text":"<p>\u4e8e\u662f\u6211\u4eec\u8003\u8651\uff0c\u53ef\u4ee5\u66f4\u6362\u62df\u5408\u7684\u635f\u5931\u51fd\u6570\uff0c\u6765\u51cf\u5c0f\u5927\u504f\u5dee\u70b9\u5e26\u6765\u7684\u5f71\u54cd\uff0c\u6bd4\u5982\u4f7f\u7528 L1 loss(\u5373\u6c42\u7edd\u5bf9\u503c)\u3002\u4e0d\u8fc7\u66f4\u597d\u7684\u662f\u4e00\u79cd\u9009\u62e9\u53eb huber loss\uff0c\u5b83\u5728\u8ddd\u79bb\u8fdc\u70b9\u8f83\u8fdc\u7684\u65f6\u5019\u6bd4\u8f83\u63a5\u8fd1 L1 loss\u3002</p> L1 &amp; L2 &amp; Huber <ul> <li>L1 loss \u5373\u76f4\u63a5\u5bf9\u504f\u5dee\u53d6\u7edd\u5bf9\u503c\uff0c\u5176\u516c\u5f0f\u4e3a \\(L_1 = |f(x)-Y|\\)\uff0c\u5176\u6700\u5927\u7684\u95ee\u9898\u5c31\u662f\u5728\u62d0\u70b9\u5904\u4e0d\u5149\u6ed1\uff0c\u5373\u4e0d\u53ef\u5bfc\uff0c\u800c\u4e14\u5176\u6536\u655b\u53ef\u80fd\u8fc7\u5feb\uff1b</li> <li>L2 loss \u5373\u5c06\u504f\u5dee\u53d6\u5e73\u65b9\uff0c\u5373 \\(L_2 = |f(x)-Y|^2\\)\uff0cL2 loss \u5728\u62d0\u70b9\u5904\u5219\u662f\u5149\u6ed1\u53ef\u5bfc\u7684\uff0c\u4e14\u6536\u655b\u76f8\u5bf9\u7a33\u5b9a\u5149\u6ed1\uff0c\u4f46\u662f\u4e14\u5728\u67d0\u4e9b\u65f6\u5019\u5177\u6709\u6bd4\u8f83\u597d\u7684\u51e0\u4f55\u610f\u4e49\uff0c\u4f46\u662f\u5bf9\u4e8e\u504f\u5dee\u8f83\u5927\u7684\u70b9\u66f4\u654f\u611f\uff1b</li> <li>Huber loss \u53c8\u53eb smooth L1 loss\uff0c\u5373\u4f7f\u7528\u5206\u6bb5\u51fd\u6570\uff0c\u5728\u62d0\u70b9\u9644\u8fd1\u4f7f\u7528 L2 loss\uff0c\u5728\u8fdc\u7aef\u4f7f\u7528 L1 loss\uff1b</li> </ul> <p></p> <ul> <li>\u76f8\u5173\u6587\u7ae0\uff1ahttps://zhuanlan.zhihu.com/p/48426076</li> </ul>"},{"location":"cour_note/D2QD_Intro2CV/Lec04/#\u968f\u673a\u62bd\u6837\u4e00\u81f4","title":"\u968f\u673a\u62bd\u6837\u4e00\u81f4","text":"<p>\u968f\u673a\u62bd\u6837\u4e00\u81f4(random sample consensus, RANSAC)\u91c7\u7528\u8fed\u4ee3\u7684\u65b9\u5f0f\u4ece\u5305\u542b\u5916\u70b9\u7684\u6570\u636e\u4e2d\u4f30\u8ba1\u6570\u5b66\u6a21\u578b\u53c2\u6570\uff0c\u662f\u4e00\u4e2a\u5bf9\u4e8e\u5b58\u5728\u660e\u663e\u5916\u70b9\u7684\u6570\u636e\u975e\u5e38\u6709\u6548\u7684\u65b9\u6cd5\u3002</p> <p>RANSAC procedure</p> <ol> <li>\u9996\u5148\u968f\u673a\u627e\u4e24\u4e2a\u70b9\u62df\u5408\u4e00\u6761\u76f4\u7ebf\uff0c\u7136\u540e\u68c0\u67e5\u6709\u591a\u5c11\u70b9\u7b26\u5408\u8fd9\u6761\u76f4\u7ebf\uff0c\u5e76\u5bf9\u5176\u8fdb\u884c vote\uff1b</li> <li>\u91cd\u590d\u8fd9\u4e2a\u6b65\u9aa4\uff0c\u6700\u540e\u9009\u62e9\u7968\u6570\u6700\u9ad8\u7684\u62df\u5408\uff1b</li> </ol> <p></p> <p>\u7531 outlier \u62df\u5408\u51fa\u6765\u7684\u76f4\u7ebf\u4e00\u822c votes \u6bd4\u8f83\u5c11\uff0c\u56e0\u4e3a outlier \u4e4b\u95f4\u5f88\u96be\u4e00\u81f4\uff1b\u4f46\u662finlier\u4e4b\u95f4\u5bb9\u6613\u4e00\u81f4\uff0c\u56e0\u800c\u5f97\u5206\u5f80\u5f80\u66f4\u9ad8\uff0c\u4e8e\u662f\u5c06\u5b83\u4eec\u533a\u5206\u5f00\u6765\u3002\u8fd9\u4e0d\u5c31\u662f Voting Tree (\u9003</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec04/#\u75c5\u6001\u95ee\u9898","title":"\u75c5\u6001\u95ee\u9898","text":"<p>\u5982\u679c\u4e00\u4e2a\u95ee\u9898\u7684\u89e3\u4e0d\u552f\u4e00\uff0c\u90a3\u4e48\u8fd9\u4e2a\u95ee\u9898\u662f\u4e00\u4e2a\u75c5\u6001\u95ee\u9898(ill-posed problem)\u3002\u7279\u522b\u7684\uff0c\u5728\u7ebf\u6027\u95ee\u9898\u4e2d\uff0c\u4e00\u4e2a\u7ebf\u6027\u65b9\u7a0b\uff08\u7ec4\uff09\u7684\u89e3\u5982\u679c\u4e0d\u552f\u4e00\uff08\u4e0d\u6ee1\u79e9\uff09\uff0c\u5219\u540c\u6837\u662f\u4e00\u4e2a\u75c5\u6001\u95ee\u9898\u3002</p> <p>\u5f53\u7136\uff0c\u5bf9\u4e8e\u7ebf\u6027\u65b9\u7a0b\u7ec4\uff0c\u6839\u636e\u7ebf\u6027\u4ee3\u6570\u7684\u77e5\u8bc6\uff0c\u6211\u4eec\u53ef\u4ee5\u589e\u52a0\u65b9\u7a0b\uff0c\u5373\u589e\u52a0\u7ea6\u675f\u3002\u800c\u8fd9\u79cd\u7ea6\u675f\u4e00\u822c\u6765\u81ea\u4e8e\u5bf9\u53d8\u91cf\u7684\u5148\u9a8c\u7ea6\u675f\uff0c\u6bd4\u5982\uff1a</p> <p>L2 regularization</p> <p>L2 norm: \\(||x||_2 = \\sum_i x_i^2\\);</p> <p>L2 regularization: \\(\\min\\limits x ||Ax-b||^2_2\\;\\;s.t. ||x||_2 \\leq 1\\);</p> <p> </p> <p>\u901a\u8fc7\u8ba9\u9009\u62e9\u7684\u89e3\u5c3d\u53ef\u80fd\u63a5\u8fd1\u539f\u70b9\uff0c\u800c\u8ba9\u6211\u4eec\u6ca1\u6709\u7528\u7684\u89e3\u7684\u7ef4\u5ea6\u5c3d\u53ef\u80fd\u63a5\u8fd1 0\uff0c\u4ee5\u51cf\u5c0f\u6ca1\u7528\u7684\u53d8\u91cf\u7684\u5f71\u54cd\uff0c\u6291\u5236\u5197\u4f59\u53d8\u91cf\u3002</p> <p>L1 regularization</p> <p>L1 norm: \\(||x||_1=\\sum_i|x_i|\\);</p> <p>L1 regularization: \\(\\min\\limits x ||Ax-b||^2_2\\;\\;s.t. ||x||_1 \\leq 1\\)</p> <p> </p> <p>L1 \u53ef\u89c6\u5316\u4e2d\u53ef\u4ee5\u53d1\u73b0\uff0c\u5750\u6807\u8f74\u4e0a\u6bd4\u8f83\u5bb9\u6613\u6293\u4f4f\u89e3\uff0c\u6b64\u65f6\u610f\u5473\u7740\u6709\u4e9b\u53d8\u91cf(\u7ef4\u5ea6)\u662f 0\uff0c\u6362\u53e5\u8bdd\u6765\u8bf4\u80fd\u8ba9\u89e3\u53d8\u5f97\u201c\u7a00\u758f(sparse)\u201d\uff0c\u5373\u5728\u7ef4\u5ea6\u4e0a\u7684\u5206\u5e03\u53ea\u6bd4\u8f83\u96c6\u4e2d\u4e8e\u4e2a\u522b\u9879\u3002</p> <p>\u4e0d\u8fc7\uff0c\u5c06\u4ed6\u4eec\u4f5c\u4e3a\u7ea6\u675f\u6761\u4ef6\u53c2\u4e0e\u6c42\u89e3\uff0c\u4e0d\u5982\u76f4\u63a5\u52a0\u8fdb\u53bb\u4f5c\u4e3a\u4e00\u4e2a\u9879\uff0c\u5176\u6548\u679c\u662f\u7b49\u4ef7\u7684\uff1a</p> \\[ \\begin{matrix}     \\text{L2 regularization:}               &amp; | &amp; \\text{or L1 regularization:}\\\\     \\min_{x}||Ax-b||^2_2+\\lambda ||x||_2^2  &amp; | &amp; \\min_{x}||Ax-b||^2_2+\\lambda ||x||_1\\\\     s.t. ||x||_2 \\leq 1                     &amp; | &amp; s.t. ||x||_1 \\leq 1 \\\\ \\end{matrix} \\]"},{"location":"cour_note/D2QD_Intro2CV/Lec04/#\u8fc7\u62df\u5408\u548c\u6b20\u62df\u5408","title":"\u8fc7\u62df\u5408\u548c\u6b20\u62df\u5408","text":"<p>\u5728\u8fd9\u4e2a\u8fc7\u7a0b\u4e2d\uff0c\u4e5f\u8981\u5c0f\u5fc3\u8fc7\u62df\u5408(overfitting)\u548c\u6b20\u62df\u5408(underfitting)\uff0c\u5b83\u4eec\u7684\u542b\u4e49\u975e\u5e38\u76f4\u767d\uff1a</p> <p></p>"},{"location":"cour_note/D2QD_Intro2CV/Lec04/#\u63d2\u503c","title":"\u63d2\u503c","text":"<p>\u63d2\u503c(interpolation)\u5176\u5b9e\u5df2\u7ecf\u5728 lec 3 \u7684\u7b14\u8bb0 \u91cc\u63d0\u5230\u8fc7\u4e86\u3002</p> <p>\u8fd9\u91cc\u5148\u7565\u8fc7\u3002</p> <ul> <li> TODO: \u518d\u7ec6\u8bf4\u3002</li> </ul> sketch <p>\u7ebf\u6027\u62df\u5408\u3001\u4e8c\u6b21\u6837\u6761\u63d2\u503c\uff08\u6bcf\u4e00\u6bb5\u90fd\u662f\u4e00\u4e2a\u4e8c\u6b21\u51fd\u6570\uff09\u3001\u4e09\u6b21\u6837\u6761\u63d2\u503c\uff08\u4e00\u9636\u5bfc\u4e8c\u9636\u5bfc\u8fde\u7eed\uff0c\u4f46\u6700\u7ec8\u662f\u4e2a\u75c5\u6001\u95ee\u9898\uff0c\u9700\u8981\u989d\u5916\u518d\u7ea6\u675f\u8d77\u70b9\u548c\u7ec8\u70b9\u4e8c\u9636\u5bfc\u4e3a\u96f6\u6216\u8005\u9650\u5b9a\u7ed9\u5b9a\u659c\u7387\u7b49\uff0c\u5c31\u9700\u8981\u4fe9\u989d\u5916\u7ea6\u675f\u6761\u4ef6\uff09\u3001</p> <p>\u4e0a\u9762\u662f\u8fde\u7eed\u4f18\u5316\u95ee\u9898\uff0c\u4e0b\u9762\u662f\u79bb\u6563\u4f18\u5316\u95ee\u9898</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec04/#\u56fe\u5272--\u9a6c\u53ef\u592b\u968f\u673a\u573a","title":"\u56fe\u5272 &amp; \u9a6c\u53ef\u592b\u968f\u673a\u573a","text":""},{"location":"cour_note/D2QD_Intro2CV/Lec04/#\u56fe\u50cf\u6807\u7b7e\u95ee\u9898","title":"\u56fe\u50cf\u6807\u7b7e\u95ee\u9898","text":"<p>\u56fe\u50cf\u6807\u7b7e\u95ee\u9898(image labeling problems)\u5373\u901a\u8fc7\u56fe\u7247\u4fe1\u606f\u7ed9\u6bcf\u4e00\u4e2a\u50cf\u7d20\u5206\u914d\u6807\u7b7e\uff0c\u5b9e\u9645\u4e0a\u5c31\u662f\u4e00\u4e2a\u5bf9\u56fe\u50cf\u5185\u5bb9\u7684\u5206\u7c7b\u548c\u8bc6\u522b\u95ee\u9898\u3002</p> <p></p> <p>\u5176\u4e2d\u4e00\u4e2a\u6bd4\u8f83\u5f3a\u7684\u5148\u9a8c(prior)\u662f\uff1a\u76f8\u90bb\u4e14\u76f8\u4f3c\u7684\u50cf\u7d20\u5e94\u5f53\u62e5\u6709\u76f8\u540c\u7684\u6807\u7b7e\u3002</p> <p>\u800c\u56fe\u5272\u548c\u9a6c\u53ef\u592b\u968f\u673a\u573a\u53ef\u4ee5\u5efa\u6a21\u8fd9\u79cd\u5148\u9a8c\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec04/#\u56fe\u5272","title":"\u56fe\u5272","text":"<p>\u56fe\u5272(Graphcut)\u7684\u6838\u5fc3\u601d\u60f3\u662f\uff0c\u628a\u4e00\u5f20\u56fe\u7247\u7684\u6bcf\u4e00\u4e2a\u50cf\u7d20\u770b\u4f5c\u4e00\u4e2a graph \u4e2d\u7684 vertex\uff0c\u5e76\u5728\u50cf\u7d20\u4e4b\u95f4\u5efa edge\uff0c\u5e76\u5c06 weight \u5b9a\u4e49\u4e3a\u4e24\u50cf\u7d20\u4e4b\u95f4\u7684\u76f8\u4f3c\u6027\u6216\u5173\u8054\u6027(affinity or similarity)\u3002</p> <p>measuring affinity</p> <p>\u6bd4\u5982\uff0c\u6211\u4eec\u53ef\u4ee5\u8fd9\u6837\u8861\u91cf\u50cf\u7d20\u7684\u76f8\u4f3c\u6027\uff1a</p> <ul> <li>\u8bbe \\(f\\) \u8868\u793a\u989c\u8272\uff1b</li> <li>\u50cf\u7d20\u5dee\u5f02(dissimilarity)\u4e3a \\(s(f_i,f_j)=\\sqrt{\\sum_k(f_{ik},f_{jk})^2}\\)\uff1b</li> <li>\u5219\u76f8\u4f3c\u6027(affinity)\u6743\u91cd\u4e3a\uff1a\\(w(i,j) = A(f_i,f_j) = e^{\\frac{-1}{2\\sigma^2}s(f_i,f_j)}\\)\uff1b</li> </ul> <p>\u518d\u63a5\u4e0b\u6765\uff0c\u901a\u8fc7\u8fd9\u6837\u7684\u65b9\u5f0f\u5c06\u56fe\u7247\u5efa\u6210\u56fe\u540e\uff0c\u5c31\u53ef\u4ee5\u628a\u95ee\u9898\u8f6c\u5316\u4e3a\u56fe\u5272\u95ee\u9898\uff0c\u6211\u4eec\u5c06\u5c0f\u6743\u7684\u8fb9\u5220\u53bb\uff0c\u6700\u7ec8\u4f1a\u5f62\u6210\u82e5\u5e72\u8fde\u901a\u5206\u91cf\uff0c\u800c\u8fd9\u4e9b\u8fde\u901a\u5206\u91cf\u90a3\u7684\u70b9\u5219\u88ab\u89c6\u4e3a\u4e00\u4e2a\u201c\u5206\u5272\u201d\u3002</p> <p>\u5177\u4f53\u6765\u8bf4\uff0c\u56fe\u5272\u7684\u4ee3\u4ef7\u4e3a\u65ad\u7684\u8fb9\u6743\u4e4b\u6743\u91cd\u548c \\(cut(V_A,V_B)= \\sum_{u\\in V_A, v\\in V_B} w(u,v)\\)\uff0c\u800c\u6211\u4eec\u9700\u8981\u627e\u4ee3\u4ef7\u5c3d\u53ef\u80fd\u5c0f\u7684\uff0c\u6ee1\u8db3\u6211\u4eec\u8981\u6c42\u7684\u56fe\u5272\u3002\u5f53\u7136\uff0c\u8fd9\u4e2a\u95ee\u9898\u4e5f\u7b49\u6548\u4e8e\u6700\u5927\u6d41\u95ee\u9898\uff1b</p> <p>Problem with min-cut</p> <p>Bias to cut small, isolated segments.</p> <p></p> <p>\u7531\u4e8e min-cut \u7684\u8fd9\u4e2a\u95ee\u9898\uff0c\u6211\u4eec\u8fd8\u9700\u8981\u8861\u91cf\u8fd9\u4e2a\u5b50\u96c6\u662f\u5426\u8db3\u591f\u7a20\u5bc6\uff0c\u6240\u4ee5\u6211\u4eec\u503e\u5411\u4e8e\u4f7f\u7528 normalized-cut\u3002</p> \\[ assoc(V_A,V) = \\sum_{u\\in V_A, v\\in V} w(u,v) \\\\ NCut(V_A,V_B) = \\frac{cut(V_A,V_B)}{assoc(V_A,V)} + \\frac{cut(V_A,V_B)}{assoc(V_B,V)} \\] <ul> <li>NP-Complete</li> <li>Approximate solution by eigenvalue decomposition</li> </ul>"},{"location":"cour_note/D2QD_Intro2CV/Lec04/#\u9a6c\u53ef\u592b\u968f\u673a\u573a","title":"\u9a6c\u53ef\u592b\u968f\u673a\u573a","text":"<p>\u9a6c\u53ef\u592b\u968f\u673a\u573a(Markov Random Field, MRF)\u662f\u4e00\u79cd\u66f4\u901a\u7528\u7684\u89e3\u51b3\u65b9\u6848\uff0c\u53ef\u60dc\u6211\u7b2c\u4e00\u6b21\u6ca1\u542c\u61c2\uff0c\u7b49\u6211\u542c\u61c2\u4e86\u518d\u6765\u8865\u5145\u8fd9\u91cc\u7684\u5185\u5bb9\u3002</p> sketch <p>Markov chains</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec05/","title":"Lecture 5 | Feature Matching and Motion Estimation","text":"<p> \u7ea6 3966 \u4e2a\u5b57  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 13 \u5206\u949f</p> <p>\u6ce8\u610f</p> <p>\u672c\u6587\u5c1a\u672a\u5b8c\u5168\u6574\u7406\u597d\uff01</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec05/#\u56fe\u50cf\u7279\u5f81\u5339\u914d","title":"\u56fe\u50cf\u7279\u5f81\u5339\u914d","text":"<p>\u672c\u8282\u7684\u8bfe\u9898\u662f\u7279\u5f81\u5339\u914d(feature matching)\uff0c\u5177\u4f53\u6765\u8bf4\u662f\u627e\u5230\u4e24\u5f20\u56fe\u50cf\u4e2d\u53ef\u80fd\u6307\u4ee3\u540c\u4e00\u5ba2\u4f53\u7684\u90e8\u5206\uff0c\u5173\u952e\u5728\u4e8e\u627e\u5230\u56fe\u7247\u4e4b\u95f4\u70b9\u548c\u70b9\u7684\u5339\u914d\u5173\u7cfb\u3002\u8be5\u95ee\u9898\u662f\u5f88\u591a\u95ee\u9898\u7684\u57fa\u77f3\uff0c\u4f8b\u5982\uff1a</p> applications <ul> <li>Image alignment / Panoramas</li> <li>3D reconstruction</li> <li>Motion tracking</li> <li>Object recognition</li> <li>Indexing &amp; database retrieval</li> <li>Robot navigation</li> <li>...</li> </ul> <p>\u5934\u8111\u98ce\u66b4</p> <p>\u7a76\u5176\u6839\u672c\uff0c\u7279\u5f81\u5339\u914d\u201c\u8054\u901a\u201d\u4e86\u4e24\u5f20\u56fe\u7247\uff0c\u4f7f\u5b83\u4eec\u539f\u672c\u5b64\u7acb\u8868\u8fbe\u7684\u4fe1\u606f\u8fde\u7ed3\u8d77\u6765\u3002</p> <p>\u7b80\u5355\u7684\u5e94\u7528\u5982\u56fe\u50cf\u62fc\u63a5\uff0c\u518d\u5f80\u540e\uff0c\u6211\u4eec\u4f1a\u53d1\u73b0\u4e09\u7ef4\u91cd\u5efa\u4e2d\u4e5f\u4f1a\u5e94\u7528\u5230\u7279\u5f81\u5339\u914d\u5230\u76f8\u5173\u5185\u5bb9\u3002</p> <p>\u6982\u62ec\u4f20\u7edf\u7279\u5f81\u5339\u914d\u4e3b\u8981\u73af\u8282\uff0c\u5927\u6982\u53ef\u4ee5\u5206\u4e3a\u5982\u4e0b\u4e09\u6b65\uff1a</p> <ol> <li>\u68c0\u6d4b(detection): \u627e\u5230\u5173\u952e\u70b9(interest points)\uff0c\u5373\u53ef\u80fd\u4f1a\u88ab\u5339\u914d\u7684\u201c\u7279\u5f81\u70b9\u201d\uff1b</li> <li>\u8868\u8fbe(description): \u63d0\u53d6\u6bcf\u4e2a\u5173\u952e\u70b9\u5468\u56f4\u7684\u5411\u91cf\u7279\u5f81\u63cf\u8ff0\u7b26(feature descriptor)\uff0c\u5373\u5c06\u201c\u7279\u5f81\u201d\u6570\u636e\u5316\uff1b</li> <li>\u5339\u914d(matching): \u51b3\u5b9a\u4e24\u4e2a\u89c6\u89d2\u4e0b\u7279\u5f81\u63cf\u8ff0\u7b26\u7684\u5173\u8054\u5e76\u5339\u914d\uff0c\u5373\u6784\u5efa\u201c\u7279\u5f81\u201d\u4e4b\u95f4\u7684\u5339\u914d\u5173\u7cfb\uff1b</li> </ol>"},{"location":"cour_note/D2QD_Intro2CV/Lec05/#\u5173\u952e\u70b9\u68c0\u6d4b","title":"\u5173\u952e\u70b9\u68c0\u6d4b","text":"<p>\u63a8\u8350\u9605\u8bfb</p> <p>\u3010\u8ba1\u7b97\u673a\u89c6\u89c9\u30112. \u7279\u5f81\u70b9\u68c0\u6d4b\uff1aHarris, SIFT, SURF, ORB</p> <p>\u68c0\u6d4b(detection)\u7684\u9996\u8981\u95ee\u9898\u662f\u5982\u4f55\u9009\u62e9\u5173\u952e\u70b9(interest points/feature points)\uff0c\u6216\u8005\u8bf4\uff0c\u4e00\u4e2a\u70b9\u4ec0\u4e48\u60c5\u51b5\u4e0b\u4f1a\u88ab\u8ba4\u4e3a\u662f\u4e00\u4e2a\u7279\u5f81\u70b9\u3002</p> <p>\u603b\u4f53\u6765\u8bf4\uff0c\u5173\u952e\u70b9\u9700\u8981\u7531\u8fd9\u4e48\u4e24\u4e2a\u7279\u5f81\uff1a</p> <ol> <li>\u72ec\u7279\u6027(uniqueness)\uff0c\u5373\u8fd9\u4e2a\u70b9\u9700\u8981\u80fd\u591f\u8868\u5f81\u4e00\u5b9a\u7279\u6027\uff1b</li> <li>\u5bf9\u4e8e\u53d8\u6362\u4e0d\u654f\u611f\uff0c\u5373\u5bf9\u4e8e\u4e00\u4e2a\u5ba2\u89c2\u4e0a\u7684\u5173\u952e\u70b9\uff0c\u5373\u4f7f\u56fe\u7247\u88ab\u65cb\u8f6c\u3001\u538b\u7f29\u3001\u9002\u5f53\u7684\u626d\u66f2\uff0c\u5b83\u90fd\u5e94\u5f53\uff08\u5c3d\u53ef\u80fd\u5730\uff09\u88ab\u8bc6\u522b\u4e3a\u5173\u952e\u70b9\uff1b</li> </ol> <p>\u5173\u952e\u70b9</p> <p>\u867d\u7136\u8bf4\u662f\u5173\u952e\u201c\u70b9\u201d\uff0c\u4f46\u662f\u5b9e\u9645\u4e0a\u6307\u7684\u662f\u4e00\u5c0f\u5757\u533a\u57df\u3002\u65e2\u7136\u4f5c\u4e3a\u4e00\u4e2a\u80fd\u8868\u8fbe\u5c40\u90e8\u7279\u5f81\u7684\u70b9\uff0c\u5b83\u5fc5\u7136\u9700\u8981\u56ca\u62ec\u4e00\u5b9a\u8303\u56f4\u5185\u7684\u4fe1\u606f\u3002</p> <p>\u9996\u5148\u6211\u4eec\u8ba8\u8bba\u5982\u4f55\u8861\u91cf\u4e00\u4e2a\u70b9\u7684\u72ec\u7279\u6027(uniqueness)\uff0c\u672c\u6587\u4f1a\u4ecb\u7ecd\u4e24\u79cd\u68c0\u6d4b\u5668\uff1a</p> <ol> <li>\u7740\u773c\u4e8e\u56fe\u50cf\u7684\u89d2\u70b9 - Harris corner detector\uff1b</li> <li>\u7740\u773c\u4e8e\u56fe\u50cf\u7684\u6591\u70b9 - Blob detector(LoG or DoG)\uff1b</li> </ol>"},{"location":"cour_note/D2QD_Intro2CV/Lec05/#\u89d2\u70b9\u68c0\u6d4b","title":"\u89d2\u70b9\u68c0\u6d4b","text":"<p>\u63a8\u8350\u9605\u8bfb</p> <p>Harris Corners @ 16-385 Computer Vision (Kris Kitani) @ Carnegie Mellon University</p> <p>\u89d2\u70b9\u68c0\u6d4b\u7684\u57fa\u672c\u601d\u8def\u662f\uff0c\u6211\u4eec\u79f0\u67d0\u4e2a\u70b9\u6bd4\u8f83\u72ec\u7279\u65f6\uff0c\u5b83\u76f8\u5bf9\u4e8e\u5468\u56f4\u4e00\u5b9a\u53c8\u4e00\u4e9b\u201c\u4e0d\u540c\u201d\u7684\u5730\u65b9\u3002\u6216\u8005\u8bf4\u5b58\u5728\u4e00\u4e9b\u9ad8\u9891\u7279\u5f81\uff0c\u800c\u4e14\u8fd9\u79cd\u9ad8\u9891\u7279\u5f81\u4e0d\u4f1a\u5404\u5411\u540c\u6027\u6216\u8005\u8bf4\u51e0\u4e2a\u5411\u540c\u6027\u3002</p> <p>\u5728\u6a21\u5f0f\u5316\u7684\u63cf\u8ff0\u8fd9\u4e2a\u601d\u8def\u5c31\u662f\uff1a</p> <p>Local measures of uniqueness(rough):</p> <p>\u6211\u4eec\u4ee5\u7a97\u53e3\u7684\u5f62\u5f0f\u5bf9\u76ee\u6807\u70b9\u53ca\u5176\u90bb\u57df\u8fdb\u884c\u91c7\u6837\uff0c\u5f53\u65e0\u8bba\u5f80\u54ea\u4e2a\u65b9\u5411\u79fb\u52a8\u7a97\u53e3\uff0c\u91c7\u6837\u7ed3\u679c\u90fd\u4f1a\u4ea7\u751f\u8f83\u5927\u53d8\u5316\u65f6\uff0c\u6211\u4eec\u5c31\u8ba4\u4e3a\u8fd9\u4e2a\u70b9\u72ec\u7279\u6027\u5f3a\u3002</p> <p></p> Flag Edge Corner \u65e0\u8bba\u5411\u54ea\u4e2a\u65b9\u5411\u79fb\u52a8\uff0c\u90fd\u4e0d\u4f1a\u6709\u592a\u5927\u53d8\u5316 \u5f53\u6cbf\u7740\u201cEdge\u201d\u7684\u65b9\u5411\u79fb\u52a8\u65f6\uff0c\u4e0d\u592a\u6709\u53d8\u5316 \u65e0\u8bba\u5411\u54ea\u4e2a\u65b9\u5411\u79fb\u52a8\uff0c\u90fd\u4f1a\u5bfc\u81f4\u8f83\u5927\u7684\u53d8\u5316 <p>\u4e0d\u8fc7\u8fd9\u4ecd\u7136\u662f\u4e00\u4e2a\u76f8\u5bf9\u6a21\u7cca\u7684\u5b9a\u4e49\uff0c\u4e3a\u4e86\u5bf9\u5176\u8fdb\u884c\u5efa\u6a21\uff0c\u6211\u4eec\u8fdb\u4e00\u6b65\u5730\u5bf9\u4e0a\u9762\u63d0\u5230\u7684\u201c\u53d8\u5316\u5e45\u5ea6\u201d\u8d4b\u4e88\u6570\u5b66\u542b\u4e49\uff1a</p> <p>Local measures of uniqueness(detail):</p> <p>\u6240\u8c13\u53d8\u5316\u5927\uff0c\u5b9e\u9645\u4e0a\u6307\u7684\u662f\u76f8\u540c\u7684\u5355\u4f4d\u957f\u5ea6\u91cc\uff0c\u8272\u5f69\u503c\u7684\u5dee\u66f4\u5927\uff0c\u4e3a\u4ec0\u4e48\u6211\u4eec\u4e0d\u7528\u68af\u5ea6\u6765\u8861\u91cf\u5462\uff1f\u5173\u6ce8\u533a\u57df\u5185\u7684\u68af\u5ea6\u5206\u5e03\uff1a</p> <p></p> <p>\u6839\u636e\u68af\u5ea6\u7684\u5206\u5e03\uff0c\u6211\u4eec\u53ef\u4ee5\u5927\u81f4\u89c2\u5bdf\u5230\u56fe\u5f62\u7684\u7279\u5f81\uff0c\uff0c\u5305\u62ec\u5b58\u5728\u591a\u5c11\u4e2a Edge \u4ee5\u53ca\u8fd9\u4e9b Edge \u7684\u65b9\u5411\u3002</p> <p>\u4e0d\u8fc7\u7eaf\u7cb9\u6839\u636e\u68af\u5ea6\u6765\u5bfb\u627e\u89d2\u70b9\u6709\u65f6\u5019\u53ef\u80fd\u4f1a\u6536\u5230\u566a\u58f0\u7684\u5f71\u54cd\uff0c\u8fdb\u4e00\u6b65\u7684\uff0c\u6211\u4eec\u53ef\u4ee5\u7528\u4e3b\u6210\u5206\u5206\u6790(Principle Component Analysis)\u6765\u4f18\u5316\u8fd9\u4e2a\u8fc7\u7a0b\u3002\u3002</p> <p>Principle Component Analysis</p> <p>\u2460 Subtract off the mean for each data point.</p> <p></p> <p>\u2461 Compute the covariance matrix at each point.</p> \\[ H = \\sum_{(u,v)}w(u,v) \\begin{bmatrix}     I_x^2 &amp; I_xI_y \\\\     I_xI_y &amp; I_y^2 \\end{bmatrix} \\text{           where  }  I_x = \\frac{\\partial f}{\\partial x}, I_y = \\frac{\\partial y}{\\partial y} \\] <p>\\(w(u,v)\\) \u4e00\u822c\u662f\u9ad8\u65af\u6743\u91cd\u3002</p> <p>\u2462 Compute eigenvalues.</p> \\[ H = \\begin{bmatrix}     a &amp; b \\\\     c &amp; d \\end{bmatrix} \\;\\;\\;\\; \\lambda_{\\pm} = \\frac{1}{2}\\left(     (a+d) \\pm \\sqrt{4bc + (a-d)^2}    \\right) \\] error function approximation <p>Carnegie Mellon University \u7684 slides P18  \u5f00\u59cb\u8fd8\u63d0\u5230\u4e86\u4e0d\u540c\u4f4d\u79fb\u4e0b\u7684\u8bef\u5dee\u51fd\u6570\uff0c\u5e76\u7ed9\u51fa\u4e86\u4e09\u79cd\u60c5\u51b5\u4e0b\u8bef\u5dee\u51fd\u6570\u7684\u70ed\u529b\u56fe\u3002</p> <p></p> <p>\u2463 Components are the eigenvectors ranked by the eigenvalues.</p> <p>\u5728\u672c\u8282\u7684\u8bed\u5883\u4e0b\uff0c\u5f62\u8c61\u5730\u53d9\u8ff0\u4e3b\u6210\u5206\u5206\u6790\u5f97\u5230\u7684\u7ed3\u679c\u5c31\u662f\uff1a\u7b2c\u4e00\u4e2a\u4e3b\u6210\u5206\u6307\u5411\u65b9\u5dee\u6700\u5927\u7684\u65b9\u5411\uff0c\u7b2c\u4e8c\u4e2a\u4e3b\u6210\u5206\u6307\u5411\u5782\u76f4\u4e8e\u7b2c\u4e00\u4e2a\u4e3b\u6210\u5206\u7684\u65b9\u5411\uff0c\u5b83\u4eec\u7684\u5927\u5c0f\u5219\u4e0e\u8fd9\u4e9b\u65b9\u5dee\u6b63\u76f8\u5173\u3002</p> <p>\u5bf9\u4e8e\u4e0a\u9762\u7684\u4e09\u79cd\u60c5\u51b5\uff0c\u5b83\u4eec\u505a\u4e3b\u6210\u5206\u5206\u6790\u540e\u5f97\u5230\u7684\u7ed3\u679c\u662f\uff1a</p> <p></p> <p>\u53ef\u4ee5\u53d1\u73b0\uff0c\u7b2c\u4e09\u4e2a\u60c5\u51b5\u7684\u4e24\u4e2a\u7279\u5f81\u503c\u90fd\u5f88\u5927\u3002</p> <p>\u6211\u4eec\u901a\u8fc7\u5224\u65ad\u4e24\u4e2a\u7279\u5f81\u503c\u7684\u5927\u5c0f\u5173\u7cfb\u60c5\u51b5\u6765\u5224\u65ad\u4e00\u4e2a\u533a\u57df\u662f\u5426\u5305\u542b\u4e00\u4e2a\u89d2(corner)\u3001\u8fb9(edge)\u6216\u5e73\u9762(flat)\uff0c\u53ef\u4ee5\u5c06\u4ed6\u4eec\u653e\u5230\u4e00\u4e2a\u76f4\u65b9\u56fe\u4e2d\uff0c\u6839\u636e\u4e24\u4e2a\u7279\u5f81\u503c\u5f62\u6210\u7684\u70b9\u5bf9\u5728\u6574\u4e2a\u8c61\u9650\u4e2d\u51fa\u73b0\u7684\u4f4d\u7f6e\u6765\u5224\u65ad\u89d2\u70b9\u60c5\u51b5\uff1a</p> <p></p> <p>Figure from Carnegie Mellon University's slides. Corner detection.</p> <p>\u4e3a\u4e86\u80fd\u591f\u91cf\u5316\u5730\u8868\u8fbe\u4e0a\u9762\u8fd9\u5f20\u56fe\u7684\u5206\u7c7b\u89c4\u5219\uff0c\u6211\u4eec\u5f15\u5165\u54c8\u91cc\u65af\u7b97\u5b50(Harris operator):</p> \\[ f = \\frac{\\lambda_1\\lambda_2}{\\lambda_1+\\lambda_2} = \\frac{determinant(H)}{trace(H)} \\] <p>\u8fd9\u91cc\u7684\u4e00\u4e2a\u7279\u6027\u662f\uff0c\u5bf9\u4e8e\u4e8c\u7ef4\u77e9\u9635\u6765\u8bf4\uff0c\u6211\u4eec\u5b9e\u9645\u4e0a\u5e76\u4e0d\u9700\u8981\u6309\u7167\u4e4b\u524d\u7684\u6b65\u9aa4\uff0c\u8fdb\u884c\u4e3b\u6210\u5206\u5206\u6790\u4ee5\u540e\u518d\u5f97\u5230\uff0c\u800c\u662f\u53ef\u4ee5\u76f4\u63a5\u901a\u8fc7\u8fd9\u4e2a\u516c\u5f0f\u5f97\u5230\u3002</p> <p>\u800c\u8fd9\u4e2a \\(f\\) \u5c31\u53eb\u505a corner response\u3002</p> reminder \\[ det\\left(\\begin{bmatrix}     a &amp; b\\\\     c &amp; d \\end{bmatrix}\\right) = ad-bc \\;\\;\\;\\;\\; trace\\left(\\begin{bmatrix}     a &amp; b\\\\     c &amp; d \\end{bmatrix}\\right) = a+d \\] <p>\u5982\u4e0a\u8fd9\u5957\u65b9\u6cd5\u5c31\u662fHarris corner detector\u7684\u5b9e\u73b0\u3002</p> <p>\u5f52\u7eb3\u4e00\u4e0b\uff0c\u5176\u6b65\u9aa4\u5c31\u662f\uff1a</p> <p>Harris detector </p> <ol> <li>\u6c42\u5bfc | Compute derivatives at each pixel.</li> <li>\u534f\u65b9\u5dee\u77e9\u9635 | Compute covariance matrix \\(H\\) in a Gaussian window around each pixel.</li> <li>\u54cd\u5e94\u51fd\u6570 | Compute corner response function \\(f\\).</li> <li>\u9608\u503c\u8fc7\u6ee4 | Threshold \\(f\\).</li> <li>\u975e\u6781\u5927\u503c\u6291\u5236 | Find local maxima of response function (nonmaximum suppression).</li> </ol> <p>\u66f4\u8be6\u7ec6\u7684\u8bf4\u660e\u53ef\u4ee5\u53c2\u8003 wiki \u4e0a\u7684\u8bf4\u660e\uff1aHarris corner detector\u3002</p> <ul> <li>C.Harris and M.Stephens. \u201cA Combined Corner and Edge Detector.\u201d Proceedings of the 4th Alvey Vision Conference: pages 147\u2014151, 1988.</li> </ul> <p>\u53e6\u4e00\u4e2a\u5173\u952e\u95ee\u9898\u662f\uff0c\u901a\u8fc7\u8fd9\u4e2a\u65b9\u6cd5\u5f97\u5230\u7684\u5173\u952e\u70b9\uff0c\u5177\u6709\u5bf9\u53d8\u6362\u4e0d\u654f\u611f\u6027\u5417\uff1f</p> <p>\u5bf9\u6b64\uff0c\u7ed3\u8bba\u662f\uff1a</p> <ol> <li>Partially invariant to affine intensity change.</li> <li>Corner response is invariant w.r.t. translation.</li> <li>Corner response is invariant w.r.t. image rotation.</li> <li>Corner response is NOT invariant to scaling.</li> </ol> <p>\u5bf9\u5c3a\u5ea6\u53d8\u5316\u654f\u611f\u7684\u89e3\u51b3\u65b9\u6848</p> <p>\u9488\u5bf9\u7ed3\u8bba 4\uff0c\u7531\u4e8e Harris detector \u5bf9\u5c3a\u5ea6\u53d8\u5316\u654f\u611f\uff0c\u6240\u4ee5\u6211\u4eec\u5728\u4f7f\u7528\u8fd9\u4e2a\u65b9\u6cd5\u7684\u8fc7\u7a0b\u4e2d\u9700\u8981\u6ce8\u610f\u5c3a\u5ea6\uff0c\u5373\u7a97\u53e3\u7684\u5927\u5c0f\u9009\u5b9a\u3002</p> <p> </p> <p>\u4e00\u79cd\u8bbe\u60f3\u7684\u65b9\u6848\u662f\uff0c\u4e0d\u65ad\u5c1d\u8bd5\u4e0d\u540c\u7684 window size\uff0c\u7136\u540e\u53d6\u5f97 response \u66f2\u7ebf\uff0c\u5047\u8bbe response \u7684\u5927\u5c0f\u53ea\u4e0e scale \u6709\u5173\uff0c\u5219\u66f2\u7ebf\u90fd\u5e94\u8be5\u662f\u5355\u5cf0\u7684\uff0c\u800c\u53d6\u51fa\u8fd9\u4e2a\u5cf0\u503c\uff08\u7279\u5f81\u6700\u660e\u663e\u7684\u65f6\u5019\uff09\uff0c\u5c31\u53ef\u4ee5\u5f53\u4ed6\u4e3a\u5bf9\u5e94\u7684 scale \u4ee5\u53ca\u5bf9\u5e94\u7684 response\u3002</p> <p>\u4e0d\u8fc7\u4e00\u822c\u5b9e\u9645\u7684\u505a\u6cd5\u662f\u56fa\u5b9a\u7a97\u53e3\u5927\u5c0f\uff0c\u800c\u6539\u53d8\u56fe\u7247\u7684\u5927\u5c0f\uff0c\u518d\u5728\u5f97\u5230\u7684\u56fe\u50cf\u91d1\u5b57\u5854\u4e0a\u8fdb\u884c\u8fd9\u4e2a\u65b9\u6cd5\u7684\u8ba1\u7b97\uff0c\u5373\u5bf9\u4e0d\u540c\u5206\u8fa8\u7387\u7684\u56fe\u7247\u4e0a\u5206\u522b\u8fdb\u884c\u54c8\u91cc\u65af\u68c0\u6d4b\u3002\uff08\u76f8\u5f53\u4e8e\u7ed9\u56fe\u7247\u589e\u52a0\u4e86\u4e00\u4e2a\u7ef4\u5ea6\uff0c\u672c\u8d28\u4e0a\u548c\u4e0a\u9762\u7684\u65b9\u6cd5\u662f\u4e00\u6837\u7684\uff0c\u53ea\u4e0d\u8fc7\u7528\u4e86\u4e00\u4e2a\u66f4\u5408\u7406\u7684\u5b9e\u73b0\u89d2\u5ea6\u3002\uff09</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec05/#\u6591\u70b9\u68c0\u6d4b","title":"\u6591\u70b9\u68c0\u6d4b","text":"<p>\u9664\u4e86\u89d2\u70b9\uff0c\u6591\u70b9(blob)\u4e5f\u662f\u4e00\u4e2a\u6bd4\u8f83\u597d\u7684\u7279\u6027\uff0c\u975e\u5e38\u9002\u5408\u4f5c\u4e3a\u5173\u952e\u70b9\u3002</p> <p>\u800c\u6591\u70b9\u7684\u5bfb\u627e\u6211\u4eec\u5219\u53ef\u4ee5\u5229\u7528\u6ee4\u6ce2\u5668\u6765\u5b9e\u73b0\uff0c\u8ba9\u6211\u4eec\u56de\u987e\u7b2c\u4e09\u7ae0\u8fb9\u7f18\u63d0\u53d6\u7684\u76f8\u5173\u5185\u5bb9\uff0c\u6211\u4eec\u53ef\u4ee5\u5229\u7528\u7c7b\u4f3c\u7684\u505a\u6cd5\uff0c\u4f7f\u7528\u4e00\u4e2a\u4e2d\u95f4\u8d1f\u56db\u5468\u6b63\u7684\u6ee4\u6ce2\u5668\u6765\u63d0\u53d6\u6591\u70b9\u3002</p> <p>\u901a\u5e38\u6765\u8bf4\uff0c\u6211\u4eec\u4f7f\u7528 Gaussian \u6ee4\u6ce2\u5668\u7684 Laplacian\uff0c\u5373 Laplacian of Gaussian Filter(LoG)\uff0c\u6765\u4f5c\u4e3a\u6ee4\u6ce2\u5668\u548c\u56fe\u50cf\u8fdb\u884c\u5377\u79ef\u3002</p> <p>\ud83d\udc49 Laplacian \u7b97\u5b50</p> <p></p> <p>\u5b9e\u9645\u4e0a\u4e5f\u7b49\u6548\u4e8e\u5148\u5bf9\u56fe\u7247\u4f5c\u9ad8\u65af\u6a21\u7cca\uff08\u51cf\u5c0f\u566a\u58f0\u5f71\u54cd\uff09\uff0c\u518d\u8ba1\u7b97\u5176\u62c9\u666e\u62c9\u65af\u7b97\u5b50\uff0c\u5373\uff1a</p> \\[ \\nabla^2(f*g) = f * \\nabla^2 g \\] <p>\u5176\u4e2d\uff0cLoG \u7684 scale \u662f\u901a\u8fc7\u9ad8\u65af\u51fd\u6570\u7684 \\(\\sigma\\) \u63a7\u5236\u7684\uff0c\u4e5f\u540c\u6837\u901a\u8fc7\u50cf\u7d20\u91d1\u5b57\u5854\u6765\u5b9e\u73b0\u3002</p> <p></p> <p>\u53c8\u6216\u8005\u53ef\u4ee5\u4f7f\u7528 Difference of Gaussian(DoG)\uff0c\u5373\u5c06 Laplacian of Gaussian Filter \u66ff\u6362\u4e3a\u4e00\u4e2a\u7531\u4e24\u4e2a\u9ad8\u65af\u51fd\u6570\u505a\u5dee\u5f97\u5230\u7684 Filter\uff0c\u76f8\u5bf9\u6765\u8bf4\u6548\u7387\u66f4\u9ad8\u3002</p> <p></p> <p></p>"},{"location":"cour_note/D2QD_Intro2CV/Lec05/#\u5173\u952e\u70b9\u8868\u8fbe","title":"\u5173\u952e\u70b9\u8868\u8fbe","text":"<p>\u9009\u5b9a\u5173\u952e\u70b9\u540e\uff0c\u6211\u4eec\u9700\u8981\u8003\u8651\u5982\u4f55\u63cf\u8ff0\u548c\u8868\u8fbe\u8fd9\u4e9b\u70b9\uff0c\u4ee5\u4f7f\u5bf9\u5e94\u5bf9\u5173\u952e\u70b9\u8868\u8fbe\u76f8\u8fd1\uff0c\u800c\u4e0d\u76f8\u5173\u5bf9\u5173\u952e\u70b9\u8868\u8fbe\u76f8\u8fdc\u3002</p> <p>\u4e00\u79cd\u6734\u7d20\u7684\u601d\u60f3\u662f\u5c06\u7a97\u53e3\u5185\u7684\u50cf\u7d20\u4f5c\u4e3a\u4e00\u4e2a\u7279\u6027\u5411\u91cf(feature vector)\u8fdb\u884c\u6bd4\u8f83\uff0c\u4f46\u662f\u8fd9\u6837\u505a\u5bf9\u504f\u79fb\u7684\u8bef\u5dee\u8fc7\u4e8e\u654f\u611f\u3002\u4e5f\u5c31\u662f\u8bf4\uff0c\u4e5f\u8bb8\u4e24\u5f20\u56fe\u7247\u5f88\u50cf\uff0c\u4f46\u662f\u56e0\u4e3a\u4e00\u70b9\u4f4d\u79fb\u8bef\u5dee\uff0c\u5bfc\u81f4\u5411\u91cf\u521a\u597d\u9519\u5f00\uff0c\u5bfc\u81f4\u7ed3\u679c\u663e\u793a\u4e24\u4e2a\u70b9\u5dee\u522b\u5f88\u5927\u3002\u8fd9\u662f\u56e0\u4e3a\u8fd9\u79cd\u505a\u6cd5\u5bf9\u50cf\u7d20\u70b9\u5728\u7a97\u53e3\u4e2d\u7684\u4f4d\u7f6e\u5f88\u654f\u611f\uff0c\u4f46\u662f\u663e\u7136\u4f4d\u7f6e\u5e76\u4e0d\u662f\u5173\u952e\u70b9\u7684\u7279\u5f81\u4e4b\u6240\u5728\u3002</p> <p> </p> <p>\u53e6\u5916\u66f4\u597d\u7684\u505a\u6cd5\u662f\u5c3a\u5ea6\u4e0d\u53d8\u7684\u7279\u5f81\u53d8\u6362(Scale Invariant Feature Transform, SIFT) descriptor\uff0c\u4e0d\u518d\u4f7f\u7528\u50cf\u7d20\u503c\uff0c\u800c\u662f\u4f7f\u7528\u533a\u57df\u4e2d\u7684\u68af\u5ea6\u7684\u5206\u5e03\u4f5c\u4e3a\u4e00\u4e2a\u63cf\u8ff0\uff0c\u53ef\u4ee5\u8868\u793a\u4e3a\u4e00\u5f20 \\([0,2\\pi)\\) \u7684\uff0c\u5faa\u73af\u7684\u76f4\u65b9\u56fe\u3002\u6b64\u65f6\u5c0f\u7684\u5e73\u79fb\u548c\u7f29\u653e\u90fd\u4e0d\u4f1a\u5bf9\u5b83\u4ea7\u751f\u5f88\u5927\u5f71\u54cd\uff0c\u800c\u65cb\u8f6c\u53ea\u4f1a\u5bfc\u81f4\u76f4\u65b9\u56fe\u7684\u5faa\u73af\u5e73\u79fb\u2014\u2014\u4e0d\u8fc7\u8fd9\u79cd\u5faa\u73af\u5e73\u79fb\u662f\u5f88\u597d\u5904\u7406\u7684\uff0c\u6bd4\u5982\u6211\u4eec\u53ef\u4ee5\u9009\u4e2d\u6700\u5927\u7684\u5206\u91cf\u4f5c\u4e3a\u53c2\u8003\uff0c\u5e76\u5c06\u6574\u4e2a\u76f4\u65b9\u56fe\u5e73\u79fb\u5bf9\u9f50\u3002\u76f8\u6bd4\u76f4\u63a5\u5c06\u50cf\u7d20\u8f6c\u5316\u4e3a\u7279\u5f81\u5411\u91cf SIFT \u9c81\u68d2\u6027\u66f4\u9ad8\u3002</p> <p></p> <p>\u5b8c\u6574\u7684 SIFT \u662f\u5305\u62ec\u300c\u68c0\u6d4b\u300d\u6b65\u9aa4\u7684\u3002</p> <p>Other detectors and descriptors:</p> <ul> <li>HOG: Histogram of oriented gradients<ul> <li>Dalal &amp; Triggs, 2005 </li> </ul> </li> <li>SURF: Speeded Up Robust Features<ul> <li>Herbert Bay, Andreas Ess, Tinne Tuytelaars, Luc Van Gool, \"SURF: Speeded Up Robust Features\", Computer Vision and Image Understanding (CVIU), Vol. 110, No. 3, pp. 346--359, 2008 </li> </ul> </li> <li>FAST (corner detector)<ul> <li>Rosten. Machine Learning for High-speed Corner Detection, 2006. </li> </ul> </li> <li>ORB: an efficient alternative to SIFT or SURF<ul> <li>Ethan Rublee, Vincent Rabaud, Kurt Konolige, Gary R. Bradski: ORB: An efficient alternative to SIFT or SURF. ICCV 2011 </li> </ul> </li> <li>Fast Retina Key- point (FREAK)<ul> <li>A. Alahi, R. Ortiz, and P. Vandergheynst. FREAK: Fast Retina Keypoint. In IEEE Conference on Computer Vision and Pattern Recognition, 2012. CVPR 2012 Open Source Award Winner.</li> </ul> </li> </ul>"},{"location":"cour_note/D2QD_Intro2CV/Lec05/#\u5173\u952e\u70b9\u5339\u914d","title":"\u5173\u952e\u70b9\u5339\u914d","text":"<p>\u6240\u8c13\u7684\u5339\u914d(matching)\u5c31\u662f\u5b57\u9762\u4e0a\u7684\u5c06\u4e24\u5f20\u56fe\u4e2d\u5bf9\u5e94\u7684\u70b9\u5efa\u7acb\u8d77\u5339\u914d\u5173\u7cfb\u3002\u800c\u8bc4\u4f30\u65b9\u6cd5\u5c31\u662f\u5bfb\u627e\u300c\u8ddd\u79bb\u300d\u6700\u63a5\u8fd1\u7684\u70b9\u3002</p> <p>\u800c\u8fd9\u91cc\u7684\u300c\u8ddd\u79bb\u51fd\u6570\u300d\u662f\u7528\u6765\u8861\u91cf\u4e24\u4e2a\u5173\u952e\u70b9\u7684\u8868\u8fbe\u7684\u5dee\u5f02\u7684\u51fd\u6570\uff0c\u4e00\u822c\u4f7f\u7528 L2 distance\uff0c\u5373 \\(||f_1 - f_2||\\)\u3002</p> <p>\u91cd\u590d\u6027\u7eb9\u7406</p> <p>\u7136\u800c\u9700\u8981\u7279\u522b\u6ce8\u610f\u70b9\u4e00\u4e2a\u95ee\u9898\u662f\uff0c\u5f88\u6709\u53ef\u80fd\u51fa\u73b0\u67d0\u4e2a\u7279\u5f81\u56fe\u6848\u91cd\u590d\u51fa\u73b0\u7684\u60c5\u51b5\uff0c\u8fd9\u7c7b\u95ee\u9898\u53eb\u505a\u91cd\u590d\u6027\u7eb9\u7406\u95ee\u9898\u3002</p> <p>\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\u53ef\u80fd\u6709\u5f88\u591a\u5173\u952e\u70b9\u80fd\u548c\u8fd9\u4e2a\u5173\u952e\u70b9\u5b9e\u73b0\u5339\u914d\uff08\u8868\u8fbe\u76f8\u8fd1\uff09\uff0c\u8fd9\u4e2a\u65f6\u5019\u6211\u4eec\u5c31\u9700\u8981\u7528 Ratio score = \\(\\frac{ ||f_1 - f_2|| }{ ||f_1 - f_2'|| }\\)\uff0c\u6bd4\u8f83\u6700\u63a5\u8fd1\u7684\u4e24\u79cd\u5339\u914d\u3002</p> <p>\u5982\u679c Ratio score \u63a5\u8fd1 1\uff0c\u8bf4\u660e \\(f_1, F_2,f_2'\\) \u7684\u8868\u8fbe\u90fd\u5f88\u63a5\u8fd1\uff0c\u8fd9\u4e2a\u5339\u914d\u5e76\u4e0d\u53ef\u9760\uff0c\u53ea\u80fd\u4e22\u6389\u8fd9\u4e2a\u5173\u952e\u70b9\u3002</p> <p>\u5728\u4f20\u7edf CV \u6280\u672f\u4e2d\uff0c\u6211\u4eec\u5f88\u96be\u5904\u7406\u8fd9\u4e00\u7c7b\u91cd\u590d\u6027\u7eb9\u7406\u7684\u95ee\u9898\uff0c\u6240\u4ee5\u9047\u5230\u8fd9\u79cd\u96be\u4ee5\u5bfb\u627e\u5339\u914d\u5173\u7cfb\u7684\u60c5\u51b5\uff0c\u6211\u4eec\u53ea\u80fd\u9009\u62e9\u4e0d\u5339\u914d\u5b83\u4eec\u3002</p> <p>\u6b64\u5916\uff0c\u4e3a\u4e86\u589e\u52a0\u5339\u914d\u7684\u51c6\u786e\u6027\uff0c\u6211\u4eec\u8fd8\u6709\u4e00\u4e2a\u5224\u5b9a\u89c4\u5219\uff1a\u4e24\u70b9\u76f8\u4e92\u6700\u76f8\u4f3c\uff0c\u5219\u8be5\u5339\u914d\u5341\u5206\u53ef\u4fe1\u3002\uff08\u5728 I2 \u4e2d\u4f60\u6700\u50cf\u6211\uff0c\u5728 I1 \u4e2d\u6211\u6700\u50cf\u4f60\uff09</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec05/#\u8fd0\u52a8\u4f30\u8ba1","title":"\u8fd0\u52a8\u4f30\u8ba1","text":"<p>\u5148\u524d\uff0c\u6211\u4eec\u7740\u773c\u4e8e\u5355\u5f20\u56fe\u7247\uff0c\u6216\u8005\u8bf4\u51e0\u5f20\u56fe\u7247\uff0c\u4ecd\u7136\u662f\u4ee5\u4e00\u4e2a\u9759\u6001\u7684\u89c6\u89d2\u6765\u89c2\u5bdf\u56fe\u50cf\u3002</p> <p>\u800c\u5f53\u6211\u4eec\u628a\u7814\u7a76\u5bf9\u8c61\u4ece\u56fe\u7247\u6539\u53d8\u4e3a\u89c6\u9891\u6216\u8005\u8bf4\u56fe\u7247\u5e8f\u5217\u7684\u65f6\u5019\uff0c\u56fe\u7247\u5c31\u88ab\u8d4b\u4e88\u4e86\u8fd0\u52a8\u7684\u5c5e\u6027\uff0c\u800c\u8fd9\u5c31\u5f15\u51fa\u4e86\u8fd0\u52a8\u4f30\u8ba1(motion estimation)\u95ee\u9898\u3002</p> <p>\u9996\u5148\uff0c\u8fd0\u52a8\u6309\u7167\u6210\u56e0\u4e3b\u8981\u53ef\u4ee5\u5206\u4e3a\u76f8\u673a\u8fd0\u52a8\u548c\u573a\u666f\u8fd0\u52a8\u4e24\u4e2a\u7ef4\u5ea6\u3002</p> \u76f8\u673a\u8fd0\u52a8 \u573a\u666f\u8fd0\u52a8 eg (\u5149\u7ebf\u53d8\u5316\u7b49\u5f71\u54cd\u89c6\u9891\u6bcf\u4e00\u5e27\u7684\u5185\u5bb9\u5b58\u5728\u5149\u5f71\u5dee\u5f02\u7b49) \u9759\u666f\u201c\u8fd0\u955c\u201d \u76d1\u63a7\u5f55\u50cf \u4f53\u80b2\u8d5b\u4e8b\u955c\u5934\u8ddf\u8e2a <p>\u800c\u9488\u5bf9\u8fd0\u52a8\u4f30\u8ba1\u95ee\u9898\uff0c\u6709\u8fd9\u4e48\u51e0\u79cd\u89e3\u51b3\u7684\u89c6\u89d2\uff1a</p> <ul> <li>\u7279\u5f81\u8ddf\u8e2a\uff0c\u5728\u6bcf\u4e00\u5e27\u4e2d\u8fdb\u884c\u5173\u952e\u70b9\u5339\u914d\uff0c\u4ee5\u8ddf\u8e2a\u7279\u5b9a\u5173\u952e\u70b9\u7684\u53d8\u5316\u2014\u2014\u8fd9\u4e00\u7c7b\u65b9\u6cd5\u5f97\u5230\u7684\u7ed3\u679c\u76f8\u5bf9\u7a00\u758f\uff0c\u6bd5\u7adf\u5173\u952e\u70b9\u603b\u662f\u5c11\u7684\uff1b</li> <li>\u5149\u6d41(optical flow)\u6280\u672f\uff0c\u901a\u8fc7\u5bf9\u76f8\u90bb\u5e27\u7684\u50cf\u7d20\u8fdb\u884c\u5339\u914d\uff0c\u4ee5\u8ddf\u8e2a\u50cf\u7d20\u7684\u53d8\u5316\u2014\u2014\u8fd9\u4e00\u7c7b\u65b9\u6cd5\u5f97\u5230\u7684\u7ed3\u679c\u76f8\u5bf9\u5bc6\u96c6\uff1b</li> </ul> <p>\u800c\u4e24\u4e2a\u89c6\u89d2\u90fd\u53ef\u4ee5\u4f7f\u7528 Lucas-Kanade method \u89e3\u51b3\u3002</p> <p>\u9996\u5148\uff0c\u6211\u4eec\u9700\u8981\u7ed9\u8fd0\u52a8\u4f30\u8ba1(motion estimation)\u95ee\u9898\u4e00\u4e2a\u66f4\u660e\u786e\u7684\u5b9a\u4e49\uff1a</p> <p>motion estimation</p> <p>Wiki: https://en.wikipedia.org/wiki/Motion_estimation</p> <p>\u8fd0\u52a8\u4f30\u8ba1\u662f\u6307\u4ece\u4e00\u4e2a 2D \u56fe\u50cf\u5230\u53e6\u4e00\u4e2a 2D \u56fe\u50cf\u7684\u8f6c\u6362\u4e2d\u786e\u5b9a\u63cf\u8ff0\u8fd0\u52a8\u7684\u8fd0\u52a8\u77e2\u91cf\u7684\u8fc7\u7a0b\uff0c\u901a\u5e38\u662f\u4ece\u89c6\u9891\u5e8f\u5217\u4e2d\u76f8\u90bb\u7684\u5e27\u4e2d\u63d0\u53d6\u3002</p> <p>\u5047\u8bbe\u6211\u4eec\u6709\u5339\u914d\u70b9 \\(P(x,y,t)\\) \u548c \\(P(x+u, y+v, t+1)\\)\uff0c\u5219\u8fd0\u52a8\u4f30\u8ba1\u5219\u662f\u6c42\u89e3 \\((u,v)\\) \u7684\u8fc7\u7a0b\u3002</p> <p>\u4e0d\u540c\u4e8e\u5173\u952e\u70b9\u7684\u5339\u914d\uff0c\u8fd0\u52a8\u4f30\u8ba1\u66f4\u4fa7\u91cd\u4e8e\u5bf9\u5173\u952e\u70b9\u7684\u65f6\u5e8f\u5173\u7cfb\u7684\u5339\u914d\u4e0e\u63cf\u8ff0\u3002</p> <p>\u800c\u6211\u4eec\u4e4b\u540e\u7684\u63a2\u8ba8\uff0c\u90fd\u9700\u8981\u57fa\u4e8e LK \u5047\u8bbe\u5c55\u5f00\uff1a</p> <p>Key Asumptions of Lucas-Kanade</p> <ol> <li>[Small motion] \u76f8\u90bb\u5e27\uff0c\u5339\u914d\u70b9\u7684\u8fd0\u52a8\u8ddd\u79bb\u5c0f\uff1b</li> <li>[Brightness constancy] \u76f8\u90bb\u5e27\uff0c\u70b9\u7684\u4eae\u5ea6\u503e\u5411\u4e8e\u4e0d\u53d8\uff0c\u5373\u53d8\u5316\u5fae\u5c0f\uff1b</li> <li>[Spatial coherence] \u76f8\u90bb\u7684\u70b9\u503e\u5411\u4e8e\u8fd0\u52a8\u76f8\u4f3c\uff1b</li> </ol> <p>\u63a5\u4e0b\u6765\uff0c\u57fa\u4e8e LK \u5047\u8bbe\uff0c\u6211\u4eec\u6765\u7814\u7a76\u8fd0\u52a8\u4f30\u8ba1\u95ee\u9898\u7684\u6c42\u89e3\u3002</p> <p>\u9996\u5148\uff0c\u6211\u4eec\u5c06\u7b2c\u4e8c\u6761\u5047\u8bbe\u8868\u8fbe\u5f0f\u5316\uff0c\u5373\u6709\uff1a</p> \\[ I(x,y,t) = I(x+u, y+v, t+1) \\] <p>\u4e3a\u4e86\u6c42\u89e3 \\(u\\) \u548c \\(v\\)\uff0cLK Method \u5bf9\u5176\u4f5c\u6cf0\u52d2\u5c55\u5f00\uff1a</p> \\[ I(x+u,y+v,t+1) \\approx I(x,y,t) + I_x\\cdot u + I_y \\cdot v + I_t \\] <p>\u79fb\u9879\uff1a</p> \\[ I(x+u,y+v,t+1) - I(x,y,t) = I_x\\cdot u + I_y \\cdot v + I_t \\] <p>\u6839\u636e\u5047\u8bbe 2\uff0c\u5f97\u5230\uff1a</p> \\[ I_x\\cdot u + I_y \\cdot v + I_t \\approx 0 \\] <p>\u5373\uff1a</p> \\[ \\nabla I \\cdot \\begin{bmatrix}     u &amp; v \\end{bmatrix}^T + I_t = 0 \\] <p>\u4e8e\u662f\u6211\u4eec\u5f97\u5230\u4e86\u5173\u4e8e \\(u\\) \u548c \\(v\\) \u7684\u4e00\u4e2a\u8f83\u7b80\u5355\u7684\u7b49\u5f0f\u3002</p> <p>\u7136\u800c\u6211\u4eec\u53ea\u6709\u4e00\u4e2a\u7b49\u5f0f\uff0c\u4f46\u9700\u8981\u6c42\u89e3\u7684\u672a\u77e5\u5143 \\(u\\) \u548c \\(v\\) \u6709\u4e24\u4e2a\u3002</p> <p>\u4e8e\u662f\u6211\u4eec\u5f15\u5165\u4e86\u5047\u8bbe 3\uff0c\u5373\u76f8\u90bb\u7684\u70b9\u503e\u5411\u4e8e\u8fd0\u52a8\u76f8\u4f3c\u3002</p> <p>\u4e8e\u662f\u6211\u4eec\u53ef\u4ee5\u628a\u7a97\u53e3\u5185\u7684\u50cf\u7d20\u90fd\u5e26\u5165\u4e0a\u9762\u90a3\u4e2a\u7b49\u5f0f\uff0c\u5c1d\u8bd5\u6765\u6c42\u89e3\uff08\u5927\u81f4\u90fd\u76f8\u4f3c\u7684\uff09\\(u\\) \u548c \\(v\\)\u3002\u6b64\u65f6\u6211\u4eec\u7684\u65b9\u7a0b\u6570\u91cf\u5c31\u975e\u5e38\u5145\u88d5\u4e86\u3002\u6b64\u65f6\u6211\u4eec\u53ef\u4ee5\u5c06\u95ee\u9898\u8f6c\u5316\u4e3a\u4f18\u5316\u95ee\u9898\u3002</p> \\[ Ad=b \\rightarrow \\min\\limits_d ||Ad-b||^2 \\] <p>Least squares solution(\u524d\u9762\u63d0\u5230\u8fc7\u7684\u6700\u5c0f\u4e8c\u4e58\u6cd5\u7684\u8fd1\u4f3c\u89e3) for d given by \\((A^TA)d = A^Tb\\).</p> <p>\u800c\u8fd9\u4e2a\u89e3\u662f\u5426\u5b58\u5728\u7684\u6761\u4ef6\u662f\uff1a</p> \\[ \\underbrace{     \\begin{bmatrix}         \\sum I_x I_x &amp; \\sum \\sum I_x I_x \\\\         \\sum I_x I_y &amp; \\sum I_y I_y     \\end{bmatrix} }_{A^T A} \\begin{bmatrix}     u \\\\     v \\end{bmatrix} = \\underbrace{     \\begin{bmatrix}         \\sum I_x I_t \\\\         \\sum I_y I_t     \\end{bmatrix} }_{A^T b} \\] <p>\u5728\u8be5\u5f0f\u4e2d\uff0c\\(A^TA\\) \u9700\u8981\u662f\u53ef\u9006\u7684\uff0c\u5e76\u4e14\u5b83\u7684\u4e24\u4e2a\u7279\u5f81\u503c\u90fd\u4e0d\u80fd\u592a\u5c0f\u3002\u4e5f\u5c31\u8be5\u70b9\u80fd\u591f\u88ab Harris corner detector \u68c0\u6d4b\u5230\u70b9\u89d2\u70b9\uff01</p> <p>\u56e0\u6b64\uff0c\u5018\u82e5\u4f7f\u7528 LK \u65b9\u6cd5\uff0c\u6211\u4eec\u9700\u8981\u4fdd\u8bc1 \\(A^TA\\) \u53ef\u9006\uff0c\u4e14\u56fe\u50cf\u4e2d\u4e0d\u80fd\u6709\u592a\u591a\u566a\u70b9\u3002</p> <p>\u6b64\u5916\uff0c\u5173\u4e8e\u5bf9\u5047\u8bbe 1 \u7684\u7ea6\u675f\uff0c\u539f\u5219\u4e0a\u4e24\u5e27\u4e4b\u95f4\u7684\u8fd0\u52a8\u5dee\u8ddd\u5e94\u8be5\u5c0f\u4e8e\u4e00\u4e2a\u50cf\u7d20\uff0c\u7136\u800c\u8fd9\u4e2a\u6761\u4ef6\u975e\u5e38\u82db\u523b\u3002\u6240\u4ee5\u6211\u4eec\u7684\u53ef\u4ee5\u5148\u5bf9\u56fe\u7247\u8fdb\u884c\u6a21\u7cca/\u7f29\u5c0f\u5904\u7406\uff0c\u50cf\u7d20\u8db3\u591f\u201c\u5927\u201d\u4e4b\u540e\u5c31\u53ef\u4ee5\u6ee1\u8db3\u8fd9\u4e2a\u5047\u8bbe 1\u3002\u7136\u800c\u5728\u8fd9\u4e2a\u8fc7\u7a0b\u4e2d\u4f1a\u4e22\u5931\u5f88\u591a\u4fe1\u606f\uff0c\u6240\u4ee5\u53ea\u6839\u636e\u8fd9\u4e2a\u6761\u4ef6\u6765\u8ba1\u7b97\u4e5f\u4e0d\u884c\uff0c\u6240\u4ee5\u6211\u4eec\u53ef\u4ee5\u5728\u50cf\u7d20\u91d1\u5b57\u5854\u4e0a\u8fdb\u884c\u9010\u5c42\u6b21\u4f30\u8ba1\uff0c\u518d\u4e0d\u65ad\u7ec6\u5316\u7684\u505a\u6cd5\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec06/","title":"Lecture 6 | Image Alignment and Stitching","text":"<p> \u7ea6 1320 \u4e2a\u5b57  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 4 \u5206\u949f</p> <p>\u6ce8\u610f</p> <p>\u672c\u6587\u5c1a\u672a\u5b8c\u5168\u6574\u7406\u597d\uff01</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec06/#\u56fe\u50cf\u62fc\u63a5","title":"\u56fe\u50cf\u62fc\u63a5","text":"<p>\u6240\u8c13\u7684\u56fe\u50cf\u62fc\u63a5\uff0c\u6a21\u5f0f\u4e0a\u5c31\u662f\u5bfb\u627e\u82e5\u5e72\u56fe\u7247\u7684\u5171\u540c\u90e8\u5206\uff0c\u5e76\u5c06\u753b\u9762\u5185\u5bb9\u8fdb\u884c\u62fc\u63a5\u548c\u5ef6\u5c55\uff0c\u5176\u672c\u8d28\u662f\u6c42\u89e3\u56fe\u50cf\u4e4b\u95f4\u7684\u53d8\u6362\u5173\u7cfb\uff0c\u4e5f\u5c31\u662f\u4e00\u4e2a\u6a21\u5f0f\u62df\u5408\u7684\u95ee\u9898\u3002\u5e94\u7528\u4e0a\u6bd4\u5982 \u5168\u666f\u56fe(panorama) \u6216 360\u00b0VR\u7b49\u3002</p> <p>\u6295\u5f71\u5e73\u9762/\u66f2\u9762</p> <p>\u5e38\u89c1\u7684\u56fe\u50cf\u62fc\u63a5\u6709\u6bd4\u5982\u5c06\u5e73\u884c\u7684\u666f\u8c61\u5728\u5e73\u9762\u4e0a\u6295\u5f71\u548c\u62fc\u63a5\uff0c\u4e5f\u6709\u5c06\u6c34\u5e73\u73af\u7ed5\u7684\u7684\u666f\u8c61\u5728\u67f1\u9762\u4e0a\u6295\u5f71\u548c\u62fc\u63a5\u7b49\u3002\u533a\u522b\u5728\u4e8e\u9700\u8981\u5bf9\u56fe\u50cf\u5185\u5bb9\u7684\u8868\u8fbe\u8fdb\u884c\u4e00\u4e2a\u201c\u53d8\u6362\u201d\uff0c\u4f46\u5b9e\u9645\u53d8\u5316\u65b9\u6cd5\u4e0d\u4f1a\u6709\u5927\u533a\u522b\uff0c\u4ecd\u7136\u662f\u5148\u68c0\u6d4b\u76f8\u540c\u90e8\u5206\u518d\u6c42\u89e3\u53d8\u6362\u5173\u7cfb\u3002</p> <p>\u5728\u8fd9\u91cc\u9700\u8981\u505a\u7684\u4e00\u4e2a\u7279\u522b\u8bf4\u660e\u662f\uff0c\u5728\u4e4b\u540e\u8be6\u7ec6\u4ecb\u7ecd\u201c\u53d8\u6362\u201d\u7684\u8fc7\u7a0b\u4e2d\uff0c\u6211\u4eec\u4f1a\u89e3\u91ca\u4e3a\u4ec0\u4e48\u624b\u673a\u62cd\u6444\u5e7f\u89d2\u7167\u7247\u65f6\uff0c\u4f1a\u8981\u6c42\u62cd\u6444\u8005\u53ea\u505a\u89c6\u89d2\u53d8\u5316\u800c\u4e0d\u505a\u4f4d\u79fb\u3002</p> <p>\u8fc7\u7a0b\u6982\u8ff0</p> <p>\u6211\u4eec\u8fd9\u91cc\u8003\u8651\u7684\u56fe\u50cf\u62fc\u63a5\u95ee\u9898\uff0c\u66f4\u591a\u6307\u7684\u662f\u4e24\u5f20\u56fe\u7247\u62e5\u6709\u5171\u540c\u523b\u753b\u76ee\u6807\u7684\u60c5\u51b5\u4e0b\u8fdb\u884c\u62fc\u63a5\uff0c\u5373\u4e24\u5f20\u7167\u7247\u5b58\u5728\u4ea4\u96c6\u3002</p> <p>\u9996\u5148\uff0c\u6211\u4eec\u901a\u8fc7\u56fe\u50cf\u7279\u5f81\u5339\u914d\u76f8\u5173\u6280\u672f\uff0c\u627e\u5230\u8fd9\u4e24\u5f20\u56fe\u7247\u7684\u5171\u540c\u90e8\u5206\uff0c\u63a5\u4e0b\u6765\u901a\u8fc7\u8f6c\u5316\u4e3a\u4f18\u5316\u95ee\u9898\uff0c\u6c42\u89e3\u8fd9\u4e9b\u5171\u540c\u90e8\u5206\u5982\u4f55\u5b9e\u73b0\u8f6c\u5316\uff08\u76f8\u5f53\u4e8e\u5728\u505a\u201c\u5bf9\u9f50\u201d\uff09\u3002</p> <ul> <li>\u56fe\u50cf\u62fc\u63a5\u7684\u4e24\u4e2a\u65b9\u9762\uff1a<ul> <li>\u5c06\u4e24\u5f20\u56fe\u7247\u5bf9\u9f50\uff0c\u627e\u5230\u91cd\u5408\u7684\u90e8\u5206 image warping (change shape of image)<ul> <li>\u4e00\u822c\u6765\u8bf4\u662f \u53c2\u6570\u5316parametric \u6216\u8005\u8bf4 \u5168\u5c40global \u7684 warping\uff0c\u7531\u4e00\u4e2a\u542b\u6709\u53c2\u6570\u7684\u65b9\u7a0b\u51b3\u5b9a\uff1a\\(p' = T(p)\\)\uff1b<ul> <li></li> <li>translation / affine / projective</li> <li> </li> <li>\u9664\u4e86\u80fd\u591f\u7528\u4eff\u5c04\u53d8\u6362\u63cf\u8ff0\u7684\u53d8\u6362\uff0c\u8fd8\u6709\u6295\u5f71\u53d8\u6362(Projective Transformation)\uff0c\u6216\u8005\u8bf4\u5355\u5e94\u53d8\u6362(Homography)\uff0c\u5b83\u65e0\u6cd5\u7528\u4eff\u5c04\u53d8\u6362\u63cf\u8ff0\u3002<ul> <li>\u5355\u5e94\u77e9\u9635\u5728\u5e73\u9762\u56fe\u5f62\u4e2d\u4e5f\u662f\u4e00\u4e2a 3*3 \u7684\u77e9\u9635\uff0c\u4f46\u662f\u6ca1\u6709\u5fc5\u987b\u4e3a 0 \u7684\u5143\u7d20\u7ea6\u675f\uff08\u533a\u522b\u4e8e\u9f50\u6b21\u5750\u6807\uff09\uff1a</li> <li>\\(\\begin{bmatrix}x'_i \\\\ y'_i \\\\ 1 \\end{bmatrix} \\cong \\begin{bmatrix} h_{00} &amp; h_{01} &amp; h_{02} \\\\ h_{10} &amp; h_{11} &amp; h_{12} \\\\ h_{20} &amp; h_{21} &amp; h_{22} \\end{bmatrix}\\begin{bmatrix}x_i \\\\ y_i \\\\ 1\\end{bmatrix}\\)\uff0c\u7531\u4e8e \\(h_{22}\\) \u5b9e\u9645\u4e0a\u53ef\u4ee5\u662f\u4efb\u610f\u5b9e\u6570\uff0c\u6240\u4ee5\u5b9e\u9645\u4e0a\u7684\u81ea\u7531\u5ea6\u4e3a 8\uff0c\u6240\u4ee5\u4e3a\u4e86\u8ba9\u89e3\u5177\u6709\u552f\u4e00\u6027\uff0c\u6211\u4eec\u7ea6\u675f \\(||\\begin{bmatrix}h_{00} &amp; h_{01} &amp; ... &amp; h_{21} &amp; h_{22}\\end{bmatrix}||_2 = 1\\)\uff0c\u8fd9\u6837\u5c31\u80fd\u4fdd\u8bc1\u81ea\u7531\u5ea6\u4e3a 8 \u4e14\u5bf9\u5e94\u7684\u89e3\u552f\u4e00\uff1b</li> <li>\u5b9e\u9645\u4e0a\uff0c\u53ef\u4ee5\u7406\u89e3\u4e3a\u5b83\u662f\u5728\u4e09\u7ef4\u7a7a\u95f4\u4e0b\uff0c\u76f8\u673a\u4e0d\u5e73\u79fb\u53ea\u65cb\u8f6c\u7684\u4e00\u4e2a\u89c6\u89d2\u53d8\u5316\uff0c\u5373 change projection plane\uff1b<ul> <li>\u5982\u679c\u76f8\u673a\u5e73\u79fb\u4e14\u65cb\u8f6c\uff0c\u90a3\u60c5\u51b5\u975e\u5e38\u590d\u6742\uff0c\u751a\u81f3\u4e0d\u4e00\u5b9a\u5177\u6709\u70b9\u70b9\u5bf9\u5e94\u5173\u7cfb\uff1b</li> <li>\u4f46\u662f\u6709\u4e00\u4e2a\u7279\u6b8a\u60c5\u51b5\uff0c\u5c31\u662f\u6211\u89c2\u6d4b\u5230\u573a\u666f\u672c\u8eab\u5c31\u662f\u5e73\u9762\uff08\u6216\u8005\u7279\u522b\u8fdc\u7684\u666f\u89c2\uff09\uff0c\u573a\u666f\u4e0d\u5b58\u5728\u906e\u6321\uff0c\u8fd9\u4e2a\u65f6\u5019\u4e5f\u53ef\u4ee5\u4f7f\u7528 homography\uff1b</li> <li>\u5982\u4e0a\u5c31\u662f\u4e3a\u4ec0\u4e48\u624b\u673a\u62cd\u6444\u5168\u666f\u7167\u7247\u65f6\u8981\u6c42\u4e0d\u8981\u79fb\u52a8\u53ea\u8f6c\u52a8\u76f8\u673a</li> </ul> </li> <li>\u5982\u4e0a\u53d8\u6362\u90fd\u6709\u9006\u53d8\u6362\uff1b</li> <li>\u5b9e\u9645\u64cd\u4f5c\u8fc7\u7a0b\u4e2d\uff0c\u6211\u4eec\u4f7f\u7528\u9006\u53d8\u6362\uff08\u6b63\u5411\u53d8\u6362\u7684\u8bdd\u50cf\u7d20\u4f4d\u7f6e\u53ef\u80fd\u4e0d\u5bf9\uff09\uff0c\u5373\u5bf9\u4e8e\u6bcf\u4e00\u4e2a\u9700\u8981\u627e\u7684\u50cf\u7d20\u70b9\uff0c\u6211\u4eec\u53bb\u627e\u53d8\u6362\u524d\u7684\u5750\u6807\uff0c\u5e76\u6839\u636e\u8fd9\u4e2a\u5750\u6807\u6765\u8fdb\u884c\u63d2\u503c\uff0c\u4e00\u822c\u4f7f\u7528\u53cc\u7ebf\u6027\u63d2\u503c\uff1b</li> </ul> </li> </ul> </li> </ul> </li> <li>\u8ba1\u7b97\u5982\u4f55\u5bf9\u9f50\u5408\u5e76\u8fd9\u4e24\u4e2a\u56fe\u7247 image stitching<ul> <li>\u5373\u7ed9\u5b9a\u4e24\u5f20\u56fe\u50cf\uff0c\u5982\u4f55\u8ba1\u7b97\u4e0a\u4e00\u6b65\u63d0\u5230\u7684 T\uff1b</li> <li>\u6b65\u9aa4\uff1a<ol> <li>image matching(each match gives an equation);</li> <li>solve T from the obtained matches;</li> </ol> </li> <li>\u4f8b\u5982\uff0c\u5bf9\u4e8e afine transformations\uff0c\u6709\u516d\u4e2a\u81ea\u7531\u5ea6\uff0c\u9700\u8981\u516d\u4e2a\u65b9\u7a0b\u4e09\u5bf9\u5339\u914d\u5173\u7cfb\uff08\u6bcf\u4e00\u5bf9\u5339\u914d\u5173\u7cfb\u63d0\u4f9b\u4e24\u4e2a\u65b9\u7a0b\uff0c\u5206\u522b\u662f\u5173\u4e8e x \u548c\u5173\u4e8e y \u7684\uff09\uff1b<ul> <li>\u5b83\u4eec\u5177\u6709\u77e9\u9635\u5f62\u5f0f\uff1a \uff08\u6284\u9ea6\u54e5\u7b14\u8bb0\uff09</li> <li>\u5b9e\u9645\u8fc7\u7a0b\u4e2d\u6211\u4eec\u5e76\u4e0d\u4f1a\u76f4\u63a5\u53bb\u201c\u89e3\u65b9\u7a0b\u201d\uff0c\u800c\u662f\u53bb\u505a\u4e00\u4e2a\u201c\u5c3d\u91cf\u76f8\u7b49\u201d\u7684\u4e00\u4e2a\u6700\u5c0f\u4e8c\u4e58\u95ee\u9898\uff0c\u8fd9\u4e2a\u95ee\u9898\u7684\u89e3\u6709\u4e00\u4e2a\u89e3\u6790\u89e3\uff1a\\(t = (A^TA)^{-1}A^Tb\\)\uff1b</li> </ul> </li> <li>\u518d\u4f8b\u5982\u5bf9\u4e8e homography\uff0c\u6709\u516b\u4e2a\u81ea\u7531\u5ea6\u5c31\u9700\u8981\u516b\u4e2a\u65b9\u7a0b\u56db\u5bf9\u5339\u914d\u5173\u7cfb\uff1b</li> <li>\u5bf9\u4e8e\u4f18\u5316\u95ee\u9898\uff1a\\(\\mathop{min}_h ||Ah||^2 \\;\\;\\; s.t. ||h|| = 1\\)\uff0c\u5176\u89e3 \\(\\hat{h}\\) \u4e3a \\(A_TA\\) \u7279\u5f81\u503c\u6700\u5c0f\u7684\u7279\u5f81\u5411\u91cf\uff1b</li> <li>\u6b64\u5916\uff0c\u8fd8\u8981\u5173\u6ce8\u5982\u4f55\u5904\u7406 outliers\uff1a\u4f7f\u7528 RANSAC\uff1b <ul> <li>\u5373\uff0c\u5229\u7528\u5c0f\u90e8\u5206\u5339\u914d\u5173\u7cfb\u8ba1\u7b97\u51fa T\uff0c\u7136\u540e\u62ff\u53bb\u68c0\u9a8c\u5176\u4ed6\u7684\u5339\u914d\u5173\u7cfb\uff1b </li> </ul> </li> </ul> </li> <li>\u7136\u800c\u4e0a\u9762\u8fd9\u4e9b\u505a\u6cd5\u90fd\u662f\u5c06\u56fe\u7247\u6295\u5f71\u5230\u4e00\u4e2a\u5e73\u9762\u4e0a\uff0c\u4e5f\u5c31\u662f\u8bf4\u5c06\u56fe\u50cf\u62fc\u63a5\u4e3a\u4e00\u4e2a\u66f4\u5927\u90fd\u5e73\u9762\u56fe\u50cf\uff1b\u4f46\u662f\u5728\u5168\u666f\u8fd9\u79cd\u6848\u4f8b\u4e2d\uff0c\u8fd9\u4e48\u505a\u4f1a\u8ba9\u8fb9\u7f18\u62c9\u4f38\u8d8a\u6765\u6108\u660e\u663e\uff08\u8fd1\u5927\u8fdc\u5c0f\uff09\uff0c\u6240\u4ee5\u5bf9\u4e8e\u8fd9\u79cd\u6848\u4f8b\uff0c\u6211\u4eec\u8981\u5148\u5c06\u5b83\u6295\u5c04\u5230\u67f1\u9762\u4e0a\uff0c\u7136\u540e\u5728\u67f1\u9762\u4e0a\u8fdb\u884c\u62fc\u63a5\uff0cTODO:\u516c\u5f0f\u8bb0\u5f97\u6284\u4e0a\u6765\uff1b</li> <li>\u8fd8\u6709\u4e00\u4e2a\u95ee\u9898\u662f\u8bef\u5dee\u7d2f\u79ef\uff0c\u5bfc\u81f4\u6f02\u79fb(drift)\uff0c\u89e3\u51b3\u529e\u6cd5\u5c31\u662f\u6700\u540e\u4e00\u5f20\u548c\u7b2c\u4e00\u5f20\u4e4b\u95f4\u4e5f\u8ba1\u7b97\u4e00\u6b21 T \u6765\u8fdb\u884c\u7ea6\u675f\uff0c\u8fd9\u79cd\u60f3\u6cd5\u53eb\u56de\u8def\u95ed\u5408\uff1b </li> </ul> </li> </ul> <p>\u62fc\u63a5\u8fc7\u7a0b\u4e2d\u4f1a\u51fa\u73b0\u8fb9\u754c\uff0c\u800c\u8fd9\u4e2a\u8fb9\u754c\u6211\u4eec\u662f\u53ef\u4ee5\u4eba\u4e3a\u9009\u62e9\u7684\uff0c\u6bd4\u5982\u6211\u4eec\u53ef\u4ee5\u9009\u62e9\u8ba9\u5b83\u5dee\u8ddd\u6700\u5c0f\u7684\u5730\u65b9\u6210\u4e3a\u8fb9\u754c\uff0c\u53c8\u6216\u8005\u662f\u4e00\u4e2a\u56fe\u5272\u95ee\u9898\uff1b</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec07/","title":"Lecture 7 | Structure From Motion","text":"<p> \u7ea6 8658 \u4e2a\u5b57  14 \u884c\u4ee3\u7801  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 29 \u5206\u949f</p> <p>\u524d\u8a00</p> <p>\u4e2a\u4eba\u611f\u89c9\u8fd9\u4e00\u7ae0\u7684\u5185\u5bb9\u867d\u7136\u8109\u7edc\u6e05\u6670\uff0c\u4f46\u662f\u9700\u8981\u4e0d\u65ad\u5f15\u5165\u65b0\u7684\u5185\u5bb9\uff0c\u5982\u679c\u76f4\u63a5\u91c7\u7528\u201c\u7528\u5230\u4ec0\u4e48\u8bb2\u4ec0\u4e48\u201d\u7684\u987a\u5e8f\u9610\u8ff0\uff0c\u53ef\u80fd\u4f1a\u6709\u4e9b\u6742\u4e71\uff0c\u4e0d\u65b9\u4fbf\u77e5\u8bc6\u7d22\u5f15\u548c\u590d\u4e60\uff0c\u6240\u4ee5\u6211\u5927\u81f4\u6309\u7167\u62d3\u6251\u6392\u5e8f\u7684\u987a\u5e8f\u6392\u5217\u5185\u5bb9\uff0c\u503e\u5411\u4e8e\u5b8c\u6574\u5730\u4ecb\u7ecd\u4e00\u4e0b\u524d\u7f6e\uff0c\u518d\u5f15\u5165\u4e4b\u540e\u7684\u5185\u5bb9\u5e76\u9636\u6bb5\u6027\u5c0f\u7ed3\uff0c\u53ef\u80fd\u770b\u8d77\u6765\u6bd4\u8f83\u5510\u7a81\uff0c\u4f46\u662f\u5927\u6982\u5bf9\u56de\u5934\u67e5\u77e5\u8bc6\u70b9\u6bd4\u8f83\u65b9\u4fbf\u3002</p> <p>\u8bf4\u660e</p> <p>\u672c\u6587\u4e2d\u63d0\u5230\u7684\u6240\u6709\u7684\u300c\u6210\u50cf\u5e73\u9762\u300d\u6307\u7684\u90fd\u662f\u6211\u4eec\u7684\u7b80\u5316\u51e0\u4f55\u6a21\u578b\u4e2d\u7684\u865a\u62df\u6210\u50cf\u5e73\u9762\uff0c\u5e76\u4e0d\u662f\u7269\u7406\u610f\u4e49\u4e0a\u5c0f\u5b54\u6210\u50cf\u6240\u5728\u7684\u90a3\u4e2a\u6210\u53cd\u5411\u5012\u7acb\u50cf\u7684\u5e73\u9762\uff01</p> <p>\u8fd0\u52a8\u63a8\u65ad\u7ed3\u6784(Structure from Motion, SfM)\u7528\u4e8e\u4f30\u8ba1\u4e8c\u7ef4\u56fe\u50cf\u4e2d\u7684\u4e09\u7ef4\u7ed3\u6784\uff0c\u901a\u8fc7\u76f8\u673a\u8fd0\u52a8\uff08\u5e73\u79fb\u3001\u65cb\u8f6c\uff09\u5f15\u8d77\u7684\u753b\u9762\u53d8\u5316\u6765\u8ba1\u7b97\u5176\u53cd\u5e94\u7684 3D \u7ed3\u6784\u3002</p> <p>\u5728\u673a\u5668\u4eba\u9886\u57df\uff0c\u4e00\u4e2a\u76f8\u5173\u7684\u9886\u57df\u662f \u540c\u65f6\u5b9a\u4f4d\u4e0e\u5730\u56fe\u6784\u5efa(Simultaneous Localization and Mapping, SLAM)\u3002</p> <p>\u4e09\u4e2a\u5173\u952e\u95ee\u9898</p> <ol> <li>\u5982\u4f55\u63cf\u8ff0\u76f8\u673a\u7684\u6295\u5f71\u884c\u4e3a\uff0c\u4e5f\u5c31\u662f\u76f8\u673a\u6a21\u578b\u7684\u76f8\u5173\u5185\u5bb9\uff0c\u672c\u5c0f\u7ed3\u6307\u900f\u89c6\u6a21\u578b\uff1b</li> <li>\u5982\u4f55\u901a\u8fc7\u56fe\u50cf\u6c42\u89e3\u76f8\u673a\u53c2\u6570\uff0c\u8fd9\u4e2a\u8fc7\u7a0b\u88ab\u79f0\u4e3a\u76f8\u673a\u6807\u5b9a(Camera Calibration)\uff0c\u4ee5\u53ca\u5982\u4f55\u6c42\u89e3\u76f8\u673a\u7684\u7a7a\u95f4\u4f4d\u7f6e\u4e0e\u671d\u5411\uff0c\u8fd9\u4e2a\u8fc7\u7a0b\u88ab\u79f0\u4e3a\u4f4d\u7f6e\u4f30\u8ba1(Pose Estimation)\uff1b</li> <li>\u5982\u4f55\u5229\u7528\u82e5\u5e72\u89c6\u89d2\u8fdb\u884c\u91cd\u5efa\uff1b</li> </ol> <p>\u5176\u4e2d\uff0c\u7b2c\u4e00\u4e2a\u547d\u9898\u7684\u5185\u5bb9\u5df2\u7ecf\u5728\u7b2c\u4e8c\u8bb2\u4e2d\u6d89\u53ca\uff0c\u6240\u4ee5\u4e0d\u518d\u5c55\u5f00\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec07/#\u76f8\u673a\u6807\u5b9a\u4e0e\u4f4d\u7f6e\u4f30\u8ba1","title":"\u76f8\u673a\u6807\u5b9a\u4e0e\u4f4d\u7f6e\u4f30\u8ba1","text":"<p>\u76f8\u673a\u6807\u5b9a(Camera Calibration)\u5373\u6c42\u89e3\u76f8\u673a\u7528\u6765\u63cf\u8ff0\u76f8\u673a\u6a21\u578b\u7684\u81ea\u8eab\u53c2\u6570\uff0c\u6362\u53e5\u8bdd\u6765\u8bf4\u5c31\u662f\u6c42\u89e3\u76f8\u673a\u7684\u5185\u53c2(Intrinsic Parameters)\uff1b\u800c\u4f4d\u7f6e\u4f30\u8ba1(Pose Estimation)\u6c42\u89e3\u76f8\u673a\u7684\u7a7a\u95f4\u4f4d\u7f6e\u4ee5\u53ca\u671d\u5411\uff0c\u4e0e\u5185\u53c2\u76f8\u5bf9\u5e94\u7684\uff0c\u5c31\u662f\u6c42\u89e3\u76f8\u673a\u7684\u5916\u53c2(Extrinsic Parameters)\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec07/#\u6210\u50cf\u8fc7\u7a0b\u7684\u5efa\u6a21","title":"\u6210\u50cf\u8fc7\u7a0b\u7684\u5efa\u6a21","text":"<p>\u89c6\u89c9\u5b9a\u4f4d\u95ee\u9898</p> <p>\u9996\u5148\uff0c\u4e3a\u4e86\u5c55\u5f00\u4e4b\u540e\u7684\u5185\u5bb9\uff0c\u6211\u4eec\u9700\u8981\u5b9a\u4e49\u89c6\u89c9\u5b9a\u4f4d\u95ee\u9898(Visual Localization Problem)\uff1a\u7ed9\u5b9a\u4e00\u4e2a\u5df2\u77e5\u7684\u4e09\u7ef4\u6a21\u578b\uff0c\u4ece\u67d0\u4e2a\u4f4d\u7f6e\u5bf9\u5176\u8fdb\u884c\u62cd\u6444\uff0c\u6c42\u89e3\u62cd\u6444\u4f4d\u7f6e\u548c\u89c6\u89d2\u3002</p> <p>\u800c\u4e3a\u4e86\u5c55\u5f00\u89c6\u89c9\u5b9a\u4f4d\u95ee\u9898\uff0c\u6211\u4eec\u9996\u5148\u9700\u8981\u5bf9\u76f8\u673a\u6210\u50cf\u8fd9\u4e2a\u8fc7\u7a0b\u8fdb\u884c\u4e00\u4e2a\u6570\u5b66\u5efa\u6a21\u2014\u2014\u66f4\u8be6\u7ec6\u7684\u6765\u8bf4\uff0c\u662f\u5efa\u6a21\u4e00\u4e2a\u7a7a\u95f4 3D \u70b9\u4e0e\u76f8\u673a\u4e0a\u7279\u5b9a\u50cf\u7d20\u533a\u57df\u7684\u8f6c\u5316\u5173\u7cfb\u3002</p> <p>\u9996\u5148\u8ba9\u6211\u4eec\u56de\u987e\u4e00\u4e0b\u6295\u5f71\u6a21\u578b\u7684\u53ef\u89c6\u5316\u8868\u793a\u4e2d\u7684\u76f8\u5173\u5185\u5bb9\uff1a</p> <p>\u56de\u987e</p> <p></p> <p>\u6211\u4eec\u53ef\u4ee5\u53d1\u73b0\uff0c\u5c0f\u5b54\u6210\u50cf\u7684\u6a21\u578b\u89c6\u56fe\u5176\u5b9e\u8fd8\u662f\u6bd4\u8f83\u9ebb\u70e6\u7684\u3002\u73b0\u5728\u6211\u4eec\u628a\u8fd9\u4e2a\u5b9a\u89d2\u76f8\u4f3c\u5bf9\u6298\uff0c\u53d8\u6210 A \u5b57\u578b\u76f8\u4f3c\u6765\u8868\u793a\u8fd9\u4e2a\u6a21\u578b\uff0c\u4ee5\u7b80\u5316\u4e0d\u5fc5\u8981\u7684\u4fe1\u606f\uff0c\u540c\u65f6\u4e5f\u80fd\u66f4\u6e05\u6670\u5730\u8868\u793a\u900f\u89c6\u5173\u7cfb\u3002</p> <p>\u89c4\u5b9a\u6211\u4eec\u8ba8\u8bba\u7684\u95ee\u9898\u4e2d\u7269\u8ddd\u603b\u662f\u5927\u4e8e\u50cf\u8ddd\uff0c\u5219\u53ef\u4ee5\u5c06\u50cf\u8868\u793a\u4e3a\u76f8\u673a\u4e2d\u5fc3\u5230\u7269\u4f53\u7684\u653e\u5c04\u8fde\u7ebf\u4e2d\u7684\u622a\u9762\u3002</p> <p>\u5b83\u6bd4\u8f83\u597d\u5730\u8868\u8fbe\u4e86\u900f\u89c6\u5173\u7cfb\uff0c\u5373 \u76f8\u673a\u4e2d\u5fc3 \u7269\u70b9B \u50cf\u70b9B' \u59cb\u7ec8\u5171\u7ebf\u3002\u8fd9\u4e5f\u662f\u5728\u4e4b\u540e\u7684\u5185\u5bb9\u4e2d\u66f4\u52a0\u5e38\u89c1\u7684\u53ef\u89c6\u5316\u8868\u73b0\u65b9\u6cd5\u3002</p> <p>\u5b83\u63d0\u4f9b\u4e86\u4e00\u79cd\u5c06\u76f8\u673a\u6a21\u578b\u6210\u50cf\u539f\u7406\u53ef\u89c6\u5316\u7684\u65b9\u6cd5\uff0c\u63a5\u4e0b\u6765\u6211\u4eec\u5c06\u5b83\u653e\u5230 3D \u7a7a\u95f4\u4e2d\uff1a</p> <p></p> <p>\u8fd9\u5f20\u56fe\u5927\u81f4\u63cf\u8ff0\u4e86\uff1a\u5728\u7279\u5b9a\u4f4d\u7f6e\u6709\u7740\u7279\u5b9a\u671d\u5411\u7684\u76f8\u673a\u6a21\u578b\u5982\u4f55\u62cd\u5230\u5df2\u77e5 3D \u666f\u8c61\u7684\u7279\u5b9a\u753b\u9762\uff0c\u4f46\u9700\u8981\u6ce8\u610f\u7684\u662f\uff0c\u8fd9\u91cc\u7684\u300cPicture\u300d\u4ee3\u8868\u7684\u662f Image Plane\uff0c\u4e5f\u5c31\u662f\u6210\u50cf\u5e73\u9762\uff0c\u6b64\u65f6\u300c\u5750\u6807\u300d\u7684\u5355\u4f4d\u662f\u957f\u5ea6\uff0c\u5982\u6beb\u7c73\u2014\u2014\u4e0e\u4ee5\u300c\u50cf\u7d20\u300d\u4e3a\u57fa\u672c\u5355\u5143\u7684\u201c\u56fe\u7247\u201d\u6709\u4e00\u5b9a\u533a\u522b\u3002</p> <p>\u4e5f\u5c31\u662f\u8bf4\uff0c\u4ece 3D \u4e2d\u7684\u67d0\u4e00\u4e2a\u70b9\uff0c\u5230\u56fe\u7247\u4e0a\u7684\u67d0\u5757\u50cf\u7d20\u533a\u57df\uff0c\u6709\u5927\u81f4\u5982\u4e0b\u51e0\u4e2a\u9636\u6bb5\uff1a</p> <pre><code>graph LR\n    A[3D \u666f\u8c61] --&gt; B[2D \u6210\u50cf\u5e73\u9762] --&gt; C[\u50cf\u7d20\u56fe\u50cf];</code></pre> <p>\u4e0d\u8fc7\u9700\u8981\u6ce8\u610f\u7684\u4e00\u70b9\u662f\uff0c\u6211\u4eec\u5728\u76f8\u673a\u6a21\u578b\u4e2d\u4ecb\u7ecd\u7684\u4e00\u7cfb\u5217\u5efa\u6a21\uff0c\u662f\u5efa\u7acb\u5728\u4ee5\u76f8\u673a\u4e3a\u53c2\u8003\u7cfb\u7684\u60c5\u51b5\u4e0b\u7684\uff0c\u800c\u5728\u89c6\u89c9\u5b9a\u4f4d\u95ee\u9898\u4e2d\uff0c\u6211\u4eec\u62e5\u6709\u7684 3D \u666f\u8c61\u4fe1\u606f\u80af\u5b9a\u4e0d\u662f\u901a\u8fc7\u76f8\u673a\u5750\u6807(Camera Coordinates)\u6765\u8868\u793a\u7684\uff0c\u800c\u662f\u7528\u4e16\u754c\u5750\u6807(World Coordinates)\uff0c\u663e\u7136\uff0c\u8fd9\u91cc\u53ea\u5305\u62ec\u5e73\u79fb\u548c\u65cb\u8f6c\uff0c\u4e5f\u5c31\u662f\u7ecf\u8fc7\u4e00\u6b21\u4eff\u5c04\u53d8\u6362\u3002</p> <p>\u6211\u4eec\u5bf9\u4e0a\u9762\u90a3\u4e2a\u6d41\u7a0b\u56fe\u7684\u7ed3\u679c\u8fdb\u884c\u4e00\u4e2a\u6539\u8fdb\uff1a</p> <pre><code>graph LR\n    A[\"(\u4e16\u754c\u5750\u6807) 3D \u666f\u8c61\"] --&gt; B[\"(\u76f8\u673a\u5750\u6807) 3D \u666f\u8c61\"] --&gt; C[\"(\u6210\u50cf\u5e73\u9762) 2D \u6620\u5c04\"] --&gt; D[\"(\u4f20\u611f\u5668\u5e73\u9762) \u50cf\u7d20\u56fe\u50cf\"];</code></pre>"},{"location":"cour_note/D2QD_Intro2CV/Lec07/#\u4e16\u754c\u5750\u6807-to-\u76f8\u673a\u5750\u6807","title":"\u4e16\u754c\u5750\u6807 to \u76f8\u673a\u5750\u6807","text":"<p>\u4e3a\u4e86\u5b9e\u73b0\u4e16\u754c\u5750\u6807\u5411\u76f8\u673a\u5750\u6807\u7684\u8f6c\u6362\uff0c\u6211\u4eec\u9700\u8981\u77e5\u9053\u76f8\u673a\u5750\u6807\u5728\u4e16\u754c\u5750\u6807\u4e2d\u7684\u65b9\u5411\u4e0e\u4f4d\u7f6e\uff0c\u4e0d\u96be\u53d1\u73b0\uff0c\u5b9e\u9645\u4e0a\u8fd9\u5c31\u8981\u6c42\u6211\u4eec\u77e5\u9053\u76f8\u673a\u7684\u5916\u53c2\u3002</p> <p></p> <p>\u66f4\u8fdb\u4e00\u6b65\u7684\uff0c\u5b9e\u9645\u4e0a\u6211\u4eec\u5c31\u662f\u5bfb\u627e\u4e00\u79cd\u53d8\u6362\uff0c\u80fd\u591f\u5b9e\u73b0\u4e16\u754c\u5750\u6807\u7cfb\u4e0b\u7684\u5750\u6807\u5411\u76f8\u673a\u5750\u6807\u7cfb\u4e0b\u5750\u6807\u7684\u8f6c\u6362\uff1a</p> \\[ \\underbrace{\\;\\mathbf{x}_w = \\begin{bmatrix}     x_w \\\\     y_w \\\\     z_w \\end{bmatrix}\\;}_{\\text{World Coordinates}} \\xrightarrow{\\text{Rotation \\&amp; Movement}} \\underbrace{\\;\\mathbf{x}_c = \\begin{bmatrix}     x_c \\\\     y_c \\\\     z_c \\end{bmatrix}\\;}_{\\text{Camera Coordinates}} \\] <p>\u6211\u4eec\u5b9a\u4e49\u5916\u53c2 \\((R,\\mathbf{c}_w)\\)\uff0c\u5206\u522b\u4ee3\u8868\u300c\u4ece\u4e16\u754c\u5750\u6807\u5411\u76f8\u673a\u5750\u6807\u7684\u65cb\u8f6c\u77e9\u9635\u300d\u548c\u300c\u5728\u4e16\u754c\u5750\u6807\u7cfb\u4e0b\u7684\u76f8\u673a\u7684\u4e2d\u5fc3\u5750\u6807\u300d\uff0c\u5219\u53d8\u6362\u540e\u7684\u5750\u6807\u5373\u4e3a\uff1a</p> \\[ \\mathbf{x}_c = R(\\mathbf{x}_w - \\mathbf{c}_w) = R \\mathbf{x}_w - R \\mathbf{c}_w = R \\mathbf{x}_w + \\mathbf{t},\\ \\ \\text{ where } \\mathbf{t} = -R \\mathbf{c}_w \\\\ \\text{i.e.} \\;\\; \\mathbf{x}_c = \\begin{bmatrix} x_c \\\\ y_c \\\\ z_c \\end{bmatrix} = \\begin{bmatrix}     r_{11} &amp; r_{12} &amp; r_{13} \\\\     r_{21} &amp; r_{22} &amp; r_{23} \\\\     r_{31} &amp; r_{32} &amp; r_{33} \\\\ \\end{bmatrix} \\begin{bmatrix}     x_w \\\\ y_w \\\\ z_w \\end{bmatrix} + \\begin{bmatrix}     t_x \\\\ t_y \\\\ t_z \\end{bmatrix} \\] <ul> <li>\u8bf4\u660e\uff1a<ol> <li>\\((\\mathbf{x}_w - \\mathbf{c}_w)\\) \u53ef\u4ee5\u7406\u89e3\u4e3a\u4ece\u76f8\u673a\u4e2d\u5fc3\u6307\u5411\u76ee\u6807\u70b9\u7684\u4e00\u4e2a\u5411\u91cf\uff1b</li> <li>\u65cb\u8f6c\u77e9\u9635 \\(R\\) \u5355\u4f4d\u6b63\u4ea4\uff1b </li> </ol> </li> </ul> <p>\u5f53\u7136\uff0c\u6211\u4eec\u53ef\u4ee5\u5c06\u5b83\u4f7f\u7528\u9f50\u6b21\u5750\u6807\u7edf\u4e00\uff1a</p> \\[ \\mathbf{\\tilde x}_c = \\begin{bmatrix} x_c \\\\ y_c \\\\ z_c \\\\ 1\\end{bmatrix} = \\underbrace{\\begin{bmatrix}     r_{11} &amp; r_{12} &amp; r_{13} &amp; t_x \\\\     r_{21} &amp; r_{22} &amp; r_{23} &amp; t_y\\\\     r_{31} &amp; r_{32} &amp; r_{33} &amp; t_z\\\\     0 &amp; 0 &amp; 0 &amp; 1 \\end{bmatrix}}_{\\text{Extrinsic Matrix}} \\begin{bmatrix}     x_w \\\\ y_w \\\\ z_w \\\\ 1 \\end{bmatrix} \\] <p>\u5916\u53c2\u77e9\u9635</p> <p>\u5176\u4e2d\uff0c\u65b0\u5f97\u5230\u7684\u8fd9\u4e2a 44 \u7684\u77e9\u9635\u5c31\u88ab\u79f0\u4e3a\u5916\u53c2\u77e9\u9635(Extrinsic Matrix)*\uff0c\u4e5f\u88ab\u5199\u4f5c\uff1a</p> \\[ M_{ext} = \\begin{bmatrix}     R_{3\\times 3} &amp; \\mathbf{t} \\\\     \\mathbf{0}_{1\\times 3} &amp; 1 \\end{bmatrix} = \\begin{bmatrix}     r_{11} &amp; r_{12} &amp; r_{13} &amp; t_x \\\\     r_{21} &amp; r_{22} &amp; r_{23} &amp; t_y\\\\     r_{31} &amp; r_{32} &amp; r_{33} &amp; t_z\\\\     0 &amp; 0 &amp; 0 &amp; 1 \\end{bmatrix} \\\\ or \\\\ M_{ext} = \\begin{bmatrix}     R_{3\\times 3} &amp; \\mathbf{t} \\\\ \\end{bmatrix} = \\begin{bmatrix}     r_{11} &amp; r_{12} &amp; r_{13} &amp; t_x \\\\     r_{21} &amp; r_{22} &amp; r_{23} &amp; t_y\\\\     r_{31} &amp; r_{32} &amp; r_{33} &amp; t_z\\\\ \\end{bmatrix} \\]"},{"location":"cour_note/D2QD_Intro2CV/Lec07/#\u76f8\u673a\u5750\u6807-to-\u6210\u50cf\u5e73\u9762","title":"\u76f8\u673a\u5750\u6807 to \u6210\u50cf\u5e73\u9762","text":"<p>\u5b9e\u9645\u4e0a\u8fd9\u4e00\u6b65\u5c31\u662f\u6211\u4eec\u5728\u76f8\u673a\u6a21\u578b\u4ecb\u7ecd\u8fc7\u7684\u5185\u5bb9\uff0c\u6211\u4eec\u5728\u4e0a\u4e00\u6b65\u5df2\u7ecf\u505a\u597d\u4e86\u9f50\u6b21\u5750\u6807\u7684\u94fa\u57ab\uff0c\u6240\u4ee5\u8fd9\u4e00\u6b65\u683c\u5916\u7b80\u5355\u3002</p> \\[ \\begin{bmatrix}     \\mathbf{x}_{i_{1 \\times 2}} \\\\ 1 \\end{bmatrix} \\cong \\begin{bmatrix}     f &amp; 0 &amp; 0 &amp; 0 \\\\     0 &amp; f &amp; 0 &amp; 0 \\\\     0 &amp; 0 &amp; 1 &amp; 0 \\end{bmatrix} \\begin{bmatrix}     x_c \\\\     y_c \\\\     z_c \\\\     1 \\end{bmatrix} \\] <p>\u6ce8\u610f</p> <p>\u8fd9\u91cc 3*4 \u7684\u77e9\u9635\u8fd8\u4e0d\u662f\u5185\u53c2\u77e9\u9635\uff01</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec07/#\u6210\u50cf\u5e73\u9762-to-\u4f20\u611f\u5668\u5e73\u9762","title":"\u6210\u50cf\u5e73\u9762 to \u4f20\u611f\u5668\u5e73\u9762","text":"<p>\u4e4b\u524d\u8bf4\u8fc7\uff0c\u6210\u50cf\u5e73\u9762\u4e0a\u7684\u5185\u5bb9\u548c\u4f20\u611f\u5668\u5e73\u9762\u4e0a\u7684\u5185\u5bb9\u6700\u5927\u7684\u4e0d\u540c\u5c31\u662f\u8ba1\u91cf\u5355\u4f4d\u4e0d\u540c\uff0c\u6240\u4ee5\u6211\u4eec\u9700\u8981\u5c06\u957f\u5ea6\u4fe1\u606f\u8f6c\u5316\u4e3a\u50cf\u7d20\u4fe1\u606f\uff1b\u6b64\u5916\uff0c\u4e2d\u5fc3\u5750\u6807\u4e5f\u9700\u8981\u53d8\u6362\u3002</p> <p>\u5047\u8bbe \\(m_x\\) \u548c \\(m_y\\) \u5206\u522b\u662f\u5355\u4f4d\u957f\u5ea6\u4e0a\u7684\u50cf\u7d20\u5bc6\u5ea6\uff08\u4ee5 px/mm \u4e3a\u4f8b\uff09\uff0c\\((c_x,c_y)\\) \u5206\u522b\u662f\u5728\u6210\u50cf\u5e73\u9762\u4e0b\u4f20\u611f\u5668\u5e73\u9762\u7684\u4e2d\u5fc3\u5750\u6807\uff0c\u5219\uff1a</p> \\[ \\left\\{     \\begin{aligned}         u &amp;= m_x \\cdot x_i + c_x\\\\         v &amp;= m_y \\cdot y_i + c_y     \\end{aligned} \\right. \\] <p>\u5e26\u5165\u4e0a\u4e00\u8282\u7684\u7ed3\u679c\uff0c\u5f97\u5230\uff08\u6ce8\u610f\uff0c\u8fd9\u91cc\u7684\u201c\u9f50\u6b21\u5750\u6807\u201d\u662f\u4e0a\u4e00\u8282\u5e26\u6765\u7684\uff0c\u8fd9\u4e00\u8282\u7684\u8ba1\u7b97\u5e76\u4e0d\u9700\u8981\u9f50\u6b21\u5750\u6807\uff09\uff1a</p> \\[ \\begin{bmatrix}     u \\\\     v \\\\     1 \\end{bmatrix} = ... \\cong \\begin{bmatrix}     u' \\\\     v' \\\\     z_c \\end{bmatrix} = \\underbrace{{\\begin{bmatrix}     m_x f &amp; 0 &amp; c_x &amp; 0 \\\\     0 &amp; m_y f &amp; c_y &amp; 0 \\\\     0 &amp; 0 &amp; 1 &amp; 0 \\end{bmatrix}}}_{\\text{Intrinsic Matrix}} \\begin{bmatrix}     x_c \\\\     y_c \\\\     z_c \\\\     1 \\end{bmatrix} \\] <p>\u5185\u53c2\u77e9\u9635</p> <p>\u8fd9\u91cc\u5f97\u5230\u7684\uff0c\u5305\u542b \\(f\\) \u548c \\(m\\) \u7684\u77e9\u9635\u624d\u662f\u5185\u53c2\u77e9\u9635(Intrinsic Matrix)\uff0c\u4e5f\u88ab\u5199\u4f5c\uff1a</p> \\[ M_{int} =  \\begin{bmatrix}     m_x f &amp; 0 &amp; c_x &amp; 0 \\\\     0 &amp; m_y f &amp; c_y &amp; 0 \\\\     0 &amp; 0 &amp; 1 &amp; 0 \\end{bmatrix} \\\\ or \\\\ K =  \\begin{bmatrix}     m_x f &amp; 0 &amp; c_x \\\\     0 &amp; m_y f &amp; c_y \\\\     0 &amp; 0 &amp; 1 \\end{bmatrix} \\]"},{"location":"cour_note/D2QD_Intro2CV/Lec07/#\u5185\u53c2\u77e9\u9635\u5916\u53c2\u77e9\u9635\u4e0e\u6295\u5f71\u77e9\u9635","title":"\u5185\u53c2\u77e9\u9635\u3001\u5916\u53c2\u77e9\u9635\u4e0e\u6295\u5f71\u77e9\u9635","text":"<p>\u7b80\u5355\u603b\u7ed3\u4e0a\u9762\u51e0\u4e2a\u6b65\u9aa4\u4e0e\u5185\u53c2\u5916\u53c2\u77e9\u9635\u7684\u5173\u7cfb\uff0c\u5c31\u662f\u4e0b\u9762\u8fd9\u5f20\u6d41\u7a0b\u56fe\uff1a</p> <pre><code>graph LR\n    subgraph EM[\"Using Extrinsic Matrix\"]\n        A[\"Coordinate Transformation\"]\n    end\n    subgraph IM[\"Using Intrinsic Matrix\"]\n        B[\"Perspective Projection\"]\n        C[\"Image Plane to Image Sensor Mapping\"]\n    end\n    A ---&gt; B\n    B ---&gt; C</code></pre>"},{"location":"cour_note/D2QD_Intro2CV/Lec07/#\u5185\u53c2\u77e9\u9635","title":"\u5185\u53c2\u77e9\u9635","text":"<p>\u6211\u4eec\u5728\u4e0a\u9762\u63d0\u5230\u7684\u5185\u53c2\u77e9\u9635\u957f\u8fd9\u6837\uff1a</p> \\[ M_{int} =  \\begin{bmatrix}     m_x f &amp; 0 &amp; c_x &amp; 0 \\\\     0 &amp; m_y f &amp; c_y &amp; 0 \\\\     0 &amp; 0 &amp; 1 &amp; 0 \\end{bmatrix} \\\\ or \\\\ K =  \\begin{bmatrix}     m_x f &amp; 0 &amp; c_x \\\\     0 &amp; m_y f &amp; c_y \\\\     0 &amp; 0 &amp; 1 \\end{bmatrix} \\] <p>\u5176\u4e2d\u4e3b\u8981\u6709 4 \u4e2a\u81ea\u7531\u5ea6\uff1a\\(m_x f\\)\u3001\\(m_y f\\)\u3001\\(c_x\\)\u3001\\(c_y\\)\u3002</p> <p>\u7136\u800c\u5b9e\u9645\u4e0a\u672a\u5fc5\u5982\u6b64\uff0c\u7531\u4e8e\u7578\u53d8\u7b49\u53ef\u80fd\u5b58\u5728\u7684\u539f\u56e0\uff0c\u5b9e\u9645\u7684\u5185\u53c2\u77e9\u9635\uff0c\u6216\u8005\u662f\u6c42\u89e3\u51fa\u6765\u7684\u5185\u53c2\u77e9\u9635\u5e76\u4e0d\u4e00\u5b9a\u5f62\u5982\u6b64\uff0c\u6211\u4eec\u5728\u540e\u9762\u4f1a\u63d0\u5230\uff0c\u7531\u4e8e\u67d0\u4e9b\u6027\u8d28\u5206\u89e3\u51fa\u6765\u7684\u5185\u53c2\u77e9\u9635\uff0c\u66f4\u591a\u7684\u662f\u4e00\u4e2a\u53f3\u4e0a\u4e09\u89d2\u9635\uff0c\u5373\u7b2c\u4e00\u884c\u7b2c\u4e8c\u5217\u7684\u5143\u7d20\u672a\u5fc5\u4e3a\u96f6\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec07/#\u5916\u53c2\u77e9\u9635","title":"\u5916\u53c2\u77e9\u9635","text":"<p>\u6211\u4eec\u5728\u4e0a\u9762\u63d0\u5230\u7684\u5916\u53c2\u77e9\u9635\u957f\u8fd9\u6837\uff1a</p> \\[ M_{ext} = \\begin{bmatrix}     R_{3\\times 3} &amp; \\mathbf{t} \\\\     \\mathbf{0}_{1\\times 3} &amp; 1 \\end{bmatrix} = \\begin{bmatrix}     r_{11} &amp; r_{12} &amp; r_{13} &amp; t_x \\\\     r_{21} &amp; r_{22} &amp; r_{23} &amp; t_y\\\\     r_{31} &amp; r_{32} &amp; r_{33} &amp; t_z\\\\     0 &amp; 0 &amp; 0 &amp; 1 \\end{bmatrix} \\\\ or \\\\ M_{ext} = \\begin{bmatrix}     R_{3\\times 3} &amp; \\mathbf{t} \\\\ \\end{bmatrix} = \\begin{bmatrix}     r_{11} &amp; r_{12} &amp; r_{13} &amp; t_x \\\\     r_{21} &amp; r_{22} &amp; r_{23} &amp; t_y\\\\     r_{31} &amp; r_{32} &amp; r_{33} &amp; t_z\\\\ \\end{bmatrix} \\] <p>\u5176\u4e2d\u4e3b\u8981\u6709 12 \u4e2a\u81ea\u7531\u5ea6\uff0c\u5305\u542b\u4e86\u65cb\u8f6c\u77e9\u9635 \\(R\\) \u548c\u65cb\u8f6c\u540e\u7684\u4f4d\u79fb\u5411\u91cf \\(\\mathbf{t}\\)\u3002</p> <p>\u7c7b\u4f3c\u4e8e\u4e0a\u4e00\u8282\u63d0\u5230\u7684\u65cb\u8f6c\u77e9\u9635\uff0c\u8fd9\u91cc\u7684\u65cb\u8f6c\u77e9\u9635\u540c\u6837\u62e5\u6709 \u6b63\u4ea4 \u548c \\(||R||_2^2 = 1\\) \u7684\u6027\u8d28\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec07/#\u6295\u5f71\u77e9\u9635","title":"\u6295\u5f71\u77e9\u9635","text":"<p>\u603b\u7ed3\u5e94\u7528\u4e24\u4e2a\u77e9\u9635\u7684\u4e24\u4e2a\u9636\u6bb5\uff1a</p> <p>Camera to Pixel: Intrinsic Matrix</p> \\[ \\mathbf{\\tilde{u}} = M_{int} \\mathbf{\\tilde{x}}_c \\;\\;\\;\\;i.e.\\;\\;\\;\\; \\begin{bmatrix}     u' \\\\ v' \\\\ z_c \\end{bmatrix} = \\begin{bmatrix}     f_x &amp; 0 &amp; c_x &amp; 0 \\\\     0 &amp; f_y &amp; c_y &amp; 0 \\\\     0 &amp; 0 &amp; 1 &amp; 0 \\end{bmatrix} \\begin{bmatrix}     x_c \\\\     y_c \\\\     z_c \\\\     1 \\end{bmatrix} \\] <p>World to Camera: Extrinsic Matrix</p> \\[ \\mathbf{\\tilde{x}}_c = M_{ext} \\mathbf{\\tilde{x}}_w \\;\\;\\;\\;i.e.\\;\\;\\;\\; \\begin{bmatrix} x_c \\\\ y_c \\\\ z_c \\\\ 1\\end{bmatrix} = \\begin{bmatrix}     r_{11} &amp; r_{12} &amp; r_{13} &amp; t_x \\\\     r_{21} &amp; r_{22} &amp; r_{23} &amp; t_y\\\\     r_{31} &amp; r_{32} &amp; r_{33} &amp; t_z\\\\     0 &amp; 0 &amp; 0 &amp; 1 \\end{bmatrix} \\begin{bmatrix}     x_w \\\\ y_w \\\\ z_w \\\\ 1 \\end{bmatrix} \\] <p>\u800c\u5c06\u5b83\u4eec\u7ed3\u5408\uff0c\u6211\u4eec\u5c31\u5f97\u5230\u4e86\u5b8c\u6574\u7684\u6295\u5f71\u77e9\u9635(Projection Matrix)\\(P\\)\uff1a</p> \\[ \\mathbf{\\tilde u} = M_{int}M_{ext} \\mathbf{\\tilde x}_w = P \\mathbf{\\tilde x} \\;\\;\\;\\; i.e. \\;\\;\\;\\; \\begin{bmatrix}     u \\\\ v \\\\ 1 \\end{bmatrix} \\cong \\begin{bmatrix}     u' \\\\ v' \\\\ z_c \\end{bmatrix} = \\underbrace{\\begin{bmatrix}     p_{11} &amp; p_{12} &amp; p_{13} &amp; p_{14} \\\\     p_{21} &amp; p_{22} &amp; p_{23} &amp; p_{24} \\\\     p_{31} &amp; p_{32} &amp; p_{33} &amp; p_{34} \\end{bmatrix}}_{\\text{Projection Matrix } P} \\begin{bmatrix}     x_w \\\\     y_w \\\\     z_w \\\\     1 \\end{bmatrix} \\]"},{"location":"cour_note/D2QD_Intro2CV/Lec07/#\u76f8\u673a\u6807\u5b9a\u4e0e\u4f4d\u7f6e\u4f30\u8ba1_1","title":"\u76f8\u673a\u6807\u5b9a\u4e0e\u4f4d\u7f6e\u4f30\u8ba1","text":"<p>\u6839\u636e\u6295\u5f71\u77e9\u9635\u6211\u4eec\u5f97\u5230\u4e86\u50cf\u7d20\u70b9\u4e0e 3D \u666f\u7269\u4e16\u754c\u5750\u6807\u7684\u8f6c\u5316\u5173\u7cfb\uff0c\u800c\u76f8\u673a\u6807\u5b9a\u4e0e\u4f4d\u7f6e\u4f30\u8ba1\u5c31\u662f\u5229\u7528\u8fd9\u4e2a\u5173\u7cfb\u5f0f\u6c42\u89e3\u6295\u5f71\u77e9\u9635\u3002\u6240\u4ee5\u8fd9\u5c31\u8981\u6c42\u6211\u4eec\u540c\u65f6\u77e5\u9053\u82e5\u5e72\u70b9\u7684\u50cf\u7d20\u70b9\u4f4d\u7f6e\u548c 3D \u666f\u7269\u4e16\u754c\u5750\u6807\uff0c\u4e00\u822c\u6765\u8bf4\u76f8\u673a\u6807\u5b9a\u4e0e\u4f4d\u7f6e\u4f30\u8ba1\u662f\u8fd9\u4e48\u5b9e\u73b0\u7684\uff1a</p> <p>\u6b65\u9aa4\u4e00</p> <p></p> <p>\u7ed9\u5b9a\u4e00\u4e2a\u51e0\u4f55\u7279\u6027\u5df2\u77e5\u7684\u6807\u5b9a\u677f\uff0c\u4eba\u4e3a\u5b9a\u4e49\u5176\u4e16\u754c\u5750\u6807\u7cfb\u3002</p> <p>\u7531\u4e8e\u5750\u6807\u90fd\u662f\u7531\u6211\u4eec\u4eba\u4e3a\u7ed9\u5b9a\u7684\uff0c\u6240\u4ee5\u6211\u4eec\u53ef\u4ee5\u6309\u7167\u5c3d\u53ef\u80fd\u65b9\u4fbf\u7684\u539f\u5219\u8fdb\u884c\u89c4\u5212\u3002\u6b64\u5916\uff0c\u4e3a\u4e86\u65b9\u4fbf\u4e4b\u540e\u7684\u8ba1\u7b97\uff0c\u6807\u5b9a\u677f\u7684\u5185\u5bb9\u4e00\u822c\u662f\u7b80\u5355\u660e\u4e86\u7684\u3002</p> <p>\u4f8b\u5982\u56fe\u4e2d\uff0c\u5b9a\u4e49\u4e16\u754c\u5750\u6807\u7cfb\u540e\uff0c\u6bcf\u4e00\u683c\u7684\u8fb9\u957f\u4e3a 5cm\uff0c\u6240\u4ee5\u7d2b\u8272\u70b9\u7684\u5750\u6807\u4e3a \\((0, 15, 20) cm\\)\u3002</p> <p>\u6b65\u9aa4\u4e8c</p> <p>\u5bfb\u627e\u7279\u5b9a\u5173\u952e\u70b9\u7684\u5bf9\u5e94\u5173\u7cfb\uff0c\u4e5f\u5c31\u662f\u505a\u7279\u5f81\u5339\u914d\uff0c\u5373\u82e5\u5e72\u70b9\u5bf9\uff0c\u6bcf\u4e00\u4e2a\u70b9\u5bf9\u90fd\u662f\u4e00\u4e2a 3D \u70b9\u548c\u4e00\u4e2a 2D \u70b9\u7684\u5bf9\u5e94\u3002</p> <p>\u9700\u8981\u8bf4\u660e\u7684\u4e00\u70b9\u662f\uff0c\u6211\u4eec\u5df2\u77e5\u7684\u7279\u5f81\u5339\u914d\u662f\u5efa\u7acb\u5728\u4e24\u5f20\u4e8c\u7ef4\u56fe\u7247\u4e0a\u7684\uff0c\u800c\u73b0\u5728\u8981\u505a\u7684\u662f 3D \u5230 2D \u7684\u5339\u914d\u3002\u4e00\u79cd\u60f3\u6cd5\u662f\uff0c\u6211\u4eec\u53ef\u4ee5\u5c06 3D \u666f\u8c61\u6309\u7167\u6211\u4eec\u5e0c\u671b\u7684\u65b9\u6cd5\u6620\u5c04\u4e3a 2D \u666f\u8c61\uff0c\u4f8b\u5982\u5728\u8fd9\u4e2a\u95ee\u9898\u4e2d\u6211\u4eec\u53ef\u4ee5\u76f4\u63a5\u62ff\u8fd9\u4e2a\u6807\u5b9a\u677f\u7684 zy \u5e73\u9762\u6765\u8fdb\u884c\u7279\u5f81\u5339\u914d\u3002</p> <p></p> <p>\u6b65\u9aa4\u4e09</p> <p>\u6839\u636e\u521a\u521a\u5f97\u5230\u7684\u82e5\u5e72\u5bf9\u5174\u8da3\u70b9\uff0c\u5efa\u7acb\u65b9\u7a0b\uff0c\u6c42\u89e3\u6295\u5f71\u77e9\u9635\u3002</p> <p>\u6bcf\u4e00\u5bf9\u5173\u952e\u70b9\u53ef\u4ee5\u5206\u522b\u6839\u636e \\(u\\) \u548c \\(v\\) \u5efa\u7acb\u4e24\u4e2a\u7b49\u5f0f\uff1a</p> \\[ \\underbrace{\\begin{bmatrix}     u^{(i)} \\\\     v^{(i)} \\\\     1 \\end{bmatrix}}_{known} =  \\underbrace{\\begin{bmatrix}     p_{11} &amp; p_{12} &amp; p_{13} &amp; p_{14} \\\\     p_{21} &amp; p_{22} &amp; p_{23} &amp; p_{24} \\\\     p_{31} &amp; p_{32} &amp; p_{33} &amp; p_{34} \\end{bmatrix}}_{unknown} \\underbrace{\\begin{bmatrix}     x_w^{(i)} \\\\     y_w^{(i)} \\\\     z_w^{(i)} \\\\     1 \\end{bmatrix}}_{known} \\\\ i.e. \\;\\;\\;\\; \\left\\{ \\begin{aligned}     u^{(i)} &amp;= \\frac{p_{11}x_w^{(i)} + p_{12}y_w^{(i)} + p_{13}z_w^{(i)} + p_{14}}{p_{31}x_w^{(i)} + p_{32}y_w^{(i)} + p_{33}z_w^{(i)} + p_{34}} \\\\     v^{(i)} &amp;= \\frac{p_{21}x_w^{(i)} + p_{22}y_w^{(i)} + p_{23}z_w^{(i)} + p_{24}}{p_{31}x_w^{(i)} + p_{32}y_w^{(i)} + p_{33}z_w^{(i)} + p_{34}} \\end{aligned} \\right. \\] <p>\u7531\u4e8e\u6295\u5f71\u77e9\u9635\u6709 12 \u4e2a\u81ea\u7531\u5ea6\uff0c\u6240\u4ee5\u81f3\u5c11\u9700\u8981 6 \u5bf9\u5173\u952e\u70b9 12 \u4e2a\u7b49\u5f0f\u3002</p> <p>\u6b65\u9aa4\u56db</p> <p>\u5c06\u82e5\u5e72\u65b9\u7a0b\u91cd\u65b0\u6392\u5217\u4e3a\u77e9\u9635\u5f62\u5f0f\uff0c\u65b9\u4fbf\u4e4b\u540e\u7684\u8ba1\u7b97\u3002</p> <p>\u5c06\u6b65\u9aa4\u4e09\u5f97\u5230\u7684\u5f0f\u5b50\u540c\u5206\u79fb\u9879\uff0c\u5f62\u6210 \\(f(...) = 0\\) \u7684\u5f62\u5f0f\uff0c\u518d\u5c06 12 \u4e2a\u5f0f\u5b50\u7ed3\u5408\u5728\u4e00\u8d77\u5c31\u5f97\u5230\u4e86\u4e0b\u9762\u8fd9\u4e2a\u5e9e\u5927\u7684\u77e9\u9635\u65b9\u7a0b\uff1a</p> \\[ \\begin{bmatrix}     x_w^{(1)} &amp; y_w^{(1)} &amp; z_w^{(1)} &amp; 1 &amp; 0 &amp; 0 &amp; 0 &amp; 0 &amp; -u_1x_w^{(1)} &amp; -u_1y_w^{(1)} &amp; -u_1z_w^{(1)} &amp; -u_1 \\\\     0 &amp; 0 &amp; 0 &amp; 0 &amp;  x_w^{(1)} &amp; y_w^{(1)} &amp; z_w^{(1)} &amp; 1 &amp; -v_1x_w^{(1)} &amp; -v_1y_w^{(1)} &amp; -v_1z_w^{(1)} &amp; -v_1 \\\\     \\vdots &amp; \\vdots &amp; \\vdots &amp; \\vdots &amp; \\vdots &amp; \\vdots &amp; \\vdots &amp; \\vdots &amp; \\vdots &amp; \\vdots &amp; \\vdots &amp; \\vdots \\\\      x_w^{(i)} &amp; y_w^{(i)} &amp; z_w^{(i)} &amp; 1 &amp; 0 &amp; 0 &amp; 0 &amp; 0 &amp; -u_ix_w^{(i)} &amp; -u_iy_w^{(i)} &amp; -u_iz_w^{(i)} &amp; -u_i \\\\     0 &amp; 0 &amp; 0 &amp; 0 &amp;  x_w^{(i)} &amp; y_w^{(i)} &amp; z_w^{(i)} &amp; 1 &amp; -v_ix_w^{(i)} &amp; -v_iy_w^{(i)} &amp; -v_iz_w^{(i)} &amp; -v_i \\\\     \\vdots &amp; \\vdots &amp; \\vdots &amp; \\vdots &amp; \\vdots &amp; \\vdots &amp; \\vdots &amp; \\vdots &amp; \\vdots &amp; \\vdots &amp; \\vdots &amp; \\vdots \\\\      x_w^{(n)} &amp; y_w^{(n)} &amp; z_w^{(n)} &amp; 1 &amp; 0 &amp; 0 &amp; 0 &amp; 0 &amp; -u_nx_w^{(n)} &amp; -u_ny_w^{(n)} &amp; -u_nz_w^{(n)} &amp; -u_n \\\\     0 &amp; 0 &amp; 0 &amp; 0 &amp;  x_w^{(n)} &amp; y_w^{(n)} &amp; z_w^{(n)} &amp; 1 &amp; -v_nx_w^{(n)} &amp; -v_ny_w^{(n)} &amp; -v_nz_w^{(n)} &amp; -v_n \\\\ \\end{bmatrix} \\begin{bmatrix}     p_{11} \\\\ p_{12} \\\\ p_{13} \\\\ p_{14} \\\\     p_{21} \\\\ p_{22} \\\\ p_{23} \\\\ p_{24} \\\\     p_{31} \\\\ p_{32} \\\\ p_{33} \\\\ p_{34} \\end{bmatrix} = \\begin{bmatrix}     0 \\\\ 0 \\\\ 0 \\\\ 0 \\\\     0 \\\\ 0 \\\\ 0 \\\\ 0 \\\\     0 \\\\ 0 \\\\ 0 \\\\ 0 \\end{bmatrix} \\] <p>\u6211\u4eec\u5c06\u5176\u7b80\u5199\uff0c\u4e5f\u5c31\u662f \\(A\\mathbf{p} = 0\\)\u3002</p> <p>\u6b65\u9aa4\u4e94</p> <p>\u6c42\u89e3 \\(A\\mathbf{p} = 0\\) \u5f97\u5230 \\(\\mathbf{p}\\)\u3002</p> <p>\u7c7b\u4f3c\u4e8e\u4e0a\u4e00\u8282\u7684\u64cd\u4f5c\uff0c\u8fd9\u91cc\u5f97\u5230\u7684 \\(mathbf{p}\\) \u4e5f\u6709\u591a\u79cd\u53ef\u80fd\uff0c\u6240\u4ee5\u6211\u4eec\u8981\u5bf9\u5b83\u8fdb\u884c\u7ea6\u675f\uff0c\u4e00\u822c\u6709\u4e24\u79cd\u9009\u62e9\uff1a</p> <ul> <li>\u4ee4 \\(p_{34} = 1\\)\uff1b</li> <li>\u4ee4 \\(||p|| = 1\\)\uff1b</li> </ul> <p>\u4e00\u822c\u6211\u4eec\u9009\u62e9\u540e\u8005\uff0c\u4e5f\u5c31\u662f\u8ba9 \\(mathbf{p}\\) \u7684\u957f\u5ea6\u4e3a 1\uff0c\u6b64\u65f6\u81ea\u7531\u5ea6\u524a\u51cf\u4e3a 11\uff0c\u4ecd\u7136\u9700\u8981\u516d\u5bf9\u5173\u952e\u70b9\u3002</p> <p>\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u5c06\u6c42\u89e3\u65b9\u7a0b \\(A\\mathbf{p} = 0\\) \u8f6c\u5316\u4e3a \\(\\mathop{minimize} \\limits_\\mathbf{p} ||A\\mathbf{p}||^2 \\;\\; \\text{ such that } ||\\mathbf{p}||^2 = 1\\) \u7684\u4f18\u5316\u95ee\u9898\uff0c\u7531\u4e8e\u548c\u4e4b\u524d\u7684\u4e00\u6837\uff0c\u6240\u4ee5\u4e0d\u518d\u8d58\u8ff0\u3002</p> <p>\u5206\u89e3\u6295\u5f71\u77e9\u9635</p> <p>\u6839\u636e\u6295\u5f71\u77e9\u9635\u7684\u76f8\u5173\u5185\u5bb9\u6211\u4eec\u77e5\u9053\uff1a  </p> <p>\u901a\u5e38\u6765\u8bf4\uff0c\u5c06\u4e00\u4e2a\u77e9\u9635\u5206\u89e3\u4e3a\u4e24\u4e2a\u7279\u5b9a\u77e9\u9635\u662f\u4e0d\u73b0\u5b9e\u7684\uff0c\u4f46\u662f\u6b64\u5904\u7684\u5185\u53c2\u77e9\u9635\u7684\u5b50\u5f0f\u5177\u6709\u201c\u4e0a\u4e09\u89d2\u9635\u201d\u8fd9\u4e2a\u6027\u8d28\uff0c\u5916\u53c2\u77e9\u9635\u4e2d\u65cb\u8f6c\u77e9\u9635\u5b50\u5f0f\u5177\u6709\u201c\u6b63\u4ea4\u201d\u8fd9\u4e2a\u6027\u8d28\uff0c\u800c\u4e14\u89c2\u5bdf 0 \u7684\u5206\u5e03\uff0c\u6211\u4eec\u53d1\u73b0 \\([p_{11} \\sim p_{33}]\\) \u7531 \\(KR\\) \u5f97\u5230\u3002\u6240\u4ee5\u6211\u4eec\u6070\u597d\u53ef\u4ee5\u4f7f\u7528QR \u5206\u89e3\u6765\u5b9e\u73b0\uff1a</p> \\[ \\begin{bmatrix}     p_{11} &amp; p_{12} &amp; p_{13} \\\\     p_{21} &amp; p_{22} &amp; p_{23} \\\\     p_{31} &amp; p_{32} &amp; p_{33} \\end{bmatrix} = \\begin{bmatrix}     f_x &amp; 0 &amp; c_x \\\\     0 &amp; f_y &amp; c_y \\\\     0 &amp; 0 &amp; 1 \\end{bmatrix} \\begin{bmatrix}     r_{11} &amp; r_{12} &amp; r_{13} \\\\     r_{21} &amp; r_{22} &amp; r_{23} \\\\     r_{31} &amp; r_{32} &amp; r_{33} \\\\ \\end{bmatrix} = KR \\] <p>\u9700\u8981\u6ce8\u610f\u7684\u662f\uff0c\u4f7f\u7528 QR \u5206\u89e3\u5f97\u5230\u7684\u4e09\u89d2\u9635\u5e76\u4e0d\u4e00\u5b9a\u5177\u6709\u7b2c\u4e00\u884c\u7b2c\u4e8c\u5217\u5143\u7d20\u4e3a 0 \u7684\u6027\u8d28\u3002</p> <p>\u6b64\u65f6\uff0c\u6211\u4eec\u5df2\u7ecf\u77e5\u9053\u4e86\u9664\u4e86 \\(t_x,t_y,t_z\\) \u4ee5\u5916\u7684\u6240\u6709\u672a\u77e5\u5143\u4e86\uff0c\u6240\u4ee5\u5f53\u7136\u53ef\u4ee5\u56de\u8fc7\u6765\u7ee7\u7eed\u6c42\u5b83\u4eec\u3002</p> \\[ \\because \\begin{bmatrix}     p_{14} \\\\ p_{24} \\\\ p_{34} \\end{bmatrix} = \\begin{bmatrix}     f_x &amp; 0 &amp; c_x \\\\     0 &amp; f_y &amp; c_y \\\\     0 &amp; 0 &amp; 1 \\end{bmatrix} \\begin{bmatrix}     t_x \\\\ t_y \\\\ t_z \\end{bmatrix} = K \\mathbf{t} \\\\ \\therefore \\mathbf{t} = K^{-1}  \\begin{bmatrix}     p_{14} \\\\ p_{24} \\\\ p_{34} \\end{bmatrix} \\] <p>\u6ce8\u610f</p> <p>\u9700\u8981\u7279\u522b\u6ce8\u610f\u7684\u4e00\u70b9\u662f\uff0c\u5728\u6211\u4eec\u4e0a\u9762\u6d89\u53ca\u7684\u8ba8\u8bba\u4e2d\uff0c\u6211\u4eec\u90fd\u6ca1\u6709\u8003\u8651\u7578\u53d8\u5e26\u6765\u7684\u5f71\u54cd\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec07/#\u591a\u70b9\u900f\u89c6\u6210\u50cf\u95ee\u9898","title":"\u591a\u70b9\u900f\u89c6\u6210\u50cf\u95ee\u9898","text":"<p>\u591a\u70b9\u900f\u89c6\u6210\u50cf\u95ee\u9898(Perspective-n-Point Problem)\uff0c\u5373 PnP \u95ee\u9898\uff0c\u6307\u7684\u662f\u5df2\u77e5\u5185\u53c2\u6c42\u5916\u53c2\u7684\u89c6\u89c9\u5b9a\u4f4d\u95ee\u9898\u3002</p> <p>\u5e38\u89c1\u7684\u89e3\u51b3\u65b9\u6848\u6709\u5982\u4e0b\u51e0\u79cd\u3002</p> <p>DLT Direct Linear Transform</p> <p>\u4e5f\u5c31\u662f\u4e0a\u9762\u63d0\u5230\u7684\u505a\u6cd5\u3002</p> <p>P3P</p> <p>\u81f3\u5c11\u9700\u8981 3 \u7ec4\u5bf9\u5e94\u5173\u7cfb\u624d\u80fd\u6c42\u89e3\u76f8\u673a\u4f4d\u7f6e\uff0c\u6b64\u5916\uff0c\u6211\u4eec\u8fd8\u9700\u8981\u4e00\u4e2a\u989d\u5916\u7684\u70b9\u6765\u4fdd\u8bc1\u7b54\u6848\u7684\u552f\u4e00\u6027\uff08\u5426\u5219\u4e00\u822c\u6765\u8bf4\u4f1a\u6709\u56db\u4e2a\u89e3\uff09</p> <p>\u5176\u4e3b\u8981\u601d\u8def\u662f\u6839\u636e\u56fe\u50cf\uff0c\u4f7f\u7528\u4f59\u5f26\u5b9a\u5f8b\u8fdb\u884c\u6c42\u89e3\u3002</p> <p>\u61d2\u5f97\u5199\u4e86\uff0c\u76f4\u63a5\u8d34\u9ea6\u54e5\u7684\u7b14\u8bb0\u4e86\uff01</p> <p>PnP</p> <p>n &gt; 3 \u7684\u60c5\u51b5\u7684\u505a\u6cd5\u3002</p> <p>\u8f6c\u5316\u4e3a\u4f18\u5316\u95ee\u9898\uff0c\u6c42\u89e3\u7406\u8bba\u548c\u5b9e\u9645\u7684\u70b9\u8bef\u5dee\u2014\u2014\u91cd\u6295\u5f71\u8bef\u5dee(reprojection error)\u6700\u5c0f\u65f6\u7684\u5916\u53c2\uff0c\u6ce8\u610f\u5c06\u9f50\u6b21\u5750\u6807\u8f6c\u5316\u4e3a\u4e8c\u7ef4\u5750\u6807\u3002</p> <p>Initialized by P3P, optimized by Gauss-Newton\u3002</p> <p>\u61d2\u5f97\u5199\u4e86\uff0c\u76f4\u63a5\u8d34\u9ea6\u54e5\u7684\u7b14\u8bb0\u4e86\uff01</p> <p>EPnP</p> <p>\u76ee\u524d\u6700\u53d7\u6b22\u8fce\u7684\u505a\u6cd5\uff0cO(N) \u5341\u5206\u9ad8\u6548\u4e5f\u5341\u5206\u51c6\u786e\uff0c\u5927\u6982\u662f\u7528\u56db\u4e2a\u63a7\u5236\u70b9\u8868\u793a\u5176\u4ed6\u70b9\u3002</p> <p>\u61d2\u5f97\u5199\u4e86\uff0c\u76f4\u63a5\u8d34\u9ea6\u54e5\u7684\u7b14\u8bb0\u4e86\uff01</p> <p>\u8bf4\u660e</p> <p>\u672c\u8282\u63a5\u4e0b\u6765\u7684\u5185\u5bb9\uff0c\u8bb2\u7684\u662f\u5982\u4f55\u4e09\u7ef4\u91cd\u5efa\u5f97\u5230\u7a00\u758f\u7684\u70b9\u4e91\uff0c\u800c\u5982\u4f55\u5f97\u5230\u7a20\u5bc6\u7684\u4e09\u7ef4\u91cd\u5efa\uff0c\u5c06\u6210\u4e3a\u4e0b\u4e00\u8282\u7684\u91cd\u70b9\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec07/#\u53cc\u76ee\u4e09\u7ef4\u91cd\u5efa","title":"\u53cc\u76ee\u4e09\u7ef4\u91cd\u5efa","text":"<p>\u53cc\u76ee\u89c6\u89c9(Stereo Vision)\uff1a\u5df2\u77e5\u4e24\u4e2a\u76f8\u673a\u7684\u5185\u53c2\uff0c\u6839\u636e\u4e24\u5f20\u56fe\u50cf\u6c42\u89e3\u4e24\u4e2a\u76f8\u673a\u7684\u5916\u53c2\u548c\u76ee\u6807\u7684 3D \u7ed3\u6784\u3002</p> <p></p>"},{"location":"cour_note/D2QD_Intro2CV/Lec07/#\u5bf9\u6781\u51e0\u4f55","title":"\u5bf9\u6781\u51e0\u4f55","text":"<p>\u5728\u524d\u4e00\u8282\u6211\u4eec\u4ecb\u7ecd\u4e86\u5982\u4f55\u5728\u300c3D \u666f\u8c61\u6a21\u578b\u5df2\u77e5\u300d\u7684\u60c5\u51b5\u4e0b\uff0c\u5bf9\u76f8\u673a\u8fdb\u884c\u6807\u5b9a\u6216\u8fdb\u884c\u672a\u77e5\u4f30\u8ba1\uff0c\u4f46\u6211\u4eec\u4ecd\u7136\u4e0d\u77e5\u9053\u5982\u4f55\u4ece 2D \u56fe\u7247\u4e2d\u91cd\u5efa\u51fa 3D \u6a21\u578b\u3002</p> <p>\u8ba9\u6211\u4eec\u8003\u8651\u53cc\u76ee\u4e09\u7ef4\u91cd\u5efa\u4e2d\u7684\u60c5\u5f62\u2014\u2014\u4e24\u4e2a\u76f8\u673a\u4e0b\u4e0d\u540c\u666f\u8c61\u4e4b\u95f4\u663e\u7136\u662f\u5b58\u5728\u4e00\u5b9a\u7684\u51e0\u4f55\u5173\u7cfb\u7684\uff0c\u800c\u5bf9\u6781\u51e0\u4f55(Epipolar Geometry)\u7740\u773c\u4e8e\u4e0b\u9762\u8fd9\u4e09\u4e2a\u76ee\u6807\u4e4b\u95f4\u7684\u51e0\u4f55\u5173\u7cfb\uff1a\u4e24\u4e2a\u76f8\u673a\u4e2d\u5fc3 \\(O_L\\) \u548c \\(O_R\\)\uff0c\u4ee5\u53ca\u666f\u7269\u4e2d\u7684\u67d0\u4e2a\u7a7a\u95f4\u70b9 \\(X\\)\uff08\u6216\u8005 \\(P\\)\uff09\u3002</p> <p>WIKI page</p> <p>https://en.wikipedia.org/wiki/Epipolar_geometry</p> <p></p> <p>Epipolar geometry is the geometry of stereo vision. When two cameras view a 3D scene from two distinct positions, there are a number of geometric relations between the 3D points and their projections onto the 2D images that lead to constraints between the image points. These relations are derived based on the assumption that the cameras can be approximated by the pinhole camera model.</p> <p>\u5bf9\u6781\u51e0\u4f55\u662f\u7acb\u4f53\u89c6\u89c9\u7684\u51e0\u4f55\u5b66\u3002\u5f53\u4e24\u4e2a\u6444\u50cf\u673a\u4ece\u4e24\u4e2a\u4e0d\u540c\u7684\u4f4d\u7f6e\u67e5\u770b 3D \u573a\u666f\u65f6\uff0c3D \u70b9\u4e0e\u5b83\u4eec\u5728 2D \u56fe\u50cf\u4e0a\u7684\u6295\u5f71\u4e4b\u95f4\u5b58\u5728\u8bb8\u591a\u51e0\u4f55\u5173\u7cfb\uff0c\u5bfc\u81f4\u56fe\u50cf\u70b9\u4e4b\u95f4\u5b58\u5728\u7ea6\u675f\u3002\u8fd9\u4e9b\u5173\u7cfb\u662f\u57fa\u4e8e\u76f8\u673a\u53ef\u4ee5\u7528\u9488\u5b54\u76f8\u673a\u6a21\u578b\u8fd1\u4f3c\u7684\u5047\u8bbe\u5bfc\u51fa\u7684\u3002</p> <p>\u2014\u2014Wiki</p> <p>\u9996\u5148\uff0c\u6211\u4eec\u9700\u8981\u4ecb\u7ecd\u5bf9\u6781\u51e0\u4f55\u4e2d\u7684\u51e0\u4e2a\u6982\u5ff5\uff0c\u6211\u4eec\u5c06\u501f\u52a9\u4e0a\u56fe\u8fdb\u884c\u8bf4\u660e\u3002</p> <p>\u57fa\u7ebf</p> <p>\u57fa\u7ebf(Baseline)\u662f\u4e24\u4e2a\u76f8\u673a\u4e2d\u5fc3\u7684\u8fde\u7ebf\uff0c\u5373 \\(OO'\\)\u3002</p> <p>\u5bf9\u6781\u70b9</p> <p>\u5bf9\u6781\u70b9(Epipole)\u6307\u7684\u662f\uff1a\u5176\u4e2d\u4e00\u4e2a\u76f8\u673a\u7684\u76f8\u673a\u4e2d\u5fc3\u5728 \u53e6\u5916\u4e00\u4e2a\u76f8\u673a\u7684\u6210\u50cf\u5e73\u9762\u4e0a\u7684\u6295\u5f71\u70b9\uff0c\u5373 \\(e_l\\) \u548c \\(e_r\\)\uff0c\u4e14\u4ed6\u4eec\u5728\u65e2\u5b9a\u7684\u5177\u4f53\u53cc\u76ee\u6a21\u578b\u4e0b\u662f\u552f\u4e00\u7684\u3002</p> <p>\u5bf9\u6781\u9762</p> <p>\u5bf9\u6781\u9762(Epipolar Plane)\u6307\u7684\u662f\u4e24\u4e2a\u76f8\u673a\u4e2d\u5fc3 \\(O_L\\) \u548c \\(O_R\\)\uff0c\u4ee5\u53ca\u666f\u7269\u4e2d\u7684\u67d0\u4e2a\u7a7a\u95f4\u70b9 \\(X\\) \u8fd9\u4e09\u4e2a\u70b9\u6240\u786e\u5b9a\u7684\u7a7a\u95f4\u5e73\u9762\u3002</p> <p>\u5176\u4e2d\u6709\u4e00\u4e2a\u6027\u8d28\uff0c\u5bf9\u6781\u9762\u603b\u662f\u7ecf\u8fc7\u76f8\u673a\u4e2d\u5fc3\u8fde\u7ebf \\(O_L O_R\\)\uff0c\u6240\u4ee5\u5bf9\u4e8e\u67d0\u4e2a\u666f\u7269\u4e2d\u7684\u70b9 \\(X_i\\)\uff0c\u5176\u5bf9\u6781\u9762\u90fd\u662f\u552f\u4e00\u7684\u3002\uff08\u663e\u7136\uff0c\u53cd\u8fc7\u6765\u4e0d\u6210\u7acb\u3002\uff09</p> <p>\u5bf9\u6781\u7ebf</p> <p>\u5bf9\u6781\u7ebf(Epipolar Line)\u662f\u5173\u4e8e\u52a8\u70b9 \\(X\\) \u6765\u8bf4\u7684\uff0c\u4f53\u73b0\u4e3a\u5bf9\u6781\u9762\u4e0e\u6210\u50cf\u5e73\u9762\u7684\u4ea4\u7ebf\u3002</p> <p>\u5047\u8bbe\u6211\u4eec\u53ea\u77e5\u9053 \\(X_L\\) \u800c\u4e0d\u77e5\u9053 \\(X_R\\)\uff0c\u90a3\u4e48 \\(X\\) \u53ef\u80fd\u5728 \\(O_L X_L\\) \u8fd9\u6761\u7ebf\u4e0a\u7684\u4efb\u4e00\u70b9\uff1b\u800c\u8fd9\u6761\u7ebf\u5728 \\(R\\) \u5e73\u9762\u4e0a\u7684\u6295\u5f71\u5c31\u662f\u4e00\u6761\u5bf9\u6781\u7ebf\uff0c\u5b83\u7684\u542b\u4e49\u662f\u53ef\u80fd\u7684 \\(X_R\\) \u7684\u8f68\u8ff9\u3002</p> <p>\u6b64\u5916\uff0c\u5bf9\u6781\u7ebf\u6709\u4e00\u4e2a\u6027\u8d28\uff1a\u5bf9\u6781\u7ebf\u5fc5\u5b9a\u7ecf\u8fc7\u5bf9\u6781\u70b9\uff0c\u800c\u7ecf\u8fc7\u5bf9\u6781\u70b9\u7684\u4efb\u610f\u4e00\u6761\u76f4\u7ebf\uff08\u5f53\u7136\u5f97\u5728\u6210\u50cf\u5e73\u9762\u4e0a\uff09\u90fd\u53ef\u4ee5\u662f\u5bf9\u6781\u7ebf\u3002</p> <p>\ud83d\udc49 WIKI\u3002</p> <p>\u5176\u4ed6\u8bf4\u660e</p> <p>\u56fe\u4e2d\u8fd8\u9700\u8981\u989d\u5916\u89e3\u91ca\u7684\u5c31\u662f \\(X_L\\) \u548c \\(X_R\\)\uff0c\u5b83\u4eec\u5206\u522b\u662f\u666f\u7269\u4e2d\u7684\u67d0\u4e2a\u7a7a\u95f4\u70b9 \\(X\\) \u5728\u4e24\u4e2a\u6210\u50cf\u5e73\u9762\u4e0a\u7684\u50cf\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec07/#\u6781\u7ebf\u7ea6\u675f","title":"\u6781\u7ebf\u7ea6\u675f","text":"<p>\u73b0\u5728\u6211\u4eec\u5173\u6ce8\u5bf9\u6781\u9762\uff0c\u7740\u773c\u4e8e\u89e3\u51b3\u4e0b\u9762\u8fd9\u6837\u4e00\u4e2a\u95ee\u9898\u3002</p> <p></p> <p>\u5176\u4e2d\u4e24\u4fa7\u7684\u76f8\u673a\u7406\u6240\u5f53\u7136\u7684\u90fd\u62e5\u6709\u81ea\u5df1\u7684\u5750\u6807\u7cfb\uff0c\u73b0\u5728\u6211\u4eec\u5bfb\u627e\u4e00\u79cd\u53d8\u6362\uff0c\u4f7f\u5f97\uff1a\\(\\mathbf{x}_l = R\\mathbf{x}_r + \\mathbf{t}\\)\uff0c\u5176\u4e2d \\(\\mathbf{t} = \\overrightarrow{O_r O_l}\\)\uff08\u56fe\u4e2d\u8c8c\u4f3c\u6807\u9519\u4e86\u65b9\u5411\uff09\uff0c\\(\\mathbf{x}_l = \\overrightarrow{O_l P}\\) \u800c \\(\\mathbf{x}_r = \\overrightarrow{O_r P}\\) \u3002</p> <p>\u4e0b\u9762\u5f00\u59cb \u53d8\u9b54\u6cd5 \u8fdb\u884c\u4e00\u4e9b\u53d8\u5316\uff1a</p> \u5f62\u5f0f \u2461 \u63a8\u7406\u8fc7\u7a0b <p>\u9996\u5148\uff0c\u5728\u540c\u4e00\u4e2a\uff08\u4efb\u4f55\u4e00\u4e2a\uff09\u7b1b\u5361\u5c14\u5750\u6807\u7cfb\u4e2d\uff0c\u90fd\u6709 \\(\\mathbf{x}_l \\cdot (\\mathbf{t} \\times \\mathbf{x}_l) = 0\\)\u3002</p> <p>\u5177\u4f53\u6765\u8bf4\uff0c\\(\\mathbf{t}\\) \u548c \\(\\mathbf{x}_l\\) \u90fd\u662f\u5bf9\u6781\u9762\u5185\u7684\u4e24\u4e2a\u4e0d\u5e73\u884c\uff08\u6211\u4eec\u5047\u5b9a\u8fd9\u4e00\u70b9\u6052\u6210\u7acb\uff09\u7684\u5411\u91cf\uff0c\u90a3\u4e48 \\(\\mathbf{t} \\times \\mathbf{x}_l\\) \u7684\u7ed3\u679c\u5fc5\u7136\u662f\u4e00\u4e2a\u5782\u76f4\u4e8e\u5bf9\u6781\u9762\u7684\u5411\u91cf\u3002\u800c\u8fd9\u4e2a\u5411\u91cf\u5fc5\u7136\u5782\u76f4\u4e8e\u5bf9\u6781\u9762\u4e0a\u4efb\u610f\u4e00\u4e2a\u5411\u91cf\uff0c\u6240\u4ee5\u4e0a\u5f0f\u7ed3\u679c\u4e3a \\(0\\)\u3002\u800c\u5c06\u8fd9\u4e2a\u5f0f\u5b50\u5199\u6210\u77e9\u9635\u5411\u91cf\u8fd0\u7b97\u7684\u5f62\u5f0f\uff0c\u5c31\u662f\uff1a</p> \\[ \\begin{bmatrix}     x_l &amp; y_l &amp; z_l \\end{bmatrix} \\left( \\begin{bmatrix}     0    &amp; -t_z &amp; t_y  \\\\     t_z  &amp; 0    &amp; -t_x \\\\     -t_y &amp; t_x  &amp; 0 \\end{bmatrix} \\begin{bmatrix}     x_l \\\\     y_l \\\\     z_l \\end{bmatrix} \\right) = 0 \\;\\;\\;\\;\\;\\left( 1 \\right) \\] <p>\u7c7b\u4f3c\u7684\uff0c\u6211\u4eec\u5c06 \\(\\mathbf{x}_l = R\\mathbf{x}_r + \\mathbf{t}\\) \u4e5f\u5199\u6210\u77e9\u9635\u548c\u5411\u91cf\u8fd0\u7b97\u7684\u5f62\u5f0f\uff1a</p> \\[ \\begin{bmatrix}     x_l \\\\     y_l \\\\     z_l         \\end{bmatrix} = \\begin{bmatrix}     r_{11} &amp; r_{12} &amp; r_{13} \\\\     r_{21} &amp; r_{22} &amp; r_{23} \\\\     r_{31} &amp; r_{32} &amp; r_{33} \\end{bmatrix} \\begin{bmatrix}     x_r \\\\     y_r \\\\     z_r \\end{bmatrix} + \\begin{bmatrix}     t_x \\\\     t_y \\\\     t_z \\end{bmatrix} \\;\\;\\;\\;\\;\\left( 2 \\right) \\] <p>\u6211\u4eec\u5c06 \\((2)\\) \u5f0f\u5e26\u5165 \\((1)\\) \u5f0f\uff0c\u5f97\u5230\uff1a</p> \\[ \\begin{bmatrix}     x_l &amp; y_l &amp; z_l \\end{bmatrix} \\begin{bmatrix}     0    &amp; -t_z &amp; t_y  \\\\     t_z  &amp; 0    &amp; -t_x \\\\     -t_y &amp; t_x  &amp; 0 \\end{bmatrix} \\left( \\begin{bmatrix}     r_{11} &amp; r_{12} &amp; r_{13} \\\\     r_{21} &amp; r_{22} &amp; r_{23} \\\\     r_{31} &amp; r_{32} &amp; r_{33} \\end{bmatrix} \\begin{bmatrix}     x_r \\\\     y_r \\\\     z_r \\end{bmatrix} + \\begin{bmatrix}     t_x \\\\     t_y \\\\     t_z \\end{bmatrix}     \\right) = 0 \\] <p>\u7a0d\u4f5c\u53d8\u5316\uff08\u628a\u542b \\(t\\) \u7684\u65b9\u9635\u62ff\u5230\u62ec\u53f7\u91cc\u9762\uff09\uff1a</p> \\[ \\begin{bmatrix}     x_l &amp; y_l &amp; z_l \\end{bmatrix} \\left( \\begin{bmatrix}     0    &amp; -t_z &amp; t_y  \\\\     t_z  &amp; 0    &amp; -t_x \\\\     -t_y &amp; t_x  &amp; 0 \\end{bmatrix} \\begin{bmatrix}     r_{11} &amp; r_{12} &amp; r_{13} \\\\     r_{21} &amp; r_{22} &amp; r_{23} \\\\     r_{31} &amp; r_{32} &amp; r_{33} \\end{bmatrix} \\begin{bmatrix}     x_r \\\\     y_r \\\\     z_r \\end{bmatrix} + \\underbrace{     \\begin{bmatrix}         0    &amp; -t_z &amp; t_y  \\\\         t_z  &amp; 0    &amp; -t_x \\\\         -t_y &amp; t_x  &amp; 0     \\end{bmatrix}     \\begin{bmatrix}         t_x \\\\         t_y \\\\         t_z     \\end{bmatrix} }_{\\mathbf{t} \\times \\mathbf{t} = 0} \\right) = 0 \\] <p>\u6211\u4eec\u5f00\u5fc3\u7684\u53d1\u73b0\u91cc\u9762\u51fa\u6765\u4e86\u4e00\u4e2a \\(0\\)\uff0c\u628a\u5b83\u6458\u6389\u4ee5\u540e\u5c31\u53d8\u6210\u4e86\uff1a</p> \\[ \\begin{bmatrix}     x_l &amp; y_l &amp; z_l \\end{bmatrix} \\underbrace{     \\begin{bmatrix}         0    &amp; -t_z &amp; t_y  \\\\         t_z  &amp; 0    &amp; -t_x \\\\         -t_y &amp; t_x  &amp; 0     \\end{bmatrix}     \\begin{bmatrix}         r_{11} &amp; r_{12} &amp; r_{13} \\\\         r_{21} &amp; r_{22} &amp; r_{23} \\\\         r_{31} &amp; r_{32} &amp; r_{33}     \\end{bmatrix} }_{\\text{Essential Matrix E}} \\begin{bmatrix}     x_r \\\\     y_r \\\\     z_r \\end{bmatrix} = 0 \\] <p>\u4e5f\u5c31\u662f\u8bf4\uff0c\u6211\u4eec\u5c06\u6c42\u89e3\u8fd9\u4e2a\u95ee\u9898\uff1a</p> <p>\u5f62\u5f0f \u2460\uff1a\u5bfb\u627e\u4e00\u79cd\u53d8\u6362\uff0c\u4f7f\u5f97\uff1a\\(\\mathbf{x}_l = R\\mathbf{x}_r + \\mathbf{t}\\)\uff0c\u5176\u4e2d \\(\\mathbf{t} = \\overrightarrow{O_r O_l}\\)\uff1b</p> <p>\u5229\u7528\u5bf9\u6781\u51e0\u4f55\u7684\u76f8\u5173\u5185\u5bb9\uff0c\u8f6c\u6362\u4e3a\u4e86\uff1a</p> <p>\u5f62\u5f0f \u2461\uff1a\u6c42\u89e3 \\(E\\) \u4f7f\u5f97 \\(\\mathbf{x}_l^T E \\mathbf{x}_r = 0\\)\uff0c\u5176\u4e2d \\(E = T_{\\times}R\\)\uff0c\u5176\u4e2d \\(T\\) \u662f \\(\\mathbf{t}\\) \u7684\u77e9\u9635\u5f62\u5f0f\uff1b</p> <p>\u7136\u800c\u6211\u4eec\u5e76\u4e0d\u77e5\u9053 \\(\\mathbf{x}_l\\) \u548c \\(\\mathbf{x}_r\\)\uff0c\u6240\u4ee5\u8fd8\u9700\u8981\u8fdb\u4e00\u6b65\u53d8\u5316\u3002</p> \u5f62\u5f0f \u2462 \u63a8\u7406\u8fc7\u7a0b <p>\u6839\u636e\u900f\u89c6\u6295\u5f71\u7684\u76f8\u5173\u5185\u5bb9\uff0c\u6211\u4eec\u53ef\u4ee5\u5f97\u5230\uff1a</p> \\[ \\small \\begin{aligned}     \\text{Left Camera} &amp;&amp; \\text{Right Camera}     \\\\     z_l      \\begin{bmatrix}     u_l \\\\ v_l \\\\ 1     \\end{bmatrix}     &amp; =     \\underbrace{     \\begin{bmatrix}     f_x^{(l)} &amp; 0 &amp; o_x^{(l)} \\\\     0 &amp; f_y^{(l)} &amp; o_y^{(l)} \\\\     0 &amp; 0 &amp; 1     \\end{bmatrix}     }_{K_l}     \\begin{bmatrix}     x_l \\\\ y_l \\\\ z_l     \\end{bmatrix}     &amp;     z_r      \\begin{bmatrix}     u_r \\\\ v_r \\\\ 1     \\end{bmatrix}     &amp;=     \\underbrace{     \\begin{bmatrix}     f_x^{(r)} &amp; 0 &amp; o_x^{(r)} \\\\     0 &amp; f_y^{(r)} &amp; o_y^{(r)} \\\\     0 &amp; 0 &amp; 1     \\end{bmatrix}     }_{K_r}     \\begin{bmatrix}     x_r \\\\ y_r \\\\ z_r     \\end{bmatrix}     \\\\     \\mathbf{x}_l^T &amp;=     \\begin{bmatrix}     u_l &amp; v_l &amp; 1     \\end{bmatrix}     z_l (K_l^{-1})^T     &amp; \\mathbf{x}_r &amp;=      K_r^{-1} z_r     \\begin{bmatrix}     u_r \\\\ v_r \\\\ 1     \\end{bmatrix} \\end{aligned} \\] <p>\u5c06\u4e0a\u5f0f\u5e26\u5165\u5230\u5f62\u5f0f \u2461 \u5f97\u5230\uff1a</p> \\[ \\begin{bmatrix}     x_l &amp; y_l &amp; z_l \\end{bmatrix} \\begin{bmatrix}     e_{11} &amp; e_{12} &amp; e_{13} \\\\     e_{21} &amp; e_{22} &amp; e_{23} \\\\     e_{31} &amp; e_{32} &amp; e_{33} \\end{bmatrix} \\begin{bmatrix}     x_r \\\\     y_r \\\\     z_r \\end{bmatrix} = 0 \\] <p>\u5c31\u53d8\u6210\u4e86\uff1a</p> \\[ \\begin{bmatrix}     u_l &amp; v_l &amp; 1 \\end{bmatrix} z_l (K_l^{-1})^T \\begin{bmatrix}     e_{11} &amp; e_{12} &amp; e_{13} \\\\     e_{21} &amp; e_{22} &amp; e_{23} \\\\     e_{31} &amp; e_{32} &amp; e_{33} \\end{bmatrix} K_r^{-1} z_r \\begin{bmatrix}     u_r \\\\ v_r \\\\ 1 \\end{bmatrix} = 0 \\] <p>\u8fd9\u65f6\uff0c\u6211\u4eec\u53d1\u73b0\uff0c\\(\\mathbf{u}_l\\) \u548c \\(\\mathbf{u}_r\\) \u7ec8\u4e8e\u662f\u6211\u4eec\u5df2\u77e5\u7684\u4e1c\u897f\u4e86\uff0c\u8fd9\u4e0b\u6211\u4eec\u53ef\u4ee5\u6c42\u89e3\u57fa\u672c\u77e9\u9635 \\(F\\)\uff0c\u800c\u7531\u4e8e\u4e24\u4e2a\u76f8\u673a\u7684\u5185\u53c2\u77e9\u9635\u4e5f\u662f\u5df2\u77e5\u7684\uff0c\u6240\u4ee5\u6211\u4eec\u8fd8\u53ef\u4ee5\u5012\u8fc7\u6765\u63a5\u7740\u5f97\u5230\u672c\u5f81\u77e9\u9635 \\(E\\)\uff0c\u6700\u540e\u901a\u8fc7 SV \u5206\u89e3\u5f97\u5230\u6211\u4eec\u60f3\u8981\u7684 \\(R\\) \u548c \\(\\mathbf{t}\\)\u3002</p> <p>\u5177\u4f53\u6765\u8bf4\uff0c\u6c42\u89e3\u57fa\u672c\u77e9\u9635\u3001\u672c\u5f81\u77e9\u9635\u3001\u5750\u6807\u53d8\u6362\u7684\u6b65\u9aa4\u5982\u4e0b\uff1a</p> \u6c42\u89e3\u6b65\u9aa4 <p>\u5bf9\u4e8e\u5173\u952e\u70b9 \\(i\\)\uff0c\u6211\u4eec\u9700\u8981\u6c42\u89e3\uff1a</p> \\[ \\begin{bmatrix}     u_l^{(i)} &amp; v_l^{(i)} &amp; 1 \\end{bmatrix} \\begin{bmatrix}     f_{11} &amp; f_{12} &amp; f_{13} \\\\     f_{21} &amp; f_{22} &amp; f_{23} \\\\     f_{31} &amp; f_{32} &amp; f_{33} \\end{bmatrix} \\begin{bmatrix}     u_r^{(i)} \\\\ v_r^{(i)} \\\\ 1 \\end{bmatrix} = 0 \\] <p>\u5c06\u5176\u5c55\u5f00\uff1a</p> \\[ \\left( f_{11} u_r^{(i)} + f_{12} v_r^{(i)} + f_13 \\right) u_l^{(i)} + \\left( f_{21} u_r^{(i)} + f_{22} v_r^{(i)} + f_23 \\right) v_l^{(i)} + f_{31} u_r^{(i)} + f_{32} v_r^{(i)} + f_33 = 0. \\] <p>\u63a5\u4e0b\u6765\u5c06\u6240\u6709\u7684 \\(m\\) \u7ec4\u65b9\u7a0b\u5408\u518d\u540c\u4e00\u4e2a\u77e9\u9635\u91cc\uff08\u6211\u4eec\u81f3\u5c11\u9700\u8981\u989d\u5916\u7684 8 \u4e2a\u65b9\u7a0b\uff0c\u4e4b\u540e\u4f1a\u8bf4\uff09\uff1a</p> \\[ \\underbrace{     \\begin{bmatrix}         u_l^{(1)}u_r^{(1)} &amp; u_l^{(1)}v_r^{(1)} &amp; u_l^{(1)} &amp; v_l^{(1)}u_r^{(1)} &amp; v_l^{(1)}v_r^{(1)} &amp; v_l^{(1)} &amp; u_r^{(1)} &amp; v_r^{(1)} &amp; 1 \\\\         \\vdots &amp; \\vdots &amp; \\vdots &amp; \\vdots &amp; \\vdots &amp; \\vdots &amp; \\vdots &amp; \\vdots &amp; \\vdots \\\\          u_l^{(i)}u_r^{(i)} &amp; u_l^{(i)}v_r^{(i)} &amp; u_l^{(i)} &amp; v_l^{(i)}u_r^{(i)} &amp; v_l^{(i)}v_r^{(i)} &amp; v_l^{(i)} &amp; u_r^{(i)} &amp; v_r^{(i)} &amp; 1 \\\\         \\vdots &amp; \\vdots &amp; \\vdots &amp; \\vdots &amp; \\vdots &amp; \\vdots &amp; \\vdots &amp; \\vdots &amp; \\vdots \\\\          u_l^{(m)}u_r^{(m)} &amp; u_l^{(m)}v_r^{(m)} &amp; u_l^{(m)} &amp; v_l^{(m)}u_r^{(m)} &amp; v_l^{(m)}v_r^{(m)} &amp; v_l^{(m)} &amp; u_r^{(m)} &amp; v_r^{(m)} &amp; 1 \\\\     \\end{bmatrix} }_{A: \\text{ Known }} \\underbrace{     \\begin{bmatrix}         f_{11} \\\\ f_{12} \\\\ f_{13} \\\\         f_{21} \\\\ f_{22} \\\\ f_{23} \\\\         f_{31} \\\\ f_{32} \\\\ f_{33} \\\\     \\end{bmatrix} }_{\\mathbf{f}: \\text{ Unknown }} = \\begin{bmatrix}     0 \\\\ 0 \\\\ 0 \\\\ 0 \\\\ 0 \\\\ 0 \\\\ 0 \\\\ 0 \\\\ 0 \\end{bmatrix} \\\\ \\text{i.e.} \\;\\;\\;\\; A\\mathbf{f}=0 \\] <p>\u5f53\u7136\uff0c\u50cf\u4e4b\u524d\u4e00\u6837\uff0c\u7531\u4e8e\u8fd9\u4e2a\u65b9\u7a0b\u53ef\u4ee5\u89e3\u51fa \\(k\\mathbf{f}, \\forall k\\in \\text{Z}\\)\uff0c\u6240\u4ee5\u6211\u4eec\u9700\u8981\u7ed9 \\(\\mathbf{f}\\) \u4e00\u4e2a\u7ea6\u675f\uff0c\u5728\u8fd9\u91cc\u6211\u4eec\u53d6 \\(||\\mathbf{f}||^2 = 1\\)\uff0c\u4e8e\u662f\u95ee\u9898\u5c31\u53c8\u53d8\u6210\u4e86\uff1a</p> \\[ \\mathop{minimize} \\limits_{\\mathbf{f}} ||A\\mathbf{f}||^2 \\text{ such that } ||\\mathbf{f}||^2 = 1 \\] <p>\u4e3a\u4e86\u6c42\u89e3 \\(F\\) \u4e2d\u7684 9 \u4e2a\u672a\u77e5\u6570\uff0c\u6211\u4eec\u5df2\u7ecf\u6709\u4e00\u4e2a\u786e\u5b9a\u7684\u7ea6\u675f\u65b9\u7a0b\u662f \\(||\\mathbf{f}||^2 = 1\\)\uff0c\u6240\u4ee5\u8fd8\u9700\u8981\u989d\u5916 8 \u4e2a\u65b9\u7a0b\u3002</p> <p>\u6c42\u89e3\u5f97\u5230 \\(F\\) \u4ee5\u540e\uff0c\u6839\u636e \\(E = K_l^T F K_r\\) \u5f97\u5230 \\(E\\)\u3002</p> <p>\u524d\u9762\u4e5f\u5df2\u7ecf\u8bf4\u8fc7\uff0c\u5bf9 \\(E\\) \u8fdb\u884c SV \u5206\u89e3\u5c31\u53ef\u4ee5\u5f97\u5230 \\(R\\) \u548c \\(T_{\\times}\\)\uff0c\u5bf9 \\(T_{\\times}\\) \u91cd\u6392\u5217\u5c31\u5f97\u5230\u4e86 \\(\\mathbf{t}\\)\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec07/#\u672c\u5f81\u77e9\u9635","title":"\u672c\u5f81\u77e9\u9635","text":"<p>\u66f4\u8fdb\u4e00\u6b65\u5316\u7b80\uff0c\u6211\u4eec\u53ef\u4ee5\u628a\u4e2d\u95f4\u4e24\u4e2a\u77e9\u9635\u5408\u8d77\u6765\uff0c\u5f97\u5230\u672c\u5f81\u77e9\u9635(Essential Matrix)\\(E\\)\uff1a</p> \\[ E=T_{\\times}R= \\begin{bmatrix}     e_{11} &amp; e_{12} &amp; e_{13} \\\\     e_{21} &amp; e_{22} &amp; e_{23} \\\\     e_{31} &amp; e_{32} &amp; e_{33} \\end{bmatrix} \\] <p>\u4e8e\u662f\u6211\u4eec\u5c31\u5f97\u5230\uff1a</p> \\[ \\begin{bmatrix}     x_l &amp; y_l &amp; z_l \\end{bmatrix} \\begin{bmatrix}     e_{11} &amp; e_{12} &amp; e_{13} \\\\     e_{21} &amp; e_{22} &amp; e_{23} \\\\     e_{31} &amp; e_{32} &amp; e_{33} \\end{bmatrix} \\begin{bmatrix}     x_r \\\\     y_r \\\\     z_r \\end{bmatrix} = 0 \\;\\;\\;\\text{i.e.} \\;\\;\\; \\mathbf{x}_l^T E \\mathbf{x}_r = 0 \\] <p>\u672c\u5f81\u77e9\u9635\u7684\u6027\u8d28</p> <p>\u7531\u4e8e Essential Matrix \u7684\u5b9a\u4e49\u5177\u6709\u5982\u4e0b\u7279\u5f81\uff1a</p> <p></p> <p>\\(T_{\\times}\\) \u53cd\u5bf9\u79f0(Skew-Symmetric)\uff0c\\(R\\) \u6b63\u4ea4(Orthonormal)\u3002</p> <p>\u6240\u4ee5\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528\u5947\u5f02\u503c\u5206\u89e3(Singular Value Decomposition)\u6216\u8005\u8bf4 SV \u5206\u89e3\u6765\u53bb\u8026\u5408\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec07/#\u57fa\u672c\u77e9\u9635","title":"\u57fa\u672c\u77e9\u9635","text":"<p>\u6211\u4eec\u53ef\u4ee5\u5c06\u5e38\u6570 \\(z_l\\) \u548c \\(z_r\\) \u7ea6\u6389\uff0c\u5e76\u4e14\u5408\u5e76\u4e2d\u95f4\u7684\u4e09\u4e2a\u77e9\u9635\uff0c\u5f97\u5230\uff1a</p> \\[ \\begin{bmatrix}     u_l &amp; v_l &amp; 1 \\end{bmatrix} \\underbrace{     (K_l^{-1})^T     \\begin{bmatrix}         e_{11} &amp; e_{12} &amp; e_{13} \\\\         e_{21} &amp; e_{22} &amp; e_{23} \\\\         e_{31} &amp; e_{32} &amp; e_{33}     \\end{bmatrix}     K_r^{-1} }_{\\text{Fundamental Matrix F}} \\begin{bmatrix}     u_r \\\\ v_r \\\\ 1 \\end{bmatrix} = 0 \\] <p>\u4e8e\u662f\u5f97\u5230\u4e86\u57fa\u672c\u77e9\u9635(Fundamental Matrix)\\(F\\)\uff1a</p> \\[ F = (K_l^{-1})^T E K_r^{-1}    = (K_l^{-1})^T      \\begin{bmatrix}         e_{11} &amp; e_{12} &amp; e_{13} \\\\         e_{21} &amp; e_{22} &amp; e_{23} \\\\         e_{31} &amp; e_{32} &amp; e_{33}     \\end{bmatrix}     K_r^{-1}   = \\begin{bmatrix}         f_{11} &amp; f_{12} &amp; f_{13} \\\\         f_{21} &amp; f_{22} &amp; f_{23} \\\\         f_{31} &amp; f_{32} &amp; f_{33}     \\end{bmatrix} \\] <p>\u8fd9\u5c31\u662f\u6211\u4eec\u7684\u5f62\u5f0f \u2462\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec07/#\u4e09\u89d2\u6d4b\u91cf","title":"\u4e09\u89d2\u6d4b\u91cf","text":"<p>\u6211\u4eec\u77e5\u9053\uff0c\u5982\u679c\u5047\u8bbe\u6570\u636e\u90fd\u662f\u51c6\u786e\u7684\uff0c\u90a3\u4e48 \\(O_l X_l\\) \u548c \\(O_r X_r\\) \u5e94\u5f53\u76f8\u4ea4\u4e8e\u7a7a\u95f4\u70b9 \\(X\\)\u3002\u800c\u4e09\u89d2\u6d4b\u91cf\u63cf\u8ff0\u7684\u5c31\u662f\u5982\u4f55\u901a\u8fc7\u8fd9\u6837\u4e00\u4e2a\u8fc7\u7a0b\u5f97\u5230\u7a7a\u95f4\u70b9 \\(X\\)\u3002</p> <p>\u6211\u4eec\u5728 \u6781\u7ebf\u7ea6\u675f \u91cc\u5df2\u7ecf\u77e5\u9053\u4e86 \\(\\mathbf{x}_l\\) \u548c \\(\\mathbf{x}_r\\) \u7684\u53d8\u6362\u5173\u7cfb\uff0c\u4e5f\u5c31\u662f\u8bf4\u6211\u4eec\u73b0\u5728\u5df2\u7ecf\u6709\u4e86 \\(O_l X_l\\) \u548c \\(O_r X_r\\) \u7684\u65b9\u7a0b\u4e86\u3002\u90a3\u4e48\u5e94\u5f53\u80fd\u591f\u89e3\u51fa\u8fd9\u4e2a \\(X\\)\uff0c\u4e0d\u8fc7\u7531\u4e8e\u5b9e\u9645\u6570\u636e\u6709\u8bef\u5dee\uff0c\u6240\u4ee5\u6211\u4eec\u53ef\u80fd\u53ea\u80fd\u901a\u8fc7\u4f18\u5316\u7684\u65b9\u6cd5\u5f97\u5230\u8fd1\u4f3c\u89e3\u3002</p> <p>\u5177\u4f53\u7684\u63a8\u7406\u6b65\u9aa4\u5982\u4e0b\uff1a</p> \u6c42\u89e3\u6b65\u9aa4 <p>\u9996\u5148\u6211\u4eec\u4f7f\u7528\u9f50\u6b21\u5750\u6807\u6539\u5199\u53d8\u6362\u65b9\u7a0b\uff0c\u5e76\u6700\u7ec8\u5199\u6210\u5173\u4e8e \\(\\mathbf{u}\\) \u7684\u5f62\u5f0f   \\begin{aligned}     \\text{Left Camera}     \\\\     \\because     \\begin{bmatrix}         u_l \\\\ v_l \\\\ 1     \\end{bmatrix}     &amp;=     \\begin{bmatrix}         f_x^{(l)} &amp; 0 &amp; o_x^{(l)} &amp; 0 \\\\         0 &amp; f_y^{(l)} &amp; o_y^{(l)} &amp; 0 \\\\         0 &amp; 0 &amp; 1 &amp; 0     \\end{bmatrix}     \\begin{bmatrix}         x_l \\\\ y_l \\\\ z_l \\\\ 1     \\end{bmatrix}     ,\\ \\      \\begin{bmatrix}         x_l \\\\ y_l \\\\ z_l \\\\ 1     \\end{bmatrix}     =     \\begin{bmatrix}         r_{11} &amp; r_{12} &amp; r_{13} &amp; t_x \\\\         r_{21} &amp; r_{22} &amp; r_{23} &amp; t_y \\\\         r_{31} &amp; r_{32} &amp; r_{33} &amp; t_z \\\\         0 &amp; 0 &amp; 0 &amp; 1     \\end{bmatrix}     \\begin{bmatrix}         x_r \\\\ y_r \\\\ z_r \\\\ 1     \\end{bmatrix}     \\\\     \\therefore     \\begin{bmatrix}         u_l \\\\ v_l \\\\ 1     \\end{bmatrix}     &amp;=     \\begin{bmatrix}         f_x^{(l)} &amp; 0 &amp; o_x^{(l)} &amp; 0 \\\\         0 &amp; f_y^{(l)} &amp; o_y^{(l)} &amp; 0 \\\\         0 &amp; 0 &amp; 1 &amp; 0     \\end{bmatrix}     \\begin{bmatrix}         r_{11} &amp; r_{12} &amp; r_{13} &amp; t_x \\\\         r_{21} &amp; r_{22} &amp; r_{23} &amp; t_y \\\\         r_{31} &amp; r_{32} &amp; r_{33} &amp; t_z \\\\         0 &amp; 0 &amp; 0 &amp; 1     \\end{bmatrix}     \\begin{bmatrix}         x_r \\\\ y_r \\\\ z_r \\\\ 1     \\end{bmatrix}     \\\\     \\text{i.e. } \\mathbf{\\tilde u}_l &amp;=      P_l \\mathbf{\\tilde x}_r     \\\\     \\text{Right Camera}     \\\\     \\begin{bmatrix}         u_r \\\\ v_r \\\\ 1     \\end{bmatrix}     &amp;=     \\begin{bmatrix}         f_x^{(r)} &amp; 0 &amp; o_x^{(r)} &amp; 0 \\\\         0 &amp; f_y^{(r)} &amp; o_y^{(r)} &amp; 0 \\\\         0 &amp; 0 &amp; 1 &amp; 0     \\end{bmatrix}     \\begin{bmatrix}         x_r \\\\ y_r \\\\ z_r \\\\ 1     \\end{bmatrix}     \\\\     \\text{i.e. } \\mathbf{\\tilde u}_r &amp;=      M_{int_r} \\mathbf{\\tilde x}_r \\end{aligned}  </p> <p>\u7a0d\u4f5c\u603b\u7ed3\uff0c\u5c31\u662f\u5f97\u5230\u4e86\u4e0b\u9762\u8fd9\u4e24\u4e2a\u5173\u7cfb\uff1a</p> \\[ \\mathbf{\\tilde u}_l = P_l \\mathbf{\\tilde x}_r \\\\ \\begin{bmatrix}     u_r \\\\ v_r \\\\ 1 \\end{bmatrix} = \\begin{bmatrix}     m_{11} &amp; m_{12} &amp; m_{13} &amp; m_{14} \\\\     m_{21} &amp; m_{22} &amp; m_{23} &amp; m_{24} \\\\     m_{31} &amp; m_{32} &amp; m_{33} &amp; m_{34} \\\\ \\end{bmatrix} \\begin{bmatrix}     x_r \\\\ y_r \\\\ z_r \\\\ 1 \\end{bmatrix} \\\\ \\\\ \\mathbf{\\tilde u}_l = M_{int_r} \\mathbf{\\tilde x}_r \\\\ \\begin{bmatrix} u_l \\\\ v_l \\\\ 1 \\end{bmatrix} = \\begin{bmatrix} p_{11} &amp; p_{12} &amp; p_{13} &amp; p_{14} \\\\ p_{21} &amp; p_{22} &amp; p_{23} &amp; p_{24} \\\\ p_{31} &amp; p_{32} &amp; p_{33} &amp; p_{34} \\\\ \\end{bmatrix} \\begin{bmatrix} x_r \\\\ y_r \\\\ z_r \\\\ 1 \\end{bmatrix} \\] <p>\u6211\u4eec\u53d1\u73b0\uff0c\u9664\u4e86 \\(\\mathbf{x}_r\\) \u7684\u90e8\u5206\u90fd\u662f\u5df2\u77e5\u7684\uff0c\u6b64\u65f6\u6211\u4eec\u5c31\u53ef\u4ee5\u300c\u8054\u7acb\u300d\u8fd9\u4e24\u4e2a\u65b9\u7a0b\uff0c\u5c06\u4ed6\u4eec\u91cd\u6392\u5217\u4e3a\u5982\u4e0b\u5f62\u5f0f\uff1a</p> \\[ \\underbrace{ \\begin{bmatrix}     u_r m_{31} - m_{11} &amp; u_r m_{32} - m_{12} &amp; u_r m_{33} - m_{13} \\\\      v_r m_{31} - m_{21} &amp; v_r m_{32} - m_{22} &amp; v_r m_{33} - m_{23} \\\\      u_l p_{31} - p_{11} &amp; u_l p_{32} - p_{12} &amp; u_l p_{33} - p_{13} \\\\       v_l p_{31} - p_{21} &amp; v_l p_{32} - p_{22} &amp; v_l p_{33} - p_{23} \\end{bmatrix} }_{A_{4\\times 3}} \\underbrace{ \\begin{bmatrix}     x_r \\\\ y_r \\\\ z_r \\end{bmatrix} }_{\\mathbf{x}_r} = \\underbrace{ \\begin{bmatrix}     m_{14} - m_{34} \\\\     m_{24} - m_{34} \\\\       p_{14} - p_{34} \\\\      p_{24} - p_{34} \\end{bmatrix} }_{\\mathbf{b}} \\] <p>\u6211\u4eec\u5df2\u77e5 \\(A_{4 \\times 3}\\) \u548c \\(\\mathbf{b}\\)\uff0c\u9700\u8981\u6c42 \\(\\mathbf{x}_r\\)\u3002</p> <p>\u6211\u4eec\u4e4b\u524d\u5df2\u7ecf\u63d0\u5230\uff0c\u7531\u4e8e\u5b9e\u9645\u6570\u636e\u5b58\u5728\u8bef\u5dee\uff0c\u6240\u4ee5\u6211\u4eec\u6ca1\u53d1\u76f4\u63a5\u6c42\u5176\u89e3\u6790\u89e3\uff0c\u800c\u662f\u53ef\u4ee5\u4f7f\u7528\u6700\u5c0f\u4e8c\u4e58\u7684\u7ed3\u8bba\uff0c\u5f97\u5230\uff1a</p> \\[ \\mathbf{x}_r = (A^TA)^{-1}A^T\\mathbf{b} \\] <p>\u8fd8\u6709\u4e00\u79cd\u6539\u8fdb\uff0c\u5c31\u662f\u5c06\u5b83\u8f6c\u5316\u6210\u6700\u5c0f\u5316\u518d\u6295\u5f71\u8bef\u5dee(Reprojection Error)\u7684\u4f18\u5316\u95ee\u9898\u3002</p> <p>\u6362\u53e5\u8bdd\u6765\u8bf4\uff0c\u5c31\u662f\u6c42\u4e00\u4e2a \\(X\\) \u4f7f\u5f97\u5b83\u5728\u4e24\u4e2a\u6210\u50cf\u5e73\u9762\u4e0a\u7684\u6295\u5f71\u548c\u5b9e\u9645\u7684\u6295\u5f71\u4e4b\u95f4\u7684\u8bef\u5dee\u6700\u5c0f\u3002</p> <p></p> <p>\u5b9a\u4e49\u518d\u6295\u5f71\u8bef\u5dee\u4e3a\uff1a</p> \\[ cost(P) = dist(\\mathbf{u}_l, \\cap{\\mathbf{u}_l})^2 + dist(\\mathbf{u}_r, \\cap{\\mathbf{u}_r})^2 \\]"},{"location":"cour_note/D2QD_Intro2CV/Lec07/#\u5177\u4f53\u6b65\u9aa4","title":"\u5177\u4f53\u6b65\u9aa4","text":"<p>\u524d\u63d0</p> <p>\u4e24\u4e2a\u76f8\u673a\u7684\u5185\u53c2\u77e9\u9635\\(K\\) \u5df2\u77e5\u3002</p> <p>\u8fd9\u610f\u5473\u7740\u6211\u4eec\u53ef\u4ee5\u6839\u636e\u8fd9\u4e9b\u53c2\u6570\u5c06\u76f8\u673a\u6210\u50cf\u53ef\u89c6\u5316\uff0c\u5982\u4e0b\u56fe\u3002</p> <p>\u5176\u4e2d\u4e0b\u6807\u4e3a \\(l\\) \u7684\u8868\u793a\u5de6\u4fa7\u76f8\u673a\u7684\u76f8\u5173\u5173\u952e\u70b9\uff0c\u4e0b\u6807\u4e3a \\(r\\) \u7684\u8868\u793a\u53f3\u4fa7\u76f8\u673a\u7684\u76f8\u5173\u5173\u952e\u70b9\u3002</p> <p></p> <p>\u6b65\u9aa4\u4e00</p> <p>\u5bf9\u4e24\u5f20\u56fe\u7247\u8fdb\u884c \u5173\u952e\u70b9\u5339\u914d\uff0c\u627e\u5230\u81f3\u5c11 8 \u5bf9\u5339\u914d\u7279\u5f81\u3002</p> <p>\u300c\u4e3a\u4ec0\u4e48\u9700\u8981 8 \u5bf9\u300d\u8fd9\u4e2a\u95ee\u9898\u6211\u4eec\u5728 #\u6781\u7ebf\u7ea6\u675f/\u6c42\u89e3\u8fc7\u7a0b \u4e2d\u5df2\u7ecf\u8bf4\u660e\u3002</p> <p></p> <p>\u6b65\u9aa4\u4e8c</p> <p>\u6309\u7167 #\u6781\u7ebf\u7ea6\u675f/\u6c42\u89e3\u8fc7\u7a0b \u63d0\u5230\u7684\u6b65\u9aa4\uff0c\u6c42\u89e3\u4e24\u4e2a\u76f8\u673a\u5750\u6807\u7684\u53d8\u6362\u53c2\u6570 \\(R\\) \u548c \\(\\mathbf{t}\\)\u3002</p> <p>\u6b65\u9aa4\u4e09</p> <p>\u63a5\u4e0b\u6765\u5bf9\u4e8e\u6bcf\u4e00\u5bf9\u5339\u914d\u7684\u5173\u952e\u70b9\uff0c\u6309\u7167 #\u4e09\u89d2\u6d4b\u91cf \u63d0\u5230\u7684\u65b9\u6cd5\uff0c\u6c42\u89e3\u7a7a\u95f4\u70b9 \\(X_i\\)\u3002</p> <p>\u4e8e\u662f\u6211\u4eec\u5c31\u5f97\u5230\u4e86\u6240\u6709\u5339\u914d\u7684\u5173\u952e\u70b9\u8ba1\u7b97\u5f97\u5230\u7684\u7a7a\u95f4\u70b9\uff0c\u6700\u7ec8\u5f97\u5230\u4e00\u4efd\u7a00\u758f\u7684\u7a7a\u95f4\u70b9\u4e91\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec07/#\u591a\u76ee\u4e09\u7ef4\u91cd\u5efa","title":"\u591a\u76ee\u4e09\u7ef4\u91cd\u5efa","text":"<p>Sequential SfM\uff1a</p> <ol> <li>\u4ece\u5176\u4e2d\u4e24\u5f20\u5f00\u59cb\uff0c\u5bf9\u573a\u666f\u8fdb\u884c\u91cd\u5efa</li> <li>\u4e4b\u540e\u4e0d\u65ad\u62ff\u51fa\u65b0\u7684\u56fe\u50cf\uff0c\u6839\u636e\u5df2\u77e5\u8ba1\u7b97 camera pose\uff0c\u518d\u8fdb\u4e00\u6b65\u4f18\u5316\u4e4b\u524d\u91cd\u5efa\u51fa\u6765\u7684 3D \u70b9\uff0c\u4ee5\u53ca\u589e\u52a0\u4e00\u4e9b\u65b0\u7684\u70b9</li> <li>\u4f7f\u7528\u96c6\u675f\u4f18\u5316\u8fdb\u4e00\u6b65\u4f18\u5316\u548c\u8c03\u6574</li> </ol>"},{"location":"cour_note/D2QD_Intro2CV/Lec07/#\u96c6\u675f\u4f18\u5316","title":"\u96c6\u675f\u4f18\u5316","text":"<p>\u96c6\u675f\u4f18\u5316(Bundle Adjustment)\u4e5f\u5c31\u662f\u5728\u591a\u76ee\u60c5\u51b5\u4e0b\uff0c\u5bf9\u4e8e\u6240\u6709\u70b9\u7684 \u518d\u6295\u5f71\u8bef\u5dee \u4f18\u5316\u95ee\u9898\uff1a</p> <p></p> \\[ \\mathop{minimize} \\limits_\\mathbf{P} E(P_{proj}, \\mathbf{P}) = \\sum^m_{i=1}\\sum^n_{j=1} dist(u_j^{(i)}, P_{proj}^{(i)}\\mathbf{P}_j)^2 \\] <p>\u5176\u6c42\u89e3\u53ef\u4ee5\u4f7f\u7528 LM algorithm\u3002</p> <p>A modern SfM system: COLMAP</p> <ul> <li>GitHub Repo: https://github.com/colmap/colmap</li> </ul> <p>COLMAP is a general-purpose Structure-from-Motion (SfM) and Multi-View Stereo (MVS) pipeline with a graphical and command-line interface. It offers a wide range of features for reconstruction of ordered and unordered image collections. </p> <p></p>"},{"location":"cour_note/D2QD_Intro2CV/Lec08/","title":"Lecture 8 | Depth Estimation &amp; 3D Reconstruction","text":"<p> \u7ea6 5007 \u4e2a\u5b57  6 \u884c\u4ee3\u7801  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 17 \u5206\u949f</p> <p>\u6ce8\u610f</p> <p>\u672c\u6587\u5c1a\u672a\u5b8c\u5168\u6574\u7406\u597d\uff01</p> <p>\u5f15\u5165</p> <p>\u5728 \u4e0a\u4e00\u7ae0 \u4e2d\uff0c\u6211\u4eec\u5df2\u7ecf\u4ecb\u7ecd\u4e86\u5982\u4f55\u91cd\u5efa\u5f97\u5230\u5173\u952e\u70b9\u7684\u70b9\u4e91\uff0c\u4f46\u662f\u6b64\u65f6\u6211\u4eec\u5f97\u5230\u7684\u53ea\u662f\u4e00\u4e2a\u7a00\u758f\u7684\u70b9\u4e91\uff0c\u800c\u672c\u7ae0\u9700\u8981\u89e3\u51b3\u7684\u95ee\u9898\u5c31\u662f\u5982\u4f55\u201c\u7a20\u5bc6\u201d\u5730\u8fdb\u884c\u91cd\u5efa\u3002</p> <p>\u800c\u5728\u7a20\u5bc6\u91cd\u5efa\u8fc7\u7a0b\u4e2d\uff0c\u6211\u4eec\u4e0d\u80fd\u5355\u5355\u7740\u773c\u4e8e\u5173\u952e\u70b9\uff0c\u800c\u662f\u8981\u5e7f\u6cdb\u5730\u9762\u5411\u56fe\u50cf\u4e2d\u7684\u6240\u6709\u50cf\u7d20\uff0c\u800c\u5176\u4e2d\u6700\u91cd\u8981\u7684\u4e00\u4e2a\u6280\u672f\u5c31\u662f\u6df1\u5ea6\u4f30\u8ba1(Depth Estimation)\u3002</p> <p>\u300c\u6df1\u5ea6\u300d\u8fd9\u4e2a\u6982\u5ff5\u548c\u5b83\u7684\u5b57\u9762\u610f\u601d\u51e0\u4e4e\u4e00\u6837\uff0c\u800c\u5728\u300c\u6df1\u5ea6\u4f30\u8ba1\u300d\u4e2d\uff0c\u6211\u4eec\u9700\u8981\u505a\u7684\u662f\u5bf9\u4e8e\u7ed9\u5b9a\u7684\u56fe\u50cf\uff0c\u6807\u8bb0\u6bcf\u4e00\u4e2a\u50cf\u7d20\u7684\u6df1\u5ea6\u3002\u800c\u5c06\u5176\u53ef\u89c6\u5316\uff0c\u5c31\u662f\u6df1\u5ea6\u56fe\u3002</p> <p></p> <p>\u53ea\u4e0d\u8fc7\u6709\u65f6\u5019\u6df1\u5ea6\u6307\u7684\u662f\u7a7a\u95f4\u70b9\u5230\u76f8\u673a\u4e2d\u95f4\u6216\u8005\u76f8\u673a\u5e73\u9762\u7684\u8ddd\u79bb\uff0c\u4e5f\u6709\u7684\u65f6\u5019\u6307\u7684\u662f\u67d0\u4e2a\u7a7a\u95f4\u5750\u6807\u8f74\u5411\u7684\u6df1\u5ea6\uff0c\u5177\u4f53\u5e94\u5f53\u6839\u636e\u5b9e\u9645\u60c5\u51b5\u6765\u3002</p> <p>\u6309\u7167\u6df1\u5ea6\u611f\u77e5\u7684\u624b\u6bb5\u5206\u7c7b\uff0c\u6709\u4e3b\u52a8\u6df1\u5ea6\u63a2\u6d4b\u65b9\u6cd5(Active depth sensing)\u548c\u88ab\u52a8\u6df1\u5ea6\u63a2\u6d4b\u65b9\u6cd5(Passive depth sensing)\u4e24\u79cd\uff0c\u5176\u4e2d\u6211\u4eec\u5c06\u8981\u5c55\u5f00\u7684\u89c6\u89c9\u65b9\u6cd5\u90fd\u662f\u88ab\u52a8\u63a2\u6d4b\u65b9\u6cd5\u3002</p> <p>\u4e3b\u52a8\u63a2\u6d4b\u65b9\u6cd5 / \u975e\u89c6\u89c9\u65b9\u6cd5</p> <ul> <li>LiDAR</li> <li>Structured light</li> <li>Active stereo</li> </ul> <p>\u88ab\u52a8\u63a2\u6d4b\u65b9\u6cd5 / \u89c6\u89c9\u65b9\u6cd5</p> <ul> <li>Stereo</li> <li>Multi-view stereo</li> <li>Monocular</li> </ul> <p>\u903b\u8f91\u94fe\uff1a</p> <p>(\u53cc\u76ee\u89c6\u89c9 -&gt; \u6df1\u5ea6\u611f\u77e5) =&gt; ((\u53cc\u89c6\u89d2\u5339\u914d\u70b9 + \u89c6\u5dee -&gt; \u6df1\u5ea6) + (\u5bf9\u6240\u6709\u50cf\u7d20\u8fdb\u884c\u5339\u914d)) =&gt; \u6781\u7ebf\u4e0a\u5bfb\u627e\u5339\u914d\u70b9</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec08/#\u7acb\u4f53\u89c6\u89c9","title":"\u7acb\u4f53\u89c6\u89c9","text":"<p>\u6211\u4eec\u5df2\u7ecf\u6709\u4e86\u7a00\u758f\u91cd\u5efa\u7684\u65b9\u6cd5\uff0c\u60f3\u8981\u5f97\u5230\u7a20\u5bc6\u91cd\u5efa\u7684\u65b9\u6cd5\uff0c\u4e00\u4e2a\u6700\u66b4\u529b\u7684\u65b9\u6cd5\u5c31\u662f\u5c1d\u8bd5\u7740\u53bb\u5339\u914d\u6240\u6709\u50cf\u7d20\uff0c\u5f53\u7136\u8fd9\u770b\u8d77\u6765\u65f6\u95f4\u5f00\u9500\u975e\u5e38\u5927\u3002\u4f46\u662f\u6bcb\u5eb8\u7f6e\u7591\u7684\u662f\uff0c\u5728\u76ee\u524d\u8fd8\u6ca1\u6709\u4ecb\u5165\u4eba\u5de5\u667a\u80fd\u6280\u672f\u7684\u60c5\u51b5\u4e0b\uff0c\u6211\u4eec\u4ecd\u7136\u9700\u8981\u50cf\u7d20\u7684\u5339\u914d\u5173\u7cfb\u3002</p> <p>\u4ee5\u53ca\u8fd8\u6709\u4e00\u4e2a\u9700\u8981\u89e3\u51b3\u7684\u95ee\u9898\u5c31\u662f\uff0c\u5982\u4f55\u5f97\u5230\u5339\u914d\u70b9\u7684\u6df1\u5ea6\u4fe1\u606f\u3002</p> <p>\u6240\u4ee5\u603b\u7ed3\u4e0b\u6765\uff0c\u6709\u4e24\u4e2a\u95ee\u9898\u9700\u8981\u89e3\u51b3\uff1a</p> <ul> <li> \u5982\u4f55\u9ad8\u6548\u5730\u5f97\u5230\u5339\u914d\u5173\u7cfb\uff1b</li> <li> \u5982\u4f55\u6839\u636e\u5339\u914d\u70b9\u8ba1\u7b97\u70b9\u6df1\u5ea6\uff1b</li> </ul> <p>\u7531\u4e8e\u5339\u914d\u4e2d\u4f1a\u6709\u90e8\u5206\u4f18\u5316\u5185\u5bb9\u6d89\u53ca\u5230\u6df1\u5ea6\u8ba1\u7b97\u7684\u5185\u5bb9\uff0c\u6240\u4ee5\u6211\u60f3\u5148\u4ece\u6df1\u5ea6\u8ba1\u7b97\u5f00\u59cb\u8bb2\uff0c\u4e5f\u5c31\u662f\u4ece\u89c6\u5dee\u5f00\u59cb\u8bb2\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec08/#\u89c6\u5dee","title":"\u89c6\u5dee","text":"<p>\u9996\u5148\uff0c\u6211\u4eec\u90fd\u77e5\u9053\u4eba\u7684\u53cc\u773c\u8d4b\u4e88\u4e86\u4eba\u7c7b\u89c6\u89c9\u4e0a\u6df1\u5ea6\u611f\u77e5\u7684\u80fd\u529b\uff0c\u4e5f\u5c31\u662f\u7acb\u4f53\u89c6\u89c9(stereo vision)\u3002\u4e00\u4e2a\u6bd4\u8f83\u5bb6\u55bb\u6237\u6653\u7684\u5b9e\u9a8c\u5c31\u662f\u5355\u773c\u7a7f\u9488\u4f1a\u53d8\u5f97\u5341\u5206\u56f0\u96be\u3002</p> <p>\u5728\u5355\u76ee\u89c6\u89c9\u4e0b\uff0c\u4f53\u73b0\u8fdc\u8fd1\u6700\u7b80\u5355\u7684\u539f\u7406\u63cf\u8ff0\u5c31\u662f\u300c\u8fd1\u5927\u8fdc\u5c0f\u300d\uff0c\u800c\u5728\u52a8\u6001\u7684\u60c5\u51b5\u4e0b\uff0c\u8fd9\u4e5f\u4f53\u73b0\u5728\u79fb\u52a8\u76f8\u540c\u7684\u8ddd\u79bb\uff0c\u8fd1\u5904\u7684\u7269\u4f53\u79fb\u52a8\u66f4\u660e\u663e\uff0c\u800c\u8fdc\u5904\u7684\u66f4\u4e0d\u660e\u663e\u3002\u7136\u800c\u8fd9\u4e2a\u4fe1\u606f\u548c\u5355\u7eaf\u7684\u201c\u5927\u5c0f\u201d\u4fe1\u606f\u662f\u53ef\u4ee5\u6df7\u6dc6\u7684\uff0c\u6216\u8005\u8bf4\u5728\u201c\u5927\u5c0f\u201d\u53d8\u5316\u4e0d\u660e\u663e\u7684\u60c5\u51b5\u4e0b\uff0c\u8fd9\u4e2a\u4fe1\u606f\u662f\u5f88\u96be\u88ab\u8bc6\u522b\u51fa\u6765\u7684\u3002</p> <p>\u800c\u5728\u53cc\u76ee\u89c6\u89c9\u4e0b\uff0c\u6211\u4eec\u6709\u6709\u4e00\u4e2a\u66f4\u8fd1\u4e00\u6b65\u7684\u539f\u7406\uff0c\u4e5f\u5c31\u662f\u89c6\u5dee(disparity)\uff0c\u901a\u8fc7\u89c6\u5dee\uff0c\u6211\u4eec\u53ef\u4ee5\u66f4\u7cbe\u786e\u5730\u611f\u53d7\u5230\u201c\u8ddd\u79bb\u201d\uff08\u5b9e\u9645\u4e0a\u4e5f\u662f\u5bf9\u6781\u51e0\u4f55\u90a3\u4e00\u5957\uff09\uff0c\u63a5\u4e0b\u6765\u9610\u8ff0\u5176\u539f\u7406\u3002</p> <p>\u9996\u5148\uff0c\u6211\u4eec\u7ed8\u5236\u4e00\u4e2a\u7b80\u5355\u7684\u6a21\u578b\uff1a</p> <p>\u5728\u8fd9\u4e2a\u6a21\u578b\u4e2d\uff0c\u6211\u4eec\u5047\u8bbe\u4e24\u4e2a\u56fe\u50cf\u4e2d\u7684\u5339\u914d\u70b9\u7b26\u5408\u4e4b\u540e\u4f1a\u5728\u7acb\u4f53\u5339\u914d\u4e00\u8282\u91cc\u63d0\u5230\u7684\u6700\u7b80\u60c5\u51b5(simplest case)\uff0c\u4f46\u662f\u53ef\u4ee5\u4e0d\u7528\u7ba1\u8fd9\u4e2a\u6700\u7b80\u60c5\u51b5\u662f\u4ec0\u4e48\uff0c\u76f4\u63a5\u5f53\u4f5c\u8fd9\u662f\u4e00\u4e2a\u4fef\u89c6\u89c6\u89d2\u4e0b\u7684\u7b80\u5316\uff0c\u76f4\u63a5\u770b\u4e0b\u9762\u7684\u6a21\u578b\u5373\u53ef\u3002</p> <p></p> <p>\u8fd9\u56fe\u6211\u753b\u4e86\u81f3\u5c11\u534a\u5c0f\u65f6 T^T\uff08\u5f3a\u8feb\u75c7\u306e\u6028\u5ff5\uff09</p> <p>(1) \u4e2d OL \u548c OR \u5206\u522b\u662f\u4e24\u76f8\u673a\u4e2d\u5fc3\uff0c\u6de1\u84dd\u8272\u7ebf\u6761\u8868\u793a\u6210\u50cf\u5e73\u9762\uff0cXL \u548c XR \u5206\u522b\u8868\u793a\u5b9e\u9645\u70b9 X \u5728\u6210\u50cf\u5e73\u9762\u4e0a\u7684\u6295\u5f71\uff0c\u6a59\u8272\u7ebf\u6761\u8868\u793a\u4ed6\u4eec\u7684\u6a2a\u5411\u5750\u6807\uff08\u5047\u8bbe\u4ed6\u4eec\u90fd\u5728\u540c\u4e00\u6c34\u5e73\u7ebf\u4e0a\uff09\uff0cz \u8868\u793a\u5b9e\u9645\u70b9 X \u5230\u57fa\u7ebf\u7684\u8ddd\u79bb\uff0c\u8fd9\u91cc\u6211\u4eec\u6682\u4e14\u79f0\u4e4b\u4e3a\u201c\u6df1\u5ea6\u201d\uff08\u53cd\u6b63\u4e0d\u7ba1\u600e\u4e48\u5b9a\u4e49\u6df1\u5ea6\uff0c\u6709 z \u90fd\u80fd\u7b97\uff09\u3002</p> <p>(2) \u4e2d\u6211\u753b\u56fe\u7684\u65f6\u5019\u5fd8\u8bb0\u533a\u5206\u4e24\u4e2a XR \u4e86\uff0c\u6240\u4ee5\u5173\u4e8e (2) \u56fe\u4e2d\u7684 XR \u4e00\u5f8b\u6307\u5de6\u8fb9\u90a3\u4e2a XR\u3002</p> <p>\u6211\u4eec\u5c06 OR \u7684\u6210\u50cf\u6a21\u578b\u5e73\u79fb\u5230\u5de6\u4fa7\uff0c\u5373\u56fe (2)\uff0c\u53d1\u73b0\u6a59\u8272\u7684\u4e09\u89d2\u5f62\u548c\u7ea2\u8272\u7684\u4e09\u89d2\u5f62\u76f8\u4f3c\uff1a\\(\\Delta O X_L X_R \\cong \\Delta X O_L O_R\\) \uff08\u6ce8\u610f\uff0c\u5b9e\u9645\u60c5\u51b5\u4e0d\u4e00\u5b9a\u7b49\u8170\uff01\uff09</p> <p>\u4e8e\u662f\u6211\u4eec\u5f97\u5230\uff0c\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff1a</p> \\[ \\frac{\\overline{X_L X_R}}{f} = \\frac{\\overline{O_L O_R}}{z} \\\\ \\text{ i.e. }\\; disparity = \\Delta{\\mathbf{x}} = |\\mathbf{x}_l - \\mathbf{x}_r| = |x_l - x_r| = \\frac{B \\cdot f}{z} \\\\ \\text{where }B\\text{ is the length of baseline} \\\\ \\text{ i.e. }\\; z = \\frac{B \\cdot f}{|x_l-x_r|} \\] <p>\u63d0\u793a</p> <p>\u867d\u7136\u662f\u4e2a\u7b80\u5316\u60c5\u51b5\uff0c\u4f46\u662f\u5728\u6700\u7b80\u60c5\u51b5(simplest case)\u4e0b\u662f\u53ef\u4ee5\u76f4\u63a5\u632a\u7528\u7ed3\u8bba\u7684\uff0c\u7a0d\u540e\u6211\u4f1a\u63d0\u9192\u56de\u987e\u8fd9\u4e00\u8282\u6765\u7406\u89e3\u8fd9\u4e00\u70b9\uff0c\u6240\u4ee5\u5b89\u5fc3\u987a\u7740\u8bfb\u4e0b\u53bb\u5373\u53ef\u3002</p> <p>\u81f3\u6b64\uff0c\u6211\u4eec\u5728\u672c\u8282\u5f00\u5934\u63d0\u5230\u7684\u4e24\u4e2a\u95ee\u9898\uff0c\u5df2\u7ecf\u89e3\u51b3\u4e00\u4e2a\u4e86\u3002</p> <ul> <li> \u5982\u4f55\u9ad8\u6548\u5730\u5f97\u5230\u5339\u914d\u5173\u7cfb\uff1b</li> <li> \u5982\u4f55\u6839\u636e\u5339\u914d\u70b9\u8ba1\u7b97\u70b9\u6df1\u5ea6\uff1b</li> </ul>"},{"location":"cour_note/D2QD_Intro2CV/Lec08/#\u7acb\u4f53\u5339\u914d","title":"\u7acb\u4f53\u5339\u914d","text":"<p>\u9996\u5148\u6211\u4eec\u505a\u4e00\u4e2a\u5047\u8bbe\uff0c\u4e5f\u5c31\u662f\u5728\u5339\u914d\u8fc7\u7a0b\u4e2d\uff0c\u6211\u4eec\u7684\u4e24\u4e2a view \u7684\u8ddd\u79bb\u76f8\u5dee\u4e0d\u5927\uff0c\u4e5f\u5c31\u662f\u8bf4\u5c40\u90e8\u7279\u5f81\u4ecd\u7136\u662f\u76f8\u4f3c\u7684\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec08/#\u641c\u7d22","title":"\u641c\u7d22","text":"<p>\u7acb\u4f53\u5339\u914d(Stereo Matching)\u7684\u539f\u7406\u5c31\u662f\uff0c\u9009\u5b9a\u7b2c\u4e00\u4e2a\u56fe\u50cf\u5185\u7684\u67d0\u4e00\u70b9\uff0c\u7136\u540e\u53bb\u53e6\u5916\u4e00\u5f20\u56fe\u50cf\u5bf9\u5e94\u7684\u5bf9\u6781\u7ebf\u4e0a\u641c\u7d22\u627e\u5230\u80fd\u591f\u548c\u5b83\u5339\u914d\u7684\u70b9\u3002\u6ca1\u9519\uff0c\u6211\u4eec\u53ea\u9700\u8981\u5728\u4e00\u6761\u76f4\u7ebf\u4e0a\u641c\u7d22\u627e\u5230\u5339\u914d\u7684\u70b9\u5373\u53ef\uff0c\u8fd9\u5927\u5927\u4f18\u5316\u4e86\u590d\u6742\u5ea6\u3002\u800c\u5b83\u7684\u6839\u636e\u6070\u597d\u5c31\u662f\u5bf9\u6781\u7ebf\u7684\u5b9a\u4e49\u3002</p> <p>\ud83d\udc49 \u56de\u987e\u5bf9\u6781\u51e0\u4f55\uff01</p> <p>\u6ca1\u9519\uff0c\u6211\u4eec\u73b0\u5728\u5df2\u77e5\u4e86 \\(X_L\\)\uff08\u7531\u6211\u4eec\u9009\u5b9a\u7684\uff09\uff0c\u90a3\u4e48 \\(X_R\\) \u7684\u8f68\u8ff9\u4fbf\u662f\u5bf9\u6781\u7ebf\uff0c\u4e8e\u662f\u6211\u4eec\u53ea\u9700\u8981\u5148\u627e\u5230\u6211\u4eec\u9009\u5b9a\u7684 \\(X_L\\) \u5728\u53e6\u5916\u4e00\u5f20\u56fe\u50cf\u4e0a\u5bf9\u5e94\u7684\u5bf9\u6781\u7ebf\uff0c\u7136\u540e\u518d\u5728\u8fd9\u6761\u7ebf\u4e0a\u641c\u7d22\u7279\u5f81\u4e0e \\(X_L\\) \u6700\u5339\u914d\u7684\u90a3\u4e2a\u70b9\u5373\u53ef\u3002\uff08\u8fd9\u91cc\u6211\u4eec\u4e5f\u6ca1\u6709\u5fc5\u8981\u4f7f\u7528 SIFT\uff0c\u76f4\u63a5\u505a\u5dee\u5c31\u591f\u4e86\uff09</p> <p>\u4f46\u662f\u8bdd\u53c8\u8bf4\u56de\u6765\uff0c\u8ba1\u7b97\u5bf9\u6781\u7ebf\u8fd9\u4ef6\u4e8b\u4e5f\u5e76\u975e\u5341\u5206\u7b80\u5355\uff0c\u5982\u679c\u5bf9\u4e8e\u6bcf\u4e2a\u70b9\u6211\u4eec\u90fd\u9700\u8981\u53bb\u8ba1\u7b97\u5bf9\u6781\u7ebf\uff0c\u90a3\u4e48\u5c06\u5e26\u6765\u4e0d\u5c0f\u7684\u5e38\u6570\uff0c\u800c\u4e14\u7531\u4e8e\u8fd9\u4ef6\u4e8b\u6ca1\u6cd5\u201c\u6574\u4f53\u5730\u9884\u5904\u7406\u201d\uff0c\u6240\u4ee5\u6211\u4eec\u8fd8\u9700\u8981\u4f18\u5316\u8fd9\u4ef6\u4e8b\u3002</p> <p>\u6700\u7b80\u60c5\u51b5</p> <p>\u9996\u5148\u8003\u8651\u6700\u7b80\u60c5\u51b5(simplest case)\u8fd9\u4e2a\u7279\u6b8a\u60c5\u51b5\uff1a</p> <p></p> <ol> <li>\u4e24\u4e2a\u76f8\u673a\u7684\u7126\u8ddd\u76f8\u540c\uff1b</li> <li>\u76f8\u673a\u4f4d\u7f6e\u5728\u540c\u4e00\u6c34\u5e73\u9762\u4e0a\uff0c\u5373\u9ad8\u5ea6\u76f8\u540c\uff1b</li> <li>\u4e24\u4e2a\u6210\u50cf\u5e73\u9762\u548c\u57fa\u7ebf\uff0c\u4e09\u8005\u76f8\u4e92\u5e73\u884c\uff0c\u6216\u8005\u8bf4\u4e24\u4e2a\u6210\u50cf\u5e73\u9762\u5171\u9762\uff08\u6b64\u65f6\u5bf9\u6781\u70b9\u4e0d\u5b58\u5728\uff09\uff1b</li> </ol> <p>\u6b64\u65f6\uff0c\u5bf9\u6781\u7ebf\u4e5f\u6c34\u5e73\uff0c\u800c\u4e14\u4e24\u6761\u5bf9\u6781\u7ebf\u4e5f\u5171\u7ebf\uff08\u53ef\u4ee5\u601d\u8003\u4e00\u4e0b\u4e3a\u4ec0\u4e48\uff09\u3002</p> <p>\u6362\u53e5\u8bdd\u6765\u8bf4\uff0c\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u5f53\u6211\u4eec\u9009\u5b9a\u5de6\u56fe\u4e2d\u7684\u67d0\u4e2a\u70b9 \\(X_L\\)\uff0c\u90a3\u4e48 \\(X_R\\) \u7684\u5019\u9009\u4f4d\u7f6e\u5c31\u5728\u53f3\u56fe\u4e2d\u540c\u4e00\u9ad8\u5ea6\u7684\u90a3\u6761\u6c34\u5e73\u7ebf\u4e0a\u3002</p> <p></p> <p>\u90a3\u4e48\u5982\u4f55\u89e3\u51b3\u8fd9\u79cd\u60c5\u51b5\u4ee5\u5916\u7684\u60c5\u51b5\u5462\uff1f\u65e2\u7136\u6211\u90fd\u8fd9\u4e48\u6392\u4e86\uff0c\u90a3\u89e3\u51b3\u529e\u6cd5\u81ea\u7136\u5c31\u662f\u8f6c\u5316\u4e3a\u6700\u7b80\u60c5\u51b5\u6765\u505a\u4e86\u3002</p> <p>\u8f6c\u5316\u601d\u60f3</p> <p>\u53c8\u662f\u4e00\u4e2a\u7a81\u7136\u7684\u60f3\u6cd5\uff0c\u5f88\u591a\u65f6\u5019\u6211\u4eec\u6216\u8bb8\u53ef\u4ee5\u4e0d\u4ece\u6574\u4f53\u53bb\u601d\u8003\uff0c\u800c\u662f\u5148\u89e3\u51b3\u4e00\u4e2a\u6700\u7b80\u60c5\u51b5\uff0c\u518d\u8f6c\u5316\u95ee\u9898\u3002</p> <p>\u4e00\u822c\u60c5\u51b5</p> <p></p> <p>\u8fd9\u4e2a\u95ee\u9898\u88ab\u79f0\u4e3a\u7acb\u4f53\u5f71\u50cf\u77eb\u6b63\uff0c\u8fd9\u91cc\u5e76\u4e0d\u5c55\u5f00\uff0c\u53ef\u4ee5\u53c2\u8003\u8fd9\u7bc7\u6587\u7ae0\uff1a</p> <p>C. Loop and Z. Zhang. Computing Rectifying Homographies for Stereo Vision. IEEE Conf. Computer Vision and Pattern Recognition, 1999.</p> <p></p> <p>\u56de\u987e</p> <p>\u76f8\u4fe1\u73b0\u5728\u4f60\u5bf9\u201c\u6700\u7b80\u60c5\u51b5\u201d\u5df2\u7ecf\u6709\u66f4\u6df1\u523b\u7684\u7406\u89e3\u4e86\uff0c\u4e0d\u59a8\u56de\u8fc7\u5934\u53bb\u7406\u89e3\u4e00\u4e0b\u4e3a\u4ec0\u4e48\u6211\u4eec\u4e4b\u524d\u63d0\u5230\u7684\u90a3\u4e2a\u7b80\u5316\u7684\u89c6\u5dee\u6a21\u578b\u53ef\u4ee5\u76f4\u63a5\u632a\u7528\u7ed3\u8bba\uff1f</p> <p>\ud83d\udc49 \u89c6\u5dee</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec08/#\u5339\u914d","title":"\u5339\u914d","text":"<p>\u6240\u8c13\u7684\u5bfb\u627e\u5339\u914d\uff0c\u5c31\u662f\u5728\u5145\u65a5\u7740\u5019\u9009\u70b9\u7684\u5bf9\u6781\u7ebf\u4e0a\u641c\u7d22\u5339\u914d\u6700\u597d\u7684\u4e00\u4e2a\u70b9\uff0c\u6216\u8005\u8bf4\u5dee\u5f02\u6700\u5c0f\u7684\u4e00\u4e2a\u70b9\u3002</p> <p>\u5e38\u89c1\u7684\u5dee\u5f02\u8861\u91cf\u65b9\u6cd5\u6709\u8fd9\u4e48\u51e0\u79cd\uff1a</p> <p>SSD: Sum of Squared Differences</p> \\[ diff = \\sum_{x,y} |W_1(x,y) - W_2(x,2)|^2 \\] <p>SAD: Sum of Absolute Differences</p> \\[ diff = \\sum_{x,y} |W_1(x,y) - W_2(x,y)| \\] <p>ZNCC: Zero-mean Normalized Cross Correlation</p> \\[ diff = \\frac{(W_1(x,y)-\\overline{W_1})(W_2(x,y)-\\overline{W_2})}{\\sigma_{W_1}\\sigma_{W_2}} \\\\ \\text{where  } \\overline{W_i} = \\frac{1}{n}\\sum_{x,y} W_i \\;\\;\\; \\sigma_{W_i} = \\sqrt{\\frac{1}{n}\\sum_{x,y}(W_i-\\overline{W_i})^2} \\] <p>\u5176\u4e2d\uff0cZNCC \u76f8\u6bd4\u5176\u4ed6\u65b9\u6cd5\uff0c\u4f18\u8d8a\u6027\u5728\u4e8e\u5b83\u5bf9\u56fe\u50cf\u6574\u4f53\u7684\u5149\u5f3a\u5ea6\u4e0d\u654f\u611f\uff0c\u56e0\u4e3a\u6211\u4eec\u53ef\u4ee5\u53d1\u73b0\uff0c\\(W_i\\) \u5728\u53c2\u4e0e\u8ba1\u7b97\u524d\u90fd\u51cf\u53bb\u4e86 \\(\\overline{W_i}\\)\uff0c\u6240\u4ee5\u6d88\u9664\u4e86\u56fe\u50cf\u6574\u4f53\u4eae\u5ea6\u5e26\u6765\u7684\u5f71\u54cd\u3002</p> \u4e2a\u4eba\u7591\u60d1 <p>\u8fd9\u91cc\u6240\u8c13\u7684\u201c\u6d88\u9664\u4eae\u5ea6\u5f71\u54cd\u201d\uff0c\u662f\u5426\u662f\u5bf9\u4e8e multi-view \u7684\u60c5\u51b5\u6765\u8bf4\u7684\uff1f\u56e0\u4e3a\u5982\u679c\u53ea\u6709\u4e24\u5f20\u56fe\u7247\uff0c\u4e14\u4eae\u5ea6\u5dee\u8ddd\u6574\u4f53\u6052\u5b9a\u7684\u8bdd\uff0c\u867d\u7136\u8ba1\u7b97\u51fa\u6765\u7684 diff \u4f1a\u504f\u5927\uff0c\u4f46\u662f\u6574\u4f53\u4e0a\u7684\u5927\u5c0f\u5173\u7cfb\u597d\u50cf\u4e5f\u6ca1\u6709\u53d8\u5316\uff1f\u6211\u6ca1\u6709\u60f3\u6e05\u695a\u8fd9\u4e00\u70b9\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec08/#\u5339\u914d\u7684\u6539\u8fdb","title":"\u5339\u914d\u7684\u6539\u8fdb","text":"<p>\u7136\u800c\uff0c\u5339\u914d\u8fc7\u7a0b\u4e2d\u8fd8\u6709\u4e00\u4e2a\u989d\u5916\u7684\u95ee\u9898\u9700\u8981\u89e3\u51b3\u3002</p> <p>\u7a97\u53e3\u641c\u7d22\u7684\u5f0a\u7aef</p> <p>\u7a97\u53e3\u641c\u7d22\u7684\u6548\u679c\u5b9e\u9645\u4e0a\u5e38\u5e38\u4e0d\u5c3d\u5982\u4eba\u610f\uff0c\u6709\u4e00\u79cd\u57fa\u4e8e\u56fe\u5272\u7684\u505a\u6cd5\uff0c\u6548\u679c\u76f8\u5bf9\u7a0d\u597d\u3002</p> <p>\u8fd9\u91cc\u6240\u8bf4\u7684\u7a97\u53e3\uff0c\u6307\u7684\u662f\u5728\u5339\u914d\u641c\u7d22\u8fc7\u7a0b\u4e2d\uff0c\u7528\u6765\u6bd4\u8f83\u76f8\u4f3c\u5ea6\u7684\u7a97\u53e3\u5927\u5c0f\u3002</p> <p></p> <p>\ud83d\udc49 Boykov et al., Fast Approximate Energy Minimization via Graph Cuts, International Conference on Computer Vision 1999.</p> <p>\u8fd8\u6709\u53e6\u5916\u4e00\u4e2a\u601d\u8def\uff0c\u90a3\u5c31\u662f\u8f6c\u5316\u4e3a\u4f18\u5316\u95ee\u9898\uff0c\u5982\u679c\u8bf4\u539f\u6765\u7684\u76ee\u6807\u51fd\u6570\u662f\u4e24\u70b9\u7684\u5339\u914d\u7a0b\u5ea6\uff0c\u90a3\u4e48\u73b0\u5728\u7684\u76ee\u6807\u51fd\u6570\u53ef\u4ee5\u662f\u5339\u914d\u7a0b\u5ea6\u548c\u5e73\u6ed1\u7a0b\u5ea6\u7684\u52a0\u6743\u548c\uff1a</p> <p></p> \\[ \\begin{aligned}     E(d) = E_d(d) + \\lambda E_s(s) \\\\     \\text{match cost:   } &amp; E_d(d) = \\sum_{(x,y)\\in I} C(x,y,d(x,y)) \\;\\;\\; \\text{e.g., SSD, SAD, ZNCC} \\\\     \\text{smoothness cost:   } &amp; E_s(d) = \\sum_{(p,q) \\in \\varepsilon} V(d_p, d_q) \\;\\;\\; \\text{where } \\varepsilon \\text{ is the set of neighboring pixels } \\end{aligned} \\] <p>\u5176\u4e2d\uff0c\\(V(d_p,d_q)\\) \u4e00\u822c\u6709\u4e24\u79cd\u9009\u62e9\uff1a</p> \\[ \\begin{aligned} \\begin{aligned}     \\text{L_1 Distance: } \\\\     V(d_p, d_q) &amp;= |d_p - d_q| \\end{aligned} &amp; &amp; \\begin{aligned}     \\text{Potts Model: } \\\\     V(d_p, d_q) &amp;=          \\left\\{             \\begin{array}{*}                 0 &amp; \\text{ if } d_p = d_q \\\\                 1 &amp; \\text{ if } d_p \\not = d_q             \\end{array}         \\right. \\end{aligned} \\end{aligned} \\] <p></p> <p>\u7279\u522b\u7684\uff0c\u5982\u679c\u6d89\u53ca\u7684\u662f\u4e00\u4e2a\u7ebf\u6027\u7684\u626b\u63cf\uff0c\u4e5f\u5c31\u662f\u5f53 \\(\\varepsilon\\) \u4e2d\u53ea\u542b\u6709\u5de6\u53f3\u4e24\u4fa7\u7684\u70b9\uff0c\u90a3\u4e48\u8fd9\u4e2a\u95ee\u9898\u53ef\u4ee5\u7528 DP \u89e3\u51b3\u3002\u800c\u8fd9\u79cd\u65b9\u5f0f\u4f18\u5316\u51fa\u6765\u7684\u56fe\u7247\u6548\u679c\u662f\u8fd9\u6837\u7684\uff1a</p> <p></p> <p>\u7136\u800c\uff0c\u5982\u679c\u4e0d\u6ee1\u8db3\u7ebf\u6027\u626b\u63cf\u8fd9\u4e2a\u6761\u4ef6\u7684\u8bdd\uff0c\u8fd9\u4e2a\u95ee\u9898\u5c31\u53d8\u6210\u4e86\u4e00\u4e2a NP-hard \u95ee\u9898\uff0c\u4e0d\u8fc7\u53ef\u4ee5\u7528\u56fe\u5272\u6c42\u8fd1\u4f3c\u89e3\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec08/#\u7efc\u5408","title":"\u7efc\u5408","text":"<p>\u81f3\u6b64\uff0c\u6211\u4eec\u5728\u672c\u8282\u5f00\u5934\u63d0\u5230\u7684\u4e24\u4e2a\u95ee\u9898\uff0c\u5df2\u7ecf\u5168\u90e8\u89e3\u51b3\u4e86\u3002</p> <ul> <li> \u5982\u4f55\u9ad8\u6548\u5730\u5f97\u5230\u5339\u914d\u5173\u7cfb\uff1b</li> <li> \u5982\u4f55\u6839\u636e\u5339\u914d\u70b9\u8ba1\u7b97\u70b9\u6df1\u5ea6\uff1b</li> </ul> <p>\u4e8e\u662f\u53cc\u76ee\u91cd\u5efa\u7684\u5927\u81f4\u6d41\u7a0b\u5982\u4e0b\u2014\u2014\u9996\u5148\u6211\u4eec\u5bf9\u76f8\u673a\u8fdb\u884c\u6807\u5b9a\uff0c\u83b7\u5f97\u76f8\u673a\u7684\u5185\u53c2\uff1b\u63a5\u4e0b\u6765\u901a\u8fc7\u7acb\u4f53\u5f71\u50cf\u77eb\u6b63\u6280\u672f\uff0c\u5c06\u4e24\u5f20\u56fe\u7247\u8f6c\u5316\u4e3a\u6700\u7b80\u60c5\u51b5\uff1b\u7136\u540e\u518d\u5bf9\u6bcf\u4e00\u4e2a\u50cf\u7d20\u8fdb\u884c\u5339\u914d\uff0c\u53ea\u9700\u8981\u5728\u540c\u9ad8\u5ea6\u7684\u5bf9\u6781\u7ebf\u4e0a\u641c\u7d22\u5339\u914d\u5c40\u90e8\u7279\u5f81\u6700\u76f8\u4f3c\u7684\u53e6\u5916\u4e00\u4e2a\u70b9\u5373\u53ef\uff1b\u63a5\u7740\u518d\u6839\u636e\u5339\u914d\u70b9\u7684\u5173\u7cfb\u8fdb\u884c\u6df1\u5ea6\u4f30\u8ba1\u5373\u53ef\u3002</p> <pre><code>graph LR;\n    A --&gt; B --&gt; C --&gt; D\n    A[\"Calibrate Cameras\"]\n    B[\"Rectify Images\"]\n    C[\"Compute Disparity\"]\n    D[\"Estimate Depth\"]</code></pre> \u5f15\u8d77\u8bef\u5dee\u7684\u53ef\u80fd\u56e0\u7d20 <p>\u8bfe\u7a0b\u5185\u8fd9\u4e2a\u5217\u8868\u5176\u5b9e\u662f\u7ed9\u5927\u4f5c\u4e1a\u7684\u63d0\u793a\uff0c\u4e2a\u4eba\u8ba4\u4e3a\u4e5f\u6709\u52a9\u4e8e\u68b3\u7406\u6574\u4e2a\u6d41\u7a0b\u3002</p> <ul> <li>Camera calibration errors</li> <li>Poor image resolution</li> <li>Occlusions</li> <li>Violations of brightness constancy (specular reflections)</li> <li>Large motions</li> <li>Textureless regions</li> </ul> <p>\u4e0b\u9762\u8be6\u7ec6\u8bf4\u660e\u51e0\u4e2a\u56e0\u7d20\u5bf9\u7ed3\u679c\u7684\u5f71\u54cd\u3002</p> <p>\u7a97\u53e3\u5927\u5c0f\u7684\u9009\u62e9\u5bf9\u7ed3\u679c\u7684\u5f71\u54cd</p> <p>\u5f53\u6211\u4eec\u4f7f\u7528\u7a97\u53e3\u641c\u7d22\u65f6\uff0c\u7a97\u53e3\u5927\u5c0f\u7684\u9009\u62e9\u4ecd\u7136\u662f\u4e2a\u96be\u9898\u2014\u2014\u7a97\u53e3\u8d8a\u5c0f\uff0c\u5f80\u5f80\u7ed3\u679c\u7684\u7ec6\u8282\u4f1a\u66f4\u591a\uff0c\u76f8\u5bf9\u7684\u566a\u58f0\u4e5f\u66f4\u591a\uff0c\u56fe\u7247\u770b\u8d77\u6765\u5c31\u5f88\u4e71\uff1b\u800c\u7a97\u53e3\u8d8a\u5927\uff0c\u5f80\u5f80\u566a\u58f0\u66f4\u5c11\u3001\u66f4\u5e73\u6ed1\uff0c\u4f46\u662f\u7ec6\u8282\u4e5f\u66f4\u5c11\uff0c\u4e5f\u5c31\u662f\u8bf4\uff0c\u8fd9\u91cc\u6709\u4e00\u4e2a\u5e73\u6ed1\u5ea6\u548c\u7cbe\u786e\u5ea6\u7684 trade off\u3002</p> <p></p> <p>W \u8868\u793a\u7a97\u53e3\u5927\u5c0f\u3002</p> <p>\u57fa\u7ebf\u5927\u5c0f\u7684\u9009\u62e9\u5bf9\u7ed3\u679c\u7684\u5f71\u54cd</p> <ul> <li>\u5982\u679c\u57fa\u7ebf\u9009\u62e9\u8fc7\u5927\uff0c\u90a3\u4e48\u4e24\u5f20\u56fe\u7247\u4e4b\u95f4\u7684\u5185\u5bb9\u5dee\u522b\u5c31\u4f1a\u8f83\u5927\uff0c\u5728\u641c\u7d22\u8fc7\u7a0b\u4e2d\u5c31\u66f4\u96be\u627e\u5230\u80fd\u591f\u5339\u914d\u7684\u70b9\uff0c\u6b64\u5916\uff0c\u6a2a\u5411\u7684\u8bef\u5dee\u4e5f\u4f1a\u589e\u5927\uff0c\u7406\u7531\u53ef\u4ee5\u53c2\u8003\u4e0b\u9762\u8fd9\u5f20\u56fe\u7684\u539f\u7406\uff1b</li> <li>\u800c\u5982\u679c\u57fa\u7ebf\u9009\u62e9\u8fc7\u5c0f\uff0c\u5219\u70b9\u7684\u6df1\u5ea6\u8bef\u5dee\u5c31\u4f1a\u5f88\u5927\uff0c\u5177\u4f53\u539f\u56e0\u53ef\u4ee5\u53c2\u8003\u4e0b\u9762\u8fd9\u5f20\u56fe\u2014\u2014\u5355\u4e00\u50cf\u7d20\u5bf9\u5e94\u7684\u5019\u9009\u70b9\u533a\u57df\u66f4\u6df1\uff0c\u610f\u5473\u7740\u5f53\u524d\u70b9\u53ef\u80fd\u662f\u8fd9\u4e00\u83f1\u5f62\u91cc\u7684\u4efb\u4f55\u70b9\uff1b</li> </ul> <p></p> <p>\u8c28\u8bb0\u6211\u53c8\u56e0\u4e3a\u753b\u56fe\u6d6a\u8d39\u534a\u4e2a\u5c0f\u65f6\u3002</p> <p>\u4e0a\u9762\u7684\u5185\u5bb9\u7ed3\u675f\u540e\uff0c\u5176\u5b9e\u8fd8\u6709\u4e00\u4e2a\u9057\u7559\u4e0b\u6765\u95ee\u9898\uff0c\u8bfb\u8005\u53ef\u4ee5\u5148\u601d\u8003\u4e00\u4e0b\u76ee\u524d\u8fd9\u4e2a\u6d41\u7a0b\u6709\u4ec0\u4e48\u95ee\u9898\uff0c\u518d\u6253\u5f00\u4e0b\u9762\u7684\u63d0\u793a\u6846\u3002</p> \u4e00\u4e2a\u5c1a\u672a\u88ab\u89e3\u51b3\u7684\u95ee\u9898 <p>\u8ba9\u6211\u4eec\u56de\u5230\u7b2c\u4e94\u7ae0\u7684\u5173\u952e\u70b9\u5339\u914d\u2014\u2014\u4e3a\u4ec0\u4e48\u6211\u4eec\u53ea\u627e\u5173\u952e\u70b9\uff1f</p> <p>\u6211\u4e2a\u4eba\u7684\u60f3\u6cd5\u662f\uff0c\u9996\u5148\uff0c\u5173\u952e\u70b9\u80fd\u591f\u4e00\u5b9a\u7a0b\u5ea6\u4e0a\u8868\u8fbe\u4e00\u4e2a\u7269\u4f53\u7684\u7279\u5f81\uff0c\u6216\u8005\u8bf4\u5b83\u662f\u52fe\u52d2\u4e00\u4e2a\u7269\u4f53\u975e\u5e38\u91cd\u8981\u7684\u4e00\u4e2a\u90e8\u5206\uff1b\u8fd8\u6709\u4e00\u4e2a\u539f\u56e0\u662f\uff0c\u5173\u952e\u70b9\u7279\u5f81\u660e\u663e\uff0c\u5176\u8868\u8fbe\u5177\u6709\u4e00\u5b9a\u7684\u72ec\u7279\u6027\uff08\u4e5f\u5c31\u662f\u5173\u952e\u70b9\u7684\u72ec\u7279\u6027(uniqueness)\uff09\u3002</p> <p>\u800c\u73b0\u5728\u6211\u4eec\u505a\u5339\u914d\u7684\u5185\u5bb9\u662f\u4efb\u610f\u7684\u3001\u5e7f\u6cdb\u7684\uff0c\u4f8b\u5982\u6211\u4eec\u73b0\u5728\u5728\u505a\u5339\u914d\u7684\u5f88\u53ef\u80fd\u662f\u4e00\u9762\u767d\u5899\u4e0a\u7684\u67d0\u4e00\u4e2a\u70b9\uff08\u5c31\u662f\u4e0a\u9762\u63d0\u5230\u8fc7\u7684 textureless regions\uff09\uff0c\u8fd9\u6837\u7684\u70b9\u53c8\u8981\u5982\u4f55\u627e\u5230\u5b83\u7684\u5339\u914d\u70b9\u5462\uff1f</p> <p>\u7b54\u6848\u5c31\u662f\uff0c\u6211\u4eec\u53ef\u4ee5\u7528\u7ed3\u6784\u5149\u6765\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\u3002</p> \u7ed3\u6784\u5149 <p>\u6211\u4eec\u518d\u68b3\u7406\u4e00\u4e0b\u95ee\u9898\u7684\u8981\u70b9\uff0c\u5c31\u4ee5\u767d\u5899\u4e3a\u4f8b\u5b50\uff0c\u5b83\u96be\u4ee5\u8fdb\u884c\u5339\u914d\u662f\u56e0\u4e3a\u5b83\u7f3a\u5c11\u7279\u5f81\u3001\u7f3a\u5c11\u7eb9\u7406\uff0c\u800c\u6211\u4eec\u7684\u76ee\u6807\u662f\u5bf9\u5176\u7ed3\u6784\u8fdb\u884c\u91cd\u5efa\u2014\u2014\u90a3\u4e48\u4e00\u4e2a\u60f3\u6cd5\u5c31\u662f\u6211\u4eec\u624b\u52a8\u7ed9\u4ed6\u300c\u4e0a\u7eb9\u7406\u300d\uff0c\u5f53\u7136\u5e76\u4e0d\u662f\u6307\u753b\u4e0a\u53bb\uff0c\u800c\u662f\u4f7f\u7528\u7ed3\u6784\u5149\uff1a</p> <p></p> <p>\u4e8e\u662f\u6211\u4eec\u7684\u56fe\u50cf\u5c31\u6709\u4e86\u7eb9\u7406\uff0c\u62e5\u6709\u4e86\u201c\u7279\u5f81\u201d\u3002</p> <p>\u4e2a\u4eba\u60f3\u6cd5</p> <p>\u6211\u5f53\u65f6\u770b\u5230\u8fd9\u4e2a idea \u7684\u65f6\u5019\uff0c\u611f\u89c9\u5f88\u523a\u6fc0\uff0c\u4f46\u662f\u53c8\u89c9\u5f97\u8fd9\u7834\u574f\u4e86\u666f\u8c61\u672c\u6765\u7684\u7eb9\u7406\uff0c\u4f46\u662f\u8f6c\u5ff5\u4e00\u60f3\uff0c\u662f\u4e0d\u662f\u4f1a\u62cd\u4e24\u5f20\uff0c\u4e00\u5f20\u7528\u6765\u4e0a\u8272\uff0c\u4e00\u5f20\u7528\u6765\u5efa\u6a21\uff1f\u6211\u6682\u65f6\u8fd8\u4e0d\u77e5\u9053\uff0c\u7ebf\u653e\u4e2a\u731c\u60f3\u5728\u8fd9\u91cc\u3002</p> <p>\u4e0d\u8fc7\u6b64\u65f6\u53c8\u6709\u4e00\u4e2a\u5f15\u7533\u51fa\u6765\u7684\u70b9\uff0c\u5c31\u662f\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u5176\u5b9e\u53ef\u4ee5\u51cf\u5c11\u4e00\u4e2a\u76f8\u673a\u3002</p> <p></p> <p>\u8fd9\u662f\u56e0\u4e3a\uff0c\u5047\u8bbe\u6211\u4eec\u628a camera 2 \u653e\u5728\u4e0e projector \u4e00\u6837\u7684\u4f4d\u7f6e\uff0c\u6b64\u65f6 camera 2 \u6536\u5230\u7684\u56fe\u50cf\u5e94\u5f53\u548c projector \u5c04\u51fa\u53bb\u7684\u662f\u4e00\u6837\u7684\uff0c\u6216\u8005\u8bf4\u662f\u7c7b\u4f3c\u7684\u3002</p> <p>\u5982\u4f55\u89e3\u91ca\uff1f</p> <p>\u8bf4\u5b9e\u8bdd\u6211\u8fd8\u662f\u4e0d\u592a\u80fd\u7406\u89e3\u8fd9\u4e00\u70b9\u3002\u5982\u679c\u8981\u6211\u5f3a\u884c\u7406\u89e3\u7684\u8bdd\uff0c\u6211\u89c9\u5f97\u5927\u6982\u662f\u53c8\u8fd9\u4e48\u4e24\u70b9\uff0c\u7b2c\u4e00\u70b9\u662f\u88ab\u7ed3\u6784\u5149\u7167\u5c04\u7684\u4e1c\u897f\u5bf9\u7ed3\u6784\u5149\u7684\u53cd\u5c04\u4ee5\u6f2b\u53cd\u5c04\u4e3a\u4e3b\uff0c\u800c\u4e14\u6240\u8c13\u7684\u201c\u4e00\u6837\u201d\u4e5f\u53ea\u662f\u7d2f\u6b7b\uff0c\u5e76\u4e0d\u80fd\u5305\u62ec\u9634\u5f71\u5173\u7cfb\u7b49\uff0c\u6240\u4ee5\u5bf9\u8fd9\u4e2a\u7ed3\u8bba\u7684\u6b63\u786e\u4e0e\u5426\u6211\u8868\u793a\u6000\u7591\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec08/#\u591a\u89c6\u89d2","title":"\u591a\u89c6\u89d2","text":"<p>\u591a\u89c6\u89d2\u7acb\u4f53(Multi-view Stereo, MVS)\u91cd\u5efa\uff0c\u987e\u540d\u601d\u4e49\u5c31\u662f\u5229\u7528\u66f4\u591a\u7684\u89c6\u89d2\u6765\u8fdb\u884c\u91cd\u5efa\uff0c\u76f8\u6bd4\u4e8e\u524d\u9762\u63d0\u5230\u7684\u53cc\u76ee\u6a21\u578b\uff0c\u5b83\u6709\u66f4\u5f3a\u7684\u7ea6\u675f\u3001\u80fd\u5728\u591a\u4e2a\u5019\u9009\u4e2d\u9009\u62e9\u6700\u5408\u9002\u7684\u65b9\u6848\uff0c\u4ee5\u53ca\u80fd\u5f97\u5230\u66f4\u5b8c\u6574\u7684 3D</p> <p>\u6211\u4eec\u5728\u53cc\u76ee\u5339\u914d\u4e2d\uff0c\u9996\u5148\u5bfb\u627e\u80fd\u591f\u5339\u914d\u7684\u70b9\u5bf9\u518d\u505a\u63a5\u4e0b\u6765\u7684\u4e8b\u60c5\uff0c\u4f46\u662f\u5728\u591a\u89c6\u89d2\u4e2d\uff0c\u627e\u5230\u300c\u5339\u914d\u7684\u4e00\u7cfb\u5217\u70b9\u300d\u662f\u6bd4\u8f83\u56f0\u96be\u4e14\u8017\u65f6\u7684\uff0c\u56e0\u4e3a n \u4e2a\u70b9\u6709 \\(C_n^2\\) \u5bf9\u5339\u914d\u5173\u7cfb\u3002\u6240\u4ee5\u6211\u4eec\u8981\u53d8\u6362\u601d\u8def\uff0c\u6211\u4eec\u9700\u8981\u4ee5\u67d0\u4e00\u4e2a\u89c6\u89d2\u4e3a\u57fa\u7840\uff0c\u5e76\u679a\u4e3e\u8fd9\u4e2a\u70b9\u7684\u6df1\u5ea6\uff0c\u8ba1\u7b97\u91cd\u6295\u5f71\u8bef\u5dee\uff0c\u627e\u5230\u4f7f\u91cd\u6295\u5f71\u8bef\u5dee\u6700\u4f18\u79c0\u7684\u90a3\u4e2a\u6df1\u5ea6\u4f5c\u4e3a\u8fd9\u4e2a\u70b9\u7684\u6df1\u5ea6\uff08\u800c\u4e0d\u662f\u5728\u6bcf\u4e00\u4e2a\u5bf9\u6781\u7ebf\u4e0a\u627e\uff0c\u53ef\u4ee5\u601d\u8003\u4e3a\u4ec0\u4e48\uff09\u3002</p> <p>\u4e2a\u4eba\u7591\u95ee</p> <p>\u8bdd\u8bf4\u8fd9\u4e2a\u91cd\u6295\u5f71\u8bef\u5dee\u6307\u7684\u662f\u4ec0\u4e48\u554a\uff0c\u662f\u9700\u8981\u5148\u7b97\u597d\u5339\u914d\u70b9\u7136\u540e L2 \u8ddd\u79bb\u7684\u8bef\u5dee\u8fd8\u662f\u76f8\u4f3c\u5ea6\u7684\u8bef\u5dee\uff1f\u5982\u679c\u662f\u76f8\u4f3c\u5ea6\u7684\u8bef\u5dee\uff0c\u90a3\u600e\u4e48\u89e3\u51b3\u5f62\u53d8\uff1f</p> <ul> <li>multi-view stereo  MVS<ul> <li>\u5177\u4f53\u505a\u6cd5\u662f<ul> <li>\u53ef\u4ee5\u4f7f\u7528 Plane-Sweep<ul> <li>\u5bf9\u4e8e\u6bcf\u4e00\u4e2a\u5176\u4ed6\u89c6\u89d2\uff0c\u6784\u9020\u4e00\u4e2a\u5173\u4e8e x-y-z \u7684\u4e09\u7ef4\u8868\uff0c\u80fd\u591f\u67e5\u8be2\u5bf9\u4e8e\u53c2\u8003\u56fe\u7247<code>[x][y]</code>\u5904\u7684\u50cf\u7d20\uff0c\u5982\u679c\u5904\u4e8e\u6df1\u5ea6<code>[z]</code>\u65f6\u7684\u60c5\u51b5</li> <li>\u5229\u7528\u4e24\u6b21\u6295\u5f71\uff0c\u5148\u5728\u201cA\u201d\u5b57\u91cc\u76f8\u4f3c\u5230\u8fdc\u5904\uff0c\u7136\u540e\u518d\u659c\u7740\u6295\u5f71\u5230\u6bcf\u4e2a\u89c6\u89d2\u91cc</li> <li>\u6bcf\u4e00\u5c42\u5c42\u626b\u8fc7\u53bb</li> <li><ul> <li>\u5728\u4e0a\u56fe\u6570\u7ec4\u91cc\u627e\u6bcf\u4e00\u4e2a<code>[x][y]</code>\u91cc\u8868\u73b0\u6700\u597d\u7684<code>[z]</code>\u4f5c\u4e3a\u90a3\u4e2a\u50cf\u7d20\u7684\u6df1\u5ea6\u3002</li> </ul> </li> <li>\u7136\u800c\u8fd9\u4e2a\u505a\u6cd5\u8fd8\u662f\u4e0d\u592a\u9ad8\u6548\uff0c\u4e00\u4e2a\u66f4\u9ad8\u6548\u7684\u505a\u6cd5\uff0c\u662f PatchMatch\u3002<ul> <li>\u968f\u5373\u521d\u59cb\u5316\uff0c\u603b\u6709\u51e0\u4e2a\u662f\u63a5\u8fd1\u6700\u4f18\u89e3\u7684</li> <li>\u5bf9\u4e8e\u8fd9\u4e9b\u6bd4\u8f83\u4f18\u7684\u89e3\uff0c\u5b83\u9644\u8fd1\u7684\u50cf\u7d20\u7b54\u6848\u5728\u8fd9\u4e2a\u7b54\u6848\u7684\u9644\u8fd1\u5bfb\u627e\uff08\u4f20\u64ad\uff09\uff0c\u7136\u540e\u518d\u5728\u5c0f\u8303\u56f4\u5185\u8fdb\u4e00\u6b65\u4f18\u5316\uff08\u641c\u7d22\uff09</li> </ul> </li> </ul> </li> </ul> </li> </ul> </li> </ul>"},{"location":"cour_note/D2QD_Intro2CV/Lec08/#3d-reconstruction","title":"3D reconstruction","text":"<p>\u5177\u4f53\u6765\u8bf4\uff0c3D \u91cd\u5efa\u5305\u62ec\u8fd9\u4e48\u4e09\u4e2a\u6b65\u9aa4\uff1a</p> <ol> <li>\u6df1\u5ea6\u8ba1\u7b97</li> <li>\u6df1\u5ea6 -&gt; 3D\u7f51\u683c\u8868\u9762</li> <li>\u7eb9\u7406\u586b\u5145</li> </ol>"},{"location":"cour_note/D2QD_Intro2CV/Lec08/#3d-representations","title":"3D representations","text":"<p>\u8865\u5145\u56fe\u7247</p> <ul> <li>\u70b9\u4e91 point cloud</li> <li>\u4f53\u7d20\uff083d\u50cf\u7d20\uff09occupancy</li> <li>signed distance function (SDF)<ul> <li>\u5927\u5c0f\u8ddd\u79bb\u8868\u9762\u7684\u8ddd\u79bb\uff0c\u5185\u90e8\u4e3a\u8d1f\uff0c\u5916\u90e8\u4e3a\u6b63</li> <li>Truncated Signed Distance Function \u622a\u65adSDF\uff0c\u5373\u4ecd\u548c\u5927\u4e8e 1 \u90fd\u8bb0\u4e3a 1\uff0c\u5c0f\u4e8e -1 \u7684\u8bb0\u4e3a -1</li> </ul> </li> <li>\u7f51\u683c mesh\uff08\u6bd4\u8f83\u5e38\u7528\uff09</li> </ul>"},{"location":"cour_note/D2QD_Intro2CV/Lec08/#3d-surface-reconstruction","title":"3D surface reconstruction","text":"<ol> <li>\u6df1\u5ea6 -&gt; \u4f53\u7d20\u8868\u793a</li> <li>\u4f53\u7d20\u8868\u793a -&gt; \u4e09\u7ef4\u7f51\u683c</li> </ol>"},{"location":"cour_note/D2QD_Intro2CV/Lec08/#\u6df1\u5ea6---\u4f53\u7d20\u8868\u793a","title":"\u6df1\u5ea6 -&gt; \u4f53\u7d20\u8868\u793a","text":"<p>\u5e38\u7528\u65b9\u6cd5\uff1a</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec08/#depth-fusion-depth-maps-to-tsdf","title":"Depth Fusion \uff08depth maps to TSDF\uff09","text":"<p>\u3010\u5bf9\u4e8e\u56fe\u4e2d\u3011\uff1a</p> <ul> <li>\u53ef\u4ee5\u8ba1\u7b97\u6bcf\u4e00\u4e2a\u4f53\u7d20\u5230\u76f8\u673a\u4e2d\u5fc3\u7684\u8ddd\u79bb \\(d_p\\)</li> <li>\u6839\u636e\u5c0f\u5b54\u6210\u50cf\u89c4\u5219\uff0c\u53ef\u4ee5\u5f97\u5230\u4e0e\u5f53\u524d\u4f53\u7d20\u6240\u5bf9\u5e94\u7684\u50cf\u7d20\uff0c\u8bb0\u5bf9\u5e94\u7684\u50cf\u7d20\u7684\u6df1\u5ea6\u4e3a \\(D_k(u)\\)</li> <li>\u5219\u8be5\u4f53\u7d20\u7684 TSDF \u503c\u622a\u65ad\u524d\u4e3a \\(D_k(u) - d_p\\)</li> <li>\u5728\u591a\u56fe\u60c5\u51b5\u4e0b\uff0c\u6bcf\u4e00\u5f20\u56fe\u7684\u7ed3\u679c\u505a\u52a0\u6743\u8ba1\u7b97</li> </ul> <p>\u601d\u8def</p> <p>\u4e4b\u524d\u4e5f\u6709\u7c7b\u4f3c\u7684\u5185\u5bb9\u3002\u4e00\u4e2a\u603b\u7ed3\u6027\u7684\u60f3\u6cd5\u662f\uff0c\u5f53\u4f60\u9700\u8981\u628a\u300c\u5206\u8fa8\u7387\u300d\u4f4e\u7684\u4e1c\u897f\u6295\u5f71\u5230\u300c\u5206\u8fa8\u7387\u300d\u9ad8\u5230\u5730\u65b9\u53bb\u65f6\uff0c\u5e94\u5f53\u679a\u4e3e\u300c\u5206\u8fa8\u7387\u300d\u9ad8\u7684\u90a3\u4e00\u4fa7\u7684\u5355\u5143\uff0c\u7136\u540e\u5229\u7528\u300c\u5206\u8fa8\u7387\u300d\u4f4e\u7684\u8fd9\u4e00\u4fa7\u53bb\u8ba1\u7b97\uff0c\u800c\u4e0d\u662f\u4ece\u4f4e\u5230\u9ad8\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec08/#poisson-reconstruction-depth-maps-to-occupancy-volume","title":"Poisson reconstruction \uff08depth maps to occupancy volume\uff09","text":"<p>\u67cf\u677e\u91cd\u5efa</p> <ul> <li>\u6df1\u5ea6\u56fe -&gt; \u5e26\u6cd5\u5411\u91cf\u7684\u70b9\u4e91<ul> <li>Oriented points \u90a3\u91cc\u7684\u7bad\u5934\u662f\u8868\u9762\u6cd5\u5411\u91cf\uff08\u6df1\u5ea6\u7684\u68af\u5ea6\uff09</li> </ul> </li> <li>\u7528\u4f18\u5316\u7684\u65b9\u5f0f\u6c42\u89e3 indicator function \uff08\u5927\u6982\u5c31\u662f\u6700\u7ec8\u7ed3\u679c\u7684\u90a3\u4e2a\u7269\u4f53\u7684\u8868\u9762\u53d1\u5411\u91cf\u51fd\u6570\uff09<ul> <li>\u8fd9\u91cc\u6709\u4e00\u4e2a\u70b9\u5c31\u662f\uff0c\u4f53\u7d20\u7684\u66f2\u9762\u662f\u95ed\u5408\u7684\uff0c\u6240\u4ee5\u4f1a\u6709\u5185\u5916\u4e4b\u5206\uff0c\u5185\u90e8\u5b9e\u5fc3\u5916\u90e8\u7a7a\u5fc3\uff0c\u6240\u4ee5 indicator function \u5c31\u662f\u60f3\u540c\u65f6\u8868\u8fbe \u8868\u9762 \u548c \u5185\u5916 \u4e24\u4ef6\u4e8b\u3002</li> </ul> </li> </ul>"},{"location":"cour_note/D2QD_Intro2CV/Lec08/#\u4f53\u7d20\u8868\u793a---\u4e09\u7ef4\u7f51\u683c","title":"\u4f53\u7d20\u8868\u793a -&gt; \u4e09\u7ef4\u7f51\u683c","text":"<p>\u5e38\u7528\u65b9\u6cd5\uff1a</p> <p>Marching cubes</p> <ul> <li>\u4ee5 2D \u4e3a\u4f8b\uff0c\u5982\u679c\u4e00\u4e2a\u300c\u8fb9\u300d\u7684\u4e24\u8fb9\uff0c\u9ed1\u767d\u4e0d\u4e00\u81f4\uff08\u9ed1\u8868\u793a\u5916\u90e8\uff0c\u767d\u8868\u793a\u5185\u90e8\uff09\uff0c\u5219\u8bf4\u660e\u8fd9\u91cc\u5b58\u5728\u4e00\u4e2a\u8fb9\u754c\uff0c\u4e8e\u662f\u6807\u4e00\u4e2a\u70b9\uff0c\u7136\u540e\u5c06\u6240\u6709\u7684\u8fd9\u6837\u7684\u70b9\u6309\u7167\u7279\u5b9a\u987a\u5e8f\u8fde\u63a5\u8d77\u6765\uff0c\u5c31\u5f97\u5230\u7684\u4e86\u8fb9\u754c\u3002</li> <li>\u5177\u4f53\u6807\u5728\u8fb9\u754c\u7684\u54ea\u4e2a\u4f4d\u7f6e\uff0c\u5982\u679c\u662f SDF \u7684\u8bdd\u53ef\u4ee5\u8ba1\u7b97\u77e5\u9053\uff0c\u5426\u5219\u53ef\u80fd\u53ea\u80fd\u5728\u4e2d\u95f4\u4e86</li> <li> <p>\u4f46\u662f\u9700\u8981\u6ce8\u610f\u4e00\u4e2a\u683c\u5b50\u5982\u679c\u6709\u591a\u4e2a\u70b9\u7684\u65f6\u5019\u600e\u4e48\u8fde\u7684\u95ee\u9898\uff0c\u6709\u4e00\u4e2a\u8868\u53ef\u4ee5\u67e5\uff0c\u6491\u6b7b\u4e5f\u5c31 2^4=16 \u79cd\u60c5\u51b5</p> </li> <li> <p>\u5728 3D \u60c5\u51b5\u4e0b\uff0c\u5c31\u662f\u5728\u7acb\u65b9\u4f53\u91cc\u8fde\u63a5\u4e09\u4e2a\u70b9\u5f62\u6210\u4e09\u89d2\u9762\uff0c\u7136\u540e\u4e5f\u6709\u4e00\u4e2a\u8868\u53ef\u4ee5\u67e5\uff0c\u6491\u6b7b\u4e5f\u5c31 2^8=256 \u79cd\u60c5\u51b5\u3002</p> </li> </ul> <p></p>"},{"location":"cour_note/D2QD_Intro2CV/Lec08/#texture-mapping","title":"Texture mapping","text":"<p>\u5c55\u5f00 get \u7eb9\u7406\u56fe\uff08\u4e8c\u7ef4\u5750\u6807\u80fd\u591f\u5bf9\u5e94\u4e00\u4e2a\u7f51\u683c\u9762\uff09 using \u53c2\u6570\u5316</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec09/","title":"Lecture 9 | Deep Learning","text":"<p> \u7ea6 1839 \u4e2a\u5b57  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 6 \u5206\u949f</p> <p>\u6ce8\u610f</p> <p>\u672c\u6587\u5c1a\u672a\u5b8c\u5168\u6574\u7406\u597d\uff01</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec09/#\u673a\u5668\u5b66\u4e60\u6982\u8ff0","title":"\u673a\u5668\u5b66\u4e60\u6982\u8ff0","text":"<p>\u8bf4\u660e</p> <p>\u672c\u8bfe\u7a0b\u4e0d\u4f1a\u8be6\u7ec6\u4ecb\u7ecd\u5173\u4e8e\u673a\u5668\u5b66\u4e60\u7684\u6240\u6709\u77e5\u8bc6\uff0c\u4f46\u4ecd\u7136\u5bf9\u57fa\u7840\u6982\u5ff5\u6709\u6240\u8981\u6c42\uff0c\u6240\u4ee5\u5728\u6b64\u4ec5\u505a\u6982\u5ff5\u6027\u5bf9\u7b80\u4ecb\u3002</p> <p>\u673a\u5668\u5b66\u4e60(Machine Learning, ML) \u7c97\u7565\u7684\u6765\u8bf4\u5c31\u662f\u901a\u8fc7\u5bf9\u5927\u91cf\u6570\u636e\u8fdb\u884c\u5b66\u4e60\uff0c\u5728\u4e00\u5b9a\u89c4\u5219\u4e0b\u751f\u6210\u7a0b\u5e8f\uff0c\u5bf9\u4e8e\u673a\u5668\u5b66\u4e60\u6765\u8bf4\uff0c\u5b66\u4e60\u51fa\u6765\u7684\u8fd9\u4e2a\u201c\u7a0b\u5e8f\u201d\u7ed3\u679c\u662f\u6a21\u578b(model)\u3002</p> <p>\u800c\u5982\u679c\u7528\u6765\u5b66\u4e60\u7684\u662f\u88ab\u6807\u6ce8\u8fc7\u7684\u6570\u636e(labeled data)\uff0c\u5219\u79f0\u4e4b\u4e3a(\u6709)\u76d1\u7763(\u7684)\u5b66\u4e60(supervised learning)\u3002</p> <p>\u65e0\u8bba\u662f\u673a\u5668\u5b66\u4e60\u6280\u672f\u8fd8\u662f\u4f20\u7edf\u7684\u7f16\u7a0b\u6280\u672f\uff0c\u90fd\u662f\u4e3a\u4e86\u89e3\u51b3\u67d0\u4e2a\u95ee\u9898\u800c\u5b58\u5728\u7684\u3002\u800c\u89e3\u51b3\u4e00\u4e2a\u590d\u6742\u95ee\u9898\u2014\u2014\u6b63\u5982\u6211\u4eec\u4e4b\u524d\u5f3a\u8c03\u7684\u2014\u2014\u9700\u8981\u5bf9\u95ee\u9898\u8fdb\u884c\u62bd\u8c61\u5efa\u6a21\u3002\u800c\u4e00\u4e2a\u673a\u5668\u5b66\u4e60\u5b66\u4e60\u51fa\u6765\u7684\u6a21\u578b(model)\u53ef\u4ee5\u88ab\u89c6\u4f5c\u4e00\u4e2a\u5173\u4e8e\u8f93\u5165\u548c\u8f93\u51fa\u7684\u63cf\u8ff0\uff1a</p> \\[ \\text{Input } X \\rightarrow f_w \\rightarrow \\text{Output } Y \\] <p>\u800c\u6839\u636e\u8fd9\u91cc\u63d0\u5230\u7684\u201c\u8f93\u51fa\u201d\u7684\u4e0d\u540c\uff0c\u6309\u7167\u8fde\u7eed\u4e0e\u79bb\u6563\uff0c\u6211\u4eec\u5c06\u6240\u89e3\u51b3\u7684\u95ee\u9898\u533a\u5206\u4e3a\u56de\u5f52(regression)\u95ee\u9898\uff08\u7ed3\u679c \\(y\\) \u662f\u8fde\u7eed\u7684\u6570\u503c\uff09\u548c\u5206\u7c7b(classification)\u95ee\u9898\uff08\u7ed3\u679c \\(y\\) \u662f\u79bb\u6563\u7684\u6807\u7b7e\uff09\uff0c</p> <p>\u66f4\u5177\u9898\u7684\u6765\u8bf4\uff0c\u4e00\u822c\u673a\u5668\u5b66\u4e60\u7684 pipeline \u662f\u8fd9\u6837\u7684\uff1a</p> <ol> <li>\u5bf9\u95ee\u9898\u8fdb\u884c\u5b9a\u4e49\uff1b</li> <li>\u6536\u96c6\uff08\u548c\u5904\u7406\uff09\u7528\u6765\u5b66\u4e60\u7684\u6570\u636e\u96c6\uff1b</li> <li>\u5bf9\u95ee\u9898\u5efa\u6a21\uff0c\u5e76\u8bbe\u8ba1\u6a21\u578b\uff1b<ul> <li>\u62bd\u8c61\u5730\u6765\u8bf4\u662f\u51b3\u5b9a\u8f93\u5165\u8f93\u51fa\u7684\u5173\u8054\u5f62\u5f0f\uff1b</li> </ul> </li> <li>\u6a21\u578b\u8bad\u7ec3\uff1b<ul> <li>\u8bbe\u8ba1\u635f\u5931\u51fd\u6570\u6765\u8bc4\u4f30\u6a21\u578b\u7684\u6548\u679c\uff1b</li> <li>\u7528\u4f18\u5316\u6280\u672f\u6c42\u89e3\u4f7f\u6a21\u578b\u6548\u679c\u6700\u597d\u7684\u53c2\u6570\uff1b</li> </ul> </li> <li>\u6a21\u578b\u6d4b\u8bd5\uff1b<ul> <li>\u4e5f\u5c31\u662f\u7528\u6d4b\u8bd5\u6570\u636e\u96c6\u6d4b\u8bd5\u5b83\u7684\u8868\u73b0\uff1b</li> </ul> </li> </ol>"},{"location":"cour_note/D2QD_Intro2CV/Lec09/#\u7ebf\u6027\u5206\u7c7b\u5668","title":"\u7ebf\u6027\u5206\u7c7b\u5668","text":"<p>\u7ebf\u6027\u5206\u7c7b\u5668(Linear Classifier)\u6700\u65e9\u53eb\u611f\u77e5\u673a(Perceptron)\uff0c\u5b83\u662f ML \u4e2d\u4e00\u4e2a\u6700\u7b80\u5355\u4e5f\u662f\u6700\u57fa\u672c\u7684\u6784\u6210\u3002</p> \\[ y = f(x, W) = W x + b \\\\ \\begin{aligned}   &amp; \\text{where } x \\text{ means inputs, such as image, } \\\\   &amp; y \\text{ means outputs, such as the class of the object, } \\\\   &amp; \\text{and } W \\text{ is the parameters matrix.} \\end{aligned} \\] <p>\u53ef\u4ee5\u53d1\u73b0\uff0c\u5176\u6570\u5b66\u63cf\u8ff0\u5c31\u89e3\u91ca\u4e86\u5b83\u4e3a\u4ec0\u4e48\u53eb\u300c\u7ebf\u6027\u300d\u5206\u7c7b\u5668\u3002</p> <p>\u66f4\u8be6\u7ec6\u7684\u89e3\u91ca\u4e0d\u5728\u8fd9\u91cc\u5c55\u5f00\uff0c\u53ef\u4ee5\u67e5\u770b cs231n \u7b14\u8bb0\u7684\u76f8\u5173\u4ecb\u7ecd</p> <p>\u4f55\u65f6\u8f93\u51fa\u6bd4\u8f83\u5927\uff1f</p> <p>\u8f93\u51fa\u5927\uff0c\u6216\u8005\u8bf4\u5bf9\u4e8e\u67d0\u884c\u5927\uff0c\u6362\u53e5\u8bdd\u6765\u8bf4\u5c31\u662f\u5206\u7c7b\u5230\u8fd9\u4e00\u884c\u7684\u53ef\u80fd\u6027\u66f4\u5927\uff0c\u4e00\u822c\u662f \\(x\\) \u4e0e \\(W\\) \u7684\u5bf9\u5e94\u884c\u76f8\u4f3c\u65f6\u3002</p> <p>\u8fd9\u91cc\u6709\u4e00\u4e2a\u7279\u6b8a\u7684\u6982\u5ff5\u662f\u51b3\u7b56\u8fb9\u754c(Decision Boundary)\uff1a</p> <ul> <li>\\(w^Tx+b = 0\\)</li> <li>It's a line in 2D, a plane in 3D or hyperplane ...</li> </ul> <p></p>"},{"location":"cour_note/D2QD_Intro2CV/Lec09/#training","title":"Training","text":"<p>\u5982\u4f55\u627e\u5230\u6700\u4f73\u7684\u53c2\u6570\uff1f</p> <ul> <li>loss function</li> <li>optimization problem</li> </ul> <p>\u6700\u5c0f\u4e8c\u4e58\u6cd5\u7684\u7f3a\u70b9</p> <ul> <li>\u5bb9\u6613\u6536\u5230\u566a\u58f0\u5f71\u54cd</li> <li>\u5bf9\u4e8e classifier \u7684\u95ee\u9898\uff0c\u5f88\u96be\u7528\u201c\u505a\u5dee\u201d\u6765\u63cf\u8ff0\u5f97\u5206\u4e0e\u7c7b\u522b\u7684\u5173\u7cfb\u2014\u2014\u8ba9\u4ed6\u4ece\u4efb\u610f\u6570\u6620\u5c04\u5230\u4e00\u4e2a <code>[0,1]</code>\uff0csigmoid\uff0c\u53ef\u4ee5\u7406\u89e3\u6210\u201c\u6982\u7387\u201d\u3002i.e. softmax operator: \\(.....\\)</li> </ul> <p>\u8bc4\u4ef7\u4e24\u4e2a\u6982\u7387\u5206\u5e03\u662f\u5426\u76f8\u4f3c\uff0c\u5e38\u7528\u7684\u662f\u4ea4\u53c9\u5dee\uff0ccross entropy as loss function</p> \\[ S \\sim S(y) \\\\ D(S,L) = -\\sum_i L_i \\log S_i \\]"},{"location":"cour_note/D2QD_Intro2CV/Lec09/#neural-networks","title":"Neural Networks","text":"<p>\u7ebf\u6027\u5206\u7c7b\u6700\u65e9\u53eb\u611f\u77e5\u673a\uff0cperceptron</p> <p>\u7136\u800c\u6709\u4e9b\u5206\u7c7b\u53ef\u80fd\u662f\u975e\u7ebf\u6027\u7684\uff0c\u5982\u56fe</p> <p></p> <p>\u8fd9\u79cd\u65f6\u5019\u6211\u4eec\u53ef\u80fd\u4f1a\u4f7f\u7528\u4e00\u4e2a\u51fd\u6570\u5c06\u5b83\u4e0e\u7ebf\u6027\u5206\u7c7b\u6620\u5c04\u8d77\u6765\uff0c\u8fd9\u79cd\u51fd\u6570\u4e00\u822c\u53eb\u6fc0\u6d3b\u51fd\u6570 activation functions</p> <ul> <li>ReLU</li> <li>Sigmoid</li> </ul> <p>\u591a\u7c7b\u522b\u8868\u793a</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec09/#\u591a\u5c42\u611f\u77e5\u673a-multi-layer-perceptron","title":"\u591a\u5c42\u611f\u77e5\u673a Multi-layer perceptron","text":"\\[ \\sigma \\text{ is a nonlinear transform.} f(x) = \\sigma(w^T x + b) \\] <p>hidden layers</p> <p>\u5982\u679c\u6ca1\u6709\u975e\u7ebf\u6027\u6fc0\u6d3b\u51fd\u6570\uff0c\u6700\u540e\u7b49\u4ef7\u4e8e\u4e00\u4e2a\u5355\u5c42\u7ebf\u6027\u611f\u77e5\u673a</p> <p>Neural Networks</p> <p>\u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc Deep Neural Networks \u5c42\u6570\u591a =&gt; </p> <ul> <li>\u8868\u8fbe\u80fd\u529b \u2b06\ufe0f</li> <li>\u53c2\u6570 \u2b06\ufe0f</li> <li>\u8bad\u7ec3\u6570\u636e \u2b06\ufe0f \u6210\u672c \u2b06\ufe0f </li> <li>\u4f18\u5316\u95ee\u9898\u6c42\u89e3\u96be\u5ea6 \u2b06\ufe0f</li> </ul> <p>\u5168\u8fde\u5c42 Fully connected layer </p> <ul> <li>\u5355\u5c42\u53c2\u6570\u91cf\u5de8\u5927\uff08W \u5927\uff09</li> </ul>"},{"location":"cour_note/D2QD_Intro2CV/Lec09/#convolution-neural-networks","title":"Convolution Neural Networks","text":"<p>What is CNN? What is convolution? Layer Types: 1. Convolutional layer 2. Pooling layer 3. Fully-connected layer</p> <p></p> <p>\u5728 CV \u4e2d\uff0c\u6709\u65f6\u5019\u56fe\u50cf\u7684\u5c40\u90e8\u7279\u5f81\u5c31\u591f\u6211\u4eec\u8fdb\u884c\u5206\u7c7b\u3002\u8fd9\u610f\u5473\u7740\u6211\u4eec\u53ef\u80fd\u4e0d\u9700\u8981\u8ba9\u7f51\u7edc\u8fde\u4e0a\u6240\u6709\u7684\u90e8\u5206\u3002</p> <p>1 \u4e2a\u7f51\u7edc -&gt; 3 \u4e2a\u7f51\u7edc\uff0cwith weight sharing\uff0c\u56e0\u4e3a 3 \u4e2a\u7f51\u7edc\u90fd\u662f\u7528\u6765\u8bc6\u522b\u540c\u6837\u7684\u4e1c\u897f\u7684\uff0c\u6216\u8005\u8bf4\u529f\u80fd\u76f8\u540c\u3002</p> \\[ y = \\sigma(x \\otimes w + b) \\] <p>padding &amp; pooling &amp; stride</p> <p>\u597d\u5904\u662f\u53c2\u6570\u6bd4\u5168\u8fde\u5c42\u5c11\u5f88\u591a</p> <p>\u611f\u53d7\u91ce Receptive fields</p> <ul> <li>\u5c42\u6570\u8d8a\u591a\uff0c\u4e00\u822c\u8d8a\u5927</li> <li> P69</li> </ul>"},{"location":"cour_note/D2QD_Intro2CV/Lec09/#\u6c60\u5316\u5c42","title":"\u6c60\u5316\u5c42","text":"<p>\u628a\u4e0d\u540c\u5730\u996d\u7684\u7ed3\u679c\u7ed3\u5408\u5728\u4e00\u8d77\uff0c\u5c06\u54cd\u5e94\u56fe\u7684\u591a\u4e2a\u7ed3\u679c\u5408\u5e76\u4e3a\u540c\u4e00\u4e2a</p> <p>CNN \u4e00\u822c\u8fc7\u7a0b </p> <p> P71</p> <p>CNN \u7ecf\u5178\u7f51\u7edc\uff1aAlexNet, VGG, </p> <p>\u4e0d\u540c channel \u5355\u72ec\u505a ----&gt; Batch Normalization</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec09/#training-neural-networks","title":"Training Neural Networks","text":"<p>\u867d\u7136\u6211\u4eec\u6ca1\u6cd5\u627e\u5230\u4e00\u4e2a\u975e\u5e38\u597d\u7684\u65b9\u6cd5\u8bbe\u8ba1\u4e00\u4e2a\u201c\u6700\u4f73\u201d\u7684\u7f51\u7edc\uff0c\u4f46\u662f\u5982\u4f55\u5bfb\u627e\u5176\u4e2d\u6700\u597d\u7684\u53c2\u6570\u5219\u662f\u6709\u4e00\u7cfb\u5217\u4e25\u683c\u7684\u65b9\u6cd5\u3002</p> <p>loss function</p> <ul> <li>classification: cross-entropy</li> <li>regression: L2 loss</li> </ul> <p>optimization</p> <p>\u6700\u5c0f\u5316 loss function\uff0c\u4f7f\u7528\u5404\u79cd\u68af\u5ea6\u4e0b\u964d</p> <p>This training method is called \u540e\u5411/\u53cd\u5411\u4f20\u64ad back-propagation</p> \\[ \\mathbf{w}^{t+1} = \\mathbf{w}^t - \\eta_t\\frac{\\partial L}{\\partial \\mathbf{w}}\\mathbf{w}^t  \\] <p>\u6c42\u68af\u5ea6-\u300b\u590d\u5408\u51fd\u6570\u6c42\u5bfc-\u300b\u94fe\u5f0f\u6cd5\u5219</p> <p>\u5bf9\u4e8e\u73b0\u5728\u7684\u6df1\u5ea6\u5b66\u4e60\u5de5\u5177\u6765\u8bf4\uff0c\u53cd\u5411\u4f20\u64ad\u4e0e\u6c42\u5bfc\u7b49\u8fc7\u7a0b\u90fd\u53ef\u4ee5\u81ea\u52a8\u5b9e\u73b0\uff0c\u4e5f\u5c31\u662f\u8bf4\u6211\u4eec\u53ea\u9700\u8981\u8bbe\u8ba1\u597d\u7f51\u7edc\u7ed3\u6784\u548c loss function \u5373\u53ef\uff0c\u800c\u4f18\u5316\u90e8\u5206\u5219\u53ef\u4ee5\u901a\u8fc7\u5de5\u5177\u5b9e\u73b0\u3002</p> <p>\u968f\u673a\u68af\u5ea6\u4e0b\u964d\uff0c\u968f\u673a\u7684\u91c7\u6837\u4e00\u90e8\u5206\u70b9\uff0c\\(\\Omega\\) @P86\uff0c</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec09/#architecture--hyper-parameters","title":"Architecture &amp; hyper-parameters","text":"<p>\u65e0\u6cd5\u901a\u8fc7\u90a3\u4e9b\u80fd\u591f\u81ea\u52a8\u8ba1\u7b97\u7684\u6743\u91cd\uff0c\u6d89\u53ca\u5230\u7f51\u7edc\u8bbe\u8ba1\u7684\u4e00\u4e9b\u5185\u5bb9\u7684\u4e00\u4e9b\u53c2\u6570\uff0c\u6210\u4e3a\u8d85\u53c2\u6570 hyper-parameters\u3002</p> <p>\u65b9\u6cd5\uff1a\u8bd5\uff08\u5f53\u7136\u4e0d\u662f\u7528\u624b\u8bd5x\uff09\uff01</p> <p>How to prevent overfitting? \u2022 Cross validation and early stop \u2022 Regularization or dropout \u2022 Data augmentation</p> <p>\u5982\u4f55\u8bc4\u4ef7\u7ed3\u679c\u201c\u597d\u201d\u8fd8\u662f\u201c\u4e0d\u597d\u201d\uff1f</p> <p>\u5982\u4f55\u5206\u5272\u6570\u636e\u96c6\uff1f(cross validation: train &amp; validation &amp; test)</p> <p>Data split idea * 3</p> <p> P89\uff08cs231n also\uff09</p> <p>\u4e00\u79cd\u8fdd\u548c\u611f\uff0cvalidation \u53c2\u4e0e\u81ea\u52a8\u53cd\u9988\uff0ctest \u96be\u9053\u4e0d\u7b97\u4e00\u79cd\u4eba\u4e3a\u53cd\u9988\u5417\uff1f</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec09/#\u6b63\u5219\u5316","title":"\u6b63\u5219\u5316","text":"<p>\u589e\u52a0\u7ea6\u675f\u4ee5\u51cf\u5c11 over fit </p>"},{"location":"cour_note/D2QD_Intro2CV/Lec09/#dropout","title":"Dropout","text":"<p>\u8bad\u7ec3\u65f6\u5ffd\u7565\u4e00\u90e8\u5206\u54cd\u5e94\uff0c\u6d4b\u8bd5\u7684\u65f6\u5019\u4ecd\u7136\u4f7f\u7528</p> <p>\u65ed\u5b9d\uff1aDropout\u8bf4\u7684\u7b80\u5355\u4e00\u70b9\u5c31\u662f\uff1a\u6211\u4eec\u5728\u524d\u5411\u4f20\u64ad\u7684\u65f6\u5019\uff0c\u8ba9\u67d0\u4e2a\u795e\u7ecf\u5143\u7684\u6fc0\u6d3b\u503c\u4ee5\u4e00\u5b9a\u7684\u6982\u7387p\u505c\u6b62\u5de5\u4f5c\uff0c\u8fd9\u6837\u53ef\u4ee5\u4f7f\u6a21\u578b\u6cdb\u5316\u6027\u66f4\u5f3a\uff0c\u56e0\u4e3a\u5b83\u4e0d\u4f1a\u592a\u4f9d\u8d56\u67d0\u4e9b\u5c40\u90e8\u7684\u7279\u5f81\u3002</p> <p>\u7edf\u8ba1\u4e0a\u7b49\u6548\u4e8e L2</p> <p>\u6211\uff1a\u56e0\u4e3a\u6bcf\u4e2a\u70b9\u90fd\u6709\u53ef\u80fd\u6982\u7387\u6027\u5931\u6548\uff0c\u6cdb\u5316\u6027\u66f4\u5f3a\uff0c\u8fd9\u4e5f\u8981\u6c42\u67d0\u4e00\u4e2a\u7279\u5f81\u7684contributes\u4f1a\u88ab\u201c\u5206\u644a\u201d\u5f00\u6765\uff0c\u6240\u4ee5\u6548\u679c\u4e0a\u6709\u70b9\u50cfL2\u7684\u90a3\u79cd\u8ba9\u6743\u91cd\u66f4\u5c0f</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec09/#\u6570\u636e\u589e\u5e7f-data-augmentation","title":"\u6570\u636e\u589e\u5e7f Data augmentation","text":"<p>overfit \u53ca\u6570\u636e\u592a\u5c11\u8bad\u7ec3\u592a\u591a\uff0c\u6240\u4ee5\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u5bf9\u5df2\u6709\u6570\u636e\u53d8\u6362\u6765\u201c\u9020\u201d\u4e00\u4e9b\u6570\u636e\u51fa\u6765\uff0c\u6bd4\u5982\u7ffb\u8f6c\u3001\u62c9\u4f38\u2026\u2026</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec09/#batch-normalization","title":"Batch Normalization","text":"<p>\u5bf9\u591a\u4e2a channel \u5bf9\u7ed3\u679c\u8fdb\u884c\u5f52\u4e00\u5316\u64cd\u4f5c</p> <p>Reduce internal covariate shift\uff0c\u4ee5\u51cf\u5c11 channal \u4e4b\u95f4\u7684\u53d1\u6563\u6027\uff0c\u66f4\u7a33\u5b9a\u66f4\u6536\u655b</p> <p>For more: https://web.eecs.umich.edu/~justincj/teaching/eecs498/FA2020/</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec09/#deep-learning-frameworks","title":"Deep Learning Frameworks","text":"<ul> <li>Caffe \u8001\u4e1c\u897f</li> <li>TF \u5f00\u53d1\u8005\u66f4\u559c\u6b22</li> <li>PyTorch \u7814\u7a76\u8005\u66f4\u559c\u6b22</li> </ul>"},{"location":"cour_note/D2QD_Intro2CV/Lec09/#network-architectures","title":"Network Architectures","text":"<p>\u65e9\u671f\u4e0d\u53d7\u6b22\u8fce\uff1a\u6548\u679c\u5dee &amp; \u53ef\u63a5\u53d7\u6027\u5dee</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec09/#resnet","title":"ResNet","text":"<p>\u5047\u8bbe\u6570\u636e\u91cf\u591f\u5927\uff0c\u662f\u4e0d\u662f\u5c42\u6570\u8d8a\u591a\u8d8a\u597d\uff1f</p> <ul> <li>\u96be\u8bad\u7ec3\uff0c\u201c\u68af\u5ea6\u6d88\u5931\u201d\uff0c\u5c42\u6570\u592a\u591a\u4ee5\u540e\uff0c\u5230\u540e\u9762\u68af\u5ea6\u5c31\u5f88\u5c0f\u4e86\uff0c\u4e0b\u964d\u4e0d\u4e0b\u53bb\u4e86</li> <li>\u4f46\u662f\u4e3a\u4ec0\u4e48\u4f1a\u53d8\u5dee\u5462\uff1f</li> <li>\u5982\u4f55\u8bbe\u8ba1\u589e\u52a0\u5c42\u6570\u800c\u81f3\u5c11\u4e0d\u53d8\u5dee\u5462\uff1f<ul> <li>ResNet: \\(H(x) = F(x) + x\\)</li> <li>\u6b8b\u5dee\u5b66\u4e60 residual learning</li> </ul> </li> </ul>"},{"location":"cour_note/D2QD_Intro2CV/Lec09/#densenet","title":"DenseNet","text":"<p>\u66f4\u52a0\u7a20\u5bc6\u7684\u94fe\u63a5\uff0c\u672c\u5c42\u53d6\u51b3\u4e8e\u524d\u9762\u6240\u6709\u5c42</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec09/#mobilenets","title":"MobileNets","text":"<p>\u901f\u5ea6\u5feb</p> <p>NAS: Neural Architecture Search \u81ea\u52a8\u5316\u7f51\u7edc\u7ed3\u6784\u8bbe\u8ba1\uff0clearning to learn</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec09/#why-deep-learning-is-powerful","title":"why deep learning is powerful?","text":"<p>End-to-end learning\uff0c\u7aef\u5230\u7aef\u5b66\u4e60</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec10/","title":"Lecture 10 | Recognition","text":"<p> \u7ea6 1509 \u4e2a\u5b57  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 5 \u5206\u949f</p> <p>\u6ce8\u610f</p> <p>\u672c\u6587\u5c1a\u672a\u5b8c\u5168\u6574\u7406\u597d\uff01</p> <p>\u4e8c\u7ef4\u56fe\u50cf\u8bc6\u522b(Recognition)\u4e0b\u6709\u5f88\u591a\u4efb\u52a1\uff0c\u4e3b\u8981\u5206\u4e3a\u8fd9\u4e48\u51e0\u79cd\uff1a</p> <ul> <li>\u5206\u7c7b Classification</li> <li>\u8bed\u4e49\u5206\u5272 Semantic segmentation</li> <li>\u5bf9\u8c61\u68c0\u6d4b Object detection</li> <li>\u5b9e\u4f8b\u5206\u5272 Instance segmentation</li> </ul>"},{"location":"cour_note/D2QD_Intro2CV/Lec10/#semantic-segmentation","title":"Semantic segmentation","text":"<p>\u6bcf\u4e2a\u50cf\u7d20\u5c5e\u4e8e\u54ea\u4e2a\u7c7b\u522b\u8fd9\u79cd\u4fe1\u606f\u53eb\u8bed\u4e49\u4fe1\u606f\u3002</p> <ul> <li>\u8f93\u5165\uff1a\u56fe\u7247</li> <li>\u8f93\u51fa\uff1a\u6bcf\u4e2a\u50cf\u7d20\u7684\u7c7b\u522b\u6807\u7b7e\uff0c\u4e0d\u9700\u8981\u533a\u5206\u540c\u4e00\u7c7b\u522b\u7684\u4e0d\u540c\u5b9e\u4f8b</li> </ul> <p>\u6700\u6734\u7d20\u7684\u505a\u6cd5\u662f sliding window\uff0c\u53d6\u51fa\u4e00\u4e2a window \u653e\u8fdb\u5206\u7c7b\u673a\u5f97\u5230\u7ed3\u679c\uff0c\u4f46\u662f\u663e\u7136\u7531\u4e8e window \u5305\u542b\u7684\u4fe1\u606f\u592a\u5c11\uff0c\u800c\u4e14\u6548\u7387\u592a\u4f4e\uff0c\u8fd9\u4e2a\u65b9\u6cd5\u975e\u5e38 naive\u3002</p> <p>\u73b0\u5728\u6807\u51c6\u7684\u505a\u6cd5\u662f\u5168\u5377\u79ef\u7f51\u7edc(Fully Convolutional Network)</p> <ul> <li>Loss function: Per-pixel cross-entropy</li> </ul> <p>\u5c40\u9650\u6027\uff1a</p> <ul> <li>Receptive field is linear in number of conv layers</li> <li>Convolution on high resolution is expensive\uff08\u8017\u65f6\uff09</li> </ul> <p>\u6539\u8fdb\uff1a</p> <ul> <li>Downsampling: pooling, strided conv</li> </ul> <p>\u4f46\u662f\u7531\u4e8e\u6211\u4eec\u6700\u540e\u5e0c\u671b\u5f97\u5230\u7684\u662f\u4e00\u4e2a\u548c\u539f\u56fe\u4e00\u6837\u5927\u7684\u4e1c\u897f\uff0c\u6240\u4ee5\u6709\u5411\u4e0b\u91c7\u6837\u5c31\u80af\u5b9a\u4f1a\u6709\u5411\u4e0a\u91c7\u6837\uff08\u56de\u5fc6\uff1a\u63d2\u503c\uff09\u3002</p> <p>\u56fe\u50cf\u5411\u4e0a\u91c7\u6837\u4ee5\u540e\u53d8\u5927\u4ee5\u540e\u53c8\u5377\u79ef\uff0c\u8fd9\u4e2aTransposed convolution</p> <p> ppt P13</p> <p>\u4f46\u662f\u5f88\u663e\u7136\uff0c\u5728\u53d8\u5c0f\u53d8\u5927\u7684\u8fc7\u7a0b\u4e2d\u80af\u5b9a\u6709\u4fe1\u606f\u635f\u5931\u3002\u6240\u4ee5\u73b0\u5728\u4e00\u4e2a\u6bd4\u8f83\u6d41\u884c\u7684\u505a\u6cd5\u662f U-Net\uff0c\u4e5f\u5c31\u662f\u5927\u91cf\u5e94\u7528 skip-connection\u3002</p> <p> ppt P14 https://web.eecs.umich.edu/~justincj/teaching/eecs498/FA2020/</p> <p>DeepLab P15</p> <p>\u8003\u8651\u76f8\u90bb\u50cf\u7d20\u4e4b\u95f4\u7684\u5173\u8054\u6027\uff0c\u4f7f\u7528 CRF(Conditional random field) \u4f18\u5316 P16</p> <p>\u9a6c\u53ef\u592b\u968f\u673a\u573a\uff1f</p> <p>Unary potential: \u4f53\u73b0\u81ea\u5df1\u7684\u7279\u6027</p> <p>Pairwise potential: \u4f53\u73b0\u5173\u8054\u6027</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec10/#\u8861\u91cf\u6307\u6807-evaluation-metric-per-pixel-intersection-over-union-iou","title":"\u8861\u91cf\u6307\u6807 Evaluation metric: Per-pixel Intersection-over-union (IoU)","text":"<p>\\(IoU=\\frac{     \\text{Ground truth \u548c prediction \u7684\u4ea4\u96c6\u9762\u79ef} }{     \\text{Ground truth \u548c prediction \u7684\u5e76\u96c6\u9762\u79ef} }\\)  P19</p> <p>mIoU \u6307\u7684\u662f\u5206\u51fa\u6765\u7684\u4e0d\u540c\u7c7b\u522b\u7684 mean IoU</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec10/#object-detection","title":"Object detection","text":"<p>Bounding box (bbox)</p> <ul> <li>Class label</li> <li>Location (x,y)</li> <li> <p>Size (w,h)</p> </li> <li> <p>\u8f93\u5165\uff1a\u56fe\u50cf</p> </li> <li>\u8f93\u51fa\uff1a\u4e00\u5806 bounding box</li> </ul> <p>\u90a3\u4e48\u5982\u4f55\u5b9e\u73b0\u5462\uff1f\u6211\u4eec\u5148\u5047\u8bbe\u4e00\u5171\u53ea\u6709 1 \u4e2a\u5bf9\u8c61\uff0c\u90a3\u4e48\u6b64\u65f6\u548c\u5206\u7c7b\u4efb\u52a1\u662f\u975e\u5e38\u63a5\u8fd1\u7684\uff0c\u53ea\u9700\u8981\u518d\u989d\u5916\u6c42\u89e3\u4e00\u4e2a\u7a97\u53e3\u4f4d\u7f6e\u5373\u53ef\u3002</p> <p>\u90a3\u4e48\u591a\u4e2a\u7a97\u53e3\u5462\uff1f</p> <p>\u89e3\u51b3\u529e\u6cd5\u8fd8\u662f\u6ed1\u52a8\u7a97\u53e3\uff0c\u53ea\u4e0d\u8fc7\u4e0d\u540c\u4e4b\u524d\u7684\uff0c\u6211\u4eec\u73b0\u5728\u91c7\u7528\u7684\u65b9\u6cd5\u57fa\u672c\u4e0a\u4e5f\u662f\u57fa\u4e8e\u6ed1\u52a8\u7a97\u53e3\u5c55\u5f00\u7684\u3002\u800c\u5728\u8fd9\u79cd\u8bed\u5883\u4e0b\uff0c\u8fd9\u6837\u7684\u4e00\u4e2a\u6ed1\u52a8\u7a97\u53e3\u88ab\u79f0\u4e3a\u4e00\u4e2a\u63d0\u8bae(proposal)\u3002</p> <p>\u4f46\u662f\u663e\u7136\uff0c\u4f7f\u7528\u6700\u6734\u7d20\u7684\u6ed1\u52a8\u7a97\u53e3\u4f1a\u5bfc\u81f4\u201c\u63d0\u8bae\u201d\u8fc7\u591a\uff0c\u5bfc\u81f4\u6548\u7387\u592a\u4f4e\u3002\u6240\u4ee5\u6211\u4eec\u8981\u4f18\u5316\u8fd9\u4e2a\u8fc7\u7a0b\u3002</p> <p>\u4e00\u822c\u8fd9\u4e9b\u4f18\u5316\u7684\u65b9\u6cd5\u90fd\u662f\u542f\u53d1\u5f0f(heuristics)\u7684\u505a\u6cd5\uff0c\u4f8b\u5982 over-segmentation\uff0c </p> <p>\u800c\u8fd9\u7c7b\u65b9\u6cd5\u5c31\u662f R-CNN (region proposal &amp; CNN) P36</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec10/#evaluation-metric","title":"Evaluation metric","text":"<p>\u5bf9\u4e8e\u5355\u4e2a\u7269\u4f53\uff0c\u4ecd\u7136\u662f IoU</p> <p>P39</p> <p>\u4e3a\u4e86\u8bc4\u4ef7\u9884\u6d4b\u7ed3\u679c\u7684\u6b63\u786e\u6027\uff0c\u6211\u4eec\u9700\u8981\u4e3a\u5b83\u8bbe\u7f6e\u4e00\u4e2a\u9608\u503c\u3002</p> <p>\u800c\u5bf9\u4e8e\u591a\u4e2a\u7269\u4f53\uff0c\u5219\u4e0d\u90a3\u4e48\u7b80\u5355\uff1aP42</p> <p>\uff08\u56de\u5fc6\u7edf\u8ba1\u5b66\u5185\u5bb9\uff09</p> <p>positive: \u80af\u5b9a\u7684\u5047\u8bbe P</p> <p>negative: \u5426\u5b9a\u7684\u5047\u8bbe N</p> <p>true: \u5047\u8bbe\u662f\u6210\u7acb\u7684 T</p> <p>false: \u5047\u8bbe\u662f\u9519\u8bef\u7684 F</p> <p>\u6211\u4eec\u901a\u8fc7\u4e0b\u9762\u4e24\u4e2a\u6807\u51c6\u6765\u8054\u5408\u5224\u65ad\u6548\u679c\u3002</p> <p>\u7cbe\u5ea6 Precision = TP/(TP+FP)\uff1a\u63cf\u8ff0\u7ed9\u5b9a\u7684 bbox \u91cc\u6709\u591a\u5c11\u662f\u6b63\u786e\u7684</p> <p>\u53ec\u56de\u7387 Recall = TP/(TP+FN)\uff1a\u63cf\u8ff0\u6240\u6709\u5bf9\u8c61\u4e2d\uff0c\u88ab\u6211\u4eec\u8bc6\u522b\u51fa\u6765\u7684\u6709\u591a\u5c11</p> <p>\u4e00\u822c\u6765\u8bf4\uff0c\u8fd9\u4fe9\u4e1c\u897f\u6709\u4e00\u4e2a trade-off\u3002\uff08\u6982\u7edf\u91cc\u5e94\u8be5\u6709\u7c7b\u4f3c\u7684\u5185\u5bb9\uff09</p> <p>https://en.wikipedia.org/wiki/Precision_and_recall</p> <p>\u800c\u6700\u7ec8\u7684\u8861\u91cf\u65b9\u6cd5\uff0c\u662f Mean Average Precision (mAP)\u3002</p> <ol> <li>Run object detector on all test images</li> <li>For each category, compute Average Precision </li> <li>(AP) = area under Precision vs Recall Curves</li> </ol> <p>PPT p52</p> <p>\u5148\u505a\u6240\u6709\u7c7b\u522b\u7684 AP\uff0c\u7136\u540e\u53d6\u5e73\u5747\u5c31\u662f mAP</p> <p>mAP@threshold = ...</p> <p>COCOmAP = average(mAP@threshold_i), for i \\in {0.5, 0.55, 0.6, \u2026, 0.95}</p> <p>Non-Max Suppression</p> <p>\u5bf9\u4e8e\u540c\u4e00\u4e2a\u5bf9\u8c61\uff0c\u6211\u6709\u53ef\u80fd\u8bc6\u522b\u51fa\u597d\u51e0\u4e2a\u8bc6\u522b\u540c\u4e00\u4e2a\u7269\u4f53\u7684 bbox\uff0c\u6240\u4ee5\u6211\u53ef\u4ee5\u8003\u8651\u8bbe\u8ba1\u4e00\u79cd\u7b97\u6cd5\u51cf\u5c11\u8fd9\u79cd\u8bc6\u522b\u3002</p> <p>\u7b80\u5355\u6765\u8bf4\uff0c\u505a\u6cd5\u5c31\u662f\u627e score \u6700\u5927\u7684\uff0c\u7136\u540e\u770b\u5176\u4ed6 bbox \u548c\u8fd9\u4e2a bbox \u7684 IoU\uff0c\u5927\u4e8e\u4e00\u5b9a\u6743\u91cd\u65f6\uff0c\u8ba4\u4e3a\u5b83\u4eec\u662f\u4e00\u81f4\u7684\uff0c\u5c31\u53ef\u4ee5\u628a\u8f83\u5c0f\u7684\u90a3\u4e2a\u5220\u6389\u4e86\u3002 </p> <p>Fast R-CNN</p> <p>RoI pool \uff08\u6ca1\u542c\u61c2\uff0c\u6574\u7406\u7684\u65f6\u5019\u518d\u4ed4\u7ec6\u5b66\u4e00\u4e0b\uff09</p> <p>Faster R-CNN</p> <p>\u7528\u7f51\u7edc\uff08Region Proposal Network, RPN\uff09\u751f\u6210\u63d0\u8bae\u9009\u6846\uff0c</p> <p>\u951a\u70b9 anchor\uff1a</p> <p>\u5728\u8ba1\u7b97\u673a\u89c6\u89c9\u4e2d\uff0c\u951a\u70b9\u662f\u7528\u4e8e\u76ee\u6807\u68c0\u6d4b\u7684\u9884\u5b9a\u4e49\u6846\u6216\u611f\u5174\u8da3\u533a\u57df\u3002\u951a\u70b9\u80fd\u591f\u5e2e\u52a9\u5377\u79ef\u795e\u7ecf\u7f51\u7edc\u8bc6\u522b\u56fe\u50cf\u4e2d\u5b58\u5728\u7684\u7269\u4f53\u53ca\u5176\u4f4d\u7f6e\uff0c\u4ece\u800c\u63d0\u9ad8\u76ee\u6807\u68c0\u6d4b\u7684\u51c6\u786e\u6027\u3002\u951a\u70b9\u901a\u5e38\u7531\u4e00\u7ec4\u9884\u5b9a\u4e49\u7684\u957f\u5bbd\u6bd4\u548c\u5c3a\u5ea6\u5b9a\u4e49\uff0c\u8fd9\u4e9b\u56e0\u7d20\u51b3\u5b9a\u4e86\u5b83\u4eec\u7684\u5927\u5c0f\u548c\u5f62\u72b6\u3002\u5728\u8bad\u7ec3\u671f\u95f4\uff0cCNN\u5b66\u4e60\u9884\u6d4b\u76f8\u5bf9\u4e8e\u8fd9\u4e9b\u951a\u70b9\u7684\u7269\u4f53\u7684\u4f4d\u7f6e\u548c\u5927\u5c0f\u3002\u4f7f\u7528\u951a\u70b9\u53ef\u4ee5\u68c0\u6d4b\u4e0d\u540c\u5927\u5c0f\u548c\u5bbd\u9ad8\u6bd4\u7684\u7269\u4f53\uff0c\u5e76\u6709\u52a9\u4e8e\u63d0\u9ad8\u76ee\u6807\u68c0\u6d4b\u5728\u590d\u6742\u573a\u666f\u4e0b\u7684\u51c6\u786e\u6027\u3002----chatGPT</p> <p>RPN \u7684\u5927\u81f4\u601d\u8def\u662f\uff0c\u628a\u751f\u6210\u9009\u6846\u95ee\u9898\u8f6c\u5316\u4e3a\u6253\u5206\u95ee\u9898\uff0c\u5177\u4f53\u6765\u8bf4\u662f\u7ed9\u6bcf\u4e2a\u50cf\u7d20\u6253\u5728\u8be5\u4f4d\u7f6e\u6709\u4e00\u4e2a\u7279\u5b9a size \u7684\u6846\u7684\u53ef\u80fd\u6027\u7684\u5206\u3002</p> <p>\u4e8c\u9636\u6bb5\u5bf9\u8c61\u68c0\u6d4b\u7b26 two-stage object detector</p> <ol> <li></li> <li></li> </ol> <p> P76 \u5404\u79cd\u65b9\u6cd5\u7684\u6548\u679c\u6392\u5e8f\u3002</p> <p>\u4e00\u79cd\u5bf9 two-stage object detector \u7684\u6539\u8fdb\u662f single-stage object detector\uff0c\u5927\u6982\u5c31\u662f\u5728\u505a RPN \u7684\u540c\u65f6\u53bb\u9884\u6d4b\u8fd9\u4e2a\u6846\u6807\u8bb0\u7684\u662f\u67d0\u4e2a\u7c7b\u522b\u7684\u6982\u7387\u3002</p> <p>single-stage \u7684\u4ee3\u8868\u6027\u5de5\u4f5c\uff1aYOLO</p> <p>two-stage v.s. single-stage</p> <ul> <li>Two-stage is generally more accurate \uff08\u6570\u636e\u91cf\u8db3\u591f\u5927\uff09</li> <li>Single-stage is faster</li> </ul> <p>\u4f46\u662f\u6211\u4eec\u4e0a\u9762\u7684\u5de5\u4f5c\u90fd\u6ca1\u8003\u8651\u5c3a\u5ea6\u53d8\u5316\uff0cFeature pyramid network \u5728\u8fd9\u65b9\u9762\u63d0\u51fa\u4e86\u89e3\u51b3\u65b9\u6848\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec10/#instance-segmentation","title":"Instance segmentation","text":"<p>Faster R-CNN + additional head</p> <p>Mask R-CNN</p> <p>Deep snake</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec10/#panoptic-segmentation","title":"Panoptic segmentation","text":"<p>Microsoft COCO dataset</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec10/#human-pose-estimation","title":"Human pose estimation","text":"<p>keypoints</p> <p>represent joint location as the heatmap // hourglass networks</p> <p>Top-down: - Detect humans and detect keypoints in each bbox - Example: Mask R-CNN - \u6700\u5927\u7684\u95ee\u9898\u8fd8\u662f\u6162</p> <p>Bottom-up: - Detect keypoints and group keypoints to form humans - Example: OpenPose \u5148\u627e kpts\uff0c\u518d\u5229\u7528 Affinity Fields \u628a\u5c5e\u4e8e\u4e00\u4e2a\u4eba\u7684 kpts \u5408\u5728\u4e00\u8d77\u3002</p> <p>Top-down is generally more accurate Bottom-up is faster\uff0c\u800c\u4e14\u5728\u906e\u6321\u60c5\u51b5\u4e0b\u4e5f\u6709\u5b83\u7684\u4f18\u52bf</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec10/#optical-flow","title":"Optical flow","text":"<p>\u5149\u6d41</p> <p>video classification</p> <p>\u4e00\u4e2a\u505a\u6cd5\u662f\u628a\u89c6\u9891\u5f53\u4f5c\u4e00\u4e2a 3d \u56fe\u50cf\u53bb\u505a\uff0c\u5373 3D CNN\u3002\u4f46\u662f\u6570\u636e\u7ef4\u5ea6\u975e\u5e38\u5927\u3002</p> <p>Temporal action localization</p> <p>Spatial-temporal detection</p> <p>\u505a\u6cd5\u4e5f\u53ef\u4ee5\u5f53\u4f5c\u4e00\u4e2a 3D \u7684 R-CNN \u53bb\u505a\u3002</p> <p>Multi-object tracking</p> <p>\u5bf9\u6bcf\u4e00\u5e27\u505a\u7269\u4f53\u68c0\u6d4b\uff0c\u7136\u540e\u5728\u6bcf\u4e00\u5e27\u4e4b\u95f4\u505a\u5173\u8054\u5339\u914d\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec11/","title":"Lecture 11 | 3D Deep Learning","text":"<p> \u7ea6 385 \u4e2a\u5b57  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 1 \u5206\u949f</p> <p>\u6ce8\u610f</p> <p>\u672c\u6587\u5c1a\u672a\u5b8c\u5168\u6574\u7406\u597d\uff01</p> <p>Deep Learning for 3D reconstruction</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec11/#feature-matching","title":"Feature matching","text":"<p>recap: SfM // Colmap</p> <p>use deep learning to improve feature matching</p> <p>\u4f20\u7edf\u65b9\u6cd5\u7684\u7f3a\u70b9\u5c31\u662f\u56e0\u4e3a\u8fd9\u4e9b\u65b9\u6cd5\u90fd\u662f handcrafted \u7684\u3002\u6240\u4ee5\u6211\u4eec\u5e0c\u671b\u80fd\u591f\u7528 deep learning \u6765\u589e\u5f3a\u6548\u679c\u3002</p> <p></p> <p>example: SuperPoint\u3001SuperGlue</p> <ul> <li>CNN-base descriptor \u597d\u6709\u610f\u601d\uff01</li> </ul> <p>\u63cf\u8ff0\u503c\uff1a</p> <ol> <li>contrastive loss</li> <li>triplet loss</li> </ol> <p>\u5b9e\u9645\u4e0a\u672c\u8d28\u7c7b\u4f3c\uff0c\u6548\u679c\u76f8\u8fd1</p> <p>\u4e3b\u6d41\u7528 MVS \u6765\u751f\u6210\u8bad\u7ec3\u6570\u636e</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec11/#object-pose-estimation","title":"Object Pose Estimation","text":"<p>\u672c\u8d28\u4e0a\u662f\u5728\u8ba8\u8bba\u7269\u4f53\u5728\u91cd\u5efa\u7a7a\u95f4\u4e2d\u7684\u5750\u6807\u7cfb\u548c\u76f8\u673a\u7a7a\u95f4\u4e2d\u7684\u5750\u6807\u7cfb\u7684\u53d8\u6362\u5173\u7cfb\u3002</p> <p>PnP</p> <p>\u53ef\u662f\u96be\u5c31\u96be\u5728\uff0c\u5982\u4f55\u5bfb\u627e 3D-2D \u7684\u5173\u7cfb\u5462\uff1f</p> <p>\u4e00\u4e2a idea \u662f\uff0c\u9996\u5148\u5f97\u5230\u4e00\u4e2a\u8f83\u597d\u7684\u91cd\u5efa\uff0c\u7136\u540e\u57fa\u4e8e\u8fd9\u4e2a\u91cd\u5efa\u6a21\u578b\uff0c\u6211\u4eec\u5c31\u53ef\u4ee5\u4ece\u522b\u7684\u601d\u8def\u6765\u770b\u8fd9\u4ef6\u4e8b\u3002</p> <p>pose refinement methods</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec11/#human-pose-estimation","title":"Human Pose Estimation","text":"<p>(Markerless) MoCap</p> <p>Monocular 3D Human Pose Estimation (eg. Vnet)</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec11/#depth-estimation","title":"Depth Estimation","text":"<p>MVSNet</p> <p>MVS</p> <p>\u79bb\u6563\u8868\u793a\u3001\u9690\u5f0f\u8868\u793a\uff08\u7528\u4e00\u4e2a\u7f51\u7edc\u6765\u8868\u793a\u4e00\u4e2a\u51fd\u6570 Implicit Neural Representations\uff0c\u4ee3\u8868\uff1aNeRF\uff09</p> <p>Replacing density field in NeRF by SDF: NeuS</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec11/#single-image-to-3d","title":"Single Image to 3D","text":""},{"location":"cour_note/D2QD_Intro2CV/Lec11/#deep-learning-for-3d-understanding","title":"Deep learning for 3D understanding","text":"<p>\u8ba1\u7b97\u5f00\u9500\u5f88\u5927</p> <p>\u8fd1\u51e0\u5e74\u63d0\u51fa\u7684\u89e3\u51b3\u65b9\u6848\uff1aSparse ConvNets</p> <p>Octree \u516b\u53c9\u6811\uff0c\u7a7a\u95f4\u5212\u5206</p> <p>\u7a00\u758f\u5377\u79ef\uff0c\u53ea\u6709\u6709\u503c\u7684\u5730\u65b9\u8fdb\u884c\u5377\u79ef</p> <p>\u7531\u4e8e\u5377\u79ef\u7b49\u64cd\u4f5c\u662f\u5efa\u7acb\u5728\u7f51\u683c\u4e0a\u7684\uff0c\u800c\u70b9\u4e91\u5e76\u4e0d\u5b9a\u4e49\u5728\u7f51\u683c\u4e0a\uff0c\u6240\u4ee5\u5bf9\u70b9\u4e91\u8fdb\u884c\u5377\u79ef\u5219\u9700\u8981\u4e00\u4e9b\u5176\u4ed6\u65b9\u6cd5\u3002</p> <p>\u4e00\u4e2a\u76f8\u5173\u5de5\u4f5c\u662f PointNet\uff0c\u4e13\u95e8\u7528\u5728\u5bf9\u70b9\u4e91\u4e0a\u3002\u8fd8\u6709 PointNet++</p> <p>3D Semantic Segmentation</p> <p>3D Object Detection</p> <p>3D Instance Segmentation</p> <p>PointRCNN</p> <p>Frustum PointNets</p> <p>\u6570\u636e\u96c6\uff1aShapeNet, PartNet,SceneNet , ScanNet</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec12/","title":"Lecture 12 | Computational Photography 1","text":"<p> \u7ea6 253 \u4e2a\u5b57  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 1 \u5206\u949f</p> <p>\u6ce8\u610f</p> <p>\u672c\u6587\u5c1a\u672a\u5b8c\u5168\u6574\u7406\u597d\uff01</p> What's \u8ba1\u7b97\u6444\u5f71\uff1f <p>...</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec12/#high-dynamic-range-imaging-hdr","title":"High Dynamic Range Imaging (HDR)","text":"<p>\u6211\u4eec\u5e0c\u671b\u4eae\u7684\u548c\u6697\u7684\u5730\u65b9\u7ec6\u8282\u90fd\u5f88\u4e30\u5bcc</p> <p>\u66dd\u5149 exposure = Gain\u589e\u76ca * Irradiance\u8f90\u7167\u5ea6 * Time\u66dd\u5149\u65f6\u95f4</p> <p>\u5206\u522b\u53d6\u51b3\u4e8e\u2026\u2026</p> <ul> <li>\u5feb\u95e8</li> <li>\u5149\u5708</li> <li>ISO \u611f\u5149\u5ea6<ul> <li>\u9ad8\uff1a\u66f4\u4eae\u3001\u66f4\u591a\u566a\u58f0</li> </ul> </li> </ul> <p>Dynamic range</p> <p>The ratio between the largest and smallest values of a certain quantity </p> <p>HRD: \u4e0d\u540c\u4eae\u5ea6\u90fd\u62cd\u4e00\u4e9b\uff0c\u7136\u540e\u5408\u6210</p> <p>12 to 8 -&gt; tone mapping</p> <p>Gamma compression</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec12/#deblurring","title":"Deblurring","text":"<p>\u6a21\u7cca\u7684\u4e24\u4e2a\u4e3b\u8981\u539f\u56e0\uff1adefocus and motion blur</p> <p>blurred image = clear image * blur kernel</p> <p>deblurring = deconvolution</p> <ul> <li>Non-blind image deconvolution, NBID</li> <li>Blind image deconvolution, BID</li> </ul> <p>inverse filter</p> <p>wiener filter</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec12/#colorization","title":"Colorization","text":"<p>\u6700\u5173\u952e\u7684\u95ee\u9898\u662f\uff0c\u5982\u4f55\u51b3\u5b9a\u4e0a\u7684\u989c\u8272</p> <p>\u4e3b\u8981\u6709\u4e24\u7c7b\u65b9\u6cd5\uff1a</p> <ol> <li>sample-based colorization</li> <li>interactive colorization</li> </ol>"},{"location":"cour_note/D2QD_Intro2CV/Lec12/#sample-based","title":"Sample-based","text":"<p>...</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec12/#interactive","title":"Interactive","text":"<p>...</p> <p>\u5bf9\u4e8e\u89c6\u9891</p> <p>Colorful Image Colorization</p> <p>GAN (Generative Adversarial Network)</p> <ul> <li>\u4e24\u4e2a\u4e00\u8d77\u8bad\u7ec3\uff0cmin-max problem  </li> <li>GAN \u5f88\u96be\u6536\u655b\uff0c\u4e0d\u597d\u8c03</li> <li>adversarial loss</li> </ul>"},{"location":"cour_note/D2QD_Intro2CV/Lec12/#more-image-synthesis-tasks","title":"more Image synthesis tasks","text":"<ul> <li>image to image translation<ul> <li>pix2pix gan</li> </ul> </li> <li>style transfer</li> <li>text-to-photo</li> <li>image dehazing</li> <li>customized gaming</li> </ul> <p>GAN \u7684\u6539\u8fdb\uff1aCycle-GAN\uff0c\u89e3\u51b3\u4e86\u7f3a\u5c11\u6210\u5bf9\u7684\u8bad\u7ec3\u6570\u636e\u7684\u95ee\u9898</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec12/#super-resolution","title":"Super Resolution","text":"<p>up sampling</p> <p>bi-cubic</p> <p>super resolution using GAN</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec13/","title":"Lecture 13 | Computational Photography 2","text":"<p> \u7ea6 90 \u4e2a\u5b57 </p> <p>\u6ce8\u610f</p> <p>\u672c\u6587\u5c1a\u672a\u5b8c\u5168\u6574\u7406\u597d\uff01</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec13/#image-based-rendering","title":"Image-based Rendering","text":"<p>rendering: from 3D models to images.</p> <p>Image-based Rendering: images -&gt; 3D Models -&gt; novel views.</p> <p>representations:</p> <ul> <li>Textured Mesh (surface-based representations)</li> <li>Light Fields and Lumigraphs<ul> <li>\u727a\u7272\u4e86\u4e00\u4e2a\u65b9\u5411\uff0c\u51cf\u5c11\u4e86\u4e00\u4e2a\u7eac\u5ea6</li> <li>\u53ea\u80fd\u5185\u91c7\u6837</li> </ul> </li> <li>Depth Warping</li> <li>Multi-plane Images (MPI) (volume-based representations)<ul> <li>rgba x multi planes</li> <li>Neural Volumes</li> </ul> </li> <li>Neural Radiance Fields</li> </ul> <p>surface-based representations</p> <ul> <li>a</li> <li>da</li> </ul> <p>volume-based representations</p> <ul> <li>a</li> <li>da</li> </ul> <p>\u81ea\u7531\u89c6\u70b9\u89c6\u9891</p>"},{"location":"cour_note/D3QD_OperatingSystem/","title":"[\u5927\u4e09\u79cb\u51ac] \u64cd\u4f5c\u7cfb\u7edf | Operating System","text":"<p> \u7ea6 247 \u4e2a\u5b57  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 1 \u5206\u949f</p> <p>\u8bfe\u7a0b\u4fe1\u606f</p> <ul> <li>\u667a\u4e91\u94fe\u63a5\uff1a\ud83d\udd17</li> <li>\u6388\u8bfe\uff1a\u5b63\u6c5f\u6c11</li> <li>\u8bfe\u672c\uff1aOperating System Concepts (10th edition)</li> </ul> <p>\u5206\u6570\u6784\u6210</p> <ul> <li>[50%] \u5e73\u65f6\u6210\u7ee9<ul> <li>[5%] HOMEWORK</li> <li>[5%] Quiz / \u70b9\u540d</li> <li>[20%] Lab \u62a5\u544a\uff08\u6bcf 5 \u884c\u4ee3\u7801\u9700\u8981\u6ce8\u91ca\uff0c\u9700\u8981\u6709\u5fc3\u5f97\u4e0e\u95ee\u9898\u8ba8\u8bba\uff0c\u5360 20%\uff09</li> <li>[20%] Lab \u9a8c\u6536</li> <li>[6%] Bonus<ul> <li>[4%] Lab 7</li> <li>[2%] \u8bfe\u5802\u56de\u7b54\u95ee\u9898\uff0c0.5/\u6b21</li> </ul> </li> </ul> </li> <li>[50%] \u671f\u672b\u6210\u7ee9\uff08\u5141\u8bb8\u643a\u5e26 3 \u5f20 A4\uff0c\u5141\u8bb8\u6253\u5370\uff09</li> </ul> <p>\u7b14\u8bb0\u53c2\u8003</p> <p>\u672c\u8bfe\u7a0b\u7684\u7b14\u8bb0\u4e3b\u8981\u53c2\u8003\u4e86\u5982\u4e0b\u8d44\u6599\uff1a</p> <ul> <li>Operating System Concepts (10th edition)</li> <li>2024 \u64cd\u4f5c\u7cfb\u7edf\u8003\u7814\u590d\u4e60\u6307\u5bfc\uff08\u738b\u9053\uff09\uff08\u540e\u5f03\u7528\uff09</li> <li>\u54b8\u9c7c\u6684\u7684\u64cd\u4f5c\u7cfb\u7edf\u7b14\u8bb0</li> </ul> <p>list</p> <ul> <li> Unit 0: \u603b\u89c8 | Overview</li> <li> Unit 1: \u8fdb\u7a0b\u7ba1\u7406 | Process Management</li> <li> Unit 2: \u540c\u6b65 | Synchronization<ul> <li> Part 1: \u540c\u6b65\u5de5\u5177 | Synchronization Tools</li> <li> Part 2: \u7ecf\u5178\u540c\u6b65\u4f8b\u5b50 | Synchronization Problems Examples</li> <li> Part 3: \u6b7b\u9501 | Deadlocks</li> </ul> </li> <li> Unit 3: \u5185\u5b58\u7ba1\u7406 | Memory Management<ul> <li> Part 1: \u4e3b\u5b58 | Main Memory</li> <li> Part 2: \u865a\u62df\u5185\u5b58 | Virtual Memory</li> </ul> </li> <li> Unit 4: \u5b58\u50a8\u7ba1\u7406 | Storage Management</li> <li> Unit 5: \u6587\u4ef6\u7cfb\u7edf | File System</li> </ul>"},{"location":"cour_note/D3QD_OperatingSystem/Unit0-brief/","title":"[\u6559\u5b66\u7248] Unit 0: \u603b\u89c8 | Overview","text":"<p> \u7ea6 3594 \u4e2a\u5b57  23 \u884c\u4ee3\u7801  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 12 \u5206\u949f</p> \u4e24\u4e2a\u4efb\u52a1 <ol> <li>\u5bf9\u64cd\u4f5c\u7cfb\u7edf\u8fdb\u884c\u4e00\u4e2a\u8f83\u4e3a\u62bd\u8c61\u7684\u4ecb\u7ecd\uff0c\u540c\u65f6\u5efa\u7acb\u8d77\u6574\u95e8\u8bfe\u7a0b\u7684\u6846\u67b6\uff0c\u65b9\u4fbf\u8bfb\u8005\u5728\u4e4b\u540e\u7684\u5b66\u4e60\u8fc7\u7a0b\u4e2d\u80fd\u6709\u4e00\u4e2a\u6bd4\u8f83\u603b\u4f53\u7684\u8ba4\u8bc6\uff0c\u80fd\u5e26\u7740\u76ee\u7684\u53bb\u5b66\u4e60\u5177\u4f53\u7684\u77e5\u8bc6\uff1b</li> <li>\u4ecb\u7ecd\u4e00\u4e9b\u6bd4\u8f83\u57fa\u7840\u7684\u5185\u5bb9\uff0c\u6216\u662f\u4e00\u4e9b\u6bd4\u8f83\u7410\u788e\u3001\u4ec5\u9700\u4e86\u89e3\u7684\u5185\u5bb9\uff1b</li> </ol> \u201c\u5b9a\u4e49\u4e0d\u5b58\u5728\u4e86\u201d <ul> <li>\u5f88\u591a\u6982\u5ff5\u90fd\u5f88\u96be\u754c\u5b9a\u4e00\u4e2a\u660e\u786e\u7684\u754c\u9650\u3002</li> </ul> \u64cd\u4f5c\u7cfb\u7edf\u6982\u8ff0 \u4f55\u4e3a\u64cd\u4f5c\u7cfb\u7edf \u2460 \u4ece\u804c\u80fd\u4e0a\u770b <p></p> <ul> <li> <p>\u4e00\u4e2a\u8bcd\u6982\u62ec\uff1a\u8d44\u6e90\u7ba1\u7406\u7cfb\u7edf\uff1b</p> </li> <li> <p>\u81ea\u4e0a\u800c\u4e0b\uff1b</p> </li> <li>\u81ea\u4e0b\u800c\u4e0a\uff1b</li> </ul> <p>\u8d44\u6e90\uff1aCPU\u3001\u5185\u5b58\u3001\u8bbe\u5907\u2026\u2026\u2026</p> <ul> <li>\u4e4b\u540e\u5c06\u56f4\u7ed5\u8981\u5982\u4f55\u7ef4\u62a4\u548c\u64cd\u4f5c\u5404\u79cd\u8d44\u6e90\u800c\u5c55\u5f00\u7684\u3002</li> </ul> \u2461 \u4ece\u5b58\u5728\u4e0a\u770b <ul> <li>\u4e00\u4e2a\u8bcd\u6982\u62ec\uff1a\u4e0d\u505c\u8fd0\u884c\u7684\uff0c\u7528\u6765\u8dd1\u8f6f\u4ef6\u7684\u8f6f\u4ef6\u7a0b\u5e8f\uff08\u53cd\u5e94\u4e86\u64cd\u4f5c\u7cfb\u7edf\u4e3a\u4f55\u8bde\u751f\uff09\uff1b</li> </ul> <p>\u5185\u6838(kernel)\u2014\u2014\u81ea\u8ba1\u7b97\u673a\u5f00\u673a\u540e\u5c31\u4e0d\u505c\u5728\u8fd0\u884c\uff08\u6211\u4eec\u5b66\u7684\u57fa\u672c\u90fd\u662f kernel \u7684\u4e1c\u897f\uff09\u3002</p> \u603b\u7ed3 <p>The common functions of controlling and allocating resources are then brought together into one piece of software: the operating system. --Operating System Concepts (10th edition)</p> \u5982\u4f55\u8bc4\u4ef7\u64cd\u4f5c\u7cfb\u7edf <ul> <li>\u53ef\u9760\u6027\u548c\u5b89\u5168\u6027\uff1b</li> <li>\u6613\u7528\u6027\uff1b</li> <li>\u9ad8\u6548\u6027\uff1b</li> <li>\u516c\u5e73\u6027\uff1b</li> <li>\u53ef\u6269\u5c55\u6027\uff0c\u6613\u7ef4\u62a4\u6027\uff1b</li> <li>...</li> </ul> <p>\u6ce8\u610f</p> <p>\u4e0a\u8ff0\u89c2\u70b9\u5e76\u4e0d\u5168\u9762\u4e5f\u4e0d\u4e00\u5b9a\u5b8c\u5168\u6b63\u786e\uff0c\u6709\u4e00\u5927\u90e8\u5206\u90fd\u662f\u6211\u7684\u4e2a\u4eba\u7406\u89e3\uff0c\u8bf7\u8bfb\u8005\u8fa8\u8bc1\u5730\u770b\u5f85\uff0c\u5982\u679c\u6709\u9519\u8bef\u8bf7\u52a1\u5fc5\u544a\u8bc9\u6211\uff01</p> \u64cd\u4f5c\u7cfb\u7edf\u7684\u6574\u4f53\u8bbe\u8ba1 \u8ba1\u7b97\u673a\u7cfb\u7edf\u67b6\u6784 \u6982\u5ff5\u8fa8\u6790 <p> \u540d\u8bcd \u5b9a\u4f4d CPU \u6267\u884c\u6307\u4ee4\u7684\u786c\u4ef6 Core CPU \u7684\u57fa\u7840\u8ba1\u7b97\u5355\u5143 Multi-core \u4e00\u4e2a CPU \u4e0a\u6709\u591a\u4e2a core Processor \u5305\u542b\u4e00\u4e2a\u6216\u591a\u4e2a CPU \u7684\u82af\u7247 Multi-processor \u591a\u4e2a processor </p> <p>\u6839\u636e\u5904\u7406\u5668\u7684\u6570\u91cf\u548c\u7ec4\u7ec7\u5f62\u5f0f\uff0c\u6211\u4eec\u8fd9\u91cc\u4ecb\u7ecd\u4e09\u79cd\u8ba1\u7b97\u673a\u7cfb\u7edf\u67b6\u6784\uff1a\u5355\u5904\u7406\u5668\u7cfb\u7edf\u3001\u591a\u5904\u7406\u5668\u7cfb\u7edf\u3001\u96c6\u7fa4\u7cfb\u7edf\u3002</p> \u2460 \u5355\u5904\u7406\u5668\u7cfb\u7edf(Single-Processor System) <p>\u6709\u4e14\u4ec5\u6709\u4e00\u4e2a\u901a\u7528\u5904\u7406\u5668(general-purpose processor)\uff0c\u5e76\u4e14\u8fd9\u4e2a processor \u53ea\u6709\u4e00\u4e2a\u6838(core)\u3002</p> <p>\u53ef\u4ee5\u6709\u82e5\u5e72\u4e13\u7528\u5904\u7406\u5668(special-purpose processor)\uff0c\u7528\u6765\u6267\u884c\u4e00\u4e9b\u7279\u5b9a\u7684\u6307\u4ee4\uff0c\u800c\u8fd9\u4e9b\u4e13\u7528\u5904\u7406\u5668\u5e76\u4e0d\u8fd0\u884c\u7ebf\u7a0b\u3002</p> \u2461 \u591a\u5904\u7406\u5668\u7cfb\u7edf(Multiprocessor System) <p>\u591a\u5904\u7406\u5668\u7cfb\u7edf\u662f\u6307\u6709\u591a\u4e2a\u5355\u6838\u901a\u7528\u5904\u7406\u5668\u7684\u7cfb\u7edf\uff0c\u8fd9\u4e9b\u5904\u7406\u5668\u5171\u4eab\u4e00\u5757\u4e3b\u5185\u5b58\uff0c\u5b83\u4eec\u901a\u8fc7\u603b\u7ebf\u6216\u4ea4\u6362\u7f51\u7edc\u8fde\u63a5\u5728\u4e00\u8d77\u3002</p> <ul> <li>\u589e\u52a0\u541e\u5410\u91cf(throughput)\uff0c\u4f46\u662f\u8fd9\u4e2a\u589e\u52a0\u5e76\u4e0d\u662f\u7ebf\u6027\u7684\uff1b</li> </ul> \u2462 \u96c6\u7fa4\u7cfb\u7edf(Cluster System) <p> </p> <ul> <li>\u5197\u4f59 -&gt; \u9ad8\u53ef\u7528\uff1b</li> <li>\u5e76\u884c -&gt; \u9ad8\u6027\u80fd\uff1b</li> <li>\u8282\u70b9(node)\u901a\u8fc7\u9ad8\u901f\u901a\u4fe1\u7f51\u7edc\u4e92\u76f8\u8fde\u63a5\u5f62\u6210\uff1b</li> <li>\u5206\u5bf9\u79f0\u548c\u4e0d\u5bf9\u79f0\u4e24\u79cd\uff1b</li> </ul> \u64cd\u4f5c\u7cfb\u7edf\u7684\u4efb\u52a1\u6267\u884c\u8bbe\u8ba1 <p>\u64cd\u4f5c\u7cfb\u7edf\u88ab\u7528\u6765\u300c\u81ea\u52a8\u5316\u201c\u8ba9\u8ba1\u7b97\u673a\u5b8c\u6210\u4e00\u7cfb\u5217\u7279\u5b9a\u4efb\u52a1\u201d\u300d\u7684\uff0c\u968f\u7740\u9700\u6c42\u4e0d\u65ad\u590d\u6742\uff0c\u4f7f\u7528\u7684\u6280\u672f\u4e5f\u4e0d\u65ad\u53d1\u5c55\u3002</p> \u2460 \u6279\u5904\u7406\u7cfb\u7edf\u9636\u6bb5 \u80cc\u666f 1 <p>\u4eba\u5de5\u901f\u5ea6\u4e25\u91cd\u9650\u5236\u4e86\u8ba1\u7b97\u673a\u7684\u5de5\u4f5c\u6548\u7387\u3002</p> \u2776 \u5355\u9053\u6279\u5904\u7406\u9636\u6bb5 <p>\u4e24\u4e2a\u5173\u952e\u8bcd\uff1a\u201c\u6279\u5904\u7406\u201d\u548c\u201c\u5355\u9053\u201d\u3002</p> <p>\u201c\u6279\u5904\u7406\u201d\u6307\u7684\u662f\uff0c\u7cfb\u7edf\u6267\u884c\u7684\u4efb\u52a1\u662f\u6210\u6279\u7684\uff0c\u82e5\u5e72\u4efb\u52a1\u88ab\u4f5c\u4e3a\u4e00\u6574\u6279\u4ea4\u4ed8\u7ed9\u64cd\u4f5c\u7cfb\u7edf\u3002\u5728\u5177\u4f53\u6267\u884c\u8fc7\u7a0b\u4e2d\uff0c\u64cd\u4f5c\u7cfb\u7edf\u81ea\u52a8\u6309\u987a\u5e8f\u4e32\u884c(serial)\u6267\u884c\u8fd9\u4e9b\u4efb\u52a1\u3002</p> <p>\u800c\u201c\u5355\u9053\u201d\u6307\u7684\u662f\uff0c\u4e00\u6bb5\u65f6\u95f4\u5185\u5185\u5b58\u4e2d\u53ea\u6709\u4e00\u9053\u7a0b\u5e8f\u5728\u8fd0\u884c\uff0c\u7cfb\u7edf\u53ea\u5904\u7406\u4e00\u9879\u4efb\u52a1\uff0c\u5728\u8fd9\u4e2a\u4efb\u52a1\u7ed3\u675f\u4e4b\u524d\uff0c\u4e0d\u4f1a\u5207\u6362\u5230\u5176\u4ed6\u4efb\u52a1\u3002</p> \u80cc\u666f 2 <ul> <li>\u89e3\u51b3\u4e86\u80cc\u666f 1\uff1a\u51cf\u5c11\u4e86\u4eba\u5de5\u64cd\u4f5c\u901f\u5ea6\u5bf9\u64cd\u4f5c\u7cfb\u7edf\u7684\u5f71\u54cd\uff1b</li> <li>\u4ea7\u751f\u4e86\u80cc\u666f 2\uff1aCPU \u5229\u7528\u7387\u4f4e\uff1b</li> </ul> \u2777 \u591a\u9053\u6279\u5904\u7406\u9636\u6bb5 <p>\u5173\u952e\u8bcd\uff1a\u201c\u591a\u9053(Multiprogramming)\u201d\uff0c\u5373\u4e00\u6bb5\u65f6\u95f4\u5185\u5185\u5b58\u4e2d\u540c\u65f6\u5b58\u5728\u591a\u4e2a\u8fdb\u7a0b\u3002</p> <p>\u4e0d\u8ba9 CPU \u95f2\u4e0b\u6765 -&gt; \u8ba9\u5b83\u5148\u53bb\u505a\u4e0b\u4e00\u4ef6\u4e8b\u3002</p> <p>\u5b8f\u89c2\u5e76\u53d1\uff0c\u5fae\u89c2\u4e32\u884c\u3002\uff08\u533a\u5206\u5e76\u53d1\u548c\u5e76\u884c\uff01\uff09</p> <p>\u6211\u4eec\u53ef\u4ee5\u7528\u7518\u7279\u56fe\u6765\u53ef\u89c6\u5316\u591a\u9053\u6279\u5904\u7406\u7cfb\u7edf\u7684\u7b56\u7565\uff08\u4e00\u79cd\u5e38\u89c1\u7684\u9898\u578b\uff09\u3002\u4ee5\u4e0b\u9762\u7684\u9898\u76ee\u4e3a\u4f8b\uff0c\u6211\u4eec\u6765\u5b9e\u8df5\u4e00\u4e0b\u3002</p> \ud83c\udf30 \u9898\u9762\u89e3\u6790 <p>\u73b0\u5728\u6709\u4e24\u4e2a\u7a0b\u5e8f A \u548c B\uff0c\u4ee5\u53ca\u4e24\u4e2a\u5206\u522b\u72ec\u7acb\u7684\u8bbe\u5907 X \u548c Y\uff0c\u4e14\u6211\u4eec\u53ea\u6709\u4e00\u4e2a CPU\uff1a</p> <ul> <li>A \u9700\u8981\u987a\u5e8f\u4f7f\u7528\u5982\u4e0b\u8d44\u6e90\uff1aCPU:10s, X:5s, CPU:5s, Y:10s, CPU:10s</li> <li>B \u9700\u8981\u987a\u5e8f\u4f7f\u7528\u5982\u4e0b\u8d44\u6e90\uff1aX:10s, CPU 10s, Y:5s, CPU:5s, Y:10s </li> </ul> <p>\u8bf7\u8ba8\u8bba\uff1a</p> <ol> <li>\u5728\u5355\u9053\u7a0b\u5e8f\u73af\u5883\u4e0b\u5148\u6267\u884c A \u518d\u6267\u884c B\uff0cCPU \u7684\u5229\u7528\u7387\u662f\u591a\u5c11\uff1f</li> <li>\u5728\u591a\u9053\u7a0b\u5e8f\u73af\u5883\u4e0b\uff0cCPU \u7684\u5229\u7528\u7387\u662f\u591a\u5c11\uff1f\u8bf7\u7ed9\u51fa\u7518\u7279\u56fe\u3002</li> </ol> <p>\u5728\u5355\u9053\u7a0b\u5e8f\u4e0b\u6267\u884c\uff0c\u5373\u6309\u987a\u5e8f\u6267\u884c A \u548c B\uff0cCPU \u7684\u5229\u7528\u7387\u5373\u5b9e\u9645 CPU \u4f7f\u7528\u65f6\u95f4\u9664\u4ee5\u5b8c\u6210\u4efb\u52a1\u7684\u603b\u65f6\u95f4\uff0c\u56e0\u6b64\uff1a</p> \\[ U = \\frac{(10+5+10)+(10+5)}{(10+5+5+10+10)+(10+10+5+5+10)} = \\frac{40}{80} = 50\\% \\] <p>\u800c\u5728\u591a\u9053\u7a0b\u5e8f\u73af\u5883\u4e0b\uff0c\u6211\u4eec\u5f97\u5230\u5982\u4e0b\u7518\u7279\u56fe\uff1a</p> <pre><code>gantt\n    title Multiprogramming\n    dateFormat ss\n    axisFormat %S\n\n    section Program A\n    CPU :a,  00,  10\n    X   :b,  10,  15\n    CPU :c,  20,  25\n    Y   :d,  25,  35\n    CPU :e,  35,  45\n\n    section Program B\n    X   :g,  00,  10\n    CPU :h,  10,  20\n    Y   :i,  20,  25\n    CPU :j,  25,  30\n    Y   :k,  35,  45</code></pre> <p>\u7531\u4e8e Mermaid \u7684\u9650\u5236\uff0c\u6211\u73b0\u5728\u662f\u628a\u6bcf\u4e2a\u7a0b\u5e8f\u7684\u4efb\u52a1\u9519\u5f00\u753b\u7684\uff0c\u5b9e\u9645\u4e0a\u505a\u9898\u7684\u65f6\u5019\u53ef\u4ee5\u76f4\u63a5\u753b\u6210\u4e24\u884c\u3002</p> <p>\u8981\u70b9\u5c31\u662f\u7eb5\u5411\u4e0d\u80fd\u540c\u65f6\u51fa\u73b0\u540c\u4e00\u4e2a\u8d44\u6e90\uff0c\u4f8b\u5982 18s \u65f6\u4e0d\u80fd A \u548c B \u90fd\u7528 CPU\uff0c\u6240\u4ee5 A \u9700\u8981\u7b49 B \u7528\u5b8c CPU \u518d\u4f7f\u7528\u3002</p> <p>\u73b0\u5728\u6211\u4eec\u518d\u6765\u7edf\u8ba1 CPU \u7684\u5229\u7528\u7387\uff1a</p> \\[ U = \\frac{10+10+5+5+10}{45} = \\frac{40}{45} = 88.89\\% \\] <p>\u7531\u4e8e\u5f15\u5165\u4e86\u591a\u9053\u6280\u672f\uff0c\u7cfb\u7edf\u590d\u6742\u7a0b\u5ea6\u4e0a\u5347\u3002</p> \u80cc\u666f 3 <ul> <li>\u89e3\u51b3\u4e86\u80cc\u666f 2\uff1a\u63d0\u9ad8\u4e86 CPU \u5229\u7528\u7387\uff1b</li> <li>\u4ea7\u751f\u4e86\u80cc\u666f 3\uff1a\u4ea4\u4e92\u6027\u5dee\uff1b</li> </ul> <p>\uff08\u5047\u8bbe\u6211\u4eec\u5ffd\u7565\u5173\u4e8e\u5c4f\u5e55\u663e\u793a\u7684 I/O\uff09\u8bd5\u60f3\uff0c\u4f60\u5e0c\u671b\u5728\u8dd1\u7a0b\u5e8f\u7684\u65f6\u5019\u653e\u4e00\u4e2a\u89c6\u9891\uff0c\u4f46\u662f\u7531\u4e8e\u4f60\u7684\u7a0b\u5e8f\u8fd8\u6ca1\u8dd1\u5b8c\uff0c\u4f60\u7684\u89c6\u9891\u5c31\u6ca1\u6cd5\u64ad\u653e\uff0c\u7a81\u7136\u4f60\u7684\u7a0b\u5e8f\u53d1\u751f\u4e86\u4e00\u6b21 I/O\uff0cCPU \u8f6c\u800c\u64ad\u653e\u5df2\u7ecf\u5b8c\u6210 I/O \u540e\u7684\u90a3\u90e8\u5206\u89c6\u9891\uff0c\u4f46\u662f\u8fd9\u4e2a\u65f6\u5019\u4f60\u7684\u7a0b\u5e8f I/O \u5f88\u5feb\u4e5f\u5b8c\u6210\u4e86\uff0c\u5374\u9700\u8981\u7b49\u5f85\u7f13\u5b58\u4e2d\u7684\u89c6\u9891\u653e\u5b8c\u624d\u80fd\u7ee7\u7eed\u6267\u884c\uff0c\u8fd9\u79cd\u7528\u6237\u4f53\u9a8c\u51e0\u4e4e\u65e0\u6cd5\u63a5\u53d7\u3002</p> <ul> <li>\u5bf9\u4e8e\u7528\u6237\u6765\u8bf4\uff0c\u6700\u597d\u80fd\u540c\u65f6\u5b9e\u73b0\u4f53\u611f\u4e0a\u7684\u5e76\u884c\uff0c\u4e5f\u5c31\u662f\u51e0\u4ef6\u4e8b\u60c5\u81f3\u5c11\u770b\u8d77\u6765\u8981\u50cf\u662f\u540c\u65f6\u53d1\uff1b</li> </ul> \u2461 \u5206\u65f6\u7cfb\u7edf\u9636\u6bb5 <ul> <li>\u5206\u65f6\u7cfb\u7edf(Time Sharing Systems)\u662f\u591a\u4efb\u52a1(Multitasking)\u7684\u4e00\u4e2a\u5177\u4f53\u5b9e\u73b0\uff1b</li> <li> <p>Multitasking \u662f Multiprogramming \u7684\u4e00\u4e2a\u903b\u8f91\u6269\u5c55\uff1b</p> <ul> <li>Multitasking \u4e5f\u662f Multiprogramming \u7684\u4e00\u79cd\uff0c\u5b83\u7b26\u5408\u5185\u5b58\u4e2d\u6709\u591a\u4e2a\u8fdb\u7a0b\uff0c\u4e00\u6bb5\u65f6\u95f4\u5185\u6709\u591a\u4e2a\u4efb\u52a1\u4e00\u8d77\u6267\u884c\u7684\u7279\u70b9\uff1b</li> </ul> </li> <li> <p>\u5206\u65f6\u7cfb\u7edf\u901a\u8fc7\u9891\u7e41\u5730\u5728\u591a\u4e2a\u8fdb\u7a0b\u95f4\u5207\u6362\u6765\u8fd1\u4f3c\u5b9e\u73b0\u5e76\u884c\uff08\u4ecd\u7136\u4e0d\u662f\u771f\u6b63\u7684\u5e76\u884c\uff09\uff1b</p> <ul> <li>\u65f6\u95f4\u7247(time slice)\uff1b</li> </ul> </li> </ul> <p>\u300a\u5341\u4e07\u4e2a\u51b7\u7b11\u8bdd\u300b\u7684 4:09 - 4:48\u3002</p> <p>\u5206\u65f6\u7528\u6237\u5141\u8bb8\u591a\u4e2a\u7528\u6237\u540c\u65f6\u4f7f\u7528\u540c\u4e00\u53f0\u8ba1\u7b97\u673a\uff0c\u6240\u6709\u4efb\u52a1\u4e4b\u95f4\u4e92\u76f8\u72ec\u7acb\uff0c\u4e92\u4e0d\u5e72\u6270\u3001\u4e92\u4e0d\u963b\u585e\uff0c\u56e0\u6b64\u4efb\u52a1\u7684\u6700\u957f\u5468\u8f6c\u65f6\u95f4\u51cf\u5c11\uff0c\u7528\u6237\u7684\u64cd\u4f5c\u4e5f\u4f1a\u88ab\u53ca\u65f6\u54cd\u5e94\uff0c\u5b9e\u73b0\u4e86\u66f4\u65b9\u4fbf\u8fdb\u884c\u4eba\u673a\u5bf9\u8bdd\u3002</p> \u64cd\u4f5c\u7cfb\u7edf\u7684\u7ed3\u6784\u8bbe\u8ba1 <p>\u968f\u7740\u64cd\u4f5c\u7cfb\u7edf\u7684\u529f\u80fd\u4e0d\u65ad\u6269\u5c55\u3001\u4f53\u91cf\u9010\u6e10\u53d8\u5927\uff0c\u6574\u4e2a\u64cd\u4f5c\u7cfb\u7edf\u8f6f\u4ef6\u7684\u7ed3\u6784\u8bbe\u8ba1\u5c31\u8d8a\u53d1\u91cd\u8981\u4e86\u3002</p> <p></p> \u5b8f\u5185\u6838 <p>\u5b8f\u5185\u6838(Monolithic-Kernels)\u4e5f\u53eb\u5355\u5185\u6838\u6216\u5927\u5185\u6838\u3002</p> <p>\u4f18\u52bf\uff1a\u64cd\u4f5c\u7cfb\u7edf\u6548\u7387\u6781\u9ad8\u3002</p> <p>\u52a3\u52bf\uff1a\u5927\u91cf\u590d\u6742\u7684\u529f\u80fd\u4e92\u76f8\u8026\u5408 -&gt; \u7ef4\u62a4\u56f0\u96be\u3001\u4e00\u635f\u5177\u635f\uff1b</p> <p> </p> \u5206\u5c42\u8bbe\u8ba1 <p>\u5206\u5c42\u8bbe\u8ba1(layer approach)\u7684\u6838\u5fc3\u601d\u60f3\u662f\u5c06\u7cfb\u7edf\u5206\u4e3a\u82e5\u5e72\u5c42\uff0c\u5e95\u5c42\u4e3a\u786c\u4ef6\uff0c\u9876\u5c42\u4e3a\u7528\u6237\u63a5\u53e3\uff0c\u7b2c \\(i\\) \u5c42\u53ea\u8c03\u7528 \\(i-1\\) \u5c42\u63d0\u4f9b\u7684\u63a5\u53e3\u3002</p> <p>\u7406\u60f3\uff1a\u4f4e\u8026\u5408\uff0c\u9636\u6bb5\u6027\u5f00\u53d1\u3002</p> <p>\u73b0\u5b9e\uff1a\u6548\u7387\u4f4e\u3001\u96be\u8bbe\u8ba1\u3002</p> <p></p> \u5fae\u5185\u6838 <p>\u5fae\u5185\u6838(Micro-Kernels)\u4e3b\u5f20\u5c06\u4e0d\u662f\u5fc5\u8981\u7684\u4e1c\u897f\u90fd\u4ece\u5185\u6838\u91cc\u62ff\u51fa\u53bb\uff0c\u653e\u5230\u7528\u6237\u7a7a\u95f4\uff0c\u4ee5\u7528\u6237\u6001\u6267\u884c\u3002</p> <p>\u6574\u4f53\u5f62\u6210\u4e00\u79cd\u5fae\u5185\u6838-\u670d\u52a1\u5668\u7684\u7ed3\u6784\uff0c\u6b64\u65f6\u5185\u6838\u53ea\u63d0\u4f9b\u901a\u8baf\u3001\u5185\u5b58\u7ba1\u7406\u3001\u8fdb\u7a0b\u7ba1\u7406\u7b49\u57fa\u672c\u529f\u80fd\uff0c\u4e5f\u53ea\u6709\u8fd9\u4e9b\u90e8\u5206\u76f4\u63a5\u8fd0\u884c\u5728\u5185\u6838\u6001\uff0c\u4f5c\u4e3a\u670d\u52a1\u5668\u7684\u5176\u5b83\u529f\u80fd\u90e8\u4ef6\u5219\u901a\u8fc7\u6d88\u606f\u4f20\u9012\u673a\u5236\u4e0e\u5185\u6838\u4e92\u52a8\u3002</p> <p>\u4f18\u52bf\uff1a\u89c4\u6a21\u51cf\u5c0f,\u8026\u5408\u964d\u4f4e -&gt; \u66f4\u65b9\u4fbf\u7ef4\u62a4\uff0c\u53ef\u9760\u6027\u589e\u52a0\u3002</p> <p>\u52a3\u52bf\uff1a\u6548\u7387\u4f4e\u3002</p> <p> </p> \u6a21\u5757\u5316\u8bbe\u8ba1 <p>\u6a21\u5757\u5316\u8bbe\u8ba1(Modules Approach)\u6307\u5c06\u64cd\u4f5c\u7cfb\u7edf\u5212\u5206\u4e3a\u82e5\u5e72\u5206\u7acb\u6a21\u5757\uff0c\u5e76\u89c4\u5b9a\u6a21\u5757\u4e4b\u95f4\u7684\u63a5\u53e3\uff0c\u751a\u81f3\u5355\u4e2a\u6a21\u5757\u4e0b\u4e5f\u53ef\u80fd\u662f\u7531\u591a\u4e2a\u6a21\u5757\u901a\u8fc7\u540c\u6837\u7684\u65b9\u5f0f\u7ec4\u7ec7\u800c\u6210\u7684\u3002\u8fd9\u79cd\u8bbe\u8ba1\u65b9\u6cd5\u4e5f\u88ab\u79f0\u4e3a\u6a21\u5757-\u63a5\u53e3\u6cd5\u3002</p> <p>\u8fa8\u6790</p> <p>\u6a21\u5757\u5316\u7684\u8bbe\u8ba1\u4e0e\u5fae\u5185\u6838\u662f\u4e0d\u540c\u7684\uff0c\u9700\u8981\u6ce8\u610f\u533a\u5206\u3002\u5fae\u5185\u6838\u8bbe\u8ba1\u4ecd\u7136\u662f\u6709\u4e2d\u5fc3\uff08\u5fae\u5185\u6838\uff09\u7684\uff0c\u4f46\u662f\u6a21\u5757\u5316\u8bbe\u8ba1\u6574\u4f53\u662f\u5206\u5c42\u7f51\u72b6\u7684\u3002</p> <p>\u7406\u60f3\uff1a\u4f4e\u8026\u5408 -&gt; \u5e76\u884c\u5f00\u53d1\uff0c\u597d\u7ef4\u62a4\u3002</p> <p>\u73b0\u5b9e\uff1a\u8bbe\u8ba1\u5341\u5206\u56f0\u96be\uff0c\u96be\u4ee5\u9012\u8fdb\u5f0f\u5f00\u53d1\u3002</p> \u6df7\u5408\u7cfb\u7edf <p>\u6df7\u5408\u7cfb\u7edf(Hybrid Systems)\u662f\u6307\u5c06\u5b8f\u5185\u6838\u548c\u5fae\u5185\u6838\u7684\u8bbe\u8ba1\u601d\u8def\u7ed3\u5408\u8d77\u6765\uff0c\u8fd9\u79cd\u8bbe\u8ba1\u6a21\u5f0f\u66f4\u73b0\u4ee3\uff0c\u4e5f\u662f\u76ee\u524d\u4e3b\u6d41\u7684\u64cd\u4f5c\u7cfb\u7edf\u7684\u6a21\u5f0f\u3002</p> \u64cd\u4f5c\u7cfb\u7edf\u7684\u8fd0\u884c\u539f\u7406 \u4e2d\u65ad <ul> <li>\u903b\u8f91\u4e0a\u7684\u8f6e\u8be2\u4e0d\u5408\u7406\uff1b</li> <li>\u5b9e\u73b0\u4e0a\u7528\u201c\u786c\u4ef6\u8f6e\u8be2\u201d\u6765\u5b9e\u73b0\u4e2d\u65ad\uff1b</li> </ul> <p>\u4e2d\u65ad\u5411\u91cf\u8868</p> <p>\u7531\u4e8e\u4e2d\u65ad\u88ab\u5e7f\u6cdb\u4f7f\u7528\uff0c\u64cd\u4f5c\u7cfb\u7edf\u9700\u8981\u9891\u7e41\u7684\u5904\u7406\u5404\u79cd\u4e2d\u65ad\uff0c\u5904\u7406\u6bcf\u4e00\u79cd\u4e2d\u65ad\u90fd\u9700\u8981\u4e00\u4e2a\u7279\u5b9a\u7684\u65b9\u6cd5\uff0c\u56e0\u6b64\uff0c\u4e00\u79cd\u5feb\u901f\u5b9a\u4f4d\u4e2d\u65ad\u5904\u7406\u65b9\u6cd5\u7684\u624b\u6bb5\u5c31\u663e\u5f97\u5c24\u4e3a\u91cd\u8981\u3002</p> <p>\u4e2d\u65ad\u5411\u91cf\u8868(Interrupt Vector Table)\u901a\u8fc7\u4e2d\u65ad\u53f7\u6765\u7d22\u5f15\u4e2d\u65ad\u5904\u7406\u65b9\u6cd5\uff0c\u5b9e\u73b0\u4e86\u4e00\u79cd\u201c\u968f\u673a\u8bbf\u95ee\u201d\uff0c\u5927\u5927\u52a0\u901f\u4e86\u4e2d\u65ad\u5904\u7406\u7684\u901f\u5ea6\u3002</p> <ul> <li>\u5916\u4e2d\u65ad\uff08CPU \u5916\u4ea7\u751f\uff09\uff1b</li> <li>\u5185\u4e2d\u65ad\uff08CPU \u5185\u4ea7\u751f\uff09\u3002</li> </ul> <p>\u7406\u60f3\u60c5\u51b5\u4e0b\uff0c\u6211\u4eec\u5e0c\u671b\u4e2d\u65ad\u4e00\u65e6\u53d1\u751f\u5c31\u7acb\u523b\u88ab\u89e3\u51b3\uff0c\u4f46\u662f\u4e2d\u65ad\u5904\u7406\u4e5f\u540c\u6837\u9700\u8981\u8d44\u6e90\uff0c\u8fd9\u610f\u5473\u7740\u4e2d\u65ad\u4e5f\u6709\u53ef\u80fd\u4ea7\u751f\u51b2\u7a81\u3002\u4e8e\u662f\uff0c\u6211\u4eec\u9700\u8981\u4e00\u7cfb\u5217\u673a\u5236\u6765\u89e3\u51b3\u8fd9\u4e9b\u95ee\u9898\u3002</p> <ol> <li>\u5206\u7ea7\u673a\u5236\uff1b</li> <li>\u5c4f\u853d\u673a\u5236\uff1b</li> </ol> <p>\u4e00\u79cd\u6bd4\u8f83\u666e\u901a\u7684\u8bbe\u8ba1\uff1a\u51c6\u5907 maskable interrupt-request line \u548c non-maskable interrupt-request line \u4e24\u6761\u4e2d\u65ad\u8bf7\u6c42\u7ebf\uff0c\u524d\u8005\u7528\u4e8e\u53ef\u5c4f\u853d\u7684\u4e2d\u65ad\uff0c\u540e\u8005\u7528\u4e8e\u4e0d\u53ef\u5c4f\u853d\u7684\u4e2d\u65ad\u3002</p> <p>\u9700\u8981\u6ce8\u610f\uff0c\u64cd\u4f5c\u7cfb\u7edf\u53d1\u73b0\u4e2d\u65ad\u540e\u5e76\u4e0d\u662f\u4e8c\u8bdd\u4e0d\u8bf4\u9a6c\u4e0a\u53bb\u5904\u7406\u4e2d\u65ad\u7684\uff0c\u4e3a\u4e86\u4fdd\u8bc1\u4e2d\u65ad\u5904\u7406\u5b8c\u6210\u540e\u4ecd\u80fd\u7ee7\u7eed\u5f53\u524d\u4efb\u52a1\uff0c\u64cd\u4f5c\u7cfb\u7edf\u9700\u8981\u4fdd\u5b58\u5f53\u524d\u4efb\u52a1\u7684\u72b6\u6001\uff08\u4e0a\u4e0b\u6587\uff09\uff0c\u4ee5\u4fbf\u5b8c\u6210\u4e2d\u65ad\u5904\u7406\u540e\u6062\u590d\u5f53\u524d\u4efb\u52a1\u7684\u72b6\u6001\u3002</p> \u8ba1\u65f6\u5668 <p>\u8ba1\u65f6\u5668(timer)\uff1a\u56fa\u5b9a\u9891\u7387\u7684\u65f6\u949f + \u8ba1\u6570\u5668\u3002</p> <ul> <li>\u65f6\u95f4\u7247\u7684\u957f\u5ea6\uff1b</li> <li>\u907f\u514d\u8fdb\u7a0b\u5360\u7528\u7cfb\u7edf\u8d44\u6e90\u8fc7\u4e45\uff1b</li> <li>...</li> </ul> \u7279\u6743\u6a21\u5f0f \u9694\u79bb <p>\u64cd\u4f5c\u7cfb\u7edf\u7684\u67d0\u4e9b\u64cd\u4f5c\u662f\u5371\u9669\u7684\uff0c\u6709\u53ef\u80fd\u5a01\u80c1\u5230\u81ea\u8eab\u6b63\u5e38\u8fd0\u4f5c\u7684\uff08\u5982\u4e0e\u786c\u4ef6\u76f4\u63a5\u76f8\u5173\u7684\u884c\u4e3a\u3001\u63a7\u5236 CPU \u8fd0\u884c\u89c4\u5219\u7684\u884c\u4e3a\u7b49\uff09\uff0c\u800c\u8fd9\u4e9b\u64cd\u4f5c\u4e0d\u5e94\u5f53\u88ab\u7528\u6237\u7a0b\u5e8f\u76f4\u63a5\u6267\u884c\u3002</p> <p>\u4e00\u79cd\u7b80\u5355\u7684\u601d\u8def\u662f\uff0c\u6211\u4eec\u5212\u5206\u5e38\u89c4\u64cd\u4f5c\u548c\u5371\u9669\u64cd\u4f5c\uff0c\u5141\u8bb8\u7528\u6237\u7a0b\u5e8f\u6267\u884c\u5e38\u89c4\u64cd\u4f5c\uff0c\u800c\u5371\u9669\u64cd\u4f5c\u5219\u9700\u8981\u59d4\u6258\u4e13\u4e1a\u4eba\u58eb\u4ee3\u4e3a\u6267\u884c\u3002\u800c\u8fd9\u5c31\u662f\u7279\u6743\u6a21\u5f0f(Privileged Mode)\u7684\u57fa\u672c\u601d\u8def\u3002</p> <p>\u5de5\u4e1a\u4e0a\u7684\u7279\u6743\u6a21\u5f0f\u53ef\u80fd\u4f1a\u6709\u591a\u79cd\u590d\u6742\u7684\u5b9e\u73b0\u5f62\u5f0f\uff0c\u4f46\u662f\u6211\u4eec\u8fd9\u91cc\u53ea\u8bb2\u6700\u7b80\u5355\u7684\u4e00\u79cd\uff0c\u5373\u53cc\u6a21\u5f0f(Dual-Mode)\u3002</p> <p>\u53cc\u6a21\u5f0f\u4e0b\uff0cCPU \u6709\u4e24\u79cd\u8fd0\u884c\u6a21\u5f0f\uff0c\u4e00\u79cd\u662f\u7528\u6237\u6001(User Mode)\uff08\u76ee\u6001\uff09\uff0c\u4e00\u79cd\u662f\u5185\u6838\u6001(Kernel Mode)\uff08\u7ba1\u6001\uff0c\u6838\u5fc3\u6001\uff09\u3002</p> <p>\u540c\u65f6\uff0c\u6211\u4eec\u5c06\u90a3\u4e9b\u201c\u5371\u9669\u201d\u7684\u6307\u4ee4\u79f0\u4e3a\u7279\u6743\u6307\u4ee4(privileged instruction)\uff0c\u4f8b\u5982 I/O \u63a7\u5236\uff0c\u8ba1\u65f6\u5668\u7ba1\u7406\uff0c\u4e2d\u65ad\u7ba1\u7406\u7b49\u3002\u8fd9\u4e9b\u6307\u4ee4\u53ea\u80fd\u5728\u5185\u6838\u6001\u4e0b\u6267\u884c\uff0c\u800c\u7528\u6237\u6001\u4e0b\u6267\u884c\u8fd9\u4e9b\u6307\u4ee4\u65f6\u4f1a\u8ba4\u4e3a\u8fd9\u6761\u6307\u4ee4\u4e0d\u5b58\u5728\u3002</p> \u95ee\u9898\u5c1a\u672a\u89e3\u51b3 <p>\u73b0\u5728\u6211\u4eec\u5c06\u5371\u9669\u64cd\u4f5c\u548c\u76f8\u5bf9\u5b89\u5168\u7684\u64cd\u4f5c\u9694\u79bb\u5f00\u6765\u4e86\uff0c\u4f46\u662f\u8fd9\u5e76\u4e0d\u610f\u5473\u7740\u7528\u6237\u7a0b\u5e8f\u5c31\u4e0d\u9700\u8981\u4f7f\u7528\u90a3\u4e9b\u5371\u9669\u64cd\u4f5c\u4e86\uff0c\u5355\u7eaf\u7684\u9694\u79bb\u5e76\u4e0d\u80fd\u89e3\u51b3\u95ee\u9898\uff0c\u7528\u6237\u7a0b\u5e8f\u4ecd\u7136\u5b58\u5728\u9700\u8981\u4f7f\u7528\u7279\u6743\u6307\u4ee4\u7684\u9700\u6c42\u3002</p> \u9694\u79bb\u800c\u975e\u9694\u7edd <p>\u8fd9\u4e9b\u9700\u6c42\u5f80\u5f80\u662f\u53ef\u4ee5\u88ab\u62bd\u8c61\u7684\u3001\u88ab\u5c01\u88c5\u7684\u3002</p> <ul> <li>\u5b9e\u73b0\u65b9\u6cd5\uff1a\u8ba9\u6e21\u63a7\u5236\u6743\u3002</li> </ul> <p>\u800c\u90a3\u4e48\u5728\u5177\u4f53\u5b9e\u73b0\u4e0a\uff0c\u8fd9\u4e00\u6b65\u662f\u901a\u8fc7 trap \u5b9e\u73b0\u7684\u3002</p> <p>  Transition from user to kernel mode. </p> \u7cfb\u7edf\u8c03\u7528 <p>  Examples of W&amp;U system calls. </p> <p>\u7cfb\u7edf\u8c03\u7528(System Call)\u662f\u7cfb\u7edf\u5411\u7528\u6237\u7a0b\u5e8f\u63d0\u4f9b\u670d\u52a1\u7684\u4e00\u4e2a\u63a5\u53e3\uff0c\u5b83\u4eec\u7ecf\u5e38\u4ee5 C/C++ \u51fd\u6570\u7684\u5f62\u5f0f\u5b58\u5728\uff0c\u5bf9\u4e8e\u67d0\u4e9b\u6bd4\u8f83\u63a5\u8fd1\u5e95\u5c42\u7684\u4efb\u52a1\uff0c\u4e5f\u53ef\u80fd\u662f\u901a\u8fc7\u6c47\u7f16\u7f16\u5199\u7684\u3002</p> <p>\u4f46\u8bf4\u5230\u5e95\uff0c\u7cfb\u7edf\u8c03\u7528\u8fd8\u662f\u76f8\u5bf9\u5e95\u5c42\u7684\u8bbe\u8ba1\uff0c\u901a\u5e38\u7684\u5f00\u53d1\u5e76\u4e0d\u57fa\u4e8e\u5982\u6b64\u5e95\u5c42\u7684\u8bbe\u8ba1\u5c55\u5f00\u3002\u66f4\u5e38\u89c1\u7684\u662f\u5229\u7528\u5404\u79cd\u62bd\u8c61\u5c42\u7ea7\u66f4\u9ad8\u7684 Application Programming Interface, API \u8fdb\u884c\u5f00\u53d1\u3002</p> <p>API \u7531\u201c\u73af\u5883\u201d\u63d0\u4f9b\uff0c\u4e5f\u5c31\u662f\u6211\u4eec\u6240\u8bf4\u7684\u8fd0\u884c\u65f6\u73af\u5883(run-time environment, RTE)\u3002</p> \u601d\u8003\u9898 \u9898\u9762\u89e3\u6790 <p>\u8fa8\u6790\u5e93\u51fd\u6570\u4e0e\u7cfb\u7edf\u8c03\u7528\uff1f</p> <p>\u5e93\u51fd\u6570\u8fd0\u884c\u5728\u7528\u6237\u7a7a\u95f4\u800c\u7cfb\u7edf\u8c03\u7528\u8fd0\u884c\u5728\u5185\u6838\u7a7a\u95f4\u3002\u5927\u90e8\u5206\u5e93\u51fd\u6570\u53ef\u80fd\u4f7f\u7528\u7cfb\u7edf\u8c03\u7528\u6765\u5b9e\u73b0\u76ee\u7684\u3002</p> \u94fe\u63a5\u5668\u548c\u88c5\u8f7d\u5668 <p>  The role of the linker and loader. </p> <p>\u8bf4\u4e86\u8fd9\u4e48\u591a\uff0c\u90a3\u4e48\u64cd\u4f5c\u7cfb\u7edf\u5230\u5e95\u662f\u5982\u4f55\u6267\u884c\u4e00\u4e2a\u7a0b\u5e8f\u7684\u5462\uff1f\u4ee5 C \u4e3a\u4f8b\uff0c\u4e00\u4e2a\u5199\u5b8c\u7684\u4ee3\u7801\u9700\u8981\u7ecf\u8fc7\u7f16\u8bd1\u3001\u94fe\u63a5\u3001\u88c5\u8f7d\u4e09\u4e2a\u6b65\u9aa4\uff0c\u624d\u80fd\u6210\u4e3a\u4e00\u4e2a\u5728\u5185\u5b58\u4e2d\u7684\uff0c\u53ef\u4ee5\u88ab\u6267\u884c\u7684\u7a0b\u5e8f\u3002</p> <ol> <li>\u7f16\u8bd1\u5668\u9996\u5148\u5c06\u82e5\u5e72 <code>.c</code> \u6e90\u6587\u4ef6\u7f16\u8bd1\u4e3a\u82e5\u5e72 <code>.o</code> \u6587\u4ef6\uff08\u8fd9\u91cc\u5408\u5e76\u4e86\u9884\u5904\u7406\u3001\u7f16\u8bd1\u3001\u6c47\u7f16\u6b65\u9aa4\uff09\uff0c\u8fd9\u4e9b <code>.o</code> \u6587\u4ef6\u88ab\u79f0\u4e3a\u53ef\u91cd\u5b9a\u4f4d\u76ee\u6807\u6587\u4ef6(relocatable object file)\uff0c\u5176\u5b58\u5728\u5f62\u5f0f\u4e3a\u673a\u5668\u7801\uff1b</li> <li>\u968f\u540e\u94fe\u63a5\u5668\u5c06\u82e5\u5e72 <code>.o</code> \u6587\u4ef6\u8fde\u5e26\u6240\u9700\u8981\u7684\u4e00\u4e9b\u5e93\u6587\u4ef6\uff08\u5982 <code>.a</code> \u6587\u4ef6\uff09\u94fe\u63a5\u4e3a\u4e00\u4e2a\u53ef\u6267\u884c\u76ee\u6807\u6587\u4ef6(executable object file)\uff1b</li> </ol> <p>\u7279\u522b\u7684\uff0c\u94fe\u63a5\u5206\u4e3a\u9759\u6001\u94fe\u63a5\u548c\u52a8\u6001\u94fe\u63a5\u4e24\u79cd\u3002\u9759\u6001\u94fe\u63a5\u5c06\u5e93\u6587\u4ef6\u7684\u4ee3\u7801\u76f4\u63a5\u5408\u5e76\u8fdb\u5165\u6700\u7ec8\u7684\u53ef\u6267\u884c\u6587\u4ef6\uff0c\u800c\u52a8\u6001\u94fe\u63a5\u4ec5\u4ec5\u5c06\u5e93\u6587\u4ef6\u7684\u5f15\u7528\u4fe1\u606f\u5199\u5165\u6700\u7ec8\u7684\u53ef\u6267\u884c\u6587\u4ef6\uff0c\u800c\u5728\u7a0b\u5e8f\u8fd0\u884c\u65f6\u518d\u53bb\u5bfb\u627e\u8fd9\u4e9b\u5e93\u6587\u4ef6\u3002</p> <pre><code>gcc -E main.c -o main.i # pre-process\ngcc -S main.i -o main.s # compile to assembly code\ngcc -c main.s -o main.o # assemble to object file\ngcc main.o -o main      # link\n./main                  # (load and) execute\n</code></pre> <p>  \u53ef\u4ee5\u53d1\u73b0\uff0c\u52a8\u6001\u94fe\u63a5\u5f97\u5230\u7684\u53ef\u6267\u884c\u6587\u4ef6\u6bd4\u9759\u6001\u94fe\u63a5\u5f97\u5230\u7684\u53ef\u6267\u884c\u6587\u4ef6\u8981\u5c0f\u4e0d\u5c11\u3002 </p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit0/","title":"Unit 0: \u603b\u89c8 | Overview","text":"<p> \u7ea6 8917 \u4e2a\u5b57  23 \u884c\u4ee3\u7801  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 30 \u5206\u949f</p> <p>\u5bfc\u8bed</p> <p>\u672c\u5355\u5143\u4e3b\u8981\u6709\u4e24\u4e2a\u4efb\u52a1\uff1a</p> <ol> <li>\u5bf9\u64cd\u4f5c\u7cfb\u7edf\u8fdb\u884c\u4e00\u4e2a\u8f83\u4e3a\u62bd\u8c61\u7684\u4ecb\u7ecd\uff0c\u540c\u65f6\u5efa\u7acb\u8d77\u6574\u95e8\u8bfe\u7a0b\u7684\u6846\u67b6\uff0c\u65b9\u4fbf\u8bfb\u8005\u5728\u4e4b\u540e\u7684\u5b66\u4e60\u8fc7\u7a0b\u4e2d\u80fd\u6709\u4e00\u4e2a\u6bd4\u8f83\u603b\u4f53\u7684\u8ba4\u8bc6\uff0c\u80fd\u5e26\u7740\u76ee\u7684\u53bb\u5b66\u4e60\u5177\u4f53\u7684\u77e5\u8bc6\uff1b</li> <li>\u4ecb\u7ecd\u4e00\u4e9b\u6bd4\u8f83\u57fa\u7840\u7684\u5185\u5bb9\uff0c\u6216\u662f\u4e00\u4e9b\u6bd4\u8f83\u7410\u788e\u3001\u4ec5\u9700\u4e86\u89e3\u7684\u5185\u5bb9\uff1b</li> </ol> <p>\u7531\u4e8e\u8bfe\u672c\u7684 Overview \u5199\u5f97\u975e\u5e38\u4e00\u8a00\u96be\u5c3d\uff0c\u6240\u4ee5\u6211\u5728\u5543\u5b8c\u540e\u8fdb\u884c\u4e86\u4e00\u4e9b\u6574\u7406\uff0c\u4f60\u53ef\u4ee5\u5728\u8fd9\u91cc\u627e\u5230\u6211\u6574\u7406\u8fc7\u7a0b\u4e2d\u5b8c\u6210\u7684\u601d\u7ef4\u5bfc\u56fe\uff0c\u4e0d\u8fc7\u8fd9\u4e2a\u601d\u7ef4\u5bfc\u56fe\u66f4\u591a\u7684\u662f\u63d0\u4f9b\u6846\u67b6\u6027\u7684\u8ba4\u77e5\uff0c\u5177\u4f53\u5230\u6bcf\u4e2a\u53f6\u5b50\u8282\u70b9\u7684\u5185\u5bb9\u5efa\u8bae\u8fd8\u662f\u4ee5\u672c\u6587\u4e3a\u4e3b\u3002\u6b64\u5916\uff0c\u672c\u6587\u5f88\u591a\u89c2\u70b9\u5177\u6709\u6bd4\u8f83\u5f3a\u70c8\u7684\u4e2a\u4eba\u7406\u89e3\u8272\u5f69\uff0c\u5982\u679c\u4f60\u5bf9\u5176\u4e2d\u7684\u8bba\u65ad\u62b1\u6709\u5f02\u8bae\uff0c\u6b22\u8fce\u8ba8\u8bba\uff01</p> <p>\u5728\u6b63\u5f0f\u5f00\u59cb\u6838\u5fc3\u5185\u5bb9\u7684\u5b66\u4e60\u4e4b\u524d\uff0c\u6211\u60f3\u5148\u505a\u4e00\u70b9\u8bf4\u660e\uff0c\u4e5f\u7b97\u662f\u4e00\u70b9\u5173\u4e8e\u5b66\u4e60\u64cd\u4f5c\u7cfb\u7edf\u7684\u7ecf\u9a8c\u4e4b\u8c08\u3002</p> <p>\u201c\u5b9a\u4e49\u4e0d\u5b58\u5728\u4e86\u201d</p> <p>\u533a\u522b\u4e8e\u81ea\u7136\u79d1\u5b66\u7684\u7814\u7a76\u5bf9\u8c61\uff0c\u64cd\u4f5c\u7cfb\u7edf\u4f5c\u4e3a\u4e00\u4e2a\u5f7b\u5f7b\u5e95\u5e95\u7684\u4eba\u9020\u7269\uff0c\u5176\u5f88\u591a\u6982\u5ff5\u90fd\u5f88\u96be\u754c\u5b9a\u4e00\u4e2a\u660e\u786e\u7684\u754c\u9650\uff0c\u8fd9\u4e5f\u6b63\u662f\u6211\u5728\u5b66\u4e60\u64cd\u4f5c\u7cfb\u7edf\u7684\u8fc7\u7a0b\u4e2d\u9047\u5230\u7684\u6700\u9996\u8981\u7684\u95ee\u9898\u3002\u6211\u4f1a\u5c3d\u529b\u7ed9\u51fa\u6211\u8ba4\u4e3a\u66f4\u7cbe\u786e\u7684\u5b9a\u4e49\uff0c\u4f46\u8fd9\u4e2a\u95ee\u9898\u4ecd\u7136\u5b58\u5728\uff0c\u6240\u4ee5\u6211\u4eec\u5c3d\u91cf\u53ea\u56f4\u7ed5\u5b9a\u4e49\u7684\u4e2d\u5fc3\u8fdb\u884c\u5b66\u4e60\u3002</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit0/#\u64cd\u4f5c\u7cfb\u7edf\u6982\u8ff0","title":"\u64cd\u4f5c\u7cfb\u7edf\u6982\u8ff0","text":"<p>\u672c\u8282\u4e3b\u8981\u5c06\u64cd\u4f5c\u7cfb\u7edf\u5f53\u4f5c\u4e00\u4e2a\u4e0d\u53ef\u62c6\u5206\u7684\u5355\u4f4d\uff0c\u6765\u8ba8\u8bba\u4ec0\u4e48\u662f\u64cd\u4f5c\u7cfb\u7edf\u3002</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit0/#\u4f55\u4e3a\u64cd\u4f5c\u7cfb\u7edf","title":"\u4f55\u4e3a\u64cd\u4f5c\u7cfb\u7edf","text":"<p>\u6574\u95e8\u8bfe\u7a0b\u6211\u4eec\u9700\u8981\u89e3\u51b3\u7684\u7b2c\u4e00\u4e2a\u95ee\u9898\uff0c\u663e\u7136\u662f\u4ec0\u4e48\u662f\u64cd\u4f5c\u7cfb\u7edf(Operating System, OS)\u3002\u63a5\u4e0b\u6765\u6211\u5c06\u4ece\u4e24\u4e2a\u65b9\u9762\u7b80\u8ff0\u4f55\u4e3a\u64cd\u4f5c\u7cfb\u7edf\u3002</p> \u2460 \u4ece\u804c\u80fd\u4e0a\u770b <p></p> <p>\u4ece\u5176\u804c\u80fd\u4e0a\u770b\uff0c\u6211\u8ba4\u4e3a\u64cd\u4f5c\u7cfb\u7edf\u662f\u4e00\u4e2a\u8d44\u6e90\u7ba1\u7406\u7cfb\u7edf\u3002</p> <p>\u53f3\u56fe\u63cf\u8ff0\u4e86\u8ba1\u7b97\u673a\u7cfb\u7edf\u7684\u62bd\u8c61\u5c42\u7ea7\uff1a\u81ea\u4e0a\u800c\u4e0b\uff0c\u7528\u6237\u901a\u8fc7\u5e94\u7528\u7a0b\u5e8f\u89e3\u51b3\u95ee\u9898\uff0c\u5e94\u7528\u7a0b\u5e8f\u5411\u64cd\u4f5c\u7cfb\u7edf\u8bf7\u6c42\u8ba1\u7b97\u673a\u8d44\u6e90\uff1b\u81ea\u4e0b\u800c\u4e0a\uff0c\u8ba1\u7b97\u673a\u786c\u4ef6\u4e3a\u8f6f\u4ef6\uff08\u5305\u62ec OS\uff09\u63d0\u4f9b\u4e86\u7269\u8d28\u57fa\u7840\uff0c\u672c\u8d28\u4e0a\uff0c\u786c\u4ef6\u63d0\u4f9b\u4e86\u8ba1\u7b97\u673a\u8d44\u6e90\u3002</p> <p>\u64cd\u4f5c\u7cfb\u7edf\u4f5c\u4e3a\u4e2d\u95f4\u5c42\uff0c\u5411\u4e0a\u4e3a\u7528\u6237\u7a0b\u5e8f\u5206\u914d\u6613\u7528\u7684\u8d44\u6e90\uff0c\u5411\u4e0b\u76f4\u63a5\u64cd\u4f5c\u786c\u4ef6\u8d44\u6e90\u7684\uff0c\u5728\u8fd9\u4e2a\u8fc7\u7a0b\u4e2d\uff0c\u64cd\u4f5c\u7cfb\u7edf\u8fd8\u9700\u8981\u516c\u5e73\u3001\u9ad8\u6548\u5730\u89e3\u51b3\u8d44\u6e90\u4e4b\u95f4\u7684\u51b2\u7a81\u95ee\u9898\u7b49\u7b49\u3002</p> <p>\u5b83\u5c31\u597d\u50cf\u836f\u623f\u67dc\u53f0\uff0c\u5404\u79cd\u836f\u54c1\u5c31\u597d\u50cf\u8ba1\u7b97\u673a\u8d44\u6e90\uff0c\u75c5\u4eba\u63d0\u4f9b\u5904\u65b9\uff0c\u67dc\u53f0\u6536\u5230\u8bf7\u6c42\uff08\u7cfb\u7edf\u8c03\u7528\uff09\u540e\u5904\u7406\u8bf7\u6c42\uff0c\u5e76\u5343\u8f9b\u4e07\u82e6\uff08\u5177\u4f53\u4f1a\u9047\u5230\u4ec0\u4e48\u95ee\u9898\u6211\u4eec\u4f1a\u5728\u4e4b\u540e\u7684\u5185\u5bb9\u4e2d\u5b66\u5230\uff09\u66ff\u4f60\u51c6\u5907\u597d\u4f60\u9700\u8981\u7684\u8d44\u6e90\uff0c\u5b8c\u6210\u4f60\u7684\u8bf7\u6c42\u3002</p> <p>\u5177\u4f53\u6765\u8bf4\uff0c\u64cd\u4f5c\u7cfb\u7edf\u7ba1\u7406\u7684\u8d44\u6e90\u6709\u8fd9\u4e9b\uff1a\u2460 CPU\uff0c\u7531\u4e8e CPU \u7684\u4e00\u4e2a\u6838(core)\u5728\u7279\u5b9a\u65f6\u523b\u53ea\u80fd\u5904\u7406\u4e00\u4ef6\u4e8b\uff0c\u6240\u4ee5\u201cCPU \u80fd\u591f\u4e3a\u6211\u6240\u7528\u201d\u662f\u4e00\u4e2a\u975e\u5e38\u91cd\u8981\u7684\u8d44\u6e90\uff1b\u2461 \u5185\u5b58\uff0c\u6267\u884c\u7a0b\u5e8f\u79bb\u4e0d\u5f00\u5185\u5b58\uff0c\u7528\u6237\u7a0b\u5e8f\u81ea\u7136\u4e5f\u9700\u8981\u5360\u7528\u4e00\u5b9a\u7684\u5185\u5b58\u6765\u89e3\u51b3\u95ee\u9898\uff1b\u2462 I/O \u8bbe\u5907\uff0c\u6253\u5370\u673a\u4e0d\u80fd\u540c\u65f6\u6253\u5370\u6bdb\u6982\u5386\u5e74\u5377\u548c\u8f6c\u4e13\u4e1a\u7533\u8bf7\u8868\uff1b\u2463\u2026\u2026</p> <p>\u7c97\u7565\u7684\u6765\u8bf4\uff0c\u672c\u8bfe\u7a0b\u4e4b\u540e\u7684\u5185\u5bb9\u57fa\u672c\u4e0a\u90fd\u662f\u56f4\u7ed5\u8981\u5982\u4f55\u7ef4\u62a4\u548c\u64cd\u4f5c\u5404\u79cd\u8d44\u6e90\u800c\u5c55\u5f00\u7684\u3002</p> \u2461 \u4ece\u5b58\u5728\u4e0a\u770b <p>\u4ece\u5176\u5b58\u5728\u6765\u770b\uff0c\u64cd\u4f5c\u7cfb\u7edf\u672c\u8d28\u4e0a\u8fd8\u662f\u4e00\u4e2a\u8f6f\u4ef6\u7a0b\u5e8f\uff0c\u662f\u4e00\u4e2a\u4e0d\u505c\u8fd0\u884c\u7740\u7684\uff0c\u7528\u6765\u6267\u884c\u7528\u6237\u7a0b\u5e8f\u7684\u8f6f\u4ef6\u3002\u8fd9\u4e2a\u89d2\u5ea6\u7684\u672c\u8d28\u540c\u65f6\u53cd\u5e94\u4e86\u64cd\u4f5c\u7cfb\u7edf\u6700\u521d\u5b58\u5728\u7684\u76ee\u7684\uff0c\u4e3a\u4e86\u63d0\u9ad8\u8ba1\u7b97\u673a\u8d44\u6e90\u7684\u5229\u7528\u6548\u7387\uff0c\u6211\u4eec\u9700\u8981\u4e00\u4e2a\u7a0b\u5e8f\u6765\u81ea\u52a8\u5316\u201c\u8ba9\u8ba1\u7b97\u673a\u5b8c\u6210\u4e00\u7cfb\u5217\u7279\u5b9a\u4efb\u52a1\u201d\u8fd9\u4ef6\u4e8b\uff0c\u800c\u4e3a\u4e86\u5b9e\u73b0\u8fd9\u4e2a\u81ea\u52a8\u5316\uff0c\u8fd9\u4e2a\u7a0b\u5e8f\u4e5f\u9700\u8981\u6210\u4e3a\u8ba1\u7b97\u673a\u786c\u4ef6\u7684\u201c\u4ee3\u7406\u4eba\u201d\uff0c\u638c\u63e1\u786c\u4ef6\u7684\u6240\u6709\u8d44\u6e90\uff0c\u5e76\u4e14\u8fd9\u4e2a\u201c\u4ee3\u7406\u4eba\u201d\u8fd8\u5f97\u60f3\u65b9\u6cd5\u8ba9\u81ea\u5df1\u597d\u597d\u201c\u6d3b\u7740\u201d\u3002</p> <p>\u64cd\u4f5c\u7cfb\u7edf\u4e2d\u6700\u57fa\u7840\u6700\u4e2d\u592e\u7684\u90e8\u5206\u662f\u5185\u6838(kernel)\uff0c\u8981\u7ed9\u51fa kernel \u7684\u7cbe\u786e\u5b9a\u4e49\u5f88\u96be\uff0c\u8fd9\u4e0e\u64cd\u4f5c\u7cfb\u7edf\u8bbe\u8ba1\u7684\u7ed3\u6784\u6709\u5173\uff08\u53c2\u8003\u5b8f\u5185\u6838\u548c\u5fae\u5185\u6838\uff09\uff0c\u5b83\u6700\u660e\u663e\u7684\u4e00\u4e2a\u7279\u70b9\u5c31\u662f\u81ea\u8ba1\u7b97\u673a\u5f00\u673a\u540e\u5c31\u4e0d\u505c\u5728\u8fd0\u884c\u3002OS \u548c kernel \u7684\u5173\u7cfb\u5c31\u597d\u50cf\u7b14\u8bb0\u672c\u7535\u8111\u548c\u5b83\u7684\u4e3b\u677f\uff0c\u5982\u679c\u5c06 OS \u4e2d\u7684\u5176\u4ed6\u90e8\u5206\u9664\u53bb\uff0ckernel \u4ecd\u7136\u81ea\u6d3d\uff0c\u4ecd\u7136\u5177\u5907\u5b83\u5e94\u6709\u7684\u5185\u5728\u7684\u529f\u80fd\uff0c\u6bd4\u5982\u5b83\u4ecd\u7136\u5177\u5907\u5bf9\u8d44\u6e90\u8fdb\u884c\u8c03\u5ea6\u7684\u80fd\u529b\uff0c\u53ea\u4e0d\u8fc7\u5b83\u53ef\u80fd\u62ff\u4e0d\u5230\u80fd\u8ba9\u5b83\u8c03\u5ea6\u7684\u8d44\u6e90\u3002\u6211\u5728\u8fd9\u91cc\u907f\u514d\u8c08\u5230 OS \u548c kernel \u7684\u533a\u522b\uff0c\u56e0\u4e3a\u8fd9\u5b9e\u5728\u96be\u4ee5\u8bf4\u6e05\uff0c\u751a\u81f3\u5728\u4e4b\u540e\u7684\u5185\u5bb9\u4e2d\uff0c\u6211\u90fd\u4f1a\u7528 OS \u6765\u4ee3\u66ff kernel \u7684\u6982\u5ff5\u3002</p> <p>\u81f3\u6b64\uff0c\u6211\u4eec\u4ece\u4e24\u4e2a\u65b9\u9762\u4e86\u89e3\u4e86\u4ec0\u4e48\u662f\u64cd\u4f5c\u7cfb\u7edf\uff0c\u73b0\u5728\u7528\u4e00\u53e5\u8bfe\u672c\u4e0a\u7684\u8bdd\u6765\u505a\u603b\u7ed3\u3002</p> <p>The common functions of controlling and allocating resources are then brought together into one piece of software: the operating system. --Operating System Concepts (10th edition)</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit0/#\u64cd\u4f5c\u7cfb\u7edf\u7684\u8bbe\u8ba1\u76ee\u6807","title":"\u64cd\u4f5c\u7cfb\u7edf\u7684\u8bbe\u8ba1\u76ee\u6807","text":"<p>\u73b0\u5728\u6211\u4eec\u77e5\u9053\u64cd\u4f5c\u7cfb\u7edf\u662f\u4ec0\u4e48\u4e1c\u897f\u4e86\uff0c\u90a3\u4e48\u5728\u6b64\u57fa\u7840\u4e0a\u6211\u4eec\u6316\u6398\u4e00\u4e0b\uff0c\u600e\u6837\u624d\u7b97\u4e00\u4e2a\u597d\u7684\u64cd\u4f5c\u7cfb\u7edf\uff0c\u4e5f\u5c31\u662f\u64cd\u4f5c\u7cfb\u7edf\u7684\u53d1\u5c55\u65b9\u5411\uff0c\u800c\u5728\u8fd9\u4e2a\u8fc7\u7a0b\u4e2d\uff0c\u6211\u4e5f\u4f1a\u7b80\u5355\u63d0\u53ca\u4e00\u4e9b\u6211\u4eec\u4e4b\u540e\u4f1a\u8bbe\u8ba1\u7684\u5185\u5bb9\uff0c\u4ee5\u4f9b\u53c2\u8003\u3002</p> <p>\u9996\u5148\uff0c\u64cd\u4f5c\u7cfb\u7edf\u672c\u8eab\u9700\u8981\u6709\u8f83\u597d\u7684\u53ef\u9760\u6027\u548c\u5b89\u5168\u6027\uff0c\u4e5f\u5c31\u662f\u6211\u4eec\u4e4b\u524d\u63d0\u5230\u7684\uff0c\u8fd9\u4e2a\u201c\u4ee3\u7406\u4eba\u201d\u8981\u5c3d\u53ef\u80fd\u8ba9\u81ea\u5df1\u597d\u597d\u201c\u6d3b\u7740\u201d\u3002\u4e00\u65b9\u9762\u5b83\u9700\u8981\u6709\u826f\u597d\u7684\u5f02\u5e38\u5904\u7406\u673a\u5236\uff08\u901a\u8fc7#\u4e2d\u65ad\u673a\u5236\u5b9e\u73b0\uff09\uff0c\u8fd9\u4e2a\u201c\u4ee3\u7406\u4eba\u201d\u9700\u8981\u6709\u5f3a\u5065\u7684\u4f53\u9b44\uff0c\u4e0d\u80fd\u4e00\u522e\u98ce\u5b83\u5c31\u75c5\u5012\u4e86\uff1b\u53e6\u4e00\u65b9\u9762\u5b83\u9700\u8981\u6709\u6743\u9650\u7ba1\u7406\u7cfb\u7edf\uff08#\u7279\u6743\u6a21\u5f0f\uff09\uff0c\u4ee5\u5c4f\u853d\u6765\u81ea\u7528\u6237\u7a0b\u5e8f\u7684\u5371\u9669\u884c\u4e3a\uff0c\u7528\u6237\u53ef\u4ee5\u5411\u201c\u67dc\u53f0\u201d\u7d22\u53d6\u6297\u751f\u7d20\uff0c\u4f46\u662f\u7528\u6237\u7d22\u53d6\u5e93\u623f\u94a5\u5319\u65f6\uff0c\u5408\u683c\u7684\u201c\u67dc\u53f0\u201d\u663e\u7136\u4e0d\u80fd\u7b54\u5e94\u8fd9\u4e2a\u8bf7\u6c42\u3002</p> <p>\u5176\u6b21\uff0c\u64cd\u4f5c\u7cfb\u7edf\u9700\u8981\u6709\u8f83\u597d\u7684\u6613\u7528\u6027\uff0c\u5b83\u9700\u8981\u5411\u7528\u6237\u63d0\u4f9b\u7b80\u4fbf\u7684\u670d\u52a1\u4ee5\u8bf7\u6c42\u7cfb\u7edf\u8d44\u6e90\uff0c\u6bd5\u7adf\u64cd\u4f5c\u7cfb\u7edf\u7684\u76ee\u7684\u4e4b\u4e00\u5c31\u662f\u65b9\u4fbf\u7528\u6237\u4f7f\u7528\u7cfb\u7edf\u8d44\u6e90\u2014\u2014\u8fd9\u610f\u5473\u7740\u6211\u4eec\u7684\u201c\u4ee3\u7406\u4eba\u201d\u5f97\u662f\u4e2a\u597d\u4ea4\u6d41\u7684\u4eba\uff0c\u800c\u7528\u6237\u7a0b\u5e8f\u8c03\u7528\u64cd\u4f5c\u7cfb\u7edf\u8d44\u6e90\u7684\u9014\u5f84\u662f\u7cfb\u7edf\u8c03\u7528\u3002</p> <p>\u5bbd\u6cdb\u4e00\u70b9\u6765\u8bb2\uff0c\u64cd\u4f5c\u7cfb\u7edf\u4e3a\u6211\u4eec\u63d0\u4f9b\u4e86\u547d\u4ee4\u63a5\u53e3\u548c\u7a0b\u5e8f\u63a5\u53e3\uff0c\u6709\u4e9b\u5730\u65b9\u4e5f\u4f1a\u63d0\u5230\u56fe\u5f62\u7528\u6237\u63a5\u53e3(Graphical User Interface, GUI)\uff0c\u4ee5\u53ca\u547d\u4ee4\u884c\u63a5\u53e3(Command Line Interface, CLI)\uff0c\u4f46\u662f\u6211\u4e2a\u4eba\u4e0d\u662f\u5f88\u559c\u6b22\u8fd9\u4e2a\u5206\u7c7b\u3002</p> <p>\u5f53\u7136\uff0c\u64cd\u4f5c\u7cfb\u7edf\u9700\u8981\u662f\u9ad8\u6548\u7684\uff0c\u4ece\u6700\u65e9\u7684\u6279\u5904\u7406\u7cfb\u7edf\u5230\u73b0\u5728\u7684\u5206\u65f6\u7cfb\u7edf\uff08#\u64cd\u4f5c\u7cfb\u7edf\u7684\u4efb\u52a1\u6267\u884c\u8bbe\u8ba1\uff09\uff0cCPU \u7684\u5229\u7528\u7387\u5728\u4e0d\u65ad\u63d0\u5347\uff0c\u5468\u8f6c\u65f6\u95f4\u4e5f\u5728\u4e0d\u65ad\u7f29\u77ed\uff0c\u5982\u4eca\u7684\u64cd\u4f5c\u7cfb\u7edf\u901a\u8fc7\u5206\u65f6\u6280\u672f\u4e5f\u5b9e\u73b0\u4e86\u4f53\u611f\u4e0a\u7684\u5e76\u884c\uff0c\u63d0\u9ad8\u6548\u7387\u7684\u540c\u65f6\u4e5f\u63d0\u9ad8\u4e86\u7528\u6237\u4f53\u9a8c\u3002</p> <p>\u8fd8\u6709\u4e00\u70b9\u4e0d\u5bb9\u5ffd\u89c6\u7684\u662f\u64cd\u4f5c\u7cfb\u7edf\u7684\uff08\u4e00\u5b9a\u7a0b\u5ea6\u4e0a\u7684\uff09\u516c\u5e73\u6027\uff0c\u5728 Unit 1: \u8fdb\u7a0b\u7ba1\u7406\u4e2d\u6211\u4eec\u4f1a\u4e86\u89e3\u5230\uff0c\u591a\u8fdb\u7a0b\u8bed\u5883\u4e0b\u6709\u5927\u91cf\u7684\u51b2\u7a81\u95ee\u9898\u9700\u8981\u89e3\u51b3\uff0c\u800c\u6211\u4eec\u5728\u5904\u7406\u8fd9\u4e9b\u51b2\u7a81\u95ee\u9898\u7684\u65f6\u5019\uff0c\u53ef\u80fd\u4f1a\u51fa\u73b0\u9965\u997f(Starvation)\uff08\u5177\u4f53\u662f\u4ec0\u4e48\u8bf7\u53c2\u8003\u4e0b\u4e00\u5355\u5143\uff09\uff0c\u800c\u64cd\u4f5c\u7cfb\u7edf\u8981\u505a\u7684\u5c31\u662f\u907f\u514d\u9965\u997f\u7684\u51fa\u73b0\uff0c\u5c31\u597d\u50cf\u7e41\u5fd9\u65f6\u6bb5\u7684\u7535\u68af\uff0c\u6211\u4eec\u4e0d\u80fd\u56e0\u4e3a\u4e8c\u697c\u6d41\u91cf\u5f88\u5927\u5c31\u4e0d\u7ba1\u4e09\u697c\u4ee5\u4e0a\u7684\u4eba\u3002</p> <p>\u4e0a\u8ff0\u76ee\u6807\u5927\u591a\u662f\u9488\u5bf9\u4f7f\u7528\u8005\u800c\u8a00\u7684\uff0c\u90a3\u4e48\u5bf9\u4e8e\u5f00\u53d1\u8005\u6765\u8bf4\uff0c\u64cd\u4f5c\u7cfb\u7edf\u7684\u53ef\u6269\u5c55\u6027\u3001\u6613\u7ef4\u62a4\u6027\u7b49\u4e5f\u662f\u975e\u5e38\u91cd\u8981\u7684\u3002\u4e0d\u540c\u7684\u8bbe\u8ba1\u601d\u8def\u9020\u5c31\u4e86\u4e0d\u540c\u7684\u64cd\u4f5c\u7cfb\u7edf\u7ed3\u6784\uff0c\u5404\u79cd\u8bbe\u8ba1\u4e5f\u5404\u81ea\u6709\u5404\u81ea\u7684\u4e3b\u6218\u573a\uff0c\u5173\u4e8e\u8fd9\u4e9b\u5185\u5bb9\uff0c\u6211\u4eec\u4f1a\u5728#\u64cd\u4f5c\u7cfb\u7edf\u7684\u7ed3\u6784\u8bbe\u8ba1\u8fd9\u4e00\u90e8\u5206\u66f4\u8be6\u7ec6\u5730\u4ecb\u7ecd\u3002</p> <p>\u8fd8\u6709\u8bb8\u591a\uff0c\u4f8b\u5982\u64cd\u4f5c\u7cfb\u7edf\u7684\u8bbe\u8ba1\u8981\u5c3d\u53ef\u80fd\u5229\u7528\u786c\u4ef6\u8d44\u6e90\u7b49\uff0c\u4f46\u5e76\u4e0d\u662f\u6211\u4eec\u5728\u672c\u8282\u60f3\u8981\u8ba8\u8bba\u7684\u91cd\u70b9\uff0c\u6240\u6709\u5c31\u63a0\u8fc7\u4e86\u3002\u4e0a\u8ff0\u89c2\u70b9\u5e76\u4e0d\u5168\u9762\u4e5f\u4e0d\u4e00\u5b9a\u5b8c\u5168\u6b63\u786e\uff0c\u6709\u4e00\u5927\u90e8\u5206\u90fd\u662f\u6211\u7684\u4e2a\u4eba\u7406\u89e3\uff0c\u8bf7\u8bfb\u8005\u8fa8\u8bc1\u5730\u770b\u5f85\uff0c\u5982\u679c\u6709\u9519\u8bef\u8bf7\u52a1\u5fc5\u544a\u8bc9\u6211\uff01</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit0/#\u64cd\u4f5c\u7cfb\u7edf\u7684\u6574\u4f53\u8bbe\u8ba1","title":"\u64cd\u4f5c\u7cfb\u7edf\u7684\u6574\u4f53\u8bbe\u8ba1","text":"<p>\u672c\u8282\u4e3b\u8981\u5c31\u4e00\u4e9b\u5173\u4e8e\u64cd\u4f5c\u7cfb\u7edf\u6574\u4f53\u8bbe\u8ba1\u7684\u95ee\u9898\u505a\u4e00\u4e9b\u8ba8\u8bba\uff0c\u4ece\u4e00\u4e2a\u76f8\u5bf9\u6bd4\u8f83\u9ad8\u7684\u89d2\u5ea6\u8c08\u4e00\u8c08\u4e00\u4e9b\u9876\u5c42\u8bbe\u8ba1\u3002</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit0/#\u8ba1\u7b97\u673a\u7cfb\u7edf\u67b6\u6784","title":"\u8ba1\u7b97\u673a\u7cfb\u7edf\u67b6\u6784","text":"<p>\u867d\u7136\u64cd\u4f5c\u7cfb\u7edf\u672c\u8eab\u662f\u8f6f\u4ef6\uff0c\u4f46\u662f\u5b83\u6bd5\u7adf\u662f\u4e0e\u786c\u4ef6\u7d27\u5bc6\u5173\u8054\u7684\uff0c\u6240\u4ee5\u6211\u4eec\u8fd8\u662f\u4f1a\u6d89\u53ca\u5230\u4e00\u4e9b\u5173\u4e8e\u786c\u4ef6\u7684\u5185\u5bb9\uff0c\u8fd9\u91cc\u7b80\u5355\u6d89\u53ca\u4e00\u4e9b\u5173\u4e8e\u8ba1\u7b97\u673a\u7cfb\u7edf\u67b6\u6784\u7684\u5185\u5bb9\u3002</p> \u6982\u5ff5\u8fa8\u6790 <p> \u540d\u8bcd \u5b9a\u4f4d CPU \u6267\u884c\u6307\u4ee4\u7684\u786c\u4ef6 Core CPU \u7684\u57fa\u7840\u8ba1\u7b97\u5355\u5143 Multi-core \u4e00\u4e2a CPU \u4e0a\u6709\u591a\u4e2a core Processor \u5305\u542b\u4e00\u4e2a\u6216\u591a\u4e2a CPU \u7684\u82af\u7247 Multi-processor \u591a\u4e2a processor </p> <p>\u6839\u636e\u5904\u7406\u5668\u7684\u6570\u91cf\u548c\u7ec4\u7ec7\u5f62\u5f0f\uff0c\u6211\u4eec\u8fd9\u91cc\u4ecb\u7ecd\u4e09\u79cd\u8ba1\u7b97\u673a\u7cfb\u7edf\u67b6\u6784\uff1a\u5355\u5904\u7406\u5668\u7cfb\u7edf\u3001\u591a\u5904\u7406\u5668\u7cfb\u7edf\u3001\u96c6\u7fa4\u7cfb\u7edf\u3002</p> \u2460 \u5355\u5904\u7406\u5668\u7cfb\u7edf(Single-Processor System) <p>\u4e66\u4e2d\u7ed9\u51fa\u7684\u5173\u4e8e\u5355\u5904\u7406\u5668\u7cfb\u7edf\u7684\u5b9a\u4e49\u662f\uff0c\u6709\u4e14\u4ec5\u6709\u4e00\u4e2a\u901a\u7528\u5904\u7406\u5668(general-purpose processor)\uff0c\u5e76\u4e14\u8fd9\u4e2a processor \u53ea\u6709\u4e00\u4e2a\u6838(core)\u3002\u4f46\u5b83\u53ef\u4ee5\u6709\u82e5\u5e72\u4e13\u7528\u5904\u7406\u5668(special-purpose processor)\uff0c\u7528\u6765\u6267\u884c\u4e00\u4e9b\u7279\u5b9a\u7684\u6307\u4ee4\uff0c\u800c\u8fd9\u4e9b\u4e13\u7528\u5904\u7406\u5668\u5e76\u4e0d\u8fd0\u884c\u7ebf\u7a0b\u3002</p> \u2461 \u591a\u5904\u7406\u5668\u7cfb\u7edf(Multiprocessor System) <p>\u591a\u5904\u7406\u5668\u7cfb\u7edf\u662f\u6307\u6709\u591a\u4e2a\u5355\u6838\u901a\u7528\u5904\u7406\u5668\u7684\u7cfb\u7edf\uff0c\u8fd9\u4e9b\u5904\u7406\u5668\u5171\u4eab\u4e00\u5757\u4e3b\u5185\u5b58\uff0c\u5b83\u4eec\u901a\u8fc7\u603b\u7ebf\u6216\u4ea4\u6362\u7f51\u7edc\u8fde\u63a5\u5728\u4e00\u8d77\u3002</p> <p>\u663e\u800c\u6613\u89c1\u7684\u662f\uff0c\u589e\u52a0\u4e86\u5904\u7406\u5668\u7684\u6570\u91cf\u80fd\u591f\u589e\u52a0\u541e\u5410\u91cf(throughput)\uff0c\u5373\u5355\u4f4d\u65f6\u95f4\u5185\u5904\u7406\u7684\u4efb\u52a1\u6570\u91cf\uff0c\u4f46\u662f\u8fd9\u4e2a\u589e\u52a0\u5e76\u4e0d\u662f\u7ebf\u6027\u7684\uff0c\u56e0\u4e3a\u5904\u7406\u5668\u4e4b\u95f4\u7684\u901a\u4fe1\u4e5f\u9700\u8981\u65f6\u95f4\uff0c\u800c\u4e14\u8fd8\u4f1a\u6709\u4e00\u4e9b\u989d\u5916\u7684\u5f00\u9500\u3002</p> \u76f8\u5173\u9605\u8bfb <ul> <li>\u5bf9\u79f0\u591a\u5904\u7406 | SMP\uff1b</li> <li>\u975e\u4e00\u81f4\u5185\u5b58\u8bbf\u95ee | NUMA\uff1b</li> </ul> <p>\u4f46\u662f multi-core \u7684\u8bbe\u8ba1\u5728\u901f\u5ea6\u548c\u6548\u80fd\u4e0a\u90fd\u66f4\u80dc\u4e00\u7b79\uff0c\u56e0\u4e3a on-chip \u7684\u901a\u4fe1\u6bd4 between-chip \u7684\u901a\u4fe1\u66f4\u5feb\uff0c\u800c\u4e14\u66f4\u7701\u7535\u3002</p> \u2462 \u96c6\u7fa4\u7cfb\u7edf(Cluster System) <p> </p> <p>\u96c6\u7fa4\u7cfb\u7edf\u901a\u8fc7\u5197\u4f59\u5b9e\u73b0\u9ad8\u53ef\u7528\u670d\u52a1\uff0c\u901a\u8fc7\u5e76\u884c\u5b9e\u73b0\u9ad8\u6027\u80fd\u8ba1\u7b97\uff0c\u5b83\u662f\u7531\u591a\u4e2a\u5404\u81ea\u72ec\u7acb\u7684\u8ba1\u7b97\u673a\u7cfb\u7edf\u4f5c\u4e3a\u8282\u70b9(node)\uff0c\u901a\u8fc7\u9ad8\u901f\u901a\u4fe1\u7f51\u7edc\u4e92\u76f8\u8fde\u63a5\u5f62\u6210\u7684\u3002</p> <p>\u96c6\u7fa4\u4e5f\u5206\u5bf9\u79f0\u548c\u4e0d\u5bf9\u79f0\u4e24\u79cd\uff0c\u5bf9\u79f0\u96c6\u7fa4\u7684\u5404\u4e2a\u8282\u70b9\u4e92\u76f8\u76d1\u7763\uff0c\u800c\u4e0d\u5bf9\u79f0\u7684\u96c6\u7fa4\u5219\u5b58\u5728\u4e00\u79cd\u7c7b\u4f3c\u201c\u66ff\u8865\u201d\u7684\u4e1c\u897f\uff0c\u7531\u201c\u66ff\u8865\u201d\u53bb\u76d1\u7763\u5de5\u4f5c\u4e2d\u7684\u8282\u70b9\uff0c\u5f53\u5de5\u4f5c\u4e2d\u7684\u8282\u70b9\u51fa\u73b0\u4e86\u95ee\u9898\uff0c\u5c31\u7531\u201c\u66ff\u8865\u201d\u6765\u63a5\u66ff\u5b83\u7684\u5de5\u4f5c\u3002</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit0/#\u64cd\u4f5c\u7cfb\u7edf\u7684\u4efb\u52a1\u6267\u884c\u8bbe\u8ba1","title":"\u64cd\u4f5c\u7cfb\u7edf\u7684\u4efb\u52a1\u6267\u884c\u8bbe\u8ba1","text":"<p>\u524d\u9762\u6211\u4eec\u8bf4\u8fc7\uff0c\u64cd\u4f5c\u7cfb\u7edf\u88ab\u7528\u6765\u300c\u81ea\u52a8\u5316\u201c\u8ba9\u8ba1\u7b97\u673a\u5b8c\u6210\u4e00\u7cfb\u5217\u7279\u5b9a\u4efb\u52a1\u201d\u300d\u7684\u3002\u4e00\u5f00\u59cb\u8fd9\u4ef6\u4e8b\u6bd4\u8f83\u7b80\u5355\uff0c\u53ea\u9700\u8981\u50cf\u961f\u5217\u4e00\u6837\uff0c\u4e00\u4e2a\u4e00\u4e2a\u7684\u6267\u884c\u5c31\u884c\uff0c\u4f46\u662f\u6162\u6162\u7684\u968f\u7740\u8ba1\u7b97\u673a\u5e94\u7528\u8303\u56f4\u7684\u6269\u5927\u4ee5\u53ca\u5404\u79cd\u9700\u6c42\u7684\u51fa\u73b0\uff0c\u8fd9\u79cd\u8bbe\u8ba1\u5c31\u4e0d\u592a\u5408\u7406\u4e86\u3002\u6309\u7167\u53d1\u5c55\u9636\u6bb5\u6f14\u8fdb\uff0c\u6211\u4eec\u5212\u5206\u51fa\u4e24\u4e2a\u9636\u6bb5\u4e09\u4e2a\u8bbe\u8ba1\uff1a\u5355\u9053\u6279\u5904\u7406\u7cfb\u7edf(Batch Processing System)\u3001\u591a\u9053\u6279\u5904\u7406\u7cfb\u7edf(Multiprogramming Batch Processing System)\u548c\u5206\u65f6\u7cfb\u7edf(Time Sharing Systems)\u3002</p> <p></p> \u2460 \u6279\u5904\u7406\u7cfb\u7edf\u9636\u6bb5 <p>\u6700\u65e9\u64cd\u4f5c\u7cfb\u7edf\u6267\u884c\u4efb\u52a1\u90fd\u9700\u8981\u4eba\u5de5\u624b\u52a8\u5e72\u9884\uff0c\u4f46\u662f\u8ba1\u7b97\u673a\u6267\u884c\u4efb\u52a1\u7684\u901f\u5ea6\u4e0e\u4eba\u5de5\u5e72\u9884\u7684\u901f\u5ea6\u76f8\u5dee\u592a\u5927\uff0c\u6362\u53e5\u8bdd\u6765\u8bf4\u4eba\u5de5\u901f\u5ea6\u4e25\u91cd\u9650\u5236\u4e86\u8ba1\u7b97\u673a\u7684\u5de5\u4f5c\u6548\u7387\uff0c\u4e8e\u662f\u64cd\u4f5c\u7cfb\u7edf\u5f00\u59cb\u51fa\u73b0\uff0c\u5176\u4e2d\u4e00\u4e2a\u6bd4\u8f83\u539f\u59cb\u7684\u5b9e\u73b0\u5c31\u662f\u6279\u5904\u7406\u7cfb\u7edf\u3002\uff08\u4f46\u4e0d\u662f\u6700\u65e9\uff0c\u4e4b\u524d\u8fd8\u6709\u8131\u673a\u5904\u7406\u4e4b\u7c7b\u7684\u4e1c\u897f\u3002\uff09</p> \u2776 \u5355\u9053\u6279\u5904\u7406\u9636\u6bb5 <p>\u6309\u7167\u64cd\u4f5c\u7cfb\u7edf\u53d1\u5c55\u8fdb\u7a0b\uff0c\u6211\u4eec\u9996\u5148\u4ecb\u7ecd\u5355\u9053\u6279\u5904\u7406\u7cfb\u7edf(Batch Processing)\u3002</p> <p>\u5355\u9053\u6279\u5904\u7406\u7cfb\u7edf\u6709\u4e24\u4e2a\u5173\u952e\u8bcd\uff0c\u201c\u6279\u5904\u7406\u201d\u548c\u201c\u5355\u9053\u201d\u3002</p> <p>\u201c\u6279\u5904\u7406\u201d\u6307\u7684\u662f\uff0c\u7cfb\u7edf\u6267\u884c\u7684\u4efb\u52a1\u662f\u6210\u6279\u7684\uff0c\u82e5\u5e72\u4efb\u52a1\u88ab\u4f5c\u4e3a\u4e00\u6574\u6279\u4ea4\u4ed8\u7ed9\u64cd\u4f5c\u7cfb\u7edf\u3002\u5728\u5177\u4f53\u6267\u884c\u8fc7\u7a0b\u4e2d\uff0c\u64cd\u4f5c\u7cfb\u7edf\u81ea\u52a8\u6309\u987a\u5e8f\u4e32\u884c(serial)\u6267\u884c\u8fd9\u4e9b\u4efb\u52a1\u3002</p> <p>\u800c\u201c\u5355\u9053\u201d\u6307\u7684\u662f\uff0c\u4e00\u6bb5\u65f6\u95f4\u5185\u5185\u5b58\u4e2d\u53ea\u6709\u4e00\u9053\u7a0b\u5e8f\u5728\u8fd0\u884c\uff0c\u7cfb\u7edf\u53ea\u5904\u7406\u4e00\u9879\u4efb\u52a1\uff0c\u5728\u8fd9\u4e2a\u4efb\u52a1\u7ed3\u675f\u4e4b\u524d\uff0c\u4e0d\u4f1a\u5207\u6362\u5230\u5176\u4ed6\u4efb\u52a1\u3002</p> <p>\u5355\u9053\u6279\u5904\u7406\u7cfb\u7edf\u521d\u6b65\u5b9e\u73b0\u4e86\u4e00\u79cd\u201c\u81ea\u52a8\u5316\u201d\uff0c\u6781\u5927\u51cf\u5c11\u4e86\u4eba\u5de5\u64cd\u4f5c\u901f\u5ea6\u5bf9\u64cd\u4f5c\u7cfb\u7edf\u7684\u5f71\u54cd\u3002\u4f46\u5b83\u5b58\u5728\u4e00\u4e2a\u975e\u5e38\u660e\u663e\u7684\u95ee\u9898\uff1a\u7531\u4e8e\u5f53\u524d\u4efb\u52a1\u7ed3\u675f\u4e4b\u524d\u4e0d\u4f1a\u5207\u6362\u5230\u5176\u5b83\u4efb\u52a1\uff0c\u6240\u4ee5\u5f53\u5f53\u524d\u4efb\u52a1\u51fa\u73b0 I/O \u8bf7\u6c42\u65f6\uff0cCPU \u5c31\u9700\u8981\u7b49\u5f85 I/O \u5b8c\u6210\u3002\u6211\u4eec\u77e5\u9053 I/O \u64cd\u4f5c\u662f\u975e\u5e38\u8017\u65f6\u7684\uff0c\u66f4\u4e25\u91cd\u7684\u662f\u4f8b\u5982\u7b49\u5f85\u952e\u76d8\u8f93\u5165\u8fd9\u79cd\u9700\u8981\u4eba\u5de5\u53c2\u4e0e\u7684 I/O\uff0c\u5355\u9053\u6279\u5904\u7406\u7cfb\u7edf\u4ecd\u7136\u6ca1\u6cd5\u907f\u514d\u8fd9\u79cd\u4eba\u5de5\u64cd\u4f5c\u5bf9\u8ba1\u7b97\u673a\u6267\u884c\u6548\u7387\u7684\u5f71\u54cd\uff0c\u8fd9\u5c31\u5bfc\u81f4 CPU \u4f1a\u957f\u65f6\u95f4\u5904\u4e8e\u7a7a\u95f2\u72b6\u6001\uff0c\u800c\u8ba9 CPU \u957f\u65f6\u95f4\u7a7a\u95f2\u8fd9\u4ef6\u4e8b\uff0c\u662f\u4e0d\u88ab\u63a5\u53d7\u7684\u3002</p> \u2777 \u591a\u9053\u6279\u5904\u7406\u9636\u6bb5 <p>\u56e0\u6b64\uff0c\u4e3a\u4e86\u4e0d\u8ba9 CPU \u95f2\u4e0b\u6765\uff0c\u4e00\u4e2a\u7b26\u5408\u76f4\u89c9\u7684\u60f3\u6cd5\u5c31\u662f\u8ba9\u5b83\u5148\u53bb\u505a\u4e0b\u4e00\u4ef6\u4e8b\uff0c\u5c31\u597d\u50cf\u4ed3\u5e93\u6b63\u5728\u6536\u96c6\u4e0a\u4e00\u4e2a\u75c5\u4eba\u6240\u9700\u8981\u7684\u836f\u54c1\u7684\u65f6\u5019\uff0c\u67dc\u53f0\u53ef\u4ee5\u5148\u53bb\u5904\u7406\u4e0b\u4e00\u4e2a\u75c5\u4eba\u7684\u8bf7\u6c42\u3002\u591a\u9053\u6279\u5904\u7406\u7cfb\u7edf(Multiprogramming Batch Processing System)\u5e94\u8fd0\u800c\u751f\u3002</p> <p>\u4ece\u540d\u5b57\u4e0a\u6765\u770b\uff0c\u591a\u9053\u6279\u5904\u7406\u7cfb\u7edf\u5389\u5bb3\u5728\u8fd9\u4e2a\u201c\u591a\u9053(Multiprogramming)\u201d\uff0c\u5373\u4e00\u6bb5\u65f6\u95f4\u5185\u5185\u5b58\u4e2d\u540c\u65f6\u5b58\u5728\u591a\u4e2a\u8fdb\u7a0b\u3002</p> <p>\u5177\u4f53\u6765\u8bf4\uff0c\u5728\u591a\u9053\u6279\u5904\u7406\u7cfb\u7edf\u4e2d\uff0c\u5f53\u524d\u4efb\u52a1\u53d1\u751f IO \u8bf7\u6c42\u65f6\uff0cCPU \u8f6c\u800c\u53bb\u6267\u884c\u5176\u5b83\u4efb\u52a1\uff0c\u4ee5\u6b64\u6765\u5b9e\u73b0\u5c3d\u91cf\u8ba9 CPU \u59cb\u7ec8\u5728\u5de5\u4f5c\u72b6\u6001\u3002\u56e0\u6b64\uff0c\u5b8f\u89c2\u4e0a\u6765\u770b\uff0c\u591a\u9053\u6279\u5904\u7406\u7cfb\u7edf\u5728\u4e00\u6bb5\u65f6\u95f4\u5185\u540c\u65f6\u6267\u884c\u82e5\u5e72\u4efb\u52a1\uff08\u5728\u4efb\u52a1 A \u5b8c\u6210\u4e4b\u524d\u4efb\u52a1 B \u4e5f\u53ef\u80fd\u5f00\u59cb\u4e86\uff09\uff0c\u6211\u4eec\u79f0\u4e4b\u4e3a\u5e76\u53d1(concurrency)\uff08\u6ce8\u610f\uff0c\u5e76\u53d1\u4e0e\u5e76\u884c\u7684\u6982\u5ff5\u5e76\u4e0d\u4e00\u81f41\uff09\uff1b\u4f46\u5728\u5fae\u89c2\u4e0a\uff0c\u591a\u9053\u6279\u5904\u7406\u7cfb\u7edf\u4ecd\u7136\u662f\u987a\u5e8f\u4e32\u884c\u7684\uff0c\u53ea\u4e0d\u8fc7\u533a\u522b\u4e8e\u5355\u9053\u6279\u5904\u7406\u7cfb\u7edf\u4ee5\u5b8c\u6574\u7684\u4efb\u52a1\u4f5c\u4e3a\u4efb\u52a1\u5355\u5143\uff0c\u591a\u9053\u6279\u5904\u7406\u7cfb\u7edf\u662f\u5c06\u5b8c\u6574\u4efb\u52a1\u6309\u7167 I/O \u7684\u53d1\u751f\u505a\u5212\u5206\uff0c\u4ee5\u8fd9\u4e9b\u5212\u5206\u540e\u7684\u90e8\u5206\u4efb\u52a1\u4f5c\u4e3a\u4efb\u52a1\u5355\u5143\u8fdb\u884c\u987a\u5e8f\u4e32\u884c(serial)\u3002</p> <p>\u6211\u4eec\u53ef\u4ee5\u7528\u7518\u7279\u56fe\u6765\u53ef\u89c6\u5316\u591a\u9053\u6279\u5904\u7406\u7cfb\u7edf\u7684\u7b56\u7565\uff08\u4e00\u79cd\u5e38\u89c1\u7684\u9898\u578b\uff09\u3002\u4ee5\u4e0b\u9762\u7684\u9898\u76ee\u4e3a\u4f8b\uff0c\u6211\u4eec\u6765\u5b9e\u8df5\u4e00\u4e0b\u3002</p> \ud83c\udf30 \u9898\u9762\u89e3\u6790 <p>\u73b0\u5728\u6709\u4e24\u4e2a\u7a0b\u5e8f A \u548c B\uff0c\u4ee5\u53ca\u4e24\u4e2a\u5206\u522b\u72ec\u7acb\u7684\u8bbe\u5907 X \u548c Y\uff0c\u4e14\u6211\u4eec\u53ea\u6709\u4e00\u4e2a CPU\uff1a</p> <ul> <li>A \u9700\u8981\u987a\u5e8f\u4f7f\u7528\u5982\u4e0b\u8d44\u6e90\uff1aCPU:10s, X:5s, CPU:5s, Y:10s, CPU:10s</li> <li>B \u9700\u8981\u987a\u5e8f\u4f7f\u7528\u5982\u4e0b\u8d44\u6e90\uff1aX:10s, CPU 10s, Y:5s, CPU:5s, Y:10s </li> </ul> <p>\u8bf7\u8ba8\u8bba\uff1a</p> <ol> <li>\u5728\u5355\u9053\u7a0b\u5e8f\u73af\u5883\u4e0b\u5148\u6267\u884c A \u518d\u6267\u884c B\uff0cCPU \u7684\u5229\u7528\u7387\u662f\u591a\u5c11\uff1f</li> <li>\u5728\u591a\u9053\u7a0b\u5e8f\u73af\u5883\u4e0b\uff0cCPU \u7684\u5229\u7528\u7387\u662f\u591a\u5c11\uff1f\u8bf7\u7ed9\u51fa\u7518\u7279\u56fe\u3002</li> </ol> <p>\u5728\u5355\u9053\u7a0b\u5e8f\u4e0b\u6267\u884c\uff0c\u5373\u6309\u987a\u5e8f\u6267\u884c A \u548c B\uff0cCPU \u7684\u5229\u7528\u7387\u5373\u5b9e\u9645 CPU \u4f7f\u7528\u65f6\u95f4\u9664\u4ee5\u5b8c\u6210\u4efb\u52a1\u7684\u603b\u65f6\u95f4\uff0c\u56e0\u6b64\uff1a</p> \\[ U = \\frac{(10+5+10)+(10+5)}{(10+5+5+10+10)+(10+10+5+5+10)} = \\frac{40}{80} = 50\\% \\] <p>\u800c\u5728\u591a\u9053\u7a0b\u5e8f\u73af\u5883\u4e0b\uff0c\u6211\u4eec\u5f97\u5230\u5982\u4e0b\u7518\u7279\u56fe\uff1a</p> <pre><code>gantt\n    title Multiprogramming\n    dateFormat ss\n    axisFormat %S\n\n    section Program A\n    CPU :a,  00,  10\n    X   :b,  10,  15\n    CPU :c,  20,  25\n    Y   :d,  25,  35\n    CPU :e,  35,  45\n\n    section Program B\n    X   :g,  00,  10\n    CPU :h,  10,  20\n    Y   :i,  20,  25\n    CPU :j,  25,  30\n    Y   :k,  35,  45</code></pre> <p>\u7531\u4e8e Mermaid \u7684\u9650\u5236\uff0c\u6211\u73b0\u5728\u662f\u628a\u6bcf\u4e2a\u7a0b\u5e8f\u7684\u4efb\u52a1\u9519\u5f00\u753b\u7684\uff0c\u5b9e\u9645\u4e0a\u505a\u9898\u7684\u65f6\u5019\u53ef\u4ee5\u76f4\u63a5\u753b\u6210\u4e24\u884c\u3002</p> <p>\u8981\u70b9\u5c31\u662f\u7eb5\u5411\u4e0d\u80fd\u540c\u65f6\u51fa\u73b0\u540c\u4e00\u4e2a\u8d44\u6e90\uff0c\u4f8b\u5982 18s \u65f6\u4e0d\u80fd A \u548c B \u90fd\u7528 CPU\uff0c\u6240\u4ee5 A \u9700\u8981\u7b49 B \u7528\u5b8c CPU \u518d\u4f7f\u7528\u3002</p> <p>\u73b0\u5728\u6211\u4eec\u518d\u6765\u7edf\u8ba1 CPU \u7684\u5229\u7528\u7387\uff1a</p> \\[ U = \\frac{10+10+5+5+10}{45} = \\frac{40}{45} = 88.89\\% \\] <p>\u901a\u8fc7\u8fd9\u9053\u9898\u6211\u4eec\u4e5f\u53ef\u4ee5\u53d1\u73b0\uff0c\u591a\u9053\u7a0b\u5e8f\u8bbe\u8ba1\u6280\u672f\u5bf9 CPU \u5229\u7528\u7387\u7684\u63d0\u5347\u6709\u591a\u9ad8\uff0c\u540c\u65f6\u4e5f\u53ef\u4ee5\u4ece\u8ba1\u7b97\u8fc7\u7a0b\u4e2d\u7684\u5206\u6bcd\u770b\u51fa\u5176\u5bf9\u7a0b\u5e8f\u541e\u5410\u91cf\u7684\u63d0\u5347\u6709\u591a\u9ad8\u3002</p> <p>\u591a\u9053\u6279\u5904\u7406\u89e3\u51b3\u4e86\u5355\u9053\u6279\u5904\u7406\u7cfb\u7edf\u53ef\u80fd\u8ba9 CPU \u95f2\u7f6e\u4e0b\u6765\u7684\u95ee\u9898\uff08\u5f53\u7136\u524d\u63d0\u662f\u6709\u4efb\u52a1\u8ba9\u5b83\u505a\uff09\uff0c\u63d0\u9ad8\u4e86 CPU \u7b49\u8d44\u6e90\u7684\u5229\u7528\u7387\uff0c\u589e\u52a0\u4e86\u541e\u5410\u91cf\uff0c\u4f46\u662f\u7531\u4e8e\u6d89\u53ca\u5230\u4e86\u8fdb\u7a0b\u7684\u5207\u6362\u95ee\u9898\uff0c\u6240\u4ee5\u5b9e\u9645\u5b9e\u73b0\u4f1a\u590d\u6742\u5f88\u591a\u3002\u5177\u4f53\u7684\u5185\u5bb9\u6211\u4eec\u4f1a\u5728 Unit 1: \u8fdb\u7a0b\u7ba1\u7406 \u4e2d\u8be6\u7ec6\u4ecb\u7ecd\u3002</p> <p>\u4f46\u662f\u65e0\u8bba\u5355\u9053\u8fd8\u662f\u591a\u9053\uff0c\u6279\u5904\u7406\u7cfb\u7edf\u5e76\u4e0d\u9002\u5408\u4f5c\u4e3a\u73b0\u4ee3\u8ba1\u7b97\u673a\u7cfb\u7edf\uff0c\u5176\u4e2d\u4e00\u4e2a\u6700\u5927\u7684\u95ee\u9898\u5c31\u662f\u5b83\u7684\u4ea4\u4e92\u6027\u975e\u5e38\u5dee\u3002\u7528\u6237\u7ed9\u5b9a\u4e00\u5b9a\u6279\u6b21\u7684\u4efb\u52a1\uff0c\u7136\u540e\u7cfb\u7edf\u4f1a\u81ea\u52a8\u8c03\u6574\u8fd9\u4e00\u6279\u4efb\u52a1\u7684\u6267\u884c\u987a\u5e8f\uff0c\u6700\u7ec8\u5b8c\u6210\u8fd9\u6279\u4efb\u52a1\uff0c\u7136\u800c\u5728\u8fd9\u6bb5\u65f6\u95f4\u91cc\uff0c\u7528\u6237\u5c31\u6ca1\u6cd5\u518d\u7528\u8ba1\u7b97\u673a\u505a\u5176\u5b83\u4e8b\u60c5\u4e86\uff0c\u540c\u65f6\u4f60\u4e5f\u6ca1\u6cd5\u63a7\u5236\u6b63\u5728\u6267\u884c\u7684\u4efb\u52a1\uff0c\u8fd9\u5bf9\u73b0\u4ee3\u8ba1\u7b97\u673a\u6765\u8bf4\u662f\u4e0d\u53ef\u60f3\u8c61\u7684\u3002</p> <p>\uff08\u5047\u8bbe\u6211\u4eec\u5ffd\u7565\u5173\u4e8e\u5c4f\u5e55\u663e\u793a\u7684 I/O\uff09\u8bd5\u60f3\uff0c\u4f60\u5e0c\u671b\u5728\u8dd1\u7a0b\u5e8f\u7684\u65f6\u5019\u653e\u4e00\u4e2a\u89c6\u9891\uff0c\u4f46\u662f\u7531\u4e8e\u4f60\u7684\u7a0b\u5e8f\u8fd8\u6ca1\u8dd1\u5b8c\uff0c\u4f60\u7684\u89c6\u9891\u5c31\u6ca1\u6cd5\u64ad\u653e\uff0c\u7a81\u7136\u4f60\u7684\u7a0b\u5e8f\u53d1\u751f\u4e86\u4e00\u6b21 I/O\uff0cCPU \u8f6c\u800c\u64ad\u653e\u5df2\u7ecf\u5b8c\u6210 I/O \u540e\u7684\u90a3\u90e8\u5206\u89c6\u9891\uff0c\u4f46\u662f\u8fd9\u4e2a\u65f6\u5019\u4f60\u7684\u7a0b\u5e8f I/O \u5f88\u5feb\u4e5f\u5b8c\u6210\u4e86\uff0c\u5374\u9700\u8981\u7b49\u5f85\u7f13\u5b58\u4e2d\u7684\u89c6\u9891\u653e\u5b8c\u624d\u80fd\u7ee7\u7eed\u6267\u884c\uff0c\u8fd9\u79cd\u7528\u6237\u4f53\u9a8c\u51e0\u4e4e\u65e0\u6cd5\u63a5\u53d7\u3002</p> <p>\u5bf9\u4e8e\u7528\u6237\u6765\u8bf4\uff0c\u6700\u597d\u80fd\u540c\u65f6\u5b9e\u73b0\u4f53\u611f\u4e0a\u7684\u5e76\u884c\uff0c\u4e5f\u5c31\u662f\u51e0\u4ef6\u4e8b\u60c5\u81f3\u5c11\u770b\u8d77\u6765\u8981\u50cf\u662f\u540c\u65f6\u53d1\u751f\u7684\uff0c\u4e8e\u662f\u51fa\u73b0\u4e86\u5206\u65f6\u7cfb\u7edf(Time Sharing Systems)\u3002</p> <p></p> \u2461 \u5206\u65f6\u7cfb\u7edf\u9636\u6bb5 <p>\u5206\u65f6\u7cfb\u7edf(Time Sharing Systems)\u662f\u591a\u4efb\u52a1(Multitasking)\u7684\u4e00\u4e2a\u5177\u4f53\u5b9e\u73b0\uff0c\u800c Multitasking \u662f Multiprogramming \u7684\u4e00\u4e2a\u903b\u8f91\u6269\u5c55\uff0c\u5373 Multitasking \u4e5f\u662f Multiprogramming \u7684\u4e00\u79cd\uff0c\u5b83\u7b26\u5408\u5185\u5b58\u4e2d\u6709\u591a\u4e2a\u8fdb\u7a0b\uff0c\u4e00\u6bb5\u65f6\u95f4\u5185\u6709\u591a\u4e2a\u4efb\u52a1\u4e00\u8d77\u6267\u884c\u7684\u7279\u70b9\u3002</p> <p>\u5206\u65f6\u7cfb\u7edf\u901a\u8fc7\u9891\u7e41\u5730\u5728\u591a\u4e2a\u8fdb\u7a0b\u95f4\u5207\u6362\u6765\u8fd1\u4f3c\u5b9e\u73b0\u5e76\u884c\uff08\u5e76\u4e0d\u662f\u771f\u6b63\u610f\u4e49\u4e0a\u7684\u5e76\u884c\uff0c\u771f\u6b63\u610f\u4e49\u4e0a\u7684\u5e76\u884c\u9700\u8981\u901a\u8fc7\u591a\u6838/\u591a\u5904\u7406\u5668\u5b9e\u73b0\uff09\u3002\u5177\u4f53\u6765\u8bf4\u662f\u6309\u7167\u65f6\u95f4\u7247(time slice)\uff0c\u8f6e\u6d41\u5c06 CPU \u5206\u914d\u7ed9\u5404\u4e2a\u8fdb\u7a0b\uff0c\u8fd9\u6837\u53ea\u8981\u65f6\u95f4\u7247\u8db3\u591f\u77ed\uff0c\u7528\u6237\u4f53\u611f\u4e0a\u5c31\u50cf\u662f\u591a\u4e2a\u4efb\u52a1\u5e76\u884c\u6267\u884c\u3002</p> <p>\u611f\u89c9\u6bd4\u8f83\u50cf\u300a\u5341\u4e07\u4e2a\u51b7\u7b11\u8bdd\u300b\u8d85\u4eba\u8fd9\u4e00\u96c6\u7684 4:09 - 4:48\u3002</p> <p>\u5206\u65f6\u7528\u6237\u5141\u8bb8\u591a\u4e2a\u7528\u6237\u540c\u65f6\u4f7f\u7528\u540c\u4e00\u53f0\u8ba1\u7b97\u673a\uff0c\u6240\u6709\u4efb\u52a1\u4e4b\u95f4\u4e92\u76f8\u72ec\u7acb\uff0c\u4e92\u4e0d\u5e72\u6270\u3001\u4e92\u4e0d\u963b\u585e\uff0c\u56e0\u6b64\u4efb\u52a1\u7684\u6700\u957f\u5468\u8f6c\u65f6\u95f4\u51cf\u5c11\uff0c\u7528\u6237\u7684\u64cd\u4f5c\u4e5f\u4f1a\u88ab\u53ca\u65f6\u54cd\u5e94\uff0c\u5b9e\u73b0\u4e86\u66f4\u65b9\u4fbf\u8fdb\u884c\u4eba\u673a\u5bf9\u8bdd\u3002</p> \u76f8\u5173\u9605\u8bfb <p>\u5173\u4e8e\u8fd9\u4e09\u4e2a\u6280\u672f\u7684\u8bf4\u660e\u4e5f\u53ef\u4ee5\u770b\u770b xyx \u662f\u600e\u4e48\u5199\u7684\uff1a\ud83d\udd17</p> <p>\u9664\u4e86\u8fd9\u51e0\u79cd\u7cfb\u7edf\u5916\uff0c\u738b\u9053\u91cc\u4e5f\u63d0\u5230\u4e86\u8fd9\u4e9b\u7cfb\u7edf\uff1a</p> <ul> <li>\u5b9e\u65f6\u7cfb\u7edf(Real-time System)\uff1a\u5728\u7279\u5b9a\u65f6\u95f4\uff08\u53ef\u80fd\u6bd4\u65f6\u95f4\u7247\u8fd8\u5c0f\uff09\u5185\u5b8c\u6210\u7279\u5b9a\u4efb\u52a1\u7684\u7cfb\u7edf\uff0c\u4f8b\u5982\u822a\u7a7a\u822a\u5929\u7cfb\u7edf\u3001\u6838\u53cd\u5e94\u5806\u63a7\u5236\u7cfb\u7edf\u7b49\uff1b</li> <li>\u5206\u5e03\u5f0f\u7cfb\u7edf(Distributed System)\uff1a\u7531\u591a\u53f0\u8ba1\u7b97\u673a\u7ec4\u6210\u7684\u7cfb\u7edf\uff0c\u8fd9\u4e9b\u8ba1\u7b97\u673a\u901a\u8fc7\u901a\u4fe1\u4ea4\u6362\u4fe1\u606f\uff0c\u5171\u540c\u5b8c\u6210\u4e00\u4e2a\u4efb\u52a1\uff0c\u4f8b\u5982\u4e91\u8ba1\u7b97\u3001\u5927\u578b\u7f51\u7ad9\u7b49\uff1b</li> </ul> <p>\u591a\u9053\u6280\u672f\u51fa\u73b0\u4e4b\u540e\uff0c\u867d\u7136\u8ba1\u7b97\u673a\u7684\u8868\u73b0\u4e0d\u65ad\u63d0\u5347\uff0c\u4f46\u662f\u591a\u9053\u6280\u672f\u672c\u8eab\u7684\u6280\u672f\u7279\u70b9\uff0c\u5404\u4e2a\u8fdb\u7a0b\u5728\u672a\u5b8c\u6210\u7684\u60c5\u51b5\u4e0b\u9700\u8981\u4e92\u76f8\u5207\u6362\uff0c\u4e00\u7cfb\u5217\u95ee\u9898\u63a5\u8e35\u800c\u6765\uff0c\u8fd9\u4e9b\u90fd\u662f\u6211\u4eec\u5728\u4e4b\u540e\u7684\u5355\u5143\u91cc\u8be6\u7ec6\u8ba8\u8bba\u7684\u5185\u5bb9\u3002</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit0/#\u64cd\u4f5c\u7cfb\u7edf\u7684\u7ed3\u6784\u8bbe\u8ba1","title":"\u64cd\u4f5c\u7cfb\u7edf\u7684\u7ed3\u6784\u8bbe\u8ba1","text":"<p>\u968f\u7740\u64cd\u4f5c\u7cfb\u7edf\u7684\u529f\u80fd\u4e0d\u65ad\u6269\u5c55\u3001\u4f53\u91cf\u9010\u6e10\u53d8\u5927\uff0c\u6574\u4e2a\u64cd\u4f5c\u7cfb\u7edf\u8f6f\u4ef6\u7684\u7ed3\u6784\u8bbe\u8ba1\u5c31\u8d8a\u53d1\u91cd\u8981\u4e86\u3002\u63a5\u4e0b\u6765\u6211\u4eec\u4ecb\u7ecd\u82e5\u5e72\u8bbe\u8ba1\u601d\u8def\u3002</p> <p></p> \u5b8f\u5185\u6838 <p> </p> <p>\u5b8f\u5185\u6838(Monolithic-Kernels)\u4e5f\u53eb\u5355\u5185\u6838\u6216\u5927\u5185\u6838\uff0c\u5b83\u7684\u6838\u5fc3\u601d\u60f3\u5341\u5206\u7b80\u5355\u7c97\u66b4\uff0c\u5c06\u6240\u6709\u4e3b\u8981\u529f\u80fd\u90fd\u7d27\u5bc6\u8026\u5408\u5728\u4e00\u8d77\u4f5c\u4e3a\u4e00\u4e2a\u5b8c\u6574\u7684\u6574\u4f53\u3002</p> <p>\u5b8f\u5185\u6838\u5e26\u6765\u7684\u597d\u5904\u662f\u64cd\u4f5c\u7cfb\u7edf\u6548\u7387\u6781\u9ad8\uff0c\u4ece\u64cd\u4f5c\u7cfb\u7edf\u7684\u53d1\u5c55\u5386\u7a0b\u6765\u770b\uff0c\u4e3b\u6d41\u64cd\u4f5c\u7cfb\u7edf\u90fd\u662f\u4ece\u5b8f\u5185\u6838\u53d1\u5c55\u8fc7\u6765\u7684\uff08\u4e0d\u8fc7\u5982\u4eca\u7684\u4e3b\u6d41\u64cd\u4f5c\u7cfb\u7edf\u66f4\u504f\u5411\u6df7\u5408\u7cfb\u7edf\uff09\u3002</p> <p>\u4f46\u662f\u5b8f\u5185\u6838\u7684\u7f3a\u70b9\u4e5f\u662f\u5341\u5206\u660e\u663e\u7684\uff0c\u5927\u91cf\u590d\u6742\u7684\u529f\u80fd\u4e92\u76f8\u8026\u5408\uff0c\u5bfc\u81f4\u64cd\u4f5c\u7cfb\u7edf\u7684\u7ef4\u62a4\u5341\u5206\u56f0\u96be\uff1b\u4e0d\u4ec5\u5982\u6b64\uff0c\u4e00\u65e6\u67d0\u4e2a\u90e8\u5206\u51fa\u73b0\u4e86\u4e25\u91cd\u95ee\u9898\uff0c\u6574\u4e2a\u7cfb\u7edf\u90fd\u4f1a\u53d7\u5230\u5f71\u54cd\uff0c\u5728\u8fd9\u65b9\u9762\uff0c\u5b8f\u5185\u6838\u7684\u8868\u73b0\u90fd\u4e0d\u5982\u5fae\u5185\u6838\u3002</p> \u5206\u5c42\u8bbe\u8ba1 <p>\u5206\u5c42\u8bbe\u8ba1(layer approach)\u7684\u6838\u5fc3\u601d\u60f3\u662f\u5c06\u7cfb\u7edf\u5206\u4e3a\u82e5\u5e72\u5c42\uff0c\u5e95\u5c42\u4e3a\u786c\u4ef6\uff0c\u9876\u5c42\u4e3a\u7528\u6237\u63a5\u53e3\uff0c\u7b2c \\(i\\) \u5c42\u53ea\u8c03\u7528 \\(i-1\\) \u5c42\u63d0\u4f9b\u7684\u63a5\u53e3\u3002\u6bcf\u4e00\u5c42\u90fd\u5b9e\u73b0\u826f\u597d\u7684\u5c01\u88c5\uff0c\u4e8e\u662f\u5f00\u53d1\u8fc7\u7a0b\u4e2d\u53ea\u9700\u8981\u9010\u6b65\u5b9e\u73b0\u5e76\u8c03\u8bd5\u9a8c\u8bc1\u6bcf\u4e00\u5c42\uff0c\u518d\u9010\u7ea7\u5411\u4e0a\u5f00\u53d1\u5373\u53ef\uff1b\u5728\u7ef4\u62a4\u6216\u6269\u5c55\u8fc7\u7a0b\u4e2d\uff0c\u53ea\u8981\u4fee\u6539\u6bcf\u4e00\u5c42\u7684\u5185\u90e8\u5b9e\u73b0\uff0c\u800c\u4e0d\u9700\u8981\u4fee\u6539\u5176\u5b83\u5c42\u7684\u4ee3\u7801\uff0c\u8fd9\u6837\u5c31\u5927\u5927\u964d\u4f4e\u4e86\u5f00\u53d1\u548c\u7ef4\u62a4\u7684\u96be\u5ea6\u3002</p> <p>\u7136\u800c\uff0c\u7531\u4e8e\u6bcf\u6b21\u6267\u884c\u4e00\u4e2a\u529f\u80fd\u90fd\u9700\u8981\u4e0a\u4e0b\u8de8\u8d8a\u591a\u5c42\uff0c\u53d1\u751f\u591a\u6b21\u63a5\u53e3\u8c03\u7528\uff0c\u5206\u5c42\u8bbe\u8ba1\u4e0b\u7684\u7cfb\u7edf\u6548\u7387\u5f80\u5f80\u90fd\u53d7\u5230\u9650\u5236\uff1b\u4e0d\u4ec5\u5982\u6b64\uff0c\u8981\u60f3\u771f\u6b63\u610f\u4e49\u4e0a\u5b9e\u73b0\u826f\u597d\u7684\u5206\u5c42\u8bbe\u8ba1\uff0c\u5c31\u9700\u8981\u5bf9\u5404\u5c42\u6709\u826f\u597d\u7684\u5b9a\u4e49\uff0c\u8fd9\u4e2a\u8bbe\u8ba1\u96be\u5ea6\u662f\u4e0d\u5c0f\u7684\u3002</p> <p></p> \u5fae\u5185\u6838 <p> </p> <p>\u5fae\u5185\u6838(Micro-Kernels)\u7684\u8bbe\u8ba1\u601d\u8def\u4e0e\u5b8f\u5185\u6838\u76f8\u53cd\uff0c\u4e3b\u5f20\u5c06\u4e0d\u662f\u5fc5\u8981\u7684\u4e1c\u897f\u90fd\u4ece\u5185\u6838\u91cc\u62ff\u51fa\u53bb\uff0c\u653e\u5230\u7528\u6237\u7a7a\u95f4\uff0c\u4ee5\u7528\u6237\u6001\u6267\u884c\u3002\u6574\u4f53\u5f62\u6210\u4e00\u79cd\u5fae\u5185\u6838-\u670d\u52a1\u5668\u7684\u7ed3\u6784\uff0c\u6b64\u65f6\u5185\u6838\u53ea\u63d0\u4f9b\u901a\u8baf\u3001\u5185\u5b58\u7ba1\u7406\u3001\u8fdb\u7a0b\u7ba1\u7406\u7b49\u57fa\u672c\u529f\u80fd\uff0c\u4e5f\u53ea\u6709\u8fd9\u4e9b\u90e8\u5206\u76f4\u63a5\u8fd0\u884c\u5728\u5185\u6838\u6001\uff0c\u4f5c\u4e3a\u670d\u52a1\u5668\u7684\u5176\u5b83\u529f\u80fd\u90e8\u4ef6\u5219\u901a\u8fc7\u6d88\u606f\u4f20\u9012\u673a\u5236\u4e0e\u5185\u6838\u4e92\u52a8\u3002</p> <p>\u7531\u4e8e\u5185\u6838\u53ea\u63d0\u4f9b\u6700\u57fa\u672c\u7684\u529f\u80fd\uff0c\u6240\u4ee5\u5185\u6838\u7684\u4f53\u79ef\u4f1a\u5927\u5927\u51cf\u5c0f\uff0c\u5185\u6838\u7684\u7ef4\u62a4\u548c\u6269\u5c55\u4e5f\u4f1a\u53d8\u5f97\u66f4\u52a0\u5bb9\u6613\uff0c\u5fae\u5185\u6838-\u670d\u52a1\u5668\u7684\u7ed3\u6784\u4e5f\u4f7f\u529f\u80fd\u6269\u5c55\u66f4\u52a0\u5bb9\u6613\uff1b\u53e6\u5916\uff0c\u7531\u4e8e\u5185\u6838\u53ea\u63d0\u4f9b\u6700\u57fa\u672c\u7684\u529f\u80fd\uff0c\u6240\u4ee5\u5185\u6838\u7684\u6548\u7387\u4e5f\u4f1a\u5927\u5927\u63d0\u5347\uff1b\u4e0d\u4ec5\u5982\u6b64\uff0c\u7531\u4e8e\u5404\u4e2a\u529f\u80fd\u4e4b\u95f4\u7684\u8026\u5408\u964d\u4f4e\uff0c\u4e14\u90fd\u8fd0\u884c\u5728\u7528\u6237\u6001\uff0c\u529f\u80fd\u4e4b\u95f4\u4ec5\u4f7f\u7528\u901a\u4fe1\u5efa\u7acb\u94fe\u63a5\uff0c\u5373\u4f7f\u67d0\u4e2a\u529f\u80fd\u90e8\u4ef6\u51fa\u73b0\u95ee\u9898\uff0c\u4e5f\u4e0d\u4f1a\u5bfc\u81f4\u6574\u4e2a\u7cfb\u7edf\u5d29\u6e83\uff0c\u76f8\u6bd4\u4e8e\u5b8f\u5185\u6838\uff0c\u7cfb\u7edf\u53ef\u9760\u6027\u5927\u5927\u63d0\u5347\u3002</p> \u6a21\u5757\u5316\u8bbe\u8ba1 <p>\u6a21\u5757\u5316\u8bbe\u8ba1(Modules Approach)\u6307\u5c06\u64cd\u4f5c\u7cfb\u7edf\u5212\u5206\u4e3a\u82e5\u5e72\u5206\u7acb\u6a21\u5757\uff0c\u5e76\u89c4\u5b9a\u6a21\u5757\u4e4b\u95f4\u7684\u63a5\u53e3\uff0c\u751a\u81f3\u5355\u4e2a\u6a21\u5757\u4e0b\u4e5f\u53ef\u80fd\u662f\u7531\u591a\u4e2a\u6a21\u5757\u901a\u8fc7\u540c\u6837\u7684\u65b9\u5f0f\u7ec4\u7ec7\u800c\u6210\u7684\u3002\u8fd9\u79cd\u8bbe\u8ba1\u65b9\u6cd5\u4e5f\u88ab\u79f0\u4e3a\u6a21\u5757-\u63a5\u53e3\u6cd5\u3002</p> <p>\u6a21\u5757\u5316\u7684\u8bbe\u8ba1\u4e0e\u5fae\u5185\u6838\u662f\u4e0d\u540c\u7684\uff0c\u9700\u8981\u6ce8\u610f\u533a\u5206\u3002\u5fae\u5185\u6838\u8bbe\u8ba1\u4ecd\u7136\u662f\u6709\u4e2d\u5fc3\uff08\u5fae\u5185\u6838\uff09\u7684\uff0c\u4f46\u662f\u6a21\u5757\u5316\u8bbe\u8ba1\u6574\u4f53\u662f\u5206\u5c42\u7f51\u72b6\u7684\u3002</p> <p>\u7406\u60f3\u7684\u6a21\u5757\u5316\u8bbe\u8ba1\u4f1a\u8ba9\u7cfb\u7edf\u8bbe\u8ba1\u53ef\u4ee5\u591a\u7ebf\u5e76\u884c\uff0c\u53ea\u9700\u8981\u4e8b\u5148\u5546\u91cf\u597d\u63a5\u53e3\uff0c\u5404\u4e2a\u5de5\u7a0b\u5e08\u5c31\u53ef\u4ee5\u72ec\u7acb\u5730\u5b9e\u73b0\u3001\u586b\u5145\u6a21\u5757\u5185\u5bb9\uff1b\u9ad8\u5185\u805a\u4f4e\u8026\u5408\u7684\u8bbe\u8ba1\u4e5f\u80fd\u8ba9\u7cfb\u7edf\u7684\u7ef4\u62a4\u548c\u6269\u5c55\u53d8\u5f97\u66f4\u52a0\u5bb9\u6613\u3002</p> <p>\u7136\u800c\u6a21\u5757\u5316\u7684\u8bbe\u8ba1\u5341\u5206\u56f0\u96be\uff0c\u6a21\u5757\u5316\u7684\u8bbe\u8ba1\u5e76\u6ca1\u6709\u4e00\u4e2a\u6e05\u6670\u7684\u5355\u5411\u4f9d\u8d56\u5173\u7cfb\uff0c\u56e0\u6b64\u65e0\u6cd5\u9012\u8fdb\u5f0f\u7684\u63a8\u8fdb\u4efb\u52a1\uff0c\u6574\u4e2a\u5f00\u53d1\u8fc7\u7a0b\u5c31\u597d\u50cf\u59cb\u7ec8\u60ac\u5728\u534a\u7a7a\uff1b\u9664\u6b64\u4e4b\u5916\uff0c\u5982\u4f55\u8bbe\u8ba1\u63a5\u53e3\u4f7f\u5f97\u6240\u6709\u9700\u6c42\u90fd\u80fd\u88ab\u5f88\u597d\u6ee1\u8db3\u4e5f\u662f\u4e2a\u96be\u4ee5\u89e3\u51b3\u7684\u95ee\u9898\u3002</p> \u6df7\u5408\u7cfb\u7edf <p>\u6df7\u5408\u7cfb\u7edf(Hybrid Systems)\u662f\u6307\u5c06\u5b8f\u5185\u6838\u548c\u5fae\u5185\u6838\u7684\u8bbe\u8ba1\u601d\u8def\u7ed3\u5408\u8d77\u6765\uff0c\u8fd9\u79cd\u8bbe\u8ba1\u6a21\u5f0f\u66f4\u73b0\u4ee3\uff0c\u4e5f\u662f\u76ee\u524d\u4e3b\u6d41\u7684\u64cd\u4f5c\u7cfb\u7edf\u7684\u6a21\u5f0f\u3002</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit0/#\u64cd\u4f5c\u7cfb\u7edf\u7684\u8fd0\u884c\u539f\u7406","title":"\u64cd\u4f5c\u7cfb\u7edf\u7684\u8fd0\u884c\u539f\u7406","text":"<p>\u672c\u8282\u6211\u4eec\u6df1\u5165\u5230\u64cd\u4f5c\u7cfb\u7edf\u7684\u4e00\u4e9b\u5177\u4f53\u8fd0\u884c\u8fc7\u7a0b\uff0c\u63a2\u7a76\u4e00\u4e9b\u6b65\u9aa4\u7684\u5177\u4f53\u5b9e\u73b0\u3002</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit0/#\u4e2d\u65ad","title":"\u4e2d\u65ad","text":"<p>\u4e2d\u65ad\uff08\u5e7f\u4e49\uff09\u662f\u8d2f\u7a7f\u73b0\u4ee3\u64cd\u4f5c\u7cfb\u7edf\u7684\u4e00\u4e2a\u91cd\u8981\u6280\u672f\uff0c\u5b83\u4f7f\u5f97\u201c\u8ba1\u5212\u4e4b\u5916\u201d\u7684\u4e8b\u60c5\u53ef\u4ee5\u53ca\u65f6\u7684\u88ab\u544a\u77e5\u5e76\u5904\u7406\u3002\u4f8b\u5982\uff0c\u7a0b\u5e8f\u7a81\u7136\u51fa\u73b0\u4e86\u81f4\u547d\u9519\u8bef\uff0c\u8fd9\u65f6\u64cd\u4f5c\u7cfb\u7edf\u5e94\u8be5\u53ca\u65f6\u5bdf\u89c9\u5e76\u5904\u7406\uff1b\u53c8\u6bd4\u5982\uff0c\u7528\u6237\u5728\u547d\u4ee4\u884c\u8f93\u5165\u4e86\u6307\u4ee4\uff0c\u6309\u4e0b\u4e86\u56de\u8f66\uff0c\u64cd\u4f5c\u7cfb\u7edf\u5e94\u5f53\u5bdf\u89c9\u5230 I/O \u5df2\u7ecf\u51c6\u5907\u597d\u4e86\u3002\u4f46\u662f\u6211\u4eec\u4e0d\u5e94\u5f53\u8ba9\u64cd\u4f5c\u7cfb\u7edf\u4e0d\u538c\u5176\u70e6\u5730\u8be2\u95ee\u4f60\u6709\u6ca1\u6709\u53d1\u751f\u9519\u8bef\uff0c\u53c8\u6216\u8005\u8fd9\u4e2a I/O \u662f\u5426\u5c31\u7eea\uff0c\u8fd9\u5f88\u4e0d\u5408\u7406\u3002</p> <p>\u4e5f\u5c31\u662f\u8bf4\uff0c\u6211\u4eec\u4e0d\u5e94\u5f53\u8ba9\u64cd\u4f5c\u7cfb\u7edf\u4e8b\u65e0\u5de8\u7ec6\u5730\u53bb\u8d1f\u8d23\u68c0\u67e5\u610f\u5916\u662f\u5426\u53d1\u751f\uff0c\u800c\u662f\u5e94\u5f53\u63d0\u4f9b\u4e00\u4e2a\u4e0a\u62a5\u610f\u5916\u7684\u63a5\u53e3\uff0c\u8ba9\u4ea7\u751f\u610f\u5916\u7684\u4eba\u81ea\u884c\u4e0a\u62a5\u8fd9\u4e9b\u610f\u5916\u3002\u5728\u5177\u4f53\u786c\u4ef6\u7684\u5b9e\u73b0\u4e0a\uff0c\u4f1a\u6709\u4e24\u6761\u4e13\u95e8\u8868\u793a\u4e2d\u65ad\u4fe1\u53f7\u7684\u7ebf\uff08\u7a0d\u5019\u4f1a\u5728\u4e2d\u65ad\u5c4f\u853d\u4e2d\u8bb2\u5230\uff09\uff0cCPU \u4f1a\u5728\u6bcf\u4e00\u6761\u6307\u4ee4\u7ed3\u675f\u540e\u68c0\u6d4b\u662f\u5426\u6709\u4e2d\u65ad\u53d1\u751f\uff0c\u800c\u5728\u8f6f\u4ef6\u4e0a\u5c31\u4f53\u73b0\u4e3a\u6bcf\u5f53\u6709\u4e2d\u65ad\u53d1\u751f\u65f6\uff0c\u64cd\u4f5c\u7cfb\u7edf\u5c31\u9700\u8981\u53bb\u5904\u7406\u3002\u7531\u4e8e\u4e2d\u65ad\u7684\u5f3a\u5927\u7279\u6027\uff0c\u4ece\u6700\u65e9\u4ec5\u7684\u5904\u7406\u786c\u4ef6\u72b6\u6001\uff0c\u5230\u5904\u7406\u8f6f\u4ef6\u9519\u8bef\u548c\u4f5c\u4e3a\u4e00\u79cd\u7c7b\u4f3c\u51fd\u6570\u7684\u624b\u6bb5\uff0c\u4e2d\u65ad\u7684\u5e94\u7528\u8303\u56f4\u8d8a\u6765\u8d8a\u5e7f\uff0c\u5b83\u7684\u6982\u5ff5\u968f\u7740\u5e94\u7528\u8303\u56f4\u4e5f\u4e0d\u65ad\u6269\u5927\u3002</p> <p>\u4e2d\u65ad\u5411\u91cf\u8868</p> <p>\u7531\u4e8e\u4e2d\u65ad\u88ab\u5e7f\u6cdb\u4f7f\u7528\uff0c\u64cd\u4f5c\u7cfb\u7edf\u9700\u8981\u9891\u7e41\u7684\u5904\u7406\u5404\u79cd\u4e2d\u65ad\uff0c\u5904\u7406\u6bcf\u4e00\u79cd\u4e2d\u65ad\u90fd\u9700\u8981\u4e00\u4e2a\u7279\u5b9a\u7684\u65b9\u6cd5\uff0c\u56e0\u6b64\uff0c\u4e00\u79cd\u5feb\u901f\u5b9a\u4f4d\u4e2d\u65ad\u5904\u7406\u65b9\u6cd5\u7684\u624b\u6bb5\u5c31\u663e\u5f97\u5c24\u4e3a\u91cd\u8981\u3002</p> <p>\u4e2d\u65ad\u5411\u91cf\u8868(Interrupt Vector Table)\u901a\u8fc7\u4e2d\u65ad\u53f7\u6765\u7d22\u5f15\u4e2d\u65ad\u5904\u7406\u65b9\u6cd5\uff0c\u5b9e\u73b0\u4e86\u4e00\u79cd\u201c\u968f\u673a\u8bbf\u95ee\u201d\uff0c\u5927\u5927\u52a0\u901f\u4e86\u4e2d\u65ad\u5904\u7406\u7684\u901f\u5ea6\u3002</p> <p>\u6839\u636e\u4e2d\u65ad\u662f\u5426\u7531\u7a0b\u5e8f\u4ea7\u751f\uff0c\u4e2d\u65ad\u53ef\u4ee5\u5206\u4e3a\u5916\u4e2d\u65ad\uff08\u72ed\u4e49\u7684\u4e2d\u65ad\uff0c\u7531\u786c\u4ef6\u4ea7\u751f\uff09\u548c\u5185\u4e2d\u65ad\uff08\u5f02\u5e38...\uff0c\u4e3b\u8981\u7531\u7a0b\u5e8f\u4ea7\u751f\uff09\u3002\u8fd9\u91cc\u6709\u5f88\u591a\u6982\u5ff5\uff1ainstruction, exception, trap, abort, ...\uff0c\u8fd9\u90e8\u5206\u533a\u5206\u8bf7\u5927\u5bb6\u81ea\u884c\u5bfb\u627e\u8d44\u6599\u53c2\u8003\uff0c\u6211\u5728\u8fd9\u91cc\u653e\u51e0\u4e2a\u53c2\u8003\u94fe\u63a5\u3002</p> \u76f8\u5173\u9605\u8bfb <ul> <li>Difference between TRAP and exceptions | StackOverflow</li> <li>Difference between Interrupt and Exception | GeeksForGeeks</li> </ul> <p>\u7406\u60f3\u60c5\u51b5\u4e0b\uff0c\u6211\u4eec\u5e0c\u671b\u4e2d\u65ad\u4e00\u65e6\u53d1\u751f\u5c31\u7acb\u523b\u88ab\u89e3\u51b3\uff0c\u4f46\u662f\u4e2d\u65ad\u5904\u7406\u4e5f\u540c\u6837\u9700\u8981\u8d44\u6e90\uff0c\u8fd9\u610f\u5473\u7740\u4e2d\u65ad\u4e5f\u6709\u53ef\u80fd\u4ea7\u751f\u51b2\u7a81\u3002\u4e8e\u662f\uff0c\u6211\u4eec\u9700\u8981\u4e00\u7cfb\u5217\u673a\u5236\u6765\u89e3\u51b3\u8fd9\u4e9b\u95ee\u9898\u3002</p> <ol> <li>\u663e\u7136\uff0c\u4e2d\u65ad\u4e4b\u95f4\u4ea6\u6709\u533a\u522b\uff0c\u6709\u7684\u7a0b\u5e8f\u53d1\u751f\u4e86\u201c\u81f4\u547d\u9519\u8bef\u201d\u8fd9\u4ef6\u4e8b\uff0c\u663e\u7136\u6bd4\u6253\u5370\u673a\u5c31\u7eea\u66f4\u91cd\u8981\uff0c\u56e0\u6b64\uff0c\u4e2d\u65ad\u9700\u8981\u5206\u7ea7\u673a\u5236\uff0c\u4ee5\u533a\u5206\u4e2d\u65ad\u7684\u4f18\u5148\u7ea7\uff0c\u8fd9\u6837\u5c31\u53ef\u4ee5\u5728\u5904\u7406\u4e2d\u65ad\u65f6\uff0c\u4f18\u5148\u5904\u7406\u4f18\u5148\u7ea7\u9ad8\u7684\u4e2d\u65ad\uff1b</li> <li>\u4e2d\u65ad\u5e76\u4e0d\u662f\u968f\u65f6\u968f\u5730\u90fd\u80fd\u53d1\u751f\u7684\uff0c\u201c\u4ee3\u7406\u4eba\u201d\u5728\u8d70\u72ec\u6728\u6865\u65f6\u4e0d\u5e94\u5f53\u6682\u505c\u53bb\u5904\u7406\u836f\u54c1\u7f3a\u8d27\u7684\u95ee\u9898\uff0c\u5bf9\u4e8e\u64cd\u4f5c\u7cfb\u7edf\u6765\u8bf4\uff0c\u6709\u8bb8\u591a\u539f\u5b50\u6027\u7684\u884c\u4e3a\u662f\u4e0d\u53ef\u88ab\u4e2d\u65ad\u7684\uff0c\u4e5f\u6709\u4e00\u4e9b\u91cd\u8981\u7684\u4efb\u52a1\u662f\u4e0d\u5e94\u5f53\u88ab\u666e\u901a\u7684\u4e2d\u65ad\u6253\u6270\u7684\uff0c\u8fd9\u5c31\u6d89\u53ca\u5230\u4e2d\u65ad\u5c4f\u853d\u95ee\u9898\uff1b</li> </ol> <p>\u5b58\u7591</p> <p>\u8fd9\u5c31\u9700\u8981\u6211\u4eec\u8c08\u5230\u4e2d\u65ad\u7684\u786c\u4ef6\u8bbe\u8ba1\uff0c\u4e00\u79cd\u6bd4\u8f83\u666e\u901a\u7684\u8bbe\u8ba1\u662f\uff0c\u51c6\u5907 maskable interrupt-request line \u548c non-maskable interrupt-request line \u4e24\u6761\u4e2d\u65ad\u8bf7\u6c42\u7ebf\uff0c\u524d\u8005\u7528\u4e8e\u53ef\u5c4f\u853d\u7684\u4e2d\u65ad\uff0c\u540e\u8005\u7528\u4e8e\u4e0d\u53ef\u5c4f\u853d\u7684\u4e2d\u65ad\uff0c\u64cd\u4f5c\u7cfb\u7edf\u5728\u6bcf\u4e2a\u6307\u4ee4\u540e\u68c0\u67e5\u8fd9\u4e2d\u65ad\u7ebf\u4e0a\u662f\u5426\u6709\u4e2d\u65ad\u8bf7\u6c42\uff0c\u800c\u5982\u679c\u6b64\u65f6\u64cd\u4f5c\u7cfb\u7edf\u5c4f\u853d\u4e86\u4e2d\u65ad\uff0c\u90a3\u4e48\u5c31\u4e0d\u4f1a\u68c0\u67e5 maskable interrupt-request line \u4e0a\u7684\u4e2d\u65ad\u8bf7\u6c42\u3002</p> <p>\u9700\u8981\u6ce8\u610f\uff0c\u64cd\u4f5c\u7cfb\u7edf\u53d1\u73b0\u4e2d\u65ad\u540e\u5e76\u4e0d\u662f\u4e8c\u8bdd\u4e0d\u8bf4\u9a6c\u4e0a\u53bb\u5904\u7406\u4e2d\u65ad\u7684\uff0c\u4e3a\u4e86\u4fdd\u8bc1\u4e2d\u65ad\u5904\u7406\u5b8c\u6210\u540e\u4ecd\u80fd\u7ee7\u7eed\u5f53\u524d\u4efb\u52a1\uff0c\u64cd\u4f5c\u7cfb\u7edf\u9700\u8981\u4fdd\u5b58\u5f53\u524d\u4efb\u52a1\u7684\u72b6\u6001\uff0c\u4ee5\u4fbf\u5b8c\u6210\u4e2d\u65ad\u5904\u7406\u540e\u6062\u590d\u5f53\u524d\u4efb\u52a1\u7684\u72b6\u6001\u3002</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit0/#\u8ba1\u65f6\u5668","title":"\u8ba1\u65f6\u5668","text":"<p>\u867d\u7136\u770b\u8d77\u6765\u5f88\u4e0d\u8d77\u773c\uff0c\u4f46\u8ba1\u65f6\u5668(timer)\u5728\u64cd\u4f5c\u7cfb\u7edf\u4e2d\u662f\u4e00\u4e2a\u975e\u5e38\u91cd\u8981\u7684\u4e1c\u897f\u3002\u8ba1\u65f6\u5668\u9700\u8981\u4e00\u4e2a\u56fa\u5b9a\u9891\u7387\u7684\u65f6\u949f\u4ee5\u53ca\u4e00\u4e2a\u8ba1\u6570\u5668\uff0c\u5728\u6bcf\u4e2a\u65f6\u949f\u5468\u671f\u4ee4\u8ba1\u6570\u5668\u51cf 1\uff0c\u5f53\u8ba1\u6570\u5668\u5f52\u96f6\u65f6\u4ea7\u751f\u4e2d\u65ad\uff0c\u544a\u8bc9\u64cd\u4f5c\u7cfb\u7edf\u5b9a\u7684\u65f6\u5df2\u7ecf\u5230\u4e86\u3002</p> <p>\u5b83\u7684\u529f\u80fd\u867d\u7136\u57fa\u7840\u4f46\u662f\u5341\u5206\u91cd\u8981\uff0c\u4f8b\u5982\u5206\u65f6\u7cfb\u7edf\u4e2d\u5c31\u9700\u8981\u8ba1\u6570\u5668\u6765\u63a7\u5236\u65f6\u95f4\u7247\u7684\u957f\u5ea6\uff0c\u53c8\u6bd4\u5982\u64cd\u4f5c\u7cfb\u7edf\u9700\u8981\u5b9a\u671f\u68c0\u67e5\u5185\u5b58\u4e2d\u7684\u8fdb\u7a0b\uff0c\u4ee5\u9632\u6b62\u8fdb\u7a0b\u4e00\u76f4\u5360\u7528\u7cfb\u7edf\u8d44\u6e90\uff0c\u8fd9\u4e9b\u90fd\u9700\u8981\u8ba1\u65f6\u5668\u7684\u5e2e\u52a9\u3002</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit0/#\u7279\u6743\u6a21\u5f0f","title":"\u7279\u6743\u6a21\u5f0f","text":"<p>\u6211\u4eec\u524d\u9762\u8bf4\u8fc7\uff0c\u64cd\u4f5c\u7cfb\u7edf\u7684\u67d0\u4e9b\u64cd\u4f5c\u662f\u5371\u9669\u7684\uff0c\u6709\u53ef\u80fd\u5a01\u80c1\u5230\u81ea\u8eab\u6b63\u5e38\u8fd0\u4f5c\u7684\uff08\u5982\u4e0e\u786c\u4ef6\u76f4\u63a5\u76f8\u5173\u7684\u884c\u4e3a\u3001\u63a7\u5236 CPU \u8fd0\u884c\u89c4\u5219\u7684\u884c\u4e3a\u7b49\uff09\uff0c\u800c\u8fd9\u4e9b\u64cd\u4f5c\u4e0d\u5e94\u5f53\u88ab\u7528\u6237\u7a0b\u5e8f\u76f4\u63a5\u6267\u884c\u3002\u4e00\u79cd\u7b80\u5355\u7684\u601d\u8def\u662f\uff0c\u6211\u4eec\u5212\u5206\u5e38\u89c4\u64cd\u4f5c\u548c\u5371\u9669\u64cd\u4f5c\uff0c\u5141\u8bb8\u7528\u6237\u7a0b\u5e8f\u6267\u884c\u5e38\u89c4\u64cd\u4f5c\uff0c\u800c\u5371\u9669\u64cd\u4f5c\u5219\u9700\u8981\u59d4\u6258\u4e13\u4e1a\u4eba\u58eb\u4ee3\u4e3a\u6267\u884c\u3002\u800c\u8fd9\u5c31\u662f\u7279\u6743\u6a21\u5f0f(Privileged Mode)\u7684\u57fa\u672c\u601d\u8def\u3002</p> <p>\u5de5\u4e1a\u4e0a\u7684\u7279\u6743\u6a21\u5f0f\u53ef\u80fd\u4f1a\u6709\u591a\u79cd\u590d\u6742\u7684\u5b9e\u73b0\u5f62\u5f0f\uff0c\u4f46\u662f\u6211\u4eec\u8fd9\u91cc\u53ea\u8bb2\u6700\u7b80\u5355\u7684\u4e00\u79cd\uff0c\u5373\u53cc\u6a21\u5f0f(Dual-Mode)\u3002\u53cc\u6a21\u5f0f\u4e0b\uff0cCPU \u6709\u4e24\u79cd\u8fd0\u884c\u6a21\u5f0f\uff0c\u4e00\u79cd\u662f\u7528\u6237\u6001(User Mode)\uff08\u76ee\u6001\uff09\uff0c\u4e00\u79cd\u662f\u5185\u6838\u6001(Kernel Mode)\uff08\u7ba1\u6001\uff0c\u6838\u5fc3\u6001\uff09\u3002Mode Bit \u4e3a 0\uff0c\u8868\u793a CPU \u5de5\u4f5c\u5728\u5185\u6838\u6001\uff0cMode Bit \u4e3a 1 \u65f6\uff0cCPU \u5de5\u4f5c\u5728\u7528\u6237\u6001\u3002</p> <p>\u540c\u65f6\uff0c\u6211\u4eec\u5c06\u90a3\u4e9b\u201c\u5371\u9669\u201d\u7684\u6307\u4ee4\u79f0\u4e3a\u7279\u6743\u6307\u4ee4(privileged instruction)\uff0c\u4f8b\u5982 I/O \u63a7\u5236\uff0c\u8ba1\u65f6\u5668\u7ba1\u7406\uff0c\u4e2d\u65ad\u7ba1\u7406\u7b49\u3002\u8fd9\u4e9b\u6307\u4ee4\u53ea\u80fd\u5728\u5185\u6838\u6001\u4e0b\u6267\u884c\uff0c\u800c\u7528\u6237\u6001\u4e0b\u6267\u884c\u8fd9\u4e9b\u6307\u4ee4\u65f6\u4f1a\u8ba4\u4e3a\u8fd9\u6761\u6307\u4ee4\u4e0d\u5b58\u5728\u3002</p> <p>\u95ee\u9898\u5c1a\u672a\u89e3\u51b3</p> <p>\u73b0\u5728\u6211\u4eec\u5c06\u5371\u9669\u64cd\u4f5c\u548c\u76f8\u5bf9\u5b89\u5168\u7684\u64cd\u4f5c\u9694\u79bb\u5f00\u6765\u4e86\uff0c\u4f46\u662f\u8fd9\u5e76\u4e0d\u610f\u5473\u7740\u7528\u6237\u7a0b\u5e8f\u5c31\u4e0d\u9700\u8981\u4f7f\u7528\u90a3\u4e9b\u5371\u9669\u64cd\u4f5c\u4e86\uff0c\u5355\u7eaf\u7684\u9694\u79bb\u5e76\u4e0d\u80fd\u89e3\u51b3\u95ee\u9898\uff0c\u7528\u6237\u7a0b\u5e8f\u4ecd\u7136\u5b58\u5728\u9700\u8981\u4f7f\u7528\u7279\u6743\u6307\u4ee4\u7684\u9700\u6c42\u3002</p> <p>\u8fd9\u4e9b\u9700\u6c42\u5f80\u5f80\u662f\u53ef\u4ee5\u88ab\u62bd\u8c61\u7684\u3001\u88ab\u5c01\u88c5\u7684\u3002\u5c31\u597d\u50cf\u300c\u201c\u7528\u6237\u201d\u5411\u201c\u67dc\u53f0\u201d\u7d22\u8981\u5e93\u623f\u94a5\u5319\uff0c\u4ee5\u4fbf ta \u80fd\u53bb\u5e93\u623f\u62ff\u7f3a\u8d27\u7684\u8d27\u7269\u300d\u8fd9\u4ef6\u4e8b\u662f\u4e0d\u5408\u7406\u7684\uff0c\u6211\u4eec\u65e0\u6cd5\u63a7\u5236\u201c\u7528\u6237\u201d\u5b9e\u9645\u62ff\u201c\u94a5\u5319\u201d\u505a\u4e86\u4ec0\u4e48\uff0c\u800c\u201c\u94a5\u5319\u201d\u7684\u6ee5\u7528\u53c8\u4f1a\u5bfc\u81f4\u201c\u67dc\u53f0\u201d\u9677\u5165\u5371\u9669\u4e2d\uff1b\u4f46\u662f\u300c\u201c\u7528\u6237\u201d\u8bf7\u6c42\u201c\u67dc\u53f0\u201d\u53bb\u5e93\u623f\u62ff ta \u9700\u8981\u7684\u8d27\u7269\u300d\u662f\u5408\u7406\u7684\u3002</p> <p>\u53cd\u8fc7\u6765\u8bb2\uff0c\u867d\u7136\u300c\u201c\u7528\u6237\u201d\u8bf7\u6c42\u201c\u67dc\u53f0\u201d\u53bb\u5e93\u623f\u62ff ta \u9700\u8981\u7684\u8d27\u7269\u300d\u8fd9\u4e2a\u4efb\u52a1\u5fc5\u987b\u4f7f\u7528\u5e93\u623f\u201c\u94a5\u5319\u201d\u624d\u80fd\u8fdb\u884c\uff0c\u4f46\u662f\u65e0\u8bba\u5982\u4f55\u8fd9\u4e2a\u201c\u94a5\u5319\u201d\u4e5f\u53ea\u4f1a\u88ab\u201c\u67dc\u53f0\u201d\u7528\u6765\u83b7\u53d6\u5e93\u623f\u91cc\u7684\u7279\u5b9a\u8d27\u7269\uff0c\u800c\u4e0d\u4f1a\u53d1\u751f\u8bf8\u5982\u201c\u7528\u6237\u201d\u5e26\u7740\u5341\u516b\u8f66\u9762\u5305\u4eba\u628a\u5e93\u623f\u6d17\u52ab\u4e00\u7a7a\u7684\u60c5\u51b5\u3002</p> <p>\u64cd\u4f5c\u7cfb\u7edf\u53ea\u9700\u8981\u5c01\u88c5\u597d\u4e00\u7cfb\u5217\u7c7b\u4f3c\u8fd9\u79cd\u7684\u9700\u6c42-\u7ed3\u679c\u7684\u5904\u7406\u65b9\u6848\uff0c\u8ba9\u7528\u6237\u5728\u6709\u9700\u8981\u7684\u65f6\u5019\u8ba9\u64cd\u4f5c\u7cfb\u7edf\u6267\u884c\u8fd9\u4e9b\u65b9\u6848\uff0c\u5728\u6267\u884c\u5f53\u524d\u4efb\u52a1\u7684\u65f6\u5019\u5c06\u63a7\u5236\u6743\u8ba9\u6e21\u7ed9\u64cd\u4f5c\u7cfb\u7edf\uff0c\u64cd\u4f5c\u7cfb\u7edf\u5b8c\u6210\u540e\u518d\u8fd8\u56de\u63a7\u5236\u6743\uff0c\u5c31\u53ef\u4ee5\u5b9e\u73b0\u5c06\u7279\u6743\u6307\u4ee4\u9694\u79bb\u5728\u5185\u6838\u6001\uff0c\u540c\u65f6\u7528\u6237\u7a0b\u5e8f\u4e5f\u80fd\u5b8c\u6210\u9700\u6c42\u3002</p> <p>\u800c\u90a3\u4e48\u5728\u5177\u4f53\u5b9e\u73b0\u4e0a\uff0c\u8fd9\u4e00\u6b65\u662f\u901a\u8fc7 trap \u5b9e\u73b0\u7684\u3002</p> <p> Transition from user to kernel mode.</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit0/#\u7cfb\u7edf\u8c03\u7528","title":"\u7cfb\u7edf\u8c03\u7528","text":"<p>  Examples of W&amp;U system calls. </p> <p>\u7cfb\u7edf\u8c03\u7528(System Call)\u662f\u7cfb\u7edf\u5411\u7528\u6237\u7a0b\u5e8f\u63d0\u4f9b\u670d\u52a1\u7684\u4e00\u4e2a\u63a5\u53e3\uff0c\u5b83\u4eec\u7ecf\u5e38\u4ee5 C/C++ \u51fd\u6570\u7684\u5f62\u5f0f\u5b58\u5728\uff0c\u5bf9\u4e8e\u67d0\u4e9b\u6bd4\u8f83\u63a5\u8fd1\u5e95\u5c42\u7684\u4efb\u52a1\uff0c\u4e5f\u53ef\u80fd\u662f\u901a\u8fc7\u6c47\u7f16\u7f16\u5199\u7684\u3002</p> <p>\u4f46\u8bf4\u5230\u5e95\uff0c\u7cfb\u7edf\u8c03\u7528\u8fd8\u662f\u76f8\u5bf9\u5e95\u5c42\u7684\u8bbe\u8ba1\uff0c\u901a\u5e38\u7684\u5f00\u53d1\u5e76\u4e0d\u57fa\u4e8e\u5982\u6b64\u5e95\u5c42\u7684\u8bbe\u8ba1\u5c55\u5f00\u3002\u66f4\u5e38\u89c1\u7684\u662f\u5229\u7528\u5404\u79cd\u62bd\u8c61\u5c42\u7ea7\u66f4\u9ad8\u7684 Application Programming Interface, API \u8fdb\u884c\u5f00\u53d1\u3002</p> <p>API \u662f\u4e00\u4e2a\u975e\u5e38\u5e38\u89c1\u7684\u6982\u5ff5\uff0c\u5728\u6211\u770b\u6765\u7cfb\u7edf\u8c03\u7528\u672c\u8eab\u4e5f\u662f\u4e00\u79cd API\u3002API \u7684\u6838\u5fc3\u601d\u60f3\u662f\u8ba9\u8c03\u7528\u8005\u53ea\u9700\u8981\u77e5\u9053\u5982\u4f55\u4e0e\u88ab\u8c03\u7528\u8005\u4ea4\u6d41\u4ee5\u5b9e\u73b0\u76ee\u7684\uff0c\u800c\u4e0d\u9700\u8981\u5173\u5fc3\u5176\u5177\u4f53\u5b9e\u73b0\u3002\u8fd9\u540c\u65f6\u4e5f\u6697\u793a\u7740\uff0c\u53ea\u8981 API \u4e00\u81f4\uff0c\u540c\u6837\u7684\u7a0b\u5e8f\u5728\u4e0d\u540c\u7684\u5e73\u53f0\u4e0a\u4e5f\u80fd\u76f4\u63a5\u7f16\u8bd1\u540e\u8fd0\u884c\u3002</p> <p>\u663e\u7136\uff0cAPI \u4e0e\u7f16\u7a0b\u8bed\u8a00\u5f80\u5f80\u662f\u5f3a\u76f8\u5173\u7684\uff0c\u7279\u5b9a\u7f16\u7a0b\u8bed\u8a00\u5728\u64cd\u4f5c\u7cfb\u7edf\u4e0a\u8fd0\u884c\u4e5f\u662f\u9700\u8981\u4e00\u5b9a\u7684\u201c\u73af\u5883\u201d\u7684\uff0c\u4e5f\u5c31\u662f\u6211\u4eec\u6240\u8bf4\u7684\u8fd0\u884c\u65f6\u73af\u5883(run-time environment, RTE)\u3002RTE \u901a\u5e38\u5305\u62ec\u4e86\u7f16\u8bd1\u5668(compilers)\u3001\u89e3\u91ca\u5668(interpreters)\u3001\u5e93(libraries)\u548c\u88c5\u8f7d\u5668(loaders)\u7b49\uff0c\u5b83\u4eec\u5171\u540c\u7ec4\u6210\u4e86\u4e00\u4e2a\u5b8c\u6574\u7684\u8fd0\u884c\u65f6\u73af\u5883\u3002</p> \u76f8\u5173\u9605\u8bfb <ul> <li>ABI | Wiki</li> <li>Difference between API and ABI | StackOverflow</li> </ul> \u601d\u8003\u9898 \u9898\u9762\u89e3\u6790 <p>\u8fa8\u6790\u5e93\u51fd\u6570\u4e0e\u7cfb\u7edf\u8c03\u7528\uff1f</p> <p>\u5e93\u51fd\u6570\u8fd0\u884c\u5728\u7528\u6237\u7a7a\u95f4\u800c\u7cfb\u7edf\u8c03\u7528\u8fd0\u884c\u5728\u5185\u6838\u7a7a\u95f4\u3002\u5927\u90e8\u5206\u5e93\u51fd\u6570\u53ef\u80fd\u4f7f\u7528\u7cfb\u7edf\u8c03\u7528\u6765\u5b9e\u73b0\u76ee\u7684\u3002</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit0/#\u94fe\u63a5\u5668\u548c\u88c5\u8f7d\u5668","title":"\u94fe\u63a5\u5668\u548c\u88c5\u8f7d\u5668","text":"<p>  The role of the linker and loader. </p> <p>\u8bf4\u4e86\u8fd9\u4e48\u591a\uff0c\u90a3\u4e48\u64cd\u4f5c\u7cfb\u7edf\u5230\u5e95\u662f\u5982\u4f55\u6267\u884c\u4e00\u4e2a\u7a0b\u5e8f\u7684\u5462\uff1f\u4ee5 C \u4e3a\u4f8b\uff0c\u4e00\u4e2a\u5199\u5b8c\u7684\u4ee3\u7801\u9700\u8981\u7ecf\u8fc7\u7f16\u8bd1\u3001\u94fe\u63a5\u3001\u88c5\u8f7d\u4e09\u4e2a\u6b65\u9aa4\uff0c\u624d\u80fd\u6210\u4e3a\u4e00\u4e2a\u5728\u5185\u5b58\u4e2d\u7684\uff0c\u53ef\u4ee5\u88ab\u6267\u884c\u7684\u7a0b\u5e8f\u3002</p> <p>\u7b80\u5355\u6765\u8bf4\uff0c\u7f16\u8bd1\u5668\u9996\u5148\u5c06\u82e5\u5e72 <code>.c</code> \u6e90\u6587\u4ef6\u7f16\u8bd1\u4e3a\u82e5\u5e72 <code>.o</code> \u6587\u4ef6\uff08\u8fd9\u91cc\u5408\u5e76\u4e86\u9884\u5904\u7406\u3001\u7f16\u8bd1\u3001\u6c47\u7f16\u6b65\u9aa4\uff09\uff0c\u8fd9\u4e9b <code>.o</code> \u6587\u4ef6\u88ab\u79f0\u4e3a\u53ef\u91cd\u5b9a\u4f4d\u76ee\u6807\u6587\u4ef6(relocatable object file)\uff0c\u5176\u5b58\u5728\u5f62\u5f0f\u4e3a\u673a\u5668\u7801\uff1b\u968f\u540e\u94fe\u63a5\u5668\u5c06\u82e5\u5e72 <code>.o</code> \u6587\u4ef6\u8fde\u5e26\u6240\u9700\u8981\u7684\u4e00\u4e9b\u5e93\u6587\u4ef6\uff08\u5982 <code>.a</code> \u6587\u4ef6\uff09\u94fe\u63a5\u4e3a\u4e00\u4e2a\u53ef\u6267\u884c\u76ee\u6807\u6587\u4ef6(executable object file)\u3002</p> <p>\u7279\u522b\u7684\uff0c\u94fe\u63a5\u5206\u4e3a\u9759\u6001\u94fe\u63a5\u548c\u52a8\u6001\u94fe\u63a5\u4e24\u79cd\u3002\u9759\u6001\u94fe\u63a5\u5c06\u5e93\u6587\u4ef6\u7684\u4ee3\u7801\u76f4\u63a5\u5408\u5e76\u8fdb\u5165\u6700\u7ec8\u7684\u53ef\u6267\u884c\u6587\u4ef6\uff0c\u800c\u52a8\u6001\u94fe\u63a5\u4ec5\u4ec5\u5c06\u5e93\u6587\u4ef6\u7684\u5f15\u7528\u4fe1\u606f\u5199\u5165\u6700\u7ec8\u7684\u53ef\u6267\u884c\u6587\u4ef6\uff0c\u800c\u5728\u7a0b\u5e8f\u8fd0\u884c\u65f6\u518d\u53bb\u5bfb\u627e\u8fd9\u4e9b\u5e93\u6587\u4ef6\u3002</p> <pre><code>gcc -E main.c -o main.i # pre-process\ngcc -S main.i -o main.s # compile to assembly code\ngcc -c main.s -o main.o # assemble to object file\ngcc main.o -o main      # link\n./main                  # (load and) execute\n</code></pre> \u4e00\u4e9b\u64cd\u4f5c <ul> <li>\u4f7f\u7528 <code>gcc -static ...</code> \u6765\u6307\u5b9a\u4f7f\u7528\u9759\u6001\u94fe\u63a5\uff1b</li> <li>\u4f7f\u7528 <code>ldd &lt;file&gt;</code> \u6765\u67e5\u770b\u6587\u4ef6\u94fe\u63a5\u4e86\u54ea\u4e9b\u5e93\uff1b</li> </ul> <p>  \u53ef\u4ee5\u53d1\u73b0\uff0c\u52a8\u6001\u94fe\u63a5\u5f97\u5230\u7684\u53ef\u6267\u884c\u6587\u4ef6\u6bd4\u9759\u6001\u94fe\u63a5\u5f97\u5230\u7684\u53ef\u6267\u884c\u6587\u4ef6\u8981\u5c0f\u4e0d\u5c11\u3002</p> <ol> <li> <p>\u5e76\u53d1\u662f\u6307\u4e24\u4e2a\u6216\u591a\u4e2a\u4e8b\u4ef6\u5728\u540c\u4e00\u65f6\u95f4\u95f4\u9694\u5185\u53d1\u751f\uff0c\u800c\u5e76\u884c\u662f\u6307\u4e24\u4e2a\u6216\u591a\u4e2a\u4e8b\u4ef6\u5728\u540c\u4e00\u65f6\u523b\u53d1\u751f\u3002\u903b\u8f91\u4e0a\uff0c\u5e76\u884c\u662f\u5e76\u53d1\u7684\u5b50\u96c6\u3002\u00a0\u21a9</p> </li> </ol>"},{"location":"cour_note/D3QD_OperatingSystem/Unit1/","title":"Unit 1: \u8fdb\u7a0b\u7ba1\u7406 | Process Management","text":"<p> \u7ea6 6600 \u4e2a\u5b57  78 \u884c\u4ee3\u7801  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 23 \u5206\u949f</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit1/#\u8fdb\u7a0b","title":"\u8fdb\u7a0b","text":"<p>\u4e00\u6bb5\u672c\u8d28\u4e0a\u7a0b\u5e8f\u662f\u9759\u6001\u7684\u3001\u5b58\u50a8\u5728\u786c\u76d8\u4e0a\u7684\u6307\u4ee4\u6570\u636e\uff0c\u800c\u5f53\u5b83\u9644\u5e26\u8fd0\u884c\u7a0b\u5e8f\u6240\u9700\u8981\u7684\u5fc5\u8981\u4fe1\u606f\u8fdb\u5165\u5185\u5b58\uff0c\u5f97\u5230\u76f8\u5173\u8d44\u6e90\u540e\uff0c\u5b83\u6210\u4e3a\u4e00\u4e2a\u52a8\u6001\u7684\u3001\u4e0e\u8ba1\u7b97\u673a\u8d44\u6e90\u4e92\u52a8\u7684\u5b9e\u4f53\uff0c\u8fd9\u4e2a\u5b9e\u4f53\u5c31\u662f\u8fdb\u7a0b(process)\u3002</p> <p>\u8fdb\u7a0b\u662f\u662f\u64cd\u4f5c\u7cfb\u7edf\u8fdb\u884c\u8d44\u6e90\u5206\u914d\u548c\u8c03\u5ea6\u7684\u4e00\u4e2a\u72ec\u7acb\u5355\u4f4d\uff0c\u5b83\u4ee5\u7279\u5b9a\u5f62\u5f0f\u5b58\u5728\u4e8e\u5185\u5b58\u4e2d\uff0c\u5177\u6709\u4e00\u5b9a\u7684\u5c01\u95ed\u6027\uff0c\u662f\u591a\u9053\u6280\u672f\u7684\u91cd\u8981\u57fa\u7840\u3002</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit1/#\u8fdb\u7a0b\u7684\u5f62\u5f0f","title":"\u8fdb\u7a0b\u7684\u5f62\u5f0f","text":"<p>\u524d\u9762\u6211\u4eec\u63d0\u5230\uff0c\u8fdb\u7a0b\u52a8\u6001\u5730\u5b58\u5728\u4e8e\u5185\u5b58\u4e2d\uff0c\u56e0\u6b64\u9664\u4e86\u547d\u4ee4\u4ee5\u5916\uff0c\u8fd8\u5305\u62ec\u5176\u8fd0\u884c\u65f6\u7684\u52a8\u6001\u4fe1\u606f\u3002\u62bd\u8c61\u6765\u8bf4\uff0c\u4e3b\u8981\u5305\u542b\u8fd9\u4e09\u4e2a\u7ef4\u5ea6\uff1a\u2460 \u7528\u6765\u8dd1\u7684\u4ee3\u7801\uff1b\u2461 \u8dd1\u7684\u8fc7\u7a0b\u4e2d\uff0c\u4e0d\u65ad\u4f1a\u88ab\u66f4\u65b0\u7684\u6570\u636e\uff1b\u2462 \u7528\u6765\u7ef4\u62a4\u3001\u63a7\u5236\u8fdb\u7a0b\u7684\u63a7\u5236\u4fe1\u606f\u3002</p> <p>\u8fdb\u7a0b\u5728\u5185\u5b58\u4e2d\u5b58\u5728\u9700\u8981\u4e00\u5757\u865a\u62df\u7684\u5730\u5740\u7a7a\u95f4\u4ee5\u5b58\u50a8\u4e0a\u8ff0\u8fd9\u4e9b\u5185\u5bb9\u3002\u5176\u5305\u542b\u4e24\u4e2a\u90e8\u5206\uff0c\u5373\u865a\u62df\u5730\u5740\u7a7a\u95f4\u4e2d\u7684\u7528\u6237\u90e8\u5206\u548c\u865a\u62df\u5730\u5740\u7a7a\u95f4\u7684\u5185\u6838\u90e8\u5206\u3002</p> <p>\u4e0b\u56fe\u662f\u8fdb\u7a0b\u5728\u865a\u62df\u5730\u5740\u7a7a\u95f4\u4e2d\u7528\u6237\u90e8\u5206\u7684\u7ec4\u6210\uff1a</p> <p>\u7528\u6237\u90e8\u5206</p> <p> </p> <ul> <li>Text section:<ul> <li>\u5b58\u50a8\u4ee3\u7801\uff1b</li> </ul> </li> <li>Data section:<ul> <li>\u5b58\u50a8\u4ee3\u7801\u4e2d\u7684\u5168\u5c40\u53d8\u91cf\u3001\u9759\u6001\u53d8\u91cf\uff1b</li> </ul> </li> <li>Heap section:<ul> <li>\u5e38\u8bf4\u7684\u201c\u5806\u201d\uff0c\u88ab\u52a8\u6001\u5206\u914d\u7684\u5185\u5b58\uff1b</li> </ul> </li> <li>Stack section:<ul> <li>\u5e38\u8bf4\u7684\u201c\u6808\u201d\uff0c\u5b58\u50a8\u4e00\u4e9b\u6682\u65f6\u6027\u7684\u6570\u636e\uff0c\u5982\u51fd\u6570\u4f20\u53c2\u3001\u8fd4\u56de\u503c\u3001\u5c40\u90e8\u53d8\u91cf\u7b49\uff1b</li> </ul> </li> </ul> <p>\u53ef\u4ee5\u53d1\u73b0\uff0cText \u548c Data \u90e8\u5206\u6240\u9700\u8981\u7684\u7a7a\u95f4\u5728\u4e00\u5f00\u59cb\u5c31\u88ab\u786e\u5b9a\uff0c\u800c Heap \u548c Stack \u90fd\u53ef\u80fd\u52a8\u6001\u7684\u6269\u5c55\u548c\u6536\u7f29\u3002\u89c2\u5bdf\u53f3\u56fe\uff0cHeap \u548c Stack \u662f\u76f8\u5411\u6269\u5c55\u7684\uff0c\u4e8e\u662f\u6574\u4e00\u5757\u7684\u5927\u5c0f\u80fd\u591f\u56fa\u5b9a\u4e0b\u6765\uff0c\u800c\u5728\u5185\u90e8\u8fdb\u884c\u6709\u9650\u5236\u7684\u52a8\u6001\u5206\u914d\u3002\u5f53\u7136\uff0cHeap \u548c Stack \u7684\u533a\u57df\u5e76\u4e0d\u4f1a\u4ea4\u53c9\u3002</p> memory layout of a C program <p></p> <p>\u4e4b\u6240\u4ee5\u628a\u6709\u521d\u59cb\u503c\u7684\u9759\u6001\u53d8\u91cf\u548c\u6ca1\u521d\u59cb\u503c\u7684\u9759\u6001\u53d8\u91cf\u5206\u5f00\u6765\uff0c\u662f\u56e0\u4e3a\u6211\u4eec\u53ef\u4ee5\u5728\u4e00\u5f00\u59cb\u53ea\u5b58\u50a8\u6ca1\u521d\u59cb\u503c\u7684\u9759\u6001\u53d8\u91cf\u7684\u5927\u5c0f\uff0c\u800c\u5728\u771f\u6b63\u7b2c\u4e00\u6b21\u8bbf\u95ee\u7684\u65f6\u5019\u624d\u5206\u914d\u5185\u5b58\uff0c\u4ee5\u6b64\u6765\u5b9e\u73b0\u51cf\u5c11\u5185\u5b58\u5360\u7528\u3002</p> <p>\u901a\u5e38\u6765\u8bf4\uff0c\u672a\u521d\u59cb\u5316\u7684\u9759\u6001\u53d8\u91cf\u4e00\u822c\u90fd\u88ab\u653e\u5728 <code>.bss</code> \u6bb5\uff0c\u800c\u5728\u88ab\u521d\u59cb\u5316\u7684\u65f6\u5019\u79fb\u52a8\u5230 <code>.data</code> \u6bb5\u30021</p> <p>\u800c\u653e\u5728\u5185\u6838\u90e8\u5206\u7684\u5185\u5bb9\uff0c\u5219\u66f4\u4fa7\u91cd\u4e8e\u8fdb\u7a0b\u7684\u63a7\u5236\u4fe1\u606f\uff0c\u5177\u4f53\u6765\u8bf4\u5c31\u662f\u8fdb\u7a0b\u63a7\u5236\u5757(Process Control Block, PCB)\u3002</p> <p>\u5185\u6838\u90e8\u5206</p> <p>\u8fdb\u7a0b\u63a7\u5236\u5757(Process Control Block, PCB)\u662f\u64cd\u4f5c\u7cfb\u7edf\u4e2d\u7528\u6765\u63cf\u8ff0\u8fdb\u7a0b\u7684\u4e00\u79cd\u6570\u636e\u7ed3\u6784\uff0c\u5b83\u5305\u542b\u4e86\u8fdb\u7a0b\u7684\u6240\u6709\u4fe1\u606f\uff0c\u662f\u64cd\u4f5c\u7cfb\u7edf\u4e2d\u6700\u91cd\u8981\u7684\u6570\u636e\u7ed3\u6784\u4e4b\u4e00\u3002\u53ef\u4ee5\u8bf4\uff0cPCB \u662f\u8fdb\u7a0b\u5b58\u5728\u7684\u552f\u4e00\u6807\u5fd7\u3002</p> <p>\u901a\u5e38\u6765\u8bf4\uff0cPCB \u53ef\u80fd\u5305\u542b\u8fd9\u4e9b\u5185\u5bb9\uff1a</p> <p> </p> <ul> <li>Process state:<ul> <li>\u8fdb\u7a0b\u7684\u72b6\u6001\uff1b</li> </ul> </li> <li>Program counter:<ul> <li>\u6807\u8bc6\u8be5\u8fdb\u7a0b\u8dd1\u5230\u4e86\u54ea\u91cc\uff0c\u7531\u4e8e\u8fdb\u7a0b\u662f\u52a8\u6001\u7684\uff0c\u6bcf\u4e00\u88ab\u5207\u6362\u90fd\u9700\u8981\u4fdd\u8bc1\u4e0b\u4e00\u6b21\u80fd\u65e0\u7f1d\u8854\u63a5\u4e4b\u524d\u7684\u8fdb\u5ea6\uff0c\u6240\u4ee5\u9700\u8981\u5b58\u50a8\u6bcf\u6b21\u7684\u5de5\u4f5c\u72b6\u6001\uff1b</li> </ul> </li> <li>CPU registers:<ul> <li>\u4fdd\u5b58\u8fdb\u7a0b\u76f8\u5173\u7684\u5bc4\u5b58\u5668\u4fe1\u606f\uff1b</li> </ul> </li> <li>CPU-scheduling information:<ul> <li>CPU \u8c03\u5ea6\u53c2\u8003\u7684\u4fe1\u606f\uff0c\u5305\u62ec\u4f18\u5148\u7ea7\u3001\u8c03\u5ea6\u961f\u5217\u7684\u6307\u9488\u3001\u8c03\u5ea6\u53c2\u6570\u7b49\uff1b</li> </ul> </li> <li>Memory-management information:<ul> <li>\u5305\u62ec\u9875\u8868\u3001\u6bb5\u8868\u7b49\u4fe1\u606f\uff0c\u5177\u4f53\u4e0e\u5b9e\u73b0\u7684\u5185\u5b58\u7cfb\u7edf\u6709\u5173\uff1b</li> </ul> </li> <li>Accounting information\uff1a<ul> <li>\u4e00\u4e9b\u5173\u4e8e\u8fdb\u7a0b\u7684\u52a8\u6001\u6570\u636e\u7684\u7edf\u8ba1\u548c\u8bb0\u5f55\uff0c\u6bd4\u5982\u603b\u5171\u5df2\u7ecf\u8dd1\u4e86\u591a\u4e45\u3001\u65f6\u95f4\u9650\u5236\u3001\u8fdb\u7a0b\u53f7\u7b49\uff1b</li> </ul> </li> <li>I/O status information:<ul> <li>\u88ab\u5206\u914d\u7ed9\u8fdb\u7a0b\u7684 I/O \u8bbe\u5907\u5217\u8868\u3001\u6253\u5f00\u7684\u6587\u4ef6\u5217\u8868\u7b49\uff1b</li> </ul> </li> </ul> <p>\u4e24\u4e2a\u90e8\u5206\u5728\u903b\u8f91\u4e0a\u7684\u5173\u7cfb\u662f\uff0c\u7528\u6237\u90e8\u5206\u5212\u5206\u5e76\u5b9e\u9645\u5b58\u50a8\u8fdb\u7a0b\u6240\u9700\u8981\u7684\u6570\u636e\u8d44\u6e90\uff08\u5305\u62ec\u7a0b\u5e8f\u8fd0\u884c\u7684\u4ee3\u7801\uff09\uff0c\u800c\u5185\u6838\u90e8\u5206\u5b58\u50a8\u8fdb\u7a0b\u7684\u5143\u6570\u636e\uff0c\u5305\u62ec\u63a7\u5236\u4fe1\u606f\u4e0e\u7528\u6237\u90e8\u5206\u4e2d\u5404\u4e2a\u90e8\u5206\u5185\u5b58\u7684\u5206\u914d\u548c\u4f7f\u7528\u60c5\u51b5\u3002</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit1/#\u8fdb\u7a0b\u7684\u72b6\u6001","title":"\u8fdb\u7a0b\u7684\u72b6\u6001","text":"<p>\u5728\u5355\u673a\u8bed\u5883\u4e0b\uff0c\u8fdb\u7a0b\u8c03\u5ea6\u4e00\u4e2a\u6bd4\u8f83\u6838\u5fc3\u7684\u90e8\u5206\u5c31\u662f\u5c06 CPU \u8d44\u6e90\u7ed9\u54ea\u4e2a\u4efb\u52a1\u7528\u3002\u800c\u5e76\u4e0d\u662f\u4efb\u4f55\u8fdb\u7a0b\u5728\u4efb\u4f55\u65f6\u523b\u90fd\u53ef\u4ee5\u76f4\u63a5\u83b7\u5f97 CPU \u8d44\u6e90\u5e76\u76f4\u63a5\u5f00\u59cb\u4f7f\u7528\u7684\uff0c\u56e0\u6b64\u6211\u4eec\u9700\u8981\u5bf9\u8fdb\u7a0b\u7684\u72b6\u6001\u8fdb\u884c\u5efa\u6a21\u3002</p> <p> </p> <ul> <li><code>new</code>:<ul> <li>\u8fdb\u7a0b\u6b63\u5728\u521b\u5efa\u8fc7\u7a0b\u4e2d\uff0c\u5305\u62ec\u7533\u8bf7 PCB\uff0c\u5206\u914d\u521d\u59cb\u8d44\u6e90\u7b49\uff1b</li> </ul> </li> <li><code>running</code>:<ul> <li>\u8fdb\u7a0b\u6b63\u5728\u8fd0\u884c\uff0c\u5373\u6b63\u5728\u4f7f\u7528 CPU \u8d44\u6e90\uff1b</li> <li>\u6709\u51e0\u4e2a\u6838\u5c31\u6700\u591a\u6709\u51e0\u4e2a\u8fdb\u7a0b\u5904\u4e8e <code>running</code> \u72b6\u6001\uff1b</li> </ul> </li> <li><code>ready</code>:<ul> <li>\u8fdb\u7a0b\u5df2\u7ecf\u51c6\u5907\u597d\u4e86\uff0c\u53ea\u5dee CPU \u8d44\u6e90\uff0c\u4e00\u65e6\u6709 CPU \u8d44\u6e90\u5f85\u5206\u914d\uff0c\u5c31\u4f1a\u6709\u5c31\u7eea\u6001\u7684\u8fdb\u7a0b\u53d8\u4e3a\u8fd0\u884c\u6001\uff1b</li> <li>\u5982\u679c\u6709\u8fdb\u7a0b\u5904\u4e8e\u5c31\u7eea\u6001\uff0c\u5c31\u4e00\u5b9a\u6709\u8fdb\u7a0b\u5904\u4e8e\u8fd0\u884c\u6001\uff1b</li> <li>CPU \u8c03\u5ea6\u5b9e\u9645\u4e0a\u6307\u7684\u5c31\u662f\u82e5\u5e72\u8fdb\u7a0b\u5728\u5c31\u7eea\u6001\u548c\u8fd0\u884c\u6001\u4e4b\u95f4\u7684\u5207\u6362\uff1b</li> </ul> </li> <li><code>waiting</code>:<ul> <li>\u8fdb\u7a0b\u6b63\u5728\u7b49\u5f85\u67d0\u4e2a\u4e8b\u4ef6\u7684\u53d1\u751f\uff0c\u6bd4\u5982\u7b49\u5f85 I/O \u5b8c\u6210\u3001\u7b49\u5f85\u67d0\u4e2a\u4fe1\u53f7\u91cf\u7b49\uff1b</li> <li>\u6b64\u65f6\u5373\u4f7f\u6709\u7a7a\u4f59\u7684 CPU \u8d44\u6e90\uff0c\u8be5\u8fdb\u7a0b\u4e5f\u65e0\u6cd5\u7ee7\u7eed\uff1b</li> <li>\u4e00\u822c\u8fdb\u7a0b\u4ece\u8fd0\u884c\u6001\u8fdb\u5165\u963b\u585e\u6001\u662f\u4e3b\u52a8\u7684\uff0c\u79bb\u5f00\u963b\u585e\u6001\u8fdb\u5165\u5c31\u7eea\u6001\u662f\u88ab\u52a8\u7684\uff1b</li> </ul> </li> <li><code>terminated</code>:<ul> <li>\u8fdb\u7a0b\u56e0\u4e3a\u67d0\u4e9b\u539f\u56e0\u7ec8\u6b62\uff0c\u7ed3\u675f\u8fd0\u884c\uff0c\u9700\u8981\u91ca\u653e\u8d44\u6e90\uff1b</li> </ul> </li> </ul> <p>\u8fdb\u7a0b\u5728\u5c31\u7eea\u6001\u9700\u8981\u7b49\u5f85 CPU \u8d44\u6e90\u7684\u6d3e\u53d1(dispatch)\uff0c\u63a5\u53d7\u8c03\u5ea6\uff1b\u5728\u963b\u585e\u6001\u9700\u8981\u7b49\u5f85\u5bf9\u5e94\u7684 I/O \u5b8c\u6210\u6216\u4e8b\u4ef6\u5b8c\u6210\uff0c\u56e0\u800c\u5b58\u5728\u4e00\u79cd\u7ed3\u6784\u9700\u8981\u53bb\u7ef4\u62a4\u8fd9\u4e9b\u201c\u76f8\u5bf9\u9759\u6b62\u201d\u7684\u8fdb\u7a0b\u3002\u901a\u5e38\u4f7f\u7528\u5c31\u7eea\u961f\u5217(ready queue)\u548c\u7b49\u5f85\u961f\u5217(wait queue)\u6765\u5b9e\u73b0\uff0c\u5176\u57fa\u672c\u7ed3\u6784\u5982\u4e0b\uff1a</p> <p></p> <p>\u5b9e\u9645\u5b9e\u73b0\u4e2d\uff0c\u7531\u4e8e\u7b49\u5f85\u7684 I/O \u6216\u4e8b\u4ef6\u4e0d\u540c\uff0c\u53ef\u80fd\u7ef4\u62a4\u591a\u4e2a\u7b49\u5f85\u961f\u5217\uff0c\u4e8e\u662f\u5b9e\u9645\u8fc7\u7a0b\u4e2d\u7684\u60c5\u51b5\u53ef\u80fd\u5982\u4e0b\uff1a</p> <p></p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit1/#\u8fdb\u7a0b\u7ba1\u7406","title":"\u8fdb\u7a0b\u7ba1\u7406","text":"<p>\u73b0\u5728\u6211\u4eec\u5df2\u7ecf\u8ba8\u8bba\u4e86\u8fdb\u7a0b\u7684\u5f62\u5f0f\u548c\u4e00\u4e2a\u4e2a\u79bb\u6563\u7684\u72b6\u6001\uff0c\u73b0\u5728\u6211\u4eec\u6765\u8bb2\u8bb2\u8fdb\u7a0b\u5728\u51e0\u4e2a\u9636\u6bb5\u7684\u52a8\u6001\u8fc7\u7a0b\u3002</p> <p>\u7528\u6237\u8fdb\u7a0b\u5728\u64cd\u4f5c\u7cfb\u7edf\u4e2d\uff0c\u603b\u4f53\u4e0a\u6765\u8bb2\u9075\u5faa\u4e00\u4e2a\u6811\u72b6\u7684\u7ec4\u7ec7\u5f62\u5f0f\uff0c\u6bcf\u4e00\u4e2a\u8fdb\u7a0b\u90fd\u6709\u4e00\u4e2a\u552f\u4e00\u6807\u8bc6\u7b26\u8fdb\u7a0b\u53f7\uff08\u901a\u5e38\u88ab\u79f0\u4e3a pid\uff0c\u4f46\u5728\u7279\u5b9a\u8bed\u5883\u4e0b\u53ef\u80fd\u6709\u4e0d\u540c\u7684\u542b\u4e49\uff09\u3002\u5982\u4e0b\u56fe\u662f Linux \u7684\u4e00\u4e2a\u8fdb\u7a0b\u6811\u3002</p> <p></p> <p>\u4f60\u4e5f\u53ef\u4ee5\u5728 Linux \u4e2d\u4f7f\u7528 <code>pstree</code> \u6765\u67e5\u770b\u8fdb\u7a0b\u6811\u3002 \u8a00\u4e0b\u4e4b\u610f\u5c31\u662f\u8fdb\u7a0b\u4e4b\u95f4\u5b58\u5728\u4e00\u79cd\u7236\u5b50\u5173\u7cfb\uff0c\u5373 child \u8fdb\u7a0b\u662f\u7531 parent \u8fdb\u7a0b\u521b\u5efa\u7684\uff0c\u56e0\u6b64\u8fdb\u7a0b\u9664\u4e86\u81ea\u5df1\u7684 <code>pid</code> \u8fd8\u6709 <code>ppid</code> \u6765\u6807\u8bc6\u5b83\u7684 parent \u8fdb\u7a0b\u3002</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit1/#\u8fdb\u7a0b\u7684\u521b\u5efa","title":"\u8fdb\u7a0b\u7684\u521b\u5efa","text":"<p>child \u8fdb\u7a0b\u7684\u8d44\u6e90\u53ef\u80fd\u76f4\u63a5\u6765\u81ea\u64cd\u4f5c\u7cfb\u7edf\u7684\u5206\u914d\uff0c\u4e5f\u53ef\u80fd\u6765\u81ea parent \u8fdb\u7a0b\u7684\u5206\u914d\uff0c\u9650\u5236\u4f7f\u7528\u540e\u8005\u7684\u597d\u5904\u662f\u80fd\u591f\u907f\u514d\u56e0\u4e3a\u521b\u5efa\u592a\u591a\u5b50\u8fdb\u7a0b\u800c\u5bfc\u81f4\u8d44\u6e90\u4e0d\u591f\u7528\u3002\u7279\u522b\u7684\uff0c\u6211\u4eec\u89c2\u5bdf\u5230\u8fd9\u68f5\u6811\u7684\u6839\u662f <code>systemd</code>\uff0c\u5386\u53f2\u4e0a\u4e5f\u66fe\u53eb\u8fc7 <code>init</code>\uff0c\u5b83\u662f\u64cd\u4f5c\u7cfb\u7edf\u542f\u52a8\u540e\u8fd0\u884c\u7684\u7b2c\u4e00\u4e2a\u7528\u6237\u8fdb\u7a0b\uff0c\u81f3\u5c11\u5728 Linux \u4e2d\uff0c\u5b83\u7684 <code>pid</code> \u88ab\u5206\u914d\u4e3a 1\uff0c\u800c\u5b83\u7684 <code>ppid</code> \u662f 0\uff0c\u53ef\u4ee5\u7406\u89e3\u4e3a\u8fd9\u4e2a\u8fdb\u7a0b\u7684 parent \u662f scheduler \u800c\u975e\u4e00\u4e2a\u8fdb\u7a0b2\u3002</p> <p>\u5728 Linux \u4e2d\uff0c\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528 <code>fork</code> \u6765\u521b\u5efa\u4e00\u4e2a child \u8fdb\u7a0b\uff0c\u5728\u8fd9\u91cc\u5148\u5f15\u5165\u5982\u4f55\u5b9e\u73b0\u662f\u4e3a\u4e86\u5f15\u5165\u4e00\u4e2a\u53ef\u4ee5\u501f\u6765\u63cf\u8ff0\u8fc7\u7a0b\u7684\u8bed\u8a00\uff0c\u6211\u4eec\u4ee5\u4e0b\u9762\u7684 C \u7a0b\u5e8f\u4e3a\u4f8b\u5c55\u5f00\u4e4b\u540e\u7684\u8ba8\u8bba\u3002</p> <pre><code>#include &lt;stdio.h&gt;\n#include &lt;unistd.h&gt;\n#include &lt;sys/wait.h&gt;\n#include &lt;sys/types.h&gt;\n\nint main() {\nprintf(\"A process starts!\\n\");\n\npid_t pid;\npid = fork();\nif (pid &lt; 0) {\nprintf(\"Fork failed!\\n\");\n} else if (pid == 0) {\n// sleep(1);\nprintf(\"pid is zero, so it's child process!\\n\");\n} else {\n// wait(NULL);\n// sleep(1);\nprintf(\"pid is nonzero thus it's parent process!\\n\");\n}\n}\n</code></pre> <p>\u7b2c 10 \u884c\u9ad8\u4eae\u7684 <code>fork()</code> \u8bed\u53e5\u521b\u5efa\u4e86\u4e00\u4e2a\u8fdb\u7a0b\uff0c\u8be5\u8fdb\u7a0b\u53ea\u6709\u8fdb\u7a0b\u53f7\u4e0e parent \u8fdb\u7a0b\u4e0d\u4e00\u6837\uff0c\u540c\u65f6\u901a\u8fc7\u68c0\u67e5\u8fd4\u56de\u503c <code>pid</code> \u6765\u5224\u65ad\u5c5e\u4e8e parent \u8fd8\u662f child\u3002</p> <p>\u5982\u679c\u7b2c 18 \u884c\u4ecd\u7136\u88ab\u6ce8\u91ca\uff0c\u90a3\u4e48 parent \u8fdb\u7a0b\u8bf6 child \u8fdb\u7a0b\u5c06\u5e76\u53d1\u6267\u884c\uff0c\u5373\u5b8c\u6210 <code>fork()</code> \u540e\u4e24\u4e2a\u8fdb\u7a0b\u90fd\u4ece 11 \u884c\u5f00\u59cb\u7ee7\u7eed\u5411\u4e0b\u5e76\u53d1\u7684\u6267\u884c\uff0c\u4e92\u4e0d\u963b\u585e\uff1b\u5982\u679c 18 \u884c\u7684\u6ce8\u91ca\u88ab\u53d6\u6d88\uff0c\u90a3\u4e48 parent \u8fdb\u7a0b\u5c06\u7b49\u5f85 child \u8fdb\u7a0b\u7ed3\u675f\u540e\u518d\u7ee7\u7eed\u3002\u8bfb\u8005\u53ef\u4ee5\u5c1d\u8bd5\u6392\u5217\u7ec4\u5408\u4e24\u4e2a\u6ce8\u91ca\u6765\u89c2\u5bdf\u7a0b\u5e8f\u8fd0\u884c\u7684\u7ed3\u679c\u4f1a\u5982\u4f55\u53d8\u5316\u3002</p> <p>\u903b\u8f91\u4e0a\u521b\u5efa\u7684\u65b0\u8fdb\u7a0b\u6709\u4e24\u79cd\u60c5\u51b5\uff1a</p> <ol> <li>\u590d\u5236 parent \u8fdb\u7a0b\u7684\u4ee3\u7801\u6570\u636e\uff1b</li> <li>\u8f7d\u5165\u65b0\u7684\u7a0b\u5e8f\u5e76\u7ee7\u7eed\u6267\u884c\uff1b</li> </ol> <p>\u800c\u5b9e\u9645\u5728 Linux \u4e2d\uff0c\u7b2c\u4e00\u79cd\u901a\u8fc7 <code>fork()</code> \u5b9e\u73b0\uff0c\u7b2c\u4e8c\u79cd\u901a\u8fc7 <code>fork()</code> \u540e <code>execXX()</code> \u5b9e\u73b0\uff0c<code>execXX()</code> \u4f1a\u8986\u76d6\u90a3\u4e2a\u8fdb\u7a0b\u7684\u5730\u5740\u7a7a\u95f4\uff0c\u4ee5\u5b9e\u73b0\u6267\u884c\u5176\u4ed6\u7a0b\u5e8f\u30023 4</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit1/#\u8fdb\u7a0b\u7684\u7ec8\u6b62","title":"\u8fdb\u7a0b\u7684\u7ec8\u6b62","text":"<p>\u5f53\u8fdb\u7a0b\u8c03\u7528 <code>exit()</code> \u8fd9\u4e2a\u7cfb\u7edf\u8c03\u7528\u65f6\uff0c\u8fd9\u4e2a\u8fdb\u7a0b\u5c06\u88ab\u7ec8\u6b62\uff0c\u8fd9\u610f\u5473\u7740\u8fd9\u4e2a\u8fdb\u7a0b\u5c06\u4e0d\u518d\u6267\u884c\uff0c\u5176\u8d44\u6e90\u5c06\u88ab\u91ca\u653e\uff0c\u540c\u65f6\u2014\u2014\u8fd4\u56de\u72b6\u6001\u503c\uff0c\u800c\u8fd9\u4e2a\u72b6\u6001\u503c\u5c06\u88ab parent \u8fdb\u7a0b\u7684 <code>wait()</code> \u63a5\u6536\u3002\u7279\u522b\u7684\uff0c\u5982\u679c parent \u8fdb\u7a0b\u5c1a\u672a\u8c03\u7528 <code>wait()</code>\uff0c\u5219\u8fd9\u4e2a child \u8fdb\u7a0b\u8fd8\u4e0d\u4f1a\u5b8c\u5168\u6d88\u5931\uff0c\u56e0\u4e3a\u8981\u8fd4\u56de\u7684\u4e1c\u897f\u8fd8\u6ca1\u8fd4\u56de\uff0c\u8fd9\u79cd\u903b\u8f91\u4e0a\u5df2\u7ecf\u7ec8\u6b62\uff0c\u4f46\u4ecd\u7136\u5360\u6709\u4e00\u90e8\u5206\u8d44\u6e90\uff0c\u7b49\u5f85 parent \u8fdb\u7a0b\u8c03\u7528 <code>wait()</code> \u7684\u8fdb\u7a0b\uff0c\u6211\u4eec\u79f0\u4e4b\u4e3a\u50f5\u5c38\u8fdb\u7a0b(zombie)\u3002\u4e00\u4e2a\u8fdb\u7a0b\u53d8\u6210\u50f5\u5c38\u8fdb\u7a0b\u662f\u5f88\u666e\u901a\u7684\uff0c\u5173\u952e\u5728\u4e8e\uff0c\u5982\u679c parent \u8fdb\u7a0b\u4e0d\u8c03\u7528 <code>wait()</code>\uff0c\u90a3\u7b49 parent \u7ec8\u6b62\u540e\uff0c\u8fd9\u4e2a\u50f5\u5c38\u8fdb\u7a0b\u53ef\u80fd\u4ecd\u7136\u4e00\u76f4\u5b58\u5728\uff0c\u6b64\u65f6\u8fd9\u4e2a\u50f5\u5c38\u8fdb\u7a0b\u540c\u65f6\u662f\u4e00\u4e2a\u5b64\u513f\u8fdb\u7a0b(orphan)\u2014\u2014\u5373\u6ca1\u6709 parent \u8fdb\u7a0b\u7684\u8fdb\u7a0b\uff0c\u8fd9\u663e\u7136\u662f\u4e0d\u5408\u7406\u7684\uff0cUNIX \u7684\u89e3\u51b3\u529e\u6cd5\u662f\uff0c\u8ba9\u6240\u6709\u5b64\u513f\u8fdb\u7a0b\u90fd\u6210\u4e3a <code>init</code>/<code>systemd</code> \u7684 child \u8fdb\u7a0b\uff0c\u7531 <code>init</code>/<code>systemd</code> \u6765 <code>wait()</code> \u5b83\u4eec\u3002</p> <p>\u5728\u67d0\u4e9b\u7cfb\u7edf\u91cc\uff0c\u64cd\u4f5c\u7cfb\u7edf\u901a\u8fc7\u7ea7\u8054\u7ec8\u6b62(cascading termination)\u6765\u907f\u514d\u5b64\u513f\u8fdb\u7a0b\u7684\u51fa\u73b0\uff0c\u5373\u5f53\u4e00\u4e2a\u8fdb\u7a0b\u88ab\u7ec8\u6b62\u65f6\uff0c\u5b83\u7684 child \u4e5f\u5e94\u5f53\u88ab\u9012\u5f52\u5730\u7ec8\u6b62\u3002</p> daemon <p>\u5b88\u62a4\u8fdb\u7a0b\u662f\u4e00\u79cd\u7279\u6b8a\u7684\u8fdb\u7a0b\uff0c\u5b83\u4eec\u5728\u201c\u540e\u53f0\u201d\u957f\u671f\u8fd0\u884c\uff0c\u4f8b\u5982\u67d0\u4e9b\u6570\u636e\u5e93\u670d\u52a1\u3001\u53cd\u4ee3\u7406\u670d\u52a1\u7b49\uff0c\u800c\u975e\u50cf\u666e\u901a\u7684\u7528\u6237\u7a0b\u5e8f\u4e00\u6837\u4f9d\u8d56\u4e8e\u7528\u6237\u4ea4\u4e92\u3002</p> <p>\u4e3a\u4e86\u5b9e\u73b0\u201c\u957f\u671f\u8fd0\u884c\u201d\uff0c\u6211\u4eec\u9700\u8981\u8ba9\u5b83\u4ee5 <code>init</code>/<code>systemd</code> \u4e3a parent\uff0c\u56e0\u4e3a\u4efb\u4f55\u5176\u5b83\u8fdb\u7a0b\u90fd\u6709\u53ef\u80fd\u5728\u64cd\u4f5c\u7cfb\u7edf\u8fd0\u884c\u7684\u65f6\u5019\u7ec8\u6b62\u3002</p> <p>\u90a3\u4e48\u4e00\u79cd\u529e\u6cd5\u5c31\u662f\u6211\u4eec\u9012\u5f52\u5730 <code>fork()</code> \u4e24\u6b21\uff0c\u7136\u540e\u7ec8\u6b62\u7b2c\u4e00\u4e2a\u8fdb\u7a0b\uff0c\u5373\u7ec8\u6b62\u7b2c\u4e8c\u4e2a\u8fdb\u7a0b\u7684 parent\uff0c\u8fd9\u6837\u5b83\u5c31\u80fd\u6210\u4e3a\u4e00\u4e2a\u5b64\u513f\u8fdb\u7a0b\uff0c\u8fdb\u800c\u88ab <code>init</code>/<code>systemd</code> \u63a5\u7ba1\u3002</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit1/#\u8fdb\u7a0b\u95f4\u901a\u4fe1","title":"\u8fdb\u7a0b\u95f4\u901a\u4fe1","text":"<p>\u5982\u679c\u4e00\u4e2a\u8fdb\u7a0b\u53d7\u5230\u5176\u5b83\u8fdb\u7a0b\u7684\u5f71\u54cd\uff0c\u6216\u4f1a\u5f71\u54cd\u5176\u5b83\u8fdb\u7a0b\uff0c\u90a3\u4e48\u6211\u4eec\u79f0\u4e4b\u4e3a\u534f\u4f5c\u8fdb\u7a0b(cooperation process)\uff0c\u800c\u8fdb\u7a0b\u95f4\u901a\u4fe1(Inter-Process Communication, IPC)\u652f\u6301\u4e86\u8fdb\u7a0b\u534f\u4f5c\uff0c\u4ee5\u5b9e\u73b0\u8fdb\u7a0b\u95f4\u7684\u6570\u636e\u4ea4\u6362\u3002</p> <ul> <li>\u4fe1\u53f7\u91cf(semaphores)\uff1b</li> <li>\u5171\u4eab\u5185\u5b58(shared memory)\uff1a<ul> <li>\u66f4\u5feb\uff0c\u9700\u8981\u7528\u5230 sys call \u7684\u5730\u65b9\u53ea\u6709\u5efa\u7acb\u5171\u4eab\u5185\u5b58\u7684\u65f6\u5019\u7528\u7684\u5230\u3002</li> </ul> </li> <li>\u6d88\u606f\u4f20\u9012(message passing)\uff1a<ul> <li>\u5728\u5206\u5e03\u5f0f\u7cfb\u7edf\u4e2d\u66f4\u5bb9\u6613\u5b9e\u73b0\uff0c\u5bf9\u4e8e\u5c11\u91cf\u6570\u636e\u901a\u4fe1\u5f88\u6709\u7528\uff08\u56e0\u4e3a\u4e0d\u9700\u8981\u5904\u7406\u51b2\u7a81\u95ee\u9898\uff09\u3002</li> </ul> </li> <li>\u6587\u4ef6 / \u7ba1\u9053(pipe)\uff1a<ul> <li>\u7ba1\u9053\u672c\u8d28\u4e0a\u4e5f\u662f\u4e00\u79cd\u6587\u4ef6\uff0c\u4f46\u4e00\u4e2a\u7ba1\u9053\u53ea\u652f\u6301\u5355\u5411\u4f20\u8f93\uff0c\u5373\u53ea\u80fd A \u5199 B \u8bfb\uff0c\u5982\u679c\u8981\u5b9e\u73b0\u53cc\u5411\u9700\u8981\u4e24\u4e2a\u7ba1\u9053\u3002</li> </ul> </li> </ul> <p> Communications models. (a) Shared memory. (b) Message passing.</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit1/#\u8fdb\u7a0b\u8c03\u5ea6","title":"\u8fdb\u7a0b\u8c03\u5ea6","text":"<p>\u591a\u9053\u6280\u672f\u5f15\u5165\u540e\uff0c\u5185\u5b58\u4e2d\u540c\u65f6\u5b58\u5728\u591a\u4e2a\u8fdb\u7a0b\uff0c\u8fdb\u7a0b\u7684\u6570\u91cf\u6211\u4eec\u79f0\u4e4b\u4e3a\u591a\u9053\u7684\u5ea6(degree of multiprogramming)\u3002\u4e00\u6bb5\u65f6\u95f4\u5185\u82e5\u5e72\u8fdb\u7a0b\u5e76\u53d1\u6267\u884c\uff0c\u56e0\u6b64\u8c03\u5ea6\u95ee\u9898(scheduling)\u2014\u2014CPU scheduler \u5c06\u51b3\u5b9a\u5728\u4f55\u65f6\u5c06 CPU \u8d44\u6e90\u5206\u914d\u7ed9\u54ea\u4e00\u4e2a\u5c31\u7eea\u8fdb\u7a0b\uff0c\u4f7f\u4e4b\u8fdb\u5165\u8fd0\u884c\u6001\u2014\u2014\u8fd9\u4e2a\u95ee\u9898\u5c31\u5f88\u91cd\u8981\u4e86\u3002\u603b\u4f53\u6765\u8bb2\uff0c\u6211\u4eec\u9700\u8981\u5b9e\u73b0\u4e00\u4e2a\u9ad8\u6548\u3001\u516c\u5e73\u7684\u7684\u8c03\u5ea6\uff0c\u4ee5\u6b64\u4fdd\u8bc1 CPU \u5229\u7528\u7387\u8db3\u591f\u9ad8\uff0c\u540c\u65f6\u53c8\u4fdd\u8bc1\u8ba1\u7b97\u673a\u529f\u80fd\u6b63\u5e38\u8fd0\u4f5c\u3002</p> <p> Diagram of process state.</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit1/#\u8c03\u5ea6\u7684\u65f6\u673a","title":"\u8c03\u5ea6\u7684\u65f6\u673a","text":"<p>\u6211\u4eec\u518d\u6b21\u5ba1\u89c6\u8fdb\u7a0b\u72b6\u6001\u7684 FSM\uff0c\u53d1\u73b0\u6240\u6709\u72b6\u6001\u90fd\u662f\u56f4\u7ed5\u7740 <code>ready</code>/<code>running</code> \u5c55\u5f00\u7684\uff0c\u800c CPU \u5177\u4f53\u8d44\u6e90\u5206\u914d\u7684\u8fc7\u7a0b\u4e5f\u6b63\u662f\u901a\u8fc7\u8fd9\u4e24\u4e2a\u72b6\u6001\u7684\u8f6c\u5316\u4f53\u73b0\u7684\u3002\u800c \u2776 \u5f53\u8fd0\u884c\u6001\u7684\u8fdb\u7a0b\u7531\u4e8e\u67d0\u4e9b\u539f\u56e0\u9700\u8981\u4e3b\u52a8\u79bb\u5f00\u8fd0\u884c\u6001\u65f6\uff0c\u6216 \u2777 \u5f53\u5c31\u7eea\u6001\u7684\u67d0\u4e2a\u8fdb\u7a0b\u9700\u8981\u7acb\u523b\u5f97\u5230 CPU \u8d44\u6e90\u65f6\uff0cscheduler \u4f1a\u8fdb\u884c\u8c03\u5ea6\u3002\u4e0a\u9762\u8fd9\u53e5\u8bdd\u53cd\u5e94\u5728\u3000FSM \u4e0a\uff0c\u5c31\u662f \u2776 \u8fdb\u7a0b\u4ece\u8fd0\u884c\u6001\u8f6c\u5316\u4e3a\u5176\u5b83\u72b6\u6001\uff0c\u5373\u7bad\u5934\u4ece <code>running</code> \u51fa\u53d1\u5411\u5916\uff1b\u2777 \u8fdb\u7a0b\u4ece\u5176\u5b83\u72b6\u6001\u8f6c\u5316\u4e3a\u5c31\u7eea\u6001\uff0c\u5373\u7bad\u5934\u4ece\u5916\u6307\u5411 <code>ready</code>\uff0c\u8fd9\u91cc\u5176\u5b9e\u8fd8\u6697\u542b\u4e86\u4e00\u4e2a <code>ready</code> \u6307\u5411 <code>ready</code> \u7684\u7bad\u5934\uff0c\u5728\u4f8b\u5982 priority aging \u7684\u60c5\u51b5\u4e0b\uff0c<code>ready</code> \u4e2d\u53ef\u80fd\u7a81\u7136\u6709\u4e00\u4e2a\u4f18\u5148\u7ea7\u8db3\u591f\u5927\u4e86\u5c31\u4f1a\u53d1\u751f\u62a2\u5360\u5f0f\u8c03\u5ea6\u3002\u4e0a\u9762\u63cf\u8ff0\u7684\u8fd9\u4e24\u79cd\u65f6\u673a\u4e0b\u4ea7\u751f\u7684\u8c03\u5ea6\uff0c\u5c31\u5206\u522b\u5b9a\u4e49\u4e3a\u975e\u62a2\u5360\u5f0f\u8c03\u5ea6(non-preemptive scheduling)\u548c\u62a2\u5360\u5f0f\u8c03\u5ea6(preemptive scheduling)\u3002</p> <p> Diagram of process state.</p> <p>\u4e24\u8005\u672c\u8d28\u4e0a\u7684\u533a\u522b\u5c31\u662f\uff0c\u975e\u62a2\u5360\u5f0f\u8c03\u5ea6\u662f\u7531\u5df2\u7ecf\u62e5\u6709\u8d44\u6e90\u7684\u8fdb\u7a0b\u4e3b\u52a8\u91ca\u653e CPU \u8d44\u6e90\u5f15\u8d77\u7684\uff0c\u800c\u62a2\u5360\u5f0f\u8c03\u5ea6\u5219\u662f\u4e0d\u5360\u6709\u8d44\u6e90\u7684\u8fdb\u7a0b\u7d22\u53d6 CPU \u8d44\u6e90\u6210\u529f\u5f15\u8d77\u7684\u3002</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit1/#\u8c03\u5ea6\u7684\u8fc7\u7a0b","title":"\u8c03\u5ea6\u7684\u8fc7\u7a0b","text":"<p>\u7531 CPU scheduler \u9009\u62e9\u54ea\u4e00\u4e2a\u5c31\u7eea\u6001\u7684\u5c06\u8981\u88ab\u6267\u884c\u540e\uff0c\u7531 dispatcher \u6765\u5b8c\u6210\u5177\u4f53\u7684\u5207\u6362\u5de5\u4f5c\u5305\u62ec\uff1a</p> <ol> <li>\u5728\u4e24\u4e2a\u8fdb\u7a0b\u95f4\u8fdb\u884c\u4e0a\u4e0b\u6587\u5207\u6362\uff1b</li> <li>\u5207\u6362\u5230\u7528\u6237\u6001\uff1b</li> <li>\u8df3\u8f6c\u5230\u7528\u6237\u7a0b\u5e8f\u4e2d\u5408\u9002\u7684\u4f4d\u7f6e\u4ee5\u7ee7\u7eed\u8fdb\u7a0b\u6267\u884c\uff1b</li> </ol> <p>\u800c\u4ece dispatcher \u505c\u6b62\u4e0a\u4e00\u4e2a\u8fd0\u884c\u65f6\u7684\u8fdb\u7a0b\uff0c\u5b8c\u6210\u4e0a\u4e0b\u6587\u5207\u6362\uff0c\u5e76\u542f\u52a8\u4e0b\u4e00\u4e2a\u8fdb\u7a0b\u7684\u5ef6\u65f6\uff0c\u79f0\u4e3a dispatch latency\u3002</p> <p></p> <p>\u4e0a\u4e0b\u6587\u5207\u6362</p> <p>\u5207\u6362\u8fdb\u7a0b\u7684\u65f6\u5019\u9700\u8981\u4fdd\u5b58\u201c\u73b0\u573a\u201d\uff0c\u5e76\u5728\u4e0b\u4e00\u6b21\u62ff\u51fa\u8fd9\u4e2a\u8fdb\u7a0b\u51c6\u5907\u6267\u884c\u4e4b\u524d\u6062\u590d\u201c\u73b0\u573a\u201d\uff0c\u4ee5\u6b64\u6765\u4fdd\u8bc1\u8fdb\u7a0b\u6267\u884c\u7684\u4e00\u81f4\u6027\u3002\u8fd9\u91cc\u63d0\u5230\u7684\u201c\u73b0\u573a\u201d\u88ab\u79f0\u4e3a\u4e0a\u4e0b\u6587(context)\uff0c\u8868\u793a\u4e00\u79cd\u201c\u8bed\u5883\u201d\uff1b\u800c\u4fdd\u62a4-\u6062\u590d\u7684\u8fc7\u7a0b\uff0c\u5c31\u662f\u4e0a\u9762\u63d0\u5230\u7684\u4e0a\u4e0b\u6587\u5207\u6362(context switch)\u3002</p> <p>\u5176\u4e2d\uff0c\u4e0a\u4e0b\u6587\u53ef\u80fd\u5305\u62ec \u2460 CPU \u5bc4\u5b58\u5668\u4e2d\u7684\u503c\uff0c\u2461 \u8fdb\u7a0b\u72b6\u6001\uff0c\u2462 \u5185\u5b58\u7684\u7ba1\u7406\u4fe1\u606f\u7b49\u3002</p> <p>\u4e0a\u4e0b\u6587\u5207\u6362\u7684\u76f8\u5173\u5185\u5bb9\u5728 Lab2 \u91cc\u6709\u6240\u6d89\u53ca\uff0c\u9700\u8981\u5b9e\u73b0\u4e00\u4e2a\u7b80\u5355\u7684\u4e0a\u4e0b\u6587\u5207\u6362\u3002</p> <p> (a) Diagram showing context switch from process to process. (b) Role of dispatcher.</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit1/#\u8c03\u5ea6\u7b97\u6cd5","title":"\u8c03\u5ea6\u7b97\u6cd5","text":"<p>\u5728\u8ba8\u8bba\u6709\u54ea\u4e9b\u8c03\u5ea6\u7b97\u6cd5\u4e4b\u524d\uff0c\u6211\u4eec\u9996\u5148\u9700\u8981\u77e5\u9053\u600e\u6837\u7b97\u4e00\u4e2a\u597d\u7684\u8c03\u5ea6\u7b97\u6cd5\u3002\u7c7b\u4f3c\u4e8e\u64cd\u4f5c\u7cfb\u7edf\u7684\u8bc4\u4ef7\uff0c\u8c03\u5ea6\u7b97\u6cd5\u7684\u8bc4\u4ef7\u6807\u51c6\u4e5f\u4e0d\u662f\u5355\u4e00\u7684\uff1b\u5bf9\u5e94\u7684\uff0c\u4e0d\u540c\u8c03\u5ea6\u7b97\u6cd5\u6709\u5404\u81ea\u7684\u4f18\u7f3a\u70b9\uff0c\u9700\u8981\u6839\u636e\u5b9e\u9645\u60c5\u51b5\u548c\u9700\u6c42\u6709\u6240\u9009\u62e9\u3002\u901a\u5e38\u6765\u8bf4\u6709\u8fd9\u4e9b\u8c03\u5ea6\u7b97\u6cd5\u7684\u6307\u6807(scheduling criteria)\uff1a</p> <ul> <li>CPU \u4f7f\u7528\u7387(CPU utilization)\uff1a<ul> <li>CPU \u4f7f\u7528\u65f6\u95f4 / \u603b\u65f6\u95f4\uff0c\u4ece CPU \u662f\u5426\u8db3\u591f\u5fd9\u788c\u6765\u770b\u786c\u4ef6\u6027\u80fd\u662f\u5426\u5145\u5206\u53d1\u6325\uff1b</li> </ul> </li> <li>\u541e\u5410\u91cf(throughput)\uff1a<ul> <li>\u5355\u4f4d\u65f6\u95f4\u5185\u5b8c\u6210\u7684\u8fdb\u7a0b\u6570\uff0c\u4ece\u7ed3\u679c\u6765\u770b\u4efb\u52a1\u5b8c\u6210\u662f\u5426\u8db3\u591f\u9ad8\u6548\uff1b</li> </ul> </li> <li>\u5468\u8f6c\u65f6\u95f4(turnaround time)\uff1a<ul> <li>\u4ece\u8fdb\u7a0b\u5f00\u59cb\u5efa\u7acb\u5230\u8fdb\u7a0b\u5b8c\u6210\u7684\u65f6\u95f4\uff0c\u5373\u5305\u62ec\u7b49\u5f85\u8fdb\u5165\u5185\u5b58\u3001\u5728\u5404\u79cd queue \u4e2d\u7684\u7b49\u5f85\u65f6\u95f4\u3001\u5728 CPU \u4e2d\u7684\u8fd0\u884c\u65f6\u95f4\u3001I/O \u65f6\u95f4\u7b49\uff0c\u901a\u8fc7\u89c2\u5bdf\u6700\u5927\u5468\u8f6c\u65f6\u95f4\uff0c\u80fd\u53cd\u5e94\u8c03\u5ea6\u7684\u6548\u7387\u548c\u201c\u516c\u5e73\u6027\u201d\uff1b</li> </ul> </li> <li>\u7b49\u5f85\u65f6\u95f4(waiting time)\uff1a<ul> <li>\u8fdb\u7a0b\u5728 ready queue \u4e2d\u7b49\u5f85\u7684\u65f6\u95f4\u7684\u603b\u548c\uff0c\u7531\u4e8e\u4efb\u52a1\u6240\u9700\u8981\u7684 CPU \u65f6\u95f4\u3001I/O \u65f6\u95f4\u4e0d\u53d7\u8c03\u5ea6\u7b97\u6cd5\u5f71\u54cd\uff0c\u6240\u4ee5\u629b\u5f00\u8fd9\u4e9b\u53ea\u770b\u5728 ready queue \u4e2d\u7684\u7b49\u5f85\u65f6\u95f4\uff0c\u80fd\u53cd\u5e94\u8c03\u5ea6\u7b97\u6cd5\u7684\u6548\u7387\uff1b</li> <li>\u5bb9\u6613\u53d1\u73b0\uff0c\u7b49\u5f85\u65f6\u95f4 = \u5468\u8f6c\u65f6\u95f4 - \u8fd0\u884c\u65f6\u95f4\uff1b</li> </ul> </li> <li>\u54cd\u5e94\u65f6\u95f4(response time)\uff1a<ul> <li>\u8fdb\u7a0b\u4ece\u53d1\u51fa\u8bf7\u6c42\u5230\u7b2c\u4e00\u6b21\u54cd\u5e94\u7684\u65f6\u95f4\uff0c\u80fd\u53cd\u5e94\u4ea4\u4e92\u5f0f\u7cfb\u7edf\u4e2d\u8c03\u5ea6\u7b97\u6cd5\u7684\u201c\u53ca\u65f6\u6027\u201d\uff1b</li> </ul> </li> </ul> <p>\u4e0a\u9762\u4e94\u4e2a\u524d\u4e24\u4e2a\u8d8a\u5927\u8d8a\u597d\uff0c\u540e\u4e09\u4e2a\u8d8a\u5c0f\u8d8a\u597d\u3002</p> <p>\u63a5\u4e0b\u6765\u6211\u4eec\u5f00\u59cb\u4ecb\u7ecd\u5404\u79cd\u8c03\u5ea6\u7b97\u6cd5\uff0c\u9700\u8981\u6ce8\u610f\u7684\u662f\uff0c\u5982\u4e0b\u8c03\u5ea6\u7b97\u6cd5\u4e2d\u5b58\u5728\u4e00\u4e9b\u7406\u60f3\u5316\u7684\u5efa\u6a21\uff08\u4f8b\u5982\u5047\u8bbe\u6211\u4eec\u77e5\u9053\u8fdb\u7a0b\u9700\u8981\u4f7f\u7528\u591a\u4e45 CPU\uff09\uff0c\u800c\u6211\u4eec\u91cd\u70b9\u9700\u8981\u638c\u63e1\u5b83\u7684\u601d\u8def\uff0c\u505a\u5230\u80fd\u753b\u7518\u7279\u56fe\u3001\u80fd\u7b97\u65f6\u95f4\u3002\u6b64\u5916\uff0c\u8fd9\u91cc\u6211\u4eec\u4ee5\u201c\u591a\u9053\u201d\u4e3a\u8bed\u5883\uff0c\u5373\u5982\u679c\u4e0d\u662f\u7279\u522b\u8bf4\u660e\uff0c\u4e0d\u8003\u8651\u5206\u65f6\u6280\u672f\u3002</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit1/#\u7b97\u6cd5--first-come-first-serve-fcfs","title":"\u7b97\u6cd5 | First-Come, First-Serve (FCFS)","text":"<p>FCFS \u662f\u6700\u57fa\u672c\u7684\u975e\u62a2\u5360\u5f0f\u8c03\u5ea6\u65b9\u6cd5\u5c31\u662f\u6309\u7167\u8fdb\u7a0b\u5148\u6765\u540e\u5230\u7684\u987a\u5e8f\u8fdb\u884c\u8c03\u5ea6\uff0c\u53ef\u4ee5\u5f88\u7b80\u5355\u5730\u901a\u8fc7\u4e00\u4e2a FIFO \u7684\u961f\u5217\u5b9e\u73b0\u3002FCFS \u6700\u5927\u7684\u4f18\u70b9\u5c31\u662f\u5b9e\u73b0\u7b80\u5355\u3002</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit1/#\u7b97\u6cd5--shortest-job-first-sjf--shortest-remaining-time-first-srtf","title":"\u7b97\u6cd5 | Shortest-Job-First (SJF) / Shortest-Remaining-Time-First (SRTF)","text":"<p>SJF \u7684\u601d\u8def\u662f\uff0c\u5f53\u6709\u591a\u4e2a\u8fdb\u7a0b\u5904\u4e8e\u5c31\u7eea\u6001\u65f6\uff0c\u9009\u62e9\u9700\u8981\u8fd0\u884c\u65f6\u95f4\u6700\u77ed\u7684\u8fdb\u7a0b\u5148\u8fd0\u884c\u3002\u8fd9\u79cd\u7b97\u6cd5\u7684\u4f18\u70b9\u662f\uff0c\u80fd\u591f\u4fdd\u8bc1\u5e73\u5747\u7b49\u5f85\u65f6\u95f4\u6700\u5c0f\uff1b\u4f46\u662f\u7f3a\u70b9\u662f\uff0c\u5982\u679c\u6709\u4e00\u4e2a\u8fdb\u7a0b\u9700\u8981\u8fd0\u884c\u65f6\u95f4\u5f88\u957f\uff0c\u90a3\u4e48\u5b83\u53ef\u80fd\u4f1a\u4e00\u76f4\u88ab\u63a8\u8fdf\uff0c\u4ece\u800c\u5bfc\u81f4\u201c\u9965\u997f\u201d\u73b0\u8c61\uff0c\u6b64\u5916\uff0c\u6211\u4eec\u5e76\u4e0d\u77e5\u9053\u8fdb\u7a0b\u8fd0\u884c\u65f6\u95f4\u6709\u591a\u4e45\u3002</p> \ud83c\udf30 \u9898\u9762\u89e3\u6790 <p>\u73b0\u5728\u6709\u4e09\u4e2a\u8fdb\u7a0b\uff0c\u5b83\u4eec\u5c06\u8981\u6267\u884c\u7684\u65f6\u95f4\u5206\u522b\u5982\u4e0b\uff1a</p> <ul> <li>P1: 24</li> <li>P2: 3</li> <li>P3: 3</li> </ul> <p>\u73b0\u5728\u5b83\u4eec\u6309\u7167\u987a\u5e8f\u8fdb\u5165 ready queue\uff0c\u8bf7\u5206\u522b\u8ba1\u7b97 FCFS \u4e0b\u548c SJF \u4e0b\u7684\u5e73\u5747\u7b49\u5f85\u65f6\u95f4\u3002</p> <p>\u9996\u5148\u770b FCFS\uff0c\u5373\u6309\u7167\u987a\u5e8f\u6267\u884c\uff0c\u753b\u51fa\u7518\u7279\u56fe\uff1a</p> <pre><code>gantt\n    title FCFS\n    dateFormat ss\n    axisFormat %S\n\n    section processes\n    P1: a, 00, 24\n    P2: b, 24, 27\n    P3: c, 27, 30</code></pre> <p>\u4e8e\u662f\u5e73\u5747\u7b49\u5f85\u65f6\u95f4\u4e3a \\((0 + 24 + 27) / 3 = 17\\)\u3002</p> <p>\u73b0\u5728\u6309\u7167 SJF \u6765\uff0c\u987a\u5e8f\u53d8\u4e3a P2 \u548c P3 \u5148\u6267\u884c\uff1a</p> <pre><code>gantt\n    title SJF\n    dateFormat ss\n    axisFormat %S\n\n    section processes\n    P2: a, 00, 03\n    P3: b, 03, 06\n    P1: c, 06, 30</code></pre> <p>\u4e8e\u662f\u5e73\u5747\u7b49\u5f85\u65f6\u95f4\u4e3a \\((0 + 3 + 6) / 3 = 3\\)\u3002</p> <p>\u53ef\u4ee5\u53d1\u73b0\uff0c\u4f7f\u7528 SJF \u4ee5\u540e\u5bf9\u4e8e\u8fd9\u79cd\u524d\u9762\u653e\u4e86\u4e2a\u5927\u4efb\u52a1\u7684\u60c5\u51b5\u5e73\u5747\u7b49\u5f85\u65f6\u95f4\u5927\u5927\u51cf\u5c11\u3002</p> <p>\u8fd9\u79cd\u505a\u6cd5\u53c8\u88ab\u79f0\u4e3a Shortest-Next-CPU-Burst\uff0c\u5b83\u662f\u4e00\u79cd\u975e\u62a2\u5360\u5f0f\u8c03\u5ea6\u7b97\u6cd5\uff0c\u4f46\u5047\u8bbe\u6211\u4eec\u5728\u6267\u884c\u4e00\u4e2a\u8fdb\u7a0b\u7684\u8fc7\u7a0b\u4e2d\uff0c\u6709\u4e00\u4e2a\u65b0\u7684\u8fdb\u7a0b\u52a0\u5165\u4e86 ready queue\uff0c\u800c\u4e14\u8fd9\u4e2a\u8fdb\u7a0b\u7684\u6267\u884c\u65f6\u95f4\u6bd4\u6b63\u5728\u8fd0\u884c\u7684\u8fdb\u7a0b\u7684\u5269\u4f59\u65f6\u95f4\u8fd8\u8981\u77ed\uff0c\u6211\u4eec\u4ecd\u7136\u9700\u8981\u7ee7\u7eed\u6267\u884c\u5b8c\u5f53\u524d\u7684\u8fdb\u7a0b\u624d\u884c\u2014\u2014\u56e0\u4e3a\u5b83\u662f\u975e\u62a2\u5360\u5f0f\u7684\u3002\u800c\u663e\u7136\u8fd9\u4e2a\u8fc7\u7a0b\u662f\u53ef\u4ee5\u901a\u8fc7\u62a2\u5360\u5f0f\u8c03\u5ea6\u6765\u4f18\u5316\u7684\uff0c\u4e8e\u662f\u6211\u4eec\u5f15\u5165\u4e86 Shortest-Remaining-Time-First (SRTF)\uff0c\u5176\u8868\u8ff0\u662f\uff1a\u603b\u662f\u6267\u884c\u5269\u4f59\u8fd0\u884c\u65f6\u95f4\u6700\u77ed\u7684\u8fdb\u7a0b\u3002\u5176\u4f18\u7f3a\u70b9\u4e0e SJF \u4e00\u81f4\u3002</p> <p>\u6211\u4eec\u53ea\u9700\u8981\u8003\u8651\u6240\u6709\u62a2\u5360\u5f0f\u8c03\u5ea6\u548c\u975e\u62a2\u5360\u5f0f\u8c03\u5ea6\u65f6\u673a\uff0c\u5e76\u9009\u62e9\u6b64\u65f6\u7684\u5269\u4f59\u8fd0\u884c\u65f6\u95f4\u6700\u77ed\u7684\u8fdb\u7a0b\u8fdb\u884c\u8c03\u5ea6\u5373\u53ef\u3002</p> <p>\u5982\u4f55\u5f97\u5230\u5269\u4f59\u65f6\u95f4</p> <p>\u6211\u4eec\u77e5\u9053\uff0c\u4e00\u4e2a\u7a0b\u5e8f\u8fd0\u884c\u6240\u9700\u8981\u7684\u65f6\u95f4\u662f\u4e00\u4e2a\u65e0\u6cd5\u5728\u8fd0\u884c\u7ed3\u675f\u524d\u5f97\u5230\u7684\u6570\u636e\uff0c\u56e0\u6b64\u4f7f\u7528\u8fd9\u4e2a\u4e1c\u897f\u8fdb\u884c\u8c03\u5ea6\u5c31\u663e\u5f97\u5341\u5206\u4e0d\u5408\u7406\u3002\u4f46\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u9884\u6d4b\u7684\u65b9\u6cd5\u4f30\u8ba1\u8fd0\u884c\u7684\u5269\u4f59\u65f6\u95f4\uff0c\u4f46\u662f\u65e2\u7136\u662f\u9884\u6d4b\u5c31\u4f1a\u6709\u4e0d\u51c6\u786e\uff0c\u6240\u4ee5 SJF/SRTF \u5e76\u4e0d\u80fd\u5b9e\u73b0\u7406\u8bba\u4e0a\u5e73\u5747\u7b49\u5f85\u65f6\u95f4\u6700\u4f18\u3002\u81f3\u4e8e\u5982\u4f55\u9884\u6d4b\uff0c\u4e66\u4e0a\u63d0\u4f9b\u4e86\u4e00\u4e2a\u53eb exponential average \u7684\u65b9\u6cd5\uff0c\u6211\u4eec\u5728\u8fd9\u91cc\u4e0d\u5c55\u5f00\u3002</p> \ud83c\udf30 \u9898\u9762\u89e3\u6790 <p>\u73b0\u5728\u6709\u4e09\u4e2a\u8fdb\u7a0b\uff0c\u5b83\u4eec\u5c06\u8981\u6267\u884c\u7684\u65f6\u95f4\u5206\u522b\u5982\u4e0b\uff1a</p> <ul> <li>P1: 8</li> <li>P2: 4</li> <li>P3: 9</li> <li>P4: 5</li> </ul> <p>\u5b83\u4eec\u5230\u8fbe ready queue \u7684\u65f6\u95f4\u5206\u522b\u5982\u4e0b\uff1a</p> <ul> <li>P1: 0</li> <li>P2: 1</li> <li>P3: 2</li> <li>P4: 3</li> </ul> <p>\u8bf7\u5206\u522b\u8ba1\u7b97 SJF \u4e0b\u548c SRTF \u4e0b\u7684\u5e73\u5747\u7b49\u5f85\u65f6\u95f4\u3002</p> <p>\u5bf9\u4e8e SJF \u6765\u8bf4\uff0c\u5728\u7b2c 0 \u65f6\u523b\uff0c\u53ea\u6709 P1 \u53ef\u7528\uff0c\u6240\u4ee5\u53ea\u80fd\u6267\u884c P1\uff1bP1 \u6267\u884c\u7ed3\u675f\u540e\u6240\u6709\u5176\u5b83\u8fdb\u7a0b\u90fd\u53ef\u7528\u4e86\uff0c\u6b64\u65f6\u6309\u7167\u6b63\u5e38\u7684 SJF \u5373\u53ef\u5f97\u5230\u7ed3\u679c\u3002</p> <pre><code>gantt\n    title SJF\n    dateFormat ss\n    axisFormat %S\n\n    section P1\n    run: a, 00, 08\n\n    section P2\n    ready: b, 01, 08\n    run: e, 08, 12\n\n    section P3\n    ready: c, 02, 17\n    run: 17, 26\n\n    section P4\n    ready: d, 03, 12\n    run: f, 12, 17</code></pre> <p>\u6b64\u65f6\u5e73\u5747\u7b49\u5f85\u65f6\u95f4\u4e3a \\((0 + 7 + 15 + 9) / 4 = 7.75\\)\u3002</p> <p>\u5bf9\u4e8e SRFT \u6765\u8bf4\uff0c\u540c\u6837\u4ece P1 \u5f00\u59cb\u6267\u884c\uff0c\u4f46\u662f\u7b2c\u4e00\u79d2 P2 \u8fdb\u5165\uff0c\u53d1\u73b0\u6b64\u65f6 P1 \u8fd8\u5269\u4e0b 7\uff0c\u800c P2 \u53ea\u9700\u8981 4\uff0c\u4e8e\u662f P2 \u9700\u8981\u62a2\u5360 P1 \u7684\u8d44\u6e90\uff1b\u4e4b\u540e\u7684\u8fc7\u7a0b\u7c7b\u4f3c</p> <pre><code>gantt\n    dateFormat ss\n    axisFormat %S\n\n    section P1\n    run: a, 00, 01\n    ready(rest 7): e, 01, 10\n    run: g, 10, 17\n\n    section P2\n    run: b, 01, 05\n\n    section P3\n    ready(rest 9): c, 02, 17\n    run: h, 17, 26\n\n    section P4\n    ready(rest 5): d, 03, 05\n    run: f, 05, 10</code></pre> <p>\u6b64\u65f6\u5e73\u5747\u7b49\u5f85\u65f6\u95f4\u4e3a \\(((0+9) + 0 + 15 + 2) / 4 = 6.5\\)\u3002</p> <p>\u53ef\u4ee5\u53d1\u73b0 SRTF \u80fd\u591f\u63d0\u5347 SJF \u7684\u6548\u7387\u3002</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit1/#\u7b97\u6cd5--round-robin-rr","title":"\u7b97\u6cd5 | Round-Robin (RR)","text":"<p>RR \u8c03\u5ea6\u5c31\u662f\u4f7f\u7528\u5206\u65f6\u6280\u672f\u540e\u7684 FCFS \u8c03\u5ea6\uff0c\u56e0\u6b64\u5b83\u4e5f\u662f\u975e\u62a2\u5360\u5f0f\u7684\u3002\u6bcf\u4e00\u4e2a\u8fdb\u7a0b\u6700\u591a\u8fde\u7eed\u6267\u884c\u4e00\u4e2a\u65f6\u95f4\u7247\u7684\u957f\u5ea6\uff0c\u5b8c\u6210\u540e\u88ab\u63d2\u5165\u5230 FIFO ready queue \u7684\u672b\u5c3e\uff0c\u5e76\u53d6\u51fa FIFO ready queue \u7684\u961f\u9996\u8fdb\u884c\u6267\u884c\u3002</p> <p>\u6211\u4eec\u4e4b\u524d\u63d0\u5230\u5206\u65f6\u7684\u65f6\u5019\u4e5f\u8bf4\u8fc7\uff0c\u5206\u65f6\u6280\u672f\u901a\u8fc7\u4f18\u5316\u54cd\u5e94\u65f6\u95f4\u89e3\u51b3\u4e86\u7528\u6237\u4ea4\u4e92\u95ee\u9898\uff0cRR \u8c03\u5ea6\u867d\u7136\u76f8\u6bd4 SJF \u6709\u4e86\u66f4\u957f\u7684\u7b49\u5f85\u65f6\u95f4\uff0c\u4f46\u662f\u6709\u4e86\u66f4\u77ed\u7684\u54cd\u5e94\u65f6\u95f4\uff0c\u800c\u5b9e\u9645\u76f4\u63a5\u5f71\u54cd\u7528\u6237\u4ea4\u4e92\u95ee\u9898\u7684\u5e94\u8be5\u662f\u54cd\u5e94\u65f6\u95f4\u3002</p> <p>\u4e00\u4e2a\u9700\u8981\u6ce8\u610f\u7684\u662f\uff0cRR \u8c03\u5ea6\u6709\u4e00\u4e2a\u201c\u8d85\u53c2\u6570\u201d\uff0c\u5373\u65f6\u95f4\u7247\u7684\u957f\u5ea6\u3002\u7406\u8bba\u4e0a\uff0c\u65f6\u95f4\u7247\u7ea6\u77ed\uff0c\u54cd\u5e94\u65f6\u95f4\u8d8a\u77ed\uff1b\u4f46\u66f4\u77ed\u7684\u65f6\u95f4\u7247\u5c06\u5e26\u6765\u66f4\u9891\u7e41\u7684\u8fdb\u7a0b\u5207\u6362\uff0c\u4ece\u800c\u5e26\u6765\u66f4\u591a\u7684 dispatch latency\u3002</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit1/#\u7b97\u6cd5--priority-scheduling","title":"\u7b97\u6cd5 | Priority Scheduling","text":"<p>\u4f18\u5148\u7ea7\u8c03\u5ea6\u7684\u601d\u8def\u662f\uff0c\u6bcf\u4e2a\u8fdb\u7a0b\u90fd\u6709\u4e00\u4e2a\u4f18\u5148\u7ea7\uff0c\u5f53\u6709\u591a\u4e2a\u8fdb\u7a0b\u5904\u4e8e\u5c31\u7eea\u6001\u65f6\uff0c\u9009\u62e9\u4f18\u5148\u7ea7\u6700\u9ad8\u7684\u8fdb\u7a0b\u5148\u8fd0\u884c\u3002\u8fd9\u79cd\u7b97\u6cd5\u7684\u4f18\u70b9\u662f\uff0c\u80fd\u591f\u4fdd\u8bc1\u4f18\u5148\u7ea7\u9ad8\u7684\u8fdb\u7a0b\u4f18\u5148\u8fd0\u884c\uff1b\u4f46\u662f\u7f3a\u70b9\u662f\uff0c\u5982\u679c\u6709\u4e00\u4e2a\u8fdb\u7a0b\u7684\u4f18\u5148\u7ea7\u5f88\u9ad8\uff0c\u90a3\u4e48\u5b83\u53ef\u80fd\u4f1a\u4e00\u76f4\u88ab\u63a8\u8fdf\uff0c\u4ece\u800c\u5bfc\u81f4\u201c\u9965\u997f\u201d\u73b0\u8c61\u3002</p> <p>\u4f60\u53ef\u80fd\u53d1\u73b0\u4e86\uff0c\u5982\u679c\u628a\u4e0a\u9762\u8fd9\u53e5\u8bdd\u7684\u201c\u4f18\u5148\u7ea7\u6700\u9ad8\u201d\u6539\u6210\u201c\u8fd0\u884c\u65f6\u95f4\u6700\u77ed\u201d/\u201c\u5269\u4f59\u8fd0\u884c\u65f6\u95f4\u6700\u77ed\u201d\uff0c\u90a3\u5c31\u548c SJF/SRTF \u4e00\u6a21\u4e00\u6837\u4e86\uff0cSJF/SRTF \u5b9e\u9645\u4e0a\u5c31\u662f\u4f18\u5148\u7ea7\u8c03\u5ea6\u7684\u4e00\u4e2a\u7279\u4f8b\uff0c\u56e0\u800c\u4f18\u5148\u7ea7\u8c03\u5ea6\u5f53\u7136\u662f\u53ef\u4ee5\u5b9e\u73b0\u62a2\u5360\u5f0f\u548c\u975e\u62a2\u5360\u5f0f\u4e24\u79cd\u7684\u3002</p> <p>\u6b64\u5916\uff0c\u4f18\u5148\u7ea7\u7684\u5206\u914d\u53ef\u4ee5\u6839\u636e\u4f7f\u7528\u9700\u6c42\u8fdb\u884c\u8bbe\u8ba1\uff0c\u5b83\u53ef\u80fd\u662f\u4e00\u4e9b\u6d4b\u91cf\u6570\u636e\uff0c\u4e5f\u53ef\u80fd\u5177\u6709\u4e00\u4e9b\u88ab\u8d4b\u4e88\u7684\u610f\u4e49\uff0c\u751a\u81f3\u53ef\u4ee5\u662f\u4e00\u4e9b\u590d\u5408\u7684\u503c\uff1b\u4f18\u5148\u7ea7\u4e5f\u5e76\u4e0d\u4e00\u5b9a\u662f\u9759\u6001\u7684\uff0c\u5148\u524d\u6211\u4eec\u63d0\u5230\u8fc7\u7684\u9965\u997f\u95ee\u9898\uff0c\u5c31\u53ef\u4ee5\u901a\u8fc7\u52a8\u6001\u7684\u4f18\u5148\u7ea7\u6765\u89e3\u51b3\uff1a\u4f18\u5148\u7ea7\u968f\u7740\u7b49\u5f85\u65f6\u95f4\u589e\u52a0\u4e0d\u65ad\u589e\u957f\uff0c\u7b49\u5f85\u8fc7\u4e45\u7684\u4efb\u52a1\u5c31\u4f1a\u88ab\u8d4b\u4e88\u8f83\u9ad8\u7684\u4f18\u5148\u7ea7\uff0c\u4ee5\u6b64\u907f\u514d\u9965\u997f\u7684\u53d1\u751f\uff0c\u8fd9\u79cd\u7b56\u7565\u53eb priority aging\u3002</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit1/#\u8bbe\u8ba1--multilevel-queue-scheduling","title":"\u8bbe\u8ba1 | Multilevel Queue Scheduling","text":"<p>\u65e2\u7136\u8c03\u5ea6\u7b97\u6cd5\u591a\u79cd\u591a\u6837\uff0c\u4ed6\u4eec\u9002\u914d\u4e0d\u540c\u7684\u9700\u6c42\uff0c\u90a3\u80fd\u5426\u53ea\u5728\u7279\u5b9a\u60c5\u51b5\u4e0b\u4f7f\u7528\u7279\u5b9a\u7b97\u6cd5\u5462\uff1f\u7b54\u6848\u662f\u80af\u5b9a\u7684\uff0c\u6211\u4eec\u53ef\u4ee5\u5c06 ready queue \u5206\u6210\u591a\u4e2a\u961f\u5217\uff0c\u6bcf\u4e2a\u961f\u5217\u4f7f\u7528\u4e0d\u540c\u7684\u8c03\u5ea6\u7b97\u6cd5\uff0c\u7136\u540e\u518d\u8fdb\u884c\u961f\u5217\u95f4\u8c03\u5ea6\uff0c\u8fd9\u79cd\u65b9\u6cd5\u88ab\u79f0\u4e3a\u591a\u7ea7\u961f\u5217\u8c03\u5ea6(multilevel queue scheduling)\u3002</p> <p>\ud83c\udf30</p> <p>\u4e00\u4e2a\u64cd\u4f5c\u7cfb\u7edf\u6309\u7167\u4f18\u5148\u7ea7\u5148\u540e\uff0c\u53ef\u80fd\u6709\u8fd9\u4e48\u4e9b\u961f\u5217\uff1a</p> <ol> <li>Real-time processes</li> <li>System processes</li> <li>Interactive processes</li> <li>Batch processes</li> </ol> <p>\u5b83\u4eec\u7684\u4f18\u5148\u7ea7\u968f\u7740 1 -&gt; 4 \u9012\u51cf\uff0c\u800c\u5f53\u4f18\u5148\u7ea7\u66f4\u9ad8\u7684\u961f\u5217\u4e2d\u5b58\u5728\u4efb\u52a1\u65f6\uff0c\u4f18\u5148\u7ea7\u4f4e\u7684\u961f\u5217\u4fbf\u4e0d\u4f1a\u53c2\u4e0e\u8c03\u5ea6\u3002\u4e0d\u4ec5\u5982\u6b64\uff0c\u9ad8\u4f18\u5148\u7ea7\u7684\u961f\u5217\u4e2d\u51fa\u73b0\u65b0\u7684\u4efb\u52a1\u65f6\uff0c\u4e5f\u4f1a\u62a2\u5360\u6b63\u5728\u8fd0\u884c\u7684\u4f4e\u4f18\u5148\u7ea7\u961f\u5217\u7684\u4efb\u52a1\u3002</p> <p>\ud83c\udf30</p> <p>\u53c8\u6bd4\u5982\uff0c\u4e00\u4e2a\u64cd\u4f5c\u7cfb\u7edf\u53ef\u80fd\u5206\u524d\u53f0(foreground)\u7a0b\u5e8f\u961f\u5217\u548c\u540e\u53f0(background)\u7a0b\u5e8f\u961f\u5217\uff0c\u800c\u6211\u4eec\u4f7f\u7528\u65f6\u95f4\u7247\u6765\u8fdb\u884c\u961f\u5217\u95f4\u8c03\u5ea6\uff0c\u4f46\u524d\u53f0\u5360\u7528 80% \u7684\u65f6\u95f4\uff0c\u800c\u540e\u53f0\u5360\u7528 20% \u7684\u65f6\u95f4\u3002</p> <p>\u800c\u5728\u961f\u5217\u5185\u90e8\uff0c\u6211\u4eec\u4e5f\u53ef\u4ee5\u6839\u636e\u9700\u6c42\u4f7f\u7528\u4e0d\u540c\u7684\u961f\u5217\u5185\u8c03\u5ea6\u7b97\u6cd5\u3002\u5728\u8fd9\u4e2a\u4f8b\u5b50\u4e2d\uff0c\u7531\u4e8e\u524d\u53f0\u7a0b\u5e8f\u5f80\u5f80\u8981\u6c42\u66f4\u597d\u7684\u54cd\u5e94\u65f6\u95f4\u8868\u73b0\uff0c\u6240\u4ee5\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528 RR \u8c03\u5ea6\uff1b\u800c\u5728\u540e\u53f0\u4f7f\u7528 FCFS \u8c03\u5ea6\u3002</p> <p>Windows XP Scheduling</p> <ul> <li>windows-xp-scheduling</li> </ul>"},{"location":"cour_note/D3QD_OperatingSystem/Unit1/#\u8bbe\u8ba1--multilevel-feedback-queue-scheduling","title":"\u8bbe\u8ba1 | Multilevel Feedback Queue Scheduling","text":"<p>\u66f4\u8fdb\u4e00\u6b65\uff0cMultilevel Feedback Queue Scheduling \u5728 Multilevel Queue Scheduling \u7684\u57fa\u7840\u4e0a\uff0c\u5141\u8bb8\u8fdb\u7a0b\u5728\u961f\u5217\u95f4\u8f6c\u79fb\uff0c\u4ee5\u6b64\u5b9e\u73b0\u66f4\u7075\u6d3b\u66f4\u79d1\u5b66\u7684\u8c03\u5ea6\u3002\u4f8b\u5982\uff0c\u4e00\u4e2a\u8fdb\u7a0b\u5982\u679c\u4f7f\u7528\u4e86\u8fc7\u957f\u7684 CPU \u65f6\u95f4\uff0c\u5b83\u53ef\u80fd\u88ab\u79fb\u52a8\u5230\u4f18\u5148\u7ea7\u66f4\u4f4e\u7684\u961f\u5217\uff1b\u76f8\u53cd\uff0c\u5982\u679c\u4e00\u4e2a\u8fdb\u7a0b\u7b49\u5f85\u4e86\u592a\u4e45\uff0c\u5b83\u53ef\u80fd\u88ab\u79fb\u52a8\u5230\u4f18\u5148\u7ea7\u66f4\u9ad8\u7684\u961f\u5217\u3002</p> <p>\u5f53\u7136\uff0c\u76f8\u5bf9\u5e94\u7684\uff0c\u7b97\u6cd5\u590d\u6742\u5ea6\u4e5f\u4f1a\u63d0\u9ad8\u4e0d\u5c11\u3002</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit1/#\u7ebf\u7a0b","title":"\u7ebf\u7a0b","text":"<p>\u7ebf\u7a0b\u662f\u4e00\u79cd\u8f7b\u91cf\u7ea7\u7684\u8fdb\u7a0b\uff0c\u5b83\u5728\u8fdb\u7a0b\u7684\u57fa\u7840\u4e0a\u8fdb\u884c\u5212\u5206\uff0c\u662f\u8fdb\u7a0b\u5185\u7684\u4e00\u4e2a\u53ef\u8c03\u5ea6\u7684\u6267\u884c\u5355\u5143\uff0c\u4ee5\u51cf\u5c0f\u8fdb\u7a0b folk \u548c\u5207\u6362\u7684\u5f00\u9500\u4e3a\u76ee\u7684\u3002</p> <p>\u540c\u4e00\u8fdb\u7a0b\u7684\u82e5\u5e72\u7ebf\u7a0b\u5171\u4eab\u4ee3\u7801\u3001\u6570\u636e\u7b49\u201c\u76f8\u5bf9\u9759\u6001\u201d\u7684\u8d44\u6e90\uff0c\u800c\u5404\u81ea\u7ef4\u62a4\u5bc4\u5b58\u5668\u3001\u6808\u3001PC \u7b49\u201c\u76f8\u5bf9\u52a8\u6001\u201d\u7684\u8d44\u6e90\uff1b\u6216\u8005\u8bf4\u7ebf\u7a0b\u53ea\u62e5\u6709\u4e00\u4e9b\u8fd0\u884c\u4e2d\u5fc5\u4e0d\u53ef\u7701\u7684\u8d44\u6e90\uff0c\u800c\u6240\u6709\u5176\u5b83\u8d44\u6e90\u90fd\u5c5e\u4e8e\u8fdb\u7a0b\uff0c\u7ebf\u7a0b\u4e0e\u8fdb\u7a0b\u4e2d\u7684\u5176\u5b83\u7ebf\u7a0b\u5171\u4eab\u8fd9\u4e9b\u8d44\u6e90\uff0c\u4ee5\u6b64\u6765\u51cf\u5c11\u8fdb\u7a0b\u521b\u5efa\u8fc7\u7a0b\u4e2d\u590d\u5236\u4ee3\u7801\u6bb5\u7b49\u8d44\u6e90\u65f6\u5e26\u6765\u7684\u4e0d\u5c0f\u5f00\u9500\u3002</p> <p></p> <p>\u7ebf\u7a0b\u5929\u751f\u548c\u540c\u4e00\u8fdb\u7a0b\u5185\u7684\u5176\u5b83\u7ebf\u7a0b\u5171\u4eab\u8d44\u6e90\uff0c\u56e0\u6b64\u540c\u8fdb\u7a0b\u5185\u7ebf\u7a0b\u5929\u751f\u5c31\u6709\u7ebf\u7a0b\u95f4\u901a\u4fe1\u7684\u80fd\u529b\u3002\u540c\u65f6\uff0c\u7531\u4e8e\u5c06\u8fdb\u7a0b\u8fdb\u884c\u4e86\u518d\u5212\u5206\uff0c\u4e00\u65b9\u9762\u5728\u786c\u4ef6\u652f\u6301\u7684\u60c5\u51b5\u4e0b\u80fd\u66f4\u597d\u5730\u9002\u914d\u5e76\u884c\uff0c\u53e6\u4e00\u65b9\u9762\u4e5f\u80fd\uff08\u4ee3\u4ef7\u66f4\u5c0f\u5730\uff09\u8ba9\u4efb\u52a1\u7684\u7c92\u5ea6\u53d8\u5c0f\uff0c\u6b64\u65f6\u53ef\u4ee5\u5c06\u6574\u4e2a\u8fdb\u7a0b\u7684\u963b\u585e\u8f6c\u79fb\u5230\u5355\u4e2a\u7ebf\u7a0b\u7684\u963b\u585e\u4e0a\uff0c\u8fdb\u4e00\u6b65\u51cf\u5c11\u54cd\u5e94\u65f6\u95f4\u3002</p> <p>\u5f53\u7136\uff0c\u7531\u4e8e\u8fd9\u91cc\u5b58\u5728\u4e00\u4e2a\u90e8\u5206\u6574\u4f53\u7684\u5173\u7cfb\uff0c\u5373\u5b58\u5728\u4e00\u4e2a\u201c\u5c06\u82e5\u5e72\u9e21\u86cb\u653e\u5728\u540c\u4e00\u4e2a\u7bee\u5b50\u91cc\u201d\u7684\u95ee\u9898\uff0c\u867d\u7136\u5c06\u82e5\u5e72\u4efb\u52a1\u90fd\u653e\u5230\u4e00\u4e2a\u8fdb\u7a0b\u7684\u591a\u7ebf\u7a0b\u53ef\u4ee5\u63d0\u9ad8\u6548\u7387\uff0c\u4f46\u662f\u4e00\u65e6\u201c\u7bee\u5b50\u201d\u574f\u4e86\uff0c\u90a3\u6240\u6709\u201c\u9e21\u86cb\u201d\u90fd\u65e0\u6cd5\u5e78\u514d\uff1b\u5176\u6b21\uff0c\u867d\u7136\u5929\u7136\u7684\u5171\u4eab\u5c5e\u6027\u8ba9\u7ebf\u7a0b\u80fd\u66f4\u65b9\u4fbf\u5730\u8fdb\u884c\u7ebf\u7a0b\u95f4\u901a\u4fe1\uff0c\u4f46\u4e5f\u5e26\u6765\u4e86\u5185\u5b58\u4fdd\u62a4\u7684\u95ee\u9898\u3002</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit1/#\u591a\u7ebf\u7a0b\u6a21\u578b","title":"\u591a\u7ebf\u7a0b\u6a21\u578b","text":"<p>\u6309\u7167\u7ebf\u7a0b\u5212\u5206\u7684\u5b9e\u73b0\u4f4d\u7f6e\uff0c\u591a\u7ebf\u7a0b\u6a21\u578b\u5206\u4e3a\u7528\u6237\u7ea7\u591a\u7ebf\u7a0b(user threads)\u548c\u5185\u6838\u7ea7\u591a\u7ebf\u7a0b(kernel threads)\u3002</p> <p>\u7528\u6237\u7ea7\u591a\u7ebf\u7a0b\u5728\u7528\u6237\u7a7a\u95f4\u5b9e\u73b0\u591a\u7ebf\u7a0b\uff0c\u5373\u4f7f\u7528\u7ebf\u7a0b\u5e93(thread library)\u5229\u7528\u5355\u4e2a\u8fdb\u7a0b\u7684\u8d44\u6e90\uff0c\u5728\u7528\u6237\u7a7a\u95f4\u7ef4\u62a4\u591a\u4e2a\u7ebf\u7a0b\uff1b\u800c\u5185\u6838\u7ea7\u591a\u7ebf\u7a0b\u5219\u662f\u7531\u5185\u6838\u652f\u6301\u591a\u7ebf\u7a0b\u64cd\u4f5c\u3002\u4e24\u8005\u5404\u6709\u4f18\u7f3a\u70b9\uff1a</p> <ul> <li>\u7528\u6237\u7ea7\u591a\u7ebf\u7a0b &gt; \u5185\u6838\u7ea7\u591a\u7ebf\u7a0b<ul> <li>\u7528\u6237\u7ea7\u591a\u7ebf\u7a0b\u4e0d\u9700\u8981\u5185\u6838\u652f\u6301\u591a\u7ebf\u7a0b\uff0c\u4e0d\u9700\u8981\u8fdb\u5165\u5185\u6838\u6001\u5b9e\u73b0\u591a\u7ebf\u7a0b\uff0c\u4e5f\u4e0d\u9700\u8981\u5360\u7528\u7ebf\u7a0b ID\uff0c\u56e0\u6b64\u7406\u8bba\u4e0a\u53ef\u4ee5\u6bd4\u5185\u6838\u7ea7\u652f\u6301\u66f4\u591a\u7684\u7ebf\u7a0b\u6570\uff1b</li> <li>\u7531\u4e8e\u5176\u5212\u5206\u662f\u9488\u5bf9\u8fdb\u7a0b\u7684\uff0c\u800c\u4e0d\u540c\u8fdb\u7a0b\u4e4b\u95f4\u7684\u7ebf\u7a0b\u5b9e\u73b0\u6ca1\u6709\u76f4\u63a5\u5173\u7cfb\uff0c\u800c\u4e14\u7531\u4e8e\u662f\u5728\u7528\u6237\u7a7a\u95f4\u5b9e\u73b0\u7b97\u6cd5\uff0c\u6240\u4ee5\u80fd\u591f\u66f4\u5bb9\u6613\u7684\u5bf9\u5355\u4e2a\u8fdb\u7a0b\u5185\u7684\u591a\u4e2a\u7ebf\u7a0b\u7684\u8c03\u5ea6\u7b97\u6cd5\u8fdb\u884c\u81ea\u5b9a\u4e49\uff1b</li> </ul> </li> <li>\u7528\u6237\u7ea7\u591a\u7ebf\u7a0b &lt; \u5185\u6838\u7ea7\u591a\u7ebf\u7a0b<ul> <li>\u7531\u4e8e\u5bf9\u5185\u6838\u6765\u8bf4\uff0c\u7528\u6237\u7ea7\u591a\u7ebf\u7a0b\u4ecd\u7136\u662f\u4e00\u4e2a\u666e\u901a\u7684\u8fdb\u7a0b\uff0c\u6240\u4ee5\u5f53\u7528\u6237\u7ea7\u7684\u7ebf\u7a0b\u51fa\u73b0\u963b\u585e\u65f6\uff0c\u5185\u6838\u4f1a\u8ba4\u4e3a\u6574\u4e2a\u8fdb\u7a0b\u90fd\u88ab\u963b\u585e\uff1b\u5185\u6838\u7ea7\u7ebf\u7a0b\u7531\u4e8e\u662f\u5185\u6838\u5b9e\u73b0\uff0c\u6240\u4ee5\u5355\u7ebf\u7a0b\u7684\u963b\u585e\u5e76\u4e0d\u4f1a\u5bfc\u81f4\u6574\u4e2a\u8fdb\u7a0b\u963b\u585e\uff1b</li> <li>\u5728\u591a\u6838\u7684\u60c5\u51b5\u4e0b\uff0c\u7528\u6237\u7ea7\u591a\u7ebf\u7a0b\u6ca1\u6cd5\u5229\u7528\u591a\u6838\u8fdb\u884c\u7ebf\u7a0b\u5e76\u884c\uff1b\u663e\u7136\u5185\u6838\u591a\u7ea7\u7ebf\u7a0b\u662f\u505a\u5f97\u5230\u8fd9\u4e00\u70b9\u7684\uff1b</li> </ul> </li> </ul> <p>\u9700\u8981\u6ce8\u610f\u7684\u662f\uff0c\u7528\u6237\u7ea7\u591a\u7ebf\u7a0b\u548c\u5185\u6838\u7ea7\u591a\u7ebf\u7a0b\u5e76\u4e0d\u51b2\u7a81\uff0c\u56e0\u800c\u6392\u5217\u7ec4\u5408\u540e\u5f97\u5230\u591a\u7ebf\u7a0b\u4e3b\u8981\u6709\u5982\u4e0b\u4e09\u79cd\u6a21\u578b\uff1a</p> <p> (a) Many-to-many model. (b) One-to-one model. (c) Many-to-one model.</p> <p>Linux \u7ebf\u7a0b</p> <ul> <li>Linux \u7ebf\u7a0b</li> </ul> <ol> <li> <p>Where memory will be allocated to \"Uninitialized Static variable\" upon initialization? \u21a9</p> </li> <li> <p>What process is the parent of the init process in Linux? \u21a9</p> </li> <li> <p>Linux CreateProcess? \u21a9</p> </li> <li> <p>Differences between fork and exec? \u21a9</p> </li> </ol>"},{"location":"cour_note/D3QD_OperatingSystem/Unit2-Part1/","title":"U2 Part 1: \u540c\u6b65\u5de5\u5177 | Synchronization Tools","text":"<p> \u7ea6 7937 \u4e2a\u5b57  215 \u884c\u4ee3\u7801  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 29 \u5206\u949f</p> <p>\u5f15\u5165</p> <p>\u9996\u5148\u6211\u4eec\u7b80\u5355\u63cf\u8ff0\u4ec0\u4e48\u662f\u540c\u6b65\u95ee\u9898\uff0c\u8bfb\u8005\u53ef\u4ee5\u62b1\u7740\u5bf9\u4e0b\u9762\u8fd9\u6bb5\u8bdd\u7684\u7591\u95ee\u53bb\u9605\u8bfb\u63a5\u4e0b\u6765\u7684\u5185\u5bb9\u3002</p> <p>\u4e0d\u5fc5\u5c1d\u8bd5\u7acb\u523b\u7406\u89e3\u8fd9\u6bb5\u8bdd\uff0c\u6211\u5e0c\u671b\u8bfb\u8005\u80fd\u591f\u5728\u770b\u7684\u8fc7\u7a0b\u4e2d\u4ee5\u4e0b\u9762\u8fd9\u6bb5\u8bdd\u4e3a\u4e3b\u7ebf\uff0c\u731c\u6d4b\u63a5\u4e0b\u6765\u5c06\u8981\u5c55\u5f00\u7684\u5185\u5bb9\uff0c\u53bb\u53d1\u73b0\u95ee\u9898\u3001\u601d\u8003\u89e3\u51b3\u529e\u6cd5\u3002</p> <p>\u5728\u652f\u6301\u5e76\u53d1\u751a\u81f3\u5e76\u884c\u7684\u7cfb\u7edf\u4e2d\uff0c\u867d\u7136\u8fdb\u7a0b\u4e4b\u95f4\u76f8\u5bf9\u9694\u79bb\uff0c\u5728\u4e00\u822c\u60c5\u51b5\u4e0b\u4e92\u4e0d\u76f4\u63a5\u5e72\u6270\uff0c\u81ea\u987e\u81ea\u8dd1\u2014\u2014\u5373\u662f\u5f02\u6b65\u7684\uff1b\u4f46\u7531\u4e8e\u5404\u4e9b\u539f\u56e0\uff08\u4f8b\u5982\u90fd\u9700\u8981\u5bf9\u4e00\u5171\u4eab\u8d44\u6e90\u7684\u4fee\u6539\uff09\uff0c\u8fdb\u7a0b\u4e4b\u95f4\u7684\u6267\u884c\u9700\u8981\u4e92\u76f8\u5236\u7ea6\uff0c\u9075\u5faa\u7279\u5b9a\u7684\u5148\u540e\u987a\u5e8f\uff0c\u56e0\u6b64\u8fdb\u7a0b\u9700\u8981\u901a\u8fc7\u67d0\u4e9b\u624b\u6bb5\uff0c\u8ba9\u534f\u4f5c\u8fdb\u7a0b\u80fd\u591f\u76f4\u63a5\u6216\u95f4\u63a5\u4e86\u89e3\u5230\u5176\u5b83\u76f8\u5173\u8fdb\u7a0b\u7684\u72b6\u6001\uff0c\u4ee5\u5b9e\u73b0\u5bf9\u5f53\u524d\u8fdb\u7a0b\u6267\u884c\u7684\u63a7\u5236\uff0c\u6700\u7ec8\u5728\u5b8f\u89c2\u4e0a\u5b9e\u73b0\u540c\u6b65\u63a7\u5236\u3002</p> <p>\u800c\u4e0a\u9762\u63d0\u5230\u7684\u201c\u5404\u79cd\u539f\u56e0\u201d\u548c\u201c\u67d0\u4e9b\u624b\u6bb5\u201d\uff0c\u5c31\u662f\u6211\u4eec\u7a0d\u540e\u5c06\u8ba8\u8bba\u7684\u4e1c\u897f\uff0c\u5176\u4e2d\uff0c\u8fd9\u91cc\u7684\u201c\u67d0\u4e9b\u624b\u6bb5\u201d\uff0c\u5c31\u662f\u6307\u6211\u4eec\u7684\u5404\u79cd\u540c\u6b65\u5de5\u5177\u3002</p> <p>\u9700\u8981\u6ce8\u610f\u7684\u662f\uff0c\u540c\u6b65\u5e76\u4e0d\u662f\u67d0\u79cd\u4e2d\u592e\u8c03\u63a7\u673a\u5236\uff0c\u800c\u66f4\u50cf\u662f\u4e00\u79cd\u201c\u534f\u8bae\u201d\uff0c\u5f53\u5404\u4e2a\u8fdb\u7a0b\u53d1\u73b0\u6709\u522b\u7684\u8fdb\u7a0b\u4e0e\u81ea\u5df1\u4ea7\u751f\u7ade\u4e89\u65f6\uff0c\u5e94\u5f53\u6709\u67d0\u79cd\u624b\u6bb5\u5141\u8bb8\u5b83\u4eec\u8fbe\u6210\u534f\u5546\uff0c\u4ee5\u51b3\u5b9a\u8c01\u5148\u8c01\u540e\u3002</p> <p>\u6211\u4eec\u6309\u7167\u95ee\u9898\u7684\u590d\u6742\u7a0b\u5ea6\uff0c\u7531\u6d45\u5165\u6df1\u5730\u8ba8\u8bba\u8fd9\u4e9b\u4e1c\u897f\u3002</p> <p>\u8bed\u5883\u95ee\u9898</p> <p>\u4e00\u4e2a\u6bd4\u8f83\u5c34\u5c2c\u7684\u95ee\u9898\u662f\uff0c\u4e66\u672c\u4e0a\u4ee5\u534f\u4f5c\u8fdb\u7a0b\u7684\u8bed\u5883\u4e3a\u5f00\u7bc7\uff0c\u4f46\u63a5\u4e0b\u6765\u8bb2\u7684\u6709\u4e9b\u5185\u5bb9\u662f\u4ee5\u7ebf\u7a0b\u540c\u6b65\u4e3a\u8bed\u5883\uff08\u5bf9\u4e8e\u8fd9\u4e2a\u95ee\u9898\u6211\u5df2\u7ecf\u653e\u5f03\u53bb\u68b3\u7406\u548c\u7ea0\u6b63\u4e66\u4e2d\u7684\u63aa\u8f9e\u4e86\uff0c\u7d2f\u4e86\uff09\uff0c\u5982\u679c\u5728\u7528\u8bcd\u4e0a\u90fd\u533a\u5206\u7ebf\u7a0b\u548c\u8fdb\u7a0b\uff0c\u90a3\u4e48\u4f1a\u53d8\u5f97\u5f88\u7e41\u6742\uff0c\u6240\u4ee5\u6211\u63a5\u4e0b\u6765\u4e00\u5f8b\u7528\u8fdb\u7a0b\u8868\u793a\uff0c\u4f46\u8bfb\u8005\u5fc3\u4e2d\u5e94\u5f53\u5bf9\u8fd9\u4e2a\u8bed\u5883\u66f4\u9002\u4e8e\u7ebf\u7a0b\u8fd8\u662f\u8fdb\u7a0b\u6709\u6240\u611f\u53d7\u3002</p> <p>\u5173\u4e8e\u8fd9\u4e9b\u65b9\u6cd5\u66f4\u9002\u5408\u5728 process \u8fd8\u662f thread \u4e0a\u88ab\u5e94\u7528\uff0c\u53ef\u4ee5\u770b\u8fd9\u4e2a\u3002</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit2-Part1/#\u7ade\u6001\u6761\u4ef6","title":"\u7ade\u6001\u6761\u4ef6","text":"<p>Links</p> <ul> <li>Race Condition | Wikipedia</li> </ul> <p>\u6211\u4eec\u9700\u8981\u610f\u8bc6\u5230\uff0c\u6211\u4eec\u65e0\u6cd5\u4e00\u6b65\u5230\u4f4d\u5730\u3001in-place \u5730\u53bb\u4fee\u6539\u4e00\u4e2a\u5185\u5b58\u4e2d\u7684\u6570\u636e\uff0c\u6362\u8a00\u4e4b\uff0c\u8981\u60f3\u4fee\u6539 <code>mem[x]</code>\uff0c\u6211\u4eec\u9700\u8981\u4e09\u4e2a\u6b65\u9aa4\uff1a</p> <ol> <li><code>reg</code> &lt;- <code>mem[x]</code>\uff1b</li> <li><code>reg</code> &lt;- update(<code>reg</code>)\uff1b</li> <li><code>mem[x]</code> &lt;- <code>reg</code>\uff1b</li> </ol> <p>\u800c\u5982\u679c\u73b0\u5728\u4e0d\u6b62\u4e00\u4e2a\u8fdb\u7a0b\u5728\u4fee\u6539 <code>mem[x]</code>\uff0c\u4f8b\u5982\u4e0b\u9762\u8fd9\u4e2a\u4f8b\u5b50\uff1a</p> <pre><code>\u250c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u252c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2510\n\u2502 process A    \u2502 process B    \u2502 mem[x] = 1 (initial)\n\u251c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u253c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2524\n\u2502 t0 &lt;- mem[x] \u2502 t0 &lt;- mem[x] \u2502 mem[x] = 1\n\u2502 t0 &lt;- t0 + 1 \u2502 t0 &lt;- t0 + 1 \u2502\n\u2502 mem[x] &lt;- t0 \u2502 t0 &lt;- t0 + 1 \u2502 mem[x] = 2, B's t0 is out of date\n\u2502              \u2502 mem[x] &lt;- t0 \u2502 mem[x] = 3, 2 is overwritten\n\u2514\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2534\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2518\n</code></pre> <p>\u5b83\u4eec\u90fd\u60f3\u8981\u66f4\u65b0 <code>mem[x]</code>\uff0c\u53c8\u597d\u5de7\u4e0d\u5de7\u7684\u5b83\u4eec\u51e0\u4e4e\u540c\u65f6\u53d1\u751f\u8bfb\u53d6\u4e86 <code>mem[x]</code>\uff0c\u90a3\u4e48\u5c31\u4f1a\u51fa\u73b0\u95ee\u9898\uff1a\u4e24\u4e2a\u8fdb\u7a0b\u540c\u65f6\u8bfb\u53d6 <code>mem[x]</code>\uff0c\u7136\u540e\u5404\u81ea\u8ba1\u7b97\u66f4\u65b0\u540e\u7684\u503c\uff0c\u7136\u540e\u5404\u81ea\u5199\u56de <code>mem[x]</code>\uff0c\u7406\u60f3\u60c5\u51b5\u4e0b\uff0c\u6700\u7ec8\u7684 <code>mem[x]</code> \u4f1a\u6bd4\u539f\u6765\u5927 3\uff0c\u4f46\u73b0\u5728\u7684 <code>mem[x]</code> \u53ea\u6bd4\u539f\u6765\u5927 2\uff0c\u5176\u4e2d process A \u5bf9\u5b83\u7684\u4fee\u6539\u5728\u7b2c 7 \u884c\u88ab\u8986\u76d6\u4e86\u3002</p> <p>\u7a76\u5176\u6839\u672c\uff0c\u7531\u4e8e\u5982\u4eca\u6211\u4eec\u5904\u5728\u5e76\u53d1\u8bed\u5883\u4e0b\uff0c\u6240\u4ee5\u4f1a\u51fa\u73b0\u82e5\u5e72\u7528\u6237\u540c\u65f6\u6301\u6709\u4e00\u4efd\u6570\u636e\u8d44\u6e90\u7684\u60c5\u51b5\uff08\u4e3a\u4e86\u53d1\u6325\u5e76\u53d1\u7684\u4f18\u52bf\uff0c\u6211\u4eec\u4e5f\u5e94\u5f53\u5c3d\u53ef\u80fd\u7684\u6ee1\u8db3\u8fd9\u79cd\u9700\u6c42\uff09\uff0c\u903b\u8f91\u4e0a\u6570\u636e\u4fee\u6539\u8fc7\u7a0b\u5e94\u5f53\u662f\u7b26\u53f7\u7684\u3001\u77ac\u95f4\u7684\u3001\u7acb\u5373\u751f\u6548\u7684\uff0c\u4f46\u5b9e\u9645\u4e0a\u6211\u4eec\u5bf9\u6570\u636e\u7684\u64cd\u4f5c\u662f\u6570\u503c\u7684\u3001\u9700\u8981\u4e00\u6bb5\u65f6\u95f4\u6765\u5b8c\u6210\u7684\u3002\u5728\u8fd9\u79cd\uff08\u540e\u8005\uff09\u8bed\u5883\u4e0b\uff0c\u5982\u679c\u6211\u4eec\u65e0\u6cd5\u4fdd\u8bc1\u8bfb\u5165\u6570\u503c\u5b8c\u6210\u5230\u5199\u5165\u6570\u503c\u5b8c\u6210\u7684\u8fc7\u7a0b\u4e2d\uff0c<code>mem[x]</code> \u4fdd\u6301\u4e0d\u53d8\uff0c\u90a3\u4e48\u8be5\u64cd\u4f5c\u5b9e\u9645\u4e0a\u662f\u4f7f\u7528\u8fc7\u65f6\u6570\u636e\u8fdb\u884c\u8ba1\u7b97\u3002</p> <pre><code>\u250c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u252c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2510\n\u2502 process A    \u2502 process B    \u2502 mem[x] = 1 (initial)\n\u251c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u253c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2524\n\u2502 t0 &lt;- mem[x] \u2502 t0 &lt;- mem[x] \u2502 mem[x] = 1\n\u2502 t0 &lt;- t0 + 1 \u2502 t0 &lt;- t0 + 1 \u2502\n\u2502 mem[x] &lt;- t0 \u2502 t0 &lt;- t0 + 1 \u2502 mem[x] = 2, B's t0 is out of date\n\u2502              \u2502 mem[x] &lt;- t0 \u2502 mem[x] = 3, 2 is overwritten\n\u2514\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2534\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2518\n</code></pre> <p>\u53ef\u4ee5\u53d1\u73b0\uff0c\u7b2c\u516d\u884c\u7684 <code>t0</code> \u4ecd\u7136\u5728\u7528\u66f4\u65b0\u4e4b\u524d\u7684 <code>mem[x]</code> \u505a\u8ba1\u7b97\uff0c\u56e0\u800c\u53ef\u4ee5\u8ba4\u4e3a\u6b64\u65f6 process B \u4e2d\u7684 <code>t0</code> \u53c2\u4e0e\u8fd0\u7b97\u7684\u3001\u6697\u542b\u7684 <code>mem[x]</code> \u7684\u6570\u636e\u5df2\u7ecf\u8fc7\u65f6\u3002</p> <p>race condition</p> <p>\u7c7b\u4f3c\u8fd9\u79cd\u7684\uff0c\u7531\u4e24\u4e2a\u4fe1\u53f7\u4ea7\u751f\u7ade\u4e89\uff0c\u5176\u7ade\u4e89\u60c5\u51b5\u5f71\u54cd\u6700\u7ec8\u7ed3\u679c\u7684\u60c5\u51b5\uff0c\u88ab\u79f0\u4e3a\u7ade\u6001\u6761\u4ef6(race condition)\u3002\u5728\u4e0a\u9762\u8fd9\u4e2a\u4f8b\u5b50\u4e2d\uff0c\u8c01\u540e\u6267\u884c\uff0c\u6700\u7ec8\u7ed3\u679c\u5c31\u662f\u8c01\u7684\u8f93\u51fa\uff0c\u800c\u53e6\u4e00\u4e2a\u7528\u6237\u7684\u8f93\u51fa\u5219\u4f1a\u88ab\u8986\u76d6\u3002</p> <p>\u9700\u8981\u6ce8\u610f\u7684\u662f\uff0c\u8fd9\u91cc\u7684\u91cd\u70b9\u5e76\u4e0d\u662f\u201c\u5982\u4f55\u63a7\u5236\u7ade\u4e89\u7ed3\u679c\u201d\uff0c\u56e0\u4e3a\u65e0\u8bba\u7ade\u4e89\u7ed3\u679c\u5982\u4f55\uff08\u751a\u81f3\u8c01\u8d62\u4e86\u7ed3\u679c\u53ef\u80fd\u90fd\u4e00\u6837\uff09\uff0c\u53ea\u8981\u8fd9\u79cd\u201c\u7ade\u4e89\u201d\u51fa\u73b0\uff0c\u90a3\u4e48\u6700\u7ec8\u7ed3\u679c\u5c31\u6709\u53ef\u80fd\u4e0d\u7b26\u5408\u9884\u671f\u7684\u3002 \u771f\u6b63\u7684\u91cd\u70b9\u5e94\u8be5\u662f\u5982\u4f55\u907f\u514d\u8fd9\u79cd\u7ade\u4e89\u7684\u51fa\u73b0\u3002</p> <p>\u5c31\u6bd4\u5982\u4e0a\u9762\u7684\u4f8b\u5b50\uff0c\u65e0\u8bba\u6700\u7ec8 <code>mem[x]</code> \u662f 3 \u8fd8\u662f 2 \u90fd\u4e0d\u5bf9\uff0c\u7406\u60f3\u60c5\u51b5\u4e0b\u5e94\u8be5\u662f 4\u2014\u2014\u65e0\u8bba\u662f\u5148\u8fdb\u884c <code>+1</code> \u8fd8\u662f\u5148\u8fdb\u884c <code>+2</code>\u3002</p> <p>\u6ce8\u610f</p> <p>\u867d\u7136\u4e0a\u9762\u7684\u4f8b\u5b50\u4e2d\u6211\u4eec\u6a21\u62df\u7684\u4e24\u4e2a\u7a0b\u5e8f\u662f\u6309\u7167\u76f8\u540c\u901f\u5ea6\uff0c\u4e00\u884c\u4e00\u4e2a\u6307\u4ee4\u6267\u884c\u7684\uff0c\u4f46\u662f\u6211\u4eec\u5728\u5e76\u884c\u8bed\u5883\u4e0b\u5bf9\u6240\u6709\u8fdb\u7a0b\u6267\u884c\u7684\u901f\u5ea6\u4e0d\u5e94\u5f53\u6709\u6240\u5047\u8bbe\uff0c\u5373\u8fdb\u7a0b A \u4e0d\u77e5\u9053\u8fdb\u7a0b B \u7684\u901f\u5ea6\u3002</p> <p>\u4e0d\u4ec5\u5982\u6b64\uff0c\u6211\u4eec\u4e5f\u5e76\u4e0d\u4e00\u5b9a\u8981\u5728\u5e76\u884c\u8bed\u5883\u4e0b\u8ba8\u8bba\u8fd9\u4e2a\u95ee\u9898\uff0c\u5728\u591a\u9053\u8bed\u5883\u4e0b\u8fd9\u4e2a\u95ee\u9898\u90fd\u4f1a\u51fa\u73b0\uff0c\u4f8b\u5982\uff1a</p> <pre><code>\u250c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2510     \u250c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2510\n\u2502 process A    \u2502     \u2502 process B    \u2502 mem[x] = 1 (initial)\n\u251c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2524     \u251c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2524\n\u2502              \u2502     \u2502 t0 &lt;- mem[x] \u2502 mem[x] = 1\n\u2502 t0 &lt;- mem[x] \u2502\u25c4\u2500\u2500\u2500\u2500\u2524 &lt;ctx switch&gt; \u2502 mem[x] = 1\n\u2502 t0 &lt;- t0 + 1 \u2502     \u2502              \u2502\n\u2502 mem[x] &lt;- t0 \u2502     \u2502              \u2502 mem[x] = 2, B's t0 is out of date\n\u2502 &lt;ctx switch&gt; \u251c\u2500\u2500\u2500\u2500\u25ba\u2502 t0 &lt;- t0 + 1 \u2502\n\u2502              \u2502     \u2502 t0 &lt;- t0 + 1 \u2502 \n\u2502              \u2502     \u2502 mem[x] &lt;- t0 \u2502 mem[x] = 3, 2 is overwritten\n\u2514\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2518     \u2514\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2518\n</code></pre> <p>\u95ee\u9898\u4f9d\u65e7\u3002</p> <p>\u6839\u636e\u4e0a\u9762\u8fd9\u4e2a\u5177\u4f53\u7684\u4f8b\u5b50\uff0c\u6211\u4eec\u53d1\u73b0\uff0c\u5982\u679c\u9700\u8981\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\uff0c\u6211\u4eec\u6709\u4e24\u79cd\u9009\u62e9\uff1a</p> <ol> <li>\u8fdb\u884c\u7b26\u53f7\u7684\u8fd0\u7b97\u800c\u975e\u6570\u503c\u7684\u8fd0\u7b97\uff0c\u8fd9\u6837\u8f93\u5165\u7684\u53d8\u5316\u80fd\u5728\u4efb\u610f\u65f6\u523b\u53cd\u6620\u5728\u8f93\u51fa\u4e0a\uff0c\u8fd9\u6837\u65f6\u65f6\u523b\u523b\u90fd\u662f\u201c\u6700\u65b0\u201d\uff0c\u800c\u4e0d\u4f1a\u51fa\u73b0\u201c\u8fc7\u65f6\u201d\uff1b</li> <li>\u4fdd\u8bc1\u8bfb\u5165\u6570\u503c\u5b8c\u6210\u5230\u5199\u5165\u6570\u503c\u5b8c\u6210\u7684\u8fc7\u7a0b\u4e2d\uff0c<code>mem[x]</code> \u4fdd\u6301\u4e0d\u53d8\uff0c\u5373\u4e24\u4e2a\u53ef\u80fd\u7ade\u4e89\u7684\u64cd\u4f5c\uff0c\u5728\u65f6\u95f4\u4e0a\u4e0d\u5e94\u8be5\u6709\u4ea4\u96c6\uff1b</li> </ol> <p>\u663e\u7136\uff0c\u6211\u4eec\u5e94\u5f53\u9009\u62e9\u7b2c\u4e8c\u79cd\u3002</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit2-Part1/#the-critical-section-problem","title":"The Critical-Section Problem","text":"<p>\u4e3a\u4e86\u66f4\u597d\u5730\u5c55\u5f00\uff0c\u6211\u4eec\u5bf9\u4e0a\u9762\u7684\u8fd9\u79cd\u60c5\u51b5\u8fdb\u884c\u5efa\u6a21\uff0c\u5e76\u7ed9\u51fa\u89e3\u51b3 race condition \u95ee\u9898\u7684\u65b9\u6cd5\u9700\u8981\u6ee1\u8db3\u7684\u8303\u5f0f\uff1a</p> <p>\u6211\u4eec\u5e94\u5f53\u4fdd\u8bc1\u5728\u4e00\u4e2a\u8fdb\u7a0b\u5728\u4fee\u6539 <code>mem[x]</code> \u7684\u65f6\u5019\uff0c\u5176\u5b83\u8fdb\u7a0b\u4e0d\u5e94\u8be5\u8bfb\u53d6 <code>mem[x]</code>\uff08\u81f3\u5c11\u4e0d\u5e94\u4ee5\u4fee\u6539 <code>mem[x]</code> \u4e3a\u76ee\u7684\u6765\u8bfb\u53d6\uff09\uff0c\u76f4\u5230\u8fd9\u4e2a\u8fdb\u7a0b\u5b8c\u6210\u4e86\u5bf9 <code>mem[x]</code> \u7684\u4fee\u6539\u3002\u6362\u53e5\u8bdd\u6765\u8bf4\uff0c<code>mem[x]</code> \u8fd9\u4e2a\u5171\u4eab\u8d44\u6e90\u5e94\u5f53\u53ea\u80fd\u88ab\u4e00\u4e2a\u7528\u6237\u6301\u6709\uff0c\u6211\u4eec\u79f0\u8fd9\u79cd\u53ea\u80fd\u88ab\u81f3\u591a\u4e00\u4e2a\u7528\u6237\u5360\u6709\u7684\u8d44\u6e90\u4e3a\u4e34\u754c\u8d44\u6e90\u3002\u800c\u7a0b\u5e8f\u4e2d\u8bbf\u95ee\u4e34\u754c\u8d44\u6e90\u7684\u4ee3\u7801\u6bb5\uff0c\u6211\u4eec\u79f0\u4e4b\u4e3a\u4e34\u754c\u533a\u6bb5(critical section, CS)\ud83d\udd17\u3002</p> <p>\u90a3\u4e48\uff0c\u5bf9\u4e8e\u4e4b\u524d\u63d0\u5230\u8fc7\u7684\u4f8b\u5b50\uff0c\u6211\u4eec\u62ff\u51fa\u6765\u5bf9\u6bd4\u6a21\u62df\u7684\u90e8\u5206\u5c31\u662f critical section\u3002</p> <p>\u800c CS \u95ee\u9898\uff0c\u6307\u7684\u5c31\u662f\u5982\u4f55\u4fdd\u8bc1\u6700\u591a\u53ea\u6709\u4e00\u4e2a\u7528\u6237\u5728\u6267\u884c\u4e34\u754c\u533a\u6bb5\u7684\u4ee3\u78011\u3002</p> <p>\u56f4\u7ed5\u4e34\u754c\u533a\u6bb5\uff0c\u6211\u4eec\u5b9a\u4e49\u80fd\u591f\u89e3\u51b3 CS \u95ee\u9898\u7684\u4ee3\u7801\u5e94\u5f53\u80fd\u591f\u505a\u5982\u4e0b\u5212\u5206\uff1a</p> <pre><code>\u250c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2510\n\u2502  Entry Section      \u2502 &lt;-- ask for &amp; wait for permission to enter CS\n\u251c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2524\n\u2502  Critical Section   \u2502 &lt;-- codes manipulating critical resources\n\u251c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2524\n\u2502  Exit Section       \u2502 &lt;-- release the critical resources\n\u251c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2524\n\u2502  Remainder Section  \u2502 &lt;-- other codes\n\u2514\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2518\n</code></pre> <p>\u8fdb\u7a0b\u9700\u8981\u5728 entry section \u5224\u65ad\u662f\u5426\u80fd\u591f\u8fdb\u5165 critical section\uff0c\u5373\u7d22\u53d6\u4e34\u754c\u8d44\u6e90\uff0c\u5982\u679c\u4e0d\u884c\u5219\u7b49\u5f85\uff1b\u800c\u5728\u8fdb\u5165 critical section \u540e\uff0c\u8fdb\u7a0b\u9700\u8981\u5728 exit section \u91ca\u653e\u4e34\u754c\u8d44\u6e90\uff1b\u7136\u540e\u8131\u79bb CS \u95ee\u9898\u7684\u8bed\u5883\uff0c\u8fdb\u5165 remainder section \u7ee7\u7eed\u6267\u884c\u3002</p> <p>Brainstorming</p> <p>\u6574\u4e2a\u8fc7\u7a0b\u6709\u70b9\u50cf\u8c03\u5ea6\uff0c\u7b49\u5f85\u4e34\u754c\u8d44\u6e90\u7684\u8fc7\u7a0b\u5c31\u597d\u50cf ready \u6001\u7b49\u5f85\u8c03\u5ea6\u8fc7\u7a0b\u4e2d\u7684 CPU \u8d44\u6e90\uff08CPU \u4e5f\u53ef\u4ee5\u8ba4\u4e3a\u662f\u4e00\u79cd\u4e34\u754c\u8d44\u6e90\uff0c\u53ea\u4e0d\u8fc7\u5b83\u4e0d\u662f\u7531\u8fdb\u7a0b\u4e3b\u52a8\u5904\u7406\u548c\u7d22\u53d6\uff09\u3002</p> <p>\u65e2\u7136\u5982\u6b64\u6211\u4eec\u53ef\u4ee5\u8fc1\u79fb\u201c\u72b6\u6001\u201d\u8fd9\u4e2a\u6982\u5ff5\u3002\u6211\u4eec\u53ea\u5173\u5fc3\u76f4\u63a5\u4e0e CS \u95ee\u9898\u6709\u5173\u7684\u72b6\u6001\uff0c\u6240\u4ee5\u6211\u5728\u8fd9\u91cc\u5b9a\u4e49\uff1a\u5c31\u7eea\u3001\u4e34\u754c\u3001\u65e0\u5173\u4e09\u4e2a\u72b6\u6001\u3002</p> <ol> <li>\u5c31\u7eea\u6001\uff1a\u8fdb\u7a0b\u968f\u65f6\u51c6\u5907\u597d\u8fdb\u5165 critical section\uff0c\u60f3\u8981\u6301\u6709\u4e34\u754c\u8d44\u6e90\uff1b</li> <li>\u4e34\u754c\u6001\uff1a\u8fdb\u7a0b\u6b63\u5728\u6267\u884c critical section\uff0c\u6301\u6709\u4e34\u754c\u8d44\u6e90\uff0c\u6216\u8fdb\u7a0b\u6267\u884c\u5b8c critical section\uff0c\u6267\u884c exit section \u6b63\u5728\u91ca\u653e\u6301\u6709\u7684\u4e34\u754c\u8d44\u6e90\u4e2d\uff1b</li> <li>\u65e0\u5173\u6001\uff1a\u4e0d\u5904\u4e8e\u5c31\u7eea\u6001\u4e5f\u4e0d\u5904\u4e8e\u4e34\u754c\u6001\uff0c\u4e0d\u60f3\u8981\u6301\u6709\u4e34\u754c\u8d44\u6e90\uff0c\u6216\u662f\u4f7f\u7528\u5b8c\u5df2\u7ecf\u91ca\u653e\uff1b</li> </ol> <p>\u6839\u636e\u6211\u4eec\u5148\u524d\u7ed9\u51fa\u7684\uff0c\u89e3\u6cd5\u9700\u8981\u6ee1\u8db3\u7684\u6027\u8d28\u4e2d\u7684 mutual exclusion\uff0c\u4e0d\u80fd\u540c\u65f6\u6709\u591a\u4e2a\u8fdb\u7a0b\u5904\u4e8e\u4e34\u754c\u6001\uff0c\u4f46\u662f\u53ef\u4ee5\u6709\u82e5\u5e72\u8fdb\u7a0b\u5904\u4e8e\u5c31\u7eea\u6001\uff0c\u800c\u65e0\u5173\u6001\u5219\u8868\u793a\u4e0d\u4f1a\u4ea7\u751f\u7ade\u4e89\uff0c\u548c\u8c03\u5ea6\u8fc7\u7a0b\u5341\u5206\u76f8\u4f3c\u3002</p> <p>\u8fd9\u4e9b\u5b9a\u4e49\u5c06\u4f1a\u5728\u6211\u4eec\u4e4b\u540e\u7684\u63a2\u7d22\u4e2d\u8d77\u4f5c\u7528\u3002</p> <p>\u540c\u65f6\uff0c\u6211\u4eec\u8981\u6c42\u89e3\u51b3\u65b9\u6848\u9700\u8981\u6ee1\u8db3\u5982\u4e0b\u6027\u8d28\uff1a</p> <p></p> <p>requirements for solution to CS problem</p> <ol> <li>\u4e34\u754c\u4e92\u65a5(mutual exclusion)\uff1a\u64cd\u4f5c\u540c\u4e00\u4e34\u754c\u8d44\u6e90\u7684\u4e34\u754c\u533a\u6bb5\u5e94\u5f53\u4e92\u76f8\u6392\u65a5\uff1b<ul> <li>\u5982\u679c\u8fdb\u7a0b \\(P_i\\) \u6b63\u5728\u6267\u884c\u5176 critical section\uff0c\u90a3\u4e48\u4e0d\u5e94\u5f53\u6709\u5176\u4ed6\u8fdb\u7a0b\u5904\u4e8e\uff08\u64cd\u4f5c\u540c\u4e00\u4e34\u754c\u8d44\u6e90\u7684\uff09critical section\uff1b</li> </ul> </li> <li>\u9009\u62e9\u65f6\u95f4\u6709\u9650(progress)\uff1a\u9009\u62e9\u4e0b\u4e00\u4e2a\u8fdb\u5165 critical section \u7684\u64cd\u4f5c\u5e94\u5f53\u53ea\u6709\u5904\u4e8e entry/critical/exit section \u7684\u8fdb\u7a0b\u53c2\u4e0e\uff0c\u4e14\u8be5\u9009\u62e9\u5e94\u5f53\u5728\u6709\u9650\u65f6\u95f4\u5185\u88ab\u6267\u884c\uff1b</li> <li>\u7b49\u5f85\u65f6\u95f4\u6709\u9650(bounded waiting)\uff1a\u8fdb\u7a0b\u7b49\u5f85\u88ab\u5141\u8bb8\u8fdb\u5165 critical section \u7684\u65f6\u95f4\u5e94\u5f53\u662f\u6709\u9650\u7684\uff1b</li> </ol> <p>\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u4ee5\u8ba8\u8bba CS \u95ee\u9898\u662f\u5982\u4f55\u89e3\u51b3\u7684\u4e3a\u4e3b\u7ebf\uff0c\u63a2\u7d22\u5982\u4f55\u89e3\u51b3 race condition\u3002</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit2-Part1/#for-kernel-code","title":"For Kernel Code","text":"<p>\u7531\u4e8e kernel code \u4e0b\u7684 CS \u95ee\u9898\u89e3\u51b3\u8f83\u4e3a\u6e05\u6670\u76f4\u63a5\uff0c\u6240\u4ee5\u5148\u884c\u4ecb\u7ecd\u3002</p> <p>For Kernel Code</p> <p>\u5728 kernel code \u4e2d\u4e5f\u666e\u904d\u5b58\u5728\u7740 race condition \u7684\u95ee\u9898\uff0c\u4f8b\u5982\uff1a</p> <p>  Race condition when assigning a pid. </p> <p>\u4e0a\u4f8b\u4e2d \\(P_0\\) \u548c \\(P_1\\) \u540c\u65f6\u8bbf\u95ee\u4e86 <code>next_available_pid</code> \u8fd9\u4e2a\u4e34\u754c\u8d44\u6e90\uff0c\u4ea7\u751f\u7ade\u4e89\uff0c\u5bfc\u81f4\u6700\u540e\u6709\u4e24\u4e2a\u8fdb\u7a0b\u4f7f\u7528\u4e86\u540c\u4e00\u4e2a <code>pid</code>\u3002</p> <p>\u6b32\u89e3\u51b3 kernel code \u4e2d\u7684 CS \u95ee\u9898\uff0c\u6211\u4eec\u53ef\u4ee5\u4fdd\u8bc1\u53ea\u6709\u4e00\u4e2a\u8fdb\u7a0b\u53ef\u4ee5\u8fd0\u884c\u5728 kernel mode\uff0c\u8fd9\u6837\u5c31\u53ef\u4ee5\u4fdd\u8bc1\u5728 kernel code \u4e2d\u8bbf\u95ee\u4e34\u754c\u8d44\u6e90\u7684\u884c\u4e3a\uff0c\u4ece\u800c\u89e3\u51b3 CS \u95ee\u9898\u3002</p> <p>\u5bf9\u4e8e\u5355\u5904\u7406\u5668\u6765\u8bf4\uff0c\u6211\u4eec\u53ea\u9700\u8981\u5728 kernel code \u4e2d\u7981\u6b62\u4e2d\u65ad\uff0c\u5c31\u53ef\u4ee5\u4fdd\u8bc1\u53ea\u6709\u4e00\u4e2a\u8fdb\u7a0b\u53ef\u4ee5\u8fd0\u884c\u5728 kernel mode\uff1b\u800c\u5bf9\u4e8e\u591a\u5904\u7406\u5668\u6765\u8bf4\uff0c\u8fd9\u79cd\u65b9\u6cd5\u5c31\u4e0d\u90a3\u4e48\u5408\u9002\u4e86\u2014\u2014\u6211\u4eec\u9700\u8981\u540c\u65f6\u544a\u8bc9\u591a\u4e2a\u5904\u7406\u5668\u4e2d\u65ad\u88ab\u7981\u6b62\uff0c\u800c\u8fd9\u4e2a\u8fc7\u7a0b\u4e2d\u7684\u65f6\u5ef6\u4ecd\u7136\u4f1a\u4ea7\u751f\u95ee\u9898\uff1b\u4e0d\u4ec5\u5982\u6b64\uff0c\u8fd9\u4e2a\u65b9\u6cd5\u4e5f\u4f1a\u5e26\u6765\u989d\u5916\u7684\u5f00\u9500\u3002\u5728\u591a\u5904\u7406\u5668\u8bed\u5883\u4e0b\uff0c\u6211\u4eec\u9700\u8981\u5b9e\u73b0\u62a2\u5360\u5f0f\u5185\u6838(preemptive kernels)\u548c\u975e\u62a2\u5360\u5f0f\u5185\u6838(non-preemptive kernels)\uff0c\u5173\u952e\u662f\u540e\u8005\u5b9e\u73b0\u4e86\u4e00\u6bb5\u65f6\u95f4\u5185\u53ea\u6709\u4e00\u4e2a\u8fdb\u7a0b\u53ef\u4ee5\u8fd0\u884c\u5728 kernel mode2\u3002</p> <p>\u63a5\u4e0b\u6765\u6211\u4eec\u63a2\u7d22\u66f4\u4e3a\u901a\u7528\u7684\u89e3\u51b3\u65b9\u6848\u3002</p> <p>\u8bf4\u660e</p> <p>\u4e3a\u4e86\u7b80\u5316\u8bf4\u660e\u4ee3\u7801\uff0c\u6211\u4eec\u7528\u5168\u5927\u5199\u6765\u8868\u793a\u4e00\u4e2a\u5171\u4eab\u8d44\u6e90\uff0c\u4f8b\u5982 <code>READY</code>\uff0c\u5b83\u80fd\u591f\u88ab\u82e5\u5e72\u8fdb\u7a0b\u8bbf\u95ee\u3002\u5b9e\u9645\u4e0a\u8fd9\u4e2a\u529f\u80fd\u5e94\u5f53\u7531\u64cd\u4f5c\u7cfb\u7edf\u63d0\u4f9b\uff0c\u5e76\u4e0d\u662f\u6211\u4eec\u5173\u6ce8\u7684\u91cd\u70b9\u3002</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit2-Part1/#petersons-algorithm","title":"Peterson\u2019s Algorithm","text":"<p>Links</p> <ul> <li>Peterson's algorithm | Wikipedia</li> </ul> <p>Peterson's algorithm \u662f\u5bf9\u53ea\u6709\u4e24\u4e2a\u8fdb\u7a0b\u53c2\u4e0e\u7684\u540c\u6b65\u95ee\u9898\u7684\u4e00\u4e2a\u89e3\u6cd5\uff0c\u5177\u6709\u4e00\u5b9a\u7684\u5c40\u9650\u6027\uff0c\u4f46\u5176\u8bbe\u8ba1\u76f8\u5bf9\u7b80\u5355\uff0c\u6240\u4ee5\u5148\u884c\u7ed9\u51fa\u3002\u5728\u672c\u8282\u4e2d\uff0c\u6211\u4eec\u5047\u8bbe \\(P_0\\) \u548c \\(P_1\\) \u662f\u53c2\u4e0e\u540c\u6b65\u95ee\u9898\u8ba8\u8bba\u7684\u4e24\u4e2a\u8fdb\u7a0b\u3002</p> <p>\u57fa\u4e8e Peterson's algorithm \u5bf9\u591a\u8fdb\u7a0b\u60c5\u51b5\u7684\u6269\u5c55\u88ab\u79f0\u4e3a filter algorithm\uff0c\u4f46 filter algorithm \u4e0d\u6ee1\u8db3 bounded waiting time \u7684\u6761\u4ef6\uff0c\u8bfb\u8005\u6709\u5174\u8da3\u53ef\u4ee5\u81ea\u884c\u4e86\u89e3\u3002</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit2-Part1/#\u7b97\u6cd5\u63cf\u8ff0","title":"\u7b97\u6cd5\u63cf\u8ff0","text":"<p>\u4e3a\u4e86\u4fdd\u8bc1\u5904\u4e8e\u4e34\u754c\u6001\u7684\u8fdb\u7a0b\u81f3\u591a\u53ea\u6709\u4e00\u4e2a\uff0c\u6211\u4eec\u5e94\u5f53\u5728\u8fdb\u7a0b\u5904\u4e8e\u5c31\u7eea\u6001\u65f6\uff0c\u786e\u8ba4\u6ca1\u6709\u5176\u4ed6\u8fdb\u7a0b\u5904\u4e8e\u4e34\u754c\u6001\u540e\u518d\u8fdb\u5165\u3002\u5176\u4e2d\u6700\u91cd\u8981\u7684\u4e00\u4ef6\u4e8b\u5c31\u662f\uff0c\u5f53\u6211\u4eec\u5904\u5728 \\(P_0\\) \u65f6\uff0c\u6211\u4eec\u5982\u4f55\u77e5\u9053 \\(P_1\\) \u662f\u5426\u6b63\u5904\u4e8e\u4e34\u754c\u6001\u5462\uff1fPeterson\u2019s Algorithm \u901a\u8fc7\u5982\u4e0b\u65b9\u5f0f\u5b9e\u73b0\u4e86\u8fd9\u4ef6\u4e8b\uff1a</p> <pre><code>// `i` is 0 or 1, indicating current pid, while `j` is another pid.\nprocess(i) {\nj = 1 - i;\n\nREADY[i] = true;                    // \u2510\nTURN = j;                           // \u2502\nwhile (READY[j] &amp;&amp; TURN == j) {}    // \u251c entry section\n// i.e. wait until:             // \u2502\n//  (1) j exits,                // \u2502\n//  (2) j is slower, so it      // \u2502\n//      should run now.         // \u2518\n\n/* operate critical resources */    // - critical section\n\nREADY[i] = false;                   // - exit section\n\n/* other things */                  // - remainder section\n}\n</code></pre> <p>\u9996\u5148\uff0c\u6211\u4eec\u8bf4\u660e entry section \u6ca1\u6709\u4e34\u754c\u8d44\u6e90\u3002<code>READY</code> \u662f\u4e00\u4e2a\u5171\u4eab\u7684\u6570\u7ec4\uff0c\u6bcf\u4e2a\u8fdb\u7a0b\u53ea\u4fee\u6539\u4e0e\u81ea\u5df1\u4e00\u4e00\u5bf9\u5e94\u7684 element\uff0c\u6240\u4ee5\u672c\u8d28\u4e0a <code>READY</code> \u4e0d\u4f1a\u51fa\u73b0 race condition\uff0c\u56e0\u800c\u4e5f\u4e0d\u662f\u4e34\u754c\u8d44\u6e90\u3002\u800c <code>TURN</code>\uff0c\u6211\u4eec\u8fd9\u91cc\u53ea\u5bf9 <code>TURN</code> \u8fdb\u884c\u5199\u7684\u64cd\u4f5c\uff0c\u4f46\u662f P1 \u548c P2 \u8c01\u5148\u8dd1\u5230\u8fd9\u4e00\u884c\u4f1a\u51b3\u5b9a <code>TURN</code> \u6700\u540e\u7684\u503c\uff0c\u6240\u4ee5\u5b9e\u9645\u4e0a\u8fd9\u91cc\u6709 race condition\u3002</p> <p>\u4f46\u8fd9\u5c31\u662f Peterson\u2019s Algorithm \u5de7\u5999\u7684\u5730\u65b9\uff0cPeterson's \u5229\u7528 race condition \u8fd9\u4e2a\u201c\u540e\u8986\u76d6\u524d\u201d\u7684\u6027\u8d28\uff0c\u5b9e\u73b0\u4e86\u6807\u8bb0\u4e86\u8fd9\u4e24\u4e2a\u8fdb\u7a0b\u7684\u5148\u6765\u540e\u5230\u7684\u6548\u679c\u3002\u6211\u4eec\u90fd\u5411\u8fd9\u4e2a <code>TURN</code> \u5199\u4e00\u4e2a\u4e92\u5f02\u7684\u503c\uff08\u6bd4\u5982\u81ea\u5df1\u7684 id\uff0c\u6216\u8005\u5bf9\u65b9\u7684 id\uff09\uff0c\u7b49\u5927\u5bb6\u90fd\u5199\u597d\u540e\u6211\u4eec\u770b\u770b\u8fd9\u4e2a\u503c\u6700\u7ec8\u662f\u8c01\u5199\u7684\uff0c\u4e8e\u662f\u5c31\u77e5\u9053\u8c01\u540e\u5230\u3002</p> <p>\u5229\u7528\u8fd9\u4e2a\u539f\u7406\uff0cPeterson's \u8fd9\u91cc\u505a\u4e86\u4e00\u4e2a\u201c\u975e\u5e38\u6709\u4e2d\u56fd\u4eba\u6c14\u8d28\u201d\u7684\u4e8b\u60c5\uff1a\\(P_0\\) \u548c \\(P_1\\) \u4e0a\u516c\u4ea4\u8f66\u540e\u540c\u65f6\u770b\u4e0a\u4e86\u4e00\u4e2a\u5ea7\u4f4d\uff0c\\(P_0\\) \u8bf4\uff1a\u201c\u4f60\u5750\u5427\u3002\u201d\uff0c \\(P_1\\) \u81ea\u7136\u4e5f\u8981\u5ba2\u6c14\u4e00\u4e0b\uff0c\u8bf4\uff1a\u201c\u8fd8\u662f\u4f60\u5750\u5427\uff01\u201d\u3002\u73b0\u5728\u4e24\u8fb9\u90fd\u5ba2\u6c14\u8fc7\u4e86\uff0c\\(P_0\\) \u5c31\u53ef\u4ee5\u5fc3\u5b89\u7406\u5f97\u5730\u5750\u4e0b\u4e86\u3002\u5bf9\u4e0a\u8ff0\u8fc7\u7a0b\uff0c\u6211\u4eec\u7ed9\u51fa \\(P_0\\) \u83b7\u5f97\u6905\u5b50\u7684\u51c6\u786e\u6761\u4ef6\u6709\uff1a</p> <ol> <li>\\(P_0\\) \u60f3\u5750\u4e0b\uff0c\\(P_1\\) \u4e5f\u60f3\u5750\u4e0b\uff0c\u5426\u5219\u5c31\u6ca1\u6709\u51b2\u7a81\u4e86\uff1b</li> <li>\\(P_0\\) \u53d1\u73b0 \\(P_1\\) \u5728\u5ba2\u6c14\uff0c\u4f46 \\(P_0\\) \u5df2\u7ecf\u5ba2\u6c14\u8fc7\u4e86\uff1b</li> </ol> <p>\u5bf9\u5e94\u5230\u4e0a\u9762\u7ed9\u51fa\u7684\u4ee3\u7801\u91cc\uff0c\u8fd9\u4e2a\u6761\u4ef6\u53ef\u4ee5\u7ffb\u8bd1\u4e3a\uff1a</p> <ol> <li><code>READY[0]</code> = <code>READY[1]</code> = <code>true</code>\uff1b</li> <li><code>TURN</code> \u2260 <code>j</code>\uff0c\u4f46\u6b64\u524d \\(P_i\\) \u5df2\u7ecf\u6267\u884c\u8fc7 <code>TURN &lt;- j</code>\uff1b</li> </ol> <p>\u8bf7\u8bfb\u8005\u4ed4\u7ec6\u601d\u8003\u4e0a\u9762\u7684\u8fc7\u7a0b\uff0c\u5e76\u9002\u5f53\u8fdb\u884c\u5168\u9762\u7684\u6a21\u62df\u4ee5\u7406\u89e3 Peterson's \u662f\u5982\u4f55\u5de5\u4f5c\u7684\u3002</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit2-Part1/#\u6027\u8d28\u8bc1\u660e","title":"\u6027\u8d28\u8bc1\u660e","text":"<p>\u73b0\u5728\u6211\u4eec\u9700\u8981\u8bc1\u660e\u8fd9\u4e2a\u7b97\u6cd5\u6ee1\u8db3\u6027\u8d28\u3002</p> <p>\u6211\u7684\u8bc1\u660e\u6bd4\u8f83\u8be6\u7ec6\u548c\u5570\u55e6\uff0c\u4f46\u6211\u8ba4\u4e3a\u5b8c\u6574\u5730\u6a21\u62df\u66f4\u52a0\u6709\u5229\u4e8e\u76f4\u89c9\u7406\u89e3\uff0c\u5982\u679c\u4f60\u60f3\u8981\u66f4\u7b80\u6d01\u7684\u8bc1\u660e\uff0c\u53ef\u4ee5\u53c2\u8003 xyx \u7684\u7b14\u8bb0\u3002</p> mutual exclusion <pre><code>// `i` is 0 or 1, indicating current pid, while `j` is another pid.\nprocess(i) {\nj = 1 - i;\n\nREADY[i] = true;                    // \u2510\nTURN = j;                           // \u2502\nwhile (READY[j] &amp;&amp; TURN == j) {}    // \u251c entry section\n// i.e. wait until:             // \u2502\n//  (1) j exits,                // \u2502\n//  (2) j is slower, so it      // \u2502\n//      should run now.         // \u2518\n\n/* operate critical resources */    // - critical section\n\nREADY[i] = false;                   // - exit section\n\n/* other things */                  // - remainder section\n}\n</code></pre> <p>lemma</p> <p>\u5982\u679c\u6b64\u65f6 i \u548c j \u540c\u5904\u4e8e\u7b2c 7 \u884c\uff0c\u90a3\u4e48\u663e\u7136\uff1a</p> <ol> <li>\u4e24\u4e2a\u8fdb\u7a0b\u90fd\u60f3\u8981\u8fdb\u5165 critical section\uff0c\u5373 <code>READY[i]</code> \u548c <code>READY[j]</code> \u90fd\u4e3a <code>true</code>\uff1b</li> <li><code>TURN</code> \u7684\u503c\u4e0d\u518d\u4f1a\u88ab\u66f4\u6539\uff1b</li> <li>\u4e24\u4e2a\u8fdb\u7a0b\u90fd\u5c1a\u672a\u8fdb\u5165 critical section\uff1b</li> </ol> <p>\u7531\u4e8e <code>TURN</code> \u5fc5\u5b9a\u4e5f\u53ea\u80fd\u4e3a i \u6216 j\uff0c\u6240\u4ee5 i \u548c j \u5fc5\u7136\u6709\u4e14\u4ec5\u6709\u4e00\u4e2a\u8fdb\u7a0b\u63a5\u4e0b\u6765\u4f1a break loop \u5e76\u8fdb\u5165 critical section\uff0c\u5728\u5b83\u7ed3\u675f\u4e4b\u524d\uff0c\u5373\u5728 <code>READY[?]</code> \u88ab\u6539\u53d8\u4e4b\u524d\uff0c\u8be5\u6761\u4ef6\u6301\u7eed\u6210\u7acb\u3002</p> <p>\u56e0\u6b64\u6211\u4eec\u5f97\u5230\u4e00\u4e2a\u7ed3\u8bba\uff1a\u5982\u679c\u6b64\u65f6 i \u548c j \u540c\u5904\u4e8e\u7b2c\u4e03\u884c\uff0c\u90a3\u4e48\u4ece\u8be5\u65f6\u523b\u5f00\u59cb\uff0c\u5230\u4e24\u4e2a\u8fdb\u7a0b\u90fd\u79bb\u5f00 critical section \u4e3a\u6b62\uff0c\u4e92\u65a5\u6027\u8d28\u90fd\u6210\u7acb\u3002</p> <p>\u73b0\u5728\u6211\u4eec\u8003\u8651 i \u5df2\u7ecf\u5148\u884c\u8fd0\u884c\u5230\u7b2c 7 \u884c\uff0c\u800c j \u8fd8\u6ca1\u8fd0\u884c\u5230\u7b2c 7 \u884c\uff1a</p> <p>Situation 1</p> <p>\u5982\u679c j \u8fd8\u6ca1\u8fdb\u5165\u7b2c 5 \u884c\uff0c\u90a3\u4e48 <code>READY[j]</code> \u4e3a <code>false</code>\uff0c\u6b64\u65f6\u6ca1\u6709\u7ade\u4e89\uff0ci \u53ef\u4ee5\u76f4\u63a5\u8fdb\u5165\u4e34\u754c\u6001\u3002\u5e76\u4e14 j \u4e4b\u540e\u8fd0\u884c\u5230\u7b2c 7 \u884c\u65f6\uff0c<code>TURN == &lt;another&gt;</code> \u59cb\u7ec8\u6210\u7acb\u3002\u6240\u4ee5 j \u4f55\u65f6\u8fdb\u5165 critical section \u5b8c\u5168\u53d6\u51b3\u4e8e <code>READY[j]</code>\uff0c\u5373 j \u4f55\u65f6\u79bb\u5f00 critical section\u3002</p> <p>\u663e\u7136\uff0c\u6b64\u65f6\u6ee1\u8db3\u4e92\u65a5\u6027\u8d28\u3002</p> <p>Situation 2</p> <p>\u5982\u679c j \u5df2\u7ecf\u8fd0\u884c\u5b8c\u7b2c 5 \u884c\uff0c\u8fd8\u6ca1\u6267\u884c\u7b2c 6 \u884c\uff0c\u90a3\u4e48\u5bf9\u4e8e i \u6765\u8bf4\uff0c<code>(READY[j] &amp;&amp; TURN == j)</code> \u4e3a <code>true</code>\uff0c\u6b64\u65f6 i \u5c06\u7b49\u5f85 j\uff0c\u8fdb\u5165 Situation 3\u3002</p> <p>\u4e5f\u5c31\u662f\u8bf4\uff0c\u8981\u4e48 i \u548c j \u4e0d\u7ade\u4e89\uff0c\u8981\u4e48\u4e24\u8005\u90fd\u8fd0\u884c\u5230\u7b2c 7 \u884c\u540e\u624d\u4f1a\u6709\u8fdb\u7a0b\u8fdb\u5165 critical section</p> <p>\u8fd9\u5c31\u597d\u50cf\u4e24\u8005\u5728\u7b2c 6 \u884c\u6bd4\u8c01\u5148\u4e3e\u624b\uff0c\u7136\u540e\u7b49\u4e24\u8005\u90fd\u4e3e\u8fc7\u624b\uff08\u90fd\u8dd1\u5b8c\u7b2c 6 \u884c\uff0c\u5230\u8fbe\u7b2c 7 \u884c\uff09\u540e\uff0c\u518d\u5224\u65ad\u8c01\u8fdb\u5165 critical section\uff0c\u800c\u8fdb\u5165\u7b2c 7 \u884c\u4ee5\u540e\u6240\u6709\u7684\u5224\u65ad\u6761\u4ef6\u90fd\u662f\u76f8\u5bf9\u9759\u6b62\u7684\u3001\u4e0d\u4f1a\u518d\u88ab\u4fee\u6539\u7684\uff0c\u56e0\u800c\u907f\u514d\u751a\u81f3\u5229\u7528\u4e86 race condition \u5bf9 selection \u7684\u5f71\u54cd\uff0c\u4fdd\u8bc1\u4e86\u4e92\u65a5\u7684\u6027\u8d28\u3002</p> progress <p>\u8fd9\u6761\u6027\u8d28\u7684\u6210\u7acb\u6bd4\u8f83\u7b26\u5408\u76f4\u89c9\uff0c\u552f\u4e00\u9700\u8981\u8bf4\u660e\u7684\u5c31\u662f\u4e0d\u4f1a\u51fa\u73b0\u4e24\u4e2a\u8fdb\u7a0b\u540c\u65f6\u5728 <code>while ()</code> \u88ab\u963b\u585e\u4f4f\u7684\u60c5\u51b5\u3002\u4f46\u662f\u8fd9\u70b9\u975e\u5e38\u663e\u7136\uff0c<code>TURN == i &amp;&amp; TURN == j</code> \u5fc5\u7136\u662f false\uff0c\u6240\u4ee5\u4e24\u4e2a\u5faa\u73af\u603b\u6709\u4e00\u4e2a\u4f1a\u88ab break\u3002</p> bounded waiting time <p>\u5728 Peterson's \u4e2d\uff0c\u7b49\u5f85\u65f6\u95f4\u4e3b\u8981\u6307\u8fd9\u90e8\u5206\u7684\u8fd0\u884c\u65f6\u95f4\uff0c\u5c24\u5176\u6307\u7b2c\u4e03\u884c\u7684 <code>while</code> \u5faa\u73af\u3002</p> <pre><code>// `i` is 0 or 1, indicating current pid, while `j` is another pid.\nprocess(i) {\nj = 1 - i;\n\nREADY[i] = true;                    // \u2510\nTURN = j;                           // \u2502\nwhile (READY[j] &amp;&amp; TURN == j) {}    // \u251c entry section\n// i.e. wait until:             // \u2502\n//  (1) j exits,                // \u2502\n//  (2) j is slower, so it      // \u2502\n//      should run now.         // \u2518\n\n/* operate critical resources */    // - critical section\n\nREADY[i] = false;                   // - exit section\n\n/* other things */                  // - remainder section\n}\n</code></pre> <p>\u6211\u4eec\u53ef\u4ee5\u53d1\u73b0\uff0c\u4e0d\u65ad\u5faa\u73af\u7684\u6761\u4ef6\u662f\uff1a<code>READY[j] &amp;&amp; TURN == j</code>\uff0c\u5982\u679c\u8be5\u5faa\u73af\u4e00\u5f00\u59cb\u5c31\u4e0d\u6210\u7acb\uff0c\u90a3\u4e48\u663e\u7136\u662f\u7b26\u5408 bounded waiting time \u7684\uff0c\u6240\u4ee5\u6211\u4eec\u8003\u8651\u8fd9\u4e2a\u6761\u4ef6\u6700\u591a\u80fd\u6301\u7eed\u591a\u4e45\u3002</p> <p>A. <code>READY[j]</code> \u4e3a <code>true</code></p> <p>\u8fd9\u9700\u8981 process j \u5df2\u7ecf\u8fd0\u884c\u8fc7\u7b2c 5 \u884c\uff0c\u5e76\u4e14\u8fd8\u6ca1\u8fd0\u884c\u7b2c 15 \u884c\uff0c\u5373 process j \u4e5f\u60f3\u8981\u8fdb\u5165\u4e34\u754c\u6001\u3002</p> <p>\u8fd9\u4e00\u6761\u662f\u5728\u5224\u65ad\u662f\u5426\u6709\u51b2\u7a81\u5b58\u5728\uff0c\u5982\u73b0\u5728\u53ea\u6709 process i \u60f3\u8981\u8fdb\u5165\u4e34\u754c\u6001\uff0c\u90a3\u65e0\u9700\u7b49\u5f85\u76f4\u63a5\u8fdb\u5165\u5373\u53ef\u3002\u901a\u8fc7\u6539\u53d8\u8fd9\u4e2a\u6761\u4ef6\u800c\u8fdb\u5165\u4e34\u754c\u6001\u6709\u4e24\u79cd\u53ef\u80fd\uff1a</p> <ol> <li>\u4e00\u5f00\u59cb\u51b2\u7a81\u5c31\u4e0d\u5b58\u5728\uff1b</li> <li>process j \u521a\u79bb\u5f00\u4e34\u754c\u6001\uff0c\u91ca\u653e\u4e86\u4e34\u754c\u8d44\u6e90\uff1b</li> </ol> <p>B. <code>TURN == j</code> \u4e3a <code>true</code></p> <p>\u6709\u4e24\u79cd\u53ef\u80fd\uff1a</p> <ol> <li>process j \u8fd8\u6ca1\u8fd0\u884c\u7b2c 6 \u884c\uff1b</li> <li>process j \u5728 process i \u4e4b\u524d\u5c31\u8fd0\u884c\u4e86\u7b2c 6 \u884c\uff1b</li> </ol> <p>\u5bf9\u4e8e\u7b2c\u4e00\u79cd\u60c5\u51b5\uff0c\u7531\u4e8e A. \u6210\u7acb\u540e\u624d\u4f1a\u5224\u65ad\u8fd9\u6761\uff0c\u6240\u4ee5 process j \u7684\u72b6\u6001\u5176\u5b9e\u662f\u521a\u8fd0\u884c\u5b8c\u7b2c 5 \u884c\u8fd8\u6ca1\u8fd0\u884c\u5b8c\u7b2c 6 \u884c\uff0c\u663e\u7136\u8fd9\u4e2a\u65f6\u95f4\u662f\u6709\u754c\u7684\u3002</p> <p>\u800c\u5bf9\u4e8e\u7b2c\u4e8c\u79cd\u60c5\u51b5\uff0c\u8bf4\u660e i \u662f\u540e\u6765\u8005\uff0cj \u5df2\u7ecf\u5ba2\u6c14\u8fc7\u4e00\u6b21\u4e86\uff0c\u6240\u4ee5\u5e94\u5f53\u8ba9 j \u8fd0\u884c\uff0ci \u7b49\u5f85 j \u79bb\u5f00\u4e34\u754c\u6001\u91ca\u653e\u8d44\u6e90\uff0c\u6b64\u65f6\u901a\u8fc7 A.2. \u6765\u8fdb\u5165\u4e34\u754c\u6001\u3002\u800c process j \u64cd\u4f5c\u4e34\u754c\u8d44\u6e90\u7684\u65f6\u95f4\u4e5f\u5e94\u5f53\u6709\u9650\u7684\u3002</p> <p>\u7efc\u4e0a\u6240\u8ff0\uff0cwaiting time \u7684\u6700\u5927\u503c\u57fa\u672c\u4e0a\u53d6\u81ea\uff1a</p> <ol> <li>process j \u6267\u884c\u7b2c 6 \u884c\u7684\u65f6\u95f4\uff1b</li> <li>process j \u64cd\u4f5c\u4e34\u754c\u8d44\u6e90\u7684\u65f6\u95f4\uff1b</li> </ol> <p>\u901a\u8fc7\u4e4b\u524d\u7684\u8bba\u8ff0\u6211\u4eec\u77e5\u9053\uff0c\u8fd9\u4e24\u4e2a\u90fd\u662f\u6709\u754c\u7684\uff0c\u4e8e\u662f\u8be5\u6027\u8d28\u5f97\u8bc1\u3002</p> <p>Oops!</p> <p>\u4f46\u662f\uff0cPeterson's \u5b9e\u9645\u4e0a\u65e0\u6cd5\u9002\u7528\u4e8e\u73b0\u4ee3\u8ba1\u7b97\u673a\u4e2d\u3002\u4e0a\u8ff0\u505a\u6cd5\u6709\u4e00\u4e2a\u5173\u952e\uff0c\u4e5f\u662f\u6211\u4eec\u5728\u8bc1\u660e\u8fc7\u7a0b\u4e2d\u4e00\u76f4\u9ed8\u8ba4\u6210\u7acb\u7684\u4e8b\u60c5\uff1a\u8fdb\u7a0b\u603b\u662f\u5148\u6267\u884c <code>READY[i] = true;</code>\uff0c\u7136\u540e\u624d\u4f1a\u6267\u884c <code>TURN = j;</code>\uff0c\u5373\u5148\u8fdb\u5165\u5c31\u7eea\u6001\uff0c\u518d\u7d22\u53d6\u4e34\u754c\u8d44\u6e90\uff0c\u8fd9\u770b\u8d77\u6765\u662f\u4e2a\u975e\u5e38\u5408\u7406\u7684\u6761\u4ef6\u3002\u4f46\u5728\u73b0\u4ee3\u8ba1\u7b97\u673a\u4e2d\uff0c\u7f16\u8bd1\u5668\u53ef\u80fd\u4f1a\u901a\u8fc7\u91cd\u6392\u5217\u90e8\u5206\u8bed\u53e5\u6765\u66f4\u597d\u5730\u5229\u7528 CPU \u8d44\u6e90\uff08\u53c2\u8003\u8ba1\u7ec4\u7684\u5404\u79cd\u7ade\u4e89\uff09\u3002\u800c\u5bf9\u7f16\u8bd1\u5668\u6765\u8bf4\uff0c\u8fd9\u4e24\u4e2a\u64cd\u4f5c\uff08\u5c31\u7eea\u548c\u8bf7\u6c42\uff09\u5e76\u6ca1\u6709\u64cd\u4f5c\u76f8\u540c\u5185\u5bb9\uff0c\u56e0\u800c\u4ea4\u6362\u987a\u5e8f\u662f\u4e0d\u4f1a\u5f71\u54cd\u7ed3\u679c\u7684\uff0c\u6240\u4ee5\u53ef\u80fd\u88ab\u7f16\u8bd1\u5668\u4ea4\u6362\u3002\u800c\u8fd9\u5c31\u6709\u53ef\u80fd\u5bfc\u81f4\u51fa\u73b0\u95ee\u9898\uff0c\u4f8b\u5982\uff1a</p> <p>  The effects of instruction reordering in Peterson\u2019s solution. </p> <p>\u5728\u68d5\u8272\u6807\u8bb0\u65f6\u523b\uff0cprocess 1 \u8fdb\u884c <code>while</code> \u5faa\u73af\u5224\u65ad\uff0c\u53d1\u73b0 <code>READY[0]</code> \u4e3a <code>false</code>\uff0c\u4f46\u6b64\u65f6 <code>TURN</code> \u6307\u5411\u5bf9\u65b9\uff0c\u6240\u4ee5\u6309\u7167\u6211\u4eec\u5148\u524d\u7684\u5206\u6790\uff0c\u6b64\u65f6 process 1 \u4f1a\u8ba4\u4e3a process 0 \u662f\u5df2\u7ecf\u8fd0\u884c\u5b8c critical section\uff0c\u5df2\u7ecf\u91ca\u653e\u4e86\u4e34\u754c\u8d44\u6e90\uff0c\u6240\u4ee5\u8fdb\u5165\u4e34\u754c\u6001\uff1b\u7136\u800c\uff0c\u5728\u7eff\u8272\u6807\u8bb0\u65f6\u523b\uff0c\u5bf9\u4e8e process 0\uff0c\u6b64\u65f6 <code>TURN</code> \u6307\u5411\u81ea\u5df1\uff0cprocess 1 \u8fd8\u6ca1\u8fd0\u884c\u5b8c\u6240\u4ee5 <code>READY[1]</code> \u8fd8\u662f <code>true</code>\uff0c\u6839\u636e\u6211\u4eec\u4e4b\u524d\u7684\u5206\u6790\uff0c\u6b64\u65f6 process 0 \u4f1a\u8ba4\u4e3a process 1 \u5728\u7b49\u5f85\u81ea\u5df1\uff0c\u6240\u4ee5\u4e5f\u8fdb\u5165\u4e86\u4e34\u754c\u6001\u3002\u4e8e\u662f\uff0c\u4e24\u4e2a\u8fdb\u7a0b\u540c\u65f6\u8fdb\u5165\u4e86\u4e34\u754c\u6001\uff0c\u8fdd\u53cd\u4e86 mutual exclusion \u7684\u6027\u8d28\u3002</p> <p>\u6240\u4ee5\uff0c\u5b9e\u9645\u4e0a Peterson's Algorithm \u4ecd\u7136\u6ca1\u6709\u89e3\u51b3\u95ee\u9898\u3002</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit2-Part1/#memory-barriers","title":"Memory Barriers","text":"<p>\u8be5\u65b9\u6cd5\u5b9e\u9645\u4e0a\u662f\u5bf9\u8f6f\u4ef6\u65b9\u6cd5\u7684\u8865\u8db3\u3002\u6211\u4eec\u5148\u524d\u63d0\u5230\uff0cPeterson's Algorithm \u5931\u6548\u7684\u539f\u56e0\u662f\u7f16\u8bd1\u5668\u4f1a\u6839\u636e\u9700\u6c42\u91cd\u6392\u5217\u4e00\u4e9b\u5185\u5b58\u64cd\u4f5c\uff0c\u800c memory barriers \u4fdd\u8bc1 barrier \u4e4b\u524d\u7684 S/L \u6307\u4ee4\u5fc5\u987b\u5728 barrier \u4e4b\u540e\u7684 S/L \u6307\u4ee4\u4e4b\u524d\u5b8c\u6210\uff0c\u4f7f\u6211\u4eec\u80fd\u591f\u4e3b\u52a8\u7981\u6b62\u7f16\u8bd1\u5668\u505a\u8fd9\u79cd\u91cd\u6392\u3002</p> <pre><code>// `i` is 0 or 1, indicating current pid, while `j` is another pid.\nprocess(i) {\nj = 1 - i;\n\nREADY[i] = true;                    // \u2510\nmemory_barrier();                   // \u2502\nTURN = j;                           // \u2502\nwhile (READY[j] &amp;&amp; TURN == j) {}    // \u251c entry section\n// i.e. wait until:             // \u2502\n//  (1) j exits,                // \u2502\n//  (2) j is slower, so it      // \u2502\n//      should run now.         // \u2518\n\n/* operate critical resources */    // - critical section\n\nREADY[i] = false;                   // - exit section\n\n/* other things */                  // - remainder section\n}\n</code></pre> <p>Memory Model</p> <p>\u4e0d\u540c\u7684\u8ba1\u7b97\u673a\u67b6\u6784\u53ef\u80fd\u4f1a\u5bf9\u7528\u6237\u7a0b\u5e8f\u64cd\u4f5c\u5185\u5b58\u7684\u4fdd\u8bc1\u6709\u6240\u4e0d\u540c\uff0c\u8fd9\u79cd\u4fdd\u8bc1\u88ab\u79f0\u4e3a memory model\u3002\u6211\u4eec\u53ef\u4ee5\u5c06\u5b83\u5206\u4e3a\u4e24\u5927\u7c7b\uff1a</p> <ol> <li>\u5f3a\u6709\u5e8f(strongly ordered)\uff1a\u8fdb\u7a0b\u5bf9\u5185\u5b58\u505a\u7684\u4fee\u6539\u7acb\u523b\u5bf9\u5176\u5b83\u5904\u7406\u5668\u53ef\u89c1\uff1b</li> <li>\u5f31\u6709\u5e8f(weakly ordered)\uff1a\u8fdb\u7a0b\u5bf9\u5185\u5b58\u505a\u7684\u4fee\u6539\u4e0d\u7acb\u523b\u5bf9\u5176\u5b83\u5904\u7406\u5668\u53ef\u89c1\uff1b</li> </ol> <p>\u6211\u4eec\u77e5\u9053\uff0c\u4e3a\u4e86\u63d0\u9ad8\u5185\u5b58\u64cd\u4f5c\u7684\u6548\u7387\uff0c\u6211\u4eec\u5f15\u5165\u4e86 cache\uff0c\u5728\u591a\u5904\u7406\u5668\u60c5\u51b5\u4e0b\uff0ccache \u673a\u5236\u7684\u5b58\u5728\u53ef\u80fd\u5bfc\u81f4\u8fdb\u7a0b A \u5bf9\u5185\u5b58\u7684\u5199\u65e0\u6cd5\u5bf9\u8fdb\u7a0b B \u7acb\u523b\u53ef\u89c1\uff0c\u8fd9\u5c31\u662f\u5f31\u6709\u5e8f\u7684\u4e00\u79cd\u4f53\u73b0\u3002</p> <p>\u8fd9\u90e8\u5206\u6211\u6ca1\u6709\u5b8c\u5168\u641e\u6e05\u695a\uff0c\u4e66\u672c\u7684\u903b\u8f91\u975e\u5e38\u7684\u8be1\u5f02\uff1a\u4e66\u672c\u8ba4\u4e3a memory barrier \u662f\u5f31\u6709\u5e8f\u95ee\u9898\u7684\u89e3\u51b3\u65b9\u6848\uff0c\u4f46\u662f\u6211\u59cb\u7ec8\u6ca1\u660e\u767d\u5b83\u4eec\u4e4b\u95f4\u7684\u903b\u8f91\u5728\u54ea\u91cc\uff0c\u4ee5\u53ca\u201c\u6709\u5e8f\u201d\u548c\u201c\u7acb\u523b\u53ef\u89c1\u201d\u7684\u6839\u672c\u8054\u7cfb\u5728\u54ea\u91cc\u3002\u8fd9\u91cc\u4e00\u5b9a\u662f\u5b58\u5728\u4e0d\u6e05\u695a\u7684\u5730\u65b9\u7684\u3002\u4f46\u662f\u8fd9\u90e8\u5206\u770b\u8d77\u6765\u4e0d\u662f\u5f88\u91cd\u8981\uff0c\u6240\u4ee5\u6211\u5c31\u5148\u653e\u7740\u4e0d\u7ba1\u4e86\u3002</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit2-Part1/#hardware-instructions","title":"Hardware Instructions","text":"<p>\u8ba8\u8bba Peterson's Algorithm \u540e\u6211\u4eec\u5e94\u5f53\u610f\u8bc6\u5230\uff0c\u540c\u6b65\u95ee\u9898\u7684\u51fa\u73b0\u662f \u2776 \u786c\u4ef6\u64cd\u4f5c\u6570\u636e\u9700\u8981\u65f6\u95f4\uff0c\u4e0e \u2777 \u6570\u636e\u5177\u6709\u5171\u4eab\u6027\u7684\u4e0d\u534f\u8c03\uff0c\u6240\u4ee5\u672c\u8d28\u4e0a\u662f\u786c\u4ef6\u4ea7\u751f\u7684\u95ee\u9898\u3002\u56e0\u800c\uff0c\u8981\u60f3\u66f4\u597d\u7684\u89e3\u51b3\u95ee\u9898\uff0c\u6211\u4eec\u8fd8\u662f\u5e94\u5f53\u4ece\u786c\u4ef6\u51fa\u53d1\u3002\u6211\u4eec\u5728\u8fd9\u91cc\u5f15\u5165\u539f\u5b50\u6027(atomic)\u8fd9\u4e2a\u6982\u5ff5\uff0c\u5b83\u7684\u57fa\u672c\u903b\u8f91\u662f\u8ba9\u201c\u9700\u8981\u65f6\u95f4\u7684\uff0c\u5bf9\u6570\u636e\u7684\u64cd\u4f5c\u201d\uff0c\u53d8\u6210\u4e00\u4e2a\u201c\u5728\u65f6\u95f4\u4e0a\u4e0d\u53ef\u5206\u5272\u3001\u4e0d\u53ef\u88ab\u6253\u65ad\u7684\uff0c\u5373\u539f\u5b50\u6027\u7684\u64cd\u4f5c\u201d\u3002\u4e0d\u540c\u786c\u4ef6\u53ef\u80fd\u63d0\u4f9b\u4e0d\u540c\u7684\u539f\u5b50\u6027\u64cd\u4f5c\uff0c\u6211\u4eec\u8fd9\u91cc\u5c06\u5b83\u4eec\u62bd\u8c61\u4e3a <code>test_and_set()</code> \u548c <code>compare_and_swap()</code> \u4e24\u7c7b\u6765\u4ecb\u7ecd\u3002</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit2-Part1/#test_and_set","title":"<code>test_and_set()</code>","text":"<p>Links</p> <ul> <li>Wikipedia</li> </ul> <pre><code>&lt;atomic&gt; test_and_set(bool * target) {\nbool ret = *target;\n*target = true;\nreturn ret;\n}\n</code></pre> <p>\u8be5\u6307\u4ee4\u7684\u529f\u80fd\u5c31\u7c7b\u4f3c\u4e0a\u9762\u8fd9\u6bb5\u4ee3\u7801\uff1a\u5c06\u76ee\u6807\u8bbe\u4e3a <code>true</code>\uff0c\u540c\u65f6\u8fd4\u56de\u5176\u65e7\u503c\u3002\u4f46\u9664\u6b64\u4e4b\u5916\uff0c\u8fd9\u4e2a\u6307\u4ee4\u9700\u8981\u4fdd\u8bc1\u539f\u5b50\u6027\uff0c\u5373\u5982\u679c\u6709\u82e5\u5e72 <code>test_and_set()</code> \u540c\u65f6\u53d1\u751f\uff0c\u90a3\u4e48\u65e0\u8bba\u5e76\u53d1\u8fd8\u662f\u5e76\u884c\uff0c\u5b83\u4eec\u90fd\u5e94\u5f53\u4e00\u4e2a\u4e00\u4e2a\u5730\u6267\u884c\uff0c\u800c\u4e0d\u80fd\u4ea7\u751f\u65f6\u95f4\u4e0a\u7684\u4ea4\u96c6\u3002</p> <p>\u53ef\u4ee5\u53d1\u73b0\uff0c\u8fd9\u79cd atomic \u7684\u64cd\u4f5c\u5929\u7136\u4fdd\u8bc1\u4e86 mutual exclusion\uff0c\u56e0\u800c\u5bf9\u4e8e\u5b9e\u73b0\u4e86 <code>test_and_set()</code> \u7684\u673a\u5668\uff0c\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528 <code>test_and_set()</code> \u6765\u89e3\u51b3 CS \u95ee\u9898\u3002</p> <pre><code>process(i) {\nwhile ( test_and_set(&amp;LOCK) ) {}    // - entry section\n/* operate critical resources */    // - critical section\n\nLOCK = false;                       // - exit section\n\n/* other things */                  // - remainder section\n}\n</code></pre> <p>\u5728\u7b2c 3 \u884c\uff0c\u5faa\u73af\u7b49\u5f85\u7684\u6761\u4ef6\u53d8\u4e3a <code>test_and_set(&amp;LOCK)</code>\uff0c\u5982\u679c <code>LOCK</code> \u7684\u65e7\u503c\u662f <code>false</code>\uff0c\u5219\u53ef\u4ee5\u7ee7\u7eed\uff0c\u5e76\u4e14\u6b64\u65f6 <code>LOCK</code> \u7684\u503c\u88ab\u539f\u5b50\u6027\u5730\u4fee\u6539\u4e3a <code>true</code>\uff1b\u800c\u5982\u679c <code>LOCK</code> \u7684\u65e7\u503c\u662f <code>true</code>\uff0c\u90a3\u4e48\u5b83\u7ecf\u8fc7 <code>test_and_set(&amp;LOCK)</code> \u540e\u7684\u503c\u4ecd\u7136\u662f <code>true</code>\uff0c\u4e14\u9700\u8981\u7b49\u5f85\uff0c\u76f4\u5230\uff1a\u5c06 <code>LOCK</code> \u6539\u6210 <code>true</code> \u7684\u90a3\u4e2a\u8fdb\u7a0b\u5728 exit section \u5c06 <code>LOCK</code> \u6539\u56de <code>false</code>\uff0c\u5373\u91ca\u653e\u9501\u3002</p> <p>\u4f46\u662f\u8bf7\u6ce8\u610f\uff0c\u4e0e\u6211\u4eec\u8ba8\u8bba Peterson's Algorithm \u65f6\u7684\u8bed\u5883\u4e0d\u540c\uff0c\u6211\u4eec\u73b0\u5728\u4e0d\u518d\u5047\u8bbe\u53c2\u4e0e\u7ade\u4e89\u7684\u8fdb\u7a0b\u53ea\u6709\u4e24\u4e2a\uff08\u8fd9\u662f Peterson's \u7684\u5c40\u9650\u6027\u4e4b\u4e00\uff09\u3002\u5728\u8fd9\u4e2a\u8bed\u5883\u4e0b\uff0c\u6211\u4eec\u518d\u6765\u8003\u8651\u5b83\u662f\u5426\u6ee1\u8db3\u4e09\u6761\u6027\u8d28\u3002</p> <p>mutual exclusion</p> <p>\u7531\u4e8e <code>test_and_set()</code> \u662f\u539f\u5b50\u6027\u7684\uff0c\u6240\u4ee5\u540c\u65f6\u6267\u884c\u7684\u4e00\u7cfb\u5217 <code>test_and_set()</code> \u4e2d\uff0c\u53ea\u6709\u4e00\u4e2a\u80fd\u8fd4\u56de <code>false</code>\uff0c\u5373\u53ea\u6709\u4e00\u4e2a\u80fd\u901a\u8fc7\u9501\uff0c\u56e0\u800c\u5929\u751f\u6ee1\u8db3\u4e86 mutual exclusion\u3002</p> <p>progress</p> <p>\u4ee3\u7801\u4e2d\u5bf9 <code>LOCK</code> \u7684\u4fee\u6539\u64cd\u4f5c\u662f\u95ed\u5408\u7684\uff0c\u5373\u8fdb\u5165 critical section \u4f1a\u5bfc\u81f4 <code>LOCK</code> \u53d8\u4e3a <code>false</code>\uff0c\u4f46\u79bb\u5f00 critical section \u5fc5\u5b9a\u5bfc\u81f4 <code>LOCK</code> \u53d8\u4e3a true\u3002\u56e0\u6b64\uff0c\u53ea\u8981\u6ca1\u6709\u8fdb\u7a0b\u5904\u4e8e critical section\uff0c\u90a3\u4e48 <code>LOCK</code> \u5fc5\u5b9a\u4e3a <code>false</code>\uff0c\u5219\u4e00\u5b9a\u6709\u5c31\u7eea\u7684\u8fdb\u7a0b\u80fd\u591f\u8fdb\u5165 critical section\uff0c\u800c\u8fd0\u884c critical section \u7684\u65f6\u95f4\u662f\u6709\u9650\u7684\uff0c\u56e0\u6b64 <code>LOCK</code> \u53c8\u4e00\u5b9a\u4f1a\u5728\u6709\u9650\u65f6\u95f4\u5185\u53d8\u4e3a <code>false</code>\uff0c\u4ece\u800c\u6ee1\u8db3 progress\u3002</p> <p>bounded waiting time</p> <p>\u5982\u679c\u53ea\u6709\u4e24\u4e2a\u8fdb\u7a0b\u53c2\u4e0e\u7ade\u4e89\uff0c\u90a3\u4e48\u901a\u8fc7\u7c7b\u4f3c\u8bc1\u660e progress \u7684\u8fc7\u7a0b\u53ef\u4ee5\u5f97\u5230 bounded waiting time \u662f\u53ef\u4ee5\u6210\u7acb\u7684\u3002A \u79bb\u5f00\u4e34\u754c\u6001\u540e\u5904\u4e8e\u5c31\u7eea\u6001\u7b49\u5f85\u7684 B \u7acb\u523b\u5c31\u80fd\u8fdb\u5165 critical section\uff0c\u5373\u53ea\u6709\u4e24\u4e2a\u4eba\u6392\u961f\u662f\u4e0d\u4f1a\u88ab\u63d2\u961f\u7684\u3002</p> <p>\u4f46\u5728\u53c2\u4e0e\u7ade\u4e89\u7684\u8fdb\u7a0b\u53d8\u591a\u4ee5\u540e\uff0c\u5c31\u5f88\u6709\u53ef\u80fd\u51fa\u73b0\u7c7b\u4f3c\u4e8e\u8c03\u5ea6\u4e2d\u201c\u9965\u997f\u201d\u7684\u73b0\u8c61\uff1a</p> <pre><code>    \u250c\u2500\u2500\u2500\u2500\u2510      \u250c\u2500\u2500\u2500\u2500\u2510      \u250c\u2500\u2500\u2500\u2500\u2510      \u250c\u2500\u2500\u2500\u2500\u2510      \nP0  \u2502 CS \u2502   \u2500\u2500\u2500\u2524 CS \u2502   \u2500\u2500\u2500\u2524 CS \u2502   \u2500\u2500\u2500\u2524 CS \u2502   \u2500\u2500\u2500 \u00b7\u00b7\u00b7\n    \u2514\u2500\u2500\u2500\u2500\u2518      \u2514\u2500\u2500\u2500\u2500\u2518      \u2514\u2500\u2500\u2500\u2500\u2518      \u2514\u2500\u2500\u2500\u2500\u2518      \n          \u250c\u2500\u2500\u2500\u2500\u2510      \u250c\u2500\u2500\u2500\u2500\u2510      \u250c\u2500\u2500\u2500\u2500\u2510      \u250c\u2500\u2500\u2500\u2500\u2510\nP1  \u2500\u2500\u2500\u2500\u2500\u2500\u2524 CS \u2502   \u2500\u2500\u2500\u2524 CS \u2502   \u2500\u2500\u2500\u2524 CS \u2502   \u2500\u2500\u2500\u2524 CS \u2502 \u00b7\u00b7\u00b7\n          \u2514\u2500\u2500\u2500\u2500\u2518      \u2514\u2500\u2500\u2500\u2500\u2518      \u2514\u2500\u2500\u2500\u2500\u2518      \u2514\u2500\u2500\u2500\u2500\u2518\n\nP2  \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 \u00b7\u00b7\u00b7\n</code></pre> <p>\u53ef\u4ee5\u53d1\u73b0\uff0c\u7531\u4e8e <code>P0</code> \u548c <code>P1</code> \u603b\u662f\u8f6e\u6d41\u83b7\u5f97\u9501\uff0c\u5bfc\u81f4 <code>P2</code> \u59cb\u7ec8\u5904\u4e8e\u5c31\u7eea\u6001\u7b49\u5f85\u9501\uff0c\u56e0\u800c\u5bf9\u4e8e <code>P2</code> \u6765\u8bf4 waiting time \u5c31\u4e0d\u518d\u6709\u9650\u4e86\u3002</p> <p>\u7cdf\u4e86\uff0c\u770b\u8d77\u6765\u5f88\u9177\u7684\u4e00\u4e2a\u65b9\u6cd5\u8c8c\u4f3c\u4e0d\u80fd\u6ee1\u8db3 CS \u89e3\u6cd5\u7684\u6027\u8d28\uff0c\u4f46\u4ed4\u7ec6\u5206\u6790\uff0c\u8fd9\u662f\u7531\u4e8e\u9501\u7684\u5206\u914d\u673a\u5236\u662f\u4e0d\u53ef\u63a7\u7684\u2014\u2014\u5728\u4e00\u4e2a\u9501\u88ab\u91ca\u653e\u540e\uff0c\u63a5\u4e0b\u6765\u5c06\u62ff\u5230\u9501\u7684\u8fdb\u7a0b\u5e94\u5f53\u662f\u63a5\u4e0b\u6765\u7b2c\u4e00\u4e2a\u5b9e\u9645\u6267\u884c <code>test_and_set()</code> \u7684\u8fdb\u7a0b\uff0c\u7136\u800c\u7531\u4e8e \u2776 \u6211\u4eec\u5bf9\u6bcf\u4e2a\u8fdb\u7a0b\u7684\u8fd0\u884c\u901f\u5ea6\uff0c\u4e0d\u5e94\u5f53\u6709\u5047\u8bbe\uff0c\u2777 \u6211\u4eec\u5bf9\u540c\u65f6\u4ea7\u751f\u7684 <code>test_and_set()</code> \u5c06\u6309\u4f55\u987a\u5e8f\u88ab\u5904\u7406\uff0c\u4e0d\u5e94\u5f53\u6709\u5047\u8bbe\uff0c\u6240\u4ee5\u6211\u4eec\u5fc5\u987b\u624b\u52a8\u7528\u67d0\u79cd\u65b9\u6cd5\u6765\u5b9e\u73b0\u8fd9\u79cd\u201c\u9501\u7684\u8c03\u5ea6\u201d\uff1a</p> <pre><code>// `i` is process id in [0, n), where `n` is the count of related process. \nprocess(i) {\nWAITING[i] = true;                                  // \u2510\nwhile ( WAITING[i] &amp;&amp; test_and_set(&amp;LOCK) ) {}      // \u251c entry sec.\n// \u2502\nWAITING[i] = false;                                 // \u2518\n\n/* operate critical resources */                    // - critical sec.\n\n// i.e. find next waiting process j                 // \u2510\nj = (i + 1) % n;                                    // \u2502\nwhile (i != j &amp;&amp; !WAITING[j]) {                     // \u251c exit sec.\nj = (i + 1) % n;                                // \u2502\n}                                                   // \u2502\n// release j's LOCK or release whole LOCK           // \u2502\nif (i == j)     LOCK = false;                       // \u2502\nelse            WAITING[j] = false;                 // \u2518\n\n/* other things */                                  // - remainder sec.\n}\n</code></pre> <p>\u6211\u4eec\u5f15\u5165\u4e86\u4e00\u4e2a <code>WAITING[]</code> \u6570\u7ec4\u6765\u8f85\u52a9 <code>LOCK</code> \u7ec6\u5316\u9501\u7684\u7c92\u5ea6\uff0c\u6b64\u65f6 <code>LOCK</code> \u8868\u793a\u7684\u201c\u662f\u5426\u5b58\u5728\u7ade\u4e89\u201d\uff0c\u800c <code>WAITING[]</code> \u5219\u6807\u8bc6\u4e86\u6240\u6709\u6b63\u5728\u7b49\u5f85\u7684\u8fdb\u7a0b\u3002\u533a\u522b\u4e8e\u4e4b\u524d\u76f4\u63a5\u91ca\u653e\u6574\u4e2a\u9501\uff0c\u8ba9\u5269\u4e0b\u7684\u8fdb\u7a0b\u53bb\u201c\u62fc\u624b\u901f\u201d\uff0c\u6211\u4eec\u8fd9\u6b21\u7531\u91ca\u653e\u9501\u7684\u8fdb\u7a0b\u6765\u9009\u62e9\u4e0b\u4e00\u4e2a\u8fdb\u5165 critical section \u7684\u662f\u8c01\u3002</p> <p>\u5728 11-14 \u884c\uff0c\u901a\u8fc7\u4e00\u4e2a\u5faa\u73af\u627e\u5230\u4e0b\u4e00\u4e2a <code>WAITING[j]</code> \u4e3a <code>true</code> \u7684 j\uff0c\u2776 \u5982\u679c\u627e\u5230\u4e86\u8fd9\u4e2a j\uff0c\u90a3\u4e48\u5c31\u5c06 <code>WAITING[j]</code> \u8bbe\u4e3a <code>false</code>\uff0819 \u884c\uff09\uff0c\u8fd9\u6837 j \u9a6c\u4e0a\u5c31\u4f1a\u5728\u7b2c 4 \u884c break\uff0c\u8fdb\u5165 critical section\uff1b\u2777 \u800c\u5982\u679c\u627e\u4e0d\u5230\u8fd9\u4e2a j\uff0c\u5373\u627e\u4e86\u4e00\u5708\u53c8\u627e\u56de\u4e86 i\uff0c\u90a3\u4e48\u8bf4\u660e i \u662f\u6700\u540e\u4e00\u4e2a\u4e86\uff0c\u6240\u4ee5\u53ef\u4ee5\u76f4\u63a5\u91ca\u653e\u6574\u4e2a\u9501\uff0817 \u884c\uff09\u3002</p> <p>\u901a\u8fc7\u4f7f\u7528\u8fd9\u79cd\u65b9\u6cd5\uff0c\u6211\u4eec\u4fdd\u8bc1\u4e86\u7b49\u5f85\u4e2d\u7684\u8fdb\u7a0b\u6700\u591a\u53ea\u9700\u8981\u7b49\u5f85 n-1 \u4e2a\u8fdb\u7a0b\u8fd0\u884c\u5b8c critical section\uff08\u7c7b\u4f3c\u4e8e\u5b9e\u73b0\u4e86\u201cFCFS\u201d\uff09\u3002</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit2-Part1/#compare_and_swap","title":"<code>compare_and_swap()</code>","text":"<p>Links</p> <ul> <li>Wikipedia</li> </ul> <p><code>compare_and_swap()</code> \u4e5f\u88ab\u7b80\u5199\u4e3a CAS \u6307\u4ee4\uff0c\u5b83\u7684\u529f\u80fd\u5982\u4e0b\uff1a</p> <pre><code>&lt;atomic&gt; compare_and_swap(int * target, int expected, int new_val) {\nint ret = *target;\n\n// *target = (*target == expected) ? new_val : *target;\nif (*target == expected) {\n*target = new_val;\n}\n\nreturn ret;\n}\n</code></pre> <p>CAS \u63a5\u53d7\u4e09\u4e2a\u503c\uff1a</p> <ol> <li><code>target</code> \u5f85\u4fee\u6539\u7684\u6570\u636e\u7684\u5730\u5740\uff1b</li> <li><code>expected</code> \u9884\u671f\u4e2d\u5f85\u4fee\u6539\u7684\u6570\u636e\u7684\u65e7\u503c\uff1b</li> <li><code>new_val</code> \u5e0c\u671b\u5c06\u6570\u636e\u4fee\u6539\u4e3a\u7684\u65b0\u503c\uff1b</li> </ol> <p>\u800c\u5f53\u4e14\u4ec5\u5f53 <code>*target</code> \u7b26\u5408\u9884\u671f\uff0c\u4e0e <code>expected</code> \u76f8\u540c\u65f6\u5019\uff0c\u624d\u4f1a\u5c06\u5b83\u6539\u4e3a <code>new_val</code>\u3002\u540c\u6837\uff0cCAS \u4e5f\u5e94\u5f53\u4fdd\u8bc1\u539f\u5b50\u6027\uff0c\u5373\u82e5\u5e72 CAS \u540c\u65f6\u53d1\u751f\u65f6\uff0c\u4e5f\u5e94\u5f53\u4e00\u4e2a\u4e00\u4e2a\u7684\u6267\u884c\uff0c\u800c\u4e0d\u80fd\u5b58\u5728\u65f6\u95f4\u4e0a\u7684\u4ea4\u96c6\u3002</p> <p>\u6211\u4eec\u6ce8\u610f\u5230\uff0c\u5b9e\u9645\u4e0a <code>test_and_set(target)</code> \u5c31\u662f <code>compare_and_swap(target, false, true)</code>\uff0c\u56e0\u800c\u5b9e\u9645\u4e0a CAS \u89e3\u51b3 CS \u95ee\u9898\u7684\u65b9\u6cd5\u4ee5\u53ca\u95ee\u9898\u548c\u4e0a\u4e00\u8282\u7684\u5185\u5bb9\u6ca1\u4ec0\u4e48\u5dee\u522b\u3002</p> <p>\u4f46\u662f\u6211\u4eec\u53d1\u73b0\uff0c<code>compare_and_swap()</code> \u76f8\u6bd4\u4e8e <code>test_and_set()</code>\uff0c\u663e\u7136\u6709\u66f4\u5927\u7684\u64cd\u4f5c\u7a7a\u95f4\uff0c\u4e5f\u66f4\u6cdb\u7528\uff0c\u8003\u8651\u5230 CAS \u6307\u4ee4\u81ea\u8eab\u5df2\u7ecf\u80fd\u591f\u652f\u6301\u539f\u5b50\u6027\u7684\u4fee\u6539\u503c\uff0c\u6211\u4eec\u8003\u8651\u80fd\u5426\u8df3\u51fa CS \u95ee\u9898\u7684\u8303\u5f0f\u6765\u8003\u8651\u95ee\u9898\u3002</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit2-Part1/#atomic-variables","title":"Atomic Variables","text":"<p>\u539f\u5b50\u53d8\u91cf(atomic variables)\u662f\u4e00\u79cd\u7528\u539f\u5b50\u6027\u64cd\u4f5c\u7ef4\u62a4\u7684\u53d8\u91cf\u3002\u6211\u4eec\u6240\u6709\u5bf9\u539f\u5b50\u53d8\u91cf\u7684\u64cd\u4f5c\u53ef\u4ee5\u901a\u8fc7 CAS \u6765\u5b9e\u73b0\uff0c\u4f8b\u5982\u81ea\u589e\u64cd\u4f5c\uff1a</p> <pre><code>increment(atomic_int * v) {\nint tmp;\ndo {\ntmp = *v;\n} while ( tmp != compare_and_swap(v, tmp, tmp+1) );\n}\n</code></pre> <p>\u4f7f\u7528 atomic variables \u540e\u5b9e\u9645\u4e0a\u5c31\u4e0d\u592a\u7b26\u5408 CS \u95ee\u9898\u7684\u6a21\u578b\u4e86\uff0c\u53ef\u4ee5\u53d1\u73b0\uff0c\u8fd9\u91cc\u5e76\u4e0d\u518d\u9700\u8981\u7ef4\u62a4\u7c7b\u4f3c <code>LOCK</code> \u7684\u4e1c\u897f\uff0c\u800c\u662f\u4ee5 <code>*target</code> \u662f\u5426\u7b26\u5408 <code>expected</code> \u7684\u9884\u8bbe\u6765\u5224\u65ad\u662f\u5426\u6709\u7ade\u4e89\u51fa\u73b0\uff0c\u4f5c\u4e3a\u4e00\u4e2a\u540c\u6b65\u5de5\u5177\uff0c\u6211\u4eec\u53ef\u4ee5\u76f4\u63a5\u4f7f\u7528\u8fd9\u79cd\u5c01\u88c5\u540e\u7684\u539f\u5b50\u6027\u64cd\u4f5c\u6765\u89e3\u51b3 race condition\uff0c\u800c\u4e0d\u9700\u8981\u518d\u533a\u5206 entry section \u6216\u662f critical section \u7b49\u3002</p> <p>\u4e66\u672c\u4e0a\u7279\u5730\u63d0\u5230\uff0c\u5728\u4f8b\u5982 producer&amp;consumer \u7684\u6a21\u578b\u4e2d\uff0c\u4f7f\u7528 atomic variables \u7ef4\u62a4 count \u5e76\u4e0d\u80fd\u89e3\u51b3 race condition\uff0c\u4f46\u6211\u8ba4\u4e3a\u8fd9\u79cd\u8ba8\u8bba\u662f\u6709\u5931\u504f\u9887\u7684\uff0c\u6240\u8c13\u7684\u201c\u539f\u5b50\u6027\u201d\u5e94\u8be5\u5305\u62ec\u6240\u6709\u64cd\u4f5c\u4e34\u754c\u8d44\u6e90\u7684\u90e8\u5206\uff0c\u4e66\u4e2d\u53ea\u7ef4\u62a4 count \u4e0d\u7ef4\u62a4 buffer \u7684\u5047\u8bbe\u6211\u89c9\u5f97\u5bf9\u4e8e atomic \u8fd9\u4e2a\u6982\u5ff5\u6765\u8bf4\u5b9e\u5728\u4e0d\u591f\u516c\u5e73\u3002\u6240\u4ee5\u6211\u5728\u8fd9\u91cc\u5c31\u4e0d\u7740\u91cd\u8bf4\u660e\u8fd9\u4e2a\u95ee\u9898\u3002</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit2-Part1/#mutex-locks","title":"Mutex Locks","text":"<p>\u7531\u6b64\u6211\u4eec\u5df2\u7ecf\u5f97\u5230\u4e86\u80fd\u5728\u786c\u4ef6\u5c42\u9762\u89e3\u51b3 race condition \u95ee\u9898\u7684\u6839\u6e90\u7684\u5de5\u5177\u4e86\uff0c\u4f46\u662f\u4e3a\u4e86\u80fd\u8ba9\u7528\u6237\u7a0b\u5e8f\u4e5f\u80fd\u66f4\u597d\u7684\u4f7f\u7528\uff0c\u6211\u4eec\u9700\u8981\u5c06\u5b83\u505a\u4e00\u6b21\u8f6f\u4ef6\u5c42\u9762\u7684\u5c01\u88c5\u3002\u4e8e\u662f\uff0c\u6211\u4eec\u8bbe\u8ba1\u4e86\u4e92\u65a5\u9501(mutex locks)\u8fd9\u4e2a\u4e1c\u897f\u3002</p> <p>\u5229\u7528\u4e92\u65a5\u9501\u907f\u514d race condition \u7684\u57fa\u672c\u601d\u8def\u4ecd\u7136\u662f\u57fa\u4e8e CS \u95ee\u9898\u7684\u5efa\u6a21\uff0c\u4f46\u5b83\u66f4\u5177\u4f53\u5730\u8ba4\u4e3a\u5728 entry section \u5c31\u8be5\u53bb\u7d22\u53d6\u4e92\u65a5\u9501\uff0c\u800c\u5728 exit section \u5c31\u5e94\u8be5\u53bb\u91ca\u653e\u4e92\u65a5\u9501\uff0c\u5373\uff1a</p> <pre><code>\u250c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2510\n\u2502  Acquire Lock       \u2502\n\u251c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2524\n\u2502  Critical Section   \u2502 &lt;-- codes manipulating critical resources\n\u251c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2524\n\u2502  Release Lock       \u2502\n\u251c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2524\n\u2502  Remainder Section  \u2502 &lt;-- other codes\n\u2514\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2518\n</code></pre> <p>\u56de\u987e\u6211\u4eec\u5728\u4ecb\u7ecd <code>test_and_set()</code> \u90e8\u5206\u7ed9\u51fa\u7684\u8fd9\u6bb5\u4ee3\u7801\uff1a</p> <pre><code>process(i) {\nwhile ( test_and_set(&amp;LOCK) ) {}    // - entry section\n/* operate critical resources */    // - critical section\n\nLOCK = false;                       // - exit section\n/* other things */                  // - remainder section\n}\n</code></pre> <p>\u6211\u4eec\u53ea\u9700\u8981\u5c06\u9ad8\u4eae\u7684\u8fd9\u4e24\u884c\u5c01\u88c5\u8d77\u6765\uff0c\u5c31\u5b9e\u73b0\u4e86 acquire LOCK \u548c release LOCK\u3002</p> <pre><code>// `available` means whether the `LOCK` is free, or whether the related resources is available\nacquire() {\nwhile ( !compare_and_swap(&amp;available, true, false) ) {}\n}\n\nrelease() {\navailable = true;\n}\n</code></pre> <p>\u4f60\u53ef\u80fd\u6ce8\u610f\u5230\u4e86\uff0c\u6211\u4eec\u5728 <code>test_and_set()</code> \u8ba8\u8bba\u4e0a\u9762\u90a3\u6bb5\u4ee3\u7801\u7684\u65f6\u5019\uff0c\u8ba8\u8bba\u8fc7\u5b83\u65e0\u6cd5\u6ee1\u8db3 bounded waiting time \u7684\u95ee\u9898\uff0c\u90a3\u65e2\u7136\u5982\u6b64\u6211\u4eec\u4e3a\u4ec0\u4e48\u4e0d\u628a <code>WAITING[]</code> \u4e5f\u4e00\u8d77\u5c01\u8fdb\u53bb\u5462\uff1f</p> <p>\u8fd9\u662f\u56e0\u4e3a\u4e66\u4e0a\u76f4\u63a5\u5ffd\u7565\u4e86\u8fd9\u4e2a\u95ee\u9898\uff0c\u76f4\u5230\u5728\u4e4b\u540e\u8bb2 semaphores \u7684\u65f6\u5019\u624d\u60f3\u8d77\u6765\uff0c\u4f46 semaphores \u548c mutex lock \u53c8\u662f\u4e24\u4e2a\u8def\u5b50\uff0c\u6211\u4e5f\u4e0d\u77e5\u9053\u5b83\u5230\u5e95\u60f3\u8bf4\u660e\u4ec0\u4e48\u95ee\u9898\u3002\u4f46\u662f\u65e2\u7136\u5b83\u73b0\u5728\u5ffd\u7565\u4e86\uff0c\u6211\u4eec\u5c31\u5148\u4e0d\u7ba1\u5b83\uff0c\u4f46\u662f\u6211\u5e0c\u671b\u8bfb\u8005\u80fd\u610f\u8bc6\u5230\u8fd9\u4e2a\u95ee\u9898\u662f\u5b58\u5728\u7684\u3002</p> <p>\u7ecf\u8fc7\u8fd9\u4e48\u957f\u7684\u94fa\u57ab\uff0c\u6211\u4eec\u73b0\u5728\u80fd\u591f\u4fdd\u8bc1\u7684\u4e00\u4ef6\u4e8b\u662f\uff0c\u6211\u4eec\u7ec8\u4e8e\u5f97\u5230\u4e86\u4e00\u4e2a\u8f6f\u4ef6\u5c42\u9762\u7684\u3001\u80fd\u591f\u907f\u514d race condition \u7684\u540c\u6b65\u5de5\u5177\u3002\u90a3\u4e48\u5b9e\u73b0\u57fa\u672c\u9700\u6c42\u4ee5\u540e\u6211\u4eec\u5c31\u5f00\u59cb\u8003\u8651\u80fd\u4e0d\u80fd\u4f18\u5316\u5b83\u3002</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit2-Part1/#\u5fd9\u7b49\u5f85","title":"\u5fd9\u7b49\u5f85","text":"<p>\u5982\u679c\u8bfb\u8005\u5bf9\u4ee3\u7801\u6709\u6bd4\u8f83\u654f\u611f\u7684\u55c5\u89c9\uff0c\u90a3\u53ef\u80fd\u770b\u8fd9\u51e0\u5343\u4e2a\u5b57\u5230\u73b0\u5728\uff0c\u4f60\u5df2\u7ecf\u4e3a\u6570\u4e0d\u6e05\u7684 <code>while()</code> \u63d0\u5fc3\u540a\u80c6\u8fc7\u5341\u591a\u6b21\u4e86\u3002\u6ca1\u9519\uff0c\u867d\u7136\u6211\u4eec\u901a\u8fc7\u903b\u8f91\u4fdd\u8bc1\u8fd9\u91cc\u4e0d\u4f1a\u51fa\u73b0\u6b7b\u5faa\u73af\uff0c\u4f46\u5bf9\u4e8e\u7b49\u5f85\u4e2d\u7684 process\uff0c\u786e\u5b9e\u8981\u5728\u6570\u4e0d\u5c3d\u7684 <code>while</code> loop \u4e2d\u6d6a\u8d39 CPU\uff0c\u6211\u4eec\u79f0\u8fd9\u79cd\u7b49\u5f85\u9501\u91ca\u653e\u7684\u884c\u4e3a\u4e3a\u5fd9\u7b49\u5f85(busy waiting)\uff0c\u5176\u4e2d\u201c\u5fd9\u201d\u6307\u7684\u5c31\u662f\u5728\u7b49\u5f85\u8fc7\u7a0b\u4e2d\u4ecd\u7136\u5360\u7528 CPU \u8d44\u6e90\u3002\u800c\u8fd9\u79cd\u4f7f\u7528\u5fd9\u7b49\u5f85\u7684\u4e92\u65a5\u9501\uff0c\u4e5f\u88ab\u79f0\u4e3a\u81ea\u65cb\u9501(spinLOCK)\u3002</p> <p>\u6211\u4eec\u5f15\u5165\u4e24\u4e2a\u8bcd\u6765\u66f4\u51c6\u786e\u7684\u63cf\u8ff0\u8fd9\u4ef6\u4e8b\uff1a</p> <p>Lock Contention</p> <p>\u5982\u679c\u4e00\u4e2a\u7528\u6237\u8bd5\u56fe\u7d22\u53d6\u67d0\u4e2a\u9501\u65f6\uff0c\u5982\u679c\u8fd9\u4e2a\u9501\u4e0d\u662f available \u7684\uff0c\u8fd9\u5c31\u610f\u5473\u7740\u6709\u7528\u6237\u6b63\u5728\u4f7f\u7528\u8fd9\u4e2a\u9501\uff0c\u800c\u5f53\u524d\u7528\u6237\u9700\u8981\u7b49\u5f85\u8fd9\u4e2a\u9501\u91cd\u65b0\u53ef\u7528\uff0c\u6b64\u65f6\u6211\u4eec\u79f0\u8fd9\u4e2a\u9501\u662f\u88ab\u4e89\u62a2\u7684(contended)\uff1b\u53cd\u4e4b\uff0c\u5982\u679c\u4e0d\u5b58\u5728\u4e89\u62a2\uff0c\u6211\u4eec\u5c31\u79f0\u4e4b\u4e3a\u4e0d\u88ab\u4e89\u62a2\u7684(uncontended)\u3002</p> <p>\u5982\u679c\u73b0\u5728\u6709\u597d\u591a\u7528\u6237\u90fd\u5728\u4e89\u62a2\u4e00\u4e2a\u9501\uff0c\u6211\u4eec\u79f0\u4e4b\u4e3a high contention\uff1b\u53cd\u4e4b\u5982\u679c\u53ea\u6709\u96f6\u661f\u51e0\u4e2a\u7528\u6237\u5728\u4e89\u62a2\u8fd9\u4e2a\u9501\uff0c\u6211\u4eec\u79f0\u4e4b\u4e3a low contention\u3002</p> <p>\u5982\u679c\u5ef6\u7528 spinLOCK\uff0c\u90a3\u4e48\u4e0d\u96be\u5f97\u5230\u7ed3\u8bba\uff1ahigh contention \u4f1a\u5bfc\u81f4\u4e25\u91cd\u7684\u6027\u80fd\u95ee\u9898\uff0c\u56e0\u4e3a\u603b\u662f\u4f1a\u6709\u5927\u91cf\u5f97\u4e0d\u5230\u9501\u7684\u7528\u6237\u5904\u4e8e busy waiting \u4e2d\u3002</p> <p>\u65e2\u7136\u5b83\u4eec\u90fd\u662f\u5728\u505a\u65e0\u610f\u4e49\u7684\u7b49\u5f85\uff0c\u90a3\u6211\u4eec\u4e3a\u4ec0\u4e48\u4e0d\u5728\u8fd9\u4e2a\u65f6\u5019\u628a\u8d44\u6e90\u8ba9\u7ed9\u6709\u9700\u8981\u7684\u4eba\u5462\uff1f</p> <p>\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u6682\u65f6\u5730\u5207\u6362\u8fdb\u7a0b\uff0c\u8ba9\u8fd9\u4e9b\u5904\u4e8e\u7b49\u5f85\u7684\u7528\u6237\u6682\u65f6\u4f11\u7720\uff0c\u7b49\u65f6\u673a\u5230\u6765\u518d\u5524\u9192\u5b83\u4eec\uff0c\u6b64\u65f6\u5c31\u9700\u8981\u7cfb\u7edf\u8c03\u7528\u7684\u4ecb\u51653\u3002\u800c\u5177\u4f53\u7684\u65b9\u6cd5\u6211\u4eec\u5728\u4e0b\u4e00\u8282\u7684\u907f\u514d\u5fd9\u7b49\u5f85\u4e2d\u4ecb\u7ecd\u3002</p> <p>\u4f46\u662f\u8bf7\u6ce8\u610f\uff0c\u6211\u4eec\u5728\u8fd9\u91cc\u9700\u8981\u4fdd\u6301\u5ba2\u89c2\uff1aspinLOCK \u5728\u7279\u5b9a\u60c5\u51b5\u4e0b\u662f\u6709\u597d\u5904\u7684\uff0c\u5728\u7b49\u5f85\u65f6\u95f4\u5e76\u4e0d\u957f\u7684\u60c5\u51b5\u4e0b\uff0c\u76f8\u6bd4\u4e8e\u62e5\u6709\u9501\u7684\u7528\u6237\u91ca\u653e\u9501\uff0c\u8fdb\u884c\u8c03\u5ea6\u9501\u9700\u8981\u7684 context switch \u7684\u5f00\u9500\u53ef\u80fd\u663e\u5f97\u8f83\u5927\uff0c\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\u6211\u4eec\u8fd8\u6ca1\u6765\u5f97\u53ca\u628a\u8d44\u6e90\u8ba9\u7ed9\u522b\u4eba\u9501\u5c31\u597d\u4e86\uff0c\u90a3\u4e48\u8fd9\u79cd\u8d44\u6e90\u8f6c\u8ba9\u8fd8\u4e0d\u5982\u4e0d\u8f6c\u3002\u800c\u4e8b\u5b9e\u4e0a\uff0c\u5728\u7279\u5b9a\u60c5\u51b5\u4e0b\uff0c\u81ea\u65cb\u9501\u4e5f\u786e\u5b9e\u662f\u4e00\u4e9b\u591a\u6838\u7cfb\u7edf\u7684\u9996\u9009\u3002</p> <p>\u4e0d\u8fc7\u5728\u8bb8\u591a\u8bed\u5883\u91cc mutex \u548c spinLOCK \u662f\u533a\u5206\u5f00\u6765\u7684\u4e24\u4e2a\u6982\u5ff5\uff0c\u5177\u4f53\u4f7f\u7528\u54ea\u4e2a\u5219\u9700\u8981\u9002\u65f6\u5224\u65ad4\u3002</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit2-Part1/#semaphores","title":"Semaphores","text":"<p>Links</p> <ul> <li>Wikipedia</li> </ul> <p>Mutex LOCK \u4e3a\u7528\u6237\u7a0b\u5e8f\u63d0\u4f9b\u4e86\u7c7b\u4f3c\u4e8e\u201c\u623f\u95f4\u7533\u8bf7\u201d\u7684\u529f\u80fd\uff0c\u9501\u7ade\u4e89\u5c31\u597d\u50cf\u5927\u5bb6\u62a2\u623f\u95f4\u7684\u4f7f\u7528\u6743\u3002\u800c\u4fe1\u53f7\u91cf(semaphores)\u5219\u662f\u7c7b\u4f3c\u4e8e\u6211\u4eec\u4e4b\u524d\u63d0\u5230\u8fc7\u7684 atomic variables\uff0c\u901a\u8fc7\u63d0\u4f9b\u6807\u51c6\u5316\u7684\u539f\u5b50\u6027\u64cd\u4f5c\uff0c\u6765\u7ef4\u62a4\u4e00\u4e9b\u53d8\u91cf\uff0c\u53ea\u4e0d\u8fc7\u5b83\u989d\u5916\u5bf9\u53d8\u91cf\u7684\u503c\u6709\u4e00\u5b9a\u7684\u7ea6\u675f\u3002</p> <p>\uff08\u8bf4\u5b9e\u8bdd\u6211\u611f\u89c9\u8fd9\u4fe9\u4e1c\u897f\u672c\u8d28\u4e0a\u771f\u6ca1\u5565\u533a\u522b\u2026\u2026\uff09</p> <p>Semaphores \u53ea\u63d0\u4f9b\u4e24\u4e2a\u6807\u51c6\u5316\u7684\u63a5\u53e3\uff1a<code>wait()</code>\uff08\u6216<code>P()</code>\uff09 \u548c <code>signal()</code>\uff08\u6216<code>V()</code>\uff09\uff0c\u5b83\u4eec\u7684\u529f\u80fd\u5982\u4e0b\uff1a</p> <pre><code>&lt;atomic&gt; wait(reference S) {\nwhile (S &lt;= 0) {} // busy wait here\nS--;\n}\n\n&lt;atomic&gt; signal(reference S) {\nS++;\n}\n</code></pre> <p>\u663e\u7136\uff0c\u8fd9\u4e24\u4e2a\u64cd\u4f5c\u7684\u5b9e\u73b0\u4e5f\u5e94\u5f53\u4fdd\u8bc1\u662f atomic \u7684\u3002</p> <p>\u533a\u522b\u4e8e\u666e\u901a\u7684 atomic variables\uff0csemaphores \u591a\u4e86\u5728\u7b2c 2 \u884c\u7684 busy wait\uff0c\u8fd9\u6697\u542b\u4e86\u4e00\u79cd\u201c\u6709\u9650\u201d\u7684\u6982\u5ff5\uff0c\u5373\u4fdd\u8bc1 \\(0 \\leq S\\)\u3002\u5728\u5b9e\u9645\u4f7f\u7528\u4e2d\uff0csemaphores \u5206\u4e3a counting semaphore \u548c binary semaphore\uff0c\u524d\u8005\u7684\u529f\u80fd\u5982\u4e0a\uff0c\u540e\u8005\u53ea\u4e0d\u8fc7\u662f\u989d\u5916\u8981\u6c42 \\(0 \\leq S \\leq 1\\)\uff0c\u4fee\u6539 loop \u7684\u6761\u4ef6\u5373\u53ef\u3002</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit2-Part1/#\u4f7f\u7528","title":"\u4f7f\u7528","text":"<p>\u4f8b\u5982\uff0c\u6211\u4eec\u53ef\u4ee5\u7528\u5982\u4e0b\u65b9\u5f0f\uff0c\u4fdd\u8bc1 <code>P0()</code> \u4e2d\u7684 section A \u5fc5\u987b\u5728 <code>P1()</code> \u7684 section B \u4e4b\u524d\u5b8c\u6210\uff1a</p> <pre><code>semaphore S = 0;\n\nP0() {\n/* Section A */\nsignal(S);\n}\n\nP1() {\nwait(S);\n/* Section B */\n}\n</code></pre> <p>\u4e0a\u9762\u7684\u4f8b\u5b50\u975e\u5e38\u5f62\u8c61\u5730\u5c55\u793a\u4e86\u4fe1\u53f7\u91cf\u662f\u5982\u4f55\u53d1\u6325\u4f5c\u7528\u7684\uff0c\u5f53\u7136\uff0c\u4e0a\u9762\u53ea\u5c55\u793a\u4e86\u7c7b\u4f3c\u8fdb\u7a0b\u95f4\u901a\u8baf\u7684\u529f\u80fd\uff0c\u4e0b\u9762\u8fd9\u4e2a\u5f62\u5f0f\u5219\u66f4\u63a5\u8fd1\u6211\u4eec\u4e0a\u6587\u4e2d\u8ba8\u8bba\u7684\u60c5\u51b5\uff0c\u5373\u5b9e\u73b0\u4e86\u4e92\u65a5\uff1a</p> <pre><code>// `i` is process id and S is the semaphores\nprocess(i) {\nwait(S);    // i.e. release the 'LOCK'\n\n/* critical section */\n\nsignal(S);  // only one process can pass this line at once\n}\n</code></pre>"},{"location":"cour_note/D3QD_OperatingSystem/Unit2-Part1/#\u907f\u514d\u5fd9\u7b49\u5f85","title":"\u907f\u514d\u5fd9\u7b49\u5f85","text":"<p>\u6211\u4eec\u5728 mutex \u4e2d\u63d0\u51fa\u5fd9\u7b49\u5f85\u7684\u65f6\u5019\u5c31\u5df2\u7ecf\u63d0\u5230\u8fc7\uff0c\u53ef\u4ee5\u901a\u8fc7\u300c\u5728\u7b49\u5f85\u7684\u65f6\u5019\u8ba9\u8fdb\u7a0b\u4f11\u7720\uff0c\u7b49\u65f6\u673a\u5408\u9002\u7684\u65f6\u5019\u518d\u5524\u9192\u300d\u7684\u65b9\u5f0f\uff0c\u6765\u51cf\u5c0f\u8f83\u957f\u7684\u5fd9\u7b49\u5f85\u5f15\u8d77\u7684\u6027\u80fd\u964d\u4f4e\u3002\u800c\u4e3a\u4e86\u5b9e\u73b0\u8fd9\u4e00\u70b9\uff0c\u6211\u4eec\u9700\u8981\u6269\u5c55 semaphores \u7684\u5185\u5bb9\uff0c\u5f15\u5165\u4e00\u4e2a\u94fe\u8868\u6765\u7ef4\u62a4\u7b49\u5f85\u4e2d\u7684\u8fdb\u7a0b\u3002</p> <pre><code>struct semaphore {\nvalue;\nwaiting_list;\n};\n\n&lt;atomic&gt; wait(reference S) {\nS-&gt;value--;\nif (S-&gt;value &lt; 0) {\nS-&gt;waiting_list.push(current process);\nsleep();\n}\n}\n\n&lt;atomic&gt; signal(reference S) {\nS-&gt;value++;\nif (S-&gt;value &lt;= 0) {\np = S-&gt;waiting_list.pop();\nwakeup(p);\n}\n}\n</code></pre> <p>\u76f8\u6bd4\u4e8e\u4e4b\u524d\u7684\u903b\u8f91\uff0c\u73b0\u5728\u7684\u903b\u8f91\u7a0d\u5fae\u6709\u70b9\u53d8\u5316\uff0c\u8bf7\u8bfb\u8005\u5c1d\u8bd5\u72ec\u7acb\u5206\u6790\u5176\u4e2d\u7684\u5965\u79d8\u3002\u8fd9\u91cc\u662f\u4e00\u4e9b\u63d0\u793a\uff1a</p> <p>\u601d\u8003\u9898</p> <ol> <li>\u73b0\u5728\u5df2\u7ecf\u6ca1\u6709 <code>while</code> \u4e86\uff0c\u53ea\u4f59\u4e0b <code>if</code>\uff0c\u73b0\u5728\u662f\u5982\u4f55\u4fdd\u8bc1\u7b49\u5f85\u4e2d\u7684\u8fdb\u7a0b\u80fd\u591f\u88ab\u53ca\u65f6\u5524\u9192\uff1f</li> <li><code>wait</code> \u539f\u5148\u662f\u5148\u7b49\u5f85\u518d\u4fee\u6539\uff0c\u73b0\u5728\u662f\u5148\u4fee\u6539\u3001\u518d\u7b49\u5f85\uff0c\u8fd9\u5bf9\u6574\u4f53\u903b\u8f91\u6709\u4f55\u5f71\u54cd\uff1f</li> <li><code>signal</code> \u4e2d\u7684\u6761\u4ef6\u8bed\u53e5\uff0c\u4e3a\u4f55\u662f <code>S-&gt;value &lt;= 0</code>\uff1f\u8fd9\u4e2a\u6761\u4ef6\u4e3a false \u65f6\u610f\u5473\u7740\u4ec0\u4e48\uff1f<ul> <li>\u8003\u8651\u5728 high contention \u7684\u60c5\u51b5\u4e0b\uff0c\u8d44\u6e90\u603b\u662f\u4e00\u51fa\u73b0\u5c31\u88ab\u62a2\u7a7a\u3002</li> </ul> </li> </ol> <ol> <li> <p>The Critical Section Problem \u21a9</p> </li> <li> <p>\u4e66\u672c\u4e2d\u5bf9 preemptive kernels \u548c non-preemptive kernels \u7684\u5b9a\u4e49\u5e76\u4e0d\u51c6\u786e\uff0c\u4e24\u8005\u6700\u672c\u8d28\u7684\u533a\u522b\u662f\u540e\u8005\u5b9e\u73b0\u4e86 Giant Lock\u3002\u540c\u65f6\u8bfb\u8005\u53ef\u4ee5\u53c2\u8003\u8fd9\u4e2a\u94fe\u63a5\uff1aWhat was the reason of the non-preemptivity of older Linux kernels? \u21a9</p> </li> <li> <p>Mutex access and system call \u21a9</p> </li> <li> <p>When should one use a spinLOCK instead of mutex? \u2b50\ufe0f\u00a0\u21a9</p> </li> </ol>"},{"location":"cour_note/D3QD_OperatingSystem/Unit2-Part2/","title":"U2 Part 2: \u540c\u6b65\u95ee\u9898\u4f8b\u5b50 | Synchronization Problems Examples","text":"<p> \u7ea6 1568 \u4e2a\u5b57  51 \u884c\u4ee3\u7801  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 6 \u5206\u949f</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit2-Part2/#the-bounded-buffer-problem","title":"The Bounded-Buffer Problem","text":""},{"location":"cour_note/D3QD_OperatingSystem/Unit2-Part2/#\u95ee\u9898\u80cc\u666f","title":"\u95ee\u9898\u80cc\u666f","text":"<ul> <li>\ud83d\udd17 Wiki</li> </ul> <p>The Bounded-Buffer Problem \u53c8\u79f0 The Producer\u2013Consumer Problem\uff0c\u5728\u8be5\u95ee\u9898\u4e2d\uff0c\u6709\u4e24\u4e2a\u89d2\u8272\uff0cproducer \u548c consumer\uff1aproducer \u4f1a\u4ea7\u751f item \u5b58\u653e\u5230 buffer \u4e2d\uff0c\u800c consumer \u53ef\u4ee5\u5c06\u6570\u636e\u4ece buffer \u4e2d\u53d6\u51fa item\u3002\u5982\u679c\u6211\u4eec\u7528 \\(n = \\# items\\) \u6765\u63cf\u8ff0 buffer \u7684\u72b6\u6001\uff0c\u90a3\u4e48\u95ee\u9898\u5c06\u62bd\u8c61\u4e3a\uff1a</p> <pre><code>void produce() {\n/* something */\n++n;\n/* something */\n}\n\nvoid consume() {\n/* something */\n--n;\n/* something */\n}\n</code></pre> <p>\u540c\u65f6\uff0c\u6211\u4eec\u9700\u8981\u4fdd\u8bc1 \\(0 \\leq n \\leq n_{max}\\)\uff0c\u6240\u4ee5\u6211\u4eec\u9700\u8981\u5728 \\(n = 0\\) \u65f6\uff0c\u8ba9 consumer \u7b49\u5f85 \\(n &gt; 0\\) \u518d <code>consume()</code>\uff1b\u5bf9\u5e94\u7684\uff0c\u5728 \\(n = \\leq n_{max}\\) \u65f6\u5019\uff0c\u8ba9 producer \u7b49\u5f85 \\(n &lt; n_{max}\\) \u518d <code>produce()</code>\u3002\u4f46\u8fd9\u5e76\u4e0d\u662f\u6211\u4eec\u5728\u672c\u5355\u5143\u63d0\u53ca\u5b83\u7684\u91cd\u70b9\uff0c\u6240\u4ee5\u6211\u4eec\u5728\u8fd9\u91cc\u8ba4\u4e3a\u5b83\u4eec\u5728 <code>/* something */</code> \u4e2d\u3002</p> <p>\u5b9e\u9645\u7684 The Bounded-Buffer Problem \u4e2d\u8fd8\u6709\u4e00\u4e9b\u5176\u5b83\u7ec6\u8282\uff0c\u4f46\u662f\u8fd9\u91cc\u6211\u4eec\u5c06\u6574\u4e2a\u95ee\u9898\u62bd\u8c61\u4e3a\u6211\u4eec\u9700\u8981\u7684\u6a21\u6837\uff0c\u8bf7\u4e0d\u8981\u8ba4\u4e3a\u4e0a\u9762\u7684\u4ee3\u7801\u5c31\u662f The Bounded-Buffer Problem \u7684\u5168\u90e8\u3002</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit2-Part2/#\u95ee\u9898\u63cf\u8ff0","title":"\u95ee\u9898\u63cf\u8ff0","text":"<p>\u8003\u8651\u5728\u5e76\u884c\u8bed\u5883\u4e0b\uff0c<code>produce()</code> \u548c <code>consume()</code> \u540c\u65f6\u53d1\u751f\uff0c\u7531\u4e8e <code>++n</code> \u548c <code>--n</code> \u8fd9\u4e9b\u64cd\u4f5c\u672c\u8d28\u4e0a\u662f\u6570\u503c\u7684\u3001\u9700\u8981\u4e00\u6bb5\u65f6\u95f4\u6765\u5b8c\u6210\u7684\uff0c\u6240\u4ee5\u5bb9\u6613\u51fa\u73b0 race condition\u95ee\u9898\u3002</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit2-Part2/#\u89e3\u51b3---semaphores","title":"\u89e3\u51b3 - semaphores","text":"<p>\u6211\u4eec\u4f7f\u7528\u4fe1\u53f7\u91cf\u6765\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\uff0c\u9700\u8981\u5b9a\u4e49\u4e09\u4e2a\u4fe1\u53f7\u91cf\uff1a</p> <pre><code>// suppose the capacity of the buffer is n\nsemaphore mutex = 1;\nsemaphore empty = n;\nsemaphore full  = 0;\n</code></pre> <p>\u903b\u8f91\u4e0a\u6211\u4eec\u8981\u6c42 <code>empty + full == n</code> \u59cb\u7ec8\u6210\u7acb\uff0c\u4f46\u662f\u5728\u5b9e\u9645\u8fd0\u884c\u8fc7\u7a0b\u4e2d\u53ef\u80fd\u4f1a\u4ea7\u751f\u4e00\u5b9a\u8bef\u5dee\uff08\u8003\u8651\u67d0\u4e2a\u539f\u8bed\u8fd8\u6ca1\u5f7b\u5e95\u6267\u884c\u5b8c\uff09\u3002\u800c\u6211\u4eec\u8fd9\u91cc\u4e4b\u6240\u4ee5\u8981\u4f7f\u7528\u4e24\u4e2a\u4fe1\u53f7\u91cf\u6765\u7ef4\u62a4\u4e00\u4e2a buffer \u7684\u5360\u7528\u72b6\u6001\uff0c\u662f\u56e0\u4e3a\u4fe1\u53f7\u91cf\u7684\u201c\u6709\u754c\u201d\u662f\u901a\u8fc7 0 \u7ef4\u62a4\u7684\uff0c\u4e5f\u5c31\u662f\u53ea\u6709\u5728\u201c\u51cf\u5c11\u201d\u7684\u65f6\u5019\u624d\u80fd\u7ef4\u62a4\uff1b\u800c\u6211\u4eec\u7684\u8981\u6c42\u662f\uff0cbuffer \u7684\u4e0a\u4e0b\u754c\u90fd\u6709\u754c\uff0c\u6240\u4ee5\u6211\u4eec\u9700\u8981\u4e24\u4e2a\u4fe1\u53f7\u91cf\u5206\u522b\u6765\u7ef4\u62a4\u4e24\u4e2a\u8fb9\u754c\u3002</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit2-Part2/#the-readerswriters-problem","title":"The Readers\u2013Writers Problem","text":""},{"location":"cour_note/D3QD_OperatingSystem/Unit2-Part2/#\u95ee\u9898\u80cc\u666f--\u95ee\u9898\u63cf\u8ff0","title":"\u95ee\u9898\u80cc\u666f &amp; \u95ee\u9898\u63cf\u8ff0","text":"<ul> <li>\ud83d\udd17 Wiki</li> </ul> <p>\u8be5\u95ee\u9898\u62bd\u8c61\u81ea\u6570\u636e\u5e93\u7684\u4f7f\u7528\u3002\u7528\u6237\u4f7f\u7528\u6570\u636e\u5e93\u4fee\u6539\u6570\u636e\uff08<code>UPDATE</code>\uff09\uff0c\u672c\u8d28\u4e0a\u4e5f\u662f\u6709\u4e09\u4e2a\u6b65\u9aa4\uff1a</p> <ol> <li>[READ] \u4ece\u6570\u636e\u5e93\u4e2d\u68c0\u7d22\u3001\u8bfb\u53d6\u6570\u636e\uff1b</li> <li>\u6570\u636e\u7ecf\u8fc7\u4e1a\u52a1\u903b\u8f91\u7684\u5904\u7406\uff0c\u5f97\u5230\u65b0\u503c\uff1b</li> <li>[WRITE] \u5c06\u65b0\u503c\u5199\u56de\u6570\u636e\u5e93\uff1b</li> </ol> <p>\u8fd9\u4e2a\u6b65\u9aa4\u4e0e\u6211\u4eec\u4fee\u6539 <code>mem[x]</code> \u7684\u8fc7\u7a0b\u9ad8\u5ea6\u76f8\u4f3c\uff0c\u56e0\u6b64\u9047\u5230\u7684\u95ee\u9898\u4e5f\u662f\u7c7b\u4f3c\u7684\u3002</p> <p>\u51b2\u7a81\u4e3b\u8981\u4f53\u73b0\u5728\u4e24\u79cd\u60c5\u51b5\uff1a</p> <ul> <li>reader \u548c writer \u7684\u51b2\u7a81\uff1b</li> <li>writer \u548c writer \u7684\u51b2\u7a81\uff1b</li> </ul> <p>\u663e\u7136\uff0creader \u548c reader \u4e0d\u4f1a\u6709\u51b2\u7a81\u3002</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit2-Part2/#\u89e3\u51b3---semaphores_1","title":"\u89e3\u51b3 - semaphores","text":"<p>\u6709\u4e24\u79cd\u79cd\u6734\u7d20\u7684\u89e3\u51b3\u529e\u6cd5\uff1a\u24f5 writer \u603b\u662f\u7b49\u5f85 reader\uff0c\u24f6 reader \u603b\u662f\u7b49\u5f85 writer\u3002\u4f46\u662f\u8fd9\u4e24\u79cd\u89e3\u51b3\u529e\u6cd5\u90fd\u4e0d\u662f\u5f88\u597d\uff0c\u56e0\u4e3a \u24f5 \u4f1a\u5bfc\u81f4 writer \u9965\u997f\uff0c\u24f6 \u4f1a\u5bfc\u81f4 reader \u9965\u997f\u3002</p> <p>\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u7ed9\u51fa\u6b63\u5f0f\u7684\u89e3\u51b3\u65b9\u6cd5\uff0c\u5f15\u5165\u4e24\u4e2a\u4fe1\u53f7\u91cf\u548c\u4e00\u4e2a\u5171\u4eab\u53d8\u91cf\uff1a</p> <pre><code>semaphores rw_mutex   = 1;\nsemaphores mutex      = 1;\nint        read_count = 0;\n</code></pre> <p>\u8003\u8651\u5230 reader \u548c reader \u4e0d\u4f1a\u51b2\u7a81\uff0c\u6240\u4ee5 readers \u4e4b\u95f4\u4e0d\u5e94\u8be5\u4e92\u65a5\u3002\u800c\u6211\u4eec\u9700\u8981\u4fdd\u8bc1\u7684\u662f\uff1a\u5355\u4e2a writer \u548c\u82e5\u5e72 readers \u4e4b\u95f4\u4e92\u65a5\uff0c\u5355\u4e2a writer \u548c\u5355\u4e2a writer \u4e4b\u95f4\u4e92\u65a5\u3002\u800c <code>rw_mutex</code> \u5c31\u662f\u7528\u4e8e\u63a7\u5236\u8fd9\u79cd\u4e92\u65a5\u3002</p> writer's code<pre><code>writer() {\nwait(rw_mutex);\n\n/* critical section */\nsignal(rw_mutex);\n}\n</code></pre> <p>\u4f46\u6b64\u65f6\u5982\u4f55\u4fdd\u8bc1 readers \u4e4b\u95f4\u4e0d\u4f1a\u4e92\u65a5\u5462\uff1f\u9996\u5148\uff0c\u5f53\u7b2c\u4e00\u4e2a reader \u8bd5\u56fe\u8fdb\u5165\u4e34\u754c\u6bb5\u65f6\uff0c\u5b83\u5e94\u5f53\u83b7\u53d6\u4e00\u4e2a <code>rw_mutex</code>\uff0c\u4ee5\u963b\u6b62\u5176\u5b83 writer \u8fdb\u5165\u4e34\u754c\u6bb5\u3002\u800c\u5bf9\u4e8e\u4e4b\u540e\u7684 reader \u6765\u8bf4\uff0c\u5982\u679c\u76ee\u524d\u83b7\u53d6\u9501\u7684\u662f\u4e00\u4e2a reader\uff0c\u90a3\u4e48\u5b83\u53ef\u4ee5\u76f4\u63a5\u8fdb\u5165\u4e34\u754c\u6bb5\uff1b\u5982\u679c\u76ee\u524d\u83b7\u53d6\u9501\u7684\u662f\u4e00\u4e2a writer\uff0c\u90a3\u4e48\u5b9e\u9645\u4e0a\u5b83\u624d\u662f\u7b2c\u4e00\u4e2a reader\u3002\u6362\u53e5\u8bdd\u6765\u8bf4\uff0c\u5bf9\u4e8e\u62ff <code>rw_mutex</code> \u6765\u8bf4\uff0c\u6211\u4eec\u53ea\u9700\u8981\u5224\u65ad\u5f53\u524d\u6709\u6ca1\u6709 reader \u6b63\u5728\u4eab\u7528\u4e34\u754c\u8d44\u6e90\u5373\u53ef\uff1b\u800c\u5bf9\u4e8e\u653e <code>rw_mutex</code> \u6765\u8bf4\uff0c\u6211\u4eec\u9700\u8981\u5224\u65ad\u5f53\u524d\u662f\u4e0d\u662f\u6700\u540e\u4e00\u4e2a reader\uff0c\u6240\u4ee5\u5b9e\u9645\u4e0a\u6211\u4eec\u9700\u8981\u7ef4\u62a4\u4e00\u4e2a\u8ba1\u6570\u5668 <code>read_count</code>\uff0c\u800c\u7531\u4e8e\u8fd9\u4e2a\u8ba1\u6570\u5668\u662f\u4e2a\u666e\u901a\u7684\u5171\u4eab\u53d8\u91cf\uff0c\u800c\u4e14\u8fd9\u4e2a\u8ba1\u6570\u5668\u672c\u8eab\u4e5f\u662f\u4e2a\u4e34\u754c\u8d44\u6e90\uff0c\u6240\u4ee5\u6211\u4eec\u8fd8\u9700\u8981\u4e00\u4e2a <code>mutex</code> \u6765\u7ef4\u62a4\u5b83\u3002</p> <p>\u6240\u4ee5\uff0c\u5b9e\u9645\u4e0a reader \u7684\u4ee3\u7801\u4e2d\u542b\u6709 3 \u4e2a\u4e34\u754c\u6bb5\uff0c\u5206\u522b\u662f\uff1a\u8ba1\u6570\u5668\u589e\u3001\u8bfb\u53d6\u4e34\u754c\u8d44\u6e90\u3001\u8ba1\u6570\u5668\u51cf\u3002</p> reader's code<pre><code>reader() {\nwait(mutex);            //   \u2510\nread_count++;           //   \u251c obtain `mutex` to increase\nif (read_count == 1) {  //   \u2502 `read_count`\nwait(rw_mutex);     // \u2510 \u2502\n}                       // \u2502 \u2502\nsignal(mutex);          // \u2502 \u2518\n// \u251c\u2500\u2500 readers share `rw_mutex` to\n/* critical section */  // \u2502   read critical resource\n// \u2502\nwait(mutex);            // \u2502 \u2510\nread_count--;           // \u2502 \u251c obtain `mutex` to decrease\nif (read_count == 0) {  // \u2502 \u2502 `read_count`\nsignal(rw_mutex);   // \u2518 \u2502\n}                       //   \u2502\nsignal(mutex);          //   \u2518\n}\n</code></pre> <p>\u903b\u8f91\u4e0a\uff0c\u91ca\u653e <code>rw_mutex</code> \u7684 reader \u4e0d\u9700\u8981\u662f\u7533\u8bf7 <code>rw_mutex</code> \u7684 reader\uff0c\u8fd9\u4e5f\u5370\u8bc1\u4e86\u8fd9\u4e2a\u9501\u7ef4\u62a4\u7684\u662f\u6574\u4e2a readers \u7fa4\u4f53\u7684\u5b58\u5728\u4e0e\u5426\uff0c\u800c\u4e0d\u662f\u201c\u67d0\u4e2a reader\u201d\u7684\u5b58\u5728\u4e0e\u5426\u3002</p> <p>\u4e3a\u4ec0\u4e48 <code>read_count</code> \u4e0d\u4f7f\u7528\u4fe1\u53f7\u91cf\uff1f</p> <p>\u6211\u4eec\u89c2\u5bdf\u5bf9 <code>read_count</code> \u7684\u64cd\u4f5c\uff0c\u4e00\u5171\u6709\u4e09\u7c7b\uff1a</p> <ol> <li><code>read_count++</code>\uff1b</li> <li><code>read_count--</code>\uff1b</li> <li><code>read_count == k</code>\uff1b</li> </ol> <p>\u5e76\u4e14 <code>read_count &gt;= 0</code> \u5e94\u5f53\u59cb\u7ec8\u6210\u7acb\uff0c\u6240\u4ee5\u5149\u770b\u524d\u4e24\u7c7b\uff0c\u5176\u5b9e\u5f88\u9002\u5408\u76f4\u63a5\u4f5c\u4e3a\u4fe1\u53f7\u91cf\u6765\u7ef4\u62a4\u3002\u4f46\u662f\u6211\u4eec\u65e0\u6cd5\u5bf9\u4fe1\u53f7\u91cf\u8fdb\u884c\u6bd4\u8f83\u64cd\u4f5c\uff0c\u6240\u4ee5\u6211\u4eec\u662f\u7528 <code>mutex</code> \u7ef4\u62a4\u4e86 <code>read_count</code>\uff0c\u53ef\u4ee5\u53d1\u73b0\uff0c\u6240\u6709\u5bf9 <code>read_count</code> \u7684\u64cd\u4f5c\u90fd\u662f\u5728 <code>mutex</code> \u7684\u4fdd\u62a4\u4e0b\u8fdb\u884c\u7684\u3002\u6362\u53e5\u8bdd\u6765\u8bf4\uff0c\u5176\u5b9e <code>read_count</code> \u548c <code>mutex</code> \u4e00\u8d77\u6784\u6210\u4e86\u4e00\u4e2a\u539f\u5b50\u53d8\u91cf\u3002</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit2-Part2/#the-dining-philosophers-problem","title":"The Dining Philosophers Problem","text":""},{"location":"cour_note/D3QD_OperatingSystem/Unit2-Part2/#\u95ee\u9898\u80cc\u666f--\u95ee\u9898\u63cf\u8ff0_1","title":"\u95ee\u9898\u80cc\u666f &amp; \u95ee\u9898\u63cf\u8ff0","text":"<ul> <li>\ud83d\udd17 Wiki</li> </ul> <p>\u5728\u8fd9\u4e2a\u95ee\u9898\u4e2d\uff0c\u6709\u4e94\u4e2a\u54f2\u5b66\u5bb6\uff0cta \u4eec\u56f4\u5750\u5728\u4e00\u5f20\u5706\u684c\u65c1\uff0c\u6bcf\u4e2a\u54f2\u5b66\u5bb6\u9762\u524d\u90fd\u6709\u4e00\u7897\u7c73\u996d\uff0c\u800c ta \u4eec\u4e24\u4e24\u4e4b\u95f4\u5206\u522b\u6709\u4e00\u6839\u7b77\u5b50\u3002</p> <p> </p> <p>\u6bcf\u5e27\u54f2\u5b66\u5bb6\u90fd\u80fd\u9009\u62e9\u6267\u884c\u4ee5\u4e0b\u4e24\u4e2a\u884c\u4e3a\u4e4b\u4e00\uff1a</p> <ol> <li>\u601d\u8003\uff1b</li> <li>\u62ff\u7b77\u5b50\uff1b</li> </ol> <p>\u54f2\u5b66\u5bb6\u5982\u679c\u60f3\u8981\u5e72\u996d\u5c31\u5fc5\u987b\u6709\u4e24\u6839\u7b77\u5b50\uff0cta \u540c\u65f6 \u62ff\u8d77 ta \u5de6\u53f3\u4fa7\u7b77\u5b50\u65f6\uff0c\u624d\u80fd\u5e72\u996d\u3002\u663e\u7136\uff0c\u4e24\u4e2a\u54f2\u5b66\u5bb6\u4e0d\u80fd\u540c\u65f6\u62ff\u8d77\u540c\u4e00\u6839\u7b77\u5b50\uff1b\u5e72\u5b8c\u996d\u54f2\u5b66\u5bb6\u4f1a\u653e\u4e0b\u7b77\u5b50\u3002\u5047\u8bbe\u54f2\u5b66\u5bb6\u4eec\u90fd\u4e0d\u5acc\u810f\u3002</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit2-Part2/#\u89e3\u51b3---semaphores_2","title":"\u89e3\u51b3 - semaphores","text":"<p>\u663e\u7136\uff0c\u6211\u4eec\u53ef\u4ee5\u7528\u4fe1\u53f7\u91cf\u6765\u7ef4\u62a4\u4e00\u4e2a\u7b77\u5b50\u662f\u5426\u53ef\u7528\uff0c\u5c31\u53ef\u4ee5\u5f97\u5230\u4e0b\u9762\uff08\u6709\u95ee\u9898\u7684\uff09\u89e3\u6cd5\uff1a</p> <pre><code>process() {\nwait(chopstick[i]);\nwait(chopstick[ (i+1) % 5 ]); // i.e. the next chopstick\n\n/* eat rice */\n\nsignal(chopstick[i]);\nsignal(chopstick[ (i+1) % 5 ]);\n}\n</code></pre> <p>\u4e0a\u8ff0\u65b9\u6848\u5b58\u5728\u95ee\u9898\uff01</p> <p>\u8003\u8651\u8fd9\u79cd\u60c5\u51b5\uff1a\u6240\u6709\u54f2\u5b66\u5bb6\u5728\u7b2c\u4e00\u5e27\u90fd\u60f3\u8981\u5e72\u996d\uff0c\u6b64\u65f6\u5b83\u4eec\u540c\u65f6\u8fd0\u884c\u5b8c\u4e86\u7b2c 2 \u884c\uff08\u4f8b\u5982\uff0c\u540c\u65f6\u62ff\u8d77\u4e86\u53f3\u624b\u8fb9\u7684\u7b77\u5b50\uff09\uff0c\u8fd9\u65f6\u6211\u4eec\u53d1\u73b0\uff0c\u6240\u6709\u7b77\u5b50\u90fd\u88ab\u5360\u6709\uff0c\u6ca1\u6709\u4efb\u4f55\u4e00\u4e2a\u4eba\u80fd\u7b49\u5230\u4e0b\u4e00\u4e2a\u7b77\u5b50\uff0c\u6b64\u65f6\uff0c\u54f2\u5b66\u5bb6\u4eec\u53d1\u751f\u4e86\u6b7b\u9501\u3002</p> <p>\u5bf9\u4e8e\u8fd9\u4e2a\u6b7b\u9501\uff0c\u4e66\u4e2d\u7ed9\u51fa\u4e86\u4e09\u79cd\u89e3\u51b3\u65b9\u6848\uff1a</p> <ol> <li>\u5141\u8bb8\u6700\u591a 4 \u4f4d\u54f2\u5b66\u5bb6\u540c\u65f6\u83b7\u53d6\u7b77\u5b50\uff1b</li> <li>\u54f2\u5b66\u5bb6\u5fc5\u987b\u540c\u65f6\u83b7\u53d6\u4e24\u4e2a\u7b77\u5b50\uff0c\u800c\u4e0d\u80fd\u6293\u4e00\u652f\u7b49\u4e00\u652f\uff1b<ul> <li>\u4e3a\u4e86\u5b9e\u73b0\u8fd9\u4e00\u70b9\uff0c\u201c\u6293\u7b77\u5b50\u201d\u8fd9\u4ef6\u4e8b\u5e94\u5f53\u5728\u4e00\u4e2a\u4e34\u754c\u6bb5\u4e2d\u5b8c\u6210\uff1b</li> </ul> </li> <li>\u5947\u6570\u54f2\u5b66\u5bb6\u5148\u62ff\u5de6\u624b\u7684\u7b77\u5b50\uff0c\u5076\u6570\u54f2\u5b66\u5bb6\u5148\u62ff\u53f3\u624b\u7684\u7b77\u5b50\uff0c\u8fd9\u6837\u4e0d\u4f1a\u4ea7\u751f\u5faa\u73af\u7b49\u5f85\uff1b</li> </ol>"},{"location":"cour_note/D3QD_OperatingSystem/Unit2-Part2/#\u89e3\u51b3---monitors","title":"\u89e3\u51b3 - monitors","text":"<ul> <li> TODO: \u4e0d\u662f\u5f88\u91cd\u8981</li> </ul>"},{"location":"cour_note/D3QD_OperatingSystem/Unit2-Part3/","title":"U2 Part 3: \u6b7b\u9501 | Deadlocks","text":"<p> \u7ea6 5215 \u4e2a\u5b57  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 17 \u5206\u949f</p> <p>\u5f15\u5165</p> <p>\u6b7b\u9501\u95ee\u9898\u5e7f\u6cdb\u5b58\u5728\u4e8e\u8ba1\u7b97\u673a\u8f6f\u4ef6\u7cfb\u7edf\u4e2d\uff0c\u800c\u6211\u4eec\u672c\u8282\u53ea\u8ba8\u8bba\u64cd\u4f5c\u7cfb\u7edf\u4e2d\u7684\u6b7b\u9501\u95ee\u9898\u3002</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit2-Part3/#\u6b7b\u9501\u5efa\u6a21","title":"\u6b7b\u9501\u5efa\u6a21","text":"<p>\u6211\u4eec\u5728\u4e0a\u4e00\u8282\u4e2d\u5df2\u7ecf\u63d0\u5230\u4e86\u4e00\u4e2a\u6b7b\u9501\u60c5\u51b5\u3002\u672c\u8282\u6211\u4eec\u4e13\u6ce8\u4e8e\u5982\u4f55\u89e3\u51b3\u64cd\u4f5c\u7cfb\u7edf\u4e2d\u7684\u6b7b\u9501(deadlock)\u95ee\u9898\u3002</p> <p>deadlock</p> <p>A deadlock is a situation in which every process in a set of processes is waiting for an event that can be caused only by another process in the set.</p> <p>\u5373\u5b58\u5728\u4e00\u4e2a\u8fdb\u7a0b/\u7ebf\u7a0b\u7684\u96c6\u5408\uff0c\u5b83\u4eec\u4e92\u76f8\u7b49\u5f85\u5bf9\u65b9\u6301\u6709\u7684\u8d44\u6e90\u3002</p> <p>\u4e0e\u4e4b\u5bf9\u5e94\u7684\uff0c\u5176\u5b9e\u8fd8\u6709\u4e00\u4e2a\u53eb\u6d3b\u9501(livelock)1\u7684\u4e1c\u897f\u3002</p> <p>\u6b7b\u9501\u4ea7\u751f\u4e8e\u8d44\u6e90\u7684\u4f7f\u7528\u8fc7\u7a0b\uff0c\u800c\u4e14\u901a\u5e38\u53ea\u5728\u7279\u5b9a\u60c5\u51b5\u4e0b\u624d\u4f1a\u53d1\u751f\uff0c\u800c\u6b63\u662f\u56e0\u4e3a\u8fd9\u79cd\u4e0d\u786e\u5b9a\u6027\uff0c\u6b7b\u9501\u95ee\u9898\u624d\u5f02\u5e38\u68d8\u624b\u3002\u4e3a\u4e86\u89e3\u51b3\u6b7b\u9501\uff0c\u6211\u4eec\u9996\u5148\u9700\u8981\u7406\u89e3\u6b7b\u9501\u4ea7\u751f\u7684\u539f\u56e0\uff0c\u4ee5\u65b9\u4fbf\u5bf9\u5b83\u8fdb\u884c\u5efa\u6a21\uff0c\u8fdb\u800c\u66f4\u597d\u5730\u63cf\u8ff0\u6b7b\u9501\u3002</p> <p>\u4ece\u8d44\u6e90\u4f7f\u7528\u7684\u89d2\u5ea6\u6765\u770b\uff0c\u6211\u4eec\u53ef\u4ee5\u5c06\u7cfb\u7edf\u7684\u884c\u4e3a\u5206\u6210\u4e09\u4e2a\u90e8\u5206\uff1a</p> <ol> <li>\u7533\u8bf7\u8d44\u6e90\uff1b</li> <li>\u4f7f\u7528\u8d44\u6e90\uff1b</li> <li>\u91ca\u653e\u8d44\u6e90\uff1b</li> </ol> <p>\u5176\u4e2d\uff0c\u7533\u8bf7\u8d44\u6e90\u548c\u91ca\u653e\u8d44\u6e90\u901a\u5e38\u901a\u8fc7\u4e0d\u540c\u7684\u7cfb\u7edf\u8c03\u7528\u5b9e\u73b0\u3002\u800c\u90e8\u5206\u8d44\u6e90\u662f\u6709\u9650\u4e14\u4e92\u65a5\u7684\uff0c\u56e0\u800c\u5982\u679c\u5728\u7f3a\u4e4f\u8d44\u6e90\u7684\u60c5\u51b5\u4e0b\uff0c\u8fdb\u7a0b/\u7ebf\u7a0b\u4ecd\u7136\u60f3\u8981\u7533\u8bf7\u8d44\u6e90\uff0c\u5c31\u53ea\u80fd\u9677\u5165\u7b49\u5f85\u3002\u800c\u6b63\u5728\u7b49\u5f85\u7684\u8d44\u6e90\u4e5f\u53ef\u80fd\u6301\u6709\u4e00\u4e9b\u8d44\u6e90\uff0c\u4e00\u65e6\u6070\u597d\u51fa\u73b0\u4e86\u4e92\u76f8\u7b49\u5f85\u7684\u60c5\u51b5\uff0c\u5c31\u4f1a\u51fa\u73b0\u6b7b\u9501\u3002\u4f8b\u5982\uff0c\u4e92\u65a5\u9501\u548c\u4fe1\u53f7\u91cf\u8fd9\u4e9b\u4e1c\u897f\u5c31\u662f\u6b7b\u9501\u4ea7\u751f\u7684\u4e00\u5927\u91cd\u8981\u6765\u6e90\u3002</p> <p>\u8ba1\u7b97\u673a\u8d44\u6e90\u5206\u4e3a\u5f88\u591a\u7c7b\uff0c\u6bcf\u4e00\u7c7b\u4e2d\u53ef\u80fd\u6709\u82e5\u5e72\u5e73\u7b49\u7684\u201c\u5b9e\u4f8b(instance)\u201d\u3002\u5bf9\u4e8e\u4e00\u4e2a\u5408\u7406\u7684\u201c\u8d44\u6e90\u5206\u7c7b\u201d\u6765\u8bf4\uff0c\u4e00\u4e2a\u8fdb\u7a0b/\u7ebf\u7a0b\u9700\u8981\u67d0\u79cd\u8d44\u6e90\u65f6\u5019\uff0c\u8fd9\u4e2a\u8d44\u6e90\u7c7b\u522b\u4e2d\u7684\u4efb\u610f\u7a7a\u95f2\u5b9e\u4f8b\u90fd\u5e94\u5f53\u53ef\u4ee5\u88ab\u7528\u4e8e\u6ee1\u8db3\u8fd9\u4e2a\u8fdb\u7a0b/\u7ebf\u7a0b\u7684\u9700\u6c42\u3002</p> <p>\u5bfc\u8bfb</p> <p>\u4e0b\u9762\u4e24\u4e2a\u90e8\u5206\u5e76\u4e0d\u4f1a\u5f88\u5feb\u5c31\u88ab\u7528\u5230\uff0c\u5c24\u5176\u662f\u5b89\u5168\u72b6\u6001\u4e0e\u4e0d\u5b89\u5168\u72b6\u6001\u662f\u88ab\u6211\u63d0\u524d\u653e\u5230\u8fd9\u91cc\u6765\u7684\uff0c\u8bfb\u8005\u53ef\u4ee5\u81ea\u884c\u8003\u8651\u662f\u76f4\u63a5\u987a\u5e8f\u9605\u8bfb\uff0c\u8fd8\u662f\u6682\u65f6\u8df3\u8fc7\uff08\u4e4b\u540e\u7528\u5230\u7684\u65f6\u5019\u6211\u4f1a\u7ed9\u51fa\u8df3\u56de\u94fe\u63a5\uff09\u3002</p> <p>\u6211\u4e2a\u4eba\u8ba4\u4e3a\u7ed3\u6784\u4e0a\u8fd9\u6837\u5b89\u6392\u66f4\u6e05\u6670\uff0c\u4f46\u8003\u8651\u5230\u4e24\u4e2a\u5185\u5bb9\u5b58\u5728\u4e00\u5b9a\u95f4\u9694\uff0c\u6240\u4ee5\u5f80\u540e\u653e\u7f6e\u4e5f\u6709\u5f80\u540e\u653e\u7f6e\u7684\u9053\u7406\u3002</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit2-Part3/#\u8d44\u6e90\u5206\u914d\u56fe","title":"\u8d44\u6e90\u5206\u914d\u56fe","text":"<p>\u6839\u636e\u4e0a\u9762\u7684\u63cf\u8ff0\uff0c\u6211\u4eec\u53ef\u4ee5\u77e5\u9053\uff0c\u5efa\u6a21\u6b7b\u9501\u53ef\u4ee5\u4ece\u8ba8\u8bba\u8fdb\u7a0b/\u7ebf\u7a0b\u4e0e\u8d44\u6e90\u7684\u6c42\u53d6\u5173\u7cfb\u5165\u624b\u3002\u6211\u4eec\u53ef\u4ee5\u7528\u8d44\u6e90\u5206\u914d\u56fe(resource-allocation graph)\u6765\u63cf\u8ff0\u8fd9\u4ef6\u4e8b\u3002</p> <p>\u9759\u6001</p> <p>\u8d44\u6e90\u5206\u914d\u56fe\u662f\u4e00\u79cd\u6709\u4e24\u7c7b\u8282\u70b9\u7684\u6709\u5411\u56fe\uff0c\u6211\u4eec\u7528\u5706\u8282\u70b9 \\(T_i\\) \u8868\u793a\u8fdb\u7a0b/\u7ebf\u7a0b\uff0c\u7528\u65b9\u8282\u70b9 \\(R_j\\) \u8868\u793a\u8d44\u6e90\uff0c\u65b9\u8282\u70b9\u4e2d\u7684\u5b9e\u5fc3\u70b9\u8868\u793a\u4e00\u4e2a\u8d44\u6e90\u7c7b\u522b\u7684\u4e00\u4e2a\u5b9e\u4f8b\u3002\u540c\u65f6\uff0c\u6211\u4eec\u79f0\u4ece\u8fdb\u7a0b/\u7ebf\u7a0b\u6307\u5411\u8d44\u6e90\u7c7b\u522b\u7684\u6709\u5411\u8fb9\u4e3a\u8bf7\u6c42\u8fb9(request edge)\uff0c\u8868\u793a\u8fdb\u7a0b/\u7ebf\u7a0b \\(T_i\\) \u6b63\u5728\u7b49\u5f85\u8fd9\u79cd\u8d44\u6e90\uff1b\u79f0\u4ece\u8d44\u6e90\u5b9e\u4f8b\u6307\u5411\u8fdb\u7a0b/\u7ebf\u7a0b\u7684\u6709\u5411\u8fb9\u4e3a\u5206\u914d\u8fb9(allocation edge)\uff0c\u8868\u793a\u8d44\u6e90 \\(R_j\\) \u88ab\u5206\u914d\u7ed9\u8fdb\u7a0b/\u7ebf\u7a0b \\(T_i\\)\uff0c\u5373\u76ee\u524d\u8fdb\u7a0b/\u7ebf\u7a0b \\(T_i\\) \u6301\u6709\u4e00\u4e2a\uff08\u4e00\u6761\u8fb9\u8868\u793a\u4e00\u4e2a\uff09\u8d44\u6e90 \\(R_j\\) \u7684\u5b9e\u4f8b\uff0c\u4f8b\u5982\u4e0b\u56fe\uff1a</p> <p>      Resource allocation graph. </p> <ul> <li>\u5f53\u8d44\u6e90\u5206\u914d\u56fe\u4e2d\u4e0d\u5b58\u5728\u73af\u65f6\uff0c\u8bf4\u660e\u4e0d\u4f1a\u51fa\u73b0\u6b7b\u9501\u72b6\u6001\uff1b</li> <li>\u5f53\u8d44\u6e90\u5206\u914d\u56fe\u4e2d\u5b58\u5728\u73af\u65f6\uff0c\u7cfb\u7edf\u53ef\u80fd\u5904\u4e8e\u6b7b\u9501\u72b6\u6001\uff0c\u4e5f\u53ef\u80fd\u4e0d\u5904\u4e8e\u6b7b\u9501\u72b6\u6001\uff1b<ul> <li>\u7279\u4f8b\uff1a\u5982\u679c\u4e0e\u73af\u76f8\u5173\u7684\u8282\u70b9\u90fd\u53ea\u6709\u4e00\u4e2a\u5b9e\u4f8b\u65f6\u5019\uff0c\u7cfb\u7edf\u5904\u4e8e\u6b7b\u9501\u72b6\u6001\uff1b</li> </ul> </li> </ul> <p>\u6362\u53e5\u8bdd\u6765\u8bf4\uff0c\u8d44\u6e90\u5206\u914d\u56fe\u4e2d\u5b58\u5728\u73af\uff0c\u662f\u7cfb\u7edf\u5904\u4e8e\u6b7b\u9501\u72b6\u6001\u7684\u5fc5\u8981\u6761\u4ef6\u3002</p> <p>\u52a8\u6001</p> <ul> <li>\u8fdb\u7a0b/\u7ebf\u7a0b\u7533\u8bf7\u67d0\u4e2a\u8d44\u6e90\u65f6\uff0c\u5728\u56fe\u4e2d\u6dfb\u52a0\u4e00\u6761\u5bf9\u5e94\u7684 request edge\uff1b</li> <li>\u5f53\u8d44\u6e90\u7d22\u53d6\u6210\u529f\u65f6\uff0c\u8fd9\u6761 request edge \u88ab\u66ff\u6362\u4e3a allocation edge\uff1b</li> <li>\u5f53\u8fdb\u7a0b\u91ca\u653e\u8fd9\u4e2a\u8d44\u6e90\u65f6\uff0c\u5219\u9700\u8981\u5c06\u8be5 allocation edge \u6d88\u9664\uff1b</li> </ul> <p>\u5728\u4e4b\u540e\u7684\u5185\u5bb9\u4e2d\uff0c\u6211\u4eec\u8fd8\u5c06\u770b\u5230\u4e00\u4e9b\u8d44\u6e90\u5206\u914d\u56fe\u7684\u53d8\u4f53\uff1a\u5f15\u5165 claim edge \u7684\u8d44\u6e90\u5206\u914d\u56fe\u7b97\u6cd5\u4ee5\u53ca\u53ea\u4fdd\u7559\u8fdb\u7a0b/\u7ebf\u7a0b\u7b49\u5f85\u5173\u7cfb\u7684 wait for graph\u3002</p> <p>\u7531\u4e8e\u552f\u4e00\u5b9e\u4f8b\u8fd9\u4e2a\u6027\u8d28\u88ab\u7834\u574f\u540e\uff0c\u6b7b\u9501\u5728\u8d44\u6e90\u5206\u914d\u56fe\u4e0a\u4e0d\u518d\u90a3\u4e48\u76f4\u89c2\u4e86\uff0c\u6240\u4ee5\u6211\u4eec\u9700\u8981\u5f15\u5165\u65b0\u7684\u5de5\u5177\u6765\u63cf\u8ff0\u6b7b\u9501\u3002</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit2-Part3/#\u5b89\u5168\u72b6\u6001\u4e0e\u4e0d\u5b89\u5168\u72b6\u6001","title":"\u5b89\u5168\u72b6\u6001\u4e0e\u4e0d\u5b89\u5168\u72b6\u6001","text":"<p>\u8be5\u90e8\u5206\u5185\u5bb9\u88ab\u4e66\u672c\u5b89\u6392\u5728\u6b7b\u9501\u907f\u514d\u4e2d\uff0c\u88ab\u6211\u63d0\u524d\uff0c\u53ef\u4ee5\u8003\u8651\u4e0d\u76f4\u63a5\u6df1\u5165\u800c\u662f\u7b49\u4e4b\u540e\u9047\u5230\u4e86\u518d\u770b\u3002</p> <p>\u5b89\u5168\u72b6\u6001(safe state)\u6307\u5b58\u5728\u5b89\u5168\u5e8f\u5217(safe sequence)\u7684\u72b6\u6001\uff0c\u7cfb\u7edf\u6309\u7167 safe sequence \u7684\u987a\u5e8f\u6267\u884c\u8fdb\u7a0b/\u7ebf\u7a0b\u548c\u5206\u914d\u8d44\u6e90\uff0c\u5c31\u4e0d\u4f1a\u51fa\u73b0\u6b7b\u9501\uff1b\u76f8\u5bf9\u5e94\u7684\uff0c\u4e0d\u662f\u5b89\u5168\u72b6\u6001\u7684\u72b6\u6001\u79f0\u4e3a\u4e0d\u5b89\u5168\u72b6\u6001(unsafe state)\u3002\u5177\u4f53\u6765\u8bf4\uff0csafe sequence \u7684\u5b9a\u4e49\u5982\u4e0b\uff1a</p> <p>safe sequence</p> <p>\u9996\u5148 high level \u5730\u8bb2\u4e00\u4e0b safe sequence \u7684\u601d\u8def\uff0csafe sequence \u4e2d\u7684\u6bcf\u4e00\u9879 \\(T_i\\) \u6240\u9700\u8981\u7684\u8d44\u6e90\uff0c\u90fd\u80fd\u901a\u8fc7\u73b0\u6709\u8d44\u6e90\u6216\u5176\u4e4b\u524d\u7684\u8fdb\u7a0b/\u7ebf\u7a0b \\(\\forall j &lt; i T_{j}\\) \u6267\u884c\u5b8c\u6bd5\u91ca\u653e\u7684\u8d44\u6e90\u6765\u6ee1\u8db3\u3002</p> <p>\u5177\u4f53\u6765\u8bf4\uff0c\u5bf9\u4e8e safe sequence \\(&lt;T_1, T_2, \\dots, T_n&gt;\\)\uff0c\u6211\u4eec\u5b9a\u4e49\u6bcf\u4e00\u9879\u8fd8\u9700\u8981\u7684 \\(R_j\\) \u8d44\u6e90\u4e3a \\(need_{i,j}\\)\u3001\u5df2\u7ecf\u88ab\u5206\u914d\u7684 \\(R_j\\) \u8d44\u6e90\u4e3a \\(allocated_{i,j}\\)\uff0c\u4ee5\u53ca\u8d44\u6e90 \\(R_j\\) \u4e2d\u8fd8\u7a7a\u95f2\u7684\u8d44\u6e90\u7684\u91cf \\(available_{j}\\)\uff0c\u5219\u5e94\u5f53\u6709\uff1a</p> \\[ \\begin{aligned}     \\forall i \\in \\{1, 2, \\dots, n\\},\\quad     \\forall j \\in \\{1, 2, \\dots, m\\}, \\\\     available_{j} + \\sum_{k=1}^{i-1} allocated_{k,j} \\geq need_{i,j} \\end{aligned} \\] <p>\u5bf9\u4e8e\u7b2c \\(i\\) \u4e2a\u8fdb\u7a0b/\u7ebf\u7a0b\u6765\u8bf4\uff0c\u5b9e\u9645\u8fd0\u884c\u65f6\u7684\u7a7a\u95f2\u8d44\u6e90\u53ef\u80fd\u6765\u81ea\u4e8e \\(allocated_{k,j}\\)\uff0c\u4f46\u8fd9\u91cc\u662f\u7528\u6765\u505a\u5224\u65ad\u7684\uff0c\u5e76\u4e0d\u662f\u4e00\u4e2a\u5728\u7ebf\u7684\u8ba1\u7b97\u8fc7\u7a0b\uff0c\u6240\u4ee5\u7528 \\(available_{j} + \\sum_{k=1}^{i-1} allocated_{k,j}\\) \u8fd9\u4e2a\u5f0f\u5b50\u6765\u7ef4\u62a4\u6b64\u65f6 \\(T_i\\) \u7684\u6700\u5927\u53ef\u7528\u8d44\u6e90\u3002</p> <p>\u601d\u8003\u5982\u4f55\u5bfb\u627e\u4e00\u4e2a safe sequence</p> <p>\u8fd9\u4e2a\u95ee\u9898\u6211\u4eec\u5728\u4e4b\u540e\u6b7b\u9501\u68c0\u6d4b\u7684\u90e8\u5206\u4f1a\u7ed9\u51fa\u7b54\u6848\uff0c\u4f46\u4e0d\u59a8\u7b80\u5355\u601d\u8003\u4e00\u4e0b\u600e\u6837\u5bfb\u627e\u4e00\u4e2a safe sequence \u5462\uff1f\u80fd\u5426\u8d2a\u5fc3\u5730\u6765\u6c42\u7b97\u8fd9\u6837\u4e00\u4e2a\u5e8f\u5217\u5462\uff1f</p> <p>\u4f46\u662f\uff0csafe state \u662f\u4e00\u4e2a\u76f8\u5bf9\u8f83\u5f3a\u7684\u7ea6\u675f\uff0c\u4e0d\u5b89\u5168\u72b6\u6001\u4e0d\u4ee3\u8868\u6b7b\u9501\u4e00\u5b9a\u4f1a\u53d1\u751f\uff0c\u7528\u97e6\u6069\u56fe\u6765\u8868\u793a\u5b83\u4eec\u7684\u5173\u7cfb\u5c31\u662f\uff1a</p> <p> </p> <p>\u5982\u679c\u6211\u4eec\u80fd\u4fdd\u8bc1\u7cfb\u7edf\u53ea\u8fd0\u884c\u5728 safe state\uff0c\u4e5f\u5c31\u80fd\u5145\u5206\u5730\u907f\u514d\u6b7b\u9501\u7684\u53d1\u751f\u3002</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit2-Part3/#\u6b7b\u9501\u7684\u6761\u4ef6","title":"\u6b7b\u9501\u7684\u6761\u4ef6","text":"<p>\u8981\u60f3\u6b7b\u9501\u51fa\u73b0\uff0c\u4e0b\u9762\u56db\u4e2a\u6761\u4ef6\u5fc5\u987b\u540c\u65f6\u6ee1\u8db3\uff1a</p> <ol> <li>\u4e92\u65a5(mutual exclusion)\uff1a\u6b7b\u9501\u4e2d\u81f3\u5c11\u6709\u4e00\u4e2a\u8d44\u6e90\u5fc5\u987b\u662f\u975e\u5171\u4eab\u7684\uff0c\u5373\u4e00\u6b21\u53ea\u80fd\u88ab\u4e00\u4e2a\u8fdb\u7a0b/\u7ebf\u7a0b\u4f7f\u7528\uff1b<ul> <li>\u6b63\u56e0\u4e3a\u4e92\u65a5\u8d44\u6e90\u65e0\u6cd5\u88ab\u540c\u65f6\u4f7f\u7528\uff0c\u6240\u4ee5\u9700\u8981\u8d44\u6e90\u7684\u8fdb\u7a0b/\u7ebf\u7a0b\u9700\u8981\u7b49\u5f85\u6301\u6709\u76ee\u6807\u8d44\u6e90\u7684\u8fdb\u7a0b/\u7ebf\u7a0b\u91ca\u653e\u8be5\u8d44\u6e90\u4ee5\u540e\u624d\u80fd\u4f7f\u7528\u76ee\u6807\u8d44\u6e90\uff1b</li> </ul> </li> <li>\u6301\u6709\u5e76\u7b49\u5f85(hold &amp; wait)\uff1a\u6b7b\u9501\u4e2d\u7684\u8fdb\u7a0b/\u7ebf\u7a0b\u5728\u7b49\u5f85\u8d44\u6e90\u7684\u540c\u65f6\uff0c\u4e5f\u5fc5\u987b\u6301\u6709\u81f3\u5c11\u4e00\u4e2a\u8d44\u6e90\uff1b<ul> <li>\u4e3a\u4e86\u4fc3\u6210\u5faa\u73af\u7b49\u5f85\uff0c\u4e00\u4e2a\u7b49\u5f85\u5176\u5b83\u8d44\u6e90\uff08\u6709\u51fa\u8fb9\uff09\u7684\u8fdb\u7a0b/\u7ebf\u7a0b\u5fc5\u987b\u6301\u6709\u81f3\u5c11\u4e00\u4e2a\u8d44\u6e90\uff0c\u8fd9\u6837\u624d\u80fd\u8ba9\u5176\u5b83\u8d44\u6e90\u4e5f\u7b49\u5f85\u5b83\uff08\u6709\u5165\u8fb9\uff09\uff1b</li> <li>\u8bf4\u767d\u4e86\u5c31\u662f\uff1a\u6301\u6709\u5bfc\u81f4\u53ef\u80fd\u88ab\u7b49\u5f85\uff0c\u7b49\u5f85\u5c31\u662f\u7b49\u5f85\uff0c\u800c\u4e00\u65e6\u4e00\u4e2a\u8282\u70b9\u65e2\u7b49\u5f85\u53c8\u88ab\u7b49\u5f85\uff0c\u5c31\u6709\u53ef\u80fd\u4fc3\u6210\u5faa\u73af\u7b49\u5f85</li> </ul> </li> <li>\u975e\u62a2\u5360(no preemption)\uff1a\u6b7b\u9501\u4e2d\u7684\u8fdb\u7a0b/\u7ebf\u7a0b\u53ea\u80fd\u5728\u4f7f\u7528\u5b8c\u8d44\u6e90\u540e\u4e3b\u52a8\u91ca\u653e\u8d44\u6e90\uff0c\u5176\u6301\u6709\u7684\u8d44\u6e90\u65e0\u6cd5\u88ab\u5176\u5b83\u8fdb\u7a0b/\u7ebf\u7a0b\u62a2\u5360\uff1b<ul> <li>\u4e3a\u4e86\u4fdd\u8bc1\u7b49\u5f85\u5173\u7cfb\u4e0d\u4f1a\u88ab\u5f3a\u884c\u7834\u574f\uff1b</li> </ul> </li> <li>\u5faa\u73af\u7b49\u5f85(circular wait)\uff1a\u6b7b\u9501\u4e2d\u7684\u8fdb\u7a0b\u5b58\u5728\u73af\u72b6\u7684\u7b49\u5f85\u8d44\u6e90\u5173\u7cfb\uff0c\u5373 wait for graph \u4e2d\u5b58\u5728\u73af\uff1b<ul> <li>\u903b\u8f91\u4e0a\u5bfc\u81f4\u6b7b\u9501\u51fa\u73b0\u7684\u76f4\u63a5\u539f\u56e0\uff0c\u4e92\u76f8\u7b49\u5f85\u5bfc\u81f4\u6ca1\u6709\u8d44\u6e90\u4f1a\u88ab\u91ca\u653e\uff0c\u5bfc\u81f4\u6b7b\u9501\u72b6\u6001\u65e0\u6cd5\u88ab\u6253\u7834\uff1b</li> </ul> </li> </ol> <p>\u53ef\u4ee5\u53d1\u73b0\uff0c\u8fd9\u56db\u4e2a\u5173\u7cfb\u5e76\u4e0d\u5b8c\u5168\u72ec\u7acb\u3002</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit2-Part3/#\u6b7b\u9501\u7684\u5904\u7406","title":"\u6b7b\u9501\u7684\u5904\u7406","text":"<p>\u5f88\u5bb9\u6613\u8ba4\u8bc6\u5230\uff0c\u6b7b\u9501\u7684\u5371\u5bb3\u662f\u5de8\u5927\u7684\uff0c\u90a3\u4e48\u5982\u4f55\u5904\u7406\u64cd\u4f5c\u7cfb\u7edf\u4e2d\u7684\u6b7b\u9501\u95ee\u9898\u5462\uff1f\u4e3b\u8981\u6709\u8fd9\u4e48\u51e0\u4e2a\u601d\u8def\uff1a</p> <ol> <li>\u4e0d\u505a\u989d\u5916\u5904\u7406\uff0c\u8981\u6c42\u7a0b\u5e8f\u5458\u4fdd\u8bc1\u903b\u8f91\u4e0a\u4e0d\u4f1a\u51fa\u73b0\u6b7b\u9501\uff1b</li> <li>\u6b7b\u9501\u9884\u9632(deadlock prevention)\uff1a\u4f7f\u7528\u67d0\u79cd\u89c4\u8303\u6216\u534f\u8bae\u6765\u4fdd\u8bc1\u6b7b\u9501\u4e0d\u4f1a\u51fa\u73b0\uff1b</li> <li>\u6b7b\u9501\u907f\u514d(deadlock avoidance)\uff1a\u7981\u6b62\u53ef\u80fd\u4ea7\u751f\u6b7b\u9501\u7684\u884c\u4e3a\u7684\u53d1\u751f\uff1b<ul> <li>\u4e0e 2. \u7684\u6700\u4e3b\u8981\u7684\u533a\u522b\u662f\uff0c2. \u5728\u89c4\u8303\u4e0b\u7684\u6240\u6709\u884c\u4e3a\u90fd\u4e0d\u4f1a\u51fa\u73b0\u6b7b\u9501\u95ee\u9898\uff1b\u800c 3. \u5219\u662f\u4e0d\u7ea6\u675f\u884c\u4e3a\uff0c\u4f46\u662f\u7981\u6b62\u53ef\u80fd\u4ea7\u751f\u6b7b\u9501\u7684\u884c\u4e3a\u6267\u884c\uff0c\u5728\u7a0d\u5019\u4ecb\u7ecd\u5177\u4f53\u5185\u5bb9\u540e\u4f1a\u66f4\u5bb9\u6613\u7406\u89e3\uff1b</li> </ul> </li> <li>\u6b7b\u9501\u68c0\u6d4b(deadlock detection)\u548c\u6b7b\u9501\u89e3\u9664(deadlock recovery)\u5141\u8bb8\u6b7b\u9501\u7684\u51fa\u73b0\uff0c\u4f46\u662f\u5f53\u68c0\u6d4b\u5230\u6b7b\u9501\u65f6\uff0c\u9700\u8981\u53bb\u6d88\u9664\u6b7b\u9501\u95ee\u9898\uff1b</li> </ol> <p>\u4e8b\u5b9e\u4e0a\uff0c\u5728\u4e3b\u6d41\u64cd\u4f5c\u7cfb\u7edf\u4e2d\uff0c\u4e00\u822c\u9009\u62e9\u4f7f\u7528\u7b2c\u4e00\u79cd\uff0c\u5373\u5c06\u95ee\u9898\u4ea4\u7ed9\u5f00\u53d1\u8005\u53bb\u89e3\u51b3\u3002</p> <p>\u63a5\u4e0b\u6765\u6211\u4eec\u6765\u4ecb\u7ecd\u4e0a\u9762\u63d0\u5230\u7684\u540e\u4e09\u4e2a\u65b9\u6cd5\u4e2d\u7684\u56db\u5757\u5185\u5bb9\u3002\u5176\u4e2d\u6709\u90e8\u5206\u5185\u5bb9\u6709\u8f83\u5927\u4ea4\u96c6\uff0c\u5b83\u4eec\u53ef\u80fd\u5c5e\u4e8e\u540c\u4e00\u7eb2\u9886\u4e0b\u5728\u4e0d\u540c\u65f6\u523b\u505a\u7684\u5904\u7406\u3002</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit2-Part3/#\u6b7b\u9501\u9884\u9632","title":"\u6b7b\u9501\u9884\u9632","text":"<p>\u6b7b\u9501\u9884\u9632(deadlock prevention)\u7684\u6838\u5fc3\u601d\u8def\u662f\u7834\u574f\u6b7b\u9501\u4ea7\u751f\u7684\u5fc5\u8981\u6761\u4ef6\u3002\u7531\u4e8e\u300c\u8981\u60f3\u6b7b\u9501\u51fa\u73b0\uff0c\u56db\u4e2a\u6761\u4ef6\u5fc5\u987b\u540c\u65f6\u6ee1\u8db3\u300d\uff0c\u6240\u4ee5\u6211\u4eec\u5982\u679c\u80fd\u4fdd\u8bc1\u56db\u4e2a\u6761\u4ef6\u4e2d\u67d0\u4e00\u4e2a\u4e00\u76f4\u4e0d\u6210\u7acb\uff0c\u90a3\u4e48\u6b7b\u9501\u5c06\u6c38\u8fdc\u4e0d\u4f1a\u4ea7\u751f\uff0c\u800c\u65e2\u7136\u6b7b\u9501\u4e0d\u4f1a\u4ea7\u751f\uff0c\u90a3\u4e5f\u5c31\u4e0d\u9700\u8981\u53bb\u5904\u7406\u6b7b\u9501\u95ee\u9898\u3002\u63a5\u4e0b\u6765\u6211\u4eec\u5bf9\u56db\u4e2a\u5fc5\u8981\u6761\u4ef6\u9010\u4e00\u5206\u6790\uff1a</p> <ol> <li>\u7834\u574f\u4e92\u65a5(mutual exclusion)\uff1a<ul> <li>\u8fd9\u4e2a\u6761\u4ef6\u51e0\u4e4e\u662f\u65e0\u6cd5\u7834\u574f\u7684\uff0c\u5f88\u591a\u8d44\u6e90\u5929\u7136\u662f\u4e92\u65a5\u7684\uff1b</li> <li>\u6709\u4e9b\u8d44\u6599\u91cc\u4e5f\u6709\u5199\u4e00\u4e9b\u65b9\u6cd5\u6765\u7834\u574f\u8fd9\u4e2a\u6761\u4ef62\uff0c\u4f46\u662f\u6211\u611f\u89c9\u8fd8\u662f\u6709\u5c40\u9650\u6027\u7684\uff0c\u53cd\u6b63\u4e66\u672c\u91cc\u8bf4\u7684\u662f\u6ca1\u6cd5\u7834\u574f\uff1b</li> </ul> </li> <li>\u7834\u574f\u6301\u6709\u5e76\u7b49\u5f85(hold &amp; wait)\uff1a<ul> <li>\u5728\u6211\u4eec\u524d\u9762\u7684\u5206\u6790\u4e2d\u77e5\u9053\uff1a\u300c\u6301\u6709\u5bfc\u81f4\u53ef\u80fd\u88ab\u7b49\u5f85\uff0c\u7b49\u5f85\u5c31\u662f\u7b49\u5f85\uff0c\u800c\u4e00\u65e6\u4e00\u4e2a\u8282\u70b9\u65e2\u7b49\u5f85\u53c8\u88ab\u7b49\u5f85\uff0c\u5c31\u6709\u53ef\u80fd\u4fc3\u6210\u5faa\u73af\u7b49\u5f85\u300d\uff1b</li> <li>\u4f46\u662f\uff0c\u5982\u679c\u6211\u4eec\u53ea\u5141\u8bb8\u4e00\u4e2a\u8282\u70b9\u53ea\u80fd\u5728\u201c\u88ab\u7b49\u5f85\u201d\u548c\u201c\u7b49\u5f85\u201d\u4e2d\u4e8c\u9009\u4e00\uff0c\u4e5f\u5c31\u662f\u8bf4\u8ba9\u4e00\u4e2a\u7ebf\u7a0b/\u8fdb\u7a0b\u4e00\u65e6\u7533\u8bf7\u8d44\u6e90\u5c31\u4e00\u6b21\u6027\u83b7\u53d6\u6240\u6709\u8d44\u6e90\uff0c\u5982\u679c\u6ca1\u6cd5\u4e00\u6b21\u6027\u83b7\u53d6\u6240\u6709\u8d44\u6e90\u5c31\u91ca\u653e\u5df2\u7ecf\u7533\u8bf7\u5230\u7684\u8d44\u6e90\uff0c\u901a\u8fc7\u8fd9\u79cd\u65b9\u6cd5\u907f\u514d\u4e86\u5faa\u73af\u7b49\u5f85\u7684\u4ea7\u751f\uff1b</li> </ul> </li> <li>\u7834\u574f\u975e\u62a2\u5360(no preemption)\uff1a<ul> <li>\u901a\u8fc7\u5141\u8bb8\u8fdb\u7a0b/\u7ebf\u7a0b\u5f3a\u884c\u62a2\u5360\u53e6\u5916\u4e00\u4e2a\u8fdb\u7a0b/\u7ebf\u7a0b\u6301\u6709\u7684\u8d44\u6e90\uff0c\u53ef\u4ee5\u7834\u574f\u88ab\u52a8\u7684\u7b49\u5f85\u5173\u7cfb\uff0c\u4ece\u800c\u907f\u514d\u6b7b\u9501\uff1b</li> <li>\u4f46\u662f\u548c\u4e92\u65a5\u5176\u5b9e\u662f\u7c7b\u4f3c\u7684\uff0c\u975e\u62a2\u5360\u4e5f\u5177\u6709\u4e00\u5b9a\u7684\u5929\u7136\u6027\uff0c\u5f3a\u884c\u62a2\u5360\u4e00\u90e8\u5206\u8d44\u6e90\u53ef\u80fd\u5bfc\u81f4\u8fdb\u884c\u5230\u4e00\u534a\u7684\u4efb\u52a1\u5931\u8d25\uff0c\u751a\u81f3\u4e00\u4e9b\u66f4\u4e25\u91cd\u7684\u540e\u679c\uff0c\u6240\u4ee5\u8fd9\u5e76\u4e0d\u662f\u4e00\u4e2a\u5f88\u597d\u7684\u529e\u6cd5\uff1b</li> <li>\u800c\u4e14\uff0c\u5141\u8bb8\u201c\u62a2\u5360\u201d\u4e5f\u4f1a\u5e26\u6765\u9965\u997f\u95ee\u9898\uff0c\u603b\u4f53\u6765\u8bf4\u96be\u4ee5\u5b9e\u73b0\u800c\u4e14\u6548\u7387\u4e0d\u9ad8\uff1b</li> </ul> </li> <li>\u7834\u574f\u5faa\u73af\u7b49\u5f85(circular wait)\uff1a<ul> <li>\u901a\u8fc7\u7ed9\u8d44\u6e90\u7f16\u53f7\uff0c\u89c4\u5b9a\u8fdb\u7a0b/\u7ebf\u7a0b\u53ea\u80fd\u6309\u7279\u5b9a\u7684\u987a\u5e8f\u7533\u8bf7\u8d44\u6e90\uff0c\u5c31\u4e0d\u4f1a\u51fa\u73b0\u5faa\u73af\u7b49\u5f85\u7684\u60c5\u51b5\uff1b</li> <li>\u7531\u4e8e\u8fdb\u7a0b/\u7ebf\u7a0b\u53ea\u80fd\u6309\u7167\u7279\u5b9a\u987a\u5e8f\u7533\u8bf7\u8d44\u6e90\uff0c\u800c\u8d44\u6e90\u7684\u7533\u8bf7\u5e94\u5f53\u662f\u4e2a\u52a8\u6001\u7684\u8fc7\u7a0b\uff0c\u6240\u4ee5\u53ef\u80fd\u4f1a\u51fa\u73b0\u300c\u8fdb\u7a0b\u5927\u534a\u90e8\u5206\u53ea\u9700\u8981\u7528\u5230 \\(R_3\\)\uff0c\u4f46\u662f\u7531\u4e8e\u6700\u540e\u9700\u8981\u7528\u4e00\u4e0b \\(R_1\\)\uff0c\u6240\u4ee5\u5fc5\u987b\u5148\u7533\u8bf7 \\(R_1\\) \u518d\u7533\u8bf7 \\(R_3\\)\uff0c\u5bfc\u81f4\u8fc7\u7a0b\u4e2d \\(R_1\\) \u4e00\u76f4\u88ab\u6301\u6709\u4f46\u4e00\u76f4\u672a\u88ab\u4f7f\u7528\u300d\u7684\u60c5\u51b5\uff0c\u6548\u7387\u582a\u5fe7\uff1b</li> <li>\u4e3a\u4e86\u89e3\u51b3\u4e0a\u9762\u8fd9\u4e2a\u95ee\u9898\uff0c\u53ef\u4ee5\u5c1d\u8bd5\u5728\u8bbe\u8ba1\u7f16\u53f7\u65f6\u5c06\u8d44\u6e90\u4f7f\u7528\u7684\u5e38\u89c4\u987a\u5e8f\u7b49\u56e0\u7d20\u7eb3\u5165\u8003\u8651\uff0c\u4f46\u7cbe\u5fc3\u8bbe\u8ba1\u7684\u8d44\u6e90\u5e8f\u53f7\u9047\u5230\u65e0\u7a77\u65e0\u5c3d\u7684\u8d44\u6e90\u7c7b\u578b\u65f6\uff0c\u53c8\u5f53\u5982\u4f55\u5462\uff1f\u7531\u4e8e\u9700\u8981\u5927\u91cf\u8bbe\u8ba1\uff0c\u6240\u4ee5\u5e26\u6765\u4e86\u8d44\u6e90\u7684\u6269\u5c55\u6027\u8f83\u5dee\u7684\u95ee\u9898\uff1b</li> </ul> </li> </ol>"},{"location":"cour_note/D3QD_OperatingSystem/Unit2-Part3/#\u6b7b\u9501\u907f\u514d","title":"\u6b7b\u9501\u907f\u514d","text":"<p>\u6b7b\u9501\u907f\u514d(deadlock avoidance)\u901a\u8fc7\u963b\u6b62\u53ef\u80fd\u8ba9\u7cfb\u7edf\u8fdb\u5165\u6b7b\u9501\u72b6\u6001\u7684\u884c\u4e3a\uff0c\u6765\u89e3\u51b3\u6b7b\u9501\u95ee\u9898\u3002\u5373\uff1a\u5982\u679c\u8fd9\u4e48\u505a\u53ef\u80fd\u5bfc\u81f4\u6b7b\u9501\uff0c\u90a3\u6211\u5c31\u4e0d\u8fd9\u4e48\u505a\uff0c\u4ee5\u6b64\u6765\u907f\u514d\u6b7b\u9501\u3002</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit2-Part3/#\u8d44\u6e90\u5206\u914d\u56fe\u7b97\u6cd5","title":"\u8d44\u6e90\u5206\u914d\u56fe\u7b97\u6cd5","text":"<p>\u524d\u7f6e\uff1a\u8d44\u6e90\u5206\u914d\u56fe\uff01</p> <p>\u8d44\u6e90\u5206\u914d\u56fe\u7b97\u6cd5\u8f83\u4e3a\u76f4\u63a5\uff0c\u5b83\u4e0e\u5b89\u5168\u72b6\u6001\u7684\u6982\u5ff5\u65e0\u5173\uff0c\u76f4\u63a5\u68c0\u6d4b\u67d0\u79cd\u5206\u914d\u662f\u5426\u4f1a\u5bfc\u81f4\u6b7b\u9501\u53d1\u751f\uff0c\u5982\u679c\u8be5\u5206\u914d\u4f1a\u5bfc\u81f4\u6b7b\u9501\u53d1\u751f\uff0c\u5219\u4e0d\u8fdb\u884c\u8be5\u5206\u914d\u3002\u4f46\u662f\u9700\u8981\u6ce8\u610f\uff0c\u8be5\u7b97\u6cd5\u53ea\u9002\u7528\u4e8e\u6bcf\u4e2a\u8d44\u6e90\u7c7b\u522b\u4e2d\u90fd\u53ea\u6709\u4e00\u4e2a\u5b9e\u4f8b\u7684\u60c5\u51b5\u3002\uff08\u56e0\u4e3a\u5b83\u4ee5\u8d44\u6e90\u5206\u914d\u56fe\u4e2d\u7684\u90a3\u4e2a\u7279\u4f8b\u4e3a\u539f\u7406\uff01\uff09</p> <p>\u6211\u4eec\u4e4b\u524d\u5df2\u7ecf\u5f15\u5165\u4e86\u8d44\u6e90\u5206\u914d\u56fe\u8fd9\u4e2a\u5de5\u5177\uff0c\u73b0\u5728\u6211\u4eec\u8981\u5728\u8d44\u6e90\u5206\u914d\u56fe\u7684\u57fa\u7840\u4e0a\uff0c\u5f15\u5165\u4e00\u6761\u8bc9\u6c42\u8fb9(claim edge)\uff0c\u7528\u865a\u7ebf\u8868\u793a\uff0c\u5b83\u4ece\u8fdb\u7a0b/\u7ebf\u7a0b \\(T_i\\) \u6307\u5411\u8d44\u6e90 \\(R_j\\)\uff0c\u8868\u793a\u8fdb\u7a0b/\u7ebf\u7a0b \\(T_i\\) \u4f1a\u5728\u672a\u6765\u7533\u8bf7\u8d44\u6e90 \\(R_j\\)\u3002</p> <p>\u4e8e\u662f\uff0c\u5728\u52a8\u6001\u8fc7\u7a0b\u4e2d\uff0c\u8d44\u6e90\u5206\u914d\u56fe\u6309\u7167\u5982\u4e0b\u89c4\u5219\u53cd\u5e94\u5206\u914d\u8fc7\u7a0b\uff1a</p> <ol> <li>\u8fdb\u7a0b/\u7ebf\u7a0b \\(T_i\\) \u88ab\u6dfb\u52a0\u5230\u8d44\u6e90\u5206\u914d\u56fe\u4e2d\u65f6\u5019\uff0c\u9700\u8981\u8fde\u597d\u6240\u6709\u76f8\u5173\u7684 claim edge\uff1b<ul> <li> <p>\u8981\u6c42\u6700\u521d\u5c31\u77e5\u9053\u9700\u8981\u7684\u6240\u6709\u8d44\u6e90\uff0c\u8fd9\u4e5f\u6784\u6210\u8fd9\u7c7b\u65b9\u6cd5\u7684\u4e00\u4e2a\u5c40\u9650\u6027\uff1b</p> </li> </ul> </li> <li>\u8fdb\u7a0b/\u7ebf\u7a0b \\(T_i\\) \u7533\u8bf7\u8d44\u6e90 \\(R_j\\) \u65f6\u5019\uff0c\u5982\u679c\u8fd9\u6761\u8fb9\u53d8\u4e3a assignment edge \u4e0d\u4f1a\u5bfc\u81f4\u6210\u73af\uff0c\u5219\u5c06 claim edge \u8f6c\u5316\u4e3a\u4e00\u6761 request edge \\(T_i \\rightarrow R_j\\)\uff1b<ul> <li> <p>\u8bf7\u6ce8\u610f\uff0c\u8fd9\u91cc\u9700\u8981\u5224\u65ad\u7684\u662f assignment edge\uff0c\u800c\u8f6c\u5316\u7684\u662f request edge\uff1b</p> </li> </ul> </li> <li>\u8fdb\u7a0b/\u7ebf\u7a0b \\(T_i\\) \u83b7\u5f97\u8d44\u6e90 \\(R_j\\) \u65f6\u5019\uff0c\u5c06 request edge \u8f6c\u5316\u4e3a\u4e00\u6761 allocation edge \\(R_j \\rightarrow T_i\\)\uff1b</li> <li>\u8fdb\u7a0b/\u7ebf\u7a0b \\(T_i\\) \u91ca\u653e\u8d44\u6e90 \\(R_j\\) \u65f6\u5019\uff0c\u5c06 allocation edge \u5220\u53bb\uff1b</li> </ol> <p>\u6211\u4eec\u5728\u4e0a\u9762\u4e5f\u8bf4\u4e86\uff1a\u300c\u8be5\u7b97\u6cd5\u53ea\u9002\u7528\u4e8e\u6bcf\u4e2a\u8d44\u6e90\u7c7b\u522b\u4e2d\u90fd\u53ea\u6709\u4e00\u4e2a\u5b9e\u4f8b\u7684\u60c5\u51b5\u300d\uff0c\u90a3\u4e48\u5982\u4f55\u89e3\u9664\u8fd9\u4e2a\u9650\u5236\u5462\uff1f\u8be5\u95ee\u9898\u6211\u4eec\u65e9\u5728\u8d44\u6e90\u5206\u914d\u56fe\u5c0f\u8282\u5c31\u5df2\u7ecf\u8ba8\u8bba\uff0c\u6211\u4eec\u4f7f\u7528\u5b89\u5168\u72b6\u6001\u4e0e\u4e0d\u5b89\u5168\u72b6\u6001\u6765\u63cf\u8ff0\u4e00\u4e2a\u7ea6\u675f\u8f83\u5f3a\u7684\u3001\u4e0d\u4f1a\u4ea7\u751f\u6b7b\u9501\u7684\u72b6\u6001\u3002</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit2-Part3/#\u94f6\u884c\u5bb6\u7b97\u6cd5","title":"\u94f6\u884c\u5bb6\u7b97\u6cd5","text":"<p>\u524d\u7f6e\uff1a\u5b89\u5168\u72b6\u6001\u4e0e\u4e0d\u5b89\u5168\u72b6\u6001\uff01</p> <p>\u94f6\u884c\u5bb6\u7b97\u6cd5(Banker's algorithm)\u5f25\u8865\u4e86\u8d44\u6e90\u5206\u914d\u56fe\u7b97\u6cd5\u53ea\u9002\u7528\u4e8e\u6bcf\u4e2a\u8d44\u6e90\u7c7b\u522b\u4e2d\u90fd\u53ea\u6709\u4e00\u4e2a\u5b9e\u4f8b\u7684\u60c5\u51b5\u7684\u7f3a\u9677\uff0c\u5b83\u652f\u6301\u6bcf\u4e2a\u8d44\u6e90\u7c7b\u522b\u4e0d\u6b62\u4e00\u4e2a\u7684\u60c5\u51b5\uff0c\u4f46\u662f\u6548\u7387\u4e0d\u5982\u5206\u914d\u56fe\u7b97\u6cd5\u3002\u7c7b\u4f3c\u4e8e\u8d44\u6e90\u5206\u914d\u56fe\u7b97\u6cd5\u9700\u8981\u5728\u6700\u5f00\u59cb\u7ed9\u51fa\u6240\u6709 claim edge\uff0c\u94f6\u884c\u5bb6\u7b97\u6cd5\u8981\u6c42\u6ca1\u4e2a\u8fdb\u7a0b/\u7ebf\u7a0b\u7ed9\u51fa\u6267\u884c\u8fc7\u7a0b\u4e2d\u6240\u9700\u8981\u7684\u5404\u7c7b\u8d44\u6e90\u7684\u6700\u5927\u91cf\uff0c\u540c\u65f6\u7ef4\u62a4\u4e00\u4e9b\u6570\u636e\u4ee5\u52a8\u6001\u5730\u8ba1\u7b97\u5b89\u5168\u72b6\u6001\u3002High level \u5730\u6765\u8bb2\uff0c\u5c31\u662f\u9700\u8981\u52a8\u6001\u5730\u68c0\u6d4b\u67d0\u4e2a\u8d44\u6e90\u7533\u8bf7\u662f\u5426\u4f1a\u5bfc\u81f4\u7cfb\u7edf\u8fdb\u5165\u4e0d\u5b89\u5168\u72b6\u6001\uff0c\u5982\u679c\u4f1a\u5bfc\u81f4\u7cfb\u7edf\u8fdb\u5165\u4e0d\u5b89\u5168\u72b6\u6001\uff0c\u5219\u7b49\u5f85\u8d44\u6e90\u8db3\u591f\u518d\u5206\u914d\u3002</p> <p>\u66f4\u5177\u4f53\u7684\u6765\u8bf4\uff0c\u9700\u8981\u7ef4\u62a4\u8fd9\u4e9b\u4e1c\u897f\uff08\u5047\u8bbe\u95ee\u9898\u4e2d\u6709 n \u4e2a\u8fdb\u7a0b/\u7ebf\u7a0b\u548c m \u79cd\u8d44\u6e90\uff09\uff1a</p> <p>data structure</p> <ul> <li><code>Available[m]</code>: number of available resources of each type.</li> <li><code>Max[n][m]</code>: maximum demand of each thread.</li> <li><code>Allocation[n][m]</code>: number of resources of each type currently allocated to each thread.</li> <li><code>Need[n][m]</code>: remaining resource need of each thread.<ul> <li><code>Need[i][j] = Max[i][j] - Allocation[i][j]</code> always holds true.</li> <li> <p>\u6240\u4ee5\u903b\u8f91\u4e0a\u8fd9\u4e2a\u5f0f\u5b50\u5e94\u5f53\u662f\u5197\u4f59\u7684\uff0c\u4f46\u662f\u53d6\u540d\u6709\u5229\u4e8e\u4e4b\u540e\u7684\u6d41\u7a0b\u9610\u8ff0\uff0c\u6240\u4ee5\u6211\u5728\u8fd9\u91cc\u4fdd\u7559\uff1b</p> </li> </ul> </li> </ul> <p>\u94f6\u884c\u5bb6\u7b97\u6cd5\u5206\u4e3a\u4e24\u4e2a\u90e8\u5206\uff0c\u5206\u522b\u662f\u5b89\u5168\u7b97\u6cd5(safety algorithm)\u548c\u8d44\u6e90\u8bf7\u6c42\u7b97\u6cd5(resource request algorithm)\u3002\u524d\u8005\u68c0\u6d4b\u5f53\u524d\u72b6\u6001\u662f\u5426\u5904\u4e8e\u4e0d\u5b89\u5168\u72b6\u6001\uff0c\u540e\u8005\u4ee5\u524d\u8005\u4e3a\u57fa\u7840\uff0c\u5224\u65ad\u662f\u5426\u5141\u8bb8\u5f53\u524d\u8d44\u6e90\u8bf7\u6c42\u53d1\u751f\u3002</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit2-Part3/#\u5b89\u5168\u7b97\u6cd5","title":"\u5b89\u5168\u7b97\u6cd5","text":"<p>\u5b89\u5168\u7b97\u6cd5\u901a\u8fc7\u5bfb\u627e\u662f\u5426\u5b58\u5728\u4e00\u4e2a\u5b89\u5168\u5e8f\u5217\u6765\u5224\u65ad\u5f53\u524d\u72b6\u6001\u662f\u5426\u5904\u4e8e\u5b89\u5168\u72b6\u6001\u3002\u5148\u524d\u5728\u5b89\u5168\u72b6\u6001\u4e0e\u4e0d\u5b89\u5168\u72b6\u6001\u4e00\u8282\u4e2d\u6211\u7559\u4e0b\u8fc7\u4e00\u4e2a\u95ee\u9898\uff1a\u300c\u80fd\u5426\u8d2a\u5fc3\u5730\u6765\u6c42\u7b97\u8fd9\u6837\u4e00\u4e2a\u5e8f\u5217\u5462\u300d\uff0c\u7b54\u6848\u662f\u53ef\u4ee5\uff0c\u6211\u4eec\u4ee5\u4e00\u79cd\u8fd1\u4f3c\u8d2a\u5fc3\u5730\u7b56\u7565\u53bb\u6a21\u62df\u5b89\u5168\u5e8f\u5217\u7684\u8d44\u6e90\u5206\u914d\u8fc7\u7a0b\uff0c\u5c31\u53ef\u4ee5\u5224\u65ad\u662f\u5426\u5b58\u5728\u5b89\u5168\u7b56\u7565\u3002</p> <p>\u56e0\u4e3a\u5bf9\u4e8e\u6240\u6709\u53ef\u4ee5\u4f5c\u4e3a\u5b89\u5168\u72b6\u6001\u4e0b\u4e00\u9879\u7684 \\(T_{i_k}\\)\uff0c\u7531\u4e8e\u6267\u884c\u5b83\u4eec\u540e\uff0c\u7b49\u5230\u8fdb\u7a0b/\u7ebf\u7a0b\u8fd0\u884c\u7ed3\u675f\uff0c\u4f59\u4e0b\u7684\u8d44\u6e90\u53ea\u4f1a\u66f4\u591a\u4e0d\u4f1a\u66f4\u5c11\uff08\u5bf9\u6bd4\u8fd0\u884c\u524d\u540e\uff0c\u4f1a\u591a\u51fa\u6765\u539f\u672c\u5206\u914d\u7ed9\u8fd9\u4e9b\u8fdb\u7a0b/\u7ebf\u7a0b\u7684\u90a3\u4e9b\u8d44\u6e90\uff09\uff0c\u56e0\u800c\u53ea\u8981\u7b26\u5408\u6761\u4ef6\uff0c\u5c31\u53ef\u4ee5\u4f5c\u4e3a\u4e0b\u4e00\u9879\uff0c\u6b65\u6b65\u53ef\u884c\u6700\u7ec8\u4e5f\u53ef\u884c\u3002</p> <p>\u8bf7\u4ed4\u7ec6\u601d\u8003\u8fd9\u4e2a\u8fc7\u7a0b\u7684\u5408\u7406\u6027\uff0c\u5c24\u5176\u662f\u6211\u4e3a\u4ec0\u4e48\u5728\u8fd9\u91cc\u63d0\u5230\u4e86\u201c\u8d2a\u5fc3\u201d\uff0c\u6211\u611f\u89c9\u6211\u67e5\u5230\u7684\u8d44\u6599\u51e0\u4e4e\u90fd\u5ffd\u7565\u4e86\u8fd9\u4e2a\u95ee\u9898\u3002</p> <p>\u5177\u4f53\u6765\u8bf4\uff0c\u5b89\u5168\u7b97\u6cd5\u7684\u6b65\u9aa4\u5982\u4e0b\uff1a</p> <p>algorithm</p> <ol> <li>\u521d\u59cb\u5316\uff1a</li> <li><code>Work[m]</code> &lt;- <code>Available[m]</code>\uff0c<code>Work[m]</code> \u8868\u793a\u5f53\u524d\u72b6\u6001\u7684\u5269\u4f59\u8d44\u6e90\u91cf\uff1b</li> <li><code>Finish[n]</code> &lt;- <code>false</code>\uff0c\u8868\u793a\u6240\u6709\u8fdb\u7a0b/\u7ebf\u7a0b\u90fd\u8fd8\u6ca1\u8fd0\u884c\uff1b</li> <li>\u627e\u5230\u4e00\u4e2a <code>i</code> \u4f7f\u5f97\uff1a</li> <li><code>(Finish[i] == false) &amp;&amp; (Need[i] &lt;= Work)</code>\uff08\u6ce8\u610f\uff0c\u7b2c\u4e8c\u4e2a term \u662f vector \u6bd4\u8f83\uff0c\u8981\u6c42\u6bcf\u4e00\u9879\u90fd\u6ee1\u8db3\uff09\uff0c\u6ee1\u8db3\u8be5\u6761\u4ef6\u8868\u793a\u8be5\u8fdb\u7a0b/\u7ebf\u7a0b\u6240\u9700\u8981\u7684\u8d44\u6e90\u53ef\u4ee5\u88ab\u6ee1\u8db3\uff1b</li> <li>\u5982\u679c\u6ca1\u6709\u8fd9\u4e2a <code>i</code>\uff0c\u5219 goto 3.\uff1b</li> <li>\u5982\u679c\u6709\u8fd9\u4e2a <code>i</code>\uff0c\u5219\u66f4\u65b0\u72b6\u6001\uff1a         - <code>Finish[i]</code> &lt;- <code>true</code>\uff0c\u8868\u793a\u8be5\u8fdb\u7a0b/\u7ebf\u7a0b\u6267\u884c\u5b8c\u6bd5\uff1b         - <code>Work</code> &lt;- <code>Work + Allocation[i]</code>\uff0c\u8868\u793a\u8fdb\u7a0b/\u7ebf\u7a0b\u6267\u884c\u5b8c\u6bd5\u540e\u91ca\u653e\u8d44\u6e90\uff1b         - repeat 2.\uff1b</li> <li>\u5982\u679c\u6240\u6709\u8fdb\u7a0b/\u7ebf\u7a0b\u90fd\u6ee1\u8db3 <code>Finish[i] == true</code>\uff0c\u5219\u7cfb\u7edf\u5904\u4e8e\u5b89\u5168\u72b6\u6001\uff0c\u5426\u5219\u7cfb\u7edf\u5904\u4e8e\u4e0d\u5b89\u5168\u72b6\u6001\uff1b</li> </ol>"},{"location":"cour_note/D3QD_OperatingSystem/Unit2-Part3/#\u8d44\u6e90\u8bf7\u6c42\u7b97\u6cd5","title":"\u8d44\u6e90\u8bf7\u6c42\u7b97\u6cd5","text":"<p>\u6709\u4e86\u5b89\u5168\u7b97\u6cd5\u4f5c\u4e3a\u57fa\u7840\uff0c\u6211\u4eec\u5c31\u53ef\u4ee5\u5728\u5b83\u7684\u57fa\u7840\u4e0a\uff0c\u5224\u65ad\u67d0\u4e2a\u8d44\u6e90\u8bf7\u6c42\u662f\u5426\u4f1a\u5bfc\u81f4\u7cfb\u7edf\u8fdb\u5165\u4e0d\u5b89\u5168\u72b6\u6001\uff0c\u8fdb\u800c\u5f97\u5230\u5b8c\u6574\u7684\u94f6\u884c\u5bb6\u7b97\u6cd5\u4e86\u3002</p> <p>\u5b89\u5168\u7b97\u6cd5\u901a\u8fc7\u6a21\u62df\u7684\u65b9\u5f0f\u5224\u65ad\u4e00\u4e2a\u72b6\u6001\u662f\u4e0d\u662f\u5b89\u5168\u72b6\u6001\uff0c\u800c\u8d44\u6e90\u8bf7\u6c42\u7b97\u6cd5\u5219\u662f\u8d1f\u8d23\u7ef4\u62a4\u8fd9\u4e2a\u201c\u72b6\u6001\u201d\uff0c\u5e76\u6839\u636e\u5b89\u5168\u7b97\u6cd5\u8fd4\u56de\u7684\u7ed3\u679c\u6765\u5224\u65ad\u67d0\u4e2a\u8bf7\u6c42\u662f\u5426\u5e94\u5f53\u88ab\u63a5\u53d7\u3002</p> <p>\u5177\u4f53\u6765\u8bf4\uff0c\u8d44\u6e90\u8bf7\u6c42\u7b97\u6cd5\u7684\u6b65\u9aa4\u5982\u4e0b\uff1a</p> <p>algorithm</p> <ol> <li>\u7528 <code>Request[n][m]</code> \u6765\u7ef4\u62a4\u8fdb\u7a0b/\u7ebf\u7a0b\u60f3\u8981\u8bf7\u6c42\u7684\u8d44\u6e90\u7684\u6570\u91cf\uff1b</li> <li>\u5728\u6bcf\u4e2a\u8bf7\u6c42\u4e2d\uff0c\u5982\u679c <code>Request[i] &lt;= Need[i]</code>\uff08\u6ce8\u610f\u5411\u91cf\u6bd4\u8f83\uff09\uff0c\u5219\u7ee7\u7eed\uff1b\u5426\u5219\u629b\u51fa\u5f02\u5e38\uff0c\u56e0\u4e3a\u6b64\u65f6\u5b83\u8bf7\u6c42\u7684\u91cf\u8d85\u8fc7\u4e86\u5b83\u9884\u671f\u9700\u8981\u7684\u8d44\u6e90\u7684\u6700\u5927\u91cf\uff1b</li> <li>\u5982\u679c <code>Request[i] &lt;= Available</code>\uff0c\u8bf4\u660e\u8d44\u6e90\u8db3\u591f\uff0c\u7ee7\u7eed\uff1b\u5426\u5219\uff0c\u8fdb\u7a0b/\u7ebf\u7a0b\u5fc5\u987b\u7b49\u5f85\u8db3\u591f\u7684\u8d44\u6e90\uff1b</li> <li>\u5047\u8bbe\u7cfb\u7edf\u5206\u914d\u4e86\u8d44\u6e90\uff0c\u5219\u9700\u8981\u66f4\u65b0\u6a21\u62df\u72b6\u6001\uff08\u6b64\u65f6\u8d44\u6e90\u8fd8\u672a\u5b9e\u9645\u5206\u914d\uff01\u53ea\u662f\u4e3a\u4e86\u4ece\u6570\u503c\u4e0a\u6d4b\u8bd5\u662f\u5426\u5b89\u5168\u800c\u4e34\u65f6\u6784\u9020\u7684\u865a\u62df\u5c40\u9762\uff01\uff09\uff1a<ul> <li><code>Available</code> &lt;- <code>Available - Request[i]</code>\uff0c\u5373\u6a21\u62df\u5269\u4f59\u8d44\u6e90\u91cf\uff1b</li> <li><code>Allocation[i]</code> &lt;- <code>Allocation[i] + Request[i]</code>\uff0c\u5373\u6a21\u62df\u5206\u914d\u5f97\u5230\u7684\u8d44\u6e90\uff1b</li> <li><code>Need[i]</code> &lt;- <code>Need[i]</code> - <code>Request[i]</code>\uff0c\u5373\u6a21\u62df\u9884\u671f\u9700\u6c42\u91cf\uff1b</li> </ul> </li> <li>\u4f7f\u7528\u5b89\u5168\u7b97\u6cd5\u5224\u65ad\uff1a<ul> <li>\u5982\u679c\u5f53\u524d\u72b6\u6001\u662f\u5b89\u5168\u7684\uff0c\u5219\u8bf7\u6c42\u88ab\u63a5\u53d7\uff1b</li> <li>\u5982\u679c\u5f53\u524d\u72b6\u6001\u662f\u4e0d\u5b89\u5168\u7684\uff0c\u8bf7\u6c42\u4e0d\u88ab\u5141\u8bb8\uff0c\u540c\u65f6\u9700\u8981\u5c06\u8fd9\u4e9b\u77e9\u9635\u56de\u6eda\u5230\u6a21\u62df\u4e4b\u524d\u7684\u72b6\u60013\uff1b</li> </ul> </li> </ol> <p>limitations</p> <p>Like the other algorithms, the Banker's algorithm has some limitations when implemented. </p> <p>Specifically, it needs to know how much of each resource a process could possibly request. In most systems, this information is unavailable, making it impossible to implement the Banker's algorithm. </p> <p>Also, it is unrealistic to assume that the number of processes is static since in most systems the number of processes varies dynamically. </p> <p>Moreover, the requirement that a process will eventually release all its resources (when the process terminates) is sufficient for the correctness of the algorithm, however it is not sufficient for a practical system. Waiting for hours (or even days) for resources to be released is usually not acceptable.</p> <p>From Banker's algorithm | Wikipedia.</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit2-Part3/#\u6b7b\u9501\u68c0\u6d4b","title":"\u6b7b\u9501\u68c0\u6d4b","text":"<p>\u6b7b\u9501\u68c0\u6d4b(deadlock detection)\u548c\u6b7b\u9501\u89e3\u9664(deadlock recovery)\u642d\u914d\u4f7f\u7528\uff0c\u5176\u6838\u5fc3\u601d\u8def\u662f\u4e0d\u5bf9\u8d44\u6e90\u8bf7\u6c42\u505a\u8fc7\u591a\u7ea6\u675f\uff0c\u800c\u662f\u5728\u68c0\u6d4b\u5230\u7cfb\u7edf\u4e2d\u5b58\u5728\u6b7b\u9501\u65f6\uff0c\u53bb\u5904\u7406\u6b7b\u9501\u3002\u5176\u4e2d\u7684\u7b2c\u4e00\u6b65\u5c31\u662f\u68c0\u6d4b\u5230\u6b7b\u9501\u3002</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit2-Part3/#\u9762\u5411\u5355\u5b9e\u4f8b\u8d44\u6e90","title":"\u9762\u5411\u5355\u5b9e\u4f8b\u8d44\u6e90","text":"<p>\u7b49\u5f85\u56fe(wait-for graph)\u662f\u8d44\u6e90\u5206\u914d\u56fe\u7684\u5316\u7b80\uff0c\u8be5\u7b97\u6cd5\u53ea\u80fd\u89e3\u51b3\u6bcf\u4e2a\u8d44\u6e90\u7c7b\u522b\u4e2d\u53ea\u6709\u4e00\u4e2a\u5b9e\u4f8b\u7684\u60c5\u51b5\u3002</p> <p>\u5728\u8d44\u6e90\u5206\u914d\u56fe\u4e00\u8282\u4e2d\u6211\u4eec\u77e5\u9053\uff0c\u5bf9\u4e8e\u6bcf\u4e2a\u8d44\u6e90\u7c7b\u522b\u4e2d\u53ea\u6709\u4e00\u4e2a\u5b9e\u4f8b\u7684\u60c5\u51b5\uff0c\u53ea\u8981\u6709\u73af\u5c31\u4f1a\u6709\u6b7b\u9501\uff0c\u800c\u53ea\u8981\u80fd\u68c0\u6d4b\u8fd9\u4e2a\u73af\uff0c\u5c31\u80fd\u68c0\u6d4b\u6b7b\u9501\u3002\u800c\u5b9e\u9645\u7684\u8d44\u6e90\u5206\u914d\u56fe\u4e2d\u8d44\u6e90\u548c\u8fdb\u7a0b/\u7ebf\u7a0b\u7684\u8282\u70b9\u4ece\u662f\u6210\u5bf9\u51fa\u73b0\u5728\u73af\u4e2d\uff0c\u800c wait-for graph \u5219\u662f\u6293\u4f4f\u4e3b\u8981\u77db\u76fe\uff0c\u53ea\u4fdd\u7559\u8fdb\u7a0b/\u7ebf\u7a0b\u7684\u8282\u70b9\uff08\u8bf7\u8bfb\u8005\u601d\u8003\u4e3a\u4ec0\u4e48\u53ef\u4ee5\u8fd9\u6837\uff09\u4ee5\u51cf\u5c0f\u70b9\u7684\u6570\u91cf\uff0c\u63d0\u9ad8\u6548\u7387\u3002</p> <p>\u6211\u4eec\u5c06\u8d44\u6e90\u5206\u914d\u56fe\u4e00\u8282\u4e2d\u7684\u8d44\u6e90\u5206\u914d\u56fe\u6539\u4e3a\u7b49\u5f85\u56fe\uff0c\u5373\u4e3a\uff1a</p> <pre><code>&lt;center&gt; ![](img/26.png) &lt;/center&gt;\nWait-for graph.\n</code></pre> <p>\u901a\u8fc7\u52a8\u6001\u5730\u7ef4\u62a4\u8fd9\u4e2a wait-for graph \u548c\u5b9a\u671f\u8c03\u7528\u4e00\u4e2a\u73af\u68c0\u6d4b\u7b97\u6cd5\uff0c\u6765\u5b9e\u73b0\u6b7b\u9501\u68c0\u6d4b\u3002</p> <p>\u663e\u800c\u6613\u89c1\u7684\uff0c\u5c31\u7b97\u629b\u5f00\u5b83\u53ea\u652f\u6301\u6bcf\u4e2a\u8d44\u6e90\u7c7b\u522b\u4ec5\u80fd\u6709\u4e00\u4e2a\u5b9e\u4f8b\u7684\u7f3a\u70b9\uff0c\u9891\u7e41\u5730\u7ef4\u62a4\u56fe\u548c\u5b9a\u671f\u8c03\u7528\u73af\u68c0\u6d4b\u7b97\u6cd5\uff0c\u90fd\u4f1a\u5e26\u6765\u8f83\u5927\u7684\u5f00\u9500\u3002\u6240\u4ee5\uff0c\u8be5\u65b9\u6cd5\u5176\u5b9e\u8868\u73b0\u5e76\u4e0d\u7406\u60f3\u3002</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit2-Part3/#\u9762\u5411\u591a\u5b9e\u4f8b\u8d44\u6e90","title":"\u9762\u5411\u591a\u5b9e\u4f8b\u8d44\u6e90","text":"<p>\u4ece\u5355\u5b9e\u4f8b\u5411\u591a\u5b9e\u4f8b\u7684\u8fc1\u79fb\u601d\u8def\u548c\u6b7b\u9501\u907f\u514d\u4e2d\u4f7f\u7528\u7684\u8fc1\u79fb\u601d\u8def\u662f\u7c7b\u4f3c\u7684\uff0c\u4f7f\u7528\u5b89\u5168\u72b6\u6001\u6765\u5224\u65ad\u800c\u975e\u627e\u73af\u3002\u56e0\u800c\u8fd9\u4e2a\u7b97\u6cd5\u7684\u5b9e\u73b0\u548c\u94f6\u884c\u5bb6\u7b97\u6cd5\u7684\u5b9e\u73b0\u4e5f\u662f\u7c7b\u4f3c\u7684\uff08\u4f46\u662f\u6709\u4e00\u5b9a\u533a\u522b\uff0c\u53c2\u8003\u4e66\u672c P339\uff09\uff0cjjm \u8868\u793a\u4e00\u822c\u53ea\u8003\u94f6\u884c\u5bb6\u7b97\u6cd5\uff0c\u6240\u4ee5\u6211\u5728\u8fd9\u91cc\u4e5f\u4e0d\u8bb2\u8fd9\u4e2a\u7b97\u6cd5\u4e86\u3002</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit2-Part3/#\u6b7b\u9501\u89e3\u9664","title":"\u6b7b\u9501\u89e3\u9664","text":"<p>\u6b7b\u9501\u89e3\u9664(deadlock recovery)\u867d\u7136\u662f \"recovery\"\uff0c\u4f46\u662f\u5b9e\u9645\u4e0a\u662f\u7834\u574f\u6b7b\u9501\u800c\u5e76\u6ca1\u6709\u6062\u590d\u5230\u4e00\u4e2a\u6b7b\u9501\u4e0d\u5b58\u5728\u7684\u72b6\u6001\uff0c\u6240\u4ee5\u7ffb\u8bd1\u4e3a\u89e3\u9664\u3002\u5bf9\u4e8e\u5df2\u7ecf\u4ea7\u751f\u7684\u6b7b\u9501\uff0c\u81f3\u5c11\u5f97\u6b7b\u4e00\u4e2a\uff0c\u6211\u4eec\u9700\u8981\u4f5c\u51fa\u51b3\u65ad\u3002\u4e66\u672c\u4e2d\u63d0\u5230\u4e86\u7ec8\u6b62\u548c\u8d44\u6e90\u62a2\u5360\u4e24\u79cd\u65b9\u6cd5\uff0c\u4f46\u6211\u8ba4\u4e3a\u672c\u8d28\u4e0a\u662f\u4e00\u6837\u7684\uff0c\u6240\u4ee5\u5e76\u5217\u5730\u7ed9\u51fa\uff1a</p> <ol> <li>\u90fd\u522b\u6d3b\uff0c\u6740\u6b7b\u6240\u6709\u6b7b\u9501\u4e2d\u7684\u8fdb\u7a0b/\u7ebf\u7a0b\uff1b<ul> <li>\u5f00\u9500\u5f88\u5927\uff0c\u56e0\u4e3a\u6240\u6709\u8fd9\u4e9b\u5de5\u4f5c\u90fd\u76f8\u5f53\u4e8e\u767d\u8d39\u4e86\uff0c\u800c\u4e14\u5e76\u4e0d\u662f\u968f\u968f\u4fbf\u4fbf\u5c31\u80fd\u6740\u7684\uff1b</li> </ul> </li> <li>\u4e00\u4e2a\u4e00\u4e2a\u6740\uff0c\u6740\u5230\u6ca1\u6709\u6b7b\u9501\uff1b<ul> <li>\u4ee5\u7279\u5b9a\u987a\u5e8f\u6740\u8fd9\u4e9b\u8fdb\u7a0b\uff0c\u53ef\u4ee5\u4f18\u5316\u8868\u73b0\uff0c\u4f8b\u5982\u6309\u7167\u4f18\u5148\u7ea7\u4ece\u4f4e\u5230\u9ad8\u6740\uff1b </li> </ul> </li> <li>\u7559\u6d3b\u547d\uff0c\u4f46\u662f\u9700\u8981\u56de\u6eda\u90e8\u5206\u8fdb\u7a0b\uff0c\u5f3a\u884c\u62a2\u5360\u5360\u6709\u7684\u8d44\u6e90\uff1b<ul> <li>\u5f88\u96be\u754c\u5b9a\u5e94\u8be5\u56de\u6eda\u5230\u54ea\u91cc\uff0c\u56de\u6eda\u4e5f\u96be\u5b9e\u73b0\uff0c\u4e3a\u4e86\u56de\u6eda\u4e5f\u9700\u8981\u5b58\u50a8\u66f4\u591a\u7684\u4fe1\u606f\uff0c\u5f00\u9500\u5f88\u5927\uff1b</li> <li>\u53c8\u770b\u5230\u62a2\u5360\u8fd9\u4e24\u4e2a\u5b57\uff0c\u6240\u4ee5\u8fd9\u91cc\u4e5f\u4f1a\u6709\u9965\u997f\u95ee\u9898\uff0c\u89e3\u51b3\u65b9\u6cd5\u4e5f\u548c\u4e4b\u524d\u4e00\u6837\uff0c\u901a\u8fc7\u8003\u8651\u4f18\u5148\u7ea7\uff0c\u5e76\u5c06\u88ab\u62a2\u5360\uff08\u88ab\u8feb\u56de\u6eda\uff09\u7684\u6b21\u6570\u7eb3\u5165\u4f18\u5148\u7ea7\u7684\u8003\u8651\u8303\u7574\u3002</li> </ul> </li> </ol> <ol> <li> <p>What's the difference between deadlock and livelock? \u21a9</p> </li> <li> <p>Deadlock Prevention \u4e00\u6587\u4e2d\u63d0\u5230\u4e86\u4f7f\u7528\u5047\u8131\u673a(spooling)\u7684\u65b9\u6cd5\u6765\u89e3\u9664\u6253\u5370\u673a\u8d44\u6e90\u7684\u4e92\u65a5\u6027\u3002\u00a0\u21a9</p> </li> <li> <p>Banker's Algorithm in Operating System (OS) \u4e00\u6587\u4e2d\u63d0\u5230\u4e86\u8981\u6062\u590d\u77e9\u9635\u72b6\u6001\uff0c\u4e66\u4e0a\u8c8c\u4f3c\u6ca1\u5199\u8fd9\u4e2a\u3002\u00a0\u21a9</p> </li> </ol>"},{"location":"cour_note/D3QD_OperatingSystem/Unit3-Part1/","title":"U3 Part 1: \u4e3b\u5b58 | Main Memory [\u672a\u5b8c\u6210]","text":"<p> \u7ea6 10 \u4e2a\u5b57 </p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit3-Part2/","title":"U3 Part 2: \u865a\u62df\u5185\u5b58 | Virtual Memory [\u672a\u5b8c\u6210]","text":"<p> \u7ea6 12 \u4e2a\u5b57 </p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit4/","title":"Unit 4: \u5b58\u50a8\u7ba1\u7406 | Storage Management [\u672a\u5b8c\u6210]","text":"<p> \u7ea6 11 \u4e2a\u5b57 </p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit5/","title":"Unit 5: \u6587\u4ef6\u7cfb\u7edf | File System [\u672a\u5b8c\u6210]","text":"<p> \u7ea6 11 \u4e2a\u5b57 </p>"},{"location":"others/","title":"\u6249\u9875","text":"<p> \u7ea6 21 \u4e2a\u5b57 </p> <p> \u300e\u305d\u306e\u6642\u3092\u5f85\u3064\u3088\u300f      \u6211\u4e0d\u80fd\u4e00\u76f4\u5728\u4f60\u8eab\u8fb9\u5e2e\u52a9\u4f60\u3002  \u2014\u2014\u67e5\u7406\u00b7\u5e03\u6717  </p>"},{"location":"others/tools/","title":"\u5de5\u5177\u6536\u96c6","text":"<p> \u7ea6 46 \u4e2a\u5b57 </p> <ul> <li> <p>\u7ed8\u56fe</p> <ul> <li>\u77e2\u91cf\u56fe\u7ed8\u5236\u8bed\u8a00 Graphviz</li> <li>\u5728\u7ebf\u77e2\u91cf\u56fe\u7ed8\u5236 draw.io</li> <li>\u5728\u7ebf\u56fe\u8bba\u4f5c\u56fe</li> <li>\u5728\u7ebf\u624b\u5199\u98ce\u4f5c\u56fe Excalidraw</li> </ul> </li> <li> <p>\u547d\u4ee4\u884c\u8f85\u52a9</p> <ul> <li>ffmpeg \u6307\u4ee4\u751f\u6210</li> </ul> </li> </ul>"},{"location":"others/reveal-md2Slides/","title":"\u4f7f\u7528 reveal-md \u6765\u5199 Slides","text":"<p> \u7ea6 4169 \u4e2a\u5b57  151 \u884c\u4ee3\u7801  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 16 \u5206\u949f</p> <p>\u524d\u8a00</p> <ul> <li>\u672c\u6587\u9762\u5411 \u8ba4\u4e3a PPT \u5e76\u4e0d\u9ad8\u6548\uff0c\u4f46\u540c\u65f6\u53c8\u786e\u5b9e\u9700\u8981\u4e00\u79cd\u300c\u6f14\u793a\u300d\u9014\u5f84 \u7684\u504f\u6280\u672f\u4eba\u5458\uff1b</li> <li>\u867d\u7136\u5de5\u5177\u57fa\u4e8e\u524d\u7aef\u6280\u672f\u6808\uff0c\u4f46\u524d\u7aef\u77e5\u8bc6\u4ec5\u51b3\u5b9a\u5de5\u5177\u4f7f\u7528\u4e0a\u9650\uff0c\u5b8c\u5168\u53ef\u4ee5\u505a\u5230\u65e0\u524d\u7aef\u57fa\u7840\u8fdb\u884c\u57fa\u7840\u4f7f\u7528\uff1b</li> <li>\u6211\u5e76\u6ca1\u6709\u5c1d\u8bd5\u8fc7\u8131\u79bb\u547d\u4ee4\u884c\u6765\u5b9e\u73b0\u8fd9\u4e9b\uff0c\u4f46\u662f\u6211\u89c9\u5f97\u5927\u6982\u201c\u504f\u6280\u672f\u201d\u4eba\u5458\u4e0d\u5e94\u5f53\u4e0d\u4f1a\u4f7f\u7528\u547d\u4ee4\u884c\uff0c\u81f3\u5c11\u4f60\u8981\u77e5\u9053\u5728\u54ea\u91cc\u80fd\u8fd0\u884c\u547d\u4ee4\uff1b\u6b64\u5916\uff0c\u60a8\u9700\u8981\u786e\u4fdd\u60a8\u7684\u547d\u4ee4\u884c\u73af\u5883\u80fd\u591f\u4f7f\u7528 npm\uff1b</li> </ul>"},{"location":"others/reveal-md2Slides/#\u7b80\u4ecb","title":"\u7b80\u4ecb","text":"<p><code>reveal-md</code> \u662f <code>reveal.js</code> \u7684\u4e00\u4e2a\u6269\u5c55\u5de5\u5177\uff0c\u7c7b\u4f3c\u4e8e\u4e00\u4e2a\u9884\u7f16\u8bd1\u5de5\u5177\u3002\u5229\u7528 <code>reveal-md</code>\uff0c\u4f60\u53ef\u4ee5\u901a\u8fc7\u7f16\u5199\u4e00\u4e2a <code>Markdown</code> \u6587\u4ef6\u6765\u5feb\u901f\u7b80\u4fbf\u5730\u751f\u6210\u4e00\u4e2a\u57fa\u4e8e\u7f51\u9875\u7684 Slides\uff0c\u4f60\u4e5f\u53ef\u4ee5\u5c06\u5b83\u5bfc\u51fa\u4e3a\u9759\u6001\u8d44\u6e90\u5e76\u90e8\u7f72\u5728\u7c7b\u4f3c github pages \u7b49\u5e73\u53f0\u6765\u5206\u4eab\u9759\u6001\u9875\u9762\u3002</p> <ul> <li><code>reveal.js</code> \u7684\u5b98\u65b9 demo\uff1a\ud83d\udd17</li> <li>\u6211\u81ea\u5df1\u5199\u7684\u4e00\u4e2a project\uff1a\ud83d\udd17</li> <li><code>reveal-md</code> \u7684 github repo\uff1a\ud83d\udd17</li> </ul>"},{"location":"others/reveal-md2Slides/#\u4e3a\u4ec0\u4e48\u6211\u4e0d\u7528-ppt-\u548c\u8bed\u96c0\u6587\u6863\u6f14\u793a\u6a21\u5f0f","title":"\u4e3a\u4ec0\u4e48\u6211\u4e0d\u7528 PPT \u548c\u8bed\u96c0\u201c\u6587\u6863\u6f14\u793a\u6a21\u5f0f\u201d","text":"<p>\u5728\u8fd9\u7bc7\u6587\u7ae0\u548c\u8bed\u5883\u4e2d\uff0c\u6211\u60f3\u5927\u6982\u5c06\u300c\u6f14\u793a\u300d\u6240\u4f7f\u7528\u7684\u5f62\u5f0f\u5206\u4e3a\u4e09\u79cd\uff1a</p> <ul> <li>PPT \u7b49\u56fe\u5f62\u5316\u7684\u300c\u6f14\u793a\u300d\u6587\u6863\u5236\u4f5c\u5e73\u53f0\uff1b</li> <li>\u4f7f\u7528<code>Beamer</code>\u3001<code>reveal.js</code>\u3001<code>nodeppt</code>\u7b49\u5de5\u5177\uff0c\u4f7f\u7528\u4ee3\u7801\u7f16\u5199\u300c\u6f14\u793a\u300d\u6587\u6863\uff1b</li> <li>\u8bed\u96c0\u7684\u300c\u6587\u6863\u6f14\u793a\u6a21\u5f0f\u300d\uff1b</li> </ul> <p>\u6070\u597d\uff0c\u8bed\u96c0\u63a8\u51fa\u6f14\u793a\u6587\u7a3f\u7684\u65f6\u5019\u6709\u8bf4\u660e\u4e3a\u4ec0\u4e48\u4ed6\u4eec\u8981\u5f00\u53d1\u8fd9\u6837\u4e00\u4e2a\u4e1c\u897f\u3002</p> <p>\u518d\u89c1PPT\uff0c\u4f60\u597d\u201c\u6587\u6863\u6f14\u793a\u6a21\u5f0f\u201d</p> <p>\u6211\u975e\u5e38\u8d5e\u540c\u8fd9\u7bc7\u6587\u7ae0\u4e2d\u5bf9\u4e8e PPT \u7684\u53d9\u8ff0\uff0c\u6211\u4e5f\u5f88\u8ba8\u538c PPT \uff0c\u5b83\u786e\u5b9e\u53ef\u4ee5\u505a\u5f88\u591a\u4e8b\uff0c\u4f46\u662f\u5bf9\u6211\u6765\u8bf4\u6ca1\u5fc5\u8981\uff0c\u6211\u4e5f\u7528\u4e0d\u5230\u3002\u800c\u4e14\u8eab\u4e3a\u7834\u5199\u4ee3\u7801\u7684\uff0c\u6211\u5bf9\u90a3\u79cd\u6240\u8c13\u7684\u9ad8\u7ea7\u611f\u5e76\u6ca1\u6709\u4ec0\u4e48\u611f\u89c9\u3002\u800c\u4e14 PPT \u6709\u4e00\u4e2a\u81f4\u547d\u7684\u7f3a\u70b9\u5c31\u662f\u5b83\u7684\u5206\u4eab\u975e\u5e38\u4e0d\u65b9\u4fbf\uff0c\u4f60\u5fc5\u987b\u8981\u901a\u8fc7\u300c\u6587\u4ef6\u300d\u6765\u4f20\u9012\u4f60\u7684\u6750\u6599\uff0c\u800c\u4e14\u8fd8\u6536\u5230\u5c55\u793a\u8bbe\u5907\u7684\u73af\u5883\u9650\u5236\uff0c\u800c\u5176\u4ed6\u4e24\u79cd\u65b9\u6cd5\u90fd\u53ef\u4ee5\u5f88\u65b9\u4fbf\u7684\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\u3002</p> <p>\u56de\u5230\u300c\u6587\u6863\u6f14\u793a\u6a21\u5f0f\u300d\uff0c\u8bda\u7136\uff0c\u5728\u67d0\u4e9b\u7279\u5b9a\u7684\u65f6\u95f4\uff0c\u6587\u6863\u6f14\u793a\u786e\u5b9e\u80fd\u4fbf\u6377\u7684\u89e3\u51b3\u8bb8\u591a\u95ee\u9898\uff0c\u4f46\u662f\u6211\u4e0d\u89c9\u5f97\u76ee\u524d\u7684\u6587\u7a3f\u6f14\u793a\u80fd\u6210\u4e3a Slides \u7684\u66ff\u4ee3\u54c1\u3002\u5b83\u786e\u5b9e\u4fbf\u6377\u4e14\u9ad8\u6548\uff0c\u4f46\u662f\u5e76\u4e0d\u597d\u770b\uff0c\u4e5f\u5e76\u4e0d\u6e05\u6670\u2014\u2014\u800c\u4e14\u8bf4\u56de\u6765\uff0c\u5176\u5b9e\u4e5f\u4e0d\u65b9\u4fbf\uff08\u4e3a\u4ec0\u4e48\u6211\u4e4b\u540e\u4f1a\u8bb2\uff09\u3002 \u7b80\u5355\u8bb2\u4e86\u4e00\u4e0b\u6211\u5bf9\u5176\u4ed6\u4e24\u79cd\u9014\u5f84\u7684\u770b\u6cd5\uff0c\u5173\u4e8e\u901a\u8fc7\u4ee3\u7801\u9014\u5f84\u7f16\u5199\u300c\u6f14\u793a\u300d\u6587\u6863\u6211\u5f53\u7136\u4e5f\u6709\u8bdd\u8bf4\uff0c\u4f46\u662f\u6211\u60f3\u628a\u4ed6\u4eec\u653e\u5728\u540e\u9762\u3002</p> <p>\u63a5\u4e0b\u6765\uff0c\u6211\u60f3\u4ece\u300c\u4f7f\u7528\u4f53\u9a8c\u300d\u7684\u89d2\u5ea6\u6765\u8bc4\u4ef7\u4e00\u4e0b\u4e0a\u9762\u5df2\u7ecf\u63d0\u8fc7\u7684\u4e24\u4e2a\u9014\u5f84\u3002</p> <p>\u5728\u6211\u770b\u6765\uff0cPPT \u4e4b\u6240\u4ee5\u7d2f\u8d58\u4e14\u4f4e\u6548\uff0c\u662f\u56e0\u4e3a\u5927\u90e8\u5206\u4eba\u6d6a\u8d39\u65f6\u95f4\u5728\u4e8e\u4e0e\u6838\u5fc3\u5185\u5bb9\u5e76\u4e0d\u76f4\u63a5\u76f8\u5173\u7684\u7f8e\u5de5\u4e0a\u3002\u800c\u4ece\u5de5\u4f5c\u6d41\u7a0b\u4e0a\u6765\u8bb2\uff0c\u9664\u975e\u6211\u7cbe\u901a PPT \u4e14\u6709\u65f6\u95f4\uff0c\u5426\u5219\u6211\u4e0d\u4f1a\u4eb2\u81ea\u53bb\u505a PPT\uff0c\u800c\u662f\u548c\u7f8e\u5de5\u5bf9\u63a5\uff0c\u8ba9\u4ed6\u4eec\u6765\u505a\u3002\u53ef\u8fd9\u6837\u4e00\u6765\u95ee\u9898\u5c31\u51fa\u73b0\u4e86\uff0c\u201c\u5bf9\u63a5\u201d\u8fd9\u4ef6\u4e8b\u672a\u5fc5\u6bd4\u505a PPT \u8f7b\u677e\u3002\u53c8\u6216\u8005\u6211\u8fd9\u4e2a PPT \u662f\u6211\u81ea\u5df1\u9700\u8981\u7684\uff0c\u90a3\u6211\u5c31\u5f97\u786c\u7740\u5934\u76ae\u82b1\u8d39\u65f6\u95f4\u53bb\u94bb\u7814\u5982\u4f55\u505a\u4e00\u4e2a\u597d\u770b\u7684 PPT\uff0c\u7ed3\u679c\u6d6a\u8d39\u5927\u628a\u65f6\u95f4\u505a\u51fa\u6765\u7684\u53ef\u80fd\u8fd8\u662f\u4e2a\u8fde\u6cb9\u817b\u90fd\u8bf4\u4e0d\u4e0a\u7684\u4e1c\u897f\u3002</p> <p>\u800c\u56de\u5230\u8bed\u96c0\u7684\u300c\u6587\u6863\u6f14\u793a\u6a21\u5f0f\u300d\uff0c\u8bf4\u6765\u53ef\u7b11\uff0c\u6211\u5199\u8fd9\u4e00\u884c\u7684\u65f6\u5019\u5c31\u53c8\u51fa\u4e86 bug\u3002\u8bda\u7136\u300c\u6587\u6863\u6f14\u793a\u6a21\u5f0f\u300d\u662f\u4e00\u4e2a\u5f88\u597d\u7684 Idea\uff0c\u4f46\u662f\u8bed\u96c0\u81ea\u8eab\u5927\u5927\u5c0f\u5c0f\u7684\u95ee\u9898\u5230\u5904\u90fd\u662f\uff0c\u672c\u6765\u4f5c\u4e3a\u4e00\u4e2a\u6548\u7387\u5de5\u5177\u5374\u603b\u662f\u5728\u610f\u6599\u4e4b\u5916\u7684\u5730\u65b9\u9047\u5230\u5f88\u7cdf\u5fc3\u7684 Bug \uff0c\u8fd9\u7740\u5b9e\u5f88\u5f71\u54cd\u6548\u7387\uff08\u5173\u4e8e\u8fd9\u65b9\u9762\u7684\u5410\u69fd\u6211\u5c31\u4e0d\u653e\u5728\u8fd9\u91cc\u8bf4\u4e86\uff0c\u4ee5\u9632\u504f\u9898\uff09\u3002</p> <p>\u5728\u8fd9\u6837\u4e00\u4e2a\u57fa\u7840\u4e0b\uff0c\u51fa\u73b0\u4e86\u95ee\u9898\u4f46\u662f\u6211\u4eec\u65e0\u6cd5\uff0c\u6216\u8005\u8bf4\u5feb\u901f\u6392\u67e5\uff0c\u6216\u8005\u8bf4\u662f\u9000\u800c\u6c42\u5176\u6b21\u5bfb\u627e\u522b\u7684\u5b9e\u73b0\u529e\u6cd5\uff0c\u90fd\u662f\u4e0d\u65b9\u4fbf\u7684\u3002\u6362\u53e5\u8bdd\u6765\u8bf4\u5c31\u662f\u8fd9\u4e2a\u529f\u80fd\u81ea\u8eab\u7684\u7a33\u5b9a\u6027\u5c31\u4e0d\u80fd\u4fdd\u8bc1\uff0c\u800c\u5176\u5b9e\u73b0\u5bf9\u4f7f\u7528\u8005\u6765\u8bf4\u4e5f\u5e76\u4e0d\u8db3\u591f\u7b80\u5355\u900f\u660e\uff0c\u5bfc\u81f4\u4f7f\u7528\u8d77\u6765\u4f1a\u9700\u8981\u627f\u62c5\u5f88\u591a\u4e0d\u786e\u5b9a\u7684\u98ce\u9669\u3002\uff08\u987a\u4fbf\u5410\u69fd\u4e00\u53e5\uff0c\u4f7f\u7528\u8bed\u96c0\u7684\u8fd9\u4e00\u5e74\u6211\u4f53\u611f\u4e0a\u5f71\u54cd\u4f53\u9a8c\u7684 Bug \u662f\u8d8a\u6765\u8d8a\u591a\u4e86\u2026\u2026\uff09</p>"},{"location":"others/reveal-md2Slides/#\u4e3a\u4ec0\u4e48\u6211\u7528-reveal","title":"\u4e3a\u4ec0\u4e48\u6211\u7528 reveal*","text":"<p>\u90a3\u4e48\uff0c\u901a\u8fc7\u4ee3\u7801\u6765\u5236\u4f5c\u300c\u6f14\u793a\u300d\u6750\u6599\u53c8\u600e\u4e48\u6837\u5462\uff1f\u9996\u5148\u662f <code>Beamer</code>\uff0c\u5927\u6982\u4e5f\u662f\u6700\u6709\u540d\u7684\uff0c\u5176\u57fa\u4e8e \\(\\LaTeX\\) \u5b9e\u73b0\uff0c\u5176\u5728\u6392\u7248\u4e0a\u7684\u53ef\u63a7\u6027\u4e0d\u8a00\u800c\u55bb\uff0c\u4f46\u662f\u5199\u8fc7\u7684\u4eba\u90fd\u77e5\u9053 \\(\\LaTeX\\) \u5199\u8d77\u6765\u591a\u8d39\u5fc3\uff1b\u800creveal.js \u4ee5\u53ca nodeppt \u662f\u6211\u627e\u5230\u8fc7\u7684\u4e24\u4e2a\u6bd4\u8f83\u6ee1\u610f\u7684\uff0c\u901a\u8fc7\u4ee3\u7801\u6765\u5199 Slides \u7684\u5de5\u5177\u3002\u6211\u5e76\u4e0d\u6253\u7b97\u5728\u8fd9\u91cc\u628a\u4ed6\u4eec\u4e24\u4e2a\u90fd\u8be6\u7ec6\u7684\u4ecb\u7ecd\u4e00\u904d\uff0c\u4f46\u662f\u6211\u5e0c\u671b\u7b80\u5355\u8868\u8fbe\u4e00\u4e0b\u6211\u5bf9\u8fd9\u4e24\u4e2a\u4e1c\u897f\u7684\u770b\u6cd5\u3002</p> <p>\u9996\u5148\uff0c\u5728\u6211\u7684\u7406\u89e3\u4e2d\uff0c<code>nodeppt</code> \u5bf9\u7f8e\u5316\u662f\u6bd4 <code>reveal.js</code> \u8981\u597d\u4e00\u4e9b\u7684\uff0c\u5373\uff0c\u629b\u5f00\u82b1\u8d39\u5728\u91cc\u9762\u7684\u65f6\u95f4\u4e0d\u8bf4\uff0c\u5c31\u7ed3\u679c\u800c\u8a00\uff0c\u4f7f\u7528 <code>nodeppt</code> \u4f1a\u6bd4 <code>reveal.js</code> \u597d\u770b\u4e00\u4e9b\uff0c\u6392\u7248\u66f4\u81ea\u7531\u4e00\u4e9b\u3002\u4f46\u662f\u4ece\u300c\u6548\u7387\u300d\u6765\u8bf4\uff0c\u6211\u503e\u5411\u4e8e <code>reveal.js</code>\u3002 \u7406\u7531\u5f88\u7b80\u5355\uff0c<code>reveal.js</code> \u7684\u5206\u9875\u903b\u8f91\u6df1\u5f97\u6211\u5fc3\uff1a</p> <p></p> <p>\u6211\u81ea\u5df1\u5199\u7684\u67d0\u4e2a Slides \u7684\u7ed3\u6784\u901f\u89c8</p> <p>\u53ef\u4ee5\u53d1\u73b0\uff0c\u9875\u9762\u6709\u7eb5\u5411\u548c\u6a2a\u5411\u4e24\u4e2a\u6269\u5c55\u65b9\u5411\uff0c\u8fd9\u975e\u5e38\u7b26\u5408\u5c42\u6b21\u5316\u7684\u601d\u7ef4\u903b\u8f91\uff0c\u4e5f\u5f88\u7b26\u5408\u6587\u6863\u7684\u7f16\u5199\u903b\u8f91\uff0c\u5e76\u4e14\u603b\u4f53\u800c\u8a00 \u6ca1\u6709\u4ec0\u4e48\u82b1\u91cc\u80e1\u54e8\u4f46\u662f\u6ca1\u5565\u7528\u7684\u4e1c\u897f\uff0c\u5177\u6709\u4e00\u79cd\u5965\u5361\u59c6\u5243\u5200\u7684\u7f8e\u611f\u3002\u7136\u800c\u8fd9\u5e76\u4e0d\u610f\u5473\u7740\u5b83\u7684\u7f8e\u5de5\u4e0a\u9650\u5f88\u4f4e\uff0c\u6070\u6070\u76f8\u53cd\uff0c\u4e0d\u4ec5 <code>reveal.js</code> \u7684\u5185\u7f6e\u52a8\u753b\u548c\u98ce\u683c\u5c31\u5f88\u8212\u9002\uff0c\u800c\u4e14\u65e0\u8bba\u662f <code>reveal.js</code> \u8fd8\u662f <code>nodeppt</code>\uff0c\u4ed6\u4eec\u7684\u672c\u8d28\u90fd\u662f\u9759\u6001\u7f51\u9875\uff0c\u4f60\u5927\u53ef\u4ee5\u7528\u4f60\u7684\u524d\u7aef\u6280\u80fd\u6765\u7f8e\u5316\u5b83\u2014\u2014\u5f53\u7136\uff0c \u5bf9\u6211\u6765\u8bf4\u8fd9\u4e9b\u4e1c\u897f\u5c31\u6ca1\u5565\u5fc5\u8981\u4e86\u3002 \u4ee5\u4e0a\u90fd\u662f\u5173\u4e8e\u6548\u679c\u7684\u53d9\u8ff0\uff0c\u90a3\u5b83\u662f\u5426\u771f\u7684\u5199\u8d77\u6765\u5f88\u65b9\u4fbf\u5462\uff1f\u5176\u5b9e\u6211\u611f\u89c9\u539f\u751f\u7684 <code>reveal.js</code> \u5199\u8d77\u6765\u5e76\u4e0d\u65b9\u4fbf\uff0c\u6211\u4e00\u5f00\u59cb\u751a\u81f3\u4e0d\u77e5\u9053\u8981\u5982\u4f55\u521b\u5efa\u4e00\u4e2a\u65b0\u7684\u6587\u6863\u3002\u4f46\u662f\u6211\u540e\u6765\u53d1\u73b0\u4e86<code>[reveal-md](https://github.com/webpro/reveal-md)</code>\u8fd9\u4e2a\u5de5\u5177\u3002\u5229\u7528<code>reveal-md</code>\uff0c\u4f60\u53ef\u4ee5\u771f\u6b63\u610f\u4e49\u4e0a\u7684\u5b9e\u73b0\u4f7f\u7528<code>markdown</code>\u8bed\u6cd5\u6765\u5199\u4e00\u4e2a Slides\u3002</p>"},{"location":"others/reveal-md2Slides/#\u5b89\u88c5\u4e0e\u6f14\u793a","title":"\u5b89\u88c5\u4e0e\u6f14\u793a","text":"<p>\u786e\u4fdd\u60a8\u7684<code>[npm](https://www.npmjs.com/)</code>\u80fd\u591f\u6b63\u5e38\u4f7f\u7528\uff0c\u63a5\u4e0b\u6765\u5b89\u88c5<code>reveal-md</code>\u4f60\u53ea\u9700\u8981\u4f7f\u7528\u5982\u4e0b\u547d\u4ee4\u5373\u53ef\u3002</p> <pre><code>npm install -g reveal-md\n</code></pre> <p></p> <p>\u5b89\u88c5\u5b8c\u6210\u540e\uff0c\u4f60\u5c31\u53ef\u4ee5\u5c06 <code>reveal-md</code> \u5f53\u4f5c\u4e00\u4e2a console app \u6765\u4f7f\u7528\uff0c\u8f93\u5165 <code>reveal-md --help</code> \u6765\u67e5\u770b\u547d\u4ee4\u8be6\u7ec6\u7684\u4f7f\u7528\u65b9\u6cd5\u3002</p> help list <pre><code>Puppeteer unavailable, unable to create featured slide image for OpenGraph metadata.\nPuppeteer unavailable, unable to generate PDF file.\nUsage: cli &lt;slides.md&gt; [options]\n\nSee https://github.com/webpro/reveal-md for more details.\n\nOptions:\n  -V, --version                               output the version number\n      --title &lt;title&gt;                         Title of the presentation\n  -s, --separator &lt;separator&gt;                 Slide separator [default: 3 dashes (---) surrounded by two blank lines]\n-S, --vertical-separator &lt;separator&gt;        Vertical slide separator [default: 4 dashes (----) surrounded by two blank lines]\n-t, --theme &lt;theme&gt;                         Theme [default: black]\n--highlight-theme &lt;theme&gt;               Highlight theme [default: zenburn]\n--css &lt;files&gt;                           CSS files to inject into the page\n      --scripts &lt;files&gt;                       Scripts to inject into the page\n      --assets-dir &lt;dirname&gt;                  Defines assets directory name [default: _assets]\n--preprocessor &lt;script&gt;                 Markdown preprocessor script\n      --template &lt;filename&gt;                   Template file for reveal.js\n      --listing-template &lt;filename&gt;           Template file for listing\n      --glob &lt;pattern&gt;                        Glob pattern to select markdown files for listing and conversion [default: **/*.md]\n--print [filename]                      Print to PDF file\n      --static [dir]                          Export static html to directory [_static]. Incompatible with --print.\n      --static-dirs &lt;dirs&gt;                    Extra directories to copy into static directory. Only used in conjunction with --static.\n  -w, --watch                                 Watch for changes in markdown file and livereload presentation\n      --disable-auto-open                     Disable auto-opening your web browser\n      --host &lt;host&gt;                           Host [default: localhost]\n--port &lt;port&gt;                           Port [default: 1948]\n--featured-slide &lt;num&gt;                  Capture snapshot from this slide (numbering starts from 1) and use it as og:image for static build. Defaults to first slide. Only used with --static.\n      --absolute-url &lt;url&gt;                    Define url used for hosting static build. This is included in OpenGraph metadata. Only used with --static.\n      --print-size                            Paper size to use in exported PDF files\n      --puppeteer-launch-args &lt;args&gt;          Customize how Puppeteer launches Chromium. The arguments are specified as a space separated list (for example --puppeteer-launch-args=\"--no-sandbox --disable-dev-shm-usage\"). Needed for some CI setups.\n      --puppeteer-chromium-executable &lt;path&gt;  Customize which Chromium executable puppeteer will launch. Allows to use a globally installed version of Chromium.\n  -h, --help                                  output usage information\n</code></pre> <p>\u5728\u6211\u81ea\u5df1\u7684\u4f7f\u7528\u8fc7\u7a0b\u4e2d\uff0c\u6211\u8ba4\u4e3a\u6bd4\u8f83\u6838\u5fc3\u7684\u4e24\u6761\u547d\u4ee4\u5982\u4e0b\uff1a</p> <pre><code>## \u6700\u57fa\u7840\u7684\u547d\u4ee4\uff0c\u6839\u636e Markdown \u6587\u4ef6\u5728\u672c\u5730 1948 \u7aef\u53e3\u751f\u6210 Slides \u670d\u52a1\u3002\n$ reveal-md your-md-file.md\n\n## \u4e3a\u4e86\u5b9e\u73b0\u5728\u7ebf\u90e8\u7f72\uff0c\u9700\u8981\u5bfc\u51fa\u4e3a\u9759\u6001\u8d44\u6e90\u3002\n$ reveal-md your-md-file.md --static your-static-dir\n</code></pre> <p>\u4e5f\u5c31\u662f\u8bf4\uff0c\u4f60\u53ea\u9700\u8981\u7f16\u5199\u4e00\u4e2amd\u6587\u4ef6\uff0c\u5e76\u4f7f\u7528\u8fd9\u4e9b\u6307\u4ee4\u5c31\u80fd\u751f\u6210 reveal.js Slides\u3002 \u63a5\u4e0b\u6765\u4ee5\u5b98\u65b9 demo \u4e3a\u4f8b\u4ecb\u7ecd\u4e00\u4e0b\u4f7f\u7528\u3002\u8fd0\u884c\u6307\u4ee4\u4ee5\u540e\u4f1a\u5728 1948 \u7aef\u53e3\u542f\u52a8\u670d\u52a1\uff0c\u4e00\u822c\u4f1a\u76f4\u63a5\u901a\u8fc7\u6d4f\u89c8\u5668\u6253\u5f00\u3002 \u5728 PC \u7aef\u53e3\uff1a</p> <ul> <li>\u901a\u8fc7\u70b9\u51fb/ \u7a7a\u683c\u6765\u9009\u62e9\u4e0b\u4e00\u9875\uff0c\u4f7f\u7528 <code>h/\u2190</code> <code>j/\u2193</code> <code>k/\u2191</code> <code>l/\u2192</code> \u6216\u8005\u70b9\u51fb\u53f3\u4e0b\u89d2\u7684\u65b9\u5411\u76d8\u6765\u8fdb\u884c\u4e0a\u4e0b\u5de6\u53f3\u5207\u6362\uff0c\u76f4\u63a5\u70b9\u51fb\u9875\u9762\u5e95\u90e8\u7684\u8fdb\u5ea6\u6761\u4e5f\u53ef\u4ee5\u5b9e\u73b0\u9875\u9762\u8df3\u8f6c\u3002</li> </ul> <p></p> <ul> <li>\u6309\u4e0b <code>f</code> \u6765\u5168\u5c4f\u663e\u793a\uff0c\u6309\u4e0b <code>Esc</code> \u6216\u8005 <code>f</code> \u9000\u51fa\u3002</li> </ul> \u6309 <code>f</code> \u4e4b\u524d\u3002 \u5168\u5c4f\u663e\u793a\u3002 <ul> <li>\u6309\u4e0b<code>s</code>\u8fdb\u5165\u6f14\u8bb2\u8005\u6a21\u5f0f\uff0c\u4e5f\u5c31\u662f\u518d\u591a\u8df3\u51fa\u6765\u4e00\u4e2a\u5f39\u7a97\uff0c\u5728\u5b9e\u9645\u4f7f\u7528\u4e2d\u53ef\u4ee5\u5728\u6295\u5f71\u4eea\u91cc\u653e\u5168\u5c4f\uff0c\u5728\u81ea\u5df1\u7535\u8111\u4e0a\u5c55\u793a\u8fd9\u4e2a\u7a97\u53e3\u3002\u4fee\u6539\u53f3\u4e0a\u89d2\u7684 Layout \u53ef\u4ee5\u4fee\u6539\u663e\u793a\u6a21\u5f0f\u3002<code>Notes</code> \u7684\u5185\u5bb9\u4f1a\u5728\u540e\u9762\u4ecb\u7ecd\uff0c\u7c7b\u4f3c\u4e8e PPT \u7684\u5907\u6ce8\u3002</li> </ul> <p></p> <ul> <li>\u6309\u4e0b<code>o</code>\u8fdb\u5165\u603b\u89c8\u89c6\u56fe\uff0c\u53ef\u4ee5\u5229\u7528\u65b9\u5411\u952e\u8fdb\u884c\u79fb\u52a8\uff0c\u56de\u8f66\u6216\u70b9\u51fb\u8fdb\u884c\u9009\u62e9\u3002\u9700\u8981\u6ce8\u610f\uff0c\u8fd9\u91cc\u663e\u793a\u7684\u5185\u5bb9\u548c\u5b9e\u9645\u5c55\u793a\u7684\u9875\u9762\u5185\u5bb9\u5728\u5e03\u5c40\u4e0a\u5b58\u5728\u5dee\u5f02\u3002</li> </ul> <p></p> <ul> <li>\u6309\u4e0b<code>v</code>\u6216<code>.</code>\u9ed1\u5c4f\u3002</li> </ul> <p>\u800c\u5728\u79fb\u52a8\u7aef\uff08\u6bd4\u5982\u8bbf\u95ee\u67d0\u4e2a\u5b9e\u4f8b\u7684\u5728\u7ebf\u90e8\u7f72\u65f6\uff09\uff0c\u57fa\u672c\u7684\u70b9\u51fb\u64cd\u4f5c\u662f\u4e00\u6837\u7684\uff0c\u6b64\u5916\uff0c\u5e26\u6709\u65b9\u5411\u7684\u6ed1\u52a8\u53ef\u4ee5\u5bf9\u5e94\u65b9\u5411\u952e\u529f\u80fd\u3002</p> <p></p>"},{"location":"others/reveal-md2Slides/#\u6587\u6863\u7f16\u5199","title":"\u6587\u6863\u7f16\u5199","text":"<p>\u5728\u8fd9\u90e8\u5206\uff0c\u6211\u5e76\u4e0d\u6253\u7b97\u6309\u7167\u6a21\u5757\u5316\u3001\u7cfb\u7edf\u5316\u7684\u6d41\u7a0b\u6765\u7f16\u5199\u6559\u7a0b\uff0c\u8fd9\u4e9b\u4f60\u5728\u5b98\u65b9\u6587\u6863\u4e2d\u90fd\u80fd\u627e\u5230\u2014\u2014\u6211\u5e76\u4e0d\u89c9\u5f97\u201c\u5b57\u5178\u201d\u662f\u4e00\u4e2a\u5f88\u597d\u7684\u5b66\u4e60\u9014\u5f84\uff0c\u5c31\u50cf\u6211\u4eec\u4e00\u822c\u4e0d\u5efa\u8bae\u7528\u300aC++ Primer\u300b\u5165\u95e8 C++\uff0c\u66f4\u4e0d\u4f1a\u5efa\u8bae\u5916\u56fd\u53cb\u4eba\u901a\u8fc7\u300a\u65b0\u534e\u5b57\u5178\u300b\u6765\u5b66\u4e60\u6c49\u8bed\u3002 \u6211\u5c06\u6309\u7167\u6211\u5bf9\u8fd9\u4e2a\u5de5\u5177\u7684\u7406\u89e3\uff0c\u6309\u7167\u7531\u6d45\u5165\u6df1\uff0c\u6309\u7167\u5fc5\u8981\u7a0b\u5ea6\u6765\u4ecb\u7ecd\u5185\u5bb9\u3002\u5b83\u53ef\u80fd\u770b\u8d77\u6765\u4f1a\u53c8\u4e9b\u6df7\u4e71\uff0c\u4f46\u662f\u6211\u89c9\u5f97\u5b83\u662f\u7b26\u5408\u5b9e\u8df5\u987a\u5e8f\u7684\uff0c\u5982\u679c\u8ba9\u4f60\u89c9\u5f97\u770b\u8d77\u6765\u5f88\u8d39\u52b2\uff0c\u53ef\u4ee5\u642d\u914d\u5b98\u65b9\u6587\u6863\u6765\u4f7f\u7528\uff0c\u6216\u8005\u76f4\u63a5\u544a\u8bc9\u6211\u3002 \u6b64\u5916\uff0c\u5176\u4e2d\u53ef\u80fd\u4e0d\u4f1a\u6d89\u53ca\u4e00\u90e8\u5206\u6211\u4e2a\u4eba\u4e0d\u592a\u559c\u6b22\u7684\u4e1c\u897f\uff0c\u6bd4\u5982\u540c\u6837\u53ef\u4ee5\u901a\u8fc7\u914d\u7f6e\u6587\u4ef6\u548c\u547d\u4ee4\u53c2\u6570\u7684\u884c\u4e3a\uff0c\u6211\u4f1a\u9009\u62e9\u53ea\u4ecb\u7ecd\u914d\u7f6e\u6587\u4ef6\u7684\u65b9\u6848\u3002\u5982\u679c\u4f60\u5bf9\u53e6\u5916\u4e00\u79cd\u65b9\u6848\u611f\u5174\u8da3\uff0c\u53ef\u4ee5\u8be6\u7ec6\u9605\u8bfb\u6587\u6863\u6216\u8005\u5e2e\u52a9\u83dc\u5355\u3002\u6b64\u5916\uff0c\u672c\u6587\u7ae0\u4e5f\u4e0d\u4f1a\u6d89\u53ca <code>reveal-md</code> \u7684\u6240\u6709\u5185\u5bb9\uff0c\u800c\u66f4\u591a\u7684\u662f\u4e00\u4e2a\u629b\u7816\u5f15\u7389\u6216\u8005\u8bf4\u57fa\u7840\u4f7f\u7528\u7684\u6559\u7a0b\u3002\u90e8\u5206\u9700\u6c42\u53ef\u80fd\u662f\u9762\u5411\u7279\u6b8a\u7528\u6237\u7fa4\u4f53\u7684\uff0c\u8fd8\u662f\u90a3\u53e5\u8bdd\uff0c\u5982\u679c\u6709\u5174\u8da3\u53ef\u4ee5\u67e5\u770b\u5b98\u65b9\u6587\u6863\u3002</p>"},{"location":"others/reveal-md2Slides/#\u5206\u9875","title":"\u5206\u9875","text":"<p>\u9996\u5148\uff0c\u5982\u679c\u4f60\u7528\u4e00\u4e2a\u518d\u666e\u901a\u4e0d\u8fc7\u7684 Markdown \u6587\u4ef6\u6765\u521b\u5efa Slides\uff0c\u6bd4\u5982\uff1a</p> <pre><code>## Part 1\n\n### Part 1.1\n\n- Orderred List\n- Next Line\n\n1. Numberred List\n2. Next Line\n\n### Part 1.2\n\n{code block here}\n\n### Part 1.3\n\n&gt; Everthings seems ok!\n</code></pre> <p>\u90a3\u4e48\u8fd0\u884c\u4ee5\u540e\u6211\u4eec\u4f1a\u5f97\u5230\u8fd9\u6837\u4e00\u4e2a\u9875\u9762\uff1a</p> <p></p> <p>\u53ef\u4ee5\u53d1\u73b0\uff0c\u5b83\u5e76\u4e0d\u50cf\u6211\u4eec\u60f3\u7684\u90a3\u6837\uff0c\u5411\u6a2a\u5411\u548c\u7eb5\u5411\u6269\u5c55\u3002\u4f46\u662f\u8fd9\u6070\u597d\u8bf4\u660e\u6240\u6709\u4e1c\u897f\u90fd\u662f\u53ef\u63a7\u7684\uff0c\u800c\u4e0d\u662f\u83ab\u540d\u5176\u5999\u7684\u6839\u636e\u67d0\u4e2a\u6807\u9898\u5c31\u81ea\u52a8\u6362\u6389\uff0c\u8fdb\u800c\u5bfc\u81f4\u4e00\u7cfb\u5217\u8be1\u5f02\u7684\u95ee\u9898\u3002</p> <p>\u5728 reveal-md \u4e2d\uff0c\u6709\u4e24\u79cd separator \u548c vertical separator \u4e24\u79cd\uff0c\u987e\u540d\u601d\u4e49\uff0c\u5206\u522b\u5bf9\u5e94\u7740\u5de6\u53f3\u5206\u9875\u548c\u4e0a\u4e0b\u5206\u9875\u3002\u9ed8\u8ba4\u60c5\u51b5\u4e0b\uff0cseparator \u662f <code>\\n---\\n</code>\uff0c\u800c vertical separator \u662f <code>\\n----\\n</code>\u3002\u6240\u4ee5\u7a0d\u5fae\u5bf9\u4e0a\u9762\u7684\u6587\u6863\u8fdb\u884c\u4e00\u4e9b\u4fee\u6539\uff1a</p> <pre><code>### Part 1\n\n---\n\n#### Part 1.1\n\n- Orderred List\n- Next Line\n\n1. Numberred List\n2. Next Line\n\n----\n\n#### Part 1.2\n\n{code block here}\n\n----\n\n#### Part 1.3\n\n&gt; Everthings seems ok!\n</code></pre> <p>\u518d\u6b21\u8fd0\u884c\u5c31\u80fd\u53d1\u73b0\u6211\u4eec\u7684 Slides \u5df2\u7ecf\u6709\u4e86\u4e8c\u7ef4\u7684\u5c42\u7ea7\u7ed3\u6784\uff1a</p> <p></p> <p>\u867d\u7136\u8fd9\u91cc\u7684\u9884\u89c8\u56fe\u91cc\u770b\u8d77\u6765\u6392\u7248\u5f88\u4e11\uff0c\u4f46\u662f\u5b9e\u9645\u5c55\u793a\u7684\u65f6\u5019\u90fd\u662f\u9ed8\u8ba4\u5c45\u4e2d\uff0c\u4e0d\u559c\u6b22\u7684\u8bdd\u53ef\u4ee5\u6539\u76f8\u5173\u8bbe\u7f6e\u6216\u8005\u7528 html \u6807\u7b7e\u4fee\u6539\u3002</p> <p>\u90a3\u4e48\u5176\u5b9e\u5230\u6b64\u4e3a\u6b62\uff0c\u4f60\u5df2\u7ecf\u80fd\u591f\u901a\u8fc7<code>reveal-md</code>\u6765\u5b9e\u73b0\u975e\u5e38\u5feb\u901f\u7684 Slides \u7f16\u5199\u4e86\u3002\u4f46\u662f\u4e3a\u4e86\u5b9a\u5236\u4e3b\u9898\uff0c\u6216\u8005\u662f\u4f7f\u7528\u4e00\u4e9b\u66f4\u9ad8\u7ea7\u7684\u4e1c\u897f\uff0c\u6211\u4eec\u8fd8\u9700\u8981\u4ecb\u7ecd\u4e00\u4e9b\u522b\u7684\u4e1c\u897f\uff0c\u5305\u62ec\u5bf9\u67d0\u4e9b\u4e1c\u897f\u7684\u81ea\u5b9a\u4e49\u3001\u67d0\u4e9b\u6a21\u5757\u7684\u6269\u5c55\u529f\u80fd\u3001\u4e0e\u539f\u751f<code>reveal.js</code>\u8bed\u6cd5\u7684\u6df7\u7528\u3002 \u5728\u6b63\u5f0f\u8fdb\u5165\u4e0b\u4e00\u4e2a\u90e8\u5206\u4e4b\u524d\uff0c\u6211\u60f3\u8865\u5145\u4ecb\u7ecd\u4e00\u4e0b\u5982\u4f55\u4fee\u6539\u9ed8\u8ba4\u7684 separator\uff1a \u6709\u4e24\u79cd\u65b9\u6848\u80fd\u5b9e\u73b0 seperator \u7684\u81ea\u5b9a\u4e49\uff0c\u4e00\u79cd\u662f\u901a\u8fc7\u5728\u547d\u4ee4\u884c\u4e2d\u7684\u9644\u52a0\u53c2\u6570\u5b9e\u73b0\uff0c\u53e6\u4e00\u79cd\u5219\u662f\u5728<code>md</code>\u6587\u4ef6\u5f00\u5934\u5199\u597d\u914d\u7f6e\u6587\u4ef6\u5b9e\u73b0\u3002</p> <p></p> <pre><code>---\nseparator: &lt;!--s--&gt;\nverticalSeparator: &lt;!--v--&gt;\n---\n</code></pre> <ul> <li>\u8fd9\u91cc\u5c06 <code>&lt;!--s--&gt;</code> \u8bbe\u4e3a separator\uff0c\u5c06 <code>&lt;!--v--&gt;</code> \u8bbe\u4e3a vertical separator\u3002</li> <li>\u8fd9\u4e00\u90e8\u5206\u5185\u5bb9\u9700\u8981\u653e\u5728 <code>md</code> \u6587\u4ef6\u7684\u5f00\u5934\uff0c\u4e4b\u540e\u4f1a\u8be6\u7ec6\u4ecb\u7ecd\u3002</li> </ul> <p>\u8fd9\u91cc\u6211\u624d\u7528\u7b2c\u4e8c\u79cd\u65b9\u6848\u6765\u6539\u88c5\u6211\u4eec\u7684 <code>md</code> \u6587\u4ef6\u73b0\u5728\u5f97\u5230\uff1a</p> <pre><code>---\nseparator: &lt;!--s--&gt;\nverticalSeparator: &lt;!--v--&gt;\n---\n\n### Part 1\n\n&lt;!--s--&gt;\n\n#### Part 1.1\n\n- Orderred List\n- Next Line\n\n1. Numberred List\n2. Next Line\n\n&lt;!--v--&gt;\n\n#### Part 1.2\n\n{code block here}\n\n&lt;!--v--&gt;\n\n#### Part 1.3\n\n&gt; Everthings seems ok!\n</code></pre> <p>\u800c\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u9664\u4e86\u5f00\u5934\u914d\u7f6e\u6587\u4ef6\u7684\u90e8\u5206\uff0c\u5176\u4ed6\u7684 <code>---</code> \u5219\u4f1a\u88ab\u8ba4\u4e3a\u662f <code>md</code> \u7684\u8bed\u6cd5\uff0c\u6e32\u67d3\u4e3a\u6b63\u5e38\u7684\u5206\u5272\u7ebf\u3002</p>"},{"location":"others/reveal-md2Slides/#\u4ee3\u7801\u6846","title":"\u4ee3\u7801\u6846","text":"<p>\u9996\u5148\uff0c\u5728 <code>reveal-md</code> \u4e2d\u4f7f\u7528\u4ee3\u7801\u6846\u548c\u5728 <code>markdown</code> \u4e2d\u4f7f\u7528\u662f\u4e00\u6837\u7684\uff0c\u53ea\u4e0d\u8fc7 <code>reveal.js</code> \u5bf9\u4ee3\u7801\u6846\u6709\u66f4\u591a\u7684\u652f\u6301\uff0c\u800c <code>reveal-md</code> \u5c06\u8fd9\u79cd\u652f\u6301\u878d\u5408\u8fdb\u4e86 <code>markdown</code> \u7684\u8bed\u6cd5\u3002\u6211\u5728\u8fd9\u91cc\u4e3b\u8981\u60f3\u4ecb\u7ecd\u7684\u662f\u4ee3\u7801\u6846\u9ad8\u4eae\u884c\u52a8\u753b\u3002</p> <p>\u4e0d\u77e5\u9053\u4f60\u6709\u6ca1\u6709\u9047\u5230\u8fc7\u8fd9\u79cd\u60c5\u51b5\uff0c\u6211\u4eec\u9700\u8981\u8d34\u51fa\u4e00\u6bb5\u4ee3\u7801\uff0c\u4f46\u662f\u6709\u4e9b\u90e8\u5206\u5e76\u4e0d\u662f\u91cd\u70b9\uff0c\u4f46\u662f\u4e0d\u653e\u4e0a\u53bb\u53c8\u89c9\u5f97\u602a\u602a\u7684\uff1b\u53c8\u6216\u8005\u4f60\u7684\u4ee3\u7801\u91cc\u6709\u591a\u4e2a\u91cd\u70b9\uff0c\u4f60\u9700\u8981\u5728\u5c55\u793a\u65f6\u624b\u52a8\u544a\u8bc9\u5927\u5bb6\u54ea\u91cc\u662f\u91cd\u70b9\uff1f<code>reveal*</code> \u53ef\u4ee5\u505a\u5230\u6309\u884c\u9ad8\u4eae\u4ee3\u7801\uff0c\u5e76\u4e14\u80fd\u591f\u5b9e\u73b0\u52a8\u753b\u3002\u8fd9\u4e48\u8bf4\u6709\u70b9\u62bd\u8c61\uff0c\u53ef\u4ee5\u4f53\u9a8c\u4e00\u4e0b\u8fd9\u4e00\u9875 Slide\u3002</p> \u53ef\u4ee5\u53d1\u73b0\uff0c\u4e0d\u4ec5\u9ad8\u4eae\u4e86\uff0c\u800c\u4e14\u8fd8\u6709\u81ea\u52a8\u6eda\u52a8\u5230\u4e2d\u5fc3\u3002 <p>\u90a3\u4e48\u8981\u5982\u4f55\u5b9e\u73b0\u5462\uff1f\u6211\u4eec\u77e5\u9053\uff0c\u5728<code>Markdown</code>\u4e2d\u4f7f\u7528\u4ee3\u7801\u6846\u7684\u8bed\u6cd5\u5982\u4e0b\uff1a</p> <pre><code>- \u524d\u9762\u7684\u6570\u5b57\u662f\u4e3a\u4e86\u6807\u8bb0\u5b83\u4eec\u5c5e\u4e8e\u4ee3\u7801\u6846\u7684\u7b2c\u51e0\u884c\u800c\u5199\u7684\uff0c\u5b9e\u9645\u4e0d\u9700\u8981\u5199\u8fd9\u4e9b\u6570\u5b57\uff08\u5e9f\u8bdd\uff09\n- \u53cd\u659c\u6760\u662f\u4e3a\u4e86\u9632\u6b62md\u6e32\u67d3\u9519\u8bef\uff0c\u5b9e\u9645\u4e0a\u4e0d\u9700\u8981\u52a0\n\n\\```cpp\n1       #include &lt;iostream&gt;\n2       int main(){\n3           std::cout &lt;&lt; \"Hello World!\\n\";\n4       return 0;\n5       }\n\\```\n</code></pre> <p>\u90a3\u4e48\uff0c\u4e3a\u4e86\u5b9e\u73b0\u9ad8\u4eae\uff0c\u6211\u4eec\u53ea\u9700\u8981\u5728\u8bed\u8a00\u540e\u9762\u52a0\u4e0a\u4e00\u4e2a\u65b9\u62ec\u53f7 <code>[...]</code> \u6765\u6807\u8bb0\u9ad8\u4eae\u884c\u5373\u53ef\uff0c\u6bd4\u5982 <code>[2-5]</code> \u5c31\u662f\u6807\u8bb0 2\uff5e5 \u884c\uff0c\u4e5f\u5c31\u662f\u6574\u4e2a <code>main()</code> \u51fd\u6570\u3002\u6b64\u5916\uff0c\u4f60\u8fd8\u53ef\u4ee5\u7528<code>|</code>\u6765\u5206\u9694\u591a\u4e2a\u9ad8\u4eae\u5757\uff0c\u6765\u5b9e\u73b0\u52a8\u753b\u7684\u6548\u679c\uff0c\u4f8b\u5982 <code>[1|2-5]</code> \u5c31\u662f\u5148\u9ad8\u4eae\u9884\u7f16\u8bd1\uff0c\u518d\u9ad8\u4eae <code>main()</code> \u51fd\u6570\u3002</p> <pre><code>---\nseparator: &lt;!--s--&gt;\nverticalSeparator: &lt;!--v--&gt;\n---\n\n### Part 1\n\n&lt;!--s--&gt;\n\n#### Part 1.1\n\n- Orderred List\n- Next Line\n\n1. Numberred List\n2. Next Line\n\n&lt;!--v--&gt;\n\n#### Part 1.2\n\n\\```cpp[1|2-5]\n#include &lt;iostream&gt;\nint main(){\n    std::cout &lt;&lt; \"Hello World!\\n\";\n    return 0;\n}\n\\```\n\n&lt;!--v--&gt;\n\n#### Part 1.3\n\n&gt; Everthings seems ok!\n</code></pre>"},{"location":"others/reveal-md2Slides/#\u683c\u5f0f\u652f\u6301","title":"\u683c\u5f0f\u652f\u6301","text":"<p>\u5728\u6587\u672c\u683c\u5f0f\u6392\u7248\u65b9\u9762\uff0c<code>Markdown</code> \u7684\u539f\u751f\u8bed\u6cd5\u90fd\u662f\u652f\u6301\u7684\uff0c\u6b64\u5916\u4f60\u5f53\u7136\u4e5f\u53ef\u4ee5\u4f7f\u7528 <code>html</code> \u6807\u7b7e\u6765\u7f16\u8f91\u4f60\u7684\u6587\u5b57\uff0c\u4f8b\u5982\u4fee\u6539\u989c\u8272\u3001\u8bbe\u7f6e\u5c45\u4e2d/\u9760\u5de6/\u9760\u53f3\u3001\u4fee\u6539\u5927\u5c0f\u2026\u2026 \u4f8b\u5982\uff0c\u4e0a\u9762\u5c55\u793a\u7684\u90a3\u5f20\u5c55\u793a\u4ee3\u7801\u9ad8\u4eae\u7684 Slide \u7684\u521d\u59cb\u4ee3\u7801\u5982\u4e0b\uff1a</p> <pre><code>### \u8f93\u51fa\u6d41\n\n\\```c[1-19|13-16]\n#ifndef __C_NEWBIE_HELPER__\n#define __C_NEWBIE_HELPER__\n/****************************************************\n * C Newbie Helper 1.0                              *\n * ------------------------------------------------ *\n * Github Repository Address:                       *\n * - https://github.com/IsshikiHugh/C-Newbie-Helper *\n ****************************************************/\n/*** Config Part ************************************/\n// MODE 0 : Logs will be write to 'CNH_log.txt' file.\n// MODE 1 : Logs will be print to console (colorful for normal terminal).\n// MODE 2 : Logs will be print to console (colorless but fine for CMD).\n#define CNH_MODE 2\n...\n\\```\n\n&lt;font size=\"6\"&gt;\n\n- \u5982\u679c\u4f60\u5bf9\u547d\u4ee4\u884c&lt;font color=\"orange\"&gt;\u6beb\u65e0\u4e86\u89e3&lt;/font&gt;\uff0c\u90a3\u4e48\u8bf7\u68c0\u67e5 &lt;font color=\"cyan\"&gt;CNH_MODE&lt;/font&gt; \u88ab\u8bbe\u7f6e\u4e3a &lt;font color=\"cyan\"&gt;2&lt;/font&gt; \uff1b\n- \u5982\u679c\u4f60\u7684\u65e5\u5fd7\u5c06\u4f1a\u88ab\u6253\u5370\u5728\u5e38\u89c4\u7684 &lt;font color=\"orange\"&gt;Terminal&lt;/font&gt; \u4e0a\uff0c\u90a3\u4e48\u6211\u4eec\u63a8\u8350\u4f60\u8bbe\u7f6e &lt;font color=\"cyan\"&gt;CNH_MODE&lt;/font&gt; \u4e3a &lt;font color=\"cyan\"&gt;1&lt;/font&gt; \uff1b\n- \u5982\u679c\u4f60\u5e0c\u671b\u4f60\u7684\u65e5\u5fd7\u5185\u5bb9\u4e0d\u88ab\u6253\u5370\uff0c\u800c\u662f\u8f93\u51fa\u5230&lt;font color=\"orange\"&gt;\u6587\u4ef6&lt;/font&gt;\u4e2d\uff0c\u5219\u53ef\u4ee5\u8bbe\u7f6e &lt;font color=\"cyan\"&gt;CNH_MODE&lt;/font&gt; \u4e3a &lt;font color=\"cyan\"&gt;0&lt;/font&gt; \uff0c\u4f46\u662f\u8bf7\u6ce8\u610f\uff0cCNH \u65e0\u6cd5\u6e05\u7a7a\u8f93\u51fa\u6587\u4ef6\uff0c\u8bf7\u5728\u6bcf\u6b21\u8f93\u51fa\u7684\u65f6\u5019\u624b\u52a8\u6e05\u7406 &lt;font color=\"yellow\"&gt;CNH_log.txt&lt;/font&gt; \uff1b\n\n&lt;/font&gt;\n</code></pre> <p>\u6839\u636e\u6211\u7684\u89c2\u5bdf\uff0c\u5982\u679c\u9700\u8981\u5728<code>html</code>\u6807\u7b7e\u91cc\u4f7f\u7528<code>Markdown</code>\u8bed\u6cd5\uff0c\u6700\u597d\u5728\u6807\u7b7e\u548c\u8bed\u6cd5\u4e4b\u95f4\u52a0\u7a7a\u884c\u3002</p>"},{"location":"others/reveal-md2Slides/#\u5b9a\u5236\u4e0e\u7f8e\u5316","title":"\u5b9a\u5236\u4e0e\u7f8e\u5316","text":"<p>\u8fd9\u91cc\u6211\u63d0\u4f9b\u4e00\u4e2a\u6211\u81ea\u5df1\u7684\u6e90<code>md</code>\u6587\u4ef6\u5f00\u5934\u914d\u7f6e\u7684\u6a21\u677f\uff1a</p> <pre><code>---\ntitle: Title\nseparator: &lt;!--s--&gt;\nverticalSeparator: &lt;!--v--&gt;\ntheme: league\nhighlightTheme: tomorrow-night-bright\nrevealOptions:\n  width: 1520\nheight: 950\nmargin: 0.04\n  transition: 'convex'\nslideNumber: true\n---\n</code></pre> <ul> <li><code>title</code> \u5373\u663e\u793a\u5728\u7f51\u9875\u6807\u7b7e\u4e0a\u5185\u5bb9\uff1b</li> <li><code>(vertical)separator</code> \u5373\u4e4b\u524d\u63d0\u5230\u8fc7\u7684\u4e24\u4e2a <code>separator</code>\uff1b</li> <li><code>theme</code> \u4e3a Slides \u4e3b\u9898\uff0c\u53ef\u4f9b\u4f7f\u7528\u7684\u5b98\u65b9\u9ed8\u8ba4\u4e3b\u9898\u53ef\u4ee5\u770b\u8fd9\u91cc\uff1a\ud83d\udd17\uff1b</li> <li><code>highlightTheme</code> \u4e3a\u4ee3\u7801\u6846\u9ad8\u4eae\u4e3b\u9898\uff0c\u5b98\u65b9\u5bf9\u9ad8\u4eae\u4e3b\u9898\u7684\u8bf4\u660e\u5728\u8fd9\u91cc\uff1a\ud83d\udd17\uff1b</li> <li><code>revealOptions</code> \u5219\u5bf9\u5e94\u4e86 <code>reveal.js</code> \u4e2d config \u7684\u5185\u5bb9\uff1b</li> <li>\u8fd9\u4e00\u5757\u4e0d\u53ea\u8fd9\u4e9b\u5185\u5bb9\uff0c\u6d89\u53ca\u7684\u5185\u5bb9\u975e\u5e38\u591a\uff0c<code>reveal.js</code> \u5b98\u65b9\u7684\u6587\u6863\u4e2d\u90fd\u6709\u8be6\u7ec6\u7684\u5185\u5bb9\uff0c\u6211\u8fd9\u91cc\u5217\u51fa\u4e86 \u5bbd\u3001\u9ad8\u3001\u8fb9\u754c\u3001\u6362\u9875\u52a8\u753b\u3001\u6807\u53f7 \u7b49\u3002</li> </ul> <p>\u6211\u8fd9\u91cc\u586b\u5199\u7684\u662f\u6211\u81ea\u5df1\u8ba4\u4e3a\u6bd4\u8f83\u8212\u670d\u800c\u4e14\u597d\u770b\u7684\u3002\u5f53\u7136\uff0c\u5982\u679c\u672c\u5730\u5bf9\u5e94\u8d44\u6e90\u6587\u4ef6\u91cc\u6709\u60a8\u81ea\u5df1\u7f16\u5199\u7684\u8d44\u6e90\u4e5f\u662f\u53ef\u4ee5\u7528\u7684\u3002\u4f46\u662f\u8fd9\u4e00\u5757\u6211\u7684\u94bb\u7814\u4e5f\u4e0d\u662f\u7279\u522b\u6df1\uff0c\u6211\u672c\u8eab\u4e5f\u4e0d\u662f\u524d\u7aef\u4eba\uff0c\u6240\u4ee5\u53ea\u80fd\u4ecb\u7ecd\u5230\u8fd9\u91cc\u4e86\u3002</p>"},{"location":"others/reveal-md2Slides/#\u901a\u8fc7-github-pages-\u5b9e\u73b0\u9759\u6001\u90e8\u7f72","title":"\u901a\u8fc7 GitHub Pages \u5b9e\u73b0\u9759\u6001\u90e8\u7f72","text":"<p>\u5728\u8fd9\u4e2a\u7ae0\u8282\u4e2d\uff0c\u6211\u5c06\u4ecb\u7ecd\u5982\u4f55\u5229\u7528 GitHub Pages \u5b9e\u73b0 Slides \u7684\u90e8\u7f72\uff0c\u5728\u8bf8\u5982 Gitee Pages \u7684\u5e73\u53f0\u5b9e\u73b0\u8fd9\u4e9b\u529f\u80fd\u7684\u6d41\u7a0b\u4e5f\u662f\u7c7b\u4f3c\u7684\u3002 \u9996\u5148\u4f60\u9700\u8981\u521b\u5efa\u4e00\u4e2a Repo \u6765\u5b58\u653e\u4f60\u7684\u9759\u6001\u8d44\u6e90\uff0c\u4f8b\u5982\u3002\u6211\u4e2a\u4eba\u7684\u505a\u6cd5\u662f\u76f4\u63a5\u628a\u521d\u59cb\u7684 <code>md</code> \u6587\u672c\u548c\u9759\u6001\u8d44\u6e90\u6587\u672c\u90fd\u653e\u5728\u4e00\u4e2a\u5730\u65b9\u4e86\u3002 \u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u9700\u8981\u5bfc\u51fa\u9759\u6001\u8d44\u6e90\uff0c\u4f7f\u7528\u7684\u662f\u8fd9\u6761\u6307\u4ee4\uff1a</p> <pre><code>reveal-md your-md-file.md --static your-static-dir\n</code></pre> <p>\u63a5\u4e0b\u6765\uff0c\u4f60\u4f1a\u5f97\u5230\u4e00\u4e2a\u6587\u4ef6\u5939\uff0c\u5305\u542b\u8fd9\u4e2a Slides \u6240\u9700\u8981\u7684\u6240\u6709\u8d44\u6e90\u3002\u4f60\u53ea\u9700\u8981\u5c06\u5b83\u4f20\u5230\u4f60\u7684 Repo \u91cc\u5373\u53ef\u3002 \u4f8b\u5982\u6211\u7684\u4ed3\u5e93\u4e2d\uff1a</p> <p></p> <p>\u8fdb\u5165<code>repo/.../static-dir</code>\uff0c\u4e5f\u5c31\u662f\u4e0a\u56fe\u7684<code>slides</code>\uff0c\u6211\u4eec\u53ef\u4ee5\u770b\u5230\u7c7b\u4f3c\u8fd9\u6837\u7684\u4e00\u4e9b\u6587\u4ef6\uff1a</p> <p></p> <p>\u5176\u4e2d\u7684 <code>index.html</code> \u548c <code>slides.html</code> \u90fd\u662f Slides \u7684 <code>html</code> \u6587\u4ef6\u3002\u533a\u522b\u8c8c\u4f3c\u662f <code>index.html</code>\u4f1a \u6709\u4e00\u4e2a\u5f39\u7a97\u544a\u8bc9\u4f60\u4f7f\u7528\u7684\u662f <code>reveal.js</code>\u3002</p> <p>\u63a5\u4e0b\u6765\uff0c\u8bbe\u7f6e pages \u670d\u52a1\u4ee5\u540e\u901a\u8fc7 <code>https://&lt;github_id&gt;.github.io/&lt;repo_name&gt;/.../slides.html</code> \u5373\u53ef\u8bbf\u95ee\u5230\u9875\u9762\u5566\uff01 \u4f8b\u5982\u4e0a\u65b9\u8fd9\u4e2a\u4ed3\u5e93\u5bf9\u5e94\u7684 <code>URL</code> \u662f <code>https://isshikihugh.github.io/myReveal-md/projectsTutorial_CNewbieHelper/slides/slides.html</code>\u3002</p> <p>\u5229\u7528 Pages \u670d\u52a1\uff0c\u5c31\u53ef\u4ee5\u5feb\u901f\u4fbf\u6377\u5730\u5206\u4eab\u4f60\u7684 Slides\uff0c\u5bf9\u4e8e\u4e0d\u61c2\u6280\u672f\u7684\u4eba\u6765\u8bf4\u4e0d\u4ec5\u8868\u73b0\u6548\u679c\u4e0d\u5dee\uff0c\u800c\u4e14\u8fd8\u6709\u4e00\u4e1d\u903c\u683c\u3002\u4e0d\u8fc7\u5728\u56fd\u5185\u6216\u8bb8\u8bbf\u95ee\u4e0d\u592a\u7a33\u5b9a\uff0c\u6240\u4ee5\u53ef\u4ee5\u8003\u8651\u4f7f\u7528 Gitee Pages \u6765\u5b9e\u73b0\u3002\u4e0d\u8fc7 Gitee Pages \u670d\u52a1\u6bcf\u4e00\u6b21\u90fd\u9700\u8981\u4f60\u81ea\u5df1\u53bb\u66f4\u65b0\u4e00\u4e0b\uff0c\u8fd8\u6709\u4e00\u4e9b\u5ba1\u6838\u673a\u5236\u3002</p>"},{"location":"others/reveal-md2Slides/#\u4e00\u4e9b\u5751","title":"\u4e00\u4e9b\u5751","text":"<p><code>reveal-md</code> \u5df2\u7ecf\u6709\u5927\u6982\u4e00\u5e74\u7684\u65f6\u95f4\u6ca1\u6709\u7ef4\u62a4\u4e86\uff0c\u5176\u4e2d\u4e5f\u9047\u5230\u4e00\u4e9b\u95ee\u9898\uff0c\u6211\u9047\u5230\u4e86\u4e00\u4e9b\u5c31\u8bb0\u4e0b\u6765\u3002</p> <ul> <li>\u8fd9\u4e2a\u95ee\u9898\u6211\u8fd8\u63d0\u4e86\u4e2a issue\uff0c\u91cc\u9762\u4e5f\u9644\u4e86\u89e3\u51b3\u7684\u529e\u6cd5\uff1a--static with --theme generate the <code>index.html</code> with the wrong path of <code>theme.css</code></li> <li>\u5728\u4f7f\u7528 gh-page \u8fdb\u884c\u90e8\u7f72\uff0c\u5e76\u4e14\u6307\u5b9a\u4e86\u989d\u5916\u7684 <code>css</code> \u6587\u4ef6\u7684\u65f6\u5019\uff0c\u4e00\u5b9a\u8981\u6dfb\u52a0 <code>--assets-dir assets</code>\uff0c\u5426\u5219\u9ed8\u8ba4\u7684\u7d20\u6750\u6587\u4ef6\u5939\u7684\u540d\u5b57\u662f <code>_assets</code>\uff0c\u800c <code>_</code> \u5f00\u5934\u7684\u6587\u4ef6\u5939\u4f1a\u88ab gh-page \u5ffd\u7565\u3002</li> </ul>"},{"location":"pape_read/","title":"\u6249\u9875","text":"<p> \u7ea6 31 \u4e2a\u5b57 </p> <p> \u300e\u305d\u306e\u6642\u3092\u5f85\u3064\u3088\u300f      \u4f60\u4eec\u8981\u52aa\u529b\u8fdb\u7a84\u95e8\uff0c\u56e0\u4e3a\u5bbd\u95e8\u548c\u9614\u8def\u5f15\u5411\u6c89\u6ca6\u3002  \u2014\u2014\u5b89\u5fb7\u70c8\u00b7\u7eaa\u5fb7\u300a\u7a84\u95e8\u300b  </p>"},{"location":"pape_read/ACTOR/","title":"[ACTOR] Action-Conditioned 3D Human Motion Synthesis with Transformer VAE","text":"<p> \u7ea6 235 \u4e2a\u5b57  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 1 \u5206\u949f</p> <p><code>3DV</code> <code>Human-Motion</code> <code>Action-Control</code></p> <p>\u6587\u7ae0\u4fe1\u606f</p> <ul> <li>\u6587\u7ae0\u9898\u76ee\uff1aAction-Conditioned 3D Human Motion Synthesis with Transformer VAE</li> <li>\u5206\u7c7b\uff1a<code>Computer Science</code> &gt; <code>Computer Vision and Pattern Recognition</code></li> <li>\u4f5c\u8005\uff1aMathis Petrovich, Michael J. Black, G\u00fcl Varol</li> <li>\u9879\u76ee\u4e3b\u9875\uff1a\ud83d\udd17</li> <li>arXiv\uff1a\ud83d\udd17 2104.05670</li> <li>\u4ee3\u7801\uff1a\ud83d\udd17</li> </ul> <p>\u76f8\u5173\u5185\u5bb9</p> <ul> <li>Transformer</li> <li>VAE</li> <li>SMPL \u4e00\u4e2a\u6027\u8d28\u826f\u597d\u7684\u4eba\u4f53\u6a21\u578b\u89c4\u8303</li> <li>MoCap</li> </ul>"},{"location":"pape_read/ACTOR/#introduction","title":"Introduction","text":"<p>In this work, our goal is to take a semantic action label like \u201cThrow\u201d and generate an infinite number of realistic 3D human motion sequences, of varying length, that look like realistic throwing (Figure 1).</p> <p>\u5e76\u4e14\u53d7\u4f7f\u7528\u573a\u666f\u9650\u5236\uff0c\u5b83\u9700\u8981\u6709\u5f3a\u7ea6\u675f\u4ee5\u53ca\u76f8\u5bf9\u7684\u9ad8\u6548\u6027\u3002</p> <p>\u6d89\u53ca\u4eba\u4f53\u76ae\u80a4\u8868\u9762\u4e0e\u4e3b\u5ba2\u4f53\u7684\u4ea4\u4e92\uff0c\u6240\u4ee5\u4f7f\u7528 SMPL \u662f\u4e00\u4e2a\u975e\u5e38\u597d\u7684\u9009\u62e9\u3002</p> <p>noisy 3D body poses</p> <p>\u540c\u6837\u91c7\u7528 Positional Encoding\uff0c\u8fd9\u4e0e NeRF \u8054\u7cfb\u8d77\u6765\u3002</p>"},{"location":"pape_read/ACTOR/#related-work","title":"Related Work","text":"<ul> <li>Future human motion prediction</li> <li>Human motion synthesis</li> <li>Monocular human motion estimation</li> <li>Transformer VAEs</li> </ul> \u7591\u60d1 <p>his allows the generation of variable length sequences without the problem of the motions regressing to the mean pose. \u8fd9\u53e5\u8bdd\u662f\u4ec0\u4e48\u610f\u601d\uff1f</p> Translate <p>\u7ffb\u8bd1\u5185\u5bb9</p>"},{"location":"pape_read/ACTOR/trans/","title":"Translate","text":"<p> \u7ea6 4848 \u4e2a\u5b57  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 16 \u5206\u949f</p>"},{"location":"pape_read/ACTOR/trans/#abstract","title":"Abstract","text":"<p>\u6211\u4eec\u89e3\u51b3\u4e86\u4ee5\u52a8\u4f5c\u4e3a\u6761\u4ef6\u751f\u6210\u903c\u771f\u591a\u6837\u7684\u4eba\u4f53\u8fd0\u52a8\u5e8f\u5217\u7684\u95ee\u9898\u3002 \u4e0e\u5b8c\u6210\u6216\u6269\u5c55\u8fd0\u52a8\u5e8f\u5217\u7684\u65b9\u6cd5\u76f8\u6bd4\uff0c\u6b64\u4efb\u52a1\u4e0d\u9700\u8981\u521d\u59cb\u59ff\u52bf\u6216\u5e8f\u5217\u3002 \u5728\u8fd9\u91cc\uff0c\u6211\u4eec\u901a\u8fc7\u8bad\u7ec3\u751f\u6210\u53d8\u5206\u81ea\u52a8\u7f16\u7801\u5668 (VAE) \u6765\u5b66\u4e60\u4eba\u4f53\u52a8\u4f5c\u7684\u52a8\u4f5c\u611f\u77e5\u6f5c\u5728\u8868\u793a\u3002 \u901a\u8fc7\u4ece\u8fd9\u4e2a\u6f5c\u5728\u7a7a\u95f4\u4e2d\u91c7\u6837\u5e76\u901a\u8fc7\u4e00\u7cfb\u5217\u4f4d\u7f6e\u7f16\u7801\u67e5\u8be2\u67d0\u4e2a\u6301\u7eed\u65f6\u95f4\uff0c\u6211\u4eec\u5408\u6210\u4e86\u4ee5\u5206\u7c7b\u52a8\u4f5c\u4e3a\u6761\u4ef6\u7684\u53ef\u53d8\u957f\u5ea6\u8fd0\u52a8\u5e8f\u5217\u3002 \u5177\u4f53\u6765\u8bf4\uff0c\u6211\u4eec\u8bbe\u8ba1\u4e86\u4e00\u4e2a\u57fa\u4e8e Transformer \u7684\u67b6\u6784 ACTOR\uff0c\u7528\u4e8e\u7f16\u7801\u548c\u89e3\u7801\u4ece\u52a8\u4f5c\u8bc6\u522b\u6570\u636e\u96c6\u4f30\u8ba1\u7684\u4e00\u7cfb\u5217\u53c2\u6570\u5316 SMPL \u4eba\u4f53\u6a21\u578b\u3002 \u6211\u4eec\u5728 NTU RGB+D\u3001HumanAct12 \u548c UESTC \u6570\u636e\u96c6\u4e0a\u8bc4\u4f30\u4e86\u6211\u4eec\u7684\u65b9\u6cd5\uff0c\u5e76\u5c55\u793a\u4e86\u5bf9\u73b0\u6709\u6280\u672f\u7684\u6539\u8fdb\u3002 \u6b64\u5916\uff0c\u6211\u4eec\u8fd8\u5c55\u793a\u4e86\u4e24\u4e2a\u7528\u4f8b\uff1a\u901a\u8fc7\u5c06\u6211\u4eec\u7684\u5408\u6210\u6570\u636e\u6dfb\u52a0\u5230\u8bad\u7ec3\u4e2d\u6765\u6539\u8fdb\u52a8\u4f5c\u8bc6\u522b\uff0c\u4ee5\u53ca\u8fd0\u52a8\u53bb\u566a\u3002 \u4ee3\u7801\u548c\u6a21\u578b\u53ef\u5728\u6211\u4eec\u7684\u9879\u76ee\u9875\u9762 [57] \u4e0a\u627e\u5230\u3002</p>"},{"location":"pape_read/ACTOR/trans/#introduction","title":"Introduction","text":"<p>\u5c3d\u7ba1\u5bf9\u4eba\u4f53\u8fd0\u52a8\u5efa\u6a21\u8fdb\u884c\u4e86\u6570\u5341\u5e74\u7684\u7814\u7a76 [4\u30015]\uff0c\u4f46\u5408\u6210\u903c\u771f\u4e14\u53ef\u63a7\u7684\u5e8f\u5217\u4ecd\u7136\u6781\u5177\u6311\u6218\u6027\u3002 \u5728\u8fd9\u9879\u5de5\u4f5c\u4e2d\uff0c\u6211\u4eec\u7684\u76ee\u6807\u662f\u91c7\u7528\u50cf\u201c\u6295\u63b7\u201d\u8fd9\u6837\u7684\u8bed\u4e49\u52a8\u4f5c\u6807\u7b7e\uff0c\u5e76\u751f\u6210\u65e0\u9650\u6570\u91cf\u7684\u903c\u771f 3D \u4eba\u4f53\u8fd0\u52a8\u5e8f\u5217\uff0c\u957f\u5ea6\u5404\u4e0d\u76f8\u540c\uff0c\u770b\u8d77\u6765\u50cf\u771f\u5b9e\u7684\u6295\u63b7\uff08\u56fe 1\uff09\u3002\u5927\u91cf\u5148\u524d\u7684\u5de5\u4f5c\u90fd\u96c6\u4e2d\u5728\u91c7\u53d6\u4e00\u4e2a\u59ff\u52bf\u6216\u4e00\u7cfb\u5217\u59ff\u52bf\uff0c\u7136\u540e\u9884\u6d4b\u672a\u6765\u7684\u8fd0\u52a8 [3\u30016\u300122\u300171\u300174]\u3002 \u8fd9\u662f\u4e00\u4e2a\u8fc7\u4e8e\u53d7\u9650\u7684\u573a\u666f\uff0c\u56e0\u4e3a\u5b83\u5047\u8bbe\u5df2\u7ecf\u6709\u4e00\u4e2a\u8fd0\u52a8\u5e8f\u5217\u5e76\u4e14\u53ea\u9700\u8981\u66f4\u591a\u3002 \u53e6\u4e00\u65b9\u9762\uff0c\u8bb8\u591a\u5e94\u7528\u7a0b\u5e8f\uff0c\u5982\u865a\u62df\u73b0\u5b9e\u548c\u89d2\u8272\u63a7\u5236 [28\u300161] \u9700\u8981\u751f\u6210\u5177\u6709\u6307\u5b9a\u6301\u7eed\u65f6\u95f4\u7684\u7ed9\u5b9a\u7c7b\u578b\uff08\u8bed\u4e49\u52a8\u4f5c\u6807\u7b7e\uff09\u7684\u52a8\u4f5c\u3002</p> <p>\u56fe1\uff1a\u76ee\u6807\uff1a\u4ee5\u52a8\u4f5c\u4e3a\u6761\u4ef6\u7684 Transformer VAE\uff08ACTOR\uff09\u5b66\u4e60\u5408\u6210\u4ee5\u5206\u7c7b\u52a8\u4f5c\u548c\u6301\u7eed\u65f6\u95f4T\u4e3a\u6761\u4ef6\u7684\u4eba\u7c7b\u8fd0\u52a8\u5e8f\u5217\u3002\u5e8f\u5217\u662f\u901a\u8fc7\u4ece\u5355\u4e00\u7684\u8fd0\u52a8\u8868\u5f81\u6f5c\u4f0f\u5411\u91cfz\u4e2d\u53d6\u6837\u4ea7\u751f\u7684\uff0c\u800c\u4e0d\u662f\u5148\u524d\u5de5\u4f5c\u4e2d\u7684\u6846\u67b6\u7ea7\u5d4c\u5165\u7a7a\u95f4\u3002</p> <p>\u6211\u4eec\u901a\u8fc7\u4f7f\u7528\u5177\u6709\u76f8\u5e94\u52a8\u4f5c\u6807\u7b7e\u7684 3D \u4eba\u4f53\u8fd0\u52a8\u6570\u636e\u8bad\u7ec3\u52a8\u4f5c\u6761\u4ef6\u751f\u6210\u6a21\u578b\u6765\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\u3002\u7279\u522b\u662f\uff0c\u6211\u4eec\u6784\u5efa\u4e86\u4e00\u4e2a\u57fa\u4e8e Transformer \u7684\u7f16\u7801\u5668-\u89e3\u7801\u5668\u67b6\u6784\uff0c\u5e76\u4f7f\u7528 VAE \u76ee\u6807\u5bf9\u5176\u8fdb\u884c\u8bad\u7ec3\u3002 \u6211\u4eec\u4f7f\u7528 SMPL [46] \u5bf9\u4eba\u4f53\u8fdb\u884c\u53c2\u6570\u5316\uff0c\u56e0\u4e3a\u5b83\u53ef\u4ee5\u8f93\u51fa\u5173\u8282\u4f4d\u7f6e\u6216\u8eab\u4f53\u8868\u9762\u3002 \u8fd9\u4e3a\u66f4\u597d\u5730\u6a21\u62df\u4e0e\u73af\u5883\u7684\u76f8\u4e92\u4f5c\u7528\u94fa\u5e73\u4e86\u9053\u8def\uff0c\u56e0\u4e3a\u8868\u9762\u662f\u6a21\u62df\u63a5\u89e6\u6240\u5fc5\u9700\u7684\u3002 \u6b64\u5916\uff0c\u8fd9\u79cd\u8868\u793a\u5141\u8bb8\u4f7f\u7528\u591a\u79cd\u91cd\u5efa\u635f\u5931\uff1a\u7ea6\u675f\u8fd0\u52a8\u6811\u4e2d\u7684\u96f6\u4ef6\u65cb\u8f6c\u3001\u5173\u8282\u4f4d\u7f6e\u6216\u8868\u9762\u70b9\u3002\u6587\u732e [40] \u548c\u6211\u4eec\u7684\u7ed3\u679c\u8868\u660e\uff0c\u635f\u5931\u7684\u7ec4\u5408\u7ed9\u51fa\u4e86\u6700\u771f\u5b9e\u7684\u751f\u6210\u8fd0\u52a8\u3002</p> <p>\u8fd0\u52a8\u5408\u6210\u7684\u5173\u952e\u6311\u6218\u662f\u751f\u6210\u5728\u611f\u77e5\u4e0a\u903c\u771f\u7684\u540c\u65f6\u5177\u6709\u591a\u6837\u6027\u7684\u5e8f\u5217\u3002\u8bb8\u591a\u8fd0\u52a8\u751f\u6210\u65b9\u6cd5\u90fd\u91c7\u7528\u81ea\u56de\u5f52\u65b9\u6cd5\uff0c\u4f8b\u5982 LSTM [16] \u548c GRU [49]\u3002\u7136\u800c\uff0c\u8fd9\u4e9b\u65b9\u6cd5\u901a\u5e38\u4f1a\u5728\u4e00\u6bb5\u65f6\u95f4\u540e\u56de\u5f52\u5230\u5e73\u5747\u59ff\u52bf [49] \u5e76\u4e14\u5bb9\u6613\u6f02\u79fb\u3002 \u6211\u4eec\u7684 Transformer \u6a21\u578b\u7684\u5173\u952e\u521b\u65b0\u662f\u4e3a\u89e3\u7801\u5668\u63d0\u4f9b\u4f4d\u7f6e\u7f16\u7801\u5e76\u7acb\u5373\u8f93\u51fa\u5b8c\u6574\u5e8f\u5217\u3002 \u6700\u8fd1\u5173\u4e8e\u795e\u7ecf\u8f90\u5c04\u573a\u7684\u5de5\u4f5c\u5df2\u7ecf\u666e\u53ca\u4e86\u4f4d\u7f6e\u7f16\u7801 [50]\uff1b \u6211\u4eec\u8fd8\u6ca1\u6709\u770b\u5230\u5b83\u50cf\u6211\u4eec\u4e00\u6837\u7528\u4e8e\u8fd0\u52a8\u751f\u6210\u3002 \u8fd9\u5141\u8bb8\u751f\u6210\u53ef\u53d8\u957f\u5ea6\u5e8f\u5217\uff0c\u800c\u4e0d\u4f1a\u51fa\u73b0\u8fd0\u52a8\u56de\u5f52\u5230\u5e73\u5747\u59ff\u52bf\u7684\u95ee\u9898\u3002 \u6b64\u5916\uff0c\u636e\u6211\u4eec\u6240\u77e5\uff0c\u6211\u4eec\u7684\u65b9\u6cd5\u662f\u7b2c\u4e00\u4e2a\u521b\u5efa\u52a8\u4f5c\u6761\u4ef6\u5e8f\u5217\u7ea7\u5d4c\u5165\u7684\u65b9\u6cd5\u3002 \u6700\u63a5\u8fd1\u7684\u5de5\u4f5c\u662f Action2Motion [21]\uff0c\u76f8\u6bd4\u4e4b\u4e0b\uff0c\u5b83\u63d0\u51fa\u4e86\u4e00\u79cd\u81ea\u56de\u5f52\u65b9\u6cd5\uff0c\u5176\u4e2d\u6f5c\u5728\u8868\u793a\u5904\u4e8e\u5e27\u7ea7\u522b\u3002 \u83b7\u5f97\u5e8f\u5217\u7ea7\u5d4c\u5165\u9700\u8981\u6c47\u96c6\u65f6\u95f4\u7ef4\u5ea6\uff1a\u6211\u4eec\u4e3a\u6b64\u76ee\u7684\u5f15\u5165\u4e86\u4e00\u79cd\u7ed3\u5408 Transformers \u548c VAE \u7684\u65b0\u65b9\u6cd5\uff0c\u8fd9\u4e5f\u663e\u7740\u63d0\u9ad8\u4e86\u57fa\u7ebf\u7684\u6027\u80fd\u3002</p> <p>\u6211\u4eec\u7684\u52a8\u4f5c\u6761\u4ef6\u751f\u6210\u95ee\u9898\u7684\u4e00\u4e2a\u7279\u5b9a\u6311\u6218\u662f\u5b58\u5728\u4e0e\u4e0d\u540c\u52a8\u4f5c\u6807\u7b7e\u914d\u5bf9\u7684\u6709\u9650\u52a8\u4f5c\u6355\u6349 (MoCap) \u6570\u636e\uff0c\u901a\u5e38\u5728 10 \u4e2a\u7c7b\u522b\u4e2d [31\u300163]\u3002 \u76f8\u53cd\uff0c\u6211\u4eec\u4f9d\u9760\u5355\u76ee\u8fd0\u52a8\u4f30\u8ba1\u65b9\u6cd5 [38] \u6765\u83b7\u5f97 3D \u52a8\u4f5c\u5e8f\u5217\uff0c\u5e76\u5728 UESTC \u52a8\u4f5c\u8bc6\u522b\u6570\u636e\u96c6 [32] \u7684 40 \u4e2a\u7ec6\u7c92\u5ea6\u7c7b\u522b\u4e0a\u5448\u73b0\u6709\u5e0c\u671b\u7684\u7ed3\u679c\u3002 \u4e0e[21]\u76f8\u53cd\uff0c\u6211\u4eec\u4e0d\u9700\u8981\u591a\u89c6\u89d2\u76f8\u673a\u6765\u8fdb\u884c\u5355\u76ee\u8f68\u8ff9\u4f30\u8ba1\uff0c\u8fd9\u4f7f\u5f97\u6211\u4eec\u7684\u6a21\u578b\u53ef\u80fd\u9002\u7528\u4e8e\u66f4\u5927\u7684\u5c3a\u5ea6\u3002 \u5c3d\u7ba1\u6709\u566a\u97f3\uff0c\u5355\u773c\u4f30\u8ba1\u88ab\u8bc1\u660e\u8db3\u4ee5\u7528\u4e8e\u8bad\u7ec3\uff0c\u5e76\u4e14\u4f5c\u4e3a\u6211\u4eec\u6a21\u578b\u7684\u989d\u5916\u597d\u5904\uff0c\u6211\u4eec\u80fd\u591f\u901a\u8fc7\u6211\u4eec\u5b66\u4e60\u7684\u8fd0\u52a8\u8868\u793a\u6765\u7f16\u7801\u89e3\u7801\u53bb\u566a\u4f30\u8ba1\u5e8f\u5217\u3002 </p> <p>\u52a8\u4f5c\u6761\u4ef6\u751f\u6210\u6a21\u578b\u53ef\u4ee5\u589e\u5f3a\u73b0\u6709\u7684 MoCap \u6570\u636e\u96c6\uff0c\u8fd9\u4e9b\u6570\u636e\u96c6\u6602\u8d35\u4e14\u5927\u5c0f\u6709\u9650 [48,63]\u3002 \u6700\u8fd1\u7684\u7814\u7a76\u63d0\u4f9b\u4e86\u7528\u4e8e\u8bad\u7ec3\u52a8\u4f5c\u8bc6\u522b\u6a21\u578b\u7684\u5408\u6210\u4eba\u7c7b\u52a8\u4f5c\u89c6\u9891 [65]\uff0c\u663e\u793a\u4e86\u52a8\u4f5c\u591a\u6837\u6027\u548c\u6bcf\u4e2a\u52a8\u4f5c\u7684\u5927\u91cf\u6570\u636e\u7684\u91cd\u8981\u6027\u3002 \u8fd9\u79cd\u65b9\u6cd5\u53ef\u4ee5\u53d7\u76ca\u4e8e\u65e0\u9650\u6e90\u52a8\u4f5c\u6761\u4ef6\u8fd0\u52a8\u5408\u6210\u3002 \u6211\u4eec\u901a\u8fc7\u52a8\u4f5c\u8bc6\u522b\u5b9e\u9a8c\u6765\u63a2\u8ba8\u8fd9\u4e2a\u95ee\u9898\u3002 \u6211\u4eec\u89c2\u5bdf\u5230\uff0c\u5c3d\u7ba1\u5b58\u5728 domain gap\uff0c\u4f46\u751f\u6210\u7684\u8fd0\u52a8\u53ef\u4ee5\u4f5c\u4e3a\u989d\u5916\u7684\u8bad\u7ec3\u6570\u636e\uff0c\u5c24\u5176\u662f\u5728\u4f4e\u6570\u636e\u8bbe\u7f6e\u4e2d\u3002 \u6700\u540e\uff0c\u7d27\u51d1\u7684\u52a8\u4f5c\u611f\u77e5\u4eba\u4f53\u8fd0\u52a8\u6f5c\u5728\u7a7a\u95f4\u53ef\u4ee5\u7528\u4f5c\u5176\u4ed6\u4efb\u52a1\u7684\u5148\u51b3\u6761\u4ef6\uff0c\u4f8b\u5982\u89c6\u9891\u4e2d\u7684\u4eba\u4f53\u8fd0\u52a8\u4f30\u8ba1\u3002</p> <p>\u6211\u4eec\u7684\u8d21\u732e\u6709\u56db\u65b9\u9762\uff1a(i) \u6211\u4eec\u4ecb\u7ecd\u4e86 ACTOR\uff0c\u8fd9\u662f\u4e00\u79cd\u65b0\u578b\u7684\u57fa\u4e8e Transformer \u7684\u6761\u4ef6 VAE\uff0c\u5e76\u8bad\u7ec3\u5b83\u901a\u8fc7\u4ece\u5e8f\u5217\u7ea7\u6f5c\u5728\u5411\u91cf\u4e2d\u91c7\u6837\u6765\u751f\u6210\u52a8\u4f5c\u6761\u4ef6\u4eba\u4f53\u8fd0\u52a8\u3002 (ii) \u6211\u4eec\u8bc1\u660e\u53ef\u4ee5\u4f7f\u7528\u4ece\u5355\u773c\u89c6\u9891\u4f30\u8ba1\u7684\u5608\u6742 3D \u4eba\u4f53\u59ff\u52bf\u6765\u5b66\u4e60\u751f\u6210\u903c\u771f\u7684 3D \u4eba\u4f53\u8fd0\u52a8\uff1b (iii) \u6211\u4eec\u5bf9\u67b6\u6784\u548c\u635f\u5931\u7ec4\u4ef6\u8fdb\u884c\u5168\u9762\u7684\u6d88\u878d\u7814\u7a76\uff0c\u5728\u591a\u4e2a\u6570\u636e\u96c6\u4e0a\u83b7\u5f97\u6700\u5148\u8fdb\u7684\u6027\u80fd\uff1b (iv) \u6211\u4eec\u4e3a\u52a8\u4f5c\u8bc6\u522b\u548c MoCap \u53bb\u566a\u6a21\u578b\u8bf4\u660e\u4e86\u4e24\u4e2a\u7528\u4f8b\u3002 \u8be5\u4ee3\u7801\u53ef\u5728\u6211\u4eec\u7684\u9879\u76ee\u9875\u9762 [57] \u4e0a\u627e\u5230\u3002</p>"},{"location":"pape_read/ACTOR/trans/#related-work","title":"Related Work","text":"<p>\u6211\u4eec\u7b80\u8981\u56de\u987e\u4e86\u6709\u5173\u8fd0\u52a8\u9884\u6d4b\u3001\u8fd0\u52a8\u5408\u6210\u3001\u5355\u773c\u8fd0\u52a8\u4f30\u8ba1\u4ee5\u53ca VAE \u80cc\u666f\u4e0b\u7684 Transformers \u7684\u76f8\u5173\u6587\u732e\u3002</p> <p>\u672a\u6765\u4eba\u4f53\u8fd0\u52a8\u9884\u6d4b\u3002\u4eba\u4f53\u8fd0\u52a8\u5206\u6790\u7684\u7814\u7a76\u5386\u53f2\u60a0\u4e45\uff0c\u53ef\u4ee5\u8ffd\u6eaf\u5230 20 \u4e16\u7eaa 80 \u5e74\u4ee3 [5,17,19,52]\u3002 \u7ed9\u5b9a\u8fc7\u53bb\u7684\u8fd0\u52a8\u6216\u521d\u59cb\u59ff\u52bf\uff0c\u9884\u6d4b\u672a\u6765\u7684\u5e27\u88ab\u79f0\u4e3a\u8fd0\u52a8\u9884\u6d4b\u3002 \u65e9\u671f\u7814\u7a76\u4e2d\u5df2\u7ecf\u91c7\u7528\u4e86\u7edf\u8ba1\u6a21\u578b [7, 18]\u3002 \u6700\u8fd1\uff0c\u968f\u7740 GANs [20] \u6216 VAEs [37] \u7b49\u795e\u7ecf\u7f51\u7edc\u751f\u6210\u6a21\u578b\u7684\u8fdb\u5c55\uff0c\u4e00\u4e9b\u5de5\u4f5c\u663e\u793a\u51fa\u53ef\u559c\u7684\u7ed3\u679c\u3002 \u793a\u4f8b\u5305\u62ec\u7528\u4e8e\u672a\u6765\u8fd0\u52a8\u9884\u6d4b\u7684 HP-GAN [6] \u548c\u5faa\u73af VAE [22]\u3002 \u5927\u591a\u6570\u5de5\u4f5c\u5c06\u8eab\u4f53\u89c6\u4e3a\u9aa8\u67b6\uff0c\u5c3d\u7ba1\u6700\u8fd1\u7684\u5de5\u4f5c\u5229\u7528\u4e86\u5b8c\u6574\u7684 3D \u8eab\u4f53\u5f62\u72b6\u6a21\u578b [3, 74]\u3002 \u4e0e [74] \u7c7b\u4f3c\uff0c\u6211\u4eec\u4e5f\u8d85\u8d8a\u4e86\u7a00\u758f\u5173\u8282\u5e76\u5c06\u9876\u70b9\u5408\u5e76\u5230\u8eab\u4f53\u8868\u9762\u3002 DLow [71] \u4fa7\u91cd\u4e8e\u4ece\u9884\u8bad\u7ec3\u6a21\u578b\u4e2d\u591a\u6837\u5316\u672a\u6765\u8fd0\u52a8\u7684\u91c7\u6837\u3002 [11] \u4f7f\u7528\u5173\u4e8e\u5bf9\u8c61\u4ea4\u4e92\u7684\u4e0a\u4e0b\u6587\u7ebf\u7d22\u6267\u884c\u6709\u6761\u4ef6\u7684\u672a\u6765\u9884\u6d4b\u3002 \u6700\u8fd1\uff0c[42] \u63d0\u51fa\u4e86\u4e00\u79cd\u57fa\u4e8e Transformer \u7684\u821e\u8e48\u751f\u6210\u65b9\u6cd5\uff0c\u8be5\u65b9\u6cd5\u4ee5\u97f3\u4e50\u548c\u8fc7\u53bb\u7684\u52a8\u4f5c\u4e3a\u6761\u4ef6\u3002 \u6bb5\u7b49\u3002 [14] \u4f7f\u7528\u53d8\u5f62\u91d1\u521a\u5b8c\u6210\u8fd0\u52a8\u3002 \u6709\u4e00\u4e2a\u5173\u4e8e\u8fd0\u52a8\u201c\u4e2d\u95f4\u201d\u7684\u76f8\u5173\u5de5\u4f5c\uff0c\u5b83\u91c7\u7528\u8fc7\u53bb\u548c\u672a\u6765\u7684\u59ff\u52bf\uff0c\u5e76\u201c\u4fee\u590d\u201d\u5b83\u4eec\u4e4b\u95f4\u7684\u5408\u7406\u8fd0\u52a8\uff1b \u6709\u5173\u66f4\u591a\u4fe1\u606f\uff0c\u8bf7\u53c2\u89c1 [23]\u3002 \u4e0e\u4e4b\u524d\u7684\u5de5\u4f5c\u76f8\u6bd4\uff0c\u6211\u4eec\u7684\u76ee\u6807\u662f\u5728\u6ca1\u6709\u4efb\u4f55\u8fc7\u53bb\u89c2\u5bdf\u7684\u60c5\u51b5\u4e0b\u5408\u6210\u8fd0\u52a8\u3002 \u4eba\u4f53\u8fd0\u52a8\u5408\u6210\u3002 \u867d\u7136\u6709\u5927\u91cf\u5173\u4e8e\u672a\u6765\u9884\u6d4b\u7684\u6587\u732e\uff0c\u4f46\u4ece\u5934\u5f00\u59cb\u7efc\u5408\u53d7\u5230\u7684\u5173\u6ce8\u76f8\u5bf9\u8f83\u5c11\u3002 \u975e\u5e38\u65e9\u671f\u7684\u5de5\u4f5c\u4f7f\u7528 PCA [51] \u548c GPLVM [64] \u6765\u5b66\u4e60\u6b65\u884c\u548c\u8dd1\u6b65\u7b49\u5faa\u73af\u8fd0\u52a8\u7684\u7edf\u8ba1\u6a21\u578b\u3002 \u5bf9\u591a\u79cd\u591a\u6837\u7684\u52a8\u4f5c\u8fdb\u884c\u6761\u4ef6\u7efc\u5408\u8981\u56f0\u96be\u5f97\u591a\u3002 DVGAN [43] \u8bad\u7ec3\u4e00\u4e2a\u751f\u6210\u6a21\u578b\uff0c\u8be5\u6a21\u578b\u4ee5\u8868\u793a MoCap \u6570\u636e\u96c6\u4e2d\u52a8\u4f5c\u7684\u77ed\u6587\u672c\u4e3a\u6761\u4ef6\uff0c\u4f8b\u5982 Human3.6M [30\u300131] \u548c CMU [63]\u3002 Text2Action [1] \u548c Language2Pose [2] \u540c\u6837\u63a2\u7d22\u4e86\u6839\u636e\u6587\u672c\u63cf\u8ff0\u8c03\u8282\u52a8\u4f5c\u751f\u6210\u3002 Music-to-Dance [39] \u548c [41] \u7814\u7a76\u97f3\u4e50\u6761\u4ef6\u751f\u6210\u3002 QuaterNet [56] \u4fa7\u91cd\u4e8e\u5728\u7ed9\u5b9a\u5730\u9762\u8f68\u8ff9\u548c\u5e73\u5747\u901f\u5ea6\u7684\u60c5\u51b5\u4e0b\u751f\u6210\u884c\u8d70\u548c\u8dd1\u6b65\u7b49\u8fd0\u52a8\u52a8\u4f5c\u3002 [69] \u63d0\u51fa\u4e86\u4e00\u79cd\u57fa\u4e8e\u5377\u79ef\u7684\u751f\u6210\u6a21\u578b\uff0c\u7528\u4e8e\u5728\u4e0d\u6307\u5b9a\u52a8\u4f5c\u7684\u60c5\u51b5\u4e0b\u5b9e\u73b0\u903c\u771f\u7684\u4f46\u4e0d\u53d7\u7ea6\u675f\u7684\u8fd0\u52a8\u3002 \u7c7b\u4f3c\u5730\uff0c[73] \u5408\u6210\u4efb\u610f\u5e8f\u5217\uff0c\u5173\u6ce8\u65f6\u95f4\u4e0a\u7684\u65e0\u754c\u8fd0\u52a8\u3002</p> <p>\u65e0\u7ea6\u675f\u8fd0\u52a8\u5408\u6210\u7684\u8bb8\u591a\u65b9\u6cd5\u5f80\u5f80\u4ee5\u6b65\u884c\u548c\u8dd1\u6b65\u7b49\u52a8\u4f5c\u4e3a\u4e3b\u5bfc\u3002\u76f8\u6bd4\u4e4b\u4e0b\uff0c\u6211\u4eec\u7684\u6a21\u578b\u80fd\u591f\u4ece\u66f4\u4e00\u822c\u7684\uff0c\u65e0\u5468\u671f\u7684\uff0c\u9884\u5b9a\u4e49\u7684\u884c\u52a8\u7c7b\u522b\uff0c\u4e0e\u884c\u52a8\u8bc6\u522b\u6570\u636e\u96c6\u517c\u5bb9\u7684\u6837\u672c\u3002\u5728\u8fd9\u65b9\u9762\uff0c[75]\u5f15\u5165\u4e86\u8d1d\u53f6\u65af\u65b9\u6cd5\uff0c\u5176\u4e2d\u9690\u85cf\u534a\u9a6c\u5c14\u53ef\u592b\u6a21\u578b\u7528\u4e8e\u8054\u5408\u8bad\u7ec3\u751f\u6210\u6a21\u578b\u548c\u5224\u522b\u6a21\u578b\u3002\u4e0e\u6211\u4eec\u7c7b\u4f3c\uff0c[75]\u8868\u660e\uff0c\u4ed6\u4eec\u751f\u6210\u7684\u52a8\u4f5c\u53ef\u4ee5\u4f5c\u4e3a\u989d\u5916\u7684\u8bad\u7ec3\u6570\u636e\u7684\u884c\u52a8\u8bc6\u522b\u3002\u7136\u800c\uff0c\u6839\u636e\u5224\u522b\u5668\u5206\u7c7b\u7ed3\u679c\uff0c\u5b83\u4eec\u751f\u6210\u7684\u5e8f\u5217\u662f\u4f2a\u6807\u8bb0\u7684\u3002\u53e6\u4e00\u65b9\u9762\uff0c\u6211\u4eec\u7684\u6761\u4ef6\u6a21\u578b\u80fd\u591f\u4ee5\u4e00\u79cd\u53d7\u63a7\u7684\u65b9\u5f0f\u5408\u6210\u8fd0\u52a8\uff0c\u4f8b\u5982\u5e73\u8861\u8bad\u7ec3\u96c6\u3002\u4e0e\u6211\u4eec\u7684\u5de5\u4f5c\u6700\u76f8\u4f3c\u7684\u662f Action2Motion [21] \uff0c\u8fd9\u662f\u4e00\u4e2a\u57fa\u4e8e GRU \u67b6\u6784\u7684\u6bcf\u5e27\u64cd\u4f5c VAE\u3002\u6211\u4eec\u7684\u5e8f\u5217\u7ea7 VAE \u6f5c\u5728\u7a7a\u95f4\uff0c\u7ed3\u5408\u57fa\u4e8e\u53d8\u538b\u5668\u7684\u8bbe\u8ba1\u63d0\u4f9b\u4e86\u663e\u8457\u7684\u4f18\u52bf\uff0c\u5982\u6211\u4eec\u7684\u5b9e\u9a8c\u6240\u793a\u3002</p> <p>\u5176\u4ed6\u6700\u8fd1\u7684\u5de5\u4f5c[25,72]\u4f7f\u7528\u89c4\u8303\u5316\u6d41\u6765\u89e3\u51b3\u4eba\u4f53\u8fd0\u52a8\u4f30\u8ba1\u548c\u751f\u6210\u95ee\u9898\u3002\u51e0\u4e2a\u4f5c\u54c1[29,36,67]\u5b66\u4e60\u4e00\u4e2a\u8fd0\u52a8\u6d41\u5f62\uff0c\u5e76\u4f7f\u7528\u5b83\u7684\u8fd0\u52a8\u53bb\u566a\uff0c\u8fd9\u662f\u6211\u4eec\u7684\u7528\u4f8b\u4e4b\u4e00\u3002\u8fd8\u6709\u4e00\u4e2a\u91cd\u8981\u7684\u56fe\u5f62\u6587\u732e\u7684\u4e3b\u9898\uff0c\u8fd9\u5f80\u5f80\u96c6\u4e2d\u5728\u52a8\u753b\u5e08\u63a7\u5236\u3002\u770b\uff0c\u4f8b\u5982\uff0c[27]\u5b66\u4e60\u52a8\u4f5c\u5339\u914d\u548c[40]\u89d2\u8272\u52a8\u753b\u3002\u8fd9\u91cc\u6700\u76f8\u5173\u7684\u662f\u76f8\u51fd\u6570\u795e\u7ecf\u7f51\u7edc[28]\u548c\u795e\u7ecf\u72b6\u6001\u673a[61]\u3002\u4e24\u8005\u90fd\u5229\u7528\u4e86\u7531\u6b63\u5f26\u51fd\u6570\u76f8\u4f4d\u9a71\u52a8\u7684\u52a8\u4f5c\u7684\u6982\u5ff5\u3002\u8fd9\u4e0e\u4f4d\u7f6e\u7f16\u7801\u7684\u601d\u60f3\u6709\u5173\uff0c\u4f46\u4e0e\u6211\u4eec\u7684\u65b9\u6cd5\u4e0d\u540c\uff0c\u5b83\u4eec\u7684\u65b9\u6cd5\u9700\u8981\u4eba\u5de5\u5206\u5272\u64cd\u4f5c\u5e76\u6784\u5efa\u8fd9\u4e9b\u76f8\u51fd\u6570\u3002</p> <p>\u5355\u76ee\u4eba\u4f53\u8fd0\u52a8\u4f30\u8ba1\u3002\u6765\u81ea\u89c6\u9891\u7684\u8fd0\u52a8\u4f30\u8ba1[35,38,47]\u6700\u8fd1\u53d6\u5f97\u4e86\u91cd\u5927\u8fdb\u5c55\uff0c\u4f46\u8d85\u51fa\u4e86\u6211\u4eec\u7684\u8303\u56f4\u3002\u5728\u8fd9\u9879\u5de5\u4f5c\u4e2d\uff0c\u6211\u4eec\u91c7\u7528 VIBE [38]\u4ece\u52a8\u4f5c\u6807\u8bb0\u7684\u89c6\u9891\u6570\u636e\u96c6\u4e2d\u83b7\u5f97\u8bad\u7ec3\u8fd0\u52a8\u5e8f\u5217\u3002</p> <p>Transformer VAE\u3002Transformer \u6700\u8fd1\u5728\u8bed\u8a00\u4efb\u52a1\u65b9\u9762\u53d6\u5f97\u7684\u6210\u529f\u589e\u52a0\u4e86\u4eba\u4eec\u5bf9\u57fa\u4e8e\u6ce8\u610f\u529b\u7684\u795e\u7ecf\u7f51\u7edc\u6a21\u578b\u7684\u5174\u8da3\u3002\u4e00\u4e9b\u5de5\u7a0b\u4f7f\u7528\u53d8\u538b\u5668\u7ed3\u5408\u751f\u6210 VAE \u57f9\u8bad\u3002\u5177\u4f53\u7684\u4f8b\u5b50\u5305\u62ec\u6545\u4e8b\u751f\u6210[15] \uff0c\u60c5\u611f\u5206\u6790[10] \uff0c\u53cd\u5e94\u751f\u6210[44]\u548c\u97f3\u4e50\u751f\u6210[33]\u3002[33]\u7684\u5de5\u4f5c\u5b66\u4e60\u6bcf\u4e2a\u65f6\u95f4\u6846\u67b6\u7684\u6f5c\u5728\u5d4c\u5165\uff0c\u800c[10]\u5e73\u5747\u7684\u9690\u85cf\u72b6\u6001\uff0c\u4ee5\u83b7\u5f97\u4e00\u4e2a\u5355\u4e00\u7684\u6f5c\u5728\u4ee3\u7801\u3002\u53e6\u4e00\u65b9\u9762\uff0c[15]\u6267\u884c\u6ce8\u610f\u529b\u5e73\u5747\u6c60\u968f\u7740\u65f6\u95f4\u7684\u63a8\u79fb\u3002\u4e0e\u8fd9\u4e9b\u5de5\u4f5c\u76f8\u53cd\uff0c\u6211\u4eec\u91c7\u7528\u53ef\u5b66\u4e60\u7684\u6807\u8bb0\uff0c\u5982[12,13]\u4e2d\u6240\u793a\uff0c\u5c06\u8f93\u5165\u603b\u7ed3\u4e3a\u5e8f\u5217\u7ea7\u5d4c\u5165\u3002</p> <p>\u56fe2\uff1a\u65b9\u6cd5\u6982\u8ff0\u3002\u6211\u4eec\u8bf4\u660e\u4e86\u6211\u4eec\u57fa\u4e8eTransformer\u7684VAE\u6a21\u578b\u7684\u7f16\u7801\u5668\uff08\u5de6\uff09\u548c\u89e3\u7801\u5668\uff08\u53f3\uff09\uff0c\u8be5\u6a21\u578b\u751f\u6210\u4e86\u52a8\u4f5c\u6761\u4ef6\u7684\u8fd0\u52a8\u3002\u7ed9\u5b9a\u4e00\u4e32\u8eab\u4f53\u59ff\u52bfP1, ... , PT\u548c\u4e00\u4e2a\u52a8\u4f5c\u6807\u7b7ea\uff0c\u7f16\u7801\u5668\u8f93\u51fa\u5206\u5e03\u53c2\u6570\uff0c\u6211\u4eec\u5728\u6b64\u57fa\u7840\u4e0a\u5b9a\u4e49KL\u635f\u5931\uff08LKL\uff09\u3002\u6211\u4eec\u4f7f\u7528\u6bcf\u4e2a\u52a8\u4f5c\u7684\u989d\u5916\u53ef\u5b66\u4e60\u6807\u8bb0\uff08\u00b5 token a \u548c \u03a3 token a \uff09\u4f5c\u4e3a\u4eceTransformer\u7f16\u7801\u5668\u83b7\u5f97\u00b5\u548c\u03a3\u7684\u65b9\u6cd5\u3002\u4f7f\u7528\u00b5\u548c\u03a3\uff0c\u6211\u4eec\u5bf9\u8fd0\u52a8\u7684\u6f5c\u5728\u8868\u5f81z\u2208M\u8fdb\u884c\u91c7\u6837\u3002\u89e3\u7801\u5668\u5c06\u6f5c\u4f0f\u5411\u91cfz\u3001\u52a8\u4f5c\u6807\u7b7ea\u548c\u6301\u7eed\u65f6\u95f4T\u4f5c\u4e3a\u8f93\u5165\u3002\u884c\u52a8\u51b3\u5b9a\u4e86\u53ef\u5b66\u4e60\u7684b\u6807\u8bb0a\u52a0\u6cd5\u6807\u8bb0\uff0c\u6301\u7eed\u65f6\u95f4\u51b3\u5b9a\u4e86\u8f93\u5165\u5230\u89e3\u7801\u5668\u7684\u4f4d\u7f6e\u7f16\u7801\uff08PE\uff09\u7684\u6570\u91cf\u3002\u89e3\u7801\u5668\u8f93\u51fa\u6574\u4e2a\u5e8f\u5217Pb1, . . . , PbT\uff0c\u5728\u6b64\u57fa\u7840\u4e0a\u8ba1\u7b97\u91cd\u5efa\u635f\u5931LP\u3002\u6b64\u5916\uff0c\u6211\u4eec\u7528\u4e00\u4e2a\u53ef\u5fae\u5206\u7684SMPL\u5c42\u8ba1\u7b97\u9876\u70b9\uff0c\u4ee5\u5b9a\u4e49\u4e00\u4e2a\u9876\u70b9\u635f\u5931\uff08LV \uff09\u3002\u5bf9\u4e8e\u8bad\u7ec3\u6765\u8bf4\uff0cz\u662f\u4f5c\u4e3a\u7f16\u7801\u5668\u7684\u8f93\u51fa\u5f97\u5230\u7684\uff1b\u5bf9\u4e8e\u751f\u6210\u6765\u8bf4\uff0c\u5b83\u662f\u4ece\u9ad8\u65af\u5206\u5e03\u4e2d\u968f\u673a\u62bd\u53d6\u7684\u3002</p>"},{"location":"pape_read/ACTOR/trans/#action-conditioned-motion-generation","title":"Action-Conditioned Motion Generation","text":"<p>\u95ee\u9898\u5b9a\u4e49\u3002\u8eab\u4f53\u8fd0\u52a8\u6240\u5b9a\u4e49\u7684\u52a8\u4f5c\u53ef\u4ee5\u662f\u8eab\u4f53\u90e8\u4f4d\u7684\u65cb\u8f6c\u62e5\u6709\u5c5e\u6027\uff0c\u4e0e\u8eab\u4efd\u7279\u5b9a\u7684\u8eab\u4f53\u5f62\u72b6\u65e0\u5173\u3002\u4e3a\u4e86\u80fd\u591f\u4ea7\u751f\u4e0e\u4e0d\u540c\u5f62\u6001\u7684\u884c\u4e3a\u8005\u7684\u8fd0\u52a8\uff0c\u8fd9\u662f\u7406\u60f3\u7684\u5206\u79bb\u59ff\u52bf\u548c\u5f62\u72b6\u3002\u56e0\u6b64\uff0c\u4e0d\u5931\u4e00\u822c\u6027\uff0c\u6211\u4eec\u91c7\u7528\u4e86 SMPL \u8eab\u4f53\u6a21\u578b[46] \uff0c\u8fd9\u662f\u4e00\u4e2a\u5206\u79bb\u7684\u8eab\u4f53\u8868\u793a(\u7c7b\u4f3c\u4e8e\u6700\u8fd1\u7684\u6a21\u578b[53,55,58,68])\u3002\u5ffd\u7565\u5f62\u72b6\uff0c\u6211\u4eec\u7684\u76ee\u6807\u662f\u751f\u6210\u4e00\u7cfb\u5217\u7684\u59ff\u6001\u53c2\u6570\u3002\u66f4\u6b63\u5f0f\u5730\u8bf4\uff0c\u7ed9\u5b9a\u4e00\u4e2a\u52a8\u4f5c\u6807\u7b7e a (\u6765\u81ea\u4e00\u7ec4\u9884\u5b9a\u4e49\u7684\u52a8\u4f5c\u8303\u7574 a \u2208 A)\u548c\u4e00\u4e2a\u6301\u7eed\u65f6\u95f4 T\uff0c\u6211\u4eec\u751f\u6210\u4e00\u4e2a\u4f53\u6784\u6210\u7684\u5e8f\u5217 R1\uff0c... \uff0cRT \u548c\u4e00\u4e2a\u6839\u5173\u8282\u7684\u5e73\u79fb\u5e8f\u5217\u8868\u793a\u4e3a\u4f4d\u79fb\uff0cD1\uff0c... \uff0cDT (\u4e0e DT \u2208 R3\uff0csomething t \u2208{1\uff0c... \uff0cT })</p> <p>\u52a8\u4f5c\u8868\u73b0\u6cd5\u3002\u6bcf\u5e27 SMPL \u59ff\u6001\u53c2\u6570\u8868\u793a\u8fd0\u52a8\u5b66\u6811\u4e2d\u768423\u4e2a\u5173\u8282\u65cb\u8f6c\u548c\u4e00\u4e2a\u5168\u5c40\u65cb\u8f6c\u3002\u91c7\u7528\u8fde\u7eed6D \u65cb\u8f6c\u8868\u793a\u6cd5\u8fdb\u884c\u8bad\u7ec3[76] \uff0c\u4f7f Rt \u2208 R24 \u00d7 6\u3002\u8bbe Pt \u662f Rt \u548c Dt \u7684\u7ec4\u5408\uff0c\u8868\u793a\u5355\u5e27\u4e2d\u8eab\u4f53\u7684\u59ff\u52bf\u548c\u4f4d\u7f6e t\u3002\u5b8c\u6574\u7684\u52a8\u4f5c\u662f P1\uff0c. . \uff0cPT\u3002\u7ed9\u5b9a\u4e00\u4e2a\u751f\u6210\u5668\u8f93\u51fa\u4f4d\u59ff Pt \u548c\u4efb\u610f\u5f62\u72b6\u53c2\u6570\uff0c\u6211\u4eec\u53ef\u4ee5\u7528[46]\u53ef\u5fae\u5730\u5f97\u5230\u4f53\u7f51\u683c\u9876\u70b9(Vt)\u548c\u4f53\u5173\u8282\u5750\u6807(Jt)\u3002</p>"},{"location":"pape_read/ACTOR/trans/#conditional-transformer-vae-for-motions","title":"Conditional Transformer VAE for Motions","text":"<p>\u6211\u4eec\u91c7\u7528\u6761\u4ef6\u53d8\u5206\u81ea\u52a8\u7f16\u7801\u5668(CVAE)\u6a21\u578b[60] \uff0c\u5e76\u5c06\u52a8\u4f5c\u7c7b\u522b\u4fe1\u606f\u8f93\u5165\u5230\u7f16\u7801\u5668\u548c\u89e3\u7801\u5668\u3002\u66f4\u5177\u4f53\u5730\u8bf4\uff0c\u6211\u4eec\u7684\u6a21\u578b\u662f\u4e00\u4e2a\u52a8\u4f5c\u6761\u4ef6\u53d8\u538b\u5668 VAE (ACTOR) \uff0c\u5176\u7f16\u7801\u5668\u548c\u89e3\u7801\u5668\u7531\u53d8\u538b\u5668\u5c42\u7ec4\u6210(\u53c2\u89c1\u56fe2\u4ee5\u83b7\u5f97\u6982\u8ff0)\u3002</p> <p>\u7f16\u7801\u5668\u3002\u8be5\u7f16\u7801\u5668\u91c7\u7528\u4efb\u610f\u957f\u5ea6\u7684\u59ff\u6001\u5e8f\u5217\uff0c\u4ee5\u52a8\u4f5c\u6807\u7b7e a \u4e3a\u8f93\u5165\uff0c\u8f93\u51fa\u8fd0\u52a8\u6f5c\u4f0f\u7a7a\u95f4\u7684\u5206\u5e03\u53c2\u6570 \u03bc \u548c \u03a3\u3002\u5229\u7528\u91cd\u53c2\u6570\u5316\u6280\u5de7[37] \uff0c\u6211\u4eec\u4ece\u8fd9\u4e2a\u5206\u5e03\u4e2d\u62bd\u6837\u51fa\u4e00\u4e2a\u6f5c\u5411\u91cf z \u2208 M\uff0c\u5176\u4e2d MdRd\u3002\u9996\u5148\u5c06\u6240\u6709\u8f93\u5165\u59ff\u6001\u53c2\u6570(R)\u548c\u5e73\u79fb(D)\u7ebf\u6027\u5d4c\u5165\u5230 Rd \u7a7a\u95f4\u4e2d\u3002\u5f53\u6211\u4eec\u5c06\u4efb\u610f\u957f\u5ea6\u7684\u5e8f\u5217\u5d4c\u5165\u5230\u4e00\u4e2a\u6f5c\u5728\u7a7a\u95f4(\u5e8f\u5217\u7ea7\u5d4c\u5165)\u65f6\uff0c\u6211\u4eec\u9700\u8981\u5408\u5e76\u65f6\u95f4\u7ef4\u6570\u3002\u5728\u5176\u4ed6\u9886\u57df\u4e2d\uff0c\u5df2\u7ecf\u5f15\u5165\u4e86[\u7c7b]\u4ee4\u724c\u7528\u4e8e\u6c60\u7684\u76ee\u7684\uff0c\u4f8b\u5982\uff0c\u5728\u5e26\u6709 BERT [12]\u7684 NLP \u4e2d\uff0c\u4ee5\u53ca\u6700\u8fd1\u5728\u5e26\u6709 ViT [13]\u7684\u8ba1\u7b97\u673a\u89c6\u89c9\u4e2d\u3002\u53d7\u6b64\u65b9\u6cd5\u7684\u542f\u53d1\uff0c\u6211\u4eec\u7c7b\u4f3c\u5730\u5728\u8f93\u5165\u524d\u9762\u52a0\u4e0a\u53ef\u5b66\u4e60\u7684\u4ee4\u724c\uff0c\u5e76\u4e14\u53ea\u4f7f\u7528\u76f8\u5e94\u7684\u7f16\u7801\u5668\u8f93\u51fa\u4f5c\u4e3a\u6c47\u96c6\u65f6\u95f4\u7ef4\u5ea6\u7684\u65b9\u6cd5\u3002\u4e3a\u6b64\uff0c\u6211\u4eec\u5728\u6bcf\u4e2a\u64cd\u4f5c\u4e2d\u5305\u62ec\u4e24\u4e2a\u989d\u5916\u7684\u53ef\u5b66\u4e60\u53c2\u6570: \u03bc \u6807\u8bb0 a \u548c \u03a3 \u6807\u8bb0 a\uff0c\u6211\u4eec\u79f0\u4e4b\u4e3a\u201c\u5206\u5e03\u53c2\u6570\u6807\u8bb0\u201d\u3002\u6211\u4eec\u5c06\u5d4c\u5165\u7684\u59ff\u52bf\u5e8f\u5217\u9644\u52a0\u5230\u8fd9\u4e9b\u6807\u8bb0\u3002\u4ea7\u751f\u7684\u53d8\u538b\u5668\u7f16\u7801\u5668\u8f93\u5165\u662f\u4f4d\u7f6e\u7f16\u7801\u7684\u6b63\u5f26\u51fd\u6570\u5f62\u5f0f\u7684\u603b\u548c\u3002\u6211\u4eec\u901a\u8fc7\u53d6\u7f16\u7801\u5668\u7684\u524d\u4e24\u4e2a\u8f93\u51fa\u5bf9\u5e94\u4e8e\u5206\u5e03\u53c2\u6570\u6807\u8bb0\u6765\u83b7\u5f97\u5206\u5e03\u53c2\u6570 \u03bc \u548c \u03a3 (\u5373\u53bb\u6389\u5176\u4f59\u7684\u6807\u8bb0)\u3002\u89e3\u7801\u5668\u3002\u7ed9\u5b9a\u4e00\u4e2a\u6f5c\u5728\u5411\u91cf z \u548c\u4e00\u4e2a\u52a8\u4f5c\u6807\u7b7e a\uff0c\u89e3\u7801\u5668\u5728\u4e00\u6b21\u62cd\u6444\u4e2d\u5728\u7ed9\u5b9a\u7684\u6301\u7eed\u65f6\u95f4\u5185\u751f\u6210\u4e00\u4e2a\u771f\u5b9e\u7684\u4eba\u4f53\u8fd0\u52a8(\u5373\uff0c\u4e0d\u662f\u81ea\u56de\u5f52)\u3002\u6211\u4eec\u4f7f\u7528\u53d8\u538b\u5668\u89e3\u7801\u5668\u6a21\u578b\uff0c\u5176\u4e2d\u6211\u4eec\u63d0\u4f9b\u7684\u65f6\u95f4\u4fe1\u606f\u4f5c\u4e3a\u4e00\u4e2a\u67e5\u8be2(\u5728 T \u6b63\u5f26\u4f4d\u7f6e\u7f16\u7801\u7684\u5f62\u5f0f) \uff0c\u548c\u6f5c\u5728\u7684\u5411\u91cf\u7ed3\u5408\u7684\u884c\u52a8\u4fe1\u606f\uff0c\u4f5c\u4e3a\u5173\u952e\u548c\u503c\u3002\u4e3a\u4e86\u5408\u5e76\u52a8\u4f5c\u4fe1\u606f\uff0c\u6211\u4eec\u7b80\u5355\u5730\u6dfb\u52a0\u4e00\u4e2a\u53ef\u5b66\u4e60\u7684\u504f\u89c1 b \u6807\u8bb0 a \u6765\u5c06\u6f5c\u5728\u8868\u5f81\u8f6c\u79fb\u5230\u4e00\u4e2a\u52a8\u4f5c\u4f9d\u8d56\u7684\u7a7a\u95f4\u3002\u53d8\u538b\u5668\u89e3\u7801\u5668\u8f93\u51fa\u4e00\u7cfb\u5217\u7684 T \u77e2\u91cf\uff0c\u4ece\u4e2d\u6211\u4eec\u53ef\u4ee5\u5f97\u5230\u6700\u7ec8\u7684 Pb1\uff0c. . \uff0cPbT \u7684\u7ebf\u6027\u6295\u5f71\u3002\u5229\u7528\u53ef\u5fae SMPL \u5c42\u83b7\u5f97\u7ed9\u5b9a\u7684\u4f4d\u59ff\u53c2\u6570\u4f5c\u4e3a\u89e3\u7801\u5668\u8f93\u51fa\u7684\u9876\u70b9\u548c\u5173\u8282\u3002</p>"},{"location":"pape_read/ACTOR/trans/#training","title":"Training","text":"<p>\u6211\u4eec\u5b9a\u4e49\u4e86\u51e0\u4e2a\u635f\u5931\u9879\u6765\u8bad\u7ec3\u6211\u4eec\u7684\u6a21\u578b\uff0c\u5e76\u5728\u7b2c 4.2 \u8282\u4e2d\u8fdb\u884c\u4e86\u6d88\u878d\u7814\u7a76\u3002 \u59ff\u52bf\u53c2\u6570 (LP) \u7684\u91cd\u5efa\u635f\u5931\u3002 \u6211\u4eec\u5728\u5730\u9762\u5b9e\u51b5\u59ff\u52bf P1,... \u4e4b\u95f4\u4f7f\u7528 L2 \u635f\u5931\u3002 . . , PT \u548c\u6211\u4eec\u7684\u9884\u6d4b Pb1, . . . , PbT \u4f5c\u4e3a LP = PT t=1\u2225Pt \u2212 Pbt\u2225 2 2 \u3002 \u8bf7\u6ce8\u610f\uff0c\u6b64\u635f\u5931\u5305\u542b SMPL \u65cb\u8f6c\u548c\u6839\u5e73\u79fb\u3002 \u5f53\u6211\u4eec\u901a\u8fc7\u4e22\u5f03\u5e73\u79fb\u8fdb\u884c\u5b9e\u9a8c\u65f6\uff0c\u6211\u4eec\u5c06\u8fd9\u4e2a\u672f\u8bed\u5206\u6210\u4e24\u90e8\u5206\uff1aLR \u548c LD\uff0c\u5206\u522b\u7528\u4e8e\u65cb\u8f6c\u548c\u5e73\u79fb\u3002</p> <p>\u9876\u70b9\u5750\u6807 (LV) \u4e0a\u7684\u91cd\u5efa\u635f\u5931\u3002 \u6211\u4eec\u5c06 SMPL \u59ff\u52bf Pt \u548c Pbt \u9988\u9001\u5230\u5177\u6709\u5e73\u5747\u5f62\u72b6\uff08\u5373 \u03b2 = \u20d70\uff09\u7684\u53ef\u5fae\u5206 SMPL \u5c42\uff08\u6ca1\u6709\u53ef\u5b66\u4e60\u53c2\u6570\uff09\u4ee5\u83b7\u5f97\u7f51\u683c Vt \u548c Vbt \u7684\u6839\u4e2d\u5fc3\u9876\u70b9\u3002 \u6211\u4eec\u901a\u8fc7\u4e0e\u5730\u9762\u5b9e\u51b5\u9876\u70b9 Vt \u6bd4\u8f83\u6765\u5b9a\u4e49 L2 \u635f\u5931\uff0c\u5373 LV = PT t=1\u2225Vt \u2212 Vbt\u2225 2 2 \u3002 \u6211\u4eec\u8fdb\u4e00\u6b65\u5728\u4e00\u7ec4\u66f4\u7a00\u758f\u7684\u70b9\u4e0a\u4f7f\u7528\u635f\u5931 LJ \u8fdb\u884c\u5b9e\u9a8c\uff0c\u4f8b\u5982\u901a\u8fc7 SMPL \u8054\u5408\u56de\u5f52\u5668\u83b7\u5f97\u7684\u8054\u5408\u4f4d\u7f6e Jbt\u3002 \u7136\u800c\uff0c\u6b63\u5982\u7b2c 4.2 \u8282\u6240\u793a\uff0c\u6211\u4eec\u6ca1\u6709\u5728\u6700\u7ec8\u6a21\u578b\u4e2d\u5305\u542b\u8be5\u672f\u8bed\u3002 KL\u635f\u5931\uff08LKL\uff09\u3002 \u4e0e\u6807\u51c6 VAE \u4e00\u6837\uff0c\u6211\u4eec\u901a\u8fc7\u9f13\u52b1\u6f5c\u5728\u7a7a\u95f4\u7c7b\u4f3c\u4e8e\u9ad8\u65af\u5206\u5e03\u6765\u89c4\u8303\u5316\u6f5c\u5728\u7a7a\u95f4\uff0c\u5176\u4e2d \u00b5 \u662f\u7a7a\u5411\u91cf\uff0c\u03a3 \u662f\u8eab\u4efd\u77e9\u9635\u3002 \u6211\u4eec\u6700\u5c0f\u5316\u7f16\u7801\u5668\u5206\u5e03\u548c\u8be5\u76ee\u6807\u5206\u5e03\u4e4b\u95f4\u7684 Kullback\u2013Leibler (KL) \u6563\u5ea6\u3002 \u7531\u6b64\u4ea7\u751f\u7684\u603b\u635f\u5931\u88ab\u5b9a\u4e49\u4e3a\u4e0d\u540c\u9879\u7684\u603b\u548c\uff1aL = LP + LV + \u03bbKLLKL\u3002 \u6211\u4eec\u51ed\u7ecf\u9a8c\u8bc1\u660e\u4e86\u5728\u6211\u4eec\u7684\u5b9e\u9a8c\u4e2d\u4f7f\u7528 \u03bbKL\uff08\u76f8\u5f53\u4e8e \u03b2-VAE [26] \u4e2d\u7684 \u03b2 \u9879\uff09\u8fdb\u884c\u52a0\u6743\u4ee5\u83b7\u5f97\u591a\u6837\u6027\u548c\u73b0\u5b9e\u4e3b\u4e49\u4e4b\u95f4\u7684\u826f\u597d\u6743\u8861\u7684\u91cd\u8981\u6027\uff08\u53c2\u89c1\u9644\u5f55 A.1 \u8282\uff09 ). \u5269\u4f59\u7684\u635f\u5931\u9879\u53ea\u662f\u7b80\u5355\u5730\u540c\u7b49\u52a0\u6743\uff0c\u901a\u8fc7\u8c03\u6574\u53ef\u80fd\u4f1a\u8fdb\u4e00\u6b65\u6539\u8fdb\u3002 \u6211\u4eec\u4f7f\u7528\u56fa\u5b9a\u5b66\u4e60\u7387\u4e3a 0.0001 \u7684 AdamW \u4f18\u5316\u5668\u3002 \u5c0f\u6279\u91cf\u5927\u5c0f\u8bbe\u7f6e\u4e3a 20\uff0c\u6211\u4eec\u53d1\u73b0\u6027\u80fd\u5bf9\u8fd9\u4e2a\u8d85\u53c2\u6570\u5f88\u654f\u611f\uff08\u53c2\u89c1\u9644\u5f55 A.2 \u8282\uff09\u3002 \u6211\u4eec\u5206\u522b\u5728 NTU-13\u3001HumanAct12 \u548c UESTC \u6570\u636e\u96c6\u4e0a\u8bad\u7ec3\u6211\u4eec\u7684\u6a21\u578b 2000\u30015000 \u548c 1000 \u4e2a\u65f6\u671f\u3002 \u603b\u7684\u6765\u8bf4\uff0c\u66f4\u591a\u7684\u65f6\u671f\u4f1a\u4ea7\u751f\u66f4\u597d\u7684\u6027\u80fd\uff0c\u4f46\u6211\u4eec\u505c\u6b62\u8bad\u7ec3\u4ee5\u4fdd\u6301\u8f83\u4f4e\u7684\u8ba1\u7b97\u6210\u672c\u3002 \u8bf7\u6ce8\u610f\uff0c\u4e3a\u4e86\u5141\u8bb8\u66f4\u5feb\u7684\u8fed\u4ee3\u3001\u635f\u5931\u548c\u67b6\u6784\u7684\u6d88\u878d\uff0c\u6211\u4eec\u5728 NTU-13 \u4e0a\u8bad\u7ec3\u4e86 1000 \u4e2a epoch\uff0c\u5728 UESTC \u4e0a\u8bad\u7ec3\u4e86 500 \u4e2a epoch\u3002 \u5176\u4f59\u7684\u5b9e\u65bd\u7ec6\u8282\u53ef\u4ee5\u5728\u9644\u5f55\u7684 C \u8282\u4e2d\u627e\u5230\u3002</p>"},{"location":"pape_read/ACTOR/trans/#experiments","title":"Experiments","text":"<p>\u6682\u7565</p>"},{"location":"pape_read/ACTOR/trans/#conclusions","title":"Conclusions","text":"<p>\u6211\u4eec\u63d0\u51fa\u4e86\u4e00\u79cd\u65b0\u7684\u57fa\u4e8e Transformer \u7684 VAE \u6a21\u578b\u6765\u5408\u6210\u4ee5\u52a8\u4f5c\u4e3a\u6761\u4ef6\u7684\u4eba\u4f53\u8fd0\u52a8\u3002\u6211\u4eec\u63d0\u4f9b\u4e86\u8be6\u7ec6\u7684\u5206\u6790\u6765\u8bc4\u4f30\u6211\u4eec\u63d0\u8bae\u7684\u65b9\u6cd5\u7684\u4e0d\u540c\u7ec4\u6210\u90e8\u5206\u3002 \u6211\u4eec\u5728\u52a8\u4f5c\u6761\u4ef6\u8fd0\u52a8\u751f\u6210\u65b9\u9762\u83b7\u5f97\u4e86\u6700\u5148\u8fdb\u7684\u6027\u80fd\uff0c\u4e0e\u4e4b\u524d\u7684\u5de5\u4f5c\u76f8\u6bd4\u6709\u4e86\u663e\u7740\u6539\u8fdb\u3002 \u6b64\u5916\uff0c\u6211\u4eec\u63a2\u7d22\u4e86\u8fd0\u52a8\u53bb\u566a\u548c\u52a8\u4f5c\u8bc6\u522b\u4e2d\u7684\u5404\u79cd\u7528\u4f8b\u3002 \u6211\u4eec\u65b9\u6cd5\u7684\u4e00\u4e2a\u7279\u522b\u5438\u5f15\u4eba\u7684\u7279\u6027\u662f\u5b83\u5728\u5e8f\u5217\u7ea7\u6f5c\u5728\u7a7a\u95f4\u4e0a\u8fd0\u884c\u3002\u56e0\u6b64\uff0c\u672a\u6765\u7684\u5de5\u4f5c\u53ef\u4ee5\u5229\u7528\u6211\u4eec\u7684\u6a21\u578b\u5bf9\u8fd0\u52a8\u4f30\u8ba1\u6216\u52a8\u4f5c\u8bc6\u522b\u95ee\u9898\u65bd\u52a0\u5148\u9a8c\u3002</p>"},{"location":"pape_read/EG3D/","title":"[EG3D] Efficient Geometry-aware 3D Generative Adversarial Networks","text":"<p> \u7ea6 479 \u4e2a\u5b57  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 2 \u5206\u949f</p> <p><code>3DV</code> <code>Generation</code></p> <p>\u6587\u7ae0\u4fe1\u606f</p> <ul> <li>\u6587\u7ae0\u9898\u76ee\uff1aEG3D: Efficient Geometry-aware 3D Generative Adversarial Networks</li> <li>\u4f5c\u8005\uff1a     Eric Ryan Chan  * 1, 2 ,      Connor Zhizhen Lin  * 1 ,      Matthew Aaron Chan  * 1 ,      Koki Nagano  * 2 ,      Boxiao Pan  1 ,      Shalini De Mello 2 ,      Orazio Gallo  2 ,      Leonidas Guibas  1 ,      Jonathan Tremblay  2 ,      Sameh Khamis  2 ,      Tero Karras  2 ,      Gordon Wetzstein  1 </li> <li>\u9879\u76ee\u4e3b\u9875\uff1a\ud83d\udd17</li> <li>arXiv\uff1a\ud83d\udd17 2112.07945</li> <li>\u4ee3\u7801\uff1a\ud83d\udd17</li> </ul>"},{"location":"pape_read/EG3D/#\u8bba\u6587\u7b14\u8bb0","title":"\u8bba\u6587\u7b14\u8bb0","text":""},{"location":"pape_read/EG3D/#tri-plane-hybrid-3d-representation","title":"Tri-plane hybrid 3D representation","text":"<p>\u8ba8\u8bba\u4e00\u4e0b NeRF \u548c Tri-plane hybrid 3D representation \u7684\u5173\u7cfb\u3002</p> <p>NeRF \u6309 ray \u4f53\u79ef\u6e32\u67d3\u8fc7\u7a0b\u4e2d\u91c7\u6837\u7684\u70b9\u4ece\u8bad\u7ec3\u597d\u7684 MLP \u91cc\u62ff\uff1b\u800c EG3D \u5219\u662f\u5f97\u5230\u4e09\u4e2a\u6295\u5f71\u65b9\u5411\u4e0a\u7684\u7279\u5f81\u5411\u91cf\uff0c\u6bcf\u4e00\u4e2a\u6295\u5f71\u65b9\u5411\u4e0a\u7684\u7279\u5f81\u5411\u91cf\u90fd\u662f\u6cbf\u7740\u6d88\u5931\u7684\u90a3\u4e2a\u7ef4\u5ea6\u805a\u5408\u5f97\u5230\u7684\uff0c\u53ef\u4ee5\u770b\u4f5c\u662f\u62ff\u5230\u4e86\u7a7a\u95f4\u4e2d\u4e09\u6761\u6b63\u4ea4\u7684\u7ebf\u7684\u7279\u5f81\uff0c\u800c\u4e4b\u540e\u7528\u4e00\u4e2a\u8f7b\u91cf MLP \u53bb\u4ece\u8fd9\u4e09\u4e2a\u7279\u5f81\u5411\u91cf\u91cc\u628a\u8fd9\u4e2a\u70b9\u7684\u989c\u8272\u5bc6\u5ea6\u62ff\u51fa\u6765\uff0c\u7c7b\u4f3c\u4e8e\u6c42\u4e09\u6761\u7ebf\u7684\u4ea4\u70b9\u3002</p> <p>\u76f8\u6bd4\u4e8e NeRF \u5c06\u6570\u636e\u53c2\u6570\u5316\uff0c\u6bcf\u6b21\u67e5\u8be2\u90fd\u9700\u8981\u8d70\u4e00\u8fb9 MLP\uff0cEG3D Sec3 \u5219\u663e\u793a\u7684\u5c06\u7279\u5f81\u5b58\u5728\u4e09\u4e2a\u4e8c\u7ef4\u8868\u91cc\uff0c\u6bcf\u6b21\u67e5\u8be2\u53ea\u9700\u8981 O(1) \u7684\u5f00\u9500\uff0c\u56e0\u6b64\u6548\u7387\u4e3b\u8981\u53d6\u51b3\u4e8e\u540e\u9762\u90a3\u4e2a\u8f7b\u91cf MLP\uff0c\u4ee5\u6b64\u6765\u5b9e\u73b0\u6548\u7387\u4e0a\u7684\u63d0\u9ad8\u3002</p> <p>\u800c\u5b9e\u73b0\u6548\u679c\u4e0a\uff0c\u6211\u80e1\u731c EG3D \u7684\u65b9\u6cd5\u597d\u7684\u539f\u56e0\uff1a</p> <ol> <li>\u7531\u4e8e\u4f7f\u7528\u4e86\u5ea7\u6807\u6295\u5f71\uff0c\u6240\u4ee5\u76f8\u5bf9\u4e8e NeRF \u7684\u53c2\u6570\u8868\u8fbe\uff0cEG3D \u5bf9\u4e8e\u67d0\u4e2a\u70b9\u7684\u7a7a\u95f4\u4f4d\u7f6e\u5177\u6709\u66f4\u5f3a\u7684\u7ea6\u675f\uff0c\u56e0\u800c\u53ef\u80fd\u5bf9\u7ec6\u8282\u7684\u628a\u63a7\u7ea6\u675f\u66f4\u76f4\u63a5\uff0c\u6216\u8005\u8bf4\u76f4\u89c9\u4e0a\u6211\u611f\u89c9 EG3D \u8fd9\u79cd\u8868\u8fbe\u5bf9\u201c\u7279\u5f81-\u5ea7\u6807\u201d\u7684\u5173\u7cfb\u66f4\u5177\u4f53\uff1b</li> <li>\u4e09\u4e2a\u6b63\u4ea4\u65b9\u5411\u585e\u8fdb\u5c0f MLP \u91cc\u5b66\uff0c\u53ef\u80fd\u4f1a\u66f4\u5bb9\u6613\u8ba9 MLP \u77e5\u9053\u53bb\u627e\u4ea4\u70b9\u9644\u8fd1\u7684\u90a3\u4e9b\u70b9\u53bb\u5b66\u4e60\uff0c\u611f\u89c9\u6709\u70b9\u7c7b\u4f3c\u4e8e\u5728\u4e00\u4e2a\u957f\u5f97\u50cf\u66fc\u54c8\u987f\u8ddd\u79bb\u90a3\u79cd\u7acb\u65b9\u4f53\u4e00\u6837\u7684\u7a7a\u95f4\u91cc\u53bb\u5b66\u4e60\u5468\u56f4\u7684\u4fe1\u606f\uff1b</li> </ol> <p>\u53c2\u8003\u8d44\u6599</p> <ul> <li>https://www.cnblogs.com/ghostcai/p/16615616.html \uff08\u7b14\u8bb0\uff09</li> </ul>"},{"location":"pape_read/MAS/","title":"[MAS] Multi-view Ancestral Sampling for 3D Motion Generation Using 2D Diffusion","text":"<p> \u7ea6 211 \u4e2a\u5b57  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 1 \u5206\u949f</p> <p><code>3DV</code> <code>Motion</code> <code>Diffusion</code></p> <p>\u6587\u7ae0\u4fe1\u606f</p> <ul> <li>\u6587\u7ae0\u9898\u76ee\uff1aMAS: Multi-view Ancestral Sampling for 3D Motion Generation Using 2D Diffusion </li> <li>\u4f5c\u8005\uff1aRoy Kapon, Guy Tevet, Daniel Cohen-Or, Amit H. Bermano</li> <li>\u9879\u76ee\u4e3b\u9875\uff1a\ud83d\udd17</li> <li>arXiv\uff1a\ud83d\udd17 2310.14729</li> </ul>"},{"location":"pape_read/MAS/#\u8bba\u6587\u7b14\u8bb0","title":"\u8bba\u6587\u7b14\u8bb0","text":"<p>\u5229\u7528\u4e00\u4e2a\u5728 2D \u5355\u76ee\u6570\u636e\u96c6\u4e0a train \u51fa\u6765\u7684 diffusion model \u505a 3D Motion \u7684\u751f\u6210\u3002</p> <ul> <li> <p>\u7531\u4e8e\u4f7f\u7528 ancestral sampling\uff0cMAS \u751f\u6210 3D motion \u7684\u6548\u7387\u5f88\u9ad8\uff1b</p> </li> <li> <p>\u6570\u636e\u8868\u793a\uff1a</p> <ul> <li>\u8868\u793a J \u4e2a joint \u5728 L \u5e27\u91cc\u7684 xyz\uff0c\u800c\u4e14\u4e0d\u5bf9\u9aa8\u68d2\u957f\u5ea6\u505a\u7ea6\u675f\uff08\u5728\u505a\u6cd5\u4e2d\u4e5f\u4e0d\u7ea6\u675f\uff09\uff1b<ul> <li>\u8fd9\u5e26\u6765\u7684\u597d\u5904\u662f\u53ef\u4ee5\u589e\u52a0\u573a\u666f\u4e2d\u66f4\u591a\u7684\u8fd0\u52a8\u7269\u4f53\uff1b</li> </ul> </li> </ul> </li> <li> <p>\u65b9\u6cd5</p> <ul> <li>\u591a\u89c6\u89d2\u7684\u4e00\u81f4\u6027\uff1a<ul> <li>\u5728\u6bcf\u4e2a diffusion denoising step \u90fd\u5229\u7528 \"triangulate\" \u8fdb\u884c\u4e00\u6b21 \\(n*2D \\rightarrow 1*3D \\rightarrow n*2D\\) \u7684\u8fc7\u7a0b\uff1b</li> <li> TODO: \u8fd9\u4e2a \"triangulate\" \u662f\u4ec0\u4e48\uff1f \u4e09\u89d2\u6d4b\u91cf\u3002</li> </ul> </li> <li>\u5b9e\u9a8c\u8ba4\u4e3a V = 3 \u5c31\u591f\u4e86\uff0c\u518d\u591a\u5f71\u54cd\u4e5f\u4e0d\u5927\uff1b</li> <li></li> </ul> </li> </ul>"},{"location":"pape_read/NSM/","title":"[NSM] Neural State Machine for Character-Scene Interactions","text":"<p> \u7ea6 1434 \u4e2a\u5b57  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 5 \u5206\u949f</p> <p><code>3DV</code> <code>Human-Motion</code> <code>Scene-Aware</code></p> <p>\u6587\u7ae0\u4fe1\u606f</p> <ul> <li>\u6587\u7ae0\u9898\u76ee\uff1aNeural State Machine for Character-Scene Interactions</li> <li>\u4f5c\u8005\uff1aSebastian Starke, He Zhang, Taku Komura, Jun Saito</li> <li>\u8bba\u6587\uff1a\ud83d\udd17</li> </ul>"},{"location":"pape_read/NSM/#\u8bba\u6587\u7b14\u8bb0","title":"\u8bba\u6587\u7b14\u8bb0","text":""},{"location":"pape_read/NSM/#\u6982\u8ff0","title":"\u6982\u8ff0","text":"<p>NSM \u63d0\u51fa\u4e00\u79cd\u65b0\u7684\u76ee\u6807\u5bfc\u5411\u81ea\u56de\u5f52\u6a21\u578b\u6765\u89e3\u51b3\u4eba\u4f53\u52a8\u4f5c\u751f\u6210\u95ee\u9898\uff0c\u80fd\u5b9e\u73b0\u8868\u73b0\u826f\u597d\u7684\u5750\u3001\u6301\u7269\u3001\u907f\u969c\u7684\u884c\u4e3a\u3002\u8be5\u95ee\u9898\u4e3b\u8981\u96be\u70b9\u5728\u4e8e\uff0c\u5b8c\u6210\u4e00\u9879\u4efb\u52a1\u6240\u9700\u8981\u751f\u6210\u7684\u52a8\u4f5c\u5e8f\u5217\u4e2d\u5305\u542b\u5468\u671f\u6027\u548c\u975e\u5468\u671f\u6027\u7684\u90e8\u5206\uff0c\u5e76\u4e14\u9700\u8981\u5bf9\u5468\u56f4\u73af\u5883\u8fdb\u884c\u611f\u77e5\u3002\u901a\u8fc7\u4f7f\u7528\u4e8c\u7ef4\u76f8\u4f4d\u8868\u793a\u7684 Kronecker \u4e58\u79ef\u3001\u4e00\u79cd\u53cc\u5411\u63a7\u5236\uff08\u76ee\u6807\u4e2d\u5fc3\u548c\u81ea\u6211\u4e2d\u5fc3\uff09\u89c4\u5219\u3001\u4ea4\u4e92\u4f53\u7d20\u4f20\u611f\u5668\u548c\u73af\u5883\u4f53\u7d20\u4f20\u611f\u5668\u7b49\u6280\u672f\u6765\u589e\u5f3a\u6548\u679c\uff0c\u66f4\u5b8f\u89c2\u7684\u8bf4\uff0cNSM \u4f7f\u7528\u4e86\u4e00\u79cd\u76ee\u6807\u9a71\u52a8\u7684\u6a21\u578b\u6765\u5b9e\u73b0\u6548\u679c\u826f\u597d\u7684\u52a8\u4f5c\u751f\u6210\u3002</p>"},{"location":"pape_read/NSM/#\u65b9\u6cd5","title":"\u65b9\u6cd5","text":"<p>\u6574\u4e2a\u4efb\u52a1\u53ef\u4ee5\u5212\u5206\u4e3a\u4e24\u4e2a\u90e8\u5206\uff0c\u7b2c\u4e00\u90e8\u5206\u662f\u5bfb\u8def\u81f3\u76ee\u6807\uff0c\u8981\u6c42\u4ee3\u7406\u4eba\u80fd\u591f\u81ea\u7136\u89c4\u907f\u969c\u788d\u5e76\u627e\u5230\u76ee\u6807\u5e76\u4e14\u6700\u7ec8\u9762\u671d\u76ee\u6807\uff0c\u8fd9\u4e00\u90e8\u5206\u4e3b\u8981\u7684\u96be\u70b9\u5c31\u662f\u9700\u8981\u80fd\u591f\u5bf9\u73af\u5883\u8fdb\u884c\u611f\u77e5\uff0c\u4e3a\u6b64 NSM \u56e2\u961f\u9009\u62e9\u4e86\u4f53\u7d20\u8868\u8fbe\uff0c\u5e76\u8bbe\u8ba1\u4e86\u73af\u5883\u4f53\u7d20\u4f20\u611f\u5668\u2014\u2014\u5176\u8303\u56f4\u8986\u76d6\u4ee5\u4ee3\u7406\u4eba\u4e3a\u4e2d\u5fc3\u7684\u4e00\u4e2a\u5706\u67f1\u5f62\u533a\u57df\uff0c\u533a\u57df\u5185\u7684\u6240\u6709\u5177\u6709\u4f53\u7d20\u7684\u7269\u4f53\u90fd\u4f1a\u88ab\u7403\u5f62\u91c7\u6837\u4e3a\u4e00\u4e2a 0~1 \u548c\u4e4b\u95f4\u7684\u503c\uff0c\u5982\u8bba\u6587\u4e2d Fig5\u3002\u800c\u8fd9\u4e9b\u503c\u88ab\u79f0\u4e3a\u73af\u5883\u8f93\u5165\uff0c\u5728\u6a21\u578b\u7684 pipeline \u4e2d\u4f5c\u4e3a\u8f93\u5165\u3002\u73af\u5883\u8f93\u5165\u6709\u6548\u589e\u52a0\u4ee3\u7406\u4eba\u5bf9\u73af\u5883\u7684\u7406\u89e3\u80fd\u529b\uff0c\u6539\u5584\u4e86\u8bf8\u5982\u4e0e\u76ee\u6807\u4ea4\u4e92\u65f6\u4ece\u80cc\u540e\u7a7f\u900f\u6905\u5b50\u5750\u4e0b\u7684\u8fd9\u79cd\u95ee\u9898\uff0c\u5982 Fig14\u3002\u6b64\u5916\uff0cNSM \u56e2\u961f\u5b66\u4e60\u4e86 PFNN\uff0c\u4f7f\u7528 phase \u6765\u5b9e\u73b0\u72b6\u6001\u673a\uff0c\u4f46\u521b\u65b0\u6027\u7684\u4f7f\u7528\u4e86\u6807\u6ce8\u79bb\u6563\u7279\u5b9a\u76f8\u4f4d\uff08\u5982\u884c\u8d70\u65f6\u5de6\u811a\u843d\u5730\u88ab\u6807\u6ce8\u4e3a \\(2k\\pi\\)\uff0c\u53f3\u811a\u843d\u5730\u88ab\u6807\u6ce8\u4e3a \\((2k+1)\\pi\\)\uff0c\u800c\u4e2d\u95f4\u8fc7\u7a0b\u901a\u8fc7\u63d2\u503c\u8ba1\u7b97\uff09\uff0c\u901a\u8fc7\u7f51\u7edc\u5b66\u4e60\u63d2\u503c\u76f8\u4f4d\u7684\u5f62\u5f0f\uff0c\u89e3\u51b3\u4e86 PFNN \u4e2d\u5148\u9a8c\u76f8\u4f4d\u5e26\u6765\u7684\uff0c\u4ee3\u7406\u4eba\u8d8b\u5411\u4e8e\u4e0d\u884c\u52a8\u7684\u7f3a\u70b9\u3002\u800c\u5728\u5bfb\u627e\u76ee\u6807\u65f6\uff0c\u4f20\u7edf\u7684\u5355\u5411\u8868\u8fbe\u5bb9\u6613\u4ea7\u751f\u8bef\u5dee\u7d2f\u8ba1\uff0c\u5bfc\u81f4\u6700\u7ec8\u76ee\u6807\u5b9a\u4f4d\u504f\u79fb\uff0cNSM \u56e2\u961f\u4f7f\u7528\u76ee\u6807\u4e2d\u5fc3\u3001\u81ea\u6211\u4e2d\u5fc3\u53cc\u5411\u8868\u8fbe\uff0c\u663e\u8457\u6539\u5584\u4e86\u8be5\u95ee\u9898\uff0c\u5b9e\u9a8c\u6548\u679c\u5982 Fig11 \u4e0a\u56fe\u3002</p> <p>\u7b2c\u4e8c\u90e8\u5206\u9700\u8981\u4ee3\u7406\u4eba\u80fd\u591f\u81ea\u7136\u7684\u548c\u76ee\u6807\u8fdb\u884c\u4ea4\u4e92\uff0c\u5982\u5728\u6905\u5b50\u4e0a\u5750\u4e0b\u3001\u6253\u5f00\u95e8\u3001\u7a7f\u8fc7\u5899\u4e0a\u7684\u6d1e\u3002\u8fd9\u9700\u8981\u4ee3\u7406\u4eba\u5bf9\u4ea4\u4e92\u76ee\u6807\u5177\u6709\u7cbe\u786e\u7684\u611f\u77e5\uff0c\u4e0e\u73af\u5883\u4f53\u7d20\u4f20\u611f\u5668\u7c7b\u4f3c\uff0cNSM \u4e5f\u63d0\u51fa\u4e86\u4ea4\u4e92\u4f53\u7d20\u4f20\u611f\u5668\uff0c\u4e3a\u4e86\u63d0\u9ad8\u7cbe\u5ea6\uff0c\u4f53\u7d20\u4f20\u611f\u5668\u4ee5 8x8x8 \u7684\u4f53\u7d20\u4e3a\u5355\u4f4d\uff0c\u540c\u6837\u91c7\u6837\u4e3a 0~1 \u4e4b\u95f4\u7684\u503c\uff0c\u88ab\u4f5c\u4e3a\u6a21\u578b\u7684\u4e00\u90e8\u5206\u8f93\u5165\u3002</p> <p>\u6574\u4f53\u6a21\u578b\u4f7f\u7528\u4e86 MoE \u6280\u672f\uff0c\u5373\u591a\u4e13\u5bb6\u6a21\u578b\uff0c\u901a\u8fc7 Gating Networks \u6765\u8ba1\u7b97\u5176\u6df7\u5408\u6743\u91cd\uff0c\u5176\u8f93\u5165\u4e3b\u8981\u4e3a\u5f53\u524d\u7684\u52a8\u4f5c\u6807\u7b7e\u548c\u4e8c\u7ef4\u76f8\u4f4d\uff08\u4ee5\u89e3\u51b3\u4e00\u7ef4\u76f8\u4f4d\u5e26\u6765\u7684\u4e0d\u53ef\u5fae\u7684\u95ee\u9898\uff09\u3002\u6a21\u578b\u9884\u6d4b\u7f51\u7edc\u5206\u4e3a\u7f16\u7801\u6a21\u5757\u548c\u9884\u6d4b\u6a21\u5757\u4e24\u90e8\u5206\uff0c\u6a21\u578b\u8f93\u5165\u5305\u542b\u56db\u4e2a\u90e8\u5206\uff1a\u5173\u4e8e\u4ee3\u7406\u4eba\u7684\u5f53\u524d\u5e27\uff08\u548c\u7a97\u53e3\u5185\u9644\u8fd1\u5e27\uff09\u7684\u4fe1\u606f\u3001\u76ee\u6807\u4fe1\u606f\uff08\u4f4d\u7f6e\u3001\u671d\u5411\u3001\u4ea4\u4e92\u52a8\u4f5c\u6807\u7b7e\uff09\u4ee5\u53ca\u5148\u524d\u63d0\u5230\u7684\u73af\u5883\u8f93\u5165\u548c\u4ea4\u4e92\u8f93\u5165\u3002\u5c06\u8f93\u51fa\u9884\u6d4b\u540e\u7684\u4ee3\u7406\u4eba\u52a8\u4f5c\u4fe1\u606f\u3001\u884c\u52a8\u8f68\u8ff9\u4fe1\u606f\u3001\u76f8\u4f4d\u4fe1\u606f\u3001\u4ea4\u4e92\u63a5\u89e6\u70b9\u4fe1\u606f\u7b49\u3002\u800c\u8fd9\u6837\u7684\u8bbe\u8ba1\u7ed9\u4e86\u6a21\u578b\u826f\u597d\u7684\u5728\u4e24\u79cd\u7528\u6237\u64cd\u4f5c\u6a21\u5f0f\uff08\u624b\u52a8\u63a7\u5236\u79fb\u52a8\u65b9\u5411\u548c\u53ea\u6307\u5b9a\u4ea4\u4e92\u76ee\u6807\uff09\u4e4b\u95f4\u5207\u6362\u7684\u80fd\u529b\uff0c\u53ea\u9700\u8981\u6539\u53d8\u76ee\u6807\u8f93\u5165\u7684\u5b9a\u4e49\u5373\u53ef\u65e0\u7f1d\u8854\u63a5\u3002</p>"},{"location":"pape_read/NSM/#\u5b9e\u9a8c\u6548\u679c\u4e0e\u548c\u76f8\u5173\u5de5\u4f5c\u7684\u5bf9\u6bd4","title":"\u5b9e\u9a8c\u6548\u679c\u4e0e\u548c\u76f8\u5173\u5de5\u4f5c\u7684\u5bf9\u6bd4","text":"<p>\u8fd9\u79cd\u8bbe\u8ba1\u901a\u8fc7\u4e86\u5b9e\u9a8c\u9a8c\u8bc1\uff0c\u5728 NSM \u56e2\u961f\u8bbe\u8ba1\u7684\u4e00\u79cd\u7279\u6b8a\u60c5\u51b5\u4e0b\u8868\u73b0\u826f\u597d\u2014\u2014\u5750\u4e0a\u4e00\u5f20\u534a\u63d2\u8fdb\u684c\u5b50\u7684\u6905\u5b50\u3002\u5e76\u4e14\u5728\u4e0e\u5176\u4ed6\u6a21\u578b\u7684\u5bf9\u6bd4\u4e2d\uff0c\u5728\u54cd\u5e94\u65f6\u95f4\u3001\u6ed1\u6b65\uff08\u4e0d\u81ea\u7136\u7684\u8d70\u52a8\uff09\u8868\u73b0\u3001\u4f4d\u7f6e\u7cbe\u5ea6\u3001\u65cb\u8f6c\u7cbe\u5ea6\u7b49\u65b9\u9762\u603b\u4f53\u8868\u73b0\u826f\u597d\uff0c\u51e0\u4e4e\u5b8c\u5168\u8d85\u8fc7\u4e86\u4ee5\u5f80\u7684\u540c\u7c7b\u5de5\u4f5c\uff0c\u6587\u7ae0\u4e5f\u5bf9\u8868\u73b0\u826f\u597d\u7684\u539f\u56e0\u8fdb\u884c\u4e86\u4e00\u4e9b\u5206\u6790\u3002</p> <p>LSTM \u6a21\u578b\u901a\u8fc7\u751f\u6210\u5927\u91cf\u77ed\u7247\u6bb5\u7684\u52a8\u4f5c\u6765\u589e\u5f3a\u6570\u636e\uff0c\u800c\u5b9e\u9645\u4e5f\u662f\u901a\u8fc7\u5c06\u8fc7\u7a0b\u4ece\u8fd9\u4e9b\u7247\u6bb5\u4e2d\u5b66\u4e60\u7684\u5185\u5bb9\u8fdb\u884c\u7ec4\u5408\u5b9e\u73b0\uff0c\u56e0\u6b64\u6269\u5c55\u6027\u8f83\u5dee\uff0c\u4e0d\u9002\u5408\u8fd0\u52a8\u6570\u636e\u4e0d\u591f\u5145\u5206\u7684\u60c5\u51b5\u3002</p> <p>\u800c\u4e0e PFNN \u76f8\u6bd4\uff0cNSM \u9650\u5236\u66f4\u5c11\uff0c\u56e0\u4e3a PFNN \u7684\u5148\u9a8c\u7684\u5916\u90e8 phase \u63a7\u5236\u673a\u5236\u8ba9\u5b83\u65e0\u6cd5\u5f88\u597d\u7684\u89e3\u51b3\u5bf9\u975e\u5468\u671f\u6027\u52a8\u4f5c\u751f\u6210\u3002</p> <p>\u800c MANN \u867d\u7136\u76f8\u5e94\u901f\u5ea6\u5feb\uff0c\u4f46\u5b58\u5728\u66f4\u660e\u663e\u7684\u6ed1\u6b65\u73b0\u8c61\uff0c\u5e76\u4e14\u5728\u63a7\u5236\u6a21\u5f0f\u53d8\u5316\u7684\u65f6\u5019\u52a8\u4f5c\u5341\u5206\u50f5\u786c\uff0c\u800c\u6b63\u662f\u56e0\u4e3a\u52a8\u4f5c\u50f5\u786c\u800c\u4ee3\u7406\u4eba\u7684\u6839\u90e8\u79fb\u52a8\u4ecd\u7136\u5b58\u5728\uff0c\u624d\u51fa\u73b0\u4e86\u66f4\u660e\u663e\u7684\u6ed1\u6b65\u73b0\u8c61\u3002</p>"},{"location":"pape_read/NSM/#\u6570\u636e\u589e\u5f3a","title":"\u6570\u636e\u589e\u5f3a","text":"<p>\u6b64\u5916\uff0c\u4e3a\u4e86\u589e\u5f3a\u6a21\u578b\u7684\u53ef\u6269\u5c55\u6027\u548c\u9002\u5e94\u6027\uff0cNSM \u56e2\u961f\u4e5f\u63d0\u51fa\u4e86\u4e00\u79cd\u65b0\u7684\u6570\u636e\u589e\u5f3a\u65b9\u6848\u3002\u6784\u5efa\u573a\u666f\u540e\u91c7\u96c6\u4e00\u7cfb\u5217\u573a\u666f\u4ea4\u4e92\u52a8\u4f5c\uff0c\u5e76\u901a\u8fc7\u955c\u50cf\u6765\u589e\u52a0\u6570\u636e\u4f53\u91cf\uff0c\u4eba\u5de5\u6807\u8bb0\u52a8\u4f5c\u6807\u7b7e\u548c\u76f8\u4f4d\u6807\u7b7e\u3002\u63a5\u4e0b\u6765\u901a\u8fc7\u6570\u636e\u589e\u5f3a\u7cfb\u7edf\u6765\u589e\u5f3a\u6570\u636e\u3002</p> <p>\u5177\u4f53\u6765\u8bf4\uff0c\u5c31\u662f\u4f7f\u7528 ShapeNet \u6570\u636e\u96c6\u4e2d\u7b26\u5408\u6a21\u578b\u7684\u7269\u4f53\u4e0d\u65ad\u66ff\u6362\u8bad\u7ec3\u7269\u4f53\uff0c\u5e76\u8fdb\u884c\u53d8\u6362\uff0c\u540c\u65f6\u8981\u6ce8\u610f\u66f4\u65b0\u63a5\u89e6\u70b9\u548c\u4ea4\u4e92\u65b9\u5411\u7b49\u3002\u4ee5\u6b64\u5728\u8bad\u7ec3\u8fc7\u7a0b\u4e2d\u63d0\u9ad8\u6a21\u578b\u8303\u7528\u6027\u3002</p>"},{"location":"pape_read/NeRF/","title":"[NeRF] Representing Scenes as Neural Radiance Fields for View Synthesis","text":"<p> \u7ea6 1701 \u4e2a\u5b57  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 6 \u5206\u949f</p> <p><code>3DV</code> <code>Reconstruction</code></p> <p>\u6587\u7ae0\u4fe1\u606f</p> <ul> <li>\u6587\u7ae0\u9898\u76ee\uff1aNeRF: Representing Scenes as Neural Radiance Fields for View Synthesis \uff08\u795e\u7ecf\u8f90\u5c04\u573a\uff09</li> <li>\u5206\u7c7b\uff1a<code>Computer Science</code> &gt; <code>Computer Vision and Pattern Recognition</code></li> <li>\u4f5c\u8005\uff1aBen Mildenhall, Pratul P. Srinivasan, Matthew Tancik, Jonathan T. Barron, Ravi Ramamoorthi, Ren Ng</li> <li>\u9879\u76ee\u4e3b\u9875\uff1a\ud83d\udd17</li> <li>arXiv\uff1a\ud83d\udd17 2003.08934</li> <li>\u4ee3\u7801\uff1a\ud83d\udd17</li> </ul>"},{"location":"pape_read/NeRF/#\u8bba\u6587\u7b14\u8bb0","title":"\u8bba\u6587\u7b14\u8bb0","text":""},{"location":"pape_read/NeRF/#\u8d21\u732e","title":"\u8d21\u732e","text":"<ol> <li>\u5c06\u590d\u6742\u96c6\u5408\u5f62\u72b6\u548c\u6750\u8d28\u7684\u8fde\u7eed\u573a\u666f\u8868\u8fbe\u4e3a 5D \u795e\u7ecf\u8f90\u5c04\u573a\u7684\u65b9\u6cd5\uff0c\u5c06\u5176\u53c2\u6570\u5316\u4e3a\u57fa\u672c\u7684 MLP \u7f51\u7edc\uff1b</li> <li>\u57fa\u4e8e\u7ecf\u5178\u4f53\u79ef\u6e32\u67d3\u6280\u672f\u7684\u53ef\u5fae\u5206\u6e32\u67d3\u7a0b\u5e8f\uff0c\u6211\u4eec\u7528\u5b83\u4ece\u6807\u51c6 RGB \u56fe\u50cf\u4e2d\u4f18\u5316\u8fd9\u4e9b\u8868\u793a\u3002\u8fd9\u5305\u62ec\u4e00\u79cd\u5206\u5c42\u91c7\u6837\u7b56\u7565\uff0c\u5c06 MLP \u7684\u5bb9\u91cf\u5206\u914d\u7ed9\u5177\u6709\u53ef\u89c1\u573a\u666f\u5185\u5bb9\u7684\u7a7a\u95f4\uff1b</li> <li>\u4f7f\u7528\u4f4d\u7f6e\u7f16\u7801(positional encoding)\uff0c\u5c06 5D \u5ea7\u6807\u6620\u5c04\u5230\u66f4\u9ad8\u7ef4\u7684\u7a7a\u95f4\uff0c\u4ee5\u5b9e\u73b0\u66f4\u9ad8\u9891\u7387\u7684\u573a\u666f\u5185\u5bb9\u7684\u8868\u793a\uff1b</li> </ol> <p>\u63d0\u51fa\u7684\u8868\u793a\u65b9\u6cd5\u6709\u5982\u4e0b\u597d\u5904\uff1a</p> <ul> <li>\u53ef\u4ee5\u8868\u8fbe\u590d\u6742\u771f\u5b9e\u7684\u51e0\u4f55\u5f62\u72b6</li> <li>\u9002\u5408\u4f7f\u7528\u6295\u5f71\u56fe\u50cf\u505a\u68af\u5ea6\u4f18\u5316<ul> <li> \u95ee\u9898\uff1a\u4ec0\u4e48\u610f\u601d\uff1f</li> </ul> </li> <li>\u964d\u4f4e\u4e86\u9ad8\u5206\u8fa8\u7387\u7a7a\u95f4\u56fe\u50cf\u7684\u5b58\u50a8\u6210\u672c</li> </ul>"},{"location":"pape_read/NeRF/#\u65b9\u6cd5","title":"\u65b9\u6cd5","text":"<p>\u4f7f\u7528\u5982\u4e0b\u4e00\u4e2a\u201c\u51fd\u6570\u201d\u6765\u8868\u793a\u4e00\u4e2a\u9759\u6001\u573a\u666f\uff1a</p> \\[ \\begin{aligned}     &amp; F_{\\Theta}:(\\mathrm{x}, \\mathrm{d}) \\rightarrow (\\mathrm{c}, \\sigma)     \\\\     &amp; \\text{where } \\mathrm{x} = (x,y,z), \\; \\mathrm{d} \\text{ is a 3D Cartesian unit vector}, \\; \\mathrm{c} = (r,g,b), \\; \\sigma \\text{ is the density}. \\end{aligned}  \\] <ul> <li>\u5168\u662f FC\uff1b</li> <li>\u8f93\u5165\u662f 5D \u5ea7\u6807\u2014\u2014\u70b9\u7684\u7a7a\u95f4\u5ea7\u6807 \\((x,y,z)\\) \u548c\u89c6\u89d2\u65b9\u5411 \\((\\theta, \\phi)\\)\uff1b</li> <li>\u8f93\u51fa\u662f\u4f53\u79ef\u5bc6\u5ea6\u4ee5\u53ca\u5bf9\u5e94\u7a7a\u95f4\u4f4d\u7f6e\u7684\u4e0e\u89c6\u89d2\u6709\u5173\u7684\u8f90\u5c04\uff08\u6216\u8005\u8bf4\u89c6\u89d2\u6709\u5173\u7684 RGB \u989c\u8272\uff09\uff1b</li> </ul> <p>\u4e3a\u4e86\u4fdd\u8bc1\u591a\u89c6\u89d2\u4e0b\u89c2\u5bdf\u5230\u7684\u5185\u5bb9\u5177\u6709\u4e00\u81f4\u6027\uff0c\u505a\u5982\u4e0b\u7ea6\u675f\uff1a</p> <ul> <li>\u5173\u4e8e\u5bc6\u5ea6 \\(\\sigma\\) \u7684\u51fd\u6570\uff0c\u4ec5\u4e0e\u70b9\u7684\u7a7a\u95f4\u4f4d\u7f6e \\(\\mathrm{x} = (x,y,z)\\) \u6709\u5173\uff0c\u800c\u4e0e\u89c6\u89d2\u65e0\u5173\uff1b</li> <li>\u5173\u4e8e\u989c\u8272 \\(\\mathrm{c}\\) \u7684\u51fd\u6570\uff0c\u4e0e\u70b9\u7684\u7a7a\u95f4\u4f4d\u7f6e \\(\\mathrm{x} = (x,y,z)\\) \u548c\u89c2\u5bdf\u65b9\u5411 \\(\\mathrm{d}\\) \u540c\u65f6\u6709\u5173\uff1b<ul> <li>\u8fd9\u5927\u6982\u4e0e NeRF \u5728\u4e0d\u540c\u89c6\u89d2\u4e0a\u5149\u5f71\u8868\u73b0\u7684\u826f\u597d\u4e5f\u6709\u8f83\u5927\u5173\u7cfb\uff1b</li> </ul> </li> <li>\u5b9e\u73b0\u4e0a\u662f\u5148\u901a\u8fc7 MLP \u7528 \\(\\mathrm{x}\\) \u8bad\u7ec3\u51fa \\(\\sigma\\) \u548c\u4e00\u4e2a\u4e2d\u95f4\u7279\u5f81\u5411\u91cf\uff0c\u518d\u5c06\u8fd9\u4e2a\u4e2d\u95f4\u5411\u91cf\u4e0e \\(\\mathrm{d}\\) \u62fc\u63a5\uff0c\u7ee7\u7eed\u653e\u5230 MLP \u4e2d\uff1b</li> </ul> <p>\u5229\u7528\u5982\u4e0a\u201c\u51fd\u6570\u201d\uff0c\u5177\u4f53\u6765\u8bf4\u64cd\u4f5c\u5982\u4e0b\uff1a</p> <ul> <li>\u5728\u573a\u666f\u4e2d\u5339\u914d\u7a7f\u8fc7\u7684\u76f8\u673a\u5149\u7ebf\u4ee5\u751f\u6210\u91c7\u6837\u7684 3D \u70b9\u96c6\u5408\uff1b</li> <li>\u4f7f\u7528\u8fd9\u4e9b\u70b9\u4ee5\u53ca\u5bf9\u5e94\u7684 2D \u89c6\u89d2\u65b9\u5411\u8f93\u5165\u5230\u7f51\u7edc\u4e2d\uff0c\u4ee5\u5f97\u5230\u989c\u8272\u548c\u5bc6\u5ea6\u96c6\u5408\uff1b</li> <li>\u4f7f\u7528\u4f20\u7edf\u7684\u4f53\u79ef\u6e32\u67d3\u6280\u672f\u7d2f\u79ef\u8fd9\u4e9b\u989c\u8272\u548c\u5bc6\u5ea6\u4ee5\u5f97\u5230 2D \u56fe\u50cf\uff1b</li> </ul> <p>\u4e3a\u4e86\u80fd\u591f\u8ba9 MLP \u8868\u793a\u66f4\u9ad8\u9891\u7387\u7684\u51fd\u6570\uff0c\u5f15\u5165\u4e86\u4f4d\u7f6e\u7f16\u7801(positional encoding)\u3002</p> <p>\u6b64\u5916\uff0c\u5173\u4e8e\u6e32\u67d3\uff0c\u4f7f\u7528\u7684\u662f\u4f20\u7edf\u7684\u4f53\u79ef\u6e32\u67d3\u65b9\u6cd5\uff0c\u7d2f\u79ef\u4e00\u6761\u5149\u7ebf\u4e0a\u7684\u989c\u8272\u548c\u5bc6\u5ea6\uff0c\u5f97\u5230\u6700\u7ec8\u7684\u989c\u8272\uff0c\u6240\u4f7f\u7528\u7684\u516c\u5f0f\u5982\u4e0b\uff1a</p> \\[ \\begin{aligned}     &amp; \\mathrm{C}(\\mathrm{r})=     \\int_{t_n}^{t_f}      T(t) \\cdot \\sigma\\left(         \\mathrm{r}(t)      \\right)  \\cdot \\mathrm{c} \\left(         \\mathrm{r}(t), \\mathrm{d}     \\right) \\cdot \\mathrm{d}t \\end{aligned},\\;\\; \\text{where } T(t) = \\exp\\left(     -\\int_{t_n}^t \\sigma\\left(\\mathrm{r}(s)\\right) \\; \\mathrm{d}s \\right) \\] <p>\u5bf9\u8fd9\u4e2a\u5f0f\u5b50\u7a0d\u4f5c\u89e3\u91ca\uff0c\\(t_n\\) \u548c \\(t_f\\) \u5206\u522b\u8868\u793a near \u548c far \u7684\u5149\u7ebf\u8fb9\u754c(bound)\uff0c\u5149\u7ebf\u7ed3\u679c \\(C(\\mathrm{r})\\) \u901a\u8fc7\u7d2f\u79ef\u8fd9\u4e24\u4e2a\u7aef\u70b9\u4e4b\u95f4\u7684\u6309\u6743\u7d2f\u79ef\u5f97\u5230\uff0c\u5176\u6743\u91cd\u4e3a \\(T(t)\\)\uff0c\u89c2\u5bdf\u5176\u5b9a\u4e49\u5f0f\u53ef\u53d1\u73b0\uff0c\u968f\u7740 \\(t\\) \u7684\u589e\u5927\uff0c\\(T(t) \\rightarrow 0\\)\uff0c\u5373\u7ea6\u5f80\u540e\u7684\u70b9\u7ea6\u4e0d\u5bb9\u6613\u88ab\u770b\u5230\uff0c\u8fd9\u4e5f\u662f\u7b26\u5408\u5e38\u8bc6\u7684\u3002\u800c\u7d2f\u79ef\u7684\u5bf9\u8c61\u4e3a \\(\\sigma(\\mathrm{r}(t)) \\cdot \\mathrm{c}(\\mathrm{r}(t), \\mathrm{d})\\)\uff0c\u5373\u5bc6\u5ea6\u548c\u989c\u8272\u7684\u4e58\u79ef\uff0c\u6ce8\u610f\u4e24\u4e2a\u53c2\u6570\u2014\u2014\u5bc6\u5ea6\u8868\u5f81\u5f62\u72b6\u7279\u5f81\uff0c\u4ec5\u4e0e\u7a7a\u95f4\u4f4d\u7f6e\u6709\u5173\uff1b\u800c\u989c\u8272\u540c\u65f6\u4e0e\u89c2\u5bdf\u89d2\u5ea6\u6709\u5173\uff0c\u8fd9\u6697\u542b\u7740\u5149\u5f71\u4fe1\u606f\u3002</p> <p>\u7136\u800c\uff0c\u7531\u4e8e\u79ef\u5206\u7684\u64cd\u4f5c\u6027\u5dee\uff0c\u6240\u4ee5\u4f7f\u7528\u4e00\u79cd\u79bb\u6563\u7684\u62bd\u6837\u7d2f\u79ef\u6765\u5b9e\u73b0\u8fd9\u4ef6\u4e8b\uff0c\u5c06\u5149\u7ebf\u5747\u5300\u5212\u5206\u4e3a \\(N\\) \u4e2a\u533a\u95f4\uff0c\u6309\u5747\u5300\u5206\u5e03\u5728\u6bcf\u4e2a\u70b9\u91c7\u6837\u4e00\u4e2a\u70b9\uff0c\u8fdb\u884c\u7d2f\u79ef\uff0c\u5373\u5bf9\u4e8e\u533a\u95f4 \\(t_i\\)\uff1a</p> \\[ t_i \\sim U \\left[      t_n + \\frac{i-1}{N} \\left( t_f - t_n \\right),      t_n + \\frac{i}{N} \\left( t_f - t_n \\right) \\right] \\] <p>\u5bf9\u5e94\u7684\u989c\u8272\u8ba1\u7b97\u516c\u5f0f\u6539\u5199\u4e3a\uff1a</p> \\[ \\begin{aligned} \\hat{C}(\\mathrm{r}) = \\sum_{i=1}^{N} T_i \\cdot (1 - \\exp(-\\sigma_i \\delta_i)) \\cdot \\mathrm{c}_i, \\;\\; \\text{where } T_i = \\exp\\left(     -\\sum_{j=1}^{i-1} \\sigma_j \\delta_j \\right) \\text{ and } \\delta_i = t_{i+1} - t_i \\end{aligned} \\] <p>\u5176\u4e2d\uff0c\\(\\sigma(\\mathrm{r}(t))\\) \u522b\u66ff\u6362\u4e3a \\((1-\\exp(-\\sigma_i\\delta_i))\\)\uff0c\u5728\u7ed3\u5408\u4e86\u533a\u95f4\u957f\u5ea6\u7684\u60c5\u51b5\u4e0b\u53c8\u91cd\u65b0\u5c06\u5bc6\u5ea6\u6620\u5c04\u56de\u4e86 \\([0,1]\\)\u3002</p> <p>\u5728\u4e4b\u540e\u7684\u7b56\u7565\u4e2d\uff0c\u8fd8\u4f1a\u5bf9\u91c7\u6837\u89c4\u5219\u505a\u8fdb\u4e00\u6b65\u4f18\u5316\u3002</p> <p>\u81f3\u6b64\u4e3a\u6b62\u662f NeRF \u4e3b\u8981\u7684\u65b9\u6cd5\uff0c\u4f46\u662f\u8fd9\u4e9b\u65b9\u6cd5\u4ecd\u7136\u4e0d\u8db3\u4ee5\u8ba9\u5b83\u8fbe\u5230\u6700\u5148\u8fdb\u7684\u6548\u679c\uff0c\u56e0\u6b64\u8fd9\u91cc\u5f15\u5165\u4e24\u4e2a\u6539\u8fdb\u63aa\u65bd\u3002</p> <ol> <li>\u4f7f\u7528\u4f4d\u7f6e\u7f16\u7801(positional encoding)\u6765\u4f7f MLP \u80fd\u591f\u652f\u6301\u66f4\u9ad8\u9891\u7684\u56fe\u50cf\u4fe1\u606f\uff1b</li> <li>\u4f7f\u7528\u7ed3\u6784\u5316\u7684\u91c7\u6837(hierarchical sampling)\u4f7f\u80fd\u591f\u66f4\u6709\u6548\u5730\u5bf9\u8fd9\u79cd\u9ad8\u9891\u8868\u793a\u8fdb\u884c\u91c7\u6837\uff1b</li> </ol> <p>\u4f4d\u7f6e\u7f16\u7801\u4e3a\u4e00\u4e2a \\(\\gamma : \\R \\rightarrow \\R^{2L}\\)\uff1a</p> \\[ \\gamma(p) = \\left( \\sin(2^0 \\pi p), \\cos(2^0 \\pi p), \\cdots, \\sin(2^{L-1} \\pi p), \\cos(2^{L-1} \\pi p) \\right) \\] <p>\u5c06 \\(\\gamma(\\cdot)\\) \u5e94\u7528\u4e8e \\(\\mathrm{x}\\) \u7684\u4e09\u4e2a\u5206\u91cf\uff08\u88ab\u6807\u51c6\u5316\u5230 \\([-1,1]\\) \u4e0a\uff09\u548c \\(\\mathrm{d}\\) \u7684\u4e24\u4e2a\u5206\u91cf\u4e0a\uff0c\u5b9e\u73b0\u7ef4\u5ea6\u63d0\u5347\uff0c\u4ee5\u6b64\u4f18\u5316\u5728\u9ad8\u9891\u5185\u5bb9\u4e0a\u7684\u8868\u73b0\u3002\u5728\u6587\u7ae0\u4e2d\u63d0\u5230\uff0c\\(L_\\mathrm{x} = 10, L_\\mathrm{d} = 4\\)\u3002</p> <p>\u800c\u5206\u5c42\u91c7\u6837\uff0c\u9488\u5bf9\u7684\u662f\u4e4b\u524d\u7684\u5747\u5300\u5212\u5206\u4e3a \\(N\\) \u4e2a\u533a\u95f4\u8fdb\u884c\u5747\u5300\u91c7\u6837\u3002\u663e\u7136\uff0c\u67d0\u4e9b\u201c\u7a7a\u6c14\u201d\u533a\u57df\u548c\u88ab\u906e\u6321\u7684\u533a\u57df\u5bf9\u6e32\u67d3\u7ed3\u679c\u5e76\u4e0d\u4f1a\u6709\u5f88\u5927\u5f71\u54cd\uff0c\u800c\u5728\u7a7a\u95f4\u4e0a\u8fd9\u4e9b\u5185\u5bb9\u53ef\u80fd\u5360\u4e86\u7edd\u5927\u90e8\u5206\uff08\u5c24\u5176\u662f\u6ca1\u6709\u534a\u900f\u660e\u7269\u4f53\u7684\u60c5\u51b5\u4e0b\uff09\uff0c\u5747\u5300\u91c7\u6837\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\u5c31\u663e\u5f97\u975e\u5e38\u4f4e\u6548\u3002</p> <p>\u5206\u5c42\u91c7\u6837\u7684\u5927\u81f4\u601d\u8def\u662f\uff0c\u9996\u5148\u4f7f\u7528\u4e00\u4e2a\u7c97\u7565(coarse)\u7684\u7f51\u7edc\uff0c\u5229\u7528 \\(N_c\\) \u4e2a\u7c97\u7565(coarse)\u7684\u5747\u5300\u91c7\u6837\u70b9\uff0c\u901a\u8fc7\u8ba1\u7b97 \\(\\hat{w}_i = normalize\\left( T_i \\cdot (1 - \\exp(-\\sigma_i \\delta_i)) \\right)\\) \u5f97\u5230\u6bcf\u4e2a\u70b9\u7684\u6743\u91cd\uff0c\u800c\u8fd9\u4e2a\u6743\u91cd\u5219\u53cd\u5e94\u4e86\u6bcf\u4e00\u4e2a\u91c7\u6837\u70b9\u9644\u8fd1\u6709\u6548\u70b9\u7684\u5206\u5e03\u60c5\u51b5\uff0c\u53ef\u4ee5\u770b\u4f5c\u4e00\u4e2a\u6982\u7387\u5bc6\u5ea6\u51fd\u6570(PDF)\u3002\u63a5\u4e0b\u6765\u6211\u4eec\u5728\u8fd9\u4e2a\u5206\u5e03\u7684\u57fa\u7840\u4e0a\u518d\u91c7\u6837\u5f97\u5230 \\(N_f\\) \u4e2a\u7cbe\u7ec6(fine)\u91c7\u6837\u70b9\uff0c\u4e0e \\(N_c\\) \u4e2a\u7c97\u7565(coarse)\u70b9\u4e00\u8d77\u653e\u5230\u7cbe\u7ec6(fine)\u7f51\u7edc\u4e2d\u8fdb\u884c\u8bad\u7ec3\u3002</p> <p>\u4f7f\u7528\u7684 loss \u5982\u4e0b\uff1a</p> \\[ \\mathcal{L} = \\sum_\\mathrm{r\\in \\text{Rays}} \\left[ \\left\\| \\hat{C}_c(\\mathrm{r}) - C_{g.t.}(\\mathrm{r}) \\right\\|_2^2 + \\left\\| \\hat{C}_f(\\mathrm{r}) - C_{g.t.}(\\mathrm{r}) \\right\\|_2^2 \\right] \\] \u53c2\u8003\u8d44\u6599 <ul> <li>https://zhuanlan.zhihu.com/p/360365941 \uff08\u7b14\u8bb0 \u5173\u4e8e\u4f53\u79ef\u6e32\u67d3\u8bb2\u5f97\u5f88\u6e05\u6670\uff09</li> <li>https://zhuanlan.zhihu.com/p/380015071 \uff08\u7b14\u8bb0\uff09</li> <li>https://wandb.ai/wandb_fc/chinese/reports/NeRF-Neural-Radiance-Fields-View-Synthesis---VmlldzozNDQxNzk \uff08\u4fa7\u91cd\u5982\u4f55\u4f7f\u7528\uff09</li> <li>https://www.youtube.com/watch?v=nCpGStnayHk\uff08\u4e0a\u9762\u90a3\u7bc7\u6587\u7ae0\u7684\u4ecb\u7ecd\u89c6\u9891\uff09</li> <li>https://blog.csdn.net/qq_43620967/article/details/124467551 \uff08\u7ffb\u8bd1\uff09</li> <li>https://blog.csdn.net/weixin_44292547/article/details/126042398 \uff08\u7ffb\u8bd1\uff09</li> <li>https://blog.csdn.net/weixin_44580210/article/details/122284120 \uff08\u7b14\u8bb0\uff09</li> </ul> <p>\u793e\u533a Pytorch \u590d\u73b0\u4ee3\u7801\u7684\u6ce8\u91ca\uff1ahttps://github.com/IsshikiHugh/nerf-pytorch</p>"},{"location":"pape_read/SA-MHR/","title":"[SA-HMR] Learning Human Mesh Recovery in 3D Scenes","text":"<p> \u7ea6 1927 \u4e2a\u5b57  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 6 \u5206\u949f</p> <p><code>3DV</code> <code>HMR</code> <code>Scene-Aware</code></p> <p>\u6587\u7ae0\u4fe1\u606f</p> <ul> <li>\u6587\u7ae0\u9898\u76ee\uff1aLearning Human Mesh Recovery in 3D Scenes</li> <li>\u4f5c\u8005\uff1a     Zehong Shen,      Zhi Cen,      Sida Peng,      Qing Shuai,      Hujun Bao,      Xiaowei Zhou</li> <li>\u9879\u76ee\u4e3b\u9875\uff1a\ud83d\udd17</li> <li>\u8bba\u6587\uff1a\ud83d\udd17</li> <li>\u4ee3\u7801\uff1a\ud83d\udd17</li> </ul>"},{"location":"pape_read/SA-MHR/#\u7b14\u8bb0","title":"\u7b14\u8bb0","text":""},{"location":"pape_read/SA-MHR/#\u4efb\u52a1\u5b9a\u4e49","title":"\u4efb\u52a1\u5b9a\u4e49","text":"<ul> <li>SA-HMR = scene-aware human mesh recovery</li> <li>\u9884\u5148\u7ed9\u5b9a\u626b\u63cf\u597d\u7684\u573a\u666f\uff0c\u518d\u6839\u636e\u5355\u5f20\u7167\u7247\u4f30\u8ba1\u4eba\u7684\u7edd\u5bf9\u4f4d\u7f6e\u548c\u59ff\u52bf</li> </ul>"},{"location":"pape_read/SA-MHR/#\u4f18\u52bf\u4e0e\u8d21\u732e","title":"\u4f18\u52bf\u4e0e\u8d21\u732e","text":"<ul> <li>\u76f8\u6bd4\u4f20\u7edf\u7684\u901a\u8fc7\u4f18\u5316\u8fed\u4ee3\u7684\u751f\u6210\u529e\u6cd5\uff0c\u672c\u65b9\u6cd5\u5728\u63a8\u65ad\u8fc7\u7a0b\u4e2d\u66f4\u52a0\u8fc5\u901f\uff1b</li> <li> \u95ee\u9898\uff1a\u6700\u4f18\u5316\u4e2d\u7684 contact regions \u7684 chamfer distance \u7ea6\u675f\u662f\u4e3a\u4e86\u4ec0\u4e48\uff1f \u5c3d\u53ef\u80fd\u589e\u52a0\u4e00\u56e2\u7684\u805a\u5408\u6027\uff1f \u662f\u3002</li> </ul> <p>\u6982\u62ec\u8d21\u732e\uff1a</p> <ol> <li>\u975e\u4f18\u5316\u505a\u6cd5\u7684\uff0c\u573a\u666f\u611f\u77e5\u7684\u3001\u5355\u7167\u7247\u3001\u9884\u7ed9\u573a\u666f\u7684\u4eba\u4f53\u7f51\u683c\u6062\u590d\u6846\u67b6\uff1b</li> <li>\u9884\u8bad\u7ec3\u7684 HMR \u7f51\u7edc\u4e0e\u5e73\u884c\u7f51\u7edc\u7684\u673a\u9047 cross-attention \u7684\u5904\u7406\u8bbe\u8ba1\uff0c\u662f\u897f\u5b89\u4e86\u5bf9\u4eba\u4f53\u59ff\u52bf\u548c\u573a\u666f\u51e0\u4f55\u7279\u5f81\u7684\u8054\u5408\u5b66\u4e60\uff1b</li> <li>\u5728\u51c6\u786e\u5ea6\u548c\u901f\u5ea6\u4e0a\u90fd\u8584\u7eb1\u4f18\u5316\u505a\u6cd5\u7684\u57fa\u7ebf\uff1b</li> </ol>"},{"location":"pape_read/SA-MHR/#\u65b9\u6cd5","title":"\u65b9\u6cd5","text":"<ul> <li>\u4f30\u8ba1\u4eba\u4f53\u7684\u5168\u5c40\u4f4d\u7f6e(absolute human position)\u3001\u573a\u666f\u63a5\u89e6\u70b9(dense scene contacts)\u3001\u4ee5\u53ca\u4e00\u4e2a\u573a\u666f\u611f\u77e5\u7684\u4eba\u4f53\u7f51\u683c(scene aware human mesh)\uff1b</li> <li>\u51c6\u5907\u5de5\u4f5c\uff1a<ul> <li>\u4eba\u4f53<ul> <li>\u4f7f\u7528 SMPL \u6765\u8868\u793a\u4eba\u4f53\uff0c\u8ba1\u7b97\u7f51\u683c\u9876\u70b9 \\(V\\in\\mathrm{R}^{6890\\times 3}\\)\uff1b</li> <li>\u4f7f\u7528 H36M \u5173\u952e\u70b9\u56de\u5f52\u77e9\u9635(joint regression matrix) \\(M \\in \\mathrm{R}^{14\\times 6890}\\)\uff1b<ul> <li> \u95ee\u9898\uff1a\u8fd9\u662f\u4ec0\u4e48\uff1f \u4e00\u4e2a from smpl to h36m \u7684\u77e9\u9635\u3002</li> </ul> </li> <li>\u8ba1\u7b97 3D \u5173\u952e\u70b9 \\(J\\in \\mathrm{R}^{14\\times 3} = MV\\)\uff1b</li> </ul> </li> <li>\u573a\u666f<ul> <li>\u7528\u4e00\u4e2a bbox \u53bb\u6846\u9009\u76ee\u6807\u4eba\u4f53\uff1b</li> <li>\u8f6c\u5316\u4e3a\u7279\u5b9a\u5927\u5c0f\u7684\u56fe\u50cf \\(I \\in \\mathrm{R}^{224\\times 224\\times 3}\\)\uff1b</li> <li>\u6839\u636e\u7ed9\u5b9a\u7684\u56fe\u50cf\u533a\u57df\u548c\u76f8\u673a\u53c2\u6570\uff0c\u5f97\u5230\u5bf9\u5e94\u4e8e\u7a7a\u95f4\u4e2d\u7684\u4e00\u4e2a\u89c6\u9525\u4f53\u7a7a\u95f4\uff0c\u9009\u53d6\u8fd9\u90e8\u5206\u70b9\u4e91\u4f5c\u4e3a\u8f93\u5165\u7684\u70b9\u4e91 \\(S \\in \\mathrm{R}^{N_S \\times 3}\\)\uff1b</li> </ul> </li> <li>\u4eba\u4e0e\u573a\u666f\u7684\u63a5\u89e6<ul> <li>\u4f7f\u7528 7 \u4e2a\u6700\u5bb9\u6613\u6210\u4e3a\u63a5\u89e6\u70b9\u7684\u533a\u57df\u548c 1 \u4e2a\u8868\u793a\u4e0d\u63a5\u89e6\u7684\u533a\u57df\uff0c\u8fd9 8 \u4e2a\u6807\u7b7e\u5728\u70b9\u4e91\u4e2d\u505a\u5206\u5272\u4efb\u52a1\uff1b</li> </ul> </li> </ul> </li> <li>\u4eba\u4f53\u6839\u4f4d\u7f6e\u548c\u573a\u666f\u63a5\u89e6\u70b9\u7684\u4f30\u8ba1\uff1a<ul> <li>\u6982\u8ff0<ul> <li>\u9996\u5148\u4f7f\u7528\u4e00\u4e2a\u7a00\u758f 3D CNN \u6765\u4f30\u8ba1\u5bc6\u5ea6\u573a\u666f\u7684\u63a5\u89e6\u70b9\u2014\u2014\u70b9\u4e91\u6807\u7b7e\u4efb\u52a1(point cloud labeling task)\u548c\u7edd\u5bf9\u7684\u4eba\u4f53\u4f4d\u7f6e\u2014\u2014\u6295\u7968\u5411\u91cf\u573a\u4fee\u6b63\u4efb\u52a1(voting vector field refinement task)\uff0c\u6839\u636e\u5f97\u5230\u7684\u7ed3\u679c\uff0c\u4ee5\u7edd\u5bf9\u4f4d\u7f6e\u4e3a\u4e2d\u5fc3\u8868\u793a\u63a5\u89e6\u70b9\uff1b<ul> <li> \u95ee\u9898\uff1a\u4ec0\u4e48\u662f voting vector field refinement task\uff1f\u540e\u9762\u6709\u5199\u3002</li> </ul> </li> </ul> </li> <li>\u7c97\u4f30\u6839<ul> <li>\u4f7f\u7528\u4e00\u4e2a CNN \u5f97\u5230\u4e00\u4e2a\u70ed\u56fe\u548c\u5f52\u4e00\u5316\u7684\u6df1\u5ea6\u56fe\uff1b</li> <li>\u4ece\u70ed\u56fe\u4e2d\u80fd\u4f7f\u7528 <code>argmax</code> \u5f97\u5230\u521d\u59cb\u7684\u4eba\u4f53\u6839\u90e8\u5ea7\u6807 \\((x,y)\\)\uff0c\u4ece\u6df1\u5ea6\u56fe\u4e2d\u4f30\u8ba1\u51fa \\(\\tilde Z\\)\uff1b</li> <li>\u5229\u7528\u76f8\u673a\u5185\u53c2\u53ef\u4ee5\u8ba1\u7b97\u51fa 3D \u7a7a\u95f4\u4e2d\u7684\u5ea7\u6807 \\((X,Y,Z)\\)\uff1a<ul> <li>\\(Z = \\tilde{Z} \\frac{f}{w},\\quad X = \\frac{x - c_x}{f} \\cdot Z,\\quad Y = \\frac{y-c_y}{f}\\cdot Z\\)</li> </ul> </li> <li>\u4ece\u7ed3\u679c\u6765\u770b\uff0c\\((x, y)\\) \u7684\u4f30\u8ba1\u662f\u6bd4\u8f83\u51c6\u786e\u7684\uff0c\u4f46 \\(\\tilde{Z}\\) \u7684\u6548\u679c\u6bd4\u8f83\u5dee\uff1b</li> </ul> </li> <li>3D \u7279\u5f81\u6784\u9020<ul> <li>\u5728\u70b9\u4e91\u4e2d\u5bfb\u627e ROI\u2014\u2014\u4ee5 \\(r=(X,Y,Z)\\) \u4e3a\u4e2d\u5fc3\uff0c\\(\\gamma_1\\) \u4e3a\u534a\u5f84\u7684\u7403\u5f62\u533a\u57df\uff0c\u7531 \\(\\tilde{Z}\\) \u7684\u4f30\u8ba1\u5e76\u4e0d\u51c6\u786e\uff0c\u6240\u4ee5\u5728\u8ddd\u79bb \\(\\gamma_2\\) \u7684\u3001\u6cbf\u7740 \\(z\\) \u8f74\u7684\u5730\u65b9\u518d\u91c7\u4e24\u4e2a\u7403\u5f62 ROI\uff1b<ul> <li> \u95ee\u9898\uff1a\u4e0d\u51c6\u786e\u7684\u662f \\(\\tilde{Z}\\)\uff0c\u53ef\u662f \\(X, Y\\) \u7684\u5f97\u5230\u4e5f\u4e0e \\(\\tilde{Z}\\) \u6709\u5173\u5440\uff1f \u900f\u89c6\u6295\u5f71\uff0c\u800c\u975e\u6b63\u4ea4\u6295\u5f71\u3002</li> </ul> </li> <li>\u63a5\u4e0b\u6765\u5c06 ROI \u4e2d\u7684\u70b9\u4e91\u4f53\u7d20\u5316\uff0c\u5e76\u4e14\u8ba1\u7b97\u5f97\u5230\u6bcf\u4e00\u4e2a\u4f53\u7d20\u7684\u7279\u5f81\uff0c\u7279\u5f81\u5305\u62ec\u4e24\u4e2a\u90e8\u5206\uff1a<ul> <li>\u7531\u4f53\u7d20\u4e2d\u5fc3 \\(\\overline{s}_i\\) \u6307\u5411\u6839 \\(r\\) \u7684\u504f\u79fb\u5411\u91cf(offset vector) \\(o_i = r - \\overline{s}_i\\)\uff1b</li> <li>\u5229\u7528\u76f8\u673a\u53c2\u6570\uff0c\u5c06 \\(\\overline{s}_i\\) \u6295\u5f71\u56de\u56fe\u7247\u540e\uff0c\u5728\u7279\u5f81 map \u4e0a\u8fdb\u884c\u53cc\u7ebf\u6027\u91c7\u6837\u5f97\u5230\u7684\u4e0d\u6295\u5f71\u56fe\u50cf\u7279\u5f81(unprojecting image feature) \\(\\hat{f}\\)\uff1b</li> </ul> </li> </ul> </li> <li>\u4f30\u8ba1\u4fee\u6b63\u6839\u548c\u573a\u666f\u63a5\u89e6\u70b9<ul> <li>\u4f7f\u7528\u4e00\u4e2a\u7a00\u758f 3D CNN \u6765\u5904\u7406 3D \u7279\u5f81\uff0c\u4ee5\u6c42\u4f18\u5316\u6839\u7684\u4f30\u8ba1\u5e76\u4f30\u8ba1\u573a\u666f\u63a5\u89e6\u4f4d\u7f6e\uff0c\u7f51\u7edc\u7684\u8f93\u51fa\u5305\u62ec\u4e09\u4e2a\u90e8\u5206\uff1a\u66f4\u65b0\u540e\u7684\u504f\u79fb\u5411\u91cf(updated offset vector) \\(o_i^*\\)\u3001\u5176\u7f6e\u4fe1\u5ea6(confidence) \\(c_i\\)\u3001\u4ee5\u53ca\u5173\u4e8e\u516b\u4e2a\u63a5\u89e6\u4f4d\u7f6e\u6216\u4e0d\u63a5\u89e6\u4f4d\u7f6e\u7684\u5206\u5272\u7ed3\u679c\uff1b</li> <li>\u4f7f\u7528 \\(r^* = \\sum \\limits_i c_i \\cdot (o^*_i + \\overline{s}_i)\\) \u6765\u8ba1\u7b97\u4f18\u5316\u540e\u7684\u6839\uff0c\u5176\u4e2d \\(i\\) \u4e3a ROI \u4e2d\u7684\u4f53\u7d20\u7684 index\uff08\u4e4b\u524d\u63d0\u5230\u7684 voting vector field refinement task\uff09\uff1b</li> <li>\u63a5\u89e6\u70b9\u5206\u7c7b\u5305\u62ec 7 \u4e2a\u6700\u5bb9\u6613\u6210\u4e3a\u63a5\u89e6\u70b9\u7684\u5206\u7c7b\uff0c\u548c 1 \u4e2a\u7528\u6765\u8868\u793a\u4e0d\u63a5\u89e6\u7684\u7c7b\u522b\uff0c\u901a\u8fc7\u53d6\u5f97\u5206\u6700\u9ad8\u7684\u5f97\u5230\u70b9\u4e91\u7684\u6807\u7b7e\uff0c\u6700\u7ec8\u5f97\u5230\u4e00\u4e2a\u6709\u6807\u7b7e\u7684\u70b9\u4e91\u6570\u636e\u4f5c\u4e3a\u4e4b\u540e\u7684\u8f93\u5165\uff08\u4e4b\u524d\u63d0\u5230\u7684 point cloud labeling task\uff09\uff1b</li> </ul> </li> </ul> </li> <li>SA-HMR\uff1a<ul> <li></li> <li>\u53d7\u6570\u636e\u96c6\u9650\u5236\uff0c\u672c\u90e8\u5206\u7684\u5de5\u4f5c\u4ee5\u9884\u8bad\u7ec3\u597d\u7684 METRO \u4e3a\u57fa\u7840 SA-HMR \u6dfb\u52a0\u4e00\u4e2a\u5e73\u884c\u7684\u573a\u666f\u76f8\u5173\u7f51\u7edc\uff0c\u4f7f\u7528\u4ea4\u53c9\u6ce8\u610f\u529b\u673a\u5236\u6765\u63d0\u9ad8 METRO \u7684\u573a\u666f\u611f\u77e5\uff1b</li> <li>METRO<ul> <li>\u4f7f\u7528\u81ea\u6ce8\u610f\u529b\u673a\u5236\u5b9e\u73b0\u5355\u76ee\u7684\u4eba\u4f53\u7f51\u683c\u6062\u590d\uff1b</li> <li>\u63d0\u53d6\u5168\u5c40\u7684 CNN \u7279\u5f81 \u27a1\ufe0f \u5c06\u7279\u5f81\u5408\u5e76\u5230\u65e0\u59ff\u52bf\u7684 SMPL \u7f51\u683c\u9876\u70b9\u4e0a \u27a1\ufe0f \u9884\u6d4b\u5305\u542b\u5f62\u4f53\u7684\u59ff\u52bf\uff1b</li> </ul> </li> <li>\u4ea4\u53c9\u6ce8\u610f\u529b\u4e0b\u7684 METRO<ul> <li>\u9996\u5148\u4f7f\u7528 METRO \u9aa8\u5e72\u90e8\u5206\u4e2d\u7684 CNN \u4ece\u56fe\u7247\u4e2d\u63d0\u53d6\u51fa\u56fe\u50cf\u7279\u5f81\uff0c\u5e76\u6620\u5c04\u3001\u6c60\u5316\u5f97\u5230\u4e0e\u4eba\u4f53 mesh \u9876\u70b9\u4e2a\u6570\u4e00\u81f4\u7684 tokens\uff1b</li> <li>\u5c06\u521d\u59cb\u9876\u70b9\u4e0e\u8fd9\u4e9b\u751f\u6210\u7684 token \u76f4\u63a5\u62fc\u63a5\uff0c\u585e\u8fdb transformer \u91cc\uff0c\u4ee5\u6b64\u6765\u8ba9 transformer \u80fd\u66f4\u597d\u7684\u6ce8\u610f\u5230\u8bed\u4e49\u4e0a\u66f4\u76f8\u5173\u7684\u90e8\u5206\uff1b</li> <li>\u4e3a\u4e86\u5c06\u7528\u6765\u4f30\u8ba1\u4eba\u4f53\u59ff\u6001\u7684 METRO \u4e0e\u9879\u76ee\u63d0\u51fa\u7684\u573a\u666f\u7f51\u7edc\u76f8\u7ed3\u5408\uff0c\u4f7f\u7528\u4e86\u4ea4\u53c9\u6ce8\u610f\u529b(cross attention)\uff1b<ul> <li>\u5373 Q \u548c K \u4e0d\u540c\u5c5e\u4e00\u4e2a\u6a21\u5757\uff0c\u5728\u672c\u9879\u76ee\u7684\u8bed\u5883\u4e0b\uff0c\u6307\u4e24\u4e2a\u6a21\u5757\u7684 Q \u548c K \u90fd\u6765\u81ea\u5bf9\u65b9\uff1b</li> </ul> </li> <li>\u8fd9\u91cc\u5bf9 METRO \u4f7f\u7528\u5171\u4eab\u6743\u91cd\u7684\u56de\u5f52\u5c42\uff0c\u5177\u4f53\u5e94\u7528\u5728\u4ece\u9010\u70b9\u7279\u5f81\u5230\u70b9\u4f4d\u7f6e\u7684\u56de\u5f52\uff1b<ul> <li>\u56e0\u6b64\uff0c\u5f53\u7279\u5f81\u76f8\u4f3c\u7684\u70b9\u88ab\u8f93\u5165\u4ee5\u540e\uff0c\u8f93\u51fa\u7684\u5ea7\u6807\u4e5f\u503e\u5411\u4e8e\u76f8\u4f3c\uff0c\u76f8\u5f53\u4e8e\u8bf4\u5728\u505a scene image \u548c real image \u7684\u7279\u5f81\u5339\u914d\uff1b</li> <li>\u8fd9\u9690\u5f0f\u5730\u5c06\u76f8\u4f3c\u7684\u4eba\u4f53\u9876\u70b9\u548c\u573a\u666f\u70b9\u5bf9\u9f50\uff0c\u4ee5\u4fbf\u4e8e transformer \u5bfb\u627e\u5bf9\u5e94\u5173\u7cfb\uff1b</li> </ul> </li> </ul> </li> </ul> </li> <li>Loss<ul> <li>\u7b2c\u4e00\u90e8\u5206 \u00b7 \u6839\u548c\u63a5\u89e6\u70b9<ul> <li>\\(L_ {RC} = L_ {R2D} + w_ {RZ} \\cdot L_ {RZ} + L_ {ROV} + L_ {R3D} + L_ {C}\\)</li> <li>\\(L_ {R2D}\\) \u662f\u6839\u7684\u70ed\u529b\u56fe\u7684 MSE loss\uff1b</li> <li>\\(L_{RZ},L_{ROV},L_{R3D}\\) \u662f\u76f8\u5bf9\u6df1\u5ea6\u3001\u504f\u79fb\u5411\u91cf\u3001\u6839\u7684 3D \u5ea7\u6807\u7684 L1 loss\uff1b</li> <li>\\(L_C\\) \u662f\u63a5\u89e6\u70b9\u7684\u6807\u7b7e\u7684\u4ea4\u53c9\u71b5 loss\uff1b</li> </ul> </li> <li>\u7b2c\u4e8c\u90e8\u5206 \u00b7 HMR<ul> <li>\\(L_{\\mathrm{HMR}}=L_\\mathrm{V}+L_\\mathrm{J}+L_{\\mathrm{CP}}+L_\\mathrm{GV}\\)</li> <li>\u56db\u4e2a term \u5206\u522b\u662f\u5e73\u79fb\u5bf9\u9f50\u7684\u4eba\u4f53\u9876\u70b9\u7684\u3001\u4eba\u4f53\u5173\u952e\u70b9\u7684\u3001\u91cd\u5efa\u7684\u63a5\u89e6\u70b9\u7684\u3001\u5168\u5c40\u4eba\u4f53\u9876\u70b9\u7684 L1 loss\uff1b</li> </ul> </li> </ul> </li> </ul>"},{"location":"pape_read/SA-MHR/#\u6570\u636e\u96c6","title":"\u6570\u636e\u96c6","text":"<ul> <li>RICH<ul> <li>\u573a\u666f\uff1a6 \u5ba4\u5916 &amp; 2 \u5ba4\u5185</li> <li>\u4e0d\u5904\u7406\u591a\u4eba\u3001\u4e0d\u5904\u7406 bbox \u51fa\u753b\u9762\u7684\u60c5\u51b5</li> </ul> </li> <li>PROX <ul> <li>\u573a\u666f\uff1a12 \u5ba4\u5185</li> </ul> </li> </ul>"},{"location":"pape_read/SA-MHR/#\u6548\u679c\u5ea6\u91cfmetrics","title":"\u6548\u679c\u5ea6\u91cf(metrics)","text":"<ul> <li>HMR<ul> <li>G-MPJPE: Global Mean-Per-Joint-Position-Error</li> <li>G-MPVE: Global Mean-Per-Vertex-Error</li> <li>\u5373\u5168\u5c40\u7684 JP \u548c V \u7684 L2 \u8bef\u5dee\uff0c\u76f8\u5bf9\u7684\uff0c\u540e\u9762\u8fd8\u6709\u4e00\u4e2a\u975e\u5168\u5c40\u7684\u8bef\u5dee\uff0c\u8868\u793a\u7684\u662f\u8282\u70b9/\u9876\u70b9\u76f8\u5bf9\u4e8e pelvis \u7684\u5ea7\u6807\u7684\u8bef\u5dee\uff0c\u5168\u5c40\u7684\u8bef\u5dee\u66f4\u80fd\u4f53\u73b0\u5728\u5168\u5c40\u8303\u56f4\u5185\u7684\u6548\u679c\uff1b</li> </ul> </li> <li>contact<ul> <li>PenE: Penetration Error <ul> <li>\u5373\u7a7f\u6a21\u8bef\u5dee\uff0c\u5bf9\u4e8e\u6240\u6709\u7a7f\u5165\u6a21\u8868\u9762\u7684\u70b9\uff0c\u7d2f\u52a0\u5176\u5230\u8868\u9762\u7684\u8ddd\u79bb\uff0c\u8d8a\u7a7f\u8d8a\u574f\uff1b</li> <li> \u95ee\u9898\uff1a\u5177\u4f53\u6765\u8bf4\u5982\u4f55\u8861\u91cf v to scene \u7684\u8ddd\u79bb\uff1f\u5982\u679c\u7a7f\u4e86\u4e00\u4e2a\u6241\u5e73\u6a21\u662f\u5426\u8868\u8fbe\u4e0d\u660e\u663e\uff1f \u662f\uff0c\u6240\u4ee5\u8fd9\u4e2a\u6807\u51c6\u53ea\u662f\u793a\u610f\uff0c\u5b9e\u9645\u5f88\u96be\u505a\u3002</li> </ul> </li> <li>ConFE: Contact Failure Error<ul> <li>\u524d\u4e00\u4e2a term \u8868\u793a\u5f53\u8fd9\u91cc\u662f\u63a5\u89e6\u65f6\uff0c\u8981\u5c3d\u53ef\u80fd\u63a5\u8fd1\uff1b\u540e\u4e00\u4e2a term \u8868\u793a\u5f53\u8fd9\u91cc\u4e0d\u63a5\u89e6\u65f6\uff0c\u8981\u5c3d\u53ef\u80fd\u4e0d\u7a7f\u6a21\uff1b</li> <li> \u95ee\u9898\uff1a\u7b2c\u4e8c\u4e2a term \u662f\u4e0d\u662f\u4e0e PenE \u7684\u529f\u80fd\u91cd\u5408\u4e86\uff1f \u6709\u4e00\u90e8\u5206\u91cd\u5408\uff0c\u4f46\u662f\u662f\u5fc5\u8981\u7684\uff0c\u5b83\u8861\u91cf\u7684\u6709\u4e24\u4e2a\u5185\u5bb9\uff1a1. \u5c5e\u4e8e\u63a5\u89e6\u70b9\u7684\uff0c\u8981\u5c3d\u53ef\u80fd\u201c\u63a5\u89e6\u201d\uff1b2. \u4e0d\u5c5e\u4e8e\u63a5\u89e6\u70b9\u7684\uff0c\u8981\u5c3d\u53ef\u80fd\u201c\u4e0d\u63a5\u89e6\u201d\uff1b</li> </ul> </li> </ul> </li> </ul>"},{"location":"pape_read/SAMP/","title":"[SAMP] Stochastic Scene-Aware Motion Prediction","text":"<p> \u7ea6 1427 \u4e2a\u5b57  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 5 \u5206\u949f</p> <p><code>3DV</code> <code>Human-Motion</code> <code>Scene-Aware</code></p> <p>\u6587\u7ae0\u4fe1\u606f</p> <ul> <li>\u6587\u7ae0\u9898\u76ee\uff1aStochastic Scene-Aware Motion Prediction</li> <li>\u4f5c\u8005\uff1aMohamed Hassan, Duygu Ceylan, Ruben Villegas, Jun Saito, Jimei Yang, Yi Zhou, and Michael Black</li> <li>\u9879\u76ee\u4e3b\u9875\uff1a\ud83d\udd17</li> <li>\u8bba\u6587\uff1a\ud83d\udd17</li> <li>Demo\uff1a\ud83d\udd17</li> <li>\u4ee3\u7801\uff1a\ud83d\udd17</li> </ul>"},{"location":"pape_read/SAMP/#\u8bba\u6587\u7b14\u8bb0","title":"\u8bba\u6587\u7b14\u8bb0","text":""},{"location":"pape_read/SAMP/#\u95ee\u9898\u4e0e\u73b0\u72b6\u4e0e\u8109\u7edc","title":"\u95ee\u9898\u4e0e\u73b0\u72b6\u4e0e\u8109\u7edc","text":"<p>\u52a8\u4f5c\u751f\u6210\u7684\u5b9e\u73b0\u5212\u5206\u4e3a\u4e09\u4e2a\u90e8\u5206\uff1a</p> <ol> <li>\u5bfc\u822a\u81f3\u4ea4\u4e92\u76ee\u6807\uff1b</li> <li>\u5bfb\u627e\u4ea4\u4e92\u63a5\u89e6\u70b9(contact point)\uff1b</li> <li>\u751f\u6210\u4ea4\u4e92\u52a8\u4f5c\uff0c\u5e76\u4e14\u9700\u8981\u4fdd\u8bc1\u751f\u6210\u7ed3\u679c\u4f1a\u81ea\u7136\u53d8\u5316\uff08\u4ee5\u7b26\u5408\u73b0\u5b9e\u611f\u89c9\uff09\uff1b</li> </ol> <p>\u7531\u4e8e\u8fd9\u4e9b\u52a8\u4f5c\u4e2d\u6709\u4e00\u90e8\u5206\u662f\u201c\u5faa\u73af\u7684(cyclic)\u201d\uff0c\u4e00\u90e8\u5206\u662f\u201c\u4e0d\u5faa\u73af\u7684(acyclic)\u201d\uff0c\u6240\u4ee5\u9700\u8981\u4e00\u4e2a\u63a8\u7406\u7cfb\u7edf\u6765\u534f\u8c03\u4e24\u8005 -&gt; \u63d0\u51fa SAMP\uff0c\u573a\u666f\u53ef\u611f\u77e5\u7684\u52a8\u4f5c\u9884\u6d4b\u7cfb\u7edf(Scene-Aware Motion Prediction)\uff1a</p> <ul> <li>\u968f\u673a\u6a21\u578b</li> <li>\u8f93\u5165 3D \u573a\u666f</li> <li>\u91c7\u6837\u6709\u6548\u4ea4\u4e92\u76ee\u6807</li> <li>\u751f\u6210\u76ee\u6807\u9650\u5236\u7684\u3001\u573a\u666f\u611f\u77e5\u7684\u3001\u903c\u771f\u7684\u4eba\u4f53\u52a8\u4f5c\u5e8f\u5217</li> </ul>"},{"location":"pape_read/SAMP/#\u8d21\u732e","title":"\u8d21\u732e","text":"<ol> <li>\u65b0\u9896\u7684\u968f\u673a\u6a21\u578b\u4ee5\u751f\u6210\u5b9e\u65f6\u7684\u3001\u591a\u6837\u7684\u3001goal driven \u7684\u4eba\u7269\u5bf9\u573a\u666f\u7684\u4ea4\u4e92\uff1b</li> <li>\uff08\u5bf9 1. \u7684\u7ec6\u5316\uff09\u7ed9\u5b9a\u76ee\u6807\u51e0\u4f55\u4f53\u540e\u751f\u6210\u53ef\u4fe1\u7684\u3001\u52a8\u4f5c\u76f8\u5173\u7684\u4ea4\u4e92\u4f4d\u7f6e\u548c\u65b9\u5411\u7684\u65b0\u5efa\u6a21\u65b9\u6cd5\uff1b</li> <li>\uff08\u5bf9 1. \u7684\u7ec6\u5316\uff09\u5c06\u5177\u4f53\u8def\u5f84\u89c4\u5212\u7eb3\u5165\u53d8\u5206\u8fd0\u52a8\u5408\u6210\u7f51\u7edc\uff0c\u5b9e\u73b0\u5728\u590d\u6742\u573a\u666f\u4e2d\u7684\u5bfc\u822a\uff1b</li> <li>\u5305\u542b\u591a\u6837\u4eba\u4f53\u573a\u666f\u4ea4\u4e92\u6570\u636e\u7684\u65b0\u7684 MoCap \u6570\u636e\u96c6\uff1b</li> </ol>"},{"location":"pape_read/SAMP/#\u65b9\u6cd5","title":"\u65b9\u6cd5","text":"<ul> <li><code>MotionNet</code>(core)\uff1a\u4e00\u4e2a cVAE\uff0c\u8f93\u5165\u76ee\u6807\u5bf9\u8c61\u548c\u52a8\u4f5c\uff0c<code>MotionNet</code> \u6bcf\u4e00\u5e27\u5c06\u91c7\u6837\u4e00\u4e2a\u6f5c\u5411\u91cf\uff0c\u8054\u5408\u524d\u4e00\u5e27\u7684\u52a8\u4f5c\u6765\u63a7\u5236\uff08\u5373\u9884\u6d4b\uff09\u4e0b\u4e00\u4e2a\u52a8\u4f5c\uff1b<ul> <li>\u5305\u542b\u4e00\u4e2a encoder \u548c\u4e00\u4e2a decoder\uff1b  </li> <li>\\(X_i\\) \u8868\u793a\u7b2c \\(i\\) \u65f6\u523b\u7684\u72b6\u6001\uff0c\\(Z\\) \u4e3a\u751f\u6210\u7684\u6f5c\u5411\u91cf\uff0c\\(I\\) \u4e3a\u4ea4\u4e92\u5bf9\u8c61(interaction objects)\uff08\u4ee5\u4eba\u7269\u4e3a\u539f\u70b9\u7684\u4f53\u7d20\u7a7a\u95f4\u8868\u8fbe\uff09\uff1b<ul> <li>encoder \u5305\u542b Interaction Encoder \u548c State Encoder\uff0c\u5206\u522b\u5c06 \\(I\\) \u548c \\(X\\) \u7f16\u7801\uff08\u4f7f\u7528 3 \u4e2a FC\uff09\u4e3a\u4f4e\u7ef4\u5ea6\u5411\u91cf\uff0c\u518d\u62fc\u63a5\u8d77\u6765\u8f93\u5165\u5230\u4e24\u4e2a\u5b8c\u5168\u76f8\u540c\u7684 FC \u4e2d\u4ee5\u9884\u6d4b \\(\\mu\\) \u548c \\(\\sigma\\) \u5373\u4e00\u4e2a\u6f5c\u5d4c\u5165\u7a7a\u95f4(latent embedding space)\uff1b</li> <li>\u4e8e\u662f\u6211\u4eec\u53ef\u4ee5\u4ece\u4ee5\u4e0a\u8ff0\u7ed3\u679c\u4e3a\u53c2\u6570\u7684\u9ad8\u65af\u5206\u5e03\u4e2d\u91c7\u6837\u51fa\u6f5c\u5411\u91cf \\(Z\\) \u4f5c\u4e3a decoder \u7684\u8f93\u5165\uff1b </li> <li> \u95ee\u9898\uff1a\u4e3a\u4ec0\u4e48\u8fd9\u91cc\u7684 \\(j^r_i\\) \u662f 6d \u7684\uff1f\uff08\u5b9e\u9645\u4e0a\u662f 9d \u65cb\u8f6c\u77e9\u9635\u4e2d\u4f1a\u53d8\u5143\u6709 6 \u4e2a\uff0c\u901a\u8fc7\u8fd9\u4e2a 6d \u7684\u5411\u91cf\u80fd\u591f\u8fd8\u539f\u51fa\u8fd9\u4e2a\u77e9\u9635\uff0c\u800c\u81f3\u4e8e\u4e3a\u4ec0\u4e48\u7528\u8fd9\u4e2a 6d \u5185\u5bb9\u800c\u975e\u89d2\u5ea6\uff0c\u53ef\u4ee5\u53c2\u8003\u8fd9\u7bc7\u6587\u7ae0\uff0c\u89d2\u5ea6\u5177\u6709\u7a81\u53d8\u4e0d\u8fde\u7eed\uff1a\\(2pi = 0\\)\uff0c\u6240\u4ee5\u90fd\u4e0d\u600e\u4e48\u7528\u4e86\uff09</li> <li>decoder \u662f\u4e00\u4e2a MoE\uff0c\u6709 Prediction Network \u548c Gating Network \u4e24\u4e2a\u90e8\u5206\uff0c\u524d\u8005\u8d1f\u8d23\u751f\u6210\u9884\u6d4b\u7ed3\u679c\uff0c\u540e\u8005\u8d1f\u8d23\u751f\u6210\u5404\u4e2a\u4e13\u5bb6\u7f51\u7edc\u7684\u7ed3\u679c\u5408\u6210\u8fc7\u7a0b\u4e2d\u7684\u6743\u91cd\uff1b</li> </ul> </li> <li>\u4f7f\u7528\u7684 loss \u4e3a \\(||\\hat{X_i} - X_i||^2_2 + \\beta_1\\mathop{KL}(Q(Z|X_i, X_{i-1}, I) || p(Z))\\)\uff1b</li> <li>\u7279\u522b\u6ce8\u610f\uff0c\u5728\u6d4b\u8bd5\u8fc7\u7a0b\u4e2d\uff0c\u6211\u4eec\u4ec5\u4ec5\u4ece\u6807\u51c6\u6b63\u6001\u5206\u5e03\u4e2d\u91c7\u6837\u6f5c\u5411\u91cf\uff1b<ul> <li> \u95ee\u9898\uff1a\u4e3a\u4ec0\u4e48\uff1f</li> </ul> </li> </ul> </li> <li><code>GoalNet</code>\uff1a\u7528\u6765\u751f\u6210\u4ea4\u4e92\u70b9\u548c\u4ea4\u4e92\u65b9\u5411(contact points and orientations)\uff0c\u5373\u76ee\u6807(goals)\uff1b<ul> <li>\u8be5\u6a21\u5757\u8ba9 SAMP \u80fd\u591f\u9002\u5e94\u4e0d\u540c\u7684\u76ee\u6807\u51e0\u4f55\u4f53\uff1b</li> <li>\u540c\u6837\u5305\u542b\u4e00\u4e2a encoder \u548c\u4e00\u4e2a decoder\uff1b  </li> <li>\\(I\\) \u4e3a\u4ea4\u4e92\u5bf9\u8c61(interaction objects)\uff08\u4ee5\u7269\u4f53\u81ea\u8eab\u4e3a\u539f\u70b9\u7684\u4f53\u7d20\u7a7a\u95f4\u8868\u8fbe\uff09\uff0c\\(\\{g^p, g^d\\}\\) \u5206\u522b\u4e3a\u76ee\u6807(goal)\u7684\u4f4d\u7f6e\u548c\u65b9\u5411\uff0c\\(Z_{goal}\\) \u4e3a\u6f5c\u5411\u91cf\uff1b</li> <li>\u4f7f\u7528\u7684 loss \u4e3a \\(||\\hat{g}^p - g^p||^2_2 + ||\\hat{g}^d - g^d||^2_2 + \\beta_2 \\mathop{KL}(Q(Z_{goal}|g^p, g^d, I) || p(Z_{goal}))\\)\uff1b</li> </ul> </li> <li><code>Path Planning Module</code>\uff1a\u4f7f\u7528 A* \u5bfb\u8def\u4ee5\u907f\u969c(obstacles)\uff1b<ul> <li>\u751f\u6210\u7684\u8def\u7ebf\u4e2d\u5c06\u4f1a\u6709\u8bb8\u591a\u8def\u70b9(way-points)\u4f5c\u4e3a\u8fc7\u7a0b\u4e2d\u7684\u76ee\u6807\u70b9(goals)\uff1b</li> <li>explicit A*\uff1b</li> <li>\u6240\u8c13\u7684\u201c\u8def\u5f84\u201d\uff0c\u5177\u4f53\u6307\u7684\u662f\u4e00\u7cfb\u5217\u8def\u70b9(way point)\uff0c\u901a\u8fc7\u8fd9\u4e9b\u201c\u5c0f\u76ee\u6807\u201d\uff0c\u6765\u4e00\u6b65\u6b65\u5f15\u5bfc\u865a\u62df\u4eba\u5230\u8fbe\u76ee\u6807\u524d\uff0c\u5728\u6700\u540e\u4e00\u4e2a\u8def\u70b9\u8fdb\u884c\u76ee\u6807\u52a8\u4f5c\u7684\u751f\u6210\uff1b</li> <li>\u8fd9\u4e00\u65b9\u9762\u4e0e NSM \u4f7f\u7528 sensor \u68c0\u6d4b\u4e0d\u540c\uff0c\u66f4\u52a0\u9ad8\u6548\uff1b</li> </ul> </li> </ul> <p>\u8fd9\u4e9b\u72ec\u7acb\u7ec4\u4ef6\u4f7f SAMP \u79f0\u4e3a\u7b2c\u4e00\u4e2a\u89e3\u51b3\u751f\u6210\u591a\u6837\u52a8\u6001\u52a8\u4f5c\u5e8f\u5217\uff0c\u5e76\u4e14\u80fd\u771f\u5b9e\u5e94\u7528\u4e8e\u590d\u6742\u573a\u666f\u4e2d\u7684\u3002 - [x] \u95ee\u9898\uff1a\u8fd9\u91cc\u6700\u5173\u952e\u7684\u662f\u54ea\u4e00\u4e2a\u90e8\u5206\uff1f\u4e0e NSM \u76f8\u6bd4\u72ec\u521b\u6027\u7684\u5730\u65b9\u5177\u4f53\u5728\u54ea\u91cc\uff1f\u5230\u5e95\u5982\u4f55\u5b9a\u4e49\u201cdiverse human-scene interactions\u201d\uff0c\u548c Motion VAE \u90a3\u79cd\u751f\u6210\u5206\u5e03\u6a21\u578b\u7684\u6709\u4ec0\u4e48\u533a\u522b\uff1f\uff08Motion VAE \u662f\u5229\u7528\u5206\u5e03\u7684\u6781\u5927\u4f3c\u7136\u4f30\u8ba1\u5f97\u5230\u7ed3\u679c\u7684\uff0cMoGlow \u8c8c\u4f3c\u548c\u573a\u666f\u6ca1\u5173\u7cfb\uff09</p> <p>\u56e0\u6b64\uff0c\u8bad\u7ec3 SAMP \u6240\u9700\u7684\u6570\u636e\u96c6\u9700\u8981\u4e30\u5bcc\u4e14\u4e0d\u540c\u7684\u573a\u666f\u4ea4\u4e92\uff0c\u73b0\u6709\u6570\u636e\u96c6\u7f3a\u5c11\u4ea4\u4e92\u884c\u4e3a -&gt; \u81ea\u5df1\u505a\u4e86\u4e00\u4e2a\u3002</p> <ul> <li> \u95ee\u9898\uff1atrajectory \u548c path \u548c pose \u7684\u533a\u522b\uff1f\u662f\u6307\u5305\u62ec\u4e86\u52a8\u4f5c\u548c\u884c\u52a8\u8def\u7ebf\u7684\u8f68\u8ff9\u5417\uff1f</li> </ul> <p>\u5982\u4f55\u8861\u91cf\u4eba\u4f53\u52a8\u4f5c\u7684\u968f\u673a\u6027(stochasticity)\u662f\u4e00\u4e2a\u6709\u5f85\u63a2\u7d22\u7684\u9886\u57df\u3002</p>"},{"location":"pape_read/SAMP/#\u8bad\u7ec3\u7b56\u7565","title":"\u8bad\u7ec3\u7b56\u7565","text":"<p>\u4f7f\u7528\u6b63\u5e38\u7684\u76d1\u7763\u8bad\u7ec3\u4f1a\u5bfc\u81f4\u9519\u8bef\u7d2f\u79ef(accumulation of error)\uff0c\u56e0\u4e3a\u4e00\u6b21\u7684\u8f93\u51fa\u4f1a\u4f5c\u4e3a\u8f93\u5165\u8fdb\u5165\u5230\u4e0b\u4e00\u4e2a\u7f51\u7edc\u3002\u6240\u4ee5 SAMP \u91c7\u7528\u9884\u8ba2\u91c7\u6837(scheduled sampling)\uff0c\u5b83\u80fd\u591f\u7a33\u5b9a\u751f\u6210\u957f\u65f6\u95f4\u7684\u52a8\u4f5c\u9884\u4f30\u3002</p> <p>\u5177\u4f53\u6765\u8bf4\uff0c\u4e0a\u4e00\u6b21\u7684\u9884\u6d4b\u7ed3\u679c\u4ee5 \\(1-P\\) \u7684\u6982\u7387\u4f5c\u4e3a\u4e0b\u4e00\u6b21\u9884\u6d4b\u7684\u8f93\u5165\uff0c\u5176\u4e2d \\(P\\) \u7684\u5b9a\u4e49\u5982\u4e0b\uff1a </p>"},{"location":"pape_read/SAMP/#\u5b9e\u9a8c\u548c\u8bc4\u4f30","title":"\u5b9e\u9a8c\u548c\u8bc4\u4f30","text":"<p>\u5728\u540c\u521d\u59cb\u6761\u4ef6\u4e0b\u591a\u6b21\u6267\u884c\u540c\u4e00\u4efb\u52a1\uff0c\u4f7f\u7528 APD(Average Pairwise Distance) \u6765\u8861\u91cf\u5176\u8fd0\u52a8\u5e45\u5ea6\uff1a </p>"},{"location":"pape_read/SAMP/#\u4ee3\u7801\u9605\u8bfb","title":"\u4ee3\u7801\u9605\u8bfb","text":""},{"location":"pape_read/SAMP/#motionnet","title":"MotionNet","text":"<p>\u516c\u5f0f\u63a8\u5bfc\uff1a</p> <p>\u6b63\u6001\u5206\u5e03\u7684\u71b5\u516c\u5f0f</p> <p>\u5047\u8bbe \\(x\\sim N(\\mu, \\sigma^2)\\)\uff0c\u4e8e\u662f\u6709\uff1a</p> <p>  \u5e76\u4e14\u6709\u7ed3\u8bba\uff1a</p> \\[ \\int_{-\\infty}^{\\infty} e^{-x^2} \\mathrm{d}x = \\sqrt{\\pi} \\] <p>\u90a3\u4e48\u6709\u5176\u71b5\u516c\u5f0f\uff1a</p> \\[ \\begin{aligned}     -\\int_{-\\infty}^{\\infty} p(x)\\ln p(x) \\mathrm{d}x     &amp;=     -\\int_{-\\infty}^{\\infty}\\frac{1}{\\sqrt{2\\pi\\sigma^2}}\\exp\\left(         -\\frac{(x-\\mu)^2}{\\sqrt{2\\sigma^2}}      \\right)     \\ln\\left[     \\frac{1}{\\sqrt{2\\pi\\sigma^2}} \\exp\\left(         -\\frac{(x-\\mu)^2}{2\\sigma^2}     \\right)     \\right]     \\mathrm{d}x \\\\     &amp;=      \\frac{1}{2}\\left(         \\ln\\left(             2\\pi\\sigma^2         \\right) + 1     \\right) \\end{aligned} \\]"},{"location":"pape_read/TRACE/","title":"[TRACE] 5D Temporal Regression of Avatars with Dynamic Cameras in 3D Environments","text":"<p> \u7ea6 1352 \u4e2a\u5b57  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 5 \u5206\u949f</p> <p><code>3DV</code> <code>HMR</code> <code>Global-Coordinates</code> <code>Track</code></p> <p>\u6587\u7ae0\u4fe1\u606f</p> <ul> <li>\u6587\u7ae0\u9898\u76ee\uff1aTRACE: 5D Temporal Regression of Avatars with Dynamic Cameras in 3D Environments</li> <li>\u4f5c\u8005\uff1aAuthors:Yu Sun, Qian Bao, Wu Liu, Tao Mei, Michael J. Black</li> <li>\u9879\u76ee\u4e3b\u9875\uff1a\ud83d\udd17</li> <li>\u8bba\u6587\uff1a\ud83d\udd17</li> <li>\u4ee3\u7801\uff1a\ud83d\udd17</li> </ul>"},{"location":"pape_read/TRACE/#\u4efb\u52a1--\u6311\u6218","title":"\u4efb\u52a1 &amp; \u6311\u6218","text":""},{"location":"pape_read/TRACE/#\u80cc\u666f","title":"\u80cc\u666f","text":"<p>\u867d\u7136\u76ee\u524d\u5bf9\u4e8e HPS(Human Pose &amp; Shape) \u7684\u4f30\u8ba1\u5df2\u7ecf\u6709\u5f88\u591a\u5f88\u597d\u7684\u5de5\u4f5c\uff0c\u4f46\u662f\u90fd\u662f\u5f97\u5230\u76f8\u673a\u5ea7\u6807\u4e0b\u7684\u7ed3\u679c\uff0c\u65e0\u6cd5\u5f88\u597d\u7684\u5f97\u5230\u5168\u5c40\u5ea7\u6807\u7cfb\u4e0b\u7684\u7ed3\u679c\u3002\u5c24\u5176\u662f\u5728\u76f8\u673a\u79fb\u52a8\u7684\u60c5\u51b5\u4e0b\uff0c\u8fd9\u4e2a\u4efb\u52a1\u5c24\u5176\u56f0\u96be\u3002\u800c\u5f97\u5230\u6062\u590d\u51fa\u6765\u7684 Human \u7684\u5168\u5c40\u5ea7\u6807\u5177\u6709\u91cd\u5927\u610f\u4e49\u3002</p>"},{"location":"pape_read/TRACE/#\u6311\u6218","title":"\u6311\u6218","text":"<ol> <li>\u9700\u8981\u89e3\u5076 human \u7684\u8fd0\u52a8\u548c camera \u7684\u8fd0\u52a8\uff0c\u8fd9\u6837\u624d\u80fd\u5728\u5168\u5c40\u5ea7\u6807\u7cfb\u4e0b\u6062\u590d human \u7684\u8f68\u8ff9\uff1b<ol> <li>\u4e00\u79cd\u65b9\u6cd5\uff1a\u4f7f\u7528 SfM \u6062\u590d\u51fa\u76f8\u673a\u5173\u4e8e rigid scene \u7684\u76f8\u5bf9\u8fd0\u52a8\uff0c\u4f46\u662f\u5728\u7279\u6b8a\u73af\u5883\uff08\u753b\u9762\u7684\u5927\u90e8\u5206\u90fd\u4e0d\u600e\u4e48 rigid\uff0c\u6bd4\u5982\u5927\u91cf\u4eba\u6d41\uff09\u4e0b\u975e\u5e38\u4e0d\u53ef\u9760\uff1b</li> <li>\u53e6\u5916\u4e00\u79cd\u6765\u81ea GLAMR \u7684\u65b9\u6cd5\uff1a\u901a\u8fc7\u5df2\u6709\u7684\u5c40\u90e8\u59ff\u6001\u6765\u63a8\u65ad\u5168\u5c40\u4f4d\u7f6e\uff0c\u5c31\u7c7b\u4f3c\u4e8e\u770b\u4f60\u8d70\u4e86\u51e0\u6b65\u7136\u540e\u4f30\u8ba1\u4f60\u52a8\u4e86\u51e0\u7c73\uff1b</li> <li>TRACE \u9009\u62e9\u4e86\u7b2c\u4e8c\u79cd\u65b9\u6cd5\u7684\u53d8\u79cd\uff0c\u901a\u8fc7\u4f7f\u7528\u6574\u4e2a\u753b\u9762\u6765\u9884\u6d4b\u79fb\u52a8\u8ddd\u79bb\uff0c\u6539\u5584\u4e86 GLAMR \u539f\u672c\u4e0d\u600e\u4e48\u597d\u7684\u6548\u679c\u3002\u4e0d\u4ec5\u5982\u6b64\uff0cGLAMR \u662f\u591a\u9636\u6bb5\u7684\uff0c\u9c81\u68d2\u6027\u4e0d\u654c TRACE\uff1b</li> </ol> </li> <li>\u5c24\u5176\u9488\u5bf9\u4e8e\u8ffd\u8e2a\u529f\u80fd\uff0c\u5728\u5bc6\u96c6\u4eba\u7fa4\u573a\u666f\uff0c\u5b58\u5728\u5f88\u4e25\u91cd\u7684\u906e\u6321\u95ee\u9898\uff1b<ol> <li>\u6700\u5e38\u89c1\u7684\u89e3\u51b3\u529e\u6cd5\u662f\u4f7f\u7528\u65f6\u5e8f\u5148\u9a8c\u5047\u8bbe\uff0c\u5982 Kalman filter\uff0c\u4f46\u662f\u5728\u590d\u6742\u573a\u666f\u4e0b\u4e5f\u5f88\u5bb9\u6613\u5931\u6548\uff1b</li> <li> \u95ee\u9898\uff1aKalman filter \u597d\u50cf\u548c\u6ee4\u6ce2\u6709\u5173\uff1f\u4e3a\u4ec0\u4e48\u8bf4\u662f temporal priors\uff1f \u4f7f\u5e73\u6ed1\u3002</li> <li>PHALP \u662f\u4e3a\u6570\u4e0d\u591a\u7684\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\u7684\u65b9\u6cd5\u4e4b\u4e00\uff0c\u4f46\u662f\u5b83\u5e76\u975e one-stage\uff0c\u800c\u4e14\u5e76\u4e0d\u5bf9\u5e8f\u5217\u8fdb\u884c\u5168\u9762\u7684\u63a8\u7406\uff1b</li> <li> \u95ee\u9898\uff1a\u9700\u8981\u4e86\u89e3\u8fd9\u4e2a\u5417\uff1f \u8df3\u8fc7\u3002</li> </ol> </li> </ol>"},{"location":"pape_read/TRACE/#\u4efb\u52a1\u4e0e\u6210\u679c","title":"\u4efb\u52a1\u4e0e\u6210\u679c","text":"<p>\u672c\u5de5\u4f5c\u5b9e\u73b0\u4e86\u52a8\u6001\u76f8\u673a\u89c6\u9891\uff08DC-videos\uff09\u4e0b\u5728\uff08\u865a\u62df\u7684\uff09\u7a7a\u95f4\u4e2d\u7684\u65f6\u5e8f\u7684\u5bf9\u4e8e K \u76ee\u6807\u7684\u5b9a\u4f4d\u68c0\u6d4b\u3001\u59ff\u6001\u4f30\u8ba1\u3001\u8ffd\u8e2a\u548c\u51b2\u7a81\u9002\u914d\uff0c\u5e76\u4e14\u80fd\u591f\u5f97\u5230\u5168\u5c40\u7684\u5ea7\u6807\u3002 - \u65f6\u5e8f &amp; \u5168\u5c40\u5ea7\u6807 &amp; \u8ffd\u8e2a\uff1b</p> <p>\u5bf9 K \u4e2a\u6709\u9650\u76ee\u6807\u8fdb\u884c\u8ffd\u8e2a\uff0c\u5373\u4f7f\u4e2d\u9014\u77ed\u6682\u7684\u5931\u914d\uff0c\u4e5f\u80fd\u5728\u4e4b\u540e\u88ab\u91cd\u65b0\u8bc6\u522b\uff08\u4e00\u5f00\u59cb\u51b3\u5b9a\u4e86\u54ea K \u4e2a\u5c31\u4e00\u76f4\u662f\u54ea K \u4e2a\u4eba\uff09\u3002</p>"},{"location":"pape_read/TRACE/#\u521b\u65b0\u70b9--\u8d21\u732e","title":"\u521b\u65b0\u70b9 &amp; \u8d21\u732e","text":"<ul> <li>\u63d0\u4f9b\u4e86 5D \u7684\u8868\u8fbe\u65b9\u5f0f\uff0c\u62bd\u8c61\u6765\u8bf4\u9700\u8981\u5305\u62ec\uff1a\u65f6(1)\u7a7a(3)\u5ea7\u6807 + \u4e3b\u4f53\u7279\u5f81(1\uff0c\u62bd\u8c61\u4e00\u70b9\u6765\u770b)\uff1b</li> <li>end2end \u5e76\u4e14 one stage \u7684\u65b9\u6cd5\uff1b</li> <li>\u53d7\u5230 BEV \u542f\u53d1\uff0c\u5f15\u5165\u4e86\u4e86\u4e00\u79cd\u9e1f\u77b0\u89c6\u89d2\u7684 2D map \u6765\u63a8\u7406 3D \u4e2d\u7684 Human\u3002\u8fd9\u4e2a map \u548c\u4e00\u4e2a\u4ee5\u56fe\u7247\u4e3a\u4e2d\u5fc3\u7684 map \u4e00\u8d77\u7528\u6765\u63a8\u7406 Human \u7684 3D \u5ea7\u6807\u3002\u7c7b\u4f3c\u7684\u8fd8\u6709\u4e00\u5806\u5176\u4ed6\u7684 map\uff1b</li> <li>\u4e00\u4e2a memory unit\uff0c\u6765\u505a\u4e00\u4e9b long-term \u7684\u4e8b\u60c5\uff0c\u6bd4\u5982\u5bf9\u906e\u6321\u751a\u81f3\u6682\u65f6\u5931\u914d\u7684\u9c81\u68d2\u7684\u8ffd\u8e2a\uff1b</li> <li>\u4e00\u4e2a\u4e3b\u8981\u7528\u5168\u666f\u89c6\u9891\u6a21\u62df  DC-video \u7684\u6570\u636e\u96c6\uff1b</li> </ul>"},{"location":"pape_read/TRACE/#\u65b9\u6cd5","title":"\u65b9\u6cd5","text":"<p>\u53c2\u8003\u6d41\u7a0b\u56fe\u505a\u89e3\u91ca\u3002</p> <ul> <li>\u8f93\u5165\u7684 Video \u6309\u5e27\u8f93\u5165\uff0c\u5373\u8f93\u5165 N \u5f20\u56fe\u7247\uff1b\u540c\u65f6 user \u6307\u5b9a\u9700\u8981\u8ffd\u8e2a\u7684\u4eba\u6570 K\uff1b</li> <li>\u968f\u540e\uff0c\u56fe\u7247\u5e8f\u5217\u5206\u522b\u901a\u8fc7 Image backbone \u548c Motion backbone \u5f97\u5230\u5355\u5e27\u7684\u7279\u5f81 map \\(F_i\\) \u548c\u5149\u6d41 map \\(O_i\\)\uff1b<ul> <li>Image backbone(HRNet-32) \u7ebf\u91cc\uff0c\u5229\u7528 \\(F_{i-1}\\) \u548c \\(F_{i}\\)\uff0c\u4ee5\u53ca\u4e0a\u4e00\u4e2a\u65f6\u5e8f\u7279\u5f81\u4f20\u64ad\u6a21(temporal feature propagation module, ConvGRU)\u5757\u5f97\u5230\u7684 \\(H_{i-1}\\)\uff0c\u9884\u6d4b\u8fd9\u4e00\u5e27\u7684\u65f6\u5e8f\u7279\u5f81\uff0c\u5e76\u5f97\u5230\u7ecf\u8fc7\u6a21\u7cca\u7684\u2014\u2014\u5305\u542b\u65f6\u5e8f\u4fe1\u606f\u7684\u7279\u5f81 map \\(F_i'\\)\uff1b<ul> <li> \u95ee\u9898\uff1a\u8fd9\u91cc\u7684 ConvGRU \u76f8\u5173\u7684\u4e0d\u662f\u5f88\u6e05\u695a\uff0c\u6bd4\u5982 \\(H_i\\) \u662f\u4ec0\u4e48\uff1f \u6682\u65f6\u8df3\u8fc7\u3002</li> </ul> </li> <li>Motion backbone(RAFT) \u8ba1\u7b97\u5149\u6d41\uff1b</li> </ul> </li> <li>\u5728\u5b8c\u6210\u65f6\u5e8f\u7279\u5f81\u63d0\u53d6(temporal feature extraction)\u4ee5\u540e\uff0c\u662f\u4e00\u7cfb\u5217\u7684 head network\uff0c\u5b83\u4eec\u5e76\u4e0d\u5b8c\u5168\u5e73\u884c\uff0c\u90e8\u5206 branch \u548c\u5176\u5b83 branch \u6709\u5148\u540e\u8981\u6c42\uff0c\u4f46\u662f\u65e2\u7136\u56fe\u90fd\u8fd9\u4e48\u753b\u4e86\uff0c\u8fd9\u91cc\u5c31\u5f53\u5e73\u884c\u7684\u6a21\u5757\u6765\u8bb2\uff1b<ul> <li>Detection \u6a21\u5757\uff0c\u4ee5\u65f6\u5e8f\u56fe\u50cf\u7279\u5f81 \\(F_i'\\) \u4e3a\u8f93\u5165\uff1b<ul> <li>\u76f8\u673a\u5ea7\u6807\u7cfb\uff1b</li> <li>\u4f7f\u7528\u6b63\u89c6\u548c\u4fef\u89c6\u4e24\u4e2a\u65b9\u5411\u7684 view maps \u5408\u6210\u9884\u6d4b\uff08\u6765\u5219 BEV\uff09\uff0c\u5f97\u5230\u4e00\u4e2a 3D \u4e2d\u5fc3 map(3D Center map) \\(M_C^{3D}\\in \\mathrm{R}^{1\\times D\\times H\\times W}\\) \u548c\u4e00\u4e2a 3D \u5b9a\u4f4d map(3D Localization map) \\(M_{L}^{3D} \\in \\mathrm{R}^{1\\times D\\times H\\times W}\\)\uff1b</li> <li>\u4ece \\(M_C^{3D}\\) \u4e2d\u5f97\u5230 K \u4e2a\u5bf9\u8c61\u7684 3D \u4e2d\u5fc3 \\(\\tilde t_{i}\\) \u53ca\u5176\u7f6e\u4fe1\u5ea6 \\(c_i\\)\uff0c\u7136\u540e\u4ece \\(M_{L}^{3D}\\) \u4e2d\u5728 \\(\\tilde t_{i}\\) \u5904\u91c7\u6837\u4ece \\(\\tilde t_{i}\\) \u6307\u5411\u7cbe\u786e\u4f4d\u7f6e\u7684\u504f\u79fb\u5411\u91cf \\(\\Delta t_i\\)\uff0c\u4e8e\u662f\u5f97\u5230\u7cbe\u786e\u7684\u4f4d\u7f6e\u4e3a \\(t_i = \\tilde{t}_i + \\Delta t\\)\uff1b<ul> <li> \u95ee\u9898\uff1a\u4e3a\u5565\u8981\u4e24\u6b65\uff0c\u4e0d\u80fd\u76f4\u63a5\u5f97\u5230\u7cbe\u786e\u4f4d\u7f6e\u5417\uff1f \u9700\u8981\u5b9e\u9a8c\u8bc1\u660e\u3002</li> </ul> </li> </ul> </li> <li>Tracking \u6a21\u5757\uff0c\u4ee5\u65f6\u5e8f\u56fe\u50cf\u7279\u5f81 \\(F_i'\\) \u548c\u5149\u6d41 \\(O_i\\) \u4e3a\u8f93\u5165\uff1b<ul> <li>\u76f8\u673a\u5ea7\u6807\u7cfb\uff1b</li> <li>\u4f7f\u7528 \\(F_i'\\) \u548c \\(O_i\\) \u9884\u6d4b 3D \u8fd0\u52a8\u504f\u79fb map(3D Motion Offset map) \\(M^{3D}_{M} \\in \\mathrm{R}^{3\\times D\\times H\\times W}\\)\uff0c\u6765\u63a8\u7406\u4eba\u5728 3D \u7a7a\u95f4\u4e2d\u7684\u4f4d\u7f6e\u504f\u79fb \\(\\Delta m_i\\)\uff0c\u8fd9\u4e2a\u504f\u79fb\u53ea\u662f\u7528\u6765\u505a tracking \u7684\uff1b</li> <li>\u5229\u7528 \\(\\Delta m_i\\)\uff0c\\(t_i\\) \u548c \\(c_i\\)\uff0c\u5728 Memory unit \u7684\u4f5c\u7528\u4e0b\u5b9e\u73b0\u8ffd\u8e2a\uff1b</li> <li>Memory unit \u7684\u5de5\u4f5c\u6d41\u7a0b\u5206\u4e09\u4e2a\u6b65\u9aa4\uff1a<ul> <li>\u521d\u59cb\u5316\uff1b</li> <li>\u5339\u914d\uff1b</li> <li>\u66f4\u65b0\uff1b</li> </ul> </li> </ul> </li> <li>Mesh \u6a21\u5757\uff0c\u4ee5\u65f6\u5e8f\u56fe\u50cf\u7279\u5f81 \\(F_i'\\) \u548c\u5149\u6d41 \\(O_i\\) \u4e3a\u8f93\u5165\uff1b<ul> <li>\u5f97\u5230 SMPL \u7ed3\u679c\uff1b</li> </ul> </li> <li>World \u6a21\u5757\uff0c\u4ee5\u65f6\u5e8f\u56fe\u50cf\u7279\u5f81 \\(F_i'\\) \u548c\u5149\u6d41 \\(O_i\\) \u4e3a\u8f93\u5165\uff1b<ul> <li>\u5373\u4e4b\u524d\u63d0\u5230\u7684\u4f7f\u7528 pose \u6765\u4f30\u8ba1\u5168\u5c40\u7684\u52a8\u4f5c\uff1b</li> </ul> </li> </ul> </li> </ul>"},{"location":"pape_read/TRACE/#\u6570\u636e\u96c6","title":"\u6570\u636e\u96c6","text":"<p>\u7565\u3002</p>"},{"location":"pape_read/TRACE/#loss","title":"Loss","text":"<p>\u7565\u3002</p>"},{"location":"tech_accu/","title":"\u6249\u9875","text":"<p> \u7ea6 15 \u4e2a\u5b57 </p> <p> \u300e\u305d\u306e\u6642\u3092\u5f85\u3064\u3088\u300f      \u9761\u4e0d\u6709\u521d\uff0c\u9c9c\u514b\u6709\u7ec8\u3002  \u2014\u2014\u300a\u8bd7\u7ecf\u300b  </p>"},{"location":"tech_accu/ai/","title":"\u6249\u9875","text":"<p> \u7ea6 15 \u4e2a\u5b57 </p> <p> \u300e\u305d\u306e\u6642\u3092\u5f85\u3064\u3088\u300f      \u9761\u4e0d\u6709\u521d\uff0c\u9c9c\u514b\u6709\u7ec8\u3002  \u2014\u2014\u300a\u8bd7\u7ecf\u300b  </p>"},{"location":"tech_accu/ai/hydra/","title":"Hydra","text":"<p> \u7ea6 1136 \u4e2a\u5b57  42 \u884c\u4ee3\u7801  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 4 \u5206\u949f</p> <p>\u76f8\u5173\u94fe\u63a5</p> <ul> <li>\u5b98\u65b9\u6587\u6863 \ud83d\udd17</li> <li>\u7b14\u8bb0 \ud83d\udd17</li> </ul> <p>\u7b80\u4ecb</p> <p>Hydra \u4ea6\u53ef\u7528\u4e8e\u5176\u5b83 Python APP\uff0c\u4f46\u672c\u6587\u53ea\u4ee5 Research \u7684\u89c6\u89d2\u6765\u8c08\u8fd9\u4e2a\u5de5\u5177\u3002</p> <p>\u5728\u8fdb\u884c\u5b9e\u9a8c\u65f6\uff0c\u6211\u4eec\u53ef\u80fd\u4f1a\u5e0c\u671b\u4e00\u4e2a\u9879\u76ee\u80fd\u652f\u6301\u5207\u6362\u5176\u4e2d\u7684\u82e5\u5e72\u90e8\u4ef6\uff0c\u5c31\u597d\u50cf\u7ed9\u673a\u5668\u4eba\u66f4\u6362\u4e0d\u540c\u7684\u90e8\u4ef6\uff0c\u6765\u6d4b\u8bd5\u5176\u6027\u80fd\u3002\u800c\u6bcf\u4e00\u4e2a\u90e8\u4ef6\u90fd\u6709\u53ef\u80fd\u6709\u81ea\u5df1\u7684\u8d85\u53c2\u6570\u9700\u8981\u8bbe\u7f6e\u3002</p> <p>\u786c\u7f16\u7801\u8bbe\u7f6e\u5f53\u7136\u4e0d\u53ef\u53d6\uff0c\u8fd9\u592a\u4e0d\u4f18\u96c5\u4e86\u3002\u6240\u4ee5\u6211\u4eec\u901a\u5e38\u4f7f\u7528\u547d\u4ee4\u884c\u53c2\u6570\uff0c\u5373 args \u6765\u5b9e\u73b0\u8d85\u53c2\u6570\u7684\u4f20\u5165\u3002\u4f46\u968f\u7740\u6a21\u578b\u8d8a\u6765\u8d8a\u590d\u6742\uff0c\u9700\u8981\u7684\u8d85\u53c2\u6570\u8d8a\u6765\u8d8a\u591a\uff0c\u547d\u4ee4\u884c\u5c31\u4f1a\u8d8a\u6765\u8d8a\u957f\uff1b\u800c\u4e14\u4e0d\u540c\u7684\u201c\u90e8\u4ef6\u201d\u53ef\u80fd\u9700\u8981\u4e0d\u540c\u7684\u8d85\u53c2\u6570\uff0c\u56e0\u6b64\uff0c\u4f7f\u7528\u547d\u4ee4\u884c\u53c2\u6570\u7075\u6d3b\u6027\u5c31\u5927\u5927\u4e0b\u964d\u4e86\u3002</p> <p>\u56e0\u6b64\uff0c\u6211\u4eec\u8003\u8651\u628a\u8fd9\u4e9b\u4e1c\u897f\u653e\u5728\u6587\u4ef6\u91cc\uff0c\u9700\u8981\u4fee\u6539\u65f6\u5c31\u76f4\u63a5\u4fee\u6539\u6587\u4ef6\uff0c\u8fd9\u6837\u4fee\u6539\u53c2\u6570\u76f8\u5bf9\u5c31\u7075\u6d3b\u4e00\u4e9b\u3002\u66f4\u8fdb\u4e00\u6b65\u7684\uff0c\u6211\u4eec\u8fd8\u53ef\u4ee5\u901a\u8fc7\u5c06\u4e0d\u540c\u7684\u7ec4\u5408\u5206\u522b\u4fdd\u5b58\u4e3a\u4e00\u4e2a\u6587\u4ef6\uff0c\u7528\u6307\u5b9a\u7279\u5b9a\u6587\u4ef6\u7684\u65b9\u5f0f\u6765\u9009\u62e9\u4e00\u4e2a\u5df2\u7ecf\u8bbe\u7f6e\u597d\u7684 pipeline\u3002</p> <p>\u4f46\u662f\u8fd9\u6837\u8fd8\u6709\u4e24\u4e2a\u95ee\u9898\uff0c\u9996\u5148\uff0c\u8fd9\u6837\u5199\u7684\u8bdd\uff0c\u914d\u7f6e\u6587\u4ef6\u7684\u590d\u7528\u7387\u662f\u6bd4\u8f83\u4f4e\u7684\uff0c\u56e0\u4e3a\u5404\u4e2a\u914d\u7f6e\u4e4b\u95f4\u5dee\u522b\u53ef\u80fd\u4e0d\u5927\uff0c\u53ef\u80fd\u4e92\u76f8\u53ea\u6709\u4e00\u5c0f\u90e8\u5206\u7684\u4e0d\u540c\uff0c\u800c\u590d\u7528\u7387\u4f4e\u7684\u574f\u5904\u5c31\u4e0d\u5fc5\u591a\u8bf4\u4e86\uff1b\u5176\u6b21\uff0c\u5c31\u7b97\u6211\u4eec\u7528\u5c42\u6b21\u5316\u7684\u914d\u7f6e\u6587\u4ef6\u6765\u89e3\u51b3\u590d\u7528\u7684\u95ee\u9898\uff0c\u6211\u4eec\u5728\u5b9e\u9645\u4ee3\u7801\u91cc\u4e5f\u9700\u8981\u4f7f\u7528\u7e41\u590d\u7684\u5206\u652f\u8bed\u53e5\u624d\u80fd\u5f88\u597d\u5730\u63a7\u5236\u914d\u7f6e\u7684\u9009\u62e9\u3002</p> <p>\u4e8e\u662f\uff0cHydra \u5e94\u8fd0\u800c\u751f\u3002Hydra \u4f1a\u4ee5\u7279\u5b9a\u7684\u65b9\u5f0f\u5904\u7406\u5c42\u6b21\u5316\u7684\u914d\u7f6e\u6587\u4ef6\uff0c\u5b83\u7684\u884c\u4e3a\u5f88\u50cf Cpp \u7684 <code>#include</code>\uff0c\u4f1a\u628a\u9009\u4e2d\u7684\u540e\u4ee3 Group \u91cc\u7684\u914d\u7f6e\u6587\u4ef6\u5d4c\u5165\u5230\u5f53\u524d\u914d\u7f6e\u6587\u4ef6\u91cc\u3002</p> <p>\u66f4\u5177\u4f53\u7684\u5173\u4e8e Hydra \u7684\u89c4\u8303\uff0c\u8bf7\u53c2\u8003\u5b98\u65b9\u6587\u6863\uff0c\u672c\u6587\u4e3b\u8981\u5bf9\u5b98\u65b9\u6587\u6863\u505a\u4e00\u4e9b\u8865\u5145\uff0c\u901a\u8fc7\u5b9e\u9a8c\u63a2\u7d22\u4e00\u4e9b Hydra \u6587\u6863\u4e2d\u6ca1\u6709\u63d0\u5230\u7684\u6027\u8d28\u3002</p>"},{"location":"tech_accu/ai/hydra/#\u5173\u4e8e-ab-\u8bed\u6cd5","title":"\u5173\u4e8e +A=B \u8bed\u6cd5","text":"<p>\u5728\u6587\u6863\u4e2d\uff0c\u6709\u4e24\u4e2a\u5730\u65b9\u63d0\u5230\u4e86 +A=B \u7684\u8bed\u6cd5\u3002\u7b2c\u4e00\u6b21\u662f\u5728\u8fd9\u91cc\uff1a</p> <p>You can add config values via the command line. The <code>+</code> indicates that the field is new.</p> <pre><code>$ python my_app.py +db.driver=mysql +db.user=omry +db.password=secret\ndb:\n  driver: mysql\n  user: omry\n  password: secret\n</code></pre> files my_app.py<pre><code>from omegaconf import DictConfig, OmegaConf\nimport hydra\n\n@hydra.main(version_base=None)\ndef my_app(cfg: DictConfig) -&gt; None:\n    print(OmegaConf.to_yaml(cfg))\n\nif __name__ == \"__main__\":\n    my_app()\n</code></pre> <p>\u7b2c\u4e8c\u6b21\u662f\u5728\u8fd9\u91cc\uff1a</p> <p>Select an item from a config group with <code>+GROUP=OPTION</code>, e.g:</p> <pre><code>$ python my_app.py +db=postgresql\ndb:\n  driver: postgresql\n  pass: drowssap\n  timeout: 10\n  user: postgres_user\n</code></pre> files Directory layout<pre><code>    \u251c\u2500 conf\n    \u2502  \u2514\u2500 db\n    \u2502      \u251c\u2500 mysql.yaml\n    \u2502      \u2514\u2500 postgresql.yaml\n    \u2514\u2500\u2500 my_app.py\n</code></pre> db/mysql.yaml<pre><code>driver: mysql\nuser: omry\npassword: secret\n</code></pre> db/postgresql.yaml<pre><code>driver: postgresql\nuser: postgres_user\npassword: drowssap\ntimeout: 10\n</code></pre> my_app.py<pre><code>from omegaconf import DictConfig, OmegaConf\nimport hydra\n\n@hydra.main(version_base=None)\ndef my_app(cfg: DictConfig) -&gt; None:\n    print(OmegaConf.to_yaml(cfg))\n\nif __name__ == \"__main__\":\n    my_app()\n</code></pre> <p>\u524d\u8005\u8868\u793a\u589e\u52a0\u4e00\u4e2a field\uff0c\u540e\u8005\u8868\u793a\u6307\u5b9a\u4e00\u4e2a group\uff0c\u5176\u542b\u4e49\u662f\u4e0d\u540c\u7684\uff0c\u800c\u770b\u8d77\u6765\u662f\u6709\u6b67\u4e49\u7684\u3002</p> <p>\u6839\u636e\u6211\u7684\u6d4b\u8bd5\uff0c<code>+A=B</code> \u5177\u4f53\u662f\u54ea\u4e00\u79cd\uff0c\u53d6\u51b3\u4e8e\u662f\u5426\u5b58\u5728\u540d\u4e3a A \u7684 folder\u3002\u5373\uff1a</p> <ul> <li>\u5982\u679c\u5b58\u5728\u540d\u4e3a A \u7684 folder\uff0c\u5219 <code>+A=B</code> \u8868\u793a\u6307\u5b9a A group \u91cc\u7684 <code>b.yaml</code> \u9879\uff1b</li> <li>\u5982\u679c\u4e0d\u5b58\u5728\u540d\u4e3a A \u7684 folder\uff0c\u5219 <code>+A=B</code> \u8868\u793a\u589e\u52a0\u4e00\u4e2a field\uff0c\u5176 key \u4e3a A\uff0cvalue \u4e3a B\uff1b</li> </ul> <p>\u66f4\u8fdb\u4e00\u6b65\u7684\uff0c\u53ea\u8981\u5f53\u524d\u76ee\u5f55\u5b58\u5728\u540d\u4e3a <code>A</code> \u7684 folder\uff0c\u90a3\u4e48\u5728\u5f53\u524d <code>yaml</code> \u6587\u4ef6\u4e2d\u5c31\u65e0\u6cd5\u5c06 <code>A</code> \u4f5c\u4e3a\u4e00\u4e2a field \u7684 key\u3002</p> <p>\u4e4b\u6240\u4ee5\u5f3a\u8c03\u5f53\u524d\uff0c\u662f\u56e0\u4e3a\u5b83\u53ef\u4ee5\u88ab\u7236\u6bcd\u7684 <code>yaml</code> \u6587\u4ef6\u4e2d\u7684\uff0c\u4ee5 <code>A</code> \u4e3a key \u7684 k-v \u5bf9\u8986\u76d6\u3002</p> <p>\u4f8b\u5982\uff0c\u867d\u7136\u6dfb\u52a0 <code>A=1</code> \u66ff\u6362\u4f5c\u4e3a group \u7684 <code>A</code> \u4f1a\u62a5\u9519\uff0c\u4f46\u662f\u6dfb\u52a0 <code>A.B=1</code> \u5374\u53ef\u4ee5\u8986\u76d6 <code>A</code> \u4e0b\u7684\u4f5c\u4e3a group \u7684 <code>B</code>\uff1b\u4ea6\u6216\u5728\u6700\u7684 <code>config.yaml</code> \u91cc\u6dfb\u52a0\u8fd9\u6837\u4e00\u6bb5\u4e5f\u53ef\u4ee5\u8d77\u5230\u540c\u6837\u7684\u6548\u679c\uff1a</p> <pre><code>A:\nB: 1\n</code></pre> <p>\u5373\uff0c\u5bf9\u4e8e\u201c\u65e0\u6cd5\u5c06 group \u8986\u76d6\u4e3a field\u201d\u8fd9\u4ef6\u4e8b\u7684\u4fdd\u62a4\uff0c\u53ea\u6709\u76ee\u5f55\u4e00\u5c42\u5185\u6709\u6548\u3002</p>"},{"location":"tech_accu/ai/hydra/#\u8986\u76d6\u5173\u7cfb","title":"\u8986\u76d6\u5173\u7cfb","text":"<p>\u9996\u5148\uff0c\u9664\u4e86\u5728\u4e0a\u4e00\u8282\u63d0\u5230\u7684\u5173\u4e8e field \u548c group \u7684\u8986\u76d6\u5173\u7cfb\uff0c\u66f4\u91cd\u8981\u7684\u662f\u5728\u4e0d\u540c\u5c42\u7684 yaml \u4e4b\u95f4\uff0c\u76f8\u540c\u952e\u7684\u503c\u7684\u8986\u76d6\u5173\u7cfb\u3002</p> <p>\u9996\u5148\uff0c\u5355\u770b defaults\uff0c\u5b98\u65b9\u5728\u6587\u6863\u4e2d\u6709\u63d0\u5230\u89c4\u5219\uff1a</p> <p>The defaults are ordered:</p> <ul> <li>If multiple configs define the same value, the last one wins.</li> <li>If multiple configs contribute to the same dictionary, the result is the combined dictionary.</li> </ul> <p>\u6b64\u5916\uff0c\u5982\u679c\u5df2\u7ecf\u5728\u5185\u5c42 defaults \u8bbe\u7f6e\u4e86\u952e\u7684\u9ed8\u8ba4\u503c\uff0c\u5c31\u4e0d\u80fd\u5728\u5916\u5c42\u4e3a\u8fd9\u4e2a\u952e\u8bbe\u7f6e\u9ed8\u8ba4\u503c\uff0c\u53cd\u4e4b\u4ea6\u7136\u3002</p> <p>\ud83c\udf30</p> <p>\u4f8b\u5982\u4e0b\u9762\u8fd9\u4e24\u4e2a\u6587\u4ef6\u4e2d\uff0c<code>- group1/group2: option1_1</code> \u548c <code>- group2: option1_1</code> \u8fd9\u4e24\u884c\u662f\u51b2\u7a81\u7684\uff0c\u53ea\u80fd\u9009\u5176\u4e00\u7684\u3002</p> config.yaml<pre><code>defaults:\n- group1: option1\n- group1/group2: option1_1\n</code></pre> group1/option1.yaml<pre><code>defaults:\n- group2: option1_1\n</code></pre> <p>\u56e0\u6b64\uff0c\u4e00\u822c\u6765\u8bf4\u5c3d\u91cf\u907f\u514d\u8ba9\u914d\u7f6e\u5c42\u6570\u8d85\u8fc7\u4e24\u5c42\u3002</p> <p>\u800c\u5173\u4e8e defaults \u4ee5\u5916\u7684\u90e8\u5206\uff0c\u89c4\u5219\u5982\u4e0b\uff1a</p> <ol> <li>\u5f53\u6700\u5916\u5c42\u7684 <code>config.yaml</code> \u548c\u5728 <code>defaults:</code> \u91cc\u6307\u5b9a\u7684 <code>yaml</code> \u914d\u7f6e\u6587\u4ef6\u5b58\u5728\u51b2\u7a81\u7684\u952e\u65f6\uff0c\u4ee5 <code>config.yaml</code> \u91cc\u7684\u4e3a\u51c6\uff0c\uff08\u65e0\u8bba\u662f\u5426\u6709 <code>GROUP=OPTION</code> \u9009\u9879\uff09\uff1b</li> <li>\u5f53\u952e\u4e0d\u5b58\u5728\u4e8e <code>defaults:</code> \u4e2d\uff0c\u800c\u53ea\u5728\u547d\u4ee4\u884c\u4e2d\u901a\u8fc7 <code>+GROUP=OPTION</code> \u9009\u4e2d\u65f6\uff0c\u4ee5 <code>OPTION.yaml</code> \u91cc\u7684\u4e3a\u51c6\uff1b</li> </ol>"},{"location":"tech_accu/ai/pytorch/","title":"PyTorch","text":"<p> \u7ea6 565 \u4e2a\u5b57  48 \u884c\u4ee3\u7801  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 2 \u5206\u949f</p> <p>\u5f03\u5751\u4e86\uff0c\u611f\u89c9\u6ca1\u5565\u5199\u7684\u5fc5\u8981</p> <ul> <li>PyTorch \u4e3b\u8981\u6709\u4e24\u4e2a\u7528\u9014\uff1a<ul> <li>\u80fd\u591f\u4f7f\u7528 GPU \u52a0\u901f\u7684 NumPy \u66ff\u4ee3\u54c1\uff1b</li> <li>\u5185\u7f6e\u7684\u81ea\u52a8\u5fae\u5206\u5e93\u7b49\u5bf9\u795e\u7ecf\u7f51\u7edc\u7684\u5b9e\u73b0\u4ea7\u751f\u8f83\u5927\u7684\u5e2e\u52a9\uff1b</li> </ul> </li> </ul> \u53c2\u8003\u8d44\u6599 <ul> <li>PyTorch \u5b98\u7f51\uff1a\ud83d\udd17</li> <li>A 60 MINUTE BLITZ\uff1a\ud83d\udd17<ul> <li>*\u672c\u6587\u4e3b\u8981\u6309\u7167\u8fd9\u7bc7\u6587\u7ae0\u7684\u601d\u8def\u6765\uff1b</li> </ul> </li> <li>PyTorch \u5b98\u65b9\u6559\u7a0b\u4e2d\u6587\u7248\uff1a\ud83d\udd17</li> <li>PyTorch\u7b80\u660e\u6559\u7a0b\uff1a\ud83d\udd17</li> </ul>"},{"location":"tech_accu/ai/pytorch/#\u5b89\u88c5","title":"\u5b89\u88c5","text":"<p>\u6839\u636e \u8fd9\u91cc \u63d0\u4f9b\u7684\u65b9\u6cd5\u83b7\u53d6\u5b89\u88c5\u9014\u5f84\uff0c\u6ce8\u610f\u9009\u62e9\u4e0e\u60a8\u7684\u73af\u5883\u76f8\u7b26\u7684\u6761\u4ef6\u3002</p> <p>\u4f9d\u8d56\u4e4b\u7c7b\u7684\u90fd\u5df2\u7ecf\u5728\u8be5\u9875\u9762\u5199\u7684\u5f88\u6e05\u695a\u4e86\u3002</p> <p>\u5b8c\u6210\u5b89\u88c5\u540e\uff0c\u6211\u4eec\u901a\u8fc7\u5982\u4e0b\u65b9\u6cd5\u6765\u68c0\u6d4b\u662f\u5426\u5b89\u88c5\u6210\u529f\uff1a</p> <pre><code>$ python\n&gt;&gt;&gt; import torch\n&gt;&gt;&gt; x = torch.rand(5, 3)\n&gt;&gt;&gt; print(x)\ntensor([[0.8577, 0.6416, 0.2632],\n        [0.3853, 0.8534, 0.4877],\n        [0.0628, 0.2360, 0.8810],\n        [0.1766, 0.8024, 0.5447],\n        [0.3938, 0.9232, 0.4407]])\n</code></pre>"},{"location":"tech_accu/ai/pytorch/#\u5f20\u91cf--tensors","title":"\u5f20\u91cf | Tensors","text":"<p>Tensors \u662f NumPy \u4e2d ndarrys \u7684\u4e00\u79cd\u65e0\u75db\u66ff\u4ee3\uff0c\u53ea\u4e0d\u8fc7 tensors \u80fd\u591f\u6709\u6548\u5229\u7528 GPU \u8fdb\u884c\u52a0\u901f\u3002</p>"},{"location":"tech_accu/ai/pytorch/#\u521d\u59cb\u5316","title":"\u521d\u59cb\u5316","text":"<p>\u663e\u7136\uff0c\u521d\u59cb\u5316\u6709\u5f88\u591a\u65b9\u6cd5\uff0c\u8fd9\u91cc\u63d0\u4f9b\u51e0\u79cd\u3002</p> \u901a\u8fc7\u6570\u636e\u751f\u6210\u901a\u8fc7 NumPy array \u751f\u6210\u901a\u8fc7\u53e6\u5916\u4e00\u4e2a tensor \u751f\u6210\u4f7f\u7528\u5e38\u6570\u6216\u968f\u673a\u521d\u59cb\u5316 <p><pre><code>data = [[1, 2], [3, 4]]\nx_data = torch.tensor(data)\nprint(x_data)\n</code></pre> \u9884\u671f\u8f93\u51fa\u5982\u4e0b\uff1a</p> <p>Output</p> <pre><code>tensor([[1, 2],\n        [3, 4]])\n</code></pre> <p><pre><code>np_array = np.array(data)\nx_np = torch.from_numpy(np_array)\nprint(x_np)\n</code></pre> \u9884\u671f\u8f93\u51fa\u5982\u4e0b\uff1a</p> <p>Output</p> <pre><code>tensor([[1, 2],\n        [3, 4]])\n</code></pre> <p><pre><code>x_ones = torch.ones_like(x_data) # retains the properties of x_data\nprint(f\"Ones Tensor: \\n {x_ones} \\n\")\n\nx_rand = torch.rand_like(x_data, dtype=torch.float) # overrides the datatype of x_data\nprint(f\"Random Tensor: \\n {x_rand} \\n\")\n</code></pre> \u9884\u671f\u8f93\u51fa\u5982\u4e0b\uff1a</p> <p>Output</p> <pre><code>Ones Tensor:\ntensor([[1, 1],\n        [1, 1]])\n\nRandom Tensor:\ntensor([[0.4557, 0.7406],\n        [0.5935, 0.1859]])\n</code></pre> <p><pre><code>    shape = (2, 3)\n    rand_tensor = torch.rand(shape)\n    ones_tensor = torch.ones(shape)\n    zeros_tensor = torch.zeros(shape)\n\n    print(f\"Random Tensor: \\n {rand_tensor} \\n\")\n    print(f\"Ones Tensor: \\n {ones_tensor} \\n\")\n    print(f\"Zeros Tensor: \\n {zeros_tensor}\")\n</code></pre> \u9884\u671f\u8f93\u51fa\u5982\u4e0b\uff1a</p> <p>Output</p> <pre><code>Random Tensor:\n tensor([[0.4434, 0.1717, 0.7331],\n        [0.4211, 0.8945, 0.2239]])\n\nOnes Tensor:\n tensor([[1., 1., 1.],\n        [1., 1., 1.]])\n\nZeros Tensor:\n tensor([[0., 0., 0.],\n        [0., 0., 0.]])\n</code></pre>"},{"location":"tech_accu/ai/pytorch/#\u5c5e\u6027","title":"\u5c5e\u6027","text":"<p>\u8fd9\u91cc\u4e3b\u8981\u6d89\u53ca\u7684\u5f20\u91cf\u7684\u5c5e\u6027\u4e3a \u5f62\u72b6(<code>shape</code>)\u3001\u6570\u636e\u7c7b\u578b(<code>dtype</code>) \u548c \u6570\u636e\u6240\u5b58\u50a8\u5728\u7684\u786c\u4ef6\u8bbe\u5907(<code>device</code>)\u3002</p> <pre><code>tensor = torch.rand(3, 4)\n\nprint(f\"Shape of tensor: {tensor.shape}\")\nprint(f\"Datatype of tensor: {tensor.dtype}\")\nprint(f\"Device tensor is stored on: {tensor.device}\")\n</code></pre> <p>\u9884\u671f\u8f93\u51fa\u5982\u4e0b\uff1a</p> <p>Output</p> <pre><code>Shape of tensor: torch.Size([3, 4])\nDatatype of tensor: torch.float32\nDevice tensor is stored on: cpu\n</code></pre>"},{"location":"tech_accu/ai/pytorch/#\u65b9\u6cd5\u4e0e\u64cd\u4f5c","title":"\u65b9\u6cd5\u4e0e\u64cd\u4f5c","text":"<p>\u5bf9\u5f20\u91cf\u7684\u64cd\u4f5c\u65b9\u6cd5\u975e\u5e38\u4e4b\u591a\uff0c\u5f88\u96be\u5728\u672c\u6587\u4e2d\u5168\u90e8\u6d89\u53ca\uff0c\u56e0\u800c\u4e5f\u53ea\u662f\u653e\u4e2a \u6587\u6863 \u5728\u8fd9\u8fb9\uff0c\u5728\u6b64\u53ea\u4ecb\u7ecd\u6bd4\u8f83\u57fa\u7840\u7684\u51e0\u4e2a\u3002</p>"},{"location":"tech_accu/ai/pytorch/#\u4f7f\u7528-gpu-\u52a0\u901f","title":"\u4f7f\u7528 GPU \u52a0\u901f","text":"<p>\u4ee4\u4eba\u5e78\u559c\u7684\u662f\uff0c\u5bf9\u5f20\u91cf\u7684\u8fd9\u4e9b\u64cd\u4f5c\u90fd\u53ef\u4ee5\u4f7f\u7528 GPU \u6765\u8fdb\u884c\u52a0\u901f\uff0c\u5f53\u7136\u5728\u6b64\u4e4b\u524d\u6211\u4eec\u9700\u8981\u5c06\u5b83\u8f6c\u79fb\u5230 GPU \u4e0a\u2014\u2014\u5982\u679c\u53ef\u4ee5\u7684\u8bdd\u3002</p> <pre><code># We move our tensor to the GPU if available\nif torch.cuda.is_available():\n    tensor = tensor.to('cuda')\n    print(f\"Device tensor is stored on: {tensor.device}\")\n</code></pre> <p>Output</p> <pre><code>Device tensor is stored on: cuda:0\n</code></pre>"},{"location":"tech_accu/ai/pytorch/#\u8fd0\u7b97","title":"\u8fd0\u7b97","text":"<p>\u6ce8\u610f</p> <p>\u5982\u679c\u4e00\u4e2a tensor \u7684\u65b9\u6cd5\u4ee5 <code>_</code> \u7ed3\u5c3e\uff0c\u90a3\u4e48\u8bf4\u660e\u8fd9\u4e2a\u8fd0\u7b97\u4f1a\u4fee\u6539\u8fd9\u4e2a tensor \u81ea\u8eab\u3002</p> <p>\u5373\uff0c<code>x.method_(...)</code> \u5c06\u4f1a\u4fee\u6539 <code>x</code> \u672c\u8eab\u3002</p> <p>PyTorch \u5bf9\u56db\u5219\u8fd0\u7b97\u7b26\u8fdb\u884c\u4e86\u4e00\u4e9b\u91cd\u8f7d\uff0c\u5176\u4e0e\u6b63\u5e38\u65b9\u6cd5\u7684\u6620\u5c04\u5173\u7cfb\u5982\u4e0b\uff1a</p> \u8fd0\u7b97\u7b26 \u7b49\u4ef7\u65b9\u6cd5 <code>+</code> <code>torch.add()</code> <code>-</code> <code>torch.sub()</code> <code>*</code> <code>torch.mul()</code> <code>/</code> <code>torch.div()</code>"},{"location":"tech_accu/ai/pytorch/#\u7d22\u5f15\u4e0e\u5207\u7247","title":"\u7d22\u5f15\u4e0e\u5207\u7247","text":"<p><pre><code>tensor = torch.ones(4, 4)\ntensor[:,1] = 0\nprint(tensor)\n</code></pre> \u9884\u671f\u8f93\u51fa\u5982\u4e0b\uff1a</p> <p>Output</p> <pre><code>tensor([[1., 0., 1., 1.],\n        [1., 0., 1., 1.],\n        [1., 0., 1., 1.],\n        [1., 0., 1., 1.]])\n</code></pre>"},{"location":"tech_accu/language/cpp/","title":"Cpp about OOP","text":"<p> \u7ea6 53 \u4e2a\u5b57 </p> <p>\u76f8\u5173\u4fe1\u606f</p> <p>\u8fd9\u4e2a\u6761\u76ee\u653e\u7684\u4e3b\u8981\u662f Cpp \u5173\u4e8e OOP \u7684\u4e00\u4e9b\u8bed\u6cd5\u3002</p> <p>\u4e3b\u8981\u8fc1\u79fb\u81ea\u5927\u4e00\u7684 yuque \u6587\u6863\uff0c\u518d\u4e4b\u540e\u4e5f\u4f1a\u6709\u4e00\u4e9b\u4fee\u6539\u3002</p> <p>\u8fc1\u79fb\u524d\u7684\u6587\u4ef6</p>"},{"location":"tech_accu/language/cpp/Part0/","title":"[pre] \u524d\u7f6e\u4e0e\u6742\u9879","text":"<p> \u7ea6 1746 \u4e2a\u5b57  74 \u884c\u4ee3\u7801  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 7 \u5206\u949f</p>"},{"location":"tech_accu/language/cpp/Part0/#1x-\u5f15\u7528reference","title":"[1.x] \u5f15\u7528reference","text":"<p>1.\u521b\u5efabinding\u5173\u7cfb</p> <p>\u9700\u8981\u7406\u89e3\u7684\u662f\uff0c\u5f15\u7528\u672c\u8d28\u5c31\u662f\u6307\u9488\u3002\u5b83\u662f\u6307\u9488\u7684\u7cd6\u3002</p> <p><code>typename &amp; refname = name;</code> \u521b\u5efa\u4e86 <code>(typename)name</code> \u7684\u5f15\u7528 <code>(reference)refname</code></p> <p>\u5728bingding\u5173\u7cfb\u5efa\u7acb\u540e\uff0c\u5728 <code>name</code> \u548c <code>refname</code> \u7684\u4f5c\u7528\u57df\u5185 <code>refname</code> \u548c <code>name</code> \u57fa\u672c\u7b49\u6548\uff08\u662f\u53d8\u91cf\u7684\u7ed1\u5b9a\u5173\u7cfb\uff0c\u800c\u975e\u50cf <code>#define</code> \u90a3\u6837\u7684\u5b57\u7b26\u66ff\u6362\u5173\u7cfb</p> <ul> <li>\u4e00\u822c\u6765\u8bf4(\u4e0d\u8003\u8651const+reference)\u80fd\u521b\u5efa\u7684\u5f15\u7528\u7684\u5fc5\u987b\u662f\u4e2a\u53d8\u91cf\uff0c\u800c\u4e0d\u80fd\u662f\u4e2a\u8868\u8fbe\u5f0f\u3001\u5e38\u91cf\u3002<ul> <li>\u6362\u53e5\u8bdd\u8bf4\uff0c\u53ea\u80fd\u7ed9\u5de6\u503c(left value)\u521b\u5efa\u5f15\u7528 \u7279\u522b\u7684\uff1a</li> </ul> </li> </ul> <pre><code>int x = 1, y = 10, *p = &amp;x, &amp;ref = *p;\n// \u6b64\u65f6 x = 1, y = 10, *p = 1, ref = 1\n\n*p = 2;\n// \u6b64\u65f6 x = 2, y = 10, *p = 2, ref = 2\n\np = &amp;y;\n// \u6b64\u65f6 x = 2, y = 10, *p = 10, ref = 2\n</code></pre> <ul> <li>\u5f15\u7528\u5728\u521b\u5efa\u7684\u65f6\u5019\u5fc5\u987b\u521d\u59cb\u5316\uff0c\u5373<code>int &amp;x;</code>\u9519\u8bef\uff1b<code>int &amp;x = y;</code>\u6b63\u786e\u3002</li> <li>Bindings\u4e00\u65e6\u5efa\u7acb\uff0c\u65e0\u6cd5\u53d6\u6d88</li> <li>reference\u672c\u8d28\u4e0a\u5c31\u662f\u53d7\u9650\u7684pointer</li> <li>reference\u4e0d\u5b58\u5728reference</li> <li>reference\u4e0d\u5b58\u5728pointer<ul> <li>\u5b9a\u4e49<code>int *p = &amp;x;</code></li> <li><code>int&amp;* ref = ...;</code>\u975e\u6cd5\uff0c<code>ref</code>\u4e0d\u80fd\u662f\u4e00\u4e2a\u5f15\u7528\u7684\u6307\u9488</li> <li><code>int*&amp; ref = p;</code>\u5408\u6cd5\uff0c<code>ref</code>\u662f\u4e00\u4e2a\u6307\u9488\u7684\u5f15\u7528</li> </ul> </li> <li>\u4e0d\u5b58\u5728reference\u6570\u7ec4</li> </ul> <p>2.\u5229\u7528reference\u4f20\u53c2</p> <p>\u5229\u7528reference\u53ef\u4ee5\u7c7b\u4f3c\u4f20\u6307\u9488\u4e00\u6837\uff0c\u5728\u53d8\u91cf\u539f\u672c\u7684\u4f5c\u7528\u57df\u5916\u5bf9\u53d8\u91cf\u8fdb\u884c\u4fee\u6539</p> <pre><code>void f(int &amp;x){\nx = 1;\n}\n\nint main(){\nint p = 0;\n// \u6b64\u65f6 p = 0\nf(p);\n// \u6b64\u65f6 p = 1\n}\n</code></pre> <p>\u4f46\u6b64\u65f6\uff0c\u4f20\u5165 <code>f(p)</code> \u7684\u5b9e\u53c2 <code>p</code> \u5fc5\u987b\u4e3a\u4e00\u4e2a\u53d8\u91cf\uff0c\u4e0d\u53ef\u4ee5\u662f\u5e38\u91cf\u3001\u8868\u8fbe\u5f0f\u7b49\u3002</p> <p>3.<code>reference</code> \u4e0e <code>const</code></p> <p>\u8fdb\u884c <code>const int &amp;refA = A;</code> \u64cd\u4f5c\u540e\uff0c\u6211\u4eec\u53d1\u73b0 <code>refA</code> \u4e0d\u53ef\u4fee\u6539\uff0c\u4f46 <code>A</code> \u53ef\u4ee5\u4fee\u6539</p> <p>\u5982\u679c <code>A</code> \u5982\u6b64\u5b9a\u4e49\uff1a<code>const int A = 1;</code>\uff0c\u90a3\u4e48\uff1a</p> <ul> <li><code>int &amp;refA = A;</code>\u975e\u6cd5</li> <li><code>const int &amp;refA = A;</code>\u5408\u6cd5</li> <li><code>const int &amp;refA = 1;</code>\u5408\u6cd5</li> <li>\u51fd\u6570\u4f20\u53c2\u540c\u7406</li> </ul>"},{"location":"tech_accu/language/cpp/Part0/#2x-\u8303\u56f4\u89e3\u6790\u8fd0\u7b97\u7b26resolver","title":"[2.x] \u8303\u56f4\u89e3\u6790\u8fd0\u7b97\u7b26resolver","text":"<ul> <li><code>&lt;Class Name&gt;::&lt;Function Name&gt;</code> \u8868\u793a\u8fd9\u4e2a <code>&lt;Function Name&gt;</code> \u662f\u4e0d\u81ea\u7531\u7684\uff0c\u5c5e\u4e8e <code>&lt;Class Name&gt;</code>\u7684\uff1b</li> <li><code>::&lt;Function Name&gt;</code> \u8868\u793a\u8fd9\u4e2a <code>&lt;Function Name&gt;</code>\u662f\u5168\u5c40\u53d8\u91cf\u4e2d\u7684\u81ea\u7531\u51fd\u6570\uff08\u53d8\u91cf\u540c\u7406\uff09\uff1b</li> </ul> <pre><code>#include&lt;iostream&gt;\nusing namespace std;\n\nclass S{\npublic:\nvoid f();\nprivate:\nint a;\n};\n\nint a;\n\nvoid f(){\ncout &lt;&lt; \"qwq\\n\";\n}\n\nvoid S::f(){ // \u8fd9\u91cc\u6b63\u5728\u5b9a\u4e49\u4e00\u4e2a\u5c5e\u4e8e\u7c7bS\u7684\u7684\u51fd\u6570\n++a;     // \u8fd9\u91cc\u5bf9\u4e00\u4e2a\u7c7bS\u7684\u6210\u5458\u53d8\u91cfa\u8fdb\u884c\u4e86\u81ea\u589e\u64cd\u4f5c\n::f();   // \u8fd9\u91cc\u8c03\u7528\u4e86\u4e00\u4e2a\u5168\u5c40\u4e0b\u7684\u81ea\u7531\u51fd\u6570\n++::a;   // \u8fd9\u91cc\u5bf9\u4e00\u4e2a\u5168\u5c40\u53d8\u91cfa\u8fdb\u884c\u4e86\u81ea\u589e\u64cd\u4f5c\ncout &lt;&lt; a &lt;&lt; \" \" &lt;&lt; ::a &lt;&lt; \"\\n\";\n}\n\nint main(){\nS k;\nk.f(); }\n</code></pre> <ul> <li>\u7c7b\u7684\u9759\u6001\u53d8\u91cf\u5c5e\u4e8e\u7c7b\u4e0d\u5c5e\u4e8e\u5b9e\u4f8b\uff0c\u4e0d\u80fd\u901a\u8fc7\u6b63\u5e38\u7684\u65b9\u5f0f\u521d\u59cb\u5316\uff0c\u53ef\u4ee5\u7528\u8fc7\u8303\u56f4\u89e3\u6790\u8fd0\u7b97\u7b26\u5728\u5168\u5c40\u521d\u59cb\u5316</li> <li>\u5b9e\u9645\u4e0a\uff0c\u7f16\u8bd1\u5668\u5c06\u5bf9\u8c61\u5bf9\u9759\u6001\u53d8\u91cf\u7684\u8bbf\u95ee\u81ea\u52a8\u8f6c\u6362\u6210\u4e86\u7c7b\u5bf9\u9759\u6001\u53d8\u91cf\u7684\u8bbf\u95ee\u3002\u56e0\u6b64\uff0c\u5efa\u8bae\u59cb\u7ec8\u4f7f\u7528<code>className::staticVar</code>\u8bbf\u95ee\u9759\u6001\u53d8\u91cf_(xxjj\u5728\u8fd9\u91cc\u8bf4\u7684)_</li> </ul>"},{"location":"tech_accu/language/cpp/Part0/#3x-\u51fd\u6570\u7684\u91cd\u8f7doverload","title":"[3.x] \u51fd\u6570\u7684\u91cd\u8f7dOverload","text":"<p>\u53ef\u4ee5\u5b58\u5728\u51fd\u6570\u540d\u76f8\u540c\u4f46\u662f\u53c2\u6570\u8868\u4e0d\u540c\u7684\u591a\u4e2a\u51fd\u6570\uff0c\u5373\u51fd\u6570\u7684\u91cd\u8f7d\u3002</p> <p>\u7c7b\u4f3cGolang\u7684interface\uff0c\u53c2\u6570\u8868\u5b8c\u5168\u7b26\u5408\u54ea\u4e2a\u5c31\u6267\u884c\u54ea\u4e2a(\u51fa\u73b0\u6b67\u4e49\u65f6\u4f1a\u629b\u51fa\u9519\u8bef)</p> <pre><code>int k(int x){ return x; }\n\nchar k(long x){ return 'a'; }\n\nint main(){\ncout &lt;&lt; k(1L);   // \u8f93\u51fa\uff1aa\ncout &lt;&lt; k(1);    // \u8f93\u51fa\uff1a1\n}\n</code></pre> <ul> <li>overload\u4e0d\u652f\u6301\u81ea\u52a8\u7c7b\u578b\u8f6c\u6362</li> </ul>"},{"location":"tech_accu/language/cpp/Part0/#4x-\u51fd\u6570\u7684\u9ed8\u8ba4\u53c2\u6570default-argument","title":"[4.x] \u51fd\u6570\u7684\u9ed8\u8ba4\u53c2\u6570Default Argument","text":"<p>\u5f62\u5f0f\uff1a<code>void fun(int a = 0);</code></p> <ul> <li>\u6b64\u65f6\u8c03\u7528<code>fun()</code>\u53ef\u4ee5\u7701\u7565\u5b58\u5728\u9ed8\u8ba4\u53c2\u6570\u7684\u53c2\u6570</li> <li>\u4f46\u662f\u4e0d\u5b58\u5728\u9ed8\u8ba4\u503c\u7684\u53c2\u6570\u5fc5\u987b\u5728\u5b58\u5728\u9ed8\u8ba4\u503c\u7684\u53c2\u6570\u524d\u9762</li> <li><code>void fun(int x, int a = 0);</code>\u5408\u6cd5</li> <li><code>void fun(int x = 0, int a);</code>\u975e\u6cd5</li> <li>\u5982\u679c\u540c\u65f6\u5b58\u5728\u51fd\u6570\u58f0\u660e\u548c\u51fd\u6570body\uff0c\u5219\u5728\u8fd9\u4e24\u90e8\u5206\u4e2dDefault Argument\u53ea\u80fd\u5728\u5176\u4e2d\u4e00\u4e2a</li> </ul> <pre><code>// \u5408\u6cd5\nvoid fun(int x,int y);\n\nvoid fun(int x = 1,int y = 2){\n// ...\n}\n</code></pre> <pre><code>// \u975e\u6cd5\uff0c\u56e0\u4e3ax\u4e0d\u80fd\u5728y\u524d\nvoid fun(int x = 1,int y); void fun(int x,int y = 2){\n// ...\n}\n</code></pre> <pre><code>// \u5408\u6cd5\nvoid fun(int x = 1,int y = 2);\n\nvoid fun(int x,int y){\n// ...\n}\n</code></pre>"},{"location":"tech_accu/language/cpp/Part0/#5x-\u5185\u8054\u51fd\u6570inline","title":"[5.x] \u5185\u8054\u51fd\u6570<code>inline</code>","text":"<p>\u4e3b\u8981\u4f5c\u7528\u662f\u5728\u51fd\u6570\u4f18\u5316\u4e0a\uff0c\u6548\u679c\u662f\u727a\u7272\u7a7a\u95f4\u6362\u6548\u7387\uff0c\u9002\u7528\u4e8e\u77ed\u5c0f\u4e14\u9891\u7e41\u4f7f\u7528\u7684\u51fd\u6570\u4ee3\u7801</p> <p>\u5b9e\u73b0\u5c31\u662f\u7f16\u8bd1\u5668\u628a\u51fd\u6570\u5185\u5bb9\u8d34\u5230\u8c03\u7528\u51fd\u6570\u7684\u5730\u65b9\u6765\u51cf\u5c11\u6808\u6d88\u8017</p> <ul> <li><code>inline</code>\u4ec5\u4ec5\u662f\u5bf9\u7f16\u8bd1\u5668\u7684\u4e00\u4e2a\u5efa\u8bae</li> <li>\ud83d\udd17\u5f15\u7528\u4e00\u4e0bxxjj\u7684\u6587\u7ae0</li> <li>\u9700\u8981\u6ce8\u610f\u7684\u662f\uff0c<code>inline</code>\u662f\u5728\u6bcf\u4e00\u4e2a\u7f16\u8bd1\u5355\u5143\u4e2d\u8fdb\u884c\u7684\uff0c\u6240\u4ee5\u8fd9\u5c31\u5bfc\u81f4\u4e86\u5185\u8054\u51fd\u6570\u7684\u539f\u578b\u5e94\u5f53\u80fd\u76f4\u63a5\u88ab\u8c03\u7528\u8be5\u51fd\u6570\u7684\u6587\u4ef6\u8bbf\u95ee\u5230\u3002</li> <li>eg.<ul> <li>\u5728<code>a.cpp</code>\u4e2d\u8c03\u7528<code>f();</code>\u5e76<code>#include \"b.h\"</code></li> <li>\u5728<code>b.h</code>\u4e2d\u58f0\u660e<code>inline void f();</code></li> <li>\u5728<code>b.cpp</code>\u4e2d\u5199\u660e<code>f()</code>\u7684body</li> </ul> </li> <li>\u7ed3\u679c\u5c31\u662f\u4f1a\u7f16\u8bd1\u9519\u8bef\u2014\u2014\u9700\u8981\u5c06<code>f()</code>\u7684body\u653e\u5230<code>a.cpp</code>\u6216\u8005<code>b.h</code>\u4e2d\u624d\u53ef\u4ee5\u2014\u2014\u56e0\u4e3a\u5728\u7f16\u8bd1\u7684\u65f6\u5019<code>a.cpp</code>\u4ec5\u548c<code>b.h</code>\u4e00\u8d77\u7f16\u8bd1\uff0c\u5e76\u4e0d\u77e5\u9053<code>f()</code>\u7684body\u5728\u54ea\u91cc\uff0c\u65e0\u6cd5\u8fdb\u884c\u201c\u5185\u8054\u201d</li> <li><code>inline</code>\u4e0e \u5b8f \u5f88\u76f8\u4f3c\uff0c\u4f46\u662f\u6709\u4e00\u4e9b\u533a\u522b\uff1a</li> </ul> <p></p> <ul> <li>\u505a\u7684\u4e8b\u60c5\u662f\u7c7b\u4f3c\u7684\uff0c\u4f46\u7528\u5b8f\u65e0\u6cd5\u5b9e\u73b0\u9690\u5f0f\u7c7b\u578b\u8f6c\u5316</li> <li>\u5bf9\u7f16\u8bd1\u5668\u6765\u8bf4<code>inline</code>\u53ea\u662f\u4e2a\u5efa\u8bae\uff0c\u7f16\u8bd1\u5668\u672a\u5fc5\u4f1a\u5b9e\u73b0</li> <li>\u5728\u4e00\u4e2a\u7c7b\u91cc\u5b9a\u4e49body\u7684\u51fd\u6570\uff0c\u5b83\u9ed8\u8ba4\u662f<code>inline</code>\u51fd\u6570</li> <li>\u5982\u679c\u5728\u7c7b\u91cc\u6ca1\u6709\u5b9a\u4e49body\uff0c\u90a3\u4e48\u8be5\u51fd\u6570\u662f\u5185\u8054\u51fd\u6570\u5f53\u4e14\u4ec5\u5f53\u524d\u9762\u6709<code>inline</code>\u5173\u952e\u8bcd</li> </ul>"},{"location":"tech_accu/language/cpp/Part0/#6x-const","title":"[6.x] const","text":"<p><code>const</code>\u5bf9\u6570\u636e\u7684\u4fdd\u62a4\u51fa\u73b0\u5728\u7f16\u8bd1\u65f6\u523b\uff0c\u5982\u679c\u5f3a\u884c\u901a\u8fc7\u67d0\u79cd\u624b\u6bb5\u83b7\u53d6\u5176\u5730\u5740\uff0c\u4ecd\u7136\u53ef\u4ee5\u4fee\u6539\uff0c\u7f16\u8bd1\u5668\u4ec5\u4ec5\u4fdd\u8bc1<code>const</code>\u4fee\u9970\u8fc7\u7684\u53d8\u91cf\u9664\u4e86\u5b9a\u4e49\u65f6\uff0c\u4e0d\u80fd\u4f5c\u4e3a\u5de6\u503c</p> <ul> <li><code>char * const p;</code>\u4fee\u9970\u7684\u662f<code>p</code></li> <li><code>const char *p;</code>\u4fee\u9970\u7684\u662f<code>*p</code></li> <li><code>char const *p;</code>\u4fee\u9970\u7684\u662f<code>*p</code></li> <li><code>const char * const p;``*p</code>\u548c<code>p</code>\u90fd\u88ab\u4fee\u9970</li> <li><code>const</code>\u51fa\u73b0\u5728<code>*</code>\u5de6\u4fa7\uff0c\u4fee\u9970\u7684\u662f<code>*p</code></li> <li><code>const</code>\u51fa\u73b0\u5728<code>*</code>\u53f3\u4fa7\uff0c\u4fee\u9970\u7684\u662f<code>p</code></li> <li>\uff08\u82e5<code>const char *p = &amp;ch;</code>\uff0c\u867d\u7136\u901a\u8fc7<code>*p</code>\u65e0\u6cd5\u66f4\u6539\u6307\uff0c\u4f46<code>ch</code>\u4ecd\u7136\u53ef\u4ee5\u4fee\u6539\uff0c\u8fdb\u4e00\u6b65\u4f53\u73b0\u8fd9\u662f\u4e2a\u7f16\u8bd1\u65f6\u523b\u884c\u4e3a\uff09</li> <li></li> <li>\u5728\u8fd9\u4e9b\u6027\u8d28\u4e0b\uff0c\u6211\u4eec\u53ef\u4ee5\u628a\u4e00\u4e2a\u975e<code>const</code>\u7684\u53d8\u91cf\u8d4b\u503c\u7ed9<code>const</code>\u53d8\u91cf\uff08\u7279\u522b\u662f\u51fd\u6570\u4f20\u53c2\uff09\uff0c\u6765\u63a7\u5236\u6307\u9488\u7684\u8bfb\u5199\u6743\u9650\uff08\u53ef\u4ee5\u7528\u6765\u51cf\u5c11\u4ee3\u7801\u5199\u9519\u7684\u60c5\u51b5\uff09</li> <li></li> <li>\u4e00\u4e2a\u88ab<code>const</code>\u4fee\u9970\u8fc7\u7684\u5bf9\u8c61\u7684\u6210\u5458\u51fd\u6570\u53ea\u6709\u5728\u8be5\u51fd\u6570\u4e5f\u88ab<code>const</code>\u4fee\u9970\u8fc7\u4e14\u7ecf\u8fc7\u7f16\u8bd1\u5668\u68c0\u6d4b\u786e\u5b9e\u4e0d\u4fee\u6539\u6210\u5458\u53d8\u91cf\u7684\u60c5\u51b5\u4e0b\u624d\u80fd\u6267\u884c</li> <li></li> <li><code>int A::fun() const;</code>\u548c<code>int A::fun();</code>\u53ef\u4ee5\u6784\u6210overload\u5173\u7cfb\uff0c\u56e0\u4e3a\u8fd9\u91cc\u7684<code>const</code>\u5b9e\u9645\u4e0a\u6307\u7684\u662f\u9690\u85cf\u7684<code>A *this</code>\u88ab<code>const</code>\u4fee\u9970\uff0c\u53c2\u6570\u8868\u4e0d\u540c\uff0c\u7b26\u5408overload\u6761\u4ef6</li> <li>\u5f53\u4e0a\u8ff0\u4e24\u4e2a\u51fd\u6570\u90fd\u5b58\u5728\u65f6\uff0c\u5f53\u4e14\u4ec5\u5f53\u5bf9\u8c61\u88ab<code>const</code>\u4fee\u9970\u624d\u4f1a\u8c03\u7528\u524d\u8005</li> <li>\u5982\u679c\u6210\u5458\u53d8\u91cf\u662f<code>const</code>\uff0c\u90a3\u5fc5\u987b\u5b58\u5728\u521d\u59cb\u5316\u65b9\u6848</li> </ul>"},{"location":"tech_accu/language/cpp/Part0/#7x-static","title":"[7.x] static","text":"<p>\u867d\u7136\u5728\u5355\u4e2a\u6587\u4ef6\u5185\uff0c\u9759\u6001\u5168\u5c40\u53d8\u91cf\u7684\u58f0\u660e\u987a\u5e8f\u53ef\u4ee5\u786e\u8ba4\uff0c\u4f46\u6587\u4ef6\u95f4\u7684\u987a\u5e8f\u65e0\u6cd5\u786e\u8ba4\uff0c\u8fd9\u53ef\u80fd\u9020\u6210\u4f9d\u8d56\u95ee\u9898\uff0c\u6240\u4ee5\u5c3d\u53ef\u80fd\u907f\u514d\u591a\u6587\u4ef6\u9759\u6001\u5168\u5c40\u53d8\u91cf\u7684\u4f9d\u8d56\u5173\u7cfb</p> <ul> <li>\u7c7b\u7684\u9759\u6001\u53d8\u91cf\u5c5e\u4e8e\u7c7b\u4e0d\u5c5e\u4e8e\u5b9e\u4f8b\uff0c\u4e0d\u80fd\u901a\u8fc7\u6b63\u5e38\u7684\u65b9\u5f0f\u521d\u59cb\u5316\uff0c\u53ef\u4ee5\u7528\u8fc7\u8303\u56f4\u89e3\u6790\u8fd0\u7b97\u7b26\u5728\u5168\u5c40\u521d\u59cb\u5316</li> <li>\u5b9e\u9645\u4e0a\uff0c\u7f16\u8bd1\u5668\u5c06\u5bf9\u8c61\u5bf9\u9759\u6001\u53d8\u91cf\u7684\u8bbf\u95ee\u81ea\u52a8\u8f6c\u6362\u6210\u4e86\u7c7b\u5bf9\u9759\u6001\u53d8\u91cf\u7684\u8bbf\u95ee\u3002\u56e0\u6b64\uff0c\u5efa\u8bae\u59cb\u7ec8\u4f7f\u7528<code>className::staticVar</code>\u8bbf\u95ee\u9759\u6001\u53d8\u91cf_(xxjj\u5728\u8fd9\u91cc\u8bf4\u7684)_</li> <li>\u7c7b\u7684\u9759\u6001\u51fd\u6570\u4e0d\u518d\u5177\u6709<code>this</code>\u6307\u9488\uff0c\u4e5f\u4e0d\u80fd\u76f4\u63a5\u8bbf\u95ee\u975e\u9759\u6001\u6210\u5458\u53d8\u91cf\u6216\u8005\u975e\u9759\u6001\u6210\u5458\u51fd\u6570</li> <li>\u4e00\u822c\u60c5\u51b5\u4e0b\uff0c\u5982\u679c\u8981\u5728<code>class</code>\u91cc\u58f0\u660e<code>static</code>\u53d8\u91cf/\u51fd\u6570\uff0c\u5219\u53ea\u5728<code>.h</code>\u6587\u4ef6\u4e2d\u51fa\u73b0\u5173\u952e\u5b57\uff0c\u4e0d\u8981\u5728<code>.cpp</code>\u4e2d\u51fa\u73b0</li> </ul>"},{"location":"tech_accu/language/cpp/Part0/#8x-\u547d\u540d\u7a7a\u95f4namespace--using\u5173\u952e\u5b57","title":"[8.x] \u547d\u540d\u7a7a\u95f4namespace &amp; using\u5173\u952e\u5b57","text":"<p>\u53ef\u4ee5\u7528<code>namespace</code>\u6765\u5c01\u88c5\u4ee3\u7801</p> <pre><code>namespace &lt;Space Name&gt;{\n// \u5185\u5bb9\n} </code></pre> <p>\u5728\u4e4b\u540e\u4f7f\u7528\u91cc\u9762\u7684\u53d8\u91cf/\u51fd\u6570\u9700\u8981\u4f7f\u7528\u8303\u56f4\u89e3\u6790\u8fd0\u7b97\u7b26<code>::</code>\uff0c\u5373<code>&lt;Space Name&gt;::&lt;Function Name&gt;();</code></p> <ul> <li><code>using namespace xxx;</code>\u540e\u53ef\u4ee5\u7701\u7565<code>&lt;Space Name&gt;::</code>\uff0c\u4f46\u662f\u8981\u6ce8\u610f\u6b67\u4e49\u95ee\u9898</li> <li><code>using xxx::yyy;</code>\u540e\u4ec5\u4ec5\u5bf9<code>yyy</code>\u6765\u8bf4\u53ef\u4ee5\u7701\u7565<code>&lt;Space Name&gt;::</code>\uff0c\u540c\u6837\u8981\u6ce8\u610f\u6b67\u4e49\u95ee\u9898</li> <li>\u4e24\u4e2a\u547d\u540d\u7a7a\u95f4\u6709\u76f8\u540c\u51fd\u6570/\u53d8\u91cf\u7684\u65f6\u5019\uff0c\u9700\u8981\u5199\u660e\u547d\u540d\u7a7a\u95f4</li> <li><code>namespace x = y;</code>\u8868\u793a\u53ef\u4ee5\u7528<code>x</code>\u6765\u8868\u793a\u547d\u540d\u7a7a\u95f4<code>y</code>\uff0c\u4f46\u662f\u5728\u6b64\u524d<code>y</code>\u5fc5\u987b\u5df2\u7ecf\u5b9a\u4e49</li> <li><code>namespace</code>\u91cc\u4e5f\u53ef\u4ee5\u6709<code>namespace</code>\uff0c\u6211\u4eec\u79f0\u4e4b\u4e3a \u7ec4\u5408</li> </ul>"},{"location":"tech_accu/language/cpp/Part0/#9x-\u5de6\u503c\u4e0e\u53f3\u503c\u53f3\u503c\u5f15\u7528","title":"[9.x] \u5de6\u503c\u4e0e\u53f3\u503c&amp;\u53f3\u503c\u5f15\u7528","text":""},{"location":"tech_accu/standard/","title":"\u6249\u9875","text":"<p> \u7ea6 15 \u4e2a\u5b57 </p> <p> \u300e\u305d\u306e\u6642\u3092\u5f85\u3064\u3088\u300f      \u9761\u4e0d\u6709\u521d\uff0c\u9c9c\u514b\u6709\u7ec8\u3002  \u2014\u2014\u300a\u8bd7\u7ecf\u300b  </p>"},{"location":"tech_accu/standard/BVH_format/","title":"BVH \u683c\u5f0f\u8be6\u89e3","text":"<p> \u7ea6 1312 \u4e2a\u5b57  116 \u884c\u4ee3\u7801  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 6 \u5206\u949f</p>"},{"location":"tech_accu/standard/BVH_format/#\u7b80\u4ecb","title":"\u7b80\u4ecb","text":"<p>BVH \u8868\u793a Biovision Hierarchy Data\uff0c\u662f Biovision \u52a8\u6355\u8bbe\u5907\u7684\u6570\u636e\u8f93\u51fa\u683c\u5f0f\uff0c\u662f BVA \u683c\u5f0f\u7684\u6539\u8fdb\uff0c\u5e7f\u6cdb\u5e94\u7528\u4e8e\u52a8\u753b\u5236\u4f5c\u8f6f\u4ef6\u3002\u800c\u8be5\u683c\u5f0f\u4ee5\u6587\u672c\u5f62\u5f0f\u50a8\u5b58\uff0c\u6240\u4ee5\u4fbf\u4e8e\u5f00\u53d1\u3002 \u4ece\u9700\u6c42\u7684\u89d2\u5ea6\u6765\u8bb2\uff0c\u4e3a\u4e86\u4f18\u96c5\u5730\u89e3\u51b3\u52a8\u753b\u5236\u4f5c\u95ee\u9898\uff0c\u5b83\u88ab\u5206\u4e3a\u4e86\u201c\u8499\u76ae\u201d\u548c\u201c\u9aa8\u9abc\u201d\u4e24\u4e2a\u90e8\u5206\u3002\u800c BVH \u5c31\u8d1f\u8d23\u5b58\u50a8 \u9aa8\u9abc\u67b6\u7ed3\u6784 \u548c \u52a8\u4f5c\u4fe1\u606f\u3002 BVH \u683c\u5f0f\u603b\u4f53\u6765\u8bf4\u6bd4\u8f83\u4f18\u79c0\uff0c\u4f46\u662f\u7f3a\u4e4f\u5bf9\u8fd0\u52a8\u65f6\u7684\u9aa8\u67b6\u59ff\u52bf\u7684\u5b8c\u6574\u89e3\u91ca\u3002\u56e0\u4e3a BVH \u662f\u901a\u8fc7 \u504f\u79fb(Offset) \u6765\u63cf\u8ff0\u8fd0\u52a8\u7684\uff0c\u5373\u4fdd\u5b58\u7684\u662f\u6bcf\u4e00\u5e27\u5173\u952e\u8282\u70b9\u5bf9\u4e8e\u7236\u8282\u70b9\u7684\u76f8\u5bf9\u4f4d\u79fb\u3002</p>"},{"location":"tech_accu/standard/BVH_format/#\u6587\u4ef6\u89e3\u6790","title":"\u6587\u4ef6\u89e3\u6790","text":"<p>A BVH file has two parts, a header section which describes the hierarchy and initial pose of the skeleton; and a data section which contains the motion data. </p> <p>BVH \u6587\u4ef6\u6570\u636e\u5206\u4e3a\u4e24\u4e2a\u90e8\u5206\uff1a</p> <ul> <li>\u9aa8\u67b6\u4fe1\u606f(header section)\uff1a\u5b9a\u4e49\u4e86\u9aa8\u67b6\u7684\u7ec4\u7ec7\u7ed3\u6784\uff0c\u6307\u5bfc\u5982\u4f55\u89e3\u6790\u6570\u636e\u5757\u3002</li> <li>\u6570\u636e\u5757(data section)\uff1a\u5305\u542b\u4e86\u6bcf\u4e00\u5e27\u5404\u90e8\u5206\u7684\u6570\u636e\u4fe1\u606f\u3002</li> </ul> <p>\u5e76\u4e14\u4ee5\u9012\u5f52\u7684\u5f62\u5f0f\u7ed9\u51fa\u5b9a\u4e49\u3002 \u4e0b\u9762\u7ed9\u51fa\u4e00\u4e2a\u793a\u4f8b\u6587\u4ef6\uff0c\u7136\u540e\u505a\u8fdb\u4e00\u6b65\u5206\u6790\u3002</p> Summary <pre><code>HIERARCHY\nROOT Hips\n{\nOFFSET  0.00    0.00    0.00\nCHANNELS 6 Xposition Yposition Zposition Zrotation Xrotation Yrotation\nJOINT Chest\n{\nOFFSET   0.00    5.21    0.00\nCHANNELS 3 Zrotation Xrotation Yrotation\nJOINT Neck\n{\nOFFSET   0.00    18.65   0.00\nCHANNELS 3 Zrotation Xrotation Yrotation\nJOINT Head\n{\nOFFSET   0.00    5.45    0.00\nCHANNELS 3 Zrotation Xrotation Yrotation\nEnd Site {\nOFFSET   0.00    3.87    0.00\n}\n}\n}\nJOINT LeftCollar\n{\nOFFSET   1.12    16.23   1.87\nCHANNELS 3 Zrotation Xrotation Yrotation\nJOINT LeftUpArm\n{\nOFFSET   5.54    0.00    0.00\nCHANNELS 3 Zrotation Xrotation Yrotation\nJOINT LeftLowArm\n{\nOFFSET   0.00   -11.96   0.00\nCHANNELS 3 Zrotation Xrotation Yrotation\nJOINT LeftHand\n{\nOFFSET   0.00   -9.93    0.00\nCHANNELS 3 Zrotation Xrotation Yrotation\nEnd Site {\nOFFSET   0.00   -7.00    0.00\n}\n}\n}\n}\n}\nJOINT RightCollar\n{\nOFFSET  -1.12    16.23   1.87\nCHANNELS 3 Zrotation Xrotation Yrotation\nJOINT RightUpArm\n{\nOFFSET  -6.07    0.00    0.00\nCHANNELS 3 Zrotation Xrotation Yrotation\nJOINT RightLowArm\n{\nOFFSET   0.00   -11.82   0.00\nCHANNELS 3 Zrotation Xrotation Yrotation\nJOINT RightHand\n{\nOFFSET   0.00   -10.65   0.00\nCHANNELS 3 Zrotation Xrotation Yrotation\nEnd Site {\nOFFSET   0.00   -7.00    0.00\n}\n}\n}\n}\n}\n}\nJOINT LeftUpLeg\n{\nOFFSET   3.91    0.00    0.00\nCHANNELS 3 Zrotation Xrotation Yrotation\nJOINT LeftLowLeg\n{\nOFFSET   0.00   -18.34   0.00\nCHANNELS 3 Zrotation Xrotation Yrotation\nJOINT LeftFoot\n{\nOFFSET   0.00   -17.37   0.00\nCHANNELS 3 Zrotation Xrotation Yrotation\nEnd Site {\nOFFSET   0.00   -3.46    0.00\n}\n}\n}\n}\nJOINT RightUpLeg\n{\nOFFSET  -3.91    0.00    0.00\nCHANNELS 3 Zrotation Xrotation Yrotation\nJOINT RightLowLeg\n{\nOFFSET   0.00   -17.63   0.00\nCHANNELS 3 Zrotation Xrotation Yrotation\nJOINT RightFoot\n{\nOFFSET   0.00   -17.14   0.00\nCHANNELS 3 Zrotation Xrotation Yrotation\nEnd Site {\nOFFSET   0.00   -3.75    0.00\n}\n}\n}\n}\n}\nMOTION\nFrames:    2\nFrame Time: 0.033333\n8.03     35.01   88.36  -3.41    14.78  -164.35  13.09   40.30  -24.60   7.88    43.80   0.00   -3.61   -41.45   5.82    10.08   0.00    10.21   97.95  -23.53  -2.14   -101.86 -80.77  -98.91   0.69    0.03    0.00   -14.04   0.00   -10.50  -85.52  -13.72  -102.93  61.91  -61.18   65.18  -1.57    0.69    0.02    15.00   22.78  -5.92    14.93   49.99   6.60    0.00   -1.14    0.00   -16.58  -10.51  -3.11    15.38   52.66  -21.80   0.00   -23.95   0.00   7.81     35.10   86.47  -3.78    12.94  -166.97  12.64   42.57  -22.34   7.67    43.61   0.00   -4.23   -41.41   4.89    19.10   0.00    4.16    93.12  -9.69   -9.43    132.67 -81.86   136.80  0.70    0.37    0.00   -8.62    0.00   -21.82  -87.31  -27.57  -100.09  56.17  -61.56   58.72  -1.63    0.95    0.03    13.16   15.44  -3.56    7.97    59.29   4.97    0.00    1.64    0.00   -17.18  -10.02  -3.08    13.56   53.38  -18.07   0.00   -25.93   0.00   </code></pre> <p>\u8be5\u6837\u4f8b\u7ed9\u51fa\u4e86\u8fd9\u6837\u4e00\u4e2a\u9aa8\u67b6\uff1a</p> <p></p> \\[ vR = vYXZ\\\\ vM= vM_{child}M_{parent}M_{grandparent}... \\]"},{"location":"tech_accu/standard/BVH_format/#header-section","title":"header section","text":"<p><code>HIERARCHY</code>\u5173\u952e\u5b57\u6807\u8bc6<code>header section</code>\u7684\u5f00\u59cb\uff0c\u968f\u540e\u5728\u4e0b\u4e00\u884c\u5b9a\u4e49\u4e86\u6839\u8282\u70b9<code>ROOT</code>\uff0c\u800c<code>Hips</code>\u5219\u662f\u8be5\u8282\u70b9\u7684\u540d\u79f0\u3002\u89c2\u5bdf\u4e0a\u65b9\u7ed9\u51fa\u7684\u9aa8\u67b6\u793a\u610f\u56fe\uff0c<code>Hips</code>\u8282\u70b9\u4f5c\u4e3a\u6574\u4e2a\u9aa8\u67b6\u7684\u6839\u8282\u70b9\uff0c\u4fdd\u8bc1\u4e86\u6574\u4e2a\u6811\u5f62\u56fe\u7684\u6700\u5927\u6df1\u5ea6\u76f8\u5bf9\u8f83\u5c0f\uff0c\u51cf\u5c0f\u8bef\u5dee\u3002</p> <p>\u5176\u540e\u7ed9\u51fa\u4e86<code>OFFSET</code>\u548c<code>CHANNELS</code>\u4e24\u4e2a\u5c5e\u6027\u3002</p> <ul> <li><code>OFFSET</code>\u8868\u793a\u76f8\u5bf9\u4e0e\u7236\u8282\u70b9\uff0c\u8be5\u8282\u70b9\u7684\u504f\u79fb\uff1b</li> <li>\u5bf9\u4e8e \u6839\u8282\u70b9 \u6765\u8bf4\uff0c\u5b83\u4e00\u822c\u662f<code>0 0 0</code>\uff1b</li> <li>\u00b7<code>CHANNELS</code>\u540e\u6709\u4e24\u4e2a\u90e8\u5206\uff0c\u9996\u5148\u662f\u4e00\u4e2a\u6570\u5b57\u8868\u793a\u540e\u9762\u6709\u51e0\u4e2a\u901a\u9053\u3002</li> <li>\u4e00\u822c\u6765\u8bf4\uff0c\u6839\u8282\u70b9 \u4f1a\u6709 6 \u4e2a\u901a\u9053\uff0c\u5982\u4e0a\u793a\u4f8b\u6709<code>Xposition Yposition Zposition Zrotation Yrotation Xrotation</code>\uff0c\u5206\u522b\u4ee3\u8868\u5728<code>data section</code>\u4e2d\uff0c\u5e27\u5e8f\u5217\u7684\u6570\u636e\u6309\u8fd9\u6837\u7684\u65b9\u5f0f\u5b58\u50a8\uff0c\u524d\u4e09\u4e2a\u4ee3\u8868\u7684\u662f \u4f4d\u79fb \u4e0b\u6bcf\u4e2a\u5206\u91cf\u7684\u987a\u5e8f\uff08\u6b64\u5904\u8868\u793a\uff1a\u4f9d\u6b21\u4e3a x \u5750\u6807\uff0c y \u5750\u6807\uff0c z \u5750\u6807\uff0c\u4e00\u822c\u53ea\u6709\u6839\u8282\u70b9\u6709\u8fd9\u4e09\u4e2a\u901a\u9053\uff0c\u7528\u6765\u8868\u793a\u9aa8\u67b6\u7684\u4f4d\u79fb\uff09\uff0c\u540e\u4e09\u4e2a\u4ee3\u8868\u7684\u662f \u65cb\u8f6c\u89d2\u5ea6 \u987a\u5e8f\uff1b</li> <li>\u800c\u5bf9\u4e8e \u975e\u6839\u8282\u70b9\uff0c\u4e00\u822c\u6709 3 \u4e2a\u901a\u9053\uff0c\u4ee3\u8868\u7684 \u65cb\u8f6c\u89d2\u5ea6 \u987a\u5e8f\uff1b</li> <li>\u6ce8\u610f\uff0c\u8fd9\u91cc\u4f7f\u7528\u7684 \u89d2\u5ea6\u5236 \u800c\u975e\u5f27\u5ea6\u5236\uff1b</li> </ul> <p>\u800c\u5728\u5176\u540e\uff0c\u4ee5<code>JOINT</code>\u4e3a\u5173\u952e\u5b57\u53c8\u8868\u793a\u4e86\u5176\u5b50\u8282\u70b9\u7684\u5b9a\u4e49\uff0c\u5373\u4ee5 \u9012\u5f52 \u7684\u5f62\u5f0f\u7ed9\u51fa\u5b9a\u4e49\u3002</p> <p></p> <ul> <li>\u5728\u8fd9\u5f20\u56fe\u4e2d\uff0c<code>Neck``LeftCollar``RightCollar</code>\u662f<code>Chest</code>\u7684\u5b50\u8282\u70b9\uff0c\u5219<code>Neck``LeftCollar``RightCollar</code>\u7684\u76f8\u5bf9\u4f4d\u7f6e\u5e94\u5f53\u4e0d\u53d8\uff0c\u4e4b\u540e\u7684\u53d8\u6362\u4ec5\u4ec5\u901a\u8fc7\u5b83\u4eec\u6574\u4f53\u76f8\u5bf9\u4e8e<code>Chest</code>\u7684\u65cb\u8f6c\u5b9e\u73b0\u3002</li> </ul> <p>\u53ef\u4ee5\u8fd9\u4e48\u7406\u89e3\uff1a</p> <ul> <li><code>ROOT</code>\u548c<code>JOINT</code>\u5728\u8bed\u6cd5\u4e0a\u57fa\u672c\u4e00\u81f4\uff0c</li> <li>\u53ea\u4e0d\u8fc7\u7b2c\u4e00\u4e2a\u51fa\u73b0\u7684\u8282\u70b9\u9700\u8981\u7528<code>ROOT</code>\u7d22\u5f15\uff0c\u4e14\u5b83\u67096\u4e2a\u901a\u9053\uff1b</li> <li>\u800c\u4e4b\u540e\u7684\u5b50\u8282\u70b9\u901a\u8fc7<code>JOINT</code>\u7d22\u5f15\uff0c\u4e14\u67093\u4e2a\u901a\u9053\u3002</li> </ul> <p>\u800c\u5728\u9012\u5f52\u5b9a\u4e49\u7684\u672b\u7aef\uff0c\u4f60\u4f1a\u53d1\u73b0\u4e00\u4e2a<code>End Site</code>\uff0c\u5b83\u53ea\u6709<code>OFFSET</code>\u5c5e\u6027\u800c\u6ca1\u6709<code>CHANNELS</code>\u5c5e\u6027\uff0c\u8fd9\u662f\u56e0\u4e3a\uff1a</p> <ul> <li>\u9aa8\u67b6\u662f\u6709\u82e5\u5e72\u201c\u9aa8\u68d2\u201d\u7ec4\u6210\u7684\uff0c\u8fd9\u4e2a\u201c\u9aa8\u68d2\u201d\u79f0\u4e3a<code>segment</code>\uff0c\u800c\u5b9a\u4e49\u4e00\u4e2a<code>segment</code>\u9700\u8981\u4e24\u4e2a\u7aef\u70b9\uff0c\u800c<code>End Site</code>\u5c31\u662f\u8fd9\u4e2a<code>segment</code>\u94fe\u7684\u672b\u7aef\uff0c\u5b83\u4e0d\u5177\u5907\u65cb\u8f6c\u4fe1\u606f\uff0c\u56e0\u4e3a\u5b83\u6ca1\u6709\u5b50\u8282\u70b9\uff0c\u4ec5\u4ec5\u7528\u6765\u901a\u8fc7\u5750\u6807\u8868\u8fbe\u6700\u540e\u4e00\u4e2a<code>segment</code>\u7684\u957f\u5ea6\u3002</li> </ul> <p>One last note about the BVH hierarchy, the world space is defined as a right handed coordinate system with the Y axis as the world up vector. Thus you will typically find that BVH skeletal segments are aligned along the Y or negative Y axis (since the characters are often have a zero pose where the character stands straight up with the arms straight down to the side).</p> <p>\u5373\u4e16\u754c\u5750\u6807\u7cfb\u4e00\u822c\u662f\u4e00\u4e2a\\(y\\)\u8f74\u671d\u4e0a\u7684\u53f3\u624b\u7cfb\uff0c\u5e76\u4e14\u9aa8\u67b6\u7684\u521d\u59cb\u59ff\u52bf\u603b\u662f T-Pose \uff0c\u5373\u4eba\u6253\u5f00\u53cc\u624b\uff0c\u50cf\u5b57\u6bcd<code>T</code>\u4e00\u6837\u7ad9\u5728\u5730\u4e0a\u3002</p>"},{"location":"tech_accu/standard/BVH_format/#data-section","title":"data section","text":"<p><code>MOTION</code>\u5173\u952e\u5b57\u6807\u8bc6<code>data section</code>\u7684\u5f00\u59cb\uff0c\u4e4b\u540e\u4e24\u884c\u5206\u522b\u662f<code>Frames</code>\u548c<code>Frame Time</code>\uff0c\u8868\u793a \u5e27\u6570 \u548c \u5e27\u6570\u957f\u5ea6\uff08\u5373\u5e27\u7387\u5012\u6570\uff0c0.033333\u5c31\u662f30\u5e27\uff09\u3002 \u800c\u518d\u4e4b\u540e\uff0c\u5219\u662f\u771f\u6b63\u7684\u52a8\u753b\u6570\u636e\uff0c\u6839\u636e<code>header section</code>\u7ed9\u51fa\u7684\u901a\u9053\u5b9a\u4e49\u4f9d\u6b21\u6765\u7ed9\u51fa\u6bcf\u4e00\u5e27\u7684\u76f8\u5bf9\u53d8\u5316\u6570\u636e\u3002 </p>"},{"location":"tech_accu/standard/BVH_format/#\u7406\u89e3","title":"\u7406\u89e3","text":"<p>\u6839\u636e\u6211\u7684\u4e2a\u4eba\u7406\u89e3\uff0c<code>header section</code>\u7c7b\u4f3c\u4e8e\u5c06\u4e00\u6839\u6839\u68d2\u710a\u63a5\u5728\u80fd\u591f\u81ea\u7531\u65cb\u8f6c\u7684\u8282\u70b9\u4e0a\uff0c\u5e76\u89c4\u5b9a\u6570\u636e\u7684\u7ec4\u7ec7\u987a\u5e8f\uff0c\u5373\u89e3\u51b3\u4e86\u9aa8\u67b6\u201c\u957f\u4ec0\u4e48\u6837\u201d\u7684\u95ee\u9898\uff0c\u5e76\u6307\u5bfc\u5982\u4f55\u63cf\u8ff0\u9aa8\u67b6\u201c\u600e\u4e48\u52a8\u201d\uff1b \u800c<code>data section</code>\u5219\u7c7b\u4f3c\u4e8e\u6309\u7167<code>header section</code>\u7ed9\u51fa\u7684\u5b9a\u4e49\uff0c\u5177\u4f53\u8be5\u5982\u4f55\u6539\u53d8\u5404\u4e2a\u8282\u70b9\u7684\u72b6\u6001\u3002 \u9664\u4e86\u53d1\u9001\u7ed9<code>ROOT</code>\u7684\u4f4d\u7f6e\u5750\u6807\u6765\u8868\u793a\u9aa8\u67b6\u7684\u4f4d\u79fb\uff08\u5e73\u79fb\u77e9\u9635\uff09\uff0c\u4e4b\u540e\u7684\u4e00\u7cfb\u5217\u6570\u636e\u90fd\u8868\u793a\u8be5\u8282\u70b9\u8be5\u5982\u4f55\u65cb\u8f6c\uff08\u65cb\u8f6c\u77e9\u9635\uff09\uff0c\u90a3\u4e48\u7406\u6240\u5f53\u7136\u7684\uff0c\u8fd9\u4e2a\u8282\u70b9\u7684\u6240\u6709\u5b50\u8282\u70b9\u90fd\u4f1a\u4ee5\u8fd9\u4e2a\u8282\u70b9\u4e3a\u4e2d\u5fc3\u8fdb\u884c\u76f8\u5e94\u7684\u65cb\u8f6c\uff1b\u6bcf\u6b21\u9012\u5f52\u90fd\u91cd\u590d\u8fd9\u6837\u7684\u64cd\u4f5c\uff0c\u6700\u7ec8\u6307\u6325\u6574\u4e2a\u9aa8\u67b6\u7684\u53d8\u6362\u3002 \u90a3\u4e48\uff0c\u5b9e\u9645\u4e0a\uff0c\u6bcf\u4e00\u4e2a\u8282\u70b9\u76f8\u5bf9\u4e8e\u6839\u8282\u70b9\u7684\u53d8\u5316\u5c31\u53ef\u4ee5\u901a\u8fc7\u8fd9\u4e9b\u53d8\u6362\u77e9\u9635\u6309\u7167\u987a\u5e8f\u7d2f\u4e58\u5f97\u5230\u3002</p>"},{"location":"tech_accu/standard/BVH_format/#\u53c2\u8003\u8d44\u6599","title":"\u53c2\u8003\u8d44\u6599","text":"<ul> <li>https://en.wikipedia.org/wiki/Biovision_Hierarchy</li> <li>https://research.cs.wisc.edu/graphics/Courses/cs-838-1999/Jeff/BVH.html</li> <li>https://blog.csdn.net/u012336923/article/details/50972968</li> <li>https://blog.csdn.net/u012336923/article/details/50979894</li> <li>https://zhuanlan.zhihu.com/p/71818887</li> <li>https://www.4k8k.xyz/article/one_2_one/97963901</li> <li>https://www.youizone.com/2015/06/04/bvh-files.html</li> </ul>"},{"location":"tech_accu/tool/","title":"\u6249\u9875","text":"<p> \u7ea6 15 \u4e2a\u5b57 </p> <p> \u300e\u305d\u306e\u6642\u3092\u5f85\u3064\u3088\u300f      \u9761\u4e0d\u6709\u521d\uff0c\u9c9c\u514b\u6709\u7ec8\u3002  \u2014\u2014\u300a\u8bd7\u7ecf\u300b  </p>"},{"location":"tech_accu/tool/Colab/","title":"Google Colaboratory","text":"<p> \u7ea6 477 \u4e2a\u5b57  6 \u884c\u4ee3\u7801  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 2 \u5206\u949f</p> <p>\u7b80\u4ecb</p> <p>Google Colab \u662f\u4e00\u4e2a\u5141\u8bb8\u7f16\u5199\u548c\u6267\u884c\u4ee3\u7801\u7684\u4ea4\u4e92\u5f0f\u73af\u5883\uff0c\u4ee5\u4e0b\u662f\u5206\u522b\u4e3a Colab \u7684\u7f51\u5740\u4ee5\u53ca\u5b98\u65b9 Q&amp;A\u3002</p> <ul> <li>Colab URL: \ud83d\udd17 </li> <li>A&amp;Q: \ud83d\udd17</li> </ul> <p>\u5bf9\u6211\u6765\u8bf4\uff0cGolab \u4e3a\u6211\u63d0\u4f9b\u4e86\u4e00\u4e2a\u6bd4\u8f83\u65b9\u4fbf\u4e14\u6709\u4e00\u5b9a\u7b97\u529b\u7684\u5728\u7ebf\u5e73\u53f0\uff0c\u800c\u4e14\u6211\u89c9\u5f97\u4f5c\u4e3a\u7b14\u8bb0\u672c\u8c8c\u4f3c\u4e5f\u633a\u597d\u7528\u7684\u3002</p> <p>\u7b80\u5355\u6765\u8bf4\uff0cColab \u4e2d\u5b58\u5728 \u6587\u672c\u5355\u5143 \u548c \u4ee3\u7801\u5355\u5143 \u8fd9\u4e24\u79cd\u6a21\u5757\u3002</p> <ul> <li>\u5728\u6587\u672c\u5355\u5143\u4e2d\uff0c\u4f60\u53ef\u7528\u96c6\u6210\\(\\LaTeX\\)\u3001<code>HTML</code>\u3001\u5bcc\u6587\u672c\u3001Markdown \u7b49\uff1b</li> <li>\u800c\u5bf9\u4e8e\u4ee3\u7801\u5355\u5143\uff0c\u4f60\u5219\u53ef\u4ee5\u76f4\u63a5\u628a\u5b83\u5f53\u4f5c\u4e00\u4e2a<code>Python</code>\u89e3\u91ca\u5668\uff1a</li> </ul> <p></p> <ul> <li>\u540c\u65f6\uff0c\u5728\u4e00\u884c\u7684\u6700\u524d\u9762\u52a0\u4e0a<code>!</code>\u8868\u793a\u8fd9\u662f\u4e00\u4e2a\u7ec8\u7aef\u547d\u4ee4</li> <li>\u4f8b\u5982\u5728 \u4ee3\u7801\u5355\u5143 \u4e2d\u8f93\u5165<code>!pwd</code>\u5c31\u7b49\u4ef7\u4e8e\u5728\u7ec8\u7aef\u4e2d\u8f93\u5165<code>pwd</code></li> <li>\u4f46\u5728 \u4ee3\u7801\u5355\u5143 \u4e2d\u8f93\u5165<code>pwd</code>\u5219\u4f1a\u62a5\u9519\uff0c\u56e0\u4e3a\u8fd9\u4e0d\u662f\u4e00\u4e2a<code>Python</code>\u547d\u4ee4</li> </ul> <p>\u4ece\u7528\u9014\u4e0a\u6765\u8bb2\uff0cColab \u5728\u6570\u636e\u79d1\u5b66\u548c\u673a\u5668\u5b66\u4e60\u8fd9\u4e24\u65b9\u9762\u6709\u8f83\u5927\u7528\u5904\u3002</p> <ul> <li>\u6570\u636e\u79d1\u5b66: \ud83d\udd17</li> <li>\u673a\u5668\u5b66\u4e60: \ud83d\udd17</li> </ul>"},{"location":"tech_accu/tool/Colab/#\u6587\u4ef6\u4e92\u52a8","title":"\u6587\u4ef6\u4e92\u52a8","text":"<p>Colab \u81ea\u5e26\u6587\u4ef6\u6d4f\u89c8\u754c\u9762</p> <p>\u901a\u8fc7\u8fd9\u4e09\u4e2a\u6309\u94ae\u53ef\u4ee5\u5b9e\u73b0 \u4e0a\u4f20\u6587\u4ef6\u3001\u5237\u65b0\u3001\u88c5\u8f7d Google \u4e91\u76d8\uff1a</p> <p></p>"},{"location":"tech_accu/tool/Colab/#\u786c\u4ef6\u52a0\u901f","title":"\u786c\u4ef6\u52a0\u901f","text":"<p>\u5173\u4e8eGPU\u52a0\u901f\u7684\u5177\u4f53\u4fe1\u606f\uff0c\u8bf7\u67e5\u770b\u8fd9\u91cc \ud83d\udd17\u3002</p>"},{"location":"tech_accu/tool/Colab/#\u8d44\u6e90\u9650\u5236","title":"\u8d44\u6e90\u9650\u5236","text":"<ul> <li> <p>\u5173\u4e8e\u8d44\u6e90\u9650\u5236\u7684\u5b98\u65b9\u8bf4\u660e: \ud83d\udd17 </p> </li> <li> <p>\u6761\u76ee\uff1a</p> <ul> <li>\u4e3a\u4ec0\u4e48 Colab \u4e0d\u80fd\u4fdd\u8bc1\u8d44\u6e90\u4f9b\u5e94\uff1f</li> <li>Colab \u7684\u7528\u91cf\u9650\u989d\u662f\u591a\u5c11\uff1f</li> <li>Colab \u63d0\u4f9b\u54ea\u4e9b\u7c7b\u578b\u7684 GPU\uff1f</li> <li>\u5728 Colab \u4e2d\uff0c\u7b14\u8bb0\u672c\u53ef\u4ee5\u8fd0\u884c\u591a\u957f\u65f6\u95f4\uff1f</li> <li>Colab \u63d0\u4f9b\u591a\u5927\u5185\u5b58\uff1f</li> <li>\u5982\u4f55\u624d\u80fd\u5145\u5206\u5229\u7528 Colab\uff1f</li> <li>\u7cfb\u7edf\u663e\u793a\u4e00\u6761\u6d88\u606f\uff0c\u63d0\u793a\u6211\u6ca1\u6709\u4f7f\u7528 GPU\u3002\u6211\u8be5\u600e\u4e48\u529e\uff1f</li> </ul> </li> </ul>"},{"location":"tech_accu/tool/Colab/#\u5947\u6280\u6deb\u5de7","title":"\u5947\u6280\u6deb\u5de7","text":""},{"location":"tech_accu/tool/Colab/#\u5360\u7528\u663e\u5b58","title":"\u5360\u7528\u663e\u5b58","text":"<p>\u5f53\u4f60\u7684\u6574\u4e2a\u9879\u76ee\u9700\u8981<code>GPU</code>\u4f46\u662f\u73b0\u5728\u4e0d\u592a\u9700\u8981\u7684\u65f6\u5019\uff0c\u53ef\u4ee5\u901a\u8fc7\u4e0b\u9762\u8fd9\u6837\u4e00\u6bb5\u4ee3\u7801\u6765\u5148\u5360\u7528\u4e00\u90e8\u5206\u663e\u5b58\u3002</p> <pre><code>import torch\n## about 1.1 GB\na = torch.Tensor([1000, 1000, 1000]).cuda()\n</code></pre>"},{"location":"tech_accu/tool/Colab/#\u67e5\u770b\u663e\u5361\u4fe1\u606f","title":"\u67e5\u770b\u663e\u5361\u4fe1\u606f","text":"<pre><code>!nvidia-smi\n</code></pre>"},{"location":"tech_accu/tool/Colab/#\u6302\u8f7d-google-drive","title":"\u6302\u8f7d Google Drive","text":"<pre><code>from google.colab import drive\ndrive.mount('/content/drive/')\n</code></pre>"},{"location":"tech_accu/tool/Colab/#\u53ef\u53c2\u8003\u8d44\u6599","title":"\u53ef\u53c2\u8003\u8d44\u6599","text":"<ul> <li>https://zhuanlan.zhihu.com/p/387509768</li> <li>https://itiandong.com/2021/colab-tips/</li> </ul>"},{"location":"tech_accu/tool/Colab/#\u5176\u4ed6\u8d44\u6599","title":"\u5176\u4ed6\u8d44\u6599","text":"<ul> <li>https://jishuin.proginn.com/p/763bfbd316dc</li> </ul>"},{"location":"tech_accu/tool/Git/","title":"Git","text":"<p> \u7ea6 67 \u4e2a\u5b57 </p> <p>Git \u662f\u4ee3\u7801\u534f\u4f5c\u7684\u91cd\u8981\u5de5\u5177\uff0c\u540c\u65f6\u4e5f\u5bf9\u4e2a\u4eba\u4ee3\u7801\u7684\u7248\u672c\u7ba1\u7406\u6709\u91cd\u8981\u4f5c\u7528\uff0c\u56e0\u6b64\u53ef\u4ee5\u8bf4 Git \u662f\u7834\u5199\u4ee3\u7801\u7684\u4eba\u7684\u5fc5\u5907\u6280\u80fd\u4e4b\u4e00\u3002</p> <p>List</p> <ul> <li> Workflow </li> <li> Commands </li> <li> Commits Convention\uff08\u8ba1\u5212\u4e2d\uff09</li> <li> Lazy Git\uff08\u8ba1\u5212\u4e2d\uff09</li> </ul>"},{"location":"tech_accu/tool/Git/Commands/","title":"Git Commands","text":"<p> \u7ea6 1464 \u4e2a\u5b57  110 \u884c\u4ee3\u7801  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 6 \u5206\u949f</p> <p>\u7b80\u4ecb</p> <p>\u672c\u6587\u5185\u5bb9\u57fa\u4e8e\u6211\u81ea\u5df1\u7684\u7406\u89e3\u548c\u4e00\u4e9b\u6587\u7ae0\uff0c\u662f\u5b66\u4e60\u7b14\u8bb0\uff0c\u4f46\u540c\u65f6\u6211\u4e5f\u5e0c\u671b\u5b83\u80fd\u88ab\u4f5c\u4e3a\u4e00\u4e2a\u5b66\u4e60\u53c2\u8003\u8d44\u6599\u3002</p> <p>\u6240\u4ee5\u5982\u679c\u6709\u9519\u8bef\u8bf7\u53ca\u65f6\u8bc4\u8bba\u6216\u8005\u8054\u7cfb\u6211\uff0c\u5e0c\u671b\u80fd\u4e3a\u5927\u5bb6\u63d0\u4f9b\u4e00\u4e2a\u6bd4\u8f83\u597d\u7684\u5b66\u4e60\u53c2\u8003\uff01</p> <p>\u56e0\u4e3a\u6211\u81ea\u5df1\u7684\u5f00\u53d1\u7ecf\u5386\u6709\u9650\uff0c\u6240\u4ee5\u5e76\u4e0d\u80fd\u4fdd\u8bc1\u81ea\u5df1\u7684\u7406\u89e3\u662f\u5408\u9002\u4e14\u6b63\u786e\u7684\uff0c\u6240\u4ee5\u5e0c\u671b\u5927\u5bb6\u72e0\u72e0\u5730 educate \u6211\uff01</p> <p>\u672c\u6761\u76ee\u5c06\u628a\u76ee\u5149\u653e\u5728\u5177\u4f53\u7684<code>git</code> \u547d\u4ee4 \u7684\u4ecb\u7ecd\u4e0e\u4f7f\u7528\uff0c\u65e8\u5728\u6307\u5bfc\u8fdb\u884c\u5177\u4f53\u7684\u5de5\u4f5c\u3002</p> <p>Git \u6709\u8bb8\u591a\u547d\u4ee4\uff0c\u4f46\u662f\u5176\u5b9e\u5e38\u7528\u7684\u5c31\u56fe\u4e2d\u7684\u8fd9\u4e48\u51e0\u4e2a\uff0c\u751a\u81f3\u5728 \u521a\u5f00\u59cb \u5b66\u4e60\u4f7f\u7528\u7684\u65f6\u5019\u53ea\u9700\u8981\u8bb0\u4f4f\u5176\u4e2d\u7684\u4e00\u4e24\u4e2a\uff0c\u4f46\u662f</p> <p>\u8fd9\u5e76\u4e0d\u662f\u8bf4\u5176\u4ed6\u547d\u4ee4\u5c31\u662f\u6ca1\u7528\u7684\uff0c\u6211\u4f1a\u5728\u8fd9\u91cc\u6309\u7167\u4f7f\u7528\u573a\u666f\u5206\u7c7b\uff0c\u5c3d\u53ef\u80fd\u5730\u4ecb\u7ecd Git \u547d\u4ee4\u3002</p> <p>  \u5e38\u7528\u547d\u4ee4 </p> <p>\u7531\u4e8e\u4e00\u822c\u6765\u8bf4\u8fd0\u884c\u547d\u4ee4\u90fd\u662f\u4ee5\u672c\u5730\u89c6\u89d2\uff0c\u6240\u4ee5\u8fd9\u91cc\u7684\u300c\u4f7f\u7528\u573a\u666f\u300d\u7684\u5212\u5206\u4e5f\u662f\u4ee5\u672c\u5730\u89c6\u89d2\u5c55\u5f00\u7684\u3002 \u5e76\u4e14\u5728\u67d0\u4e9b\u9700\u8981\u6d89\u53ca\u8fdc\u7a0b\u4ed3\u5e93\u7684\u5730\u65b9\u4e3b\u8981\u4ee5 Github \u7684\u4f7f\u7528\u4e3a\u53c2\u8003\u3002</p>"},{"location":"tech_accu/tool/Git/Commands/#\u7b80\u6d01\u7248\u672c","title":"\u7b80\u6d01\u7248\u672c","text":"<p>\u8be5\u6761\u76ee\u4e3b\u8981\u9002\u7528\u4e8e\u521d\u5b66\u4e0e\u7b80\u5355\u4f7f\u7528 Git \uff0c\u5e76\u4e0d\u9002\u5408\u957f\u671f\u7ef4\u62a4\u7684\u5927\u578b\u9879\u76ee\u3002</p> \u5feb\u9910 <pre><code># \u5728 Github \u521b\u5efa\u4ed3\u5e93\n# \u83b7\u53d6\u4ed3\u5e93\u7684 http / SSH clone \u547d\u4ee4\n\n# \u4ece\u8fdc\u7a0b\u5c06\u4ed3\u5e93\u514b\u9686\u5230\u672c\u5730\ngit clone &lt;repo-url&gt;\n\n# \u5b8c\u6210\u4ee3\u7801\u4fee\u6539\u540e\u5c06\u4fee\u6539\u6dfb\u52a0\u5230\u6682\u5b58\u533a\ngit add -A # \u6dfb\u52a0\u6240\u6709\u4fee\u6539\ngit add .  # \u6dfb\u52a0\u5f53\u524d\u76ee\u5f55\u4e0b\u7684\u4fee\u6539\n\n# \u63d0\u4ea4\u4fee\u6539\ngit commit -m \"Write commit message here.\"\n\n# push \u5230\u8fdc\u7a0b\u4ed3\u5e93\ngit push origin\n</code></pre>"},{"location":"tech_accu/tool/Git/Commands/#\u914d\u7f6e","title":"\u914d\u7f6e","text":"<p>Git \u7684\u914d\u7f6e\u6587\u4ef6\u540d\u53eb <code>.gitconfig</code>\uff0c\u7528\u6765\u5b58\u653e\u4e00\u4e9b\u914d\u7f6e\u4fe1\u606f\uff0c\u5728\u7528\u6237\u76ee\u5f55\u4e0b\u7684\u4e3a\u5168\u5c40\u914d\u7f6e\u4fe1\u606f\uff0c\u800c\u5728\u9879\u76ee\u76ee\u5f55\u4e0b\u7684\u5219\u4e3a\u9879\u76ee\u914d\u7f6e\u4fe1\u606f\u3002</p> <pre><code># \u663e\u793a\u914d\u7f6e\ngit config --list\n</code></pre>"},{"location":"tech_accu/tool/Git/Commands/#\u751f\u6210\u672c\u5730\u4ed3\u5e93","title":"\u751f\u6210\u672c\u5730\u4ed3\u5e93","text":"<p>\u672c\u5730\u751f\u6210\u4ed3\u5e93\u4e3b\u8981\u6709\u4e24\u79cd\u9014\u5f84\uff0c\u4e00\u662f\u5728\u672c\u5730\u76f4\u63a5\u65b0\u5efa\u4e00\u4e2a\u4ed3\u5e93\uff0c\u800c\u662f\u514b\u9686\u4e00\u4e2a\u8fdc\u7a0b\u4ed3\u5e93\u3002</p> <pre><code># \u5728\u5f53\u524d\u76ee\u5f55 . \u65b0\u5efa\u4e00\u4e2a\u4ed3\u5e93\ngit init\n\n# \u521b\u5efa\u4e00\u4e2a\u540d\u4e3a &lt;dir-name&gt; \u7684\u76ee\u5f55\uff0c\u5c06\u5176\u521d\u59cb\u5316\u4e3a\u4e00\u4e2a Git \u4ed3\u5e93\ngit init &lt;dir-name&gt;\n\n# \u4ece &lt;repo-url&gt; \u514b\u9686\u4e00\u4e2a\u8fdc\u7a0b\u4ed3\u5e93\uff08\u5305\u62ec\u6240\u6709\u7684 git \u4fe1\u606f\uff09\ngit clone &lt;repo-url&gt;\n</code></pre> <p>\u4ece\u6587\u4ef6\u89d2\u5ea6\u6765\u8bb2\uff0c\u5b9e\u9645\u4e0a\u5b83\u662f\u751f\u6210\u4e86\u4e00\u4e2a\u6709<code>.git</code>\u6587\u4ef6\u5939\u7684\u6587\u4ef6\u5939\uff0c\u800c<code>.git</code>\u6587\u4ef6\u5939\u5b58\u50a8\u4e86 Git \u6240\u9700\u8981\u7684\u5927\u90e8\u5206\u4fe1\u606f\u3002 \u4f7f\u7528\u5e38\u89c1\u7684 shell \u8fdb\u5165\u4ed3\u5e93\u6587\u4ef6\u5939\u540e\uff0c\u4e00\u822c\u4f1a\u6709\u4e00\u4e2a label \u8868\u793a\u4f60\u5df2\u7ecf\u8fdb\u5165\u4e86\u4e00\u4e2a\u4ed3\u5e93\u7684\u67d0\u4e2a\u5206\u652f\u4e86\u3002\u6bd4\u5982\u8fdb\u5165\u4e00\u4e2a\u65b0\u7684\u4ed3\u5e93\u65f6\uff0c\u4f1a\u6709\u4e00\u4e2amaster\u7684 label \uff0c\u5177\u4f53\u8868\u73b0\u5f62\u5f0f\u4e3b\u8981\u770b\u4f60\u7684 shell \u548c\u4e3b\u9898\u4e86\u3002</p> <p>\u9700\u8981\u6ce8\u610f\u7684\u662f\uff0c\u5728\u672c\u5730\u76f4\u63a5\u521b\u5efa\u7684\u4ed3\u5e93\u4ec5\u4ec5\u53ea\u662f\u4e00\u4e2a\u672c\u5730\u4ed3\u5e93\uff0c\u4e0d\u5177\u5907\u8fdc\u7a0b\u534f\u4f5c\u529f\u80fd\uff0c\u9700\u8981\u8fdb\u884c\u5bf9\u5e94\u7684\u914d\u7f6e\uff0c\u53c2\u8003 \"Git Workflow\" \u6761\u76ee\uff1b\u800c\u4e00\u822c\u4ece\u8fdc\u7a0b\u4ed3\u5e93\u514b\u9686\u4e0b\u6765\u7684\u4ed3\u5e93\u90fd\u5df2\u7ecf\u7ecf\u8fc7\u8bbe\u7f6e\uff0c\u53ef\u4ee5\u76f4\u63a5\u8fdb\u884c\u8fdc\u7a0b\u534f\u4f5c\u3002</p>"},{"location":"tech_accu/tool/Git/Commands/#\u7248\u672c\u7ba1\u7406","title":"\u7248\u672c\u7ba1\u7406","text":"<p>Git \u57fa\u4e8e\u7248\u672c\u4e4b\u95f4\u7684\u5dee\u5f02\u8fdb\u884c\u4ee3\u7801\u7ba1\u7406\uff0c\u4f7f\u7528 Git \u8fdb\u884c\u4ee3\u7801\u7ba1\u7406\u4e3b\u8981\u6307\u5728\u505a\u5b8c\u7279\u5b9a\u4fee\u6539\u4ee5\u540e\u5c06\u5176\u6dfb\u52a0\u5230\u5bf9\u5e94\u5206\u652f\u4e2d\u3002 \u5728\u8003\u8651 Git \u64cd\u4f5c\u4e4b\u524d\uff0c\u4f60\u53ef\u4ee5\u653e\u5fc3\u5730\u8fdb\u884c\u4f60\u7684\u4ee3\u7801\u7f16\u8f91\u5de5\u4f5c\uff0c\u4e0d\u8fc7\u8bb0\u5f97\u5728\u5408\u9002\u7684\u65f6\u673a\u8fdb\u884c\u7248\u672c\u7ba1\u7406\u3002</p>"},{"location":"tech_accu/tool/Git/Commands/#\u67e5\u770b\u5dee\u5f02\u6587\u4ef6","title":"\u67e5\u770b\u5dee\u5f02\u6587\u4ef6","text":"<p>\u901a\u8fc7\u5982\u4e0b\u6307\u4ee4\u53ef\u4ee5 \u67e5\u770b\u5dee\u5f02\u6587\u4ef6\uff1a</p> <pre><code># \u663e\u793a\u68c0\u6d4b\u5230\u5dee\u5f02\u7684\u6587\u4ef6\uff0c\u5b83\u4eec\u6b63\u5728\u7b49\u5f85\u88ab\u63d0\u4ea4\ngit status\n</code></pre>"},{"location":"tech_accu/tool/Git/Commands/#\u6dfb\u52a0\u5230\u6682\u5b58\u533a","title":"\u6dfb\u52a0\u5230\u6682\u5b58\u533a","text":"<p>\u5728\u5b8c\u6210\u4ee3\u7801\u4fee\u6539\u5de5\u4f5c\u540e\u9700\u8981\u5c06\u4ee3\u7801 \u6dfb\u52a0 \u5230\u6682\u5b58\u533a\uff1a</p> <pre><code># \u5c06 &lt;target&gt; \u4e2d\u7684\u4fee\u6539\u6dfb\u52a0\u7684\u6682\u5b58\u533a\uff0c\u6587\u4ef6\u5939\u548c\u6587\u4ef6\u540c\u7406\uff0c'.' \u540c\u7406 \ngit add &lt;target&gt;\n\n# \u5bf9\u4e8e\u6240\u6709\u7684\u4fee\u6539\u4f9d\u6b21\u8fdb\u884c\u6dfb\u52a0\u786e\u8ba4\uff08\u5305\u62ec\u5355\u4e00\u6587\u4ef6\u7684\u591a\u5904\u4fee\u6539\uff09\ngit add -p\n\n# \u7528\u4ea4\u4e92\u5f0f\u7684\u65b9\u6cd5\u8fdb\u884c\u6dfb\u52a0\ngit add -i\n</code></pre>"},{"location":"tech_accu/tool/Git/Commands/#\u63d0\u4ea4\u5230\u4ed3\u5e93","title":"\u63d0\u4ea4\u5230\u4ed3\u5e93","text":"<p>\u6dfb\u52a0\u5b8c\u540e\u9700\u8981\u8fdb\u884c \u63d0\u4ea4\uff0c\u5728\u4ed3\u5e93\u4e2d\u5f62\u6210\u4e00\u4e2a\u8282\u70b9\uff1a</p> <pre><code># \u63d0\u4ea4\u5230\u4ed3\u5e93\ngit commit -m \"Write commit message here.\"\n\n# \u4fee\u6b63\u4e0a\u4e00\u6b21\u63d0\u4ea4\uff0c\u610f\u601d\u662f\u8bf4\u4f1a\u6269\u5145\u5e76\u66ff\u4ee3\u4e0a\u4e00\u6b21\u63d0\u4ea4\n# \u5e94\u7528\u573a\u666f\u5982\uff1a\u4e0a\u4e00\u6b21\u63d0\u4ea4\u6709\u9057\u6f0f\u3001\u4e0a\u4e00\u6b21\u63d0\u4ea4\u7684\u63d0\u4ea4\u4fe1\u606f\u6709\u95ee\u9898\u7b49\ngit commit --amend -m \"Write commit message here.\"\n</code></pre>"},{"location":"tech_accu/tool/Git/Commands/#\u67e5\u770b\u63d0\u4ea4\u8bb0\u5f55","title":"\u67e5\u770b\u63d0\u4ea4\u8bb0\u5f55","text":"<p>\u5b8c\u6210\u63d0\u4ea4\u540e\u8fd9\u4e00\u6b21\u4fee\u6539\u5c31\u4f1a\u88ab\u5199\u5165\u5386\u53f2\u8bb0\u5f55\u4e2d\uff0c\u4f60\u53ef\u4ee5\u901a\u8fc7<code>log</code>\u6765 \u67e5\u770b\uff1a</p> <pre><code>git log\n</code></pre>"},{"location":"tech_accu/tool/Git/Commands/#\u56de\u6eaf--\u62b5\u6d88\u8bb0\u5f55","title":"\u56de\u6eaf / \u62b5\u6d88\u8bb0\u5f55","text":"<p>\u5728<code>log</code>\u4e2d\u53ef\u4ee5\u67e5\u8be2\u5f97\u5230\u6bcf\u4e00\u6b21<code>commit</code>\u7684\u54c8\u5e0c\uff0c\u5f97\u5230\u8fd9\u4e9b\u54c8\u5e0c(\u4e5f\u53ef\u4ee5\u4f7f\u7528\u6807\u7b7e)\u4ee5\u540e\u6211\u4eec\u53ef\u4ee5\u7528\u5b83\u6765\u8fdb\u884c \u56de\u6eaf \u548c \u62b5\u6d88 \u64cd\u4f5c\uff1a</p> <pre><code># \u56de\u6eaf\u5230\u7279\u5b9a commit \uff0c\u6bd4\u8f83\u5371\u9669\ngit reset HEAD                  # \u56de\u6eaf\u5230\u4e0a\u4e00\u4e2a commit \uff0c\u6548\u679c\u4e0a\u6e05\u7a7a\u4e86\u6682\u5b58\u533a\uff0c\u4e0d\u5f71\u54cd\u5de5\u4f5c\u533a\ngit reset --hard &lt;commit-id&gt;    # \u629b\u5f03\u5f53\u524d\u7684\u5de5\u4f5c\u533a\u5e76\u56de\u6eaf\u5230\u67d0\u4e2a\u7248\u672c\n\n# \u62b5\u6d88\u4e00\u6b21 commit \uff0c\u4ea7\u751f\u4e00\u4e2a\u4e0e\u76ee\u6807 commit \u4e92\u9006\u7684 commit\ngit revert HEAD                     # \u62b5\u6d88\u4e0a\u4e00\u6b21 commit\ngit revert &lt;commit-id&gt;              # \u62b5\u6d88\u7279\u5b9a commit\n</code></pre>"},{"location":"tech_accu/tool/Git/Commands/#\u5220\u9664--\u79fb\u52a8\u91cd\u547d\u540d","title":"\u5220\u9664 / \u79fb\u52a8(\u91cd\u547d\u540d)","text":"<p>\u5220\u9664 \u6587\u4ef6\u548c \u79fb\u52a8(\u91cd\u547d\u540d) \u6587\u4ef6\u53ef\u4ee5\u4f7f\u7528<code>rm</code>\u548c<code>mv</code>\uff0c\u5173\u4e8e<code>rm</code>(<code>mv</code>)\u548c<code>git rm</code>(<code>git mv</code>)\u7684\u533a\u522b\u53ef\u4ee5\u770b\u8fd9\u91cc\u3002 \u7b80\u5355\u6765\u8bf4\u5c31\u662f\uff0c<code>git rm &lt;file&gt;</code>\u7b49\u4ef7\u4e8e<code>rm &lt;file&gt; ; git add &lt;file&gt;</code>\uff1b<code>mv</code>\u540c\u7406\uff0c\u4f46\u662f\u4f60\u65e0\u6cd5\u628a\u4e00\u4e2a\u6587\u4ef6\u901a\u8fc7<code>git mv</code>\u79fb\u52a8\u5230 repo dir \u4e4b\u5916\u3002</p> <pre><code># \u5220\u9664\u67d0\u4e2a\u6587\u4ef6\ngit rm &lt;file&gt;\n# \u79fb\u52a8(\u91cd\u547d\u540d)\u67d0\u4e2a\u6587\u4ef6\ngit mv &lt;from&gt; &lt;to&gt;\n\n# \u4f7f\u7528\u5982\u4e0b\u547d\u4ee4\u8fd8\u53ef\u4ee5\u505c\u6b62\u5bf9\u67d0\u4e2a\u6587\u4ef6\u7684\u8ffd\u8e2a\uff0c\u6700\u5e38\u7528\u7684\u60c5\u51b5\u4e00\u822c\u548c`.gitignore`\u6709\u5173\ngit rm --cache &lt;file&gt;\n</code></pre>"},{"location":"tech_accu/tool/Git/Commands/#\u6807\u7b7e\u64cd\u4f5c","title":"\u6807\u7b7e\u64cd\u4f5c","text":"<p>\u4e0a\u9762\u8bb8\u591a\u6d89\u53ca\u5b9a\u4f4d\u7279\u5b9a commit \u7684\u64cd\u4f5c\u90fd\u9700\u8981\u83b7\u53d6 commit \u7684\u54c8\u5e0c\u3002\u4e0d\u8fc7\u5982\u679c\u5bf9\u67d0\u4e9b\u7279\u5b9a\u7248\u672c\u8fdb\u884c\u4e00\u4e9b\u6807\u7b7e\u7ba1\u7406\uff0c\u90a3\u6211\u4eec\u5c31\u53ef\u4ee5\u901a\u8fc7\u8bbf\u95ee\u6807\u7b7e\u6765\u7d22\u5f15\u7279\u5b9a commit \uff0c\u56e0\u800c\uff0ctag \u5b9e\u9645\u4e0a\u662f\u4e0d\u53ef\u91cd\u590d\u7684\u3002</p> <pre><code># \u4e3a\u7279\u5b9a commit \u6dfb\u52a0 tag\ngit tag &lt;tag name&gt; &lt;commit id&gt;\n\n# \u5220\u9664\u7279\u5b9a tag\ngit tag -d &lt;tag name&gt;\n</code></pre> <p>\u53e6\u5916\uff0c\u9700\u8981\u63d0\u9192\u7684\u662f\uff0c\u9ed8\u8ba4\u60c5\u51b5\u4e0b<code>git push</code>\u4e0d\u4f1a\u5c06 tag \u4e0a\u4f20\u5230\u8fdc\u7a0b\u4ed3\u5e93\uff0c\u9700\u8981\u5728\u547d\u4ee4\u540e\u52a0\u5165<code>--tags</code>\u6765\u4e00\u6b21\u6027 push \u6240\u6709\u7684 tag \u6216\u8005\u6dfb\u52a0<code>&lt;tag name&gt;</code>\u6765\u4e0a\u4f20 tag \u3002</p>"},{"location":"tech_accu/tool/Git/Commands/#\u8fdc\u7a0b\u534f\u4f5c","title":"\u8fdc\u7a0b\u534f\u4f5c","text":"<p>\u8fdc\u7a0b\u7ba1\u7406\u4e3b\u8981\u6307\u591a\u4eba\u9879\u76ee\u65f6\u9700\u8981\u901a\u8fc7\u8fdc\u7a0b\u4ed3\u5e93\u6765\u5b8c\u6210\u534f\u4f5c\u3002\u8fd9\u91cc\u4ee5 GitHub \u4e3a\u4f8b\u3002 \u5f53\u4f60\u5728 Github \u521b\u5efa\u4e00\u4e2a\u7a7a repo \u4ee5\u540e\uff0c\u4f1a\u6709\u8fd9\u6837\u4e00\u4e2a\u9ed8\u8ba4\u9875\u9762\uff1a</p> <p> IsshikiHugh \u662f\u6211\u7684 User ID\uff0cnothing \u662f\u6211\u7684 Repo Name</p> <p>\u6211\u4eec\u91cd\u70b9\u5173\u6ce8\u4e2d\u95f4\u4e24\u4e2a\u4ee3\u7801\u6846\uff0c\u5199\u7684\u5df2\u7ecf\u975e\u5e38\u6e05\u695a\u4e86\u3002</p> <p><code>create a new repository on the command line</code>\u6307\u5bfc\u4f60\u5728\u672c\u5730\u521b\u5efa\u4e00\u4e2a\u65b0\u7684\u7a7a\u4ed3\u5e93\uff0c\u5e76\u4e0e\u8fdc\u7a0b\u4ed3\u5e93\u94fe\u63a5\uff1b</p> <p><code>push an existing repository from the command line</code>\u6307\u5bfc\u4f60\u5982\u4f55\u5c06\u8fdc\u7a0b\u4ed3\u5e93\u548c\u672c\u5730\u4ed3\u5e93\u94fe\u63a5\u8d77\u6765\uff0c\u5e76 push \u3002</p>"},{"location":"tech_accu/tool/Git/Commands/#\u8fdc\u7a0b\u4ed3\u5e93\u7ba1\u7406","title":"\u8fdc\u7a0b\u4ed3\u5e93\u7ba1\u7406","text":"<p>\u6765\u81ea GitHub \u7684\u6307\u5bfc\u6587\u4ef6\u4e2d\u6700\u6838\u5fc3\u7684\u4e00\u6761\u6307\u4ee4\u662f\u5982\u4f55\u94fe\u63a5\u672c\u5730\u4ed3\u5e93\u4e0e\u8fdc\u7a0b\u4ed3\u5e93\uff1a</p> <p><pre><code># \u5728\u672c\u5730\u6dfb\u52a0\u8fdc\u7a0b\u4ed3\u5e93\uff0c\u547d\u540d\u4e3a &lt;remote name&gt; \uff0c\u6ce8\u610f\u8fd9\u91cc\u7684 &lt;url&gt; \u5e76\u4e0d\u662f\u6d4f\u89c8\u5668\u4e0a\u9762\n# \u90a3\u4e2a\uff0c\u800c\u662f\u4ece github \u590d\u5236\u8fc7\u6765\u7684 http \u6216\u8005 ssh \u63a8\u9001\ngit remote add &lt;remote name&gt; &lt;url&gt;\n# \u5e38\u7528\u7684 &lt;remote name&gt; \u662f origin\n</code></pre> \u9664\u6b64\u4e4b\u5916\uff0c\u5173\u4e8e\u8fdc\u7a0b\u4ed3\u5e93\u7684\u76f8\u5173\u547d\u4ee4\u8fd8\u6709\u5982\u4e0b\uff1a <pre><code>git remote -v                  # \u663e\u793a\u8fdc\u7a0b\u4ed3\u5e93(\u8be6\u7ec6\u4fe1\u606f)\ngit remote rm &lt;remote name&gt;    # \u89e3\u9664\u4e0e\u5bf9\u5e94\u8fdc\u7a0b\u4ed3\u5e93\u7684\u7ed1\u5b9a\u5173\u7cfb\ngit remote rename &lt;from&gt; &lt;to&gt;  # \u91cd\u547d\u540d\u7279\u5b9a\u8fdc\u7a0b\u4ed3\u5e93\n</code></pre></p>"},{"location":"tech_accu/tool/Git/Commands/#\u672c\u5730\u4ece\u8fdc\u7a0b\u4ed3\u5e93\u62c9\u53d6\u5185\u5bb9","title":"\u672c\u5730\u4ece\u8fdc\u7a0b\u4ed3\u5e93\u62c9\u53d6\u5185\u5bb9","text":"<p>\u4e3b\u8981\u6709\u4e24\u79cd\u65b9\u5f0f\uff0c\u5373<code>pull</code>\u548c<code>fetch</code>\uff0c\u533a\u522b\u5728\u4e8e<code>fetch</code>\u5e76\u4e0d\u4f1a\u5408\u5e76\u5185\u5bb9\uff0c\u800c\u4ec5\u4ec5\u662f\u4e0b\u8f7d\u8fdc\u7a0b\u4ed3\u5e93\u4e2d\u7684\u53d8\u52a8\u4fe1\u606f\u3002\u7b80\u5355\u6765\u8bf4\u5c31\u662f<code>pull</code>\u7b49\u6548\u4e8e<code>fetch</code>\u5e76<code>merge</code>\u3002</p> <pre><code># \u4ece\u8fdc\u7a0b\u4ed3\u5e93\u4e0b\u8f7d\u53d8\u52a8\u5185\u5bb9\ngit fetch &lt;remote name&gt;\n\n# \u4ece\u8fdc\u7a0b\u4ed3\u5e93\u62c9\u53d6\u53d8\u52a8\u5185\u5bb9\u5e76\u4e14\u5408\u5e76\u5230\u6307\u5b9a\u5206\u652f\ngit pull &lt;remote name&gt; &lt;branch&gt;\n</code></pre>"},{"location":"tech_accu/tool/Git/Commands/#\u672c\u5730\u5411\u8fdc\u7a0b\u4ed3\u5e93\u63a8\u9001\u5185\u5bb9","title":"\u672c\u5730\u5411\u8fdc\u7a0b\u4ed3\u5e93\u63a8\u9001\u5185\u5bb9","text":"<p>\u5728\u672c\u5730\u5b8c\u6210 commit \u64cd\u4f5c\u540e\uff0c\u5c31\u53ef\u4ee5 push \u5230\u8fdc\u7a0b\u4ed3\u5e93\uff1a</p> <pre><code># \u63a8\u9001 &lt;branch&gt; \u7684\u5185\u5bb9\u5230 &lt;remote&gt; \uff0c\u5e76\u81ea\u52a8\u8bbe\u7f6e\u4e0a\u6e38\uff0c\u8fd9\u610f\u5473\u7740\u5728\u8fd9\u4e2a\u5206\u652f\u91cc\uff0c\n# \u4e0b\u4e00\u6b21 push \u53ea\u9700\u8981\u8f93\u5165 git push \u5373\u53ef\ngit push -u &lt;remote&gt; &lt;branch&gt;\n# eg: \u63a8\u9001 master \u5206\u652f\u7684\u5185\u5bb9\u5230 origin \uff0c\u5e76\u81ea\u52a8\u8bbe\u7f6e\u4e0a\u6e38\ngit push -u origin master\n\ngit push --force    # \u5f3a\u5236\u63a8\u9001\u5f53\u524d\u5206\u652f\uff0c\u5373\u4f7f\u6709\u51b2\u7a81\u5b58\u5728\n--all      # \u63a8\u9001\u6240\u6709\u5206\u652f\u7684\u5185\u5bb9\n</code></pre>"},{"location":"tech_accu/tool/Git/Commands/#\u5206\u652f\u7ba1\u7406","title":"\u5206\u652f\u7ba1\u7406","text":""},{"location":"tech_accu/tool/Git/Commands/#\u67e5\u770b\u5206\u652f","title":"\u67e5\u770b\u5206\u652f","text":"<pre><code>git branch        # \u663e\u793a\u672c\u5730\u6240\u6709\u5206\u652f\n-r     # \u663e\u793a\u8fdc\u7a0b\u6240\u6709\u5206\u652f\n-a     # \u663e\u793a\u6240\u6709\u5206\u652f\n</code></pre>"},{"location":"tech_accu/tool/Git/Commands/#\u65b0\u5efa\u5206\u652f--\u5207\u6362\u5206\u652f--\u8bbe\u7f6e\u4e0a\u6e38","title":"\u65b0\u5efa\u5206\u652f / \u5207\u6362\u5206\u652f / \u8bbe\u7f6e\u4e0a\u6e38","text":"<pre><code># \u65b0\u5efa\u4e00\u4e2a\u540d\u4e3a &lt;branch name&gt; \u7684\u65b0\u5206\u652f\uff0c\u4f46\u4e0d\u5207\u6362\ngit branch &lt;branch name&gt;\n# \u901a\u8fc7 checkout \u6765\u5207\u6362\u5206\u652f\uff0c\u6bd4\u5982\u8fdb\u5165\u5230\u521a\u521a\u521b\u5efa\u7684\u5206\u652f\u6c47\u603b\ngit checkout &lt;branch&gt;         # \u8be5\u547d\u4ee4\u4f1a\u66f4\u65b0\u5de5\u4f5c\u533a\n# \u521b\u5efa\u5b8c\u5206\u652f\u540e\u901a\u8fc7\u5982\u4e0b\u547d\u4ee4\u8bbe\u7f6e\u4e0a\u6e38\ngit branch --set-upstream &lt;local branch&gt; &lt;remote branch&gt;\n\n# \u5c06\u4e0a\u9762\u7684\u547d\u4ee4\u8fdb\u884c\u96c6\u6210\uff0c\u6709\uff1a\n\n# \u76f4\u63a5\u65b0\u5efa\u4e00\u4e2a\u540d\u4e3a &lt;branch name&gt; \u7684\u65b0\u5206\u652f\u5e76\u5207\u6362\ngit checkout -b &lt;branch name&gt;\n# \u65b0\u5efa\u4e00\u4e2a\u540d\u4e3a &lt;local branch&gt; \u7684\u65b0\u5206\u652f\uff0c\u5e76\u8bbe &lt;remote branch&gt; \u4e3a\u4e0a\u6e38\ngit branch --track &lt;local branch&gt; &lt;remote branch&gt;\n</code></pre>"},{"location":"tech_accu/tool/Git/Commands/#\u5206\u652f\u5408\u5e76","title":"\u5206\u652f\u5408\u5e76","text":"<pre><code># \u5c06\u6307\u5b9a\u5206\u652f\u5408\u5e76\u5230\u5f53\u524d\u5206\u652f\uff0c\u9700\u8981\u5904\u7406\u51b2\u7a81\u90e8\u5206\uff08\u6c9f\u901a\u534f\u5546\u3001\u624b\u52a8\u89e3\u51b3\uff09\ngit merge &lt;branch&gt;\n\n# \u5c06\u7279\u5b9a commit \u5408\u5e76\u8fdb\u5f53\u524d\u5206\u652f\ngit cherry-pick &lt;commit id&gt;\n</code></pre>"},{"location":"tech_accu/tool/Git/Commands/#\u5206\u652f\u5220\u9664","title":"\u5206\u652f\u5220\u9664","text":"<pre><code># \u5220\u9664\u672c\u5730\u5206\u652f\ngit branch -d &lt;branch&gt;\n\n# \u5220\u9664\u8fdc\u7a0b\u5206\u652f\ngit push &lt;remote&gt; --delete &lt;branch&gt;\ngit branch -dr &lt;remote&gt;/&lt;branch&gt;\n# eg:\ngit branch -dr origin/testbrach\n</code></pre>"},{"location":"tech_accu/tool/Git/Commands/#\u4f60\u53ef\u80fd\u8fd8\u8981\u4e86\u89e3\u7684--\u672c\u6587\u8fd8\u6ca1\u8bb2\u7684\u4e1c\u897f","title":"\u4f60\u53ef\u80fd\u8fd8\u8981\u4e86\u89e3\u7684 / \u672c\u6587\u8fd8\u6ca1\u8bb2\u7684\u4e1c\u897f","text":"<ul> <li><code>.gitignore</code>\u6587\u4ef6</li> <li>\u8054\u7cfb<code>git rm --cached &lt;file&gt;</code></li> <li>\u201c\u8ffd\u8e2a\u201d\u7684\u6982\u5ff5</li> <li><code>HEAD</code></li> <li>git stash</li> </ul>"},{"location":"tech_accu/tool/Git/Commands/#\u53c2\u8003\u8d44\u6599--ref","title":"\u53c2\u8003\u8d44\u6599 | Ref","text":"<ul> <li>https://www.ruanyifeng.com/blog/2015/12/git-cheat-sheet.html</li> <li>https://www.cnblogs.com/lance-ehf/p/3871643.html</li> <li>https://blog.csdn.net/Lakers2015/article/details/111318801</li> </ul>"},{"location":"tech_accu/tool/Git/Workflow/","title":"Git Workflow","text":"<p> \u7ea6 1267 \u4e2a\u5b57  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 4 \u5206\u949f</p> <p>\u7b80\u4ecb</p> <p>\u672c\u6587\u5185\u5bb9\u57fa\u4e8e\u6211\u81ea\u5df1\u7684\u7406\u89e3\u548c\u4e00\u4e9b\u6587\u7ae0\uff0c\u662f\u5b66\u4e60\u7b14\u8bb0\uff0c\u4f46\u540c\u65f6\u6211\u4e5f\u5e0c\u671b\u5b83\u80fd\u88ab\u4f5c\u4e3a\u4e00\u4e2a\u5b66\u4e60\u53c2\u8003\u8d44\u6599\u3002</p> <p>\u6240\u4ee5\u5982\u679c\u6709\u9519\u8bef\u8bf7\u53ca\u65f6\u8bc4\u8bba\u6216\u8005\u8054\u7cfb\u6211\uff0c\u5e0c\u671b\u80fd\u4e3a\u5927\u5bb6\u63d0\u4f9b\u4e00\u4e2a\u6bd4\u8f83\u597d\u7684\u5b66\u4e60\u53c2\u8003\uff01</p> <p>\u56e0\u4e3a\u6211\u81ea\u5df1\u7684\u5f00\u53d1\u7ecf\u5386\u6709\u9650\uff0c\u6240\u4ee5\u5e76\u4e0d\u80fd\u4fdd\u8bc1\u81ea\u5df1\u7684\u7406\u89e3\u662f\u5408\u9002\u4e14\u6b63\u786e\u7684\uff0c\u6240\u4ee5\u5e0c\u671b\u5927\u5bb6\u72e0\u72e0\u5730 educate \u6211\uff01</p> <p>\u672c\u6761\u76ee\u4e3b\u8981\u4ecb\u7ecd\u6709\u5173 Git Workflow \u7684\u6982\u5ff5\u6027\u8d28\u548c\u6307\u5bfc\u6027\u8d28\u7684\u4e00\u4e9b\u5185\u5bb9\uff0c\u5b83\u4eec\u5e76\u4e0d\u5177\u4f53\uff0c\u4f46\u662f\u4f1a\u6307\u5bfc\u60a8\u7684\u4f7f\u7528\u3002</p> <p>\u7531\u4e8e mkdocs \u5e76\u6ca1\u6709\u6807\u7b7e\u529f\u80fd\uff0c\u6240\u4ee5\u5176\u5b9e\u8fd8\u662f\u8bed\u96c0\u4e0a\u7684\u6587\u7ae0\u66f4\u597d\u770b\uff0c\u4f46\u662f\u6211\u5e76\u4e0d\u6253\u7b97\u66f4\u65b0\u8bed\u96c0\u4e86\uff0c\u6545\u8fd9\u91cc\u53ea\u653e\u4e00\u4e2a\u4ee5\u524d\u7684\u6307\u8def\u94fe\u63a5\uff1a\ud83d\udd17\u3002</p> <p>Git branch \u53ef\u89c6\u5316\u7ec3\u4e60\u7f51\u7ad9\uff1ahttps://note.isshikih.top/tech_accu/tool/Git/Workflow/</p>"},{"location":"tech_accu/tool/Git/Workflow/#\u4f55\u4e3a-git-workflow","title":"\u4f55\u4e3a 'Git Workflow'","text":"<p>Git Workflow \u662f\u4e00\u79cd\u89c4\u8303\u7684\u5de5\u4f5c\u6d41\u7a0b\uff0c\u800c\u5e76\u4e0d\u662f\u4e00\u4e2a\u5177\u4f53\u7684\u5de5\u5177\u6216\u8005\u6280\u672f\uff0c\u5f53\u7136\u8c8c\u4f3c\u6709\u4e00\u4e2a\u53eb\u505a Gitflow \u7684\u5de5\u5177\uff0c\u4f46\u5728\u672c\u6587\u4e2d\u6682\u65f6\u4e0d\u4ecb\u7ecd\u3002 \u73b0\u5728\u88ab\u5e7f\u6cdb\u4f7f\u7528\u7684 Workflow \u4e3b\u8981\u6709\u4e09\u79cd\uff1a</p> <ul> <li>Git Workflow</li> <li>Github Workflow</li> <li>Gitlab Workflow</li> </ul> <p>\u4ed6\u4eec\u7684\u5173\u7cfb\u662f\uff0c\u4f9d\u6b21\u5438\u6536\u4e0e\u6539\u8fdb\uff0c\u5404\u6709\u7279\u70b9\uff0c\u4e14\u4e0e\u5bf9\u5e94\u7684\u4f7f\u7528\u5e73\u53f0\u76f8\u9002\u5e94\uff0c\u4e0b\u9762\u5c06\u5206\u6761\u6982\u8ff0\u3002 \u5728\u4e0d\u540c\u7684 Workflow \u4e2d\uff0c\u6700\u4e3b\u8981\u7684\u533a\u522b\u5c31\u662f\u4e0d\u540c\u5206\u652f\u95f4\u7684\u5408\u4f5c\u5f62\u5f0f\u548c\u7ec4\u7ec7\u5f62\u5f0f\uff0c\u5982\u679c\u4f60\u5bf9 Git \u7684\u5206\u652f\u8fd8\u4e0d\u662f\u5f88\u719f\u6089\uff0c\u8bf7\u5148\u53c2\u8003 Git Commands \u7684\u90e8\u5206\u5185\u5bb9\uff0c\u7b80\u5355\u4e86\u89e3\u4e00\u4e0b\u57fa\u7840\u6307\u4ee4\u3002</p>"},{"location":"tech_accu/tool/Git/Workflow/#git-workflow_1","title":"Git Workflow","text":"<p> [Source] https://gitbook.tw/chapters/gitflow/why-need-git-flow</p> <p>Tips: \u5728\u9605\u8bfb\u63a5\u4e0b\u6765\u7684\u4e00\u4e9b\u8bf4\u660e\u65f6\uff0c\u53ef\u4ee5\u8054\u7cfb\u4e0a\u65b9\u8fd9\u5f20\u56fe\u8fdb\u884c\u7406\u89e3\u3002</p> <p>\u5728 Git Workflow \u4e2d\uff0c\u4e3b\u8981\u6709 5 \u7c7b\u5206\u652f\uff0c\u4ed6\u4eec\u5206\u522b\u662f master hotfix release develop feature\uff0c\u5b83\u4eec\u6709\u7740\u4e0d\u540c\u7684\u4f5c\u7528\u548c\u4f7f\u7528\u89c4\u8303\u3002\u5176\u4e2dmasterdevelop\u662f\u957f\u671f\u5206\u652f\uff0c\u4ed6\u4eec\u4f1a\u968f\u7740\u9879\u76ee\u7684\u7ef4\u62a4\u4e00\u76f4\u5b58\u5728\uff0c\u800chotfixreleasefeature\u8fd9\u4e9b\u77ed\u671f\u5206\u652f\u5219\u4f1a\u5728\u5b8c\u6210\u5bf9\u5e94\u5f00\u53d1\u540e\u88ab\u5408\u5e76\u6216\u8005\u5220\u9664\u3002</p>"},{"location":"tech_accu/tool/Git/Workflow/#master-\u5206\u652f\u4e3b\u5206\u652f","title":"Master \u5206\u652f\uff08\u4e3b\u5206\u652f\uff09","text":"<p>\u76f4\u63a5\u9762\u5411\u4f7f\u7528\u65b9\u7684\u5206\u652f\uff0c\u5728master\u4e2d\u5b58\u653e\u7684\u5e94\u5f53\u662f\u53ef\u4ee5\u4f7f\u7528\u7684\u7a33\u5b9a\u7248\u672c\uff0c\u56e0\u800c\u901a\u5e38\u4e5f\u4f1a\u5728\u5176\u4e2d\u6dfb\u52a0\u7248\u672c\u7f16\u53f7\u3002 \u6211\u4eec\u5e0c\u671b master \u4e2d\u7684\u4ee3\u7801\u603b\u662f\u4ece\u522b\u7684\u5206\u652f\u4e2d\u5408\u5e76\u8fc7\u6765\u7684\uff0c\u800c\u5e76\u4e0d\u5e0c\u671b\u4efb\u4f55\u4eba\u76f4\u63a5 commit \u5230 master \u4e2d\u3002</p>"},{"location":"tech_accu/tool/Git/Workflow/#develop-\u5206\u652f\u5f00\u53d1\u5206\u652f","title":"Develop \u5206\u652f\uff08\u5f00\u53d1\u5206\u652f\uff09","text":"<p>\u6240\u6709\u5f00\u53d1\u5de5\u4f5c\u90fd\u57fa\u4e8e\u8be5\u5206\u652f\u8fdb\u884c\uff0c\u53ef\u4ee5\u7406\u89e3\u4e3a\u9879\u76ee\u4ee3\u7801\u7684\u6c47\u6d41\u5904\uff0c\u800c master \u5219\u662f develop \u4e2d\u7279\u5b9a\u8282\u70b9\u53ef\u7528\u53d1\u884c\u3002 \u5f53\u9700\u8981\u6dfb\u52a0\u65b0\u7684\u529f\u80fd\u65f6\uff0c\u6211\u4eec\u9700\u8981\u65b0\u5efa\u4e00\u4e2a feature (\u5982\u56fe)\uff0c\u7136\u540e\u5728\u5b8c\u6210\u5bf9\u5e94\u5f00\u53d1\u540e\u5408\u5e76\u56de develop\u3002</p>"},{"location":"tech_accu/tool/Git/Workflow/#hotfix-\u5206\u652f\u8865\u4e01\u5206\u652f","title":"Hotfix \u5206\u652f\uff08\u8865\u4e01\u5206\u652f\uff09","text":"<p>\u5f53 master \u4e2d\u51fa\u73b0\u95ee\u9898\uff0c\u6211\u4eec\u9700\u8981\u4ee5\u51fa\u95ee\u9898\u7684\u8282\u70b9\u4e3a\u57fa\u7840\u521b\u5efa\u4e00\u4e2a hotfix\uff0c\u7136\u540e\u5728\u8fd9\u4e2a hotfix \u4e2d\u8fdb\u884c bug \u7684\u4fee\u590d\u5de5\u4f5c\u3002 \u5728\u5b8c\u6210\u4fee\u590d\u540e\uff0c\u6211\u4eec\u9700\u8981\u628a\u8fd9\u4e2a hotfix \u540c\u65f6\u5408\u5e76\u5230 master \u548c develop(\u5982\u56fe)\uff0c\u4e00\u65b9\u9762\u786e\u4fdd\u4e0b\u4e00\u4e2a\u7a33\u5b9a\u7248\u672c\u53ef\u7528\uff0c\u4e00\u65b9\u9762\u786e\u4fdd\u672a\u6765\u7684\u7248\u672c\u4e5f\u4fee\u590d\u4e86\u8be5 bug\u3002</p>"},{"location":"tech_accu/tool/Git/Workflow/#release-\u5206\u652f\u9884\u53d1\u5206\u652f","title":"Release \u5206\u652f\uff08\u9884\u53d1\u5206\u652f\uff09","text":"<p>\u5f53 develop \u8db3\u591f\u6210\u719f\u65f6\uff0c\u6211\u4eec\u4f1a\u5e0c\u671b\u5b83\u88ab\u5408\u5e76\u5230 master \u4e2d\u4f5c\u4e3a\u4e00\u4e2a\u7a33\u5b9a\u7248\u672c\u53d1\u5e03\uff0c\u4f46\u5728\u8fd9\u4e4b\u524d\uff0c\u6211\u4eec\u9700\u8981\u5728 release \u4e2d\u8fdb\u884c\u6700\u540e\u7684\u6d4b\u8bd5\u548c\u4fee\u6b63\u3002 \u5728\u5b8c\u6210\u8fd9\u4e9b\u5de5\u4f5c\u540e\uff0c\u6211\u4eec\u9700\u8981\u628a release \u540c\u65f6\u5408\u5e76\u5230 master \u548c develop (\u5982\u56fe)\uff0c\u4e00\u65b9\u9762\u786e\u4fdd\u4e0b\u4e00\u4e2a\u7a33\u5b9a\u7248\u672c\u53ef\u7528\uff0c\u4e00\u65b9\u9762\u786e\u4fdd\u672a\u6765\u7684\u7248\u672c\u4e5f\u4fee\u590d\u4e86\u8fd9\u4e9b\u95ee\u9898\u3002</p> <p>hotfix\u548crelease\u662f\u7c7b\u4f3c\u7684\uff0c\u4ed6\u4eec\u4e00\u4e2a\u662f\u57fa\u4e8emaster\u5bf9\u4e24\u4e2a\u957f\u671f\u5206\u652f\u8fdb\u884c\u7ef4\u62a4\uff0c\u4e00\u4e2a\u662f\u57fa\u4e8edevelop\u3002</p>"},{"location":"tech_accu/tool/Git/Workflow/#feature-\u5206\u652f\u529f\u80fd\u5206\u652f","title":"Feature \u5206\u652f\uff08\u529f\u80fd\u5206\u652f\uff09","text":"<p>\u5f53\u6211\u4eec\u9700\u8981\u5f00\u53d1\u65b0\u7684\u529f\u80fd\uff0c\u6216\u8005\u8bf4\u5bf9\u4e8e\u5927\u90e8\u5206\u5f00\u53d1\u5de5\u4f5c\uff0c\u5728\u5408\u7406\u7684\u6a21\u5757\u5212\u5206\u540e\uff0c\u5c31\u9700\u8981\u521b\u5efa\u5408\u9002\u7684 feature \u5206\u652f\u6765\u8fdb\u884c\u5bf9\u5e94\u7684\u5f00\u53d1\u5de5\u4f5c\u3002\u56e0\u4e3a feature \u5f80\u5f80\u6bd4\u8f83\u591a\uff0c\u6240\u4ee5\u8981\u6c42\u5404\u4e2afeature\u4e4b\u95f4\u8026\u5408\u7a0b\u5ea6\u4e0d\u5b9c\u8fc7\u9ad8\uff0c\u4ee5\u51cf\u5c11\u51b2\u7a81\uff0c\u8fd9\u5c31\u9700\u8981\u8fdb\u884c\u5408\u7406\u7684\u5212\u5206\u3002</p>"},{"location":"tech_accu/tool/Git/Workflow/#github-workflow","title":"Github Workflow","text":"<ul> <li>\u8fd9\u91cc\u7684 Workflow \u4e0e Github Action \u4e2d\u7684 Workflow \u6709\u533a\u522b\uff01</li> </ul> <p>Github Workflow \u5bf9 Git Workflow \u8fdb\u884c\u4e86\u7b80\u5316\uff0c\u5728 Github Workflow \u4e0b\u4ec5\u4ec5\u533a\u5206 master \u548c branch\uff0c\u800c\u5177\u4f53\u529f\u80fd\u7531\u5404\u4e2a branch \u7684\u547d\u540d\u6765\u4f53\u73b0\uff0c\u5373\u8981\u6c42 branch \u7684\u547d\u540d\u5177\u6709\u53d9\u4e8b\u6027\u3002</p> <p>\u6700\u91cd\u8981\u7684\u662f\uff0c\u6ca1\u6709\u4e86 develop \u5206\u652f\u4ee5\u540e\uff0c\u957f\u671f\u7ef4\u62a4\u7684\u5c31\u53ea\u6709 master \u4e86\uff0c\u8fd9\u5c31\u610f\u5473\u7740\u53d1\u5e03\u7684\u4ee3\u7801\u4e00\u822c\u90fd\u662f\u8fdb\u5ea6\u6700\u65b0\u7684\u4ee3\u7801\u3002\u800c\u8fd9\u4ef6\u4e8b\u662f\u6709\u597d\u6709\u574f\u7684\u3002 \u57fa\u4e8e Github Workflow \u7684\u5de5\u4f5c\u6d41\u7a0b\u4e3b\u8981\u5982\u4e0b\uff1a</p> <ol> <li>\u521b\u5efa\u5206\u652f (create a branch or fork)\uff1b</li> <li>\u5728\u5206\u652f\u4e2d\u8fdb\u884c\u5f00\u53d1\u5e76\u5b8c\u6210\u63d0\u4ea4 (add commits)\uff1b</li> <li>\u53d1\u9001 Pull Request (open a pull request)\uff1b</li> <li>\u4eba\u5de5\u5ba1\u6838\u4ee3\u7801\u3001\u6c9f\u901a\u4ea4\u6d41\uff0c\u4ee5\u53ca\u5fc5\u8981\u7684\u6d4b\u8bd5 (discuss and review)\uff1b</li> <li>\u5408\u5e76\u8fdb master (merge)</li> </ol> <p>\u56e0\u800c\uff0c\u5728\u8fd9\u6837\u4e00\u4e2a\u5de5\u4f5c\u6d41\u7a0b\u4e0b\uff0c\u5408\u4f5c\u8005\u4e4b\u95f4\u7684\u4ea4\u6d41\u5c31\u66f4\u52a0\u91cd\u8981\u4e86\u3002</p>"},{"location":"tech_accu/tool/Git/Workflow/#gitlab-workflow","title":"Gitlab Workflow","text":"<ul> <li> \u5495\u5495\u5495</li> </ul>"},{"location":"tech_accu/tool/Git/Workflow/#\u53c2\u8003\u8d44\u6599--ref","title":"\u53c2\u8003\u8d44\u6599 | Ref","text":"<ul> <li>https://nvie.com/posts/a-successful-git-branching-model/</li> <li>https://www.ruanyifeng.com/blog/2015/12/git-workflow.html</li> <li>https://gitbook.tw/chapters/gitflow/why-need-git-flow</li> <li>https://medium.com/i-think-so-i-live/git\u4e0a\u7684\u4e09\u7a2e\u5de5\u4f5c\u6d41\u7a0b-10f4f915167e</li> <li>https://github.com/xirong/my-git/blob/master/git-workflow-tutorial.md</li> <li>https://about.gitlab.com/topics/version-control/what-is-git-workflow/</li> </ul>"},{"location":"tech_accu/tool/Shell/","title":"Shell","text":"<p> \u7ea6 4930 \u4e2a\u5b57  462 \u884c\u4ee3\u7801  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 22 \u5206\u949f</p> <p>\u6587\u7ae0\u76ee\u6807</p> <p>\u5728\u5b8c\u6210\u672c\u6587\u5b66\u4e60\u540e\uff0c\u6211\u4eec\u671f\u5f85\u60a8\u5bf9 Shell \u80fd\u6709\u66f4\u5177\u4f53\u7684\u8ba4\u8bc6\uff0c\u5e76\u80fd\u505a\u5230\u901a\u8fc7 Command Line \u5b9e\u73b0\u57fa\u7840\u4ea4\u4e92\u5e76\u4e86\u89e3\u5982\u4f55\u5b66\u4e60 Shell\u3002\u9664\u6b64\u4e4b\u5916\uff0c\u4e5f\u53ef\u4ee5\u901a\u8fc7\u64b0\u5199 Shell \u811a\u672c\u6765\u5b9e\u73b0\u4e00\u4e9b\u81ea\u52a8\u5316\u3002</p> <p>\u6b64\u5916\uff0c\u4ece Shell \u5165\u95e8\u5230\u547d\u4ee4\u884c\u5927\u5e08\uff0c\u5176\u4e2d\u80af\u5b9a\u6709\u5f88\u957f\u7684\u8def\u8981\u8d70\uff0c\u6211\u4eec\u6ca1\u6cd5\u6d89\u53ca Shell \u7684\u5168\u90e8\u77e5\u8bc6\u70b9\uff0c\u5149\u547d\u4ee4\u5c31\u80fd\u8bb2\u4e0a\u5f88\u4e45\uff0c\u6240\u4ee5\u4e00\u5b9a\u8981\u5b66\u4f1a\u5982\u4f55\u5229\u7528\u624b\u518c\u548c\u6587\u6863\u7b49\u67e5\u8be2\u547d\u4ee4\u7684\u4f7f\u7528\u65b9\u6cd5\uff0c\u672c\u6587\u5e0c\u671b\u505a\u5230\u7684\u662f\u6388\u4eba\u4ee5\u6e14\u800c\u975e\u6388\u4eba\u4ee5\u9c7c\u3002</p> <p>\u6b64\u5916\uff0c\u6211\u4f1a\u5728\u6587\u4e2d\u591a\u6b21\u5c06 Shell \u4e0e C \u8bed\u8a00\u7684\u4e00\u4e9b\u5185\u5bb9\u76f8\u8054\u7cfb\uff0c\u5982\u679c\u60a8\u6709 C \u7684\u57fa\u7840\uff0c\u90a3\u5c06\u518d\u597d\u4e0d\u8fc7\u3002</p>"},{"location":"tech_accu/tool/Shell/#\u6982\u8ff0","title":"\u6982\u8ff0","text":""},{"location":"tech_accu/tool/Shell/#\u7b80\u4ecb","title":"\u7b80\u4ecb","text":"<p>Shell \u7684\u4e2d\u6587\u540d\u79f0\u4e3a\u201c\u58f3\u5c42\u201d\uff0c\u987e\u540d\u601d\u4e49\u5c31\u662f\u201c\u6700\u5916\u5c42\u201d\u3002Wiki \u5bf9\u5176\u63cf\u8ff0\u4e3a\uff1a</p> <p>It is named a shell because it is the outermost layer around the operating system.</p> <p>\u7b80\u5355\u6765\u8bf4\uff0cShell \u5c06\u8bfb\u5165\u6765\u81ea Keyboard \u7684\u5185\u5bb9\uff0c\u5e76\u5c06\u6307\u4ee4\u53d1\u9001\u7ed9 OS \u4ee5\u8c03\u7528\u7cfb\u7edf\u670d\u52a1\u3002</p> <p>\u5728\u5e38\u89c1\u7684\u65e5\u7528\u64cd\u4f5c\u7cfb\u7edf\uff0c\u5982 Windows \u4e0e MacOS\uff0c\u4f60\u53ef\u80fd\u5c1d\u8bd5\u8fc7\u4f7f\u7528 GUI(Graphical User Interface)\uff0c\u5373\u56fe\u5f62\u7528\u6237\u754c\u9762\u6765\u4e0e\u4f60\u7684\u7cfb\u7edf\u6109\u5feb\u73a9\u800d\uff1b\u4e0e\u4e4b\u5bf9\u5e94\u7684\uff0cShell \u5219\u662f\u4e00\u79cd CLI(Command Line Interface)\uff0c\u4e0d\u540c\u4e8e GUIs \u901a\u8fc7\u70b9\u51fb\u6309\u94ae\u7b49\u64cd\u4f5c\u4e0e\u7cfb\u7edf\u4ea4\u4e92\u7b49\u65b9\u5f0f\uff0cCLI \u8981\u6c42\u7528\u6237\u901a\u8fc7\u547d\u4ee4\u884c\u6765\u4e0e\u7cfb\u7edf\u4ea4\u4e92\u3002\u800c\u4f5c\u4e3a\u4e00\u4e2a\u5408\u683c\u7684\u7a0b\u5e8f\u5458\uff0c\u6211\u4eec\u63a5\u89e6\u5230\u7684\u5927\u591a\u6570\u751f\u4ea7\u573a\u666f\u4e2d\uff0c\u4f7f\u7528 CLI \u662f\u4e00\u79cd\u66f4\u52a0\u9ad8\u6548\u7684\u9009\u62e9\uff0c\u4e8b\u5b9e\u4e0a\u4f60\u4e5f\u5f88\u96be\u907f\u514d\u5b83\u2014\u2014\u56e0\u800c\uff0c\u6211\u4eec\u9700\u8981\u638c\u63e1 Shell \u7684\u57fa\u672c\u4f7f\u7528\u3002</p> <p>\u5982\u4eca\uff0c\u5df2\u7ecf\u6709\u975e\u5e38\u591a\u7684 Shell \u53ef\u4ee5\u4f7f\u7528\uff0c\u800c\u4ed6\u4eec\u57fa\u672c\u4e0a\u90fd\u4ee5 <code>sh</code> \u7ed3\u5c3e\uff0c\u4f8b\u5982\u5e38\u89c1\u7684 <code>bash</code> \u548c <code>zsh</code> ,\u518d\u6bd4\u5982\u8bb8\u591a\u57fa\u4e8e Alpine \u7684 Docker Image\uff0c\u5185\u7f6e\u7684 Shell \u90fd\u662f <code>sh</code>\u3002\u5176\u4ed6\u7684\u8fd8\u6709 <code>dash</code> <code>csh</code> <code>ksh</code> \u7b49\u7b49\u3002</p>"},{"location":"tech_accu/tool/Shell/#shell-vs-terminal","title":"Shell vs Terminal","text":"<p>\u5728\u6b63\u5f0f\u5f00\u59cb\u4ecb\u7ecd Shell \u4e4b\u524d\uff0c\u6211\u8ba4\u4e3a\u6709\u5fc5\u8981\u505a\u4e00\u4e9b\u8fa8\u6790\u3002</p> <p>\u5728\u73b0\u4ee3\u7684\u8ba1\u7b97\u673a\u7cfb\u7edf\u4e2d\uff0c\u60f3\u8981\u4f7f\u7528 Shell\uff0c\u4f60\u9700\u8981\u501f\u52a9 Terminal\uff0c\u5373\u7ec8\u7aef\uff08\u66f4\u51c6\u786e\u7684\u8bf4\uff0c\u662f terminal emulator\uff0c\u4e0d\u8fc7\u5728\u672c\u6587\u4e2d\u6211\u4eec\u5e76\u4e0d\u4f1a\u5c31\u6b64\u5c55\u5f00\uff09\u3002Terminal \u4e4b\u4e8e Shell\uff0c\u5c31\u597d\u50cf\u7535\u8bdd\u4e4b\u4e8e\u901a\u8baf\u670d\u52a1\u3002</p> <p></p> <p>\u4f8b\u5982\uff0c\u56fe\u4e2d\u6253\u5f00\u7684\u8fd9\u4e2a\u201c\u7a97\u53e3\u201d\u5c31\u662f\u4e00\u4e2a\u53eb\u505a iTerm2 \u7684 terminal emulator\uff0c\u800c\u6211\u4f7f\u7528\u7684 <code>fish</code> \u5219\u662f\u4e00\u79cd Shell\u3002</p> <p>\u80fd\u4e0e\u8fd9\u4e24\u4e2a\u4e1c\u897f\u8fdb\u884c\u6bd4\u8f83\u548c\u8fa8\u6790\u7684\u4e1c\u897f\u5176\u5b9e\u8fd8\u6709\u5f88\u591a\uff0c\u4f46\u5e76\u975e\u672c\u6587\u4e3b\u9898\uff0c\u6240\u4ee5\u4e0d\u518d\u5c55\u5f00\u3002</p>"},{"location":"tech_accu/tool/Shell/#\u4ee5-bash-\u4e3a\u4f8b","title":"\u4ee5 Bash \u4e3a\u4f8b","text":"<p><code>bash</code> \u5168\u79f0 Bourne Again Shell\uff0c\u662f\u5982\u4eca\u6700\u5e38\u7528\u7684 Shell \u4e4b\u4e00\uff0c\u4e14\u5927\u90e8\u5206 Linux \u90fd\u4f1a\u5185\u7f6e bash\uff0c\u8fd9\u4e5f\u907f\u514d\u4e86\u66f4\u591a\u7684\u73af\u5883\u914d\u7f6e\u8d1f\u62c5\uff0c\u6240\u4ee5\u5728\u672c\u7ae0\u79cd\uff0c\u6211\u4eec\u5c06\u4ee5 <code>bash</code> \u4e3a\u4f8b\uff0c\u4ecb\u7ecd\u4e00\u4e9b Shell \u5e38\u7528\u6307\u4ee4\u548c\u6280\u5de7\u3002</p> <p>\u6b64\u5916\uff0c\u6211\u4eec\u63a5\u4e0b\u6765\u63d0\u4f9b\u7684\u5927\u591a\u6570\u8bba\u65ad\u4e3b\u8981\u57fa\u4e8e Linux \u7cfb\u7edf\u3002\u90e8\u5206\u7ed3\u8bba\u5728 Windows \u7b49\u7cfb\u7edf\u4e2d\u53ef\u80fd\u5e76\u4e0d\u6210\u7acb\u3002\u5982\u679c\u60a8\u6709\u5174\u8da3\uff0c\u53ef\u4ee5\u81ea\u884c\u67e5\u8be2\u8d44\u6599\u3002</p>"},{"location":"tech_accu/tool/Shell/#\u51c6\u5907\u5de5\u4f5c","title":"\u51c6\u5907\u5de5\u4f5c","text":"<p>\u5728\u5f00\u59cb\u4e4b\u524d\uff0c\u6211\u5e0c\u671b\u60a8\u786e\u4fdd\u60a8\u672c\u5730\u5df2\u6709\u53ef\u7528\u7684 <code>bash</code> \u73af\u5883\uff0c\u4ee5\u4fbf\u4e8e\u60a8\u80fd\u8ddf\u7740\u6559\u7a0b\u8fb9\u5b9e\u8df5\u8fb9\u5b66\u4e60\u3002</p> <p>\u5728\u8fd9\u91cc\uff0c\u6211\u5c06\u63d0\u4f9b\u4e00\u79cd\u7b80\u5355\u7684\u914d\u7f6e <code>bash</code> \u73af\u5883\u7684\u65b9\u6848\uff1a</p> <ul> <li>\u5982\u679c\u60a8\u662f Linux/MacOS \u7528\u6237\uff0c\u90a3\u4e48\u60a8\u7684\u7cfb\u7edf\u4e00\u822c\u90fd\u4f1a\u81ea\u5e26 Terminal \u7a0b\u5e8f\uff0c\u76f4\u63a5\u6253\u5f00\u5e76\u8f93\u5165 bash \u4ee5\u542f\u7528 bash\uff1b</li> <li>\u5982\u679c\u60a8\u662f Windows \u7528\u6237\uff0c\u90a3\u4e48\u60a8\u53ef\u4ee5\u9009\u62e9\u76f4\u63a5\u4e0b\u8f7d Git Bash\uff1b</li> </ul> <p>\u5f53\u7136\uff0c\u6211\u4eec\u6700\u63a8\u8350\u7684\u8fd8\u662f\u60a8\u53ef\u4ee5\u914d\u7f6e\u4e00\u4e2a Linux \u73af\u5883\u4ee5\u8fdb\u884c\u5b9e\u8df5\u548c\u5b66\u4e60\u3002</p> <p>\u5f53\u60a8\u5b8c\u6210\u8fd9\u4e9b\u5de5\u4f5c\u540e\uff0c\u60a8\u53ef\u80fd\u770b\u5230\u7c7b\u4f3c\u4e8e\u5982\u4e0b\u5217\u4e3e\u7684\u5185\u5bb9\u7684\u60c5\u51b5\uff1a</p> <pre><code># \u4e5f\u8bb8\u662f\u8fd9\u6837\nxxx:~$ {\u4f60\u7684\u5149\u6807\u5728\u8fd9\u91cc}\n# \u6216\u8005\u8fd9\u6837\n[xxx@yyy]~$ {\u4f60\u7684\u5149\u6807\u5728\u8fd9\u91cc}\n# \u53c8\u6216\u8005\u8fd9\u6837\nxxxx yyyy ~\n$ {\u4f60\u7684\u5149\u6807\u5728\u8fd9\u91cc}\n# ...\n</code></pre> <p>\u5b9e\u9645\u60c5\u51b5\u8fd8\u6709\u5f88\u591a\u79cd\uff0c\u56e0\u4e3a\u8fd9\u4e9b\u201c\u5f62\u5f0f\u201d\u90fd\u662f\u53ef\u4ee5\u88ab\u8bbe\u7f6e\u7684\u3002\u6bd4\u5982\u8fd9\u91cc\u7684 <code>$</code> \u88ab\u79f0\u4e3a prompt\uff0c\u5728\u672c\u6587\u7b2c\u4e00\u5f20\u56fe\u7247\u4e2d\u6211\u5c31\u5c06\u5b83\u8bbe\u7f6e\u4e3a\u4e86\u4e00\u4e2a Emoji \u56fe\u6807\u3002\u800c\u6211\u4eec\u53d1\u73b0\u8fd9\u91cc\u8fd8\u6709\u4e00\u4e2a <code>~</code> \uff0c\u5b83\u8868\u793a\u7684\u662f\u60a8\u7684\u201c\u5bb6\u76ee\u5f55\u201d\u3002\u66f4\u51c6\u786e\u7684\u8bf4\uff0c\u5b83\u7684\u542b\u4e49\u662f\u60a8\u5f53\u524d\u6240\u5728\u7684\u4f4d\u7f6e\u662f\u60a8\u7684\u5bb6\u76ee\u5f55\u3002\u5173\u4e8e\u8fd9\u4e00\u70b9\u6211\u4eec\u5c06\u5728\u63a5\u4e0b\u6765\u5c55\u5f00\u3002</p> <p>\u6b64\u5916\uff0c\u5982\u679c\u60a8\u5bf9 Linux \u7cfb\u7edf\u6709\u4e00\u5b9a\u8ba4\u8bc6\uff0c\u90a3\u65e0\u7591\u4f1a\u5e2e\u52a9\u60a8\u7406\u89e3\u672c\u6587\u3002</p> <p>\u90a3\u4e48\u63a5\u4e0b\u6765\uff0c\u8ba9\u6211\u4eec\u5f00\u59cb\u5427\uff01</p>"},{"location":"tech_accu/tool/Shell/#\u5e2e\u52a9\u624b\u518c","title":"\u5e2e\u52a9\u624b\u518c","text":"<p>\u5de6\u601d\u53f3\u60f3\uff0c\u6700\u540e\u6211\u8fd8\u662f\u628a\u8fd9\u6761\u6307\u4ee4\u653e\u5230\u4e86\u6700\u524d\u6765\u8bb2\u3002\u6211\u4eec\u4e0d\u53ef\u80fd\u4ec5\u4ec5\u901a\u8fc7\u4e00\u7bc7\u6587\u7ae0\u5c31\u4e86\u89e3\u547d\u4ee4\u884c\u7684\u5168\u90e8\u77e5\u8bc6\uff0c\u6240\u4ee5\u6211\u89c9\u5f97\u628a <code>man</code> \u653e\u5230\u6700\u524d\u9762\u6765\u8bb2\u662f\u5f88\u6709\u610f\u4e49\u7684\u3002</p> <p><code>man</code> \u7684\u4f5c\u7528\u662f\u6253\u5f00\u4e00\u4e2a user manual\u3002\u4f8b\u5982\uff0c\u5982\u679c\u6211\u4eec\u5728\u7ec8\u7aef\u4e2d\u8f93\u5165 <code>man man</code>\uff0c\u5c31\u4f1a\u5f97\u5230\u5982\u4e0b\u7ed3\u679c\uff0c\u5373\u4f7f\u7528 <code>man</code> \u6253\u5f00\u4e86 <code>man</code> \u7684\u624b\u518c\uff1a</p> <pre><code>man(1)                                     General Commands Manual                                    man(1)\n\nNAME\n       man - format and display the on-line manual pages\n\nSYNOPSIS\n       man [-acdfFhkKtwW] [--path] [-m system] [-p string] [-C config_file] [-M pathlist] [-P pager] [-B\n       browser] [-H htmlpager] [-S section_list] [section] name ...\n\nDESCRIPTION\n       man formats and displays the on-line manual pages.  If you specify section, man only looks in that\n       section of the manual.  name is normally the name of the manual page, which is typically the name of\n       a command, function, or file.  However, if name contains a slash (/) then man interprets it as a file\n       specification, so that you can do man ./foo.5 or even man /cd/foo/bar.1.gz.\n\n       See below for a description of where man looks for the manual page files.\n\n......\n</code></pre> <ul> <li>\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528\u9f20\u6807\u6eda\u8f6e/\u624b\u52bf\u7ffb\u9875/\u56de\u8f66\u7b49\u9014\u5f84\u53ef\u4ee5\u67e5\u770b\u63a5\u4e0b\u6765\u7684\u5185\u5bb9\uff0c\u6309\u4e0b <code>q</code> \u79bb\u5f00\u624b\u518c\u9875\u9762\u3002</li> <li>\u6b64\u5916\uff0cuser manual \u7684\u5185\u5bb9\u53ef\u80fd\u4f1a\u6839\u636e\u4f7f\u7528\u7684 Shell \u4e0d\u540c\u800c\u4e0d\u540c\uff0c\u751a\u81f3\u5728\u4e00\u4e9b Shell \u90fd\u4e0d\u4e00\u5b9a\u6709 user manual\u3002</li> </ul> <p>\u4e3a\u4e86\u5b9e\u73b0\u629b\u7816\u5f15\u7389\u7684\u76ee\u7684\uff0c\u73b0\u5728\u6211\u4eec\u4ec5\u4ec5\u4ecb\u7ecd <code>man</code> \u7684\u8fd9\u4e9b\u90e8\u5206\uff0c\u5b9e\u9645\u4e0a\u5149\u770b manual \u7684\u6587\u672c\u91cf\u5c31\u80fd\u611f\u53d7\u5230\uff0c <code>man</code> \u8fdc\u4e0d\u6b62\u5982\u6b64\uff0c\u4f46\u672c\u6587\u5e76\u4e0d\u6253\u7b97\u5c31\u6b64\u6df1\u5165\u3002\u800c\u5728\u8fd9\u91cc\u4ecb\u7ecd <code>man</code> \u7684\u76ee\u7684\uff0c\u4e00\u65b9\u9762\u662f\u5e0c\u671b\u5927\u5bb6\u5728\u5b66\u4e60\u4e4b\u540e\u7684\u547d\u4ee4\u65f6\uff0c\u53ef\u4ee5\u53c2\u8003 user manual\uff0c\u4e8b\u5b9e\u4e0a\u672c\u6587\u6d89\u53ca\u7684\u547d\u4ee4\u4e5f\u5e76\u4e0d\u4f1a\u4ecb\u7ecd\u5176\u5168\u90e8\u7528\u6cd5\uff1b\u53e6\u4e00\u65b9\u9762\u662f\u9f13\u52b1\u5927\u5bb6\u5728\u9047\u5230\u4e3a\u6b62\u7684\u6307\u4ee4\u65f6\uff0c\u901a\u8fc7\u624b\u518c\u7b49\u9014\u5f84\u5148\u67e5\u8be2\u5176\u884c\u4e3a\u3001\u7528\u6cd5\uff0c\u518d\u4f7f\u7528\u5b83\u3002</p>"},{"location":"tech_accu/tool/Shell/#\u6253\u5370\u5b57\u7b26\u4e32--echo","title":"\u6253\u5370\u5b57\u7b26\u4e32 | echo","text":"<p><code>echo</code> \u5373\u56de\u54cd\uff0c\u8fd9\u4e2a\u5355\u8bcd\u975e\u5e38\u5f62\u8c61\u5730\u63cf\u8ff0\u4e86\u8fd9\u4e2a\u547d\u4ee4\u7684\u4f5c\u7528\uff0c\u5c06\u5176\u63a5\u53d7\u5230\u7684\u5185\u5bb9\u201c\u56de\u54cd\u201d\u51fa\u6765\u3002</p> <pre><code># echo \u4f1a\u5c06\u5b83\u62ff\u5230\u7684\u53c2\u6570\u5168\u90fd\u5f53\u4f5c\u5b57\u7b26\u4e32\u6253\u5370\u51fa\u6765\uff0c\u4f46\u6210\u5bf9\u5f15\u53f7\u5e76\u4e0d\u4f1a\n$ echo &lt;something&gt;\n$ echo \"something 1 2 3\"\nsomething 1 2 3\n$ echo something 1 2 3\nsomething 1 2 3\n\n# \u5982\u679c\u4f60\u53ea\u8f93\u5165\u4e86\u4e00\u4e2a\u5f15\u53f7\uff0c\u5b83\u4f1a\u7b49\u4f60\u628a\u4ed6\u8865\u5b8c\u518d\u8f93\u51fa\n# \u5982\u679c\u60f3\u8f93\u51fa\u5f15\u53f7\uff0c\u9700\u8981\u4f7f\u7528 \\\" \u8f6c\u4e49\n$ echo \"\nFine, \\\"I\\\" will finish the string.\n\"\nFine, \"I\" will finish the string.\n\n# echo \u652f\u6301\u8f93\u51fa\u53c2\u6570\uff0c\u4ee5 $ \u5f00\u5934\uff0c\u5728\u547d\u4ee4\u884c\u73af\u5883\u4e0b\u4ed6\u4eec\u6307\u73af\u5883\u53d8\u91cf\uff0c\u5728\u811a\u672c\u73af\u5883\u4e0b\u8fd8\u53ef\u4ee5\u8fdb\u884c\u4e00\u4e9b\u53c2\u6570\u4f20\u9012\n# \u4e0b\u9762\u7684\u547d\u4ee4\u8f93\u51fa\u4e86\u5f53\u524d\u7528\u6237\uff0cUSER \u662f\u4e00\u4e2a\u503c\u4e3a\u5f53\u524d\u7528\u6237\u7684\u7528\u6237\u540d\u7684\u73af\u5883\u53d8\u91cf\u3002\necho $USER\nisshikih\n</code></pre>"},{"location":"tech_accu/tool/Shell/#\u67e5\u770b\u5f53\u524d\u8def\u5f84--pwd","title":"\u67e5\u770b\u5f53\u524d\u8def\u5f84 | pwd","text":"<p>\u5728\u8fd9\u91cc\u6211\u4eec\u60f3\u4ecb\u7ecd\u7684\u7b2c\u4e8c\u4e2a\u6307\u4ee4\u662f <code>pwd</code>\uff0c\u5b83\u7684\u6548\u679c\u662f\u8f93\u51fa\u60a8\u5f53\u524d\u7684\u4f4d\u7f6e\u3002</p> <pre><code>$ pwd\n# \u6bd4\u5982\u6211\u7684\u73af\u5883\u4e0b\uff0c\u5728 ~ \u4e0b\u8f93\u51fa\u5982\u4e0b\n/Users/isshikih\n# \u8868\u793a\u6211\u5f53\u524d\u7684\u4f4d\u7f6e\u662f /Users/isshikih\n</code></pre> <p>\u4e00\u5207\u7686\u6587\u4ef6 \u662f Linux \u7684\u8bbe\u8ba1\u7406\u5ff5\uff0c\u800c Shell \u7684\u4f7f\u7528\u6709\u76f8\u5f53\u4e00\u90e8\u5206\u662f\u57fa\u4e8e\u6587\u4ef6\u4f53\u7cfb\u7684\u3002\u800c\u5982\u4f55 \u7d22\u5f15 \u4e00\u4e2a\u6587\u4ef6\u5462\uff1f\u6211\u4eec\u9700\u8981\u63d0\u4f9b\u8fd9\u4e2a\u6587\u4ef6\u7684\u8def\u5f84\u548c\u6587\u4ef6\u540d\uff01\u4f8b\u5982\uff0c\u60a8\u9700\u8981\u53bb\u4e00\u53f0 Windows \u7535\u8111\u4e2d\u627e\u5230\u60a8\u4e0a\u5b66\u671f\u7684\u8bfe\u7a0b\u4f5c\u4e1a\uff0c\u5b83\u7684\u6587\u4ef6\u540d\u4e3a <code>myHomework.pdf</code> \uff0c\u4e5f\u8bb8\u4f60\u9700\u8981\u6253\u5f00D\u76d8\u4e2d\u7684 Homework \u6587\u4ef6\u5939\u3002\u90a3\u4e48\u62bd\u8c61\u5730\u6765\u8bf4\uff0c\u8fd9\u4e2a\u6587\u4ef6\u7684\u8def\u5f84\u4e3a <code>D:\\Homework\\myHomework.pdf</code> \uff08\u8fd9\u662f\u5728 Windows \u4e0a\u7684\u5199\u6cd5\uff09\u3002\u8fd9\u79cd\u5f62\u5f0f\u7684\u201c\u4f4d\u7f6e\u201d\u88ab\u79f0\u4e3a \u7edd\u5bf9\u8def\u5f84\uff0c\u5373\u6211\u4eec\u9700\u8981\u586b\u5199\u6587\u4ef6\u7684\u5b8c\u6574\u8def\u5f84\u624d\u80fd\u627e\u5230\u8fd9\u4e2a\u6587\u4ef6\u3002\u5728\u4e4b\u540e\u7684\u90e8\u5206\u4e2d\uff0c\u6211\u4eec\u63d0\u5230\u7684<code>&lt;filename&gt;&lt;dirname&gt;</code>\u7b49\u90fd\u5305\u62ec\u4e86\u6587\u4ef6\u7684\u8def\u5f84\u3002</p> <p>\ud83d\udc49\u00a0\u4e8b\u5b9e\u4e0a\uff0c\u6709\u76f8\u5f53\u4e00\u90e8\u5206 Shell \u8bed\u6cd5\u662f\u56f4\u7ed5\u7740\u6587\u4ef6\u5c55\u5f00\u7684\u3002</p>"},{"location":"tech_accu/tool/Shell/#\u5207\u6362\u76ee\u5f55--cd","title":"\u5207\u6362\u76ee\u5f55 | cd","text":"<p><code>cd</code> \u662f change directory \u7684\u7f29\u5199\uff0c\u5b83\u7684\u6548\u679c\u662f\u5c06\u60a8\u5f53\u524d\u7684\u4f4d\u7f6e\u8f6c\u79fb\u5230\u76ee\u6807\u76ee\u5f55\u4e2d\u3002\u5b83\u7684\u5199\u6cd5\u5982\u4e0b\uff1a</p> <pre><code>cd {target directory}\n\n# eg 1: =========================================\n$ pwd\n/home/username\n\n$ cd /home/username/aaa\n$ pwd\n/home/username/aaa\n\n# eg 2: =========================================\n$ pwd\n/home/username\n\n$ cd ./aaa/bbb\n$ pwd\n/home/username/aaa/bbb\n\n# eg 3: =========================================\n$ pwd\n/home/username\n\n$ cd ./../aaa\n$ pwd\n/home/aaa\n</code></pre> <p>\u63a5\u4e0b\u6765\u5bf9\u4e0a\u9762 eg \u7684\u90e8\u5206\u7b26\u53f7\u505a\u4e00\u4e0b\u89e3\u91ca\uff1a</p> <ul> <li><code>.</code> \u8868\u793a\u5f53\u524d\u8def\u5f84\uff1b</li> <li><code>..</code> \u8868\u793a\u4e0a\u7ea7\u8def\u5f84\uff08\u6307\u4e0a\u4e00\u4e2a\uff09 \uff1b</li> </ul> <p>\u6b64\u5916\uff0c\u8fd9\u91cc\u8fd8\u6709\u4e00\u4e9b\u5feb\u6377\u65b9\u5f0f\uff1a</p> <ul> <li>\u5982\u679c\u53ea\u6709 <code>cd</code> \uff0c\u5219\u8fd4\u56de\u5bb6\u76ee\u5f55 <code>~</code> \uff08\u53ef\u4ee5\u53d1\u73b0 eg 4 \u548c eg 5 \u7b49\u4ef7\uff09\uff1b</li> <li><code>cd -</code> \u8fd4\u56de\u4e0a\u4e00\u6b21 <code>cd</code> \u4e4b\u524d\u6240\u5728\u7684\u4f4d\u7f6e\uff1b</li> <li><code>cd ~username</code> \u5207\u6362\u5230\u76ee\u6807\u7528\u6237\u7684\u5bb6\u76ee\u5f55\uff1b</li> </ul>"},{"location":"tech_accu/tool/Shell/#\u7f57\u5217\u76ee\u5f55\u4e0b\u5185\u5bb9--ls","title":"\u7f57\u5217\u76ee\u5f55\u4e0b\u5185\u5bb9 | ls","text":"<p><code>ls</code> \u6307\u4ee4\u7528\u6765\u67e5\u770b\u76ee\u6807\u76ee\u5f55\u4e0b\u7684\u6587\u4ef6\u3002\u5e38\u7528\u7684\u53c2\u6570\u4e3b\u8981\u6709 <code>-l</code> \uff08\u957f\u683c\u5f0f\uff09\u548c <code>-a</code> \uff08\u663e\u793a\u5168\u90e8\uff09\u3002</p> <p>\u5177\u4f53\u5199\u6cd5\u5982\u4e0b\uff1a</p> <pre><code># \u5047\u8bbe\u6211\u4eec\u5f53\u524d\u5728\u6587\u4ef6\u5939 my_ \u4e0b\uff0c\u6587\u4ef6\u5939\u5185\u6709\u4e24\u4e2a\u6587\u4ef6\u548c\u4e00\u4e2a\u6587\u4ef6\u5939\n# \u6587\u4ef6 .hidden \u548c\u6587\u4ef6 file1.md\n# \u6587\u4ef6\u5939 dir1\uff0c\u91cc\u9762\u6709\u4e2a\u6587\u4ef6 file2.md\n\n$ ls\ndir1        file1.md\n\n$ ls -a\n.               ..      .hiden1     dir1        file1.md\n\n$ ls -l\ndrwxr-xr-x  2 isshikih  staff  64 10 12 12:15 dir1\n-rw-r--r--  1 isshikih  staff   7 10 12 12:16 file1.md\n\n$ ls -la\ndrwxr-xr-x  5 isshikih  staff  160 10 12 12:15 .\ndrwxr-xr-x  6 isshikih  staff  192 10 12 12:14 ..\n-rw-r--r--  1 isshikih  staff    0 10 12 12:15 .hiden1\ndrwxr-xr-x  2 isshikih  staff   96 10 12 12:15 dir1\n-rw-r--r--  1 isshikih  staff    7 10 12 12:16 file1.md\n\n# \u5982\u679c\u540e\u9762\u8ddf\u7740\u4e00\u4e2a\u6587\u4ef6\u5939\uff0c\u5219\u663e\u793a\u76ee\u6807\u8def\u5f84\u4e0b\u7684\u5185\u5bb9\uff0c\u5426\u5219\u663e\u793a\u5f53\u524d\u8def\u5f84\u4e0b\u7684\u5185\u5bb9\u3002\n$ ls dir1\nfile2.md\n</code></pre> <ul> <li>\u6709\u65f6\uff0c\u6211\u4eec\u4f1a\u4e3a <code>ls -l</code> \u8bbe\u7f6e\u4e00\u4e2a alias\uff0c\u5373 <code>alias ll=\"ls -l\"</code> \uff0c\u8fd9\u6837\uff0c\u6211\u4eec\u5c31\u53ef\u4ee5\u66f4\u65b9\u4fbf\u7684 <code>ll</code> \u4e86\u3002</li> <li>\u5176\u4e2d\uff0c <code>l</code> \u4e2d\u7684\u5177\u4f53\u683c\u5f0f\u5982\u4e0b\uff1a</li> </ul> <pre><code>-rw-------   1 me       me            576 Apr 17  2019 weather.txt\ndrwxr-xr-x   6 me       me           1024 Oct  9  2019 web_page\n-rw-rw-r--   1 me       me         276480 Feb 11 20:41 web_site.tar\n-rw-------   1 me       me           5743 Dec 16  2018 xmas_file.txt\n\n----------  -------  -------     -------- ------------ -------------\n|          |        |            |         |             |\n|          |        |            |         |\n|          |        |            |         |           \u6587\u4ef6\u540d\n|          |        |            |         |\n|          |        |            |         +---       \u4fee\u6539\u65f6\u95f4\n|          |        |            |\n|          |        |            +-------------   \u6587\u4ef6\u5927\u5c0f(in bytes)\n|          |        |\n|          |        +--------------------------       \u6240\u5c5e\u7528\u6237\u7ec4\n|          |\n|          +-----------------------------------       \u6240\u5c5e\u7528\u6237\n|\n+----------------------------------------------       \u6587\u4ef6\u6743\u9650\n# Edited from https://linuxcommand.org/lc3_lts0030.php\n</code></pre> <ul> <li>\u5173\u4e8e\u8fd9\u90e8\u5206\u5177\u4f53\u90e8\u5206\u5b57\u6bb5\u7684\u5177\u4f53\u89e3\u91ca\uff0c\u8bf7\u53c2\u8003\u76f8\u5173\u8d44\u6599\uff0c\u4e0d\u5c5e\u4e8e\u672c\u6587\u7684\u8303\u7574\u3002</li> </ul>"},{"location":"tech_accu/tool/Shell/#\u6253\u5370\u6587\u4ef6\u5185\u5bb9--cat","title":"\u6253\u5370\u6587\u4ef6\u5185\u5bb9 | cat","text":"<p><code>cat</code> \u6307\u4ee4\u4f1a\u8fde\u63a5\u6587\u4ef6\u5e76\u5c06\u5185\u5bb9\u6253\u5370\u5230\u6807\u51c6\u8f93\u51fa\u6d41\u3002</p> <pre><code># &lt;filename&gt; \u662f\u76ee\u6807\u6587\u4ef6\u7684\u540d\u5b57\u3002\n$ cat &lt;filename&gt;\n</code></pre> <ul> <li>\u800c\u5b9e\u9645\u4e0a <code>cat</code> \u547d\u4ee4\u6700\u91cd\u8981\u7684\u4f5c\u7528\u5e76\u4e0d\u662f \u663e\u793a \u6587\u4ef6\u5185\u5bb9\uff0c\u4ed4\u7ec6\u89c2\u5bdf\u63cf\u8ff0\uff0c\u5b83\u7684\u4f5c\u7528\u662f \u6253\u5370\u5230\u6807\u51c6\u8f93\u51fa\u6d41\uff0c\u5176\u4f5c\u7528\u5728\u4e4b\u540e\u4ecb\u7ecd\u4e86\u91cd\u5b9a\u5411\u4e4b\u540e\u4f1a\u51f8\u663e\u51fa\u6765\u3002</li> </ul>"},{"location":"tech_accu/tool/Shell/#\u6253\u5370\u6587\u4ef6\u9996\u5c3e\u5185\u5bb9--head--tail","title":"\u6253\u5370\u6587\u4ef6\u9996\u5c3e\u5185\u5bb9 | head &amp; tail","text":"<p><code>head</code> \u548c <code>tail</code> \u8bed\u6cd5\u7c7b\u4f3c\uff0c\u529f\u80fd\u7c7b\u4f3c\uff0c\u5206\u522b\u4e3a\u67e5\u770b\u76ee\u6807\u6587\u4ef6\u7684\u5f00\u5934\u90e8\u5206\u7684\u5185\u5bb9\u548c\u7ed3\u5c3e\u90e8\u5206\u7684\u5185\u5bb9\u3002\u4e0d\u8fc7\u7531\u4e8e\u6211\u4eec\u5bf9\u6587\u672c\u6587\u4ef6\u9664\u4e86\u8bfb\u5199\uff0c\u8fd8\u6709\u4e00\u4e2a\u53eb\u505a\u201c\u8ffd\u52a0\u201d\u7684\u64cd\u4f5c\uff08\u7c7b\u6bd4 C \u8bed\u8a00\u4e2d <code>fopen()</code> \u7684 <code>\u2018a\u2019</code> \u6a21\u5f0f\uff09 <code>tail</code> \u4f1a\u6301\u7eed\u6253\u5370\u65b0\u8ffd\u52a0\u8fdb\u6587\u4ef6\u7684\u5185\u5bb9\uff0c\u6240\u4ee5\u82b1\u6837\u7a0d\u5fae\u6bd4 <code>head</code> \u591a\u4e00\u70b9\u3002</p> <pre><code># `head` \u548c `tail` \u90fd\u6709\u9ed8\u8ba4\u53c2\u6570 `-n 10`\n# \u4e5f\u5c31\u662f\uff0c\u4e0b\u9762\u4e24\u4e2a\u6307\u4ee4\u662f\u7b49\u4ef7\u7684\uff0c\u5b83\u4eec\u90fd\u4f1a\u6253\u5370\u76ee\u6807\u6587\u4ef6\u7684\u524d 10 \u884c\n$ head &lt;filename&gt;\n$ head -n 10 &lt;filename&gt;\n# \u4e0b\u9762\u8fd9\u4e24\u6761\u6307\u4ee4\u4e5f\u662f\u7b49\u4ef7\u7684\uff0c\u5b83\u4eec\u90fd\u4f1a\u6253\u5370\u76ee\u6807\u6587\u4ef6\u7684\u672b 10 \u884c\n$ tail &lt;filename&gt;\n$ tail -n 10 &lt;filename&gt;\n\n# \u5c06 10 \u6539\u6210\u5176\u4ed6\u6570\u5b57\u5c31\u53ef\u4ee5\u4fee\u6539\u663e\u793a\u7684\u884c\u6570\uff0c\u4f8b\u5982\u4e0b\u9762\u7684\u6307\u4ee4\u4f1a\u6253\u5370\u76ee\u6807\u6587\u4ef6\u7684\u9996/\u672b 4 \u884c\n$ head -n 4 &lt;filename&gt;\n$ tail -n 4 &lt;filename&gt;\n\n# \u9664\u4e86\u884c\u6570\uff0c\u4f60\u4e5f\u53ef\u4ee5\u6307\u5b9a\u6253\u5370\u7684\u5b57\u8282\u6570\uff0c\u5982\u4e0b\u9762\u6307\u4ee4\u4f1a\u6253\u5370\u76ee\u6807\u6587\u4ef6\u7684\u9996/\u672b 20 \u4e2a\u5b57\u8282\n$ head -c 20 &lt;filename&gt;\n$ tail -c 20 &lt;filename&gt;\n</code></pre> <p><pre><code># `tail` \u6bd4 `head` \u8fd8\u8981\u591a\u4e00\u4e9b\u53c2\u6570\uff0c\u6bd4\u5982 `-f`\n# `-f` \u5728\u6253\u5370\u5b8c\u5df2\u6709\u7684\u6587\u4ef6\u5185\u5bb9\u540e\u4f1a\u963b\u585e\uff0c\u7b49\u5f85\u76ee\u6807\u6587\u4ef6\u7684\u66f4\u65b0\n# \u4e00\u65e6\u6709\u5185\u5bb9\u8ffd\u52a0\u8fdb\u76ee\u6807\u6587\u4ef6\uff0c`tail` \u5c31\u4f1a\u5c06\u5b83\u6253\u5370\u51fa\u6765\n$ tail -f &lt;filename&gt;\n</code></pre> </p> <p>\u6ce8\u610f\uff0c\u8fd9\u91cc\u7684 echo \u5f00\u5934\u7684\u8bed\u53e5\u662f\u5728\u505a\u8ffd\u52a0\u64cd\u4f5c\uff0c\u4e4b\u540e\u4f1a\u8bb2\u5230\u3002</p> <p>\u800c\u81f3\u4e8e\u5177\u4f53\u7684\u5f15\u7528\u573a\u666f\uff0c\u6bd4\u5982\u6709\u4e9b\u5de5\u5177\u7684\u65e5\u5fd7\u4f1a\u4e0d\u65ad\u8ffd\u52a0\u5230\u67d0\u4e2a\u65e5\u5fd7\u6587\u4ef6\u4e2d\uff0c\u8fd9\u65f6\u5019\u5c31\u53ef\u4ee5\u7528 <code>tail -f</code> \u6765\u5b9e\u65f6\u8ddf\u8e2a\u65e5\u5fd7\u4fe1\u606f\u3002</p>"},{"location":"tech_accu/tool/Shell/#\u67e5\u770b\u6587\u672c\u6587\u4ef6\u5185\u5bb9--less","title":"\u67e5\u770b\u6587\u672c\u6587\u4ef6\u5185\u5bb9 | less","text":"<p><code>less</code> \u5219\u662f\u771f\u6b63\u7528\u6765\u663e\u793a\u6587\u4ef6\u5185\u5bb9\u7684\u6307\u4ee4\uff0c\u5b83\u4f1a\u4ee5\u6587\u672c\u6587\u4ef6\u7684\u5f62\u5f0f\u5c55\u793a\u6587\u4ef6\u5185\u5bb9\u2014\u2014\u8fd9\u610f\u5473\u7740\u4f60\u5982\u679c\u5f3a\u884c\u4f7f\u7528 <code>less</code> \u6765\u67e5\u770b\u4e00\u4e2a\u4e8c\u8fdb\u5236\u6587\u4ef6\uff0c\u5219\u4f1a\u5f97\u5230\u4e00\u5806\u4e71\u7801\u3002</p> <pre><code># &lt;textFilename&gt; \u4e3a\u76ee\u6807\u6587\u4ef6\u7684\u540d\u5b57\n$ less &lt;textFilename&gt;\n</code></pre> <p>\u4f7f\u7528 <code>less</code> \u67e5\u770b\u6587\u4ef6\u65f6\uff0c\u4f60\u4f1a\u53d1\u73b0\u4f60\u6253\u5f00\u4e86\u4e00\u4e2a\u5f88\u50cf <code>man</code> \u7684\u754c\u9762\uff08\u76f8\u4fe1\u4f60\u5df2\u7ecf\u6ce8\u610f\u5230\u4e86\u8fd9\u4e2a\u8bf4\u6cd5\u6709\u70b9\u672c\u672b\u98a0\u5012\uff09\uff0c\u90a3\u5b9e\u9645\u4e0a\u6d4f\u89c8\u7684\u65b9\u5f0f\u4e5f\u662f\u7c7b\u4f3c\u7684\uff0c\u8fd9\u91cc\u518d\u591a\u4ecb\u7ecd\u4e00\u4e9b\u5728\u6d4f\u89c8\u6587\u4ef6\u7684\u65f6\u5019\u53ef\u80fd\u7528\u5230\u7684\u6280\u5de7\uff1a</p> <ul> <li>\u9f20\u6807\u6eda\u8f6e / \u89e6\u63a7\u677f\u624b\u52bf\uff1a\u7ffb\u9875\u6d4f\u89c8\uff1b</li> <li><code>[space]</code> / <code>PageDown</code> \uff1a\u5f80\u540e\u7ffb\u4e00\u9875\uff1b</li> <li><code>b</code> / <code>PageUp</code> \uff1a\u5f80\u524d\u7ffb\u4e00\u9875\uff1b</li> <li><code>shift</code> + <code>g</code> \uff08\u8f93\u5165 <code>G</code>\uff09\uff1a\u8df3\u8f6c\u7684\u6587\u672b\uff1b</li> <li>1,\u00a0<code>shift</code> + <code>g</code> \uff08\u8f93\u5165 <code>1G</code>\uff09\uff1a\u8df3\u8f6c\u5230\u6587\u9996\uff1b</li> <li><code>/{something}</code> , <code>Enter</code> \uff1a\u641c\u7d22 <code>{something}</code> \uff0c\u7c7b\u4f3c\u4e8e\u5e38\u89c1\u8f6f\u4ef6\u7684 <code>Ctrl</code> + <code>f</code> \uff1b</li> <li><code>n</code> \uff1a\u91cd\u590d\u4e0a\u4e00\u6b21\u641c\u7d22\u64cd\u4f5c\uff0c\u9002\u5408\u5728\u641c\u7d22\u5185\u5bb9\u6709\u591a\u4e2a\u7684\u65f6\u5019\uff0c\u8df3\u8f6c\u5230\u4e0b\u4e00\u4e2a\u641c\u7d22\u7ed3\u679c\uff1b</li> <li><code>h</code> \uff1a\u5e2e\u52a9\u624b\u518c\uff1b</li> <li><code>q</code> \uff1a\u9000\u51fa\uff1b</li> </ul>"},{"location":"tech_accu/tool/Shell/#\u4fee\u6539\u6587\u4ef6\u65f6\u95f4\u5c5e\u6027\u521b\u5efa\u6587\u4ef6--touch","title":"\u4fee\u6539\u6587\u4ef6\u65f6\u95f4\u5c5e\u6027(\u521b\u5efa\u6587\u4ef6) | touch","text":"<p><code>touch</code>\u5b9e\u9645\u4e0a\u662f\u7528\u6765\u4fee\u6539\u6587\u4ef6\u548c\u76ee\u5f55\u7684\u65f6\u95f4\u5c5e\u6027\u7684\uff0c\u4f46\u662f\u7531\u4e8e\u5b83\u5177\u6709\u201c\u5982\u679c\u6587\u4ef6\u4e0d\u5b58\u5728\u5219\u521b\u5efa\u4e00\u4e2a\u201d\u7684\u7279\u6027\uff0c\u6240\u4ee5\u4e5f\u5e38\u5e38\u7528\u6765\u521b\u5efa\u4e00\u4e2a\u65b0\u6863\u6848\u3002</p> <pre><code>$ ls -l\ntotal 0\n\n# \u5982\u679c\u5f53\u524d\u76ee\u5f55\u4e0b\u6ca1\u6709\u53eb\u505a &lt;filename&gt; \u7684\u6587\u4ef6\uff0c\u5219\u521b\u5efa\u4e00\u4e2a &lt;filename&gt;\n$ touch file\n$ ls -l\ntotal 0\n-rw-r--r--  1 isshikih  staff  0 10 25 10:07 file\n# \u5176\u4e2d\u6587\u4ef6\u7684\u65f6\u95f4\u4e3a\u7cfb\u7edf\u7684\u5f53\u524d\u65f6\u95f4\n\n# \u5982\u679c\u6b64\u65f6\u518d\u6b21 touch &lt;filename&gt;\uff0c\u5219\u4f1a\u66f4\u65b0\u5176\u65f6\u95f4\u4e3a\u5f53\u524d\u7cfb\u7edf\u65f6\u95f4\n$ touch file\n$ ls -l\ntotal 0\n-rw-r--r--  1 isshikih  staff  0 10 25 10:10 file\n</code></pre>"},{"location":"tech_accu/tool/Shell/#\u521b\u5efa\u6587\u4ef6\u5939--mkdir","title":"\u521b\u5efa\u6587\u4ef6\u5939 | mkdir","text":"<p><code>mkdir</code>\u662f make directory \u7684\u7f29\u5199\uff0c\u4e5f\u5c31\u662f\u521b\u5efa\u4e00\u4e2a\u201c\u6587\u4ef6\u5939\u201d\u3002</p> <pre><code># &lt;dirname&gt; \u53ef\u4ee5\u662f\u4e00\u4e2a\u590d\u6742\u8def\u5f84\u4e0b\u7684\u76ee\u5f55\uff0c\u4f46\u662f\u4e00\u5b9a\u8981\u6c42\u5176\u524d\u7f6e\u76ee\u5f55\u90fd\u5b58\u5728\n$ mkdir &lt;dirname&gt;\n$ ls -l\ntotal 0\n$ mkdir dir1/dir2\nmkdir: dir1: No such file or directory\n# \u8bf4\u660e\u76ee\u6807\u76ee\u5f55 dir2 \u7684\u524d\u7f6e\u8def\u5f84 ./dir1 \u7f3a\u5931\n\n# \u6211\u4eec\u53ef\u4ee5\u4f9d\u6b21\u521b\u5efa\u8fd9\u4e9b\u76ee\u5f55\n$ mkdir dir1 dir1/dir2\n$ tree      # \u8be5\u6307\u4ee4\u4f1a\u663e\u793a\u5f53\u524d\u7684\u6587\u4ef6\u7ed3\u6784\n.\n\u251c\u2500\u2500 dir1\n\u2502\u00a0\u00a0 \u251c\u2500\u2500 dir2\n\u2502\u00a0\u00a0 \u2502\u00a0\u00a0 \u2514\u2500\u2500 file2\n\u2502\u00a0\u00a0 \u2514\u2500\u2500 file1\n\u2514\u2500\u2500 newDir\n    \u251c\u2500\u2500 dir2\n    \u2502\u00a0\u00a0 \u2514\u2500\u2500 file2\n    \u2514\u2500\u2500 file1\n\n4 directories, 4 files\n\n# \u6216\u8005\u4f7f\u7528 -p \u53c2\u6570\uff0c\u5b83\u5141\u8bb8\u521b\u5efa\u5d4c\u5957\u76ee\u5f55\uff0c\u5373\u5982\u679c\u524d\u7f6e\u76ee\u5f55\u4e0d\u5b58\u5728\u5b83\u4f1a\u521b\u5efa\u4e00\u4e2a\n$ mkdir -p dir1/dir2\n$ tree      # \u8be5\u6307\u4ee4\u4f1a\u663e\u793a\u5f53\u524d\u7684\u6587\u4ef6\u7ed3\u6784\n.\n\u251c\u2500\u2500 dir1\n\u2502\u00a0\u00a0 \u251c\u2500\u2500 dir2\n\u2502\u00a0\u00a0 \u2502\u00a0\u00a0 \u2514\u2500\u2500 file2\n\u2502\u00a0\u00a0 \u2514\u2500\u2500 file1\n\u2514\u2500\u2500 newDir\n    \u251c\u2500\u2500 dir2\n    \u2502\u00a0\u00a0 \u2514\u2500\u2500 file2\n    \u2514\u2500\u2500 file1\n\n4 directories, 4 files\n</code></pre>"},{"location":"tech_accu/tool/Shell/#\u79fb\u52a8\u91cd\u547d\u540d--mv","title":"\u79fb\u52a8(\u91cd\u547d\u540d) | mv","text":"<p><code>mv</code>\u5373 move\uff0c\u542b\u4e49\u5f88\u660e\u663e\uff0c\u5373\u6539\u53d8\u6587\u4ef6\u6216\u76ee\u5f55\u7684\u4f4d\u7f6e\u3002\u4e0d\u8fc7\u7531\u4e8e\u201c\u4f4d\u7f6e\u201d\u8fd9\u4ef6\u4e8b\uff0c\u5b9e\u9645\u4e0a\u4e5f\u53ef\u4ee5\u5305\u542b\u6587\u4ef6\u672c\u8eab\u7684\u540d\u5b57\uff0c\u6240\u4ee5\u4e5f\u53ef\u4ee5\u7528\u6765\u505a\u91cd\u547d\u540d\uff0c\u5b9e\u9645\u4e0a\u5c31\u662f\u4fee\u6539\u76ee\u6807\u4f4d\u7f6e\u5230\u540c\u4e00\u4e2a\u8def\u5f84\u4e0b\u7684\u53e6\u5916\u4e00\u4e2a\u540d\u5b57\u3002</p> <pre><code># \u6ce8\u610f\uff0c\u6211\u4eec\u5728\u8fd9\u4e00\u8282\u4e34\u65f6\u628a &lt;path&gt; \u4ece &lt;filename&gt; \u548c &lt;dirname&gt; \u4e2d\u62c6\u51fa\u6765\n# \u8be5\u6307\u4ee4\u4f1a\u5c06 &lt;target1&gt; \u79fb\u52a8\u5230 &lt;path2&gt; \u5e76\u6539\u540d\u4e3a &lt;target2&gt;\uff0c\u5f53\u7136\u5141\u8bb8\u540c\u540d\n$ mv &lt;path1&gt;/&lt;target1&gt; &lt;path2&gt;/&lt;target2&gt;\n\n# \u7701\u7565 &lt;target2&gt;\uff0c\u5219\u4f1a\u79fb\u52a8\u6587\u4ef6\u4f4d\u7f6e\u4f46\u4e0d\u4fee\u6539\u6587\u4ef6\u540d\uff0c\u5373\u4e0b\u9762\u4e24\u4e2a\u6307\u4ee4\u7b49\u4ef7\n$ mv &lt;path1&gt;/&lt;target1&gt; &lt;path2&gt;\n$ mv &lt;path1&gt;/&lt;target1&gt; &lt;path2&gt;/&lt;target1&gt;\n\n# \u79fb\u52a8\u5230\u540c\u4e00\u76ee\u5f55\uff0c\u5373\u5b9e\u73b0\u91cd\u547d\u540d\uff0c\u5f53\u7136 &lt;path1&gt;/ \u53ef\u4ee5\u7701\u7565\uff0c\u5373\u6b64\u65f6 &lt;path1&gt; \u4e3a .\n$ mv &lt;path1&gt;/&lt;target1&gt; &lt;path1&gt;/&lt;target2&gt;\n</code></pre>"},{"location":"tech_accu/tool/Shell/#\u590d\u5236--cp","title":"\u590d\u5236 | cp","text":"<p><code>cp</code>\u5373 copy\uff0c\u7528\u6765\u590d\u5236\u6587\u4ef6\u6216\u76ee\u5f55\uff0c\u57fa\u672c\u8bed\u6cd5\u548c<code>mv</code>\u7c7b\u4f3c\uff0c\u6211\u4eec\u518d\u591a\u4ecb\u7ecd\u4e00\u4e2a<code>-r</code>\u53c2\u6570\u3002</p> <pre><code># \u8be5\u6307\u4ee4\u4f1a\u590d\u5236\u4e00\u4e2a\u6587\u4ef6 &lt;filename&gt; \u5230 &lt;path&gt; \u4e0b\n$ cp &lt;filename&gt; &lt;path&gt;\n\n# cp \u65e0\u6cd5\u590d\u5236\u6587\u4ef6\u5939\n$ cp &lt;dir&gt; &lt;path&gt;\ncp: &lt;dir&gt; is a directory (not copied).\n# \u4f46\u662f\u4f7f\u7528 -r \u53c2\u6570\u53ef\u4ee5\u590d\u5236 &lt;path1&gt; \u4e0b\u6240\u6709\u5185\u5bb9\u5230 &lt;path2&gt; \u4e0b\n$ cp -r &lt;path1&gt; &lt;path2&gt;\n$ cp -r dir1 newDir\n$ tree      # \u8be5\u6307\u4ee4\u4f1a\u663e\u793a\u5f53\u524d\u7684\u6587\u4ef6\u7ed3\u6784\n.\n\u251c\u2500\u2500 dir1\n\u2502\u00a0\u00a0 \u251c\u2500\u2500 dir2\n\u2502\u00a0\u00a0 \u2502\u00a0\u00a0 \u2514\u2500\u2500 file2\n\u2502\u00a0\u00a0 \u2514\u2500\u2500 file1\n\u2514\u2500\u2500 newDir\n    \u251c\u2500\u2500 dir2\n    \u2502\u00a0\u00a0 \u2514\u2500\u2500 file2\n    \u2514\u2500\u2500 file1\n\n4 directories, 4 files\n</code></pre>"},{"location":"tech_accu/tool/Shell/#\u5220\u9664--rm","title":"\u5220\u9664 | rm","text":"<p>\u628a<code>rm</code>\u653e\u5728\u6700\u540e\u8bb2\u662f\u6709\u539f\u56e0\u7684\uff0c\u6216\u8bb8\u4f60\u542c\u8bf4\u8fc7 <code>rm / -rf</code> \u8fd9\u6761\u6307\u4ee4\uff0c\u5374\u4e0d\u77e5\u9053\u5b83\u7684\u542b\u4e49\uff0c\u90a3\u4e48\u770b\u5b8c\u8fd9\u4e00\u5c0f\u8282\u4f60\u5c31\u77e5\u9053\u8fd9\u4e2a\u6307\u4ee4\u6709\u591a\u6050\u6016\u4e86\uff08\u5343\u4e07\u4e0d\u8981\u8dd1\u8fd9\u6761\u6307\u4ee4\uff09\u3002</p> <p>\u9996\u5148\u6211\u4eec\u9700\u8981\u77e5\u9053\uff0cLinux \u4e0b<code>rm</code>\u6307\u4ee4\u5e76\u4e0d\u5b58\u5728\u201c\u5783\u573e\u7bb1\u201d\u8fd9\u4e2a\u673a\u5236\uff0c\u5373\u7528<code>rm</code>\u5220\u6389\u7684\u4e1c\u897f\u662f\u6ca1\u6cd5\u901a\u8fc7\u6b63\u5e38\u624b\u6bb5\u590d\u539f\u7684\uff0c\u800c\u4e0a\u9762\u90a3\u6761\u6307\u4ee4\u7684\u610f\u601d\u5c31\u662f\u5f3a\u5236\u9012\u5f52\u5220\u9664\u7cfb\u7edf\u6839\u76ee\u5f55\u4e0b\u6240\u6709\u5185\u5bb9\uff0c\u4e5f\u5c31\u662f \u5565\u90fd\u5220\u5149\u4e86\u3002</p> <p>\u6240\u4ee5\uff0c\u4e00\u822c\u6211\u4eec\u90fd\u4f1a\u5efa\u8bae\u4f7f\u7528<code>alias</code>\u4fdd\u62a4<code>rm</code>\u6307\u4ee4\uff08\u6211\u5199\u8fc7<code>fish</code>\u7684<code>rmalias</code>\u4fdd\u62a4\u6d41\u7a0b\uff0c\u53ef\u4ee5\u53c2\u8003\u8fd9\u7bc7\u6587\u7ae0\uff09\u3002</p> <p><code>rm</code>\u5373 remove\uff0c\u987e\u540d\u601d\u4e49\u5c31\u662f\u7528\u6765\u5220\u9664\u4e1c\u897f\u7684\uff0c\u8fd9\u662f\u4e2a\u975e\u5e38\u5371\u9669\u7684\u6307\u4ee4\u3002\u5e38\u7528\u7684\u53c2\u6570\u6709<code>-r</code>\u548c<code>-f</code>\uff0c\u5206\u522b\u8868\u793a\u9012\u5f52\u5220\u9664\u548c\u5f3a\u5236\u5220\u9664\uff1b\u6b64\u5916\uff0c\u6211\u4eec\u8fd8\u5c06\u4ecb\u7ecd\u4e00\u4e2a<code>-i</code>\u53c2\u6570\u3002</p> <pre><code># \u5220\u9664\u4e00\u4e2a\u6587\u4ef6\n$ rm &lt;filename&gt;\n\n# \u5220\u9664 &lt;dirname&gt; \u4e0b\u6240\u6709\u7684\u4e00\u7ea7\u6587\u4ef6\n$ rm &lt;dirname&gt;/*\n\n$ tree\n.\n\u251c\u2500\u2500 dir2\n\u2502\u00a0\u00a0 \u2514\u2500\u2500 file3\n\u251c\u2500\u2500 file1\n\u2514\u2500\u2500 file2\n\n1 directory, 3 files\n$ rm ./*\nrm: ./dir2: is a directory\n$ tree\n.\n\u2514\u2500\u2500 dir2\n    \u2514\u2500\u2500 file3\n\n1 directory, 1 file\n# \u53ef\u4ee5\u53d1\u73b0\uff0c\u4e2d\u9014\u62a5\u9519\u8bf4 dir2 \u662f\u4e2a\u76ee\u5f55\u5e76\u4e14\u6ca1\u6709\u5220\u6389\uff0c\u5b9e\u9645\u4e0a\uff0c\u5982\u679c dir2 \u662f\u4e2a\u7a7a\u76ee\u5f55\uff0c\u90a3\u5b83\u662f\u4f1a\u88ab\u5220\u6389\u7684\n# \u800c\u5982\u679c\u8981\u771f\u6b63\u5220\u9664\u8fd9\u4e2a\u76ee\u5f55\u4e0b\u6240\u6709\u7684\u5185\u5bb9\uff0c\u5c31\u9700\u8981\u6211\u4eec\u201c\u9012\u5f52\u201d\u5220\u9664\uff0c\u5373\u4f7f\u7528 -r\n\n# \u9012\u5f52\u5220\u9664 &lt;dirname&gt; \u4e0b\u6240\u6709\u5185\u5bb9\n$ rm -r &lt;dirname&gt;/*\n\n# \u9012\u5f52\u5220\u9664 &lt;dirname&gt;\n$ rm -r &lt;dirname&gt;\n\n# \u5371\u9669\uff1a\u5f3a\u5236\u9012\u5f52\u5220\u9664 &lt;dirname&gt;\n$ rm -rf &lt;dirname&gt;\n\n# \u63a8\u8350\uff1a\u9012\u5f52\u5220\u9664\u65f6\u9010\u4e00\u786e\u8ba4\n$ rm -ri dir2\nexamine files in directory dir2/? y     # \u8fd9\u91cc\u8f93\u5165\u7684 y \u8868\u793a\u786e\u8ba4\uff0c\u5426\u5219\u90fd\u4e0d\u4f1a\u6267\u884c\u5220\u9664\nremove dir2//file3? y                                   # \u8fd9\u91cc\u8f93\u5165\u7684 y \u8868\u793a\u786e\u8ba4\uff0c\u5426\u5219\u90fd\u4e0d\u4f1a\u6267\u884c\u5220\u9664\nremove dir2/? y                                             # \u8fd9\u91cc\u8f93\u5165\u7684 y \u8868\u793a\u786e\u8ba4\uff0c\u5426\u5219\u90fd\u4e0d\u4f1a\u6267\u884c\u5220\u9664\n</code></pre>"},{"location":"tech_accu/tool/Shell/#\u91cd\u5b9a\u5411\u76f8\u5173-","title":"\u91cd\u5b9a\u5411\u76f8\u5173 \ud83d\udca1","text":"<p>\u53ef\u4ee5\u8bf4\u8fd9\u662f Shell \u4e2d\u6700\u6709\u610f\u601d\u7684\u77e5\u8bc6\u70b9\u4e4b\u4e00\u4e86\u3002\u91cd\u5b9a\u5411\uff0c\u987e\u540d\u601d\u4e49\u5c31\u662f\u91cd\u65b0\u5b9a\u5411\uff0c\u66f4\u51c6\u786e\u7684\u6765\u8bf4\u662f\u7ed9\u6570\u636e\u6d41\u91cd\u65b0\u5b9a\u5411\u3002\u9996\u5148\uff0c\u6211\u4eec\u6765\u770b\u770b\u8fd9\u5f20\u56fe\uff0c\u5b83\u63cf\u8ff0\u4e86\u547d\u4ee4\u8fd0\u884c\u65f6\u7684\u6570\u636e\u4ea4\u4e92\u3002</p> <pre><code>flowchart TD;\ninput[\"file, keyboard, etc\"] \ncommand\noutput[\"file, screen, etc\"]\nerror[\"file, screen, etc\"]\n\ninput --&gt;|\"Standard Input (stdin)\"| command\ncommand --&gt;|\"Standard Output (stdout)\"| output\ncommand --&gt;|\"Standard Error (stderr)\"| error</code></pre> <p>\u7b80\u5355\u7684\u63cf\u8ff0\u4e00\u4e0b\uff0c\u547d\u4ee4\u4ece\u6807\u51c6\u8f93\u5165\u6d41 <code>stdin</code> \u4e2d\u8bfb\u53d6\u8f93\u5165\u6570\u636e\uff0c\u5904\u7406\u8fc7\u7a0b\u4e2d\u6216\u8005\u662f\u5904\u7406\u7ed3\u675f\u540e\uff0c\u4f1a\u5411\u6807\u51c6\u8f93\u51fa\u6d41 <code>stdout</code> \u548c\u6807\u51c6\u9519\u8bef\u6d41 <code>stderr</code> \u4e2d\u5199\u5165\u6570\u636e\uff0c\u4e00\u822c\u6765\u8bf4 <code>stdout</code> \u627f\u8f7d\u7684\u662f\u6b63\u5e38\u7684\u8f93\u51fa\u6570\u636e\uff0c\u800c <code>stderr</code> \u627f\u8f7d\u7684\u662f\u62a5\u9519\u7b49\u4fe1\u606f\u3002</p> <p>\u800c\u6240\u8c13\u7684\u91cd\u5b9a\u5411\uff0c\u6b63\u662f\u6307\u91cd\u5b9a\u5411\u8fd9\u4e09\u4e2a\u6d41\uff0c\u800c\u4e14\u66f4\u591a\u7684\u6307\u7684\u662f\u91cd\u5b9a\u5411 <code>stdin</code> \u548c <code>stdout</code>\u3002</p> <p>\u800c\u5728 Shell \u4e2d\uff0c\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u4ed6\u4eec\u7684\u4ee3\u7801\u6765\u6307\u4ee3\u4ed6\u4eec\uff0c\u5177\u4f53\u5185\u5bb9\u672c\u6587\u4e0d\u4f1a\u8fc7\u591a\u6d89\u53ca\uff0c\u5982\u679c\u60f3\u8981\u6df1\u5165\u4e86\u89e3\u53ef\u4ee5\u4ed4\u7ec6\u770b\u770b\u201c\u5408\u5e76\u201d\u8fd9\u4e00\u8282\u7684\u5185\u5bb9\u3002</p> Stream: stdin stdout stderr Code: 0 1 2"},{"location":"tech_accu/tool/Shell/#\u6807\u51c6\u8f93\u51fa\u6d41\u91cd\u5b9a\u5411---","title":"\u6807\u51c6\u8f93\u51fa\u6d41\u91cd\u5b9a\u5411 | &gt; &gt;&gt;","text":"<p>\u57fa\u672c\u4e0a\u6240\u6709\u8bed\u8a00\u7684\u6559\u7a0b\u4e2d\u90fd\u4f1a\u5148\u4ecb\u7ecd\u5982\u4f55\u8f93\u51fa \u201dHello World!\u201c\uff08\u5f53\u7136\u4ed6\u4eec\u4e5f\u53ef\u80fd\u66f4\u60f3\u548c\u522b\u4eba\u6253\u62db\u547c\uff09\u3002\u603b\u800c\u8a00\u4e4b\uff0c\u8f93\u51fa\u5bf9\u4e00\u4e2a\u547d\u4ee4\u3001\u4e00\u4e2a\u7a0b\u5e8f\u662f\u81f3\u5173\u91cd\u8981\u7684\u3002\u4f46\u662f\u4f60\u4f1a\u53d1\u73b0\uff0c\u8fd9\u4e9b\u6307\u4ee4\u90fd\u53ea\u662f\u5c06\u5185\u5bb9\u6253\u5370\u5230\u4f60\u7684\u7ec8\u7aef\u91cc\uff0c\u5373 <code>stdout</code> \u91cc\uff0c\u53ea\u4e0d\u8fc7\u4e00\u822c\u88ab\u9001\u8fdb <code>stdout</code> \u7684\u4e1c\u897f\u4f1a\u88ab\u6253\u5370\u5728 screen \u4e0a\u3002</p> <p>\u4f46\u662f\u73b0\u5728\u6211\u4eec\u60f3\u8981\u5b83\u88ab\u5199\u5165\u5230\u4e00\u4e2a\u53eb <code>chat.txt</code> \u7684\u6587\u4ef6\u91cc\uff0c\u4f60\u5f53\u7136\u53ef\u4ee5\u4f7f\u7528 <code>fopen()</code> \u4e4b\u7c7b\u7684\u4e1c\u897f\u6765\u5b9e\u73b0\uff0c\u4f46\u662f\u73b0\u5728\u6211\u4eec\u60f3\u7528 Shell \u6765\u5b9e\u73b0\u8fd9\u4e2a\u6548\u679c\u3002</p> <p>\u6211\u4eec\u518d\u6b21\u56de\u5fc6\u6574\u4e2a\u8fc7\u7a0b\u4e2d\u6570\u636e\u7684\u6d41\u52a8\uff1a\u7a0b\u5e8f\u4e2d\u7684\u6570\u636e \u2192 <code>stdout</code> \u2192 screen\uff0c\u800c\u91cd\u5b9a\u5411\u505a\u7684\u4e8b\u60c5\u5c31\u662f\u6539\u53d8 <code>stdout</code> \u2192 screen \u8fd9\u4e2a\u6b65\u9aa4\u3002</p> <pre><code># \"command\" \u7684\u8f93\u51fa\u4f1a\u88ab\u8986\u5199\u8fdb \"file\"\n$ command &gt; file\n\n# \u4e0b\u9762\u8fd9\u6761\u6307\u4ee4\u5c31\u5b9e\u73b0\u4e86\u5c06 \"Hello World!\" \u5199\u5165\u4e86 chat.txt\n$ echo \"Hello World!\" &gt; chat.txt\n$ cat chat.txt\nHello World!\n\n# \"command\" \u7684\u8f93\u51fa\u4f1a\u88ab\u8ffd\u52a0\u8fdb \"file\"\n$ command &gt;&gt; file\n\n# \u4e0b\u9762\u8fd9\u6761\u6307\u4ee4\u5c31\u5b9e\u73b0\u4e86\u5c06 \"Hello World!\" \u8ffd\u52a0\u8fdb chat.txt\n$ echo \"Hello Human!\" &gt;&gt; chat.txt\n$ cat chat.txt\nHello World!\nHello Human!\n\n# \u4e0b\u9762\u8fd9\u6761\u6307\u4ee4\u5b9e\u73b0\u4e86\u5c06\u5f53\u524d\u76ee\u5f55\u4e0b\u7684\u6587\u4ef6/\u6587\u4ef6\u5939\u5217\u8868\u5199\u5165 \"index.txt\"\n$ ls -al &gt; index.txt\n</code></pre> <p>\u8bf6\u7b49\u7b49\uff0c\u4e0a\u9762\u600e\u4e48\u7a81\u7136\u51fa\u73b0\u4e86\u201c\u8ffd\u52a0\u201d\u8fd9\u4e2a\u8bcd\uff1f\u522b\u6025\u3002\u8ba9\u6211\u4eec\u56de\u987e\u4e00\u4e0b <code>fopen()</code> \u3002\u5982\u679c\u9700\u8981\u521b\u5efa\u4e00\u4e2a\u53ef\u5199\u6587\u4ef6\uff0c<code>fopen()</code> \u7684\u6a21\u5f0f\u53c2\u6570\u4e00\u822c\u662f <code>w</code> \uff0c\u6216\u8005\u662f <code>a</code>\u3002\u4ed6\u4eec\u5206\u522b\u4ee3\u8868 write \u548c append\uff0c\u5373\u8986\u5199\u548c\u8ffd\u52a0\u3002\u524d\u8005\u5c06\u76ee\u6807\u6587\u4ef6\u7684\u5185\u5bb9\u5168\u90e8\u8986\u76d6\uff0c\u5199\u5165\u65b0\u7684\u5185\u5bb9\uff0c\u5373\u76f8\u5f53\u4e8e\u6e05\u7a7a\u76ee\u6807\u6587\u4ef6\u7136\u540e\u5199\u5165\u5185\u5bb9\uff1b\u540e\u8005\u662f\u5728\u76ee\u6807\u6587\u4ef6\u7684\u5c3e\u90e8\u5f00\u59cb\u5199\u5165\u65b0\u5185\u5bb9\uff0c\u65e7\u7684\u5185\u5bb9\u4ecd\u7136\u4fdd\u7559\u3002\u6240\u4ee5\u4e0a\u9762\u7684\u4ee3\u7801\u4f1a\u51fa\u73b0 \u201cHello Human!\u201d \u88ab\u8ffd\u52a0\u5728 \u201cHello World!\u201d \u540e\u9762\u7684\u60c5\u51b5\u3002</p> <p>\u73b0\u5728\uff0c\u5982\u679c\u4f60\u60f3\u8ba9\u4f60\u7684 <code>a.exe</code> \u8f93\u51fa\u7684\u4e1c\u897f\u88ab\u5199\u5165 <code>out.txt</code> \u4e2d\uff0c\u4e5f\u53ef\u4ee5\u5c1d\u8bd5\u8fd9\u6837\u8fd0\u884c\u5b83\uff1a</p> <pre><code>$ a.exe &gt; out.txt\n</code></pre>"},{"location":"tech_accu/tool/Shell/#\u6807\u51c6\u8f93\u5165\u6d41\u91cd\u5b9a\u5411--","title":"\u6807\u51c6\u8f93\u5165\u6d41\u91cd\u5b9a\u5411 | &lt;","text":"<p>\u4e0e\u8f93\u51fa\u76f8\u5bf9\u5e94\uff0c\u5982\u679c\u6211\u4eec\u60f3\u4ece\u6587\u4ef6\u4e2d\u8bfb\u53d6\u6570\u636e\u800c\u975e\u4ece Keyboard \u5199\u5165\u7684\u7f13\u51b2\u533a\u8bfb\u53d6\u5185\u5bb9\uff0c\u800c\u662f\u4ece\u67d0\u4e2a\u6587\u4ef6\uff0c\u6211\u4eec\u4e5f\u53ef\u4ee5\u4f7f\u7528 <code>&lt;</code> \u6765\u91cd\u5b9a\u5411\u8f93\u5165\u3002</p> <pre><code>// \u5047\u8bbe a.exe \u7684\u6e90\u7801\u662f\u8fd9\u6837\u7684\n#include &lt;stdio.h&gt;\nint main(){\nchar str[1024];\nscanf(\"%s\", str);\nprintf(\"Hello %s!\", str);\n}\n</code></pre> <pre><code>// \u5047\u8bbe in.txt \u4e2d\u7684\u5185\u5bb9\u4e3a\u5982\u4e0b\nisshikih\n</code></pre> <pre><code># \"file\" \u4f1a\u88ab\u5f53\u4f5c \"command\" \u7684\u8f93\u5165\u53c2\u6570\n$ command &lt; file\n\n# \"a.exe\" \u4f1a\u8bfb\u5165 \"chat.txt\" \u7684\u5185\u5bb9\u4f5c\u4e3a\u8f93\u5165\n$ a.exe &lt; in.txt\nHello isshikh!\n\n# \u7efc\u5408\u8d77\u6765\uff0c\u6211\u4eec\u8fd8\u53ef\u4ee5\u8fd9\u6837\n$ a.exe &lt; in.txt &gt; out.txt\n$ cat out.txt\nHello isshikih! </code></pre>"},{"location":"tech_accu/tool/Shell/#\u6807\u51c6\u9519\u8bef\u6d41\u91cd\u5b9a\u5411--2-2","title":"\u6807\u51c6\u9519\u8bef\u6d41\u91cd\u5b9a\u5411 | 2&gt; 2&gt;&gt;","text":"<p><code>stderr</code> \u7684\u91cd\u5b9a\u5411\u57fa\u672c\u4e0a\u548c <code>stdout</code> \u662f\u4e00\u6837\u7684\u3002</p> <pre><code># \"command\" \u7684\u9519\u8bef\u6d41\u4f1a\u88ab\u8986\u5199\u8fdb \"file\"\n$ command 2&gt; file\n\n# \"command\" \u7684\u9519\u8bef\u6d41\u4f1a\u88ab\u8ffd\u52a0\u8fdb \"file\"\n$ command &gt;&gt; file\n</code></pre> <p>\u4f46\u5bf9\u4e8e <code>stderr</code> \uff0c\u6211\u4eec\u4f7f\u7528\u91cd\u5b9a\u5411\u7684\u76ee\u7684\u4e5f\u53ef\u80fd\u662f\u4e3a\u4e86\u8ba9\u4ed6\u4e0d\u8981\u5728\u5c4f\u5e55\u4e0a\u663e\u793a\u51fa\u6765\uff0c\u5373\u5c06\u5b83\u91cd\u5b9a\u5411\u5230\u522b\u7684\u5730\u65b9\u53bb\u3002</p> <p>\u8fd9\u91cc\u9700\u8981\u4ecb\u7ecd\u4e00\u4e2a\u7279\u6b8a\u7684\u201c\u6587\u4ef6\u201d\uff0c <code>/dev/null</code> \u2014\u2014\u4efb\u4f55\u5199\u5165\u5230\u5b83\u7684\u5185\u5bb9\u90fd\u4f1a\u88ab\u4e22\u5f03\u3002\u4e5f\u5c31\u662f\u8bf4\uff0c\u53ea\u8981\u6211\u4eec\u5c06 <code>stderr</code> \u91cd\u5b9a\u5411\u5230 <code>/dev/null</code> \uff0c\u5c31\u80fd\u5b9e\u73b0\u7c7b\u4f3c\u4e8e\u201c\u5ffd\u7565\u9519\u8bef\u6d41\u201d\u7684\u6548\u679c\u3002 </p> <pre><code># \"command\" \u7684\u9519\u8bef\u4fe1\u606f\u90fd\u4f1a\u88ab\u4e22\u5f03\n$ command 2&gt; /dev/null\n</code></pre>"},{"location":"tech_accu/tool/Shell/#\u5408\u5e76--","title":"\u5408\u5e76 | &lt;&amp; &gt;&amp;","text":"<p>\u6b64\u5916\uff0c\u8fd8\u6709 <code>&lt;&amp;</code> \u548c <code>&gt;&amp;</code> \u8fd9\u4e24\u4e2a\u7b26\u53f7\uff0c\u7531\u4e8e\u7bc7\u5e45\u6709\u9650\uff0c\u6211\u4e0d\u6253\u7b97\u5c55\u5f00\u8bb2\u8fd9\u4ef6\u4e8b\u3002\u8fd9\u91cc\u5f15\u7528\u8fd9\u4e00\u6279\u56de\u7b54\uff1a</p> <ul> <li>shell - What does \u201csh a.sh &lt;&amp;0 &gt;&amp;0\u201d mean? - Unix &amp; Linux Stack Exchange</li> </ul> <p><code>n&gt;&amp;p</code>\u00a0and\u00a0<code>n&lt;&amp;p</code>\u00a0are the same operator and are for duplicating the file descriptor (fd)\u00a0<code>p</code>\u00a0onto the file descriptor\u00a0<code>n</code>. Or said otherwise, they redirect the file descriptor\u00a0<code>n</code>\u00a0to whatever resource fd\u00a0<code>p</code>\u00a0is redirected to.</p> <p>The\u00a0<code>&lt;</code>\u00a0and\u00a0<code>&gt;</code>\u00a0are not used to determine what direction (reading or writing) the redirected file descriptor will be used.\u00a0<code>n</code>\u00a0will get the same direction as\u00a0<code>p</code>. That is, if\u00a0<code>p</code>\u00a0was open for writing, so will be\u00a0<code>n</code>\u00a0even if the\u00a0<code>n&lt;&amp;p</code>\u00a0operator is used.</p> <p>The only difference between the two operators is when\u00a0<code>n</code>\u00a0is not specified.\u00a0<code>&gt;&amp;p</code>\u00a0redirects stdout (is like\u00a0<code>1&gt;&amp;p</code>\u00a0or\u00a0<code>1&lt;&amp;p</code>) and\u00a0<code>&lt;&amp;p</code>\u00a0redirects stdin (is like\u00a0<code>0&lt;&amp;p</code>\u00a0or\u00a0<code>0&gt;&amp;p</code>).</p> <p>So\u00a0<code>&lt;&amp;0</code>\u00a0is like\u00a0<code>0&lt;&amp;0</code>, so redirects stdin to whatever resource stdin was redirected to, so does nothing useful, it's usually a no-op and doesn't make much sense.</p> <p>But not always a no-op, not in every shell. When job control is disabled, POSIX requires stdin of command in the background to be redirected to\u00a0<code>/dev/null</code>\u00a0or an equivalent file. In Bash (tested in 4.4.12)\u00a0<code>&lt;&amp;0</code>\u00a0overrides this. Compare\u00a0<code>(ls -l /proc/self/fd/0 &amp;)</code>\u00a0and\u00a0<code>(&lt;&amp;0 ls -l /proc/self/fd/0 &amp;)</code>. In some cases this is useful.</p> <p><code>&gt;&amp;0</code>\u00a0duplicates the fd 0 onto the fd 1. Because the fd 1 (stdout), is by convention only used for writing, that\u00a0<code>&gt;&amp;0</code>\u00a0only makes sense if fd 0 was open in read+write mode.</p> <p>That would be the case in cases where fd 0 points to the terminal device, because terminal emulators or\u00a0<code>getty</code>\u00a0would generally open the terminal device in read+write mode and assign fds 0, 1 and 2 to it.</p> <p>So maybe whoever wrote that wanted to redirect stdout to the terminal assuming that stdin was pointing to it.</p> <p>One place where\u00a0<code>n&gt;&amp;n</code>\u00a0makes sense is with zsh and its\u00a0<code>mult_IOs</code>\u00a0feature. In\u00a0<code>zsh</code>:</p> <pre><code>some-cmd &gt;&amp;1 &gt; some-file\n# that is: some-cmd 1&gt;&amp;1 1&gt; some-file\n</code></pre> <p>Redirects the standard output of\u00a0<code>some-cmd</code>\u00a0to both whatever stdout was before (&amp;1) and\u00a0<code>some-file</code>, as if you had written:</p> <pre><code>some-cmd | tee some-file\n</code></pre> <p>While</p> <pre><code>some-cmd &lt;&amp;0 &lt; some-file\n# that is: some-cmd 0&lt;&amp;0 0&lt; some-file\n</code></pre> <p>would feed first the original stdin and then\u00a0<code>some-file</code>\u00a0as input to\u00a0<code>some-cmd</code>\u00a0as if you had written:</p> <pre><code>cat - some-file | some-cmd\n</code></pre> <p>But in\u00a0<code>cmd &lt;&amp;0 &gt;&amp;0</code>, fd 0 is redirected only once, so that does not apply.</p> <p><code>n&gt;&amp;n</code>\u00a0can also have an interesting side effect in some shells (<code>ksh</code>,\u00a0<code>zsh</code>, not\u00a0<code>dash</code>,\u00a0<code>bash</code>\u00a0nor\u00a0<code>yash</code>) in that it triggers an error and gives up running the command if the file descriptor\u00a0<code>n</code>\u00a0is not open. So, in those shells,</p> <pre><code>cmd 0&lt;&amp;0\n</code></pre> <p>would avoid running\u00a0<code>cmd</code>\u00a0in the pathological condition where\u00a0<code>stdin</code>\u00a0is closed:</p> <pre><code>$ ksh -c 'cat file - &lt;&amp;0' &lt;&amp;-\nksh: 0: cannot open [Bad file descriptor]\n$ mksh -c 'cat file - &lt;&amp;0' &lt;&amp;-\nmksh: &lt;&amp;0 : bad file descriptor\n$ zsh -c 'cat file - &lt;&amp;0' &lt;&amp;-\nzsh:1: 0: bad file descriptor\n\n$ bash -c 'cat file - &lt;&amp;0' &lt;&amp;-\ncontents of file\ncat: -: Bad file descriptor\ncat: closing standard input: Bad file descriptor\n</code></pre> <ul> <li>Copy from the top answer from: https://unix.stackexchange.com/questions/84620/what-does-sh-a-sh-0-0-mean</li> </ul>"},{"location":"tech_accu/tool/Shell/#\u7ba1\u9053\u7b26--","title":"\u7ba1\u9053\u7b26 | |","text":"<p>\u524d\u9762\u8bb2\u4e86\u5982\u4f55\u5c06\u8f93\u5165\u8f93\u51fa\u91cd\u5b9a\u5411\u81f3 \u6587\u4ef6\uff0c\u5373\u6570\u636e\u7684\u6d41\u52a8\u662f \u4ece\u547d\u4ee4\u5230\u6587\u4ef6 \u6216\u662f \u4ece\u6587\u4ef6\u5230\u547d\u4ee4\u3002\u800c\u7ba1\u9053\u7b26 <code>|</code> \u5219\u5b9e\u73b0\u4e86\u5c06\u6570\u636e\u7684\u6d41\u52a8\u5b9a\u5411\u4e3a \u4ece\u547d\u4ee4\u5230\u547d\u4ee4\u3002</p> <pre><code># \"command_1\" \u7684\u8f93\u51fa\u4f1a\u4f5c\u4e3a \"command_2\" \u7684\u8f93\u5165\n$ command_1 | command_2\n\n# \u4f7f\u7528 less \u6765\u67e5\u770b\u5f53\u524d\u76ee\u5f55\u4e0b\u7684\u6587\u4ef6/\u6587\u4ef6\u5939\u5217\u8868\n$ ls -al | less\n\n# \u4e00\u4e2a\u5e38\u7528\u7684\u7528\u6cd5\u662f\u642d grep \u5728\u65e5\u5fd7\u4e2d\u627e\u5230\u4f60\u60f3\u8981\u7684\u4e00\u884c\n# \u6bd4\u5982\u4e0b\u9762\u7684\u547d\u4ee4\u4f1a\u5728 xxx.log \u6587\u4ef6\u4e2d\u627e\u5230\u5e26\u6709\u5173\u952e\u8bcd \"lean_shell\" \u7684\u82e5\u5e72\u884c\n$ cat xxx.log | grep \"lean_shell\"\nLet us learn_shell together!\nLearn_shell means learn_shell and learn_shell!\n$ cat xxx.log\nCommand line is powerful!\nLet us learn_shell together!\nHave you ever see this?\nLearn_shell means learn_shell and learn_shell!\n\n# \u53c8\u6216\u8005\u8ba1\u7b97\u5f53\u524d\u76ee\u5f55\u4e0b\u6709\u591a\u5c11\u6587\u4ef6\u5939\u548c\u6587\u4ef6\n$ ls -a | wc -w\n5\n$ ls -a\n.   ..  x   xx  xxx.log\n\n# \u518d\u6bd4\u5982\uff0c\u7edf\u8ba1\u5f53\u524d\u76ee\u5f55\u4e0b\u5404\u4e2a\u6587\u4ef6\u5939\u7684\u5927\u5c0f\uff0c\u5e76\u8f93\u51fa\u4ece\u5927\u5230\u5c0f\u7684 10 \u9879\n$ du | sort -nr | head\n# \u627e\u51fa\u5f53\u524d\u76ee\u5f55\u4e0b\uff08\u9012\u5f52\uff09\u6240\u6709\u53eb\u505a \"xxx\" \u7684\u6587\u4ef6\u5e76\u5220\u9664\n$ find . -name \"xxx\"  | xargs rm -f\n</code></pre>"},{"location":"tech_accu/tool/Shell/#\u7b5b\u9009\u5668","title":"\u7b5b\u9009\u5668","text":"<p>\u53ef\u4ee5\u53d1\u73b0\uff0c\u91cd\u5b9a\u5411\u7684\u529f\u80fd\u975e\u5e38\u5f3a\u5927\u3002\u540c\u65f6\uff0c\u8fd9\u91cc\u4e5f\u6709\u5f88\u591a\u7b5b\u9009\u5668\u4f9b\u4f60\u9009\u62e9\uff0c\u4ed6\u4eec\u7ecf\u5e38\u642d\u914d\u7ba1\u9053\u7b26\u4f7f\u7528\uff0c\u4ee5\u8f85\u52a9\u7ba1\u9053\u7b26\u8fdb\u884c\u4e00\u4e9b\u66f4\u590d\u6742\u7684\u5de5\u4f5c\u3002</p> <p></p> <p>Source: https://linuxcommand.org/lc3_lts0070.php</p>"},{"location":"tech_accu/tool/Shell/#\u811a\u672c-shell","title":"\u811a\u672c Shell","text":"<p>\u7b80\u5355\u6765\u8bf4\uff0cShell \u811a\u672c\u53ef\u4ee5\u770b\u4f5c\u4e00\u6761\u6761 Shell \u6307\u4ee4\u7684\u96c6\u5408\uff0c\u6211\u4eec\u5728\u8fd0\u884c Shell \u811a\u672c\u65f6\uff0cShell \u811a\u672c\u4e2d\u7684\u6307\u4ee4\u6309\u7167\u7279\u5b9a\u987a\u5e8f\u4e00\u884c\u4e00\u884c\u7684\u88ab\u6267\u884c\u4e0b\u6765\u3002</p> <p>Shell \u811a\u672c\u4e00\u822c\u662f\u4ee5 <code>.sh</code> \u4e3a\u540e\u7f00\u7684\u7eaf\u6587\u672c\u6587\u4ef6\uff0c\u800c\u6267\u884c Shell \u811a\u672c\u7684\u65b9\u6cd5\u5927\u81f4\u6709\u4e09\u79cd\uff1a</p> <ul> <li><code>./script.sh</code> \uff08\u9700\u8981\u811a\u672c\u5177\u6709\u53ef\u6267\u884c\u6743\u9650\uff09</li> <li><code>source script.sh</code></li> <li><code>bash script.sh</code> / <code>sh script.sh</code> / ...</li> </ul> <p>\u4ed6\u4eec\u7684\u533a\u522b\u4e3b\u8981\u5982\u4e0b\uff1a</p> <ul> <li>\u4f7f\u7528 <code>bash script.sh</code> / <code>sh script.sh</code> / ... \u7684\u65b9\u5f0f\u6267\u884c\u811a\u672c\uff0c\u4e3b\u8fdb\u7a0b\u4f1a\u4f11\u7720\uff0c\u5e76\u5f00\u59cb\u4e00\u4e2a\u65b0\u8fdb\u7a0b\u6765\u6267\u884c\u811a\u672c\u5185\u5bb9\uff1b</li> <li>\u4f7f\u7528 <code>source script.sh</code> \u7684\u65b9\u5f0f\u6267\u884c\u811a\u672c\uff0c\u811a\u672c\u5185\u5bb9\u4f1a\u5728\u4e3b\u8fdb\u7a0b\u8fdb\u884c\uff0c\u8fd9\u4e5f\u662f\u4e3a\u4ec0\u4e48\u6211\u4eec\u5728\u66f4\u65b0\u5b8c <code>.bashrc</code> \u8fd9\u79cd\u6587\u4ef6\u4ee5\u540e\u4f1a\u4f7f\u7528 <code>source</code> \u6765\u6267\u884c\u5b83\u4ee5\u6c42\u6548\u679c\u9a6c\u4e0a\u88ab\u52a0\u8f7d\u51fa\u6765\uff1b</li> </ul>"},{"location":"tech_accu/tool/Shell/#\u6d41\u7a0b\u63a7\u5236---\u6761\u4ef6\u8bed\u53e5","title":"\u6d41\u7a0b\u63a7\u5236 - \u6761\u4ef6\u8bed\u53e5","text":"<pre><code># \u6761\u4ef6\u5206\u652f\u8bed\u53e5\nif condition1\nthen\ncommands\nelif condition2\nthen\ncommands else\ncommands\nfi\n</code></pre> <pre><code># \u5f53 $var \u4e3a \"A\" \u65f6\u6267\u884c\u7b2c\u4e00\u5757\uff0c\u5f53 $var \u4e3a \"B\" \u65f6\u6267\u884c\u7b2c\u4e8c\u5757\uff0c*) \u5373\u5176\u4ed6\u60c5\u51b5\ncase $var in \"A\")\ncommands\n    ;;\n\"B\")\ncommands\n    ;; *)\ncommands\n    ;;\nesac\n</code></pre>"},{"location":"tech_accu/tool/Shell/#\u6d41\u7a0b\u63a7\u5236---\u5faa\u73af\u8bed\u53e5","title":"\u6d41\u7a0b\u63a7\u5236 - \u5faa\u73af\u8bed\u53e5","text":"<pre><code># \u4f9d\u6b21\u679a\u4e3e\u82e5\u5e72 item\uff0cvar \u8868\u793a\u6b63\u5728\u679a\u4e3e\u7684\u5185\u5bb9\nfor var in item1 item2 ... itemN\ndo\ncommands\ndone\n</code></pre> <pre><code># \u8fd0\u884c\u5230 condition \u4e3a\u5047\u65f6\u7ed3\u675f\nwhile condition\ndo\ncommands\ndone\n</code></pre> <pre><code># \u8fd0\u884c\u5230 condition \u4e3a\u771f\u65f6\u7ed3\u675f\nuntil condition\ndo\ncommands\ndone\n</code></pre>"},{"location":"tech_accu/tool/Shell/#\u6d41\u7a0b\u63a7\u5236---\u51fd\u6570","title":"\u6d41\u7a0b\u63a7\u5236 - \u51fd\u6570","text":"<pre><code># \u5b9a\u4e49\u4e86\u4e00\u4e2a\u53eb\u505a foo \u7684\u51fd\u6570\uff0cfunction \u53ef\u4ee5\u4e0d\u5199\nfunction foo(){\ncommands\n}\n</code></pre>"},{"location":"tech_accu/tool/Shell/#\u53c2\u6570\u4f20\u9012","title":"\u53c2\u6570\u4f20\u9012","text":"<p>\u5bf9\u4e8e\u51fd\u6570\u6216\u547d\u4ee4\u53ef\u4ee5\u7528 <code>$n</code> \u6765\u83b7\u53d6\u7b2c n \u4e2a\u53c2\u6570\u3002\u4f46\u5f53 n \u4e0d\u6b62\u4e00\u4f4d\u6570\u65f6\uff0c\u53ef\u4ee5\u4f7f\u7528 <code>${n}</code> \u7684\u65b9\u5f0f\u6765\u83b7\u53d6\u7b2c n \u4e2a\u53c2\u6570\u3002</p> <ul> <li>\u5047\u8bbe <code>script.sh</code> \u7684\u5185\u5bb9\u5982\u4e0b</li> </ul> <pre><code>#! /bin/bash\necho $1\necho $2\necho $3\necho $4\necho $5\necho $6\necho $7\necho $8\necho $9\necho $10\necho ${10}\n</code></pre> <ul> <li>\u5219\u5982\u4e0b\u8fd0\u884c\u7ed3\u679c\u5982\u4e0b\uff1a</li> </ul> <pre><code>$ ./foo.sh a b c d e f g h i j\na\nb\nc\nd\ne\nf\ng\nh\ni\na0\nj\n</code></pre> <ul> <li>\u5047\u8bbe <code>script.sh</code> \u7684\u5185\u5bb9\u5982\u4e0b</li> </ul> <pre><code>#! /bin/bash\nfunction foo(){\necho $1\necho $2\necho $3\necho $4\necho $5\necho $6\necho $7\necho $8\necho $9\necho $10\necho ${10}\n}\n\nfoo a b c d e f g h i j\n</code></pre> <ul> <li>\u5219\u5982\u4e0b\u8fd0\u884c\u7ed3\u679c\u5982\u4e0b\uff1a</li> </ul> <pre><code>$ ./script.sh\na\nb\nc\nd\ne\nf\ng\nh\ni\na0\nj\n</code></pre>"},{"location":"tech_accu/tool/Shell/#\u5c06\u547d\u4ee4\u7ed3\u679c\u4f5c\u4e3a\u53c2\u6570\u5217\u8868","title":"\u5c06\u547d\u4ee4\u7ed3\u679c\u4f5c\u4e3a\u53c2\u6570\u5217\u8868","text":"<p>\u56de\u5fc6\u5faa\u73af\u8bed\u53e5\u7684\u7ed3\u6784\uff0c\u6211\u4eec\u9700\u8981\u5199\u51fa\u679a\u4e3e\u7684\u6bcf\u4e00\u4e2a\u9879\u76ee\u3002\u663e\u7136\uff0c\u5728\u5927\u91cf\u679a\u4e3e\u76ee\u6807\u7684\u60c5\u51b5\u4e0b\uff0c\u624b\u5199\u51fa\u5168\u90e8\u7684\u679a\u4e3e\u53ef\u80fd\u4e0d\u592a\u73b0\u5b9e\uff0c\u6240\u4ee5\u6211\u4eec\u53ef\u80fd\u4f1a\u60f3\u8981\u4f7f\u7528\u6587\u4ef6\u503c\u6216\u662f\u547d\u4ee4\u7684\u8f93\u51fa\u6765\u5b9e\u73b0\u3002\u8fd9\u4e2a\u65f6\u5019\uff0c\u6211\u4eec\u53ef\u4ee5\u7528 ``` \u628a\u628a\u547d\u4ee4\u7ed9\u62ec\u8d77\u6765\u3002</p> <ul> <li>\u5047\u8bbe <code>file</code> \u7684\u5185\u5bb9\u5982\u4e0b</li> </ul> <pre><code>A\nB\nC\n</code></pre> <ul> <li>\u6267\u884c\u4e0b\u5217\u8bed\u53e5</li> </ul> <pre><code>for var in `cat file`\ndo\necho - var done\n</code></pre> <ul> <li>\u7ed3\u679c\u4e3a</li> </ul> <pre><code>- A\n- B\n- C\n</code></pre>"},{"location":"tech_accu/tool/Shell/#\u6307\u5b9a\u6267\u884c\u811a\u672c\u6240\u4f7f\u7528\u7684-shell","title":"\u6307\u5b9a\u6267\u884c\u811a\u672c\u6240\u4f7f\u7528\u7684 Shell","text":"<p>\u53ef\u4ee5\u53d1\u73b0\uff0c\u5728\u524d\u9762\u7ed9\u51fa\u7684\u82e5\u5e72\u811a\u672c\u6837\u4f8b\u4e2d\uff0c\u6211\u4eec\u7684\u7b2c\u4e00\u884c\u90fd\u6709\u4e00\u884c\u5947\u602a\u7684\u6ce8\u91ca\uff1a</p> <pre><code>#! /bin/bash\n</code></pre> <p>\u8fd9\u53e5\u8bdd\u7684\u610f\u601d\u662f\uff0c\u6307\u5b9a\u8be5\u811a\u672c\u9ed8\u8ba4\u4f7f\u7528 <code>/bin/bash</code> \u6765\u6267\u884c\u3002\u8fd9\u91cc\u9700\u8981\u4f7f\u7528\u7edd\u5bf9\u8def\u5f84\u6765\u7d22\u5f15 Shell \u7684\u53ef\u6267\u884c\u6587\u4ef6\u3002</p>"},{"location":"tech_accu/tool/Shell/#\u4e00\u4e2a\u6a21\u677f","title":"\u4e00\u4e2a\u6a21\u677f","text":"<p>\u8fd9\u91cc\u518d\u8d34\u4e00\u4e2a\u6211\u81ea\u5df1\u5199 Shell \u811a\u672c\u7684\u65f6\u5019\u4f1a\u91c7\u7528\u7684\u6a21\u677f\u3002</p> <pre><code>#! /bin/bash\n\n# get current direction\ncurDir=`pwd`\n# get shell direction\nworkDir=$(cd \"$(dirname \"$0\")\";pwd)\n\ncd $workDir\n\n# Write your script here.\n\ncd $curDir\n</code></pre>"},{"location":"tech_accu/tool/Shell/#\u5176\u4ed6","title":"\u5176\u4ed6","text":"<p>\u547d\u4ee4\u884c\u5e38\u89c1\u5feb\u6377\u952e\uff0cSource: https://lym.readthedocs.io/en/latest/startingcommands.html?highlight=mkdir#moving-around-in-the-command-line</p> <ul> <li>Linux \u547d\u4ee4\u5927\u5168</li> </ul>"},{"location":"tech_accu/tool/Shell/#\u76f8\u5173\u8d44\u6599","title":"\u76f8\u5173\u8d44\u6599","text":"<ul> <li>Shell (computing) - Wikipedia</li> <li>Terminal emulator - Wikipedia</li> <li>Introducing the Shell \u2013 Introduction to the Command Line for Genomics (datacarpentry.org)</li> <li>LinuxCommand.org: Learning the shell.</li> <li>\u8bfe\u7a0b\u6982\u89c8\u4e0e shell \u00b7 the missing semester of your cs education (missing-semester-cn.github.io)</li> <li>man command in Linux with Examples - GeeksforGeeks</li> <li>Shell commands \u2014 Linux command line for you and me 0.1 documentation (lym.readthedocs.io)</li> </ul>"},{"location":"tech_accu/tool/Shell/#\u76f8\u5173\u77e5\u8bc6\u70b9","title":"\u76f8\u5173\u77e5\u8bc6\u70b9","text":"<ul> <li>Linux</li> <li>vi / vim</li> </ul>"}]}
\ No newline at end of file
+{"config":{"lang":["en"],"separator":"[\\s\\-\\.]+","pipeline":["stemmer"]},"docs":[{"location":"","title":"\u6b22\u8fce\uff01","text":"<p> \u7ea6 108 \u4e2a\u5b57 </p> <p> \u300e\u305d\u306e\u6642\u3092\u5f85\u3064\u3088\u300f      \u6211\u4eec\u767b\u4e0a\u9ad8\u5854\uff0c\u770b\u5230\u7684\u5374\u53ea\u6709\u9ed1\u591c\u3002  \u2014\u2014\u5b89\u5fb7\u70c8\u00b7\u7eaa\u5fb7\u300a\u5730\u7cae\u300b  </p> <p> \ud83e\udd7a \u5982\u679c\u975e\u8981\u652f\u6301\u4e00\u4e0b\u7684\u8bdd\u2026\u2026\u8fd9\u4e2a\u4e8c\u7ef4\u7801\u4e5f\u4e0d\u662f\u4e0d\u53ef\u4ee5\u626b\uff01 </p> <p>\u63a8\u8350\u9605\u8bfb</p> <ul> <li>\ud83d\udcc4 \u4f7f\u7528 reveal-md \u6765\u5199 Slides</li> <li>\ud83d\uddc2\ufe0f Git Something</li> <li>\ud83d\uddc2\ufe0f \u6570\u5b57\u903b\u8f91\u8bbe\u8ba1 | Digital Design</li> <li>\ud83d\uddc2\ufe0f \u9ad8\u7ea7\u6570\u636e\u7ed3\u6784 | Advanced Data Structure</li> <li>\ud83d\uddc2\ufe0f \u64cd\u4f5c\u7cfb\u7edf | Operating System\uff08\u66f4\u65b0\u4e2d\uff09</li> </ul> <p>\u7ad9\u70b9\u7edf\u8ba1</p> <p> \u672c\u7ad9\u76ee\u524d\u5171 96 \u9875\uff0c\u7d2f\u8ba1 194561 \u5b57\uff01 </p>"},{"location":"coming/","title":"\u5185\u5bb9\u6b63\u5728\u7f16\u8f91\u4e2d\u2026\u2026","text":"<p> \u7ea6 47 \u4e2a\u5b57 </p> <p>Missing</p> <p>\u672c\u90e8\u5206\u7684\u5185\u5bb9\u6b63\u5728\u7f16\u8f91\u4e2d\uff0c\u5c1a\u672a\u4e0a\u4f20\uff01</p> \u81ea\u5b9a\u4e49 admonition <p>definition</p> <p>proof</p> <p>property</p> <p>extra</p> <p>section</p> <p>key-point</p> <p>advice</p> <p>not-advice</p> <p>eg</p>"},{"location":"link/","title":"\u4f60\u597d\uff01","text":"<p> \u7ea6 177 \u4e2a\u5b57  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 1 \u5206\u949f</p> <p>\ud83d\udcdc \u4ecb\u7ecd</p> <p>\u4f60\u597d\uff01\u6211\u60f3\u4e3a\u8fd9\u4e2a\u5c0f\u7f51\u7ad9\u8d4b\u4e88\u4e00\u4e9b\u793e\u4ea4\u4ef7\u503c\uff0c\u60f3\u8ba4\u8bc6\u66f4\u591a\u5389\u5bb3\u7684\u4eba\uff01\u6b22\u8fce\u5927\u5bb6\u5728\u8fd9\u91cc\u804a\u5929\uff0c\u6216\u662f\u7559\u4e0b\u53cb\u94fe\u4ea4\u6362\uff01</p> <p>\ud83d\udd17 \u53cb\u94fe</p> <p> \u9889\u65f6\u4eba\u5f71 \u8fd9\u662f\u6211\u7684\u535a\u5ba2\uff01\u65f6\u4e0d\u65f6\u66f4\u65b0\u4e00\u4e9b\u548c\u6280\u672f\u6ca1\u5173\u7cfb\u7684\u6587\u7ae0\u3002 </p> <p> \u54b8\u9c7c\u6684 \u7684 \u4ee3\u7801\u7a7a\u95f4 \u81ed\u5149\u5934\uff0c\u66b4\u63cdxyx\uff01 </p> <p> \u9e64\u7fd4\u4e07\u91cc \u7684 \u7b14\u8bb0\u672c  \ud83e\udd24 xg \u6559\u6b7b\u6211\uff01 </p> <p> Zicx \u7684 \u7b14\u8bb0\u672c  \ud83e\udd24 \u662f\u8d85\u5f3a\u65ed\u5b9d\uff01 </p> <p> sakuratsuyu \u7684 \u7b14\u8bb0\u672c  \ud83e\udd24 \u65e0\u654c\u9ea6\u54e5\u5e26\u5e26\u6211\uff01 </p> <p> Bowling \u7684 \u7b14\u8bb0\u672c  \u88ab\u795e\u4ed9\u5b66\u5f1f\u8584\u7eb1 orz  </p> <p> MinJoker \u7684 \u7b14\u8bb0\u672c  \u88ab\u795e\u4ed9\u5b66\u5f1f\u8584\u7eb1 orz  </p> <p> Zizheng's Blog  \u4f6c\uff01  </p> \ud83d\udd17 \u6709\u610f\u601d\u7684\u94fe\u63a5 <p>\u5728\u8fd9\u91cc\u6536\u96c6\u4e00\u4e9b\u6709\u610f\u601d\u7684\u94fe\u63a5\uff01</p> <ul> <li>https://quickref.me/</li> </ul>"},{"location":"cour_note/","title":"\u6249\u9875","text":"<p> \u7ea6 20 \u4e2a\u5b57 </p> <p> \u300e\u305d\u306e\u6642\u3092\u5f85\u3064\u3088\u300f      \u4e00\u5207\u5b89\u4e50\uff0c\u65e0\u4e0d\u6765\u81ea\u56f0\u82e6\u3002  \u2014\u2014\u590f\u76ee\u6f31\u77f3\u300a\u5fc3\u300b  </p>"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/","title":"\ud83d\udd2e \u6982\u7387\u8bba\u4e0e\u6570\u7406\u7edf\u8ba1","text":"<p> \u7ea6 164 \u4e2a\u5b57  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 1 \u5206\u949f</p> <p>\u8bfe\u7a0b\u4fe1\u606f</p> <ul> <li>\u667a\u4e91\u94fe\u63a5\uff1a\ud83d\udd17</li> <li>\u6388\u8bfe\uff1a\u5434\u56fd\u6862</li> <li>\u6559\u6750\uff1a\u300a\u6982\u7387\u8bba\u4e0e\u6570\u7406\u7edf\u8ba1\u300b\uff0c\u5f20\u5e3c\u594b\uff0c\u9ad8\u7b49\u6559\u80b2\u51fa\u7248\u793e</li> <li>\u8f85\u52a9\u6559\u6750\uff1a\u300a\u6982\u7387\u8bba\u4e0e\u6570\u7406\u7edf\u8ba1\u6559\u7a0b \u7b2c\u4e09\u7248\u300b\uff0c\u8306\u8bd7\u677e\uff0c\u9ad8\u7b49\u6559\u80b2\u51fa\u7248\u793e\uff08\u540e\u7b80\u79f0\u6a59\u4e66\uff09</li> </ul> <p>Notes</p> <ul> <li> [1.x] \u6982\u7387\u8bba\u7684\u57fa\u672c\u6982\u5ff5</li> <li> [2.x] \u968f\u673a\u53d8\u91cf\u53ca\u5176\u6982\u7387\u5206\u5e03</li> <li> [3.x] \u591a\u5143\u968f\u673a\u53d8\u91cf\u53ca\u5176\u5206\u5e03</li> <li> [4.x] \u968f\u673a\u53d8\u91cf\u7684\u6570\u5b57\u7279\u5f81</li> <li> [5.x] \u5927\u6570\u5b9a\u5f8b\u53ca\u4e2d\u5fc3\u6781\u9650\u5b9a\u7406</li> <li> [6.x] \u7edf\u8ba1\u91cf\u4e0e\u62bd\u6837\u5206\u5e03</li> <li> [7.x] \u53c2\u6570\u4f30\u8ba1</li> <li> [8.x] \u5047\u8bbe\u68c0\u9a8c</li> </ul>"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap01/","title":"[1.x] \u6982\u7387\u8bba\u7684\u57fa\u672c\u6982\u5ff5","text":"<p> \u7ea6 1144 \u4e2a\u5b57  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 4 \u5206\u949f</p>"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap01/#\u6837\u672c\u7a7a\u95f4\u4e0e\u968f\u673a\u4e8b\u4ef6","title":"\u6837\u672c\u7a7a\u95f4\u4e0e\u968f\u673a\u4e8b\u4ef6","text":"<p>\u968f\u673a\u8bd5\u9a8c(random experiment)\u7684\u7279\u70b9\uff1a</p> <ol> <li>\u53ef\u4ee5\u590d\u73b0\uff1b</li> <li>\u6bcf\u6b21\u8bd5\u9a8c\u7684\u7ed3\u679c\u4e0d\u5b9a\uff0c\u4f46\u4e8b\u5148\u53ef\u4ee5\u77e5\u9053\u8bd5\u9a8c\u7684\u6240\u6709\u53ef\u80fd\u7ed3\u679c\uff1b</li> </ol> <p>\u800c\u968f\u673a\u8bd5\u9a8c\u7684\u6240\u6709\u53ef\u80fd\u7ed3\u679c\u6784\u6210\u7684\u96c6\u5408\u4e3a\u6837\u672c\u7a7a\u95f4(sample space)\uff0c\u8bb0\u4e3a \\(S\\)\uff0c\u5176\u4e2d\u7684\u6bcf\u4e00\u4e2a\u5143\u7d20\u4e3a\u6837\u672c\u70b9(sample point)\u3002\u800c\u6837\u672c\u7a7a\u95f4\u7684\u4efb\u4e00\u5b50\u96c6\u6210\u4e3a\u968f\u673a\u4e8b\u4ef6(random event)\uff0c\u7b80\u79f0\u4e8b\u4ef6\u3002</p> <ul> <li>\u7279\u522b\u7684\uff0c\u53ea\u542b\u6709\u4e00\u4e2a\u6837\u672c\u7684\u5b50\u96c6\u79f0\u4e3a\u57fa\u672c\u4e8b\u4ef6\u3002</li> </ul> <p>\u4e8b\u4ef6\u7684\u76f8\u4e92\u5173\u7cfb</p> <p> \u4ece\u5de6\u5230\u53f3\u5206\u522b\uff1a\u5305\u542b | \u548c\u4e8b\u4ef6 | \u79ef\u4e8b\u4ef6 | \u9006\u4e8b\u4ef6 | \u5dee\u4e8b\u4ef6</p> <ul> <li>\u4e24\u4e92\u9006\u4e8b\u4ef6\u53c8\u79f0\u5bf9\u7acb\u4e8b\u4ef6\u3002</li> <li>\u82e5 \\(AB=\\varnothing\\)\uff0c\u5219\u79f0\u4e24\u4e8b\u4ef6\u4e0d\u76f8\u5bb9\uff08\u6216\u4e92\u65a5\uff09</li> <li>\u82e5 \\(A\\subset B \\;and\\;B\\subset A\\)\uff0c\u5219\u79f0\u4e24\u4e8b\u4ef6\u76f8\u7b49</li> </ul> <p>\u5176\u4e2d\uff0c\u548c\u3001\u4ea4\u3001\u9006\u4e8b\u4ef6\u6709\u5982\u4e0b\u8fd0\u7b97\u89c4\u5f8b\uff1a</p> <ul> <li>\u4ea4\u6362\u5f8b\uff1a\\(A\\cup B=B\\cup A\\;,\\;A\\cap B=B\\cap A\\)\uff1b</li> <li>\u7ed3\u5408\u5f8b\uff1a\\(A\\cup(B\\cup C)=(A\\cup B)\\cup C\\;,\\;A(BC)=(AB)C\\)\uff1b</li> <li>\u5206\u914d\u5f8b\uff1a\\(A(B\\cup C)=(AB)\\cup(AC)\\;,\\;(AB)\\cup C=(A\\cup C)(B\\cup C)\\)\uff1b</li> <li>\u5bf9\u5076\u5f8b / \u5fb7\u6469\u6839\u5b9a\u5f8b(De Morgan's law)\uff1a\\(\\overline{\\bigcup\\limits^n_{j=1}A_j}=\\bigcap\\limits^n_{j=1}\\overline{A_j}\\;,\\;\\overline{\\bigcap\\limits^n_{j=1}A_j}=\\bigcup\\limits^n_{j=1}\\overline{A_j}\\)\uff1b</li> </ul> <p>\u4e32\u8054\u7cfb\u7edf\u4e0e\u5e76\u8054\u7cfb\u7edf\uff1a</p> <ul> <li>\u4e32\u8054\u7cfb\u7edf\uff1a\\(A=\\bigcap\\limits_{i=1}^nA_i\\)</li> <li>\u5e76\u8054\u7cfb\u7edf\uff1a\\(A=\\bigcup\\limits_{i=1}^nA_i\\)</li> </ul>"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap01/#\u9891\u7387\u4e0e\u6982\u7387","title":"\u9891\u7387\u4e0e\u6982\u7387","text":"<p>\u9891\u7387 = \u9891\u6570 / \u8bd5\u9a8c\u603b\u6b21\u6570</p> <p>\u82e5\u6837\u672c\u7a7a\u95f4 \\(S\\) \u4e2d\u7684\u4efb\u4e00\u4e8b\u4ef6 \\(A\\)\uff0c\u5b9a\u4e49\u6982\u7387 \\(P(A)\\) \u6ee1\u8db3\u4ee5\u4e0b\u4e09\u6761\u516c\u7406\uff1a</p> <ol> <li>\u975e\u8d1f\u6027 \\(P(A)\\geq0\\)\uff1b</li> <li>\u89c4\u8303\u6027 / \u6b63\u5219\u6027 \\(P(S)=1\\)\uff1b</li> <li>\u53ef\u5217\u53ef\u52a0\u6027\uff1a\u5bf9\u4e8e \\(S\\) \u4e2d\u4e0d\u76f8\u5bb9\u7684\u4e8b\u4ef6 \\(A_i\\)\uff0c\u6709 \\(P(\\bigcup\\limits^{+\\infty}_{j=1}A_j)=\\sum\\limits_{j=1}^{+\\infty}P(A_j)\\)\uff1b</li> </ol> <p>\u7531\u6b64\u5f97\u5230\u5982\u4e0b\u51e0\u6761\u6982\u7387\u7684\u6027\u8d28\uff1a</p> <ol> <li>\u5bf9\u4e8e\u6709\u9650\u4e2a\u4e24\u4e24\u4e0d\u76f8\u5bb9\u7684\u4e8b\u4ef6\u7684\u548c\u4e8b\u4ef6\uff0c\u6709 \\(P(\\bigcup\\limits^n_{j=1}A_j)=\\sum\\limits_{j=1}^nP(A_j)\\)\uff1b</li> <li>\\(P(A)=1-P(\\overline A)\\)\uff1b\u7279\u522b\u7684\uff0c\u53ef\u4ee5\u5f97\u5230 \\(P(\\varnothing)=0\\)\uff1b</li> <li>\u5f53 \\(A\\supset B\\) \u65f6\uff0c\\(P(A-B) = P(A)-P(B)\\) \u4e14 \\(P(A)\\geq P(B)\\)\uff1b</li> <li>\u6982\u7387\u7684\u52a0\u6cd5\u516c\u5f0f\uff1a\\(P(A\\cup B)=P(A)+P(B)-P(AB)\\)\uff1b\u63a8\u5e7f\u5373\u5bb9\u65a5\u539f\u7406\uff1b</li> <li>\u52a0\u6cd5\u516c\u5f0f\u7684\u63a8\u8bba\uff1a\\(P(A\\cup B)\\leq P(A)+P(B)\\)\uff1b</li> </ol>"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap01/#\u7b49\u53ef\u80fd\u6982\u578b","title":"\u7b49\u53ef\u80fd\u6982\u578b","text":"<p>\u5982\u679c\u968f\u673a\u4e8b\u4ef6\u6ee1\u8db3\uff1a</p> <ol> <li>\\(S\\) \u4e2d\u6837\u672c\u70b9\u6570\u6709\u9650\uff1b</li> <li>\\(\\forall i,j \\in\\{1,2,...,n\\},\\;P(e_i) = P(e_j)\\)\uff0c\u5373\u7b49\u53ef\u80fd\uff1b</li> </ol> <p>\u5219\u8be5\u8bd5\u9a8c\u95ee\u9898\u4e3a\u7b49\u53ef\u80fd\u6982\u578b\uff08\u53e4\u5178\u6982\u578b\uff09\u6709\u5982\u4e0b\u6027\u8d28\uff1a\u82e5\u603b\u4e8b\u4ef6\u4e2a\u6570\u4e3a \\(N\\)\uff0c\\(A\\) \u4e3a \\(n\\) \u4e2a\u57fa\u672c\u4e8b\u4ef6\u7684\u548c\u4e8b\u4ef6\uff0c\u5219 \\(P(A)=\\frac{n}{N}\\)\u3002</p>"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap01/#\u6761\u4ef6\u6982\u7387","title":"\u6761\u4ef6\u6982\u7387","text":"<p>\u5982\u679c \\(P(B)&gt;0\\)\uff0c\u90a3\u4e48\u5b9a\u4e49\u5728 \\(B\\) \u53d1\u751f\u7684\u6761\u4ef6\u4e0b \\(A\\) \u53d1\u751f\u7684\u6761\u4ef6\u6982\u7387(contidional probability)\u4e3a\uff1a\\(P(A|B)=\\frac{P(AB)}{P(B)}\\)</p> <p>\u6761\u4ef6\u6982\u7387\u662f\u5728\u65b0\u7684\u6837\u672c\u7a7a\u95f4\u4e0b\u7684\u6982\u7387\u5ea6\u91cf\uff0c\u5b83\u6ee1\u8db3\u6982\u7387\u7684\u5b9a\u4e49\u548c\u6027\u8d28\u3002</p> <p>\u5b9a\u4e49\u5b8c\u5907\u4e8b\u4ef6\u7ec4\u4e3a \\(S\\) \u7684\u4e00\u4e2a\u5212\u5206 \\(B_1,B_2,...,B_n\\)\uff0c\u5b83\u6ee1\u8db3\u5982\u4e0b\u6027\u8d28\uff1a</p> <ol> <li>\\(B_iB_j=\\varnothing,i,j,...,n,i\\not=j\\)\uff1b</li> <li>\\(\\bigcup\\limits^n_{i=1}B_i=S\\)\uff1b</li> </ol> <p>\u8bbe \\(S\\) \u4e3a\u4e00\u6837\u672c\u7a7a\u95f4\uff0c\\(A\\) \u4e3a\u8be5\u8bd5\u9a8c\u7684\u4e8b\u4ef6\uff0c\\(\\{B_i\\}\\) \u4e3a \\(S\\) \u7684\u4e00\u4e2a\u5212\u5206\uff0c\u5219\u6709\uff1a</p> <ul> <li>\u82e5 \\(A_1,...,A_n,...\\) \u4e92\u4e0d\u76f8\u5bb9\uff0c\u5219 \\(P(\\cup_{n=1}^{\\infty}A_n|B)=\\sum\\limits_{n=1}^{\\infty}P(A_n|B)\\)\uff1b</li> <li>\u4e58\u6cd5\u516c\u5f0f\uff1a\u5f53 \\(P(A)\\not=0\\;\\,\\;P(B)\\not=0\\) \u65f6\uff0c\u6709 \\(P(AB)=P(A)*P(B|A)=P(B)*P(A|B)\\)\uff1b</li> <li>\u5168\u6982\u7387\u516c\u5f0f\uff1a\\(P(A)=\\sum\\limits_{j=1}^nP(B_j)P(A|B_j)\\)\uff1b</li> <li>\u8d1d\u53f6\u65af\u516c\u5f0f\uff1a\\(P(B_k|A)=\\frac{P(B_kA)}{P(A)}=\\frac{P(B_k)P(A|B_k)}{\\sum\\limits_{j=1}^nP(B_j)P(A|B_j)}\\)\uff1b</li> <li>\u5176\u4e2d\uff0c\u6211\u4eec\u79f0 \\(P(B_j)\\) \u8fd9\u79cd\u4e8b\u5148\u77e5\u9053\u7684\u6982\u7387\u4e3a\u5148\u9a8c\u6982\u7387\uff1b\u800c \\(P(B_j|A)\\) \u8fd9\u79cd\uff0c\u5f53\u4e8b\u4ef6 \\(A\\) \u53d1\u751f\u540e\u9700\u8981\u4fee\u6b63 \\(B_j\\) \u7684\u6982\u7387\u6210\u4e3a\u540e\u9a8c\u6982\u7387\u3002</li> </ul>"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap01/#\u4e8b\u4ef6\u72ec\u7acb\u6027\u4e0e\u72ec\u7acb\u8bd5\u9a8c","title":"\u4e8b\u4ef6\u72ec\u7acb\u6027\u4e0e\u72ec\u7acb\u8bd5\u9a8c","text":"<p>\u8bbe \\(A,B\\) \u4e3a\u4e24\u4e2a\u968f\u673a\u4e8b\u4ef6\uff0c\u82e5\u6709 \\(P(AB)=P(A)*P(B)\\)\uff0c\u5219 \\(A,B\\) \u76f8\u4e92\u72ec\u7acb(independent)\u5176\u5b9e\u9645\u610f\u4e49\u662f\uff0c\u4e8b\u4ef6 \\(A\\) \u7684\u53d1\u751f\u4e0e\u4e8b\u4ef6 \\(B\\) \u7684\u53d1\u751f\u4e92\u4e0d\u5f71\u54cd\u3002\u90a3\u4e48\u5c31\u6709\u7ed3\u8bba\uff1a\\(while\\;\\;P(AB)=P(A)*P(B)\\;\\;,\\;\\;P(A|B)=P(A)\\)\uff1b</p> <p>\u5f53\u51fa\u73b0\u4e24\u4e2a\u4ee5\u4e0a\u7684\u968f\u673a\u4e8b\u4ef6\u65f6\uff0c\u5982\u4e09\u4e2a\u968f\u673a\u4e8b\u4ef6 \\(A,B,C\\)\uff0c\u5f53\uff1a\\(P(AB)=P(A)*P(B)\\;,\\;P(AC)=P(A)*P(C)\\;,\\;P(BC)=P(B)*P(C)\\) \u90fd\u6210\u7acb\uff0c\u5219\u79f0\u4e8b\u4ef6 \\(A,B,C\\) \u4e24\u4e24\u72ec\u7acb\uff1b\u5982\u679c\u540c\u65f6\u8fd8\u6ee1\u8db3\uff1a\\(P(ABC)=P(A)P(B)P(C)\\) \u5219\u79f0\u4e8b\u4ef6 \\(A,B,C\\) \u76f8\u4e92\u72ec\u7acb\u3002</p> <ul> <li>\u663e\u7136\u6709\uff1a\u76f8\u4e92\u72ec\u7acb \\(\\Rightarrow\\) \u4e24\u4e24\u72ec\u7acb</li> </ul> <p>\u66f4\u666e\u904d\u7684\uff1a\u5b9a\u4e49 \\(\\{A_i\\}\\) \u76f8\u4e92\u72ec\u7acb\u5f53\u4e14\u4ec5\u5f53 \\(\\forall{i_j},\\;P(\\prod_{j=1}^k A_{i_j})=\\prod_{j=1}^kP(A_{i_j})\\)</p> <p>\u72ec\u7acb\u8bd5\u9a8c\u4e0e\u91cd\u590d\u8bd5\u9a8c\uff1a</p> <ul> <li>\u72ec\u7acb\u8bd5\u9a8c\u5404\u4e2a\u8bd5\u9a8c\u7ed3\u679c\u4e92\u4e0d\u5f71\u54cd\uff1b</li> <li>\u91cd\u590d\u8bd5\u9a8c\u7684\u6bcf\u4e00\u6b21\u5b50\u8bd5\u9a8c\u90fd\u5728\u76f8\u540c\u60c5\u51b5\u4e0b\u8fdb\u884c\uff1b</li> </ul>"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap02/","title":"[2.x] \u968f\u673a\u53d8\u91cf\u53ca\u5176\u6982\u7387\u5206\u5e03","text":"<p> \u7ea6 1166 \u4e2a\u5b57  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 4 \u5206\u949f</p> <p>\u968f\u673a\u53d8\u91cf\u662f\u5b9a\u4e49\u5728\u6837\u672c\u7a7a\u95f4 \\(S\\) \u4e0a\u7684\u5b9e\u503c\u5355\u503c\u51fd\u6570\u3002\u5e38\u7528\u5927\u5199\u5b57\u6bcd \\(X,Y,Z\\) \u6765\u8868\u793a\u968f\u673a\u53d8\u91cf\uff0c\u7528\u5c0f\u5199\u5b57\u6bcd \\(x,y,z\\) \u8868\u793a\u5176\u53d6\u503c\u3002</p>"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap02/#\u79bb\u6563\u578b\u968f\u673a\u53d8\u91cf","title":"\u79bb\u6563\u578b\u968f\u673a\u53d8\u91cf","text":"<p>\u79bb\u6563\u578b\u968f\u673a\u53d8\u91cf(discrete random variable)\u5982\u679c\u968f\u673a\u53d8\u91cf\u53d6\u6709\u9650\u4e2a\u6216\u53ef\u5217\u4e2a\u503c\uff0c\u5219\u6b64\u968f\u673a\u53d8\u91cf\u4e3a\u79bb\u6563\u578b\u968f\u673a\u53d8\u91cf\uff0c\u800c\u82e5\u5176\u53ef\u80fd\u53d6\u503c\u4e3a \\(\\{x_i\\}\\)\uff0c\u5219\u79f0 \\(P\\{X=x_k\\}=p_k\\;,\\;k=1,2,...\\) \u4e3a \\(X\\) \u7684\u6982\u7387\u5206\u5e03\u5f8b(probability mass function)\uff0c\u4e5f\u53ef\u4ee5\u7528\u5217\u8868\u7684\u65b9\u5f0f\u8868\u8fbe\u3002\u56e0\u4e3a\u6837\u672c\u7a7a\u95f4 \\(S=\\{X=x_1,X=x_2,\\,...\\,,X=x_n\\,...\\,\\}\\) \u4e2d\u5404\u6837\u672c\u70b9\u4e24\u4e24\u4e0d\u76f8\u5bb9\uff0c\u6240\u4ee5\uff1a\\(1=P(S)=\\sum\\limits_{i=1}^{+\\infty}P(X=x_i)=\\sum\\limits_{i=1}^{+\\infty}{p_i}\\)</p>"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap02/#\u4e24\u70b9\u5206\u5e03","title":"\u4e24\u70b9\u5206\u5e03","text":"<p>\u5982\u679c\u968f\u673a\u53d8\u91cf \\(X\\) \u7684\u6982\u7387\u5206\u5e03\u5f8b\u4e3a\uff1a</p> <p> x 0 1 P 1-p p </p> \\[ P\\{X=k\\}=p^k(1-p)^{1-k}\\;,\\;\\;\\;k=0\\;or\\;1 \\] <p>\u5219\u79f0 \\(X\\) \u4e3a\u670d\u4ece\u53c2\u6570\u4e3a \\(p\\) \u7684 \\(0-1\\) \u5206\u5e03\uff0c\u4e5f\u79f0\u4e3a\u4e24\u70b9\u5206\u5e03\uff0c\u5e76\u8bb0\u4e3a \\(X\\sim B(1,p)\\) \u6216\u8005 \\(X\\sim 0-1(p)\\)</p> <p>\u5b9a\u4e49\u4f2f\u52aa\u5229(Bernoulli)\u8bd5\u9a8c\u4e3a\uff1a\u5728 \\(n\\) \u6b21\u72ec\u7acb\u91cd\u590d\u8bd5\u9a8c\u4e2d\uff0c\u6bcf\u6b21\u53ea\u6709 \\(A\\) \u548c \\(\\overline A\\) \u4e24\u79cd\u7ed3\u679c\uff0c\u4e14\u6982\u7387\u4e0d\u53d8\uff0c\u5219\u8fd9\u4e00\u7cfb\u5217\u8bd5\u9a8c\u4e3a\u4f2f\u52aa\u5229\u8bd5\u9a8c\u3002</p>"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap02/#\u4e8c\u9879\u5206\u5e03","title":"\u4e8c\u9879\u5206\u5e03","text":"<p>\u82e5\u968f\u673a\u53d8\u91cf \\(X\\) \u8868\u793a \\(n\\) \u91cd\u8d1d\u52aa\u529b\u5b9e\u9a8c\u4e2d\u4e8b\u4ef6A\u53d1\u751f\u7684\u6b21\u6570\uff0c\u5176\u6982\u7387\u5206\u5e03\u5f8b\u4e3a\uff1a</p> \\[ P\\{X=k\\}={\\rm C}_n^kp^k(1-p)^{n-k}\\;,\\;\\;k=0,1,2,...,n \\] <p>\u5219\u79f0 \\(X\\) \u4e3a\u670d\u4ece\u53c2\u6570\u4e3a \\((n,p)\\) \u7684\u4e8c\u9879\u5206\u5e03(binomial distribution)\uff0c\u5e76\u8bb0\u4e3a \\(X\\sim B(n,p)\\)</p> <p>\u6839\u636e\u4e8c\u9879\u5f0f\u5b9a\u7406\uff0c\u4e8c\u9879\u5206\u5e03\u6709\u5982\u4e0b\u6027\u8d28\uff1a</p> \\[ \\sum\\limits_{k=0}^n{\\rm C}_n^kp^k(1-p)^{n-k}=1 \\] <ul> <li>\u5982\u679c\u9047\u5230\u6765\u81ea\u4e8e\u4e24\u70b9\u5206\u5e03\u7684\u603b\u4f53\u7684\uff0c\u5bb9\u91cf\u4e3a \\(n\\) \u7684\u6837\u672c\u7684\u5747\u503c \\(\\overline X\\)\uff0c\u5219\u6709 \\(n\u00b7\\overline X=\\sum\\limits_{i=1}^n X_i \\sim B(n,p)\\)</li> </ul>"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap02/#\u6cca\u677e\u5206\u5e03","title":"\u6cca\u677e\u5206\u5e03","text":"<p>\u5982\u679c\u968f\u673a\u53d8\u91cf \\(X\\) \u7684\u6982\u7387\u5206\u5e03\u5f8b\u4e3a\uff1a</p> \\[ P(X=k)=\\frac{e^{-\\lambda}\\lambda^k}{k!}\\;,\\;\\;\\;k=0,1,2,... \\] <p>\u5176\u4e2d \\(\\lambda &gt; 0\\)\uff0c\u5219\u79f0 \\(X\\) \u670d\u4ece\u53c2\u6570\u4e3a \\(\\lambda\\) \u7684\u6cca\u677e\u5206\u5e03(Poisson distribution)\uff0c\u8bb0\u505a \\(X \\sim P(\\lambda)\\)</p> <p>\u5f53 \\(n\\) \u8db3\u591f\u5927\uff0c\\(p\\) \u5145\u5206\u5c0f(\u4e00\u822c\u8981\u6c42 \\(p&lt;0.1\\))\uff0c\u4e14 \\(np\\) \u4fdd\u6301\u9002\u5f53\u5927\u5c0f\u65f6\uff0c\u53c2\u6570\u4e3a \\((n,p)\\) \u7684\u4e8c\u9879\u5206\u5e03\u53ef\u4ee5\u7528\u6cca\u677e\u5206\u5e03\u8fd1\u4f3c\u63cf\u8ff0\uff0c\u5176\u4e2d \\(\\lambda = np\\)\uff0c\u5373\uff1a</p> \\[ {\\rm C}_n^kp^k(1-p)^{n-k} \\sim \\frac{e^{-\\lambda}\\lambda^k}{k!}\\;\\;\\;\\;\\;(n\\rightarrow\\infty,p&lt;\\varepsilon,\\lambda=np) \\]"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap02/#\u8d85\u51e0\u4f55\u5206\u5e03","title":"\u8d85\u51e0\u4f55\u5206\u5e03","text":"<p>\u5982\u679c\u968f\u673a\u53d8\u91cf \\(X\\) \u7684\u6982\u7387\u5206\u5e03\u5f8b\u4e3a\uff1a</p> \\[ P\\{X=k\\}=\\frac{{\\rm C}_a^k{\\rm C}_b^{n-k}}{{\\rm C}_{a+b}^n}\\;,\\;\\;\\;k=l_1,l_1+1,...,l_2 \\] <p>\u5219\u79f0 \\(X\\) \u4e3a\u670d\u4ece\u8d85\u51e0\u4f55\u5206\u5e03(hypergeometric distribution)\uff0c\u5e76\u8bb0\u4e3a \\(X\\sim H(n,a,p)\\)</p> <ul> <li>\u5176\u610f\u4e49\u4e3a\uff0c\u5982\uff1a\\(a\\) \u767d\u7403\uff0c\\(b\\) \u7ea2\u7403\uff0c\u53d6 \\(n\\) \u6b21\u5f97\u5230 \\(X\\) \u4e2a\u767d\u7403</li> </ul> <p>\u5982\u679c\u968f\u673a\u53d8\u91cf \\(X\\) \u7684\u6982\u7387\u5206\u5e03\u5f8b\u4e3a\uff1a</p> \\[ P\\{X=k\\}=p(1-p)^{k-1}\\;,\\;\\;\\;k=1,2,... \\] <p>\u5219\u79f0 \\(X\\) \u4e3a\u670d\u4ece\u53c2\u6570\u4e3a \\(p\\) \u7684\u51e0\u4f55\u5206\u5e03(geometric distribution)\u3002</p>"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap02/#\u8fde\u7eed\u578b\u968f\u673a\u53d8\u91cf","title":"\u8fde\u7eed\u578b\u968f\u673a\u53d8\u91cf","text":"<p>\u5b9a\u4e49\uff1a\u8bbe \\(X\\) \u4e3a\u968f\u673a\u53d8\u91cf\uff0c\\(x\\) \u4e3a\u4efb\u610f\u5b9e\u6570\uff0c\u51fd\u6570 \\(F(x)=P\\{X\\leq x\\}\\) \u4e3a\u968f\u673a\u53d8\u91cf \\(X\\) \u7684\u6982\u7387\u5206\u5e03\u51fd\u6570\uff0c\u7b80\u79f0\u4e3a\u5206\u5e03\u51fd\u6570(distribution function)\u3002\uff08\u79bb\u6563\u968f\u673a\u53d8\u91cf\u540c\u6837\u53ef\u4ee5\u6709\u5206\u5e03\u51fd\u6570\uff09</p> <p>\u5219\u6709\u4ee5\u4e0b\u7ed3\u8bba\uff1a</p> \\[ P\\{x_1&lt;X\\leq x_2\\}=P\\{X\\leq x_2\\}-P\\{X\\leq x_1\\}=F(x_2)-F(x_1) \\] <p>\u5f53 \\(X\\) \u4e3a\u79bb\u6563\u578b\u968f\u673a\u53d8\u91cf\u65f6\uff0c\u8bbe \\(X\\) \u7684\u6982\u7387\u5206\u5e03\u5f8b\u4e3a \\(P\\{X=x_i\\}=p_i\\;,\\;\\;i=1,2,...\\)\uff0c\u5219 \\(X\\) \u7684\u5206\u5e03\u51fd\u6570\u4e3a\uff1a</p> \\[ F(x) = P\\{X\\leq x\\}=\\sum\\limits_{x_i\\leq x}P\\{X=x_i\\} \\] <p>\u5173\u4e8e \\(F(x)\\) \u6709\u4ee5\u4e0b\u7ed3\u8bba\uff1a</p> <ol> <li>\\(F(x)\\) \u5355\u8c03\u4e0d\u51cf\uff1b</li> <li>\\(0\\leq F(x) \\leq 1\\) \u4e14 \\(F(-\\infty)=0\\)\uff0c\\(F(+\\infty)=1\\)\uff1b</li> <li>\\(F(x)\\) \u53f3\u8fde\u7eed\uff0c\u5373 \\(F(x+0)=F(x)\\)\uff1b</li> <li>\\(P(a&lt;X\\leq b)=F(b)-F(a)\\)\uff1b</li> </ol> <p>\u5982\u679c\u5bf9\u4e8e\u968f\u673a\u53d8\u91cf \\(X\\)\uff0c\u5176\u5206\u5e03\u51fd\u6570\u4e3a \\(F(x)\\)\uff0c\u82e5\u5b58\u5728\u4e00\u4e2a\u975e\u8d1f\u7684\u5b9e\u51fd\u6570 \\(f(x)\\)\uff0c\u4f7f\u5bf9\u4e8e\u4efb\u610f\u5b9e\u6570 \\(x\\)\uff0c\u6709\uff1a</p> \\[ F(x) = \\int_{-\\infty}^{x}f(t)dt \\] <p>\u5219\u79f0 \\(X\\) \u4e3a\u8fde\u7eed\u578b\u968f\u673a\u53d8\u91cf\uff0c\u5e76\u4e14\u79f0 \\(f(x)\\) \u4e3a \\(X\\) \u7684\u6982\u7387\u5bc6\u5ea6\u51fd\u6570(probability density function)\uff0c\u7b80\u79f0\u4e3a\u5bc6\u5ea6\u51fd\u6570\u3002</p> <p>\u5173\u4e8e \\(f(x)\\) \u6709\u4ee5\u4e0b\u7ed3\u8bba\uff1a</p> <ol> <li>\\(f(x) \\geq 0\\)\uff1b</li> <li>\\(\\int_{-\\infty}^{\\infty}f(x)dx=1\\)\uff1b</li> <li>\\(\\forall x_1,x_2\\in \\mathbf{R}\\;\\;(x_1&lt;x_2)\\;,\\;\\;P\\{x_1&lt;X\\leq x_2\\}=F(x_2)-F(x_1)=\\int^{x_2}_{x_1}f(t)dt\\)\uff1b</li> <li>\u5728\\(f(x)\\) \u7684\u8fde\u7eed\u70b9 \\(x\\) \u5904\uff0c\\(F'(x)=f(x)\\)</li> <li>\\(P\\{X=a\\} = 0\\)\uff0c\u5373\u8fde\u7eed\u578b\u968f\u673a\u53d8\u91cf\u4efb\u53d6\u4e00\u4e2a\u5b9a\u503c\u7684\u6982\u7387\u4e3a\u96f6\uff0c\u56e0\u6b64\u8fde\u7eed\u578b\u968f\u673a\u53d8\u91cf\u843d\u5728\u5f00\u533a\u95f4\u4e0e\u76f8\u5e94\u95ed\u533a\u95f4\u4e0a\u7684\u6982\u7387\u76f8\u7b49\uff1b</li> </ol>"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap02/#\u5747\u5300\u5206\u5e03","title":"\u5747\u5300\u5206\u5e03","text":"<p>\u8bbe\u968f\u673a\u53d8\u91cf \\(X\\) \u5c31\u6709\u5bc6\u5ea6\u51fd\u6570\uff1a</p> \\[ f(x)=\\begin{cases} \\frac{1}{b-a}, &amp; x\\in(a,b) \\\\[1ex] 0, &amp; \\text{else} \\end{cases} \\] <p>\u5219\u79f0 \\(X\\) \u670d\u4ece\u533a\u95f4 \\((a,b)\\) \u4e0a\u7684\u5747\u5300\u5206\u5e03\uff0c\u5e76\u8bb0\u4e3a \\(X\\sim U(a,b)\\)</p> <p>\u800c\u5f97\u5230\u5bf9\u5e94\u7684\u5206\u5e03\u51fd\u6570\u4e3a\uff1a</p> \\[ F(x)=\\begin{cases} 0, &amp; x&lt;a \\\\[1ex] \\frac{x-a}{b-a}, &amp; a\\leq x&lt;b \\\\[1ex] 1, &amp; x\\geq b \\end{cases} \\] <p></p>"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap02/#\u6307\u6570\u5206\u5e03","title":"\u6307\u6570\u5206\u5e03","text":"<p>\u82e5\u968f\u673a\u53d8\u91cf \\(X\\) \u5177\u6709\u5bc6\u5ea6\u51fd\u6570\uff1a</p> \\[ f(x)=\\begin{cases} \\lambda e^{-\\lambda x}, &amp; x&gt;0 \\\\[1ex] 0\uff0c&amp; x\\leq0  \\end{cases} \\] <p>\u4e5f\u6709\u5730\u65b9\u5199\u6210\u8fd9\u6837\uff1a</p> \\[ f(x)=\\begin{cases} \\frac{1}{\\theta} e^{-\\frac{1}{\\theta} x}, &amp; x&gt;0 \\\\[1ex] 0\uff0c&amp; x\\leq0 \\end{cases} \\] <p>\u5176\u4e2d \\(\\lambda &gt; 0\\)\uff0c\u5219\u79f0 \\(X\\) \u670d\u4ece\u53c2\u6570\u4e3a \\(\\lambda\\) \u7684\u6307\u6570\u5206\u5e03(exponential distribution)\uff0c\u8bb0\u4e3a \\(X\\sim E(\\lambda)\\)</p> <p>\u6307\u6570\u5206\u5e03\u5bf9\u5e94\u7684\u5206\u5e03\u51fd\u6570\u4e3a\uff1a</p> \\[ F(x)=\\int_{-\\infty}^{x}f(t)\\mathrm{d}t= \\begin{cases} 1-e^{-\\lambda x}, &amp; x&gt;0 \\\\[1ex] 0\uff0c&amp; x\\leq0 \\end{cases} \\] <p>\u6307\u6570\u5206\u5e03\u5177\u6709\u65e0\u8bb0\u5fc6\u6027\uff0c\u5373 \\(P(X&gt;s | X&gt;t_0)=P(X&gt;s-t_0)\\)\u3002</p>"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap02/#\u6b63\u6001\u5206\u5e03","title":"\u6b63\u6001\u5206\u5e03","text":"<p>\u5982\u679c\u968f\u673a\u53d8\u91cf \\(X\\) \u5177\u6709\u5bc6\u5ea6\u51fd\u6570\uff1a</p> \\[ f(x)=\\frac{1}{\\sqrt{2\\pi}\\sigma}e^{-\\frac{(x-\\mu)^2}{2\\sigma^2}}\\;, \\;\\;\\; |x|&lt;+\\infty \\] <p>\u5176\u4e2d \\(\\sigma&gt;0\\;,\\;|\\mu|&lt;+\\infty\\) \u4e3a\u5e38\u6570\uff0c\u5219\u79f0 \\(X\\) \u670d\u4ece\u53c2\u6570\u4e3a \\((\\mu,\\sigma)\\) \u7684\u6b63\u6001\u5206\u5e03(normal distribution / Gauss distribution)\uff0c\u6216\u8005\u79f0 \\(X\\) \u4e3a\u6b63\u6001\u53d8\u91cf\uff0c\u8bb0\u4e3a \\(X\\sim N(\\mu,\\sigma^2)\\)\u3002</p> <p>\u5176\u5bf9\u5e94\u7684\u5206\u5e03\u51fd\u6570\u4e3a\uff1a</p> \\[ F(x)=\\int_{-\\infty}^{x}\\frac{1}{\\sqrt{2\\pi}\\sigma}e^{-\\frac{(t-\\mu)^2}{2\\sigma^2}}dt \\] <p>\u5728\u4e0a\u9762\u51fa\u73b0\u7684\u5f0f\u5b50\u4e2d\uff0c\\(\\mu\\) \u4e3a\u4f4d\u7f6e\u53c2\u6570\uff0c\u51b3\u5b9a\u4e86\u5206\u5e03\u56fe\u50cf\u7684\u5bf9\u79f0\u8f74\u4f4d\u7f6e\uff1b\\(\\sigma\\) \u4e3a\u5c3a\u5ea6\u53c2\u6570\uff0c\u51b3\u5b9a\u4e86\u5f62\u72b6\uff0c\\(\\sigma\\) \u8d8a\u5c0f\uff0c\u56fe\u50cf\u8d8a\u96c6\u4e2d\u3002</p> <p>\u7279\u522b\u7684\uff0c\u5f53 \\(\\mu=0\\;,\\;\\sigma=1\\) \u65f6\uff0c\u5982\u679c\u8bb0\u8fd9\u65f6\u7684\u6b63\u592a\u53d8\u91cf\u4e3a \\(Z\\)\uff0c\u5373 \\(Z\\sim N(0,1)\\) \u5219\u5b83\u670d\u4ece\u6807\u51c6\u6b63\u6001\u5206\u5e03(standard normal distribution)\u3002\u5219\u5176\u5bc6\u5ea6\u51fd\u6570\u4e3a\uff1a</p> \\[ \\varphi(x)=\\frac{1}{\\sqrt{2\\pi}}e^{-\\frac{x^2}{2}}\\;, \\;\\;\\;|x|&lt;+\\infty \\] <p>\u5219\u5bf9\u5e94\u7684\u5206\u5e03\u51fd\u6570\u4e3a\uff1a</p> \\[ \\Phi(x) = \\int_{-\\infty}^{x}\\frac{1}{\\sqrt{2\\pi}}e^{-\\frac{t^2}{2}}dt \\] <ul> <li>\u5219\u663e\u7136\u6709 \\(\\Phi(x)+\\Phi(-x)=1\\)</li> <li>\u7136\u800c\u7531\u4e8e\u5176\u65e0\u6cd5\u8ba1\u7b97\uff0c\u6240\u4ee5\u6211\u4eec\u9700\u8981\u67e5\u8868\u83b7\u5f97\u5177\u4f53\u503c\uff0c\u4ee5\u4e0b\u4e3a\u6807\u51c6\u6b63\u6001\u5206\u5e03\u8868\uff1a<ul> <li>https://www.shuxuele.com/data/standard-normal-distribution-table.html</li> <li>https://www.chip1stop.com/sp/knowledge/019_normal-distribution-table_zh</li> </ul> </li> </ul> <p>\u800c\u5bf9\u4e8e\u4e0d\u662f\u6807\u51c6\u6b63\u6001\u5206\u5e03\u7684\u6b63\u6001\u5206\u5e03\uff0c\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u7ebf\u6027\u53d8\u6362\uff08\u6807\u51c6\u5316\uff09\u6765\u8f6c\u6362\u4e3a\u6807\u51c6\u6b63\u6001\u5206\u5e03\uff1a</p> <ul> <li>\u82e5 \\(X\\sim N(\\mu,\\sigma^2)\\)\uff0c\u5219 \\(P\\{a&lt;X&lt;b\\}= P\\{\\frac{a-\\mu}{\\sigma}&lt; \\frac{X-\\mu}{\\sigma} &lt; \\frac{b-\\mu}{\\sigma} \\}=\\Phi(\\frac{b-\\mu}{\\sigma})-\\Phi(\\frac{a-\\mu}{\\sigma})\\)</li> <li>\u7279\u522b\u7684\uff1a\u82e5 \\(X\\sim N(\\mu,\\sigma^2)\\)\uff0c\u5219 \\(P\\{|X-\\mu|&lt;k\\sigma\\} = \\Phi(k)-\\Phi(-k)=2\\Phi(k)-1\\)</li> <li>\\(3\\sigma\\) \u6cd5\u5219</li> </ul>"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap02/#\u968f\u673a\u53d8\u91cf\u51fd\u6570\u7684\u5206\u5e03","title":"\u968f\u673a\u53d8\u91cf\u51fd\u6570\u7684\u5206\u5e03","text":"<p>\u5982\u679c\uff1a</p> <ul> <li>\\(X\\) \u4e3a\u8fde\u7eed\u578b\u968f\u673a\u53d8\u91cf\uff0c\u4e14\u5176\u5bc6\u5ea6\u51fd\u6570\u4e3a \\(f_X(x)\\)\uff1b</li> <li>\u968f\u673a\u53d8\u91cf \\(Y=g(X)\\)\uff1b</li> <li>\u51fd\u6570 \\(y=g(x)\\) \u4e3a\u4e00\u4e25\u683c\u5355\u8c03\uff08\u589e/\u51cf\uff09\u51fd\u6570\uff0c\u5e76\u4e14\u53ef\u5fae\uff1b</li> </ul> <p>\u5219\u8bb0 \\(y=g(x)\\) \u7684\u53cd\u51fd\u6570\u4e3a \\(x=h(y)\\)\uff0c\u5f97\u5230 \\(Y\\) \u7684\u5bc6\u5ea6\u51fd\u6570\u4e3a\uff1a</p> \\[ f_Y(y)=\\begin{cases} f_X(h(y))\u00b7|h'(y)|\\;, &amp; y\\in D,\\\\[1ex] 0, &amp; y\\not\\in D \\end{cases} \\] <ul> <li>\u5176\u4e2d \\(D\\) \u4e3a \\(y=g(x)\\) \u7684\u503c\u57df\u3002</li> </ul> <p>\u6709\u5173\u6b63\u6001\u5206\u5e03\u7684\u91cd\u8981\u7ed3\u8bba\uff1a</p> <p>\u82e5 \\(X\\sim N(\\mu,\\sigma^2)\\)\uff0c\u5219 \\(Y=aX+b \\sim N(a\\mu+b,a^2\\sigma^2)\\)</p> <ul> <li>\u6807\u51c6\u5316\uff1a\u7279\u522b\u7684\uff0c\u82e5 \\(X\\sim N(\\mu,\\sigma^2)\\)\uff0c\u5219 \\(\\frac{X-\\mu}{\\sigma}\\sim N(0,1)\\)\uff1b</li> <li>\u5373\u6b63\u6001\u5206\u5e03\u7684\u968f\u673a\u53d8\u91cf\u7ebf\u6027\u53d8\u6362\u540e\u6b63\u6001\u6027\u4e0d\u53d8\uff1b</li> </ul>"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap03/","title":"[3.x] \u591a\u5143\u968f\u673a\u53d8\u91cf\u53ca\u5176\u5206\u5e03","text":"<p> \u7ea6 406 \u4e2a\u5b57  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 1 \u5206\u949f</p>"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap03/#\u4e8c\u7ef4\u79bb\u6563\u578b\u968f\u673a\u53d8\u91cf","title":"\u4e8c\u7ef4\u79bb\u6563\u578b\u968f\u673a\u53d8\u91cf","text":""},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap03/#\u8054\u5408\u5206\u5e03\u5f8b","title":"\u8054\u5408\u5206\u5e03\u5f8b","text":"<ul> <li>\u8054\u5408\u5206\u5e03\u5f8b\uff08Joint Mass Function\uff09 \\(P(X=x_i,Y=y_j)=p_{ij}, \\; i,j=1,2,\\dots\\)\uff1b</li> </ul>"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap03/#\u8fb9\u9645\u5206\u5e03\u5f8b","title":"\u8fb9\u9645\u5206\u5e03\u5f8b","text":"<ul> <li>\u8fb9\u9645\u5206\u5e03\u5f8b\uff08Marginal Mass Function\uff09\u662f\u8054\u5408\u5206\u5e03\u5f8b\u7684\u884c/\u5217\u6c42\u548c\uff1b</li> <li>\\(P(X=x_i)=P(X=x_1,\\bigcup_{j=1}^{\\infty}(Y=y_j))=\\sum_{j=1}^{\\infty}p_{ij}:=p_{i\u00b7}\\)\uff1b</li> <li>\\(P(Y=y_j)=P(\\bigcup_{j=1}^{\\infty}(X=x_i),Y=y_j)=\\sum_{i=1}^{\\infty}p_{ij}:=p_{\u00b7j}\\)\uff1b</li> </ul>"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap03/#\u6761\u4ef6\u5206\u5e03\u5f8b","title":"\u6761\u4ef6\u5206\u5e03\u5f8b","text":"<ul> <li>\u6761\u4ef6\u5206\u5e03\u5f8b\uff08Conditional Mass Function\uff09 \\(P\\{X=x_i|Y=y_j\\}=\\frac{P(X=x_i,Y=y_j)}{P(Y=y_j)}=\\frac{p_{ij}}{p_{\u00b7j}}\\;\\;i,j=1,2,...\\)\uff1b</li> <li>\\(P\\{X&lt;x|Y&lt;y\\}=\\frac{P\\{X&lt;x,Y&lt;y\\}}{P\\{Y&lt;y\\}}\\)\uff0c\u7136\u540e\u6839\u636e\u8054\u5408\u5206\u5e03\u5f8b\u548c\u8fb9\u9645\u5206\u5e03\u5f8b\u8bfb\u8868\u8ba1\u7b97\uff1b</li> </ul>"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap03/#\u4e8c\u7ef4\u968f\u673a\u53d8\u91cf\u7684\u5206\u5e03\u51fd\u6570","title":"\u4e8c\u7ef4\u968f\u673a\u53d8\u91cf\u7684\u5206\u5e03\u51fd\u6570","text":""},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap03/#\u8054\u5408\u5206\u5e03\u51fd\u6570","title":"\u8054\u5408\u5206\u5e03\u51fd\u6570","text":"<p>\\(F(x,y)=P\\{X\\leq x,Y\\leq y\\}\\) \u4e3a \\((X,Y)\\) \u7684\u8054\u5408\u6982\u7387\u5206\u5e03\u51fd\u6570\uff0c\u7b80\u79f0\u8054\u5408\u5206\u5e03\u51fd\u6570\uff08Joint Distribution Function\uff09\uff0c\u5176\u5177\u6709\u5982\u4e0b\u6027\u8d28\uff1a</p> <ol> <li>\u56fa\u5b9a\u5176\u4e2d\u4e00\u4e2a\u53d8\u91cf\uff0c\u5219\u8be5\u4e8c\u5143\u51fd\u6570\u5173\u4e8e\u53e6\u5916\u4e00\u4e2a\u53d8\u91cf\u5355\u8c03\u4e0d\u51cf\uff1b</li> <li>\\(0\\leq F(x,y)\\leq 1\\)\uff0c\u4e14 \\(F(x,-\\infty)=F(-\\infty,y)=F(-\\infty,-\\infty)=0\\;,\\;F(+\\infty,+\\infty)=1\\)\uff1b</li> <li>\\(F(x,y)\\) \u5173\u4e8e \\(x\\) \u548c \\(y\\) \u5206\u522b\u53f3\u8fde\u7eed\uff08\u79bb\u6563\uff09\uff1b</li> <li>\\(x_1&lt;x_2\\;,\\;y_1&lt;y_2\\) \u65f6\uff0c\u6709\uff1a \\(P\\{x_1&lt;X\\leq x_2\\;,\\;y_1&lt;Y\\leq y_2\\}=F(x_2,y_2)-F(x_1,y_2)-F(x_2,y_1)+F(x_1,y_1)\\geq 0\\)</li> </ol> <ul> <li>Tips\uff1a\u8003\u8651\u51e0\u4f55\u610f\u4e49\uff01</li> </ul>"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap03/#\u8fb9\u9645\u5206\u5e03\u51fd\u6570","title":"\u8fb9\u9645\u5206\u5e03\u51fd\u6570","text":"<p>\\(F_X(x)=P\\{X\\leq x\\}=P\\{X\\leq x ,Y&lt;+\\infty\\}=F(x,+\\infty)=\\int_{-\\infty}^{+\\infty}f(x,y)dy\\) \u4e3a \\(X\\) \u5173\u4e8e\u8054\u5408\u5206\u5e03\u51fd\u6570 \\(F(x,y)\\) \u7684\u8fb9\u9645\u5206\u5e03\u51fd\u6570\uff08Marginal Distribution Function\uff09\u3002</p> <ul> <li>\u5bf9 \\(y\\) \u6765\u8bf4\u540c\u7406\u3002</li> </ul>"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap03/#\u6761\u4ef6\u5206\u5e03\u51fd\u6570","title":"\u6761\u4ef6\u5206\u5e03\u51fd\u6570","text":"<p>\\(F_{Y|X}(y|x)=P\\{Y\\leq y | X = x\\}=\\frac{P\\{Y\\leq y,X=x\\}}{P\\{X=x\\}}\\) \u4e3a \\(\\{ X=x \\}\\) \u6761\u4ef6\u4e0b \\(Y\\) \u7684\u6761\u4ef6\u5206\u5e03\u51fd\u6570\uff08Conditional Distribution Function\uff09\u3002</p> <p>\u8fdb\u4e00\u6b65\u63a8\u5e7f\uff0c\u82e5 \\(P(X=x)=0\\)\uff0c\u4f46\u5bf9\u4efb\u610f\u7ed9\u5b9a\u7684 \\(\\epsilon\\)\uff0c\\(P(x&lt;X\\leq x+\\epsilon)&gt;0\\)\uff0c\u5219\u5728 \\(\\{ X=x \\}\\) \u6761\u4ef6\u4e0b\uff0c\\(Y\\) \u7684\u6761\u4ef6\u5206\u5e03\u51fd\u6570\u4e3a \\(F_{Y|X}(y|x)=\\lim_{\\epsilon \\rarr 0^+}P\\{Y\\leq y|x&lt;X\\leq x+\\epsilon \\}\\)\uff0c\u4ecd\u8bb0\u4e3a \\(P\\{Y\\leq y | X = x\\}\\)\u3002</p>"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap03/#\u4e8c\u7ef4\u8fde\u7eed\u578b\u968f\u673a\u53d8\u91cf","title":"\u4e8c\u7ef4\u8fde\u7eed\u578b\u968f\u673a\u53d8\u91cf","text":""},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap03/#\u8054\u5408\u5bc6\u5ea6\u51fd\u6570","title":"\u8054\u5408\u5bc6\u5ea6\u51fd\u6570","text":"<p>\u8bbe\u4e8c\u5143\u968f\u673a\u53d8\u91cf \\((X,Y)\\) \u7684\u8054\u5408\u5206\u5e03\u51fd\u6570\u4e3a \\(F(x,y)\\)\uff0c\u82e5\u5b58\u5728\u4e8c\u5143\u51fd\u6570 \\(f(x,y)\\geq 0\\)\uff0c\u5219\u5bf9\u4e8e\u4efb\u610f\u7684\u5b9e\u6570 \\(x\\)\uff0c\\(y\\) \u6709 \\(F(x,y)=\\int_{-\\infty}^x\\int_{-\\infty}^yf(u,v)\\mathrm{d}u\\mathrm{d}v\\)\uff0c\u5219\u79f0 \\((X,Y)\\) \u4e3a\u4e8c\u7ef4\u8fde\u7eed\u578b\u968f\u673a\u53d8\u91cf\uff08Bivariate Continuous Random Variable\uff09\uff0c\u79f0 \\(f(x,y)\\) \u4e3a \\((X,Y)\\) \u7684\u8054\u5408\u6982\u7387\u5bc6\u5ea6\u51fd\u6570\uff08Joint Probability Density Function\uff09\uff0c\u7b80\u79f0\u4e3a\u8054\u5408\u5bc6\u5ea6\u51fd\u6570\u3002 \u5176\u5177\u6709\u4ee5\u4e0b\u6027\u8d28\uff1a</p> <ol> <li>\\(f(x,y)\\geq 0\\)\uff1b</li> <li>\\(F(+\\infty,+\\infty)=\\int_{-\\infty}^{+\\infty}\\int_{-\\infty}^{+\\infty}f(u,v)\\mathrm{d}u\\mathrm{d}v=1\\)\uff1b</li> <li>\u5728 \\(f(x,y)\\) \u7684\u8fde\u7eed\u70b9 \\((x,y)\\) \u4e0a\u6709 \\(\\frac{\\partial^2F(x,y)}{\\partial x\\partial y}=f(x,y)\\)\uff1b</li> <li>\\((X,Y)\\) \u843d\u5165 \\(xOy\\) \u5e73\u9762\u4efb\u610f\u533a\u57df \\(D\\) \u7684\u6982\u7387\u4e3a\uff1a\\(P\\{(X,Y)\\in D\\}=\\iint \\limits_{D} f(x,y)\\mathrm{d}x\\mathrm{d}y\\)\uff1b</li> <li>\u7531\u4e8e\u5176\u51e0\u4f55\u610f\u4e49\u4e3a\u843d\u5728\u4ee5 \\(D\\) \u4e3a\u5e95\uff0c\u4ee5\u66f2\u9762 \\(z=f(x,y)\\) \u4e3a\u9876\u9762\u7684\u67f1\u4f53\u4f53\u79ef\uff0c\u6240\u4ee5\u5f53 \\(D\\) \u9762\u79ef\u4e3a \\(0\\) \u65f6\u6982\u7387\u4e3a \\(0\\)\uff1b</li> <li><code>eg</code>\uff1a\\(P(X=1,Y=1)=0\\)\uff0c\\(P(X+Y=1)=0\\)\uff0c\\(P(X^2+Y^2=1)\\not =0\\)\uff1b</li> </ol>"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap03/#\u8fb9\u9645\u5bc6\u5ea6\u51fd\u6570","title":"\u8fb9\u9645\u5bc6\u5ea6\u51fd\u6570","text":"<p>\\(f_X(x)=\\int_{-\\infty}^{+\\infty}f(x,y)dy\\) \u4e3a\u8fb9\u9645\u6982\u7387\u5bc6\u5ea6\u51fd\u6570\uff08Marginal Probability Density Function\uff09\uff0c\u7b80\u79f0\u8fb9\u9645\u5bc6\u5ea6\u51fd\u6570\u3002</p>"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap03/#\u6761\u4ef6\u5bc6\u5ea6\u51fd\u6570","title":"\u6761\u4ef6\u5bc6\u5ea6\u51fd\u6570","text":"<p>\u5728\u7ed9\u5b9a \\(\\{X=x\\}\\) \u7684\u6761\u4ef6\u4e0b\uff0c\\(Y\\) \u7684\u6761\u4ef6\u6982\u7387\u5bc6\u5ea6\u51fd\u6570\uff08Conditional Prob-ability Density Function\uff09\u4e3a \\(f_{Y|X}(y|x)=\\frac{\\int^y_{-\\infty}f(x,v)\\mathrm{d}v}{f_X(x)}=\\frac{f(x,y)}{f_X(x)}\\;,\\;\\;f_X(x)\\not= 0\\)\uff0c\u7b80\u79f0\u6761\u4ef6\u5bc6\u5ea6\u51fd\u6570\u3002</p> <ul> <li>\u5bf9 \\(Y\\) \u6765\u8bf4\u540c\u7406\u3002</li> </ul>"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap03/#\u4e8c\u7ef4\u5747\u5300\u5206\u5e03\u4e0e\u4e8c\u7ef4\u6b63\u6001\u5206\u5e03","title":"\u4e8c\u7ef4\u5747\u5300\u5206\u5e03\u4e0e\u4e8c\u7ef4\u6b63\u6001\u5206\u5e03","text":"<p>\u5747\u5300\u5206\u5e03</p> <p>\u5982\u679c\u4e8c\u5143\u968f\u673a\u53d8\u91cf \\((X,Y)\\) \u5728\u4e8c\u7ef4\u6709\u754c\u533a\u95f4 \\(D\\) \u4e0a\u53d6\u503c\uff0c\u4e14\u5177\u6709\u8054\u5408\u5bc6\u5ea6\u51fd\u6570\uff1a</p> \\[ f(x,y)= \\begin{cases} \\frac{1}{\\text{Area of } D},&amp;(x,y)\\in D\\\\[1ex] 0,&amp;\\text{else} \\end{cases} \\] <p>\u5219\u79f0 \\((X,Y)\\) \u670d\u4ece \\(D\\) \u4e0a\u7684\u5747\u5300\u5206\u5e03\u3002\u5f97\u5230\uff1a</p> \\[ P\\{(X,Y)\\in D\\}=\\frac{\\text{Area of }D_1}{\\text{Area of }D}\\;,\\;\\;\\text{while }D_1\\subset D \\] <p>\u6b63\u6001\u5206\u5e03</p> <p>\u5982\u679c\u4e8c\u5143\u968f\u673a\u53d8\u91cf \\((X,Y)\\) \u5177\u6709\u8054\u5408\u5bc6\u5ea6\u51fd\u6570\uff1a</p> \\[ f(x,y)= \\frac{1}{ 2 \\pi \\sigma_1 \\sigma_2 \\sqrt{1-\\rho^2} } \\exp \\{   \\frac{-1}{ 2(1-\\rho^2) }   [     \\frac{ (x-\\mu)^2 }{ \\sigma_1^2 } - 2\\rho\\frac{ (x-\\mu_1)(y-\\mu_2) }{ \\sigma_1\\sigma_2 } + \\frac{ (y-\\mu_2)^2 }{ \\sigma_2^2 }   ] \\} \\] <p>\u4e14\u6709 \\(|\\mu_1|&lt;+\\infty\\)\uff0c\\(|\\mu_2|&lt;+\\infty\\)\uff0c\\(\\sigma_1&gt;0\\)\uff0c\\(\\sigma_2&gt;0\\)\uff0c\\(|\\rho|&lt;1\\)</p> <p>\u5219\u79f0 \\((X,Y)\\) \u670d\u4ece\u53c2\u6570\u4e3a \\((\\mu_1,\\mu_2,\\sigma_1^2,\\sigma_2^2,\\rho)\\) \u7684\u4e8c\u5143\u6b63\u6001\u5206\u5e03\uff08Bivariate Normal Distribution\uff09\uff0c\u8bb0\u505a \\((X,Y)\\sim N(\\mu_1,\\mu_2,\\sigma_1^2,\\sigma_2^2,\\rho)\\)\u3002</p> <ul> <li>\u4e8c\u7ef4\u6b63\u6001\u5206\u5e03\u7684\u4e24\u4e2a\u8fb9\u9645\u5206\u5e03\u90fd\u662f\u5bf9\u5e94\u53c2\u6570\u7684\u4e00\u7ef4\u6b63\u6001\u5206\u5e03\uff0c\u4e0e \\(\\rho\\) \u65e0\u5173\u3002</li> </ul>"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap03/#\u968f\u673a\u53d8\u91cf\u7684\u72ec\u7acb\u6027","title":"\u968f\u673a\u53d8\u91cf\u7684\u72ec\u7acb\u6027","text":"<p>\u5982\u679c\u5bf9\u4e8e\u4efb\u610f\u7684\u4e24\u4e2a\u5b9e\u6570\u96c6\u5408\\(D_1,D_2\\)\uff0c\u6709\\(P\\{X\\in D_1,Y\\in D_2\\}=P\\{X\\in D_1\\}\u00b7P\\{Y\\in D_2\\}\\)\uff0c\u5219\u79f0\u968f\u673a\u53d8\u91cf\\(X,Y\\)\u76f8\u4e92\u72ec\u7acb\uff0c\u5373\\(X,Y\\)\u72ec\u7acb\u3002\u5373\u540c\u65f6\u6709\\(P\\{X\\leq x,Y\\leq y\\}=P\\{X\\leq x\\}\u00b7P\\{Y\\leq y\\}\\)\uff0c\u5373\\(F(x,y)=F_X(x)\u00b7F_Y(y)\\)\u65f6\uff0c\\(X,Y\\)\u72ec\u7acb\u3002</p>"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap03/#\u5377\u79ef\u516c\u5f0f","title":"\u5377\u79ef\u516c\u5f0f","text":"<p>\u5f53 \\(X\\) \u548c \\(Y\\) \u76f8\u4e92\u72ec\u7acb\u65f6\uff0c\\(Z=X+Y\\) \u7684\u6761\u4ef6\u4e0b\uff1a</p> <ol> <li> <p>\\(F_Z(z) = \\iint \\limits_{x+y\\leq z}f(x,y)\\mathrm{d}x\\mathrm{d}y=\\int_{-\\infty}^{+\\infty}[\\int_{-\\infty}^{z-x}f(x,u-x)\\mathrm{d}y]\\mathrm{d}x = \\int_{-\\infty}^{+\\infty}[\\int_{-\\infty}^{z}f(x,u-x)\\mathrm{d}u]\\mathrm{d}x=\\int_{-\\infty}^{z}[\\int_{-\\infty}^{+\\infty}f(x,u-x)\\mathrm{d}x]\\mathrm{d}u =\\int_{-\\infty}^{z}f_Z(u)\\mathrm{d}y\\)\uff1b</p> </li> <li> <p>\u5176\u5bc6\u5ea6\u51fd\u6570\u516c\u5f0f\u79f0\u4e3a\u5377\u79ef\u516c\u5f0f\uff1a\\(f_X*f_Y=\\int_{-\\infty}^{+\\infty}f_X(x)f_Y(z-x)\\mathrm{d}x=\\int_{-\\infty}^{+\\infty}f_X(z-y)f_Y(y)\\mathrm{d}y\\)\uff1b</p> </li> </ol> <p>\\(M=max(X,Y)\\;\\;and\\;\\;N=min(X,Y)\\) \u7684\u5206\u5e03\uff1a</p> <ul> <li>\\(F_{max}(z)=P(M\\leq z)=P(X\\leq z,Y\\leq z)\\xlongequal{\\text{X,Y independent}}P(X\\leq z)P(Y\\leq z)=F_X(z)F_Y(z)\\)\uff1b</li> <li>\\(F_{min}(z)=P(N\\leq z)=1-P(N&gt;z)=1-P(X&gt;z,Y&gt;z)\\xlongequal{\\text{X,Y independent}}1-P(X&gt;z)P(Y&gt;z)=1-(1-F_X(z))(1-F_Y(z))\\)\uff1b</li> </ul>"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap04/","title":"[4.x] \u968f\u673a\u53d8\u91cf\u7684\u6570\u5b57\u7279\u5f81","text":"<p> \u7ea6 1668 \u4e2a\u5b57  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 6 \u5206\u949f</p> <p>\u8bbe\u79bb\u6563\u968f\u673a\u53d8\u91cf\\(X\\)\u7684\u6982\u7387\u5206\u5e03\u7387\u4e3a\\(P\\{X=x_i\\}=p_i,\\;\\;i=1,2,...\\)\uff0c\u82e5\u7ea7\u6570\\(\\sum_{i=1}^{+\\infty}=|x_i|p_i&lt;+\\infty\\)\uff08\u7edd\u5bf9\u6536\u655b\uff09\uff0c\u5219\u79f0\u7ea7\u6570\\(\\sum_{i=1}^{+\\infty}x_ip_i\\)\u4e3a\\(X\\)\u7684\u6570\u5b66\u671f\u671b\uff08Mathematical Expectation\uff09\u6216\u5747\u503c\uff08Mean\uff09\uff0c\u7b80\u79f0\u4e3a\u671f\u671b\uff0c\u8bb0\\(E(X)=\\sum_{i=1}^{+\\infty}x_ip_i\\)\u3002\u5982\u679c\\(\\sum_{i=1}^{+\\infty}=|x_i|p_i=+\\infty\\)\u5219\u79f0\u968f\u673a\u53d8\u91cf\\(X\\)\u7684\u6570\u5b66\u671f\u671b\u4e0d\u5b58\u5728\u3002</p> <p>\u8bbe\u8fde\u7eed\u968f\u673a\u53d8\u91cf\\(X\\)\u7684\u5bc6\u5ea6\u51fd\u6570\u4e3a\\(f(x)\\)\uff0c\u82e5\\(\\int^{+\\infty}_{-\\infty}|x|f(x)\\mathrm{d} x&lt;+\\infty\\)\uff0c\u5219\u79f0\u79ef\u5206\\(\\int^{+\\infty}_{-\\infty}xf(x)\\mathrm{d} x\\)\u4e3a\\(X\\)\u7684\u6570\u5b66\u671f\u671b\u6216\u5747\u503c\uff0c\u7b80\u79f0\u4e3a\u671f\u671b\uff0c\u8bb0\\(E(X)=\\int^{+\\infty}_{-\\infty}xf(x)\\mathrm{d} x\\)\u3002\u5982\u679c\\(\\int^{+\\infty}_{-\\infty}|x|f(x)\\mathrm{d} x=+\\infty\\)\u5219\u79f0\u968f\u673a\u53d8\u91cf\\(X\\)\u7684\u6570\u5b66\u671f\u671b\u4e0d\u5b58\u5728\u3002</p> <p>\u6cca\u677e\u5206\u5e03\u7684\u6570\u5b66\u671f\u671b\u8bbe\u968f\u673a\u53d8\u91cf\\(X\\)\u670d\u4ece\u6cca\u677e\u5206\u5e03\\(P(\\lambda)\\;(\\lambda&gt;0)\\)\uff0c\u5219\uff1a\\(E(X)=\\sum_{k=0}^{+\\infty}k\u30fb P\\{X=k\\}=\\sum_{k=0}^{+\\infty}k\u30fb\\frac{\\lambda^{k}}{k!}e^{-\\lambda}=\\lambda\\sum_{k=1}^{+\\infty}\\frac{\\lambda^{k-1}}{(k-1)!}e^{-\\lambda}=\\lambda\\) \u7531\u6b64\u5f0f\u53ef\u77e5\uff0c\u5df2\u77e5\u6cca\u677e\u5206\u5e03\u7684\u6570\u5b66\u671f\u671b\u53ef\u4ee5\u786e\u5b9a\u6cca\u677e\u5206\u5e03\u3002</p> <p>\u6307\u6570\u5206\u5e03\u7684\u6570\u5b66\u671f\u671b\u8bbe\u968f\u673a\u53d8\u91cf\\(X\\)\u670d\u4ece\u6307\u6570\u5206\u5e03\\(E(\\lambda)\\;(\\lambda&gt;0)\\)\uff0c\u5219\uff1a\\(E(X)=\\int_{-\\infty}^{+\\infty}xf(x)\\mathrm{d}x=\\int_{0}^{+\\infty}x\\lambda e^{-\\lambda x}\\mathrm{d}x=-\\int_{0}^{+\\infty}x\\mathrm{d}e^{-\\lambda x}\\\\=-(xe^{-\\lambda x})\\big|_{0}^{+\\infty}+\\int_{0}^{+\\infty}e^{-\\lambda x}\\mathrm{d}x=\\frac{1}{\\lambda}\\) \u7531\u6b64\u5f0f\u53ef\u77e5\uff0c\u5df2\u77e5\u6307\u6570\u5206\u5e03\u7684\u6570\u5b66\u671f\u671b\u53ef\u4ee5\u786e\u5b9a\u6307\u6570\u5206\u5e03\u3002</p> <p>\u6807\u51c6\u6b63\u6001\u5206\u5e03\u7684\u6570\u5b66\u671f\u671b\u8bbe\u968f\u673a\u53d8\u91cf\\(X\\)\u670d\u4ece\u6807\u51c6\u6b63\u6001\u5206\u5e03\\(N(0,1)\\)\uff0c\u6ce8\u610f\u5230\u5176\u7684\u5bc6\u5ea6\u51fd\u6570\uff1a\\(\\varphi(x)=\\frac{1}{\\sqrt{2\\pi}}e^{-x^2/2},\\;x\\in \\R\\)\u4e3a\u5076\u51fd\u6570\uff0c\u90a3\u4e48\\(x\\varphi(x)\\)\u662f\u5947\u51fd\u6570\uff0c\u6240\u4ee5\\(E(x)=0\\)</p> <p>\u5bf9\u4e8e\u968f\u673a\u53d8\u91cf\u51fd\u6570\uff0c\u53ea\u9700\u8981\u5c06\u5b9a\u4e49\u4e2d\\(x_i\\)\u6362\u4e3a\\(g(x_i)\\)\u5373\u53ef\uff0c\u5f53\u7136\u9700\u8981\u4fdd\u8bc1\u671f\u671b\u5b58\u5728\u3002\u800c\u9664\u4e86\u5b9a\u4e49\u8ba1\u7b97\uff0c\u4e5f\u6709\u4e00\u4e9b\u6027\u8d28\u53ef\u4ee5\u7b80\u5316\u8ba1\u7b97\u3002</p> <p>\u6570\u5b66\u671f\u671b\u7684\u6027\u8d28\uff1a</p> <ol> <li>\u82e5\\(C\\)\u662f\u5e38\u6570\uff0c\u5219\\(E(C) = C\\)\uff1b</li> <li>\u8bbe\\(X\\)\u662f\u968f\u673a\u53d8\u91cf\uff0c\\(C\\)\u662f\u5e38\u6570\uff0c\u5219\\(E(C\u30fbX)=C\u30fbE(X)\\)\uff1b</li> <li>\u8bbe\\(X,Y\\)\u662f\u4e24\u4e2a\u968f\u673a\u53d8\u91cf\uff0c\u5219\\(E(X+Y)=E(X)+E(Y)\\)\uff1b</li> <li>\u8fd9\u4e00\u6027\u8d28\u53ef\u4ee5\u63a8\u5e7f\u5230\u4efb\u610f\u6709\u9650\u4e2a\u968f\u673a\u53d8\u91cf\u7ebf\u6027\u7ec4\u5408\u7684\u60c5\u51b5\uff1a\\(E(\\sum^n_i{c_i\u30fbX_i})=\\sum^n_i c_i\u30fbE(X_i)\\)\uff1b</li> <li>\u4e0a\u8ff0\u4e09\u6761\u5408\u5e76\u8d77\u6765\u5c31\u662f\\(E(aX+bY+c)=aE(X)+bE(Y)+c\\)\uff1b</li> <li>\u8bbe\\(X,Y\\)\u662f\u76f8\u4e92\u72ec\u7acb\u7684\u968f\u673a\u53d8\u91cf\uff0c\u5219\\(E(X\u30fbY)=E(X)\u30fbE(Y)\\)\uff0c\u4f46\u9006\u547d\u9898\u4e0d\u6210\u7acb\uff1b</li> <li>\u8fd9\u4e00\u6027\u8d28\u53ef\u4ee5\u63a8\u5e7f\u5230\u4efb\u610f\u6709\u9650\u4e2a\u968f\u673a\u53d8\u91cf\uff1a\\(E(\\prod_i^nX_i)=\\prod_i^nE(X_i)\\)\uff1b</li> </ol> <p>\u8bbe\\(X\\)\u4e3a\u968f\u673a\u53d8\u91cf\uff0c\u82e5\\(E\\{[X-E(X)]^2\\}\\)\u5b58\u5728\uff0c\u5219\u79f0\u5176\u4e3a\\(X\\)\u7684\u65b9\u5dee\uff0c\u8bb0\u4f5c\\(Var(X)\\)\u6216\\(D(X)\\)\uff0c\u5373\\(Var(X)=E\\{[X-E(X)]^2\\}\\)\u3002\u8bb0\\(\\delta(X)=\\sqrt{(Var(X))}\\)\u4e3a\\(X\\)\u7684\u6807\u51c6\u5dee\u6216\u5747\u65b9\u5dee\u3002</p> <p>\u6570\u5b66\u671f\u671b\u5b58\u5728\u662f\u65b9\u5dee\u5b58\u5728\u7684\u5fc5\u8981\u4f46\u4e0d\u5145\u5206\u5b58\u5728\u3002</p> <p>\u65b9\u5dee\u523b\u753b\u4e86\\(X\\)\u53d6\u503c\u7684\u5206\u6563\u7a0b\u5ea6\uff1a</p> <ul> <li>\u82e5\\(X\\)\u53d6\u503c\u96c6\u4e2d\uff0c\u5219\\(Var(X)\\)\u8f83\u5c0f\uff1b</li> <li>\u82e5\\(X\\)\u53d6\u503c\u5206\u6563\uff0c\u5219\\(Var(X)\\)\u8f83\u5927\uff1b</li> </ul> <p>\u800c\u5176\u8ba1\u7b97\u65b9\u6cd5\u53ef\u4ee5\u5229\u7528\u671f\u671b\u7684\u6027\u8d28\uff0c\u8bb0\\(g(X)=(X-E(X))^2\\)\uff0c\u7136\u540e\u8ba1\u7b97\\(E(g(X))\\)\u3002\u5177\u4f53\u7684\uff1a</p> <ul> <li>\u79bb\u6563\u578b\uff1a\\(Var(X)=E\\{[X-E(X)]^2\\}=\\sum_{i=1}^{+\\infty}[x_i-E(X)]^2p_i\\)\uff1b</li> <li>\u8fde\u7eed\u578b\uff1a\\(Var(X)=E\\{[X-E(X)]^2\\}=\\int_{-\\infty}^{+\\infty}[x-E(X)]^2f(x)\\mathrm dx\\)\uff1b</li> <li>\u800c\u5229\u7528\u671f\u671b\u7684\u6027\u8d28\uff0c\u53ef\u4ee5\u5f97\u5230\\(Var(X)=E(X^2)-E^2(X)\\)\uff1b</li> </ul> <p>\u6cca\u677e\u5206\u5e03\u7684\u65b9\u5dee\\(\\because E(X^2)=E(X(X-1)+X)=E(X(X-1))+E(X)=\\sum_{k=0}^{\\infty}k(k-1)\\frac{\\lambda^ke^{-\\lambda}}{k!}+\\lambda=\\lambda^2+\\lambda\\\\ \\therefore Var(X)=E(X^2)+E^2(X)=\\lambda\\)</p> <p>\u6307\u6570\u5206\u5e03\u7684\u65b9\u5dee\\(\\because E(X^2)=\\int_{-\\infty}^{+\\infty}x^2f(x)\\mathrm dx=\\int_0^{+\\infty}x^2\\lambda e^{-\\lambda x}\\mathrm d x=-x^2e^{-\\lambda x}\\big|^{+\\infty}_0+\\int^{+\\infty}_{0}2xe^{-\\lambda x}\\mathrm dx=\\frac{2}{\\lambda^2}\\\\ \\therefore Var(X)=E(X^2)-E^2(X)=\\frac{1}{\\lambda^2}\\)</p> <p>\u65b9\u5dee\u7684\u6027\u8d28\uff1a</p> <ol> <li>\u82e5\\(C\\)\u662f\u5e38\u6570\uff0c\u5219\\(Var(C) = 0\\)\uff1b</li> <li>\u8bbe\\(X\\)\u662f\u968f\u673a\u53d8\u91cf\uff0c\\(C\\)\u662f\u5e38\u6570\uff0c\u5219\\(Var(C\u30fbX)=C^2\u30fbVar(X)\\)\uff1b</li> <li>\u8bbe\\(X,Y\\)\u662f\u4e24\u4e2a\u968f\u673a\u53d8\u91cf\uff0c\u5219\\(Var(X\\pm Y)=Var(X)+Var(Y)\\pm2E\\{[X-E(X)][Y-E(Y)]\\}\\\\=Var(X)+Var(Y)\\pm 2Cov(X,Y)\\)\uff1b</li> <li>\u7279\u522b\u7684\uff0c\u5982\u679c\\(X,Y\\)\u76f8\u4e92\u72ec\u7acb\uff0c\u5219\\(Var(X\\pm Y)=Var(X)+Var(Y)\\)\uff1b</li> <li>\u8fdb\u4e00\u6b65\u7684\uff0c\u5982\u679c\\(X_i\\;(i=1,2,...,n)\\)\u5f7c\u6b64\u72ec\u7acb\uff0c\u5219\\(Var(c_1X_1\\pm c_2X_2\\pm...\\pm c_nX_n)=c_1^2Var(X_1)+c_2^2Var(X_2)+...+c_n^2Var(X_n)\\)</li> <li>\u4e0a\u8ff0\u4e09\u6761\u5408\u5e76\u8d77\u6765\u5c31\u662f\\(Var(aX+bY+c)=a^2Var(X)+b^2Var(Y)\\)\uff1b</li> <li>\\(Var(X)\\leq E((X-c)^2)\\)\uff0c\u5e76\u4e14\u5f53\u4e14\u4ec5\u5f53\\(E(X)=c\\)\u65f6\u7b49\u53f7\u6210\u7acb\uff1b</li> <li>\\(Var(X)=0 \\;\\;\\;\\;\\;\\Leftrightarrow \\;\\;\\;\\;\\;P(X=c)=1 \\;\\;\\;and\\;\\;\\;c=E(X)\\)\uff1b</li> </ol> <p>\u53d8\u5f02\u7cfb\u6570\u53c8\u53eb\u201c\u6807\u51c6\u5dee\u7387\u201d\uff0c\u662f\u8861\u91cf\u8d44\u6599\u4e2d\u5404\u89c2\u6d4b\u503c\u53d8\u5f02\u7a0b\u5ea6\u7684\u53e6\u5916\u4e00\u4e2a\u6570\u5b57\u7279\u5f81\u3002\u53d8\u5f02\u7cfb\u6570\\(Cv(X)=\\frac{\\sqrt{Var(X)}}{E(X)}\\)\u540c\u6837\u63cf\u8ff0\u79bb\u6563\u7a0b\u5ea6\uff0c\u5b83\u53ef\u4ee5\u6d88\u9664\u5355\u4f4d\u6216\u5e73\u5747\u6570\u4e0d\u540c\u5bf9\u4e24\u4e2a\u6216\u591a\u4e2a\u8d44\u6599\u53d8\u5f02\u7a0b\u5ea6\u6bd4\u8f83\u7684\u5f71\u54cd\u3002</p> <p>\u968f\u673a\u53d8\u91cf\\(X,Y\\)\u7684\u534f\u65b9\u5dee\\(Cov(X,Y)=E\\{[X-E(X)][Y-E(Y)]\\}=E(XY)-E(X)E(Y)\\)</p> <p>\u968f\u673a\u53d8\u91cf\\(X,Y\\)\u7684\u76f8\u5173\u7cfb\u6570\\(\\rho _{_{XY}}=\\frac{Cov(X,Y)}{\\sqrt{Var(X)Var(Y)}}\\)</p> <p>\u534f\u65b9\u5dee\u7684\u6027\u8d28\uff1a</p> <ol> <li>\\(Cov(X,Y)=Cov(Y,X)\\)\uff1b</li> <li>\\(Cov(X,Y)=E(XY)-E(X)E(Y)\\)\uff1b</li> <li>\\(Cov(aX,bY)=abCov(X,Y)\\;,\\;\\;a,b\\in\\R\\)\uff1b</li> <li>\\(Cov(X+Y,Z)=Cov(X,Z)+Cov(Y,Z)\\)\uff1b</li> <li>\\(Cov(X,X)=Var(X)\\)\uff1b</li> <li>\\(Cov(c,Y)=E(cY)-E(c)E(Y)=0\\;,\\;\\;c\\in\\R\\)\uff1b</li> <li>\\(Cov(X+Y,X-Y)=Cov(X,X)-Cov(Y,Y)=Var(X)-Var(Y)\\)\uff1b</li> <li>\\(Cov(X^*,Y^*)=Cov(\\frac{X-E(X)}{\\sqrt{Var(X)}},\\frac{Y-E(Y)}{\\sqrt{Var(Y)}})=\\frac{Cov(X,Y)}{\\sqrt{Var(X)}\\sqrt{Var(Y)}}=\\rho_{_{XY}}\\)\uff1b</li> <li>\\(Cov(aX+bY,cX+dY)=acVar(X)+bdVar(Y)+(ad+bc)Cov(X,Y)\\)\uff1b</li> <li>\\(D(aX+bY)=a^2Var(X)+b^2Var(Y)+2abCov(X,Y)\\)\uff1b</li> </ol> <p>\u76f8\u5173\u7cfb\u6570\u7684\u6027\u8d28</p> <ol> <li>\\(|\\rho_{_{XY}}|\\leq 1\\)\uff1b</li> <li>\\(|\\rho_{_{XY}}|=1 \\;\\;\\; \\Leftrightarrow \\;\\;\\; \\exists a,b\\in \\R,\\;s.t.\\;P(Y=a+bX)=1|\\)\uff1b</li> <li>\\(\\rho_{_{XY}}=1\\)\u65f6\uff0c\\(b&gt;0\\)\uff1b</li> <li>\\(\\rho_{_{XY}}=-1\\)\u65f6\uff0c\\(b&lt;0\\)\uff1b</li> </ol> <p>\u76f8\u5173\u7cfb\u6570\\(\\rho_{_{XY}}\\)\u662f\u7528\u6765\u8868\u5f81\\(X,Y\\)\u4e4b\u95f4\u7ebf\u6027\u5173\u7cfb\u7d27\u5bc6\u7a0b\u5ea6\u7684\u91cf\uff1a</p> <ul> <li>\\(|\\rho_{_{XY}}|\\)\u6bd4\u8f83\u5927\u65f6\uff0c\u8bef\u5dee\u8f83\u5c0f\uff0c\u8868\u793a\\(X,Y\\)\u7ebf\u6027\u5173\u7cfb\u7684\u7a0b\u5ea6\u597d\uff1b</li> <li>\\(|\\rho_{_{XY}}|=1\\)\u65f6\uff0c\u8bef\u5dee\u4e3a\\(0\\)\uff0c\u8868\u793a\\(X,Y\\)\u4e4b\u95f4\u4ee5\u6982\u7387\\(1\\)\u5b58\u5728\u7ebf\u6027\u5173\u7cfb\uff1b</li> <li>\\(|\\rho_{_{XY}}|\\)\u6bd4\u8f83\u5c0f\u65f6\uff0c\u8bef\u5dee\u8f83\u5927\uff0c\u8868\u660e\\(X,Y\\)\u7ebf\u6027\u5173\u7cfb\u7684\u7a0b\u5ea6\u5dee\uff1b</li> <li>\\(\\rho_{_{XY}}&gt;0\\)\u65f6\uff0c\\(X,Y\\)\u6b63\u76f8\u5173\uff1b</li> <li>\\(\\rho_{_{XY}}&lt;0\\)\u65f6\uff0c\\(X,Y\\)\u8d1f\u76f8\u5173\uff1b</li> <li>\\(\\rho_{_{XY}}=0\\)\u65f6\uff0c\u79f0\\(X,Y\\)\u4e0d\u76f8\u5173\u6216\u96f6\u76f8\u5173\uff08\u4ec5\u4ec5\u5bf9\u4e8e\u7ebf\u6027\u5173\u7cfb\u6765\u8bf4\uff0c\u4e0e\u72ec\u7acb\u7684\u542b\u4e49\u4e0d\u540c\uff09\uff1b</li> <li>\u6b64\u65f6\u6709\uff1a</li> <li>\\(Cov(X,Y)=0\\)\uff1b</li> <li>\\(E(XY)=E(X)E(Y)\\)\uff1b</li> <li>\\(Var(X\\pm Y)=Var(X)+Var(Y)\\)\uff1b</li> <li>\u4e8e\u662f\u6709\u7ed3\u8bba\uff1a</li> </ul> <p>\\(X,Y\\text{\u4e92\u76f8\u72ec\u7acb} \\;\\; \\Rightarrow \\;\\; X,Y\\text{\u4e0d\u76f8\u5173}\\\\ X,Y\\text{\u4e0d\u72ec\u7acb}\\;\\;\\Leftarrow \\;\\;X,Y\\text{\u76f8\u5173}\\)</p> <p>\u591a\u5143\u968f\u673a\u53d8\u91cf\u7684\u6570\u5b57\u7279\u5f81\u8bbe\\(n\\)\u5143\u968f\u673a\u53d8\u91cf\\(X=(X_1,X_2,...,X_n)^T\\)\uff0c\u82e5\u6bcf\u4e00\u4e2a\u5206\u91cf\u7684\u6570\u5b66\u671f\u671b\u90fd\u5b58\u5728\uff0c\u5219\u79f0\\(E(X)=(E(X_1),E(X_2),...,E(X_n))^T\\)\u4e3a\\(n\\)\u5143\u968f\u673a\u53d8\u91cf\\(X\\)\u7684\u6570\u5b66\u671f\u671b\uff08\u5411\u91cf\uff09\u3002</p> <p>\u8bbe\\(n\\)\u7ef4\u968f\u673a\u53d8\u91cf\\(\\vec{X}=(X_1,X_2,...,X_n)^T\\)\uff0c\\(Cov(X_i,X_j)\\;\\;(i,j=1,2,...,n)\\)\u90fd\u5b58\u5728\uff0c\u5219\uff1a\\(\\begin{bmatrix}  Var(X_1) &amp; Cov(X_1,X_2) &amp; ... &amp; Cov(X_1,X_n)\\\\  Cov(X_2,X_1) &amp; Var(X_2) &amp; ... &amp; Cov(X_2,X_n)\\\\ ... &amp; ... &amp; ...  &amp; ... \\\\ Cov(X_n,X_1) &amp; Cov(X_n,X_2) &amp; ... &amp; Var(X_n) \\end{bmatrix}\\) \u79f0\u4e4b\u4e3a\\(\\vec{X}\\)\u7684\u534f\u65b9\u5dee\u77e9\u9635\u3002\u5b83\u662f\u4e00\u4e2a\u5bf9\u79f0\u7684\u975e\u8d1f\u5b9a\u77e9\u9635\u3002</p> <p>\\(n\\)\u7ef4\u6b63\u6001\u53d8\u91cf\u91cd\u8981\u6027\u8d28</p> <ol> <li>\\(n\\)\u7ef4\u6b63\u6001\u53d8\u91cf\\((X_1,X_2,...,X_n)\\)\u7684\u6bcf\u4e00\u4e2a\u5206\u91cf\\(X_i\\)\u90fd\u662f\u6b63\u6001\u53d8\u91cf\uff1b</li> <li>\u53cd\u4e4b\uff0c\u5982\u679c\\(X_i\\)\u90fd\u662f\u6b63\u6001\u53d8\u91cf\uff0c\u4e14\u76f8\u4e92\u72ec\u7acb\uff0c\u5219\\((X_1,X_2,...,X_n)\\)\u662f\\(n\\)\u7ef4\u6b63\u6001\u53d8\u91cf\uff1b</li> <li>\\(n\\)\u7ef4\u968f\u673a\u53d8\u91cf\\((X_1,X_2,...,X_n)\\)\u670d\u4ece\\(n\\)\u7ef4\u6b63\u6001\u5206\u5e03\u7684\u5145\u8981\u6761\u4ef6\u8bbe\u4e0d\u5168\u4e3a\\(0\\)\u7684\\(l_i\\)\u5e38\u6570\uff0c\u5747\u6709\\(\\sum_i^n l_iX_i\\)\u670d\u4ece\u4e00\u7ef4\u6b63\u6001\u5206\u5e03\uff1b</li> <li>\u82e5\\((X_1,X_2,...,X_n)\\)\u670d\u4ece\\(n\\)\u7ef4\u6b63\u6001\u5206\u5e03\uff0c\u8bbe\\(Y_1,Y_2,...,Y_k\\)\u662f\\(X_i\\)\u7684\u7ebf\u578b\u51fd\u6570\uff0c\u5219\\((Y_1,Y_2,...,Y_k)\\)\u4e5f\u670d\u4ece\u591a\u7ef4\u6b63\u6001\u5206\u5e03\uff1b</li> <li>\u82e5\\((X_1,X_2,...,X_n)\\)\u670d\u4ece\\(n\\)\u7ef4\u6b63\u6001\u5206\u5e03\uff0c\u5219\\(X_i\\)\u4e92\u76f8\u72ec\u7acb\u7684\u5145\u8981\u6761\u4ef6\u662f\\(X_i\\)\u4e24\u4e24\u4e0d\u76f8\u5173\uff1b</li> </ol>"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap05/","title":"[5.x] \u5927\u6570\u5b9a\u5f8b\u53ca\u4e2d\u5fc3\u6781\u9650\u5b9a\u7406","text":"<p> \u7ea6 1172 \u4e2a\u5b57  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 4 \u5206\u949f</p>"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap05/#\u4f9d\u6982\u7387\u6536\u655b","title":"\u4f9d\u6982\u7387\u6536\u655b","text":"<p>\u4f9d\u6982\u7387\u6536\u655b\u8bbe\\(\\{Y_n,n\\geq1\\}\\)\u4e3a\u4e00\u968f\u673a\u53d8\u91cf\u5e8f\u5217\uff0c\\(c\\)\u4e3a\u4e00\u5e38\u6570\u3002\u82e5\\(\\forall\\varepsilon&gt;0\\;\\;\\;s.t. \\;\\;\\lim_{n\\to+\\infty}P\\{|Y_n-c|\\geq\\varepsilon\\}=0\\)\uff0c\u5219\u79f0\\(\\{Y_n,n\\geq1\\}\\)\u4f9d\u6982\u7387\u6536\u655b(Convergence in Probability)\u4e8e\\(c\\)\uff0c\u8bb0\u505a\\(Y_n\\xrightarrow{P} c\\;,\\;\\;n\\to+\\infty\\)\u3002\u7b49\u4ef7\u7684\uff0c\u4e5f\u53ef\u4ee5\u5c06\u6761\u4ef6\u5199\u6210\\(\\forall\\varepsilon&gt;0\\;\\;\\;s.t. \\;\\;\\lim_{n\\to+\\infty}P\\{|Y_n-c|&lt;\\varepsilon\\}=1\\)\u3002</p> <ul> <li>\u8fd9\u79cd\u6536\u655b\u4e0d\u662f\u6570\u5b66\u610f\u4e49\u4e0a\u7684\u4e00\u822c\u6536\u655b\uff0c\u800c\u662f\u6982\u7387\u610f\u4e49\u4e0b\u7684\u4e00\u79cd\u6536\u655b</li> <li>\u5176\u542b\u4e49\u662f\uff1a\\(Y_n\\)\u5bf9\\(c\\)\u7684\u7edd\u5bf9\u504f\u5dee\u4e0d\u5c0f\u4e8e\u4efb\u4f55\u4e00\u4e2a\u7ed9\u5b9a\u91cf\u7684\u53ef\u80fd\u6027\u968f\\(n\\)\u7684\u589e\u5927\u800c\u8d8a\u6765\u8d8a\u5c0f\uff1b\u6216\u8005\u7edd\u5bf9\u504f\u5dee\\(|Y_n-c|\\)\u5c0f\u4e8e\u4efb\u4f55\u4e00\u4e2a\u7ed9\u5b9a\u91cf\u7684\u53ef\u80fd\u6027\u968f\\(n\\)\u7684\u589e\u5927\u65f6\u800c\u8d8a\u6765\u8d8a\u63a5\u8fd1\u4e8e\\(1\\)</li> </ul> <p>\u4f9d\u6982\u7387\u6536\u655b\u6709\u5982\u4e0b\u91cd\u8981\u6027\u8d28\uff1a\u82e5\uff1a</p> <ol> <li>\\(\\left\\{ \\begin{aligned} X_n\\xrightarrow{P} a\\\\ Y_n\\xrightarrow{P} b \\end{aligned} \\right. \\;\\;,\\;\\;n\\to+\\infty\\;\\;,\\;\\;a,b\\in\\mathbf{R}\\)\uff1b</li> <li>\u4e8c\u5143\u51fd\u6570\\(g(x,y)\\)\u5728\u70b9\\((a,b)\\)\u8fde\u7eed\uff08\u4f8b\u5982\u56db\u5219\u8fd0\u7b97\uff09\uff1b</li> </ol> <p>\u5219\u6709\uff1a</p> <ul> <li>\\(g(X_n,Y_n)\\xrightarrow{P}g(a,b)\\)\u3002</li> </ul> <p>\u8be5\u6027\u8d28\u5373\u4f9d\u6982\u7387\u6536\u655b\u53ef\u4ee5\u5728\u53cc\u76ee\u8fd0\u7b97\u7b26\u4e2d\u8fdb\u884c\u4e0b\u653e\u3002</p> <p>\u9a6c\u5c14\u53ef\u592b(Markov)\u4e0d\u7b49\u5f0f\u82e5\u968f\u673a\u53d8\u91cf\\(Y\\)\u7684\\(k\\)\u9636\uff08\u539f\u70b9\uff09\u77e9\u5b58\u5728\uff08\\(k\\geq1\\)\uff09\uff0c\u5219\\(\\forall \\varepsilon &gt; 0\\)\uff0c\u6709\uff1a\\(P \\{ |Y| \\geq \\varepsilon \\}\\leq \\frac{E(|Y|^k)}{\\varepsilon^k}\\;\\; or \\;\\; P\\{|Y| &lt; \\varepsilon \\} \\geq 1 - \\frac{E(|Y|^k)}{\\varepsilon^k}\\) \u7279\u522b\u5730\uff0c\u5f53\\(Y\\)\u53d6\u975e\u8d1f\u503c\u7684\u968f\u673a\u53d8\u91cf\u4e14\u5b83\u7684\\(k\\)\u9636\u77e9\u5b58\u5728\u65f6\uff0c\u6709\uff1a\\(P\\{Y\\geq \\varepsilon\\} \\leq \\frac{E(Y^k)}{\\varepsilon^k}\\)</p> <p>\u5207\u6bd4\u96ea\u592b(Chebyshev)\u4e0d\u7b49\u5f0f\u662f\u9a6c\u5c14\u53ef\u592b\u4e0d\u7b49\u5f0f\u7684\u63a8\u8bba\u82e5\u968f\u673a\u53d8\u91cf\\(X\\)\u7684\u6570\u5b66\u671f\u671b\u548c\u65b9\u5dee\u5b58\u5728\uff0c\u5206\u522b\u8bb0\\(E(X)=\\mu\\;,\\; Var(X) = \\sigma^2\\)\uff0c\u5219\\(\\forall \\varepsilon &gt; 0\\)\uff0c\u6709\uff1a\\(P\\{ |X-\\mu|\\geq \\varepsilon \\} \\leq \\frac{\\sigma^2}{\\varepsilon^2}\\;\\;or\\;\\;P\\{ |X-\\mu|&lt; \\varepsilon \\} \\geq1- \\frac{\\sigma^2}{\\varepsilon^2}\\) \u53ef\u4ee5\u8bb0\u5fc6\u4e3a\\(P\\{ \\sigma^2\\geq \\varepsilon^2 \\} \\leq \\frac{\\sigma^2}{\\varepsilon^2}\\;\\;or\\;\\;P\\{ \\sigma^2&lt; \\varepsilon^2 \\} \\geq1- \\frac{\\sigma^2}{\\varepsilon^2}\\) </p>"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap05/#\u5927\u6570\u5b9a\u7406","title":"\u5927\u6570\u5b9a\u7406","text":"<ul> <li>\u4e3b\u8981\u8ba8\u8bba\u4ec0\u4e48\u6761\u4ef6\u4e0b\uff0c\u968f\u673a\u53d8\u91cf\u5e8f\u5217\u7684\u7b97\u672f\u5e73\u5747\u4f9d\u6982\u7387\u6536\u655b\u5230\u5176\u5747\u503c\u7684\u7b97\u672f\u5e73\u5747\u3002</li> </ul> <p>\u5927\u6570\u5b9a\u7406\uff08\u4e00\u822c\u5f62\u5f0f\uff09\u8bbe\\(\\{Y_i,i\\geq1\\}\\)\u4e3a\u4e00\u968f\u673a\u53d8\u91cf\u5e8f\u5217\uff0c\u82e5\u5b58\u5728\u5e38\u6570\u5e8f\u5217\\({c_n,n\\geq 1}\\)\uff0c\u4f7f\\(\\forall \\varepsilon &gt; 0\\)\uff0c\u6709;\\(\\lim_{n\\to+\\infty}P\\{|\\frac{1}{n}\\sum_{i=1}^{n}Y_i-c_n|\\geq \\varepsilon\\}=0 \\;\\; or \\;\\; \\lim_{n\\to+\\infty}P\\{|\\frac{1}{n}\\sum_{i=1}^{n}Y_i-c_n|&lt; \\varepsilon\\}=1\\) \u5373\uff1a\\((\\frac{1}{n}\\sum_{i=1}^{n}Y_i-c_n)\\xrightarrow{P}0\\;\\;,\\;\\;n\\to+\\infty\\)\uff0c\u5219\u79f0\u968f\u673a\u53d8\u91cf\u5e8f\u5217\\(\\{Y_i,i\\geq1\\}\\)\u670d\u4ece\u5f31\u5927\u6570\u5b9a\u7406(Weak Law of Large Numbers)\uff0c\u7b80\u79f0\u670d\u4ece\u5927\u6570\u5b9a\u5f8b\u3002\u89c2\u5bdf\u5230\u5982\u679c\u4ee4\\(Z_n=\\frac{1}{n}\\sum_{i=1}^{n}Y_i\\)\uff0c\u5219\u8868\u8fbe\u5f0f\u7684\u542b\u4e49\u4e3a\\(Z_n\\xrightarrow{P}c\\;\\;,\\;\\;n\\to+\\infty\\)\uff0c\u5373\u5927\u6570\u5b9a\u5f8b\u4e5f\u53ef\u4ee5\u8868\u8ff0\u4e3a\uff1a</p> <ul> <li>\u968f\u673a\u53d8\u91cf\u5e8f\u5217\u524d\\(n\\)\u4e2a\u53d8\u91cf\u7684\u7b97\u672f\u5e73\u5747\u4f9d\u6982\u7387\u6536\u655b\u4e8e\\(c\\)\uff0c \u5219\u8fd9\u4e2a\u968f\u673a\u53d8\u91cf\u5e8f\u5217\u670d\u4ece\u5927\u6570\u5b9a\u5f8b\u3002</li> </ul> <p>\u6a59\u4e66\u7ed9\u51fa\u7684\u5b9a\u4e49\u5f0f\u662f\uff1a\\(\\lim_{n\\to \\infty}P\\big(\\big|   \\frac{1}{n}\\sum_{i=1}^{n}X_i-\\frac{1}{n}\\sum_{i=1}^{n}E(X_i)  \\big|&lt;\\varepsilon\\big)=1\\)</p> <ul> <li>\u63a5\u4e0b\u6765\u7ed9\u51fa\u7684\u5927\u6570\u5b9a\u5f8b\u7684\u533a\u522b\u4f53\u73b0\u5728\u6761\u4ef6\u4e0a\uff1a\u6709\u4e9b\u662f\u76f8\u4e92\u72ec\u7acb\u7684\u968f\u673a\u53d8\u91cf\uff0c\u6709\u4e9b\u662f\u76f8\u4f9d\u7684\u968f\u673a\u53d8\u91cf\uff0c\u6709\u4e9b\u662f\u540c\u5206\u5e03\u7684\u968f\u673a\u53d8\u91cf\uff0c\u6709\u4e9b\u662f\u4e0d\u540c\u5206\u5e03\u7684\u968f\u673a\u53d8\u91cf\u3002</li> </ul> <p>\u4f2f\u52aa\u5229(Bernoulli)\u5927\u6570\u5b9a\u5f8b\u8bbe\\(n_A\\)\u8868\u793a\\(n\\)\u91cd\u8d1d\u52aa\u529b\u5b9e\u9a8c\u4e2d\u4e8b\u4ef6\\(A\\)\u53d1\u751f\u7684\u6b21\u6570\uff0c\u5e76\u8bb0\\(P(A)=p\\)\uff0c\u5219\\(\\forall \\varepsilon &gt; 0\\)\uff0c\u6709\uff1a\\(\\lim_{n\\to+\\infty}P\\{|\\frac{n_A}{n}-p|\\geq \\varepsilon\\}=0\\)</p> <p>\u8f9b\u94a6(Khinchin)\u5927\u6570\u5b9a\u5f8b*\u5373\u4f7f\u968f\u673a\u53d8\u91cf\u7684\u65b9\u5dee\u4e0d\u5b58\u5728\uff0c\u671f\u671b\u5b58\u5728\u5373\u53ef\u8bbe\\(\\{X_i,i\\geq 1\\}\\)\u4e3a\u72ec\u7acb\u540c\u5206\u5e03\u7684\u968f\u673a\u53d8\u91cf\u5e8f\u5217\uff0c\u4e14\u6570\u5b66\u671f\u671b\u4e3a\\(\\mu\\)\uff0c\u5219\\(\\forall\\varepsilon&gt;0\\)\uff0c\u6709\uff1a\\(\\lim_{n\\to+\\infty}P\\{|\\frac{1}{n}\\sum_{i=1}^{n}X_i-\\mu|\\geq \\varepsilon\\}=0\\;\\;\\;or\\;\\;\\;\\frac{1}{n}\\sum_{i=1}^{n}X_i\\xrightarrow{P}\\mu\\;\\;,\\;\\;n\\to+\\infty\\)</p> <p>\u8f9b\u94a6\u5927\u6570\u5b9a\u5f8b\u6709\u5982\u4e0b\u63a8\u8bba\uff1a\u8bbe\\(\\{X_i,i\\geq 1\\}\\)\u4e3a\u72ec\u7acb\u540c\u5206\u5e03\u7684\u968f\u673a\u53d8\u91cf\u5e8f\u5217\uff0c\u82e5\\(h(x)\\)\u4e3a\u8fde\u7eed\u51fd\u6570\uff0c\u4e14\\(E(|h(X_1)|)&lt;+\\infty\\)\uff0c\u5219\\(\\forall\\varepsilon&gt;0\\)\uff0c\u6709\uff1a\\(\\lim_{n\\to+\\infty}P\\{|\\frac{1}{n}\\sum^{n}_{i=1}h(X_i)-a|\\geq\\varepsilon\\}=0\\;\\;\\;or\\;\\;\\;\\frac{1}{n}\\sum_{i=1}^{n}h(X_i)\\xrightarrow{P}a\\;\\;,\\;\\;n\\to+\\infty \\\\ where\\;\\;\\;a=E(|h(X_1)|)\\)</p>"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap05/#\u4e2d\u5fc3\u6781\u9650\u5b9a\u7406","title":"\u4e2d\u5fc3\u6781\u9650\u5b9a\u7406","text":"<ul> <li>\u8ba8\u8bba\u4ec0\u4e48\u6761\u4ef6\u4e0b\uff0c\u72ec\u7acb\u968f\u673a\u53d8\u91cf\u548c\u7684\u5206\u5e03\u51fd\u6570\\(Y=\\sum X_i\\)\u7684\u5206\u5e03\u51fd\u6570\u4f1a\u6536\u655b\u4e8e\u6b63\u6001\u5206\u5e03\u3002</li> </ul>"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap05/#\u72ec\u7acb\u540c\u5206\u5e03\u65f6","title":"\u72ec\u7acb\u540c\u5206\u5e03\u65f6","text":"<p>\u6797\u5fb7\u4f2f\u683c-\u83b1\u7ef4\u4e2d\u5fc3\u6781\u9650\u5b9a\u7406\u8bbe\\(\\{X_i,i\\geq 1\\}\\)\u4e3a\u72ec\u7acb\u540c\u5206\u5e03\u7684\u968f\u673a\u53d8\u91cf\u5e8f\u5217\uff0c\u4e14\\(E(X_i)=\\mu\\;\\;,\\;\\;Var(X_i)=\\sigma^2\\;\\;(\\sigma&gt;0)\\)\uff0c\u5219\\(\\forall x\\in \\mathbf{R}\\)\uff0c\u6709\uff1a</p> \\[ \\begin{aligned} \\lim_{n\\to+\\infty}P\\left\\{ \\frac{ \\begin{aligned}     \\sum_{i=1}^{n}X_i-E(\\sum_{i=1}^{n}X_i) \\end{aligned} }{\\begin{aligned}     \\sqrt{\\mathrm{Var}(\\sum_{i=1}^{n}X_i)} \\end{aligned}}\\leq x\\right\\}&amp;= \\lim_{n\\to+\\infty}P\\left\\{ \\frac{ \\begin{aligned}     \\sum_{i=1}^{n}X_i-n\\mu \\end{aligned} }{\\begin{aligned}     \\sigma\\sqrt{n} \\end{aligned}}\\leq x\\right\\} \\\\ &amp;=\\frac{1}{\\sqrt{2\\pi}}\\int_{-\\infty}^{x}e^{-\\frac{t^2}{2}}\\mathrm{d}t \\\\ &amp;=\\Phi(x) \\end{aligned} \\] <p>\u6362\u53e5\u8bdd\u6765\u8bf4\uff0c\\(E(X_i)=\\mu\\;\\;,\\;\\;Var(X_i)=\\sigma^2\\;\\;(\\sigma&gt;0)\\)\u7684\u72ec\u7acb\u540c\u5206\u5e03\u7684\u968f\u673a\u53d8\u91cf\u5e8f\u5217\u7684\u90e8\u5206\u548c\\(\\sum_{i=1}^{n}X_i\\)\u7684\u6807\u51c6\u5316\u91cf</p> \\[ \\frac{ \\begin{aligned}     \\sum_{i=1}^{n}X_i-n\\mu \\end{aligned} }{\\begin{aligned}     \\sigma\\sqrt{n} \\end{aligned}} \\overset{\\text{approximately}}{\\sim} N(0,1)\\;\\;,\\;\\;\\text{where }n\\text{ is big enough} \\] <p>\uff0c\u5f53\u7136\u4e5f\u53ef\u4ee5\u5199\u6210\uff1a</p> \\[ \\frac{ \\begin{aligned}     \\frac{1}{n}\\sum_{i=1}^{n}X_i-\\mu \\end{aligned} }{\\begin{aligned}     \\frac{\\sigma}{\\sqrt{n}} \\end{aligned}} \\overset{\\text{approximately}}{\\sim} N(0,1)\\;\\;,\\;\\;\\text{where }n\\text{ is big enough} \\]"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap05/#\u4e8c\u9879\u5206\u5e03\u7684\u6b63\u6001\u8fd1\u4f3c","title":"\u4e8c\u9879\u5206\u5e03\u7684\u6b63\u6001\u8fd1\u4f3c","text":"<p>\u6797\u5fb7\u4f2f\u683c-\u83b1\u7ef4\u4e2d\u5fc3\u6781\u9650\u5b9a\u7406\u6709\u5982\u4e0b\u63a8\u8bba\uff1a\u68e3\u83ab\u5f17-\u62c9\u666e\u62c9\u65af\u4e2d\u5fc3\u6781\u9650\u5b9a\u7406\u8bbe\\(n_A\\)\u8868\u793a\\(n\\)\u91cd\u8d1d\u52aa\u529b\u5b9e\u9a8c\u4e2d\u4e8b\u4ef6\\(A\\)\u53d1\u751f\u7684\u6b21\u6570\uff0c\u5e76\u8bb0\\(P(A)=p\\)\uff0c\u5219</p> \\[ \\forall x\\in\\mathbf{R}$\uff0c\u6709\uff1a&lt;br /&gt;$\\lim_{n\\to+\\infty}P\\{\\frac{n_A-np}{\\sqrt{np(1-p)}}\\leq x\\}=\\frac{1}{\\sqrt{2\\pi}}\\int_{-\\infty}^{x}e^{-\\frac{t^2}{2}}\\mathrm{d}t=\\Phi(x) \\]"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap05/#\u72ec\u7acb\u4e0d\u540c\u5206\u5e03\u65f6\u4e0d\u8981\u6c42","title":"\u72ec\u7acb\u4e0d\u540c\u5206\u5e03\u65f6(\u4e0d\u8981\u6c42)","text":"<p>\u674e\u96c5\u666e\u8bfa\u592b\u4e2d\u5fc3\u6781\u9650\u5b9a\u7406\u8bbe\\(\\{X_i,i\\geq 1\\}\\)\u4e3a\u76f8\u4e92\u72ec\u7acb\u7684\u968f\u673a\u53d8\u91cf\u5e8f\u5217\uff0c\u4e14\\(E(X_i)=\\mu_i\\;\\;,\\;\\;Var(X_i)=\\sigma_i^2\\;\\;(\\sigma&gt;0)\\)\uff0c\u82e5\\(\\exists\\varepsilon&gt;0\\)\u4f7f\u5f97\uff1a\\(\\lim_{+\\infty}\\frac{1}{B_n^{2+\\varepsilon}}\\sum_{i=1}^{n}E|X_i-\\mu_i|^{2+\\varepsilon}=0\\;\\;\\;where\\;\\;\\;B_n^{2}=\\sum_{i=1}^{n}\\sigma_i^2\\) \u5219\uff1a </p>"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap06/","title":"[6.x] \u7edf\u8ba1\u91cf\u4e0e\u62bd\u6837\u5206\u5e03","text":"<p> \u7ea6 1586 \u4e2a\u5b57  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 5 \u5206\u949f</p>"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap06/#\u6982\u5ff5","title":"\u6982\u5ff5","text":"<p>\u603b\u4f53(Population)\u4e2a\u4f53(Individual)\u603b\u4f53\u5bb9\u91cf\u6709\u9650\u603b\u4f53(Finite Population)\u65e0\u9650\u603b\u4f53(Infinite Population)\u6837\u672c(Sample)</p> <ul> <li>\u6709\u4ee3\u8868\u6027</li> <li>\u6709\u72ec\u7acb\u6027</li> </ul> <p>\u6837\u672c\u5bb9\u91cf\u968f\u673a\u6837\u672c(Random Sample)\u7b80\u5355\u968f\u673a\u6837\u672c(Simple Random Sample)\u6837\u672c\u503c / \u89c2\u5bdf\u503c\u6837\u672c\u7684\u8054\u5408\u5206\u5e03\u51fd\u6570\uff1a\\(F(x_1,x_2,...,x_n)=\\prod_{i=1}^{n} F(x_i).\\)</p> <p>\u5b9a\u4e49\u8bbe\u603b\u4f53\\(X\\)\u662f\u5177\u6709\u5206\u5e03\u51fd\u6570\\(F(\u00b7)\\)\u7684\u968f\u673a\u53d8\u91cf\uff0c\\(X_1,X_2,...,X_n\\)\u662f\u6765\u81ea\u603b\u4f53\\(X\\)\u7684\u968f\u673a\u6837\u672c\uff0c\u82e5\u6ee1\u8db3\uff1a</p> <ol> <li>\\(X_1,X_2,...,X_n\\)\u662f\u662f\u76f8\u4e92\u72ec\u7acb\u7684\u968f\u673a\u53d8\u91cf\uff1b</li> <li>\u6bcf\u4e00\u4e2a\\(X_i\\)\u4e0e\\(X\\)\u6709\u76f8\u540c\u7684\u5206\u5e03\u51fd\u6570\uff1b</li> </ol> <p>\u5219\u79f0\\(X_1,X_2,...,X_n\\)\u4e3a\u53d6\u81ea\u603b\u4f53\\(X\\)\u7684\u7b80\u5355\u968f\u673a\u6837\u672c\u3002</p>"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap06/#\u7edf\u8ba1\u91cf\u53ca\u5176\u5206\u5e03","title":"\u7edf\u8ba1\u91cf\u53ca\u5176\u5206\u5e03","text":"<p>\u7edf\u8ba1\u91cf(Statistic)\u8bbe\\(X_1,X_2,...,X_n\\)\u662f\u6765\u81ea\u603b\u4f53\\(X\\)\u7684\u4e00\u4e2a\u6837\u672c\uff0c\\(g(X_1,X_2,...,X_n)\\)\u662f\u6837\u672c\\(X_1,X_2,...,X_n\\)\u7684\u51fd\u6570\uff0c\u82e5\\(g\\)\u4e2d\u4e0d\u542b\u672a\u77e5\u53c2\u6570\uff0c\u5219\u79f0\\(g(X_1,X_2,...,X_n)\\)\u662f\u4e00\u7edf\u8ba1\u91cf\u3002</p> <ul> <li>\u5c3d\u7ba1\u7edf\u8ba1\u91cf\u4e0d\u4f9d\u8d56\u4e8e\u672a\u77e5\u53c2\u6570\uff0c\u4f46\u662f\u4ed6\u4eec\u7684\u5206\u5e03\u4f9d\u8d56\u4e8e\u672a\u77e5\u53c2\u6570\u3002</li> </ul> <p>\u5982\u4e0b\u4e3a\u51e0\u79cd\u5e38\u89c1\u7684\u91cd\u8981\u7edf\u8ba1\u91cf\uff1a</p> <ol> <li>\u6837\u672c\u5747\u503c\uff08\u5e38\u4f5c\u4e3a\u603b\u4f53\u503c\\(\\mu\\)\u7684\u4f30\u8ba1\uff09</li> </ol> <p>\\(\\overline{X}=\\frac{1}{n}\\sum_{i=1}^{n}X_i\\) \\(E(\\overline x)=\\mu\\;\\;,\\;\\;Var(\\overline x)=\\sigma^2/n\\)</p> <ul> <li>\u6027\u8d28\uff1a<ol> <li>\\(\\sum_{i=1}^{n}(x_i-\\overline{x})=0\\)\uff1b</li> <li>\u6570\u636e\u89c2\u6d4b\u503c\u4e0e\u6837\u672c\u5747\u503c\u7684\u504f\u5dee\u5e73\u65b9\u548c\u6700\u5c0f\uff0c\u5373\u5728\u5f62\u5982\\(\\sum(x_i-c)^2\\)\u7684\u51fd\u6570\u4e2d\uff0c\\(\\sum(x_i-\\overline x)^2\\)\u6700\u5c0f\uff1b</li> <li>\u82e5\u603b\u4f53\u670d\u4ece\\(N(\\mu,\\sigma^2)\\)\uff0c\u5219\\(\\overline x\\)\u7684\u7cbe\u786e\u5206\u5e03\u4e3a\\(N(\\mu,\\sigma^2/n)\\)\uff1b </li> <li>\u82e5\u603b\u4f53\u5206\u5e03\u672a\u77e5\u6216\u4e0d\u662f\u6b63\u6001\u5206\u5e03\uff0c\u5219\u5f53\\(n\\)\u8f83\u5927\u65f6\uff0c\\(\\overline x\\)\u8fd1\u4f3c\u670d\u4ece\\(N(\\mu,\\sigma^2/n)\\)\uff1b</li> </ol> </li> <li>\u6837\u672c\u65b9\u5dee\uff08\u5e38\u4f5c\u4e3a\u603b\u4f53\u65b9\u5dee\\(\\sigma^2\\)\u7684\u65e0\u504f\u4f30\u8ba1\uff09</li> </ul> \\[ S^2=\\frac{1}{n-1}\\sum_{i=1}^{n}(X_i-\\overline{X})^2=\\frac{1}{n-1}(\\sum_{i=1}^{n}X_i^2-n\\overline{X}^2) \\] \\[ E(S^2)=\\sigma^2 \\] <ul> <li>\u5bf9\u4e8e\u6837\u672c\u504f\u5dee\u5e73\u65b9\u548c\u6709\u4e09\u4e2a\u5e38\u7528\u7684\u8868\u8fbe\u5f0f\uff1a</li> </ul> <p>\\(\\sum(x_i-\\overline x)^2=\\sum x_i^2-\\frac{(\\sum x_i)^2}{n}=\\sum x_i^2-n\\overline x^2\\)</p> <ol> <li>\u6837\u672c\u6807\u51c6\u5dee</li> </ol> <p>\\(S=\\sqrt{S^2}=\\sqrt{\\frac{1}{n-1}\\sum_{i=1}^{n}(X_i-\\overline{X})^2}\\)</p> <ol> <li>\u6837\u672c\\(k\\)\u9636\uff08\u539f\u70b9\uff09\u77e9\uff08\u5e38\u4f5c\u4e3a\u603b\u4f53\u539f\u70b9\u77e9\\(\\mu_k\\)\u7684\u4f30\u8ba1\uff09</li> </ol> <p>\\(A_k=\\frac{1}{n}\\sum_{i=1}^{n}X_i^k,\\;\\;k=1,2,...\\)</p> <ol> <li>\u6837\u672c\\(k\\)\u9636\u4e2d\u5fc3\u8ddd\uff08\u5e38\u4f5c\u4e3a\u603b\u4f53\u4e2d\u5fc3\u77e9\\(\\nu_k\\)\u7684\u4f30\u8ba1\uff09\uff08\\(B_2\\)\u53ef\u4f5c\u4e3a\u603b\u4f53\u65b9\u5dee\\(\\sigma^2\\)\u7684\u6709\u504f\u4f30\u8ba1\uff09</li> </ol> <p>\\(B_k=\\frac{1}{n}\\sum_{i=1}^{n}(X_i-\\overline{X})^k,\\;\\;k=2,3,...\\)</p> <ul> <li>\u603b\u4f53\u7684\u4efb\u610f\u4e00\u4e2a\u672a\u77e5\u53c2\u6570\u53ef\u4ee5\u6709\u591a\u4e2a\u4e0d\u540c\u7684\u4f30\u8ba1\uff0c\u56e0\u6b64\u53c2\u6570\u4f30\u8ba1\u4e0d\u552f\u4e00\uff1b</li> <li>\u5047\u8bbe\\(X_1,X_2,...,X_n\\)\u662f\\(X\\)\u4e2d\u62bd\u53d6\u7684\u7b80\u5355\u968f\u673a\u6837\u672c\uff0c\\(\\mu_k=E(X^k)\\)\u5b58\u5728\uff0c\u7531\u8f9b\u94a6\u5927\u6570\u5b9a\u5f8b\u53ef\u77e5\uff1a</li> </ul> <p>\\(A_k=\\frac{1}{n}\\sum_{i=1}^{n}X_i^k\\xrightarrow{P}\\mu_k,\\;\\;k=1,2,...\\)</p>"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap06/#\u4e09\u5927\u62bd\u6837\u5206\u5e03","title":"\u4e09\u5927\u62bd\u6837\u5206\u5e03","text":"<p>\u7edf\u8ba1\u91cf\u7684\u5206\u5e03\u6210\u4e3a\u62bd\u6837\u5206\u5e03(Sampling Distribution)\uff0c\u5728\u4f7f\u7528\u7edf\u8ba1\u91cf\u8fdb\u884c\u63a8\u65ad\u65f6\u9700\u8981\u77e5\u9053\u62bd\u6837\u5206\u5e03\u3002</p>"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap06/#\u03c7\u00b2\u5206\u5e03--\u5361\u65b9\u5206\u5e03","title":"\u03c7\u00b2\u5206\u5e03 / \u5361\u65b9\u5206\u5e03","text":"<p>\\(\\chi^2\\)\u5206\u5e03 / \u5361\u65b9\u5206\u5e03\u8bbe\\(X_1,X_2,...,X_n\\)\u4e3a\u72ec\u7acb\u540c\u5206\u5e03\u670d\u4ece\\(N(0,1)\\)\u3002\u8bb0\\(Y=X_1^2+X_2^2+...+X_n^2\\)\uff0c\u5219\u79f0\\(Y\\)\u670d\u4ece\u81ea\u7531\u5ea6\u4e3a\\(n\\)\u7684\\(\\chi^2\\)\u5206\u5e03\uff0c\u8bb0\\(Y\\sim \\chi^2(n)\\)\u3002\\(\\chi^2\\)\u5206\u5e03\u7684\u5bc6\u5ea6\u51fd\u6570\u4e3a\uff1a</p> \\[ f_{\\chi^2}(x)= \\left\\{ \\begin{aligned} &amp;\\frac{1}{2^\\frac{n}{2}\\Gamma(\\frac{n}{2})}x^{\\frac{n}{2}-1}e^{-\\frac{x}{2}},&amp;x&gt;0, \\\\ &amp;0,&amp;other, \\end{aligned} \\right. \\] <p>\\(\\chi^2\\)\u5206\u5e03\u6709\u5982\u4e0b\u6027\u8d28\uff1a</p> <ol> <li>\\(\\chi^2\\)\u5206\u5e03\u53ef\u52a0\uff1a\u8bbe\\(Y_1 \\sim \\chi^2(m),\\;Y_2\\sim\\chi^2(n)\\)\uff0c\u4e14\u4e24\u8005\u4e92\u76f8\u72ec\u7acb\uff0c\u5219\\(Y_1+Y_2\\sim \\chi^2(m+n)\\)\uff1b</li> <li>\\(\\chi^2\\)\u5206\u5e03\u7684\u6570\u5b66\u671f\u671b\u4e0e\u65b9\u5dee\uff1a\\(E(\\chi^2(n))=n,\\;Var(\\chi^2(n))=2n\\)\uff1b</li> <li>\\(\\chi^2\\)\u5206\u5e03\u5206\u4f4d\u6570\uff1a\u5bf9\u4e8e\u7ed9\u5b9a\u7684\u6b63\u6570\\(\\alpha,\\;0&lt;\\alpha&lt;1\\)\uff0c\u79f0\u6ee1\u8db3\u6761\u4ef6\\(P\\{\\chi^2&gt;\\chi^2_\\alpha(n)\\}=\\int^{+\\infty}_{\\chi^2_\\alpha(n)}f_{\\chi^2}(x)\\mathrm{d}x=\\alpha\\)\u7684\u70b9\\(\\chi^2_{\\alpha}(n)\\)\u4e3a\\(\\chi^2(n)\\)*\u4fa7\uff09\\(\\alpha\\)\u5206\u4f4d\u6570*\u3002</li> </ol> <p></p> <ol> <li>\u8bbe\\(X_1,X_2,...,X_n\\)\u4e3a\u6765\u81ea\u6b63\u6001\u603b\u4f53\\(N(\\mu,\\sigma^2)\\)\u7684\u7b80\u5355\u968f\u673a\u6837\u672c\uff0c\\(\\overline{X}\\)\u662f\u6837\u672c\u5747\u503c\uff0c\\(S^2\\)\u662f\u6837\u672c\u65b9\u5dee\uff0c\u5219\u6709\uff1a</li> <li>\\(\\overline X\\)\u4e0e\\(S^2\\)\u76f8\u4e92\u72ec\u7acb\uff1b</li> <li>\\(\\overline X\\sim  N(\\mu,\\sigma^2/n)\\)\uff1b</li> <li>\\(\\frac{\\sum_{i=1}^n(X_i-\\overline X)^2}{\\sigma^2}=\\frac{(n-1)S^2}{\\sigma^2}\\sim \\chi^2(n-1)\\)\uff1b</li> </ol>"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap06/#t-\u5206\u5e03--\u5b66\u751f\u6c0f\u5206\u5e03","title":"t \u5206\u5e03 / \u5b66\u751f\u6c0f\u5206\u5e03","text":"<p>\\(t\\)\u5206\u5e03 / \u5b66\u751f\u6c0f(Student)\u5206\u5e03\u8bbe\\(X\\sim N(0,1),Y\\sim\\chi^2(n)\\)\uff0c\u4e14\\(X,Y\\)\u76f8\u4e92\u72ec\u7acb\uff0c\u5219\u79f0\u968f\u673a\u53d8\u91cf\\(t=\\frac{X}{\\sqrt{Y/n}}\\)\u670d\u4ece\u81ea\u7531\u5ea6\u4e3a\\(n\\)\u7684\\(t\\)\u5206\u5e03\uff0c\u8bb0\u505a\\(t\\sim t(n)\\)\uff0c\u5176\u5bc6\u5ea6\u51fd\u6570\u4e3a\uff1a</p> \\[ f_t(x)=\\frac{\\Gamma[(n+1)/2]}{\\sqrt{\\pi n}\\Gamma(\\frac{n}{2})}(1+\\frac{x^2}{n})^{-\\frac{n+1}{2}},\\;\\;-\\infty&lt;x&lt;+\\infty \\] <p>\u5176\u4e2d\\(\\Gamma(\\alpha)=\\int_0^{+\\infty}t^{\\alpha-1}e^{-t}\\mathrm{d}t\\)\uff0c\\(\\Gamma(\\alpha+1)=\\alpha\\Gamma(\\alpha)=\\alpha!(if\\;\\alpha\\in\\Z)\\)\uff0c\\(\\Gamma(0.5)=\\sqrt{\\pi}\\) \\(t\\)\u5206\u5e03\u6709\u5982\u4e0b\u6027\u8d28\uff1a</p> <ol> <li>\\(t\\)\u5206\u5e03\u7684\u5bc6\u5ea6\u51fd\u6570\\(f_t(x)\\)\u662f\u5076\u51fd\u6570\uff0c\u5173\u4e8e\\(y\\)\u8f74\u5bf9\u79f0\uff1b</li> <li>\u7531\\(t\\)\u5206\u5e03\u7684\u5bc6\u5ea6\u51fd\u6570\u53ef\u4ee5\u5f97\u5230\uff1a\\(\\lim_{n\\to+\\infty}f_t(x)=\\frac{1}{\\sqrt{2\\pi}}e^{-{x^2}/{2}}\\)\uff1b</li> <li>\u5f53\\(n\\)\u8db3\u591f\u5927\u65f6\uff0c\\(t\\)\u5206\u5e03\u8fd1\u4f3c\u4e8e\u6807\u51c6\u6b63\u6001\u5206\u5e03\\(N(0,1)\\)\uff1b</li> <li>\\(t\\)\u5206\u5e03\u5206\u4f4d\u6570\uff0c\u5bf9\u4e8e\u7ed9\u5b9a\u7684\u6b63\u6570\\(\\alpha,\\;\\;0&lt;\\alpha&lt;1\\)\uff0c\u79f0\u6ee1\u8db3\u6761\u4ef6\\(P\\{t&gt;t_\\alpha(n)\\}=\\int_{t_\\alpha(n)}^{+\\infty}f_t(x)\\mathrm{d}x=\\alpha\\)\u7684\u70b9\\(t_\\alpha(n)\\)\u4e3a\\(t(n)\\)\u5206\u5e03\u7684\u4e0a\uff08\u4fa7\uff09\\(\\alpha\\)\u5206\u4f4d\u6570\uff1b</li> </ol> <p></p> <ol> <li>\\(t^2\\sim F(1,n)\\)\uff1b</li> <li>\u81ea\u7531\u5ea6\u4e3a\\(1\\)\u7684\\(t\\)\u5206\u5e03\u5c31\u662f\u6807\u51c6\u67ef\u897f\u5206\u5e03\uff0c\u5176\u5747\u503c\u4e0d\u5b58\u5728\uff1b</li> <li>\\(n&gt;1\\)\u65f6\\(t\\)\u5206\u5e03\u7684\u6570\u5b66\u671f\u671b\u5b58\u5728\u4e14\u4e3a\\(0\\)\uff1b</li> <li>\\(n&gt;2\\)\u65f6\\(t\\)\u5206\u5e03\u7684\u65b9\u5dee\u5b58\u5728\u4e14\u4e3a\\(\\frac{n}{n-2}\\)\uff1b</li> <li>\u5f53\u81ea\u7531\u5ea6\u6bd4\u8f83\u5927\u65f6\uff0c\\(t\\)\u5206\u5e03\u53ef\u4ee5\u7528\\(N(0,1)\\)\u5206\u5e03\u8fd1\u4f3c\uff1b</li> </ol> <p>\u63a8\u8bba\uff1a</p> <ul> <li>\u8bbe\\(x_1,x_2,x_3,..,x_n\\)\u662f\u6765\u81ea\u6b63\u6001\u5206\u5e03\\(N(\\mu,\\sigma^2)\\)\u7684\u4e00\u4e2a\u6837\u672c\uff0c\\(\\overline x\\)\u548c\\(S^2\\)\u5206\u522b\u662f\u8be5\u6837\u672c\u7684\u6837\u672c\u5747\u503c\u4e0e\u6837\u672c\u65b9\u5dee\uff0c\u5219\u6709\\(t=\\frac{\\overline x-\\mu}{S/\\sqrt n}\\sim t(n-1)\\)\uff1b</li> </ul>"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap06/#f-\u5206\u5e03","title":"F \u5206\u5e03","text":"<p>\\(F\\)\u5206\u5e03\u8bbe\\(U\\sim\\chi^2(n_1)\\)\uff0c\\(V\\sim \\chi^2(n_2)\\)\uff0c\u4e14\\(U\\)\u548c\\(V\\)\u76f8\u4e92\u72ec\u7acb\uff0c\u5219\u79f0\u968f\u673a\u53d8\u91cf\\(F=\\frac{U/n_1}{V/n_2}\\)\u670d\u4ece\u81ea\u7531\u5ea6\u4e3a\\((n_1,n_2)\\)\u7684\\(F\\)\u5206\u5e03\uff0c\u8bb0\\(F\\sim F(n_1,n_2)\\)\u3002\u5176\u5bc6\u5ea6\u51fd\u6570\u4e3a  \\(F\\)\u5206\u5e03\u6709\u5982\u4e0b\u6027\u8d28\uff1a</p> <ol> <li>\u5982\u679c\\(F\\sim F(n_1,n_2)\\)\uff0c\u5219\\(\\frac{1}{F}\\sim F(n_2,n_1)\\)\uff1b</li> <li>\u5982\u679c\\(X\\sim t(n)\\)\uff0c\u5219\\(X^2\\sim F(1,n)\\)\uff1b</li> </ol> <p></p> <p>\u8bbe\\(X_1,X_2,...,X_n\\)\u4e3a\u6765\u81ea\u6b63\u6001\u603b\u4f53\\(N(\\mu,\\sigma^2)\\)\u7684\u7b80\u5355\u968f\u673a\u6837\u672c\uff0c\\(\\overline{X}\\)\u662f\u6837\u672c\u5747\u503c\uff0c\\(S^2\\)\u662f\u6837\u672c\u65b9\u5dee\uff0c\u5219\u6709\uff1a</p> <ol> <li>\\(\\frac{(n-1)S^2}{\\sigma^2}\\sim \\chi^2(n-1)\\)\uff1b</li> <li>\\(\\overline{X}\\)\u4e0e\\(S^2\\)\u76f8\u4e92\u72ec\u7acb\uff1b</li> <li>\\(\\frac{\\overline X - \\mu}{S/\\sqrt n}\\sim t(n-1)\\)\uff1b</li> </ol> <p>\u8bbe\\(X_1,X_2,...,X_n\\)\u548c\\(Y_1,Y_2,...,Y_n\\)\u4e3a\u6765\u81ea\u6b63\u6001\u603b\u4f53\\(N(\\mu_1,\\sigma_1^2)\\)\u548c\\(N(\\mu_2,\\sigma_2^2)\\)\u7684\u4e24\u4e2a\u76f8\u4e92\u72ec\u7acb\u7684\u7b80\u5355\u968f\u673a\u6837\u672c\uff0c\\(\\overline{X},\\overline Y\\)\u662f\u6837\u672c\u5747\u503c\uff0c\\(S_1^2,S_2^2\\)\u662f\u6837\u672c\u65b9\u5dee\uff0c\u5219\u6709\uff1a</p> <ol> <li>\\(\\frac{S_1^2/\\sigma_1^2}{S_2^2/\\sigma^2_2}\\sim F(n_1-1,n_2-2)\\)\uff1b</li> <li>\u5f53\\(\\sigma_1^2=\\sigma_2^2=\\sigma^2\\)\u65f6\uff1a</li> </ol> <p>\\(\\frac{ (\\overline X - \\overline Y) - (\\mu_1-\\mu_2) }{ S_\\omega\\sqrt{\\frac{1}{n_1}+\\frac{1}{n_2}} }\\sim t(n_1+n_2-2)\\) \u5176\u4e2d\\(S^2_\\omega=\\frac{(n_1-1)S_1^2+(n_2-n_1)S^2_2}{n_1+n_2-2}\\)</p>"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap07/","title":"[7.x] \u53c2\u6570\u4f30\u8ba1","text":"<p> \u7ea6 1368 \u4e2a\u5b57  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 5 \u5206\u949f</p>"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap07/#\u70b9\u4f30\u8ba1","title":"\u70b9\u4f30\u8ba1","text":"<p>\u8bbe\u603b\u4f53\\(X\\)\u7684\u5206\u5e03\u51fd\u6570\u4e3a\\(F(x;\\theta)\\)\uff0c\\(\\theta\\)\u662f\u5f85\u4f30\u53c2\u6570\uff0c\\(X_1,X_2,...,X_n\\)\u662f\\(X\\)\u7684\u4e00\u4e2a\u6837\u672c\u3002\u70b9\u4f30\u8ba1\u5c31\u662f\u8981\u6784\u9020\u4e00\u4e2a\u9002\u5f53\u7684\u7edf\u8ba1\u91cf\\(\\hat{\\theta}(X_1,X_2,...,X_n)\\)\uff0c\u7528\u6765\u4f30\u8ba1\u672a\u77e5\u53c2\u6570\\(\\theta\\)\uff0c\u6211\u4eec\u79f0\\(\\hat{\\theta}(X_1,X_2,...,X_n)\\)\u4e3a\\(\\theta\\)\u7684\u4f30\u8ba1\u91cf\u3002\u5982\u679c\u628a\u5176\u4e2d\u7684\u6837\u672c\u503c\u7528\\(x_1,x_2,...,x_n\\)\u4ee3\u66ff\uff0c\u5219\u79f0\\(\\hat\\theta(x_1,x_2,...,x_n)\\)\u4e3a\\(\\theta\\)\u7684\u4e00\u4e2a\u4f30\u8ba1\u503c\u3002\u5728\u4e0d\u5bfc\u81f4\u6df7\u6dc6\u7684\u60c5\u51b5\u4e0b\uff0c\u4e24\u8005\u90fd\u53ef\u4ee5\u88ab\u79f0\u4e3a\u201c\u4f30\u8ba1\u201d\uff0c\u5e76\u90fd\u53ef\u4ee5\u7b80\u8bb0\u4e3a\\(\\hat\\theta\\)\u3002</p>"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap07/#\u77e9\u6cd5","title":"\u77e9\u6cd5","text":"<p>\u505a\u9898\u6b65\u9aa4\uff1a</p> <ol> <li>\u5047\u8bbe\u6709\\(k\\)\u4e2a\u5f85\u6c42\u672a\u77e5\u53c2\u6570\uff1b</li> <li>\u5217\u5173\u4e8e\\(\\mu_1,\\mu_2,...,\\mu_k\\)\u7684\u65b9\u7a0b\u7ec4\uff1b</li> <li>\u4ece\u65b9\u7a0b\u7ec4\u4e2d\u89e3\u51fa\u8fd9\\(k\\)\u4e2a\u53c2\u6570\uff1b</li> <li>\u5982\u679c\u65b9\u7a0b\u4e2d\u5b58\u5728\u6052\u7b49\u5f0f\uff0c\u5219\u53ef\u4ee5\u987a\u5ef6\u6c42\\(\\mu_{k+1}\\)\uff1b</li> <li>\u7406\u8bba\u4e0a\u4efb\u610f\\(k\\)\u4e2a\u5173\u4e8e\\(\\mu_i\\)\u7684\u65b9\u7a0b\u7ec4\u90fd\u53ef\u4ee5\uff0c\u4f46\u8003\u8bd5\u8981\u6c42\u524d\\(k\\)\u4e2a\u624d\u7b97\u5bf9\uff1b</li> </ol>"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap07/#\u6781\u5927\u4f3c\u7136\u6cd5","title":"\u6781\u5927\u4f3c\u7136\u6cd5","text":"<p>\u505a\u9898\u6b65\u9aa4\uff1a</p> <ol> <li>\u6784\u9020\u5bf9\u6570\u4f3c\u7136\u51fd\u6570(Likelihood Function)\\(L(\\theta)=\\ln p(x_1,...,x_n,\\theta)\\)\uff1b</li> <li>\u6c42\\(\\hat\\theta\\;\\;s.t.\\;\\;L(\\hat\\theta;x_1,x_2,...,x_n)=\\max_{\\theta\\in\\Theta}L(\\theta;x_1,x_2,...,x_n)\\)\uff1b</li> <li>\u89e3\u5bf9\u6570\u4f3c\u7136\u65b9\u7a0b(Log-likelihood Equation)\\(\\frac{\\mathrm{d}L(\\theta)}{\\mathrm{d}\\theta}=0\\)\uff0c\u68c0\u9a8c\u6781\u5927\u503c\u70b9\uff1b</li> <li>\u68c0\u9a8c\u7aef\u70b9\uff1b</li> <li>\u6c42\u6700\u5927\u503c\u70b9\uff1b</li> </ol> <p>\u6027\u8d28\uff1a</p> <ul> <li>\u6781\u5927\u4f3c\u7136\u4f30\u8ba1\u7684\u4e0d\u53d8\u6027</li> <li>\u8bbe\u53c2\u6570\\(\\theta\\)\u7684\u6781\u5927\u4f3c\u7136\u4f30\u8ba1\u4e3a\\(\\hat\\theta\\)\uff0c\\(\\theta^*=g(\\theta)\\)\u662f\\(\\theta\\)\u7684\u8fde\u7eed\u51fd\u6570\uff0c\u5219\u53c2\u6570\\(\\theta^*\\)\u7684\u6781\u5927\u4f3c\u7136\u4f30\u8ba1\u4e3a\\(\\hat\\theta^*=g(\\hat\\theta)\\)\uff1b</li> </ul>"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap07/#\u4f30\u8ba1\u91cf\u7684\u8bc4\u4ef7\u51c6\u8005","title":"\u4f30\u8ba1\u91cf\u7684\u8bc4\u4ef7\u51c6\u8005","text":""},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap07/#\u65e0\u504f\u6027\u51c6\u5219","title":"\u65e0\u504f\u6027\u51c6\u5219","text":"<p>\u8bbe\\(\\theta\\)\u662f\u603b\u4f53\\(X\\)\u7684\u5f85\u4f30\u53c2\u6570\uff0c\\(X_1,X_2,...,X_n\\) \u662f\u6765\u81ea\u603b\u4f53\\(X\\)\u7684\u6837\u672c\uff0c\u82e5\u4f30\u8ba1\u91cf\\(\\hat\\theta=\\hat\\theta(X_1,X_2,...,X_n)\\)\u7684\u6570\u5b66\u671f\u671b\u5b58\u5728\uff0c\u6ee1\u8db3\\(E(\\hat\\theta)=\\theta,\\;\\;\\forall\\theta\\in\\Theta\\)\uff0c\u5219\u79f0\\(\\hat\\theta\\)\u662f\\(\\theta\\)\u7684\u65e0\u504f\u4f30\u8ba1\u91cf\u6216\u65e0\u504f\u4f30\u8ba1(Unbiased Estimation)\u3002</p> <ul> <li>\u82e5\\(E(\\hat\\theta)\\not=\\theta\\)\uff0c\u5219\u79f0\\(E(\\hat\\theta)-\\theta\\)\u4e3a\u4f30\u8ba1\u91cf\\(\\hat\\theta\\)\u7684\u504f\u5dee\uff1b</li> <li>\u82e5\\(E(\\hat\\theta)\\not=\\theta\\)\uff0c\u4f46\u82e5\u6ee1\u8db3\\(\\lim_{x\\to+\\infty}E(\\hat\\theta)=0\\)\uff0c\u5219\u79f0\\(\\hat\\theta\\)\u662f\\(\\theta\\)\u7684\u6e10\u8fdb\u65e0\u504f\u4f30\u8ba1(Asymptotic Unbiased Estimation)\uff1b</li> </ul>"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap07/#\u6709\u6548\u6027\u51c6\u5219","title":"\u6709\u6548\u6027\u51c6\u5219","text":"<p>\u8bbe\\(\\theta_1\\)\u548c\\(\\theta_2\\) \u662f\u53c2\u6570\\(\\theta\\)\u7684\u65e0\u504f\u4f30\u8ba1\uff0c\u82e5\\(\\forall \\theta\\in\\Theta\\)\uff0c\\(Var_\\theta(\\hat\\theta_1)\\leq Var_\\theta(\\hat\\theta_2)\\)\uff0c\u4e14\u4e0d\u6052\u53d6\u201c=\u201d\uff0c\u5219\u79f0\\(\\hat\\theta_1\\)\u6bd4\\(\\hat\\theta_2\\)\u6709\u6548\u3002</p>"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap07/#\u5747\u65b9\u8bef\u5dee\u51c6\u5219","title":"\u5747\u65b9\u8bef\u5dee\u51c6\u5219","text":"<p>\\(E[(\\hat\\theta-\\theta)^2] =Var(\\hat\\theta)+(E(\\hat\\theta)-\\theta)^2\\)\u662f\u4f30\u8ba1\u91cf\\(\\hat\\theta\\)\u7684\u5747\u65b9\u8bef\u5dee(Mean Square Error)\uff0c\u8bb0\u4e3a\\(Mse(\\hat\\theta)\\)\u3002\u82e5\\(Mse(\\hat\\theta_1)\\leq Mse(\\hat\\theta_2)\\)\u4e14\u4e0d\u6052\u53d6\u201c=\u201d\uff0c\u5219\u79f0\\(\\hat\\theta_1\\)\u4f18\u4e8e\\(\\hat\\theta_2\\)\u3002</p> <ul> <li>\u82e5\\(\\hat\\theta\\)\u662f\u53c2\u6570\\(\\theta\\)\u7684\u65e0\u504f\u4f30\u8ba1\u91cf\uff0c\u5219\u6709\\(Mse(\\hat\\theta)=Var(\\hat\\theta)\\)\uff1b</li> <li>\u56e0\u800c\u5747\u65b9\u8bef\u5dee\u51c6\u5219\u5e38\u7528\u4e8e\u6709\u504f\u4f30\u8ba1\u91cf\u4e4b\u95f4\uff0c\u6216\u6709\u504f\u4f30\u8ba1\u91cf\u4e0e\u65e0\u504f\u4f30\u8ba1\u91cf\u4e4b\u95f4\u7684\u6bd4\u8f83\uff1b</li> </ul>"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap07/#\u76f8\u5408\u6027\u51c6\u5219","title":"\u76f8\u5408\u6027\u51c6\u5219","text":"<p>\u82e5\\(\\lim_{n\\to+\\infty}P\\{|\\hat\\theta_n-\\theta|&lt;\\varepsilon\\}=1\\)\uff0c\u5373\\(\\hat\\theta _n \\xrightarrow{P}\\theta\\)\uff0c\u5219\u79f0\\(\\hat\\theta_n\\)\u662f\\(\\theta\\)\u7684\u76f8\u5408\u4f30\u8ba1\u91cf(Consistent Estimation)\u3002\u6709\u5982\u4e0b\u5b9a\u7406\uff1a</p> <ul> <li>\u8bbe\\(\\hat\\theta_n=\\hat\\theta_n(x_1,x_2,...,x_n)\\)\u662f\\(\\theta\\)\u7684\u4e00\u4e2a\u4f30\u8ba1\u91cf\uff0c\u82e5\\(\\lim_{n\\to \\infty}E(\\hat\\theta)=\\theta,\\;\\;\\;\\lim_{n\\to\\infty}Var(\\hat\\theta_n)=0,\\)\u5219\\(\\hat\\theta_n\\)\u662f\\(\\theta\\)\u7684\u76f8\u5408\u4f30\u8ba1\u3002</li> </ul>"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap07/#\u533a\u95f4\u4f30\u8ba1","title":"\u533a\u95f4\u4f30\u8ba1","text":"<ul> <li>\u6a59\u4e66 P300</li> <li>\u7eff\u4e66 P190</li> <li>\u8fd9\u91cc\u53ea\u7ed9\u51fa\u7279\u5b9a\u4f30\u8ba1\u7684\u8868\u8fbe\u5f0f</li> </ul>"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap07/#\u5355\u4e2a\u6b63\u6001\u603b\u4f53\u53c2\u6570\u7684\u7f6e\u4fe1\u533a\u95f4","title":"\u5355\u4e2a\u6b63\u6001\u603b\u4f53\u53c2\u6570\u7684\u7f6e\u4fe1\u533a\u95f4","text":"<p>\u91c7\u7528\u4e0a\u4fa7\u5206\u4f4d\u6570\\(X\\sim N(\\mu,\\sigma^2)\\)</p> <p>\\(\\sigma\\)\u5df2\u77e5\u65f6\\(\\mu\\)\u7684\u7f6e\u4fe1\u533a\u95f4\\(\\overline x \\sim N(\\mu,\\sigma^2/n)\\;\\;\\rightarrow\\;\\; \\frac{\\overline x-\\mu}{\\sigma/\\sqrt{n}}\\sim N(0,1)\\) \\([\\hat\\theta_L,\\hat\\theta_U]=[\\;\\;\\overline x-\\frac{z_{\\alpha/2}\u00b7\\sigma}{\\sqrt{n}}\\;\\;,\\;\\;\\overline x + \\frac{z_{\\alpha/2}\u00b7\\sigma}{\\sqrt{n}}\\;\\;]\\) \\(\\sigma\\)\u672a\u77e5\u65f6\\(\\mu\\)\u7684\u7f6e\u4fe1\u533a\u95f4\\(\\frac{\\sqrt{n}(\\overline x - \\mu)}{\\sqrt{s^2} }\\sim t(n-1)\\) \\([\\hat\\theta_L,\\hat\\theta_U]=\\left[\\;\\; \\overline x - \\frac{t_{\\alpha/2}(n-1)s}{\\sqrt{n}} \\;\\;,\\;\\; \\overline x + \\frac{t_{\\alpha/2}(n-1)s}{\\sqrt{n}} \\;\\;\\right]\\) \\(\\sigma^2\\)\u7684\u7f6e\u4fe1\u533a\u95f4\uff08\u5f53\u4f5c\\(\\mu\\)\u672a\u77e5\uff09\\(\\frac{(n-1)s^2}{\\sigma^2}\\sim \\chi^2(n-1)\\) \\([\\hat\\theta_L,\\hat\\theta_U]=\\left[\\;\\; \\frac{(n-1)s^2}{\\chi^2_{\\alpha/2}(n-1)} \\;\\;,\\;\\; \\frac{(n-1)s^2}{\\chi^2_{1-\\alpha/2}(n-1)} \\;\\;\\right]\\)</p>"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap07/#\u4e24\u4e2a\u6b63\u6001\u603b\u4f53\u4e0b\u7684\u7f6e\u4fe1\u533a\u95f4","title":"\u4e24\u4e2a\u6b63\u6001\u603b\u4f53\u4e0b\u7684\u7f6e\u4fe1\u533a\u95f4","text":"<p>\\(\\sigma_1^2,\\sigma_2^2\\)\u5df2\u77e5\u65f6\\(\\mu_1-\\mu_2\\)\u7684\u7f6e\u4fe1\u533a\u95f4\\(\\overline x - \\overline y \\sim N(\\mu_1-\\mu_2,\\frac{\\sigma_1^2}{n_1},\\frac{\\sigma_2^2}{n_2})\\) \\([\\hat\\theta_L,\\hat\\theta_U]=\\left[\\;\\;\\overline x - \\overline y+ z_{\\alpha/2}\\sqrt{\\frac{\\sigma_1^2}{n_1}+\\frac{\\sigma_2^2}{n_2}}\\;\\;,\\;\\;\\overline x - \\overline y- z_{\\alpha/2}\\sqrt{\\frac{\\sigma_1^2}{n_1}+\\frac{\\sigma_2^2}{n_2}}\\;\\;\\right]\\) \\(\\sigma_1^2,\\sigma_2^2\\)\u672a\u77e5\u4f46\u76f8\u540c(\\(\\sigma_1^2=\\sigma_2^2=\\sigma^2\\))\u65f6\\(\\mu_1-\\mu_2\\)\u7684\u7f6e\u4fe1\u533a\u95f4\u53d6\\(\\sigma^2\\)\u7684\u65e0\u504f\u4f30\u8ba1\u91cf\\(S^2_w=\\frac{(n_1-1)S_1^2+(n_2-1)S_2^2}{n_1+n_2-2}\\) \\(\\frac{(\\overline x -\\overline y)-(\\mu_1-\\mu_2)}{S_w\\sqrt{\\frac{1}{n_1}+\\frac{1}{n_2}}}\\sim t  (n_1+n_2-2)\\) \\([\\hat\\theta_L,\\hat\\theta_U]=\\left[\\;\\; \\overline x - \\overline y\\pm t_{\\alpha/2}(n_1+n_2-2)S_w\\sqrt{\\frac{1}{n_1}+\\frac{1}{n_2}} \\;\\;\\right]\\) \\(\\sigma_1^2,\\sigma_2^2\\)\u672a\u77e5\u4e14\u4e0d\u540c(\\(\\sigma_1^2\\not=\\sigma_2^2\\))\u65f6\\(\\mu_1-\\mu_2\\)\u7684\u7f6e\u4fe1\u533a\u95f4</p> <ul> <li>\u5f53\u6837\u672c\u5bb9\u91cf\\(n_1,n_2\\)\u8db3\u591f\u5927\u65f6\uff0c\u6709\\(\\frac{(\\overline x -\\overline y)-(\\mu_1 - \\mu_2)}{\\sqrt{\\frac{S_1^2}{n_1}+\\frac{S_2^2}{n_2}}}\\sim N(0,1)\\)</li> <li>\\([\\hat\\theta_L,\\hat\\theta_U]=\\left[\\;\\; \\overline x - \\overline y\\pm z_{\\alpha/2}\\sqrt{\\frac{S_1^2}{n_1}+\\frac{S_2^2}{n_2}} \\;\\;\\right]\\)</li> <li>\u800c\u5bf9\u4e8e\u5bb9\u91cf\u4e0d\u5927\u7684\u5c0f\u6837\u672c\uff0c\u6709\u5982\u4e0b\u7ed3\u8bba\uff1a</li> <li>\\(\\frac{(\\overline X-\\overline Y)-(\\mu_1-\\mu_2)}{\\sqrt{\\frac{S_1^2}{n_1}+\\frac{S_2^2}{n_2}}}\\sim t(k)\\;\\;where \\;\\; k=\\frac{(\\frac{S_1^2}{n_1}+\\frac{S_2^2}{n_2})^2}{\\frac{(S_1^2)^2}{n_1^2(n_1-1)}+\\frac{(S_2^2)^2}{n_2^2(n_2-1)}}\\)\uff1b</li> <li>\\([\\hat\\theta_L,\\hat\\theta_U]=\\left[\\;\\; \\overline x - \\overline y\\pm t_{\\alpha/2}(k)\\sqrt{\\frac{S_1^2}{n_1}+\\frac{S_2^2}{n_2}} \\;\\;\\right]\\)</li> </ul> <p>\\(\\frac{\\sigma^2_1}{\\sigma_2^2}\\)\u7684\u533a\u95f4\u4f30\u8ba1\\(\\frac{S_1^2/S_2^2}{\\sigma^2_1/\\sigma_2^2}\\sim F(n_1-1,n_2-1)\\)</p> \\[ [\\hat\\theta_L,\\hat\\theta_U]=\\left[\\;\\; \\frac{S_1^2/S_2^2}{F_{\\alpha/2}(n_1-1,n_2-1)} \\;\\;,\\;\\; \\frac{S_1^2/S_2^2}{F_{1-\\alpha/2}(n_1-1,n_2-1)} \\;\\;\\right] \\]"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap08/","title":"[8.x] \u5047\u8bbe\u68c0\u9a8c","text":"<p> \u7ea6 133 \u4e2a\u5b57 </p> <ul> <li>\u6a59\u4e66 P314</li> <li>\u7eff\u4e66 P211</li> </ul>"},{"location":"cour_note/D1CX_ProbabilityAndStatistics/Chap08/#\u5904\u7406\u5047\u8bbe\u68c0\u9a8c\u95ee\u9898\u7684\u57fa\u672c\u6b65\u9aa4","title":"\u5904\u7406\u5047\u8bbe\u68c0\u9a8c\u95ee\u9898\u7684\u57fa\u672c\u6b65\u9aa4","text":"<ol> <li>\u63d0\u51fa\u539f\u5047\u8bbe\u548c\u5907\u62e9\u5047\u8bbe\uff1b</li> <li>\u9009\u62e9\u68c0\u9a8c\u540c\u8ba1\u91cf\uff0c\u7ed9\u51fa\u62d2\u7edd\u57df\u5f62\u5f0f\uff1b</li> <li>\u9009\u62e9\u663e\u8457\u6027\u6c34\u5e73\uff0c\u6c42\u62d2\u7edd\u57df\u4e2d\u7684\u4e34\u754c\u503c\uff08\u7ed9\u51fa\u62d2\u7edd\u57df\uff09\uff1b</li> <li>\u6839\u636e\u5b9e\u9645\u6837\u672c\u4f5c\u51fa\u5224\u65ad\uff1b</li> </ol> <p>\u6216\u8005</p> <ol> <li>\u63d0\u51fa\u539f\u5047\u8bbe\u548c\u5907\u62e9\u5047\u8bbe\uff1b</li> <li>\u9009\u62e9\u68c0\u9a8c\u540c\u8ba1\u91cf\uff0c\u7ed9\u51fa\u62d2\u7edd\u57df\u5f62\u5f0f\uff1b</li> <li>\u8ba1\u7b97\u68c0\u9a8c\u7edf\u8ba1\u91cf\u7684\u89c2\u5bdf\u503c\u548c\\(P\\_\\)\u503c\uff1b</li> <li>\u6839\u636e\u7ed9\u5b9a\u7684\u663e\u8457\u6c34\u5e73\\(\\alpha\\)\u4f5c\u51fa\u5224\u65ad\uff1b</li> </ol> <p></p>"},{"location":"cour_note/D1QD_CXiaoCheng/","title":"\ud83d\udd2e C\u5c0f\u7a0b \u7410\u788e\u77e5\u8bc6\u70b9\u6574\u7406","text":"<p> \u7ea6 4826 \u4e2a\u5b57  53 \u884c\u4ee3\u7801  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 17 \u5206\u949f</p> <p>\u7528\u6765\u6574\u7406C\u5c0f\u7a0b\u7684\u4e00\u4e9b\u7ec6\u788e\u77e5\u8bc6\u70b9\u3002 \u6392\u7248\u6ca1\u6709\u903b\u8f91\uff0c\u5185\u5bb9\u4e5f\u4e0d\u5b8c\u6574\u3002 \u8be5\u6587\u6863\u9488\u5bf9\u6211\u4e2a\u4eba\u3002 \u6709\u4e00\u4e9b\u4e0d\u5728\u8003\u8bd5\u8303\u56f4\u5185\u7684\u4e1c\u897f\uff0c\u6211\u89c9\u5f97\u6709\u610f\u601d\u4e5f\u4e22\u4e0a\u53bb\u4e86\u3002</p>"},{"location":"cour_note/D1QD_CXiaoCheng/#\u60f3\u4e0d\u51fa\u6807\u9898\u7684\u90fd\u653e\u8fd9","title":"\u60f3\u4e0d\u51fa\u6807\u9898\u7684\u90fd\u653e\u8fd9","text":"<ul> <li>\u51af\u00b7\u8bfa\u4f9d\u66fc\u7ed3\u6784\uff1a\u4e00\u79cd\u5c06\u7a0b\u5e8f\u6307\u4ee4\u5b58\u50a8\u5668\u548c\u6570\u636e\u5b58\u50a8\u5668\u5408\u5e76\u5728\u4e00\u8d77\u7684\u7535\u8111\u8bbe\u8ba1\u6982\u5ff5\u7ed3\u6784\u3002   </li> <li>\u95ee\u4f60\u4e00\u4e2a<code>char</code>\u578b\u53d8\u91cf\u7684\u503c\u662f\u591a\u5c11\uff0c\u8981\u4e48\u8bb0\u5f97 \u5f15\u53f7\uff0c\u8981\u4e48\u8bb0\u5f97\u7528 ASCII </li> <li>C\u8bed\u8a00\u7a0b\u5e8f \u6613\u4e8e\u79fb\u690d <ul> <li>\u4e0e\u786c\u4ef6\u6709\u5173\u7684\u56e0\u7d20\u88ab\u4ece\u8bed\u8a00\u4e3b\u4f53\u4e2d\u5206\u79bb\u51fa\u6765   </li> </ul> </li> <li>C\u8bed\u8a00\u6570\u636e\u7c7b\u578b\u68c0\u67e5\u4e0d\u4e25\u683c    </li> <li>C\u8bed\u8a00\u8868\u8fbe\u5f0f\u51fa\u73b0\u4e8c\u4e49\u6027    </li> <li>C\u8bed\u8a00\u4e0d\u80fd\u81ea\u52a8\u68c0\u67e5\u6570\u636e\u8d8a\u754c   </li> <li>\u6570\u636e\u6587\u4ef6\u53ef\u5206\u4e3a \u6587\u672c\u6587\u4ef6 \u548c \u4e8c\u8fdb\u5236\u6587\u4ef6 </li> <li>\u6587\u4ef6\u7684\u6570\u636e\u6d41\u53c8\u5206\u4e3a \u5b57\u7b26\u6d41 \u548c \u4e8c\u8fdb\u5236\u6d41 </li> <li>\u4e0b\u9762\u8fd9\u4e9b\u8bf4\u6cd5\u90fd\u6ca1\u9519\uff0c\u4f46\u662f\u6211\u60f3\u5230\u4e86\u66f4\u597d\u7684\u8bf4\u6cd5\u6240\u4ee5\u5212\u4e86\u4ed6\u4eec    </li> <li><code>typedef</code>\u6570\u7ec4\u7684\u683c\u5f0f\u5982\u4e0b\uff1a<ul> <li><code>typedef int array[10];</code></li> </ul> </li> <li>\u5219\u4e0b\u9762\u4e24\u4e2a\u7b49\u6548\uff1a<ul> <li>int a[10];</li> <li>array a;</li> </ul> </li> <li>\u4f46\u7cfb\u7edf\u5bf9\u4ed6\u4eec\u7684\u7c7b\u578b\u8ba4\u5b9a\u4e0d\u540c\uff0c<code>array</code>\u4f5c\u4e3a\u4e00\u4e2a\u65b0\u7684<code>~~type~~</code>\u5b58\u5728 </li> <li><code>typedef</code>\u7684\u5b9a\u4e49 \u7c7b\u4f3c \u4e8e\u53d8\u91cf\u7684\u5b9a\u4e49\uff1a<ul> <li>\u300ceg\u300d\u4e8c\u7ea7\u6307\u9488\u6570\u7ec4\uff1a<code>typedef int **P[10];</code> \u4e4b\u540e\u4f60\u53ef\u4ee5\u7528<code>P</code>\u4ee3\u8868\u4e00\u4e2a \u6307\u5411 \u4e00\u4e2a\u6307\u5411\u6574\u578b\u7684\u6307\u9488 \u7684\u6307\u9488 \u7684 10\u7ef4\u6570\u7ec4 \u7684 \u7c7b\u578b\uff0810\u4e2a\u4e8c\u7ea7\u6307\u9488\uff09</li> <li>\u300ceg\u300d\u4e00\u7ea7\u6570\u7ec4\u6307\u9488\uff1a<code>typedef int (*P)[10];</code> \u4e4b\u540e\u4f60\u53ef\u4ee5\u7528<code>P</code>\u4ee3\u8868\u4e00\u4e2a \u6307\u5411 10\u7ef4\u6570\u7ec4 \u7684\u6307\u9488 \u7684 \u7c7b\u578b(1\u4e2a\u4e00\u7ea7\u6307\u9488)</li> <li>\u76f8\u5173\u5185\u5bb9\uff1a\u8fd9\u91cc</li> </ul> </li> <li><code>typedef</code>\u7684\u5185\u5bb9 \u4e00\u822c \u7528 \u5927\u5199\u5355\u8bcd(\u6bd4\u5982FILE)\u8868\u793a\u8fd9\u662f\u4e00\u4e2a\u81ea\u5b9a\u4e49\u7c7b\u578b\uff0c\u4f46\u4e0d\u7528\u5927\u5199\u4e5f\u4e0d\u4f1a\u51fa\u9519    </li> <li><code>break;</code>\u53ef\u4ee5\u51fa\u73b0\u5728 loop \u6216\u8005 switch \u5185    </li> <li>\u8981\u5c0f\u5fc3\u85cf\u5728\u53c2\u6570\u8868\u91cc\u7684\u7c7b\u578b\u8f6c\u6362    </li> </ul> \u9898\u9762\u7b54\u6848 <ul> <li>\u5982\u4e0b\u7a0b\u5e8f\u7684\u8f93\u51fa\u4e3a___\u3002</li> </ul> <pre><code>#include &lt;stdio.h&gt;\n\ndouble myFunction(int x){\nreturn x;\n}\n\nint main(){\nprintf(\"%lf\",myFunction(3.14));\n}\n</code></pre> <ul> <li>3</li> <li>\u56e0\u4e3a 3.14 \u5728\u4f20\u5165 <code>myFunction(int)</code> \u65f6\u53d1\u751f\u4e86\u7c7b\u578b\u8f6c\u6362\u3002   </li> </ul> <ul> <li>\u5b57\u7b26\u4e32\u6570\u7ec4\u4ee5<code>\\0</code>\u4e3a\u7ed3\u675f\u7b26</li> <li> <p>\u53ef\u4ee5\u76f4\u63a5\u7528<code>[]</code>\u8bbf\u95ee\u5b57\u7b26\u4e32\u5e38\u91cf\u7684\u67d0\u4e2a\u5b57\u7b26</p> <ul> <li>\u5982<code>\"ABC\"[1] = 'B'</code> </li> </ul> </li> <li> <p>\u5c0f\u5fc3 \u9690\u85cf \u7684\u201c0\u201d\uff1a</p> </li> <li><code>int a[3][4] = {{1,2,3},{1,2,3}}</code>\u5b9e\u9645\u4e0a\u7b49\u6548\u4e8e<code>int a[3][4] = {{1,2,3,0},{1,2,3,0},{0,0,0,0}}</code></li> <li><code>EOF</code>\u5b9e\u9645\u4e0a\u5c31\u662f<code>-1</code> </li> <li><code>NULL</code>\u5b9e\u9645\u4e0a\u5c31\u662f<code>0LL</code> </li> <li>\u5b9a\u4e49\u51fd\u6570\u65f6\u7701\u7565\u51fd\u6570\u7684\u8fd4\u56de\u7c7b\u578b\uff0c\u5219\u5b9e\u9645\u8fd4\u56de\u7c7b\u578b\u662f<code>int</code></li> <li><code>puts()</code>\u53ea\u80fd\u8f93\u51fa\u5b57\u7b26\u4e32(\u8f93\u51fa\u7684\u4e1c\u897f\u5fc5\u987b\u6709<code>\\0</code>\u5426\u5219\u4f1a\u6302\uff0c\u610f\u601d\u662f\u8bf4 \u6570\u5b57\u3001\u5b57\u7b26 \u90fd\u4e0d\u53ef\u4ee5)    </li> </ul> <p> </p> <ul> <li> <p>\u8fd9\u4e2a\u62a5\u9519 <pre><code>#include&lt;stdio.h&gt;\n\n{}\n\nint main(){\n}\n</code></pre></p> </li> <li> <p>\u8fd9\u4e2a\u4e0d\u62a5\u9519 <pre><code>#include&lt;stdio.h&gt;\n\nint main(){\n{}\n}\n</code></pre></p> </li> </ul>"},{"location":"cour_note/D1QD_CXiaoCheng/#\u6570\u636e\u7c7b\u578b\u4e0e\u5b57\u8282\u5206\u914d","title":"\u6570\u636e\u7c7b\u578b\u4e0e\u5b57\u8282\u5206\u914d","text":"\u6570\u636e\u7c7b\u578b \u5b57\u8282\u6570 \u8bf4\u660e char 1 int 4 short 2 long 4 long long 8 unsigned 8 float 4 \u6709\u6548\u4f4d\u6570\u4e00\u822c\u57287~8\u4f4d double 8 \u6709\u6548\u4f4d\u7f6e\u4e00\u822c\u572815~16\u4f4d \u6240\u6709 \u6307\u9488(64x/32x) 8/4 struct\u3001\u6570\u7ec4 - \u5185\u5b58\u4e3a\u6240\u6709\u6210\u5458\u53d8\u91cf\u7684\u5185\u5b58\u548c\uff08\u4f46\u662f\u9700\u8981\u8003\u8651\u5bf9\u9f50\uff09 <ul> <li>\u5bf9\u4e8e\u5e38\u6570\uff1a<ul> <li><code>sizeof(1) = 4</code></li> <li><code>sizeof(1ll) = 8</code></li> <li><code>sizeof(1.0) = 8</code></li> <li><code>sizeof(1.0f) = 4</code></li> </ul> </li> <li><code>sizeof()</code>\u662f\u4e00\u4e2a\u8fd0\u7b97\u7b26\uff0c\u4e0d\u662f\u51fd\u6570\uff0c\u800c\u4e14\u5728\u7f16\u8bd1\u9636\u6bb5\u5c31\u5b8c\u6210\u66ff\u6362\u3002<ul> <li>\u5982\u679c<code>k</code>\u7684\u7c7b\u578b\u53608B\u5185\u5b58\uff0c\u5219<code>sizeof(++k)</code>\u5728\u7f16\u8bd1\u9636\u6bb5\u88ab\u66ff\u6362\u4e3a8\uff0c\u800c<code>k</code>\u7684 \u503c\u4e0d\u4f1a\u6539\u53d8</li> </ul> </li> </ul>"},{"location":"cour_note/D1QD_CXiaoCheng/#\u7f16\u8bd1\u7f16\u8bd1\u9884\u5904\u7406","title":"\u7f16\u8bd1\u3001\u7f16\u8bd1\u9884\u5904\u7406","text":"<ul> <li>\u7f16\u8bd1\u9884\u5904\u7406<ul> <li>\u7f16\u8bd1\u9884\u5904\u7406\u662f C \u8bed\u8a00\u7f16\u8bd1\u7a0b\u5e8f\u7684\u7ec4\u6210\u90e8\u5206\uff0c\u7528\u4e8e\u89e3\u91ca\u5904\u7406 C \u8bed\u8a00\u7a0b\u5e8f\u4e2d\u7684\u9884\u5904\u7406\u6307\u4ee4\uff08\u7279\u5f81\u662f\u4ee5<code>#</code>\u5f00\u5934\uff0c\u5b83\u4eec\u4e0d\u662f\u771f\u6b63\u7684 C \u8bed\u53e5\uff09</li> <li>\u7f16\u8bd1\u9884\u5904\u7406\u5728\u6b63\u5f0f\u7f16\u8bd1\u4e4b\u524d</li> </ul> </li> <li><code>#include</code><ul> <li>\u5982\u679c\u540e\u9762\u662f<code>&lt;xxx&gt;</code>\uff0c\u5219\u5c06\u4f7f\u7528 C \u8bed\u8a00\u7684 \u6807\u51c6\u5934\u6587\u4ef6</li> <li>\u5982\u679c\u540e\u9762\u662f<code>\"xxx\"</code>\uff0c\u5c06\u5148\u5230\u5f53\u524d\u5de5\u4f5c\u76ee\u5f55\u5bfb\u627e\u88ab\u5305\u542b\u7684\u6587\u4ef6\uff0c\u627e\u4e0d\u5230\u5219\u53bb\u7cfb\u7edf<code>include</code>\u76ee\u5f55\u5bfb\u627e</li> </ul> </li> <li>\u5b8f<ul> <li>\u57fa\u672c\u683c\u5f0f <code>#define \u5b8f\u540d(\u5b8f\u53c2) \u5b8f\u5b9a\u4e49\u5b57\u7b26\u4e32</code></li> <li>\u5b8f\u53ea\u662f\u7eaf\u7cb9\u7684\u5bf9\u4ee3\u7801\u7684\u5b57\u7b26\u4e32\u66ff\u6362\uff01</li> </ul> </li> <li> <p>\u6761\u4ef6\u7f16\u8bd1   <pre><code>#define FLAG 1\n#if FLAG\n//\u7a0b\u5e8f\u6bb51\n#else\n//\u7a0b\u5e8f\u6bb52\n#endif\n</code></pre></p> </li> <li> <p>\u7531\u4e8e\u8fd9\u4e9b\u90fd\u5728\u9884\u7f16\u8bd1\u4e2d\u5904\u7406\uff1a</p> <ul> <li><code>#if</code>\u540e\u9762\u7684\u6761\u4ef6\u53ea\u80fd\u662f\u5b8f\u540d</li> <li>\u4e0d\u5728\u6761\u4ef6\u9009\u62e9\u8303\u56f4\u5185\u7684\u4ee3\u7801\u4e0d\u4f1a\u88ab\u7f16\u8bd1   </li> </ul> </li> <li> <p>\u7f16\u8bd1\u7a0b\u5e8f \u9996\u5148\u8981\u5bf9 \u6e90\u7a0b\u5e8f \u8fdb\u884c \u8bcd\u6cd5\u5206\u6790\uff0c\u7136\u540e\u8fdb\u884c \u8bed\u6cd5\u5206\u6790 \u548c \u8bed\u4e49\u5206\u6790</p> </li> <li>\u7f16\u5199\u7a0b\u5e8f  -&gt;  \u7f16\u8bd1\u751f\u6210\u4e8c\u8fdb\u5236obj\u76ee\u6807\u7a0b\u5e8f\u6587\u4ef6  -&gt; \u4e0e\u5e93\u51fd\u6570\u8fdb\u884c\u8fde\u63a5\uff0c\u5f62\u6210exe\u53ef\u6267\u884c\u6587\u4ef6</li> </ul>"},{"location":"cour_note/D1QD_CXiaoCheng/#\u8f93\u5165\u8f93\u51fa\u4e2d\u7684\u683c\u5f0f\u63a7\u5236\u7b26","title":"\u8f93\u5165\u8f93\u51fa\u4e2d\u7684\u683c\u5f0f\u63a7\u5236\u7b26","text":"\u63a7\u5236\u7b26 \u8bf4\u660e <code>%d</code> \u5341\u8fdb\u5236\u6574\u578b <code>%ld</code> \u5341\u8fdb\u5236\u957f\u6574\u578b <code>%md</code> \uff08\\(m \\in \\text{R}\\)\uff0c\u5982<code>%2d</code>\uff09 m \u4e3a\u6307\u5b9a\u7684\u8f93\u51fa\u5b57\u6bb5\u7684\u5bbd\u5ea6\u3002\u5982\u679c\u6570\u636e\u7684\u4f4d\u6570\u5c0f\u4e8e m\uff0c\u5219\u5de6\u7aef\u8865\u4ee5\u7a7a\u683c\uff0c\u82e5\u5927\u4e8e m\uff0c\u5219\u6309\u5b9e\u9645\u4f4d\u6570\u8f93\u51fa\u3002\u5982\u679c\u52a0<code>-</code>\u8868\u793a\u5de6\u5bf9\u9f50\uff1b\u5982\u679c\u52a0<code>+</code>\u6216\u4e0d\u52a0\u8868\u793a\u53f3\u5bf9\u9f50\u3002 \u5982<code>%-2d</code>\uff0c<code>%+3d</code> <code>%u</code> \u5341\u8fdb\u5236\u65e0\u7b26\u53f7\u6574\u578b <code>%lu</code> \u5341\u8fdb\u5236\u65e0\u7b26\u53f7\u957f\u6574\u578b <code>%c</code> \u5b57\u7b26 <code>%f</code> <code>%e</code> \u5bf9\u4e8e<code>scanf</code>\u4ec5\u8868\u793a\u5355\u7cbe\u5ea6\u6d6e\u70b9\u6570\u5bf9\u4e8e<code>printf</code>\u4e0e<code>%lf</code>\u7b49\u4ef7\u3002\u4e0d\u6307\u5b9a\u5b57\u6bb5\u5bbd\u5ea6\uff0c\u7531\u7cfb\u7edf\u81ea\u52a8\u6307\u5b9a\uff0c\u6574\u6570\u90e8\u5206\u5168\u90e8\u8f93\u51fa\uff0c\u5c0f\u6570\u90e8\u5206\u8f93\u51fa 6 \u4f4d\uff0c\u8d85\u8fc7 6 \u4f4d\u7684 \u56db\u820d\u4e94\u5165 <code>%.mf</code>\uff08\uff0c\u5982<code>%.6f</code>\uff09 \u8f93\u51fa\u5b9e\u6570\u65f6 \u5c0f\u6570\u70b9\u540e \u4fdd\u7559 m \u4f4d <code>%lf</code> <code>%le</code> \u5bf9\u4e8e<code>scanf</code>\u4ec5\u8868\u793a\u53cc\u7cbe\u5ea6\u6d6e\u70b9\u6570\u5bf9\u4e8e<code>printf</code>\u4e0e<code>%f</code>\u7b49\u4ef7\u3002\u4e0d\u6307\u5b9a\u5b57\u6bb5\u5bbd\u5ea6\uff0c\u7531\u7cfb\u7edf\u81ea\u52a8\u6307\u5b9a\uff0c\u6574\u6570\u90e8\u5206\u5168\u90e8\u8f93\u51fa\uff0c\u5c0f\u6570\u90e8\u5206\u8f93\u51fa 6 \u4f4d\uff0c\u8d85\u8fc7 6 \u4f4d\u7684 \u56db\u820d\u4e94\u5165 <code>%.mlf</code>\uff08\uff0c\u5982<code>%.6lf</code>\uff09 \u8f93\u51fa\u5b9e\u6570\u65f6 \u5c0f\u6570\u70b9\u540e \u4fdd\u7559 m \u4f4d <code>%p</code> \u5730\u5740 <code>%s</code> \u5b57\u7b26\u4e32 <code>%o</code> \u516b\u8fdb\u5236\u6574\u578b <code>%lo</code> \u516b\u8fdb\u5236\u957f\u6574\u578b <code>%x</code> <code>%X</code> <code>%#x</code> <code>%#X</code> \u5341\u516d\u8fdb\u5236\u6574\u578b <code>%lx</code> <code>%lX</code> \u5341\u516d\u8fdb\u5236\u957f\u6574\u578b"},{"location":"cour_note/D1QD_CXiaoCheng/#\u5e38\u89c1\u8f6c\u4e49\u5b57\u7b26","title":"\u5e38\u89c1\u8f6c\u4e49\u5b57\u7b26","text":"\u8f6c\u4e49\u5b57\u7b26 \u610f\u4e49 ASCII\uff08Dec\uff09 ASCII\uff08Hex\uff09 <code>\\b</code> \u9000\u683c(BS) \uff0c\u5c06\u5f53\u524d\u4f4d\u7f6e\u79fb\u5230\u524d\u4e00\u5217 008 0x08 <code>\\n</code> \u6362\u884c(LF) \uff0c\u5c06\u5f53\u524d\u4f4d\u7f6e\u79fb\u5230\u4e0b\u4e00\u884c\u5f00\u5934 010 0x10 <code>\\r</code> \u56de\u8f66(CR) \uff0c\u5c06\u5f53\u524d\u4f4d\u7f6e\u79fb\u5230\u672c\u884c\u5f00\u5934 013 0x13 <code>\\t</code> \u6c34\u5e73\u5236\u8868(HT) 009 0x09 <code>\\'</code> \u5355\u5f15\u53f7 039 0x27 <code>\\\"</code> \u53cc\u5f15\u53f7 034 0x22 <code>\\\\</code> \u53cd\u659c\u6760 092 0x5C <code>\\ddd</code> 1~3\u4f4d\u7684\u516b\u8fdb\u5236\u6574\u6570\u6240\u4ee3\u8868\u7684ASCII\u7b26\u6bd4\u5982<code>\\041</code>\u6216\u8005<code>\\41</code>\u8868\u793a<code>!</code> - - <code>\\xhh</code> 1~2\u4f4d\u7684\u5341\u516d\u8fdb\u5236\u6574\u6570\u6240\u8868\u793a\u7684ASCII\u7b26\u6bd4\u5982<code>\\x21</code>\u8868\u793a<code>!</code> - -"},{"location":"cour_note/D1QD_CXiaoCheng/#\u5e38\u7528\u6570\u5b66\u51fd\u6570","title":"\u5e38\u7528\u6570\u5b66\u51fd\u6570","text":"<ul> <li><code>sqrt(x)</code> \\(\\sqrt x\\)\uff0c\u8fd4\u56de<code>double</code>\u7c7b\u578b</li> <li><code>pow(x,n)</code> \\(x^n\\)\uff0c\u8fd4\u56de<code>double</code>\u7c7b\u578b</li> <li><code>exp(x)</code> \\(e^x\\)\uff0c\u8fd4\u56de<code>double</code>\u7c7b\u578b</li> <li><code>fabs(x)</code> \\(|x|\\)\uff0c\u8fd4\u56de<code>double</code>\u7c7b\u578b</li> <li><code>log(x)</code> \\(\\ln{x}\\)\uff0c\u8fd4\u56de<code>double</code>\u7c7b\u578b</li> </ul>"},{"location":"cour_note/D1QD_CXiaoCheng/#\u5faa\u73af\u8bed\u53e5","title":"\u5faa\u73af\u8bed\u53e5","text":"<p>\u5982\u4e0b\u7684\u5faa\u73af\u8bed\u53e5\uff1a <pre><code>for(\u8868\u8fbe\u5f0f1;\u8868\u8fbe\u5f0f2;\u8868\u8fbe\u5f0f3){\n\u8bed\u53e5\n}\n</code></pre> \u5176\u6d41\u7a0b\u5e94\u5f53\u5982\u4e0b\uff1a</p> <pre><code>graph LR\n    A[\u8868\u8fbe\u5f0f1] --&gt; B{\u8868\u8fbe\u5f0f2};\n    B --&gt;|Yes| C[\u8bed\u53e5];\n    C --&gt; D[\u8868\u8fbe\u5f0f3];\n    D --&gt; B;\n    B ----&gt;|No| E[\u7ed3\u675f\u5faa\u73af];</code></pre>"},{"location":"cour_note/D1QD_CXiaoCheng/#\u5206\u652f\u8bed\u53e5","title":"\u5206\u652f\u8bed\u53e5","text":"<ul> <li>\u5206\u652f\u8bed\u53e5\u6d4b\u8bd5\u6570\u636e\u81f3\u5c11\u9700\u8981\u51e0\u7ec4\u95ee\u9898\uff1a\u8981\u6ce8\u610f\u6570\u636e\u8fb9\u754c\u4e5f\u8981\u7b97\u4e00\u7ec4:<ul> <li>\u5982\u4e0b\u5206\u652f\u8bed\u53e5\u9700\u8981\u8bbe\u8ba1\u81f3\u5c11___\u7ec4\u6d4b\u8bd5\u6570\u636e\uff1f</li> </ul> </li> </ul> \u9898\u9762\u7b54\u6848 <pre><code>if(x &lt; 60){\n//\u8bed\u53e5\n}\n</code></pre> <ul> <li>\u7b54\u6848\uff1a3</li> <li>\u89e3\u6790\uff1a<code>x &lt; 60</code> <code>x = 60</code> <code>x &gt; 60</code></li> </ul> <ul> <li><code>switch()</code>\u8bed\u53e5<ul> <li>\u9664\u4e86\u5e26\u5f15\u53f7\u7684\u5b57\u7b26\uff0c<code>case</code>\u540e\u9762\u8981\u6253\u7a7a\u683c\uff0c\u4e0d\u6253\u7a7a\u683c\u53ef\u80fd\u80fd\u8fc7\u7f16\u8bd1\u4f46\u662f\u65e0\u6cd5\u6b63\u5e38\u5224\u65ad</li> <li><code>case 'a'</code> \u6709\u6548</li> <li><code>case'a'</code> \u6709\u6548</li> <li><code>casea</code> \u65e0\u6548</li> <li><code>case1</code> \u65e0\u6548</li> <li><code>case</code>\u540e\u8ddf\u7684\u5fc5\u987b\u662f\u4e0d\u91cd\u590d\u7684\u5e38\u91cf\u8868\u8fbe\u5f0f\uff0c\u4e0d\u53ef\u4ee5\u662f\u53d8\u91cf\u53c2\u4e0e\u7684\u8868\u8fbe\u5f0f</li> <li>\u4e0d\u6253<code>break</code>\u4f1a\u4ece\u7b26\u5408\u6761\u4ef6\u7684<code>case</code>\u5f00\u59cb\u4e00\u76f4\u5f80\u4e0b\u5230\u5e95\u6216\u8005\u4e4b\u540e\u7b2c\u4e00\u4e2a<code>break</code></li> </ul> </li> <li> <p>\u6240\u4ee5<code>break;</code>\u4e0d\u4e00\u5b9a\u53ea\u80fd\u51fa\u73b0\u5728\u5faa\u73af\u91cc   </p> </li> <li> <p>C\u8bed\u8a00\u7684\u903b\u8f91\u8fd0\u7b97\u5177\u6709\u7701\u7565\u7279\u6027\uff1a\u5f53\u524d\u4e00\u4e2a\u8868\u8fbe\u5f0f\u5df2\u7ecf\u80fd\u591f\u51b3\u5b9a\u6574\u4e2a\u8868\u8fbe\u5f0f\u7684\u503c\u7684\u65f6\u5019\uff0c\u4e0d\u8ba1\u7b97\u540e\u9762\u90a3\u4e2a\u8868\u8fbe\u5f0f</p> </li> </ul> \u9898\u9762\u7b54\u6848 <ul> <li>\u4e0b\u5217\u7a0b\u5e8f\u6bb5\u7ed3\u675f\u540e<code>x</code>\u548c<code>y</code>\u7684\u503c\u5206\u522b\u4e3a___ \uff0c ___\u3002</li> </ul> <pre><code>int x = 0 , y = 0;\nif((++x) || (++y)){\n//\u8bed\u53e5\n}\n</code></pre> <ul> <li>\u7b54\u6848\uff1a1\uff0c0</li> </ul>"},{"location":"cour_note/D1QD_CXiaoCheng/#\u53d8\u91cf\u7684\u751f\u547d\u5468\u671f\u4f5c\u7528\u57df","title":"\u53d8\u91cf\u7684\u751f\u547d\u5468\u671f&amp;\u4f5c\u7528\u57df","text":"\u9759\u6001\u53d8\u91cf \u81ea\u52a8\u53d8\u91cf \u8fd9\u4e00\u7ec4\u5173\u7cfb\u7684\u7740\u91cd\u70b9\u5728\u5185\u5b58 \u5b58\u50a8\u4f4d\u7f6e \u548c \u751f\u547d\u5468\u671f \u7684\u95ee\u9898 \u5168\u5c40\u53d8\u91cf \u5c40\u90e8\u53d8\u91cf \u8fd9\u4e00\u7ec4\u5173\u7cfb\u7684\u7740\u91cd\u70b9\u5728 \u4f5c\u7528\u57df <ul> <li>\u5c40\u90e8\u53d8\u91cf \u7684\u6709\u6548\u4f7f\u7528\u8303\u56f4\u6700\u5927\u7a0b\u5ea6\u4fdd\u8bc1\u4e86\u5404\u90e8\u5206\u4e4b\u95f4\u7684\u72ec\u7acb\u6027\uff0c\u964d\u4f4e\u4e86\u5404\u4e2a\u6a21\u5757\u4e4b\u95f4\u7684\u8026\u5408\u5ea6</li> <li> <p>\u5168\u5c40\u53d8\u91cf \u7684 \u4f5c\u7528\u57df \u662f\u4ece \u5b9a\u4e49\u5f00\u59cb\u5230\u6587\u4ef6\u7ed3\u675f</p> </li> <li> <p>\u4e00\u65e6\u5728\u7a0b\u5e8f\u4e2d\u5b9a\u4e49\u4e86\u53d8\u91cf\uff0c\u8ba1\u7b97\u673a\u5728\u6267\u884c\u8fc7\u7a0b\u4e2d\u4f1a\u6839\u636e\u53d8\u91cf\u7684\u7c7b\u578b\u5206\u914d\u76f8\u5e94\u7684\u5185\u5b58\u5355\u5143\u4f9b\u53d8\u91cf\u4fdd\u5b58\u6570\u636e</p> </li> <li>\u81ea\u52a8\u53d8\u91cf\u7684\u5b9a\u4e49\u4e3a\uff1a<code>auto \u7c7b\u578b \u53d8\u91cf\u8868;</code> \u4e00\u822c\u60c5\u51b5\u4e0b<code>auto</code>\u53ef\u4ee5\u7701\u7565</li> <li>\u81ea\u52a8\u53d8\u91cf\u4f1a \u81ea\u52a8\u5206\u914d\u56de\u6536\u5185\u5b58</li> </ul> \u7cfb\u7edf\u5b58\u50a8\u533a \u7528\u6237\u5b58\u50a8\u533a \u7a0b\u5e8f\u533a\uff08\u4ee3\u7801\u5185\u5bb9\uff09 \u6570\u636e\u533a \u9759\u6001\u5b58\u50a8\u533a \u5168\u5c40\u53d8\u91cf \u9759\u6001\u5c40\u90e8\u53d8\u91cf \u52a8\u6001\u5b58\u50a8\u533a \u5404\u4e2a\u6a21\u5757\u4e0b\u7684\u52a8\u6001\u5c40\u90e8\u53d8\u91cf \u5404\u4e2a\u6a21\u5757\u4e0b\u7684\u52a8\u6001\u5c40\u90e8\u53d8\u91cf ... <ul> <li>\u9759\u6001\u5c40\u90e8\u53d8\u91cf\u7684\u5185\u5b58\u5b58\u50a8\u5728 \u9759\u6001\u5b58\u50a8\u533a \u4e2d\uff0c\u751f\u547d\u5468\u671f\u6301\u7eed\u5230\u7a0b\u5e8f\u7ed3\u675f\uff0c\u4e0d\u4f1a\u5728\u9000\u51fa\u51fd\u6570\u7684\u65f6\u5019\u88ab\u56de\u6536\uff0c\u4e0b\u4e00\u6b21\u4f7f\u7528\u540e\u4f1a\u88ab\u91cd\u65b0\u6fc0\u6d3b</li> <li>\u4e0e\u52a8\u6001\u5168\u5c40\u53d8\u91cf\u76f8\u6bd4\uff0c\u9759\u6001\u5168\u5c40\u53d8\u91cf\u7684\u4f5c\u7528\u57df\u5728\u5f53\u524d\u6587\u4ef6\u5185\uff0c\u52a8\u6001\u5168\u5c40\u53d8\u91cf\u5728\u591a\u6587\u4ef6\u9879\u76ee\u4e2d\u5728\u6bcf\u4e00\u4e2a\u6587\u4ef6\u90fd\u53ef\u4ee5\u7528</li> <li>\u9759\u6001\u53d8\u91cf\u7684\u5b9a\u4e49\u4e3a\uff1a<code>static \u7c7b\u578b \u53d8\u91cf\u8868;</code></li> <li>\u9759\u6001\u53d8\u91cf\u521d\u503c\u9ed8\u8ba4\u4e3a <code>0</code></li> </ul>"},{"location":"cour_note/D1QD_CXiaoCheng/#\u8865\u7801","title":"\u8865\u7801","text":"<ul> <li>\u4e3a\u4e86\u65b9\u4fbf\u8ba1\u7b97\u673a\u5185\u7684\u8fd0\u7b97\uff0c\u4e00\u822c\u7528 \u8865\u7801 \u8868\u793a\u6570\u503c</li> <li>\u8865\u7801 \u7684\u8ba1\u7b97\uff1a\u8d1f\u6570 \u9664\u4e86\u7b26\u53f7\u4f4d \u53d6\u53cd\u52a0\u4e00<ul> <li>\u300ceg\u300d\u4e24\u4e2a\u5b57\u8282\u5b58\u50a8-17\uff1a</li> <li>\u539f\u7801\uff1a<code>1000``0000</code> <code>0001``0001</code></li> <li>\u53cd\u7801\uff1a<code>1111``1111</code> <code>1110``1110</code></li> <li>\u8865\u7801\uff1a<code>1111``1111</code> <code>1110``1111</code></li> </ul> </li> <li>\u4f7f\u7528 \u8865\u7801 \u65b9\u4fbf\u7684\u539f\u56e0\u662f\uff1a\u5904\u7406\u8d1f\u6570\u548c\u6574\u6570\u76f8\u52a0\uff0c\u5b9e\u9645\u4e0a\u662f\u505a\u540c\u4f59\u8fd0\u7b97\uff1a<ul> <li>\\(-3\\) = \\((1101)_{\u8865\u7801}\\)</li> <li>\\(6\\) = \\((0110)_{\u8865\u7801}\\)</li> <li>\\(-3 + 6\\) = \\((1101)_{\u8865\u7801} + (0110)_{\u8865\u7801}\\) =  \\((0011)_{\u8865\u7801}\\) =  \\(3\\)</li> <li>\u4f46\u662f\u5982\u679c\u628a\u8865\u7801\u90fd\u5f53\u505a\u662f\u67d0\u4e2a\u6570\u7684\u539f\u7801\u5462\uff1f</li> <li>\\((1101)_{\u539f\u7801}\\) = \\(13\\)</li> <li>\\((0110)_{\u539f\u7801}\\) = \\(6\\) </li> <li>\\((0110)_{\u539f\u7801}\\) + \\((1101)_{\u539f\u7801}\\) = \\(13+6\\) = \\(19\\) = \\((0011)_{\u539f\u7801} + (10000)_{\u539f\u7801}\\)</li> <li>\u663e\u7136\uff0c\u8fd9\u91cc\u7684<code>10000</code>\u6ea2\u51fa\u4e86\uff0c\u662f\u4e0d\u662f\u5f88\u50cf\u53d6\u6a21\uff1f</li> <li>\\(19 \\equiv 3 \\mod 16\\)</li> <li>\u800c\u8fd9\u4e2a<code>16</code>\u5c31\u662f\\(2^4\\)\uff0c\u8fd9\u4e2a<code>4</code>\u662f\u4ec0\u4e48\u663e\u800c\u6613\u89c1</li> <li>\u6240\u4ee5\u5b9e\u9645\u4e0a\u7684\u903b\u8f91\u5c31\u662f\uff1a</li> <li>\u5229\u7528\u7b26\u53f7\u4f4d\u628a<code>x</code>\u4e2a\u5b57\u8282\u7684\u50a8\u5b58\u5b57\u8282\u5206\u6210\u4e24\u90e8\u5206\uff0c\u5176\u4e2d\\(0 \\;\\;\\sim\\;\\; (2^{8x-1}-1)\\)\u8868\u793a\u975e\u8d1f\u6570\u7684\u5b58\u50a8\u8303\u56f4\uff0c \\(2^{8x-1} \\;\\;\\sim\\;\\; (2^{8x}-1)\\)\u8868\u793a\u8d1f\u6570\u7684\u5b58\u50a8\u8303\u56f4\uff0c\u5e76\u901a\u8fc7\u4e0a\u9762\u63d0\u5230\u7684\u8f6c\u6362\u65b9\u5f0f\u5bf9\u8d1f\u6570\u8fdb\u884c\u987a\u5e8f\u6620\u5c04</li> <li>\u8fdb\u884c\u8fd0\u7b97\u65f6\uff0c\u7b97\u4e0a\u7b26\u53f7\u4f4d\u53c2\u4e0e\u8fd0\u7b97\uff0c\u7b97\u51fa\u6765\u7684\u4e1c\u897f\u6574\u4e2a\u518d\u4f5c\u4e3a\u7b54\u6848\u7684\u8865\u7801</li> <li>\u4e00\u8a00\u4ee5\u853d\u4e4b\uff0c\u5728\u5bf916\u53d6\u4f59\u2014\u2014\u4ea6\u5373\u8d85\u8fc74Bits\u90fd\u5c06\u6ea2\u51fa \u7684\u60c5\u51b5\u4e0b\uff0c\u201c+13\u201d\u4e0e\u201c-3\u201d\u662f\u7b49\u4ef7\u7684\uff0c\u8fd9\u5c31\u662f\u4ece\u53d6\u6a21\u89d2\u5ea6\u6765\u7406\u89e3\u201c\u8865\u7801\u201d\u3002</li> </ul> </li> <li> <p>\u800c\u65e0\u7b26\u53f7\u6574\u6570\u5c31\u662f\u5c06\u539f\u6765\u5b58\u50a8\u8d1f\u6570\u7684\u8fd9\u90e8\u5206\u4f5c\u4e3a\u6574\u6570\u7684\u5ef6\u7eed\u90e8\u5206</p> </li> <li> <p>\u5bf9\u4e8e\u5404\u7c7b\u578b\u6574\u578b\u6570\u636e\u7684\u957f\u5ea6\u4ec5\u6709\u5df2\u4e0b\u8981\u6c42\uff1a</p> <ul> <li>\\(sizeof(\\text{short}) \\leq sizeof(\\text{int}) \\leq sizeof(\\text{long})\\) </li> </ul> </li> <li> <p>\u6574\u578b\u5e38\u91cf\u7684\u89c4\u5219\uff1a</p> <ul> <li>\u524d\u7f00\uff1a</li> <li>\u5341\u8fdb\u5236 \u9996\u4f4d\u6570\u5b57\u5fc5\u987b\u975e0   \u300ceg\u300d\uff1a<code>114514</code></li> <li>\u516b\u8fdb\u5236 \u9996\u4f4d\u6570\u5b57\u5fc5\u987b\u662f0   \u300ceg\u300d\uff1a<code>01616210</code></li> <li>\u5341\u516d\u8fdb\u5236 \u5f00\u5934\u5fc5\u987b\u662f0x\u62160X   \u300ceg\u300d\uff1a<code>0xfff</code></li> <li>\u540e\u7f00\uff1a\uff08\u5927\u5c0f\u5199\u4e0d\u654f\u611f\uff09</li> <li>L \u8868\u793a\u957f\u6574\u578b   \u300ceg\u300d\uff1a<code>123456L</code></li> <li>LL \u8868\u793a\u957f\u957f\u6574\u578b   \u300ceg\u300d\uff1a<code>123456LL</code></li> <li>U \u8868\u793a\u65e0\u7b26\u53f7\u6574\u578b   \u300ceg\u300d\uff1a<code>123456U</code></li> <li>U\u548cL\u53ef\u4ee5\u6df7\u5408\u4f7f\u7528\uff0c\u4e0d\u654f\u611f\u987a\u5e8f</li> </ul> </li> </ul>"},{"location":"cour_note/D1QD_CXiaoCheng/#\u8fd0\u7b97","title":"\u8fd0\u7b97","text":"<ul> <li>\u7b97\u6570\u8fd0\u7b97\u7b26\u7684\u51e0\u4e2a\u89c4\u5219\uff1a<ul> <li>\u6574\u6570\u9664\u6cd5\u5f97\u5230\u6574\u6570 (\u5206\u5b50\u6216\u5206\u6bcd\u4efb\u610f\u4e00\u4e2a\u4e3a\u6d6e\u70b9\u6570\u5373\u53ef\u81ea\u52a8\u7c7b\u578b\u8f6c\u6362\u540e\u505a\u6d6e\u70b9\u8fd0\u7b97)</li> <li>\u53d6\u4f59 \u8fd0\u7b97\u4ec5\u5bf9 \u6574\u578b \u6570\u636e\u4f7f\u7528</li> <li><code>+</code> <code>-</code>\u53ef\u505a\u5355\u76ee\u8fd0\u7b97\u7b26\u8868\u793a\u6b63\u8d1f</li> <li>\u53cc\u76ee\u8fd0\u7b97\u7b26\u4f1a\u4fdd\u8bc1\u4e24\u4fa7\u7684\u6570\u636e \u7c7b\u578b\u76f8\u540c(\u5bf9\u4e8e\u4e0d\u540c\u7684\u8f93\u5165\u6570\u636e\u4f1a\u8fdb\u884c\u81ea\u52a8\u7c7b\u578b\u8f6c\u6362)</li> <li>\u81ea\u52a8\u7c7b\u578b\u8f6c\u6362\uff1a<ul> <li>\u975e\u8d4b\u503c\u8fd0\u7b97\uff1a\u603b\u662f\u7531\u4f4e\u5411\u9ad8\u8f6c\u6362  </li> <li>\u8d4b\u503c\u8fd0\u7b97\uff1a\u8f6c\u6362\u4e3a\u88ab\u8d4b\u503c\u7684\u53d8\u91cf\u7c7b\u578b</li> </ul> </li> </ul> </li> </ul>"},{"location":"cour_note/D1QD_CXiaoCheng/#\u8fd0\u7b97\u7b26\u4f18\u5148\u7ea7\u540c\u7ea7\u9075\u5faa\u7ed3\u5408\u65b9\u5411\u89c4\u5f8b","title":"\u8fd0\u7b97\u7b26\u4f18\u5148\u7ea7(\u540c\u7ea7\u9075\u5faa\u7ed3\u5408\u65b9\u5411\u89c4\u5f8b)","text":"<p>\u5982\u6709\u51b2\u7a81\uff0c\u8bf7\u4f18\u5148\u53c2\u8003 \u8fd9\u91cc\u3002</p> \u4f18\u5148\u7ea7 \u8fd0\u7b97\u7b26 \u540d\u79f0\u6216\u542b\u4e49 \u4f7f\u7528\u5f62\u5f0f \u7ed3\u5408\u65b9\u5411 1 [] \u6570\u7ec4\u4e0b\u6807 \u6570\u7ec4\u540d[\u5e38\u91cf\u8868\u8fbe\u5f0f] \u5de6\u5230\u53f3 () \u5706\u62ec\u53f7 \uff08\u8868\u8fbe\u5f0f\uff09/\u51fd\u6570\u540d(\u5f62\u53c2\u8868) . \u6210\u5458\u9009\u62e9\uff08\u5bf9\u8c61\uff09 \u5bf9\u8c61.\u6210\u5458\u540d -&gt; \u6210\u5458\u9009\u62e9\uff08\u6307\u9488\uff09 \u5bf9\u8c61\u6307\u9488-&gt;\u6210\u5458\u540d ++ \u540e\u7f6e\u81ea\u589e\u8fd0\u7b97\u7b26 \u53d8\u91cf\u540d++ -- \u540e\u7f6e\u81ea\u51cf\u8fd0\u7b97\u7b26 \u53d8\u91cf\u540d-- 2 - \u8d1f\u53f7\u8fd0\u7b97\u7b26 -\u8868\u8fbe\u5f0f \u53f3\u5230\u5de6 (\u7c7b\u578b) \u5f3a\u5236\u7c7b\u578b\u8f6c\u6362 (\u6570\u636e\u7c7b\u578b)\u8868\u8fbe\u5f0f ++ \u524d\u7f6e\u81ea\u589e\u8fd0\u7b97\u7b26 ++\u53d8\u91cf\u540d -- \u524d\u7f6e\u81ea\u51cf\u8fd0\u7b97\u7b26 --\u53d8\u91cf\u540d * \u53d6\u503c\u8fd0\u7b97\u7b26 *\u6307\u9488\u53d8\u91cf &amp; \u53d6\u5730\u5740\u8fd0\u7b97\u7b26 &amp;\u53d8\u91cf\u540d ! \u903b\u8f91\u975e\u8fd0\u7b97\u7b26 !\u8868\u8fbe\u5f0f ~ \u6309\u4f4d\u53d6\u53cd\u8fd0\u7b97\u7b26 ~\u8868\u8fbe\u5f0f sizeof() \u957f\u5ea6\u8fd0\u7b97\u7b26 sizeof(\u8868\u8fbe\u5f0f) 3 / \u9664 \u8868\u8fbe\u5f0f/\u8868\u8fbe\u5f0f \u5de6\u5230\u53f3 * \u4e58 \u8868\u8fbe\u5f0f*\u8868\u8fbe\u5f0f % \u4f59\u6570\uff08\u53d6\u6a21\uff09 \u6574\u578b\u8868\u8fbe\u5f0f/\u6574\u578b\u8868\u8fbe\u5f0f 4 + \u52a0 \u8868\u8fbe\u5f0f+\u8868\u8fbe\u5f0f \u5de6\u5230\u53f3 - \u51cf \u8868\u8fbe\u5f0f-\u8868\u8fbe\u5f0f 5 &lt;&lt; \u5de6\u79fb \u53d8\u91cf&lt;&lt;\u8868\u8fbe\u5f0f \u5de6\u5230\u53f3 &gt;&gt; \u53f3\u79fb \u53d8\u91cf&gt;&gt;\u8868\u8fbe\u5f0f 6 &gt; \u5927\u4e8e \u8868\u8fbe\u5f0f&gt;\u8868\u8fbe\u5f0f \u5de6\u5230\u53f3 &gt;= \u5927\u4e8e\u7b49\u4e8e \u8868\u8fbe\u5f0f&gt;=\u8868\u8fbe\u5f0f &lt; \u5c0f\u4e8e \u8868\u8fbe\u5f0f&lt;\u8868\u8fbe\u5f0f &lt;= \u5c0f\u4e8e\u7b49\u4e8e \u8868\u8fbe\u5f0f&lt;=\u8868\u8fbe\u5f0f 7 == \u7b49\u4e8e \u8868\u8fbe\u5f0f==\u8868\u8fbe\u5f0f \u5de6\u5230\u53f3 != \u4e0d\u7b49\u4e8e \u8868\u8fbe\u5f0f!= \u8868\u8fbe\u5f0f 8 &amp; \u6309\u4f4d\u4e0e \u8868\u8fbe\u5f0f&amp;\u8868\u8fbe\u5f0f \u5de6\u5230\u53f3 9 ^ \u6309\u4f4d\u5f02\u6216 \u8868\u8fbe\u5f0f^\u8868\u8fbe\u5f0f \u5de6\u5230\u53f3 10 | \u6309\u4f4d\u6216 \u8868\u8fbe\u5f0f|\u8868\u8fbe\u5f0f \u5de6\u5230\u53f3 11 &amp;&amp; \u903b\u8f91\u4e0e \u8868\u8fbe\u5f0f&amp;&amp;\u8868\u8fbe\u5f0f \u5de6\u5230\u53f3 12 || \u903b\u8f91\u6216 \u8868\u8fbe\u5f0f||\u8868\u8fbe\u5f0f \u5de6\u5230\u53f3 13 ?: \u6761\u4ef6\u8fd0\u7b97\u7b26 \u8868\u8fbe\u5f0f1? \u8868\u8fbe\u5f0f2: \u8868\u8fbe\u5f0f3 \u53f3\u5230\u5de6 14 = \u8d4b\u503c\u8fd0\u7b97\u7b26 \u53d8\u91cf=\u8868\u8fbe\u5f0f \u53f3\u5230\u5de6 /= \u9664\u540e\u8d4b\u503c \u53d8\u91cf/=\u8868\u8fbe\u5f0f *= \u4e58\u540e\u8d4b\u503c \u53d8\u91cf*=\u8868\u8fbe\u5f0f %= \u53d6\u6a21\u540e\u8d4b\u503c \u53d8\u91cf%=\u8868\u8fbe\u5f0f += \u52a0\u540e\u8d4b\u503c \u53d8\u91cf+=\u8868\u8fbe\u5f0f -= \u51cf\u540e\u8d4b\u503c \u53d8\u91cf-=\u8868\u8fbe\u5f0f &lt;&lt;= \u5de6\u79fb\u540e\u8d4b\u503c \u53d8\u91cf&lt;&lt;=\u8868\u8fbe\u5f0f &gt;&gt;= \u53f3\u79fb\u540e\u8d4b\u503c \u53d8\u91cf&gt;&gt;=\u8868\u8fbe\u5f0f &amp;= \u6309\u4f4d\u4e0e\u540e\u8d4b\u503c \u53d8\u91cf&amp;=\u8868\u8fbe\u5f0f ^= \u6309\u4f4d\u5f02\u6216\u540e\u8d4b\u503c \u53d8\u91cf^=\u8868\u8fbe\u5f0f |= \u6309\u4f4d\u6216\u540e\u8d4b\u503c \u53d8\u91cf|=\u8868\u8fbe\u5f0f 15 , \u9017\u53f7\u8fd0\u7b97\u7b26 \u8868\u8fbe\u5f0f,\u8868\u8fbe\u5f0f,\u2026 \u5de6\u5230\u53f3"},{"location":"cour_note/D1QD_CXiaoCheng/#\u6307\u9488\u76f8\u5173","title":"\u6307\u9488\u76f8\u5173","text":"<ul> <li>C\u8bed\u8a00\u89c4\u5b9a\uff0c\u6570\u7ec4\u540d\u8868\u793a\u8be5\u6570\u7ec4\u6240\u5206\u914d\u8fde\u7eed\u5185\u5b58\u7a7a\u95f4\u4e2d\u7b2c\u4e00\u4e2a\u5355\u5143\u7684\u5730\u5740\uff0c\u5373 \u9996\u5730\u5740</li> <li>\u4e8c\u7ef4\u6570\u7ec4\u7684\u5185\u5b58\u5b58\u653e\u4ecd\u7136\u91c7\u53d6\u987a\u5e8f\u5b58\u653e\uff0c\u5373\u6570\u7ec4<code>a[3][2]</code>\u4e2d<code>a[1][1]</code>\u7684\u5730\u5740\u4e0e<code>a[2][0]</code>\u76f8\u90bb</li> <li>\u4e8c\u7ef4\u6570\u7ec4\u7533\u8bf7\u65f6\u5982\u679c\u521d\u59cb\u5316\u53ef\u4ee5\u7701\u7565\u884c\u957f\u5ea6\uff0c\u5982<code>a[][3] = {1,2,3,4,5,6,7}</code></li> <li>\u5bf9\u4e8e\u4e8c\u7ef4\u6570\u7ec4<code>a[x][y]</code>\uff1a\uff08x,y\u662f\u4e24\u4e2a\u5e38\u6570\uff09<ul> <li><code>&amp;a</code>\u8868\u793a\u6570\u7ec4\u5730\u5740\uff0c<code>&amp;a+1</code>\u8868\u793a\u7684\u6570\u7ec4\u672b\u5c3e\u540e\u7684\u5730\u5740    <ul> <li>\u5373\uff1a<code>&amp;a+1</code> = (<code>&amp;a</code>) + \\(1\\times x\\times y\\times sizeof(\\text{element})\\)</li> </ul> </li> <li><code>a</code>\u6216\u8005<code>&amp;a[0]</code>\u8868\u793a\u6570\u7ec4\u9996\u884c\u5730\u5740\uff0c<code>a+1</code>\u8868\u793a\u6570\u7ec4\u4e0b\u4e00\u884c\u5730\u5740<ul> <li>\u5373\uff1a<code>a+1</code> =  (<code>a</code>) + \\(1\\times y\\times sizeof(\\text{element})\\) <code>a</code>\u5b9e\u9645\u4e0a\u662f\u4e00\u4e2a<code>x</code>\u7ef4 \u6570\u7ec4\u7684\u6307\u9488\uff0c\u8be5\u6570\u7ec4\u7684 \u5143\u7d20 \u4e3a\u82e5\u5e72<code>y</code> \u7ef4\u6570\u7ec4</li> </ul> </li> <li><code>&amp;a[0][0]</code>\u6216\u8005<code>a[0]</code>\u8868\u793a\u6570\u7ec4\u9996\u5143\u7d20\u5730\u5740\uff0c\u4e5f\u53eb\u5217\u5730\u5740\uff0c<code>&amp;a[0][0]+1</code>\u8868\u793a\u6570\u7ec4\u4e0b\u4e00\u5143\u7d20\u5730\u5740<ul> <li>\u5373\uff1a<code>&amp;a[0][0]+1</code> =  (<code>&amp;a[0][0]</code>) + \\(sizeof(\\text{element})\\)</li> </ul> </li> <li>\u4f46\u4e0a\u9762\u51e0\u4e2a\u6307\u9488\u7684 \u503c \u90fd\u4e00\u6837</li> <li><code>a[i][j]</code>\u7b49\u6548\u4e8e<code>*( *(a+i) + j )</code></li> </ul> </li> <li><code>int *p[5]</code>\u5b9a\u4e49\u4e86\u4e00\u4e2asize\u4e3a5\u7684\u6574\u578b \u6307\u9488\u7684\u6570\u7ec4 (\u8fd9\u91cc\u6709\u4e94\u4e2a\u6307\u9488)</li> <li> <p><code>int (*p)[5]</code>\u5b9a\u4e49\u4e86\u4e00\u4e2asize\u4e3a5\u7684 \u6570\u7ec4\u7684\u6307\u9488 (\u8fd9\u91cc\u53ea\u6709\u4e00\u4e2a\u6307\u9488)</p> </li> <li> <p>\u7ed9\u6307\u9488\u8d4b\u503c\u7684\u529e\u6cd5\uff1a</p> <ul> <li><code>p = &amp;x;</code></li> <li><code>p = 0;</code></li> <li><code>p = NULL;</code></li> <li><code>p = (int *)1732;</code></li> </ul> </li> <li> <p>\u6307\u9488\u8fd0\u7b97\uff1a</p> <ul> <li><code>*p+1;</code> <code>++*p;</code>\u7684\u64cd\u4f5c\u5bf9\u8c61\u90fd\u662f<code>p</code>\u6307\u5411\u7684 \u5143\u7d20\u503c</li> <li><code>*p++;</code>\u7684\u64cd\u4f5c\u5bf9\u8c61\u5219\u662f \u6307\u9488\u672c\u8eab\uff0c\u542b\u4e49\u662f\u6307\u5411\u4e0b\u4e00\u4e2a\u5730\u5740</li> <li>\u5f53\u51fa\u73b0\u4e0a\u8ff0\u8bed\u53e5\u53c2\u4e0e\u590d\u6742\u8868\u8fbe\u5f0f\u65f6\uff0c<code>*p++</code>\u4f1a\u5728\u8f93\u51fa<code>*p</code>\u540e\u518d\u6307\u5411\u4e0b\u4e00\u4e2a\u5730\u5740</li> </ul> </li> <li> <p>\u53ef\u4ee5\u901a\u8fc7\u5c06\u4e00\u4e2a \u5b57\u7b26\u4e32\u5e38\u91cf \u8d4b\u503c\u7ed9\u4e00\u4e2a\u6307\u9488\u7684\u65b9\u5f0f\u6765\u7ed9\u8be5\u5b57\u7b26\u4e32\u5206\u914d\u5730\u5740</p> <ul> <li>\u5373\u4f8b\u5982<code>char *p;   p = \"awa\";</code>\u662f\u5408\u7406\u7684</li> </ul> </li> <li><code>*strcpy(char *to,char *from)</code>\u51fd\u6570\u7684\u4f5c\u7528\u662f\uff0c\u628a \u5b57\u7b26\u6570\u7ec4 <code>from[]</code>\u590d\u5236\u5230<code>to[]</code>\u4e2d\u5e76\u8fd4\u56de<code>to[]</code></li> <li><code>*strcat(char *to,char *from)</code>\u51fd\u6570\u7684\u4f5c\u7528\u662f\uff0c\u628a \u5b57\u7b26\u6570\u7ec4 <code>from[]</code>\u6dfb\u52a0\u5230<code>to[]</code>\u672b\u5c3e\u5e76\u8fd4\u56de<code>to[]</code><ul> <li>\u8865\u5145\uff1a\u6240\u8c13\u7684\u6dfb\u52a0\uff0c\u5c31\u662f\u7528<code>from[]</code>\u53bb\u66ff\u6362<code>to[]</code>\u7b2c\u4e00\u4e2a<code>\\0</code>\u4e4b\u540e\u7684\u5143\u7d20</li> </ul> </li> <li><code>strcmp(char *a,char *b)</code>\u51fd\u6570\u7684\u4f5c\u7528\u662f\uff0c\u6bd4\u8f83 \u5b57\u7b26\u6570\u7ec4 <code>a[]</code>\u548c<code>b[]</code>\u5728<code>\\0</code>\u524d\u7684\u5185\u5bb9\u662f\u5426\u7b49\u4ef7<ul> <li>\u5982\u679c\u7b49\u4ef7 \u8fd4\u56de0</li> <li>\u5982\u679ca&lt;b \u8fd4\u56de-1</li> <li>\u5982\u679ca&gt;b \u8fd4\u56de1</li> </ul> </li> <li> <p><code>strlen(char *s)</code>\u51fd\u6570\u7684\u4f5c\u7528\u662f\uff0c\u8fd4\u56de \u5b57\u7b26\u6570\u7ec4 <code>s[]</code>\u5728<code>\\0</code>\u524d\u7684\u5143\u7d20\u4e2a\u6570</p> </li> <li> <p>\u5173\u4e8e\u6307\u9488\u548c\u7ed3\u6784\u4f53\u7684\u5173\u7cfb\uff0c\u53ea\u9700\u8981\u8bb0\u4f4f \u53d6\u503c\u7b26<code>*</code> \u7684\u4f18\u5148\u7ea7 \u4f4e\u4e8e \u6210\u5458\u8bbf\u95ee\u7b26<code>.</code> \u7684\u4f18\u5148\u7ea7</p> </li> <li> <p><code>void *malloc(size_t size)</code>\u7533\u8bf7<code>size</code>\u5927\u5c0f\u7684\u5185\u5b58\uff0c\u4ee5\u5b57\u8282\u4e3a\u5355\u4f4d\uff0c\u8fd4\u56de\u4e00\u4e2a\u6307\u5411\u8fd9\u4e2a\u5185\u5b58\u7684\u6307\u9488</p> </li> <li> <p><code>void free(void *ptr)</code>\u91ca\u653e\u6307\u9488<code>ptr</code>\u6240\u6307\u7684\u5185\u5b58</p> </li> <li> <p>\u5bf9\u4e8e\u8fd4\u56de\u6307\u9488\u7684\u51fd\u6570\uff0c\u4e0d\u80fd\u8fd4\u56de\u5728\u51fd\u6570\u5185\u5b9a\u4e49\u7684 \u5c40\u90e8\u53d8\u91cf \u7684\u6307\u9488</p> </li> <li> <p>\u51fd\u6570\u6307\u9488\u7684\u5b9a\u4e49\uff1a<code>\u7c7b\u578b\u540d(*\u53d8\u91cf\u540d)(\u53c2\u6570\u7c7b\u578b\u8868)</code></p> <ul> <li>\u300ceg\u300d<code>int(*fun)(int,int)</code></li> </ul> </li> </ul> <p>\u4e22\u4e00\u4e2axxjj\u7684\u6587\u7ae0\u5728\u8fd9\u91cc\u00a0\u00a0\u70b9\u51fb\u8df3\u8f6c</p> <ul> <li><code>FILE *fp;</code>\u7533\u8bf7\u4e86\u4e00\u4e2a\u6587\u4ef6\u6307\u9488</li> </ul>"},{"location":"cour_note/D1QD_CXiaoCheng/#\u547d\u4ee4\u884c\u53c2\u6570","title":"\u547d\u4ee4\u884c\u53c2\u6570","text":"<ul> <li><code>main()</code>\u53ef\u4ee5\u6709\u4e24\u4e2a\u53c2\u6570\uff1a<ul> <li><code>main(int argc,char *argv[])</code></li> <li><code>argc</code>\u8868\u793a\u547d\u4ee4\u884c\u53c2\u6570\u6570\u91cf</li> <li><code>argv[]</code>\u6307\u5411\u5404\u4e2a\u547d\u4ee4\u884c\u53c2\u6570</li> <li><code>argv[0]</code>\u6307\u5411\u547d\u4ee4</li> <li><code>argv[1,]</code>\u6307\u5411\u53c2\u6570 </li> <li>\u300ceg\u300d\u547d\u4ee4\u884c\u8f93\u5165<code>./code.exe hello world</code></li> <li>\u5728\u7a0b\u5e8f\u4e2d\uff1a</li> <li><code>argc = 3</code></li> <li><code>*argv[] = {\"./code.exe\\0\",\"hello\\0\",\"world\\0\"}</code></li> </ul> </li> </ul>"},{"location":"cour_note/D1QD_CXiaoCheng/#\u6587\u4ef6\u64cd\u4f5c","title":"\u6587\u4ef6\u64cd\u4f5c","text":"<ul> <li><code>FILE *fp;</code>\u7533\u8bf7\u4e00\u4e2a\u6587\u4ef6\u6307\u9488</li> <li><code>fp = fopen(\"\u6587\u4ef6\u540d\",\"\u4f7f\u7528\u65b9\u5f0f\");</code>\u94fe\u63a5\u6307\u9488<code>fp</code>\u5230\u6587\u4ef6\u5e76\u6307\u5b9a\u6a21\u5f0f</li> </ul> \u6587\u672c\u6587\u4ef6 \u4e8c\u8fdb\u5236\u6587\u4ef6 \u4f7f\u7528\u65b9\u5f0f \u542b\u4e49 \u4f7f\u7528\u65b9\u5f0f \u542b\u4e49 \"r\" \u6253\u5f00 &amp; \u53ea\u8bfb \"rb\" \u6253\u5f00 &amp; \u53ea\u8bfb \"w\" \u65b0\u5efa(\u6e05\u7a7a) &amp; \u53ea\u5199 \"wb\" \u65b0\u5efa &amp; \u53ea\u5199 \"a\" \u6253\u5f00 &amp; \u8ffd\u52a0 \"ab\" \u6253\u5f00 &amp; \u8ffd\u52a0 \"r+\" \u6253\u5f00 &amp; \u8bfb\u5199 \"rb+\" \u6253\u5f00 &amp; \u8bfb\u5199 \"w+\" \u65b0\u5efa(\u6e05\u7a7a) &amp; \u8bfb\u5199 \"wb+\" \u65b0\u5efa &amp; \u8bfb\u5199 \"a+\" \u6253\u5f00 &amp; \u8bfb &amp; \u8ffd\u52a0 \"ab+\" \u6253\u5f00 &amp; \u8bfb &amp; \u8ffd\u52a0 \u8bf4\u660e \u4f7f\u7528<code>\"w\"</code>/<code>\"w+\"</code>\u65f6\uff0c\u6587\u4ef6\u5185\u5bb9\u4f1a\u88ab\u8986\u76d6\uff08\u56e0\u4e3a\u6e05\u7a7a\u540e\u518d\u5199\u5165\uff09 \u4f7f\u7528<code>\"a\"</code>/<code>\"a+\"</code>\u65f6\uff0c\u8f93\u5165\u5185\u5bb9\u4f1a\u5199\u5728\u6587\u4ef6\u5185\u5bb9\u540e\u9762 <ul> <li>\u8f93\u5165\u6587\u4ef6\u540d\u65f6\u53ef\u4ee5\u5199\u8def\u5f84\uff0c\u8def\u5f84\u4e2d\u8981\u4f7f\u7528<code>\\\\</code>\u6765\u533a\u5206\u5c42\u7ea7</li> <li><code>fprintf(fp,\"\u683c\u5f0f\u5b57\u7b26\u4e32\",\u53d8\u91cf\u8868);</code>\u5199\u5165\u6570\u636e\u5230<code>fp</code>\u6307\u5411\u7684\u6587\u4ef6\uff0c\u540e\u4e24\u4e2a\u53c2\u6570\u7684\u683c\u5f0f\u548c<code>printf()</code>\u4e00\u6837</li> <li><code>fclose()</code>\u5173\u95ed\u6587\u4ef6\u5e76\u5237\u65b0\u7f13\u5b58\u533a<ul> <li>\u987a\u5229\u6267\u884c\u4e86\u6587\u4ef6\u5173\u95ed\u64cd\u4f5c\u65f6\uff0c<code>fclose()</code>\u51fd\u6570\u7684\u8fd4\u56de\u503c\u662f<code>0</code>\uff0c\u5426\u5219\u8fd4\u56de<code>EOF</code></li> </ul> </li> <li><code>rewind(fp)</code>\u8ba9<code>fp</code>\u8fd4\u56de<code>fp</code>\u6240\u6307\u7684\u6587\u4ef6\u7684\u5f00\u5934\u5730\u5740</li> <li><code>rtell(fp)</code>\u8ba9<code>fp</code>\u8fd4\u56de<code>fp</code>\u7684\u5f53\u524d\u4f4d\u7f6e(<code>long int</code>\u7c7b\u578b\uff0c\u4ece<code>0</code>~<code>len</code>)\uff0c\u6210\u529f\u8fd4\u56de\u5f53\u524d\u503c(\u4e00\u5f00\u59cb\u662f0\uff0c\u6bcf\u5411\u540e\u79fb\u52a8\u4e00\u6b21+1)\uff0c\u5426\u5219\u8fd4\u56de<code>-1L</code></li> <li><code>fseek(FILE *fp,\"\u504f\u79fb\u91cf\",\"\u8d77\u59cb\u4f4d\u7f6e\")</code>\u5c06<code>fp</code>\u4ece<code>\"\u8d77\u59cb\u4f4d\u7f6e\"</code>\u5f00\u59cb\u5411\u540e\u79fb\u52a8<code>\"\u504f\u79fb\u91cf\"</code><ul> <li>\u53ef\u9009\u7684<code>\"\u8d77\u59cb\u4f4d\u7f6e\"</code>\uff1a</li> <li><code>SEEK_SET</code>\u6587\u4ef6\u5f00\u5934</li> <li><code>SEEK_CUR</code>\u5f53\u524d\u4f4d\u7f6e</li> <li><code>SEEK_END</code>\u6587\u4ef6\u672b\u5c3e</li> <li>\u300ceg\u300d\u79fb\u52a8\u6307\u9488<code>fp</code>\u5230\u6587\u4ef6\u672b\u5c3e\uff1a<code>fseek(fp,0L,SEEK_END);</code></li> </ul> </li> <li><code>feof(fp)</code>\u5982\u679c<code>fp</code>\u5230\u8fbe\u4e86<code>EOF</code>\uff0c\u8fd4\u56de\u975e\u96f6\u503c\uff0c\u5426\u5219\u8fd4\u56de<code>0</code></li> <li><code>fflush(fp)</code>\u5237\u65b0<code>fp</code>\u7684\u7f13\u51b2\u533a\uff0c\u6210\u529f\u8fd4\u56de<code>0</code>\uff0c\u5426\u5219\u8fd4\u56de<code>EOF</code></li> <li><code>fgets((char*)str,limt,fp)</code>\u4ece<code>fp</code>\u8bfb\u5165\u4e00\u884c\u7684<code>limit-1</code>\u4e2a\u5b57\u7b26\u5e76\u5b58\u5165<code>str</code>\u4e2d\uff0c\u5e76\u5728\u672b\u5c3e\u52a0<code>\\0</code>\uff0c\u7136\u540e\u8fd4\u56de\u8bfb\u5165\u7684\u5185\u5bb9(\u5982\u679c\u6ca1\u8bfb\u5b8c<code>limit-1</code>\u4e2a\u5b57\u7b26\u5c31\u9047\u5230\u4e86\u884c\u672b\u5c31\u5230\u6b64\u4e3a\u6b62)</li> <li><code>fputc(ch,fp)</code>\u5728<code>fp</code>\u4e2d\u5199\u5165\u5355\u4e2a\u5b57\u7b26<code>ch</code>\uff0c\u6210\u529f\u8fd4\u56de<code>ch</code>\uff0c\u5426\u5219\u8fd4\u56de<code>EOF</code></li> <li> <p><code>fgetc(fp)</code>\u83b7\u53d6\u4e0b\u4e00\u4e2a\u5b57\u7b26(\u5982\u679c\u5230\u8fbe<code>EOF</code>\u5c31\u8bfb\u5165\u4e86<code>-1</code>\uff0c\u53c2\u8003\u8fd9\u91cc)</p> </li> <li> <p>C\u7a0b\u5e8f\u5bf9\u6587\u4ef6\u5f85\u5904\u7406\u91c7\u7528\u5185\u5b58\u7f13\u51b2\u6587\u4ef6\u7cfb\u7edf\u7684\u65b9\u5f0f\u8fdb\u884c</p> </li> <li>\u4f7f\u7528\u7f13\u51b2\u6587\u4ef6\u7cfb\u7edf\u53ef\u4ee5\u5927\u5927\u63d0\u9ad8\u6587\u4ef6\u64cd\u4f5c\u901f\u5ea6</li> <li>\u6587\u4ef6\u4fdd\u5b58\u5728\u78c1\u76d8\u4e0a\uff0c\u78c1\u76d8\u6570\u636e\u7684\u7ec4\u7ec7\u65b9\u5f0f\u6309\u6247\u533a\u8fdb\u884c\uff0c\u89c4\u5b9a \u6bcf\u4e2a\u6247\u533a\u5927\u5c0f\u4e3a512B</li> <li>\u4e00\u822c\u5fae\u578b\u8ba1\u7b97\u673a\u4e2d\u7684C\u8bed\u8a00\u7cfb\u7edf\u4e5f\u5c06\u7f13\u51b2\u533a\u5927\u5c0f\u5b9a\u4e3a512B</li> <li>\u8fdb\u884c\u6570\u636e\u5199\u5165\u5de5\u4f5c\u65f6:<ul> <li>\u628a\u6570\u636e\u5199\u5165\u6587\u4ef6\u7f13\u51b2\u533a</li> <li>\u5199\u6ee1512B\u4ee5\u540e\uff0cOS\u81ea\u52a8\u628a\u6570\u636e\u5199\u5165\u78c1\u76d8\u7684\u4e00\u4e2a\u6247\u533a\uff0c\u7136\u540e\u6e05\u7a7a\u6587\u4ef6\u7f13\u51b2\u533a</li> <li>\u91cd\u590d\u4e0a\u8ff0\u884c\u4e3a</li> </ul> </li> <li>\u6587\u4ef6\u6253\u5f00\u7684\u5b9e\u8d28\u662f\u628a\u78c1\u76d8\u6587\u4ef6\u548c\u6587\u4ef6\u7f13\u51b2\u533a\u5bf9\u5e94\u8d77\u6765\uff0c\u5177\u4f53\u6d41\u7a0b\u5982\u4e0b;</li> <li>\u5728\u78c1\u76d8\u4e2d\u627e\u5230\u6307\u5b9a\u6587\u4ef6</li> <li>\u5728\u5185\u5b58\u4e2d\u5206\u914d\u4fdd\u5b58\u4e00\u4e2aFILE\u7c7b\u578b\u7ed3\u6784\u7684\u5355\u5143\uff0816B\uff09</li> <li>\u5728\u5185\u5b58\u4e2d\u5206\u914d\u6587\u4ef6\u7f13\u51b2\u533a\u5355\u5143\uff08512B\uff09</li> <li> <p>\u8fd4\u56deFILE\u7684\u7ed3\u6784\u5730\u5740</p> </li> <li> <p><code>FILE</code>\u672c\u8d28\u4e0a\u662f\u4e00\u4e2a\u7ed3\u6784\u4f53\u7c7b\u578b\uff0c\u5b9a\u4e49\u5982\u4e0b\uff1a <pre><code>typedef struct{\nshort            level;       /*\u7f13\u51b2\u533a\u4f7f\u7528\u91cf*/\nunsigned         flags;       /*\u6587\u4ef6\u72b6\u6001\u6807\u5fd7*/\nchar             fd;          /*\u6587\u4ef6\u63cf\u8ff0\u7b26*/\nshort            bsize;       /*\u7f13\u51b2\u533a\u5927\u5c0f*/\nunsigned char    *buffer;     /*\u6587\u4ef6\u7f13\u51b2\u533a\u9996\u5730\u5740*/\nunsigned char    *curp;       /*\u6307\u5411\u6587\u4ef6\u7f13\u51b2\u533a\u7684\u5de5\u4f5c\u6307\u9488*/\nunsigned char    hold;        /*\u5176\u4ed6\u4fe1\u606f*/\nunsigned         istemp;\nshort            token;\n} FILE;\n</code></pre></p> </li> </ul>"},{"location":"cour_note/D1QD_CXiaoCheng/#\u5176\u4ed6","title":"\u5176\u4ed6","text":"<p>\u8d34\u4e00\u4e9b\u5176\u4ed6\u5b66\u957f\u7684\u6587\u7ae0\uff1a</p> <ul> <li>https://blog.zhanghai.me/c-exam-notes/</li> <li>https://blog.yzsun.me/c-traps-and-pitfalls/</li> </ul>"},{"location":"cour_note/D1SJ_Intro2CS/","title":"\ud83d\udd2e \u8ba1\u7b97\u673a\u7cfb\u7edf\u6982\u8bba | Introduction to Computing Systems","text":"<p> \u7ea6 12 \u4e2a\u5b57 </p> <ul> <li>https://www.yuque.com/isshikixiu/codes/ics</li> </ul>"},{"location":"cour_note/D1SJ_StanfordCS231n/","title":"\ud83d\udd2e Deep Learning for Computer Vision | CS231N","text":"<p> \u7ea6 3443 \u4e2a\u5b57  17 \u884c\u4ee3\u7801  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 12 \u5206\u949f</p> \u8bfe\u7a0b\u4ecb\u7ecd <ul> <li>\u56e0\u4e3a\u6211\u53ea\u80fd\u627e\u5230 17 \u5e74\u7684\u89c6\u9891\uff0c\u6240\u4ee5\u662f\u8ddf\u7740 17 \u5e74\u7684\u7248\u672c\u5b66\u3002</li> </ul> <p>Course Website: \ud83d\udd17</p> <p>Course Video: \ud83d\udd17</p> <p>Course Description</p> <ul> <li>Computer Vision has become ubiquitous in our society, with applications in search, image understanding, apps, mapping, medicine, drones, and self-driving cars. Core to many of these applications are visual recognition tasks such as image classification, localization and detection. Recent developments in neural network (aka \u201cdeep learning\u201d) approaches have greatly advanced the performance of these state-of-the-art visual recognition systems. This course is a deep dive into the details of deep learning architectures with a focus on learning end-to-end models for these tasks, particularly image classification. During the 10-week course, students will learn to implement and train their own neural networks and gain a detailed understanding of cutting-edge research in computer vision. Additionally, the final assignment will give them the opportunity to train and apply multi-million parameter networks on real-world vision problems of their choice. Through multiple hands-on assignments and the final course project, students will acquire the toolset for setting up deep learning tasks and practical engineering tricks for training and fine-tuning deep neural networks.</li> </ul> <p>Assignments</p> <ul> <li>Assignment 1: \ud83d\udd17</li> <li>Assignment 2: \ud83d\udd17</li> <li>Assignment 3: \ud83d\udd17</li> </ul> \u53c2\u8003\u8d44\u6599 <ul> <li>\u5b66\u957f\u7b14\u8bb0\uff1a\ud83d\udd17</li> </ul>"},{"location":"cour_note/D1SJ_StanfordCS231n/#lecture-1-introduction-to-convolutional-neural-networks-for-visual-recognition","title":"Lecture 1: Introduction to Convolutional Neural Networks for Visual Recognition","text":"<ul> <li>Video: \ud83d\udd17 </li> <li>Slides: \ud83d\udd17 </li> </ul> <ul> <li>\u4e00\u4e9b\u65e9\u671f\u7684\u5173\u4e8e CV \u7684\u601d\u8003</li> </ul> <ul> <li>\u65e9\u671f\u5bf9\u5982\u4f55\u8868\u793a\u7269\u4f53\uff0c\u8d85\u8d8a\u300cBlock World\u300d\u7684\u8868\u793a\u65b9\u6cd5</li> </ul> <p> \u5176\u6838\u5fc3\u601d\u60f3\u662f\u5c06\u590d\u6742\u7684\u89c6\u89c9\u4fe1\u606f\u7b80\u5316\u4e3a\u7b80\u5355\u5bf9\u8c61\u7684\u7ec4\u5408\u3002</p> <p>\u4eba\u4eec\u610f\u8bc6\u5230\u76f4\u63a5\u8bc6\u522b\u7269\u4f53\u6bd4\u8f83\u56f0\u96be\uff0c\u4e8e\u662f\u60f3\u5230\u4e86 \u5206\u5272\u56fe\u5f62(image segmentation) \u2014\u2014\u5373\u5148\u505a\u5c06\u50cf\u7d20\u5206\u7ec4\uff1a</p> <p></p> <ul> <li>\u542f\u53d1\uff1a\u89c6\u89c9\u8bc6\u522b\u7684\u91cd\u70b9\u53ef\u4ee5\u4ece\u8bc6\u522b\u5bf9\u8c61\u7684\u4e00\u4e9b\u5177\u6709\u8bc6\u522b\u529b\u548c\u4e0d\u6613\u53d8\u5316\u7684\u90e8\u5206\u5f00\u59cb</li> </ul> <p></p> <p>\u6709\u7aef\u8054\u60f3 FDS \u7684 Voting Tree</p> <ul> <li>\u603b\u7684\u800c\u8a00 \u5bf9\u8c61\u8bc6\u522b \u662f CV \u9886\u57df\u7684\u4e00\u4e2a\u91cd\u8981\u8bdd\u9898</li> <li>\u8be5\u8bfe\u7a0b\u91cd\u70b9\u4e3a \u5377\u79ef\u795e\u7ecf\u7f51\u7edc(Convolutional Neural Network / CNN)</li> <li>\u5177\u4f53\u7740\u773c\u70b9\u4e3a \u56fe\u50cf\u5206\u7c7b\u95ee\u9898(image classification)</li> <li>\u4e5f\u5c06\u6d89\u53ca \u5bf9\u8c61\u68c0\u6d4b(object detection)\u3001\u56fe\u50cf\u5b57\u5e55(image captioning) \u7b49\u95ee\u9898</li> </ul>"},{"location":"cour_note/D1SJ_StanfordCS231n/#lecture-2-image-classification-pipeline","title":"Lecture 2: Image Classification Pipeline","text":"<ul> <li>Video: \ud83d\udd17 </li> <li>Slides: \ud83d\udd17 </li> <li>CIFAR-10 &amp; CIFAR-100: \ud83d\udd17 </li> <li>\u524d\u7f6e\uff1aPython Numpy Tutorial: \ud83d\udd17</li> </ul> <ul> <li>\u8bed\u4e49\u9e3f\u6c9f(semantic gap)</li> </ul>"},{"location":"cour_note/D1SJ_StanfordCS231n/#data-driven-approach","title":"Data-Driven Approach","text":"<ol> <li>Collect a dataset of images and labels;</li> <li>Use Machine Learning to train a classifier;</li> <li>Evaluate the classifier on new images;</li> <li>\u5f97\u5230\u7684\u6a21\u578b\u6709\u4e24\u4e2a\u6838\u5fc3 API\uff1a\u4e00\u4e2a\u7528\u4e8e \u8bad\u7ec3(train)\uff0c\u4e00\u4e2a\u7528\u4e8e \u9884\u6d4b(predict)\u3002</li> <li>\u4e00\u822c\u60c5\u51b5\u4e0b\uff0c\u6211\u4eec\u4e0d\u4ecb\u610f\u8bad\u7ec3\u65f6\u95f4\u957f\uff0c\u4f46\u5e0c\u671b\u9884\u6d4b\u6548\u7387\u9ad8\u3002</li> </ol> <p>CIFAR-10 &amp; CIFAR-100: \ud83d\udd17 </p> <p>Distance Metric to compare images</p> <p></p> <p>\u6211\u4eec\u5c06\u5206\u7c7b\u95ee\u9898\u770b\u4f5c\u5728\u201c\u7a7a\u95f4\u201d\u4e2d\u7684\u67d3\u8272\u95ee\u9898\uff0c\u70b9\u8868\u793a\u8bad\u7ec3\u6570\u636e\uff0c\u5176\u989c\u8272\u8868\u793a\u5176\u88ab\u6807\u8bb0\u7684\u5206\u7c7b\uff1b\u800c\u753b\u677f\u4e2d\u5176\u4ed6\u90e8\u5206\u7684\u989c\u8272\u5219\u8868\u793a\u5f53\u70b9\u843d\u5728\u8fd9\u4e2a\u4f4d\u7f6e\u65f6\u5019\u4f1a\u88ab\u5206\u7c7b\u4e3a\u54ea\u4e00\u79cd\u3002</p> <p></p> <p>\u4e2d\u95f4\u201c\u9ec4\u8272\u90e8\u5206\u201d\u8fd9\u79cd\u5b64\u7acb\u7684\u5c0f\u5c9b\u5728\u5b9e\u9645\u5bf9\u6570\u636e\u8fdb\u884c\u9884\u6d4b\u5de5\u4f5c\u65f6\u53ef\u80fd\u4e0d\u662f\u5f88\u597d\u3002</p> <p></p> <p>\u8fd9\u4e9b\u90e8\u5206\u53ef\u80fd\u6709\u566a\u58f0\u6216\u662f\u865a\u5047\u7684\u3002             </p> L1 (Manhattan) distance:  (stupid in most cases)L2 (Euclidean ) distance:  (better by comparison) <ul> <li>\\(d_1(I_1,I_2)=\\sum_{p}|I_1^{p}-I_2^{p}|\\)</li> </ul> <p> </p> <ul> <li>\u5982\u679c\u56fe\u50cf\u65cb\u8f6c\uff0c\u9884\u6d4b\u7ed3\u679c\u4f1a\u53d1\u751f\u6539\u53d8\u3002</li> </ul> <ul> <li>\\(d_2(I_1,I_2)=\\sum_{p}\\sqrt{(I_1^p-I_2^p)^2}\\)</li> </ul> <p> </p> <p>K-Nearest Neighbors: \ud83d\udd17</p> <p>Interactive Demo: \ud83d\udd17</p> <p>Instead of copying label from nearest neighbor, take majority vote from K closest points.</p> <p></p> <p>\u4f8b\u5982\uff0cK=1 \u65f6\u4e2d\u95f4\u7684\u9ec4\u8272\u533a\u57df\u7531\u4e8e\u9644\u8fd1\u90fd\u662f\u7eff\u70b9\uff0c\u6240\u4ee5\u5728 K \u589e\u957f\u7684\u65f6\u5019\u7eff\u8272\u5728\u8ba1\u7b97\u4e2d\u7684\u6743\u91cd\u53d8\u5927\uff0c\u6240\u4ee5\u6700\u540e\u88ab\u6807\u8bb0\u4e3a\u7eff\u8272\u3002s</p> <ul> <li>\u5f53\u7136\uff0c\u8fd9\u79cd\u901a\u8fc7\u6bd4\u8f83\u201c\u8ddd\u79bb\u201d\u7684\u5206\u7c7b\u65b9\u6848\u5e76\u4e0d\u4ec5\u9650\u4e8e\u56fe\u7247\u7b49\uff0c\u5bf9\u4e8e\u4efb\u4f55\u9700\u8981\u5206\u7c7b\u7684\u6570\u636e\uff0c\u4f8b\u5982\u6587\u672c\uff0c\u53ea\u8981\u80fd\u5b9a\u4e49\u80fd\u591f\u91cf\u5316\u7684\u201c\u8ddd\u79bb\u201d\u4ee5\u53ca\u4e00\u7cfb\u5217\u76f8\u5e94\u7684\u89c4\u5219\uff0c\u5c31\u80fd\u4f7f\u7528\u8fd9\u79cd\u65b9\u6cd5\u6765\u8fdb\u884c\u5206\u7c7b\u3002</li> <li>\u7136\u800c\uff0cK-\u4e34\u8fd1\u7b97\u6cd5 \u5728\u56fe\u50cf\u5206\u7c7b\u4e0a\u51e0\u4e4e\u4e0d\u600e\u4e48\u4f7f\u7528\uff0c\u4e3b\u8981\u662f\u56e0\u4e3a\u5b83\u5b9e\u9645\u4f7f\u7528\u8d77\u6765\uff0c\u9884\u6d4b\u6548\u7387\u8f83\u4f4e\uff1b\u4e14\u201c\u8ddd\u79bb\u5ea6\u91cf\u201d\u5e76\u4e0d\u975e\u5e38\u9002\u5408\u56fe\u50cf\u5904\u7406\uff08\u5b83\u65e0\u6cd5\u5b8c\u6574\u63cf\u8ff0\u56fe\u50cf\u4e0a\u7684\u8ddd\u79bb\u4fe1\u606f\u6216\u56fe\u50cf\u4e4b\u95f4\u7684\u5dee\u5f02\uff09\uff1b\u6b64\u5916\u5b83\u8fd8\u6709\u4e00\u4e2a\u6bd4\u8f83\u4e25\u91cd\u7684\u95ee\u9898\uff1a\u7ef4\u6570\u707e\u96be(curse of dimensionality) \ud83d\udd17 \uff08\u56e0\u4e3a\u53ea\u6709\u8bad\u7ec3\u6837\u672c\u8db3\u591f\u5bc6\u96c6\uff0cK-\u4e34\u8fd1\u7b97\u6cd5\u624d\u80fd\u6b63\u5e38\u8fd0\u884c\uff09\u3002</li> </ul>"},{"location":"cour_note/D1SJ_StanfordCS231n/#hyperparameters","title":"Hyperparameters","text":"<ul> <li> <p>Choices about the algorithm that we set rather than learn.</p> </li> <li> <p>eg: best k to use; best distance to use (L1/L2);</p> </li> </ul> <p>Setting Hyperparameters (\u8c03\u53c2)</p> <p></p> <p>\u5373\uff0c\u6211\u4eec\u9700\u8981\u786e\u4fdd\u8db3\u591f\u7684\u8bad\u7ec3\u96c6\uff0c\u5e76\u901a\u8fc7\u9a8c\u8bc1\u96c6\u8fdb\u884c\u8c03\u53c2\uff0c\u5e76\u5728\u4e00\u5207\u90fd\u5b8c\u6210\u4ee5\u540e\u624d\u4f7f\u7528\u6d4b\u8bd5\u96c6\u6765\u9a8c\u8bc1\u6a21\u578b\u7684\u51c6\u786e\u5ea6\u3002</p> <p></p>"},{"location":"cour_note/D1SJ_StanfordCS231n/#linear-classification","title":"Linear Classification","text":"<p>Parametric Approach</p> \\[ f(x,W)=Wx+b \\] <p></p> <p>\u8fd9\u91cc\u7684 10 numbers \u8868\u793a\u7684\u662f CIFAR-10 \u4e2d\u7684 10 \u4e2a\u7c7b\u522b\u5bf9\u5e94\u7684\u5f97\u5206\u3002</p> <ul> <li>\u5373\uff0c\u6211\u4eec\u6784\u9020\u4e00\u4e2a\u51fd\u6570\uff0c\u8f93\u5165\u5305\u542b\u56fe\u50cf\u6570\u636e \\(x\\) \u548c\u6743\u91cd\u53c2\u6570 \\(W\\)\uff0c\u6ee1\u8db3\u5176\u8ba1\u7b97\u7ed3\u679c\u4e3a\u5404\u4e2a\u7c7b\u522b\u7684\u9884\u6d4b\u5f97\u5206</li> <li>\u6700\u7ec8\u5f97\u5230\u4e00\u4e2a\u6a21\u7248\uff0c\u5b83\u5c06\u5c1d\u8bd5\u6027\u5730\u9002\u5e94\u8be5\u7c7b\u91cc\u5c3d\u53ef\u80fd\u591a\u7684\u6837\u672c</li> </ul> <p></p> <p></p> <p>\u5982\u679c\u5c06\u9ad8\u7ef4\u7a7a\u95f4\u7684\u60c5\u51b5\u6620\u5c04\u5230\u5e73\u9762\u7684\u51e0\u4f55\u89d2\u5ea6\u6765\u7406\u89e3\uff0c\u5c31\u597d\u50cf\u5728\u5212\u4e00\u9053\u9053\u76f4\u7ebf\u6765\u8fdb\u884c\u5212\u5206\u3002</p> <ul> <li>\u4ece\u8fd9\u79cd\u89d2\u5ea6\u6765\u7406\u89e3\u5c31\u5f88\u5bb9\u6613\u53d1\u73b0\uff0c\u5355\u4e00\u7684\u7ebf\u6027\u5206\u7c7b\u5177\u6709\u5c40\u9650\u6027\uff0c\u4f8b\u5982\u5bf9\u4e8e\u591a\u6a21\u6001\u7684\u6570\u636e\uff0c\u4f7f\u7528\u5355\u4e00\u7684\u7ebf\u6027\u5206\u7c7b\u53ef\u80fd\u4f1a\u6bd4\u8f83\u5403\u529b\u3002</li> </ul>"},{"location":"cour_note/D1SJ_StanfordCS231n/#lecture-3-loss-functions-and-optimization","title":"Lecture 3: Loss Functions and Optimization","text":"<ul> <li>Video: \ud83d\udd17 </li> <li>Slides: \ud83d\udd17 </li> </ul> <ul> <li>Linear classifier is an example of parametric classifier.</li> <li> <p>\u6211\u4eec\u53ef\u4ee5\u8fd9\u6837\u7406\u89e3 Linear Classifation \u4e2d\u7684 \\(W\\)\uff1a\u77e9\u9635\u4e2d\u7684\u6bcf\u4e00\u4e2a\u53c2\u6570\u8868\u793a\u4e86\u6bcf\u4e00\u4e2a\u50cf\u7d20\u70b9(\u5355\u4e2a\u989c\u8272\u901a\u9053)\u5bf9\u4e8e\u8bc6\u522b\u67d0\u4e2a\u7c7b\u7684\u8d21\u732e\u6743\u91cd\u3002</p> </li> <li> <p>A loss function that quantifies our unhappiness with the scores across the training data, tells how good our current classifier is. </p> </li> <li>Given a dataset of examples \\(\\{(x_1,y_i)\\}_{i=1}^N\\), where \\(x_i\\) is image and \\(y_i\\) is label. And loss over the dataset is a sum of loss over examples: \\(L = \\frac{1}{N}\\sum L_i(f(xi,W),y_i)\\).</li> <li>Loss function \u662f\u7528\u6765\u5ea6\u91cf \\(W\\) \u7684\u5408\u9002\u7a0b\u5ea6\u7684\uff0c\u6211\u4eec\u901a\u8fc7\u5bfb\u627e\u5728 \\(W\\) \u7a7a\u95f4\u4e2d\u635f\u5931\u51fd\u6570\u53d6\u6700\u503c\u65f6\u7684 \\(W\\) \u6765\u627e\u5230\u6211\u4eec\u8ba4\u4e3a\u6700\u5408\u9002\u7684 \\(W\\)\u3002</li> </ul>"},{"location":"cour_note/D1SJ_StanfordCS231n/#multi-class-svm-loss","title":"Multi-class SVM Loss","text":"<p>\u5982\u4f55\u7406\u89e3\u90a3\u5f20\u56fe\uff1f(hinge loss?)</p> <p>Let \\(s = f(x_i,W)\\), then SVM loss is:</p> \\[ L_i = \\sum_{j \\not = y_i } \\left\\{     \\begin{align*}         &amp;0              &amp;\\text{if } s_{y_i} \\geq s_j + 1\\\\         &amp;s_j-s_{y_i}+1  &amp;\\text{otherwise}     \\end{align*} \\right. = \\sum_{j \\not = y_i } \\text{max}(0,s_j-s_{y_i}+1) \\] <ul> <li>\u4e5f\u5c31\u662f\u8bf4\uff0c\u5bf9\u4e8e\u67d0\u4e00\u4e2a\u6837\u672c\uff0c\u5b83\u5b9e\u9645\u7c7b\u522b\u5bf9\u5e94\u7684\u5f97\u5206\u5982\u679c\u8fdc\u5927\u4e8e\uff08\u6211\u4eec\u9700\u8981\u4e00\u4e2a\u8fb9\u754c \uff0c\u5c31\u662f\u4e0a\u56fe\u4e2d\u7684\\(+1\\)\uff09\u67d0\u4e2a\u5176\u4ed6\u7c7b\u522b\u7684\u5f97\u5206\uff0c\u90a3\u4e48\u8be5\u201c\u5176\u4ed6\u7c7b\u522b\u201d\u5bf9\u635f\u5931\u51fd\u6570\u7684\u8d21\u732e\u5373\u4e3a\\(0\\)\uff1b\u53cd\u4e4b\uff0c\u5982\u679c\u5e76\u6ca1\u6709\u8fdc\u5927\u4e8e\u5176\u4ed6\u67d0\u4e2a\u7c7b\u522b\u7684\u5f97\u5206\uff0c\u5219\u9700\u8981\u5c06\u8fd9\u4e2a\u504f\u5dee\u4f5c\u4e3a\u5bf9\u635f\u5931\u51fd\u6570\u7684\u8d21\u732e\u3002</li> </ul> <p> </p> <pre><code>def L_i_Vectorized(x, y, W):\n    scores = W.dot(x)\n    margins = np.maximum(0, scores - scores[y] + 1)\n    margins[y] = 0\n    loss_i = np.sum(margins)\n    return loss_i\n</code></pre> <ul> <li>Overview</li> </ul> \\[ f(x,W) = Wx\\\\ L = \\frac{1}{N}\\sum_{i=1}^{n}\\sum_{j\\not = y_i}\\text{max}(0,f(x;W)_j-f(x_i;W)_{y_i}+1) \\] <p></p> <ul> <li>However, for that we only calculate a loss in terms of the data, some strange things like overfitting will happen.</li> </ul> <p></p> <ul> <li>\u84dd\u70b9\u4e3a\u6a21\u578b\u8bad\u7ec3\u6570\u636e\uff0c\u7eff\u8272\u7684\u4e3a\u9a8c\u8bc1\u6216\u8005\u5b9e\u9645\u6570\u636e\u7b49\u3002</li> <li>\u84dd\u8272\u7684\u4e3a\u8fc7\u62df\u5408\u540e\u6a21\u578b\u8bad\u7ec3\u51fa\u6765\u7684\u9884\u6d4b\u8d8b\u52bf\uff0c\u4ed6\u4eec\u5b8c\u5168\u7b26\u5408\u8bad\u7ec3\u6a21\u578b\u7684\u6570\u636e\uff0c\u4f46\u662f\u53ef\u4ee5\u53d1\u73b0\uff0c\u7eff\u8272\u7684\u7ebf\u6761\u624d\u662f\u5b9e\u9645\u7684\u6211\u4eec\u5e0c\u671b\u5f97\u5230\u7684\u8d8b\u52bf\u3002</li> <li>\u8fd9\u79cd\u9884\u6d4b\u7ed3\u679c\u8fc7\u5ea6\u62df\u5408\u4e86\u8bad\u7ec3\u6570\u636e\u7684\u884c\u4e3a\u53ca\u4e3a\u8fc7\u62df\u5408\u3002</li> </ul> <p>To solve it, we use regularization.</p> <p></p> <p>The regularization term.</p> <p></p> <p>Occam's Razor</p> <ul> <li>The regularization term encourages the model to somehow pick a simpler \\(W\\) depending on the dask and the model.</li> </ul> <p>So your standard loss function usually has two terms, a data loss and a regularization loss, and there's a hyperparameter(mentioned already in L2) here, lambda, which trades off between the two.</p>"},{"location":"cour_note/D1SJ_StanfordCS231n/#regularization","title":"Regularization","text":"<p>There are many regularizations used in practice, and the most common one is probably L2 regularization or weight decay. </p> <p>In common use:</p> <ul> <li>L2 regularization: \\(R(W) = \\sum_{k}\\sum_lW_{k,l}^2\\);</li> <li>L1 regularization: \\(R(W) = \\sum_k\\sum_l |W_{k,l}|\\);</li> <li>Elastic net (L1+L2): \\(R(W) = \\sum_k\\sum_l (\\beta W_{k,l}^2+|W_{k,l}|)\\);</li> <li>Max norm regularization</li> <li>Dropout</li> <li>Fancier: Batch normalization, stochastic depth...</li> </ul> <p>The whole idea of regularization is just any thing that you do to your model, that sort of penalizes somehow the complexity of the model, rather than explicitly trying to fit the training data. Each regularization has its own feature, you should choose them depends on the problems.</p>"},{"location":"cour_note/D1SJ_StanfordCS231n/#softmax-classifier-multinomial-logistic-regression","title":"Softmax Classifier (Multinomial Logistic Regression)","text":"<ul> <li>It normalizes the scores to a probability distribution.</li> <li>Then we just want the probablity of the true class is high and as close to one.</li> <li>scores = unnormalized log probabilities of the classes</li> <li>\\(P(Y=k|X=x_i)=\\frac{e^{s_k}}{\\sum_j e^{s_j}}\\;,\\;\\;where\\;s=f(x_i;W)\\);</li> <li>That is \\(L_i=-\\log P(Y=y_i|X=x_i)=-\\log(\\frac{e^{s_k}}{\\sum_j e^{s_j}})\\);</li> </ul> <p>eg for Softmax Classifier.</p> <p></p> <p>Compare the two.</p> <ul> <li>\u5728\u5b9e\u9645\u4f7f\u7528\u4e2d\uff0cSVM \u5728\u4fdd\u8bc1\u771f\u5b9e\u6807\u7b7e\u5bf9\u5e94\u7684\u5f97\u5206\u9ad8\u4e8e\u5176\u4ed6\u5f97\u5206\u4e00\u5b9a\u91cf\u540e\u5c31\u63a5\u53d7\u4e86\uff0c\u5373\u5b58\u5728\u4e00\u4e2a\u660e\u786e\u7684\u7a81\u53d8\u6807\u51c6\uff1b\u800c\u5bf9\u4e8e Softmax \u6765\u8bf4\uff0c\u5b83\u4f1a\u5728\u8fd9\u4e2a\u8fc7\u7a0b\u4e2d\u4e0d\u65ad\u5c06\u6b63\u786e\u6807\u7b7e\u5bf9\u5e94\u7684\u6982\u7387\u5411\\(1\\)\u903c\u8fd1\uff0c\u4e0d\u65ad\u4f18\u5316\u81ea\u5df1\u3002</li> </ul> <p></p>"},{"location":"cour_note/D1SJ_StanfordCS231n/#optimization","title":"Optimization","text":"<ul> <li>Strategy #1: A first _very bad _idea solution: Random search</li> <li>Strategy #2: Gradient Descent / Follow the slope(gradient\\(\\nabla\\))</li> <li>Always use analytic gradient, but check implementation with numerical gradient. This is called a gradient check.</li> </ul> <p><pre><code>## Vanilla Gradient Descent\n\nwhile True:\n    weights_grad = evaluate_gradient(loss_fun, data, weight)\n    weights += - step_size * weights_grad ## perform parameter update\n</code></pre> <code>step_size</code> is a hyperparameter here, it's also called a learning rate sometimes. Stochastic Gradient Descent (SGD) - The basic Gradient Descent will be messy when \\(N\\) is large! - So we need to start with approximate sum using a minibatch of examples.    - 32 / 64 / 128 common</p> <pre><code>## Vanilla Gradient Descent\n\nwhile True:\n    data_batch = sample_training_data(data, 256) ## sample 256 examples\n    weights_grad = evaluate_gradient(loss_fun, data_batch, weight)\n    weights += - step_size * weights_grad ## perform parameter update\n</code></pre> <ul> <li>Online Demo: \ud83d\udd17</li> </ul>"},{"location":"cour_note/D1SJ_StanfordCS231n/#aside-image-features","title":"Aside: Image Features","text":""},{"location":"cour_note/D1SJ_StanfordCS231n/#lecture-4-introduction-to-neural-networks","title":"Lecture 4: Introduction to Neural Networks","text":"<ul> <li>Video: \ud83d\udd17 </li> <li>Slides: \ud83d\udd17 </li> </ul>"},{"location":"cour_note/D1SJ_StanfordCS231n/#computational-graphs","title":"Computational graphs","text":"<p>eg. for the linear classifier.</p>"},{"location":"cour_note/D1SJ_StanfordCS231n/#backpropagation","title":"Backpropagation","text":"<p>\u901a\u8fc7\u5c06\u7b97\u5f0f\u5199\u6210\u8fd9\u79cd\u201c\u8282\u70b9\u56fe\u201d\u7684\u5f62\u5f0f\uff0c\u53ef\u4ee5\u8fdb\u4e00\u6b65\u8ba9\u6211\u4eec\u770b\u6e05\u8ba1\u7b97\u8fc7\u7a0b\u5e76\u65b9\u4fbf\u6211\u4eec\u8ba1\u7b97\u68af\u5ea6\u3002\u5177\u4f53\u6765\u8bf4\uff0c\u4f8b\u5982 \\(f(x,y,z)=(x+y)z\\)\uff0c\u5c06\u5176\u5199\u6210\u8282\u70b9\u56fe\u5982\u4e0b\uff0c\u5e76\u8ba1\u7b97\u6240\u9700\u8981\u7684\u53c2\u6570\u3002</p> <p> </p> <p>\u7136\u540e\u6211\u4eec\u4ece\u56fe\u7684\u672b\u7aef\u5f00\u59cb\u8ba1\u7b97\uff0c\u5f97\u5230\u8fd9\u4e9b\u8282\u70b9\u6570\u636e\uff1a</p> <p>\\(\\left\\{ \\begin{aligned} &amp;\\frac{\\partial{f}}{\\partial{f}}=1,\\\\ &amp;\\frac{\\partial{f}}{\\partial{z}}=q=3,\\\\ &amp;\\frac{\\partial{f}}{\\partial{q}}=z=-4,\\\\ &amp;\\frac{\\partial{f}}{\\partial{x}}=\\frac{\\partial{f}}{\\partial{q}}\\frac{\\partial{q}}{\\partial{x}}=-4,\\\\ &amp;\\frac{\\partial{f}}{\\partial{y}}=\\frac{\\partial{f}}{\\partial{q}}\\frac{\\partial{q}}{\\partial{y}}=-4 \\end{aligned} \\right.\\)</p> <p></p> <p></p> <p>backprop (red lines)</p> <p>\u53ef\u4ee5\u53d1\u73b0\uff0c\u6211\u4eec\u5728\u8ba1\u7b97\u8fc7\u7a0b\u4e2d\u53ea\u9700\u8981\u5c06\u201c\u76f8\u90bb\u201d\u68af\u5ea6\u4e58\u4ee5\"local gradient\"\u5373\u53ef\u8ba1\u7b97\u51fa\u6240\u9700\u8981\u7684\u65b0\u7684\"local gradient\"\u3002\u800c\u53ea\u9700\u8981\u518d\u6cbf\u7740\u8def\u5f84\u518d\u5c06\u6240\u6709\u7684\"local gradient\"\u7d2f\u4e58\u8d77\u6765\uff0c\u5c31\u80fd\u5f97\u5230\u6bcf\u4e00\u4e2a\u53d8\u91cf\u5173\u4e8e\u8868\u8fbe\u5f0f\u7684\u68af\u5ea6\u3002</p> <p></p> <p>\u7279\u522b\u7684\uff0c\u7531\u4e8e\u8282\u70b9\u662f\u6211\u4eec\u8ba4\u4e3a\u5b9a\u4e49\u7684\uff0c\u800c\u4e14\u8be5\u65b9\u6cd5\u6240\u4f9d\u8d56\u201c\u94fe\u5f0f\u6cd5\u5219\u201d\u4e5f\u5141\u8bb8\u51fd\u6570\u7684\u81ea\u7531\u7ec4\u5408\uff0c\u6240\u4ee5\u6211\u4eec\u53ef\u4ee5\u4eba\u4e3a\u201c\u5408\u5e76/\u5206\u5272\u201d\u4e00\u4e9b\u8282\u70b9\uff0c\u4f8b\u5982\u5728\u4e0a\u9762\u90a3\u4e2a\u4f8b\u5b50\u4e2d\uff0c\u6211\u4eec\u53ef\u4ee5\u5c06\u6700\u540e\u56db\u4e2a\u8282\u70b9\u5408\u5e76\u4e3a\u4e00\u4e2a\"sigmoid function\"(i.e. \\(\\frac{1}{1+e^{-x}}\\))\u3002</p> <p></p>"},{"location":"cour_note/D1SJ_StanfordCS231n/#patterns-in-backward-flow","title":"Patterns in backward flow","text":"<p>\u53e6\u5916\u4e00\u79cd\u7406\u89e3\u7b97\u7b26\u5728\u8ba1\u7b97\u56fe\u4e2d\u7684\u4f5c\u7528\u7684\u601d\u8def\u3002</p> <p>\u53ef\u4ee5\u53d1\u73b0\uff0c<code>max()</code> \u8fd0\u7b97\u5728\u68af\u5ea6\u4f20\u9012\u8fc7\u7a0b\u4e2d\u53ea\u8d77\u5230\u8def\u7531\u5668\u7684\u4f5c\u7528\uff0c\u4e5f\u5c31\u662f\u8bf4\u5c06\u5176\u4f20\u9012\u5230\u8f83\u5927\u7684\u90a3\u4e2a\u53d8\u91cf\u90a3\u4e00\u4fa7\uff0c\u4f46\u4e0d\u6539\u53d8\u68af\u5ea6\u7684\u503c\uff1b\u800c\u5bf9\u4e8e\u8f83\u5c0f\u7684\u90a3\u4e2a\u53d8\u91cf\uff0c\u68af\u5ea6\u4f20\u9012\u88ab\u963b\u65ad\uff0c\u76ee\u6807\u53d8\u91cf\u7684\u68af\u5ea6\u4e3a \\(0\\)\u3002</p> <p>\u5c06\u8fd9\u4e2a\u6d41\u7a0b\u8fc1\u79fb\u5230\u795e\u7ecf\u7f51\u7edc\u4e0a\uff0c\u6211\u4eec\u53ea\u9700\u8981\u5c06\u8fd9\u4e9b\u6570\u5b57\u53d8\u4e3a Jacobian matrix \u5373\u53ef\u3002</p> <p></p> <ul> <li>Always check: The gradient with respect to a variable should have the same shape as the variable.</li> <li>Because each element of your gradient is quantifying how much that element is contributing to your final output.</li> </ul> <p>\u5728\u5177\u4f53\u5b9e\u73b0\u4e2d\uff0c\u6211\u4eec\u4e00\u822c\u4f1a\u5b9e\u73b0\u4e00\u4e2a <code>forward()</code> \u7528\u4e8e\u8ba1\u7b97\u51fd\u6570\u7684\u8f93\u51fa\uff0c\u4ee5\u53ca\u4e00\u4e2a <code>backward()</code> \u7528\u4e8e\u6309\u7167\u4e0a\u9762\u63d0\u5230\u7684\u65b9\u6cd5\u8ba1\u7b97\u68af\u5ea6\u3002</p> <p></p> <p>Summary</p> <ul> <li>Neural nets will be very large: impractical to write down gradient formula by hand for all parameters.</li> <li>Backpropagation = recursive application of the chain rule along a computational graph to compute the gradients of all inputs/parameters/intermediates.</li> <li>Implementations maintain a graph structure, where the nodes implement the <code>forward()</code> / <code>backward()</code> API.</li> <li>Forward: compute result of an operation and save any intermediates needed for gradient computation in memory.</li> <li>Backward: apply the chain rule to compute the *gradient *of the loss function with respect to the inputs.</li> </ul>"},{"location":"cour_note/D1SJ_StanfordCS231n/#neural-networks","title":"Neural Networks","text":"<p>\u901a\u8fc7\u51fd\u6570\u53e0\u52a0\u7684\u65b9\u5f0f\u6765\u5b9e\u73b0\u795e\u7ecf\u7f51\u7edc\u3002</p> <p></p> <p>\u4e0e\u751f\u7269\u795e\u7ecf\u7684\u4e00\u4e2a\u7c7b\u6bd4</p> <p></p> <p></p> <p>Summary</p> <ul> <li>We arrange neurons into fully-connected layers.</li> <li>The abstraction of a layer has the nice property that it allows us to use efficient vectorized code (e.g. matrix multiplies).</li> <li>Neural networks are not really neural.</li> </ul>"},{"location":"cour_note/D1SJ_StanfordCS231n/#lecture-5-convolutional-neural-networks","title":"Lecture 5: Convolutional Neural Networks","text":"<ul> <li>Video: \ud83d\udd17</li> <li>Slides: \ud83d\udd17</li> </ul>"},{"location":"cour_note/D1SJ_StanfordCS231n/#convolutional-neural-networks","title":"Convolutional Neural Networks","text":"<p>\u4e4b\u524d\u63d0\u5230\u8fc7\u7684 Fully Connected Layer \u4f1a\u5c06\u591a\u7ef4\u7684\u6570\u636e\u62c9\u4f38\u4e3a\u5411\u91cf\u7684\u5f62\u5f0f\uff0c\u76f8\u6bd4\u4e4b\u4e0b\uff0c Convolution Layer \u5219\u4f1a\u4fdd\u7559\u8f93\u5165\u6570\u636e\u7684\u5f62\u72b6 \u7279\u5f81\uff0c\u4e00\u822c\u6765\u8bf4\uff0cfilter \u4f1a\u4e0e\u6570\u636e\u5177\u6709\u76f8\u540c\u7684\u6df1\u5ea6\uff08\u4f8b\u5982 input \u662f 32x32x3\uff0c\u90a3\u4e48 filter \u53ef\u4ee5\u4e3a 5x5x3\uff09\u3002\u901a\u8fc7\u5c06 filter \u4e0e input \u7684\u67d0\u4e00\u4e2a\u540c\u5f62\u72b6\u7684\u5b50\u533a\u57df\u505a\u70b9\u79ef\uff0c\u6211\u4eec\u5c31\u53ef\u4ee5\u5f97\u5230\u4e00\u4e2a\u6570\u5b57\u3002</p> <ul> <li>Convolve the filter with the image. (i.e. \"slide over the image spatially, computing dot products\")</li> </ul> <p></p> <p>\u5728\u67d0\u4e2a\u4f4d\u7f6e\u83b7\u5f97\u70b9\u79ef\uff0c\u5373 filter \u5982\u4f55\u4f5c\u7528\u4e8e input</p> <p></p> <p>\u91c7\u7528\u591a\u4e2a filters \u5e76\u5c06\u7ed3\u679c\u53e0\u52a0\uff0c\u6211\u4eec\u5c31\u53ef\u4ee5\u5f97\u5230\u591a\u4e2a\u6fc0\u6d3b\u56fe(activation maps)\uff0c\u4f5c\u4e3a\u4e00\u4e2a\u5904\u7406\u540e\u7684\u6570\u636e\u3002 - ConvNet is a sequence of Convolution Layers, interspersed with activation functions.</p> <p></p> <p>\u5173\u4e8e\u8f93\u51fa\u7684\u6fc0\u6d3b\u56fe\u7684\u5927\u5c0f\uff0c\u6709\u5982\u4e0a\u516c\u5f0f\u3002</p> <p>\u901a\u8fc7\u9009\u62e9\u6b65\u957f\uff0c\u6211\u4eec\u53ef\u4ee5\u63a7\u5236\u6ed1\u52a8\u7684\u901f\u7387\u3002\u4ece\u67d0\u79cd\u610f\u4e49\u4e0a\u6765\u8bb2\u8fd9\u4e5f\u662f\u5728\u63a7\u5236\u6ed1\u52a8\u7ed3\u679c\u7684\u5206\u8fa8\u7387\uff0c\u4e5f\u662f\u6c60\u5316\u64cd\u4f5c\u80cc\u540e\u7684\u601d\u60f3\u4e4b\u4e00\u3002\u800c\u5177\u4f53\u9009\u62e9\u5927\u6b65\u957f\u8fd8\u662f\u5c0f\u6b65\u957f\u662f\u4f60\u9700\u8981\u5bf9\u5404\u79cd\u56e0\u7d20\u8fdb\u884c\u8003\u91cf\u51b3\u5b9a\u7684\u3002</p> <p>\u53ef\u4ee5\u53d1\u73b0\uff0c\u6b65\u957f\u4e3a 3 \u65f6\u65e0\u6cd5\u5339\u914d\u3002\u800c\u5728\u5b9e\u8df5\u8fc7\u7a0b\u4e2d\uff0c\u6211\u4eec\u6709\u4e00\u4e9b\u624b\u6bb5\u6765\u89e3\u51b3\u8fd9\u79cd\u65e0\u6cd5\u5339\u914d\u7684\u60c5\u51b5\uff0c\u5982\"zero pad to borders\"\u4ee5\u4f7f\u5927\u5c0f\u7b26\u5408\u6b65\u957f\u3002</p> <ul> <li>The zero padding does add some sort of extraneous features at the corners, and we're doing our best to get some value and do, like process that region of the image. And so zero padding is kind of one way to do this. There's also other ways to do this that, you know, you can try and like, mirror the values here or extend them, and so it doesn't have to be zero padding, but in practice this is one thing that works reasonably.</li> </ul> <p></p> <p>\u6ce8\u610f\uff0c\u91c7\u7528\u96f6\u6269\u5c55\u4ee5\u540e\u4e0a\u4e00\u5f20\u56fe\u7684\u516c\u5f0f\u5c31\u65e0\u6cd5\u4f7f\u7528\u4e86\u3002\u8fd9\u4e5f\u6b63\u662f\u96f6\u6269\u5c55\u7684\u4e00\u4e2a\u7279\u70b9\uff0c\u5b83\u53ef\u4ee5\u8ba9\u56fe\u50cf\u7684\u5f62\u72b6\u4e0d\u5fc5\u7f29\u5c0f\u3002</p> <p>\u4e00\u9053\u6d4b\u8bd5\u9898\uff1a</p> \u9898\u9762\u7b54\u6848 <p></p> <p>\u8ba1\u7b97\u8fd9\u6837\u4e00\u5c42\u4e2d\u6709\u591a\u5c11\u53c2\u6570\u3002</p> <p>Ans</p> <ul> <li>Each filter has \\(5\\times5\\times3_{\\text{(depth)}} + 1_{\\text{(for bias)}} = 76\\) params.</li> <li>So the total number is \\(76\\times 10 = 760\\).</li> </ul>"},{"location":"cour_note/D1SJ_StanfordCS231n/#pooling-layer","title":"Pooling layer","text":"<ul> <li>makes the representations smaller and more manageable</li> <li>operates over each activation map independently:</li> </ul> <p>just downsample</p> <p>A common way to do this is max pooling:</p> <p></p> <p>just take the max value</p> <p>\u5bf9\u4e8e\u6c60\u5316\u5c42\uff0c\u5728\u8fdb\u884c\u6ed1\u52a8\u7a97\u53e3\u65f6\u6211\u4eec\u66f4\u5e0c\u671b\u6b65\u957f\u7684\u8bbe\u7f6e\u80fd\u4f7f filter \u6ca1\u6709\u91cd\u53e0\uff0c\u4ee5\u6ee1\u8db3\u5c0f\u8282\u5f00\u5934\u63d0\u5230\u7684\"independently\"\u3002</p>"},{"location":"cour_note/D1SJ_StanfordCS231n/#fully-connected-layer-fc-layer","title":"Fully Connected Layer (FC layer)","text":"<ul> <li>Contains neurons that connect to the entire input volume, as in ordinary Neural Networks.</li> </ul>"},{"location":"cour_note/D2CX_AdvancedDataStructure/","title":"\ud83d\udc8e \u9ad8\u7ea7\u6570\u636e\u7ed3\u6784 | Advanced Data Structure","text":"<p> \u7ea6 148 \u4e2a\u5b57 </p> <p>\u8bfe\u7a0b\u4fe1\u606f</p> <p>\u7ffb\u8f6c\u8bfe\u5802*</p> <p>\u5206\u6570\u6784\u6210\uff1a</p> <ul> <li>5% = HW</li> <li>5% = Quiz\uff08\u5212\u5206\u5230\u54ea\u91cc\u8fd8\u4e0d\u77e5\u9053\uff09</li> <li>10% = Discussions</li> <li>30% = Research Project &amp; Peer Review</li> <li>10% = max(\u671f\u4e2d\uff0c\u671f\u672b)</li> <li>40% = \u671f\u672b</li> </ul> <p>\u7b14\u8bb0\u76f8\u5173</p> <p>\u53c2\u8003\u7b14\u8bb0\uff1a</p> <ul> <li>https://www.yuque.com/xianyuxuan/saltfish_shop/course_res_index#cIhfl</li> </ul> <p>List</p> <ul> <li> Lecture 1 | AVL Trees &amp; Splay Trees &amp; Amortized Analysis</li> <li> Lecture 2 | Red Black Tree &amp; B+ Tree</li> <li> Lecture 3 | Inverted File Index</li> <li> Lecture 4 | Leftist Heaps &amp; Skew Heaps</li> <li> Lecture 5 | Binominal Trees</li> <li> Lecture 6 | Backtracing</li> <li> Lecture 7 | Divide &amp; Conquer</li> <li> Lecture 8 | Dynamic Programming</li> <li> Lecture 9 | Greedy Algorithms</li> <li> Lecture 10 | NP Completeness</li> <li> Lecture 11 | Approximation</li> <li> Lecture 12 | Local Search</li> <li> Lecture 13 | Randomized Algorithms</li> <li> Lecture 14 | Parallel</li> <li> <p> Lecture 15 | External Sorting</p> </li> <li> <p> Topic 1 | Amortized Analysis</p> </li> </ul>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Ex01/","title":"Topic 1 | Amortized Analysis","text":"<p> \u7ea6 1041 \u4e2a\u5b57  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 3 \u5206\u949f</p> <p>\u8bf4\u660e</p> <p>\u8ba1\u5212\u5728\u4e00\u6bb5\u65f6\u95f4\u5185\u91cd\u5199\u8fd9\u4e00\u90e8\u5206\u7684\u5185\u5bb9\uff0c\u73b0\u5728\u7684\u5185\u5bb9\u662f\u4ece\u539f\u6765\u7684 Lec01 \u91cc\u76f4\u63a5\u8fc1\u79fb\u8fc7\u6765\u7684\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Ex01/#\u644a\u8fd8\u5206\u6790","title":"\u644a\u8fd8\u5206\u6790","text":"<p>link</p> <p>Wikipedia: https://zh.wikipedia.org/wiki/%E5%B9%B3%E6%91%8A%E5%88%86%E6%9E%90</p> <p>\u4e0d\u597d\u610f\u601d</p> <p>\u6211\u5b9e\u5728\u4e0d\u77e5\u9053\u600e\u4e48\u6e05\u6670\u5730\u8bb2\u660e\u767d\u201c\u644a\u8fd8\u201d\u662f\u4ec0\u4e48\uff0c\u611f\u89c9\u8bb2\u4e0d\u592a\u6e05\u695a\uff0c\u6240\u4ee5\u5c31\u6bd4\u8f83\u7b80\u5355\u7684\u4ecb\u7ecd\u4e86\uff0c\u4f46\u662f\u6211\u4ecd\u7136\u4f1a\u6307\u51fa\u6211\u5b66\u4e60\u8fc7\u7a0b\u4e2d\u8ba4\u4e3a\u5bf9\u6211\u542f\u53d1\u6027\u6bd4\u8f83\u5927\u7684\u5730\u65b9\u3002</p> <p>\u6240\u8c13\u7684\u644a\u8fd8\u5206\u6790\uff0c\u5206\u6790\u7684\u662f\u644a\u8fd8\u8fb9\u754c\uff0c\u6216\u8005\u8bf4\u644a\u8fd8\u65f6\u95f4\u590d\u6742\u5ea6\u3002\u5e73\u5e38\u6211\u4eec\u5206\u6790\u65f6\u95f4\u590d\u6742\u5ea6\u65f6\uff0c\u9488\u5bf9\u7684\u5f80\u5f80\u662f\u67d0\u4e2a\u5177\u4f53\u7684\u64cd\u4f5c\u3002\u800c\u644a\u8fd8\u5206\u6790\u7684\u5bf9\u8c61\u5219\u662f\u4e00\u4e2a\u6570\u636e\u7ed3\u6784\u7684\u4e00\u7cfb\u5217\u64cd\u4f5c\uff0c\u800c\u8fd9\u4e00\u7cfb\u5217\u64cd\u4f5c\u4e2d\u6709\u6210\u672c\u8f83\u4f4e\u7684\uff0c\u4e5f\u6709\u6210\u672c\u8f83\u9ad8\u7684\uff0c\u800c\u4e14\u64cd\u4f5c\u4e4b\u95f4\u4e5f\u53ef\u80fd\u6709\u4e92\u76f8\u5f71\u54cd\u3002</p> <p>\u800c\u644a\u8fd8\u5206\u6790\u5219\u662f\u4ee5\u4e00\u4e2a\u66f4\u5168\u5c40\u7684\u89d2\u5ea6\u6765\u8ba1\u7b97\u201c\u5e73\u5747\u201d\u7684\u64cd\u4f5c\u4ee3\u4ef7\uff0c\u5b83\u8ba1\u7b97\u7684\u662f\u4ece\u521d\u59cb\u72b6\u6001\u5f00\u59cb\uff0c\u8fde\u7eed\u7684 M \u6b21\u4efb\u610f\u64cd\u4f5c\u6700\u591a\u6709 \u7684\u4ee3\u4ef7\u3002\u9700\u8981\u6ce8\u610f\u7684\u662f\uff0c\u5b83\u4e0d\u540c\u4e8e\u5e73\u5747\u65f6\u95f4\u5206\u6790\uff08\u6240\u6709\u53ef\u80fd\u7684\u64cd\u4f5c\u51fa\u73b0\u6982\u7387\u5e73\u5747\uff0c\u4e5f\u5c31\u662f\u76f4\u63a5\u6c42\u5e73\u5747\uff09\u548c\u6982\u7387\u7b97\u6cd5\u7684\u6982\u7387\u5206\u6790\uff08\u5e73\u5747\u8bdd\u6240\u6709\u53ef\u80fd\u7684\u968f\u673a\u9009\u62e9\uff0c\u4e5f\u5c31\u662f\u52a0\u6743\u6c42\u5e73\u5747\uff09\u4e0d\u540c\uff0c\u644a\u8fd8\u5206\u6790\u548c\u6982\u7387\u5b8c\u5168\u65e0\u5173\u3002</p> <p>\u5bb9\u6613\u5f97\u5230\u5982\u4e0b\u7b49\u5f0f\uff1a</p> \\[ \\text{worst-case bound} \\geq \\text{amortized bound} \\geq \\text{average-case bound} \\] <p>\u6211\u4eec\u77e5\u9053\uff0c\u7531\u4e8e amortized bound \u9650\u5236\u4e86\u6240\u6709\u7684 M \u6b21\u64cd\u4f5c\uff0c\u6240\u4ee5\u5176\u4e0a\u754c\u5c31\u7b49\u4e8e\u6700\u5dee\u7684\u60c5\u51b5\u53d1\u751f M \u6b21\uff08\u5f53\u7136\uff0c\u5f88\u591a\u60c5\u51b5\u4e0b\u4e0d\u4e00\u5b9a\u80fd\u53d6\u5230\u5168\u90fd\u662f\u6700\u5dee\u60c5\u51b5\uff09\uff1b\u540c\u6837\u7684\uff0c\u7531\u4e8e\u9700\u8981\u5bf9\u4efb\u610f\u7ec4\u5408\u90fd\u6210\u7acb\uff0c\u6240\u4ee5\u4e00\u5b9a\u4e0d\u4f1a\u5c0f\u4e8e\u7edf\u8ba1\u5b66\u610f\u4e49\u4e0a\u7684\u5e73\u5747\u60c5\u51b5\u3002</p> <p>\u521a\u5f00\u59cb\u5b66\u5230\u644a\u8fd8\u5206\u6790\u7684\u65f6\u5019\uff0c\u770b\u7740\u8fd9\u4e9b\u5185\u5bb9\u6709\u4e00\u79cd\u83ab\u540d\u5176\u5999\u7684\u611f\u89c9\uff0c\u4e0d\u77e5\u9053\u5b83\u5728\u5e72\u561b\uff0c\u540e\u6765\u6211\u624d\u53d1\u73b0\u6211\u8bef\u89e3\u4e86\u644a\u8fd8\u5206\u6790\u7684\u76ee\u7684\u3002\u6240\u4ee5\u6211\u611f\u89c9\u8fd8\u662f\u9700\u8981\u5c31\u6b64\u7ed9\u51fa\u6211\u81ea\u5df1\u7684\u7406\u89e3\u3002</p> <p>\u644a\u8fd8\u5206\u6790</p> <p>\u5728\u6211\u7406\u89e3\u4e2d\uff0c\u644a\u8fd8\u5206\u6790\u5b9e\u9645\u4e0a\u662f\u4e00\u7cfb\u5217\u8bc1\u660e\u65b9\u6cd5\uff0c\u66f4\u8fdb\u4e00\u6b65\u7684\u8bf4\uff0c\u5728\u6211\u4eec\u4e4b\u540e\u4f1a\u8bb2\u5230\u7684\u4e09\u4e2a\u5206\u6790\u65b9\u6cd5\u4e2d\uff0c\u6709\u4e00\u4e9b\u53ef\u80fd\u96be\u4ee5\u76f4\u63a5\u5f97\u5230\u644a\u8fd8\u590d\u6742\u5ea6\u3002\u4f46\u662f\u5b9e\u9645\u4e0a\uff0c\u4ed6\u4eec\u7684\u8fc7\u7a0b\u66f4\u50cf\u662f\u5df2\u77e5\u4e00\u4e2a\u644a\u8fd8\u8fb9\u754c\uff0c\u5e76\u8bc1\u660e\u5b83\u786e\u5b9e\u662f\u8fb9\u754c\u3002</p> <p>\u5e38\u89c1\u7684\u644a\u8fd8\u5206\u6790\u6709\u4e09\u79cd\uff1a\u805a\u5408(aggregate)\u6cd5\u3001\u6838(accounting)\u6cd5\u3001\u52bf\u80fd(potential)\u6cd5\uff0c\u63a5\u4e0b\u6765\u4e00\u4e00\u4ecb\u7ecd\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Ex01/#\u805a\u5408\u6cd5","title":"\u805a\u5408\u6cd5","text":"<p>\u805a\u5408\u6cd5\u76f8\u5bf9\u7b80\u5355\uff0c\u5c31\u662f\u76f4\u63a5\u7d2f\u79ef\u8fde\u7eed M \u6b21\u64cd\u4f5c\u7684\u4ee3\u4ef7\uff0c\u518d\u9664\u4ee5 M\u3002</p> \\[ T_{amortized} = \\frac{\\sum_i{T_i}}{n} \\]"},{"location":"cour_note/D2CX_AdvancedDataStructure/Ex01/#\u6838\u6cd5","title":"\u6838\u6cd5","text":"<p>link</p> <p>\u5173\u4e8e Accounting Analysis \u53ef\u4ee5\u53c2\u8003\u8fd9\u7bc7\u6587\u7ae0\uff1ahttps://www.baeldung.com/cs/amortized-analysis</p> <p>\u505a\u4e00\u4e2a\u6bd4\u55bb\u7684\u8bdd\uff0c\u53ef\u4ee5\u8fd9\u4e48\u7406\u89e3\uff1a</p> <p>\u4f60\u53bb\u5403\u5348\u996d\uff0c\u5403\u7d20\u83dc\u8981 \u00a51\uff08\u5bf9\u6807\u6d88\u8017\u8f83\u5c0f\u7684\u64cd\u4f5c\uff09\uff0c\u5403\u8364\u83dc\u8981 \u00a54\uff08\u5bf9\u6807\u6d88\u8017\u8f83\u5927\u7684\u64cd\u4f5c\uff09\uff0c\u73b0\u5728\u4f60\u77e5\u9053\u4f60\u6bcf\u5929\u5403\u5348\u996d\u7684\u644a\u8fd8\u5f00\u9500\u4e3a \u00a52\uff08\u4ece\u8bc1\u660e\u7684\u89d2\u5ea6\u6765\u7406\u89e3\uff09\uff0c\u5e76\u4e14\u6211\u65e0\u8111\u7684\u8ba4\u4e3a\u6bcf\u4e2a\u64cd\u4f5c\u7684\u644a\u8fd8\u4ee3\u4ef7\u90fd\u662f \u00a52\uff08\u5728\u6838\u6cd5\u4e2d\uff0c\u6574\u4f53\u7684\u644a\u8fd8\u5f00\u9500\u548c\u5355\u4e2a\u64cd\u4f5c\u7684\u644a\u8fd8\u5f00\u9500\u662f\u4e0d\u4e00\u6837\u7684\uff0c\u5355\u4e2a\u64cd\u4f5c\u7684\u644a\u8fd8\u5f00\u9500\u662f\u53ef\u80fd\u4e92\u4e0d\u4e00\u6837\u7684\uff0cM \u4e2a\u64cd\u4f5c\u6c42\u548c\u53d6\u5e73\u5747\u4ee5\u540e\u624d\u662f\u6574\u4f53\u7684\u644a\u8fd8\u4ee3\u4ef7\uff09\u3002\u90a3\u4e48\u4f60\u4eca\u5929\u5403\u7d20\u83dc\uff0c\u8d26\u6237\u5165\u8d26 \u00a51\uff082 - 1 = 1\uff09\uff1b\u660e\u5929\u4f60\u4e5f\u5403\u7d20\u83dc\uff0c\u8d26\u6237\u4e5f\u5165\u8d26 \u00a51\uff1b\u540e\u5929\u4f60\u5403\u8364\u83dc\u4e86\uff0c\u90a3\u4e48\u8d26\u6237\u5c31\u51fa\u8d26 \u00a52\uff082 - 4 = -2\uff09\u2026\u2026</p> <p>\u6838\u6cd5\u5927\u6982\u5c31\u662f\u6309\u7167\u8fd9\u4e48\u4e00\u4e2a\u601d\u8def\u6765\u8bc1\u660e\uff0c\u4e0d\u8fc7\u5177\u4f53\u7ec6\u8282\u548c\u4e0a\u9762\u8fd9\u4e2a\u6848\u4f8b\u8fd8\u662f\u6709\u533a\u522b\u7684\uff0c\u53ef\u4ee5\u8be6\u7ec6\u53c2\u8003\u4e0a\u9762\u90a3\u7247\u6587\u7ae0\uff0c\u6211\u89c9\u5f97\u914d\u56fe\u548c\u8bf4\u660e\u90fd\u5f88\u8be6\u7ec6\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Ex01/#\u52bf\u80fd\u6cd5","title":"\u52bf\u80fd\u6cd5","text":"<p>link</p> <p>\u5173\u4e8e Potential Analysis \u53ef\u4ee5\u53c2\u8003\u8fd9\u7bc7\u6587\u7ae0\uff1ahttps://en.wikipedia.org/wiki/Potential_method \u4ee5\u53ca ltgg \u7684\u8fd9\u671f\u5468\u62a5\u8bb2\u7684\u4e5f\u5f88\u597d\uff1ahttps://www.yuque.com/xianyuxuan/saltfish_shop/weekly002_amortized_analysis#KmnY6</p> <p>\u52bf\u80fd\u6cd5\u5f3a\u63a8 ltgg \u7684\u8fd9\u7bc7\u6587\u7ae0\uff0c\u8bb2\u7684\u975e\u5e38\u597d\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec01/","title":"Lecture 1 | AVL Trees &amp; Splay Trees","text":"<p> \u7ea6 7119 \u4e2a\u5b57  385 \u884c\u4ee3\u7801  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 29 \u5206\u949f</p> <p>\u8bf4\u660e</p> <p>\u539f\u5148\u5b89\u6392\u5728\u8fd9\u4e00\u7ae0\u8282\u7684\u644a\u8fd8\u5206\u6790\u73b0\u5728\u88ab\u8fc1\u79fb\u5230\u4e86\u8fd9\u4e2a\u5730\u65b9\uff1aTopic 1 | Amortized Analysis\u3002</p> <p>\u9605\u8bfb\u6280\u5de7</p> <p>\u56e0\u4e3a\u6ca1\u6cd5\u5728\u8fd9\u91cc\u7528\u4ee3\u7801\u5199\u52a8\u753b\uff0c\u6240\u4ee5\u6211\u7528 Tab \u6a21\u62df\u4e86\u4e00\u4e0b\u52a8\u753b\u5e27\uff0c\u53ef\u4ee5\u624b\u52a8\u5207\u6362\u8fd9\u4e9b\u6807\u7b7e\u6765\u52a8\u6001\u89c2\u5bdf\u3002\u4e00\u822c\u8fd9\u79cd\u5185\u5bb9\u7684 Tab \u6807\u9898\u90fd\u4f1a\u662f <code>Frame {}</code>\u3002</p> Frame 1Frame 2Frame 3 <p>Like</p> <p>Like this</p> <p>Like this!</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec01/#avl-\u6811","title":"AVL \u6811","text":""},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec01/#\u6982\u5ff5","title":"\u6982\u5ff5","text":"<p>link</p> <p>OI Wiki: https://oi-wiki.org/ds/avl/</p> <p>\u6211\u4eec\u77e5\u9053\uff0c\u5bf9\u4e8e\u4e00\u68f5\u4e8c\u53c9\u641c\u7d22\u6811\uff0c\u5176\u5bf9\u70b9\u7684\u64cd\u4f5c\u4ee3\u4ef7\u4e3a \\(O(\\log n)\\)\u3002\u7136\u800c\u5728\u6700\u574f\u60c5\u51b5\u4e0b\uff0c\u5b83\u4f1a\u9000\u5316\u6210 \\(O(n)\\)\uff0c\u4f8b\u5982\u8fd9\u662f\u4e00\u68f5\u53ea\u6709\u5de6\u5b69\u5b50\u6811\u7684\u94fe\u578b\u4e8c\u53c9\u6811\uff0c\u90a3\u4e48\u64cd\u4f5c\u8fd9\u91cc\u552f\u4e00\u7684\u53f6\u5b69\u5b50\u8282\u70b9\u5c31\u662f \\(O(n)\\)\u3002</p> <p>\u6362\u53e5\u8bdd\u6765\u8bf4\uff0c\u4e00\u68f5\u4e8c\u53c9\u6811\u7684\u7ef4\u62a4\u6210\u672c\u57fa\u672c\u4e0a\u4e0e\u5176\u9ad8\u5ea6\u6b63\u76f8\u5173\u3002\u56e0\u800c\u4e00\u4e2a\u5f88\u81ea\u7136\u7684\u60f3\u6cd5\u662f\uff0c\u5982\u679c\u6211\u4eec\u60f3\u8ba9\u4e00\u68f5\u4e8c\u53c9\u6811\u597d\u7ef4\u62a4\uff0c\u90a3\u4e48\u5c31\u5e0c\u671b\u5b83\u7684\u9ad8\u5ea6\u5c3d\u53ef\u80fd\u4f4e\uff0c\u800c\u5728\u70b9\u6570\u56fa\u5b9a\u7684\u60c5\u51b5\u4e0b\uff0c\u4e00\u79cd\u6734\u7d20\u7684\u601d\u60f3\u662f\u8ba9\u8282\u70b9\u5c3d\u53ef\u80fd\u201c\u5747\u5300\u201d\u5730\u5206\u5e03\u5728\u6811\u4e0a\u3002</p> <p>height of a tree</p> <p>\u6811\u7684\u9ad8\u5ea6(Height of Tree)\u7b49\u4e8e\u5176\u6839\u8282\u70b9\u5230\u53f6\u5b69\u5b50\u8282\u70b9\u7684\u82e5\u5e72\u8def\u5f84\u4e2d\uff0c\u6700\u5927\u7684\u8ddd\u79bb\uff08\u5373\u8fb9\u7684\u6570\u91cf\uff09\uff0c\u4e5f\u5c31\u662f\u6df1\u5ea6\u6700\u6df1\u7684\u8282\u70b9\u5230\u6839\u8282\u70b9\u5230\u8ddd\u79bb\u3002</p> <p>\u7279\u522b\u7684\uff0c\u4e00\u68f5\u7a7a\u6811\u7684\u9ad8\u5ea6\u4e3a -1\u3002</p> <p>\u8bf4\u7684\u901a\u4fd7\u4e00\u4e9b\uff0c\u5c31\u662f\u6811\u7684\u5c42\u6570\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec01/#avl-\u6811_1","title":"AVL \u6811","text":"<p>\u800c AVL Tree \u662f\u4e00\u79cd\u5e73\u8861(balanced)\u7684\u4e8c\u53c9\u641c\u7d22\u6811\uff0c\u901a\u8fc7\u300c\u9ad8\u5ea6\u300d\u8fd9\u4e2a\u91cf\uff0c\u5b9a\u4e49\u4e86\u300c\u5e73\u8861\u300d\u8fd9\u4ef6\u4e8b\u3002</p> <p>AVL Tree</p> <ol> <li>\u4e00\u4e2a\u7a7a\u4e8c\u53c9\u6811\u662f\u4e00\u4e2a AVL \u6811\uff1b</li> <li>\u5982\u679c\u4e8c\u53c9\u6811 \\(T\\) \u662f\u4e00\u4e2a AVL \u6811\uff0c\u5219\u5176\u5de6\u53f3\u5b69\u5b50\u6811 \\(T_l\\) \u548c \\(T_r\\) \u4e5f\u90fd\u5e94\u8be5\u662f AVL \u6811\uff0c\u4e14\u6709 \\(|h(T_l) - h(T_r)| \\leq 1\\)\uff1b</li> </ol> <p>Balance Factor</p> <p>\u4e00\u4e2a\u8282\u70b9\u7684\u5e73\u8861\u56e0\u5b50(Balance Factor, BF)\u7528\u6765\u63cf\u8ff0\u4e00\u4e2a\u8282\u70b9\u7684\u5e73\u8861\u72b6\u6001\uff0c\u5bf9\u4e8e\u8282\u70b9 \\(T_p\\)\uff0c\u5b83\u7684\u5de6\u5b69\u5b50\u6811\u4e3a \\(T_l\\)\uff0c\u53f3\u5b69\u5b50\u6811\u4e3a \\(T_r\\)\uff0c\u5219\uff1a</p> \\[ BF(T_p) = h(T_l) - h(T_r) \\] <p>\u6240\u4ee5\u4e0a\u9762\u7684\u7b2c 2 \u6761\u53c8\u53ef\u4ee5\u5199\u6210\uff1a</p> <ul> <li>\u5982\u679c\u4e8c\u53c9\u6811 \\(T\\) \u662f\u4e00\u4e2a AVL \u6811\uff0c\u5219\u5176\u5de6\u53f3\u5b69\u5b50\u6811 \\(T_l\\) \u548c \\(T_r\\) \u4e5f\u90fd\u5e94\u8be5\u662f AVL \u6811\uff0c\u4e14\u6709 \\(BF(T_p) \\in \\{0, \\pm 1\\}\\)\uff1b</li> </ul> <p>\u8bf4\u7684\u901a\u4fd7\u4e00\u4e9b\u5c31\u662f\uff0cAVL \u6811\u7684\u6bcf\u4e00\u4e2a\u70b9\u90fd\u5e73\u8861\uff0c\u800c\u5e73\u8861\u4e0e\u5426\u53d6\u51b3\u4e8e\u8282\u70b9\u7684\u4e24\u4e2a\u5b69\u5b50\u6811\u5c42\u6570\u4e4b\u5dee\u662f\u5426\u8d85\u8fc7 1\u3002</p> <p>\u5728\u8fd9\u79cd\u5b9a\u4e49\u4e0b\uff0cAVL \u6811\u7684\u9ad8\u5ea6\u53ef\u4ee5\u8bc1\u660e\u4e3a \\(O(\\log N)\\)\uff0c\u8bc1\u660e\u5982\u4e0b\uff1a</p> <p>Height of AVL Trees</p> <pre><code>graph TD;\nA((\"Root\"))\nB[/\"Left Subtree\"\\]\nC[/\"Right Subtree\"\\]\nA === B\nA === C</code></pre> <p>\u6211\u4eec\u8bb0 \\(n_h\\) \u662f\u9ad8\u5ea6\u4e3a \\(h\\) \u7684 AVL \u6811\u6240\u5305\u542b\u7684\u6700\u5c11\u8282\u70b9\u6570\uff0c\u5219\u6709\u5982\u4e0b\u9012\u63a8\u5173\u7cfb\uff1a</p> \\[ n_h = \\left\\{     \\begin{array}{l}         1                       &amp; (h = 0) \\\\         2                       &amp; (h = 1) \\\\         n_{h-1} + n_{h-2} + 1   &amp; (h &gt; 1)     \\end{array} \\right. \\] <p>\u53d1\u73b0 \\(n_h + 1\\) \u7b26\u5408 Fibonacci \u6570\u5217\u7684\u9012\u63a8\u516c\u5f0f\uff08\u4f46\u662f\u521d\u59cb\u6761\u4ef6\u4e0d\u4e00\u6837\uff09\uff0c\u6240\u4ee5\u6211\u4eec\u53ef\u4ee5\u7528 Fibonacci \u5bf9\u5176\u8fdb\u884c\u4e00\u4e2a\u4f30\u8ba1\u3002</p> <p>\u800c\u5bf9\u4e8e\u5982\u4e0b Fibonacci \u6570\u5217\uff1a</p> \\[ F_i = \\left\\{     \\begin{array}{l}         1                   &amp; (i = 1) \\\\         1                   &amp; (i = 2) \\\\         F_{i-1} + F_{i-2}   &amp; (i &gt; 2)     \\end{array} \\right. \\] <p>\u5176\u901a\u9879\u4e3a\uff1a</p> \\[ \\begin{aligned}     F_n &amp;= \\frac{1}{\\sqrt{5}} \\left( \\left( \\frac{1 + \\sqrt{5}}{2} \\right)^n - \\left( \\frac{1 - \\sqrt{5}}{2} \\right)^n \\right) \\\\         &amp;\\approx \\frac{1}{\\sqrt{5}} \\left( \\frac{1 + \\sqrt{5}}{2} \\right)^n \\\\     \\log{(F_n)} &amp;\\approx n \\end{aligned} \\] <p>\u800c \\(n_h + 1 \\approx F_{h+2}\\)\uff0c\u6240\u4ee5 \\(h \\approx \\log{(n_h)}\\)\uff0c\u4e5f\u5c31\u662f\u8bf4 \\(h \\approx \\log{N}\\)\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec01/#\u89c6\u89d2","title":"\u89c6\u89d2","text":"<p>\u800c\u6211\u4eec\u8c08\u8bba AVL \u6811\u65f6\uff0c\u6211\u4eec\u5e0c\u671b\u4ee5\u4e00\u4e2a\u52a8\u6001\u7684\u89c6\u89d2\u6765\u8c08\u8bba AVL \u6811\uff0c\u5373\u8ba8\u8bba\uff1a\u67d0\u4e00\u68f5\u6811\u662f\u5426\u662f AVL \u6811\uff1b\u5728\u67d0\u4e2a\u64cd\u4f5c\u540e\uff0c\u5b83\u662f\u5426\u4ecd\u7136\u662f AVL \u6811\uff1b\u82e5\u539f\u5148\u662f\uff0c\u800c\u7ecf\u8fc7\u64cd\u4f5c\u540e\u4e0d\u518d\u662f\uff0c\u90a3\u8981\u5982\u4f55\u5c06\u5b83\u91cd\u65b0\u53d8\u4e3a AVL \u6811\u3002</p> <p>\u4ee5\u4e0a\u4e09\u4e2a\u6b65\u9aa4\u662f\u7b80\u5316\u540e\u7684\u5efa\u6a21\uff0c\u5b83\u6210\u4e3a\u6211\u4eec\u89e3\u51b3\u5176\u4ed6\u95ee\u9898\u7684\u6700\u5c0f\u5355\u5143\u548c\u57fa\u7840\u3002</p> <p>\u6240\u4ee5\u5728\u8fd9\u79cd\u6a21\u578b\u4e0b\uff0c\u6211\u4eec\u9700\u8981\u5b9a\u4e49\u4e24\u4e2a\u4e1c\u897f\uff1a</p> <p>Trouble Maker &amp; Trouble Finder</p> <p>\u4ee5 \ud83c\udf30 \u6765\u8bf4\u660e\u3002</p> Frame 1Frame 2 <p>\u4e0b\u56fe\u4e3a\u4e00\u4e2a AVL \u6811\uff1a</p> <pre><code>graph TD;\nA((\"8, BF=1\"))\nB((\"4, BF=0\"))\nC((\"9, BF=0\"))\nD((\"2, BF=0\"))\nE((\"6, BF=0\"))\nA === B\nA === C\nB === D\nB === E</code></pre> <p>\u73b0\u5728\u6211\u4eec\u63d2\u5165 <code>5</code>\uff1a</p> <pre><code>graph TD;\nA((\"8, BF=2\"))\nB((\"4, BF=-1\"))\nC((\"9, BF=0\"))\nD((\"2, BF=0\"))\nE((\"6, BF=1\"))\nF((\"5, BF=0\"))\nA === B\nA === C\nB === D\nB === E\nE === F\nE === NULL</code></pre> <p>\u6211\u4eec\u53d1\u73b0\uff0c\u6b64\u65f6 <code>8</code> \u7684\u300c\u5e73\u8861\u56e0\u5b50\u300d\u53d8\u6210\u4e862\uff0c\u4e0d\u518d\u7b26\u5408 AVL \u6811\u7684\u8981\u6c42\uff0c\u800c\u8fd9\u4e00\u5207\u90fd\u662f <code>5</code> \u7684\u63d2\u5165\u5bfc\u81f4\u7684\u2014\u2014\u4e8e\u662f\u6211\u4eec\u79f0\u50cf\u8fd9\u91cc\u7684 <code>8</code> \u4e00\u6837\uff0c\u7531\u4e8e\u67d0\u4e2a\u70b9\u7684\u63d2\u5165\uff0c\u5176\u300c\u5e73\u8861\u56e0\u5b50\u300d\u4e0d\u518d\u7b26\u5408\u8981\u6c42\u7684\u70b9\uff0c\u4e3a Trouble Finder\uff1b\u800c\u50cf\u8fd9\u91cc\u7684 <code>5</code> \u4e00\u6837\uff0c\u5bfc\u81f4 Trouble Finder \u51fa\u73b0\u7684\u70b9\uff0c\u88ab\u79f0\u4e4b\u4e3a Trouble Maker\u3002</p> <p>\u5f62\u8c61\u5730\u63cf\u8ff0\u8fd9\u4ef6\u4e8b\u5c31\u662f\uff0c\u5728\u52a8\u6001\u63d2\u5165 <code>5</code> \u8fd9\u4e2a\u8fc7\u7a0b\u4e2d\uff0c\u51fa\u73b0\u4e86\u4e00\u4e2a \"Trouble\"\uff0c\u5bfc\u81f4\u8fd9\u4e2a\u6811\u4e0d\u518d\u662f AVL \u6811\uff0c\u800c <code>5</code> \u662f\u8fd9\u4e2a \"Trouble\" \u7684 \"Maker\"\uff0c<code>8</code> \u662f \"Finder\"\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec01/#\u64cd\u4f5c","title":"\u64cd\u4f5c","text":"<p>\u672c\u5c0f\u8282\u6240\u9700\u8981\u8bb2\u7684\u5185\u5bb9\u5c31\u662f#\u89c6\u89d2\u4e2d\u63d0\u5230\u7684\u201c\u91cd\u65b0\u53d8\u4e3a AVL \u6811\u201d\u8fd9\u4e00\u89c6\u89d2\uff0c\u4e5f\u5c31\u662f AVL \u6811\u7684\u7ef4\u62a4\u3002</p> <p>\u9996\u5148\uff0c \u6211\u4eec\u9700\u8981\u5bf9 AVL \u6811\u7684\u7834\u574f\u60c5\u51b5\u8fdb\u884c\u5206\u7c7b\uff0c\u6839\u636e \"Trouble Finder\"\u3001\"Related Trouble Finder's Child\"\u3001\"Trouble Maker\"\u8fd9\u4e09\u4e2a\u70b9\u7684\u76f8\u5bf9\u5173\u7cfb\uff0c\u5206\u4e3a <code>LL</code>\u3001<code>RR</code>\u3001<code>LR</code>\u3001<code>RL</code> \u56db\u79cd\uff1a</p> <p>\u540c\u5fc3\u5706\u8868\u793a\u8fd9\u4e2a\u70b9\u662f\u9700\u8981\u6211\u4eec\u5728\u540e\u7eed\u64cd\u4f5c\u4e2d\u5173\u6ce8\u7684\u3002</p> <p>\u6b64\u5916\uff0c\u867d\u7136\u5b9e\u9645\u60c5\u51b5\u4e0b\u53ef\u80fd\u51fa\u73b0\u591a\u4e2a Trouble Finder\uff0c\u4f46\u662f\u6211\u4eec\u53ea\u5173\u6ce8\u4ee5\u300c\u8ddd\u79bb\u6848\u53d1\u73b0\u573a\u6700\u8fd1\u7684 Trouble Finder\u300d\u4e3a\u6839\u7684\u5b69\u5b50\u6811\uff08\u8fd9\u53e5\u8bdd\u975e\u5e38\u91cd\u8981\uff09\u3002</p> LLRRLRRL <pre><code>flowchart TD\n    A(((\"Trouble\\nFinder\")))\n    B(((\"Left\\nChild\")))\n    C((\"Right\\nChild\"))\n    D((\"L Left\\nChild\"))\n    DA[/\"Left and Right Subtrees\"\\]\n    E((\"L Right\\nChild\"))\n    EA[/\"Left and Right Subtrees\"\\]\n    F((\"R Left\\nChild\"))\n    FA[/\"Left and Right Subtrees\"\\]\n    G((\"R Right\\nChild\"))\n    GA[/\"Left and Right Subtrees\"\\]\n    H((\"Trouble\\nMaker\"))\n    A === B\n    A === C\n    B === D === DA === H\n    B === E === EA\n    C === F === FA\n    C === G === GA</code></pre> <pre><code>flowchart TD\n    A(((\"Trouble\\nFinder\")))\n    B((\"Left\\nChild\"))\n    C(((\"Right\\nChild\")))\n    D((\"L Left\\nChild\"))\n    DA[/\"Left and Right Subtrees\"\\]\n    E((\"L Right\\nChild\"))\n    EA[/\"Left and Right Subtrees\"\\]\n    F((\"R Left\\nChild\"))\n    FA[/\"Left and Right Subtrees\"\\]\n    G((\"R Right\\nChild\"))\n    GA[/\"Left and Right Subtrees\"\\]\n    H((\"Trouble\\nMaker\"))\n    A === B\n    A === C\n    B === D === DA\n    B === E === EA\n    C === F === FA\n    C === G === GA === H</code></pre> <pre><code>flowchart TD\n    A(((\"Trouble\\nFinder\")))\n    B(((\"Left\\nChild\")))\n    C((\"Right\\nChild\"))\n    D((\"L Left\\nChild\"))\n    DA[/\"Left and Right Subtrees\"\\]\n    E(((\"L Right\\nChild\")))\n    EA[/\"Left and Right Subtrees\"\\]\n    F((\"R Left\\nChild\"))\n    FA[/\"Left and Right Subtrees\"\\]\n    G((\"R Right\\nChild\"))\n    GA[/\"Left and Right Subtrees\"\\]\n    H((\"Trouble\\nMaker\"))\n    A === B\n    A === C\n    B === D === DA\n    B === E === EA === H\n    C === F === FA\n    C === G === GA</code></pre> <pre><code>flowchart TD\n    A(((\"Trouble\\nFinder\")))\n    B((\"Left\\nChild\"))\n    C(((\"Right\\nChild\")))\n    D((\"L Left\\nChild\"))\n    DA[/\"Left and Right Subtrees\"\\]\n    E((\"L Right\\nChild\"))\n    EA[/\"Left and Right Subtrees\"\\]\n    F(((\"R Left\\nChild\")))\n    FA[/\"Left and Right Subtrees\"\\]\n    G((\"R Right\\nChild\"))\n    GA[/\"Left and Right Subtrees\"\\]\n    H((\"Trouble\\nMaker\"))\n    A === B\n    A === C\n    B === D === DA\n    B === E === EA\n    C === F === FA === H\n    C === G === GA</code></pre> <p>\u7a0d\u4f5c\u89e3\u91ca\uff0c\u4f8b\u5982 <code>LR</code>\uff0c\u8868\u793a\u7684\u662f Trouble Maker \u5728 Trouble Finder \u7684 L \u5b69\u5b50\u8282\u70b9\u7684 R \u5b69\u5b50\u6811\u4e2d\u3002</p> <p>\u53e6\u5916\uff0c\u5bf9\u4e8e\u6211\u53ea\u5728 <code>LR</code> \u548c <code>RL</code> \u4e2d\u7740\u91cd\u4e8c\u7ea7\u5b69\u5b50\u8282\u70b9\uff0c\u5e76\u4e0d\u662f\u7b14\u8bef\u3002\u4e4b\u540e\u4f1a\u8be6\u7ec6\u4ecb\u7ecd\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec01/#ll--rr","title":"LL &amp; RR","text":"<p>\u5e9f\u8bdd</p> <p>\u5927\u90e8\u5206\u6559\u6750\u90fd\u503e\u5411\u4e8e\u7ee7\u7eed\u7528\u201c\u65cb\u8f6c\u201d\u6765\u6982\u62ec\u8fd9\u4e9b\u65b9\u6cd5\uff0c\u786e\u5b9e\u5176\u5b9e\u4ece\u62bd\u8c61\u89d2\u5ea6\u6765\u8bb2\u81f3\u5c11 <code>LL</code> \u548c <code>RR</code> \u90e8\u5206\u4e5f\u8fd8\u662f\u50cf\u7684\uff0c\u4f46\u662f\u6211\u89c9\u5f97\u8fd9\u5e76\u4e0d\u5229\u4e8e\u8bb0\u5fc6\u548c\u7406\u89e3\u8fd9\u4e2a\u8fc7\u7a0b\uff0c\u5c24\u5176\u662f\u5bf9\u4e8e <code>LR</code> \u548c <code>RL</code> \u7684\u90e8\u5206\u3002</p> <p>\u6240\u4ee5\u5728 <code>LL</code> \u548c <code>RR</code> \u90e8\u5206\uff0c\u6211\u8fd8\u662f\u4f1a\u5148\u4ecb\u7ecd\u4e00\u4e0b\u6bd4\u8f83\u4f20\u7edf\u7684\uff0c\u7528\u201c\u65cb\u8f6c\u201d\u7684\u65b9\u5f0f\u6765\u7406\u89e3\uff0c\u4e4b\u540e\u6211\u5c06\u5c1d\u8bd5\u7740\u7528\u6211\u81ea\u5df1\u7684\u601d\u8def\u6765\u8bb2\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec01/#\u65cb\u8f6c\u89c6\u89d2","title":"\u201c\u65cb\u8f6c\u201d\u89c6\u89d2","text":"<p><code>LL</code> \u548c <code>RR</code> \u8fd9\u4e24\u79cd\u60c5\u51b5\u76f8\u5bf9\u76f4\u89c2\u3002\u7531\u4e8e\u5b83\u4eec\u7684\u64cd\u4f5c\u662f\u5bf9\u79f0\u7684\uff0c\u6240\u4ee5\u6211\u8fd9\u91cc\u4ee5 <code>LL</code> \u4e3a\u4f8b\u3002</p> <pre><code>    flowchart TD\n        A(((\"Trouble\\nFinder\")))\n        C[/\"Right Subtree\"\\]\n\n        subgraph SA[\"New Left Subtree\"]\n\n            subgraph SB[\"New L Left Subtree\"]\n                D[/\"L Left Subtree\"\\]\n                H((\"Trouble\\nMaker\"))\n            end\n\n            B(((\"Left\\nChild\")))\n            E[/\"L Right Subtree\"\\]\n        end\n\n        A === B\n        A === C\n        B === D === H\n        B === E</code></pre> <p>\u6839\u636e\u76f8\u5173\u6027\u8d28\uff0c\u6211\u4eec\u5f97\u5230\u8fd9\u4e2a\u6a21\u578b\u6709\u5982\u4e0b\u6027\u8d28\uff1a</p> <p>\u4e00\u4e9b\u6027\u8d28</p> <ol> <li>\\(BF(\\text{Trouble Finder}) = h(\\text{New Left Subtree}) - h(\\text{Right Subtree}) = 2\\)\uff1b</li> <li>\\(h(\\text{New L Left Subtree}) - h(\\text{L Right Subtree}) = 1\\)\uff1b<ul> <li>\u5982\u679c\u6b64\u5dee\u4e3a 0\uff0c\u5219\u4e0d\u5e94\u5f53\u6210\u4e3a Trouble Maker\uff0c\u82e5\u6b64\u5dee\u4e3a 2\uff0c\u5219 Left Child \u5e94\u5f53\u4e3a Trouble Finder\uff1b</li> </ul> </li> </ol> <p>\u73b0\u5728\u6211\u4eec\u5e0c\u671b\u5728\u4fdd\u7559\u4e8c\u53c9\u641c\u7d22\u6811\u7684\u6027\u8d28\u4e0b\uff0c\u8981\u8ba9 \\(|BF(\\text{Trouble Finder})|\\) \u53d8\u5c0f\uff0c\u4e00\u4e2a\u5f88\u81ea\u7136\u7684\u60f3\u6cd5\u5c31\u662f\u8ba9 \\(h(\\text{New Left Subtree})\\) \u53bb -1\uff0c\u8ba9 \\(h(\\text{Right Subtree})\\) \u53bb +1\u3002</p> <p>\u4e8e\u662f\u6211\u4eec\u53d1\u73b0\uff0c\u8fd9\u6837\u7684\u64cd\u4f5c\u521a\u597d\uff1a</p> <p>LL Single Rotation</p> <p>\u5728 Frame 2 \u548c Frame 3 \u4e4b\u95f4\u6dfb\u52a0\u7684\u7ec6\u7ebf\u662f\u4e3a\u4e86\u8868\u793a\u8fd9\u91cc L Right Subtree \u7684\u8f6c\u79fb\u65b9\u6cd5\uff0c\u8ba9 2 ~ 3 \u5e27\u7684\u201c\u65cb\u8f6c\u201d\u8fc7\u7a0b\u4e2d\u66f4\u52a0\u6e05\u6670\u3002</p> <p>\u6b64\u5916\uff0c\u8fd9\u91cc\u8981\u7d20\u7684\u547d\u540d\u90fd\u662f\u57fa\u4e8e Frame 1 \u7684\uff0c\u5bf9\u4e8e Frame 4 \u6765\u8bf4 L Right Subtree \u663e\u7136\u5df2\u7ecf\u4e0d\u662f L Right Subtree \u4e86\u3002</p> Frame 1Frame 2Frame 3Frame 4 <pre><code>    flowchart TD\n        A(((\"Trouble\\nFinder\")))\n        B(((\"Left\\nChild\")))\n        C[/\"Right Subtree\"\\]\n        D[/\"L Left Subtree\"\\]\n        H((\"Trouble\\nMaker\"))\n        E[/\"L Right Subtree\"\\]\n\n        A === B\n        A === C\n        B === D === H\n        B === E</code></pre> <pre><code>    flowchart TD\n        A(((\"Trouble\\nFinder\")))\n        B(((\"Left\\nChild\")))\n        C[/\"Right Subtree\"\\]\n        D[/\"L Left Subtree\"\\]\n        E[/\"L Right Subtree\"\\]\n        H((\"Trouble\\nMaker\"))\n\n        A === B\n        A --- E\n        A === C\n        B === D === H\n        B === E</code></pre> <pre><code>    flowchart TD\n        A(((\"Trouble\\nFinder\")))\n        B(((\"Left\\nChild\")))\n        C[/\"Right Subtree\"\\]\n        D[/\"L Left Subtree\"\\]\n        E[/\"L Right Subtree\"\\]\n        H((\"Trouble\\nMaker\"))\n\n        B === D === H\n        B --- E\n        B === A\n        A === E\n        A === C\n</code></pre> <pre><code>    flowchart TD\n        A(((\"Trouble\\nFinder\")))\n        B(((\"Left\\nChild\")))\n        C[/\"Right Subtree\"\\]\n        D[/\"L Left Subtree\"\\]\n        E[/\"L Right Subtree\"\\]\n        H((\"Trouble\\nMaker\"))\n\n        B === D === H\n        B === A\n        A === E\n        A === C\n</code></pre> <p>\u4f60\u751a\u81f3\u80fd\u4ece\u6574\u4e2a\u6846\u5728 2 ~ 3 \u5e27\u7684\u53d8\u77ed\u611f\u53d7\u5230\u8fd9\u4e2a\u6811\u7684\u9ad8\u5ea6\u51cf\u5c11\u4e86x\uff08\u9003\uff09</p> <p>\u90a3\u4e48\u8fd8\u6709\u4e00\u4e2a\u95ee\u9898\u662f\uff0c\u5982\u4f55\u8bc1\u660e\u8fd9\u6837\u53d8\u6362\u80fd\u591f\u4fdd\u6301 AVL \u7684\u6027\u8d28\u5462\uff1f</p> <p>\u6211\u4e2a\u4eba\u8ba4\u4e3a\u4e3b\u8981\u6709\u4e24\u4e2a\u7ef4\u5ea6\uff0c\u4e00\u662f\u4fdd\u6301\u4e8c\u53c9\u641c\u7d22\u6811\u7684\u6027\u8d28\uff0c\u4e8c\u662f\u4fdd\u6301\u5e73\u8861\u7684\u6027\u8d28\uff0c\u6211\u7684\u8bc1\u660e\u5185\u5bb9\u6298\u53e0\u8d77\u6765\u4e86\uff0c\u5efa\u8bae\u8bfb\u8005\u53ef\u4ee5\u5148\u81ea\u5df1\u601d\u8003\u4e00\u4e0b\u518d\u5c55\u5f00\u770b\u770b\u6211\u7684\u60f3\u6cd5\u3002</p> \u4e8c\u53c9\u641c\u7d22\u6811\u6027\u8d28\u7684\u4fdd\u6301 <p></p> <p>\u4e0d\u77e5\u9053\u8bfb\u8005\u662f\u5426\u53d1\u73b0\uff0c\u5bf9\u4e8e\u4e00\u4e2a\u6392\u5217\u5f97\u5f53\u7684\u4e8c\u53c9\u641c\u7d22\u6811\uff0c\u5982\u679c\u6211\u4ece\u5de6\u5230\u53f3\uff0c\u4f7f\u7528\u4e00\u6761\u7ad6\u76f4\u7684\u626b\u63cf\u7ebf\u626b\u63cf\u6574\u4e2a\u6811\uff0c\u5c06\u4f1a\u5f97\u5230\u4e00\u4e2a\u5355\u8c03\u5e8f\u5217\uff0c\u8fd9\u4e5f\u6b63\u5bf9\u5e94\u7740\u8fd9\u4e2a\u4e8c\u53c9\u641c\u7d22\u6811\u6240\u7ef4\u62a4\u7684\u6709\u5e8f\u6570\u5217\u3002</p> <p>\u57fa\u4e8e\u8fd9\u79cd\u8bba\u8c03\uff0c\u518d\u56de\u5934\u770b\u4e0a\u9762\u90a3\u4e2a\u52a8\u6001\u7684\u8fc7\u7a0b\uff0c\u751a\u81f3\u662f\u89c2\u5bdf\u6211\u5728 2 ~ 3 \u5e27\u753b\u51fa\u6765\u7684\u8fd9\u4e2a\u4e09\u89d2\u5f62\u7684\u65cb\u8f6c\uff0c\u5c31\u4f1a\u53d1\u73b0\u8fd9\u79cd\u65cb\u8f6c\u5b9e\u9645\u4e0a\u53ea\u662f\u5728\u5c06\u8282\u70b9\u4e0a\u4e0b\u79fb\u52a8\uff0c\u6240\u4ee5\u4e0d\u6539\u53d8\u4e8c\u53c9\u641c\u7d22\u6811\u7684\u6027\u8d28\u3002</p> \u5e73\u8861\u7684\u4fdd\u6301 <p>\u8ba9\u6211\u4eec\u5148\u56de\u987e\u4e00\u4e0b\u5728\u4e0a\u9762\u7ed9\u51fa\u7684\u4e00\u4e9b\u6027\u8d28\u4e2d\u7684\u7b2c 2 \u6761\uff1a \\(h(\\text{New L Left Subtree}) - h(\\text{L Right Subtree}) = 1\\)\u3002</p> <p>\u5728\u4ed4\u7ec6\u601d\u8003\u6574\u4e2a\u65cb\u8f6c\u8fc7\u7a0b\u4e2d\u6bcf\u4e00\u4e2a Subtree \u7684\u9ad8\u5ea6\u7684\u53d8\u5316\uff0c\u5373\u53ef\u5f97\u5230\u8bc1\u660e\u3002    </p> <p>\u800c RR Single Rotation \u5b8c\u5168\u5bf9\u79f0\uff0c\u6240\u4ee5\u4e0d\u518d\u8d58\u8ff0\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec01/#\u6362\u6839\u89c6\u89d2","title":"\u201c\u6362\u6839\u201d\u89c6\u89d2","text":"<p>\u73b0\u5728\u6211\u60f3\u5c1d\u8bd5\u7740\u7528\u6211\u81ea\u5df1\u7684\u65b9\u5f0f\u6765\u7406\u89e3\u8fd9\u4e2a\u95ee\u9898\u3002</p> <p>\u9996\u5148\u8ba9\u6211\u4eec\u4eba\u529b\u52a8\u753b\u4e00\u4e0b\u8fd9\u4e2a\u8fc7\u7a0b\uff08\u5212\u6389\uff09\uff1a</p> <p>LL Single Rotation</p> <p>\u6b64\u5916\uff0c\u8fd9\u91cc\u8981\u7d20\u7684\u547d\u540d\u90fd\u662f\u57fa\u4e8e Frame 1 \u7684\uff0c\u5bf9\u4e8e Frame 4 \u6765\u8bf4 L Right Subtree \u663e\u7136\u5df2\u7ecf\u4e0d\u662f L Right Subtree \u4e86\u3002</p> Frame 1Frame 2Frame 3Frame 4Frame 5 <pre><code>    flowchart TD\n        A(((\"Trouble\\nFinder\")))\n        B(((\"Left\\nChild\")))\n        C[/\"Right Subtree\"\\]\n        D[/\"L Left Subtree\"\\]\n        H((\"Trouble\\nMaker\"))\n        E[/\"L Right Subtree\"\\]\n\n        A === B\n        A === C\n        B === D === H\n        B === E</code></pre> <pre><code>    flowchart TD\n        A(((\"Trouble\\nFinder\")))\n        B(((\"Left\\nChild\")))\n        C[/\"Right Subtree\"\\]\n        D[/\"L Left Subtree\"\\]\n        H((\"Trouble\\nMaker\"))\n        E[/\"L Right Subtree\"\\]\n\n        A --- B\n        A === C\n        B === D === H\n        B === E</code></pre> <pre><code>    flowchart TD\n        B(((\"Left\\nChild\")))\n        D[/\"L Left Subtree\"\\]\n        E[/\"L Right Subtree\"\\]\n        H((\"Trouble\\nMaker\"))\n        A(((\"Trouble\\nFinder\")))\n        C[/\"Right Subtree\"\\]\n\n        A === C\n        B === D === H\n        B === E</code></pre> <pre><code>    flowchart TD\n        B(((\"Left\\nChild\")))\n        D[/\"L Left Subtree\"\\]\n        E[/\"L Right Subtree\"\\]\n        H((\"Trouble\\nMaker\"))\n        A(((\"Trouble\\nFinder\")))\n        C[/\"Right Subtree\"\\]\n\n        A === C\n        B === D === H\n        A === E</code></pre> <pre><code>    flowchart TD\n        A(((\"Trouble\\nFinder\")))\n        B(((\"Left\\nChild\")))\n        C[/\"Right Subtree\"\\]\n        D[/\"L Left Subtree\"\\]\n        E[/\"L Right Subtree\"\\]\n        H((\"Trouble\\nMaker\"))\n\n        B === D === H\n        B === A\n        A === E\n        A === C\n</code></pre> <p>\u9996\u5148\uff0c\u6211\u4eec\u9047\u5230\u7684\u95ee\u9898\u662f\u4ec0\u4e48\uff1f\u662f Trouble Maker \u8fdb\u6765\u4ee5\u540e\uff0cTrouble Finder \u53d1\u73b0 \\(h(T_l) - h(T_r) = 2\\)\u4e86\uff0c\u7528\u901a\u4fd7\u7684\u8bdd\u6765\u8bf4\u5c31\u662f\u5de6\u5b69\u5b50\u6811\u592a\u9ad8\u4e86\uff0c\u7136\u800c\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u5de6\u5b69\u5b50\u6811\u4f9d\u7136\u8fd8\u7ad9\u5728\u4e00\u4e2a\u53f0\u5b50\uff08Trouble Finder\uff09\u4e0a\u548c Trouble Finder \u6bd4\u8eab\u9ad8\uff0c\u6240\u4ee5\u6211\u4eec\u9700\u8981\u5c06\u5b83\u4ece\u53f0\u5b50\u4e0a\u8bf7\u4e0b\u6765\u3002\u4e5f\u5c31\u662f\u8bf4\uff0c\u65e2\u7136\u5de6\u5b69\u5b50\u6811\u592a\u9ad8\u4e86\uff0c\u90a3\u4e48\u6211\u4eec\u5c31\u4e0d\u5e0c\u671b\u8ba9\u5b83\u518d\u6210\u4e3a\u8c01\u7684\u5b69\u5b50\u6811\uff0c\u56e0\u4e3a\u6210\u4e3a\u8c01\u7684\u5b69\u5b50\u6811\u5fc5\u7136\u610f\u5473\u7740\u8fd9\u6761\u8def\u5f84\u4f1a\u66f4\u957f\u3002</p> <p>\u90a3\u4e48\u73b0\u5728\u6211\u4eec\u628a\u5b83\u4ece\u53f0\u5b50\u4e0a\u8bf7\u4e0b\u6765\uff0c\u4e5f\u5c31\u662f\u8bf4\u5272\u88c2\u5b83\u548c Trouble Finder \u7684\u4eb2\u5b50\u5173\u7cfb\uff08\u5bf9\u5e94 Frame 2\uff09\u8ba9\u5b83\u4eec\u540c\u53f0\u201c\u5bf9\u6297\u201d\uff08\u8fd9\u4e00\u6b65\u5728 <code>LL</code> \u548c <code>RR</code> \u53ef\u80fd\u663e\u5f97\u6bd4\u8f83\u591a\u4f59\uff0c\u4f46\u662f\u5728 <code>LR</code> \u548c <code>RL</code> \u5c31\u4f1a\u8ba9\u95ee\u9898\u6e05\u6670\u5f88\u591a\uff09\u3002</p> <p>\u7136\u800c\u6211\u4eec\u4ecd\u7136\u9700\u8981\u8ba9\u8fd9\u4e2a\u68ee\u6797\u91cd\u65b0\u53d8\u56de\u4e00\u4e2a\u6811\uff0c\u6240\u4ee5\u5c31\u9700\u8981\u91cd\u65b0\u4ece\u91cc\u9762\u627e\u5230\u6839\u8282\u70b9\uff0c\u663e\u7136\uff0c\u53ea\u80fd\u9009\u62e9 Trouble Finder \u65c1\u8fb9 \u7684 Left Child\u3002\u4f46\u662f\u4e3a\u4e86\u7ee7\u7eed\u7ef4\u62a4\u4e8c\u53c9\u641c\u7d22\u6811\u7684\u6027\u8d28\uff0c\u6240\u4ee5\u6211\u4eec\u9700\u8981\u5c06 L Right Subtree \u79fb\u690d\u5230 Trouble Finder \u5fc5\u5b9a\u7a7a\u7f3a\uff08\u56e0\u4e3a\u8fd9\u91cc\u539f\u5148\u662f Left Child\uff09\u7684\u5de6\u6307\u9488\u4e0a\u3002</p> <p>OK\uff0c\u4f60\u53ef\u80fd\u89c9\u5f97\u8fd9\u4e2a\u89e3\u91ca\u5bf9\u4e8e LL Single Rotation \u6765\u8bf4\u663e\u5f97\u5341\u5206\u591a\u6b64\u4e00\u4e3e\uff0c\u4f46\u662f\u8fd9\u90fd\u662f\u4e3a\u4e86\u7ed9\u540e\u9762\u505a\u7684\u94fa\u57ab\uff0c\u867d\u7136\u8fd9\u4e2a\u65b9\u6cd5\u770b\u8d77\u6765\u7e41\u7410\u5197\u4f59\uff0c\u4f46\u662f\u5df2\u7ecf\u8db3\u4ee5\u89e3\u91ca\u539f\u5148\u7684 Single Rotation \u65e0\u6cd5\u89e3\u91ca\u7684 LR &amp; RL \u64cd\u4f5c\u65b9\u6cd5\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec01/#lr--rl","title":"LR &amp; RL","text":"<p>\u9996\u5148\u6211\u4eec\u9700\u8981\u77e5\u9053\u4e3a\u4ec0\u4e48\u4e4b\u524d\u7684\u65b9\u6cd5\u4e0d\u884c\uff0c\u4e5f\u662f\u6211\u89c9\u5f97\u201c\u65cb\u8f6c\u201d\u8fd9\u4e2a\u505a\u6cd5\u5728\u8fd9\u4e2a\u63a8\u8fdb\u8fc7\u7a0b\u4e2d\u6bd4\u8f83\u5272\u88c2\u7684\u5730\u65b9\uff1a\uff08\u5bf9\u7167 #\u65cb\u8f6c\u89c6\u89d2 \u7684\u5185\u5bb9\u9605\u8bfb\uff09\u6211\u4eec\u53d1\u73b0\uff0c\u7531\u4e8e LL \u4e2d\u7684 Trouble Maker \u5728\u5de6\u4fa7\u5b69\u5b50\u6811\u4e0a\uff0c\u6240\u4ee5\u5728\u65cb\u8f6c\u8fc7\u7a0b\u4e2d\uff0c\u76f8\u5f53\u4e8e\u628a\u5b83\u201c\u62fd\u201d\u4e0a\u6765\u4e86\u3002\u7136\u800c\u5bf9\u4e8e L Right Subtree\uff0c\u65e0\u8bba\u662f\u65cb\u8f6c\u524d\u8fd8\u662f\u65cb\u8f6c\u540e\uff0c\u4e3a\u4e86\u7ef4\u62a4\u4e8c\u53c9\u641c\u7d22\u6811\u7684\u6027\u8d28\uff0c\u5b83\u90fd\u88ab\u63a5\u5728\u4e86\u6df1\u5ea6\u4e3a 1 \u7684\u8282\u70b9\u4e0a\uff0c\u6362\u53e5\u8bdd\u6765\u8bf4 L Right Subtree \u8d21\u732e\u7684\u9ad8\u5ea6\u5e76\u6ca1\u6709\u6539\u53d8\u3002\u5bf9\u4e8e RL \u7684\u60c5\u51b5\u4e5f\u662f\u540c\u7406\u7684\u3002\u6240\u4ee5\u6211\u4eec\u5e76\u4e0d\u80fd\u4f7f\u7528 LL Single Rotation \u7684\u65b9\u6cd5\u6765\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\u3002</p> <p>\u5173\u4e8e\u65cb\u8f6c\u89c6\u89d2</p> <p>\u5982\u679c\u4ece\u65cb\u8f6c\u89c6\u89d2\u6765\u8003\u8651\uff0c\u786e\u5b9e\u4e5f\u80fd\u8003\u8651\u8fd9\u4e2a\u8fc7\u7a0b\uff0c\u4f46\u4e00\u65b9\u9762\u8fc7\u4e8e\u590d\u6742\uff0c\u4e00\u65b9\u9762\u5b9e\u9645\u5b9e\u73b0\u8fc7\u7a0b\u4e2d\u4e5f\u5b8c\u5168\u53ef\u4ee5\u88ab\u4f18\u5316\uff0c\u6240\u4ee5\u6211\u5e0c\u671b\u4f7f\u7528\u6362\u6839\u7684\u89c6\u89d2\u6765\u7406\u89e3\u8fd9\u4e2a\u95ee\u9898\u3002</p> <p>\u90a3\u4e48\u6211\u4eec\u6362\u4e00\u4e2a\u601d\u8def\uff0c\u7528\u201c\u6362\u6839\u201d\u89c6\u89d2\u6765\u770b\u5f85\u8fd9\u4e2a\u95ee\u9898\uff1a</p> <p>LR Rotation</p> <p>\u8fd9\u91cc\u4e24\u4e2a Subtree \u63a5\u5230\u540c\u4e00\u4e2a Trouble Maker \u7684\u610f\u601d\u662f Trouble Maker \u53ef\u4ee5\u51fa\u73b0\u5728\u4e24\u8005\u4efb\u4e00\u4e2d\u3002</p> Frame 1Frame 2Frame 3Frame 4Frame 5 <pre><code>    flowchart TD\n        A(((\"Trouble\\nFinder\")))\n        B(((\"Left\\nChild\")))\n        C[/\"Right Subtree\"\\]\n        D((\"L Left\\nChild\"))\n        DA[/\"L Left Subtree\"\\]\n        H((\"Trouble\\nMaker\"))\n        E(((\"L Right\\nChild\")))\n        EA[/\"L Left Subtree\"\\]\n        EB[/\"L Right Subtree\"\\]\n\n        A === B\n        A === C\n        B === D === DA\n        B === E === EA --- H\n        E === EB --- H</code></pre> <pre><code>    flowchart TD\n        A(((\"Trouble\\nFinder\")))\n        B(((\"Left\\nChild\")))\n        C[/\"Right Subtree\"\\]\n        D((\"L Left\\nChild\"))\n        DA[/\"L Left Subtree\"\\]\n        H((\"Trouble\\nMaker\"))\n        E(((\"L Right\\nChild\")))\n        EA[/\"L Left Subtree\"\\]\n        EB[/\"L Right Subtree\"\\]\n\n        A --- B\n        A === C\n        B === D === DA\n        B --- E === EA --- H\n        E === EB --- H</code></pre> <pre><code>    flowchart TD\n\n        B(((\"Left\\nChild\")))\n        D((\"L Left\\nChild\"))\n        DA[/\"L Left Subtree\"\\]\n        H((\"Trouble\\nMaker\"))\n        E(((\"L Right\\nChild\")))\n        EA[/\"L Left Subtree\"\\]\n        EB[/\"L Right Subtree\"\\]\n        A(((\"Trouble\\nFinder\")))\n        C[/\"Right Subtree\"\\]\n\n        A === C\n        B === D === DA\n        E === EA --- H\n        E === EB --- H</code></pre> <pre><code>    flowchart TD\n\n        B(((\"Left\\nChild\")))\n        D((\"L Left\\nChild\"))\n        DA[/\"L Left Subtree\"\\]\n        H((\"Trouble\\nMaker\"))\n        E(((\"L Right\\nChild\")))\n        EA[/\"L Left Subtree\"\\]\n        EB[/\"L Right Subtree\"\\]\n        A(((\"Trouble\\nFinder\")))\n        C[/\"Right Subtree\"\\]\n\n        A === C\n        B === D === DA\n        E --- EA --- H\n        E --- EB --- H</code></pre> <pre><code>    flowchart TD\n\n        D((\"L Left\\nChild\"))\n        B(((\"Left\\nChild\")))\n        DA[/\"L Left Subtree\"\\]\n        E(((\"L Right\\nChild\")))\n        EA[/\"L Left Subtree\"\\]\n        EB[/\"L Right Subtree\"\\]\n        H((\"Trouble\\nMaker\"))\n        A(((\"Trouble\\nFinder\")))\n        C[/\"Right Subtree\"\\]\n\n        E === B\n        E === A\n        B === D === DA\n        B === EA --- H\n        A === EB --- H\n        A === C</code></pre> \u5173\u4e8e\u8bb0\u5fc6 <p>\u8bb0\u5fc6\u8fd9\u4e2a\u64cd\u4f5c\u5982\u4f55\u505a\u7684\u8bdd\uff0c\u6211\u7684\u8bb0\u5fc6\u65b9\u6cd5\u662f\u8fd9\u6837\u7684\uff1a</p> Frame 1Frame 2Frame 3Frame 4 <pre><code>    flowchart TD\n        A(((\"Trouble\\nFinder\")))\n        B(((\"Left\\nChild\")))\n        C[/\"Right Subtree\"\\]\n        D((\"L Left\\nChild\"))\n        DA[/\"L Left Subtree\"\\]\n        H((\"Trouble\\nMaker\"))\n        E(((\"L Right\\nChild\")))\n        EA[/\"L Left Subtree\"\\]\n        EB[/\"L Right Subtree\"\\]\n\n        A === B\n        A === C\n        B === D === DA\n        B === E === EA --- H\n        E === EB --- H</code></pre> <pre><code>    flowchart TD\n        A(((\"Trouble\\nFinder\")))\n        B(((\"Left\\nChild\")))\n        C[/\"Right Subtree\"\\]\n        D((\"L Left\\nChild\"))\n        DA[/\"L Left Subtree\"\\]\n        H((\"Trouble\\nMaker\"))\n        E(((\"L Right\\nChild\")))\n        EA[/\"L Left Subtree\"\\]\n        EB[/\"L Right Subtree\"\\]\n\n        A --- B\n        A --- E\n        A === C\n        B === D === DA\n        B --- E === EA --- H\n        E === EB --- H</code></pre> <pre><code>    flowchart TD\n        A(((\"Trouble\\nFinder\")))\n        B(((\"Left\\nChild\")))\n        D((\"L Left\\nChild\"))\n        DA[/\"L Left Subtree\"\\]\n        H((\"Trouble\\nMaker\"))\n        E(((\"L Right\\nChild\")))\n        EA[/\"L Left Subtree\"\\]\n        EB[/\"L Right Subtree\"\\]\n        C[/\"Right Subtree\"\\]\n\n        A --- B\n        E --- B \n        E --- A\n        B === D === DA\n        B --- EA --- H\n        A --- EB --- H\n        A === C</code></pre> <pre><code>    flowchart TD\n        A(((\"Trouble\\nFinder\")))\n        B(((\"Left\\nChild\")))\n        D((\"L Left\\nChild\"))\n        DA[/\"L Left Subtree\"\\]\n        H((\"Trouble\\nMaker\"))\n        E(((\"L Right\\nChild\")))\n        EA[/\"L Left Subtree\"\\]\n        EB[/\"L Right Subtree\"\\]\n        C[/\"Right Subtree\"\\]\n\n        E --- B \n        E --- A\n        B === D === DA\n        B --- EA --- H\n        A --- EB --- H\n        A === C</code></pre> <p>\u7528\u8bed\u8a00\u6982\u62ec\u5c31\u662f\uff0c\u627e\u5230\u5173\u952e\u7684\u90a3\u4e09\u4e2a\u70b9\uff0c\u7136\u540e\u628a\u6700\u4e0b\u9762\u7684\u9876\u5230\u4e0a\u9762\u53bb\uff0c\u5269\u4e0b\u4e24\u4e2a\u4f5c\u4e3a\u5de6\u53f3\u5b69\u5b50\u6811\uff0c\u539f\u5148\u7684\u90a3\u4e2a\u70b9\u7684\u5de6\u53f3\u5b69\u5b50\u6811\u5219\u5bf9\u5e94\u5730\uff0c\u5de6\u5b69\u5b50\u6811\u63a5\u5230\u5de6\u8fb9\u7a7a\u7f3a\u7684\u53f3\u5b69\u5b50\u6811\u4e0a\uff0c\u53f3\u5b69\u5b50\u6811\u63a5\u5230\u53f3\u8fb9\u7a7a\u7f3a\u7684\u5de6\u5b69\u5b50\u6811\u4e0a\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec01/#\u5176\u4ed6\u95ee\u9898","title":"\u5176\u4ed6\u95ee\u9898","text":"<p>\u5982\u679c\u4e00\u4e2a Trouble \u4ea7\u751f\u540e\uff0c\u51fa\u73b0\u4e86\u591a\u4e2a Trouble Finder\uff0c\u8be5\u5982\u4f55\u5904\u7406\uff1f</p> <p>\u9996\u5148\uff0c\u8bf7\u56de\u987e\u4e00\u4e0b #\u64cd\u4f5c \u4e2d\u88ab\u52a0\u7c97\u7684\u8fd9\u4e00\u53e5\u8bdd\uff0c\u300c\u4ee5\u300e\u8ddd\u79bb\u6848\u53d1\u73b0\u573a\u6700\u8fd1\u7684 Trouble Finder\u300f\u4e3a\u6839\u7684\u5b69\u5b50\u6811\u300d\u3002\u4e5f\u5c31\u662f\u8bf4\uff0c\u6211\u4eec\u73b0\u5728\u5df2\u7ecf\u6709\u4e86\u89e3\u51b3\u6700\u8fd1\u7684 Trouble Finder \u7684\u65b9\u6848\u3002</p> <p>\u611f\u6027\u7684\u601d\u8003\uff0cAVL \u7684\u201c\u5e73\u8861\u201d\u53ef\u4ee5\u7531\u9012\u5f52\u5f62\u5f0f\u5b9a\u4e49\uff0c\u5177\u4f53\u6765\u8bf4\u8861\u91cf\u7684\u662f\u5de6\u53f3\u5b69\u5b50\u6811\u7684\u201c\u9ad8\u5ea6\u201d\u5dee\u3002\u5f53\u6211\u4eec\u89e3\u51b3\u4e86\u4e00\u4e2a Trouble Finder\uff0c\u610f\u5473\u7740\u6211\u4eec\u8ba9 Trouble Finder \u7684\u6700\u9ad8\u7684\u90a3\u4e2a\u5b69\u5b50\u6811\u9ad8\u5ea6 -1\uff0c\u8fd9\u4e5f\u610f\u5473\u7740\u4ee5 Trouble Finder \u4e3a\u6839\u7684\u90a3\u4e2a\u5b69\u5b50\u6811\u9ad8\u5ea6 -1\uff0c\u8fd9\u4e5f\u610f\u5473\u7740\u5176\u6240\u6709\u7236\u8282\u70b9\u7684\u5e73\u8861\u56e0\u5b50\u90fd\u4f1a\u76f8\u5e94\u5730\u53d8\u5316\u3002</p> <p>\u4e00\u4e2a Trouble \u5f53\u4e14\u4ec5\u6709\u4e00\u4e2a Trouble Maker\uff0c\u800c\u4e14\u5b83\u5fc5\u5b9a\u662f Trouble Finder \u6240\u5173\u6ce8\u7684\u90a3\u4e2a\u201c\u6700\u957f\u8def\u5f84\u201d\u7684\u7aef\u70b9\uff0c\u8fd9\u4e5f\u610f\u5473\u7740\u6240\u6709\u7684\u5b50 Trouble Finder \u90fd\u5728\u5bf9\u5e94\u7684\u7236 Trouble Finder \u7684\u201c\u6700\u957f\u8def\u5f84\u201d\u4e0a\u3002\u800c\u73b0\u5728\u6211\u4eec\u8ba9\u5b50 Trouble Finder \u552f\u4e00\uff08\u5982\u679c\u4e0d\u552f\u4e00\uff0c\u90a3\u5728\u8fd9\u4e2a Trouble Maker \u5230\u6765\u4e4b\u524d\u5c31\u5df2\u7ecf\u5b58\u5728 Trouble \u4e86\uff09\u7684\u6700\u957f\u8def\u5f84\u4e5f\u5e94\u5f53\u4f1a -1\u3002\u800c\u8fd9\u5fc5\u5c06\u5bfc\u81f4\u5176\u5e73\u8861\u56e0\u5b50\u7684\u7edd\u5bf9\u503c -1\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec01/#splay-\u6811","title":"Splay \u6811","text":"<p>link</p> <p>OI Wiki: https://oi-wiki.org/ds/splay/</p> <p>Splay \u6811\uff0c\u5373\u4f38\u5c55\u6811\uff0c\u60f3\u8981\u89e3\u51b3\u7684\u95ee\u9898\u548c AVL \u6811\u7c7b\u4f3c\uff0c\u53ea\u4e0d\u8fc7 Splay \u6811\u5e0c\u671b\u8fbe\u5230\u7684\u76ee\u6807\u662f\u5728\u644a\u8fd8(Amortized)\u590d\u6742\u5ea6\\(O(\\log N)\\)\u7684\u60c5\u51b5\u4e0b\u5b8c\u6210\u5927\u90e8\u5206\u5bf9\u70b9\u64cd\u4f5c\u3002</p> <p>\u6211\u4eec\u77e5\u9053\uff0c\u4e3a\u4f7f AVL \u4fdd\u6301\u5e73\u8861\uff0c\u6211\u4eec\u9700\u8981\u7ef4\u62a4\u4ece\u6839\u8282\u70b9\u5230 Trouble Maker \u8fd9\u6761\u8def\u5f84\u4e0a\u6240\u6709\u70b9\u7684\u5e73\u8861\u56e0\u5b50\u3002\u800c Splay \u5219\u4e0d\u518d\u7ef4\u62a4\u8fd9\u4e9b\u4fe1\u606f\uff0c\u8fd9\u610f\u5473\u7740\u6211\u4eec\u65e0\u6cd5\u4fdd\u8bc1 Splay \u6811\u7684\u72b6\u6001\u90fd\u662f\u5e73\u8861\u7684\uff0c\u4f46\u662f\u6211\u4eec\u5e0c\u671b\u5b83\u5c3d\u53ef\u80fd\u5e73\u8861\u3002\u5177\u4f53\u6765\u8bf4\u5c31\u662f\u5bf9\u4e8e \\(M\\) \u6b21\u4efb\u610f\u64cd\u4f5c\uff0c\u5176\u65f6\u95f4\u590d\u6742\u5ea6\u90fd\u4e3a \\(O(M\\log N)\\)\uff0c\u5747\u644a\u4e0b\u6765\u8fd9 \\(M\\) \u4e2a\u64cd\u4f5c\u6bcf\u4e00\u4e2a\u90fd\u9700\u8981 \\(O(\\log N)\\)\u3002</p> <p>\u5bf9\u4e8e\u4e00\u4e2a\u6811\uff0c\u6211\u4eec\u5bf9\u5176\u8282\u70b9\u8fdb\u884c\u7684\u64cd\u4f5c\u53ef\u80fd\u662f\uff1a\u589e\u70b9\u3001\u5220\u70b9\u3001\u6539\u70b9\u3001\u67e5\u70b9\u7b49\u7b49\uff0c\u800c\u4e0d\u540c\u7c7b\u578b\u7684\u64cd\u4f5c\u5f00\u9500\u53ef\u80fd\u4e0d\u5c3d\u76f8\u540c\u3002\u7b80\u5355\u7684\u8ba1\u7b97\u5176\u5e73\u5747\u503c\u5219\u5ffd\u7565\u4e86\u8fd9\u4e9b\u64cd\u4f5c\u4e4b\u95f4\u4e92\u76f8\u7684\u5f71\u54cd\u6216\u8005\u662f\u64cd\u4f5c\u9891\u7387\u7684\u95ee\u9898\uff0c\u6240\u4ee5\u6211\u4eec\u8fd9\u91cc\u4f7f\u7528\u644a\u8fd8\u590d\u6742\u5ea6\u6765\u63cf\u8ff0\u5176\u6548\u7387\u3002</p> <p>\u5173\u4e8e\u644a\u8fd8\u7684\u95ee\u9898\u6211\u4eec\u8fd8\u4f1a\u5728\u4e4b\u540e\u8fdb\u4e00\u6b65\u6df1\u5165\u3002</p> <p>\u90a3\u4e48\u8bf4\u4e86\u8fd9\u4e48\u591a\uff0cSplay \u662f\u600e\u4e48\u5b9e\u73b0\u8fd9\u4e00\u76ee\u6807\u7684\u5462\uff1f</p> <p>Splay \u7684\u6838\u5fc3\u601d\u60f3\u5c31\u662f\uff0c\u6bcf\u5f53\u6211\u4eec\u8bbf\u95ee\u4e00\u4e2a\u8282\u70b9\uff08\u6bd4\u5982\u67e5\u8be2\u67d0\u4e2a\u70b9\u3001\u63d2\u5165\u67d0\u4e2a\u70b9\uff0c\u751a\u81f3\u662f\u5220\u9664\u67d0\u4e2a\u70b9\uff09\uff0c\u6211\u4eec\u5c31\u901a\u8fc7\u4e00\u7cfb\u5217\u64cd\u4f5c\u5c06\u76ee\u6807\u70b9\u8f6c\u79fb\u5230\u6839\u90e8\uff0c\u5f62\u8c61\u4e0a\u7406\u89e3\u5c31\u662f\u4e0d\u65ad\u65cb\u8f6c\u6574\u4e2a\u6811\u7684\u6784\u9020\uff0c\u77e5\u9053\u628a\u70b9\u8f6c\u5230\u6839\u90e8\u3002</p> <p>\u4f8b\u5982\u6211\u4eec\u67e5\u8be2\u70b9 \\(k_1\\)\uff0c\u5219\u4f1a\u901a\u8fc7\u65cb\u8f6c\u5c06\u5b83\u8f6c\u5230\u6839\u3002</p> Frame 1Frame 2Frame 3 <p></p> <p></p> <p></p> <p>\u53ef\u4ee5\u53d1\u73b0\uff0cFrame 1 ~ 2 \u5c31\u662f\u6211\u4eec\u524d\u9762\u63d0\u5230\u8fc7\u7684 LR Rotation\uff0c\u800c Frame 2 ~ 3 \u5c31\u662f\u7ecf\u8fc7\u4e86\u4e24\u6b21 LL Rotation\u3002\u5f53\u7136\uff0c\u5728 Splay \u91cc\u8fd9\u4e9b\u64cd\u4f5c\u90fd\u6709\u4e86\u65b0\u7684\u540d\u5b57\u3002</p> <p>\u8fd9\u4e2a\u4f8b\u5b50\u53ea\u662f\u4e3a\u4e86\u7ed9\u8bfb\u8005\u4e00\u4e2a\u521d\u59cb\u5370\u8c61\uff0c\u4e4b\u540e\u6211\u4eec\u5c06\u66f4\u8be6\u7ec6\u3001\u51c6\u786e\u7684\u4ecb\u7ecd\u64cd\u4f5c\u3002</p> <p>\uff08\u6ca1\u73a9\u8fc7\u53ef\u80fd\u542c\u4e0d\u592a\u61c2\uff09\u4e0d\u77e5\u9053\u5927\u5bb6\u6709\u6ca1\u6709\u73a9\u8fc7\u90a3\u79cd\u7535\u5b50\u6e38\u620f\uff0c\u5c31\u662f\u6709\u597d\u591a\u8f6c\u76d8\uff0c\u76f8\u90bb\u8f6c\u76d8\u4e4b\u95f4\u6709\u4ea4\u754c\u5904\uff0c\u8fd9\u4e9b\u4ea4\u754c\u70b9\u4e0a\u90fd\u4f1a\u6709\u5706\u7403\uff0c\u5f53\u4e00\u4e2a\u8f6c\u76d8\u65cb\u8f6c\u7684\u65f6\u5019\uff0c\u5176\u5706\u5468\u4e0a\u7684\u7403\u4f53\u90fd\u4f1a\u8ddf\u7740\u8fd9\u4e2a\u5706\u5468\u8f6c\u52a8\u3002\u901a\u8fc7\u4e0d\u505c\u8f6c\u52a8\u76f8\u90bb\u7684\u5706\u76d8\uff0c\u6211\u4eec\u53ef\u4ee5\u5b9e\u73b0\u628a\u67d0\u4e2a\u4f4d\u7f6e\u7684\u5706\u7403\u8f6c\u79fb\u5230\u53e6\u5916\u4e00\u4e2a\u4f4d\u7f6e\u3002\u800c Splay \u5dee\u4e0d\u591a\u662f\u8fd9\u4e48\u4e2a\u611f\u89c9\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec01/#\u57fa\u672c\u64cd\u4f5c","title":"\u57fa\u672c\u64cd\u4f5c","text":"<p>\u9996\u5148\u6211\u4eec\u505a\u4e00\u4e2a\u7ea6\u5b9a\uff0c\u5bf9\u4e8e\u4efb\u610f\u4e00\u4e2a\u8282\u70b9 X\uff0c\u6211\u4eec\u8bb0\u5176\u7236\u8282\u70b9\u4e3a P(Parent)\uff0c\u5176\u7236\u8282\u70b9\u7684\u7236\u8282\u70b9\u4e3a G(Grandparent)\u3002</p> <ul> <li>\u5f53\u6211\u4eec\u8bbf\u95ee\u5230\u67d0\u4e2a\u70b9 X \u65f6\uff1a<ul> <li>\u5982\u679c P \u662f\u6839\u8282\u70b9\uff0c\u5219\u76f4\u63a5\u8fdb\u884c\u4e00\u6b21 Single Rotation\uff0c\u5c06 X \u8f6c\u5230\u6839\u8282\u70b9\uff1b</li> <li>\u5982\u679c P \u4e0d\u662f\u6839\u8282\u70b9\uff1a<ul> <li>\u5f53\u60c5\u51b5\u4e3a LR / RL \u65f6\uff0c\u8fdb\u884c\u4e00\u6b21 LR Rotation \u6216 RL Rotation\uff0c\u6211\u4eec\u79f0\u4e4b\u4e3a zig-zag\uff1b</li> <li>\u5f53\u60c5\u51b5\u4e3a LL / RR \u65f6\uff0c\u8fdb\u884c\u4e24\u6b21 Single Rotation\uff0c\u4f7f\u5f97 X\u3001P\u3001G \u7684\u987a\u5e8f\u9006\u8f6c\uff0c\u50cf\u8df7\u8df7\u677f\u4e00\u6837\uff0c\u6211\u4eec\u79f0\u4e4b\u4e3a zig-zig\uff1b</li> </ul> </li> <li>\u4e0d\u65ad\u5bf9 X \u8fdb\u884c Splay \u64cd\u4f5c\uff0c\u76f4\u5230 X \u6210\u4e3a\u6839\u8282\u70b9\uff1b</li> </ul> </li> </ul> <p></p> <p>\u53ef\u4ee5\u53d1\u73b0\uff0c\u5176\u5177\u4f53\u64cd\u4f5c\u57fa\u672c\u5c31\u548c AVL \u6811\u7684\u76f8\u5173\u64cd\u4f5c\u6709\u5f88\u5927\u91cd\u5408\u3002</p> <p>\u6548\u679c</p> <p>Splaying not only moves the accessed node to the root, but also roughly halves the depth of most nodes on the path.</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec01/#\u5bf9\u70b9\u64cd\u4f5c","title":"\u5bf9\u70b9\u64cd\u4f5c","text":"<p>\u7531\u4e8e Splay Tree \u9664\u4e86\u5728\u5b8c\u6210\u6240\u6709\u64cd\u4f5c\u4ee5\u540e\u90fd\u9700\u8981\u8fdb\u884c\u4e00\u6b21 Splay \u64cd\u4f5c\uff0c\u5176\u4ed6\u90e8\u5206\u90fd\u548c BST \u4e00\u6837\uff0c\u6240\u4ee5\u8fd9\u91cc\u53ea\u7b80\u5355\u4ecb\u7ecd\u4e00\u4e0b Splay \u7684\u90e8\u5206\u3002</p> <p>Find X</p> <p>\u6839\u636e BST \u7684\u6027\u8d28\uff0c\u53ef\u4ee5\u5728 \\(O(\\log N)\\) \u7684\u65f6\u95f4\u91cc\u627e\u5230 \\(X\\)\uff0c\u63a5\u4e0b\u6765\u901a\u8fc7\u65cb\u8f6c\u64cd\u4f5c\uff0c\u5c06 \\(X\\) \u4e0d\u65ad\u65cb\u8f6c\u81f3\u6839\uff0c\u6700\u7ec8\u76f4\u63a5\u53d6\u51fa Root \u5373\u4e3a\u7ed3\u679c\u3002   </p> <p>Remove X</p> <p>\u6839\u636e BST \u7684\u6027\u8d28\uff0c\u53ef\u4ee5\u5728 \\(O(\\log N)\\) \u7684\u65f6\u95f4\u91cc\u627e\u5230 \\(X\\)\uff0c\u63a5\u4e0b\u6765\u901a\u8fc7\u65cb\u8f6c\u64cd\u4f5c\uff0c\u5c06 \\(X\\) \u4e0d\u65ad\u65cb\u8f6c\u81f3\u6839\uff0c\u63a5\u4e0b\u6765\u5220\u9664 Root \u8282\u70b9\uff0c\u5e76\u5728\u7ef4\u62a4 BST \u6027\u8d28\u7684\u60c5\u51b5\u4e0b\u9012\u5f52\u5730\u5408\u5e76\u5de6\u53f3\u5b69\u5b50\u6811\u5373\u53ef\u3002</p> <p>Find Max</p> <p>\u6839\u636e BST \u7684\u6027\u8d28\uff0c\u53ef\u4ee5\u5728 \\(O(\\log N)\\) \u7684\u65f6\u95f4\u91cc\u627e\u5230\u6700\u5927\u503c\uff0c\u5c06\u5b83\u65cb\u8f6c\u5230\u6839\u90e8\u4ee5\u540e\uff0c\u53ef\u4ee5\u53d1\u73b0\u5b83\u6ca1\u6709\u53f3\u5b69\u5b50\u6811\uff0c\u76f4\u63a5\u5220\u6389\u5c31\u884c\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec01/#\u644a\u8fd8\u5206\u6790","title":"\u644a\u8fd8\u5206\u6790","text":"<p>\u524d\u7f6e\u9605\u8bfb</p> <p>\u5173\u4e8e\u644a\u8fd8\u5206\u6790\u7684\u57fa\u672c\u77e5\u8bc6\uff0c\u8bf7\u67e5\u770b Topic 1 | Amortized Analysis\u3002</p> <p>\u6b64\u5904\uff0c\u6211\u4eec\u5c06\u4f7f\u7528\u52bf\u80fd\u6cd5\u6765\u5206\u6790 Splay \u7684\u644a\u8fd8\u590d\u6742\u5ea6\uff0c\u7531\u4e8e\u8bfe\u4ef6\u7701\u7565\u4e86\u5f88\u591a\u7ec6\u8282\u4e0a\u7684\u89e3\u91ca\uff0c\u6240\u4ee5\u6211\u8fd9\u91cc\u4f1a\u8865\u5145\u975e\u5e38\u591a\u5185\u5bb9\u3002</p> <p>reference</p> <p>http://www2.hawaii.edu/~nodari/teaching/f19/scribes/notes06.pdf</p> <p>\u5f00\u59cb\u5206\u6790\u4e4b\u524d\uff0c\u6211\u4eec\u9996\u5148\u9700\u8981\u660e\u786e\u5206\u6790\u7684\u76ee\u6807\uff1a</p> <p>\u5bf9\u4e8e Splay\uff0c\u5b83\u4e0d\u50cf\u6211\u4eec\u5728 Topic 1 | Amortized Analysis \u63d0\u5230\u7684\u90a3\u4e9b\u6848\u4f8b\u4e00\u6837\uff0c\u5b58\u5728\u660e\u663e\u7684\u51cf\u52bf\u548c\u589e\u52bf\u884c\u4e3a\u3002\u5bf9\u4e8e Splay \u6765\u8bf4\uff0c\u6240\u6709\u6211\u4eec\u63d0\u5230\u7684\u64cd\u4f5c\u90fd\u4f9d\u8d56\u4e8e\u5c06\u76ee\u6807\u70b9\u65cb\u8f6c\u5230\u6839\u6765\u5b9e\u73b0\uff0c\u800c\u8fd9\u4e5f\u6210\u4e3a\u5176\u4e3b\u8981\u5f00\u9500\uff08\u90e8\u5206\u5e38\u6570\u64cd\u4f5c\u663e\u7136\u88ab\u8986\u76d6\uff0c\u63d2\u5165\u4e4b\u7c7b\u7684\u64cd\u4f5c\u4e4b\u6240\u4ee5\u80fd\u88ab\u5ffd\u7565\u7684\u539f\u56e0\uff0c\u53ef\u4ee5\u53c2\u8003 ltgg \u7684\u8fd9\u7bc7\u6587\u7ae0\uff09\u3002\u5176\u4e2d\u6211\u4eec\u4f1a\u7528\u5230\u82e5\u5e72\u6b21 <code>zig</code>\u3001<code>zig-zag</code>\u3001<code>zig-zig</code> \u7684\u64cd\u4f5c\u3002</p> <p>\u56e0\u6b64\u6211\u4eec\u53ef\u4ee5\u8ba4\u4e3a\uff0c\u6211\u4eec\u8981\u5206\u6790\u7684\u76ee\u6807\u4e3a\uff1a</p> \\[ T_{\\text{rotate }x\\text{ to root}} = T_{\\text{zig}} + \\sum{ {T_{\\text{zig-zag}}}_i } + \\sum{ {T_{\\text{zig-zig}}}_i } \\] <p>\u4e0a\u9762\u4e09\u4e2a\u90e8\u5206\u6bcf\u4e00\u4e2a\u90fd\u6709\u53ef\u80fd\u662f \\(0\\)\uff0c\u800c <code>zig</code> \u6700\u591a\u53ea\u4f1a\u53d1\u751f\u4e00\u6b21\uff01</p> <p>\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u9700\u8981\u8bbe\u8ba1\u4e00\u4e2a\u52bf\u80fd\u51fd\u6570 \\(\\Phi(x)\\)\uff0c\u5e76\u4e14\u6839\u636e\u6211\u4eec\u63d0\u5230\u8fc7\u7684\u52bf\u80fd\u5206\u6790\u6cd5\u7684\u7279\u6027\uff0c\\(\\Phi(x)\\) \u5e94\u8be5\u5177\u6709\u8fd9\u4e48\u51e0\u4e2a\u7279\u5f81\uff1a</p> <ul> <li>\u5f00\u9500\u5927\u7684\u64cd\u4f5c\u5e94\u5f53\u503e\u5411\u8ba9\u52bf\u80fd\u964d\uff0c\u5f00\u9500\u5c0f\u7684\u64cd\u4f5c\u5e94\u5f53\u503e\u5411\u8ba9\u52bf\u80fd\u5347\uff1b</li> <li>\u52bf\u80fd\u9ad8\u503e\u5411\u4e8e\u8ba9\u67d0\u4e9b\u64cd\u4f5c\u5f00\u9500\u5927\uff0c\u52bf\u80fd\u4f4e\u503e\u5411\u4e8e\u8ba9\u67d0\u4e9b\u64cd\u4f5c\u5f00\u9500\u5c0f\uff1b</li> <li>\\(\\Phi(final) &gt; \\Phi(initial)\\)\uff1b</li> </ul> <p>\u4e8e\u662f\u8fd9\u91cc\u6211\u4eec\u8bbe\u8ba1\u7684\u52bf\u80fd\u51fd\u6570\u4e3a\uff1a</p> \\[ \\Phi(T) = \\sum_{des \\in T} \\log Size(des) = \\sum_{des \\in T} Rank(des)\\\\ \\begin{aligned}     &amp;\\text{Where } des \\text{ means the descendant of } T \\text{,}\\\\     &amp;\\text{and } Size(des) \\text{ means the number of the nodes of } des \\text{.} \\\\     &amp;\\text{And we note } Rank(des) = \\log Size(des) \\approx Height(des) \\text{.} \\end{aligned} \\] <p>\u7528\u8bed\u8a00\u63cf\u8ff0\u4e00\u4e0b\u5c31\u662f\uff0c\u5bf9\u4e8e\u67d0\u4e2a\u5b69\u5b50\u6811 \\(T\\)\uff0c\u5176\u52bf\u80fd\u51fd\u6570 \\(\\Phi(T)\\) \u7b49\u4e8e\u4ee5\u6240\u6709\u5b83\u7684\u540e\u4ee3\u4e3a\u6839\u7684\u5b69\u5b50\u6811\u7684\u5927\u5c0f\u53d6\u5bf9\u6570\u4ee5\u540e\u6c42\u548c\u3002</p> <p>Rank v.s. Height</p> <p>\u8fd9\u91cc\u9700\u8981\u6ce8\u610f\u7684\u4e00\u4e2a\u70b9\u662f\uff0c\u867d\u7136 \\(Rank(des) \\approx Height(des)\\)\uff0c\u4f46\u662f\u6211\u4eec\u4e0d\u5e94\u8be5\u7528 \\(Height()\\) \u6765\u4ee3\u66ff \\(Rank()\\)\uff0c\u4e3b\u8981\u539f\u56e0\u662f\u5728\u65cb\u8f6c\u8fc7\u7a0b\u4e2d\uff0c\\(Rank()\\) \u4e0d\u4f1a\u53d8\u5316\uff08\u56e0\u4e3a \\(Size()\\) \u4e0d\u4f1a\u53d8\u5316\uff09\uff0c\u4f46\u662f \\(Height()\\) \u53ef\u80fd\u53d8\u5316\u3002\u6362\u53e5\u8bdd\u6765\u8bf4\uff0c\u5982\u679c\u9009\u7528 \\(Height()\\) \u4f5c\u4e3a\u52bf\u80fd\u51fd\u6570\uff0c\u6211\u4eec\u5c31\u4e0d\u5f97\u5df2\u8003\u8651\u6574\u68f5\u6811\uff0c\u800c\u975e\u53ea\u9700\u8981\u8003\u8651\u5f53\u524d\u65cb\u8f6c\u6d89\u53ca\u7684\u5b69\u5b50\u6811\u3002</p> <p>\u5173\u4e8e\u6b63\u786e\u6027\u7684\u8bf4\u660e\uff0c\u6211\u4f1a\u653e\u5728\u4e4b\u540e\u7684\u8fc7\u7a0b\u4e2d\u4e00\u4e2a\u4e2a\u63d2\u5165\uff0c\u5b83\u4eec\u4f1a\u88ab\u5305\u88f9\u5728 <code>key-point</code> \u6587\u5b57\u6846\u4e2d\uff0c\u8bf7\u6ce8\u610f\u8fd9\u4e9b\u5185\u5bb9\u3002\u63a5\u4e0b\u6765\u6211\u4eec\u5c31\u53ef\u4ee5\u5f00\u59cb\u5206\u6790\u4e86\uff0c\u6839\u636e\u6211\u4eec\u7ed9\u5b9a\u7684\u76ee\u6807\uff1a</p> \\[ T_{\\text{rotate }x\\text{ to root}} = T_{\\text{zig}} + \\sum{ {T_{\\text{zig-zag}}}_i } + \\sum{ {T_{\\text{zig-zig}}}_i } \\] <p>\u6211\u4eec\u5229\u7528\u5747\u644a\u5206\u6790\uff0c\u9700\u8981\u5f97\u5230\u4e00\u4e2a\u5e73\u6ed1\u4e0a\u754c\uff1a</p> \\[ \\hat{c}_{\\text{rotate }x\\text{ to root}} = \\hat{c}_{\\text{zig}} + \\sum{ {\\hat{c}_{\\text{zig-zag}}}_i } + \\sum{ {\\hat{c}_{\\text{zig-zig}}}_i } \\] <p>\u800c\u6211\u4eec\u9700\u8981\u8bc1\u660e \\(\\hat{c}_{\\text{rotate }x\\text{ to root}} = O(\\log{N})\\)\uff0c\u73b0\u5728\u6211\u4eec\u9700\u8981\u5206\u522b\u5206\u6790 <code>zig</code>\u3001<code>zig-zag</code>\u3001<code>zig-zig</code>\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec01/#zig","title":"zig","text":"<p>Amortized Analysis for Zig</p> <p></p> \\[ \\begin{aligned}     {\\hat{c}_{\\text{zig}}}_i     &amp;= {c_{\\text{zig}}}_i + \\Phi_{i}(X) - \\Phi_{i-1}(P) \\\\     &amp;= 1 + Rank_{i}(X) - Rank_{i-1}(X) +  Rank_{i}(P) - Rank_{i-1}(P) \\end{aligned} \\] <p>\u89c2\u5bdf\u914d\u56fe\uff0c\\(X\\) \u591a\u4e86 \\(P\\) \u548c \\(C\\) \u4f5c\u4e3a\u5b50\u55e3\uff0c\u800c \\(P\\) \u60b2\u60e8\u5730\u5931\u53bb\u4e86 \\(X\\) \u4e00\u65cf\uff0c\u751a\u81f3\u6210\u4e86 \\(X\\) \u7684\u540e\u4ee3\uff0c\u5373 \\(X\\) \u76db \\(P\\) \u8870\uff0c\u56e0\u6b64\u5c31\u6709\u4e0d\u7b49\u5f0f\uff1a</p> \\[ \\left\\{     \\begin{aligned}         &amp; Rank_{i}(X) - Rank_{i-1}(X) \\geq 0\\\\         &amp; Rank_{i}(P) - Rank_{i-1}(P) \\leq 0     \\end{aligned}     \\right. \\] <p>\u6240\u4ee5\u6211\u4eec\u53ef\u4ee5\u505a\u7b80\u5355\u7684\u7f29\u653e\uff1a</p> \\[ \\begin{aligned}     {\\hat{c}_{\\text{zig}}}_i     &amp;= 1 + \\underbrace{Rank_{i}(X) - Rank_{i-1}(X)}_{\\geq 0} + \\underbrace{Rank_{i}(P) - Rank_{i-1}(P)}_{\\leq 0} \\\\     &amp;\\leq 1 + Rank_{i}(X) - Rank_{i-1}(X) \\end{aligned} \\] <p>\u4e3a\u4ec0\u4e48\u4e0d\u662f\u53e6\u5916\u4e00\u79cd\u9009\u62e9 / \u4e3a\u4f55\u8fd9\u6837\u7f29\u653e\uff1f</p> <p>\u8fd9\u4e00\u90e8\u5206\u5728 cy \u7684 PPT \u91cc\u5e76\u6ca1\u6709\u8be6\u7ec6\u8bf4\u660e\uff0c\u4f46\u662f\u6211\u8ba4\u4e3a\u8fd9\u662f\u8fd9\u4e2a\u5206\u6790\u65b9\u6cd5\u6210\u7acb\u4e00\u4e2a\u975e\u5e38\u91cd\u8981\u7684\u56e0\u7d20\uff01</p> <p>\u4e5f\u8bb8\u4f60\u5df2\u7ecf\u6ce8\u610f\u5230\u4e86\uff0c\u53c8\u6216\u8005\u4f60\u4e86\u89e3\u4e86\u4e4b\u540e\u4e24\u79cd\u5206\u6790\uff0c\u53c8\u56de\u8fc7\u5934\u6765\u601d\u8003\u53d1\u73b0\uff0c\u8fd9\u91cc\u5176\u5b9e\u5b58\u5728\u53e6\u5916\u4e00\u79cd\u66f4\u7d27\u51d1\u7684\u7f29\u653e\u65b9\u6cd5\uff08\u751a\u81f3\u4e0d\u80fd\u8bf4\u201c\u7f29\u653e\u201d\uff09\uff0c\u89c2\u5bdf\u5230 \\(Size_{i}(X) =Size_{i-1}(P)\\)\uff0c\u6240\u4ee5\uff1a</p> \\[ \\begin{aligned}     {\\hat{c}_{\\text{zig}}}_i     &amp;= 1 + Rank_{i}(P) - Rank_{i-1}(X) + \\underbrace{Rank_{i}(X) - Rank_{i-1}(P)}_{= 0} \\\\     &amp;= 1 + Rank_{i}(P) - Rank_{i-1}(X) \\end{aligned} \\] <p>\u4f46\u662f\u8fd9\u4e0d\u4fbf\u4e8e\u6211\u4eec\u4e4b\u540e\u7684\u4f20\u9012\u3002\u8fd8\u8bb0\u5f97\u6211\u4eec\u8981\u6c42\u7684\u76ee\u6807\u5417\uff1f</p> \\[ \\hat{c}_{\\text{rotate }x\\text{ to root}} = \\hat{c}_{\\text{zig}} + \\sum{ {\\hat{c}_{\\text{zig-zag}}}_i } + \\sum{ {\\hat{c}_{\\text{zig-zig}}}_i } \\] <p>\u6211\u4eec\u4e4b\u540e\u9700\u8981\u5bf9\u5404\u79cd \\(\\hat{c}\\) \u8fdb\u884c\u6c42\u548c\uff0c\u800c\u6bcf\u4e00\u6b21\u7684 \\(X,\\;P,\\;G\\) \u90fd\u662f\u4e0d\u540c\u7684\uff0c\u4e3a\u4e86\u5728\u6c42\u548c\u7684\u65f6\u5019\u5b9e\u73b0\u9519\u4f4d\u76f8\u51cf\uff0c\u6211\u4eec\u5fc5\u987b\u4fdd\u8bc1\u7f29\u653e\u5f97\u5230\u7684\u7ed3\u679c\u5177\u6709\u4e00\u5b9a\u7684\u4f20\u9012\u6027\u8d28\uff0c\u6216\u8005\u8bf4\u5728\u6c42\u548c\u8fc7\u7a0b\u4e2d\u80fd\u591f\u8fbe\u5230\u88c2\u9879\u76f8\u6d88\u7684\u6548\u679c\u3002</p> <p>\u800c\u5bf9\u4e8e Splay \u6765\u8bf4\uff0c\u6211\u4eec\u7684\u64cd\u4f5c\u4f20\u9012\uff0c\u6b63\u662f\u901a\u8fc7\u4e0d\u65ad\u5c06\u6211\u4eec\u5173\u6ce8\u7684 \\(X\\) \u70b9\u9012\u5f52\u5730\u5411\u4e0a\u65cb\u8f6c\u5b9e\u73b0\u7684\u3002\u6362\u53e5\u8bdd\u6765\u8bf4\uff0c\\(\\Phi_{i}(X)\\) \u4e2d\u7684 \\(X\\)\uff0c\u5c31\u662f \\(\\Phi_{i-1}(X)\\) \u4e2d\u7684 \\(X\\)\uff0c\u5982\u6b64\u6211\u4eec\u6700\u7ec8\u53ef\u4ee5\u5f97\u5230 \\(\\Phi_{n}(X) - \\Phi_{0}(X)\\)\uff0c\u800c\u5176\u4e2d\u4e00\u4e2a\u662f\u6839\uff0c\u4e00\u4e2a\u662f\u6211\u4eec\u4e00\u5f00\u59cb\u6253\u7b97\u64cd\u4f5c\u7684\u90a3\u4e2a\u70b9\u3002</p> <p>\u4e8e\u662f\u6211\u4eec\u7406\u60f3\u7684\u7f29\u653e\u76ee\u6807\u5c31\u662f \\(k(Rank_{i}(X) - Rank_{i-1}(X)) \\;\\; \\text{where } k \\text{ is fixed for all the terms}\\)\u3002</p> <p>\u4e0d\u8fc7\u4f60\u53ef\u80fd\u53c8\u8981\u63d0\u95ee\u4e86\uff0c<code>zig</code> \u5206\u6790\u7684\u7ed3\u679c\u91cc\u4e0d\u662f\u6709\u4e2a \\({c_{\\text{zig}}}_i = 1\\) \u5417\uff1f</p> <p>\u8fd9\u662f\u56e0\u4e3a <code>zig</code> \u6700\u591a\u53ea\u53d1\u751f\u4e00\u6b21\uff0c\u6240\u4ee5\u8fd9\u4e2a\u5e38\u6570\u662f\u6ca1\u6709\u5f71\u54cd\u7684\u3002</p> <p>\u771f\u7684\u9700\u8981\u90fd\u7f29\u653e\u5230\u76f8\u540c\u7684 k \u5417</p> <p>\u968f\u4e4b\u800c\u6765\u7684\uff0c\u4e00\u4e2a\u9700\u8981\u8ba8\u8bba\u7684\u95ee\u9898\u662f\u300c\\(\\text{where } k \\text{ is fixed for all the terms}\\)\u300d\u771f\u7684\u91cd\u8981\u5417\uff0c\u6362\u53e5\u8bdd\u6765\u8bf4\uff0c\u6211\u4eec\u5fc5\u987b\u4fdd\u8bc1\u4e09\u4e2a\u90e8\u5206\u7f29\u653e\u51fa\u6765\u90fd\u5177\u6709\u76f8\u540c\u7684 \\(k\\) \u5417\uff1f</p> <p>\u9996\u5148\uff0c\u91cd\u8981\u80af\u5b9a\u662f\u91cd\u8981\u7684\uff0c\u53ea\u4e0d\u8fc7\u5728\u8fd9\u4e2a\u95ee\u9898\u4e2d\uff0c\u7531\u4e8e\u6211\u4eec\u65cb\u8f6c\u7684\u65b9\u5411\u90fd\u662f\u5411\u4e0a\uff0c\u6240\u4ee5 \\(Rank_{i}(X) \\geq Rank_{i-1}(X)\\)\uff0c\u56e0\u6b64\u6211\u4eec\u53ea\u9700\u8981\u6700\u540e\u5c06\u5b83\u4eec\u4e00\u8d77\u90fd\u7f29\u653e\u5230 \\(k_{overall} = \\max\\{k_\\text{zig}, k_\\text{zig-zag}, k_\\text{zig-zig} \\}\\) \u5c31\u53ef\u4ee5\u4e86\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec01/#zig-zag","title":"zig-zag","text":"<p>Amortized Analysis for Zig-Zag</p> <p></p> \\[ \\begin{aligned}     {\\hat{c}_{\\text{zig-zag}}}_i      &amp;= {c_{\\text{zig-zag}}}_i + \\Phi_{i}(X)- \\Phi_{i-1}(G) \\\\     &amp;= 2 + Rank_{i}(X) - Rank_{i-1}(X) + Rank_{i}(P) - Rank_{i-1}(P) + Rank_{i}(G) - Rank_{i-1}(G) \\end{aligned} \\] <p>\u89c2\u5bdf\u914d\u56fe\uff0c\\(X\\) \u53c8\u4e00\u6b21\u7edd\u5730\u53cd\u51fb\uff0c\u6210\u4e3a\u5b83\u5bb6\u957f\u548c\u5b83\u5bb6\u957f\u7684\u5bb6\u957f\u5171\u540c\u7684\u5bb6\u957f\uff1b\\(G\\) \u635f\u5931\u6700\u60e8\u91cd\uff0c\u4e22\u6389\u4e86 \\(A,\\;B\\) \u4e24\u65cf\u5b50\u55e3\u3002</p> <p>\u5728\u8fd9\u6b21\u7684\u7f29\u653e\u4e2d\uff0c\u6839\u636e\u6211\u4eec\u4e4b\u524d\u5728 <code>key-point</code> \u91cc\u63d0\u5230\u7684\uff0c\u6211\u4eec\u9700\u8981\u5c06\u5b83\u7f29\u653e\u5230 \\(k(Rank_{i}(X) - Rank_{i-1}(X))\\) \u7684\u5f62\u5f0f\uff0c\u5e76\u4e14\u7531\u4e8e <code>zig-zig</code> \u4f1a\u591a\u6b21\u53d1\u751f\uff0c\u6240\u4ee5\u6211\u4eec\u4e5f\u5f97\u60f3\u529e\u6cd5\u641e\u6389\u8fd9\u91cc\u7684 \\({c_{\\text{zig-zag}}}_i = 2\\)\uff0c\u5426\u5219\u6700\u540e\u5c31\u4f1a\u51fa\u73b0\u4e00\u4e2a \\(2p(n)\\) \u7684 term\uff0c\u800c\u6211\u4eec\u7684\u8bc1\u660e\u76ee\u6807\u662f \\(\\log{N}\\)\uff0c\u6240\u4ee5\u6211\u4eec\u5fc5\u987b\u5c06\u8fd9\u4e2a \\(2\\) \u6d88\u6389\u3002\u800c\u4e3a\u4e86\u6d88\u9664\u8fd9\u4e2a \\(2\\)\uff0c\u6211\u4eec\u9700\u8981\u5148\u5f15\u5165\u4e00\u4e2a\u5f15\u7406\uff1a</p> <p>Lemma 1</p> <p>\u7531\u4e8e \\(y = \\log{x}\\) \u662f\u5355\u8c03\u7684\u51f8\u51fd\u6570\uff0c\u6240\u4ee5\u6709 \\(\\frac{\\log{x} + \\log{b}}{2} \\leq \\log {\\frac{a+b}{2}}\\)\u3002</p> <p>\u800c\u5728 Splay \u7684\u5747\u644a\u590d\u6742\u5ea6\u5206\u6790\u8fc7\u7a0b\u4e2d\uff0c\u6211\u4eec\u7684 \\(\\log{x}\\) \u6307\u7684\u662f \\(\\log_2{x}\\)\uff0c\u56e0\u6b64\u6709\uff1a</p> \\[ \\begin{aligned}     \\log{a} + \\log{b}      &amp;= 2\\left( \\frac{\\log{a} + \\log{b}}{2} \\right) \\\\     &amp;\\leq 2\\left( \\log{\\frac{a+b}{2}} \\right) \\\\     &amp;= 2\\left( \\log{(a+b)} - \\log{2} \\right) \\\\     &amp;= 2 \\log{(a+b)} - 2 \\\\ \\end{aligned} \\] <p>\u770b\u5230\u8fd9\u91cc\u51fa\u73b0\u4e86\u4e00\u4e2a \\(-2\\) \u6211\u4eec\u5c31\u80fd\u957f\u8212\u4e00\u53e3\u6c14\u4e86\uff0c\u8fd9\u4e0b \\({c_{\\text{zig-zag}}}_i = 2\\) \u6b7b\u5230\u4e34\u5934\u54af\uff01\u5bf9\u7167\u914d\u56fe\u770b\uff0c\u6211\u4eec\u53ef\u4ee5\u5f97\u5230\uff1a</p> \\[ \\begin{aligned}     Rank_{i}(P) + Rank_{i}(G)   &amp;= \\log{Size_{i}(P)} + \\log{Size_{i}(G)} \\\\                                 &amp;\\leq 2\\log{\\left(Size_{i}(P)+Size_{i}(G)\\right)} - 2 &amp; \\text{(Lemma 1)}\\\\                                 &amp;\\leq 2\\log{\\left(Size_{i}(P)+Size_{i}(G)+1\\right)} - 2 \\\\                                 &amp;\\leq 2\\log{Size_{i}(X)} - 2 \\\\                                 &amp;\\leq 2Rank_{i}(X) - 2 \\\\ \\end{aligned} \\] <p>\u56e0\u6b64\uff0c\u6211\u4eec\u80fd\u591f\u5f97\u5230\u8fd9\u4e9b\u76f8\u7b49\u6216\u4e0d\u7b49\u5173\u7cfb\uff1a</p> \\[ \\left\\{     \\begin{aligned}         Rank_{i}(X) &amp;= Rank_{i-1}(G) \\\\         Rank_{i}(P) + Rank_{i}(G) &amp;\\leq 2Rank_{i}(X) - 2 \\\\         Rank_{i-1}(P) + Rank_{i-1}(X) &amp;\\geq 2Rank_{i-1}(X)     \\end{aligned} \\right. \\] <p>\u4e8e\u662f\u6211\u4eec\u53ef\u4ee5\u5b9e\u73b0\u7f29\u653e\uff1a</p> \\[ \\begin{aligned}     {\\hat{c}_{\\text{zig-zag}}}_i      &amp;= 2 + Rank_{i}(X) - Rank_{i-1}(X) + Rank_{i}(P) - Rank_{i-1}(P) + Rank_{i}(G) - Rank_{i-1}(G) \\\\     &amp;= 2 + \\left( Rank_{i}(X) - Rank_{i-1}(G)\\right )           + \\left( Rank_{i}(P) + Rank_{i}(G) \\right)          - \\left( Rank_{i-1}(P) + Rank_{i-1}(X) \\right) \\\\     &amp;\\leq 2 + 0 + 2Rank_{i}(X) - 2 + 2Rank_{i-1}(X) \\\\     &amp;= 2\\left(Rank_{i}(X) - Rank_{i-1}(X)\\right) \\end{aligned} \\] <p>\u7686\u5927\u6b22\u559c\uff01</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec01/#zig-zig","title":"zig-zig","text":"<p>Amortized Analysis for Zig-Zig</p> <p></p> \\[ \\begin{aligned}     {\\hat{c}_{\\text{zig-zig}}}_i      &amp;= {c_{\\text{zig-zig}}}_i + \\Phi_{i}(X)- \\Phi_{i-1}(G) \\\\     &amp;= 2 + Rank_{i}(X) - Rank_{i-1}(X) + Rank_{i}(P) - Rank_{i-1}(P) + Rank_{i}(G) - Rank_{i-1}(G) \\end{aligned} \\] <p>\u4e3a\u4e86\u5b9e\u73b0 <code>zig-zig</code> \u7684\u7f29\u653e\uff0c\u6211\u4eec\u8fd8\u9700\u8981\u5bf9 Lemma 1 \u8fdb\u884c\u4e00\u4e2a\u6d3b\u7528\u3002\u5bf9\u7167\u914d\u56fe\uff0c\u5f97\u5230\uff1a</p> \\[ \\begin{aligned}     Rank_{i}(G) + Rank_{i-1}(X)          &amp;\\leq 2\\log{\\left(              \\underbrace{Size_{i}(G)}_{\\mathbf{C}+\\mathbf{D}+G}           + \\underbrace{Size_{i-1}(X)}_{\\mathbf{A}+\\mathbf{B}+X}         \\right)} - 2 &amp; \\text{(Lemma 1)} \\\\         &amp;\\leq 2\\log{\\left( Size_{i}(G) + Size_{i-1}(X) + 1 \\right)} - 2 &amp; \\\\         &amp;= 2\\log{\\left( Size_{i}(X) \\right)} - 2 \\\\         &amp;= 2Rank_{i}(X) - 2 \\\\     Rank_{i}(G)          &amp;\\leq 2Rank_{i}(X) - Rank_{i-1}(X) - 2 \\end{aligned} \\] <p>\u8fd9\u4e00\u6b65\u5f88\u96be\u60f3\uff0c\u4f46\u662f\u4e5f\u975e\u5e38\u5173\u952e\u3002</p> <p>\u4e8e\u662f\uff0c\u6211\u4eec\u6709\u5982\u4e0b\u8fd9\u4e9b\u4e0d\u7b49\u5f0f\uff1a</p> \\[ \\left\\{     \\begin{aligned}         Rank_{i}(X) &amp;= Rank_{i-1}(G) \\\\         Rank_{i}(G) &amp;\\leq 2Rank_{i}(X) - Rank_{i-1}(X) - 2 \\\\         Rank_{i}(P) &amp;\\leq Rank_{i}(X) \\\\         Rank_{i-1}(P) &amp;\\geq Rank_{i-1}(X)     \\end{aligned} \\right. \\] <p>\u4e8e\u662f\u6211\u4eec\u5c31\u53ef\u4ee5\u5bf9\u5176\u8fdb\u884c\u8be1\u5f02\u7684\u7f29\u653e\uff1a</p> \\[ \\begin{aligned}     {\\hat{c}_{\\text{zig-zig}}}_i      &amp;= 2 + Rank_{i}(X) - Rank_{i-1}(X) + Rank_{i}(P) - Rank_{i-1}(P) + Rank_{i}(G) - Rank_{i-1}(G) \\\\     &amp;= 2 + \\left( Rank_{i}(X) - Rank_{i-1}(G) \\right)          + Rank_{i}(G)          + Rank_{i}(P)          - Rank_{i-1}(P)          - Rank_{i-1}(X) \\\\     &amp;\\leq 2 + 0              + \\left( 2Rank_{i}(X) - Rank_{i-1}(X) - 2 \\right)              + Rank_{i}(X)             - Rank_{i-1}(X)             - Rank_{i-1}(X) \\\\     &amp;= 3\\left( Rank_{i}(X) - Rank_{i-1}(X) \\right) \\end{aligned} \\] <p>\ud83d\ude29 \u81f3\u6b64\uff0c\u6211\u4eec\u603b\u7b97\u662f\u628a\u725b\u9b3c\u86c7\u795e\u7684 <code>zig-zig</code> \u7684\u8bc1\u660e\u4e5f\u7ed9\u641e\u5b9a\u4e86\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec01/#\u7ed3\u8bba","title":"\u7ed3\u8bba","text":"<p>Amortized Analysis for Splay</p> <p>\u81f3\u6b64\uff0c\u5bf9\u4e8e\u4e09\u79cd\u64cd\u4f5c\uff0c\u6211\u4eec\u90fd\u5f97\u5230\u4e86\u5b83\u4eec\u7684\u5747\u644a\u4e0a\u754c\uff1a</p> \\[ \\begin{aligned}     {\\hat{c}_{\\text{zig}}}_i &amp;\\leq 1 + Rank_{i}(X) - Rank_{i-1}(X) \\\\     {\\hat{c}_{\\text{zig-zag}}}_i &amp;\\leq 2\\left(Rank_{i}(X) - Rank_{i-1}(X)\\right) \\\\     {\\hat{c}_{\\text{zig-zig}}}_i &amp;\\leq 3\\left(Rank_{i}(X) - Rank_{i-1}(X)\\right) \\end{aligned} \\] <p>\u6839\u636e\u6211\u4eec\u5728 <code>key-point</code> \u6846\u300c\u771f\u7684\u9700\u8981\u90fd\u7f29\u653e\u5230\u76f8\u540c\u7684 k \u5417\u300d\u4e2d\u7684\u5185\u5bb9\uff0c\u6211\u4eec\u63a5\u4e0b\u6765\u53ef\u4ee5\u5c06\u5b83\u4eec\u7684 \\(k\\) \u90fd\u7f29\u653e\u4e3a \\(3\\)\uff1a</p> \\[ \\begin{aligned}     {\\hat{c}_{\\text{zig}}}_i &amp;\\leq 1 + 3\\left( Rank_{i}(X) - Rank_{i-1}(X) \\right) \\\\     {\\hat{c}_{\\text{zig-zag}}}_i &amp;\\leq 3\\left( Rank_{i}(X) - Rank_{i-1}(X) \\right) \\\\     {\\hat{c}_{\\text{zig-zig}}}_i &amp;\\leq 3\\left( Rank_{i}(X) - Rank_{i-1}(X) \\right) \\end{aligned} \\] <p>\u4e8e\u662f\uff0c\u6211\u4eec\u5c31\u53ef\u4ee5\u5f97\u5230\u6700\u7ec8\u7684\u5747\u644a\u4e0a\u754c\uff1a</p> \\[ \\begin{aligned}     \\hat{c}_{\\text{rotate }x\\text{ to root}}          &amp;= \\hat{c}_{\\text{zig}} + \\sum{ {\\hat{c}_{\\text{zig-zag}}}_i } + \\sum{ {\\hat{c}_{\\text{zig-zig}}}_i } \\\\         &amp;= O(1) + 3\\left( Rank_{N}(X) - Rank_{0}(X) \\right) \\\\         &amp;= O(\\log{N}) \\end{aligned} \\] <p>\u53ef\u4ee5\u4ed4\u7ec6\u60f3\u60f3\u6c42\u548c\u5f0f\u662f\u5982\u4f55\u201c\u76f8\u6d88\u201d\u5f97\u5230\u6700\u540e\u7684\u5f0f\u5b50\u7684\uff0c\u8fd9\u91cc\u7684 \\(\\sum {\\hat{c}_\\text{...}}_i\\) \u7684 \\(i\\) \u5e76\u4e0d\u662f\u5728\u6c42\u548c\u5f0f\u4e2d\u5404\u81ea\u8fde\u7eed\u7684\uff0c\u4f46\u662f\u4e09\u4e2a term \u653e\u5728\u4e00\u8d77\uff0c\u5219\u53ef\u4ee5\u56ca\u62ec \\(i\\in\\{1,2,...,N\\}\\)</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec02/","title":"Lecture 2 | Red Black Tree &amp; B+ Tree","text":"<p> \u7ea6 4971 \u4e2a\u5b57  43 \u884c\u4ee3\u7801  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 17 \u5206\u949f</p> <p>\u8bf4\u660e</p> <p>\u800c\u4e3a\u4e86\u63d0\u9ad8\u7b14\u8bb0\u6574\u7406\u6548\u7387\uff0c\u53ef\u80fd\u4f1a\u8003\u8651\u7528\u66f4\u591a\u7684\u5f15\u7528\u548c\u66f4\u7b80\u5355\u7684\u8bed\u8a00\u3002\u5982\u679c\u60a8\u89c9\u5f97\u6709\u54ea\u91cc\u8bf4\u7684\u4e0d\u591f\u6e05\u695a\uff0c\u8bf7\u76f4\u63a5\u5728\u8bc4\u8bba\u533a\u72e0\u72e0 blame \u6211\uff01</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec02/#\u7ea2\u9ed1\u6811","title":"\u7ea2\u9ed1\u6811","text":"<p>link</p> <p>OI Wiki: https://oi-wiki.org/ds/rbtree/</p> <p>Wikipedia: https://en.wikipedia.org/wiki/Red%E2%80%93black_tree</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec02/#\u6982\u5ff5","title":"\u6982\u5ff5","text":"<p>\u987e\u540d\u601d\u4e49\uff0c\u7ea2\u9ed1\u6811(Red Black Tree)\u5c31\u662f\u4e00\u79cd\u8282\u70b9\u5206\u7c7b\u4e3a\u7ea2\u9ed1\u4e24\u8272\u7684\uff0c\u6bd4\u8f83\u5e73\u8861\u7684\u4e8c\u53c9\u641c\u7d22\u6811\u3002\u53ea\u4e0d\u8fc7\u4e0d\u540c\u4e8e AVL \u6811\uff0c\u7ea2\u9ed1\u6811\u7684\u201c\u5e73\u8861\u201d\u6027\u8d28\u662f\u901a\u8fc7\u9ed1\u9ad8(black height)\u6765\u5b9a\u4e49\u7684\u3002\u63a5\u4e0b\u6765\u4f9d\u6b21\u7ed9\u51fa\u7ea2\u9ed1\u6811\u7684\u5b9a\u4e49\u548c\u9ed1\u9ad8\u7684\u5b9a\u4e49\u3002</p> <p>Red Black Tree</p> <p> </p> <p>\u7ea2\u9ed1\u6811\u662f\u6ee1\u8db3\u5982\u4e0b\u6027\u8d28\u7684\u4e00\u79cd\u4e8c\u53c9\u641c\u7d22\u6811\uff1a</p> <p>Properties of RBTree</p> <p>@cy's PPT</p> <ol> <li>Every node is either red or black.</li> <li>The root is black.</li> <li>Every leaf (<code>NIL</code>) is black.</li> <li>if a node is red, then both its children are black.</li> <li>For each node, all simple paths from the node to descendant leaves contain the same number of black nodes.</li> </ol> <p>ch \u8001\u5e08\u8bf4\uff0c\u5e0c\u671b\u6211\u4eec\u80fd\u628a\u8fd9\u4e94\u6761\u6027\u8d28\u719f\u7ec3\u8bb0\u4f4f\uff0c\u600e\u4e48\u53ef\u80fd\uff08\u9003\uff09\u3002</p> <p>\u8bf4\u660e</p> <p>\u7531\u4e8e\u8fd9\u91cc\u7684\u201c\u53f6\u5b50\u7ed3\u70b9\u201d\u88ab\u91cd\u65b0\u5b9a\u4e49\u4e86\uff0c\u4e3a\u4e86\u63cf\u8ff0\u65b9\u4fbf\uff0c\u6211\u73b0\u5728\u79f0\u6240\u6709\u4e24\u4e2a\u5b50\u7ed3\u70b9\u90fd\u662f <code>NIL</code> \u7684\u7ed3\u70b9\u4e3a\u672b\u7aef\u7ed3\u70b9\uff08\u4e5f\u5c31\u662f\u901a\u4fd7\u610f\u4e49\u4e0a\u7684\u53f6\u5b50\u7ed3\u70b9\uff09\u3002\u800c\u8fd9\u4e2a\u5b9a\u4e49\u53ea\u662f\u6211\u81ea\u5df1\u8bf4\u8bf4\u7684\uff01</p> @Wiki <ol> <li>Every node is either red or black.</li> <li>All <code>NIL</code> nodes (figure above) are considered black.</li> <li>A red node does not have a red child.</li> <li>Every path from a given node to any of its descendant <code>NIL</code> nodes goes through the same number of black nodes.</li> </ol> @OI Wiki <ol> <li>\u6bcf\u4e00\u4e2a\u8282\u70b9\u8981\u4e48\u662f\u7ea2\u8272\uff0c\u8981\u4e48\u662f\u9ed1\u8272\uff1b</li> <li><code>NIL</code> \u8282\u70b9\uff08\u7a7a\u53f6\u5b50\u8282\u70b9\uff09\u4e3a\u9ed1\u8272\uff1b</li> <li>\u7ea2\u8272\u8282\u70b9\u7684\u5b50\u8282\u70b9\u5fc5\u987b\u4e3a\u9ed1\u8272\uff1b</li> <li>\u4ece\u6839\u8282\u70b9\u5230 <code>NIL</code> \u8282\u70b9\u7684\u6bcf\u6761\u8def\u5f84\u4e0a\u7684\u9ed1\u8272\u8282\u70b9\u6570\u91cf\u76f8\u540c\uff1b</li> </ol> <p>black height, bh</p> <p>\u7279\u5b9a\u8282\u70b9\u7684\u9ed1\u9ad8\uff0c\u7b49\u4e8e\u8be5\u8282\u70b9\u5230\u53f6\u7ed3\u70b9\u5230\u7b80\u5355\u8def\u5f84\u4e2d\uff08\u4e0d\u5305\u62ec\u81ea\u8eab\uff09\uff0c\u9ed1\u8272\u8282\u70b9\u7684\u6570\u91cf\u3002</p> <p>\u63a5\u4e0b\u6765\u4e3a\u4e86\u52a0\u6df1\u7406\u89e3\uff0c\u6709\u4e00\u4e9b\u8fa8\u6790\u53ef\u4ee5\u505a\uff1a</p> T1T2 \u9898\u9762\u7b54\u6848 <p>\u4e0b\u56fe\u7684\u7ea2\u9ed1\u6811\u662f\u5426\u5408\u6cd5\uff1f</p> <p></p> <p>\u4e0d\u5408\u6cd5\u3002</p> <p><code>16</code> \u53f7\u8282\u70b9\u7684\u53f3\u513f\u5b50\u662f\u4e00\u4e2a\u9ed1\u53f6\u5b50\uff0c\u800c\u8fd9\u4e2a\u53f6\u5b50\u5230\u6839\u7684\u8def\u5f84\u4e0a\u53ea\u6709 3 \u4e2a\u9ed1\u8282\u70b9\uff0c\u800c\u5176\u4ed6\u53f6\u5b50\u5230\u6839\u90fd\u6709 4 \u4e2a\u9ed1\u8282\u70b9\u3002</p> <p>\u6240\u4ee5\u6211\u4eec\u9700\u8981\u8b66\u60d5\u53ea\u6709\u4e00\u4e2a\u975e\u53f6\u513f\u5b50\u7684\u7ea2\u8272\u8282\u70b9\u3002</p> \u9898\u9762\u7b54\u6848 <p>\u4e0b\u56fe\u7684\u7ea2\u9ed1\u6811\u662f\u5426\u5408\u6cd5\uff1f</p> <p></p> <p>\u5408\u6cd5\u3002</p> <p>\u6839\u636e T1 \u7684\u89e3\u6790\uff0c\u6211\u4eec\u5f97\u5230\u8fd9\u6837\u4e00\u4e2a\u7ed3\u8bba\uff1a</p> <p>\u5408\u6cd5\u7ea2\u9ed1\u6811\u4e0d\u5b58\u5728\u53ea\u6709\u4e00\u4e2a\u975e\u53f6\u5b50\u8282\u70b9\u7684\u7ea2\u8272\u8282\u70b9\uff01</p> <p>or</p> <p>\u5408\u6cd5\u7ea2\u9ed1\u6811\u7684\u7ea2\u8272\u8282\u70b9\u7684\u4e24\u4e2a\u5b50\u8282\u70b9\u4e00\u5b9a\u90fd\u662f\u53f6\u5b50\u6216\u90fd\u4e0d\u662f\u53f6\u5b50\uff01</p> <p>\u6b64\u5916\uff0c\u5173\u4e8e\u7ea2\u9ed1\u6811\u7684\u9ad8\uff0c\u6211\u4eec\u6709\u5982\u4e0b\u6027\u8d28\uff1a</p> <p>property about height of RBTree</p> <p>\u4e00\u4e2a\u6709 \\(N\\) \u4e2a\u5185\u90e8\u8282\u70b9\uff08\u4e0d\u5305\u62ec\u53f6\u5b50\u7ed3\u70b9\uff09\u7684\u7ea2\u9ed1\u6811\uff0c\u5176\u9ad8\u5ea6\u6700\u5927\u4e3a \\(2\\log_2 (N+1)\\)\u3002</p> the proof of the property <p>\u5173\u4e8e\u9ed1\u9ad8\u548c\u70b9\u6570\u7684\u5173\u7cfb\u3002</p> <ol> <li>\u9996\u5148\u6211\u4eec\u6709 \\(N \\geq 2^{bh}-1\\)\uff0c\u4e5f\u5c31\u662f \\(bh \\leq \\log_2 (N+1)\\)\uff1b</li> <li>\u7136\u540e\u663e\u7136\u6709 \\(2 bh(Tree) &gt;= h(Tree)\\)</li> </ol>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec02/#\u64cd\u4f5c","title":"\u64cd\u4f5c","text":"<p>\u63d0\u9192</p> <p>\u6211\u4eec\u8fd9\u91cc\u4ecb\u7ecd\u7684\u90fd\u662f bottom-up \u7684\u601d\u8def\uff0c\u4e0d\u540c\u4e8e AVL \u6811\uff0c\u7ea2\u9ed1\u6811\u662f\u5b58\u5728 top-down \u7684\u64cd\u4f5c\u65b9\u6cd5\u7684\uff0c\u800c\u8fd9\u4e5f\u662f\u7ea2\u9ed1\u6811\u4e00\u4e2a\u975e\u5e38\u5f3a\u5927\u7684\u4f18\u52bf\uff0c\u5b58\u5728 top-down \u7684\u5904\u7406\u65b9\u6cd5\u610f\u5473\u7740\u6211\u4eec\u53ef\u4ee5\u8fdb\u884c\u66f4\u5feb\u7684\u5e76\u884c\u64cd\u4f5c\u3002\u4f46\u662f\u6211\u4eec\u4e0d\u5728\u8fd9\u91cc\u8be6\u7ec6\u5c55\u5f00\u3002</p> <p>\u540c AVL \u6811\u7684\u8c03\u6574\u64cd\u4f5c\u7c7b\u4f3c\uff0c\u7ea2\u9ed1\u6811\u7684\u8c03\u6574\u64cd\u4f5c\u4e5f\u662f\u5de6\u53f3\u5bf9\u79f0\u7684\uff0c\u6240\u4ee5\u6211\u4eec\u4e5f\u4ecd\u7136\u53ea\u8ba8\u8bba\u4e00\u4fa7\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec02/#\u63d2\u5165","title":"\u63d2\u5165","text":"<p>\u6211\u4eec\u77e5\u9053\uff0c\u5bf9\u9ed1\u9ad8\u6709\u8d21\u732e\u7684\u53ea\u6709\u9ed1\u8272\u8282\u70b9\uff0c\u56e0\u6b64 <code>NIL</code> \u8282\u70b9\u88ab\u4e00\u4e2a\u7ea2\u8272\u8282\u70b9\u7f6e\u6362\u5e76\u4e0d\u4f1a\u6539\u53d8\u4e00\u9897\u7ea2\u9ed1\u6811\u7684\u9ed1\u9ad8\uff0c\u56e0\u4e3a\u7ea2\u8272\u8282\u70b9\u8fd8\u4f1a\u6709\u4e00\u5c42 <code>NIL</code> \u5b50\u8282\u70b9\uff1b\u7136\u800c\u5bf9\u4e8e\u7ea2\u8272\u8282\u70b9\uff0c\u5374\u6709\u7740\u7ea2\u8272\u7ed3\u70b9\u4e92\u4e0d\u76f8\u90bb\u7684\u9650\u5236\u3002</p> <p>\u56e0\u6b64\uff0c\u201c\u63d2\u5165\u201d\u64cd\u4f5c\u7684\u4e3b\u8981\u601d\u8def\u5c31\u662f\uff0c\u5148\u5c06\u6574\u4e2a\u7ea2\u9ed1\u6811\u5f53\u4f5c\u4e00\u4e2a\u666e\u901a\u7684\u4e8c\u53c9\u641c\u7d22\u6811\uff0c\u5c06\u76ee\u6807\u6570\u636e\u63d2\u5165\u5230\u6811\u7684\u672b\u7aef\uff08\u4e5f\u5c31\u662f\u7f6e\u6362\u4e00\u4e2a <code>NIL</code> \u8282\u70b9\uff09\uff0c\u5e76\u5c06\u5b83\u67d3\u4e3a\u7ea2\u8272\uff0c\u518d\u8c03\u6574\u4f7f\u4e4b\u5728\u4fdd\u8bc1\u9ed1\u9ad8\u4e0d\u53d8\u7684\u60c5\u51b5\u4e0b\uff0c\u6ee1\u8db3\u7ea2\u8272\u8282\u70b9\u4e0d\u80fd\u76f8\u90bb\u7684\u8981\u6c42\u3002</p> <p>\u73b0\u5728\uff0c\u6211\u4eec\u8bb0\u8fd9\u4e2a\u88ab\u63d2\u5165\u7684\u8282\u70b9\u4e3a <code>x</code>\uff0c\u4efb\u610f\u4e00\u4e2a\u8282\u70b9 <code>node</code> \u7684\u5bb6\u957f\u8282\u70b9\u4e3a <code>node.p</code>\uff0c\u5219\uff1a</p> <ol> <li>\u5982\u679c <code>x.p</code> \u662f\u9ed1\u8272\u7684\uff0c\u90a3\u4e48\u6211\u4eec\u4e0d\u9700\u8981\u505a\u4efb\u4f55\u8c03\u6574\uff1b</li> <li>\u5982\u679c <code>x.p</code> \u662f\u7ea2\u8272\u7684\uff0c\u90a3\u4e48\u6211\u4eec\u9700\u8981\u8fdb\u884c\u8c03\u6574\uff1b<ul> <li>\u6b64\u65f6\u56e0\u4e3a\u539f\u6765\u7684\u6811\u7b26\u5408\u7ea2\u9ed1\u6027\u8d28\uff0c<code>x.p.p</code> \u5fc5\u5b9a\u5b58\u5728\uff08\u7ea2 <code>x.p</code> \u4e0d\u80fd\u662f\u6839\uff09\u4e14\u5fc5\u5b9a\u662f\u9ed1\u8272\u7684\uff1b</li> </ul> </li> </ol> <p>\u6839\u636e\u8fd9\u4e9b\u8ba8\u8bba\uff0c\u6211\u4eec\u5c31\u80fd\u5217\u4e3e\u51fa\u6765\u4e00\u4e2a\u7ea2\u8272\u7684\u70b9\u88ab\u63d2\u5165\u540e\uff0c\u5728 <code>2.</code> \u7684\u60c5\u51b5\u4e0b\u6240\u6709\u7684\u521d\u59cb\u60c5\u51b5\uff0c\u5373\u4e0b\u9762\u7b2c\u4e00\u5f20\u56fe\u3002</p> <p></p> <p>\u7531\u4e8e\u7ea2\u9ed1\u6811\u7684\u64cd\u4f5c\u4e2d\uff0c\u6709\u4e00\u90e8\u5206\u9700\u8981\u8fdb\u884c\u9012\u5f52\u8f6c\u79fb\uff0c\u800c\u5176\u4e2d\u4e2d\u95f4\u6b65\u9aa4\u51fa\u73b0\u4e86\u5f88\u591a\u540c\u6784\u7684\u7ed3\u6784\uff0c\u6240\u4ee5\u4e3a\u4e86\u7b80\u5316\u8bf4\u660e\uff0c\u6211\u4eec\u5bf9\u5176\u8fdb\u884c\u7edf\u4e00\uff0c\u6240\u6709\u60c5\u51b5\u90fd\u88ab\u5f52\u7eb3\u4e3a\u4e0a\u9762\u7b2c\u4e8c\u5f20\u56fe\u3002</p> <p>\u800c\u7b2c\u4e8c\u5f20\u56fe\u4e2d\u63d0\u5230\u7684\u6a59\u8272\u7ed3\u70b9\uff0c\u4e5f\u5c31\u662f\u6807\u4e3a\u201c\u88ab\u63d2\u5165\u7684\u7ea2\u8272\u8282\u70b9\u201d\u7684\u7ed3\u70b9\uff0c\u5b9e\u9645\u8fc7\u7a0b\u4e2d\u5e76\u4e0d\u4e00\u5b9a\u6307\u7684\u662f\u88ab\u300c\u63d2\u5165\u300d\u7684\u90a3\u4e2a\u70b9\uff0c\u4e5f\u53ef\u80fd\u662f\u5728 case 1 \u5411\u4e0a\u9012\u5f52\u65f6\uff0c\u7b80\u5316\u7684\u539f\u6765\u90a3\u9897\u5b50\u6811\u3002\u6362\u53e5\u8bdd\u6765\u8bf4\uff0c\u8fd9\u91cc\u7684\u201c\u88ab\u63d2\u5165\u7684\u7ea2\u8272\u8282\u70b9\u53ca\u5176\u5b50\u6811\u201d\uff0c\u5b9e\u9645\u4e0a\u53ef\u80fd\u662f\u6307\u300c\u5bfc\u81f4\u7ea2\u9ed1\u6027\u8d28\u88ab\u7834\u574f\u7684\u7ea2\u6839\u5b50\u6811\u300d\u3002</p> <p>\u63a5\u4e0b\u6765\u6211\u4eec\u6765\u8ba8\u8bba\u5404\u79cd\u60c5\u51b5\u8981\u600e\u4e48\u5904\u7406\u3002</p> <p>\u8bf4\u660e</p> <p>\u8fd9\u91cc case 1 ~ case 3 \u7684\u7f16\u53f7\u4e3b\u8981\u662f\u4e3a\u4e86\u548c\u8bfe\u7a0b ppt \u5bf9\u6807\uff0c\u4f46\u662f\u63a5\u4e0b\u6765\u4f60\u4f1a\u53d1\u73b0\u6211\u662f\u6309\u7167 case 3 -&gt; case 1 \u6765\u4ecb\u7ecd\u64cd\u4f5c\u7684\uff0c\u8fd9\u662f\u56e0\u4e3a\u6211\u89c9\u5f97\u8fd9\u6837\u5b89\u6392\u66f4\u5408\u7406\uff0c\u800c\u975e\u6392\u7248\u6df7\u4e71\u3002</p> Insertion / case 3 <p>\u5bf9\u4e8e case 3\uff0c \u6211\u4eec\u9ad8\u5174\u5730\u53d1\u73b0\uff0c\u8fd9\u6837\u7684\u4e00\u6b21\u67d3\u8272\u548c\u4e00\u6b21\u65cb\u8f6c\u521a\u597d\u80fd\u8ba9\u8fd9\u68f5\u5b50\u6811\u5b8c\u6210\u8c03\u6574\uff01</p> <p></p> Insertion / case 2 <p>\u5bf9\u4e8e case 2\uff0c\u6211\u4eec\u53ef\u4ee5\u76f4\u63a5\u8fdb\u884c\u4e00\u4e2a Rotation \u64cd\u4f5c\u5c06\u5b83\u8f6c\u5316\u4e3a case 3\u3002</p> <p>\u4f46\u662f\u5b9e\u9645\u4e0a\uff0c\u7ec6\u5fc3\u7684\u5c0f\u670b\u53cb\u5df2\u7ecf\u53d1\u73b0\u4e86\uff0c\u4ece case 2 -&gt; case 3 -&gt; done \u7684\u8fc7\u7a0b \u5b9e\u9645\u4e0a\u5c31\u662f\u4e00\u4e2a LR Rotation\uff01</p> <p></p> Insertion / case 1 <p>\u5bf9\u4e8e case 1\uff0c\u56fe\u4e2d\u7684\u4e24\u79cd\u60c5\u51b5\u662f\u7b49\u4ef7\u7684\u3002\u6240\u4ee5\u6211\u4eec\u53ea\u5c55\u793a\u5176\u4e2d\u4e00\u79cd\u3002</p> <p>\u6211\u4eec\u53ea\u9700\u8981\u5c06\u56fe\u4e2d\u7684\u6839\u8282\u70b9\u67d3\u7ea2\uff0c\u5c06\u6839\u7684\u4e24\u4e2a\u5b50\u8282\u70b9\u67d3\u9ed1\uff0c\u7c7b\u4f3c\u4e8e\u5c06\u9ed1\u8282\u70b9\u201c\u4e0b\u653e\u201d\u3002</p> <p></p> <p>\u901a\u8fc7\u7b2c\u4e00\u6b65\u64cd\u4f5c\uff0c\u6211\u4eec\u53ef\u4ee5\u4fdd\u8bc1\u8fd9\u6574\u4e2a\u5b50\u6811\u5fc5\u5b9a\u5e73\u8861\u3001\u4e0d\u5f71\u54cd\u5bb6\u957f\u8282\u70b9\u7684\u9ed1\u9ad8\uff08\u9664\u4e86\u5bb6\u957f\u662f\u6839\u7684\u60c5\u51b5\uff09\u4e14\u7ea2\u70b9\u4e0d\u90bb\u7684\u3002</p> <p>\u7136\u800c\u6211\u4eec\u5e76\u4e0d\u77e5\u9053\u8fd9\u4e2a\u6839\u7684\u5bb6\u957f\u8282\u70b9\u662f\u5426\u662f\u7ea2\u8272\u8282\u70b9\uff0c\u56e0\u6b64\u505a\u5206\u7c7b\u8ba8\u8bba\u3002\u5018\u82e5\u5176\u6839\u7684\u5bb6\u957f\u8282\u70b9\u662f\u7ea2\u8272\u8282\u70b9\uff0c\u90a3\u4e48\u6211\u4eec\u8fd8\u9700\u8981\u5411\u4e0a\u9012\u5f52\uff0c\u7ee7\u7eed\u8c03\u6574\uff0c\u6839\u636e\u5b9e\u9645\u60c5\u51b5\u8f6c\u5316\u4e3a\u5176\u4ed6 case\uff1b\u82e5\u8fd9\u5b50\u6811\u7684\u6839\u6ca1\u6709\u5bb6\u957f\u8282\u70b9\uff0c\u5219\u76f4\u63a5\u67d3\u9ed1\u7ea2\u6839\u5373\u53ef\uff1b\u800c\u5018\u82e5\u5b50\u6811\u6839\u8282\u70b9\u7684\u5bb6\u957f\u8282\u70b9\u662f\u9ed1\u8282\u70b9\uff0c\u90a3\u4e48\u6211\u4eec\u5c31\u8c03\u6574\u5b8c\u6bd5\u4e86\u3002</p> <p>\u5728\u8fd9\u4e09\u4e2a\u8fc7\u7a0b\u4e2d\uff0c\u6211\u4eec\u89c2\u5bdf\u5230\uff0c\u53ea\u6709 case 1 \u7684\u8f6c\u5316\u4f1a\u5bfc\u81f4\u6211\u4eec\u9012\u5f52\u5411\u4e0a\uff0c\u800c case 2 \u5411 case 3 \u7684\u8f6c\u5316\u5e76\u4e0d\u4f1a\u5bfc\u81f4\u6211\u4eec\u6539\u53d8\u5173\u6ce8\u7684\u5b50\u6811\u7684\u8303\u56f4\u3002</p> <p>\u4e3a\u4e86\u66f4\u6e05\u6670\u5730\u770b\u51fa\u5404\u4e2a\u65b9\u6cd5\u4e4b\u95f4\u7684\u8f6c\u5316\u5173\u7cfb\uff0c\u4e8e\u662f\u6211\u4eec\u53ef\u4ee5\u753b\u4e00\u4e2a\u72b6\u6001\u673a\uff1a</p> <pre><code>graph LR;\nA[\"case 1\"]\nB[\"case 2\"]\nC[\"case 3\"]\nD([\"finish\"])\n\nA ===&gt;|\"C\"| B ---&gt;|\"R\"| C\nA ===&gt;|\"C\"| A ---&gt;|\"C\"| D\nA ===&gt;|\"C\"| C ---&gt;|\"C&amp;R\"| D</code></pre> <p>\u6ce8\u610f\uff0c\u72b6\u6001\u673a\u4e2d\u7684\u7c97\u7ebf\u8868\u793a\u8f6c\u6362\u8fc7\u7a0b\u4e2d\uff0c\u6211\u4eec\u5173\u6ce8\u7684\u201c\u5b50\u6811\u201d\u5411\u4e0a\u6500\u5347\u4e86\u4e00\u7ea7\uff1b\u800c\u7ec6\u7ebf\u8868\u793a\u6211\u4eec\u5173\u6ce8\u7684\u5b50\u6811\u4ecd\u7136\u662f\u8fd9\u4e00\u5c42\u7684\u90a3\u4e00\u68f5\u3002\u4ee5\u53ca\uff0c<code>C</code> \u8868\u793a\u67d3\u8272\u64cd\u4f5c\uff0c<code>R</code> \u8868\u793a\u65cb\u8f6c\u64cd\u4f5c\u3002</p> <p>\u5176\u4e2d\uff0c\u4efb\u4f55\u4e00\u4e2a\u60c5\u51b5\u90fd\u53ef\u4ee5\u4f5c\u4e3a\u4e00\u4e2a\u521d\u59cb\u60c5\u51b5\u3002\u6240\u4ee5\u53ef\u4ee5\u6570\u51fa\uff0c\u5230\u8fbe finish \u7684\u8def\u5f84\u4e2d\uff0c\u6700\u591a\u51fa\u73b0 2 \u6b21 Rotation\uff08case 2 -&gt; case 3 -&gt; finish\uff09\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec02/#\u5220\u9664","title":"\u5220\u9664","text":"<p>\u5173\u4e8e\u5220\u9664\u64cd\u4f5c\uff0c\u4e0b\u9762\u8fd9\u4e2a\u89c6\u9891\u8bb2\u7684\u5f88\u6e05\u6670\uff01\u53ea\u4e0d\u8fc7 case 1 \u53ef\u80fd\u8fd8\u6709\u4e9b\u7ec6\u8282\u9700\u8981\u6ce8\u610f\u3002</p> <p>\ud83d\udc49 \u7ea2\u9ed1\u6811\u5feb\u901f\u5165\u95e8 - 04\u5220\u9664</p> <p>\u8981\u5220\u9664\u67d0\u4e2a\u8282\u70b9 x\uff0c\u6211\u4eec\u9996\u5148\u8981\u627e\u5230\u5b83\uff0c\u5728 BST \u4e2d\u627e\u5230\u67d0\u4e2a x \u7684\u5f00\u9500\u4e3a \\(O(\\log N)\\)\u3002\u63a5\u4e0b\u6765\u6211\u4eec\u8981\u5220\u9664\u8fd9\u4e2a\u4efb\u610f\u4f4d\u7f6e\u7684\u8282\u70b9\uff0c\u8fd9\u52bf\u5fc5\u8ba9\u7ea2\u9ed1\u6811\u7684\u7ed3\u6784\u53d1\u751f\u53d8\u5316\u3002\u6b64\u5916\uff0c\u7ea2\u9ed1\u6027\u8d28\u7684\u7ef4\u62a4\u4e5f\u662f\u4e00\u4e2a\u8ba9\u4eba\u5934\u75bc\u7684\u95ee\u9898\uff0c\u56e0\u6b64\uff0c\u6211\u4eec\u5bf9\u8fd9\u4e9b\u60c5\u51b5\u505a\u5206\u7c7b\u8ba8\u8bba\uff1a</p> \u6ca1\u6709\u975e<code>NIL</code>\u5b50\u8282\u70b9 \u6709\u4e00\u4e2a\u975e<code>NIL</code>\u5b50\u8282\u70b9 \u6709\u4e24\u4e2a\u975e<code>NIL</code>\u5b50\u8282\u70b9 \u76f4\u63a5\u7528<code>NIL</code>\u66ff\u4ee3 \u76f4\u63a5\u5220\u9664\uff0c\u7528\u5b50\u8282\u70b9\u66ff\u4ee3\u5b83 \u5c06\u503c\u4e0e\u5de6\u5b50\u6811\u6700\u5927\u503c\u6216\u53f3\u5b50\u6811\u6700\u5c0f\u503c\u4ea4\u6362\uff0c\u989c\u8272\u4e0d\u6362\uff0c\u7136\u540e\u5220\u9664\u76ee\u6807\u70b9 <p>\u5176\u4e2d\uff0c\u6bcf\u4e00\u9879\u64cd\u4f5c\u90fd\u4f1a\u5bfc\u81f4\u4e00\u4e2a\u70b9\u7684\u6d88\u5931\uff08\u6bd5\u7adf\u662f\u5220\u9664\uff09\uff0c\u800c\u5982\u679c\u6d88\u5931\u7684\u662f\u7ea2\u8272\u8282\u70b9\uff0c\u90a3\u4e48\u5c06\u4e0d\u4f1a\u5f71\u54cd\u9ed1\u9ad8\uff1b\u800c\u5982\u679c\u6d88\u5931\u7684\u662f\u9ed1\u8272\u8282\u70b9\uff0c\u90a3\u4e48\u5c06\u4f1a\u5bfc\u81f4\u9ed1\u9ad8\u51cf\u5c11\u4e00\uff0c\u6b64\u65f6\u6211\u4eec\u9700\u8981\u505a\u8fdb\u4e00\u6b65\u64cd\u4f5c\u3002</p> <ul> <li> TODO: \u8fd9\u91cc\u9700\u8981\u914d\u56fe\u8bb2\u6e05\u695a\u8282\u70b9\u7684\u5177\u4f53\u53d8\u6362\u5230\u5e95\u662f\u600e\u4e48\u6837\u7684\uff0c\u5c24\u5176\u662f\u8282\u70b9\u989c\u8272\u53d8\u5316\u5230\u5e95\u662f\u600e\u4e48\u4e00\u56de\u4e8b\uff0c\u4e4b\u540e\u5927\u6982\u9700\u8981\u91cd\u5199</li> </ul> <p>\u8bf4\u660e</p> <p>\u867d\u7136\u6211\u60f3\u5c3d\u53ef\u80fd\u62df\u5408 cy \u7684 ppt\uff0c\u4f46\u662f\u6211\u7b2c\u4e00\u904d\u5b9e\u5728\u6ca1\u770b\u61c2\uff0c\u6240\u4ee5 case \u7684\u7f16\u53f7\u6211\u5c31\u6309\u7167\u4e0a\u9762\u90a3\u4e2a\u89c6\u9891\u6765\u4e86\u3002</p> <p>\u8fd9\u662f case \u5e8f\u53f7\u7684\u5bf9\u5e94\u5173\u7cfb\uff1a</p> my cy's my cy's case 1 case 2 case 2 case 4 case 3 case 3 case 4 case 1 <p>\u6211\u4eec\u6839\u636e\u60c5\u51b5\uff0c\u5c06\u60c5\u51b5\u5206\u4e3a\u56db\u79cd\uff1a</p> <p></p> <p>\u9700\u8981\u505a\u4e00\u4e0b\u7b80\u5355\u8bf4\u660e\uff0c\u7c7b\u6bd4\u6211\u4eec\u5728#\u63d2\u5165\uff0c\u5728\u5220\u9664\u8fc7\u7a0b\u4e2d\u4e5f\u5b58\u5728\u9700\u8981\u5411\u4e0a\u9012\u5f52\u7684\u60c5\u51b5\u3002\u4e0e\u300c\u88ab\u63d2\u5165\u7684\u7ea2\u8272\u8282\u70b9\u300d\u7c7b\u4f3c\u7684\uff0c\u6211\u4eec\u8fd9\u91cc\u7684\u300c\u9700\u8981\u88ab\u5220\u9664\u7684\u76ee\u6807\u70b9\u300d\uff0c\u4e5f\u5e94\u5f53\u88ab\u770b\u4f5c\u300c\u5bfc\u81f4\u8c03\u6574\u51fa\u73b0\u7684\u5b50\u6811\u300d\uff0c\u66f4\u8fdb\u4e00\u6b65\u7684\uff0c\u53ef\u4ee5\u5b9a\u4e49\u6210\u300c\u7531\u4e8e\u5220\u9664\u4e86\u67d0\u4e2a\u7ed3\u70b9\uff0c\u9ed1\u9ad8 -1 \u7684\u5b50\u6811\u300d\uff0c\u8bf7\u8bb0\u4f4f\u8fd9\u4e2a\u5b9a\u4e49\uff0c\u8fd9\u4f1a\u8ba9\u4e4b\u540e\u7684\u9012\u5f52\u64cd\u4f5c\u53d8\u5f97\u81ea\u7136\u3002</p> <p>\u4f55\u65f6\u5220\u9664\u90a3\u4e2a\u7ed3\u70b9\uff1f</p> <p>\u867d\u7136\u6211\u4eec\u5bf9\u300c\u9700\u8981\u88ab\u5220\u9664\u7684\u76ee\u6807\u70b9\u300d\u8fdb\u884c\u4e86\u9012\u5f52\u7684\u6269\u5c55\u5b9a\u4e49\uff0c\u4f46\u662f\u5728\u7b2c\u4e00\u5c42\u6211\u4eec\u5c31\u53ef\u4ee5\u76f4\u63a5\u5c06\u5b83\u5220\u6389\u4e86\u3002\u800c\u8fd9\u4e2a\u70b9\u88ab\u5220\u9664\u9020\u6210\u7684\u5f71\u54cd\uff0c\u5df2\u7ecf\u7531\u300c\u7531\u4e8e\u5220\u9664\u7ed3\u70b9\uff0c\u9ed1\u9ad8 -1 \u7684\u5b50\u6811\u300d\u7ee7\u627f\u4e86\u3002</p> <p>\u5728\u4e4b\u540e\u7684\u914d\u56fe\u4e2d\uff0c\u6211\u4eec\u90fd\u4e0d\u4f1a\u5c55\u793a x \u662f\u5982\u4f55\u88ab\u5220\u6389\u7684\uff0c\u800c\u662f\u5728\u7ed3\u679c\u56fe\u4e2d\u4fdd\u7559 x\u3002\u5982\u679c\u8bf4 x \u5c31\u662f\u6211\u4eec\u4e00\u5f00\u59cb\u8981\u5220\u9664\u7684\u90a3\u4e2a\u70b9\uff0c\u90a3\u4e48\u6211\u4eec\u5e94\u5f53\u5220\u6389 x\uff0c\u76f4\u63a5\u6362\u6210 <code>NIL</code>\uff1b\u5982\u679c x \u662f\u5728\u4f20\u9012\u8fc7\u7a0b\u4e2d\uff0c\u8868\u793a\u300c\u9ed1\u9ad8 -1 \u7684\u5b50\u6811\u300d\u7684\u6839\uff0c\u90a3\u4e48\u4e0d\u7528\u505a\u989d\u5916\u5904\u7406\u3002</p> <p>\u7c7b\u4f3c\u4e8e\u6211\u4eec\u5728\u300cInsertion / case 3\u300d\u91cc\u63d0\u5230\u7684\u201c\u4e0b\u653e\u201d\u9ed1\u8282\u70b9\uff0c\u5220\u9664\u64cd\u4f5c\u7684\u601d\u8def\u57fa\u672c\u4e0a\u662f\u201c\u4e0a\u653e\u201d\u9ed1\u8282\u70b9\uff0c\u6216\u8005\u8bf4\u201c\u5438\u7eb3\u201d\u9ed1\u8282\u70b9\u3002\u8fd9\u4e2a\u201c\u5438\u7eb3\u201d\u7684\u884c\u4e3a\uff0c\u6307\u7684\u662f\u4e00\u4e2a\u9ed1\u70b9\uff0c\u539f\u6765\u53ea\u4e3a\u53f3\u5b50\u6811\u4e2d\u7684\u6240\u6709\u8def\u5f84\u63d0\u4f9b\u4e86\u9ed1\u9ad8\uff0c\u73b0\u5728\u7531\u4e8e\u5b83\u7684 sibling \u5b50\u6811\u4e2d\u5c11\u4e86\u4e00\u4e2a\u9ed1\u8272\u8282\u70b9\uff0c\u6211\u4eec\u5c06\u8fd9\u4e2a\u9ed1\u8272\u8282\u70b9\u8f6c\u79fb\u5230\u5b83\u4eec\u7684\u5bb6\u957f\u8282\u70b9\u8282\u70b9\uff0c\u4e8e\u662f\u8fd9\u4e2a\u8282\u70b9\u540c\u65f6\u4e3a\u5de6\u53f3\u5b50\u6811\u7684\u6240\u6709\u8def\u5f84\u90fd\u8d21\u732e\u4e86\u9ed1\u9ad8\u3002</p> <p>\u63a5\u4e0b\u6765\u6211\u4eec\u9010\u4e2a\u5206\u6790\u53d8\u5316\uff1a</p> <p>Deletion / case 1</p> <p>\u867d\u7136\u5927\u90e8\u5206\u6559\u7a0b\u90fd\u628a case 1 \u5f53\u4f5c\u4e00\u4e2a case\uff0c\u4f46\u662f\u6211\u89c9\u5f97\u5b8c\u5168\u53ef\u4ee5\u628a\u5b83\u6309\u7167 a \u8282\u70b9\u7684\u7ea2\u9ed1\uff0c\u5206\u4e3a\u4e24\u79cd\u60c5\u51b5\u3002</p> <p></p> <p>Deletion / case 1.1</p> <p>\u5f53 a \u4e3a\u7ea2\u6839\u65f6\uff0c\u7531\u4e8e x \u8d21\u732e\u4e86\uff08\u76f8\u5bf9\u4e8e\u539f\u7ea2\u9ed1\u6811\uff09-1 \u7684\u9ed1\u9ad8\uff0c\u4e3a\u4e86\u4fdd\u8bc1\u6574\u4e2a\u5b50\u6811\u8d21\u732e\u7684\u9ed1\u9ad8\u4e0d\u53d8\uff0c\u6211\u4eec\u8003\u8651\u628a w \u7684\u9ed1\u9ad8\u201c\u4e0a\u653e\u201d\u5230 a \u4e0a\uff0c\u4e5f\u5c31\u662f\u4ece\u4e0b\u9762\u201c\u5438\u7eb3\u201d\u4e0a\u6765\u3002</p> <p></p> <p>Deletion / case 1.2</p> <p>\u5f53 a \u4e3a\u9ed1\u6839\u65f6\uff0c\u6211\u4eec\u6ca1\u6709\u7a7a\u4f59\u7684\u4f4d\u7f6e\u6765\u201c\u5438\u7eb3\u201d w \u7684\u9ed1\u9ad8\uff0c\u4f46\u662f\u5de6\u5b50\u6811\u548c\u53f3\u5b50\u6811\u7684\u4e0d\u5e73\u8861\u662f\u5fc5\u987b\u89e3\u51b3\u7684\uff0c\u800c\u6211\u4eec\u7edd\u4e0d\u80fd\u5bc4\u5e0c\u671b\u4e8e\u201c\u5728\u4e0d\u77e5\u9053\u6709\u6ca1\u6709\u7ea2\u8272\u8282\u70b9\u7684 b \u548c c \u7684\u5b50\u6811\u4e2d\u53bb\u5bfb\u627e\u7ea2\u8272\u8282\u70b9\u201d\u8fd9\u4e2a\u60f3\u6cd5\u3002</p> <p>\u6240\u4ee5\u6211\u4eec\u53ef\u4ee5\u4eff\u7167\u300cInsertion / case 3\u300d\uff0c\u5c06\u6574\u4e2a\u6811\u6807\u8bb0\u4e3a\u7070\u8272\u2014\u2014\u300c\u7531\u4e8e\u5220\u9664\u7ed3\u70b9\uff0c\u9ed1\u9ad8 -1 \u7684\u5b50\u6811\u300d\uff0c\u7136\u540e\u8fdb\u4e00\u6b65\u6839\u636e\u5176\u5bb6\u957f\u8282\u70b9\u7684\u60c5\u51b5\u9012\u5f52\u5230\u5176\u4ed6 case\u3002\u5176\u4e2d\uff0c\u5f53\u6211\u4eec\u9012\u5f52\u5230 a \u662f\u6574\u4e2a\u6811\u7684\u6839\u65f6\u53ef\u4ee5\u9000\u51fa\uff0c\u56e0\u4e3a\u8fd9\u76f8\u5f53\u4e8e\u6574\u4e2a\u6811\u7684\u9ed1\u9ad8 -1\uff0c\u4e0d\u5f71\u54cd\u7ea2\u9ed1\u6027\u8d28\u3002</p> <p></p> <p>Deletion / case 2</p> <p>\u753b\u4e0d\u52a8\u56fe\u4e86\uff0c\u5148\u8bed\u8a00\u63cf\u8ff0\u4e00\u4e0b\u3002</p> <ol> <li>\u5c06 w \u67d3\u4e3a a \u7684\u989c\u8272\uff0c\u518d\u5c06 a \u548c c \u67d3\u6210\u9ed1\u8272\uff1b</li> <li>\u5c06 a \u5de6\u65cb\uff0c\u4f7f w \u6210\u4e3a\u8fd9\u4e2a\u5b50\u6811\u65b0\u7684\u6839\uff0ca \u6210\u4e3a w \u7684\u5de6\u513f\u5b50\uff0cb \u6210\u4e3a a \u7684\u53f3\u513f\u5b50\uff1b</li> <li>\u8c03\u6574\u7ed3\u675f\uff1b</li> </ol> <p>Deletion / case 3</p> <p>\u753b\u4e0d\u52a8\u56fe\u4e86\uff0c\u5148\u8bed\u8a00\u63cf\u8ff0\u4e00\u4e0b\u3002</p> <ol> <li>\u4ea4\u6362 b \u548c w \u7684\u989c\u8272\uff1b</li> <li>\u5c06 w \u53f3\u65cb\uff0c\u4f7f b \u6210\u4e3a a \u7684\u53f3\u513f\u5b50\uff0cw \u6210\u4e3a b \u7684\u53f3\u513f\u5b50\uff0cb \u7684\u53f3\u513f\u5b50\u6210\u4e3a w \u7684\u5de6\u513f\u5b50\uff1b</li> <li>\u6b64\u65f6\u60c5\u51b5\u8f6c\u5316\u4e3a case 2\uff1b</li> </ol> <p>Deletion / case 4</p> <p>\u753b\u4e0d\u52a8\u56fe\u4e86\uff0c\u5148\u8bed\u8a00\u63cf\u8ff0\u4e00\u4e0b\u3002</p> <ol> <li>\u4ea4\u6362 a \u548c w \u7684\u989c\u8272\uff1b</li> <li>\u5c06 a \u5de6\u65cb\uff0c\u4f7f w \u6210\u4e3a\u8fd9\u4e2a\u5b50\u6811\u65b0\u7684\u6839\uff0ca \u6210\u4e3a w \u7684\u5de6\u513f\u5b50\uff0cb \u6210\u4e3a a \u7684\u53f3\u513f\u5b50\uff1b</li> <li>\u6b64\u65f6\u6839\u636e\u5b50\u6811 a \u7684\u60c5\u51b5\uff0c\u8f6c\u5316\u4e3a case 1.1 / case 2 / case 3\uff1b</li> </ol> \u533a\u5206 case 1.1 \u548c case 1.2\u4e0d\u533a\u5206 case 1.1 \u548c case 1.2 <pre><code>graph LR;\nA1[\"case 1.1\"]\nA2[\"case 1.2\"]\nB[\"case 2\"]\nC[\"case 3\"]\nD[\"case 4\"]\nE[\"finish\"]\n\nA1 ---&gt;|\"C\"| E\nA2 ===&gt;|\"C\"| A1\nA2 ===&gt;|\"C\"| A2\nA2 ===&gt;|\"C\"| B\nA2 ===&gt;|\"C\"| C\nA2 ===&gt;|\"C\"| D\nC ---&gt;|\"C&amp;R\"| B ---&gt;|\"C&amp;R\"| E\nD ===&gt;|\"C&amp;R\"| A1\nD ===&gt;|\"C&amp;R\"| B\nD ===&gt;|\"C&amp;R\"| C</code></pre> <pre><code>graph LR;\nA[\"case 1\"]\nB[\"case 2\"]\nC[\"case 3\"]\nD[\"case 4\"]\nE[\"finish\"]\n\nA ---&gt;|\"C\\nfrom case 1.1\"| E\nA ===&gt;|\"C\\nfrom case 1.2\"| A\nA ===&gt;|\"C\\nfrom case 1.2\"| B\nA ===&gt;|\"C\\nfrom case 1.2\"| C\nA ===&gt;|\"C\\nfrom case 1.2\"| D\nC ---&gt;|\"C&amp;R\"| B ---&gt;|\"C&amp;R\"| E\nD ===&gt;|\"C&amp;R\\nto case 1.1 \"| A\nD ===&gt;|\"C&amp;R\"| B\nD ===&gt;|\"C&amp;R\"| C</code></pre> <p>\u6ce8\u610f\uff0c\u72b6\u6001\u673a\u4e2d\u7684\u7c97\u7ebf\u8868\u793a\u8f6c\u6362\u8fc7\u7a0b\u4e2d\uff0c\u6211\u4eec\u5173\u6ce8\u7684\u201c\u5b50\u6811\u201d\u5411\u4e0a\u6216\u5411\u4e0b\u8f6c\u79fb\u4e86\u4e00\u7ea7\uff08\u7531 case 4 \u51fa\u53d1\u65f6\u4e0b\u964d\uff0c\u7531 case 1.2 \u51fa\u53d1\u65f6\u4e0a\u5347\uff09\uff1b\u800c\u7ec6\u7ebf\u8868\u793a\u6211\u4eec\u5173\u6ce8\u7684\u5b50\u6811\u4ecd\u7136\u662f\u8fd9\u4e00\u5c42\u7684\u90a3\u4e00\u68f5\u3002\u4ee5\u53ca\uff0c<code>C</code> \u8868\u793a\u67d3\u8272\u64cd\u4f5c\uff0c<code>R</code> \u8868\u793a\u65cb\u8f6c\u64cd\u4f5c\u3002</p> <p>\u5176\u4e2d\uff0c\u4efb\u4f55\u4e00\u4e2a\u60c5\u51b5\u90fd\u53ef\u4ee5\u4f5c\u4e3a\u4e00\u4e2a\u521d\u59cb\u60c5\u51b5\u3002\u6240\u4ee5\u53ef\u4ee5\u6570\u51fa\uff0c\u5230\u8fbe finish \u7684\u8def\u5f84\u4e2d\uff0c\u6700\u591a\u51fa\u73b0 3 \u6b21 Rotation\uff08case 4 -&gt; case 3 -&gt; case 2 -&gt; finish\uff09\u3002</p> <p>\u6839\u636e\u524d\u9762\u72b6\u6001\u673a\u7684\u76f8\u5173\u5185\u5bb9\uff0c\u6211\u4eec\u4e0d\u96be\u5f97\u5230\u8fd9\u5f20\u8868\u683c\uff0c\u5b83\u7edf\u8ba1\u7684\u662f Rotation \u5728\u4e0d\u540c\u6570\u636e\u7ed3\u6784\u3001\u4e0d\u540c\u64cd\u4f5c\u4e2d\u51fa\u73b0\u7684\u6570\u91cf\uff1a</p> Option AVL Tree RB Tree Insertion \\(\\leq 2\\) \\(\\leq 2\\) Deletion \\(O(\\log N)\\) \\(\\leq 3\\)"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec02/#b-tree","title":"B+ Tree","text":"<p>link</p> <p>OI Wiki: https://oi-wiki.org/ds/bplus-tree/</p> <p>Wiki: https://en.wikipedia.org/wiki/B%2B_tree</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec02/#\u6982\u5ff5_1","title":"\u6982\u5ff5","text":"<p>B+ \u6811\u662f\u4e00\u79cd\u7528\u6811\u72b6\u5f62\u5f0f\u7ef4\u62a4\u6709\u5e8f\u6570\u5217\u6bd4\u8f83\u4fe1\u606f\u7684\u6570\u636e\u7ed3\u6784\uff0c\u5176\u589e\u6539\u64cd\u4f5c\u62e5\u76f8\u5bf9\u4e8e\u4e8c\u53c9\u6811\u7ed3\u6784\u66f4\u52a0\u7a33\u5b9a\u7684\u5bf9\u6570\u65f6\u95f4\u590d\u6742\u5ea6\uff0c\u901a\u5e38\u7528\u4e8e\u6570\u636e\u5e93\u548c\u64cd\u4f5c\u7cfb\u7edf\u7684\u6587\u4ef6\u7cfb\u7edf\u4e2d\u3002</p> <p>B+ Tree</p> <p>\u5982\u4e0b\u56fe\u5c31\u662f\u4e00\u9897 \\(M=4\\) \u7684 B+ \u6811\uff0c\u53ef\u4ee5\u5bf9\u7167\u7740\u8fd9\u4e2a\u4f8b\u5b50\u6765\u7406\u89e3\u6027\u8d28\u3002</p> <p></p> <p>\u66f4\u4e00\u822c\u5730\u6765\u8bf4\uff0cB+ \u6811\u6ee1\u8db3\u5982\u4e0b\u6027\u8d28\uff1a</p> <p>property of B+ Tree</p> <p>@cy's PPT</p> <ol> <li>The root is either a leaf or has between \\(2\\) and \\(M\\) children.</li> <li>All nonleaf nodes (except the root) have between \\(\\lceil M/2 \\rceil\\) and M children.</li> <li>All leaves are at the same depth.</li> </ol> <p>Assume each nonroot leaf also has between \\(\\lceil M/2 \\rceil\\) and \\(M\\) children.</p> <p>\u6240\u6709\u771f\u5b9e\u7684\u6570\u636e\u90fd\u88ab\u5b58\u50a8\u5728\u53f6\u5b50\u7ed3\u70b9\u4e2d\uff0c\u5f62\u6210\u4e00\u4e2a\u6709\u5e8f\u7684\u6570\u5217\u3002\u800c\u975e\u53f6\u5b50\u7ed3\u70b9\u4e2d\u7b2c <code>i</code> \u4e2a\u952e\u503c\u7b49\u4e8e\u5176\u7b2c <code>i+1</code> \u68f5\u5b50\u6811\u7684\u6700\u5c0f\u503c\uff08\u5728\u4e0a\u56fe\u4e2d\u8868\u73b0\u4e3a\u989c\u8272\u76f8\u540c\u7684\u4e00\u5bf9\u4e0a\u4e0b\u7ed3\u70b9\uff09\uff0c\u56e0\u6b64\u975e\u53f6\u7ed3\u70b9\u6700\u591a\u5b58 \\(M-1\\) \u4e2a\u503c\u3002</p> \u53d1\u73b0 <p>\u4e8e\u662f\u6211\u4eec\u53d1\u73b0\u8fd9\u6837\u4e00\u4e2a\u6027\u8d28\uff1a\u5728\u5b58\u50a8\u6570\u503c\u4e0d\u91cd\u590d\u7684\u60c5\u51b5\u4e0b\uff0c\u975e\u53f6\u7ed3\u70b9\u5b58\u50a8\u7684\u952e\u503c\u90fd\u4e0d\u76f8\u540c\u3002</p> <p>\u8bc1\u660e\u5f88\u7b80\u5355\uff0c\u5bf9\u4e8e\u4efb\u610f\u4e00\u4e2a\u975e\u53f6\u5b50\u7ed3\u70b9\uff0c\u5b83\u5b58\u50a8\u7684\u503c\u5fc5\u5b9a\u4e0d\u4f1a\u88ab\u5b83\u7684\u5b50\u8282\u70b9\u5b58\u50a8\uff08\u5982\u679c\u5b83\u7684\u5b50\u8282\u70b9\u4e0d\u662f\u53f6\u5b50\uff09\uff0c\u56e0\u4e3a\u5b83\u5b58\u7684\u662f\u5b83\u7684\u5b50\u8282\u70b9\u7684\u7b2c\u4e00\u4e2a\u5b50\u6811\u7684\u6700\u5c0f\u503c\uff0c\u800c\u5b83\u7684\u5b50\u8282\u70b9\u5b58\u7684\u662f\u7b2c\u4e8c\u4e2a\u5b50\u6811\u5f00\u59cb\u7684\u6700\u5c0f\u503c\u3002</p> <p>\u6211\u4eec\u79f0\u8fd9\u6837\u7684\u6811\u4e3a\u4e00\u4e2a \\(M\\) \u9636(order) B+ \u6811\u3002\u5bf9\u4e8e\u5e38\u89c1\u7684 \\(M\\)\uff0c\u6bd4\u5982\u4e00\u68f5 \\(4\\) \u9636 B+ \u6811\uff0c\u6211\u4eec\u4e5f\u79f0\u4e4b\u4e3a\u4e00\u68f5 2-3-4 \u6811\uff0c\u4e00\u822c \\(M\\) \u7684\u9009\u62e9\u4e3a 3 \u6216 4\u3002</p> <p>\u7279\u522b\u8bf4\u660e\uff0c\u5bf9\u4e8e B+ \u6811\uff0c\u5c06\u5b83\u7684\u53f6\u5b50\u7ed3\u70b9\u62fc\u63a5\u8d77\u6765\uff0c\u5b9e\u9645\u4e0a\u5c31\u662f\u4e00\u4e2a\u6709\u5e8f\u6570\u5217\u3002</p> <p>\u62bd\u8c61\u5730\u6765\u8bf4\u5c31\u662f\uff0c\u6211\u4eec\u628a\u4e00\u4e2a\u6570\u5217\u76f8\u5bf9\u5747\u5300\u7684\u5206\u4e3a \\(m\\) \u5757\uff0c\u7136\u540e\u628a\u5206\u754c\u7684\u6570\u62ff\u51fa\u6765\u3002\u5f53\u6211\u4eec\u53bb\u67e5\u627e\u6216\u63d2\u5165\u65f6\uff0c\u53ea\u9700\u8981\u548c\u8fd9\u4e9b\u8fb9\u754c\u6570\u8fdb\u884c\u6bd4\u8f83\uff0c\u5c31\u77e5\u9053\u5b83\u5e94\u8be5\u653e\u5728\u54ea\u4e00\u5757\u91cc\u3002\u518d\u4e0d\u65ad\u7ec6\u5316\u7c92\u5ea6\uff0c\u7528\u7c7b\u4f3c\u4e8e\u201c\\(m\\) \u5206\u201d\u7684\u601d\u60f3\u6765\u627e\u5230\u76ee\u6807\u4f4d\u7f6e\u3002</p> <p>\u5728\u6211\u770b\u6765\u8fd9\u4e2a\u5b9a\u4e49\u975e\u5e38\u6e05\u6670\uff0c\u5c31\u662f\u5c06\u6574\u4e2a\u5e8f\u5217\u6309\u7167\u4e0d\u540c\u7c92\u5ea6\u5212\u5206\uff0c\u7136\u540e\u7531\u5927\u5230\u5c0f\u8fdb\u884c\u903c\u8fd1\u3002</p> <p>depth of B+ Tree</p> <p>\u7531\u4e8e\u5b83\u5728\u7a7a\u95f4\u6700\u6d6a\u8d39\u7684\u60c5\u51b5\u4e0b\u662f\u4e00\u68f5 \\(\\lceil M/2 \\rceil\\) \u53c9\u6811\uff0c\u6240\u4ee5 B+ \u6811\u7684\u6df1\u5ea6\u662f \\(O(\\lceil \\log_{\\lceil M/2 \\rceil} N \\rceil)\\)\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec02/#\u64cd\u4f5c_1","title":"\u64cd\u4f5c","text":"<p>\u7531\u4e8e B+ \u6811\u7684\u6027\u8d28\u5341\u5206\u81ea\u7136\uff0c\u6240\u4ee5\u5b83\u7684\u64cd\u4f5c\u4ece\u601d\u60f3\u5c42\u9762\u4e0a\u6765\u8bf4\u4e5f\u975e\u5e38\u7b80\u5355\u3002\u5176\u66f4\u591a\u7684\u96be\u5ea6\u5728\u4e8e\u5b9e\u73b0\u4e0a\u3002</p> <p>\u5173\u4e8e\u5b9e\u73b0\u7684\u5efa\u8bae</p> <p>\u7531\u4e8e B+ \u6811\u5173\u4e8e\u5185\u90e8\u8282\u70b9\u548c\u53f6\u5b50\u7684\u5b9a\u4e49\u5341\u5206\u5272\u88c2\uff08\u867d\u7136\u7ea2\u9ed1\u6811\u53f6\u4e5f\u5f88\u5272\u88c2\uff0c\u4f46\u662f\u6bd5\u7adf\u7ea2\u9ed1\u6811\u7684\u53f6\u5b50\u4e0d\u9700\u8981\u4ec0\u4e48\u64cd\u4f5c\uff0c\u4f46\u662f B+ \u6811\u9700\u8981\uff09\uff0c\u6240\u4ee5\u5728\u5b9e\u73b0\u8fc7\u7a0b\u4e2d\u4f1a\u9047\u5230\u4e00\u4e9b\u9ebb\u70e6\u3002</p> <p>\u6211\u4e2a\u4eba\u5efa\u8bae\uff0c\u5982\u679c\u4f60\u5341\u5206\u719f\u6089 oop\uff0c\u90a3\u4e48\u53ef\u4ee5\u5c1d\u8bd5\u7528\u591a\u6001\u6765\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\u3002\u53cd\u6b63\u6211\u5b9e\u73b0 B+ \u6811\u7684\u65f6\u5019\u5bf9 cpp \u7684 oop \u6211\u8bf4\u4e0d\u4e0a\u5341\u5206\u719f\u7ec3\uff0c\u6240\u4ee5\u6211\u76f4\u63a5\u65e0\u8111\u4f7f\u7528 <code>struct</code> with tag \u5b9e\u73b0\u4e86\u3002</p> <p>\u800c\u5728\u5f00\u59cb\u5199\u4ee3\u7801\u4e4b\u524d\uff0c\u6211\u5f3a\u70c8\u5efa\u8bae\u5927\u5bb6\u6309\u7167\u6211\u4e0b\u9762\u505a\u56fe\u7684\u683c\u5f0f\uff0c\u6a21\u62df\u4e00\u904d\u5404\u4e2a\u64cd\u4f5c\uff01\u5e76\u5728\u6a21\u62df\u8fc7\u7a0b\u4e2d\uff0c\u89c2\u5bdf\u6570\u636e\u7684\u6d41\u52a8\u4ee5\u53ca\u8282\u70b9\u7684\u7ed3\u6784\u53d8\u5316\u3002</p> <p>\u6b64\u5916\uff0c\u5728\u8ba8\u8bba\u8fd9\u4e9b\u64cd\u4f5c\u65f6\uff0c\u5148\u8ba9\u6211\u4eec\u5ffd\u7565\u5982\u4f55\u4ece\u7a7a\u5efa\u7acb\u8d77\u4e00\u4e2a B+ \u6811\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec02/#\u67e5\u627e","title":"\u67e5\u627e","text":"<p>\u548c\u4e8c\u53c9\u6811\u7684\u67e5\u627e\u5341\u5206\u76f8\u4f3c\uff0c\u6240\u4ee5\u8fd9\u91cc\u53ea\u6a21\u62df\u4e00\u4e0b\u4e3e\u4e2a\u4f8b\u5b50\u3002</p> <p></p> <p>\u4f8b\u5982\uff0c\u6211\u4eec\u5728\u4e0a\u9762\u8fd9\u68f5\u6811\u4e2d\u627e <code>43</code> \u8fd9\u4e2a\u503c\uff0c\u6a59\u8272\u90e8\u5206\u8868\u793a\u6211\u4eec\u7684\u7126\u70b9\u3002</p> <p>Find(43)</p> Frame 1Frame 2Frame 3 <p></p> <p>\u6211\u4eec\u53d1\u73b0\u6709 \\(21 \\leq 43 &lt; 48\\)\uff0c\u6240\u4ee5\u987a\u7740\u6807\u8bc6\u7684\u6a59\u8272\u6307\u9488\u5411\u4e0b\u3002</p> <p></p> <p>\u6211\u4eec\u53d1\u73b0\u6709 \\(41 \\leq 43\\)\uff0c\u6240\u4ee5\u987a\u7740\u6807\u8bc6\u7684\u6a59\u8272\u6307\u9488\u5411\u4e0b\u3002</p> <p></p> <p>\u5df2\u7ecf\u8d70\u5230\u53f6\u5b50\u7ed3\u70b9\uff0c\u6700\u540e\u53d1\u73b0\u6211\u4eec\u8981\u627e\u7684 <code>43</code>\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec02/#\u63d2\u5165_1","title":"\u63d2\u5165","text":"<p>\u63d2\u5165\u7684\u65b9\u6cd5\u4e5f\u76f8\u5bf9\u6734\u7d20\u7b80\u5355\uff0c\u5c31\u662f\u627e\u5230\u8be5\u63d2\u5165\u7684\u5730\u65b9\u4ee5\u540e\u63d2\u5165\u5373\u53ef\u3002</p> <p>\u53ea\u4e0d\u8fc7\u9700\u8981\u6ce8\u610f\u4e00\u4ef6\u4e8b\uff0c\u5f53\u8fd9\u4e2a\u63d2\u5165\uff0c\u5bfc\u81f4\u4e86 B+ \u6811\u7684\u6027\u8d28\u4e0d\u518d\u6210\u7acb\u65f6\uff0c\u5373\u5bfc\u81f4\u5176\u5bb6\u957f\u8282\u70b9\u7684\u5b50\u8282\u70b9\u6570\u91cf\u4e3a \\(M+1\\) \u65f6\uff0c\u6211\u4eec\u9700\u8981\u5c06\u8fd9\u4e2a\u7ed3\u70b9\u5e73\u5747\u5206\u88c2\u6210\u4e24\u4e2a\uff0c\u6b64\u65f6\u663e\u7136\u6709\u4e24\u4e2a\u5b50\u6811\u7684\u8282\u70b9\u6570\u91cf\u90fd\u4e0d\u5c0f\u4e8e \\(\\lceil M+1 \\rceil\\)\u3002\u4f46\u8fd9\u8fd8\u4e0d\u591f\uff0c\u5206\u88c2\u5bfc\u81f4\u5bb6\u957f\u8282\u70b9\u7684\u5bb6\u957f\u8282\u70b9\u7684\u5b50\u8282\u70b9\u53d8\u591a\uff0c\u6240\u4ee5\u6211\u4eec\u8fd8\u5f97\u5411\u4e0a\u9012\u5f52\u3002</p> <p>\u4f9d\u7136\u662f\u8fdb\u884c\u4e00\u4e2a\u6a21\u62df\uff0c\u6211\u4eec\u6a21\u62df\u63d2\u5165 <code>46</code> \u548c <code>44</code>\u3002</p> <p>Insert(46), no split</p> Frame 1Frame 2Frame 3 <p></p> <p>\u540c\u67e5\u627e\uff0c\u7565\u3002</p> <p></p> <p>\u540c\u67e5\u627e\uff0c\u7565\u3002</p> <p></p> <p>\u627e\u5230\u8981\u585e\u7684\u4f4d\u7f6e\u4e86\uff0c\u53d1\u73b0\u8981\u585e\u7684\u5730\u65b9\u662f <code>45</code> \u7684\u540e\u9762\uff0c\u63d2\u5165\u4ee5\u540e\u53d1\u73b0\u4e00\u5171 4 \u4e2a\u6570\uff0c\u800c \\(M=4\\)\uff0c\u4e0d\u9700\u8981\u5206\u88c2\u3002</p> <p>Insert(44), split</p> Frame 1Frame 2Frame 3Frame 4Frame 5Frame 6 <p></p> <p>\u540c\u67e5\u627e\uff0c\u7565\u3002</p> <p></p> <p>\u540c\u67e5\u627e\uff0c\u7565\u3002</p> <p></p> <p>\u627e\u5230\u8981\u585e\u7684\u4f4d\u7f6e\u4e86\uff0c\u53d1\u73b0\u8981\u585e\u7684\u5730\u65b9\u662f <code>45</code> \u7684\u524d\u9762\uff0c\u63d2\u5165\u4ee5\u540e\u53d1\u73b0\u4e00\u5171 5 \u4e2a\u6570\uff0c\u800c \\(M=4\\)\uff0c\u9700\u8981\u5206\u88c2\uff01</p> <p></p> <p>\u5411\u4e0a\u9012\u5f52\uff0c\u6211\u4eec\u60b2\u75db\u5730\u53d1\u73b0\uff0c\u8fd9\u4e2a\u8282\u70b9\u5728\u5206\u88c2\u540e\u6709\u4e86 <code>5</code> \u4e2a\u5b50\u8282\u70b9\uff0c\u4e0d\u5f97\u4e0d\u518d\u6b21\u5206\u88c2\u3002</p> <p></p> <p>\u5411\u4e0a\u9012\u5f52\uff0c\u6211\u7684\u8001\u5929\u7237\u5440\uff0c\u600e\u4e48\u8fd8\u6ca1\u5230\u5934\uff01\u8fd9\u4e0b\u6211\u4eec\u8981\u5206\u88c2\u6839\u90e8\u4e86\uff01</p> <p></p> <p>\u7531\u4e8e\u6839\u90e8\u88ab\u88c2\u5f00\u4e86\uff0c\u6240\u4ee5\u6211\u4eec\u9700\u8981\u6dfb\u52a0\u4e00\u4e2a\u65b0\u7684\u6839\uff0c\u8fd9\u4e5f\u610f\u5473\u7740\u6811\u7684\u5c42\u6570\u589e\u9ad8\u4e86\u3002</p> <p>\u73b0\u5728\uff0c\u6211\u4eec\u7ec8\u4e8e\u5b8c\u6210\u4e86\u63d2\u5165\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec03/","title":"Lecture 3 | Inverted File Index","text":"<p> \u7ea6 1461 \u4e2a\u5b57  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 5 \u5206\u949f</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec03/#\u5012\u6392\u7d22\u5f15","title":"\u5012\u6392\u7d22\u5f15","text":"<p>\u5012\u6392\u7d22\u5f15\uff08inverted file index\uff09\u662f\u4e00\u79cd\u5e38\u89c1\u7684\u6587\u672c\u68c0\u7d22\u6280\u672f\uff0c\u7528\u4e8e\u5feb\u901f\u67e5\u627e\u5305\u542b\u7279\u5b9a\u5355\u8bcd\u6216\u77ed\u8bed\u7684\u6587\u6863\u3002\u5b83\u901a\u8fc7\u5c06\u5355\u8bcd\u6216\u77ed\u8bed\u4f5c\u4e3a\u5173\u952e\u5b57\uff0c\u5e76\u5c06\u5b83\u4eec\u51fa\u73b0\u5728\u6587\u6863\u4e2d\u7684\u4f4d\u7f6e\u8bb0\u5f55\u5728\u4e00\u4e2a\u7d22\u5f15\u4e2d\uff0c\u4ece\u800c\u652f\u6301\u5feb\u901f\u7684\u6587\u672c\u68c0\u7d22\u3002\u5728\u641c\u7d22\u8fc7\u7a0b\u4e2d\uff0c\u7cfb\u7edf\u53ef\u4ee5\u5feb\u901f\u5730\u5b9a\u4f4d\u5305\u542b\u6307\u5b9a\u5355\u8bcd\u6216\u77ed\u8bed\u7684\u6587\u6863\uff0c\u5e76\u8fd4\u56de\u5b83\u4eec\u7684\u76f8\u5173\u4fe1\u606f\u3002\u5012\u6392\u7d22\u5f15\u5e7f\u6cdb\u5e94\u7528\u4e8e\u641c\u7d22\u5f15\u64ce\u3001\u6570\u636e\u5e93\u7cfb\u7edf\u548c\u4fe1\u606f\u68c0\u7d22\u7b49\u9886\u57df\u3002</p> <p>\u2014\u2014 ChatGPT</p> <p>Info</p> <p>Wiki: https://en.wikipedia.org/wiki/Inverted_index</p> <p>\u6240\u8c13\u7684\u5012\u6392\u7d22\u5f15\uff0c\u6240\u6709\u7684\u601d\u60f3\u90fd\u51dd\u7ed3\u5728\u4e86\u201c\u5012\u201d\uff0c\u4e5f\u5c31\u662f inverted\u3002\u5982\u679c\u53ef\u4ee5\uff0c\u6211\u89c9\u5f97\u7528\u201c\u9006\u201d\u66f4\u5408\u9002\u3002\u8fd9\u91cc\u7684\u7d22\u5f15\u5bf9\u8c61\u6307\u7684\u662f\u201c\u6587\u6863\u201d\u548c\u201c\u5355\u8bcd\u201d\u4e4b\u95f4\u7684\u5173\u7cfb\uff0c\u800c\u5012\u6392\u7d22\u5f15\u7684\u610f\u601d\u662f\uff0c\u5bf9\u4e8e\u6bcf\u4e00\u4e2a\u5355\u8bcd\uff0c\u6211\u4eec\u8bb0\u5f55\u5b83\u51fa\u73b0\u5728\u54ea\u4e9b\u6587\u6863\u4e2d\uff0c\u4ee5\u53ca\u8bb0\u5f55\u4ed6\u4eec\u51fa\u73b0\u7684\u6b21\u6570\uff08\u9891\u7387\uff09\u3002</p> <p>\u641c\u7d22\u5f15\u64ce\u662f\u4e00\u4e2a\u975e\u5e38\u5e38\u89c1\u7684\uff0c\u5012\u6392\u7d22\u5f15\u7684\u5e94\u7528\u6848\u4f8b\uff0c\u6211\u4eec\u901a\u8fc7\u8f93\u5165\u6211\u4eec\u5173\u6ce8\u7684\u8bcd\u8bed\uff0c\u6765\u7d22\u5f15\u5305\u542b\u8fd9\u4e2a\u8bcd\u7684\u6240\u6709\u6587\u6863\u3002 \u5f53\u7136\uff0c\u5728\u8fd9\u91cc\u6211\u4eec\u8003\u8651\u7684\u662f\u82f1\u6587\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec03/#\u5012\u6392\u7d22\u5f15\u7684\u5b9e\u73b0","title":"\u5012\u6392\u7d22\u5f15\u7684\u5b9e\u73b0","text":"<p>\u77e5\u9053\u4e86\u5012\u6392\u7d22\u5f15\u7684\u601d\u60f3\u4e4b\u540e\uff0c\u5176\u5b9e\u73b0\u5c31\u53d8\u5f97\u975e\u5e38\u76f4\u89c2\u4e86\u3002\u6211\u4eec\u53ef\u4ee5\u7528\u4e00\u4e2a\u5b57\u5178\u6765\u63cf\u8ff0\u4e00\u7c7b\u5173\u7cfb\uff0c\u5176\u4e3b\u952e\u4e3a\u5355\u8bcd\uff0c\u952e\u503c\u4e3a\u8fd9\u4e2a\u5355\u8bcd\u51fa\u73b0\u7684\u6240\u6709\u4f4d\u7f6e\u3002</p> <p>\u6700\u6734\u7d20\u7684\u7248\u672c\u5c31\u662f\u8ba9\u952e\u503c\u4e3a\u5355\u8bcd\u51fa\u73b0\u8fc7\u7684\u6587\u6863\u7684\u5e8f\u53f7\u5e8f\u5217\uff0c\u800c\u5982\u679c\u6211\u4eec\u8fd8\u9700\u8981\u77e5\u9053\u8bcd\u6c47\u51fa\u73b0\u7684\u4f4d\u7f6e\uff0c\u5219\u53ef\u4ee5\u8ba9\u952e\u503c\u662f\u4e00\u4e2a\u4e8c\u5143\u7ec4\u7684\u5e8f\u5217\uff0c\u5176\u4e2d\u7b2c\u4e00\u4e2a\u5143\u7d20\u662f\u6587\u6863\u7684\u5e8f\u53f7\uff0c\u7b2c\u4e8c\u4e2a\u5143\u7d20\u662f\u5355\u8bcd\u5728\u6587\u6863\u4e2d\u51fa\u73b0\u7684\u4f4d\u7f6e\u3002</p> <p>\u4e00\u4e2a \ud83c\udf30</p> <p>\u4f8b\u5982\u6211\u4eec\u6709\u5982\u4e0b\u6587\u4ef6\u96c6\uff1a</p> <p>\u6587\u6863\u96c6</p> Doc Text 1 Gold silver truck 2 Shipment of gold damaged in a fire 3 Delivery of silver arrived in a silver truck 4 Shipment of gold arrived in a truck <p>\u90a3\u4e48\u6211\u4eec\u53ef\u4ee5\u5f97\u5230\u5982\u4e0b\u7684\u5012\u6392\u7d22\u5f15\uff1a</p> <p>\u5012\u6392\u7d22\u5f15</p> No. Term Times; (Doc ID: Places) 1 a {3; (2;6),(3;6),(4;6)} 2 arrived {2; (3;4),(4;4)} 3 damaged {1; (2;4)} 4 delivery {1; (3;1)} 5 fire {1; (2;7)} 6 gold {3; (1;1),(2;3),(4;3)} 7 of {3; (2;2),(3;2),(4;2)} 8 in {3; (2;5),(3;5),(4;5)} 9 shipment {2; (2;1),(4;1)} 10 silver {2; (1;2),(3;3,7)} 11 truck {3; (1;3),(3;8),(4;7)} <p>\u6240\u4ee5\u5b9e\u9645\u4e0a\u975e\u5e38\u7b80\u5355\uff0c\u6211\u4eec\u53ea\u9700\u8981\u626b\u63cf\u6587\u6863\uff0c\u7136\u540e\u5b58\u4e0b\u6bcf\u4e00\u4e2a\u6587\u4ef6\u5728\u54ea\u91cc\u51fa\u73b0\u8fc7\u5373\u53ef\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec03/#\u6539\u8fdb","title":"\u6539\u8fdb","text":"<p>\u90a3\u4e48\u5230\u6b64\u4e3a\u6b62\u4e86\u5417\uff1f\u975e\u4e5f\u3002\u5018\u82e5\u6beb\u65e0\u8282\u5236\u7684\u5c06\u6240\u6709\u8bcd\u90fd\u5b58\u5230\u5012\u6392\u7d22\u5f15\u4e2d\uff0c\u90a3\u4e48\u6211\u4eec\u7684\u5012\u6392\u7d22\u5f15\u5c31\u4f1a\u53d8\u5f97\u975e\u5e38\u5927\uff0c\u5176\u4e2d\u5fc5\u7136\u6709\u5f88\u591a\u5197\u4f59\u4fe1\u606f\u5b58\u5728\uff0c\u6240\u4ee5\u6211\u4eec\u9700\u8981\u5bf9\u5012\u6392\u7d22\u5f15\u8fdb\u884c\u4e00\u4e9b\u6539\u8fdb\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec03/#\u505c\u7528\u8bcd","title":"\u505c\u7528\u8bcd","text":"<p>\u6211\u4eec\u89c2\u5bdf\u5230\uff0c\u6211\u4eec\u5b58\u4e0b\u6765\u7684\u8fd9\u4e9b\u5185\u5bb9\u4e2d\uff0c\u6709\u4e00\u4e9b\u4e1c\u897f\u9891\u7e41\u5730\u51fa\u73b0\u5728\u6240\u6709\u6587\u6863\u4e2d\uff0c\u5728\u7279\u5b9a\u60c5\u51b5\u4e0b\uff0c\u8fd9\u4e9b\u8bcd\u53ef\u80fd\u5e76\u4e0d\u4f1a\u6210\u4e3a\u4e00\u4e2a\u7d22\u5f15\uff0c\u4f8b\u5982\u6b63\u5e38\u7684\u82f1\u6587\u6587\u7ae0\u4e2d\u7684 <code>a</code>\uff0c<code>the</code> \u7b49\u3002\u6240\u4ee5\uff0c\u5bf9\u4e8e\u8fd9\u4e00\u7c7b\u8bcd\u2014\u2014\u6211\u4eec\u79f0\u4e4b\u4e3a\u505c\u7528\u8bcd(stop words)\uff0c\u5bf9\u4e8e\u505c\u7528\u8bcd\uff0c\u6211\u4eec\u5c31\u4e0d\u9700\u8981\u5c06\u4ed6\u4eec\u5b58\u4e0b\u4e86\u3002</p> <p>\u54ea\u4e9b\u8bcd\u4f1a\u6210\u4e3a\u505c\u7528\u8bcd\uff1f</p> <p>\u4e00\u822c\u4e00\u4e2a\u8bcd\u6210\u4e3a\u505c\u7528\u8bcd\uff0c\u662f\u56e0\u4e3a\u5b83\u65e0\u6cd5\u6210\u4e3a\u4e00\u4e2a\u6709\u6548\u7684\u68c0\u7d22\u5173\u952e\u5b57\uff0c\u5b83\u53ef\u80fd\u662f\u5728\u5927\u91cf\u8d44\u6599\u4e2d\u5927\u91cf\u51fa\u73b0\uff0c\u5bfc\u81f4\u6211\u4eec\u65e0\u6cd5\u5229\u7528\u5b83\u627e\u51fa\u6211\u4eec\u60f3\u8981\u7684\u8d44\u6599\u3002\u6362\u53e5\u8bdd\u6765\u8bf4\uff0c\u4e00\u4e2a\u5171\u901a\u70b9\u662f\u5b83\u4eec\u901a\u5e38\u90fd\u6709\u7740\u76f8\u5f53\u9ad8\u7684\u51fa\u73b0\u9891\u7387\u3002</p> <p>\u4f46\u662f\u6211\u4eec\u4e5f\u4e0d\u80fd\u76f2\u76ee\u5730\u5c06\u6240\u6709\u7684\u8bcd\u90fd\u4f5c\u4e3a\u505c\u7528\u8bcd\uff0c\u56e0\u4e3a\u6709\u4e9b\u8bcd\u5b83\u5728\u67d0\u4e9b\u542b\u4e49\u4e0b\u9002\u5408\u4f5c\u4e3a\u4e00\u79cd\u505c\u7528\u8bcd\uff0c\u4f46\u662f\u5728\u53e6\u4e00\u4e9b\u542b\u4e49\u4e0b\uff0c\u5b83\u5c31\u4e0d\u9002\u5408\u4f5c\u4e3a\u505c\u7528\u8bcd\u4e86\uff0c\u4e0d\u8fc7\u8fd9\u4e2a\u95ee\u9898\u5c31\u53d8\u5f97\u6bd4\u8f83\u590d\u6742\u4e86\uff0c\u6240\u4ee5\u8fd9\u91cc\u5e76\u4e0d\u5c55\u5f00\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec03/#\u8bcd\u5e72\u5206\u6790","title":"\u8bcd\u5e72\u5206\u6790","text":"<p>\u8bcd\u5e72\u5206\u6790(word stemming)\u662f\u4e00\u79cd\u5c06\u5355\u8bcd\u8f6c\u6362\u4e3a\u5176\u8bcd\u5e72\u7684\u6280\u672f\u3002\u4f8b\u5982\uff0c\u8bcd\u5e72\u5206\u6790\u53ef\u4ee5\u5c06\u5355\u8bcd <code>trouble</code>\uff0c<code>troubled</code>\uff0c<code>troubles</code>\uff0c<code>troubling</code> \u90fd\u8f6c\u6362\u4e3a <code>trouble</code>\uff08\u751a\u81f3\u662f <code>troubl</code>\uff0c\u6838\u5fc3\u76ee\u7684\u662f\u8ba9\u5b83\u4eec\u53d8\u6210\u540c\u4e00\u4e2a\u5355\u8bcd\uff09\u3002\u76f8\u540c\u8bcd\u5e72\u7684\u8bcd\u6709\u7740\u7c7b\u4f3c\u7684\u542b\u4e49\uff0c\u5728\u68c0\u7d22 <code>troubled</code> \u7684\u65f6\u5019\uff0c\u5f53\u7136\u4e5f\u53ef\u80fd\u60f3\u627e\u5230\u5305\u542b <code>trouble</code> \u7684\u6587\u6863\u3002\u8fd9\u79cd\u6280\u672f\u4e5f\u53ef\u4ee5\u8ba9\u591a\u4e2a\u5355\u8bcd\u5171\u4eab\u540c\u4e00\u6761\u7d22\u5f15\u8bb0\u5f55\uff0c\u5728\u5b58\u548c\u627e\u7684\u8fc7\u7a0b\u4e2d\u90fd\u80fd\u4f18\u5316\u6548\u679c\u3002</p> <p>\u4e0d\u8fc7\u5728\u5177\u4f53\u64cd\u4f5c\u65b9\u9762\uff0c\u8fd9\u4e2a\u4e1c\u897f\u5c31\u663e\u5f97\u6bd4\u8f83\u7e41\u6742\u548c\u66b4\u529b\u4e86\uff0c\u6211\u4eec\u53ea\u80fd\u6839\u636e\u8bed\u6cd5\u89c4\u8303\u8fdb\u884c\u66b4\u529b\u5339\u914d\u548c\u5224\u65ad\uff0c\u8fd9\u91cc\u6211\u4eec\u5c31\u4e0d\u5c55\u5f00\u4e86\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec03/#\u5206\u5e03\u5f0f","title":"\u5206\u5e03\u5f0f","text":"<p>\u53ef\u60f3\u800c\u77e5\uff0c\u5bf9\u4e8e\u4e00\u4e2a\u641c\u7d22\u5f15\u64ce\u6765\u8bf4\uff0c\u5b83\u6240\u9700\u8981\u7d22\u5f15\u7684\u6587\u6599\u662f\u975e\u5e38\u5e9e\u5927\u7684\uff0c\u6240\u4ee5\u6211\u4eec\u901a\u5e38\u9700\u8981\u5c06\u5176\u5206\u5e03\u5f0f\u5730\u5b58\u50a8\u548c\u7d22\u5f15\u3002</p> <p>\u800c\u8fd9\u91cc\u6709\u4e24\u79cd\u5206\u5e03\u5f0f\u7684\u7b56\u7565\uff0c\u5176\u4e00\u662f\u6839\u636e\u5355\u8bcd\u7684\u5b57\u5178\u5e8f\u8fdb\u884c\u5206\u5e03\u5f0f\uff0c\u5176\u4e8c\u662f\u6839\u636e\u6587\u6863\u8fdb\u884c\u5206\u5e03\u5f0f\u3002</p> <p>\u663e\u7136\u6839\u636e\u5355\u8bcd\u7684\u5185\u5bb9\u8fdb\u884c\u5206\u5e03\u5f0f\uff0c\u80fd\u591f\u63d0\u9ad8\u7d22\u5f15\u6548\u7387\uff0c\u4f46\u662f\u8fd9\u6837\u7684\u8bdd\uff0c\u6211\u4eec\u5c31\u9700\u8981\u5c06\u6240\u6709\u5f62\u5f0f\u63a5\u8fd1\u7684\u5355\u8bcd\u90fd\u5b58\u50a8\u5728\u4e00\u4e2a\u5730\u65b9\uff0c\u8fd9\u6837\u5c31\u4f1a\u9020\u6210\u5355\u70b9\u6545\u969c\uff0c\u5bb9\u707e\u80fd\u529b\u5f88\u5dee\uff0c\u6240\u4ee5\u8fd9\u79cd\u65b9\u5f0f\u5e76\u4e0d\u662f\u5f88\u597d\u3002</p> <p>\u800c\u7b2c\u4e8c\u79cd\u529e\u6cd5\u5219\u6709\u8f83\u5f3a\u7684\u5bb9\u707e\u6027\u80fd\u3002\u5373\u4f7f\u4e00\u53f0\u673a\u5668\u65e0\u6cd5\u5de5\u4f5c\uff0c\u4e5f\u4e0d\u4f1a\u5267\u70c8\u5f71\u54cd\u5230\u6574\u4e2a\u7cfb\u7edf\u7684\u5de5\u4f5c\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec03/#\u6027\u80fd\u8bc4\u4f30","title":"\u6027\u80fd\u8bc4\u4f30","text":"<p>\u548c\u7edf\u8ba1\u5b66\u7684\u5047\u8bbe\u68c0\u9a8c\u7c7b\u4f3c\uff0c\u4e5f\u548c\u673a\u5668\u5b66\u4e60\u9886\u57df\u7684 Average Precision \u7c7b\u4f3c\u3002</p> <p>\u8fd9\u4e9b\u5185\u5bb9\u53ef\u4ee5\u5f88\u597d\u7684\u7c7b\u6bd4\uff0c\u6682\u65f6\u4e0d\u518d\u5c55\u5f00\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec04/","title":"Lecture 4 | Leftist Heap &amp; Skew Heap","text":"<p> \u7ea6 4406 \u4e2a\u5b57  97 \u884c\u4ee3\u7801  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 16 \u5206\u949f</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec04/#leftist-heap","title":"Leftist Heap","text":"<p>link</p> <p>OI Wiki: https://oi-wiki.org/ds/leftist-tree/</p> <p>Wikipedia: https://en.wikipedia.org/wiki/Leftist_tree</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec04/#\u6982\u5ff5","title":"\u6982\u5ff5","text":"<p>\u5de6\u504f\u5806\uff0c\u6216\u8005\u8bf4\u5de6\u504f\u5806(Leftist Heap)\uff0c\u5b83\u76f8\u6bd4\u4e8e\u666e\u901a\u7684\u5806\uff0c\u66f4\u597d\u7684\u4e00\u70b9\u5728\u4e8e\u5b83\u652f\u6301\u5feb\u901f\u7684\u5806\u5408\u5e76\u64cd\u4f5c\u3002\u201c\u5de6\u504f\u201d\uff0c\u5e76\u4e0d\u65ad\u5c06\u65b0\u7684\u4e1c\u897f\u5f80\u53f3\u4fa7\u5408\u5e76\uff0c\u6765\u5b9e\u73b0\u6bcf\u6b21\u90fd\u662f\u5f80\u76f8\u5bf9\u5c0f\u7684\u90a3\u4e00\u4fa7\u585e\u8fdb\u4e1c\u897f\uff0c\u8fdb\u800c\u4fdd\u76f8\u5bf9\u8bc1\u4e86\u8fd9\u4e2a</p> <p>\u7531\u4e8e\u5de6\u504f\u5806\u4e0d\u518d\u662f\u4e00\u4e2a\u5b8c\u5168\u4e8c\u53c9\u6811\uff0c\u6240\u4ee5\u6211\u4eec\u4e0d\u80fd\u518d\u50cf\u7ef4\u62a4\u5927\u6839\u5806\u5c0f\u8ddf\u5806\u90a3\u6837\u7528\u6570\u7ec4\u6765\u7ef4\u62a4\u5b83\u4e86\u3002</p> <p>\u4e00\u4e2a\u5de6\u504f\u5806\u7684\u7ed3\u70b9\u7ef4\u62a4\u4e86\u5de6\u53f3\u5b50\u5806\u7684\u5730\u5740\u3001\u81ea\u8eab\u7684\u952e\u503c\u3001\u548c\u4e00\u4e2a\u201c\u8ddd\u79bb(dist)\u201d\u3002</p> <pre><code>struct LeftistHeapNode {\nElementType val;\nint dist;\nLeftistHeapNode * ls, * rs;\n};\n</code></pre> <p>'dist' in leftist heap</p> <ol> <li>\u5982\u679c\u4e00\u4e2a\u7ed3\u70b9\u7684\u5de6\u5b69\u5b50\u6216\u53f3\u5b69\u5b50\u4e3a\u7a7a\u7ed3\u70b9\uff0c\u5219\u8be5\u7ed3\u70b9\u7684 dist \u4e3a \\(0\\)\uff0c\u8fd9\u79cd\u7ed3\u70b9\u88ab\u79f0\u4e3a\u5916\u7ed3\u70b9\uff1b</li> <li>\u5982\u679c\u4e00\u4e2a\u7ed3\u70b9\u7684\u5de6\u5b69\u5b50\u548c\u53f3\u5b69\u5b50\u90fd\u4e0d\u4e3a\u7a7a\uff0c\u5219\u8be5\u7ed3\u70b9\u7684 dist \u4e3a \\(\\min{(dist_\\text{left child}, dist_\\text{right child})} + 1\\)\uff1b</li> </ol> <p>eg</p> <p> </p> <p>\u800c\u5de6\u504f\u5806\u5c31\u5efa\u7acb\u5728\u8fd9\u4e9b\u6027\u8d28\u4e0a\uff1a</p> <p>Leftist Heap</p> <p>\u5de6\u504f\u5806\u662f\u7ed3\u70b9\u7684\u952e\u503c\u5e94\u5f53\u4e0d\u5927\u4e8e\uff08\u4e0d\u5c0f\u4e8e\uff09\u5176\u5b69\u5b50\u7ed3\u70b9\u7684\u952e\u503c\u7684\u4e8c\u53c9\u6811\uff08\u5373\u5806\u7684\u6027\u8d28\uff09\uff0c\u4e14\u6ee1\u8db3\u300c\u5de6\u504f\u300d\u6027\u8d28\u2014\u2014\u7ed3\u70b9\u7684\u5de6\u5b69\u5b50\u7684 dist \u4e0d\u5c0f\u4e8e\u53f3\u5b69\u5b50\u7684 dist\u3002</p> <p>\u56e0\u6b64\uff0c\u56de\u987e dist \u7684\u5b9a\u4e49\uff0c\u6211\u4eec\u53ef\u4ee5\u5f97\u5230\u6269\u5c55\u6027\u8d28\uff1a</p> <p>properties</p> <ol> <li>\u7ed3\u70b9\u7684 dist \u7b49\u4e8e \\(dist_\\text{right child} + 1\\)\uff08\u5047\u8bbe \\(dist_\\text{NULL} = -1\\)\uff09\uff1b</li> <li>\u5982\u679c \\(dist_i = N\\)\uff0c\u5219\u4ee5 \\(i\\) \u4e3a\u6839\u7684\u5b50\u6811\u81f3\u5c11\u662f\u4e00\u4e2a \\(N+1\\) \u5c42\u7684\u5b8c\u7f8e\u4e8c\u53c9\u6811\uff0c\u81f3\u5c11\u6709 \\(2^{N+1}-1\\) \u4e2a\u7ed3\u70b9\uff1b</li> </ol> <p> </p> <p>\u6ce8\u610f\uff0c\u5728\u793a\u610f\u56fe\u4e2d\u6211\u4eec\u7701\u7565\u4e86\u7ed3\u70b9\u81ea\u8eab\u952e\u503c\u7684\u6807\u8bb0\uff0c\u4f46\u65e2\u7136\u4f5c\u4e3a\u4e00\u4e2a\u5806\uff0c\u5b83\u5c31\u9700\u8981\u6ee1\u8db3\u5806\u7684\u6027\u8d28\uff0c\u5373\u7ed3\u70b9\u7684\u952e\u503c\u4e0d\u5927\u4e8e\uff08\u4e0d\u5c0f\u4e8e\uff09\u5176\u5b69\u5b50\u7ed3\u70b9\u7684\u952e\u503c\u3002\u5728\u5b9e\u9645\u4f7f\u7528\u8fc7\u7a0b\u4e2d\uff0c\u952e\u503c\u5f88\u53ef\u80fd\u4e0d\u518d\u662f\u5355\u7eaf\u7684\u6570\uff0c\u5927\u5c0f\u5173\u7cfb\u53ef\u80fd\u8f6c\u5316\u4e3a\u504f\u5e8f\u5173\u7cfb\u3002</p> <p>\u7b80\u5355\u601d\u8003\u4e00\u4e0b\uff0c\u4e3a\u4ec0\u4e48\u5de6\u504f\u5806\u4f1a\u8fd9\u4e48\u8bbe\u8ba1\u5462\uff1f\u5b9e\u9645\u4e0a\uff0c\u5408\u5e76\u5806\u9700\u8981\u8003\u8651\u7684\u975e\u5e38\u91cd\u8981\u7684\u4e00\u4e2a\u70b9\u5c31\u662f\u8981\u80fd\u5728\u4e4b\u540e\u7684\u64cd\u4f5c\u4e2d\u5c3d\u53ef\u80fd\u5730\u7ef4\u62a4\u5806\u7684\u201c\u5e73\u8861\u201d\uff0c\u5426\u5219\u6211\u4eec\u628a\u5806\u7ef4\u62a4\u6210\u4e86\u4e00\u4e2a\u94fe\uff0c\u90a3\u663e\u7136\u662f\u975e\u5e38\u7cdf\u7cd5\u7684\u3002</p> <p>\u800c\u5de6\u504f\u5806\u901a\u8fc7\u7ef4\u62a4\u6574\u4e2a\u5806\u201c\u5de6\u504f\u201d\uff0c\u5e76\u4e0d\u65ad\u5f80\u53f3\u4fa7\u5408\u5e76\uff0c\u6765\u5b9e\u73b0\u6bcf\u6b21\u90fd\u662f\u5f80 dist \u76f8\u5bf9\u5c0f\u7684\u90a3\u4e00\u4fa7\u585e\u8fdb\u4e1c\u897f\uff0c\u8fdb\u800c\u4fdd\u8bc1\u4e86\u8fd9\u4e2a\u5806\u7684\u76f8\u5bf9\u5e73\u8861\u6027\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec04/#\u64cd\u4f5c","title":"\u64cd\u4f5c","text":"<p>\u5de6\u504f\u5806\u7684\u6838\u5fc3\u64cd\u4f5c\u5c31\u662f\u5408\u5e76\u3002\u800c\u5176\u5b83\u64cd\u4f5c\u90fd\u53ef\u4ee5\u770b\u4f5c\u662f\u5408\u5e76\u7684\u7279\u6b8a\u60c5\u51b5\u3002\u56e0\u6b64\u6211\u4eec\u9996\u5148\u8ba8\u8bba\u4efb\u610f\u4e24\u4e2a\u5de6\u504f\u5806\u7684\u5408\u5e76\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec04/#\u5408\u5e76","title":"\u5408\u5e76","text":"<p>\u4f5c\u4e3a\u5de6\u504f\u5806\u7684\u6838\u5fc3\u64cd\u4f5c\uff0c\u5408\u5e76\u64cd\u4f5c\u81ea\u7136\u5c31\u662f\u8981\u5728\u6ee1\u8db3\u6027\u8d28\u7684\u6761\u4ef6\u4e0b\uff0c\u5408\u5e76\u4e24\u4e2a\u5de6\u504f\u5806\u3002\u5927\u81f4\u601d\u8def\u5c31\u662f\u5148\u7ef4\u62a4\u5806\u7684\u6027\u8d28\uff0c\u5728\u56de\u6eaf\u65f6\u7ef4\u62a4\u5de6\u504f\u6027\u8d28\uff0c\u6240\u4ee5\u5b9e\u9645\u4e0a\u5b83\u662f\u4e00\u4e2a\u5148\u81ea\u4e0a\u800c\u4e0b\u518d\u81ea\u4e0b\u800c\u4e0a\u7684\u8fc7\u7a0b\u3002</p> <p>\u6309\u7167\u5b9e\u73b0\u65b9\u6cd5\uff0c\u5de6\u504f\u5806\u7684\u5408\u5e76\u53ef\u4ee5\u5206\u4e3a\u9012\u5f52\u5f0f\u548c\u8fed\u4ee3\u5f0f\u4e24\u79cd\u3002\u5176\u4e2d\u524d\u8005\u53ef\u80fd\u66f4\u4e3a\u76f4\u89c9\uff0c\u800c\u540e\u8005\u53ef\u89c6\u5316\u540e\u5219\u66f4\u4e3a\u76f4\u89c2\u3002</p> <p>\u4e3a\u4e86\u65b9\u4fbf\u540e\u7eed\u7684\u4ee3\u7801\u63cf\u8ff0\uff0c\u6211\u4eec\u9996\u5148\u7ed9\u51fa\u5de6\u504f\u5806\u7ed3\u70b9\u5728\u672c\u6587\u4e2d\u7684\u5b9a\u4e49\uff1a</p> <pre><code>struct LeftistHeapNode {\nElementType val;\nint dist;\nLeftistHeapNode * ls, * rs;\n};\n</code></pre>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec04/#\u9012\u5f52\u5f0f","title":"\u9012\u5f52\u5f0f","text":"<p>\u9012\u5f52\u5f0f\u5148\u6bd4\u8f83\u5f53\u524d\u4e24\u4e2a\u5f85\u5408\u5e76\u5b50\u6811\u7684\u6839\u7ed3\u70b9\u7684\u952e\u503c\uff0c\u9009\u62e9\u8f83\u5c0f\uff08\u8f83\u5927\uff09\u7684\u90a3\u4e2a\u4f5c\u4e3a\u6839\u7ed3\u70b9\uff0c\u5176\u5de6\u5b50\u6811\u4f9d\u7136\u4e3a\u5de6\u5b50\u6811\uff0c\u53f3\u5b50\u6811\u66f4\u65b0\u4e3a\u300c\u53f3\u5b50\u6811\u548c\u53e6\u4e00\u4e2a\u5f85\u5408\u5e76\u5b50\u6811\u7684\u5408\u5e76\u7ed3\u679c\u300d\u3002</p> <p>\u5f53\u7136\uff0c\u5728\u9012\u5f52\u5730\u66f4\u65b0\u5b8c\u540e\uff0c\u6211\u4eec\u9700\u8981\u68c0\u67e5\u5de6\u5b50\u6811\u548c\u53f3\u5b50\u6811\u662f\u5426\u6ee1\u8db3 \\(dist_\\text{left child} \\geq dist_\\text{right child}\\) \u7684\u6027\u8d28\uff0c\u5982\u679c\u4e0d\u6ee1\u8db3\uff0c\u6211\u4eec\u5219\u9700\u8981\u4ea4\u6362\u5de6\u53f3\u5b50\u6811\u6765\u7ef4\u6301\u6027\u8d28\u3002</p> <pre><code>LeftistHeapNode * merge(LeftistHeapNode * x, LeftistHeapNode * y) {\n// Recursive exit. If any is NULL, return the other as the new root of subtree.\nif (x == NULL) return y;\nif (y == NULL) return x;\n\n// If `x`'s val is smaller than `y`'s, swap them, which means we always operates on `x`.\nif (x-&gt;val &gt; y-&gt;val) {\nswap(x, y);\n}\n\n// Merge `x`'s right subtree and `y`, and set `x`'s right subtree to the result.\nx-&gt;rs = merge(x-&gt;rs, y);\n\n// If `x`'s left subtree's dist is smaller than `x`'s right subtree's dist, swap them.\nif (x-&gt;ls-&gt;dist == NULL || x-&gt;ls-&gt;dist &lt; x-&gt;rs-&gt;dist) {\nswap(x-&gt;ls, x-&gt;rs);\n}\n\n// Update x's dist.\nx-&gt;dist = x-&gt;rs-&gt;dist + 1;\n\n// Return x as the new root of subtree.\nreturn x;\n}\n</code></pre> <p>\ud83c\udf30</p> <p>\u73b0\u5728\u6211\u4eec\u6a21\u62df\u4e00\u4e0b\u8fd9\u4e2a\u8fc7\u7a0b\uff0c\u73b0\u5728\u6211\u4eec\u6709\u4e0b\u9762\u4e24\u4e2a\u5de6\u504f\u5806\uff0c\u5c1d\u8bd5\u5408\u5e76\u5b83\u4eec\u3002</p> Frame 0Frame 1Frame 2Frame 3Frame 4Frame 5 <p></p> <p></p> <p>\u6211\u4eec\u53d1\u73b0\uff0c\u7ecf\u8fc7\u6bd4\u8f83\uff0c\u2776 \u66f4\u5c0f\uff0c\u6240\u4ee5\u6211\u4eec\u5c06 \u2776 \u4f5c\u4e3a\u5408\u5e76\u540e\u7684\u6839\u7ed3\u70b9\uff0c\u5de6\u5b50\u6811\u4e0d\u53d8\uff0c\u53f3\u5b50\u6811\u66f4\u65b0\u4e3a\u300c\u7eff\u6811\u53f3\u5b50\u6811\u548c\u84dd\u6811\u7684\u5408\u5e76\u7ed3\u679c\u300d\u3002</p> <p></p> <p>\u7ecf\u8fc7\u6bd4\u8f83\uff0c\u2777 \u66f4\u5c0f\uff0c\u6240\u4ee5\u6211\u4eec\u5c06 \u2777 \u4f5c\u4e3a\u5408\u5e76\u540e\u7684\u6839\u7ed3\u70b9\uff0c\u5de6\u5b50\u6811\u4e0d\u53d8\uff0c\u53f3\u5b50\u6811\u66f4\u65b0\u4e3a\u300c\u84dd\u6811\u53f3\u5b50\u6811\u548c\u7eff\u6811\u7684\u5408\u5e76\u7ed3\u679c\u300d\u3002</p> <p></p> <p>\u6700\u540e\u8fd8\u5269\u4e0b\u4e24\u4e2a\u7ed3\u70b9\u5566\uff01\u5b9e\u9645\u4e0a\u8fd9\u91cc\u76f4\u63a5\u6a21\u62df\u4e86\u4e24\u4e2a\u6b65\u9aa4\uff0c\u9996\u5148\u662f\u6bd4\u8f83 \u277a \u548c \u277b\uff0c\u5e76\u9009\u62e9\u4e86 \u277a \u4f5c\u4e3a\u65b0\u6839\uff1b\u63a5\u4e0b\u6765\u5728\u9012\u5f52\u7684\u8fc7\u7a0b\u4e2d\u53d1\u73b0\u9700\u8981\u5408\u5e76 <code>NULL</code> \u548c \u277b\uff0c\u6240\u4ee5\u76f4\u63a5\u8fd4\u56de\u4e86 \u277b\u3002</p> <p>\u7136\u800c\u8fd8\u6ca1\u6709\u7ed3\u675f\uff0c\u6211\u4eec\u8fd8\u9700\u8981\u5904\u7406\u5de6\u53f3\u5b50\u6811 dist \u5927\u5c0f\u5173\u7cfb\u95ee\u9898\u3002</p> <p></p> <p>\u6211\u4eec\u53d1\u73b0 \u277a \u7684\u5de6\u5b69\u5b50\u4e3a <code>NULL</code>\uff0c\u6211\u4eec\u8bb0 \\(dist_\\text{NULL} = -1\\)\uff0c\u53f3\u5b69\u5b50 \u277b \u6709 \\(dist_\\text{right child}=0\\)\uff0c\u6240\u4ee5\u9700\u8981\u4ea4\u6362\u4e24\u4e2a\u5b69\u5b50\u3002</p> <p></p> <p>\u8fd9\u91cc\u4e5f\u8df3\u8fc7\u4e86\u4e24\u4e2a\u6b65\u9aa4\uff1a</p> <p>\u5f80\u56de\u8d70\uff0c\u53d1\u73b0 \u277a \u7684 dist \u5c0f\u4e8e \u2779 \u7684 dist\uff0c\u6ee1\u8db3\u6027\u8d28\uff0c\u4e0d\u9700\u8981\u6539\u53d8\u3002</p> <p>\u7ee7\u7eed\u5f80\u56de\u8d70\uff0c\u53d1\u73b0 \u2777 \u548c \u2778 \u7684 dist \u76f8\u540c\uff0c\u6ee1\u8db3\u6027\u8d28\uff0c\u4e5f\u4e0d\u9700\u8981\u6539\u53d8\u3002</p> <p>\u4ece\u8fd9\u91cc\u4e5f\u53ef\u4ee5\u770b\u51fa\u6765\uff0c\u5e76\u4e0d\u662f\u770b\u4e0a\u53bb\u66f4\u5927\u7684\u5b50\u6811\u4e00\u5b9a\u5728\u5de6\u4fa7\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec04/#\u8fed\u4ee3\u5f0f","title":"\u8fed\u4ee3\u5f0f","text":"<p>\u8fed\u4ee3\u5f0f\u662f\u6839\u636e\u5b83\u7684\u5b9e\u73b0\u65b9\u6cd5\u6765\u547d\u540d\u7684\uff0c\u4f46\u662f\u6211\u8ba4\u4e3a\u4ece\u53ef\u89c6\u5316\u7684\u89d2\u5ea6\u6765\u7406\u89e3\u8fed\u4ee3\u5f0f\u53ef\u80fd\u66f4\u6709\u610f\u601d\u3002\u4e8b\u5b9e\u4e0a\u5728\u5f88\u591a\u9898\u76ee\u4e2d\u6211\u89c9\u5f97\u8fd9\u4e2a\u65b9\u6cd5\u505a\u9898\u66f4\u52a0\u65b9\u4fbf\u3002</p> <p>\u8fed\u4ee3\u5f0f\u7ef4\u62a4\u4e24\u4e2a\u989d\u5916\u7684\u6307\u9488\uff0c\u5206\u522b\u6307\u5411\u4e24\u68f5\u6811\u8fd8\u6ca1\u88ab\u5408\u5e76\u7684\u5b50\u6811\u7684\u6839\uff0c\u5e76\u4e0d\u65ad\u9009\u62e9\u8f83\u5c0f\u7684\u90a3\u4e2a\u5408\u5e76\u8fdb\u53bb\uff0c\u76f4\u5230\u4e24\u4e2a\u6307\u9488\u90fd\u4e3a\u7a7a\u3002\u53ef\u4ee5\u53d1\u73b0\uff0c\u8fd9\u4e2a\u8fc7\u7a0b\u548c\u5f52\u5e76\u6392\u5e8f\u7684\u540e\u534a\u90e8\u5206\u975e\u5e38\u76f8\u4f3c\uff0c\u5b9e\u9645\u4e0a\u5f53\u6211\u4eec\u4ece\u53ef\u89c6\u5316\u7684\u89d2\u5ea6\u53bb\u770b\u8fd9\u4ef6\u4e8b\u4ee5\u540e\uff0c\u4f1a\u53d1\u73b0\u8fd9\u91cc\u505a\u7684\u5c31\u662f\u4e00\u4e2a\u5f52\u5e76\u3002</p> <pre><code>LeftistHeapNode * merge(LeftistHeapNode * x, LeftistHeapNode * y) {\n// `tx` &amp; `ty` are the pointers to the roots of the subtrees that haven't been merged.\nLeftistHeapNode * tx = x, * ty = y;\n// `res` is the root of the merged final tree, while `cur` is the latest node that has been merged.\nLeftistHeapNode * res = NULL, * cur = NULL;\n\n// Begin merging.\nwhie (tx != NULL &amp;&amp; ty != NULL) {\n// If `tx`'s val is smaller than `ty`'s, swap them, which means we always operates on `tx`.\nif (tx-&gt;val &gt; ty-&gt;val) {\nswap(tx, ty);\n}\n\n// Specially mark the root on the first merge.\nif (res == NULL) {\nres = tx;\ncur = tx;\n} else {\ncur-&gt;rs = tx;\ncur = cur-&gt;rs;\n}\n\n// Go on.\ntx = tx-&gt;rs;\n}\n\n// Merge the rest of the tree.\nwhile (ty != NULL) {\n// Specially mark the root on the first merge. (rarely happens but not impossible)\nif (res == NULL) {\nres = ty;\ncur = ty;\n} else {\ncur-&gt;rs = ty;\ncur = cur-&gt;rs;\n}\n\n// Go on.\nty = ty-&gt;rs;\n}\n\n// Adjust the left and right subtrees of all the nodes according to the properties of `dist`. \n// It does the same work as the adjust part in the recursive version. I ignore it here.\nres = adjust(res);\n\nreturn res;\n}\n</code></pre> <p>\u4f9d\u65e7\u662f\u4ee5\u4e0a\u9762\u8fdb\u884c\u6a21\u62df\u7684\u90a3\u4e2a\u5408\u5e76\u4e3a \ud83c\udf30 \u8fdb\u884c\u6a21\u62df\u3002</p> <p>\ud83c\udf30</p> <p>\u9996\u5148\uff0c\u6211\u4eec\u5bf9\u56fe\u7247\u7684\u6392\u7248\u7a0d\u5fae\u505a\u4e00\u4e9b\u6539\u53d8\uff0c\u6211\u4eec\u4e0d\u518d\u6309\u7167\u4e4b\u524d\u753b\u5806\u7684\u65b9\u5f0f\u53bb\u753b\uff0c\u800c\u662f\u201c\u5de6\u504f\u201d\u5730\u53bb\u753b\uff1a</p> <p></p> <p>\u53ef\u4ee5\u53d1\u73b0\uff0c\u5728\u8c03\u6574\u4e4b\u524d</p> Frame 0Frame 1Frame 2Frame 3Frame 4Frame 5 <p></p> <p>\u7eff\u8272\u548c\u84dd\u8272\u7684\u7bad\u5934\u5206\u522b\u8868\u793a\u4e24\u4e2a\u5f85\u5408\u5e76\u5b50\u6811\u5c1a\u672a\u5408\u5e76\u7684\u5b50\u6811\u7684\u6839\uff0c\u7d2b\u8272\u7bad\u5934\u8868\u793a\u6700\u8fd1\u7684\u5408\u5e76\u53d1\u751f\u7684\u4f4d\u7f6e\u3002</p> <p></p> <p>\u6bd4\u8f83 \u2776 \u548c \u2777\uff0c\u53d1\u73b0 \u2776 \u66f4\u5c0f\uff0c\u6240\u4ee5\u6211\u4eec\u5c06 \u2776 \u4f5c\u4e3a\u5408\u5e76\u540e\u7684\u6839\u7ed3\u70b9\uff0c\u5de6\u5b50\u6811\u968f\u4e4b\u5408\u5e76\u8fdb\u53bb\uff0c\u540c\u65f6\u66f4\u65b0\u7eff\u8272\u7bad\u5934\u6307\u5411\u5c1a\u672a\u5408\u5e76\u8fdb\u53bb\u7684 \u277a\u3002</p> <p></p> <p>\u548c\u4e0a\u4e00\u6b65\u7c7b\u4f3c\u7684\uff0c\u6bd4\u8f83 \u277a \u548c \u2777\uff0c\u53d1\u73b0 \u2777 \u66f4\u5c0f\uff0c\u6240\u4ee5\u6211\u4eec\u5c06 \u2777 \u4f5c\u4e3a\u5408\u5e76\u540e\u7684\u6839\u7ed3\u70b9\uff0c\u5de6\u5b50\u6811\u968f\u4e4b\u5408\u5e76\u8fdb\u53bb\uff0c\u540c\u65f6\u66f4\u65b0\u84dd\u8272\u7bad\u5934\u6307\u5411\u5c1a\u672a\u5408\u5e76\u8fdb\u53bb\u7684 \u277b\u3002</p> <p></p> <p>\u4f9d\u7136\u7c7b\u4f3c\u5730\uff0c\u6bd4\u8f83 \u277a \u548c \u277b\uff0c\u53d1\u73b0 \u277a \u66f4\u5c0f\uff0c\u6240\u4ee5\u6211\u4eec\u5c06 \u277a \u4f5c\u4e3a\u5408\u5e76\u540e\u7684\u6839\u7ed3\u70b9\uff0c\u5de6\u5b50\u6811\u968f\u4e4b\u5408\u5e76\u8fdb\u53bb\uff0c\u540c\u65f6\u66f4\u65b0\u7eff\u8272\u7bad\u5934\u6307\u5411 <code>NULL</code>\u3002</p> <p></p> <p>\u8fd9\u65f6\u5019\u6211\u4eec\u53d1\u73b0\u5df2\u7ecf\u6709\u4e00\u4e2a\u6307\u9488\u7a7a\u4e86\uff0c\u4e5f\u5c31\u662f\u7eff\u8272\u6307\u9488\u5df2\u7ecf\u6307\u5411\u4e86 <code>NULL</code>\uff0c\u8fd9\u4e2a\u65f6\u5019\u6211\u4eec\u53ea\u9700\u8981\u6309\u987a\u5e8f\u628a\u84dd\u8272\u6307\u9488\u6307\u5411\u7684\u5185\u5bb9\u90fd\u63a8\u8fdb\u53bb\u5373\u53ef\u3002</p> <p></p> <p>\u63a5\u4e0b\u6765\u6211\u4eec\u8fd8\u9700\u8981\u7ef4\u62a4 dist \u4fe1\u606f\u5e76\u6839\u636e\u6027\u8d28\u4ea4\u6362\u5de6\u53f3\u5b50\u6811\u3002\u8fd9\u4e00\u90e8\u5206\u548c\u4e4b\u524d\u4e00\u6837\uff0c\u5c31\u4e0d\u518d\u8d58\u8ff0\u4e86\u3002</p> <p>\ud83c\udf30/\ud83d\udd25</p> <p>\u5f53\u7136\uff0c\u8fd9\u4e48\u6765\u770b\u53ef\u80fd\u8fd8\u662f\u5f88\u4e71\uff0c\u8054\u60f3\u6211\u4eec\u4e4b\u524d\u53d1\u73b0\u5b83\u548c\u5f52\u5e76\u6392\u5e8f\u5f88\u50cf\uff0c\u6211\u4eec\u8fd8\u53ef\u4ee5\u7528\u4e00\u4e2a\u66f4\u52a0\u76f4\u89c2\u7684\u65b9\u5f0f\u6765\u770b\u8fd9\u4e2a\u8fc7\u7a0b\uff1a</p> Frame 0Frame 1Frame 2 <p></p> <p>\u540c\u6837\u4ece\u8fd9\u5f20\u56fe\u5f00\u59cb\uff0c\u7531\u4e8e\u6211\u4eec\u4e4b\u524d\u63d0\u5230\u7684\uff0c\u5b83\u7c7b\u4f3c\u4e8e\u4e00\u4e2a\u9012\u5f52\u6392\u5e8f\u7684\u540e\u534a\u90e8\u5206\uff0c\u5177\u4f53\u6765\u8bf4\u662f\u6307\u5408\u5e76\u4e24\u4e2a\u6709\u5e8f\u6570\u5217\u7684\u8fc7\u7a0b\u3002</p> <p>\u4e5f\u5c31\u662f\u8bf4\uff0c\u6211\u4eec\u53ef\u4ee5\u5c06\u8fd9\u4e24\u4e2a\u5de6\u504f\u5806\u6539\u5199\u6210\u4e24\u4e2a\u6709\u5e8f\u6570\u5217\uff01</p> <p></p> <p>\u7531\u4e8e\u6211\u4eec\u5728\u5408\u5e76\u8fc7\u7a0b\u4e2d\u603b\u662f\u627e\u53f3\u5b69\u5b50\uff0c\u6240\u4ee5\u6211\u4eec\u5c31\u6cbf\u7740\u6700\u53f3\u6cbf\u8def\u5f84\u628a\u6ca1\u4e2a\u5de6\u504f\u5806\u62c6\u6210\u8fd9\u79cd\u201c\u60ac\u540a\u201d\u7684\u5e26\u72b6\u5f62\u5f0f\uff0c\u6bcf\u4e00\u201c\u6761\u201d\u7684\u503c\u53d6\u51b3\u4e8e\u6839\u7684\u952e\u503c\uff0c\u4e5f\u5c31\u662f\u8fd9\u4e00\u201c\u6761\u201d\u7684\u6700\u9876\u90e8\u3002</p> <p>\u5728\u8fd9\u5f20\u56fe\u4e2d\uff0c\u6211\u4eec\u5f97\u5230\u7684\u4e24\u4e2a\u6709\u5e8f\u6570\u7ec4\u5206\u522b\u662f [1, 5] \u548c [2, 6]\uff0c\u63a5\u4e0b\u6765\u6211\u4eec\u5c06\u5b83\u4eec\u8fdb\u884c\u6392\u5e8f\u3002</p> <p> </p> <p>\u7ecf\u8fc7\u6392\u5e8f\uff0c\u5c31\u4f1a\u53d1\u73b0\u5b83\u4eec\u521a\u597d\u7b26\u5408\u6211\u4eec\u5728\u4e0a\u9762\u6b65\u9aa4\u5f97\u5230\u7684\u7ed3\u679c\uff08\u53ef\u4ee5\u5bf9\u6bd4\u7740\u4e0a\u9762\u7684 Frame 4 \u770b\uff09\u3002\u5b9e\u9645\u4e0a\uff0c\u53ea\u8981\u4f60\u56de\u987e\u4e00\u4e0b\u5f52\u5e76\u6392\u5e8f\u7684\u8fc7\u7a0b\uff0c\u518d\u5bf9\u6bd4\u7740\u770b\u4e0a\u9762\u7684\u8fc7\u7a0b\uff0c\u5c31\u4f1a\u53d1\u73b0\u4e00\u6a21\u4e00\u6837\u3002</p> <p>\u518d\u6b21\u63d0\u9192\uff0c\u8fd9\u4e00\u5c0f\u8282\u8bb2\u7684\u90e8\u5206\u90fd\u5ffd\u7565\u4e86\u4e4b\u540e\u8c03\u6574\u5b50\u6811\u5de6\u504f\u6027\u8d28\u7684\u8fc7\u7a0b\uff0c\u5b9e\u9645\u4e0a\u8fd9\u4e5f\u5c31\u5355\u7eaf\u662f\u4e00\u4e2a\u7ef4\u62a4\u5806\u6027\u8d28\u7684\u8fc7\u7a0b\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec04/#\u5355\u70b9\u63d2\u5165","title":"\u5355\u70b9\u63d2\u5165","text":"<p>\u63d2\u5165\u7ed3\u70b9\u53ef\u4ee5\u770b\u4f5c\u5408\u5e76\u4e00\u4e2a\u53ea\u6709\u4e00\u4e2a\u7ed3\u70b9\u7684\u5de6\u504f\u5806\uff0c\u6240\u4ee5\u6211\u4eec\u53ef\u4ee5\u76f4\u63a5\u590d\u7528\u5408\u5e76\u8fc7\u7a0b\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec04/#\u5355\u70b9\u5220\u9664","title":"\u5355\u70b9\u5220\u9664","text":"<p>\u8ba9\u6211\u4eec\u4e00\u822c\u6027\u5730\u8003\u8651\u4e00\u4e2a\u7ed3\u70b9\uff0c\u4e0e\u5b83\u76f8\u5173\u7684\u4e3b\u8981\u6709\u4e09\u4e2a\u65b9\u5411\uff1a\u7236\u7ed3\u70b9\u548c\u4e24\u4e2a\u5b69\u5b50\u7ed3\u70b9\u3002</p> <p>\u800c\u5355\u70b9\u5220\u9664\u7684\u64cd\u4f5c\u4e5f\u5f88\u7b80\u5355\uff0c\u53ea\u9700\u8981\u5408\u5e76\u9700\u8981\u88ab\u5220\u9664\u7684\u7ed3\u70b9\u7684\u4e24\u4e2a\u5b50\u7ed3\u70b9\uff0c\u7136\u540e\u5c06\u8fd9\u4e2a\u65b0\u7684\u6811\u7684\u6839\u4ee3\u66ff\u88ab\u5220\u9664\u7684\u7ed3\u70b9\uff0c\u518d\u5728\u56de\u6eaf\u7684\u8fc7\u7a0b\u4e2d bottom-up \u5730\u66f4\u65b0 dist \u5373\u53ef\u3002</p> <pre><code>LeftistHeapNode * del(LeftistHeapNode * cur, ElementType x) {\nif (cur-&gt;val == x) {\n// Just return the merge of the children.\nreturn merge(cur-&gt;l, cur-&gt;r);\n} else {\n// Not this subtree.\nif (cur-&gt;val &gt; x) return cur;\n\n// Otherwise, search the `x`.\nif (cur-&gt;l != NULL) del(cur-&gt;l, x);\nif (cur-&gt;r != NULL) del(cur-&gt;r, x);\n\n// Adjust the dist bottom-up.\nadjust(cur);\n}\n}\n</code></pre>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec04/#skew-heap","title":"Skew Heap","text":"<p>link</p> <p>Wikipedia: https://en.wikipedia.org/wiki/Skew_heap</p> <p>\u659c\u5806(Skew Hea)\u662f\u6bd4\u5de6\u504f\u5806\u66f4\u4e3a\u4e00\u822c\u7684\u6570\u636e\u7ed3\u6784\uff0c\u5b83\u540c\u6837\u6709\u7740\u80fd\u591f\u5feb\u901f\u5408\u5e76\u7684\u6027\u8d28\u3002</p> <p>\u5934\u8111\u98ce\u66b4</p> <p>\u8ba9\u6211\u4eec\u56de\u987e\u4e00\u4e0b\u5de6\u504f\u5806\uff0c\u7531\u4e8e\u9700\u8981\u81ea\u4e0b\u800c\u4e0a\u5730\u7ef4\u62a4 dist\uff0c\u6240\u4ee5\u6211\u4eec\u65e0\u6cd5\u8fdb\u884c\u5e76\u53d1\u64cd\u4f5c\u3002\u56de\u987e AVL \u6811\uff0c\u540c\u6837\u4e3a\u4e86\u7ef4\u62a4\u5b83\u6bd4\u8f83\u4e25\u683c\u7684\u5e73\u8861\u6027\u8d28\uff0c\u6211\u4eec\u4e5f\u65e0\u6cd5\u8fdb\u884c\u5e76\u53d1\u64cd\u4f5c\uff0c\u800c\u7ea2\u9ed1\u6811\u5219\u901a\u8fc7\u4e00\u4e2a\u80fd\u591f\u4ec5\u4ec5\u901a\u8fc7\u53d8\u8272\u5c31\u80fd\u8c03\u6574\u7684\u9ed1\u9ad8\u6765\u89c4\u907f\u4e86\u5fc5\u987b\u81ea\u4e0b\u800c\u4e0a\u7ef4\u62a4\u7684\u95ee\u9898\uff0c\u5b9e\u73b0\u4e86\u5e76\u53d1\u3002</p> <p>\u6362\u53e5\u8bdd\u6765\u8bf4\uff0c\u8981\u60f3\u5c06\u5de6\u504f\u5806\u6539\u53d8\u5730\u80fd\u591f\u8fdb\u884c\u81ea\u4e0a\u800c\u4e0b\u7ef4\u62a4\uff0c\u5c31\u9700\u8981\u6539\u53d8\u751a\u81f3\u653e\u5f03\u5b83\u7684\u5de6\u504f\u6027\u8d28\u7684\u4e25\u683c\u6027\u2014\u2014\u800c\u8fd9\u5c31\u662f\u659c\u5806\u7684\u7531\u6765\u3002</p> <p>\u659c\u5806\u4e5f\u9700\u8981\u6ee1\u8db3\u5927\u6839\u5806\uff08\u5c0f\u6839\u5806\uff09\u7684\u6027\u8d28\uff0c\u800c\u5b83\u7684\u5408\u5e76\u548c\u5de6\u504f\u5806\u7684\u5408\u5e76\u4e5f\u5341\u5206\u7c7b\u4f3c\uff0c\u53ea\u4e0d\u8fc7\u6211\u4eec\u8fd9\u6b21\u65e0\u6761\u4ef6\u7684\u4ea4\u6362\u5de6\u53f3\u5b50\u6811\uff0c\u6362\u53e5\u8bdd\u6765\u8bf4\uff0c\u4e0d\u7ba1\u5de6\u504f\u6027\u8d28\u5982\u4f55\u53d8\u5316\uff0c\u6211\u4eec\u90fd\u4f1a\u9009\u62e9\u4ea4\u6362\u53c2\u4e0e\u5408\u5e76\u7684\u5de6\u53f3\u5b50\u6811\uff0c\u8fd9\u6837\u6211\u4eec\u5c31\u4e0d\u9700\u8981\u5728\u56de\u6eaf\u7684\u65f6\u5019\u624d\u8fdb\u884c\u5de6\u53f3\u5b50\u6811\u7684\u4ea4\u6362\uff0c\u4e8e\u662f\u5c31\u5b9e\u73b0\u4e86\u5b8c\u5168\u7684\u81ea\u4e0a\u800c\u4e0b\u3002</p> <p>\u8ba9\u6211\u4eec\u6765\u770b\u770b wiki \u91cc\u7ed9\u51fa\u7684 \ud83c\udf30\uff1a</p> <p>\ud83c\udf30 from wikipedia</p> Frame 0Frame 1 <p></p> <p>\u8fd9\u662f\u6211\u4eec\u9700\u8981\u5408\u5e76\u7684\u4e24\u4e2a\u5806\u3002</p> <p></p> <p>\u7701\u7565\u4e86\u4e2d\u95f4\u7684\u6b65\u9aa4\uff0c\u53ef\u4ee5\u5c1d\u8bd5\u6a21\u62df\u4e00\u4e0b\uff0c\u6bcf\u4e00\u6b21\u5408\u5e76\u64cd\u4f5c\u7ed3\u675f\u4e4b\u540e\u90fd\u4ea4\u6362\u5de6\u53f3\u5b50\u6811\u3002</p> <p>\u6211\u4eec\u603b\u662f\u5148\u5f80\u53f3\u4fa7\u5b50\u6811\u9012\u5f52\u4e0b\u53bb\u5730\u5408\u5e76\uff0c\u6ca1\u5b8c\u6210\u4e00\u6b21\u5408\u5e76\u5c31\u4ea4\u6362\u8fd9\u4e2a\u5b50\u6811\u548c\u5b83\u7684\u5144\u5f1f\u59d0\u59b9\uff0c\u800c\u5b83\u7684\u5144\u5f1f\u59d0\u59b9\u5728\u8fd9\u6b21\u4ea4\u6362\u5b8c\u4ee5\u540e\u5c31\u4e0d\u4f1a\u518d\u53d1\u751f\u6539\u53d8\uff0c\u800c\u8fd9\u4e2a\u5b50\u6811\u5219\u4f1a\u7ee7\u7eed\u8fdb\u884c\u4e0b\u4e00\u6b21\u5408\u5e76\u3002</p> <p>\u7701\u7565\u4e0a\u9762\u7684\u7ed8\u56fe\u663e\u7136\u662f\u6211\u61d2\u5f97\u753b\u4e86\uff0c\u76f8\u4fe1\u5927\u5bb6\u5728\u4e86\u89e3\u5de6\u504f\u5806\u7684\u5408\u5e76\u4ee5\u540e\u4e5f\u80fd\u5f88\u5feb\u611f\u53d7\u5230\u659c\u5806\u662f\u5982\u4f55\u5408\u5e76\u7684\u3002</p> <p>\u5f53\u7136\uff0c\u5b83\u4e5f\u662f\u652f\u6301\u8fed\u4ee3\u7684\u5199\u6cd5\u7684\uff0c\u548c\u662f\u548c\u4e4b\u524d\u7684\u505a\u6cd5\u7c7b\u4f3c\uff0c\u6211\u4eec\u53ef\u4ee5\u6392\u5e8f\u6bcf\u4e00\u201c\u6761\u201d\uff0c\u7136\u540e\u518d\u5408\u5e76\u3002Wikipedia \u4e0a\u63d0\u4f9b\u4e86\u4e00\u7cfb\u5217\u7684\u8fc7\u7a0b\u56fe\uff0c\u4f46\u662f\u90a3\u4e2a\u8fc7\u7a0b\u56fe\u6709\u70b9\u81ea\u4e0b\u800c\u4e0a\u7684\u610f\u601d\uff0c\u4f46\u662f\u5b9e\u9645\u4e0a\u81ea\u4e0a\u800c\u4e0b\u505a\u4e5f\u662f\u4e00\u6837\u7684\u3002\u5982\u679c\u6709\u5174\u8da3\u53ef\u4ee5\u53bb\u770b\u770b Wiki \u4e0a\u7684\u8fc7\u7a0b\uff1a\ud83d\udd17\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec04/#\u5408\u7406\u6027\u5206\u6790","title":"\u5408\u7406\u6027\u5206\u6790","text":"<p>\u7136\u800c\uff0c\u968f\u4e4b\u51fa\u73b0\u7684\u4e00\u4e2a\u95ee\u9898\u4e0a\uff0c\u6211\u4eec\u7528\u4e86\u8fd9\u79cd\u770b\u8d77\u6765\u6709\u70b9\u4e0d\u7ba1\u4e09\u4e03\u4e8c\u5341\u4e00\u7684\u505a\u6cd5\uff0c\u90a3\u5b83\u7684\u6b63\u786e\u6027\u5982\u4f55\u4fdd\u8bc1\u5462\uff1f</p> <p>\u9996\u5148\u8fdb\u884c\u611f\u6027\u7684\u7406\u89e3\u3002\u6211\u4eec\u6bcf\u5408\u5e76\u4e24\u4e2a\u5806\u90fd\u662f\u6cbf\u7740\u6700\u53f3\u4fa7\u8def\u5f84\u5408\u5e76\uff08\u867d\u7136\u4e2d\u95f4\u4f1a\u88ab\u4e0d\u505c\u8f6c\u5230\u5de6\u8fb9\uff09\uff0c\u5373\u6bcf\u6b21\u4f1a\u88ab\u6539\u53d8\u7684\u5b50\u6811\u5de6\u53f3\u987a\u5e8f\u7684\u8282\u70b9\u90fd\u662f\u6700\u53f3\u4fa7\u7684\u8282\u70b9\uff0c\u800c\u518d\u5408\u5e76\u8fc7\u7a0b\u4e2d\u5982\u679c\u6bcf\u6b21\u5408\u5e76\u90fd\u5c06\u53d1\u751f\u7684\u53d8\u5316\u8f6c\u5230\u5de6\u4fa7\uff0c\u4ee5\u6b64\u6765\u51cf\u5c0f\u5408\u5e76\u64cd\u4f5c\u5e26\u6765\u7684\u9ad8\u5ea6\u201c\u7d2f\u79ef\u201d\u3002</p> <p>\u8fdb\u4e00\u6b65\u89e3\u91ca</p> <p>\u4ee5\u6bcf\u6b21\u53ea\u63d2\u5165\u4e00\u4e2a\u70b9\u4e3a\u4f8b\u5b50\u8bf4\u660e\u95ee\u9898\u3002</p> <p>\u8fdb\u4e00\u6b65\u5bf9\u9012\u5f52\u65cb\u8f6c\u5230\u5de6\u4fa7\u505a\u89e3\u91ca\uff0c\u9012\u5f52\u6027\u5730\u8f6c\u5230\u5de6\u4fa7\uff0c\u4f7f\u5f97\u672c\u6765\u6700\u53f3\u4fa7\u7684\u8def\u5f84\u53d8\u5230\u6700\u5de6\u4fa7\uff0c\u5373\u4f7f\u4e4b\u540e\u4ea4\u6362\u4f1a\u91cd\u65b0\u8bbf\u95ee\u5230\u8fd9\u4e2a\u5b50\u6811\uff0c\u4f46\u6b64\u65f6\u9664\u4e86\u6839\uff0c\u5176\u4ed6\u90e8\u5206\u4f9d\u7136\u662f\u6700\u5de6\u4fa7\u7684\u8def\u5f84\uff0c\u4e5f\u4e0d\u4f1a\u518d\u8f7b\u6613\u5730\u8bbf\u95ee\u5230\u8fd9\u6b21\u8def\u5f84\u3002</p> <p>\u7528\u56fe\u6765\u505a\u89e3\u91ca\u7684\u8bdd\uff0c\u5c31\u662f\u8fd9\u6837\uff1a</p> <p></p> <p>\u6211\u4eec\u53ea\u5173\u6ce8\u4e00\u5f00\u59cb\u4f5c\u4e3a\u6700\u53f3\u4fa7\u7684\u8fd9\u4e09\u4e2a\u7ea2\u70b9\uff0c\u53ef\u4ee5\u53d1\u73b0\uff0c\u5728\u4e24\u6b21\u64cd\u4f5c\u540e\uff0c\u9664\u4e86\u76f4\u63a5\u4f5c\u4e3a\u6839\u7684\u5b50\u6811\u7684\u90a3\u4e2a\u8282\u70b9\u88ab\u8f6c\u4e86\u8fc7\u6765\uff0c\u5176\u4ed6\u7684\u4e4b\u540e\u7684\u8282\u70b9\u90fd\u662f\u4f5c\u4e3a\u201c\u6700\u5de6\u4fa7\u201d\u7684\u8282\u70b9\u51fa\u73b0\u7684\uff0c\u867d\u7136\u56fe\u4e2d\u53ea\u6709\u8fd9\u4e00\u4e2a\uff0c\u4f46\u662f\u5f53\u6811\u7684\u89c4\u6a21\u53d8\u5927\u540e\uff0c\u8fd9\u4e2a\u4f18\u52bf\u4f1a\u66f4\u52a0\u660e\u663e\u3002</p> <p>\u6839\u636e\u8fd9\u4e2a\u7279\u70b9\uff0c\u6211\u4eec\u53ef\u4ee5\u975e\u5e38\u7b80\u5355\u5730\u7406\u89e3\u4e0b\u9762\u8fd9\u9053\u9898\uff1a</p> \u9898\u9762\u7b54\u6848 &amp; \u89e3\u91ca <p>The result of inserting keys \\(1\\) to \\(2^k\u22121\\) for any \\(k&gt;4\\) in order into an initially empty skew heap is always a full binary tree. (T/F)</p> <p>\u5373\u5bf9\u4e8e\u4efb\u610f\u7684 \\(k&gt;4\\) \u7684\u60c5\u51b5\uff0c\u6309\u987a\u5e8f\u5f80\u4e00\u4e2a\u659c\u5806\u91cc\u63d2\u5165 \\(1\\sim2^k-1\\) \u8fd9\u4e9b\u6570\uff0c\u5f97\u5230\u7684\u7ed3\u679c\u90fd\u4f1a\u662f\u4e00\u4e2a\u6ee1\u4e8c\u53c9\u6811\u3002\uff08\u5bf9/\u9519\uff09</p> <p>\u7b54\u6848\u662f T\u3002</p> <p>\u9996\u5148\uff0c\u4ece\u63d2\u5165\u7684\u5143\u7d20\u7684\u6570\u91cf\u6765\u770b\uff0c\u662f\u6ee1\u8db3\u6ee1\u4e8c\u53c9\u6811\u7684\u5fc5\u8981\u6761\u4ef6\u7684\u3002</p> <p>\u800c\u6839\u636e\u6211\u4eec\u4e0a\u9762\u63cf\u8ff0\u7684\uff0c\u8df3\u8fc7\u80af\u5b9a\u6210\u7acb\u7684\u521d\u59cb\u60c5\u51b5\uff0c\u6211\u4eec\u53ef\u4ee5\u505a\u4e00\u4e2a\u7b80\u5355\u7684\u5f52\u7eb3\uff0c\u8fc7\u7a0b\u5e76\u4e0d\u5b8c\u6574\u4e0e\u4e25\u8c28\uff0c\u4f46\u662f\u5927\u6982\u5c31\u662f\u8fd9\u4e48\u4e2a\u610f\u601d\u3002</p> <p>\u5bf9\u4e8e\u4e00\u4e2a\u6ee1\u4e8c\u53c9\u6811\uff0c\u6211\u4eec\u73b0\u5728\u8981\u63d2\u5165\u4e00\u4e2a\u6570\uff0c\u663e\u7136\u8fd9\u4e2a\u6570\u6bd4\u6811\u91cc\u4efb\u4f55\u4e00\u4e2a\u90fd\u8981\u5927\u3002\u800c\u5f53\u8fd9\u4e2a\u6570\u88ab\u63d2\u5165\u540e\uff0c\u5b83\u6210\u4e3a\u6574\u4e2a\u5806\uff0c\u6216\u8005\u8bf4\u6574\u4e2a\u6811\u6700\u5de6\u4fa7\u7684\u4e00\u6761\u3002\u800c\u5728\u63a5\u4e0b\u6765\u7684\u4ea4\u6362\u8fc7\u7a0b\u4e2d\uff0c\u5b83\u4f1a\u4e0d\u65ad\u88ab\u7529\u6765\u7529\u53bb\uff0c\u6700\u7ec8\u7ecf\u8fc7 2^k \u6b21\u540e\u88ab\u7529\u5230\u6700\u53f3\u8fb9\uff0c\u4e5f\u5c31\u662f\u8fce\u63a5\u5b83\u7684\u7b2c\u4e00\u4e2a\u5b69\u5b50\u3002\u663e\u7136\uff0c\u5bf9\u4e8e\u8be5\u5c42\u7684\u6240\u6709\u8282\u70b9\u6765\u8bf4\u90fd\u9700\u8981 2^k \u6b21\u624d\u4f1a\u8fdb\u5165\u5230\u6700\u53f3\u4fa7\u8def\u5f84\u3002</p> <p>\uff08\u8fd9\u4e2a\u8fc7\u7a0b\u53ef\u4ee5\u7c7b\u6bd4\u4e8c\u8fdb\u5236\u6570\u7684\u81ea\u589e\uff0c\u4f60\u53ef\u4ee5\u6839\u636e\u8fd9\u4e2a\u8282\u70b9\u7684\u6bcf\u4e2a\u524d\u9a71\u5206\u522b\u662f\u5de6\u5b69\u5b50\u8fd8\u662f\u53f3\u5b69\u5b50\u6765\u5206\u914d\u5bf9\u5e94\u7684\u4f4d\u5b50\u662f <code>0</code> \u8fd8\u662f <code>1</code>\u3002\uff09</p> <p>\u5f53\u7136\uff0c\u5982\u4e0a\u7684\u6027\u8d28\u53ea\u80fd\u5e2e\u52a9\u6211\u4eec\u611f\u6027\u7684\u7406\u89e3\u8fd9\u4e2a\u6b63\u786e\u6027\u3002\u63a5\u4e0b\u6765\u6211\u4eec\u4ece\u644a\u8fd8\u5206\u6790\u7684\u89d2\u5ea6\u6765\u5206\u6790\u5176\u6b63\u786e\u6027\uff0c\u5373\u5176\u5747\u644a\u590d\u6742\u5ea6\u4e3a \\(O(\\log N)\\)\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec04/#\u644a\u8fd8\u5206\u6790","title":"\u644a\u8fd8\u5206\u6790","text":"<ul> <li>\u524d\u60c5\u63d0\u8981\uff1aTopic 1 | \u644a\u8fd8\u5206\u6790</li> </ul> <p>\u8fd9\u91cc\u6211\u4eec\u91c7\u7528\u52bf\u80fd\u6cd5\u8fdb\u884c\u5206\u6790\u3002</p> <p>\u5206\u6790 skew heap \u7684\u5747\u644a\u590d\u6742\u5ea6\uff0c\u4e3b\u8981\u5c31\u662f\u5206\u6790\u5408\u5e76\u64cd\u4f5c\u7684\u590d\u6742\u5ea6\uff0c\u56e0\u4e3a\u5176\u4ed6\u64cd\u4f5c\u90fd\u53ef\u4ee5\u8f6c\u5316\u4e3a\u5408\u5e76\u64cd\u4f5c\u3002</p> <p>\u63a5\u4e0b\u6765\u6211\u4eec\u9700\u8981\u5b9a\u4e49\u52bf\u80fd\u51fd\u6570\uff1a</p> <p>\u52bf\u80fd\u51fd\u6570</p> <p>\u6211\u4eec\u5b9a\u4e49 \\(\\Phi(Heap) = \\text{number of heavy node in } Heap\\)\u3002</p> <p>\u5176\u4e2d\uff0c\u989d\u5916\u9700\u8981\u5b9a\u4e49 heavy node \u548c light node\uff1a</p> <p>heavy node &amp; light node</p> <p>\u5bf9\u4e8e\u4e00\u4e2a\u5b50\u5806 \\(H\\)\uff0c\u5982\u679c \\(size(H.\\text{right\\_descendant}) \\geq \\frac{1}{2}size(H)\\)\uff0c\u5219 \\(H\\) \u662f heavy node\uff0c\u5426\u5219\u662f light node\u3002 </p> @ cy'ppt <p>A node p is heavy if the number of descendants of p\u2019s right subtree is at least half of the number of descendants of p, and light otherwise.  Note that the number of descendants of a node includes the node itself.</p> <p>\u663e\u7136\uff0c\u5bf9\u4e8e heavy node \u548c light node\uff0c\u4ee5\u53ca\u5408\u5e76\u64cd\u4f5c\uff0c\u6709\u8fd9\u4e48\u4e00\u4e9b\u6027\u8d28\uff1a</p> <p>properties</p> <ol> <li>\u5982\u679c\u4e00\u4e2a\u8282\u70b9\u662f heavy node\uff0c\u5e76\u4e14\u5728\u5176\u53f3\u5b50\u6811\u53d1\u751f\u4e86\u5408\u5e76\uff08\u5305\u62ec\u7ffb\u8f6c\uff09\uff0c\u90a3\u4e48\u5b83\u4e00\u5b9a\u53d8\u4e3a\u4e00\u4e2a light node\uff1b</li> <li>\u5982\u679c\u4e00\u4e2a\u8282\u70b9\u662f light node\uff0c\u5e76\u4e14\u5728\u5176\u53f3\u5b50\u6811\u53d1\u751f\u4e86\u5408\u5e76\uff08\u5305\u62ec\u7ffb\u8f6c\uff09\uff0c\u90a3\u4e48\u5b83\u53ef\u80fd\u53d8\u4e3a\u4e00\u4e2a heavy node\uff1b</li> <li>\u5408\u5e76\u8fc7\u7a0b\u4e2d\uff0c\u5982\u679c\u4e00\u4e2a\u8282\u70b9\u7684 heavy/light \u53d1\u751f\u53d8\u5316\uff0c\u90a3\u4e48\u5b83\u539f\u5148\u4e00\u5b9a\u5728\u5806\u7684\u6700\u53f3\u4fa7\u8def\u5f84\u4e0a\uff1b</li> </ol> <p>\u5217\u51fa\u516c\u5f0f\uff1a</p> \\[ \\hat{c} = c + \\Phi(H_{merged}) - \\Phi(H_x) - \\Phi(H_y) \\] <p>\u5176\u4e2d\uff0c\\(c\\) \u4e3a\u5408\u5e76\u64cd\u4f5c\u7684\uff08\u6700\u574f\uff09\u590d\u6742\u5ea6\uff0c\\(H_{merged}\\) \u4e3a\u5408\u5e76\u540e\u7684\u5806\u7684\u52bf\u80fd\uff0c\\(H_x\\) \u548c \\(H_y\\) \u5206\u522b\u4e3a\u5408\u5e76\u524d\u7684\u4e24\u4e2a\u5806\u7684\u52bf\u80fd\u3002</p> <p>\u6839\u636e property 3\uff0c\u5728\u5408\u5e76\u8fc7\u7a0b\u4e2d\u5e76\u975e\u6240\u6709\u8282\u70b9\u90fd\u6536\u5230\u5f71\u54cd\u3002\u6211\u4eec\u53ef\u4ee5\u5355\u72ec\u8bb0\u5f55 \\(l_{x}\\) \u4e3a \\(H_x\\) \u6700\u53f3\u4fa7\u8def\u5f84\u4e0a\u7684 light node \u6570\u91cf\uff0c\\(h_{x}\\) \u4e3a \\(H_x\\) \u6700\u53f3\u4fa7\u8def\u5f84\u4e0a\u7684 heavy node \u6570\u91cf\uff0c\\(h^0_{x}\\) \u4e3a \\(H_x\\) \u6240\u6709\u4e0d\u5728\u6700\u53f3\u4fa7\u8def\u5f84\u4e0a\u7684 heavy node \u6570\u91cf\uff08\u5373 \\(\\text{count of heavy nodes of } H_x = H_x + H^0_x\\)\uff09\u3002</p> <p>\u4e8e\u662f\uff0c\u6211\u4eec\u53ef\u4ee5\u5c06\u4e0a\u5f0f\u5199\u5f00\uff1a</p> \\[ \\left\\{     \\begin{aligned}         c &amp;= l_x + h_x + l_y + h_y &amp;(1)\\\\         \\Phi(H_{merged}) &amp;\\leq l_x + h^0_x + l_y + h^0_y &amp;(2)\\\\         \\Phi(H_x) &amp;= h_x + h^0_{x} &amp;(3)\\\\         \\Phi(H_y) &amp;= h_y + h^0_{y} &amp;(4)     \\end{aligned} \\right. \\] <p>\u5176\u4e2d\u7a0d\u5fae\u505a\u4e00\u4e9b\u89e3\u91ca\uff1a</p> <ol> <li>\\((1)\\)\uff1a\\(c\\) \u4e3a\u5408\u5e76\u64cd\u4f5c\u7684\uff08\u6700\u574f\uff09\u590d\u6742\u5ea6\uff0c\u5373\u6211\u4eec\u7684\u679a\u4e3e\u6d89\u53ca\u4e86\u4e24\u4e2a\u5806\u6240\u6709\u7684\u53f3\u4fa7\u8def\u5f84\uff1b</li> <li>\\((2)\\)\uff1a\u5728\u5408\u5e76\u64cd\u4f5c\u4ee5\u540e\uff0c\u6839\u636e property 1 \u548c property 2\uff0c\u53ef\u4ee5\u5f97\u5230\u8fd9\u4e2a\u4e0d\u7b49\u5f0f\uff1b</li> <li>\\((3)\\) \u548c \\((4)\\)\uff1a\u6839\u636e\u52bf\u80fd\u51fd\u6570\u7684\u5b9a\u4e49\u5f97\u5230\uff1b</li> </ol> <p>\u4e8e\u662f\uff0c\u5c06\u5b83\u4eec\u4ee3\u5165\u5f97\u5230\u7ed3\u679c\uff1a</p> \\[ \\begin{aligned} \\hat{c}      &amp;= c + \\Phi(H_{merged}) - \\Phi(H_x) - \\Phi(H_y) \\\\     &amp;\\leq (l_x + h_x + l_y + h_y)     + (l_x + h^0_x + l_y + h^0_y)     - (h_x + h^0_{x})     - (h_y + h^0_{y}) \\\\     &amp;\\leq 2(l_x + l_y) \\\\ \\hat{c}     &amp;= O(\\log{N}) \\end{aligned} \\]"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec05/","title":"Lecture 5 | Binomial Queue","text":"<p> \u7ea6 2196 \u4e2a\u5b57  12 \u884c\u4ee3\u7801  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 7 \u5206\u949f</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec05/#binomial-queue","title":"Binomial Queue","text":"<p>\u5806\u7684\u5176\u4e2d\u4e00\u4e2a\u5e94\u7528\u5c31\u662f\u4f18\u5148\u961f\u5217\u3002\u672c\u8282\u8981\u4ecb\u7ecd\u7684\u4e8c\u9879\u961f\u5217(Binomial Queue)\u4e5f\u662f\u4f18\u5148\u961f\u5217\u7684\u4e00\u79cd\u5b9e\u73b0\uff0c\u53ea\u4e0d\u8fc7\u4e0d\u540c\u4e8e\u4e4b\u524d\u6211\u4eec\u7528\u4e00\u4e2a\u5806\u7ef4\u62a4\u4f18\u5148\u961f\u5217\uff0c\u4e8c\u9879\u961f\u5217\u540c\u65f6\u7ef4\u62a4\u4e86\u5177\u6709\u4e0d\u540c\u7279\u5f81\u7684\u82e5\u5e72\u961f\u5217\u3002</p> <p>link</p> <p>Wikipedia: https://en.wikipedia.org/wiki/Binomial_heap</p> <p>YouTube: https://www.youtube.com/watch?v=6JxvKfSV9Ns \uff08\u867d\u7136\u8fd9\u4e2a\u89c6\u9891\u662f\u8bb2\u89e3\u6590\u6ce2\u90a3\u5951\u5806\u7684\uff0c\u4f46\u662f\u4e2d\u95f4\u5148\u8bb2\u4e86\u4e8c\u9879\u5806\u3002\uff09</p> <p>\u5b66\u4e60\u5efa\u8bae</p> <p>\u5728\u6b63\u5f0f\u5f00\u59cb\u672c\u8282\u5185\u5bb9\u4e4b\u524d\uff0c\u8bf7\u5e26\u7740\u8fd9\u6837\u4e00\u4e2a\u5ff5\u5934\uff1a\u5c3d\u529b\u601d\u8003\u4e8c\u9879\u961f\u5217\u4e0e\u4e8c\u8fdb\u5236\u7684\u5173\u7cfb\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec05/#\u6982\u5ff5","title":"\u6982\u5ff5","text":"<p>\u4e8c\u9879\u961f\u5217(Binomial Queue)\u672c\u8d28\u4e0a\u662f\u4e00\u7cfb\u5217\u4e8c\u9879\u6811(Binomial Tree)\u7684\u96c6\u5408\u3002\u6240\u4ee5\u6211\u4eec\u9996\u5148\u7ed9\u5b9a\u4e8c\u9879\u6811(Binomial Tree)\u7684\u5b9a\u4e49\uff1a</p> <p>Binomial Tree</p> <p>\u4e8c\u9879\u6811\u6ee1\u8db3\u5806\u7684\u6027\u8d28\uff0c\u5373 parent \u8282\u70b9\u7684\u503c\u5c0f\u4e8e\uff08\u5927\u4e8e\uff09 child \u8282\u70b9\u7684\u503c\u3002</p> <p>\u4e00\u4e2a\u975e\u5e38\u5173\u952e\u7684\u6027\u8d28\u662f\uff0c\\(k\\) \u9636\u4e8c\u9879\u6811\u90fd\u662f\u540c\u6784\u7684\uff0c\u4e14 \\(k\\) \u9636\u4e8c\u9879\u6811\u662f\u4e24\u4e2a \\(k-1\\) \u9636\u4e8c\u9879\u6811\u5408\u5e76\u5f97\u5230\u7684\u3002\u800c\u5176\u5408\u5e76\u65b9\u5f0f\u662f\u76f4\u63a5\u4ee4\u5176\u4e2d\u4e00\u68f5\u6210\u4e3a\u53e6\u5916\u4e00\u68f5\u7684\u6839\u7684\u65b0 child\uff0c\u8fd9\u4e5f\u51b3\u5b9a\u4e86\u4e8c\u9879\u6811\u7684\u6839\u6bcf\u4e00\u4e2a child \u672c\u8eab\u4e5f\u90fd\u662f\u4e00\u4e2a\u4e8c\u9879\u6811\u3002</p> <p> </p> <p>\u663e\u7136\u80fd\u591f\u5f97\u5230\uff0c\u4e8c\u9879\u6811\u5e76\u975e\u4e8c\u53c9\u6811\uff1b\u66f4\u8fdb\u4e00\u6b65\u7684\uff0c\\(k\\) \u9636\u4e8c\u9879\u6811 \\(B_k\\) \u7684\u6839\u6709 \\(k\\) \u4e2a child\uff0c\\(2^k\\) \u4e2a\u8282\u70b9\uff1b\u518d\u8fdb\u4e00\u6b65\u7684\uff0c\\(B_k\\) \u7684\u7b2c \\(d\\) \u5c42\u4e00\u5171\u6709 \\(C_k^d = \\binom{k}{d}\\) \u4e2a\u8282\u70b9\uff0c\u6709\u8da3\u7684\u662f\uff0c\u6240\u6709\u5c42\u7684\u8282\u70b9\u52a0\u8d77\u6765\u521a\u597d\u7b26\u5408\u4e8c\u9879\u5f0f\u5b9a\u7406\uff0c\u6b64\u6761\u5b9a\u7406\u53ef\u4ee5\u7531\u6570\u5b66\u5f52\u7eb3\u6cd5\u5f88\u5bb9\u6613\u5730\u8bc1\u660e\uff0c\u4e0d\u518d\u8d58\u8ff0\u3002</p> <p>\u5173\u4e8e\u5b9e\u73b0</p> <p>\u53ef\u4ee5\u53d1\u73b0\uff0c\u4e8c\u9879\u6811\u662f\u4e00\u4e2a \\(N\\) \u53c9\u6811\uff0c\u6240\u4ee5\u901a\u5e38\u6211\u4eec\u4f7f\u7528\u94fe\u8868 sibling \u7684\u5f62\u5f0f\u6765\u8868\u793a\u4e00\u4e2a\u8282\u70b9\u7684 children\u3002</p> <p>\u518d\u5bf9\u4e8c\u9879\u6811\u505a\u4e00\u4e2a\u7b80\u5355\u7684\u603b\u7ed3\uff0c\\(k\\) \u9636\u4e8c\u9879\u6811\u7ed3\u6784\u552f\u4e00\u786e\u5b9a\uff0c\u4e24\u4e2a \\(k\\) \u9636\u4e8c\u9879\u6811\u5408\u5e76\u540e\u5f97\u5230\u4e00\u4e2a \\(k+1\\) \u9636\u4e8c\u9879\u6811\uff0c\u800c\u4e8c\u9879\u6811\u672c\u8eab\u4e5f\u5177\u6709\u5806\u7684\u6027\u8d28\u3002</p> <p>\u4f46\u662f\uff0c\u867d\u7136\u4e8c\u9879\u6811\u5177\u6709\u5806\u7684\u6027\u8d28\uff0c\u770b\u4f3c\u80fd\u72ec\u7acb\u5b8c\u6210\u4f18\u5148\u961f\u5217\u7684\u529f\u80fd\uff0c\u4f46\u662f\u4e8c\u9879\u6811\u5bf9\u70b9\u7684\u6570\u91cf\u5177\u6709\u6bd4\u8f83\u4e25\u683c\u7684\u8981\u6c42\uff0c\u53ea\u6709\u70b9\u7684\u6570\u91cf\u7b26\u5408 \\(2^k\\) \u65f6\uff0c\u624d\u80fd\u4f7f\u7528\u4e8c\u9879\u6811\u8868\u793a\u3002\u56e0\u6b64\uff0c\u89c2\u5bdf\u4e00\u4e2a\u4e8c\u9879\u6811\u80fd\u627f\u8f7d\u7684\u70b9\u7684\u6570\u91cf\u7279\u5f81\uff0c\u6211\u4eec\u8054\u60f3\u5230\u4e8c\u8fdb\u5236\u5bf9\u6570\u7684\u8868\u793a\u2014\u2014\u6211\u4eec\u53ef\u4ee5\u7528\u4e00\u7cfb\u5217\u4e8c\u9879\u6811\u6765\u7ef4\u62a4 \\(N\\) \u4e2a\u8282\u70b9\u7684\u4f18\u5148\u961f\u5217\uff0c\u800c\u5177\u4f53\u7528\u51e0\u9636\u4e8c\u9879\u6811\uff0c\u5219\u53d6\u51b3\u4e8e \\(N\\) \u7684\u4e8c\u8fdb\u5236\u8868\u8fbe\u4e2d\uff0c\u4e3a <code>1</code> \u7684\u662f\u54ea\u51e0\u4f4d\u3002</p> <p>Binomial Queue</p> <p>\u4e8c\u9879\u961f\u5217(Binomial Queue)\u662f\u4e00\u7cfb\u5217\u4e8c\u9879\u6811(Binomial Tree)\u7684\u96c6\u5408\uff0c\u5176\u4e2d\u6bcf\u4e2a\u4e8c\u9879\u6811\u7684\u9636\u6570 \\(k\\) \u90fd\u662f\u4e0d\u540c\u7684\uff0c\u53cd\u8fc7\u6765\u8bb2\u8fd9\u53e5\u8bdd\uff0c\u96c6\u5408\u4e2d \\(k\\) \u9636\u7684\u4e8c\u9879\u6811\u8981\u4e48\u53ea\u6709\u4e00\u4e2a\uff0c\u8981\u4e48\u6ca1\u6709\u3002</p> <p>\ud83c\udf30</p> <p> </p> <p>\u9898\u76ee\u5b9e\u73b0\u7684\u4e8c\u9879\u961f\u5217\u4e0d\u4e00\u5b9a\u6709 min \u6307\u9488\uff01\u6ce8\u610f\u9762\u5411\u9898\u9762\u548c\u9009\u9879\u5224\u65ad\u5b9e\u73b0\u3002</p> <p>\u800c\u4e3a\u4f55\u8981\u8fd9\u4e48\u8bbe\u8ba1\u4e8c\u9879\u961f\u5217\u7684\u7ed3\u6784\uff0c\u5177\u4f53\u4f53\u73b0\u5728\u64cd\u4f5c\u7684\u8bbe\u8ba1\u4e2d\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec05/#\u64cd\u4f5c","title":"\u64cd\u4f5c","text":"<p>\u5728\u4e8c\u9879\u961f\u5217\u4e2d\uff0c\u5408\u5e76\u662f\u4e00\u4e2a\u975e\u5e38\u57fa\u7840\u7684\u64cd\u4f5c\uff0c\u4e5f\u662f\u7cbe\u9ad3\u6240\u5728\u3002</p> <p>\u800c\u4e3a\u4e86\u611f\u53d7\u8fd9\u4e9b\u64cd\u4f5c\u7684\u7cbe\u9ad3\uff0c\u5728\u7406\u89e3\u4e8c\u9879\u961f\u5217\u8fc7\u7a0b\u4e2d\uff0c\u53ef\u4ee5\u8bd5\u56fe\u4ece\u4e24\u4e2a\u7eac\u5ea6\u540c\u65f6\u7406\u89e3\u8fd9\u4e9b\u64cd\u4f5c\uff1a</p> <ol> <li>\u6811/\u5806\u7684\u7eac\u5ea6\uff0c\u5177\u4f53\u89c2\u5bdf\u6570\u636e\u7684\u8f6c\u79fb\u4e0e\u53d8\u5316\u8fc7\u7a0b\uff1b</li> <li>\u4e8c\u8fdb\u5236\u7684\u7eac\u5ea6\uff0c\u5c06 \\(k\\) \u9636\u4e8c\u9879\u6811\u62bd\u8c61\u4e3a bit vector \u7b2c \\(k\\) \u4f4d\u7684 <code>1</code>\uff0c\u4ece\u4e8c\u8fdb\u5236\u52a0\u6cd5\u7684\u89d2\u5ea6\u7406\u89e3\uff1b</li> </ol> <p>\u4e3a\u4e86\u65b9\u4fbf\u540e\u9762\u9610\u8ff0\uff0c\u6211\u4eec\u7b80\u5355\u505a\u4e00\u4e0b\u8bf4\u660e\uff1a</p> <p>\u7279\u5f81\u6bd4\u7279\u5411\u91cf</p> <p>\u5bf9\u4e8e\u4e00\u4e2a\u4e8c\u9879\u961f\u5217\uff0c\u5b9a\u4e49\u5b83\u7684\u7279\u5f81\u6bd4\u7279\u5411\u91cf\uff08\u6211\u81ea\u5df1\u53e3\u80e1\u7684\u4e1c\u897f\uff0c\u4e0d\u662f\u672f\u8bed\uff09\u662f\u5b83\u7684\u5143\u7d20\u6570\u91cf\u7684\u4e8c\u8fdb\u5236\u8868\u793a\uff08\u53cd\u8fc7\u6765\u8bf4\uff0c\u7279\u5f81\u6bd4\u7279\u5411\u91cf\u7684\u771f\u503c\u8868\u793a\u961f\u5217\u4e2d\u7684\u5143\u7d20\u6570\u91cf\uff09\u3002</p> <p>\ud83c\udf30</p> <p>\u4f8b\u5982\u4e0b\u56fe\u7684\u4f8b\u5b50\uff0c\u4e00\u5171\u6709 11 \u4e2a\u8282\u70b9\uff0c\u5176\u7279\u5f81\u6bd4\u7279\u5411\u91cf\u4e3a <code>1011</code>\uff0c\u521a\u597d\u5bf9\u5e94 \\(B_3\\) \\(B_1\\) \\(B_0\\)\u3002</p> <p> </p> <p>\u4e5f\u5c31\u662f\u8bf4\uff0c\u7279\u5f81\u6bd4\u7279\u5411\u91cf\u8c61\u5f81\u4e86\u4e8c\u9879\u961f\u5217\u7684\u96c6\u5408\u4e2d\u6709\u54ea\u51e0\u9636\u7684\u4e8c\u9879\u6811\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec05/#\u961f\u5217\u5408\u5e76","title":"\u961f\u5217\u5408\u5e76","text":"<p>\u5408\u5e76\u4e24\u4e2a\u4e8c\u9879\u961f\u5217\uff0c\u5b9e\u9645\u4e0a\u5c31\u662f\u5408\u5e76\u4e24\u4e2a\u96c6\u5408\uff0c\u5408\u5e76\u8fc7\u7a0b\u4e2d\uff0c\u6211\u4eec\u5206\u522b\u5408\u5e76\u6bcf\u4e00\u4e2a \\(k\\) \u9636\u4e8c\u9879\u6811\uff0c\u5f53\u4e24\u4e2a\u4e8c\u9879\u961f\u5217\u90fd\u5b58\u5728 \\(k\\) \u9636\u4e8c\u9879\u6811\u65f6\uff0c\u5b83\u4eec\u5408\u5e76\u4e3a\u4e00\u68f5 \\(k+1\\) \u9636\u4e8c\u9879\u6811\u3002\u53ef\u4ee5\u8054\u60f3\uff0c\u8fd9\u9879\u64cd\u4f5c\u201c\u5bf9\u5e94\u201d\u7740\u7279\u5f81\u6bd4\u7279\u5411\u91cf\u7684\u76f8\u52a0\uff0c\u800c\u5408\u5e76\u64cd\u4f5c\u5219\u7c7b\u4f3c\u4e8e\u8fdb\u4f4d\u3002</p> <p>\u56e0\u6b64\uff0c\u5b83\u5c31\u7c7b\u4f3c\u4e8e\u4e00\u4e2a 1bit \u7684\u5168\u52a0\u5668\u3002</p> <pre><code>graph LR;\nA([\"T1.B[k]\"])\nB([\"T2.B[k]\"])\nC([\"T.carry[k-1]\"])\nD([\"T.result[k]\"])\nE([\"T.carry[k]\"])\nADD[\"Adder\"]\nA ---&gt; ADD\nB ---&gt; ADD\nC ---&gt; ADD\nADD ---&gt; D\nADD ---&gt; E</code></pre> <p>\u4e8e\u662f\uff0c\u6839\u636e\u4e00\u4e2a carry \u4f4d\u3001\u4e00\u4e2a\u88ab\u5408\u5e76\u6811\u548c\u4e00\u4e2a\u5408\u5e76\u6811\u7684\u60c5\u51b5\uff0c\u6709\u4e00\u5171 \\(2^3=8\\) \u79cd\u53ef\u80fd\u3002</p> <p>\ud83c\udf30</p> <p>\u5047\u8bbe\u6211\u4eec\u73b0\u5728\u6709\u8fd9\u6837\u4e24\u4e2a\u4e8c\u9879\u961f\u5217\u9700\u8981\u5408\u5e76\uff1a</p> <p> </p> <p>\u5219\u5176\u5408\u5e76\u7684\u64cd\u4f5c\u53ef\u4ee5\u8fd9\u6837\u63cf\u8ff0\u3002</p> \u7279\u5f81\u6bd4\u7279\u5411\u91cf\u89c6\u89d2\u5177\u4f53\u89c6\u89d2 <p>\u7eff\u8272\u4e8c\u9879\u961f\u5217\u7684\u7279\u5f81\u6bd4\u7279\u5411\u91cf\u4e3a <code>1011</code>\uff0c\u84dd\u8272\u7684\u4e3a <code>1001</code>\uff0c\u4e24\u8005\u76f8\u52a0\u5f97\u5230 <code>10100</code>\u3002</p> Frame 1Frame 2Frame 3Frame 4Frame 5Frame 6 <p> </p> <p>\\(B_0\\) \u5408\u5e76\uff0c\u7531\u4e8e \\(T_{green}.B_0\\) \u548c \\(T_{blue}.B_0\\) \u90fd\u5b58\u5728\uff0c\u6240\u4ee5\u5408\u5e76\u4ea7\u751f\u4e3a \\(T.C_0\\)\uff0c\\(T.R_0\\) \u4e3a\u7a7a\u3002</p> <p> </p> <p>\\(B_1\\) \u5408\u5e76\uff0c\u7531\u4e8e \\(T_{green}.B_1\\) \u548c \\(T.C_0\\) \u5b58\u5728\uff0c\u6240\u4ee5\u5408\u5e76\u4ea7\u751f\u4e3a \\(T.C_1\\)\uff0c\\(T.R_1\\) \u4e3a\u7a7a\u3002</p> <p> </p> <p>\\(B_2\\) \u5408\u5e76\uff0c\u7531\u4e8e\u53ea\u6709 \\(T.C_1\\) \u5b58\u5728\uff0c\u6240\u4ee5\u76f4\u63a5\u4ee4 \\(T.R_2 = T.C_1\\)\uff0c\\(T.C_2\\) \u4e3a\u7a7a\u3002</p> <p> </p> <p>\\(B_3\\) \u5408\u5e76\uff0c\u7531\u4e8e \\(T_{green}.B_1\\)\uff0c\\(T_{blue}.B_1\\) \u548c \\(T.C_2\\) \u90fd\u4e0d\u5b58\u5728\uff0c\u6240\u4ee5 \\(T.R_3\\) \u4e3a\u7a7a\uff0c\\(T.C_1\\) \u4e3a\u7a7a\u3002</p> <p> </p> <p>\\(B_4\\) \u5408\u5e76\uff0c\u7531\u4e8e \\(T_{green}.B_4\\) \u548c \\(T.C_3\\) \u90fd\u5b58\u5728\uff0c\u6240\u4ee5\u5408\u5e76\u4ea7\u751f\u4e3a \\(T.C_4\\)\uff0c\\(T.R_4\\) \u4e3a\u7a7a\u3002</p> <p> </p> <p>\\(B_5\\) \u5408\u5e76\uff0c\u7531\u4e8e\u53ea\u6709 \\(T.C_4\\) \u5b58\u5728\uff0c\u6240\u4ee5\u76f4\u63a5\u4ee4 \\(T.R_5 = T.C_4\\)\uff0c\\(T.C_5\\) \u4e3a\u7a7a\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec05/#\u5355\u70b9\u63d2\u5165","title":"\u5355\u70b9\u63d2\u5165","text":"<p>\u63d2\u5165\u7ed3\u70b9\u53ef\u4ee5\u770b\u4f5c\u5408\u5e76\u4e00\u4e2a\u53ea\u6709\u4e00\u4e2a\u7ed3\u70b9\u7684\u5de6\u504f\u5806\uff0c\u6240\u4ee5\u6211\u4eec\u53ef\u4ee5\u76f4\u63a5\u590d\u7528\u5408\u5e76\u8fc7\u7a0b\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec05/#\u67e5\u8be2\u961f\u9996","title":"\u67e5\u8be2\u961f\u9996","text":"<p>\u4e8c\u9879\u961f\u5217\u7684\u961f\u9996\uff0c\u4e5f\u5c31\u662f\u6574\u4e2a\u961f\u5217\u7684\u6700\u5c0f\u503c\uff08\u6700\u5927\u503c\uff09\uff0c\u5c31\u662f\u8fd9\u82e5\u5e72\u4e2a\uff08\\(O(\\log N)\\) \u4e2a\uff09\u4e8c\u9879\u6811\u7684\u6839\u4e2d\u6700\u5c0f\uff08\u6700\u5927\uff09\u7684\u90a3\u4e2a\u3002\u6240\u4ee5\u5176\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a \\(O(\\log N)\\)\u3002</p> <p>\u4e0d\u8fc7\u6709\u65f6\u5019\u6211\u4eec\u4e5f\u4f1a\u989d\u5916\u7ef4\u62a4\u4e00\u4e2a\u6307\u9488\uff0c\u6307\u5411\u5f53\u524d\u6700\u5c0f\u7684\u90a3\u4e2a\u6839\uff0c\u6b64\u65f6\u5176\u590d\u6742\u5ea6\u4e3a \\(O(1)\\)\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec05/#\u961f\u9996\u51fa\u961f","title":"\u961f\u9996\u51fa\u961f","text":"<p>\u961f\u9996\u51fa\u961f\u9996\u5148\u8981\u627e\u5230\u961f\u9996\uff0c\u8fd9\u4ef6\u4e8b\u6211\u4eec\u5728#\u67e5\u8be2\u961f\u9996\u5df2\u7ecf\u8ba8\u8bba\u8fc7\u4e86\u3002</p> <p>\u627e\u5230\u961f\u9996\u540e\uff0c\u6211\u4eec\u5c06\u5176\u4ece\u4e8c\u9879\u961f\u5217\u4e2d\u79fb\u9664\uff0c\u6211\u4eec\u77e5\u9053\uff0c\u961f\u9996\u5fc5\u7136\u662f\u67d0\u4e2a\u4e8c\u9879\u6811\u7684\u6839\uff0c\u6240\u4ee5\u5220\u6389\u8fd9\u4e2a\u961f\u9996\u4ee5\u540e\uff0c\u5c31\u4f1a\u4ea7\u751f \\(k\\) \u4e2a\u65b0\u7684\u5b50\u6811\u3002</p> <p>\u800c\u8ba9\u6211\u4eec\u56de\u987e\u4e8c\u9879\u6811\u7684\u5408\u5e76\u8fc7\u7a0b\uff0c\u53ef\u4ee5\u53d1\u73b0\uff0c\u6839\u7684\u6240\u6709\u513f\u5b50\u90fd\u662f\u4e00\u4e2a\u5b8c\u6574\u7684 \\(k\\) \u9636\u4e8c\u9879\u6811\u5408\u5e76\u8fc7\u6765\u7684\uff0c\u6240\u4ee5\u5f53\u6211\u4eec\u5220\u6389\u8fd9\u4e2a\u6839\uff0c\u4ea7\u751f\u7684\u6240\u6709\u5b50\u6811\u90fd\u662f\u4e8c\u9879\u6811\u3002</p> <p>\u56e0\u6b64\u6211\u4eec\u8054\u60f3\u5230\uff0c\u5c06\u961f\u9996\u51fa\u961f\u95ee\u9898\u8f6c\u5316\u4e3a\u5408\u5e76\u4e8c\u9879\u961f\u5217\u7684\u95ee\u9898\u2014\u2014\u5047\u8bbe \\(T\\) \u7684\u961f\u9996\u662f \\(B_k\\) \u7684\u6839\uff0c\u5219\u961f\u9996\u51fa\u961f\u53ef\u4ee5\u8f6c\u5316\u4e3a\u6c42\u89e3 \\(merge(T-B_k, B_k.root.children)\\) \u7684\u95ee\u9898\u3002</p> <p>\ud83c\udf30</p> <p>\u5047\u8bbe\u6211\u4eec\u6709\u5982\u4e0b\u7684\u4e8c\u9879\u961f\u5217\uff0c\u73b0\u5728\u8fdb\u884c\u5f39\u51fa\u961f\u9996\u7684\u64cd\u4f5c\u3002</p> <p> </p> \u7279\u5f81\u6bd4\u7279\u89c6\u89d2\u5177\u4f53\u89c6\u89d2 <p>\u5982\u4e0a\u961f\u5217\uff0c\u5176\u7279\u5f81\u6bd4\u7279\u5411\u91cf\u4e3a <code>10100</code>\uff0c\u5171 20 \u4e2a\u8282\u70b9\u3002\u73b0\u5728\u5220\u6389\u4e00\u4e2a\uff0c\u5e94\u5f53\u6709 19 \u4e2a\u8282\u70b9\u3002</p> <p>\u66f4\u5177\u4f53\u7684\uff0c<code>10100</code> = <code>10000</code> + <code>100</code>\uff0c\u5206\u522b\u4ee3\u8868\u4e24\u4e2a\u4e8c\u9879\u6811\uff0c\u800c\u6211\u4eec\u7684\u6700\u5c0f\u503c\u662f\u4ece <code>10000</code> \u6240\u4ee3\u8868\u7684\u6811\u91cc\u5220\u9664\u7684\uff0c\u6240\u4ee5\u65b0\u7684\u7279\u5f81\u6bd4\u7279\u5411\u91cf\u4e3a\uff1a(<code>10000</code> - 1) + <code>100</code> = <code>1111</code> + <code>100</code> = <code>10011</code>\uff0c\u5373 19 \u4e2a\u3002</p> <p>\u6ce8\u610f\u89c2\u5bdf\u8fd9\u91cc <code>10000</code> - 1 = <code>1111</code> \u7684\u53d8\u5316\uff0c\u5bfb\u627e\u5b83\u4e0e\u5177\u4f53\u89c6\u89d2\u4e2d\u7684\u5173\u7cfb\u3002</p> Frame 1Frame 2Frame 3Frame 4 <p> </p> <p>\u9996\u5148\u627e\u5230\u961f\u9996\uff0c\u5373\u6b64\u65f6 min \u6307\u9488\u6307\u5411\u7684\u5730\u65b9\u3002\u89c2\u5bdf\u5b83\u7684\u7ed3\u6784\uff0c\u6211\u4eec\u53d1\u73b0\u5b83\u5177\u6709\u56db\u4e2a\u5b50\u6811\uff0c\u5206\u522b\u662f \\(B_0 \\sim B_3\\)\uff0c\u5bf9\u5e94\u4e86\u6211\u4eec\u4e4b\u524d\u63d0\u5230\u7684\u300c\u6839\u7684\u6240\u6709\u513f\u5b50\u90fd\u662f\u4e00\u4e2a\u5b8c\u6574\u7684 \\(k\\) \u9636\u4e8c\u9879\u6811\u5408\u5e76\u8fc7\u6765\u7684\u300d\u3002</p> <p> </p> <p>\u4e8e\u662f\u6211\u4eec\u5c06\u8fd9\u4e2a\u5b50\u6811\u63d0\u53d6\u51fa\u6765\uff0c\u5c06\u539f\u672c\u7684\u4e8c\u9879\u961f\u5217\u62c6\u6210\u4e3a\u4e24\u4e2a\u4e8c\u9879\u961f\u5217\u3002</p> <p> </p> <p>\u73b0\u5728\u6211\u4eec\u5220\u9664\u201c\u961f\u9996\u201d\uff0c\u53d1\u73b0\u90a3\u68f5\u6811\u5206\u88c2\u6210\u4e86\u56db\u4e2a\u8fde\u7eed\u7684\u4e8c\u9879\u6811\uff08<code>10000</code> - 1 = <code>1111</code>\uff09\u3002</p> <p> </p> <p>\u73b0\u5728\u95ee\u9898\u5c31\u8f6c\u5316\u4e3a\u4e86\u4e24\u4e2a\u4e8c\u9879\u961f\u5217\u5408\u5e76\u7684\u95ee\u9898\u3002\u5728\u6b64\u7701\u7565\u3002</p> <p>\u6ce8\u610f\u89c2\u5bdf\u5b8c\u6210\u7684\u4e8c\u9879\u961f\u5217\u7684\u7279\u5f81\u6bd4\u7279\u5411\u91cf\u548c\u4e0a\u9762\u7684\u7279\u5f81\u6bd4\u7279\u5411\u91cf\u89c6\u89d2\u7684\u7ed3\u679c\u3002</p> <p>\u63d0\u793a</p> <p>\u652f\u6301\u7740\u961f\u9996\u51fa\u961f\u53ef\u4ee5\u8fd9\u6837\u8fdb\u884c\u7684\u6027\u8d28\u5c31\u662f\uff0c\u6bcf\u4e00\u4e2a\u4e8c\u9879\u6811\u7684\u6839\u7684 children \u672c\u8eab\u4e5f\u90fd\u662f\u4e8c\u9879\u6811\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec05/#\u644a\u8fd8\u5206\u6790","title":"\u644a\u8fd8\u5206\u6790","text":""},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec05/#project-fibonacci-queue","title":"Project: Fibonacci Queue","text":"<p>Link</p> <p>YouTube: https://www.youtube.com/watch?v=6JxvKfSV9Ns</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec06/","title":"Lecture 6 | Backtracing","text":"<p> \u7ea6 459 \u4e2a\u5b57  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 2 \u5206\u949f</p> <p>link</p> <p>OI Wiki: https://oi-wiki.org/search/backtracking/</p> <p>Wikipedia: https://en.wikipedia.org/wiki/Backtracking</p> <p>\u8fd9\u4e00\u8282\u7684\u5185\u5bb9\u6bd4\u8f83\u6563\uff0c\u56e0\u4e3a\u56de\u6eaf\u662f\u4e00\u4e2a\u5f88\u57fa\u7840\u800c\u4e14\u5f88\u6cdb\u7528\u7684\u4e1c\u897f\uff0c\u6240\u4ee5\u611f\u89c9\u600e\u4e48\u8bb2\u90fd\u4e0d\u592a\u5408\u9002\u3002\u66f4\u591a\u7684\u662f\u9700\u8981\u5728\u5177\u4f53\u95ee\u9898\u3001\u5177\u4f53\u6a21\u578b\u4e2d\u53bb\u4f53\u4f1a\u3002</p> <p>\u52a0\u4e0a\u5982\u679c\u6bcf\u4e00\u4e2a\u5185\u5bb9\u90fd\u8981\u5f80\u6b7b\u91cc\u53bb\u53d9\u8ff0\u7684\u8bdd\u5b9e\u5728\u592a\u7d2f\u4e86\uff0c\u6240\u4ee5\u56de\u6eaf\u8fd9\u4e00\u7ae0\u60f3\u5077\u4e2a\u61d2\uff0c\u5c31\u7b80\u5355\u8bb0\u5f55\u4e00\u4e0b\u8bfe\u4e0a\u63d0\u5230\u8fc7\u7684\u4e00\u4e9b\u6a21\u578b\u5427\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec06/#\u516b\u7687\u540e","title":"\u516b\u7687\u540e","text":"<p>\u975e\u5e38\u7ecf\u5178\u7684\u95ee\u9898\uff0c\u76f8\u4fe1\u63a5\u89e6\u8fc7\u7b97\u6cd5\u7684\u540c\u5b66\u57fa\u672c\u4e0a\u90fd\u7ed5\u4e0d\u5f00\u8fd9\u4e2a\u4e1c\u897f\u3002</p> <p>link</p> <p>Wikipedia: https://en.wikipedia.org/wiki/Eight_queens_puzzle</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec06/#\u6848\u4f8b-the-turnpike-reconstruction-problem","title":"[\u6848\u4f8b] The Turnpike Reconstruction Problem","text":"<p>\u6536\u8d39\u7ad9\u91cd\u5efa\u95ee\u9898(The Turnpike Reconstruction Problem)\u63cf\u8ff0\u7684\u662f\u4e00\u6761\u88ab\u62bd\u8c61\u4e3a\u76f4\u7ebf\u7684\u516c\u8def\u4e0a\uff0c\u6709 \\(N\\) \u4e2a\u6536\u8d39\u7ad9\uff08\\(x_1, x_2, ..., x_N\\)\uff09\u3002\u73b0\u5728\u7ed9\u51fa\u4efb\u610f\u4e24\u4e2a\u6536\u8d39\u7ad9\u4e4b\u95f4\u7684\u8ddd\u79bb\u7684\u53ef\u91cd\u96c6\u5408 \\(D\\)\uff0c\uff08\u53ef\u60f3\u800c\u77e5\uff0c\u4e00\u5171\u6709 \\(\\frac{N(N-1)}{2}\\) \u4e2a\u5143\u7d20\uff09\uff0c\u6c42\u6536\u8d39\u7ad9\u7684\u4f4d\u7f6e\uff0c\u5373\u7ed9\u5b9a\u4efb\u610f\u4e24\u70b9\u7684\u8ddd\u79bb\u96c6\u5408\uff0c\u6c42\u51fa\u8fd9\u4e9b\u70b9\u7684\u5750\u6807\u3002</p> <p>solution</p> <p>\u5927\u6982\u601d\u8def\u5c31\u662f\uff0c\u9996\u5148\u5047\u8bbe \\(x_1 = 0\\)\uff0c\u90a3\u4e48\u5f88\u663e\u7136 \\(x_N = \\mathop{max} \\{D\\}\\)\u3002\u540c\u65f6\u6211\u4eec\u4e5f\u5f97\u5230\u8fd9\u6761\u7ebf\u6bb5\u7684\u957f\u5ea6\u4e3a \\(\\mathop{max} \\{D\\}\\)\u3002\u63a5\u4e0b\u6765 \\(D\\) \u4e2d\u4ece\u5927\u5230\u5c0f\u53d6\u51fa\u5143\u7d20\uff0c\u5219\u5fc5\u5b9a\u8ffd\u52a0\u5728 \\(x_1\\) \u53f3\u4fa7\u6216 \\(x_N\\) \u5de6\u4fa7\uff0c\u4ee5\u6b64\u7c7b\u63a8\u3002\uff08\u53cd\u8bc1\u6cd5\u53ef\u4ee5\u8bc1\u660e\u5728\u5b8c\u5168\u5b89\u6392\u597d\u4e4b\u524d\u90fd\u662f\u8ffd\u52a0\u5728\u5de6\u4fa7\u6216\u8005\u53f3\u4fa7\u7684\u65e2\u5b9a\u8fb9\u754c\u4e4b\u95f4\u7684\uff09\u3002\u800c\u6bcf\u4e00\u6b21\u8ffd\u52a0\u7684\u9009\u62e9\u90fd\u4ee3\u8868\u51b3\u7b56\u6811\u4e2d\u7684\u4e00\u4e2a\u5206\u652f\uff0c\u53ef\u4ee5\u5229\u7528\u5176\u5b83\u6761\u4ef6\u8fdb\u884c\u526a\u679d\uff08\u4f8b\u5982 \\(D\\) \u4e2d\u6709 \\(x_p - x_0\\) \u5c31\u4e00\u5b9a\u6709 \\(x_N - x_p\\)\uff09\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec06/#\u0251-\u03b2-\u526a\u679d","title":"\u0251-\u03b2 \u526a\u679d","text":"<p>link</p> <p>Wikipedia: https://en.wikipedia.org/wiki/Alpha%E2%80%93beta_pruning</p> <ul> <li>\u5b9e\u9645\u4e0a\u5c31\u7c7b\u4f3c\u4e8e\u6c42\u89e3\u4e0d\u80fd\u8fde\u7eed\u5411\u53f3\u7684\uff0c\u4ece\u6839\u5230\u53f6\u5b50\u7684\u8def\u5f84\u3002</li> </ul>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec07/","title":"Lecture 7 | Divide &amp; Conquer","text":"<p> \u7ea6 3626 \u4e2a\u5b57  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 12 \u5206\u949f</p> <p>\u611f\u89c9\u8fd9\u51e0\u8282\u8bfe\u4e0a\u7684\u5185\u5bb9\u90fd\u633a\u5bbd\u6cdb\u7684\u554ax</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec07/#\u6982\u8ff0","title":"\u6982\u8ff0","text":"<p>link</p> <p>Wikipedia: https://en.wikipedia.org/wiki/Divide-and-conquer_algorithm</p> <p>\u5957\u7528 Wiki \u4e0a\u7684\u8bf4\u6cd5\uff0c\u5206\u6cbb\u6cd5(Divide-and-conquer algorithm)\u5c5e\u4e8e\u4e00\u79cd\u7b97\u6cd5\u8303\u578b\uff0c\u5b83\u7684\u57fa\u672c\u601d\u60f3\u662f\u5c06\u4e00\u4e2a\u95ee\u9898\u5206\u89e3\u4e3a\u82e5\u5e72\u4e2a\u89c4\u6a21\u8f83\u5c0f\u7684\u76f8\u540c\u95ee\u9898\uff0c\u7136\u540e\u9012\u5f52\u5730\u89e3\u51b3\u8fd9\u4e9b\u5b50\u95ee\u9898\uff0c\u6700\u540e\u5c06\u8fd9\u4e9b\u5b50\u95ee\u9898\u7684\u89e3\u5408\u5e76\u5f97\u5230\u539f\u95ee\u9898\u7684\u89e3\uff0c\u4e00\u4e2a\u6bd4\u8f83\u7ecf\u5178\u7684\u6848\u4f8b\u5c31\u662f\u5f52\u5e76\u6392\u5e8f\u3002</p> <p>\u672c\u8282\u7684\u91cd\u70b9\u5b9e\u9645\u4e0a\u4e5f\u5e76\u4e0d\u662f\u805a\u7126\u4e8e\u5206\u6cbb\u672c\u8eab\uff0c\u800c\u662f\u5176\u590d\u6742\u5ea6\u5206\u6790\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec07/#\u6848\u4f8b-closet-points-problem","title":"[\u6848\u4f8b] Closet Points Problem","text":"<p>\u4e8c\u7ef4\u6700\u8fd1\u70b9\u95ee\u9898(Closet Points Problem)\uff0c\u6307\u7684\u662f\u7ed9\u5b9a\u5e73\u9762\u4e0a\u7684 n \u4e2a\u70b9\uff0c\u627e\u51fa\u5176\u4e2d\u8ddd\u79bb\u6700\u8fd1\u7684\u4e24\u4e2a\u70b9\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec07/#\u6734\u7d20\u65b9\u6cd5","title":"\u6734\u7d20\u65b9\u6cd5","text":"<p>\u6700\u6734\u7d20\u7684\u505a\u6cd5\u5f53\u7136\u662f\u679a\u4e3e\u6240\u6709\u7684\u70b9\u5bf9\uff0c\u4e00\u5171\u9700\u8981 \\(C_{N}^{2} = {{N}\\choose{2}} = \\frac{N(N-1)}{2}\\) \u5373\u590d\u6742\u5ea6\u4e3a \\(O(N^2)\\)\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec07/#\u5206\u6cbb\u65b9\u6cd5","title":"\u5206\u6cbb\u65b9\u6cd5","text":"<p>\u73b0\u5728\u6211\u4eec\u7c7b\u6bd4\u6700\u5927\u5b50\u5e8f\u5217\u548c\u95ee\u9898\u7684\u5206\u6cbb\u505a\u6cd5\u3002</p> \u6700\u5927\u5b50\u5e8f\u5217\u548c\u7684\u5206\u6cbb\u505a\u6cd5 <ol> <li>\u5c06\u5e8f\u5217\u5206\u4e3a\u5de6\u53f3\u4e24\u90e8\u5206\uff0c\u5206\u522b\u6c42\u89e3\u6700\u5927\u5b50\u5e8f\u5217\u548c\uff1b</li> <li>\u6c42\u89e3\u8de8\u8d8a\u4e2d\u70b9\u7684\u6700\u5927\u5b50\u5e8f\u5217\u548c\uff1b</li> <li>\u6bd4\u8f83\u4e09\u8005\u7684\u5927\u5c0f\uff0c\u53d6\u6700\u5927\u503c\uff1b</li> </ol> <p>\u6211\u4eec\u53ef\u4ee5\u5c06\u6574\u4e2a\u5e73\u9762\u5206\u4e3a\u4e24\u4e2a\u90e8\u5206\uff0c\u5373\u5982\u56fe\u4e2d\u7eff\u8272\u7ebf\u5c06\u70b9\u5bf9\u5212\u5206\u4e3a\u4e24\u4e2a\u90e8\u5206\u3002</p> <p> </p> <p>\u63a5\u4e0b\u6765\u6211\u4eec\u540c\u6837\u5206\u4e3a\u8fd9\u4e48\u4e09\u6b65\uff1a</p> <ol> <li>\u5c06\u70b9\u5bf9\u5206\u4e3a\u5de6\u53f3\u4e24\u90e8\u5206\uff0c\u5206\u522b\u6c42\u89e3\u6700\u8fd1\u70b9\u5bf9\uff1b</li> <li>\u5bfb\u627e\u8de8\u8d8a\u5206\u754c\u7ebf\u7684\u70b9\u5bf9\uff0c\u4ece\u4e2d\u5bfb\u627e\u6700\u8fd1\u70b9\u5bf9\uff1b</li> <li>\u6bd4\u8f83\u4e09\u8005\u7684\u5927\u5c0f\uff0c\u53d6\u6700\u5c0f\u503c\uff1b</li> </ol> <p>\u663e\u7136\uff0c\u6211\u4eec\u73b0\u5728\u9700\u8981\u89e3\u51b3\u7684\u5c31\u662f\u8981\u5982\u4f55\u8bbe\u8ba1\u7b2c\u4e8c\u6b65\u7684\u5b9e\u73b0\uff0c\u4ee5\u6c42\u66f4\u4f18\u7684\u590d\u6742\u5ea6\u3002</p> <p>\u9996\u5148\u6211\u4eec\u5047\u8bbe\u5728\u7b2c\u4e00\u6b65\u4e2d\uff0c\u6211\u4eec\u6c42\u5f97\u4e24\u8fb9\u6c42\u5f97\u7684\u6700\u5c0f\u8ddd\u79bb\u4e2d\u8f83\u5c0f\u7684\u90a3\u4e2a\u4e3a \\(\\delta\\)\uff0c\u6362\u53e5\u8bdd\u6765\u8bf4\uff0c\u5982\u679c\u7b54\u6848\u5728\u7b2c\u4e8c\u6b65\u4e2d\u88ab\u66f4\u65b0\uff0c\u90a3\u4e48\u5b83\u7684\u8ddd\u79bb\u9700\u8981\u5c0f\u4e8e \\(\\delta\\)\u3002\u800c\u6211\u4eec\u77e5\u9053\uff0c\u5728\u7b2c\u4e8c\u6b65\u4e2d\u88ab\u62ff\u51fa\u6765\u7684\u70b9\u5bf9\uff0c\u4e00\u5b9a\u662f\u4e00\u4e2a\u5728\u5206\u754c\u7ebf\u5de6\u4fa7\u4e00\u4e2a\u5728\u5206\u754c\u7ebf \\(L\\) \u53f3\u4fa7\u3002\u6734\u7d20\u7684\u6765\u60f3\uff0c\u5728\u8ddd\u79bb\u5206\u754c\u7ebf \\(\\delta\\) \u4ee5\u5916\u7684\u70b9\u5bf9\u4e2d\uff0c\u6211\u4eec\u662f\u4e0d\u9700\u8981\u8003\u8651\u7684\u3002\u800c\u5728\u8ddd\u79bb\u5206\u754c\u7ebf \\(\\delta\\) \u4ee5\u5185\u7684\u70b9\uff0c\u90fd\u5b58\u5728\u6210\u4e3a\u7b54\u6848\u70b9\u5bf9\u70b9\u53ef\u80fd\u3002</p> <p> </p> <p>\u5982\u56fe\uff0c\u73b0\u5728\u6211\u4eec\u77e5\u9053\uff0c\u53ea\u6709\u843d\u5728\u4e24\u6761\u6df1\u7eff\u8272\u4e4b\u95f4\u7684\u70b9\u624d\u53ef\u80fd\u4f1a\u66f4\u65b0\u7b54\u6848\u3002</p> <p>\u73b0\u5728\u6211\u4eec\u9700\u8981\u505a\u7684\u662f\uff0c\u4ece\u5206\u754c\u7ebf\u5de6\u4fa7\u7684\u533a\u57df\u91cc\u62ff\u4e00\u4e2a\u70b9\uff0c\u548c\u5206\u754c\u7ebf\u53f3\u8fb9\u7684\u4e00\u4e2a\u70b9\u505a\u5339\u914d\uff0c\u7136\u540e\u53d6\u6240\u6709\u7ed3\u679c\u4e2d\u7684\u6700\u5c0f\u70b9\u3002\u4e0d\u8fc7\u8fd9\u4ef6\u4e8b\u4ecd\u7136\u53ef\u4ee5\u4f18\u5316\u2014\u2014\u5728\u4e8c\u7ef4\u7684\u6570\u636e\u4e2d\uff0c\u4ec5\u5bf9\u4e00\u4e2a\u7eac\u5ea6\u505a\u7ea6\u675f\u5f80\u5f80\u4f1a\u5bfc\u81f4\u4e8b\u60c5\u53d8\u5f97\u4e0d\u90a3\u4e48\u7a33\u5b9a\uff0c\u6240\u4ee5\u6211\u4eec\u540c\u6837\u8003\u8651\u5728\u53e6\u5916\u4e00\u4e2a\u65b9\u5411\u505a\u7ea6\u675f\u3002</p> <p>\u4e5f\u662f\u57fa\u4e8e\u8303\u56f4\u7ea6\u675f\u7684\u8003\u8651\u3002\u5047\u8bbe\u6211\u4eec\u4ee5\u5de6\u4fa7\u7684\u70b9\u4e3a\u57fa\u51c6\uff0c\u4ece\u4e0a\u5f80\u4e0b\u505a\u904d\u5386\u8fd9\u4e9b\u70b9\uff0c\u90a3\u4e48\u5bf9\u4e8e\u70b9 \\(p_{l_i}\\)\uff0c\u5177\u6709\u80fd\u591f\u66f4\u65b0\u7b54\u6848\u7684\uff0c \\(\\mathop{dis} (p_{l_i}, p_{r_j}) \\leq \\delta\\) \u7684 \\(p_{r_j}\\)\uff0c\u4e00\u5b9a\u6709 \\(\\mathop{dis_{\\parallel bound}}(p_{l_i}, p_{r_j}) \\leq \\delta\\)\uff08\u76f4\u89d2\u4e09\u89d2\u5f62\u659c\u8fb9\u6700\u957f\uff09\u3002</p> <p>\u56e0\u6b64\uff0c\u5bf9\u4e8e\u9009\u5b9a\u70b9 \\(p_{l_i}\\)\uff0c\u5176\u6240\u6709\u53ef\u80fd\u5bfc\u81f4\u7b54\u6848\u66f4\u65b0\u7684\u70b9\u90fd\u88ab\u6846\u5b9a\u5728\u4e00\u4e2a \\(2\\delta \\times \\delta\\) \u7684\u77e9\u5f62\u4e2d\u3002</p> <p>\u800c\u66f4\u5947\u5999\u7684\u662f\uff0c\u8fd9\u4e2a\u7531\u53c2\u6570 \\(\\delta\\) \u6307\u5b9a\u7684\u77e9\u5f62\uff0c\u5de7\u5999\u5730\u7ea6\u675f\u4e86\u843d\u5728\u77e9\u5f62\u4e2d\u7684\u70b9\u7684\u6700\u5927\u6570\u91cf\u3002</p> <p> </p> <p>\u5728\u8fd9\u6837\u4e00\u4e2a\u533a\u57df\u4e2d\uff0c\u6211\u4eec\u9700\u8981\u7ea6\u675f\u6240\u6709\u843d\u5728 \\(\\delta \\times \\delta\\) \u7684 L \u533a\u57df\u4e2d\u7684\u70b9\uff0c\u4e92\u76f8\u7684\u8ddd\u79bb\u90fd\u5927\u4e8e\u7b49\u4e8e \\(\\delta\\)\uff0c\u5bf9 R \u533a\u57df\u4e2d\u7684\u70b9\u4e5f\u6709\u76f8\u540c\u7684\u7ea6\u675f\u3002\u4e0d\u96be\u53d1\u73b0\uff0c\u5728\u6700\u7406\u60f3\u6700\u7406\u60f3\u7684\u60c5\u51b5\u4e0b\u2014\u2014\u95ed\u533a\u95f4\u3001\u5141\u8bb8\u70b9\u91cd\u5408\u7684\u60c5\u51b5\u4e0b\uff0c\u8fd9\u4e2a\u77e9\u5f62\u6700\u591a\u4e5f\u53ea\u80fd\u653e\u516b\u4e2a\u70b9\uff08\u4e24\u8fb9\u5404\u56db\u4e2a\uff09\uff1a</p> <p> </p> <p>\u800c\u66f4\u4e00\u822c\u7684\u60c5\u51b5\u4e0b\uff0c\u6700\u591a\u4e5f\u53ea\u80fd\u653e\u516d\u4e2a\u70b9\uff08\u4e24\u8fb9\u5404\u4e09\u4e2a\uff09\u3002</p> <p>\u65e0\u8bba\u5982\u4f55\uff0c\u6211\u4eec\u53ef\u4ee5\u5f97\u5230\u7ed3\u8bba\uff0c\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u5bf9\u4e8e\u6bcf\u4e00\u4e2a\u9009\u5b9a\u7684 \\(p_{l_i}\\)\uff0c\u5bfb\u627e\u5176\u53ef\u80fd\u5bfc\u81f4\u7b54\u6848\u66f4\u65b0\u7684\u70b9\u7684\u590d\u6742\u5ea6\u90fd\u662f\u5e38\u6570\u7ea7\u7684\u3002</p> <p>\u800c\u679a\u4e3e\u8fd9\u4e9b\u201c\u9009\u5b9a\u70b9\u201d\uff0c\u4e5f\u5c31\u662f\u679a\u4e3e \\(p_{l_i}\\)\uff0c\u5176\u590d\u6742\u5ea6\uff08\u6491\u6b7b\uff09\u662f \\(O(N)\\)\u3002</p> <p>\u4e8e\u662f\u6211\u4eec\u80fd\u5f97\u5230\u8fd9\u4e2a\u5206\u6cbb\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u8ba1\u7b97\u9012\u63a8\u516c\u5f0f\uff1a</p> \\[ T(N) = \\underbrace{2\\; T(\\frac{N}{2})}_{\\text{Step 1. divide}} + \\underbrace{O(N)}_{\\text{Step 2. across}} = O(N\\log N) \\] <p>\u800c\u6211\u4eec\u63a5\u4e0b\u6765\u8981\u89e3\u51b3\u7684\u5c31\u662f\uff0c\u5982\u4f55\u901a\u8fc7\u8fd9\u4e2a\u9012\u63a8\u5f0f\u5f97\u5230\u7ed3\u679c\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec07/#\u590d\u6742\u5ea6\u5206\u6790","title":"\u590d\u6742\u5ea6\u5206\u6790","text":"<p>\u5728\u5f00\u59cb\u63a5\u4e0b\u6765\u7684\u5185\u5bb9\u4e4b\u524d\uff0c\u6211\u4eec\u9700\u8981\u7ed9\u51fa\u66f4\u4e00\u822c\u7684\uff0c\u6211\u4eec\u60f3\u8981\u89e3\u51b3\u7684\u95ee\u9898\uff0c\u5373\u6c42\u89e3\u65f6\u95f4\u590d\u6742\u5ea6\u9012\u63a8\u516c\u5f0f\u5f62\u5982\u4e0b\u5f0f\u7684\u7b97\u6cd5\u7684\u65f6\u95f4\u590d\u6742\u5ea6\uff1a</p> \\[ T(N) = aT(\\frac{N}{b}) + f(N) \\;\\;\\;\\; a,b \\in Z^+ \\] <p>\u4f8b\u5982\uff0c\u4e0a\u9762\u7684\u6700\u8fd1\u70b9\u5bf9\u95ee\u9898\uff0c\u5c31\u662f \\(a = 2,\\; b = 2,\\; f(N) = O(N)\\) \u7684\u60c5\u51b5\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec07/#\u4ee3\u6362\u6cd5","title":"\u4ee3\u6362\u6cd5","text":"<p>\u4ee3\u6362\u6cd5(substitution method)\u7684\u601d\u8def\u975e\u5e38\u76f4\u767d\uff0c\u9996\u5148\u6211\u4eec\u901a\u8fc7\u67d0\u4e9b\u624b\u6bb5\uff08\u6bd4\u5982\u5927\u773c\u89c2\u5bdf\u6cd5\ud83d\udc40\uff09\u6765\u5f97\u5230\u4e00\u4e2a\u9884\u8bbe\u7684\u7ed3\u679c\uff0c\u63a5\u4e0b\u6765\u901a\u8fc7\u4ee3\u5165\u3001\u5f52\u7eb3\u7684\u65b9\u6cd5\u6765\u8bc1\u660e\u8fd9\u4e2a\u7ed3\u679c\u3002</p> <p>\u5927\u80c6\u731c\u6d4b\uff0c\u5c0f\u5fc3\u6c42\u8bc1\uff01</p> <p>\ud83c\udf30</p> \u9898\u9762\u89e3\u7b54 <p>\u6c42\u89e3\u590d\u6742\u5ea6\uff1a</p> \\[ T(N) = 2\\; T(\\frac{N}{2}) + N \\] <p>\u9884\u8bbe\uff1a</p> \\[ T(N) = O(N\\log N) \\] <p>\u4ee3\u5165\uff1a</p> <ul> <li>\u5bf9\u4e8e\u8db3\u591f\u5c0f\u7684 \\(m &lt; N\\)\uff0c\u6709\uff1a</li> </ul> \\[ T(\\frac{m}{2}) = O(\\frac{m}{2}\\log \\frac{m}{2}) \\leq c \\frac{m}{2}\\log \\frac{m}{2} \\] <ul> <li>\u5c06\u4e0a\u5f0f\u4ee3\u5165\uff1a</li> </ul> \\[ T(m) = 2\\; T(\\frac{m}{2}) + m \\] <ul> <li>\u5f97\uff1a</li> </ul> \\[ T(m) \\leq 2\\; c \\frac{m}{2}\\log \\frac{m}{2} + m \\leq c m \\log m \\text{ for } c \\geq 1 \\] <p>\u5bf9\u4e8e\u8db3\u591f\u5c0f\u7684 \\(m = 2\\) \u5f0f\u5b50\u5c31\u53ef\u4ee5\u6210\u7acb\uff0c\u7531\u5f52\u7eb3\u6cd5\u5f97\u7ed3\u8bba\u6210\u7acb\u3002</p> <p>\u4e0d\u8fc7\u5f88\u663e\u7136\uff0c\u5728\u67d0\u4e9b\u60c5\u51b5\u4e0b\u6211\u4eec\u6c42\u8bc1\u4e86\u4e00\u4e2a\u590d\u6742\u5ea6\u7684\u5047\u8bbe\u6210\u7acb\uff0c\u4f46\u5b83\u5e76\u4e0d\u4e00\u5b9a\u8db3\u591f\u7d27\uff0c\u8fd9\u662f\u731c\u89e3\u6cd5\u7684\u901a\u75c5\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec07/#\u9012\u5f52\u6811\u6cd5","title":"\u9012\u5f52\u6811\u6cd5","text":"<p>\u9012\u5f52\u6811\u6cd5(recursion-tree method)\u7684\u601d\u8def\u662f\uff0c\u6211\u4eec\u901a\u8fc7\u753b\u51fa\u9012\u5f52\u6811\u6765\u5206\u6790\u7b97\u6cd5\u7684\u65f6\u95f4\u590d\u6742\u5ea6\uff0c\u5b9e\u9645\u4e0a\u548c\u76f4\u63a5\u6570\u5b66\u63a8\u7406\u7684\u533a\u522b\u4e0d\u662f\u5f88\u5927\uff0c\u4e3b\u8981\u5c31\u662f\u901a\u8fc7\u89c2\u5bdf\u9012\u5f52\u8fc7\u7a0b\u4e2d\u6570\u636e\u589e\u957f\u7684\u6a21\u5f0f\u6765\u8fdb\u884c\u5206\u6790\u3002</p> some mathematical tools \\[ a^{\\log_b N} = \\exp^{\\frac{\\ln N}{\\ln b} \\ln a} = \\exp^{\\frac{\\ln a}{\\ln b} \\ln N} = N^{\\log_b a} \\] <p>\u5c31\u7c7b\u4f3c\u4e8e\u76f4\u63a5\u5c55\u5f00\u5f0f\u5b50\uff0c\u53ea\u4e0d\u8fc7\u901a\u8fc7\u6811\u72b6\u56fe\u7684\u5f62\u5f0f\u6216\u8bb8\u66f4\u52a0\u76f4\u89c2\u3002</p> <p>\u5bf9\u4e8e\u4e00\u4e2a\u9012\u63a8\u5f0f\uff0c\u6211\u4eec\u5c06\u5b83\u4e0d\u65ad\u5c55\u5f00\u4ee5\u540e\uff0c\u5176\u5f62\u5f0f\u5927\u6982\u4f1a\u662f\u8fd9\u6837\uff1a</p> \\[ T(N) = ... =  \\underbrace{\\sum_{leaf_i}^{leaves}T(N_{leaf_i})}_{conquer} +  \\underbrace{\\sum_{node_i}^{non-leaf-nodes}f(N_{node_i})}_{combine} \\] <p>\u5176\u4e2d\uff0c\u7531\u4e8e\u672b\u7aef\u5b50\u95ee\u9898\u7684\u89c4\u6a21\u4e00\u822c\u90fd\u8db3\u591f\u5c0f\uff0c\u53ef\u4ee5\u8ba4\u4e3a \\(T(N_{leaf_i})\\) \u90fd\u662f\u5e38\u6570\uff0c\u4e8e\u662f\u4e0a\u5f0f\u53c8\u53ef\u4ee5\u53d8\u5316\u4e3a\uff1a</p> \\[ T(N) = ... =  \\underbrace{c\\; N_{leaves}}_{conquer} +  \\underbrace{\\sum_{node_i}^{non-leaf-nodes}f(N_{node_i})}_{combine} \\] <p>\u5177\u4f53\u6765\u8bf4\u89e3\u91ca\u5176\u542b\u4e49\uff0ccombine \u90e8\u5206\u5c31\u662f\u5728\u6bcf\u4e00\u6b21\u201c\u5206\u6cbb\u201d\u7684\u5904\u7406\u65f6\u95f4\uff0c\u5982\u5408\u5e76\u5f53\u524d\u7684\u5b50\u95ee\u9898\u5206\u6cbb\u540e\u7684\u7ed3\u679c\uff0c\u4f53\u73b0\u5728\u9012\u63a8\u5f0f\u7684 \\(f(N)\\) \u90e8\u5206\uff1b\u800c conquer \u90e8\u5206\u6307\u7684\u662f\u5f53\u201c\u5206\u6cbb\u201d\u7684\u201c\u6cbb\u201d\u5728\u201c\u5206\u201d\u7684\u672b\u7aef\u7684\u4f53\u73b0\uff0c\u5373\u5bf9\u4e8e\u8db3\u591f\u5c0f\u7684\u89c4\u6a21\u7684\u95ee\u9898\uff0c\u4e0d\u518d\u9700\u8981\u7ee7\u7eed\u201c\u5206\u201d\u7684\u65f6\u5019\uff0c\u5bf9\u5176\u5904\u7406\u7684\u5f00\u9500\u3002</p> <p>\u5b9e\u9645\u4e0a\u5728\u4ee3\u7801\u5c42\u9762\u8fd9\u4e24\u90e8\u5206\u53ef\u80fd\u533a\u522b\u4e0d\u5927\uff08\u53ef\u80fd\u5c31\u662f\u4e00\u4e2a\u5206\u652f\u7684\u4e8b\u60c5\uff09\uff0c\u4e0d\u8fc7\u5728\u6570\u5b66\u610f\u4e49\u4e0a\uff0c\u5bf9\u4e8e\u4e00\u4e2a\u9012\u63a8\u5f0f\u5b50\u6c42\u89e3\u6211\u4eec\u4e00\u822c\u662f\u9700\u8981\u201c\u9996\u9879\u201d\u7684\uff0c\u6216\u8005\u8bf4\u662f\u201c\u6700\u5e95\u5c42\u201d\u7684\uff0c\u800c\u8fd9\u4e2a\u201c\u6700\u5e95\u5c42\u201d\u7684\u90e8\u5206\u5c31\u662f conquer \u90e8\u5206\u3002</p> <p>\u63a5\u4e0b\u6765\u7ed3\u5408 \ud83c\udf30 \u6765\u5206\u6790\u4e00\u4e0b\uff1a</p> <p>\ud83c\udf30</p> <p></p> <p>From cy's ppt.</p> <p><code>\\underbrace</code> \u4e0b\u9762\u90a3\u4e2a\u7b49\u5f0f\u7684\u8bc1\u660e\u5728\u4e0a\u9762\u7684 \"some mathematical tools\"\u3002</p> <p>\u53ef\u4ee5\u53d1\u73b0\uff0c\u6b64\u60c5\u51b5\u4e0b \\(a = 3,\\; b = 4,\\; f(N) = \\Theta(N^2)\\)\uff0c\u4e5f\u5c31\u662f\u8bf4\u6bcf\u6b21\u5206\u4e3a \\(3\\) \u4e2a\u5b50\u95ee\u9898\uff0c\u5b50\u95ee\u9898\u7684\u89c4\u6a21\u662f \\(\\frac{N}{4}\\)\uff0c\u800c\u5408\u5e76\u5f00\u9500\u4e3a \\(\\Theta(N^2)\\)\u3002</p> <p>\u6b64\u65f6\u7531\u4e8e\u5206\u6cbb\u7684\u7b56\u7565\u662f\u76f8\u5bf9\u5747\u5300\u7684\uff0c\u6240\u4ee5\u6211\u4eec\u53ef\u4ee5\u8ba4\u4e3a\u5f97\u5230\u7684\u662f\u4e00\u4e2a\u5b8c\u7f8e\u4e09\u53c9\u6811\u3002</p> <p>\u663e\u7136\uff0c\u6811\u9ad8\u4e3a \\(\\log_4 N\\)\uff0c\u6839\u8bb0\u4e3a \\(0\\)\uff0c\u6bcf\u4e2a\u5206\u6cbb\u8282\u70b9\u7684 combine \u5f00\u9500\u5df2\u7ecf\u6807\u6ce8\u5728\u56fe\u7684\u8282\u70b9\u4f4d\u7f6e\uff0c\u6a2a\u5411\u7bad\u5934\u6807\u8bb0\u7684\u662f\u5bf9\u8be5\u5c42\u6240\u6709\u8282\u70b9\u7684\u5f00\u9500\u7684\u6c42\u548c\u3002\u7279\u522b\u7684\uff0c\u5bf9\u4e8e\u6700\u5e95\u5c42\uff0c\u5373\u53f6\u5b50\u5c42\uff0c\u5b83\u8868\u793a\u7684\u662f conquer \u90e8\u5206\u7684\u5f00\u9500\uff08\u867d\u7136\u6211\u4e2a\u4eba\u89c9\u5f97\u6ca1\u5fc5\u8981\u533a\u5206\u8fd9\u4fe9\uff09\u3002</p> <p>\u4e8e\u662f\u6211\u4eec\u53ef\u4ee5\u6839\u636e\u4e0b\u5f0f\u7684\u5f62\u5f0f\uff0c\u5bf9\u5176\u8fdb\u884c\u6c42\u548c\uff0c\u5f97\u5230\u56fe\u7247\u4e2d\u4e0b\u65b9\u7684\u5f0f\u5b50\u3002</p> \\[ T(N) = ... =  \\underbrace{c\\; N_{leaves}}_{conquer} +  \\underbrace{\\sum_{node_i}^{non-leaf-nodes}f(N_{node_i})}_{combine} \\]"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec07/#\u4e3b\u65b9\u6cd5","title":"\u4e3b\u65b9\u6cd5","text":"<p>link</p> <p>OI Wiki: https://oi-wiki.org/basic/complexity/#\u4e3b\u5b9a\u7406-master-theorem</p> <p>Wikipedia: https://en.wikipedia.org/wiki/Master_theorem_(analysis_of_algorithms)</p> <p>\u4e3b\u65b9\u6cd5(master method)\u4e4b\u6240\u4ee5\u53eb\u201c\u4e3b\u201d\uff0c\u662f\u56e0\u4e3a\u5b83\u5206\u6790\u7684\u662f combine \u548c conquer \u90e8\u5206\u5b70\u4e3a\u4e3b\u5bfc\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec07/#\u5f62\u5f0f\u4e00","title":"\u5f62\u5f0f\u4e00","text":"<p>Form 1</p> <p>\u5bf9\u4e8e\u5f62\u5982 \\(T(N)=aT(N/b)+f(N)\\) \u7684\u9012\u63a8\u5f0f\uff1a</p> <ol> <li>\u82e5 \\(f(N)=O(N^{(\\log_b{a})-\\varepsilon}), \\text{ for }\\varepsilon&gt;0\\)\uff0c\u90a3\u4e48 \\(T(N)=\\Theta(N^{\\log_b{a}})\\)\uff1b</li> <li>\u82e5 \\(f(N)=\\Theta(N^{\\log_b{a}})\\)\uff0c\u90a3\u4e48 \\(T(N)=\\Theta(N^{\\log_b{a}}\\log{N})\\)\uff1b</li> <li>\u82e5 \\(f(N)=\\Omega(N^{(\\log_b{a})+\\varepsilon}), \\text{ for }\\varepsilon&gt;0\\) \u4e14 \\(af(\\frac{N}{b})&lt;cf(N), \\text{ for } c&lt;1 \\text{ and } \\forall N &gt; N_0\\)\uff0c\u90a3\u4e48 \\(T(N)=\\Theta(f(N))\\)\uff1b</li> </ol> <p>\u60c5\u51b5\u4e09\u7684\u540e\u9762\u90a3\u4e2a\u6761\u4ef6\u53c8\u53eb regularity condition\u3002</p> <p>\u56de\u987e\u6211\u4eec\u5728\u524d\u9762\u8bf4\u7684\u90a3\u53e5\u8bdd\uff0c\u300c\u4e3b\u65b9\u6cd5(master method)\u4e4b\u6240\u4ee5\u53eb\u201c\u4e3b\u201d\uff0c\u662f\u56e0\u4e3a\u5b83\u5206\u6790\u7684\u662f combine \u548c conquer \u90e8\u5206\u5b70\u4e3a\u4e3b\u5bfc\u300d\uff0c\u89c2\u5bdf\u4e09\u79cd\u60c5\u51b5\u7684\u533a\u5206\u6761\u4ef6\u90fd\u662f\u6bd4\u8f83 \\(f(N)\\)\uff08\u6bcf\u4e00\u6b21\u7684 combine \u5f00\u9500\uff09 \u548c \\(N^{\\log_b{a}}\\)\uff08\u5373\u6c42\u548c\u5f0f\u4e2d\u7684 conquer \u7684\u5f00\u9500\uff09\uff0c\u5f53 \\(f(N)\\) \u8db3\u591f\u5c0f\u65f6\uff0c\u4ee5 conquer \u5f00\u9500\u4e3a\u4e3b\uff08i.e. case 1\uff09\uff1b\u5f53\u8db3\u591f\u5927\u65f6\uff0c\u4ee5 combine \u4e3a\u4e3b\uff08i.e. case 3\uff09\uff1b\u800c\u5176\u4e2d\u8fd8\u6709\u4e00\u4e2a\u4e2d\u95f4\u72b6\u6001\uff08i.e. case 2\uff09\u3002</p> examples for form 1 <ul> <li>\u3010eg1\u3011\\(a = b = 2,\\; f(N) = N\\)\uff1b<ul> <li>\\(f(N) = N = \\Theta(N^{\\log_2{2}})\\)\uff0c\u9002\u7528\u4e8e\u60c5\u51b5 2\uff1b</li> <li>\u56e0\u6b64\u5f97\u5230\u7ed3\u679c \\(T(N) = \\Theta(N \\log N)\\)\uff1b</li> </ul> </li> <li>\u3010eg2\u3011\\(a = b = 2,\\; f(N) = N \\log N\\)\uff1b<ul> <li>\\(f(N) = N \\log N\\)\uff0c\u867d\u7136 \\(N \\log N = \\Omega(N^{\\log_2{2}})\\)\uff0c\u4f46\u662f \\(N \\log N \\neq \\Omega(N^{(\\log_2{2}) - \\varepsilon})\\)\uff0c\u6240\u4ee5\u4e0d\u9002\u7528\u4e8e\u60c5\u51b5 3\uff1b<ul> <li>\u5177\u4f53\u6765\u8bf4\uff0c\\(\\lim \\limits_{N\\to \\infty} \\frac{N \\log N}{N^{1+\\varepsilon}}=\\lim \\limits_{N\\to \\infty} \\frac{\\log N}{N^{\\varepsilon}} = 0 \\text{ for fixed } \\varepsilon &gt; 0\\)\uff1b</li> <li>\u8fd9\u4e2a\u4f8b\u5b50\u4f53\u73b0\u51fa\u4e86 \\(\\varepsilon\\) \u7684\u4e00\u5b9a\u4f5c\u7528\uff1b</li> </ul> </li> </ul> </li> </ul>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec07/#\u8bc1\u660e","title":"\u8bc1\u660e","text":"<p>proof for form 1</p> <p>\u5bf9\u4e8e\u5f62\u5982 \\(T(N)=aT(N/b)+f(N)\\) \u7684\u9012\u63a8\u5f0f\uff0c\u6211\u4eec\u9700\u8981\u4f9d\u6b21\u8bc1\u660e\uff0c\u6b64\u5904\u6211\u4eec\u4f7f\u7528\u9012\u5f52\u6811\u6cd5\u8fdb\u884c\u8bc1\u660e\u3002</p> \u60c5\u51b5\u4e00 <p>\ud83c\udfaf \u76ee\u6807\uff1a\u82e5 \\(f(N)=O(N^{(\\log_b{a})-\\varepsilon}), \\text{ for }\\varepsilon&gt;0\\)\uff0c\u90a3\u4e48 \\(T(N)=\\Theta(N^{\\log_b{a}})\\)\uff1b</p> <p>\ud83e\udea7 \u8bc1\u660e\uff1a\u6211\u4eec\u9996\u5148\u9700\u8981\u7ed8\u5236\u51fa\u5bf9\u5e94\u7684\u9012\u5f52\u6811\uff0c\u6216\u8005\u641e\u6e05\u695a\u5c55\u5f00\u540e\u7684\u60c5\u51b5\uff0c\u56e0\u4e3a\u61d2\u5f97\u753b\u56fe\u6240\u4ee5\u6211\u8fd9\u91cc\u91c7\u7528\u6587\u5b57\u53d9\u8ff0\u3002</p> <p>\u6811\u9ad8 \\(\\log_b{N}\\)\uff0c\u5171 \\(\\log_b{N} + 1\\) \u5c42\uff0c\u5219\u6709\uff1a</p> <ul> <li>\u7b2c \\(0\\) \u5c42\uff08\u6839\uff09\u4e00\u5171 \\(1\\) \u9879\uff0ccombine \u7684\u5f00\u9500\u4e3a \\(f(N)\\)\uff1b</li> <li>\u7b2c \\(1\\) \u5c42\u4e00\u5171 \\(a\\) \u9879\uff0ccombine \u7684\u5f00\u9500\u4e3a \\(a\\times f(\\frac{N}{b})\\)\uff1b</li> <li>\u7b2c \\(2\\) \u5c42\u4e00\u5171 \\(a^2\\) \u9879\uff0ccombine \u7684\u5f00\u9500\u4e3a \\(a^2 \\times f(\\frac{N}{b^2})\\)\uff1b</li> <li>......</li> <li>\u7b2c \\(j\\) \u5c42\u4e00\u5171 \\(a^j\\) \u9879\uff0ccombine \u7684\u5f00\u9500\u4e3a \\(a^j \\times f(\\frac{N}{b^j})\\)\uff1b</li> <li>......</li> <li>\u7b2c \\((\\log_b{N}) - 1\\) \u5c42\u4e00\u5171 \\(a^{(\\log_b{N}) - 1}\\) \u9879\uff0ccombine \u7684\u5f00\u9500\u4e3a \\(a^{(\\log_b{N}) - 1} \\times f(\\frac{N}{b^{(\\log_b{N}) - 1}})\\)\uff1b</li> <li>\u7b2c \\(\\log_b{N}\\) \u5c42\uff0c\u5373\u4e3a\u53f6\u5b50\u5c42\uff0c\u4e00\u5171 \\(a^{\\log_b{N}} = N^{\\log_b{a}}\\) \u9879\uff0cconquer \u7684\u5f00\u9500\u4e3a \\(N^{\\log_b{a}} \\times \\Theta(1) = \\Theta(N^{\\log_b{a}})\\)\uff1b</li> </ul> <p>\u5f97\u5230\u6c42\u548c\u5f0f\uff1a</p> \\[ T(N) = \\Theta(N^{\\log_b{a}}) + \\sum_{j = 0}^{(\\log_b{N})-1} a^j f(\\frac{N}{b^j}) \\] <p>\u800c\u6211\u4eec\u6709\u6761\u4ef6 \\(f(N)=O(N^{(\\log_b{a})-\\varepsilon}), \\text{ for }\\varepsilon&gt;0\\)\uff0c\u5c06\u5b83\u4ee3\u5165\u5230\u4e0a\u5f0f\u4e2d\u5f97\u5230\uff1a</p> \\[ \\begin{aligned} T(N)  &amp;= \\Theta(N^{\\log_b{a}}) + \\sum_{j = 0}^{(\\log_b{N})-1} a^j O\\left(\\left(\\frac{N}{b^j}\\right)^{(\\log_b{a})-\\varepsilon}\\right)\\\\ &amp;= \\Theta(N^{\\log_b{a}}) + O\\left(     N^{(\\log_b{a}) - \\varepsilon}     \\times     \\sum_{j = 0}^{(\\log_b{N})-1} \\left(\\frac{a}{b^{(\\log_b{a})-\\varepsilon}}\\right)^j \\right) \\\\ &amp;= \\Theta(N^{\\log_b{a}}) + O\\left(     N^{(\\log_b{a}) - \\varepsilon}     \\times     \\sum_{j = 0}^{(\\log_b{N})-1} (b^{\\varepsilon})^j \\right) \\\\ &amp;= \\Theta(N^{\\log_b{a}}) + O\\left(     N^{(\\log_b{a}) - \\varepsilon}     \\times     \\frac{1\\times(1-(b^\\varepsilon)^{\\log_b{N}})}{1-b^\\varepsilon} \\right) \\\\ &amp;= \\Theta(N^{\\log_b{a}}) + O\\left(     N^{(\\log_b{a}) - \\varepsilon}     \\times     \\frac{N^\\varepsilon-1}{b^\\varepsilon-1} \\right) \\\\ &amp;= \\Theta(N^{\\log_b{a}}) + O\\left(     N^{(\\log_b{a}) - \\varepsilon}     \\times     N^\\varepsilon \\right) \\\\ &amp;= \\Theta(N^{\\log_b{a}}) + O\\left(     N^{\\log_b{a}} \\right) \\\\ &amp;= \\Theta(N^{\\log_b{a}}) \\end{aligned} \\] <p>\u81f3\u6b64\uff0c\u60c5\u51b5\u4e00\u8bc1\u660e\u5b8c\u6bd5\u3002</p> \u60c5\u51b5\u4e8c <p>\ud83c\udfaf \u76ee\u6807\uff1a\u82e5 \\(f(N)=\\Theta(N^{\\log_b{a}})\\)\uff0c\u90a3\u4e48 \\(T(N)=\\Theta(N^{\\log_b{a}}\\log{N})\\)\uff1b</p> <p>\ud83e\udea7 \u8bc1\u660e\uff1a\u524d\u9762\u7684\u90e8\u5206\u548c\u60c5\u51b5\u4e00\u7684\u7c7b\u4f3c\uff0c\u6211\u4eec\u901a\u8fc7\u76f8\u540c\u7684\u6b65\u9aa4\u5f97\u5230\u76f8\u540c\u7684\u6c42\u548c\u5f0f\uff1a</p> \\[ T(N) = \\Theta(N^{\\log_b{a}}) + \\sum_{j = 0}^{(\\log_b{N})-1} a^j f(\\frac{N}{b^j}) \\] <p>\u800c\u6211\u4eec\u6709\u6761\u4ef6 \\(f(N)=\\Theta(N^{\\log_b{a}})\\)\uff0c\u5c06\u5b83\u4ee3\u5165\u5230\u4e0a\u5f0f\u4e2d\u5f97\u5230\uff1a</p> \\[\\begin{aligned} T(N) &amp;= \\Theta(N^{\\log_b{a}}) + \\sum_{j=0}^{(\\log_b{N})-1}a^j\\Theta\\left(\\left(\\frac{N}{b^j}\\right)^{\\log_b{a}}\\right) \\\\ &amp;= \\Theta(N^{\\log_b{a}}) + \\Theta\\left(     N^{\\log_b{a}} \\times     \\sum_{j=0}^{(\\log_b{N})-1}\\left(\\frac{a}{b^{\\log_b{a}}}\\right)^j \\right) \\\\ &amp;= \\Theta(N^{\\log_b{a}}) + \\Theta\\left(     N^{\\log_b{a}} \\times     \\log_b{N} \\right) \\\\ &amp;= \\Theta(N^{\\log_b{a}}\\log{N}) \\end{aligned}\\] <p>\u81f3\u6b64\uff0c\u60c5\u51b5\u4e8c\u8bc1\u660e\u5b8c\u6bd5\u3002</p> \u60c5\u51b5\u4e09 <p>\ud83c\udfaf \u76ee\u6807\uff1a\u82e5 \\(f(N)=\\Omega(N^{(\\log_b{a})+\\varepsilon}), \\text{ for }\\varepsilon&gt;0\\) \u4e14 \\(af(\\frac{N}{b})&lt;cf(N), \\text{ for } c&lt;1 \\text{ and } \\forall N &gt; N_0\\)\uff0c\u90a3\u4e48 \\(T(N)=\\Theta(f(N))\\)\uff1b</p> <p>\ud83e\udea7 \u8bc1\u660e\uff1a\u60c5\u51b5\u4e09\u7684\u8bc1\u660e\uff0c\u4ece\u6761\u4ef6\u7684\u53d8\u5316\u5c31\u53ef\u4ee5\u770b\u51fa\u6765\u548c\u524d\u9762\u7a0d\u8bb8\u6709\u4e9b\u4e0d\u540c\u4e86\u3002\u4e0d\u8fc7\u6c42\u548c\u5f0f\u7684\u5f97\u5230\u8fd8\u662f\u4e00\u6837\uff0c\u901a\u8fc7\u548c\u4e4b\u524d\u4e00\u6837\u7684\u65b9\u6cd5\uff0c\u6211\u4eec\u9996\u5148\u5f97\u5230\u6c42\u548c\u5f0f\uff1a</p> \\[ T(N) = \\Theta(N^{\\log_b{a}}) + \\sum_{j = 0}^{(\\log_b{N})-1} a^j f(\\frac{N}{b^j}) \\] <p>\u63a5\u4e0b\u6765\u7684\u6b65\u9aa4\u548c\u4e4b\u524d\u4e0d\u540c\u3002\u5728\u7ee7\u7eed\u4e4b\u524d\uff0c\u6211\u4eec\u9996\u5148\u89c2\u5bdf\u4e0d\u7b49\u5f0f \\(af(\\frac{N}{b})&lt;cf(N)\\)\uff0c\u5728\u6211\u4eec\u7684\u6c42\u548c\u5f0f\u4e2d\uff0c\u6211\u4eec\u89c2\u5bdf\u5230\u6211\u4eec\u6709\u5927\u91cf\u7684\u5f62\u5982 \\(a^jf(\\frac{N}{b^j})\\) \u7684\u9879\uff0c\u800c\u8fd9\u4e9b\u9879\u90fd\u53ef\u4ee5\u901a\u8fc7\u8fed\u4ee3\u4e0a\u9762\u90a3\u4e2a\u4e0d\u7b49\u5f0f\u6765\u5b9e\u73b0\uff0c\u5373\uff1a</p> \\[ a^jf(\\frac{N}{b^j}) &lt; c\\times a^{j-1}f(\\frac{N}{b^{j-1}}) &lt; ... &lt; c^j f(N) \\] <p>\u5c06\u8fd9\u4e2a\u4e0d\u7b49\u5f0f\u5e94\u7528\u4e8e\u6c42\u548c\u5f0f\u4e2d\uff0c\u6211\u4eec\u80fd\u591f\u5f97\u5230\uff1a</p> \\[ \\begin{aligned}     T(N)      &amp;&lt; \\Theta(N^{\\log_b{a}}) + \\sum_{j=0}^{(\\log_b{N})-1}c^j f(N) \\\\     &amp;= \\Theta(N^{\\log_b{a}}) + f(N) \\sum_{j=0}^{(\\log_b{N})-1}c^j \\\\     &amp;= \\Theta(N^{\\log_b{a}}) + f(N) \\times \\frac{c^{1-\\log_b{N}}}{1-c} \\\\     &amp;= \\Theta(N^{\\log_b{a}}) + f(N) \\times \\frac{1-N^{\\log_b{c}}}{1-c} \\end{aligned}         \\] <p>\u800c\u7531\u4e8e \\(c&lt;1\\)\uff0c\u6240\u4ee5 \\(\\log_b{c} &lt; 0\\)\uff1b\u800c \\(N &gt; 0\\)\uff0c\u800c\u4e14\u4e00\u822c\u975e\u5e38\u5927\uff0c\u6240\u4ee5 \\(N^{\\log_b{c}} \\in (0,1)\\)\u3002\u56e0\u6b64\uff0c\u5bf9\u4e8e\u786e\u5b9a\u7684\u5e38\u6570 \\(c\\)\uff0c\u6211\u4eec\u6709 \\(\\frac{1-N^{\\log_b{c}}}{1-c} \\in \\left(0, \\frac{1}{1-c}\\right)\\)\uff1b</p> <p>\u56e0\u6b64\uff0c\u4e0a\u5f0f\u4fbf\u80fd\u6539\u53d8\u4e3a\uff1a</p> \\[ \\begin{aligned}     T(N)      &amp;&lt; \\Theta(N^{\\log_b{a}}) + f(N) \\times \\frac{1-N^{\\log_b{c}}}{1-c} \\\\     &amp;&lt; \\Theta(N^{\\log_b{a}}) + f(N) \\times \\frac{1}{1-c} \\end{aligned} \\] <p>\u5e76\u4e14\uff0c\u7531\u4e8e \\(f(N)=\\Omega(N^{(\\log_b{a})+\\varepsilon}), \\text{ for }\\varepsilon&gt;0\\)\uff0c\u6240\u4ee5\u6839\u636e\u7b26\u53f7\u5b9a\u4e49\u53ef\u4ee5\u5f97\u5230 \\(T(N) = O(f(N))\\)\u3002</p> <p>\u800c\u6211\u4eec\u77e5\u9053\uff0c\u8981\u8bc1\u660e \\(T(N) = \\Theta(f(N))\\) \u8fd8\u9700\u8981\u8bc1\u660e \\(T(N) = \\Omega(f(N))\\)\uff1a</p> \\[ \\begin{aligned} T(N) &amp;= \\Theta(N^{\\log_b{a}}) + \\sum_{j = 0}^{(\\log_b{N})-1} a^j f(\\frac{N}{b^j}) &amp;\\geq \\sum_{j = 0}^{(\\log_b{N})-1} a^j f(\\frac{N}{b^j}) &amp;\\geq f(N) \\end{aligned} \\] <p>\u7531\u6b64\u5f97\u5230 \\(T(N) = \\Omega(f(N))\\)\uff0c\u6700\u7ec8\u8bc1\u5f97 \\(T(N) = \\Theta(f(N))\\)\uff0c\u81f3\u6b64\uff0c\u60c5\u51b5\u4e09\u8bc1\u660e\u5b8c\u6bd5\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec07/#\u5f62\u5f0f\u4e8c","title":"\u5f62\u5f0f\u4e8c","text":"<p>Form 2</p> <p>\u5bf9\u4e8e\u5f62\u5982 \\(T(N) = aT(\\frac{N}{b}) + f(N)\\) \u7684\u9012\u63a8\u5f0f\uff1a</p> <ol> <li>\u82e5 \\(af(\\frac{N}{b}) = \\kappa f(N) \\text{ for fixed } \\kappa &lt; 1\\)\uff0c\u90a3\u4e48 \\(T(N) = \\Theta(f(N))\\)\uff1b</li> <li>\u82e5 \\(af(\\frac{N}{b}) = \\Kappa f(N) \\text{ for fixed } \\Kappa &gt; 1\\)\uff0c\u90a3\u4e48 \\(T(N) = \\Theta(N^{\\log_b{a}}) = \\Theta(a^{\\log_b{N}})\\)\uff08\u4e2a\u4eba\u611f\u89c9\u540e\u9762\u90a3\u4e2a\u5f0f\u5b50\u66f4\u65b9\u4fbf\u76f4\u89c2\u8bb0\u5fc6\uff09\uff1b</li> <li>\u82e5 \\(af(\\frac{N}{b}) = f(N)\\)\uff0c\u90a3\u4e48 \\(T(N) = \\Theta(f(N) \\log_b N)\\)\uff1b</li> </ol>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec07/#\u8bc1\u660e_1","title":"\u8bc1\u660e","text":"<p>proof for form 2</p> <p>\u5bf9\u4e8e\u5f62\u5982 \\(T(N)=aT(N/b)+f(N)\\) \u7684\u9012\u63a8\u5f0f\uff0c\u57fa\u4e8e\u7ebf\u6027\u5173\u7cfb\u7684\u5f62\u5f0f\u4e8c\u7684\u8bc1\u660e\u5b9e\u9645\u4e0a\u548c\u5f62\u5f0f\u4e00\u7684\u7b2c\u4e09\u79cd\u60c5\u51b5\u7684\u8bc1\u660e\u975e\u5e38\u76f8\u50cf\u3002</p> <p>\u5047\u8bbe\u6211\u4eec\u6709 \\(af(\\frac{N}{b}) = c f(N)\\)\uff0c\u53ea\u9700\u8981\u8ba8\u8bba \\(c\\) \u7684\u53d6\u503c\u8303\u56f4\u5bf9\u7ed3\u679c\u7684\u5f71\u54cd\uff0c\u5c31\u53ef\u4ee5\u4e00\u6b21\u6027\u5f97\u5230\u7ed3\u679c\u3002</p> <p>\u7c7b\u4f3c\u4e8e\u5f62\u5f0f\u4e00\u7684\u7b2c\u4e09\u79cd\u60c5\u51b5\u7684\u8bc1\u660e\uff0c\u6211\u4eec\u8fed\u4ee3\u8be5\u5173\u7cfb\u5f0f\uff0c\u5f97\u5230\u5173\u7cfb\uff1a</p> \\[ a^j f(\\frac{N}{b^j}) = c^j f(N) \\] <p>\u4e8e\u662f\uff0c\u6211\u4eec\u6709\uff1a</p> \\[ \\begin{aligned}     T(N)     &amp;= \\Theta(N^{\\log_b{a}}) + \\sum_{j = 0}^{(\\log_b{N})-1} a^j f(\\frac{N}{b^j}) \\\\     &amp;= \\Theta(N^{\\log_b{a}}) + \\sum_{j = 0}^{(\\log_b{N})-1} c^j f(N) \\\\     &amp;= \\Theta(N^{\\log_b{a}}) + f(N) \\sum_{j = 0}^{(\\log_b{N})-1} c^j \\\\     &amp;= \\Theta(N^{\\log_b{a}}) + f(N) \\times \\frac{1-N^{\\log_b{c}}}{1-c} \\\\ \\end{aligned} \\] <p>\u5929\u5450\uff0c\u8fd9\u4e0d\u5c31\u662f\u5f62\u5f0f\u4e00\u91cc\u7b2c\u4e09\u79cd\u60c5\u51b5\u7684\u5f0f\u5b50\u5417\uff1f\u7136\u800c\u5f53\u6211\u4eec\u6ee1\u5fc3\u6b22\u559c\u5730\u6253\u7b97\u7167\u7740\u5b83\u8bc1\u660e\u5f62\u5f0f\u4e8c\u7684\u60c5\u51b5\u4e00\u65f6\u4f1a\u53d1\u73b0\uff0c\u6761\u4ef6\u597d\u50cf\u4e0d\u591f\u3002\u6211\u4eec\u73b0\u5728\u5e76\u6ca1\u6709\u663e\u5f0f\u7684 \\(f(N) = \\Omega(N^{\\log_b {a}} + \\epsilon)\\) \u7684\u6761\u4ef6\uff0c\u800c\u8fd9\u4e2a\u6761\u4ef6\u6700\u7ec8\u51b3\u5b9a conquer \u90e8\u5206\u548c combine \u90e8\u5206\u8c01\u5360\u4e3b\u5bfc\u5730\u4f4d\u3002\u4f46\u662f\uff0c\u6211\u4eec\u5b9e\u9645\u4e0a\u53ea\u9700\u8981\u5f97\u5230 \\(f(N)\\) = \\(\\Omega(N^{\\log_b {a}})\\) \u5c31\u591f\u4e86\u3002\u5176\u5b9e \\(af(\\frac{N}{b}) \\sim c f(N)\\) \u8fd9\u4ef6\u4e8b\u672c\u8eab\u5c31\u6697\u542b\u4e86\u5b83\u4e0e \\(N^{\\log_b {a}}\\) \u7684\u5173\u7cfb\uff1a</p> <p>\u4e3a\u4e86\u91cd\u590d\u5229\u7528\u8fc7\u7a0b\uff0c\u6211\u76f4\u63a5\u7528 \\(\\sim\\) \u6765\u4ee3\u66ff \\(&lt;,&gt;,=\\) \u4e86\uff0c\u8fc7\u7a0b\u4e2d\u4fdd\u6301\u4f20\u9012\u6027\u3002</p> \\[ c f(N) \\sim a f(\\frac{N}{b}) \\sim ... \\sim a^L f(\\frac{N}{b^L}) \\] <p>\u53ef\u4ee5\u53d1\u73b0\uff0c\u8fd9\u4e00\u6b65\u8fd8\u662f\u548c\u5f62\u5f0f\u4e00\u7684\u7b2c\u4e09\u79cd\u60c5\u51b5\u7684\u8bc1\u660e\u8fc7\u7a0b\u9ad8\u5ea6\u76f8\u4f3c\u3002\u53ea\u4e0d\u8fc7\u73b0\u5728\u6211\u4eec\u8981\u66f4\u8fdb\u4e00\u6b65\u5730\u770b\u8fd9\u4e2a\u5f0f\u5b50\u3002</p> <p>\u5f53 \\(c &lt; 1\\) \u65f6\uff0c\u5b9e\u9645\u4e0a\u6709 \\(f(N) &gt; af(\\frac{N}{b})\\)\uff1b\u5f53 \\(c = 1\\) \u65f6\uff0c\u5b9e\u9645\u4e0a\u6709 \\(f(N) = af(\\frac{N}{b})\\)\uff1b \\(c &gt; 1\\) \u65f6\uff0c\u5b9e\u9645\u4e0a\u6709 \\(f(N) &lt; af(\\frac{N}{b})\\)\uff1b</p> <p>\u6211\u4eec\u5047\u8bbe \\(\\frac{N}{b^L}\\) \u8db3\u591f\u5c0f\uff08\u5373\u9012\u5f52\u5230\u6700\u672b\u7aef\uff0c\u53ea\u9700\u8981\u8fdb\u884c conquer \u7684\u65f6\u5019\uff09\uff0c\u5373 \\(\\frac{N}{b^L} = \\Theta(1)\\)\uff0c\u90a3\u4e48\u5c31\u6709 \\(L = \\Theta(\\log_b{N})\\)\u3002\u4e8e\u662f\uff0c\u6211\u4eec\u6709\uff1a</p> \\[ f(N) \\sim \\Theta(a^{\\log_b{N}}) = \\Theta(N^{\\log_b{a}}) \\] <p>\u7686\u5927\u6b22\u559c\uff01\u4e09\u4e2a\u613f\u671b\uff0c\u4e00\u6b21\u6ee1\u8db3\uff01</p> <p>\u5269\u4e0b\u7684\u8bc1\u660e\u8fc7\u7a0b\u6211\u5c31\u4e0d\u518d\u8d58\u8ff0\u4e86\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec07/#\u5f62\u5f0f\u4e09","title":"\u5f62\u5f0f\u4e09","text":"<p>Form 3</p> <p>\u7b2c\u4e09\u79cd\u5f62\u5f0f\u662f\u5bf9\u4e8e \\((N)\\) \u7684\u7279\u522b\u5f62\u5f0f\uff0c\u5f53\u9012\u63a8\u5173\u7cfb\u6ee1\u8db3\uff1a</p> \\[ \\begin{aligned} &amp; T(N) = a T(\\frac{n}{b}) + \\Theta(N^k \\log^p{N}) &amp; \\text{Where } a \\geq 1,\\; b &gt; 1,\\; p \\geq 0 \\end{aligned} \\] <p>\u5176\u590d\u6742\u5ea6\u6709\u7ed3\u8bba\uff1a</p> \\[ T(N) = \\left\\{     \\begin{aligned}         &amp; O(N^{\\log_b{a}}) &amp; \\text{if } a &gt; b^{k} \\\\         &amp; O(N^k \\log^{p+1}{N}) &amp; \\text{if } a = b^{k} \\\\         &amp; O(N^k \\log^{p}{N}) &amp; \\text{if } a &lt; b^{k}     \\end{aligned} \\right. \\] <p>\u5b9e\u9645\u4e0a\u8fd9\u4e2a\u5f0f\u5b50\u4e5f\u975e\u5e38\u597d\u8ba4\uff0c\u5c5e\u4e8e\u5f62\u5f0f\u4e8c\u7684\u4e00\u79cd\u7279\u6b8a\u5f62\u5f0f\u3002\u53ef\u4ee5\u5bf9\u7167\u7740\u770b\uff0c\u975e\u5e38\u5bb9\u6613\u770b\u51fa\u5173\u7cfb\u3002</p> <p>\u53ea\u4e0d\u8fc7\u5bf9\u4e8e\u7279\u6b8a\u60c5\u51b5\uff0c\u8fd9\u4e2a\u5f62\u5f0f\u7684\u7ea6\u675f\u66f4\u52a0\u7cbe\u786e\uff0c\u8bc1\u660e\u8fc7\u7a0b\u6709\u7f18\u518d\u8865\u5427x</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec08/","title":"Lecture 8 | Dynamic Programming","text":"<p> \u7ea6 4 \u4e2a\u5b57 </p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec09/","title":"Lecture 9 | Greedy Algorithms","text":"<p> \u7ea6 895 \u4e2a\u5b57  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 3 \u5206\u949f</p> <p>\u679c\u7136\u8d8a\u6765\u8d8a\u5bbd\u6cdb\u4e86</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec09/#\u6982\u5ff5","title":"\u6982\u5ff5","text":"<p>\u8d2a\u5fc3\u7b97\u6cd5(Greedy Algorithms)\u662f\u4e00\u79cd\u5728\u6c42\u89e3\u4f18\u5316\u95ee\u9898\u65f6\u91c7\u7528\u7684\u7b56\u7565\uff0c\u5b83\u5728\u6bcf\u4e2a\u51b3\u7b56\u9636\u6bb5\u90fd\u9009\u62e9\u5f53\u524d\u770b\u8d77\u6765\u6700\u4f18\u7684\u89e3\u51b3\u65b9\u6848\uff0c\u4ece\u800c\u5e0c\u671b\u80fd\u591f\u8fbe\u5230\u5168\u5c40\u6700\u4f18\u89e3\u3002\u8d2a\u5fc3\u7b97\u6cd5\u7684\u6838\u5fc3\u601d\u60f3\u662f\u5c40\u90e8\u6700\u4f18\u9009\u62e9\uff0c\u901a\u8fc7\u4e00\u7cfb\u5217\u5c40\u90e8\u6700\u4f18\u7684\u9009\u62e9\uff0c\u6765\u8fbe\u5230\u5168\u5c40\u6700\u4f18\u7684\u76ee\u6807\u3002\u8d2a\u5fc3\u7b97\u6cd5\u6613\u4e8e\u5b9e\u73b0\uff0c\u4f46\u5e76\u4e0d\u603b\u662f\u80fd\u591f\u5f97\u5230\u5168\u5c40\u6700\u4f18\u89e3\uff0c\u56e0\u6b64\u5728\u4f7f\u7528\u8d2a\u5fc3\u7b97\u6cd5\u65f6\u9700\u8981\u5206\u6790\u95ee\u9898\u7684\u7279\u6027\u4ee5\u786e\u4fdd\u5176\u9002\u7528\u6027\u3002</p> <p>\u2014\u2014ChatGPT</p> <p>\u8d2a\u5fc3\u601d\u60f3\u548c\u5b83\u7684\u540d\u5b57\u4e00\u6837\u7b80\u5355\u66b4\u529b\uff0c\u5c31\u662f\u5728\u6bcf\u4e00\u4e2a\u6b65\u9aa4\u4e2d\u90fd\u91c7\u53d6\u5c40\u90e8\u6700\u4f18\u89e3\uff0c\u6700\u7ec8\u6c42\u5f97\u6700\u4f18\u89e3\u3002\u4f46\u662f\u663e\u7136\u8fd9\u4e2a\u65b9\u6cd5\u5e76\u4e0d\u603b\u80fd\u201c\u6700\u7ec8\u6c42\u5f97\u6700\u4f18\u89e3\u201d\u3002\u56e0\u6b64\u867d\u7136\u8fd9\u4e2a\u65b9\u6cd5\u770b\u8d77\u6765\u76f4\u63a5\u66b4\u529b\uff0c\u4f46\u662f\u5982\u4f55\u627e\u5230\u7528\u300c\u8d2a\u5fc3\u300d\u89e3\u51b3\u95ee\u9898\u7684\u8def\u5f84\uff0c\u5f80\u5f80\u662f\u9700\u8981\u52a8\u52a8\u8111\u5b50\u7684\u3002</p> <p>\u548c dp \u4e00\u6837\uff0c\u8d2a\u5fc3\u662f\u4e00\u4e2a\u6bd4\u8f83\u601d\u60f3\u6027\u8d28\u7684\u4e1c\u897f\uff0c\u6240\u4ee5\u6211\u4eec\u9700\u8981\u501f\u52a9\u8bb8\u591a\u6848\u4f8b\u6765\u8fdb\u884c\u5206\u6790\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec09/#\u6848\u4f8b-activity-selection-problem","title":"[\u6848\u4f8b] Activity Selection Problem","text":"<p>\u5728\u8bfe\u4ef6\u4e0a\uff0c\u6d3b\u52a8\u9009\u62e9\u95ee\u9898(Activity Selection Problem)\u7684\u9648\u8ff0\u5982\u4e0b\uff1a</p> <p>Activity Selection Problem</p> <p>Given a set of activities \\(S = { a_1, a_2, ..., a_n }\\) that wish to use a resource (e.g. a classroom).  Each \\(a_i\\) takes place during a time interval \\([s_i, f_i)\\).</p> <p>Activities \\(a_i\\) and \\(a_j\\) are compatible if \\(s_i \\geq f_j\\) or \\(s_j \\geq f_i\\) (i.e. their time intervals do not overlap).</p> <p>Goal: Select a maximum-size subset of mutually compatible activities.</p> <ul> <li>Assume \\(f_1\\geq f_2 \\geq ... \\geq f_n\\).</li> </ul> <p>\u62bd\u8c61\u6765\u8bf4\u5c31\u662f\u4e00\u4e2a\u4e00\u7ef4\u7684\u5bc6\u94fa\u95ee\u9898\u3002\u7ed9\u5b9a\u65f6\u95f4\u7ebf\u4e0a\u7684\u82e5\u5e72\u533a\u95f4 \\([s_i, f_i)\\)\uff0c\u6c42\u51fa\u6700\u591a\u80fd\u4e0d\u91cd\u53e0\u5730\u5728\u8fd9\u4e2a\u65f6\u95f4\u7ebf\u4e0a\u653e\u7f6e\u591a\u5c11\u4e2a\u533a\u95f4\u3002\u9898\u76ee\u989d\u5916\u4fdd\u8bc1\u4e86\u8f93\u5165\u6570\u636e\u662f\u6839\u636e \\(f_i\\) \u6709\u5e8f\u7684\uff0c\u4e0d\u8fc7\u8fd9\u4e0d\u662f\u5f88\u91cd\u8981\u3002</p> <p>bad try 1</p> <p>\u4e00\u4e2a\u975e\u5e38 naive \u7684\u60f3\u6cd5\u5c31\u662f\uff0c\u54ea\u95e8\u8bfe\u5148\u5f00\u59cb\u6211\u5148\u9009\u54ea\u95e8\u8bfe\uff0c\u8fd9\u4e2a\u60f3\u6cd5\u975e\u5e38\u7684\u8282\u7701\u8111\u7ec6\u80de\uff0c\u4f46\u662f\u663e\u7136\u4e0d\u5bf9\u3002\u6211\u968f\u968f\u4fbf\u4fbf\u6765\u4e2a\u6700\u65e9\u5f00\u59cb\u6700\u665a\u7ed3\u675f\u7684\u8bfe\uff0c\u5c31\u80fd\u76f4\u63a5 hack \u6389\u8fd9\u4e2a\u65b9\u6cd5\u3002</p> <p>bad try 2</p> <p>\u518d\u6765\u4e00\u4e2a\u5929\u771f\u7684\u60f3\u6cd5\uff0c\u6211\u6bcf\u6b21\u90fd\u9009\u533a\u95f4\u957f\u5ea6\u6700\u5c11\u7684\uff0c\u867d\u7136\u770b\u8d77\u6765\u80fd\u8ba9\u5b83\u201c\u76f8\u5bf9\u6bd4\u8f83\u591a\u201d\uff0c\u4f46\u662f\u663e\u7136\u4e5f\u65e0\u6cd5\u4fdd\u8bc1\u7ed3\u679c\u7684\u6700\u4f18\u6027\uff0c\u4e5f\u975e\u5e38\u597d hack\u3002</p> <p>search</p> <p>\u800c\u53e6\u5916\u4e00\u4e2a\u66b4\u529b\u7684\u60f3\u6cd5\u5c31\u662f\uff0c\u6211\u53bb\u679a\u4e3e\u6bcf\u4e00\u79cd\u53ef\u80fd\uff0c\u4e5f\u5c31\u662f\u6211\u4eec\u4fd7\u79f0\u7684\u66b4\u641c\uff0c\u8fd8\u53ef\u4ee5\u7528\u4e0a\u526a\u679d\u7b49\u64cd\u4f5c\uff0c\u867d\u7136\u53ef\u4ee5\uff0c\u4f46\u662f\u592a\u4e0d\u4f18\u96c5\u4e86\uff0c\u800c\u4e14\u65f6\u95f4\u590d\u6742\u5ea6\u672a\u5fc5\u662f\u6211\u4eec\u80fd\u63a5\u53d7\u7684\u3002</p> <p>dp</p> <p>\u65e2\u7136\u66b4\u641c\u4e0d\u884c\uff0c\u90a3\u8bd5\u8bd5 dp \u5462\uff1f\u5728\u8fd9\u4e2a\u95ee\u9898\u4e2d\uff0c\u6211\u4eec\u53ef\u4ee5\u5199\u51fa\u5982\u4e0b\u8f6c\u79fb\u65b9\u7a0b\uff1a</p> \\[ dp_i = \\left\\{     \\begin{aligned}         &amp;1 &amp; i = 1 \\\\         &amp;\\max\\{             dp_{i-1},             dp_{f(i)} + 1         \\} &amp; i &gt; 1     \\end{aligned} \\right. \\] <p>\u5176\u4e2d\uff0c\\(dp_i\\) \u8868\u793a\u5230\u7b2c \\(i\\) \u4e2a\u533a\u95f4\u622a\u6b62\u7684\u65f6\u95f4\u4e3a\u6b62\uff0c\u6700\u591a\u6709\u591a\u5c11\u4e2a\u9879\u76ee\u53ef\u4ee5\u88ab\u5b89\u6392\uff1b\\(f(i)\\) \u662f\u6700\u5927\u7684\u6ee1\u8db3 \\(f_j \\leq s_i\\) \u7684\u533a\u95f4\u7684\u7f16\u53f7 \\(j\\)\uff0c\u4e5f\u5c31\u662f\u80fd\u591f\u4e0d\u91cd\u53e0\u653e\u4e0b\u7684\uff0c\u6700\u665a\u7684\u90a3\u4e2a\u6d3b\u52a8\u3002</p> <p>\u6211\u4eec\u53d1\u73b0\uff0c\u8fd9\u4e48\u505a\u662f\u53ef\u4ee5\u7684\u3002\u53ea\u4e0d\u8fc7\u8fd9\u6837\u505a\u7684\u8bdd\uff0c\u5176\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a \\(O(N^2)\\)\u3002</p> <p>greedy</p> <p>\u663e\u7136\uff0c\u8fd9\u4e2a\u6848\u4f8b\u653e\u5728\u8fd9\u4e2a\u5730\u65b9\u80af\u5b9a\u662f\u6709\u8d2a\u5fc3\u89e3\u7684\u3002\u800c\u4e14\u9898\u76ee\u7684 \u201cAssume\u201d \u63d0\u793a\u6027\u5df2\u7ecf\u5f88\u5f3a\u4e86\u3002\u6211\u4eec\u53ea\u9700\u8981\u6309\u7167\u7ed3\u675f\u65f6\u95f4\uff0c\u904d\u5386\u8fd9\u4e9b\u533a\u95f4\uff0c\u80fd\u585e\u4e0b\u5c31\u585e\uff0c\u5373\u53ef \\(O(N)\\) \u8d2a\u5fc3\u6c42\u89e3\u3002</p> <p>TODO:</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec10/","title":"Lecture 10 | NP Completeness","text":"<p> \u7ea6 3027 \u4e2a\u5b57  10 \u884c\u4ee3\u7801  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 10 \u5206\u949f</p> <p>\u5bfc\u8bfb</p> <p>\u7531\u4e8e\u672c\u8282\u6d89\u53ca\u8f83\u591a\u6982\u5ff5\uff0c\u5e76\u4e14\u77e5\u8bc6\u6811\u957f\u7684\u5f88\u84ec\u677e\uff0c\u6240\u4ee5\u6211\u51b3\u5b9a\u5c1d\u8bd5\u975e\u7ebf\u6027\u7ec4\u7ec7\u5185\u5bb9\uff0c\u56e0\u6b64\u672c\u6587\u7684\u9605\u8bfb\u987a\u5e8f\u53ef\u80fd\u4e5f\u5e76\u4e0d\u4f1a\u662f\u7ebf\u6027\u7684\u3002</p> <p>\u6240\u6709\u63d0\u5230\u7684\u3001\u5e76\u4e14\u672c\u6587\u4f1a\u4ecb\u7ecd\u7684\u76f8\u5173\u5185\u5bb9\uff0c\u90fd\u4f1a\u4ee5\u94fe\u63a5\u548c\u653e\u5927\u955c\ud83d\udd0d\u7684\u5f62\u5f0f\u51fa\u73b0\u3002\u63a8\u8350\u4f7f\u7528\u9f20\u6807\u4e2d\u952e\u7b49\u65b9\u5f0f\u6253\u5f00\u65b0\u6807\u7b7e\u9875\u67e5\u770b\uff0c\u65b9\u4fbf\u56de\u6eaf\u3002</p> <p>\u63a8\u8350\u7684\u9605\u8bfb\u987a\u5e8f\u662f\uff0c\u987a\u7740\u8bfb\u4e0b\u53bb\uff0c\u6bcf\u6b21\u51fa\u73b0 \ud83d\udd0d \u90fd\u8fdb\u884c\u6df1\u5ea6\u4f18\u5148\u641c\u7d22\u5f0f\u7684\u5b66\u4e60\uff0c\u76f4\u81f3\u770b\u5b8c\u5168\u6587\u3002</p> <p>\u5176\u4e2d\uff0c\u5728 \u76f8\u5173\u6982\u5ff5 \u4e4b\u540e\u7684\u90e8\u5206\uff0c\u6211\u4f1a\u4fdd\u8bc1\u5728\u524d\u9762\u90fd\u6709\u63d0\u53ca\uff0c\u800c\u5176\u4e4b\u524d\u7684\u5185\u5bb9\uff0c\u63a8\u8350\u90fd\u5728\u987a\u5e8f\u9605\u8bfb\u4e2d\u6d89\u53ca\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec10/#\u6982\u8ff0","title":"\u6982\u8ff0","text":"<p>Links</p> <p>OI Wiki: https://oi-wiki.org/misc/cc-basic/</p> <p>Wikipedia: https://en.wikipedia.org/wiki/P_versus_NP_problem</p> <p>Wikipedia: https://en.wikipedia.org/wiki/NP-completeness</p> <p>Wikipedia: https://en.wikipedia.org/wiki/NP-hardness</p> <p>\u6839\u636e\u95ee\u9898\u7684\u96be\u5ea6\uff0c\u7531\u4e0d\u540c\u7684\u5b9a\u4e49\u5212\u5206\uff0c\u95ee\u9898\u53ef\u4ee5\u5206\u4e3a\uff1a</p> <p>P \u95ee\u9898(polynomial time)\u3001NP \u95ee\u9898(nondeterministic polynomial time)\u3001NPC \u95ee\u9898(NP complete)\u3001NPH \u95ee\u9898(NP hard)\u3002\u9664\u6b64\u4e4b\u5916 \uff0c\u6211\u4eec\u8fd8\u9700\u8981\u989d\u5916\u4e86\u89e3\u4e0d\u53ef\u8ba1\u7b97\u95ee\u9898(undecidable)\u3002</p> <p>\u7531\u4e8e\u4e0d\u53ef\u8ba1\u7b97\u95ee\u9898\u6bd4\u8f83\u7279\u6b8a\uff0c\u6240\u4ee5\u6211\u5148\u653e\u5728\u524d\u9762\u4ecb\u7ecd\u3002</p> Undecidable Problem <p>Links</p> <p>Wikipedia: https://en.wikipedia.org/wiki/Undecidable_problem</p> <p>\u4e0d\u53ef\u5224\u5b9a\u95ee\u9898(undecidable problem)\u662f\u4e00\u7c7b\u7279\u6b8a\u7684\u51b3\u5b9a\u6027\u95ee\u9898\uff0c\u5b83\u7684\u7279\u70b9\u662f\u6211\u4eec\u65e0\u6cd5\u8bbe\u8ba1\u4e00\u4e2a\u7b97\u6cd5\u6765\u6c42\u89e3\u5b83\u7684\u7ed3\u679c\u3002</p> <p>\u5176\u4e2d\u4e00\u4e2a\u6bd4\u8f83\u5178\u578b\u7684\u4f8b\u5b50\u5c31\u662f\u505c\u673a\u95ee\u9898\ud83d\udd0d\u3002</p> <p>\u6211\u4eec\u53ef\u4ee5\u7528\u8fd9\u6837\u4e00\u5f20\u56fe\u6765\u8868\u793a\u5176\u4ed6\u51e0\u4e2a\u6982\u5ff5\u7684\u5173\u7cfb\uff1a</p> <p> </p> <p>Source: https://en.wikipedia.org/wiki/NP-hardness</p> <p>\u53ef\u4ee5\u7c97\u6d45\u7684\u6309\u7167\u56fe\u4e2d\u7684\u201cComplexity\u201d\u8f74\u6765\u7406\u89e3\u5176\u4e2d\u7684\u8f6c\u5316\u5173\u7cfb\uff0c\u63a5\u4e0b\u6765\u7ed9\u51fa\u5b83\u4eec\u7684\u8be6\u7ec6\u5b9a\u4e49\uff1a</p> <p>P</p> <p>P \u53d6\u81ea polynomial time\uff0c\u6307\u7684\u662f\u53ef\u4ee5\u7528\u786e\u5b9a\u578b\u56fe\u7075\u673a\ud83d\udd0d\u5728\u591a\u9879\u5f0f\u65f6\u95f4\u5185\u89e3\u51b3\u7684\u95ee\u9898\u3002</p> <p>\u4e5f\u5c31\u662f\u6211\u4eec\u901a\u5e38\u610f\u4e49\u4e0b\u6240\u8bf4\u7684\uff0c\u53ef\u4ee5\u5728\u591a\u9879\u5f0f\u65f6\u95f4\u5185\u89e3\u51b3\u7684\u95ee\u9898\u3002</p> <p>NP</p> <p>NP \u5373 nondeterministic polynomial time\uff0c\u6307\u7684\u662f\u53ef\u4ee5\u7528\u975e\u786e\u5b9a\u578b\u56fe\u7075\u673a\ud83d\udd0d\u5728\u591a\u9879\u5f0f\u65f6\u95f4\u5185\u89e3\u51b3\u7684\u95ee\u9898\u3002\u8fd9\u4e2a\u8bf4\u6cd5\u7b49\u4ef7\u4e8e\u53ef\u4ee5\u7528\u786e\u5b9a\u578b\u56fe\u7075\u673a\ud83d\udd0d\u5728\u591a\u9879\u5f0f\u65f6\u95f4\u5185\u9a8c\u8bc1\uff08\u5224\u65ad\u7b54\u6848\u662f\u5426\u6b63\u786e\uff09\u3002</p> <p>\u4e5f\u5c31\u662f\u6211\u4eec\u901a\u5e38\u610f\u4e49\u4e0b\u6240\u8bf4\u7684\uff0c\u53ef\u4ee5\u5728\u591a\u9879\u5f0f\u65f6\u95f4\u5185\u9a8c\u8bc1\u7684\u95ee\u9898\u3002</p> <p>NPC</p> <p>NPC \u5373 NP complete\uff0cNP \u5b8c\u5168\uff0c\u662f NP \u4e2d\u6700\u96be\u7684\u51b3\u5b9a\u6027\u95ee\u9898\uff08\u5e76\u4e0d\u662f\u65e0\u9650\u5b9a\u8bcd\u7684\u6700\u96be\u7684\u95ee\u9898\uff01\uff09\u3002\u800c\u6211\u4eec\u79f0\u6ee1\u8db3\u5982\u4e0b\u6761\u4ef6\u7684\u95ee\u9898\u4e3a NPC \u95ee\u9898\uff1a</p> <ol> <li>\u662f\u4e00\u4e2a NP \u95ee\u9898\uff1b</li> <li>\u6240\u6709 NP \u95ee\u9898\u90fd\u53ef\u4ee5\u591a\u9879\u5f0f\u65f6\u95f4\u5f52\u7ea6\ud83d\udd0d\u4e3a\u8be5\u95ee\u9898\uff1b</li> </ol> <p>\u7531 2 \u53ef\u4ee5\u6709\u7ed3\u8bba\uff0c\u6240\u6709\u7684 NPC \u95ee\u9898\u96be\u5ea6\u76f8\u540c\u2014\u2014\u4e00\u65e6\u6709\u4e00\u4e2a NPC \u95ee\u9898\u88ab\u89e3\u51b3\uff0c\u90a3\u4e48\u6240\u6709 NPC \u95ee\u9898\uff0c\u4e43\u81f3\u6240\u6709 NP \u95ee\u9898\u90fd\u80fd\u88ab\u89e3\u51b3\u3002</p> <p>\u5982\u679c\u6211\u4eec\u8bd5\u56fe\u8bc1\u660e\u4e00\u4e2a\u95ee\u9898\u662f NPC \u95ee\u9898\uff0c\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u8fd9\u79cd\u624b\u6bb5\uff1a</p> <ol> <li>\u5224\u5b9a\u8be5\u95ee\u9898\u662f\u4e00\u4e2a NP \u95ee\u9898\uff1b</li> <li>\u5224\u5b9a\u4e00\u4e2a\u5df2\u77e5\u7684 NPC \u95ee\u9898\u53ef\u4ee5\u591a\u9879\u5f0f\u65f6\u95f4\u5f52\u7ea6\ud83d\udd0d\u4e3a\u8be5\u95ee\u9898\uff0c\u6216\u5224\u5b9a\u8be5\u95ee\u9898\u662f NPH\uff08\u5728\u4e0b\u9762\uff09\u95ee\u9898\uff1b</li> </ol> <p>\u7b2c\u4e00\u4e2a\u88ab\u8bc1\u660e\u662f NPC \u7684\u95ee\u9898\u662f Circuit-SAT\ud83d\udd0d \u95ee\u9898\u3002</p> <p>P ?= NP &amp; NPC</p> <p>\u5173\u4e8e P \u548c NP \u7684\u5173\u7cfb\uff0c\u6211\u4eec\u4ecd\u7136\u4e0d\u77e5\u9053 P \u662f\u5426\u80fd\u7b49\u4e8e NP\uff0c\u5373\u6211\u4eec\u4ecd\u7136\u4e0d\u77e5\u9053\u662f\u5426\u5b58\u5728\u591a\u9879\u5f0f\u7b97\u6cd5\u53ef\u4ee5\u89e3\u51b3\u4e00\u5207 NP \u95ee\u9898\u3002</p> <p>\u800c\u5176\u4e2d\u7684\u5173\u952e\u5c31\u662f\uff0c\u5982\u679c\u6211\u4eec\u80fd\u627e\u5230 NPC \u95ee\u9898\u7684\u591a\u9879\u5f0f\u89e3\u6cd5\uff0c\u90a3\u4e48\u5c31\u53ef\u4ee5\u8bc1\u660e P = NP\u3002</p> <p>NPH</p> <p>NPH \u5373 NP hard\uff0cNP \u56f0\u96be\uff0c\u5b83\u4e0d\u4e00\u5b9a\u9700\u8981\u662f NP \u95ee\u9898\u3002\u800c\u6240\u6709 NP \u95ee\u9898\u90fd\u53ef\u4ee5\u591a\u9879\u5f0f\u65f6\u95f4\u5f52\u7ea6\ud83d\udd0d\u4e3a NPH \u95ee\u9898\u3002</p> <p>\u4e5f\u5c31\u662f\u8bf4 \\(NPC = NP \\cap NPH\\)\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec10/#\u8bfe\u5185\u6848\u4f8b","title":"\u8bfe\u5185\u6848\u4f8b","text":"<p>\u63a5\u4e0b\u6765\u7684\u5185\u5bb9\u90fd\u662f\u8bfe\u4ef6\u4e2d\u63d0\u5230\u7684\u4e00\u4e9b\u5177\u4f53\u95ee\u9898\u548c\u6848\u4f8b\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec10/#halting-problem","title":"Halting Problem","text":"<p>Links</p> <p>Wikipedia: https://en.wikipedia.org/wiki/Halting_problem</p> <p>\u505c\u673a\u95ee\u9898\u662f\u4e00\u4e2a\u5178\u578b\u7684\u4e0d\u53ef\u8ba1\u7b97\u95ee\u9898\uff0c\u5b83\u6307\u7684\u662f\uff0c\u5bf9\u4e8e\u4efb\u610f\u4e00\u4e2a\u7a0b\u5e8f\uff0c\u6211\u4eec\u65e0\u6cd5\u8bbe\u8ba1\u4e00\u4e2a\u7b97\u6cd5\u6765\u5224\u65ad\u5b83\u662f\u5426\u4f1a\u5728\u6709\u9650\u65f6\u95f4\u5185\u505c\u673a\uff08\u5373\u5224\u65ad\u7a0b\u5e8f\u662f\u5426\u4f1a\u6b7b\u5faa\u73af\uff09\u3002</p> <p>\u6211\u4eec\u901a\u8fc7\u53cd\u8bc1\u6cd5\u53ef\u4ee5\u8bc1\u660e\uff1a</p> <p>\u5047\u8bbe\u5b58\u5728\u51fd\u6570 <code>willHalt(func F)</code> \u53ef\u4ee5\u5224\u65ad\u51fd\u6570 F \u662f\u5426\u4f1a\u505c\u673a\uff0c\u5982\u679c\u4f1a\uff0c\u5219\u8fd4\u56de <code>true</code>\uff0c\u5426\u5219\u8fd4\u56de <code>false</code>\u3002\u90a3\u4e48\u6211\u4eec\u53ef\u4ee5\u6784\u9020\u4e00\u4e2a\u8fd9\u6837\u7684\u51fd\u6570 <code>foo()</code>\uff1a</p> <pre><code>void foo() {\nif ( willHalt(foo) ) {\nwhile (true) {} // Endless loop.\n}\nreturn;\n}\n</code></pre> <p>\u63a5\u4e0b\u6765\uff0c\u5982\u679c\u6211\u4eec\u60f3\u77e5\u9053 <code>foo()</code> \u662f\u5426\u4f1a\u505c\u673a\uff0c\u5c31\u4f1a\u6267\u884c <code>willHalt(foo)</code>\u3002\u7136\u800c\u5728 <code>foo()</code> \u5185\u90e8\u4e5f\u6709\u4e00\u4e2a <code>willHalt(foo)</code>\uff0c\u5982\u679c\u5b83\u8ba4\u4e3a <code>foo()</code> \u4f1a\u505c\u673a\uff0c\u5219\u6784\u9020\u4e00\u4e2a\u6b7b\u5faa\u73af\uff1b\u800c\u5982\u679c\u5b83\u8ba4\u4e3a <code>foo()</code> \u4e0d\u4f1a\u505c\u673a\uff0c\u5219\u9009\u62e9\u8ba9\u5b83\u7acb\u523b\u505c\u673a\uff0c\u4e8e\u662f\u8fd9\u91cc\u5c31\u4ea7\u751f\u4e86\u77db\u76fe\u3002</p> <p>\u7406\u89e3\u4e0a\u9762\u8fd9\u6bb5\u5185\u5bb9\u7684\u5173\u952e\u5c31\u662f\uff0c\u8fd9\u91cc\u867d\u7136\u4e0d\u5b58\u5728\u4e8b\u5b9e\u610f\u4e49\u4e0a\u7684\u201c\u6b7b\u5faa\u73af\u201d\uff0c\u4f46\u53ef\u4ee5\u7406\u89e3\u4e3a\u8fd9\u91cc\u5b58\u5728\u4e00\u4e2a\u903b\u8f91\u4e0a\u7684\u9012\u5f52\uff0c\u800c\u8fd9\u79cd\u201c\u903b\u8f91\u4e0a\u7684\u9012\u5f52\u201d\uff0c\u6b63\u662f\u5bfc\u81f4\u505c\u673a\u95ee\u9898\u6210\u4e3a\u4e00\u4e2a\u4e0d\u53ef\u8ba1\u7b97\u95ee\u9898\u7684\u539f\u56e0\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec10/#hamilton-cycle-problem","title":"Hamilton Cycle Problem","text":"<p>links</p> <p>Wikipedia: https://en.wikipedia.org/wiki/Hamiltonian_path_problem</p> <p>OI Wiki: https://oi-wiki.org/graph/hamilton</p> <p>\u54c8\u5bc6\u987f\u56de\u8def\u95ee\u9898</p> <p>\u7ed9\u5b9a\u4e00\u4e2a\u56fe\uff0c\u5224\u65ad\u662f\u5426\u5b58\u5728\u4e00\u6761\u8def\u5f84\uff0c\u4f7f\u5f97\u5b83\u7ecf\u8fc7\u56fe\u4e2d\u7684\u6bcf\u4e2a\u70b9\u6070\u597d\u4e00\u6b21\uff0c\u4e14\u6700\u540e\u56de\u5230\u8d77\u70b9\u3002</p> <p>\u54c8\u5bc6\u987f\u56de\u8def\u95ee\u9898\u662f\u4e00\u4e2a NPC \u95ee\u9898\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec10/#traveling-salesman-problem","title":"Traveling Salesman Problem","text":"<p>Links</p> <p>Wikipedia: https://en.wikipedia.org/wiki/Travelling_salesman_problem</p> <p>\u65c5\u884c\u5546\u95ee\u9898</p> <p>\u65c5\u884c\u5546\u95ee\u9898\u6709\u4e24\u79cd\u5b9a\u4e49\uff0c\u5176\u4e2d\u524d\u8005\u662f NPH\uff0c\u800c\u88ab\u79f0\u4e3a\u201c\u5224\u5b9a\u7248\u672c\u201d\u7684\u540e\u8005\u662f NPC\u3002</p> \u539f\u59cb\u5b9a\u4e49\u5224\u5b9a\u7248\u672c <p>\u7ed9\u5b9a\u4e00\u4e2a\u5b8c\u5168\u56fe\uff0c\u5224\u65ad\u662f\u5426\u5b58\u5728\u4e00\u6761\u8def\u5f84\uff0c\u4f7f\u5f97\u5b83\u7ecf\u8fc7\u56fe\u4e2d\u7684\u6bcf\u4e2a\u70b9\u6070\u597d\u4e00\u6b21\uff0c\u4e14\u6700\u540e\u56de\u5230\u8d77\u70b9\uff0c\u4e14\u8def\u5f84\u957f\u5ea6\u6700\u77ed\u3002</p> <p>\"Given a list of cities and the distances between each pair of cities, what is the shortest possible route that visits each city exactly once and returns to the origin city?\"</p> <p>From Wikipedia</p> <p>\u8be5\u7248\u672c\u7684 TSP \u95ee\u9898\u662f\u4e00\u4e2a NPH \u95ee\u9898\uff0c\u5e38\u5e38\u51fa\u73b0\u5728\u7ec4\u5408\u4f18\u5316\u7684\u8bed\u5883\u4e2d\u3002</p> <p>\u7ed9\u5b9a\u4e00\u4e2a\u5b8c\u5168\u56fe\uff0c\u5224\u65ad\u662f\u5426\u5b58\u5728\u4e00\u6761\u8def\u5f84\uff0c\u4f7f\u5f97\u5b83\u7ecf\u8fc7\u56fe\u4e2d\u7684\u6bcf\u4e2a\u70b9\u6070\u597d\u4e00\u6b21\uff0c\u4e14\u6700\u540e\u56de\u5230\u8d77\u70b9\uff0c\u4e14\u8def\u5f84\u957f\u5ea6\u4e0d\u8d85\u8fc7 \\(k\\)\u3002</p> <p>\u8be5\u7248\u672c\u7684 TSP \u95ee\u9898\u662f\u4e00\u4e2a NPC \u95ee\u9898\uff0c\u5e38\u5e38\u51fa\u73b0\u5728\u590d\u6742\u5ea6\u7406\u8bba\u7684\u8bed\u5883\u4e2d\u3002</p> <p>\u9700\u8981\u6ce8\u610f\uff0c\u63a5\u4e0b\u6765\u6211\u4eec\u8c08\u8bba\u7684\u90fd\u662f\u5224\u5b9a\u7248\u672c\u7684 TSP\uff01</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec10/#\u5224\u5b9a\u7248\u672c\u7684-npc-\u8bc1\u660e","title":"\u5224\u5b9a\u7248\u672c\u7684 NPC \u8bc1\u660e","text":"<p>\u73b0\u5728\uff0c\u5047\u8bbe\u6211\u4eec\u5df2\u77e5 Hamilton Cycle Problem \u95ee\u9898\u662f\u4e00\u4e2a NPC \u95ee\u9898\uff0c\u5c1d\u8bd5\u901a\u8fc7\u591a\u9879\u5f0f\u65f6\u95f4\u5f52\u7ea6\ud83d\udd0d\u7684\u65b9\u5f0f\u6765\u8bc1\u660e TSP \u4e5f\u662f\u4e00\u4e2a NPC \u95ee\u9898\u3002</p> <p>Recommended Reading</p> <p>https://opendsa-server.cs.vt.edu/ODSA/Books/Everything/html/hamiltonianCycle_to_TSP.html</p> <p>\u9996\u5148\u56de\u987e\u8bc1\u660e NPC \u7684\u6b65\u9aa4\uff1a</p> <ol> <li>\u5224\u5b9a\u8be5\u95ee\u9898\u662f\u4e00\u4e2a NP \u95ee\u9898\uff1b</li> <li>\u5224\u5b9a\u4e00\u4e2a\u5df2\u77e5\u7684 NPC \u95ee\u9898\u53ef\u4ee5\u591a\u9879\u5f0f\u65f6\u95f4\u5f52\u7ea6\ud83d\udd0d\u4e3a\u8be5\u95ee\u9898\uff0c\u6216\u8005\u8bf4\u5224\u5b9a\u8be5\u95ee\u9898\u662f NPH \u95ee\u9898\uff1b</li> </ol> <p>\u4ee3\u5165\u5230\u8fd9\u4e2a\u95ee\u9898\u4e2d\uff0c\u4e5f\u5c31\u662f\u6211\u4eec\u9700\u8981\u8bc1\u660e\uff1a</p> <ol> <li>TSP \u662f\u4e00\u4e2a NP \u95ee\u9898\uff1b</li> <li>Hamilton Cycle Problem \u53ef\u4ee5\u591a\u9879\u5f0f\u65f6\u95f4\u5f52\u7ea6\ud83d\udd0d\u4e3a TSP\uff1b</li> </ol> <p>TSP is NP</p> <p>\u8bc1\u660e TSP \u662f\u4e00\u4e2a NP \u95ee\u9898\u5373\u8bc1\u660e TSP \u7684\u89e3\u53ef\u4ee5\u5728\u591a\u9879\u5f0f\u65f6\u95f4\u5185\u88ab\u9a8c\u8bc1\u3002\u800c\u9a8c\u8bc1\u4e00\u4e2a\u89e3\u662f TSP \u95ee\u9898\u7684\u89e3\uff0c\u9700\u8981\u8bc1\u660e\u4e0b\u9762\u4e24\u4e2a\u70b9\uff1a</p> <ol> <li>\u8fd9\u6761\u8def\u5f84\u7ecf\u8fc7\u4e86\u6240\u6709\u8282\u70b9\u6070\u597d\u4e00\u6b21\uff1b</li> <li>\u8fd9\u6761\u8def\u5f84\u957f\u5ea6\u4e0d\u8d85\u8fc7\\(k\\)\uff1b</li> </ol> <p>\u663e\u7136\uff0c\u8fd9\u4e24\u6761\u90fd\u53ea\u9700\u8981 \\(O(N)\\) \u7684\u5f00\u9500\u5c31\u80fd\u9a8c\u8bc1\u3002</p> <p>\u4e8e\u662f\uff0c\u6211\u4eec\u5f97\u5230\u7ed3\u8bba\uff1a\\(\\text{TSP} \\in \\text{NP}\\)\u3002</p> <p>TSP is NPH</p> <p>\u8981\u8bc1\u660e TSP \u662f\u4e00\u4e2a NPH \u95ee\u9898\uff0c\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u8bc1\u660e Hamilton Cycle Problem(HCP) \u53ef\u4ee5\u591a\u9879\u5f0f\u65f6\u95f4\u5f52\u7ea6\ud83d\udd0d\u4e3a TSP\u3002</p> <p>\u4e3a\u6b64\uff0c\u6211\u4eec\u9700\u8981\u5bf9\u6bd4 HCP \u548c TSP \u7684\u5dee\u5f02\u3002</p> <p>\u4ee5 HCP \u4e3a\u57fa\u7840\u63cf\u8ff0 TSP\uff0c\u5b9e\u9645\u4e0a\u5c31\u662f\u5728\u4e00\u5f20\u5b8c\u5168\u56fe\u4e0a\u5bfb\u627e\u603b\u957f\u4e0d\u8d85\u8fc7 \\(k\\) \u7684\u54c8\u5bc6\u987f\u73af\u8def\uff0c\u5177\u4f53\u6765\u8bf4\uff1a</p> HCP TSP \u56fe \\(G(V,E)\\) \u5b8c\u5168\u56fe \\(G'(V',E')\\) \u65e0\u8fb9\u6743 \u6709\u8fb9\u6743 - \\(\\sum v_i \\leq k\\) <p>\u800c\u4e3a\u4e86\u8bc1\u660e \\(\\text{HCP} \\leq_p \\text{TCP}\\)\uff0c\u6211\u4eec\u8bbe\u8ba1\u4e00\u4e2a\u591a\u9879\u5f0f\u65f6\u95f4\u7684\u65b9\u6cd5 <code>f()</code> \u5b9e\u73b0 \\(G(V,E) \\to G'(V',E')\\)\uff0c\u5177\u4f53\u6765\u8bf4\uff0c\u5b83\u505a\u8fd9\u4e9b\u4e8b\uff1a</p> <ol> <li>\u8fde\u63a5 \\(G\\) \u4e2d\u6240\u6709\u6ca1\u8fde\u4e0a\u7684\u8fb9\uff0c\u4f7f \\(G\\) \u6210\u4e3a\u4e00\u5f20\u65e0\u6743\u5b8c\u5168\u56fe\uff1b</li> <li>\u5bf9\u4e8e\u65e0\u6743\u5b8c\u5168\u56fe\u4e2d\u7684\u6bcf\u4e00\u6761\u8fb9 \\(v^c_i\\)\uff0c\u5982\u679c\u5728 \\(G\\) \u4e2d\u4e5f\u6709\u8fd9\u6761\u8fb9\uff0c\u90a3\u4e48\u4ee4\u5b83\u8fb9\u6743\u4e3a 0\uff0c\u5426\u5219\u4ee4\u5b83\u8fb9\u6743\u4e3a 1\uff0c\u4e8e\u662f\u5f97\u5230\u6709\u6743\u5b8c\u5168\u56fe \\(G'(V',E')\\)\uff1b</li> </ol> <p> </p> <p>\u53f3\u56fe\u4e2d\u6240\u6709\u7684\u84dd\u8fb9\u8fb9\u6743\u90fd\u4e3a 0\uff0c\u7eff\u8fb9\u8fb9\u6743\u90fd\u4e3a 1\u3002</p> <p>\u7531\u4e8e\u5b8c\u5168\u56fe\u7684\u8fb9\u6570\u4e3a \\(\\frac{n(n-1)}{2}\\)\uff0c\u6240\u4ee5\u8fd9\u4e2a\u6b65\u9aa4\u663e\u7136\u662f\u591a\u9879\u5f0f\u65f6\u95f4\u7684\u3002</p> <p>\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u53d1\u73b0\uff0c\u539f\u95ee\u9898\u4e3a\u5728 \\(G\\) \u4e0a\u5bfb\u627e\u54c8\u5bc6\u987f\u73af\uff0c\u7b49\u4ef7\u4e8e\u5728 \\(G' = f(G)\\) \u4e0a\u505a \\(k = 0\\) \u7684 TSP\u3002\u7531\u6b64\u8bc1\u660e \\(\\text{HCP} \\leq_{p} \\text{TSP}\\)\uff0c\u5373 \\(\\text{TSP} \\in \\text{NPH}\\)\u3002</p> <p>\u7efc\u4e0a\u6240\u8ff0\uff0c\u7531\u4e8e \\(\\text{TSP} \\in \\text{NP}\\) \u4e14 \\(\\text{TSP} \\in \\text{NPH}\\)\uff0c\u6240\u4ee5 \\(\\text{TSP} \\in \\text{NPC}\\)\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec10/#circuit-sat","title":"Circuit-SAT","text":"<p>Links</p> <p>Wikipedia: https://en.wikipedia.org/wiki/Circuit_satisfiability_problem</p> <p>Circuit-SAT \u53c8\u53eb circuit satisfiability problem\uff0c\u5b83\u662f\u6700\u65e9\u88ab\u8bc1\u660e\u662f NPC \u7684\u95ee\u9898\uff0c\u5373\u901a\u8fc7 NPC \u95ee\u9898\u7684\u5b9a\u4e49\u8bc1\u660e\u3002</p> <p>\u5176\u5177\u4f53\u63cf\u8ff0\u5982\u4e0b\uff1a</p> <p>Circuit-SAT</p> <p>Circuit-SAT \u5373\u4e3a\u786e\u5b9a\u7ed9\u5b9a\u5e03\u5c14\u7535\u8def\u662f\u5426\u5177\u6709\u4f7f\u8f93\u51fa\u4e3a\u771f\u7684\u8f93\u5165\u5206\u914d\u7684\u51b3\u7b56\u7684\u95ee\u9898\u3002</p> <p></p> <p>Source: https://en.wikipedia.org/wiki/Circuit_satisfiability_problem</p> <p>\u4e0a\u56fe\u4e2d\uff0c\u5de6\u4fa7\u7535\u8def\u6ee1\u8db3\u6761\u4ef6\uff0c\u53f3\u4fa7\u7535\u8def\u4e0d\u6ee1\u8db3\u6761\u4ef6\u3002</p> <p>\u6216\u8005\uff0c\u66f4\u62bd\u8c61\u7684\u6765\u8bf4\uff0c\u662f\u5224\u65ad\u4e00\u4e2a\u5177\u6709 \\(n\\) \u4e2a\u5e03\u5c14\u53d8\u91cf\u7684\u5e03\u5c14\u8868\u8fbe\u5f0f\u662f\u5426\u5177\u6709\u7ed3\u679c\u4e3a True \u7684\u89e3\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec10/#3-sat","title":"3-SAT","text":"<p>Links</p> <p>Wikipedia: https://en.wikipedia.org/wiki/Boolean_satisfiability_problem#3-satisfiability</p> <p>3-SAT \u6307\u7684\u662f Circuit-SAT \u95ee\u9898\u7684\u4e00\u4e2a\u7279\u4f8b\uff0c\u5b83\u5bf9\u5e03\u5c14\u7535\u8def\uff0c\u6216\u8005\u8bf4\u5e03\u5c14\u8868\u8fbe\u5f0f\u7684\u5f62\u5f0f\u6709\u7279\u6b8a\u8981\u6c42\uff0c\u5177\u4f53\u6765\u8bf4\uff0c\u5b83\u8981\u6c42\u5e03\u5c14\u8868\u8fbe\u5f0f\u5f62\u5982\uff1a</p> \\[ (x_1 \\vee x_2 \\vee x_3) \\wedge (x_4 \\vee x_5 \\vee x_6) \\wedge \\cdots \\wedge (x_{n-2} \\vee x_{n-1} \\vee x_n) \\] <ul> <li>\u53d8\u91cf\u662f\u5426\u91cd\u590d\u3001\u662f\u5426\u53d6\u975e\u4e0d\u662f\u91cd\u70b9\uff0c\\(x_1\\) \u53ef\u4ee5\u548c \\(x_6\\) \u662f\u540c\u4e00\u4e2a\u53d8\u91cf\uff0c\u4e5f\u53ef\u4ee5\u662f\u67d0\u4e2a\u53d8\u91cf\u7684\u975e\uff0c\u91cd\u70b9\u662f\u8fd9\u91cc\u7684\u4e09\u4e2a\u4e00\u7ec4\u7684\u5f62\u5f0f\u3002</li> </ul>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec10/#a-formal-language-framework","title":"A formal-language Framework","text":"<ul> <li> TODO: Finish this part.</li> </ul>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec10/#\u76f8\u5173\u6982\u5ff5","title":"\u76f8\u5173\u6982\u5ff5","text":"<p>\u8bf4\u660e</p> <p>\u4ee5\u4e0b\u90e8\u5206\u7684\u5185\u5bb9\u662f\u4e3a\u4e86\u8fdb\u4e00\u6b65\u8bf4\u660e\u4e0a\u6587\u4e2d\u90e8\u5206\u5185\u5bb9\u800c\u4ecb\u7ecd\u7684\u6982\u5ff5\uff0c\u5e76\u4e0d\u5177\u6709\u7ec4\u7ec7\u7ed3\u6784\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec10/#\u56fe\u7075\u673a","title":"\u56fe\u7075\u673a","text":"<p>Links</p> <p>Wikipedia: https://en.wikipedia.org/wiki/Turing_machine</p> <p>Wikipedia: https://en.wikipedia.org/wiki/Nondeterministic_Turing_machine</p> <p>\u56fe\u7075\u673a\u6709\u4e00\u4e9b\u53d8\u4f53\uff0c\u800c\u6211\u4eec\u5728\u8fd9\u91cc\u5f15\u5165\u56fe\u7075\u673a\u662f\u4e3a\u4e86\u4ecb\u7ecd P/NP\uff0c\u53ea\u4ecb\u7ecd\u786e\u5b9a\u578b\u56fe\u7075\u673a\u548c\u975e\u786e\u5b9a\u578b\u56fe\u7075\u673a\u3002</p> <p>\u56fe\u7075\u673a\u7531\u4e00\u4e2a\u65e0\u9650\u957f\u7684\u7eb8\u5e26\u548c\u4e00\u4e2a\u8bfb\u5199\u5934\u7ec4\u6210\u3002\u7eb8\u5e26\u88ab\u5212\u5206\u4e3a\u4e00\u4e2a\u4e2a\u683c\u5b50\uff0c\u6bcf\u4e2a\u683c\u5b50\u4e0a\u6709\u4e00\u4e2a\u7b26\u53f7\uff0c\u8bfb\u5199\u5934\u53ef\u4ee5\u5728\u7eb8\u5e26\u4e0a\u79fb\u52a8\uff0c\u8bfb\u5199\u5934\u53ef\u4ee5\u8bfb\u53d6\u5f53\u524d\u683c\u5b50\u4e0a\u7684\u7b26\u53f7\uff0c\u4e5f\u53ef\u4ee5\u6539\u53d8\u5f53\u524d\u683c\u5b50\u4e0a\u7684\u7b26\u53f7\u3002\u56fe\u7075\u673a\u7684\u72b6\u6001\u662f\u4e00\u4e2a\u6709\u9650\u96c6\u5408\uff0c\u6bcf\u4e2a\u72b6\u6001\u90fd\u6709\u4e00\u4e2a\u8f6c\u79fb\u51fd\u6570\uff0c\u8f6c\u79fb\u51fd\u6570\u7684\u8f93\u5165\u662f\u5f53\u524d\u72b6\u6001\u548c\u5f53\u524d\u683c\u5b50\u4e0a\u7684\u7b26\u53f7\uff0c\u8f93\u51fa\u662f\u4e0b\u4e00\u4e2a\u72b6\u6001\u3001\u4e0b\u4e00\u4e2a\u683c\u5b50\u4e0a\u7684\u7b26\u53f7\u548c\u8bfb\u5199\u5934\u7684\u79fb\u52a8\u65b9\u5411\u3002</p> <p>\u66f4\u672c\u8d28\u7684\u6765\u8bf4\uff0c\u56fe\u7075\u673a\u662f\u4e00\u79cd\u8ba1\u7b97\u6a21\u578b\uff0c\u6211\u4eec\u53ef\u4ee5\u7528\u5b83\u6765\u8868\u793a\u4efb\u4f55\u6709\u9650\u903b\u8f91\u6570\u5b66\u8fc7\u7a0b\u3002\u786e\u5b9a\u578b\u56fe\u7075\u673a\u4e0e\u6211\u4eec\u5e38\u89c4\u7406\u89e3\u7684\u8ba1\u7b97\u673a\u903b\u8f91\u7c7b\u4f3c\uff0c\u5373\u4e0b\u4e00\u6b65\u8981\u505a\u4ec0\u4e48\u53ef\u4ee5\u6839\u636e\u5f53\u524d\u72b6\u6001\u786e\u5b9a\u3002\u800c\u975e\u786e\u5b9a\u578b\u56fe\u7075\u673a\u5219\u7c7b\u4f3c\u4e8e\u80fd\u591f\u8fdb\u884c\u65e0\u9650\u5e76\u884c\uff0c\u5e76\u4e14\u6700\u7ec8\u603b\u662f\u9009\u62e9\u901a\u5411\u6b63\u786e\u7b54\u6848\u7684\u65b9\u5411\u7684\u90a3\u6761\u8def\uff08\u6709\u70b9\u7c7b\u4f3c\u4e8e\u5b83\u80fd\u5f00\u5e73\u884c\u5b87\u5b99\uff0c\u5e76\u4e14\u603b\u662f\u8ba9\u4f60\u89c2\u6d4b\u5230\u6b63\u786e\u7684\u90a3\u4e00\u4e2a\u5e73\u884c\u5b87\u5b99\uff09\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec10/#\u591a\u9879\u5f0f\u65f6\u95f4\u5f52\u7ea6","title":"\u591a\u9879\u5f0f\u65f6\u95f4\u5f52\u7ea6","text":"<p>Links</p> <p>Wikipedia: https://en.wikipedia.org/wiki/Polynomial-time_reduction</p> <p>\u6211\u4eec\u5f15\u5165 P/NP \u7b49\u8fd9\u4e9b\u6982\u5ff5\uff0c\u662f\u4e3a\u4e86\u8861\u91cf\u95ee\u9898\u7684\u590d\u6742\u7a0b\u5ea6\uff0c\u800c\u5982\u4f55\u5728\u5177\u4f53\u7684\u201c\u95ee\u9898\u201d\u95f4\u4f20\u9012\u3001\u6bd4\u8f83\u8fd9\u79cd\u201c\u590d\u6742\u7a0b\u5ea6\u201d\uff0c\u5c31\u662f\u591a\u9879\u5f0f\u65f6\u95f4\u5f52\u7ea6(polynomial reduce)\u7684\u76ee\u7684\u3002</p> <pre><code>graph LR;\nA[\"\u95ee\u9898 A\"]\nB[\"\u95ee\u9898 B\"]\nA ===&gt;|\"\u591a\u9879\u5f0f\u65f6\u95f4\u8f6c\u5316\"| B</code></pre> <p>\u5982\u679c\u6211\u4eec\u80fd\u5728\u591a\u9879\u5f0f\u65f6\u95f4\u7684\u590d\u6742\u5ea6\u5185\uff0c\u5c06\u95ee\u9898 A \u8f6c\u5316\u4e3a\u95ee\u9898 B\uff0c\u5219\u79f0\u95ee\u9898 A \u53ef\u4ee5\u591a\u9879\u5f0f\u65f6\u95f4\u5f52\u7ea6(polynomial reduce)\u4e3a B\uff0c\u8bb0\u4e3a \\(A \\leq_{p} B\\)\uff0c\u8868\u793a A \u4e0d\u4f1a\u6bd4 B \u96be\u3002</p> <p>\u800c\u91c7\u53d6\u6570\u5b66\u8bed\u8a00\u6765\u63cf\u8ff0\uff0c\u5219\u662f\uff1a</p> \\[ \\begin{aligned} A \\leq_{p} B  \\;\\;\\Leftrightarrow\\;\\; &amp; \\exist f() \\text{ which runs in polynomial time}, \\\\ &amp; s.t.    \\;\\; \\forall x \\in A,\\; f(x) \\in B \\\\ &amp; \\text{and}\\; \\forall f(x) \\in B,\\; y \\in A \\end{aligned} \\]"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec11/","title":"Lecture 11 | Approximation","text":"<p> \u7ea6 5372 \u4e2a\u5b57  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 18 \u5206\u949f</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec11/#\u8fd1\u4f3c\u7b97\u6cd5","title":"\u8fd1\u4f3c\u7b97\u6cd5","text":"<p>links</p> <p>Wikipedia: https://en.wikipedia.org/wiki/Approximation_algorithm</p> <p>\u5728\u4e0a\u4e00\u7ae0\u4e2d\u6211\u4eec\u4ecb\u7ecd\u4e86 P/NP \u95ee\u9898\uff0c\u800c\u5927\u5bb6\u666e\u904d\u8ba4\u4e3a P \u2260 NP\uff0c\u8fd9\u5c31\u610f\u5473\u7740\u5bf9\u4e8e\u67d0\u4e9b\u95ee\u9898\uff0c\u6211\u4eec\u65e0\u6cd5\u4f7f\u7528\u591a\u9879\u5f0f\u65f6\u95f4\u89e3\u51b3\uff0c\u800c\u5728\u95ee\u9898\u89c4\u6a21\u53d8\u5927\u65f6\uff0c\u8d8a\u53d1\u4e0d\u53ef\u63a5\u53d7\u3002</p> <p>\u56e0\u6b64\uff0c\u6211\u4eec\u8003\u8651\u80fd\u5426\u9000\u800c\u6c42\u5176\u6b21\uff0c\u5728\u591a\u9879\u5f0f\u65f6\u95f4\u5185\u6c42\u4e00\u4e2a\u6bd4\u8f83\u4f18\u7684\u89e3\u3002\u66f4\u5177\u4f53\u7684\u6765\u8bf4\uff0c\u6211\u4eec\u5c1d\u8bd5\u5bfb\u627e\u4e00\u79cd\u591a\u9879\u5f0f\u7b97\u6cd5\uff0c\u4f7f\u5f97\u5176\u7ed3\u679c\u59cb\u7ec8\u5728\u5173\u4e8e\u51c6\u786e\u89e3\u7684\u53ef\u63a5\u53d7\u504f\u5dee\u8303\u56f4\u5185\uff0c\u5bf9\u4e8e\u8fd9\u79cd\u7b97\u6cd5\uff0c\u6211\u4eec\u79f0\u4e4b\u4e3a\u8fd1\u4f3c\u7b97\u6cd5(approximation algorithm)\u3002</p> <p>\u6211\u4eec\u8bbe \\(f(n, x)\\) \u662f\u5bf9\u8f93\u5165\u5927\u5c0f\u4e3a \\(n\\) \u7684\u60c5\u51b5\u4e0b\uff0c\u5bf9\u7ed3\u679c \\(x\\) \u7684\u6700\u574f\u60c5\u51b5\u7684\u4e00\u4e2a\u76f4\u89c2\u91cf\u5316\uff08\u4f8b\u5982 dist, weight...\uff09\uff0c\u82e5\u8bbe \\(x^*\\) \u4e3a\u51c6\u786e\u89e3\uff0c\\(x\\) \u4e3a\u7ed9\u5b9a\u7b97\u6cd5\u7ed3\u679c\uff0c\u5219\u6211\u4eec\u5b9a\u4e49\u8fd1\u4f3c\u6bd4(Approximation Ratio)\\(\\rho\\)\uff1a</p> \\[ \\forall n \\rho = \\max\\left\\{\\frac{f(n, x)}{f(n, x^*)}, \\frac{f(n, x^*)}{f(n, x)}\\right\\} \\] <p>\u5219\u79f0\u7ed9\u5b9a\u7b97\u6cd5\u4e3a \\(\\rho\\) \u8fd1\u4f3c\u7b97\u6cd5(\\(\\rho\\)-approximation algorithm)\u3002</p> <p>\u8fd1\u4f3c\u7b97\u6cd5 v.s. \u968f\u673a\u7b97\u6cd5</p> <p>\u5728\u770b\u5230\u8fd1\u4f3c\u7b97\u6cd5\u65f6\uff0c\u6211\u8111\u5b50\u91cc\u4e00\u4e0b\u5b50\u6d6e\u73b0\u51fa\u4e86\u968f\u673a\u7b97\u6cd5\u7684\u6982\u5ff5\uff0c\u540c\u6837\u662f\u6c42\u51c6\u786e\u89e3\u7684\u8fd1\u4f3c\u89e3\uff0c\u4e24\u8005\u6709\u4f55\u533a\u522b\u5462\uff1f</p> hint: \u6700\u574f\u60c5\u51b5 <p>\u8fd1\u4f3c\u7b97\u6cd5\u548c\u968f\u673a\u7b97\u6cd5\u6700\u5927\u7684\u533a\u522b\u5c31\u662f\uff0c\u5f53\u6211\u4eec\u8bbe\u8ba1\u3001\u5206\u6790\u3001\u8ba8\u8bba\u8fd1\u4f3c\u7b97\u6cd5\u7684\u65f6\u5019\uff0c\u6211\u4eec\u5173\u6ce8\u7684\u90fd\u662f\u5b83\u7684\u6700\u574f\u60c5\u51b5\u3002\u4e5f\u5c31\u662f\u8bf4\uff0c\u8fd1\u4f3c\u7b97\u6cd5\u662f\u5b8c\u5168\u53ef\u63a7\u7684\uff0c\u800c\u7eaf\u7cb9\u7684\u968f\u673a\u7b97\u6cd5\u5219\u662f\u901a\u8fc7\u6982\u7387\u6765\u51cf\u5c11\u574f\u60c5\u51b5\u51fa\u73b0\u7684\u53ef\u80fd\uff0c\u5e76\u6ca1\u6709\u4e25\u683c\u7684\u7ea6\u675f\u3002\u8fd1\u4f3c\u7b97\u6cd5\u6700\u574f\u4e5f\u5c31\u574f\u5230 \\(\\rho\\)\uff0c\u800c\u968f\u673a\u7b97\u6cd5\u6700\u574f\u53ef\u4ee5\u574f\u5230\u6d77\u62c9\u9c81\u5927\u9646\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec11/#\u8fd1\u4f3c\u8303\u5f0f","title":"\u8fd1\u4f3c\u8303\u5f0f","text":"<p>links</p> <p>Wikipedia: https://en.wikipedia.org/wiki/Polynomial-time_approximation_scheme</p> <p>\u8fd1\u4f3c\u8303\u5f0f(approximation scheme)\u6307\u7684\u662f\u5bf9\u4e8e\u67d0\u4e2a\u4f18\u5316\u95ee\u9898\u7684\u4e00\u65cf\u76f8\u540c\u6a21\u5f0f\u7684\u7b97\u6cd5\uff0c\u5b83\u4eec\u6ee1\u8db3\u5bf9\u4e8e\u786e\u5b9a\u7684 \\(\\epsilon &gt; 0\\)\uff0c\u7b97\u6cd5\u7684\u8fd1\u4f3c\u6bd4\u4e3a \\(1+\\epsilon\\)\u3002</p> <p>\u53ef\u4ee5\u7c97\u7cd9\u5730\u7406\u89e3\u4e3a\uff1a\u201c\u8303\u5f0f\u201d\u662f\u4e00\u4e2a\u8f93\u51fa\u4e3a\u7b97\u6cd5\u7684\u7279\u6b8a\u51fd\u6570\uff0c\u800c \\(\\epsilon\\) \u662f\u201c\u8303\u5f0f\u201d\u7684\u4e00\u4e2a\u53c2\u6570\uff0c\u5bf9\u4e8e\u7279\u5b9a\u7684 \\(\\epsilon\\)\uff0c\u201c\u8303\u5f0f\u201d\u8f93\u51fa\u4e00\u4e2a\u7279\u5b9a\u7684\u7b97\u6cd5\uff08\u8fd9\u4e9b\u7b97\u6cd5\u6709\u7740\u76f8\u540c\u7684\u6a21\u5f0f\uff09\uff0c\u800c\u8fd9\u4e9b\u201c\u8303\u5f0f\u201d\u8f93\u51fa\u7684\u7b97\u6cd5\uff0c\u90fd\u89e3\u51b3\u540c\u4e00\u4e2a\u95ee\u9898\uff0c\u5e76\u4e14\u5bf9\u4e8e\u4efb\u610f\u56fa\u5b9a\u7684 \\(\\epsilon\\) \u5176\u8fd1\u4f3c\u6bd4\u4e3a \\(1+\\epsilon\\)\u3002</p> <p>\u800c\u5173\u4e8e \\(\\epsilon &gt; 0\\) \u8fd9\u4e2a\u7ea6\u675f\uff0c\u662f\u56e0\u4e3a\u8fd1\u4f3c\u6bd4\u5fc5\u5b9a\u5927\u4e8e 1\u3002</p> <p>\u800c\u6b64\u65f6\uff0c\u8fd9\u4e00\u65cf\u7684\u7b97\u6cd5\u7684\u590d\u6742\u5ea6\u53ef\u4ee5\u8868\u793a\u4e3a \\(O(f(n, \\epsilon))\\)\uff0c\u5982 \\(O(n^{2/\\epsilon}), O((\\frac{1}{\\epsilon})^2n^3)\\)\u3002\u5f53 \\(f(n, \\epsilon)\\) \u5173\u4e8e \\(n\\) \u662f\u591a\u9879\u5f0f\u65f6\uff0c\u6211\u4eec\u79f0\u5176\u4e3a\u591a\u9879\u5f0f\u65f6\u95f4\u8fd1\u4f3c\u8303\u5f0f(polynomial-time approximation scheme, PTAS)\u3002\u5f53 \\(f(n, \\epsilon)\\) \u5173\u4e8e \\(n\\) \u548c \\(\\frac{1}{\\epsilon}\\) \u90fd\u662f\u591a\u9879\u5f0f\u65f6\uff0c\u6211\u4eec\u79f0\u5176\u4e3a\u5b8c\u5168\u591a\u9879\u5f0f\u65f6\u95f4\u8fd1\u4f3c\u8303\u5f0f(fully polynomial-time approximation scheme, FPTAS)\u3002</p> <p>\u4e3a\u4ec0\u4e48\u8981\u533a\u5206 PTAS \u548c FPTAS \u5462\uff1f\u6211\u4eec\u89c2\u5bdf \\(\\epsilon\\) \u5bf9\u7b97\u6cd5\u7684\u5f71\u54cd\uff1a\u968f\u7740 \\(\\epsilon\\) \u7684\u51cf\u5c0f\uff0c\u8fd1\u4f3c\u6bd4\u9010\u6e10\u53d8\u5c0f\uff0c\u5373\u51c6\u786e\u5ea6\u63d0\u9ad8\uff1b\u800c \\(\\frac{1}{\\epsilon}\\) \u53d8\u5927\uff0c\u800c\u901a\u5e38\u6765\u8bf4 \\(\\frac{1}{\\epsilon}\\) \u4e0e\u7b97\u6cd5\u590d\u6742\u5ea6\u90fd\u662f\u6b63\u76f8\u5173\u7684\uff0c\u56e0\u6b64\u4f1a\u5bfc\u81f4\u7b97\u6cd5\u590d\u6742\u5ea6\u5347\u9ad8\u3002\u5982\u679c\u8bf4\u8fd9\u4e2a\u8fd1\u4f3c\u8303\u5f0f\u662f FPTAS\uff0c\u90a3\u4e48\u4e3a\u4e86\u63d0\u9ad8\u51c6\u786e\u5ea6\u800c\u7f29\u5c0f \\(\\epsilon\\)\uff0c\u5bfc\u81f4\u7684\u590d\u6742\u5ea6\u53d8\u5316\u662f\u76f8\u5bf9\u53ef\u63a5\u53d7\u7684\uff08\u591a\u9879\u5f0f\u7ea7\u7684\u53d8\u5316\uff0c\u5982 \\((\\frac{1}{\\epsilon})^2n^3\\) \u5173\u4e8e \\(\\frac{1}{\\epsilon}\\) \u662f\u591a\u9879\u5f0f\u7ea7\u7684\uff09\uff1b\u7136\u800c\u5982\u679c\u5b83\u4e0d\u662f FPTAS\uff0c\u90a3\u4e48 \\(\\epsilon\\) \u7684\u7f29\u5c0f\u53ef\u80fd\u5e26\u6765\u6050\u6016\u7684\u590d\u6742\u5ea6\u589e\u52a0\uff08\u5982 \\(n^{2/\\epsilon}\\) \u5173\u4e8e \\(\\epsilon\\) \u662f\u6307\u6570\u7ea7\u7684\uff09\u3002</p> <p>\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u4ee5\u82e5\u5e72\u5177\u4f53\u4f8b\u5b50\u505a\u5206\u6790\uff0c\u4ee5\u4fbf\u66f4\u597d\u5730\u7406\u89e3\u8fd1\u4f3c\u7b97\u6cd5\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec11/#\u6848\u4f8b-approximate-bin-packing","title":"[\u6848\u4f8b] Approximate Bin Packing","text":"<p>links</p> <p>Wikipedia: https://en.wikipedia.org/wiki/Bin_packing</p> <p>\u88c5\u7bb1\u95ee\u9898\u6307\u7684\u662f\uff0c\u7ed9\u5b9a \\(N\\) \u4e2a item\uff0c\u7b2c \\(i\\in [1,N]\\) \u4e2a item \u7684 size \u4e3a \\(S_i \\in (0,1]\\)\uff0c\u4e00\u4e2a bin \u7684\u5927\u5c0f\u4e3a \\(1\\)\uff0c\u5c1d\u8bd5\u5bfb\u627e\u6700\u5c11\u7684\uff0c\u80fd\u591f\u88c5\u8f7d\u6240\u6709 item \u7684 bin \u7684\u6570\u91cf\u3002</p> \ud83c\udf30 \u4f8b\u5b50 <p>\u7ed9\u5b9a 7 \u4e2a item\uff0csize \u5206\u522b\u4e3a \\(0.2, 0.5, 0.4, 0.7, 0.1, 0.3, 0.8\\)\uff0c\u5219\u6700\u5c11\u9700\u8981 3 \u4e2a bin\uff08\u51c6\u786e\u89e3\uff09\uff1a</p> <ul> <li>bin 1: \\(0.2 + 0.8\\);</li> <li>bin 2: \\(0.7 + 0.3\\);</li> <li>bin 3: \\(0.4 + 0.1 + 0.5\\);</li> </ul> <p>\u8fd9\u662f\u4e00\u4e2a NP hard \u95ee\u9898\uff0c\u73b0\u5728\u6211\u4eec\u8003\u8651\u4e09\u79cd\u8fd1\u4f3c\u89e3\u6cd5\u3002\u9700\u8981\u6ce8\u610f\u7684\u662f\uff0c\u8fd9\u4e09\u79cd\u90fd\u662f\u5728\u7ebf(online)\u89e3\u6cd5\uff0c\u5373\u5904\u7406 \\(item_i\\) \u65f6\u6211\u4eec\u4e0d\u77e5\u9053 \\(item_{i+1}\\sim item_{N}\\) \u7684\u60c5\u51b5\u3002\u4e4b\u540e\u6211\u4eec\u4f1a\u518d\u8ba8\u8bba\u79bb\u7ebf(offline)\u505a\u6cd5\uff0c\u4e5f\u5c31\u662f\u6211\u4eec\u77e5\u9053\u6240\u6709 item \u7684\u60c5\u51b5\u4ee5\u540e\u518d\u7ed9\u51fa\u7b56\u7565\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec11/#online-next-fit-nf","title":"(online) Next Fit (NF)","text":"<p>links</p> <p>Wikipedia: https://en.wikipedia.org/wiki/Next-fit_bin_packing</p> <p>NF \u7b56\u7565\u603b\u662f\u9009\u62e9\u5f53\u524d\u6700\u540e\u4e00\u4e2a bin\uff0c\u82e5\u80fd\u591f\u5bb9\u7eb3\uff0c\u5219\u5c06\u5f53\u524d item \u653e\u5165\u5176\u4e2d\uff0c\u5426\u5219\u65b0\u5f00\u4e00\u4e2a bin\u3002</p> <p>NF \u7b56\u7565\u603b\u662f\u4f7f\u7528\u4e0d\u8d85\u8fc7 \\(2M-1\\) \u4e2a bin\uff0c\u5176\u4e2d \\(M\\) \u8868\u793a\u51c6\u786e\u89e3\u7684 \\(\\#bin\\)\u3002</p> proof for 2M-1 <p>\u6211\u4eec\u4ece NF \u7684\u7ed3\u679c\u51fa\u53d1\uff0c\u8bc1\u660e\u5f53 NF \u7684\u7ed3\u679c\u4e3a\u9700\u8981 \\(2M-1\\) \u6216 \\(2M\\) \u4e2a bin \u65f6\uff0c\u51c6\u786e\u89e3\u4e3a\u81f3\u5c11\u9700\u8981 \\(M\\) \u4e2a bin\u3002</p> <p>\u5047\u8bbe \\(S(B_i)\\) \u8868\u793a\u7b2c \\(i\\) \u4e2a bin \u7684 size\uff0c\u5219\u6839\u636e NF \u7684\u5b9a\u4e49\uff0c\u6709\uff1a\\(S(B_{i}) + S(B_{i+1}) &gt; 1\\)\uff08\u662f NF \u7684\u5fc5\u8981\u4e0d\u5145\u5206\u6761\u4ef6\uff09\u3002\u7a0d\u4f5c\u89e3\u91ca\uff0c\u4f7f\u7528\u53cd\u8bc1\u6cd5\uff0c\u5047\u8bbe \\(S(B_{i}) + S(B_{i+1}) \\leq 1\\)\uff0c\u8fd9\u8bf4\u660e\u65e0\u8bba \\(B_{i+1}\\) \u4e2d\u6709\u591a\u5c11 item\uff0c\u90fd\u4e00\u5b9a\u80fd\u653e\u8fdb \\(B_i\\)\uff0c\u800c\u8fd9\u4e0e NF \u201c\\(B_i\\) \u653e\u4e0d\u4e0b\u4e86\u624d\u5f00\u59cb\u653e \\(B_{i+1}\\)\u201d \u7684\u6027\u8d28\u76f8\u8fdd\u80cc\u3002\u4e8e\u662f\u6211\u4eec\u5c06\u6240\u6709\u6876\u4e24\u4e24\u914d\u5bf9\uff1a</p> <p>1.\u5f53 NF \u7684\u7ed3\u679c\u662f\u9700\u8981 \\(2M-1\\) \u4e2a bin \u65f6\uff1a</p> \\[ \\left\\{ \\begin{aligned}     S(B_1) + S(B_2) &amp;&gt; 1 \\\\     S(B_3) + S(B_4) &amp;&gt; 1 \\\\     \\vdots \\\\     S(B_{2M-3}) + S(B_{2M-2}) &amp;&gt; 1 \\\\     S(B_{2M-1}) &amp;\\leq 1 \\end{aligned} \\right. \\\\ \\begin{aligned}     &amp;\\therefore \\sum_{i=1}^{2M-1} &gt; \\sum_{i=1}^{2M-2} &gt; M-1 \\\\     &amp;\\therefore \\sum_{i=1}^{2M-1} \\geq M \\end{aligned} \\] <p>\u5373 item \u7684\u603b size \u81f3\u5c11\u4e3a M\uff0c\u5373\u81f3\u5c11\u9700\u8981 \\(M\\) \u4e2a bin\u3002</p> <p>2.\u800c\u5f53 NF \u7684\u7ed3\u679c\u662f\u9700\u8981 \\(2M\\) \u4e2a bin \u65f6\uff0c\u53ef\u4ee5\u8f6c\u5316\u4e3a \\(2M-1\\) \u7684\u60c5\u51b5\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec11/#online-first-fit-ff","title":"(online) First Fit (FF)","text":"<p>links</p> <p>Wikipedia: https://en.wikipedia.org/wiki/First-fit_bin_packing</p> <p>FF \u7b56\u7565\u603b\u662f\u9009\u62e9\u7b2c\u4e00\u4e2a\u80fd\u653e\u4e0b\u5f53\u524d item \u7684 bin\uff0c\u82e5\u6240\u6709 bin \u90fd\u65e0\u6cd5\u5bb9\u7eb3\u5f53\u524d item\uff0c\u5219\u65b0\u5f00\u4e00\u4e2a bin\u3002</p> <p>NF \u7b56\u7565\u603b\u662f\u4f7f\u7528\u4e0d\u8d85\u8fc7 \\(\\lfloor 1.7M \\rfloor\\) \u4e2a bin\uff0c\u5e76\u4e14\u5b58\u5728\u4e00\u65cf\u80fd\u5bf9\u8fb9\u754c\u53d6\u7b49\u7684\u8f93\u5165\uff0c\u5176\u4e2d \\(M\\) \u8868\u793a\u51c6\u786e\u89e3\u7684 \\(\\#bin\\)\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec11/#online-best-fit-bf","title":"(online) Best Fit (BF)","text":"<p>links</p> <p>Wikipedia: https://en.wikipedia.org/wiki/Best-fit_bin_packing</p> <p>BF \u7b56\u7565\u603b\u662f\u9009\u62e9\u80fd\u591f\u5bb9\u7eb3\u5f53\u524d item \u4e14\u5269\u4f59\u7a7a\u95f4\u6700\u5c0f\u7684 bin\uff08\u5373 tightest\uff09\uff0c\u82e5\u6240\u6709 bin \u90fd\u65e0\u6cd5\u5bb9\u7eb3\u5f53\u524d item\uff0c\u5219\u65b0\u5f00\u4e00\u4e2a bin\u3002</p> <p>NF \u7b56\u7565\u4e5f\u603b\u662f\u4f7f\u7528\u4e0d\u8d85\u8fc7 \\(\\lfloor 1.7M \\rfloor\\) \u4e2a bin\uff0c\u5e76\u4e14\u5b58\u5728\u4e00\u65cf\u80fd\u5bf9\u8fb9\u754c\u53d6\u7b49\u7684\u8f93\u5165\uff0c\u5176\u4e2d \\(M\\) \u8868\u793a\u51c6\u786e\u89e3\u7684 \\(\\#bin\\)\u3002</p> <p>\u867d\u7136\u5728\u7ebf\u505a\u6cd5\u7531\u4e8e\u5bf9\u4fe1\u606f\u628a\u63e1\u7684\u4e0d\u5168\u9762\uff0c\u5728\u4e0d\u7279\u6b8a\u6784\u9020\u8f93\u5165\u7684\u60c5\u51b5\u4e0b\u751a\u81f3\u51e0\u4e4e\u4e0d\u53ef\u80fd\u8fbe\u5230\u6700\u4f18\u89e3\uff0c\u4f46\u662f\u73b0\u5b9e\u4e16\u754c\u4e2d\u6709\u5f88\u591a\u80fd\u5efa\u6a21\u4e3a\u88c5\u7bb1\u95ee\u9898\u7684\u95ee\u9898\uff0c\u90fd\u8981\u6c42\u4f7f\u7528\u5728\u7ebf\u505a\u6cd5\u89e3\u51b3\u3002\u56e0\u6b64\uff0c\u7814\u7a76\u5728\u7ebf\u505a\u6cd5\u8fd8\u662f\u6709\u5176\u610f\u4e49\u7684\u3002</p> <p>\u6b64\u5916\uff0c\u5173\u4e8e\u5728\u7ebf\u505a\u6cd5\uff0c\u6709\u4e00\u4e2a\u7ed3\u8bba\uff1a</p> <p>theorem</p> <p>\u5bf9\u4e8e\u88c5\u7bb1\u95ee\u9898\uff0c\u5982\u679c\u9650\u5b9a\u4f7f\u7528\u5728\u7ebf\u505a\u6cd5\uff0c\u5219\u6700\u4f18\u7684\u8fd1\u4f3c\u89e3\u6cd5\uff0c\u5176\u6700\u574f\u60c5\u51b5\u7684\u7ed3\u679c\u4e5f\u81f3\u5c11\u9700\u8981\u51c6\u786e\u89e3\u7684 \\(\\frac{5}{3}\\)\u3002</p> <p>PPT \u4e0a\u7684\u539f\u8bdd\u662f\uff0c\u65e0\u8bba\u54ea\u79cd\u5728\u7ebf\u505a\u6cd5\u4e5f\u81f3\u5c11\u9700\u8981\u4f7f\u7528 \\(\\frac{5}{3}\\) \u7684\u51c6\u786e\u89e3\u7ed9\u51fa\u7684\u6570\u91cf\uff0c\u4f46\u662f\u663e\u7136\u8fd9\u4e2a \\(\\frac{5}{3}\\) \u662f\u9488\u5bf9\u6700\u574f\u89e3\u7684\u8ba8\u8bba\u3002\u56de\u987e\u300c\u8fd1\u4f3c\u7b97\u6cd5 v.s. \u968f\u673a\u7b97\u6cd5\u300d\u8fd9\u4e2a block \u91cc\u7684\u5185\u5bb9\uff0c\u6211\u4eec\u5206\u6790\u8fd1\u4f3c\u89e3\uff0c\u90fd\u662f\u9488\u5bf9\u5176\u6700\u574f\u60c5\u51b5\u6765\u8bf4\u7684\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec11/#offline-first-fit-decreasing-ffd","title":"(offline) First Fit Decreasing (FFD)","text":"<p>\u79bb\u7ebf\u505a\u6cd5\u7684\u4f18\u52bf\u5728\u4e8e\u5b83\u80fd\u591f\u83b7\u5f97\u6240\u6709 item \u7684\u4fe1\u606f\u4ee5\u6c42\u7edf\u7b79\u89c4\u5212\u3002\u8fd9\u91cc\u7ed9\u51fa\u7684\u8fd1\u4f3c\u505a\u6cd5\u662f\uff0c\u5c06 item \u6309\u7167 size \u964d\u5e8f\u6392\u5e8f\uff0c\u800c\u540e\u4f7f\u7528 FF\uff08\u6216 BF\uff0c\u7531\u4e8e\u5355\u8c03\u6027\uff0c\u4e24\u8005\u7b49\u4ef7\uff09\u3002</p> \ud83c\udf30 \u4f8b\u5b50 <p>\u7ed9\u5b9a 7 \u4e2a item\uff08\u540c\u4e4b\u524d\u7684 \ud83c\udf30\uff09\uff0c\u7ecf\u8fc7\u6392\u5e8f\u540e\uff0c\u5b83\u4eec\u7684 size \u5206\u522b\u4e3a $0.8, 0.7, 0.5, 0.4, 0.3, 0.2, 0.1\uff0c\u5219\u6700\u5c11\u9700\u8981 3 \u4e2a bin\uff08\u51c6\u786e\u89e3\uff09\uff1a</p> <ul> <li>bin 1: \\(0.8 + 0.2\\);</li> <li>bin 2: \\(0.7 + 0.3\\);</li> <li>bin 3: \\(0.5 + 0.4 + 0.1\\);</li> </ul> <p>FFD \u7b56\u7565\u603b\u662f\u4f7f\u7528\u4e0d\u8d85\u8fc7 \\(\\frac{11}{9}M + \\frac{6}{9}\\) \u4e2a bin\uff08\u4e3a\u5565\u5c31\u8fde wiki \u4e5f\u4e0d\u7ea6 6/9\uff09\uff0c\u5e76\u4e14\u5b58\u5728\u4e00\u65cf\u80fd\u5bf9\u8fb9\u754c\u53d6\u7b49\u7684\u8f93\u5165\uff0c\u5176\u4e2d \\(M\\) \u8868\u793a\u51c6\u786e\u89e3\u7684 \\(\\#bin\\)\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec11/#\u6848\u4f8b-knapsack-problem","title":"[\u6848\u4f8b] Knapsack Problem","text":"<p>link</p> <p>Wikipedia: https://en.wikipedia.org/wiki/Knapsack_problem</p> <p>\u4e00\u4e2a\u4e0e\u88c5\u7bb1\u95ee\u9898\u5f88\u50cf\u7684\u95ee\u9898\u662f\u80cc\u5305\u95ee\u9898\u3002\u5176\u5927\u81f4\u63cf\u8ff0\u5982\u4e0b\uff1a\u7ed9\u5b9a\u4e00\u4e2a\u5bb9\u91cf\u4e3a \\(M\\) \u7684\u80cc\u5305\uff0c\u4ee5\u53ca \\(N\\) \u4e2a item\uff0c\u7b2c \\(i\\) \u4e2a item \u7684\u91cd\u91cf\u4e3a \\(w_i\\)\uff0c\u5176\u5229\u6da6\u4e3a \\(p_i\\)\u3002\u8981\u6c42\u5728\u4e0d\u8d85\u8fc7\u80cc\u5305\u5bb9\u91cf\u7684\u524d\u63d0\u4e0b\uff0c\u4f7f\u5f97\u80cc\u5305\u4e2d\u7684\u5229\u6da6\u6700\u5927\u5316\u3002\uff08\u6211\u4e5f\u4e0d\u77e5\u9053\u4e3a\u4ec0\u4e48 PPT \u4e0a\u4f1a\u628a\u5bb9\u91cf\u548c\u91cd\u91cf\u5173\u8054\u8d77\u6765\uff0canyway\uff0c\u5bb9\u91cf\u9650\u5236\u4e86 item \u7684\u91cd\u91cf\u548c\u3002\uff09</p> <p>\u6ce8\u610f</p> <p>\u6216\u8bb8\u5728\u5b66\u4e60 dp \u7684\u65f6\u5019\u4f60\u5df2\u7ecf\u63a5\u89e6\u8fc7\u80cc\u5305\u95ee\u9898\u4e86\uff0c\u4f46\u662f\u8bf7\u6ce8\u610f\uff0c\u6211\u4eec\u8fd9\u91cc\u8ba8\u8bba\u7684\u80cc\u5305\u95ee\u9898\u6709\u4e00\u4e2a\u975e\u5e38\u91cd\u8981\u7684\u7279\u70b9\u5c31\u662f\uff0c\u5bb9\u91cf\u548c\u5229\u6da6\u90fd\u662f\u5b9e\u6570\uff0c\u66f4\u76f4\u767d\u7684\u6765\u8bf4\uff0c\u4f60\u6ca1\u529e\u6cd5\u901a\u8fc7\u5c06\u5bb9\u91cf\u6216\u5229\u6da6\u4f5c\u4e3a\u72b6\u6001\u6765 dp \u6c42\u51c6\u786e\u89e3\u3002</p> <p>\u800c\u6839\u636e\u6bcf\u4e00\u4e2a\u7269\u54c1\u80fd\u5426\u81ea\u7531\u62c6\u5206\uff0c\u80cc\u5305\u95ee\u9898\u5206\u4e3a fractional version \u548c 0-1 version \u4e24\u7c7b\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec11/#fractional-version","title":"Fractional Version","text":"<p>\u5982\u679c\u6211\u4eec\u8bb0 \\(x_i\\in[0,1]\\) \u4e3a\u7b2c \\(i\\) \u4e2a item \u7684\u9009\u4e2d\u91cf\uff08\u5373\u5047\u8bbe item \u90fd\u662f\u8fde\u7eed\u53ef\u5206\u7684\uff09\uff0c\u5219\u7ea6\u675f\u6761\u4ef6\u53ef\u4ee5\u8868\u8ff0\u4e3a \\(\\sum_{i}^N w_ix_i \\leq M\\)\uff0c\u73b0\u5728\u6c42 \\(\\sum_{i}^{N} p_ix_i\\) \u7684\u6700\u5927\u503c\u3002</p> \ud83c\udf30 \u4f8b\u5b50 <p>\u5047\u8bbe\u73b0\u5728 \\(M = 20.0\\)\uff0c\u5e76\u4e14 \\(N = 3\\)\uff0c\u5206\u522b\u662f\uff1a</p> <ul> <li>item 1: \\(w_1 = 18.0, p_1 = 25.0\\); </li> <li>item 2: \\(w_2 = 15.0, p_2 = 24.0\\);</li> <li>item 3: \\(w_3 = 10.0, p_3 = 15.0\\);</li> </ul> <p>\u5219\u6700\u4f18\u89e3\u4e3a \\(x_1 = 0, x_2 = 1, x_3 = \\frac{1}{2}\\)\uff0c\u6b64\u65f6 \\(\\sum_{i}^{N} p_ix_i = 31.5\\)\u3002</p> <p>\u7531\u4e8e \\(x_i\\in[0,1]\\)\uff0c\u7ed9\u4e86\u6211\u4eec\u6781\u5927\u7684\u9009\u62e9\u81ea\u7531\uff0c\u6211\u4eec\u53ef\u4ee5\u9009\u62e9\u4efb\u610f\u591a\u7684\u67d0\u4e2a\u7269\u54c1\u3002\u90a3\u4e48\u975e\u5e38\u6734\u7d20\u7684\u4e00\u4e2a\u60f3\u6cd5\u5c31\u662f\uff0c\u5c3d\u53ef\u80fd\u591a\u5730\u9009\u62e9\u201c\u6027\u4ef7\u6bd4\u201d\u9ad8\u7684\u7269\u54c1\u3002\u4e5f\u5c31\u662f\u8bf4\uff0c\u6211\u4eec\u53ef\u4ee5\u6309\u7167 \\(\\frac{p_i}{w_i}\\)\uff08PPT \u79f0\u4e4b\u4e3a profit density\uff09\u964d\u5e8f\u6392\u5e8f\uff0c\u800c\u540e\u4ece\u5927\u5230\u5c0f\u4f9d\u6b21\u9009\u62e9\u7269\u54c1\uff0c\u76f4\u5230\u80cc\u5305\u88c5\u6ee1\u4e3a\u6b62\u3002</p> <p>\u4e0d\u8fc7\u8be5\u505a\u6cd5\u5df2\u7ecf\u662f\u51c6\u786e\u89e3\u4e86\uff0c\u6240\u4ee5\u6211\u4eec\u4e0d\u5bf9\u5b83\u8fdb\u884c\u5173\u4e8e\u8fd1\u4f3c\u7b97\u6cd5\u7684\u8ba8\u8bba\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec11/#0-1-version","title":"0-1 Version","text":"<p>\u76f8\u8f83\u4e8e fractional version\uff0c0-1 version \u8981\u6c42 \\(x_i \\in \\{0,1\\}\\)\uff0c\u6362\u53e5\u8bdd\u8bf4\u6bcf\u4e00\u4e2a\u7269\u54c1\u8981\u4e48\u9009\u8981\u4e48\u4e0d\u9009\u3002\u8fd9\u662f\u4e00\u4e2a\u7ecf\u5178\u7684 NPC \u95ee\u9898\uff0c\u6211\u4eec\u5c1d\u8bd5\u4f7f\u7528\u8fd1\u4f3c\u7b97\u6cd5\u6765\u6c42\u8f83\u4f18\u89e3\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec11/#\u8d2a\u5fc3\u505a\u6cd5","title":"\u8d2a\u5fc3\u505a\u6cd5","text":"<p>\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528\u8d2a\u5fc3\u7b97\u6cd5\uff0c\u8d2a\u5fc3\u7b56\u7565\u53ef\u4ee5\u662f\u603b\u662f\u9009\u53ef\u4ee5\u653e\u5f97\u4e0b\u7684\u3001\u8fd8\u6ca1\u653e\u5165\u4e2d\u7684\uff0c\u5229\u6da6\u6700\u5927\u7684\u6216 \\(\\frac{p_i}{w_i}\\) \u6700\u5927\u7684\u3002\u8fd9\u4e9b\u505a\u6cd5\u7684\u8fd1\u4f3c\u6bd4\u90fd\u662f 2\u3002</p> proof for rho = 2 <p>\u6211\u4eec\u7528 \\(p_\\text{max}\\) \u8868\u793a\u6240\u6709 item \u4e2d\u6700\u5927\u7684\u5229\u6da6\uff0c\u7528 \\(P_\\text{optimal}\\) \u8868\u793a\u51c6\u786e\u89e3\uff0c\\(P_\\text{greedy}\\) \u8868\u793a\u6211\u4eec\u4f7f\u7528\u8d2a\u5fc3\u505a\u6cd5\u5f97\u5230\u7684\u7b54\u6848\u3002\u5728\u8be5\u95ee\u9898\u4e2d\uff0c\u8fd1\u4f3c\u6bd4\u7684\u8ba1\u7b97\u8868\u8fbe\u5f0f\u4e3a\uff1a</p> \\[ \\rho = \\max(     \\frac{P_\\text{optimal}}{P_\\text{greedy}},     \\frac{P_\\text{greedy}}{P_\\text{optimal}} ) \\] <p>\u4e0b\u9762\u662f\u8bc1\u660e\u8fc7\u7a0b\uff1a</p> \\[ \\left\\{ \\begin{aligned}     &amp; p_\\text{max} \\leq P_\\text{greedy} &amp; (1)\\\\     &amp; P_\\text{optimal} \\leq P_\\text{greedy} + p_\\text{max} &amp; (2) \\end{aligned} \\right. \\] <p>\u5c06 \\((1)\\) \u5f0f\u4e24\u4fa7\u540c\u9664\u4ee5 \\(P_\\text{greedy}\\) \u5f97\uff1a</p> \\[ \\frac{p_\\text{max}}{P_\\text{greedy}} \\leq 1 \\quad (3) \\] <p>\u5c06 \\((2)\\) \u5f0f\u4e24\u4fa7\u540c\u9664\u4ee5 \\(P_\\text{greedy}\\)\uff0c\u5e76\u4ee3\u5165 \\((3)\\) \u5f97\uff1a</p> \\[ \\frac{P_\\text{optimal}}{P_\\text{greedy}} \\leq 1 + \\frac{p_\\text{max}}{P_\\text{greedy}} \\leq 2 \\] <p>PPT \u7684\u8bc1\u660e\u8fc7\u7a0b\u4e2d\u8fd8\u6709\u4e00\u4e2a\u4e0d\u7b49\u5f0f\uff0c\u867d\u7136\u6210\u7acb\uff0c\u4f46\u662f\u597d\u50cf\u6ca1\u8d77\u5230\u4f5c\u7528\uff0c\u6211\u5c31\u6269\u5c55\u4e00\u4e0b\u5199\u5728\u8fd9\u91cc\u6c42\u4e2a\u773c\u719f\u4e86\uff1a</p> \\[ p_\\text{max} \\leq P_\\text{greedy} \\leq P_\\text{optimal} \\leq P_\\text{frac} \\] <p>\u5176\u4e2d \\(P_\\text{frac}\\) \u6307\u7684\u662f\u540c\u6837\u7684\u6570\u636e\u4e0b fractional version \u7684\u7b54\u6848\u3002</p> <p>\u8865\u5145\u7ed3\u8bba\uff1a\u80cc\u5305\u95ee\u9898\u5177\u6709 FPTAS\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec11/#\u52a8\u6001\u89c4\u5212\u505a\u6cd5","title":"\u52a8\u6001\u89c4\u5212\u505a\u6cd5","text":"<p>\uff08\u771f\u662f\u6df7\u4e71\uff09</p> \\[ W_{i,p} = \\text{the minimum weight of a collection from } \\{1, \u2026, i\\} \\text{ with total profit being  exactly } p \\\\ W_{i,p} = \\left\\{ \\begin{aligned}     &amp;\\infty &amp;&amp; i = 0 \\\\     &amp;W_{i-1, p} &amp;&amp; p_i &gt; p \\\\     &amp;\\min\\{W_{i-1, p}, w_i + W_{i-1, p-p_i}\\} &amp;&amp; otherwise         \\end{aligned} \\right.\\\\ i = 1, ..., n; p = 1, ..., n\\cdot p_\\text{max} \\\\ O(n^2p_\\text{max}) \\] <p>\u5982\u679c \\(p_\\text{max}\\) \u5f88\u5927\uff0c\u53ef\u4ee5\u8003\u8651\u5c06\u5b83\u4eec\u8fd1\u4f3c\u53d6\u6574\uff0c\u7c7b\u4f3c\u4e8e\u5c06\u6d6e\u70b9\u6570\u5411\u4e0a\u53d6\u6574\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec11/#\u6848\u4f8b-the-k-center-problem","title":"[\u6848\u4f8b] The K-center Problem","text":"<p>link</p> <p>Berkeley's: https://ugtcs.berkeley.edu/src/approx-sp19/scribe-notes-2.pdf</p> <p>\uff08\u4e8c\u7ef4\uff09K \u4e2d\u5fc3\u95ee\u9898\u6307\uff1a\u7ed9\u5b9a\u5e73\u9762\u4e0a\u7684\u4e00\u7cfb\u5217 site\uff08\u5373\u70b9\uff09\uff0c\u5728\u5e73\u9762\u4e2d\u627e\u51fa \\(k\\) \u4e2a\u4e0d\u540c\u7684 center\uff0c\u8bb0 \\(site_i\\) \u5230\u79bb\u5b83\u6700\u8fd1\u7684 center \u7684\u8ddd\u79bb\u4e3a \\(dis_i\\)\uff0c\u6c42 \\(\\max \\{dis_i\\}\\) \u7684\u6700\u5c0f\u503c\u3002</p> <p>\u6570\u5b66\u8bed\u8a00\u8868\u8fbe</p> <p>\u8bbe \\(C = \\{c_1, c_2, ..., c_k\\}\\) \u4e3a \\(k\\) \u4e2a center\uff0c\\(S = \\{s_1, s_2, ..., s_n\\}\\) \u4e3a \\(n\\) \u4e2a site\uff0c\u6211\u4eec\u5b9a\u4e49 site \u5230\u5173\u4e8e center \u7684\u96c6\u5408 \\(C\\) \u7684\u8ddd\u79bb\u4e3a\uff1a</p> \\[ dis(s_i, C) = \\min_{c_i\\in C} \\{ dis(s_i, c_i) \\} \\] <p>\u5373 \\(s_i\\) \u5230\u8ddd\u79bb\u5b83\u6700\u8fd1\u7684 center \u7684\u8ddd\u79bb\u3002</p> <p>\u5b9a\u4e49\u6700\u5927\u7684\u6700\u5c0f\u8986\u76d6\u534a\u5f84\u4e3a\uff1a</p> \\[ r(C) = \\max_{s_i\\in S} \\{ dis(s_i, C) \\} \\\\ \\] <p>\u73b0\u5728\u8981\u5bfb\u627e\u4e00\u4e2a \\(C\\) \u4f7f\u5f97 \\(r(C)\\) \u6700\u5c0f\uff08\\(|C| = k\\)\uff09\u3002</p> <p>\u5f88\u7ed5\uff0c\u975e\u5e38\u7ed5\u3002\u63a5\u4e0b\u6765\u5f00\u59cb\u8bf4\u4eba\u8bdd\u3002</p> <p>\u5e73\u9762\u7684\u95ee\u9898\u6211\u4eec\u5c31\u7528\u5e73\u9762\u7684\u601d\u8def\u6765\u770b\uff0c\u5c31\u662f\u4e00\u4e2a\u5e73\u9762\u4e0a\u6709\u4e00\u5806\u70b9\uff0c\u73b0\u5728\u6211\u8981\u5728\u4e0a\u9762\u627e \\(k\\) \u4e2a\u4e2d\u5fc3\u53bb\u753b\u5706\uff0c\u4f7f\u5f97\u8fd9 \\(k\\) \u4e2a\u5706\u80fd\u8986\u76d6\u6240\u6709\u7684\u70b9\u3002\u73b0\u5728\u8981\u6c42\u6700\u5927\u7684\u90a3\u4e2a\u5706\u7684\u534a\u5f84\u6700\u5c0f\u80fd\u591a\u5c0f\u3002</p> \u5173\u4e8e\u8ddd\u79bb <p>PPT \u4e0a\u5bf9\u8ddd\u79bb\u505a\u4e86\u66f4\u8fdb\u4e00\u6b65\u7684\u8bf4\u660e\uff0c\u4f46\u662f\u5176\u5b9e\u5e76\u4e0d\u662f\u8fd9\u4e2a\u95ee\u9898\u7684\u91cd\u70b9\uff0c\u4f46\u662f\u4e3a\u4e86\u4e25\u8c28\u6027\uff0c\u6211\u8fd8\u662f\u5728\u8fd9\u91cc\u653e\u4e0a\u4e09\u6761\u6027\u8d28\uff1a</p> <p>3 property of 'distance'</p> \\[ \\begin{aligned}     &amp; dis(x,x) = 0 &amp;&amp; \\text{(identity)} \\\\     &amp; dis(x,y) = dis(y,x) &amp;&amp; \\text{(symmetry)} \\\\     &amp; dis(x,y) \\leq dis(x,z) + dis(z,y) &amp;&amp; \\text{(triangle inequality)} \\end{aligned} \\] <p>\u788e\u788e\u5ff5</p> <p>\u8fd9\u4e2a\u4e1c\u897f\u548c\u805a\u7c7b\u6709\u70b9\u50cf\u3002\u4e3b\u8981\u96be\u70b9\u5c31\u5728\u4e8e\uff0c\u6211\u4eec\u4e0d\u77e5\u9053\u5e94\u8be5\u4ee5\u4f55\u79cd\u7b56\u7565\u53bb\u8986\u76d6\u8fd9\u4e9b\u70b9\uff0c\u8981\u662f\u628a\u4e24\u4e2a\u8ddd\u79bb\u5f88\u8fdc\u7684\u70b9\u5212\u5728\u540c\u4e00\u4e2a\u5706\u5185\uff0c\u90a3\u7b54\u6848\u80af\u5b9a\u5c0f\u4e0d\u4e86\u3002</p> <p>\u63a5\u4e0b\u6765\u6211\u4eec\u6765\u5c1d\u8bd5\u89e3\u51b3\u7684\u8fd9\u4e2a\u95ee\u9898\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec11/#naive-greedy","title":"Naive Greedy","text":"<p>\u4e00\u4e2a\u505a\u6cd5\u662f\uff0c\u6211\u4eec\u6bcf\u6b21\u90fd\u9009\u62e9\u6700\u53ef\u80fd\u6210\u4e3a\u4e2d\u5fc3\u7684\u90a3\u4e2a\u70b9\uff0c\u5177\u4f53\u6765\u8bf4\uff1a</p> <ol> <li>\u5982\u679c\u662f\u7b2c\u4e00\u4e2a\u70b9\uff0c\u5c31\u9009\u53d6\u6240\u6709\u70b9\u7684\u4e2d\u5fc3\uff1b</li> <li>\u5982\u679c\u4e0d\u662f\u7b2c\u4e00\u4e2a\u70b9\uff0c\u5c31\u9009\u53d6\u80fd\u4e00\u4e2a\u6700\u80fd\u8ba9 \\(r(C)\\) \u4e0b\u964d\u7684\uff1b</li> </ol> <p>\u8fd9\u4e2a\u505a\u6cd5\u7684 bug \u6bd4\u8f83\u5927\uff0c\u5047\u8bbe\u6211\u4eec\u7684\u70b9\u662f\u805a\u7c7b\u975e\u5e38\u660e\u663e\u7684\u4e24\u4e2a\u70b9\u4e91\uff0c\u90a3\u4e48\u7b2c\u4e00\u4e2a\u70b9\u5c31\u4f1a\u843d\u5728\u4e24\u4e2a\u70b9\u4e91\u4e4b\u95f4\uff0c\u8fd9\u5f88\u8822\uff0c\u6240\u4ee5\u6211\u4eec\u4e0d\u6d6a\u8d39\u8fc7\u591a\u65f6\u95f4\u5728\u8fd9\u4e2a\u65b9\u6cd5\u4e0a\u3002</p> <p>\u6ce8\u610f\uff0c\u968f\u7740 center \u7684\u589e\u52a0\uff0c\u539f\u6765\u4ee5 \\(c_i\\) \u4e3a center \u7684 site \u5f88\u53ef\u80fd\u4ee5\u6700\u65b0\u63d2\u5165\u7684 \\(c_j\\) \u4e3a center\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec11/#2r-greedy","title":"2r-Greedy","text":"<p>\u65e2\u7136\u6b63\u5411\u505a\u5f88\u56f0\u96be\uff0c\u90a3\u6211\u4eec\u80fd\u4e0d\u80fd\u53cd\u7740\u505a\u5462\uff1f\u6709\u4e00\u79cd\u5957\u8def\u53eb\u4e8c\u5206\u7b54\u6848\uff0c\u5373\u5148\u731c\u7b54\u6848\uff0c\u518d\u9a8c\u8bc1\u662f\u5426\u662f\u7b54\u6848\u3002\u5728\u8fd9\u4e2a\u95ee\u9898\u4e2d\u6211\u4eec\u53ef\u4ee5\u8fc1\u79fb\u8fd9\u4e2a\u601d\u60f3\uff0c\u5373\u5148\u731c\u4e00\u4e2a \\(r\\)\uff0c\u7136\u540e\u5c1d\u8bd5\u7528 \\(k\\) \u4e2a\u534a\u5f84\u4e3a \\(r\\) \u7684\u5706\u53bb\u8986\u76d6\u5269\u4e0b\u7684\u6240\u6709\u70b9\u3002</p> <p>\u66f4\u5177\u4f53\u7684\u6765\u8bf4\uff0c\u5047\u8bbe\u51c6\u786e\u89e3\u5bf9\u5e94\u7684\u4e00\u4e2a center \u96c6\u5408\u4e3a \\(C^*\\)\uff0c\u90a3\u4e48 \\(\\forall r(C_x) \\geq r(C^*)\\) \u7684 \\(C_x\\) \u90fd\u5fc5\u5b9a\u5b58\u5728\u8986\u76d6\u65b9\u6848\uff1b\u53cd\u8fc7\u6765\u8bf4\uff0c\u5982\u679c\u6211\u4eec\u80fd\u591f\u9a8c\u8bc1\u5bf9\u4e8e \\(C_x\\) \u80fd\u591f\u8986\u76d6\u6240\u6709\u7684\u70b9\uff0c\u90a3\u4e48\u5c31\u53ef\u4ee5\u7ea6\u675f\u51c6\u786e\u89e3 \\(r(C^*) \\leq r(C_x)\\)\u3002</p> <p>\u5982\u4f55\u201c\u9a8c\u8bc1\u201d</p> <p>\u53ef\u662f\uff0c\u4ed4\u7ec6\u4e00\u60f3\u6211\u4eec\u53d1\u73b0\uff0c\u4e8c\u5206\u7b54\u6848\u7684\u8fc7\u7a0b\u4e2d\uff0c\u201c\u9a8c\u8bc1\u5bf9\u4e8e \\(C_x\\) \u80fd\u591f\u8986\u76d6\u6240\u6709\u7684\u70b9\u201d\u8fd9\u4ef6\u4e8b\u4e5f\u4e0d\u597d\u505a\uff0c\u867d\u7136\u6211\u4eec\u6709\u534a\u5f84\uff0c\u4f46\u662f\u6211\u4eec\u4e5f\u5f88\u96be\u627e\u5230\u4e00\u4e2a\u6700\u597d\u7684\u65b9\u6848\u6765\u8986\u76d6\u6240\u6709\u7684\u70b9\u3002</p> hint: \u8fd1\u4f3c\u7b97\u6cd5 <p>\u4e8e\u662f\u6211\u4eec\u7684\u8fd1\u4f3c\u7b97\u6cd5\u5c31\u53ef\u4ee5\u5927\u5c55\u62f3\u811a\u4e86\u3002\u4f46\u662f\u9700\u8981\u6ce8\u610f\uff0c\u8fd9\u91cc\u6240\u8c13\u7684\u8fd1\u4f3c\u7b97\u6cd5\uff0c\u6307\u7684\u662f\u4f7f\u7528\u4e8c\u5206\u7b54\u6848\u6c42\u89e3 \\(r(C)\\) \u8fd9\u4e2a\u7b97\u6cd5\uff0c\u800c\u975e\u5224\u65ad \\(k\\) \u4e2a\u534a\u5f84\u4e3a \\(r\\) \u7684\u5706\u80fd\u5426\u8986\u76d6\u6240\u6709\u70b9\u7684\u7b97\u6cd5\u3002\u8fd9\u4e00\u70b9\u975e\u5e38\u91cd\u8981\uff01</p> <p>\u800c\u5173\u4e8e\u7b97\u6cd5\u5177\u4f53\u5982\u4f55\u64cd\u4f5c\uff0c\u8bf7\u63a5\u7740\u770b\u3002 </p> <p>\u9996\u5148\uff0c\u6211\u4eec\u518d\u6b21\u68b3\u7406\u4e00\u4e0b\u8fd9\u4e2a\u7b97\u6cd5\uff0c\u5b83\u5305\u542b\u5185\u5916\u4e24\u5c42\uff0c\u9996\u5148\u5916\u90e8\u901a\u8fc7\u5728\u7b54\u6848\u7684\u5019\u9009\u533a\u95f4\uff08\u5373 \\((0, r_\\text{max}]\\)\uff0c\\(r_\\text{max}\\) \u4e3a\u6700\u8fdc\u7684\u4e24\u4e2a\u70b9\u7684\u8ddd\u79bb\uff09\u4e8c\u5206\u5019\u9009\u503c\uff0c\u63a5\u7740\u901a\u8fc7\u5224\u5b9a\u7b97\u6cd5\u6765\u5224\u5b9a\u63a5\u4e0b\u6765\u7684\u4e8c\u5206\u65b9\u5411\u3002</p> <p>\u7136\u800c\uff0c\u7531\u4e8e\u6211\u4eec\u5f88\u96be\u5728\u591a\u9879\u5f0f\u65f6\u95f4\u5b9e\u73b0\u51c6\u786e\u7684\u201c\u5224\u5b9a\u201d\uff0c\u6240\u4ee5\u6211\u4eec\u91c7\u53d6\u8fd9\u6837\u4e00\u4e2a\u542f\u53d1\u5f0f\u7684\u7b56\u7565\u6765\u8fdb\u884c\u5bbd\u6cdb\u7684\u5fc5\u8981\u6761\u4ef6\u7b5b\u9009\uff1a</p> <p>\u6d41\u7a0b\u63cf\u8ff0</p> <p>\u8bbe \\(C_x\\) \u8868\u793a\u9009\u4e2d\u7684 center\uff0c\\(S_x\\) \u8868\u793a\u5c1a\u672a\u88ab\u4efb\u4f55\u5706\u8986\u76d6\u7684 site\uff0c\\(r_x\\) \u8868\u793a\u5f53\u524d\u4e8c\u5206\u51fa\u6765\u7684\uff0c\u8981\u6211\u4eec\u5224\u65ad\u7684\u534a\u5f84\uff0c\\(S\\) \u4f9d\u7136\u8868\u793a\u6240\u6709 site \u7684\u96c6\u5408\uff1a</p> <ol> <li>\u521d\u59cb\u5316 \\(C_x = \\emptyset\\)\uff1b</li> <li>\u5f53 \\(S_x \\not = \\emptyset\\) \u65f6\uff08\u5373\u8fd8\u6709\u70b9\u6ca1\u88ab\u8986\u76d6\u65f6\uff09\uff0c\u91cd\u590d\u8fd9\u4e9b\u64cd\u4f5c\uff1a<ol> <li>\u968f\u673a\u9009\u53d6\u4e00\u4e2a site \\(s_i \\in S_x\\)\uff0c\u5c06\u5176\u63d2\u5165 \\(C_x\\)\uff08\u5373\u5c06 \\(s_i\\) \u5f53\u4f5c\u4e00\u4e2a center\uff09\uff0c\u5e76\u4ece \\(S_x\\) \u4e2d\u5c06 \\(s_i\\) \u5220\u9664\uff08\u5373 \\(s_i\\) \u5fc5\u5b9a\u88ab\u8986\u76d6\uff09\uff1b</li> <li>\u5220\u9664 \\(S_x\\) \u4e2d\u6240\u6709\u8ddd\u79bb \\(s_i\\) \u4e0d\u8db3 \\(r_x\\) \u7684\u70b9\uff08\u5373\u5220\u9664\u6ee1\u8db3 \\(dis(s_i, s_j) \\leq r_x\\) \u7684\u6240\u6709 \\(s_k \\in S_x\\)\uff09\uff1b</li> </ol> </li> <li>\u5f53\u6240\u6709\u70b9\u90fd\u88ab\u8986\u76d6\u540e\uff1a<ol> <li>\u5982\u679c \\(|C_x| \\leq k\\)\uff0c\u5219\u8fd4\u56de yes\uff1b</li> <li>\u5426\u5219\u8fd4\u56de no\uff1b</li> </ol> </li> </ol> <p>\u5982\u679c\u8fd4\u56de yes\uff0c\u5219\u4e0b\u4e00\u4e2a \\(r_x\\) \u5e94\u5f53\u53d6\u66f4\u5c0f\u7684 \\(r_x\\)\uff1b\u5982\u679c\u8fd4\u56de no\uff0c\u4e0b\u4e00\u6b21\u5e94\u8be5\u53d6\u66f4\u5927\u7684 \\(r_x\\)\uff08\u7a0d\u5019\u4f1a\u89e3\u91ca\u4e3a\u4ec0\u4e48\uff09\u3002</p> <p>\u73b0\u5728\u5bf9\u5176\u505a\u8fdb\u4e00\u6b65\u89e3\u91ca\u3002\u8fd9\u662f\u4e00\u4e2a\u542f\u53d1\u5f0f\u7684\u505a\u6cd5\uff0c\u65e8\u5728\u6bcf\u6b21\u5bfb\u627e\u8fd8\u6ca1\u88ab\u8986\u76d6\u7684\u70b9\u4f5c\u4e3a\u65b0\u7684 center\uff0c\u7528\u4e00\u4e2a\u534a\u5f84\u4e3a \\(2r_x\\) \u7684\u5706\u53bb\u8986\u76d6\u5269\u4e0b\u7684\u70b9\u3002\u901a\u8fc7\u5224\u65ad\u8fd9\u6837\u6240\u9700\u8981\u7684 center \u6570\u91cf\u662f\u5426\u8d85\u8fc7 \\(k\\) \u6765\u5224\u65ad\u662f\u5426\u80fd\u591f\u8986\u76d6\u3002\u63a5\u4e0b\u6765\u5f88\u7ed5\uff0c\u8bf7\u4e00\u6b65\u4e00\u6b65\u7684\u770b\uff1a</p> <ol> <li>\u5f53\u8fd9\u4e2a\u542f\u53d1\u5f0f\u641c\u7d22\u6210\u529f\u65f6\uff0c\u8bf4\u660e \\(2r_x \\geq r(C^*)\\)\uff0c\u5373 \\(k\\) \u4e2a \\(2r_x\\) \u7684\u5706\u53ef\u4ee5\u8986\u76d6\u6240\u6709\u70b9\uff1b</li> <li>\u5f53\u8fd9\u4e2a\u542f\u53d1\u5f0f\u641c\u7d22\u5931\u8d25\u65f6\uff0c\u4e0d\u80fd\u8bf4\u660e \\(2r_x \\geq r(C^*)\\)\uff0c\u5373 \\(k\\) \u4e2a \\(2r_x\\) \u7684\u5706\u4e0d\u80fd\u8986\u76d6\u6240\u6709\u70b9\uff0c\u56e0\u4e3a\u542f\u53d1\u5f0f\u65b9\u6848\u5e76\u4e0d\u662f\u6700\u4f18\u65b9\u6848\uff1b\u4f46\u662f\u80fd\u8bf4\u660e\u5fc5\u5b9a\u4e0d\u5b58\u5728 \\(r_x\\) \u7684\u8986\u76d6\uff0c\u5373 \\(r_x \\leq r(C^*)\\)\uff08\u8bc1\u660e\u89c1\u4e0b\u65b9 lemma\uff09\uff1b</li> </ol> lemma <p>\u5047\u8bbe\u534a\u5f84\u4e3a \\(r\\)\uff0c\u4ee5 \\(c\\) \u4e3a\u5706\u5fc3\u7684\u5706 \\(C\\) \u8986\u76d6\u4e86 \\(S\\) \u4e2d\u7684\u6240\u6709\u70b9\u3002</p> <p>\u90a3\u4e48\uff0c\u5bf9\u4e8e\u56fa\u5b9a\u7684\u534a\u5f84 \\(r'\\)\uff0c\u8981\u60f3\u53d6\u4efb\u610f\u7684 \\(s_i \\in S\\) \u4e3a\u5706\u5fc3\uff0c\u5f62\u6210\u7684\u5706 \\(C_i\\)\uff0c\u603b\u662f\u80fd\u8986\u76d6 \\(S\\) \u4e2d\u7684\u6240\u6709\u70b9\uff0c\u5219 \\(r' \\geq 2r\\)\u3002</p> <p>lemma \u7684\u8bc1\u660e\u5c31\u4e0d\u5728\u8fd9\u91cc\u5c55\u5f00\u4e86\uff0c\u8bc1\u660e\u7684\u5173\u952e\u662f\u8003\u8651\u4e24\u70b9\u5206\u5e03\u5728\u76f4\u5f84\u4e24\u7aef\u7684\u60c5\u51b5\u3002</p> <p>\u8fd9\u4e2a\u5f15\u7406\u7684\u9644\u52a0\u7ed3\u8bba\u5c31\u662f\uff1a</p> \\[ \\forall i \\quad C \\subset C_i \\] <p>\u5373\u4ee5 \\(r\\) \u4e3a\u534a\u5f84\u7684\u6700\u4f18\u8986\u76d6\u5706\uff0c\u4e00\u5b9a\u80fd\u88ab\u4ee5\u4efb\u610f \\(s_i\\) \u4e3a\u5706\u5fc3\u3001\\(2r\\) \u4e3a\u534a\u5f84\u7684\u5706\u6240\u8986\u76d6\u3002</p> <p> </p> <p>\u5f53\u6211\u4eec\u53d1\u73b0\u6211\u4eec\u5904\u4e8e\u60c5\u51b5 <code>1.</code> \u65f6\uff0c\u6211\u4eec\u5f00\u5fc3\u7684\u53d1\u73b0\u6211\u4eec\u786e\u5b9e\u5f97\u5230\u4e86\u4e00\u4e2a\u8ddd\u79bb \\(r(C^*)\\) \u66f4\u8fd1\u7684\u4e0a\u754c \\(2r_x\\)\uff0c\u7531\u4e8e\u4e8c\u5206\u7684\u6027\u8d28\uff0c\u6211\u4eec\u6bcf\u6b21\u901a\u8fc7 <code>1.</code> \u786e\u5b9a\u7684\u4e0a\u754c\uff0c\u603b\u662f\u8d8a\u6765\u8d8a\u7d27\u7684\u3002</p> <p>\u5f53\u6211\u4eec\u5904\u4e8e\u60c5\u51b5 <code>2.</code> \u65f6\uff0c\u6211\u4eec\u4e0d\u77e5\u9053 \\(2r_x\\) \u548c \\(r(C^*)\\) \u7684\u5927\u5c0f\u5173\u7cfb\uff0c\u4f46\u662f\u77e5\u9053 \\(r_x\\) \u548c \\(r(C^*)\\) \u7684\u5173\u7cfb\uff0c\u7531\u4e8e\u4e8c\u5206\u7684\u6027\u8d28\uff0c\u6211\u4eec\u6bcf\u6b21\u901a\u8fc7 <code>2.</code> \u786e\u5b9a\u7684\u4e0b\u754c\uff0c\u4e5f\u603b\u662f\u8d8a\u6765\u8d8a\u7d27\u7684\u3002</p> <p>\u800c\u6700\u7ec8\uff0c\u6211\u4eec\u4f1a\u5f97\u5230\u4e00\u4e2a\u6700\u7ec8\u7684 \\(r_{x_0}\\)\uff0c\u6ee1\u8db3\uff1a\\(r_{x_0} \\leq r(C^*) \\leq 2r_{x_0}\\)\uff08\u5f0f\u4e2d\u54ea\u8fb9\u80fd\u53d6\u7b49\u53d6\u51b3\u4e8e\u6700\u540e\u843d\u5728 <code>1.</code> \u8fd8\u662f <code>2.</code>\uff09\u3002</p> <p>\u800c\u6211\u4eec\u6700\u7ec8\u7ed9\u51fa\u7684\u7b54\u6848\u662f \\(2r_{x_0}\\)\uff08\u56e0\u4e3a \\(r_{x_0}\\) \u4e0d\u6ee1\u8db3\u6761\u4ef6\uff0c\u4e0d\u662f\u89e3\uff0c\u66f4\u4e0d\u662f\u8fd1\u4f3c\u89e3\uff09\u3002</p> <p>\u73b0\u5728\uff0c\u6211\u4eec\u6765\u8ba1\u7b97\u8fd1\u4f3c\u6bd4\uff1a</p> \\[ \\begin{aligned}     &amp; \\begin{aligned}         \\because \\;\\;\\;         &amp; r_{x_0} \\leq r(C^*) \\leq 2r_{x_0} \\\\         &amp; \\frac{1}{2} \\leq \\frac{r(C^*)}{2r_{x_0}} \\leq 1 \\\\         &amp; 1 \\leq \\frac{2r_{x_0}}{r(C^*)} \\leq 2     \\end{aligned} \\\\     &amp; \\therefore \\; \\rho = \\max\\{             \\frac{ 2 r_{x_0} }{ r(C^*) },             \\frac{ r(C^*) }{ 2 r_{x_0} }         \\} = 2 \\end{aligned} \\]"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec11/#smarter-greedy","title":"Smarter Greedy","text":"<p>\u6211\u4eec\u5173\u6ce8\u5230\uff0c\u4e0a\u9762\u90a3\u4e2a\u505a\u6cd5\u603b\u662f\u968f\u673a\u7684\u9009\u53d6\u65b0\u7684 \\(c_i\\)\uff0c\u4f46\u662f\u5bf9\u4e8e center \u7684\u9009\u53d6\uff0c\u6211\u4eec\u5176\u5b9e\u53ef\u4ee5\u603b\u662f\u9009\u62e9\u8ddd\u79bb\u5df2\u6709\u7684 center \u6700\u8fdc\u7684\u70b9\uff0c\u6b64\u5916\uff0c\u5f53 \\(|C| &gt; k\\) \u65f6\uff0c\u6211\u4eec\u4e5f\u6ca1\u5fc5\u8981\u7ee7\u7eed\u505a\u4e86\u3002</p> <p>\u6d41\u7a0b\u63cf\u8ff0</p> <ol> <li>\u521d\u59cb\u5316 \\(C_x = \\emptyset\\)\uff0c\\(S_x = S\\)\uff1b</li> <li>\u968f\u673a\u9009\u53d6\u4e00\u4e2a site \\(s_i \\in S_x\\)\uff0c\u5c06\u5176\u63d2\u5165 \\(C_x\\)\uff0c\u5e76\u4ece \\(S_x\\) \u4e2d\u5c06 \\(s_i\\) \u5220\u9664\uff1b</li> <li>\u5f53 \\(|C_x| \\leq k\\) \u4e14 \\(S_x \\not = \\emptyset\\) \u65f6\uff0c\u91cd\u590d\u4ee5\u4e0b\u6b65\u9aa4\uff1a<ol> <li>\u9009\u53d6\u4e00\u4e2a site \\(s_i \\in S_x\\)\uff0c\u8fd9\u4e2a site \u6ee1\u8db3 \\(\\forall s_j \\in S_x \\quad dis(s_i, C_x) \\geq dis(s_j, C_x)\\)\uff08\u5373\u8fd9\u4e2a\u70b9\u662f\u8fd8\u6ca1\u88ab\u8986\u76d6\u7684\u70b9\u4e2d\u8ddd\u79bb \\(C_x\\) \u6700\u8fdc\u7684\u70b9\uff09\uff1b</li> <li>\u5c06 \\(s_i\\) \u63d2\u5165 \\(C_x\\)\uff0c\u5e76\u4ece \\(S_x\\) \u4e2d\u5c06 \\(s_i\\) \u5220\u9664\uff1b</li> </ol> </li> <li>\u5982\u679c \\(|C_x| \\leq k\\) \u4e14 \\(S_x = \\emptyset\\)\uff0c\u5219\u8fd4\u56de yes\uff1b\u5426\u5219\u8fd4\u56de no\u3002</li> </ol> <p>\u7531\u4e8e\u8fd9\u4e2a\u505a\u6cd5\u5b9e\u9645\u4e0a\u53ea\u662f\u4f18\u5316\u4e86\u4e00\u4e0b\u542f\u53d1\u5f0f\u7684\u7b56\u7565\uff0c\u5e76\u6ca1\u6709\u6539\u53d8\u5185\u6838\uff0c\u6240\u4ee5\u5176\u8fd1\u4f3c\u6bd4\u4ecd\u7136\u662f \\(2\\)\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec11/#\u603b\u7ed3","title":"\u603b\u7ed3","text":"<p>\u5173\u4e8e\u7b97\u6cd5\u7684\u8bbe\u8ba1\uff0c\u6211\u4eec\u8003\u8651\u8fd9\u4e09\u4e2a\u7ef4\u5ea6\uff1a</p> <ol> <li>\u6700\u4f18\u6027(optimality)\uff1a\u5373\u80fd\u6c42\u51c6\u786e\u89e3\uff1b</li> <li>\u9ad8\u6548\u6027(efficiency)\uff1a\u5373\u7b97\u6cd5\u662f\u5426\u9ad8\u6548\uff1b</li> <li>\u666e\u904d\u6027(all instances)\uff1a\u5373\u7b97\u6cd5\u662f\u5426\u666e\u904d\u9002\u7528\u4e8e\u6240\u6709\u7684\u60c5\u51b5\uff1b</li> </ol> <p>\u5018\u82e5\u4e00\u4e2a\u89e3\u6cd5\uff1a</p> <ol> <li>\u540c\u65f6\u6ee1\u8db3\u6700\u4f18\u6027\u548c\u9ad8\u6548\u6027\uff0c\u90a3\u4e48\u8fd9\u4e2a\u7b97\u6cd5\u5bf9\u7279\u6b8a\u60c5\u51b5\u80fd\u9ad8\u6548\u6c42\u51c6\u786e\u89e3\uff1b</li> <li>\u540c\u65f6\u6ee1\u8db3\u6700\u4f18\u6027\u548c\u666e\u904d\u6027\uff0c\u90a3\u4e48\u8fd9\u4e2a\u7b97\u6cd5\u5bf9\u6240\u6709\u60c5\u51b5\u90fd\u80fd\u6c42\u51c6\u786e\u89e3\uff1b</li> <li>\u540c\u65f6\u6ee1\u8db3\u9ad8\u6548\u6027\u548c\u666e\u904d\u6027\uff0c\u90a3\u4e48\u8fd9\u4e2a\u7b97\u6cd5\u53ef\u80fd\u662f\u4e2a\u8fd1\u4f3c\u7b97\u6cd5\uff1b</li> </ol> <p>\u5c31\u7b97 N=NP \u6210\u7acb\uff0c\u6211\u4eec\u4ecd\u7136\u65e0\u6cd5\u4fdd\u8bc1\u4e09\u4e2a\u613f\u671b\u4e00\u6b21\u6ee1\u8db3\u3002</p> <p>\u4e0d\u662f\u5f88\u660e\u767d\u6700\u540e\u4e00\u53e5\u8bdd\u5982\u4f55\u7406\u89e3\uff0c\u4f46\u662f\u8fd9\u4e00\u90e8\u5206\u5e94\u8be5\u5c31\u662f\u770b\u4e2a\u773c\u719f\uff0c\u4e0d\u662f\u5f88\u91cd\u8981\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec12/","title":"Lecture 12 | Local Search","text":"<p> \u7ea6 365 \u4e2a\u5b57  17 \u884c\u4ee3\u7801  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 1 \u5206\u949f</p> <p>\u65f6\u95f4\u5306\u5fd9\uff0c\u5185\u5bb9\u7b80\u7565</p> <ul> <li>local optimum is a best solution in a neighborhood</li> <li>start with a feasible solution and search a better one within the neighborhood</li> <li>a local optimum is achieved if no improvement is possible</li> </ul> <p>\u5373\u5148\u627e\u5230\u4e00\u4e2a\u53ef\u884c\u89e3\uff0c\u4ee5\u53ca\u91cf\u5316\u5176\u4f18\u7a0b\u5ea6\u7684\u76ee\u6807\u51fd\u6570\uff0c\u518d\u5728\u8fd9\u4e2a\u53ef\u884c\u89e3\u4e0a\u5bfb\u6c42\u4f18\u5316\uff0c\u76f4\u5230\u8fbe\u5230\u5c40\u90e8\u6700\u4f18\u89e3\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec12/#\u6848\u4f8b-the-vertex-cover-problem","title":"[\u6848\u4f8b] The Vertex Cover Problem","text":"<p>\u9876\u70b9\u8986\u76d6\u95ee\u9898(vertex cover problem)\u6307\u7ed9\u5b9a\u4e00\u4e2a\u65e0\u5411\u56fe \\(G=(V,E)\\)\uff0c\u627e\u5230\u4e00\u4e2a\u6700\u5c0f\u7684\u9876\u70b9\u96c6 \\(S\\subseteq V\\)\uff0c\u4f7f\u5f97\u6bcf\u6761\u8fb9 \\((u,v)\\) \u90fd\u81f3\u5c11\u6709\u4e00\u4e2a\u7aef\u70b9\u5728 \\(S\\) \u4e2d\uff08\u5373 \\(u\\in S \\lor v\\in S\\)\uff09\u3002</p> <p>\u8fd9\u4e2a\u95ee\u9898\u7684\u53ef\u884c\u89e3\u4e3a \\(S = V\\)\uff0c\u5373\u5b8c\u5168\u8986\u76d6\uff0c\u5176\u76ee\u6807\u51fd\u6570\u4e3a \\(cost(S) = |S|\\)\u3002\u5373\uff0c\u6211\u4eec\u5c1d\u8bd5\u4f7f\u7528 local search \u6765\u964d\u4f4e \\(|S|\\)\u3002</p> <p>\u7ed9\u51fa\u51e0\u79cd\u6848\u4f8b\u4ee5\u53ca\u53ef\u89c6\u5316\uff0c\u8bf4\u660e\u5c40\u90e8\u641c\u7d22\u5bb9\u6613\u5931\u6548\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec12/#\u6885\u7279\u7f57\u6ce2\u5229\u65af\u7b97\u6cd5","title":"\u6885\u7279\u7f57\u6ce2\u5229\u65af\u7b97\u6cd5","text":"<p>\u6885\u7279\u7f57\u6ce2\u5229\u65af\u7b97\u6cd5(the Metropolis algorithm)\u7684\u8fc7\u7a0b\uff1a</p> <p>\u51d1\u5408\u4e00\u4e0b\uff0c\u4e4b\u540e\u6709\u7a7a\u518d\u6539\u3002</p> <pre><code>SolutionType Metropolis() {   Define constants k and T;\nStart from a feasible solution S \\in FS ;\nMinCost = cost(S);\nwhile (1) {\nS\u2019 = Randomly chosen from N(S); CurrentCost = cost(S\u2019);\nif ( CurrentCost &lt; MinCost ) {\nMinCost = CurrentCost;    S = S\u2019;\n}\nelse {\nWith a probability e^{-\\Delta cost / (kT)}, let S = S\u2019;\nelse  break;\n}\n}\nreturn S;\n}\n</code></pre> <p>\u6ce8\uff1a\u5bf9\u4e8ecase 1\uff0c\u6709\u4e00\u5b9a\u6982\u7387\u53ef\u4ee5\u8df3\u51falocal optimum\u5f97\u5230\u6b63\u786e\u89e3\u3002\u4f46\u662f\u5bf9case 0\uff0c\u6709\u53ef\u80fd\u5728\u52a01\u548c\u51cf1\u4e4b\u95f4\u65e0\u9650\u9707\u8361\u2026\u2026 \u6ce8\uff1a\u5f53\uff08\u6e29\u5ea6\uff09T\u5f88\u9ad8\u65f6\uff0c\u4e0a\u5761\u7684\u6982\u7387\u51e0\u4e4e\u4e3a1\uff0c\u5bb9\u6613\u5f15\u8d77\u5e95\u90e8\u9707\u8361\uff1b\u5f53T\u63a5\u8fd10\u65f6\uff0c\u4e0a\u5761\u6982\u7387\u51e0\u4e4e\u4e3a0\uff0c\u63a5\u8fd1\u539f\u59cb\u7684\u68af\u5ea6\u4e0b\u964d\u6cd5\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec12/#\u6a21\u62df\u9000\u706b","title":"\u6a21\u62df\u9000\u706b","text":"<p>\u6a21\u62df\u9000\u706b(simulated annealing)</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec12/#\u6848\u4f8b-hopfield-neural-networks","title":"[\u6848\u4f8b] Hopfield Neural Networks","text":"<p>links</p> <p>Wikipedia: https://en.wikipedia.org/wiki/Hopfield_network</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec12/#\u6848\u4f8b-the-maximum-cut-problem","title":"[\u6848\u4f8b] The Maximum Cut Problem","text":"<p>links</p> <p>Wikipedia: https://en.wikipedia.org/wiki/Maximum_cut</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec13/","title":"Lecture 13 | Randomized Algorithms","text":"<p> \u7ea6 25 \u4e2a\u5b57 </p> <p>\u65f6\u95f4\u5306\u5fd9\uff0c\u5185\u5bb9\u7b80\u7565</p> <p>\u4e00\u4e9b\u6982\u5ff5\u8bf4\u660e</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec13/#the-hiring-problem","title":"The Hiring Problem","text":""},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec13/#modified-quick-sort","title":"Modified Quick Sort","text":""},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec14/","title":"Lecture 14 | Parallel","text":"<p> \u7ea6 3 \u4e2a\u5b57 </p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec15/","title":"Lecture 15 | External Sorting","text":"<p> \u7ea6 6424 \u4e2a\u5b57  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 21 \u5206\u949f</p> <p>link</p> <p>Wikipedia: https://en.wikipedia.org/wiki/External_sorting</p> <p>\u5916\u6392\u5e8f\u4e0e\u6570\u636e\u5e93\u7cfb\u7edf\u4e2d\u7684\u76f8\u5173\u5185\u5bb9\u6709\u4ea4\u53c9\u5173\u7cfb\uff0c\u5f53\u9700\u8981\u6392\u5e8f\u7684\u6570\u636e\u8fc7\u5927\uff0c\u800c\u65e0\u6cd5\u88ab\u5b8c\u5168\u653e\u5728\u5185\u5b58\u65f6\uff0c\u666e\u901a\u7684\u6392\u5e8f\u7b97\u6cd5\u65e0\u6cd5\u88ab\u5e94\u7528\u3002\u6b64\u65f6\u9700\u8981\u4f7f\u7528\u5916\u6392\u5e8f\uff0c\u7b80\u5355\u6765\u8bf4\u5c31\u662f\u5728\u66f4\u5927\u7684\u5c3a\u5ea6\u4e0a\u8fdb\u884c\u7c7b\u4f3c\u5f52\u5e76\u7684\u64cd\u4f5c\u3002</p> <p>\u800c\u6b63\u56e0\u4e3a\u6b64\uff0c\u5916\u90e8\u6392\u5e8f\u7684\u8fc7\u7a0b\u4e0e\u786c\u4ef6\u8bbe\u8ba1\u6709\u4e00\u5b9a\u5173\u7cfb\u3002</p> \u4e0e\u786c\u4ef6\u76f8\u5173\u7684\u4e00\u4e9b\u8bf4\u660e <p>\u5177\u4f53\u6765\u8bf4\uff0c\u666e\u901a\u7684\u6392\u5e8f\u7b97\u6cd5\u6392\u5e8f\u7684\u5bf9\u8c61\u90fd\u662f\u653e\u5728\u5185\u5b58\u91cc\u7684\u4e00\u4e9b\u6570\u636e\uff0c\u4f8b\u5982\u4e00\u4e2a <code>int</code> \u6570\u7ec4\u3002\u7136\u800c\u5916\u90e8\u6392\u5e8f\u6392\u5e8f\u7684\u5bf9\u8c61\uff0c\u6216\u8005\u8bf4\u8981\u6392\u5e8f\u7684\u90a3\u4e2a\u201c\u6570\u7ec4\u201d\uff0c\u6ca1\u6cd5\u88ab\u5b8c\u6574\u5730\u5b58\u5728\u5185\u5b58\u91cc\uff0c\u5b83\u4eec\u90fd\u88ab\u5b58\u50a8\u5728\u786c\u76d8\u4e4b\u7c7b\u7684\u975e\u6613\u5931\u4ecb\u8d28\u4e2d\uff0c\u800c\u4ece\u8fd9\u79cd\u4ecb\u8d28\u91cc\u8bfb\u53d6\u6570\u636e\u5f80\u5f80\u5177\u6709\u8f83\u5927\u7684\u5f00\u9500\uff0c\u6240\u4ee5\u6211\u4eec\u603b\u662f\u201c\u4e00\u5757\u4e00\u5757\u201d\u4ece\u91cc\u9762\u90a3\u6570\u636e\u3002</p> <p>\u6253\u4e2a\u6bd4\u65b9\uff0c\u4f60\u73b0\u5728\u9700\u8981\u5bf9\u4e00\u6574\u4e2a\u56fe\u4e66\u9986\uff08\u786c\u76d8\uff09\u7684\u4e66\u505a\u6392\u5e8f\uff0c\u4f46\u662f\u4f60\u7684\u684c\u5b50\uff08\u5185\u5b58\uff09\u4e0a\u6700\u591a\u653e\u4e0b\u4e09\u5341\u672c\u4e66\uff0c\u6362\u53e5\u8bdd\u6765\u8bf4\uff0c\u4f60\u4e00\u6b21\u6700\u591a\u5904\u7406\u4e09\u5341\u672c\u4e66\u3002\u800c\u4e3a\u4e86\u4ece\u56fe\u4e66\u9986\u4e2d\u83b7\u53d6\u9700\u8981\u6392\u7684\u4e66\uff0c\u4f60\u5f97\u5148\u627e\u5230\u8fd9\u4e9b\u4e66\u5728\u54ea\uff08seek\uff09\uff0c\u7136\u540e\u518d\u628a\u8fde\u7eed\u7684\u4e09\u5341\u672c\u4e66\u62ff\u51fa\u6765\uff08block transfer\uff09\uff0c\u653e\u5230\u4f60\u7684\u684c\u5b50\uff08\u5185\u5b58\uff09\u4e0a\u518d\u6392\u5e8f\uff0c\u800c\u4e3a\u4e86\u7ed9\u63a5\u4e0b\u6765\u4e09\u5341\u672c\u4e66\u817e\u4f4d\u7f6e\uff0c\u4f60\u8fd8\u5f97\u628a\u6392\u597d\u7684\u4e09\u5341\u672c\u4e66\u518d\u653e\u56de\u53bb\uff08\u5373\u8bb0\u5f55\u4e0b\u6392\u5e8f\u7ed3\u679c\uff0c\u540c\u6837\u4e5f\u662f\u4e00\u6b21 block transfer\uff09\u3002</p> <p>\u7efc\u4e0a\u6240\u8ff0\uff0c\u5916\u90e8\u6392\u5e8f\u4e3b\u8981\u89e3\u51b3\u7684\u5c31\u662f\uff0c\u6309\u7167\u600e\u6837\u7684\u7b56\u7565\u6765\u5bf9\u8fd9\u4e9b\u6570\u636e\u8fdb\u884c\u6392\u5e8f\u3002</p> <p>\u5bfc\u8bfb</p> <p>\u7531\u4e8e ADS \u4ecb\u7ecd\u7684\u5916\u6392\u5e8f\u548c\u540c\u65f6\u671f\u6570\u636e\u5e93\u7cfb\u7edf\u8fd9\u95e8\u8bfe\u4ecb\u7ecd\u7684\u5916\u6392\u5e8f\u6709\u540c\u6709\u5f02\uff0c\u6240\u4ee5\u6211\u6253\u7b97\u5148\u5728\u5927\u6982\u8bb2\u5916\u6392\u5e8f\u7684\u6838\u5fc3\u601d\u8def\uff0c\u518d\u5c55\u5f00 ADS \u8bfe\u7a0b\u4e2d\u7684\u5177\u4f53\u8fc7\u7a0b\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec15/#\u6982\u8ff0","title":"\u6982\u8ff0","text":"<p>\u5916\u6392\u5e8f\u7684\u57fa\u672c\u601d\u8def\u5c31\u662f\u5c06\u6570\u636e\u5206\u4e3a\u82e5\u5e72\u4e2a\u5c0f\u5757\uff0c\u7136\u540e\u5bf9\u6bcf\u4e2a\u5c0f\u5757\u8fdb\u884c\u6392\u5e8f\uff0c\u6700\u540e\u518d\u5c06\u8fd9\u4e9b\u5c0f\u5757\u5408\u5e76\u8d77\u6765\u3002\u800c\u6211\u4eec\u5e38\u8bf4\u7684\u5f52\u5e76\u6392\u5e8f\uff0c\u6307\u7684\u662f\u9012\u5f52\u5730\u5c06\u4e24\u5757\u5408\u6210\u4e00\u5757\uff0c\u800c\u6240\u8c13\u7684 \\(k\\) \u8def\uff08\\(k\\)-way\uff09\u5f52\u5e76\uff0c\u5c31\u662f\u5c06 \\(k\\) \u5757\u5408\u6210\u4e00\u5757\u3002</p> <p>\u90a3\u4e48\u5982\u4f55\u5f52\u5e76\u5462\uff1f\u6211\u5c06\u4ece\u4e24\u4e2a\u7ef4\u5ea6\u6765\u7b80\u5355\u9610\u8ff0\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec15/#\u903b\u8f91\u7ef4\u5ea6","title":"\u903b\u8f91\u7ef4\u5ea6","text":"<p>\u5916\u90e8\u6392\u5e8f\u6240\u4f7f\u7528\u7684\u5f52\u5e76\u6392\u5e8f\u4ece\u903b\u8f91\u4e0a\u6765\u8bb2\u548c\u666e\u901a\u7684\u5f52\u5e76\u6392\u5e8f\u4e00\u81f4\uff0c\u603b\u662f\u5c06 \\(k\\) \u4e2a\u6709\u5e8f\u5e8f\u5217\u5408\u5e76\u4e3a 1 \u4e2a\u6709\u5e8f\u5e8f\u5217\u3002</p> <p>\u800c\u8fd9\u91cc\u7684\u201c\u6709\u5e8f\u5e8f\u5217\u201d\uff0c\u5728\u5916\u6392\u5e8f\u4e2d\u88ab\u79f0\u4e3a\u201crun\u201d\uff0c\u5373\u6bcf\u6b21\u5f52\u5e76\u6211\u4eec\u53e6 \\(k\\) \u4e2a run \u53d8\u6210\u4e00\u4e2a run\u3002\u6b63\u7740\u8bf4\u5c31\u662f\uff1a</p> <p>run</p> <p>\u4e00\u4e2a run \u6307\u7684\u662f\u4e00\u6bb5\u8fc7\u7a0b\u4e2d\u7684\u6570\u636e\uff0c\u5728\u672c\u6587\u4e2d\u7279\u6307\u5f85\u5f52\u5e76\u7684\u6709\u5e8f\u7684\u5e8f\u5217\uff0c\u5728 \\(k\\)-way merge \u4e2d\uff0c\u6211\u4eec\u603b\u662f\u5c06 \\(k\\) \u4e2a run \u5408\u5e76\u4e3a 1 \u4e2a run\u3002</p> <p>\u8bf4\u660e</p> <p>\u8fd9\u91cc\u7684 run \u7684\u5b9a\u4e49\u662f\u6211\u81ea\u5df1\u8111\u8865\u51fa\u6765\u7684\uff0c\u5e76\u4e0d\u786e\u5b9a\u662f\u5426\u4e25\u683c\uff0c\u4f46\u662f\u53ef\u4ee5\u4fdd\u8bc1\u7684\u662f\uff1a \u4e00\u4e2a run \u5728\u53c2\u4e0e merge \u4e4b\u524d\u80af\u5b9a\u5df2\u7ecf\u6709\u5e8f\u4e86\uff0c\u53ef\u4ee5\u7406\u89e3\u4e3a \"have already run\"\uff0c\u800c\u4e3a\u4e86\u4e0d\u6405\u7cca\u8bfb\u8005\u7684\u8111\u5b50\uff0c\u6211\u8fd9\u91cc\u5c31\u4ee5\u8fd9\u4e2a\u5b9a\u4e49\u4e3a\u51c6\u3002</p> <p>\u4ece\u6267\u884c\u7684\u987a\u5e8f\u6765\u8bf4\uff0c\u5185\u6392\u5e8f\u4e2d\u7684\u5f52\u5e76\u6392\u5e8f\u662f\u4e00\u4e2a\u81ea\u4e0a\u800c\u4e0b\u4e0d\u65ad \\(\\frac{1}{k}\\) \u5730\u5212\u5206\uff0c\u518d\u81ea\u4e0b\u800c\u4e0a\u4e0d\u65ad\u5f52\u5e76\u7684\u8fc7\u7a0b\u3002\u76f8\u53cd\uff0c\u5916\u6392\u5e8f\u7531\u4e8e\u5176\u7279\u6027\u9650\u5236\uff0c\u5176\u201c\u5f52\u5e76\u6bb5\u201d\u5e76\u4e0d\u662f\u81ea\u4e0a\u800c\u4e0b \\(\\frac{1}{k}\\) \u5212\u5206\u51fa\u6765\u7684\uff0c\u800c\u662f\u6839\u636e\u786c\u4ef6\u5904\u7406\u80fd\u529b\uff0c\u76f4\u63a5\u5212\u5206\u597d\u6700\u5c0f\u7684\u5f52\u5e76\u6bb5\uff0c\u7136\u540e\u76f4\u63a5\u81ea\u4e0b\u800c\u4e0a\u5f52\u5e76\u3002</p> <p>\u800c\u8fd9\u6837\u4e00\u4e2a\u5c06 \\(k \\cdot c\\) \u4e2a run merge \u6210 \\(c\\) \u4e2a run \u7684\u8fc7\u7a0b\uff0c\u6211\u4eec\u79f0\u4e4b\u4e3a\u4e00\u4e2a <code>pass</code>\u3002\uff08\u5728\u5f52\u5e76\u6811\u4e0a\u4f53\u73b0\u4e3a\u4e00\u5c42\u3002\uff09</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec15/#\u7269\u7406\u7ef4\u5ea6","title":"\u7269\u7406\u7ef4\u5ea6","text":"<p>\u5173\u4e8e\u7269\u7406\u7ef4\u5ea6\uff0c\u6d89\u53ca\u5230\u4e00\u4e9b\u786c\u4ef6\u77e5\u8bc6\uff0c\u5728 ADS \u4e2d\u4e3a\u4e86\u65b9\u4fbf\u8bf4\u660e\u4f1a\u5c06\u5176\u7b80\u5316\uff0c\u6709\u5173 block \u7684\u6982\u5ff5\u5c06\u88ab\u62bd\u8c61\u5316\u4e3a\u201c\u6570\u636e\u5355\u4f4d\u201d\u3002</p> <p>\u6211\u4eec\u77e5\u9053\uff0c\u5185\u5b58\u7684\u5927\u5c0f\u662f\u6709\u9650\u7684\uff0c\u5212\u5206\u7ed9\u5f52\u5e76\u6570\u636e\u7684\u5185\u5b58\u4e5f\u5e94\u5f53\u662f\u6709\u9650\u7684\uff0c\u6211\u4eec\u7528 \\(M\\) \u6765\u8bb0\u5b83\uff0c\u5373\u5185\u5b58\u4e2d\u4e00\u6b21\u53ea\u80fd\u5904\u7406 \\(M\\) \u4e2a\u5355\u4f4d\u7684\u6570\u636e\u3002</p> <p>\u66f4\u7ec6\u8282\u7684\uff0c\u6211\u4eec\u5e94\u5f53\u66f4\u5177\u7269\u7406\u5927\u5c0f\u6765\u8ba1\u7b97 \\(M\\)\uff0c\u4f8b\u5982\u4e00\u6761\u6570\u636e\u7684\u5927\u5c0f\u662f \\(l \\text{Bytes}\\)\uff0c\u800c\u5185\u5b58\u7684\u5927\u5c0f\u662f \\(m \\text{Bytes}\\)\uff0c\u90a3\u4e48\u4e00\u4e2a\u5185\u5b58\u80fd\u591f\u5bb9\u7eb3\u7684\u6570\u636e\u6570\u91cf\u5e94\u5f53\u4e3a \\(\\lfloor \\frac{m}{l} \\rfloor\\)\u3002</p> <p>\u4f46\u662f\u65e2\u7136\u8981\u5f52\u5e76\uff0c\u6211\u4eec\u5c31\u9700\u8981\u5c06 \\(k\\) \u8def\u7684\u6570\u636e\u8bfb\u5165\u5230\u5185\u5b58\u4e2d\uff0c\u6700\u7406\u60f3\u7684\u60c5\u51b5\u4e0b\u6211\u4eec\u80af\u5b9a\u5e0c\u671b\u8fd9 \\(k\\) \u8def\u90fd\u80fd\u8bfb\u5165\u5230\u5185\u5b58\u4e2d\uff0c\u4f46\u662f\u663e\u7136\u8fd9\u662f\u4e0d\u5207\u5b9e\u9645\u7684\uff0c\u6211\u4eec\u6700\u591a\u516c\u5e73\u5730\u8bfb\u5165\u6bcf\u4e00\u8def\u7684\u524d \\(\\lfloor \\frac{M}{k} \\rfloor\\) \u4e2a\u6570\u636e\u2014\u2014\u4f46\u8fd9\u5df2\u7ecf\u8db3\u591f\u2014\u2014\u5bf9\u4e8e \\(k\\) \u4e2a\u6709\u5e8f\u5e8f\u5217\u7684\u5408\u5e76\u64cd\u4f5c\uff0c\u5176\u5408\u5e76\u8fc7\u7a0b\u4e2d\u4e5f\u6070\u597d\u53ea\u4e0e\u6700\u9760\u524d\u7684\u3001\u672a\u6392\u5e8f\u7684\u4e00\u90e8\u5206\u6570\u636e\u6709\u5173\u3002</p> <p>\u8bf4\u660e</p> <p>\u4e4b\u540e\u6240\u63d0\u5230\u7684\uff0c\u6709\u5173\u4e8e\u6392\u5e8f\u6570\u636e\u7684\u201c\u5185\u5b58\u201d\uff0c\u6307\u7684\u90fd\u662f\u5212\u5206\u7ed9\u7b97\u6cd5\uff0c\u7528\u6765\u5b58\u653e\u5f52\u5e76\u6570\u636e\u7684\u5185\u5b58\uff01</p> <p>example</p> <p>\u4e3e\u4f8b\u6765\u8bf4\uff0c\u5047\u8bbe\u73b0\u5728\u6709\u4e24\u4e2a run\uff0c\u5206\u522b\u4e3a\uff1a</p> <ol> <li><code>1</code> <code>3</code> <code>5</code> <code>7</code> <code>9</code></li> <li><code>0</code> <code>2</code> <code>4</code> <code>6</code> <code>8</code></li> </ol> <p>\u4f46\u662f\u5185\u5b58\u53ea\u80fd\u653e 4 \u4e2a\u5355\u4f4d\u6570\u636e\uff0c\u6240\u4ee5\u5bf9\u4e8e\u6bcf\u4e2a run \u603b\u662f\u53ea\u6709\u524d 2 \u4e2a\u6570\u636e\u662f\u53ef\u89c1\u7684\u3002\u4f46\u662f\u8fd9\u5e76\u4e0d\u5f71\u54cd\u6211\u4eec\u53ef\u4ee5\u786e\u5b9a\u8fd9\u4e24\u4e2a run \u5408\u5e76\u7684\u7ed3\u679c\u4e2d\uff0c\u524d\u4e00\u90e8\u5206\u662f <code>0</code> <code>1</code> <code>2</code>\uff0c\u800c\u81f3\u4e8e <code>2</code> \u540e\u9762\u6392\u4ec0\u4e48\uff0c\u5219\u8981\u4ece <code>run2</code> \u4e2d\u53d6\u51fa\u4e4b\u540e\u7684\u6570\u636e\uff0c\u518d\u4e0e <code>run1</code> \u4f59\u4e0b\u7684 <code>_</code> <code>3</code> \u5408\u5e76\u3002</p> <p>\u6613\u9519\u70b9</p> <p>\u6ce8\u610f\uff0c\u5f53\u5176\u4e2d\u4e00\u4e2a\u6bb5\u7684 buffer \u7a7a\u4e86\u4ee5\u540e\uff0c\u6211\u4eec\u4e0d\u80fd\u76f4\u63a5\u628a\u5176\u4ed6\u6bb5\u7684 buffer \u76f4\u63a5\u6392\u5e8f\u8fdb\u53bb\uff0c\u800c\u5fc5\u987b\u5148\u586b\u5145\u8fd9\u4e2a\u7a7a buffer \u7684\u5185\u5bb9\uff0c\u518d\u7ee7\u7eed\u6392\u5e8f\u3002</p> <p>\u60f3\u8c61\u8fd9\u6837\u4e00\u4e2a\u60c5\u51b5\uff0c\u7a7a buffer \u5c06\u8981\u8f7d\u5165\u7684\u4e0b\u4e00\u6bb5\u6570\u636e\u662f <code>3</code> <code>4</code> <code>5</code>\uff0c\u800c\u53e6\u5916\u4e00\u4e2a buffer \u5269\u4e0b\u7684\u6570\u636e\u662f <code>7</code>\uff0c\u90a3\u4e48\u663e\u7136\uff0c<code>3</code> <code>4</code> <code>5</code> \u5e94\u8be5\u5148\u4e8e <code>7</code> \u88ab\u6392\u5e8f\u3002</p> <p>\u800c\u8fd9\u4e2a\u8fc7\u7a0b\u4e5f\u6b63\u662f\u5916\u6392\u5e8f\u80fd\u591f\u8fdb\u884c\u7684\u4e00\u4e2a\u91cd\u8981\u57fa\u7840\u3002</p> <p>\u5176\u4e2d\u6bd4\u8f83\u7279\u522b\u7684\u6b65\u9aa4\u5c31\u662f\uff0c\u6700\u5f00\u59cb\u7684\u6392\u5e8f\uff0c\u5373\u7b2c\u4e00\u4e2a pass\u3002\u5148\u524d\u6211\u4eec\u5728#\u903b\u8f91\u7ef4\u5ea6\u91cc\u63d0\u5230\u4e86\uff0c\u5916\u6392\u5e8f\u7684\u7b2c\u4e00\u4e2a pass \u4f1a\u76f4\u63a5\u5212\u5206\u597d\u6700\u5c0f\u7684\u5f52\u5e76\u6bb5\uff0c\u800c\u8fd9\u4e2a\u201c\u6700\u5c0f\u5f52\u5e76\u6bb5\u201d\u7684\u5927\u5c0f\u5c31\u662f \\(M\\)\u3002\u7528\u8bed\u8a00\u63cf\u8ff0\uff0c\u5c31\u662f\u6700\u65e9\u7684 run \u7684\u5927\u5c0f\u5c31\u662f\u5e73\u5747\u6bcf\u4e00\u8def\u80fd\u591f\u5728\u5185\u5b58\u4e2d\u5904\u7406\u7684\u6700\u5927\u6570\u636e\u5355\u4f4d\u91cf\u3002</p> <p>\u7136\u800c\u95ee\u9898\u51fa\u73b0\u4e86\uff0c\u6839\u636e\u6211\u4e4b\u524d\u7ed9\u51fa\u7684\u5b9a\u4e49\uff0crun \u5e94\u5f53\u662f\u6709\u5e8f\u7684\uff0c\u4f46\u662f\u4ece\u539f\u59cb\u6570\u636e\u91cc\u8bfb\u51fa\u6765\u7684\u201c\u6700\u5c0f\u5f52\u5e76\u6bb5\u201d\u662f\u65e0\u5e8f\u7684\u3002\u4f46\u662f\u5bf9\u4e8e\u6700\u521d\u7684 run\uff0c\u5b83\u5fc5\u7136\u80fd\u591f\u6574\u6bb5\u653e\u5230\u5185\u5b58\u91cc\uff08\u66f4\u8fdb\u4e00\u6b65\u7684\uff0c\u4e5f\u53ea\u6709\u6700\u521d\u7684 run \u80fd\u591f\u5b8c\u6574\u5730\u653e\u5230\u5185\u5b58\u91cc\uff09\uff0c\u56e0\u6b64\u76f4\u63a5\u5bf9\u5176\u8fdb\u884c\u5185\u6392\u5e8f\u5373\u53ef\u3002</p> <p>\u903b\u8f91\u8054\u7cfb</p> <ul> <li>\u56e0\u4e3a\u5185\u6392\u5e8f\u5f88\u5feb\uff0c\u6240\u4ee5\u8981\u5c3d\u53ef\u80fd\u5229\u7528\u5185\u6392\u5e8f\uff1b</li> <li>\u6240\u4ee5\u4e00\u5f00\u59cb\u5c31\u8981\u5c06\u80fd\u5185\u6392\u5e8f\u505a\u7684\u4e8b\u60c5\u90fd\u7528\u5185\u6392\u5e8f\u89e3\u51b3\uff1b</li> <li>\u6240\u4ee5\u6700\u521d\u7684 run \u7684\u5927\u5c0f\u662f \\(M\\)\u3002</li> </ul> <p>\u4e2d\u7ee7</p> <p>\u4ee5\u4e0a\u5185\u5bb9\u662f\u5bf9\u5916\u6392\u5e8f\u6838\u5fc3\u601d\u60f3\u7684\u4e00\u4e2a\u7b80\u5355\u4ecb\u7ecd\uff0c\u63a5\u4e0b\u6765\u6211\u4eec\u5c06\u4ee5 ADS \u6240\u4ecb\u7ecd\u7684\u5916\u6392\u5e8f\u8303\u5f0f\uff0c\u6765\u4ecb\u7ecd\u4e00\u4e0b\u5177\u4f53\u7684\u8fc7\u7a0b\u548c\u4e00\u4e9b\u6539\u8fdb\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec15/#\u5177\u4f53\u5206\u6790","title":"\u5177\u4f53\u5206\u6790","text":"<p>ADS \u4e2d\u76f8\u6bd4\u4e0a\u9762\u4ecb\u7ecd\u7684\u90e8\u5206\uff0c\u53c8\u5f15\u5165\u4e86\u4e00\u4e2a\u53eb tape \u7684\u6982\u5ff5\uff0ctape \u7684\u4e2d\u6587\u662f\u78c1\u5e26\uff0c\u800c\u5728\u8fd9\u4e2a\u6846\u67b6\u4e2d\uff0c\u6211\u66f4\u503e\u5411\u4e8e\u628a\u5b83\u5f53\u4f5c\u4e00\u4e2a\u62bd\u8c61\u7684\u6982\u5ff5\u3002</p> <p>\u76f8\u5bf9\u5e94\u7684\uff0c\u5176\u5b9e\u9645\u8fc7\u7a0b\u4e0e\u4e0a\u9762\u63cf\u8ff0\u7684\u65b9\u6cd5\u53ef\u80fd\u6709\u4e00\u4e9b\u611f\u53d7\u4e0a\u7684\u5dee\u522b\uff0c\u5982\u679c\u53ea\u662f\u4e86\u89e3\u601d\u60f3\u7684\u8bdd\u4e0a\u534a\u90e8\u5206\u5df2\u7ecf\u8db3\u591f\uff08\u5f53\u7136\u540e\u9762\u8fd8\u6709\u4e00\u4e9b\u57fa\u4e8e\u5982\u4e0b\u6a21\u578b\u7684\u4f18\u5316\u8ba8\u8bba\uff09\uff0c\u4f46\u662f\u6bd5\u7adf\u8fd8\u662f\u9762\u5411\u8003\u8bd5\uff0c\u6240\u4ee5\u8fd8\u662f\u9700\u8981\u4ee5 ADS \u8bfe\u4ef6\u7684\u65b9\u6cd5\u518d\u4ecb\u7ecd\u4e00\u6b21\u3002</p> <p>\u8bf4\u660e</p> <p>\u6211\u4e4b\u540e\u4f1a\u4ee5 run \u4e3a\u5355\u4f4d\uff0c\u6765\u63cf\u8ff0\u5408\u5e76\u8fc7\u7a0b\u3002\u4f46\u662f\u5b9e\u9645\u53d1\u751f\u5728\u8ba1\u7b97\u673a\u91cc\u7684\u6b65\u9aa4\u66f4\u52a0\u590d\u6742\uff1a</p> <p>\u9700\u8981\u5148\u5c06\u6bcf\u4e00\u6761 tape \u7684\u4e00\u90e8\u5206\u6570\u636e\u8bfb\u5165\u5185\u5b58\u7684 buffer \u4e2d\uff0c\u7136\u540e\u5229\u7528\u8fd9\u4e9b buffer \u6765\u8fdb\u884c\u6392\u5e8f\uff1b\u5f53\u67d0\u4e2a buffer \u7a7a\u4e86\u4ee5\u540e\u8981\u7acb\u523b\u5c06\u5bf9\u5e94 tape \u7684\u4e0b\u4e00\u90e8\u5206\u6570\u636e\u8bfb\u5165\uff0c\u76f4\u5230\u6ca1\u6709\u6570\u636e\u53ef\u4ee5\u586b\u5145\u4e3a\u6b62\u3002</p> <p>\u4e5f\u6b63\u662f#\u7269\u7406\u7ef4\u5ea6\u6240\u8bf4\u7684\u90a3\u4e9b\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec15/#\u6734\u7d20\u8fc7\u7a0b\u5206\u6790","title":"\u6734\u7d20\u8fc7\u7a0b\u5206\u6790","text":"<p>\u6211\u4eec\u4ee5 2-way merge \u4e3a\u4f8b\uff0c\u7ed3\u5408 ADS \u8bfe\u4ef6\u4e2d\u7684\u914d\u56fe\u6765\u8bf4\u660e\u3002</p> \u51c6\u5907 <p> </p> <p>\u56fe\u4e2d \\(T_1\\) \u662f\u4e00\u6761 tape \u7684\u7f16\u53f7\uff0c\u6211\u4eec\u53ef\u4ee5\u7406\u89e3\u4e3a\u4e00\u4e2a\u5e8f\u5217\u7684\u7269\u7406\u5730\u5740\uff0c\u6216\u66f4\u901a\u4fd7\u7684\u6765\u8bf4\uff0c\u53ef\u4ee5\u5f53\u4f5c\u4e00\u4e2a\u6570\u7ec4\uff0c\u53ea\u4e0d\u8fc7\u5b83\u7684\u5b9e\u9645\u6570\u636e\u662f\u5728\u786c\u76d8\u4e2d\u3002\u6362\u53e5\u8bdd\u6765\u8bf4\uff0c\u8fd9\u91cc\u7684 tape \u8868\u793a\u7684\u90fd\u662f\u786c\u76d8\u4e2d\u7684\u6570\u636e\u3002</p> <p>\u8fd9\u6761 tape \u4e2d\u6709 13 \u4e2a\u5143\u7d20\uff0c\u6211\u4eec\u8bb0\u5176\u4e3a \\(N = 13\\)\u3002\u800c\u8fd9\u6761\u539f\u59cb\u7684 tape \u88ab\u5212\u5206\u4e3a\u4e86 5 \u6bb5\uff0c\u6bcf\u4e00\u6bb5\u90fd\u6709\u4e0d\u8d85\u8fc7 3 \u4e2a\u5143\u7d20\uff0c\u6b64\u65f6 \\(M = 3\\)\u3002\u5373\u6709 \\(\\lceil \\frac{N}{M} \\rceil = 5\\)\u3002</p> Pass 1 <p>\u73b0\u5728\u6211\u4eec\u8981\u5f00\u59cb merge \u4e86\u3002\u5bf9\u4e8e\u8fd9\u6bb5\u6570\u636e\u6765\u8bf4\uff0c\u8fd9\u662f\u610f\u4e49\u91cd\u5927\u7684\u201c\u4eba\u751f\u7b2c\u4e00\u6b21\u201d\uff0c\u76f8\u6bd4\u4e8e\u5176\u4ed6\u5f52\u5e76\u90fd\u662f\u4ece 2 \u4e2a tape \u5f00\u59cb\u7684 pass\uff0c\u8fd9\u4e00\u6b21\u663e\u5f97\u6709\u4e9b\u7279\u6b8a\u3002</p> <p>\u5728\u7b2c\u4e00\u8f6e\u4e2d\uff0c\u9762\u5bf9\u5168\u90e8\u90fd\u662f\u65e0\u5e8f\u7684\u6570\u636e\uff0c\u6211\u4eec\u5c06\u8fd9 \\(\\lceil \\frac{N}{M} \\rceil = 5\\) \u4e2a\u6bb5\u5747\u5206\u5230\u4e24\u6761 tape \u4e0a\uff082-way\uff09\uff0c\u8fd9\u91cc\u7ecf\u5386\u4e24\u4e2a\u6b65\u9aa4\uff1a</p> <ol> <li>\u4f9d\u6b21\u8bfb\u53d6 \\(T_1\\) \u4e2d\u6bcf\u4e00\u6bb5\u6570\u636e\uff08\u521a\u597d\u5360\u6ee1\u5185\u5b58\uff09\uff0c\u5e76\u5bf9\u5b83\u4eec\u8fdb\u884c\u5185\u6392\u5e8f\uff1b</li> <li>\u5c06\u6392\u5e8f\u5b8c\u7684\u6bb5\uff0c\u8ffd\u52a0\u5199\u5230 \\(T_2\\) \u6216 \\(T_3\\) \u4e2d\uff08\u5177\u4f53\u6bcf\u4e00\u4e2a tape \u5199\u51e0\u6761\uff0c\u4f1a\u6709\u4e13\u95e8\u7b56\u7565\u505a\u8c03\u6574\uff0c\u76ee\u524d\u5148\u5e73\u5206\u7740\u653e\uff09\uff1b</li> </ol> <p>\u4e8e\u662f\uff0c\\(T_1\\) \u4e2d\u7684\u6570\u636e\u4fbf\u88ab\u8f6c\u79fb\u5230\u4e86 \\(T_2\\) \u548c \\(T_3\\)\u3002\u4e3a\u4e86\u91cd\u590d\u5229\u7528 tape\uff0c\u6b64\u65f6\u7684 \\(T_1\\) \u88ab\u770b\u4f5c\u53ef\u4ee5\u7528\u7684\u7a7a\u78c1\u76d8\u4e86\u3002</p> <p> </p> <p>\u4e8e\u662f\uff0c\u5b8c\u6210\u4e86\u7b2c\u4e00\u4e2a pass\u3002</p> Pass 2 <p>\u4e4b\u540e\u7684 pass \u5219\u57fa\u672c\u9075\u5faa\u540c\u6837\u7684\u89c4\u5219\uff0c\u4e0d\u65ad\u53d6\u6bcf\u4e00\u8def\u7684\u7b2c\u4e00\u4e2a run \u5e76 merge\uff0c\u5e76\u4e14\u5c06\u7ed3\u679c\u5199\u5230\u4e24\u4e2a\uff08k \u4e2a\uff09\u95f2\u7f6e\u7684 tape \u4e0a\uff08\u548c\u524d\u9762\u8bf4\u8fc7\u7684\u4e00\u6837\uff0c\u8fd9\u91cc\u6682\u4e14\u5c06\u5206\u914d\u7b56\u7565\u5b9a\u4e3a\u5e73\u5206\u5230\u6bcf\u4e00\u4e2a tape \u4e0a\uff09\u3002</p> <p>\u4f8b\u5982\uff0c\u6211\u4eec\u8981\u53d6 \\(T_2\\) \u548c \\(T_3\\) \u7684\u7b2c\u4e00\u6bb5\uff0c\u6267\u884c\u5f52\u5e76\u64cd\u4f5c\uff0c\u5f97\u5230\u4e00\u4e2a\u65b0\u7684\uff0c\u6709 6 \u4e2a\u6570\u636e\u7684 run\uff0c\u5e76\u5199\u5230\u95f2\u7f6e\u7684 \\(T_1\\) \u4e0a\uff1b\u63a5\u4e0b\u6765\u53d6 \\(T_2\\) \u548c \\(T_3\\) \u7684\u7b2c\u4e8c\u6bb5\uff0c\u5f52\u5e76\u5f97\u5230\u65b0\u7684 run\uff0c\u6b64\u65f6\u6211\u4eec\u53d1\u73b0\uff0c\\(T_1\\)\u3001\\(T_2\\)\u3001\\(T_3\\) \u90fd\u4e0d\u662f\u95f2\u7f6e\u7684\uff0c\u6240\u4ee5\u6211\u4eec\u9700\u8981\u4e00\u4e2a\u65b0\u7684 tape\uff0c\u5199\u5230 \\(T_4\\) \u4e0a\u3002</p> <p> </p> <p>\u4e8e\u662f\uff0c\u5b8c\u6210\u4e86\u7b2c\u4e8c\u4e2a pass\u3002</p> Pass 3 <p>pass 3 \u548c pass 2 \u7684\u8fc7\u7a0b\u57fa\u672c\u4e00\u81f4\u3002\u73b0\u5728\u7684 tape \u72b6\u6001\u662f \\(\\{T_2, T_3\\}\\) \u95f2\u7f6e\uff0c\u6211\u4eec\u53d6 \\(T_1\\) \u548c \\(T_4\\) \u7684\u7b2c\u4e00\u6bb5\uff0c\u5f97\u5230\u4e00\u4e2a\u65b0\u7684 run\uff0c\u5305\u542b 12 \u4e2a\u5143\u7d20\uff1b\u53d6 \\(T_1\\) \u548c \\(T_4\\) \u7684\u7b2c\u4e8c\u6bb5\uff0c\u5f97\u5230\u4e00\u4e2a\u65b0\u7684 run\uff0c\u5305\u542b 1 \u4e2a\u5143\u7d20\u3002\u8fd9\u4e24\u6bb5\u88ab\u5206\u914d\u5230\u4e24\u6761\u7a7a\u95f2 tape \u4e0a\uff0c\u5373 \\(T_2\\) \u548c \\(T_3\\)\u3002</p> <p> </p> <p>\u4e8e\u662f\uff0c\u5b8c\u6210\u4e86\u7b2c\u4e09\u4e2a pass\u3002</p> Pass 4 <p>\u540c\u6837\uff0cpass 4 \u548c\u524d\u9762\u4e24\u4e2a pass \u7684\u8fc7\u7a0b\u4e5f\u662f\u4e00\u81f4\u6027\u7684\uff0c\u4e0d\u505a\u8fc7\u591a\u89e3\u91ca\uff0c\u5bf9\u4e8e\u89c4\u6a21\u66f4\u5927\u7684\u6570\u636e\u4e5f\u662f\u4e00\u6837\uff0c\u9664\u4e86\u7b2c\u4e00\u4e2a pass \u6bd4\u8f83\u7279\u6b8a\uff0c\u5176\u5b83 pass \u90fd\u662f\u4e00\u6837\u7684\u3002\u6700\u7ec8\u5f97\u5230\u53ea\u5269\u4e0b\u4e00\u4e2a tape \u4e2d\u5305\u542b\u552f\u4e00\u7684 run \u65f6\uff0c\u6392\u5e8f\u5c31\u7ed3\u675f\u4e86\u3002</p> <p> </p> <p>\u81f3\u6b64\uff0c\u6392\u5e8f\u7ed3\u675f\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec15/#\u4f18\u5316\u7a7a\u95f4","title":"\u4f18\u5316\u7a7a\u95f4","text":"<p>\u53ef\u4ee5\u4f18\u5316\u7684\u90e8\u5206\u4e3b\u8981\u6709\u8fd9\u4e48\u51e0\u4e2a\uff1a</p> <ul> <li>\u4e00\u4e2a pass \u610f\u5473\u7740\u82e5\u5e72\u6b21 seek\uff0c\u6240\u4ee5\u51cf\u5c11 pass \u53ef\u4ee5\u662f\u4e00\u4e2a\u65b9\u5411\uff1b<ul> <li>#pass-\u6570\u91cf\u5206\u6790\u4e0e\u4f18\u5316</li> </ul> </li> <li>merge \u7684\u8fc7\u7a0b\u4e2d\u4f1a\u591a\u6b21\u8bfb\u53d6 tape \u4e2d\u7684\u6570\u636e\uff0c\u800c\u5bf9\u4e8e\u8ba1\u7b97\u673a\u6765\u8bf4\u5355\u6b21\u5927\u91cf\u8bfb\u53d6\u6bd4\u591a\u6b21\u5c0f\u91cf\u8bfb\u53d6\u66f4\u9ad8\u6548\uff0c\u5982\u4f55\u4f18\u5316\u6570\u636e\u8bfb\u53d6\u4e5f\u662f\u4e00\u4e2a\u65b9\u5411\uff1b<ul> <li>#tape-\u6570\u91cf\u5206\u6790\u4e0e\u4f18\u5316</li> </ul> </li> <li>\u5982\u4f55\u66f4\u9ad8\u6548\u7684\u5728 \\(k\\)-way merge \u8fc7\u7a0b\u4e2d\uff0c\u5f52\u5e76 M \u4e2a\u5206\u522b\u6765\u81ea k \u4e2a\u5e8f\u5217\u7684\u6570\u636e\uff0c\u5373\u5185\u6392\u5e8f\u7684\u7b56\u7565\uff0c\u4e5f\u4e0a\u4f18\u5316\u7684\u4e00\u4e2a\u65b9\u5411\uff1b<ul> <li>#k-\u8def\u5185\u6392\u5e8f\u4f18\u5316</li> </ul> </li> <li>\u8bfb\u5165\u3001\u5185\u6392\u5e8f\u3001\u8f93\u51fa\uff0c\u8fd9\u4e09\u4e2a\u4e8b\u52a1\u76ee\u524d\u662f\u505c\u673a\u4e32\u884c\u7684\uff0c\u8003\u8651\u5c06\u5176\u5e76\u884c\u5316\u4e5f\u662f\u4e00\u4e2a\u65b9\u5411\uff1b<ul> <li> TODO</li> </ul> </li> </ul>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec15/#pass-\u6570\u91cf\u5206\u6790\u4e0e\u4f18\u5316","title":"pass \u6570\u91cf\u5206\u6790\u4e0e\u4f18\u5316","text":"<p>\u4f8b\u5b50\u4e2d\u4e00\u5171\u7ecf\u8fc7\u4e86 4 \u6b21 pass\u3002\u5982\u679c\u6211\u4eec\u8bb0 \\(max(\\#run)\\) \u4e3a \\(\\#run\\) \u6700\u591a\u7684 tape \u7684 \\(\\#run\\)\uff0c\u5219\u6bcf\u4e00\u6b21 pass \u4f1a\u4ee4 \\(max(\\#run)\\) \u7f29\u5c0f\u4e00\u534a\uff0c\u76f4\u5230 \\(max(\\#run)\\) \u53d8\u4e3a 1\uff0c\u4e14\u53ea\u6709\u5b83\u4e00\u6761 tape \u8fd8\u6709\u6570\u636e\uff0c\u6807\u5fd7\u7740\u6392\u5e8f\u7ed3\u675f\u3002</p> <p>\u5982\u679c\u4e13\u6ce8\u4e8e \\(\\#run\\) \u7684\u53d8\u5316\uff0c\u90a3\u4e48\u4e0a\u9762\u7684\u6a21\u62df\u6b65\u9aa4\u5927\u81f4\u662f\u8fd9\u4e48\u4e00\u4e2a\u8fc7\u7a0b\uff1a</p> <p>Pass 1</p> <p>\u539f\u5148 \\(T_1\\) \u4e0a \\(\\#run = 5\\)\uff0c\u73b0\u5c06\u5b83\u5206\u914d\u5230\u4e24\u6761 tape \u4e0a\uff0c\u4e8e\u662f\u6709\uff1a</p> <ul> <li>\\(T_2\\) \u4e0a \\(\\#run = 3\\)\uff1b</li> <li>\\(T_3\\) \u4e0a \\(\\#run = 2\\)\uff1b</li> </ul> <p>Pass 2</p> <p>\u4f9d\u6b21\u53d6 \\(T_2\\) \u548c \\(T_3\\) \u7684\u7b2c\u4e00\u6bb5\uff0c\u5f52\u5e76\u5f97\u5230\u65b0\u7684 run\uff0c\u5747\u5206\u5230\u53e6\u5916\u4e24\u6761 tape \u4e0a\uff08\u672a\u4f18\u5316\u7684\u505a\u6cd5\uff0c\u4f18\u5316\u505a\u6cd5\u53c2\u8003#tape-\u4f18\u5316\uff09\uff0c\u4e8e\u662f\u6709\uff1a</p> <ul> <li>\\(T_2\\) \u4e0a \\(\\#run = 3-1 = 2\\)\uff1b</li> <li>\\(T_3\\) \u4e0a \\(\\#run = 2-1 = 1\\)\uff1b</li> <li>\\(T_1\\) \u4e0a \\(\\#run = 0+1 = 1\\)\uff1b</li> <li>\\(T_4\\) \u4e0a \\(\\#run = 0\\)\uff1b</li> </ul> <p>\u7ee7\u7eed\u53d6\uff0c\u5373\uff1a</p> <ul> <li>\\(T_2\\) \u4e0a \\(\\#run = 2-1 = 1\\)\uff1b</li> <li>\\(T_3\\) \u4e0a \\(\\#run = 1-1 = 0\\)\uff1b</li> <li>\\(T_1\\) \u4e0a \\(\\#run = 1\\)\uff1b</li> <li>\\(T_4\\) \u4e0a \\(\\#run = 0+1 = 1\\)\uff1b</li> </ul> <p>\\(T_3\\) \u4e0a\u5df2\u7ecf\u6ca1\u6709\u4e86\uff0c\u4f46\u662f \\(T_2\\) \u8fd8\u6ca1\u53d6\u5b8c\uff0c\u6240\u4ee5\u53ea\u4ece \\(T_2\\) \u62ff\uff1a</p> <ul> <li>\\(T_2\\) \u4e0a \\(\\#run = 1-1 = 0\\)\uff1b</li> <li>\\(T_3\\) \u4e0a \\(\\#run = 0\\)\uff1b</li> <li>\\(T_1\\) \u4e0a \\(\\#run = 1+1 = 2\\)\uff1b</li> <li>\\(T_4\\) \u4e0a \\(\\#run = 1\\)\uff1b</li> </ul> <p>\u6a21\u62df\u5230\u4ece\u8fd9\u91cc\u5176\u5b9e\u5df2\u7ecf\u53ef\u4ee5\u770b\u51fa\u6765\u4e86\uff0c\u5bf9\u4e8e 2-way merge \u6765\u8bf4\uff0c\u6392\u9664\u672b\u6bb5\u60c5\u51b5\uff0c\u4ece\u7b2c\u4e8c\u4e2a pass \u5f00\u59cb\uff0c\u57fa\u672c\u4e0a\u6bcf\u6b21\u90fd\u662f\u4ece 2 \u8def\u4e2d\u5404\u53d6 1 \u4e2a run\uff0c\u5e76\u5408\u5e76\u4e3a 1 \u4e2a run\u3002\u6362\u53e5\u8bdd\u6765\u8bf4\uff0c\u6bcf\u4e00\u4e2a pass \u4f1a\u8ba9 \\(total(\\#run)\\) \u7f29\u5c0f\u4e3a\u539f\u6765\u7684 \\(\\frac{1}{2}\\)\u3002</p> <p>\u90a3\u4e48\uff0c\u5bf9\u4e8e \\(k\\)-way merge \u6765\u8bf4\uff0c\u5c31\u662f\u4ece\u7b2c\u4e8c\u4e2a pass \u5f00\u59cb\uff0c\u6bcf\u6b21\u4ece \\(k\\) \u8def\u4e2d\u5404\u53d6 1 \u4e2a run\uff0c\u5e76\u5408\u5e76\u4e3a 1 \u4e2a run\uff0c\u6bcf\u4e00\u4e2a pass \u4f1a\u8ba9 \\(total(\\#run)\\) \u7f29\u5c0f\u4e3a\u539f\u6765\u7684 \\(\\frac{1}{k}\\)\u3002</p> <p>\u56e0\u6b64\uff0c\u6211\u4eec\u53ef\u4ee5\u5f52\u7eb3\u5f97\u5230\u5982\u4e0b\u8ba1\u7b97\u5f0f\uff1a</p> \\[ \\begin{aligned} \\#pass &amp;= \\underbrace{         1     }_{\\text{pass 1}}     +      \\underbrace{         \\lceil \\log_{k}{(\\#run)}\\rceil     }_{\\text{rest passes}} \\\\     &amp;= \\underbrace{         1     }_{\\text{pass 1}}     +      \\underbrace{         \\lceil \\log_{k}{             \\lceil \\frac{N}{M} \\rceil         }\\rceil     }_{\\text{rest passes}}  \\end{aligned} \\] <p>\u5176\u4e2d\uff0c\\(k\\) \u8868\u793a\u5f52\u5e76\u8def\u6570\uff0c\\(N\\) \u8868\u793a\u6570\u636e\u91cf\uff0c\\(M\\) \u8868\u793a\u5185\u5b58\u4e00\u6b21\u80fd\u5904\u7406\u7684\u6570\u636e\u91cf\u3002</p> <p>\u90a3\u4e48\uff0c\u51cf\u5c11 pass \u7684\u65b9\u6cd5\u4e5f\u5f88\u76f4\u89c2\u4e86\uff0c\u53ea\u9700\u8981\u589e\u52a0 \\(k\\) \u5373\u53ef\uff0c\u5373\u91c7\u53d6\u66f4\u591a\u8def\u7684\u5f52\u5e76\uff0c\u5c31\u80fd\u51cf\u5c11 pass\u3002</p> <p>\u7136\u800c\uff0c\u5176\u4e2d\u5fc5\u7136\u5b58\u5728\u4e00\u4e2a trade-off \u7684\u5173\u7cfb\uff0c\u867d\u7136 \\(k\\) \u589e\u52a0\u53ef\u4ee5\u51cf\u5c11 \\(\\#pass\\)\uff0c\u4f46\u662f\u5728\u63a5\u4e0b\u6765\u4e00\u8282\u4e2d\u6211\u4eec\u4f1a\u77e5\u9053\uff0c\\(k\\) \u8fc7\u5927\u4f1a\u5bfc\u81f4 tape \u9700\u6c42\u91cf\u589e\u52a0\uff0c\u6b64\u5916\uff0c\\(k\\) \u7684\u589e\u52a0\u4e5f\u4f1a\u5bfc\u81f4\u5185\u6392\u5e8f\u7684\u590d\u6742\u5ea6\u589e\u52a0\uff0c\u4e5f\u4f1a\u589e\u52a0 pass \u5185\u7684 seek \u6b21\u6570\u3002</p> <p>\u5f53\u7136\uff0c\u9664\u4e86\u66b4\u529b\u7684\u589e\u52a0 \\(k\\) \u4ee5\u5916\uff0c\u6211\u4eec\u8fd8\u53ef\u4ee5\u901a\u8fc7\u4f7f\u7528\u66ff\u6362\u9009\u62e9(Replacement Selection)\u7b97\u6cd5\uff0c\u6765\u751f\u6210\u6bd4 \\(M\\) \u5927\u7684\u521d\u59cb run\uff0c\u4ee5\u76f8\u5bf9\u51cf\u5c11 pass \u6570\u91cf\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec15/#\u66ff\u6362\u9009\u62e9\u7b97\u6cd5","title":"\u66ff\u6362\u9009\u62e9\u7b97\u6cd5","text":"<p>\u66ff\u6362\u9009\u62e9(Replacement Selection) \u5728 hw15 \u4e2d\u88ab\u5e03\u7f6e\u4e3a\u7f16\u7a0b\u9898\uff0c\u6240\u4ee5\u5176\u5b9e\u73b0\u8fc7\u7a0b\u53ef\u4ee5\u7ed3\u5408\u90a3\u9053\u9898\u76ee\u6765\u5b66\u4e60\u3002</p> Replacement Selection @ PTA <p>When the input is much too large to fit into memory, we have to do external sorting instead of internal sorting. One of the key steps in external sorting is to generate sets of sorted records (also called runs) with limited internal memory. The simplest method is to read as many records as possible into the memory, and sort them internally, then write the resulting run back to some tape. The size of each run is the same as the capacity of the internal memory.</p> <p>Replacement Selection sorting algorithm was described in 1965 by Donald Knuth. Notice that as soon as the first record is written to an output tape, the memory it used becomes available for another record. Assume that we are sorting in ascending order, if the next record is not smaller than the record we have just output, then it can be included in the run.</p> <p>For example, suppose that we have a set of input { 81, 94, 11, 96, 12, 99, 35 }, and our memory can sort 3 records only. By the simplest method we will obtain three runs: { 11, 81, 94 }, { 12, 96, 99 } and { 35 }. According to the replacement selection algorithm, we would read and sort the first 3 records { 81, 94, 11 } and output 11 as the smallest one. Then one space is available so 96 is read in and will join the first run since it is larger than 11. Now we have { 81, 94, 96 }. After 81 is out, 12 comes in but it must belong to the next run since it is smaller than 81. Hence we have { 94, 96, 12 } where 12 will stay since it belongs to the next run. When 94 is out and 99 is in, since 99 is larger than 94, it must belong to the first run. Eventually we will obtain two runs: the first one contains { 11, 81, 94, 96, 99 } and the second one contains { 12, 35 }.</p> <p>Your job is to implement this replacement selection algorithm.</p> <p>\u5229\u7528\u66ff\u6362\u9009\u62e9\u7b56\u7565\u4ee5\u540e\uff0c\u6bcf\u4e00\u6b21\u751f\u6210\u7684 run \u4e00\u5b9a\u4e0d\u5c0f\u4e8e \\(M\\)\uff08\u672b\u7aef\u4f59\u6570\u9664\u5916\uff09\uff0c\u4e8e\u662f\u76f8\u5bf9\u6765\u8bf4 \\(\\#pass\\) \u5c31\u4f1a\u51cf\u5c11\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec15/#tape-\u6570\u91cf\u5206\u6790\u4e0e\u4f18\u5316","title":"tape \u6570\u91cf\u5206\u6790\u4e0e\u4f18\u5316","text":"<p>\u5982\u679c\u4f7f\u7528#\u6734\u7d20\u8fc7\u7a0b\u5206\u6790\u4e2d\u7684\u65b9\u6cd5\uff0c\u90a3\u4e48\u6211\u4eec\u4f7f\u7528 \\(k\\)-way merge \u81f3\u5c11\u9700\u8981 \\(2k\\) \u4e2a tape\u3002</p> <p>\u8fd9\u5176\u5b9e\u5f88\u597d\u7406\u89e3\uff0c\u6211\u4eec\u6bcf\u4e00\u4e2a pass \u9700\u8981 \\(k\\) \u4e2a tape \u6765\u5b58\u653e\u6bcf\u4e00\u8def\u7684\u5e8f\u5217\uff0c\u800c\u5176\u7ed3\u679c\u8981\u5e73\u5206\u653e\u590d\u5236\u5230\u4e0b\u4e00\u4e2a pass \u6240\u9700\u8981\u7684 \\(k\\) \u4e2a pass \u4e2d\uff0c\u6240\u4ee5\u81f3\u5c11\u9700\u8981 \\(2k\\) \u4e2a tape \u8f6e\u6362\u7740\u6765\u5b58\u50a8\u6570\u636e\u3002</p> <p>\u800c\u8fd9\u4e0d\u5229\u4e8e\u6211\u4eec\u901a\u8fc7\u589e\u52a0 \\(k\\) \u6765\u51cf\u5c11 \\(\\#pass\\)\uff0c\u56e0\u6b64\u6211\u4eec\u8003\u8651\u67d0\u79cd\u7b56\u7565\u6765\u4f18\u5316 tape \u7684\u4f7f\u7528\u3002</p> <p>\u5728#\u6734\u7d20\u8fc7\u7a0b\u5206\u6790\u4e2d\u6211\u591a\u6b21\u6697\u793a\uff0c\u4e4b\u540e\u4f1a\u5bf9\u300c\u5c06\u5f52\u5e76\u540e\u7684 run \u5e73\u5206\u5230\u5404 tape\u300d\u8fd9\u4ef6\u4e8b\u505a\u4f18\u5316\u3002</p> <p>\u6211\u4eec\u53ef\u4ee5\u8003\u8651\uff0c\u4e0d\u5e73\u5747\u7684\u5c06\u5f52\u5e76\u540e\u7684 run \u5206\u914d\u5230\u5404\u4e2a tape \u4e0a\uff0c\u5373\u603b\u6709\u4e00\u4e9b tape \u6bd4\u522b\u7684 tape \u591a\u4e00\u4e9b run\u3002\u867d\u7136\u5728\u5e73\u5206\u7684\u7b56\u7565\u4e2d\uff0c\u4e5f\u6709\u53ef\u80fd\u4f1a\u6709\u591a\u51fa\u6765\u7684 run\uff0c\u4f46\u662f\u53ea\u4f1a\u591a\u4e00\u4e2a\uff08\u4e5f\u5c31\u662f\u5c06 \\(x \\mod k\\) \u7684\u4f59\u6570\u5206\u914d\u5230\u5176\u4e2d\u51e0\u4e2a tape \u4e0a\uff09\u3002\u6b64\u65f6\u8fd9\u4e9b\u591a\u51fa\u6765\u7684 run \u53ef\u80fd\u5c31\u662f\u5355\u7eaf\u7684\u4ece\u4e00\u4e2a tape \u522b\u590d\u5236\u5230\u53e6\u5916\u4e00\u4e2a tape \u4e0a\uff0c\u770b\u8d77\u6765\u662f\u4e2a\u975e\u5e38\u6ca1\u5fc5\u8981\u7684\u64cd\u4f5c\uff0c\u4e3a\u4ec0\u4e48\u4e0d\u76f4\u63a5\u7559\u4e0b\u5b83\uff0c\u5c06\u5f53\u524d tape \u62ff\u5230\u4e0b\u4e00\u8f6e\u7528\u5462\uff1f</p> <p>\u4f46\u662f\u7531\u4e8e\u5e73\u5206\u7b56\u7565\u4e0b\uff0c\u8fd9\u4e2a\u60c5\u51b5\u7684\u51fa\u73b0\u5e76\u4e0d\u53ef\u63a7\uff0c\u800c\u4e14\u603b\u662f\u4f1a\u5f15\u8d77\u60ac\u6b8a\u7684 tape \u95f4\u7684\u6570\u91cf\u5dee\uff0c\u6240\u4ee5\u6211\u4eec\u8003\u8651\u80fd\u4e0d\u80fd\u4e3b\u52a8\u5229\u7528\u8fd9\u4e2a\u6027\u8d28\u3002</p> <p>\u5b9e\u5728\u60f3\u4e0d\u5230\u600e\u4e48\u8fc7\u5ea6\u4e86\uff0c\u800c\u4e14\u6025\u6025\u6025\uff0c\u6240\u4ee5\u76f4\u63a5\u4e0a\u7ed3\u8bba\u3002</p> <p>\u6211\u4eec\u6309\u7167 Fibonacci \u6570\u5217\u7684\u9879\u6765\u5206\u914d\u6bcf\u4e2a tape \u7684 \\(\\#run\\)\uff0c\u6b64\u65f6\u6bcf\u4e00\u4e2a pass \u53ea\u9700\u8981\u4e00\u4e2a\u6709\u4e00\u4e2a\u7a7a\u95f2\u7684 tape \u5373\u53ef\u3002</p> <p>example</p> \\[ \\text{Fibonacci}: {1,1,2,3,5,8,13,21,...} \\] <p>\u5047\u8bbe\u6211\u4eec\u73b0\u5728\u6709\u4e24\u4e2a tape\uff0c\u5206\u522b\u6709 23 \u4e2a run \u548c 13 \u4e2a run\uff0c\u5219\uff1a</p> \\(T_1\\) \\(T_2\\) \\(T_3\\) \u8bf4\u660e 21 13 - \u521d\u59cb\u60c5\u51b5 8 - 13 \\(T_1\\) \u7684\u524d 13 \u4e2a\u4e0e \\(T_2\\) \u5f52\u5e76\uff0c\u7ed3\u679c\u5199\u5165 \\(T_3\\) - 8 5 \\(T_3\\) \u7684\u524d 8 \u4e2a\u4e0e \\(T_1\\) \u5f52\u5e76\uff0c\u7ed3\u679c\u5199\u5165 \\(T_2\\) 5 3 - \u7565 2 - 3 \u7565 - 2 1 \u7565 1 1 - \u7565 0 - 1 \u7565 <p>\u4f7f\u7528 Fibonacci \u6211\u4eec\u603b\u53ef\u4ee5\u6eda\u52a8\u7740\u5c06 \\(\\#run\\) \u7684\u89c4\u6a21\u7f29\u5c0f\u3002</p> k-way merge with k-order Fibonacci Sequence <p>\u5bf9\u4e8e \\(k\\)-way merge\uff0c\u6211\u4eec\u53ea\u9700\u8981\u6784\u9020 k \u9636 Fibonacci \u6570\u5217\uff0c\u7136\u540e\u6309\u7167\u8fd9\u4e2a\u6570\u5217\u6765\u5206\u914d\u6bcf\u4e2a tape \u7684 \\(\\#run\\) \u5373\u53ef\u3002</p> <p>k-order Fibonacci Sequence</p> <p>\u7ed9\u51fa k \u9636 Fibonacci \u6570\u5217\uff08\u4e0e PPT \u7565\u6709\u4e0d\u540c\uff0c\u4e3b\u8981\u4f53\u73b0\u5728\u4e0b\u6807\u4ece\u8c01\u5f00\u59cb\uff0c\u65e0\u4f24\u5927\u96c5\uff09\uff1a</p> \\[ \\left\\{ \\begin{aligned}     F^k_1 &amp;= 1 \\\\     F^k_2 &amp;= 1 \\\\     &amp; \\vdots\\\\     F^k_n &amp;= F^k_{n-1} + F^k_{n-2} + \\cdots + F^k_{n-k} \\quad (n &gt; k) \\end{aligned} \\right. \\] <p>\u8fd9\u4e2a\u7ed3\u8bba\u770b\u8d77\u6765\u5f88\u81ea\u7136\uff0c\u4f46\u662f\u5b9e\u9645\u4e0a\u662f\u600e\u4e48\u64cd\u4f5c\u7684\u5462\uff1fPPT \u538b\u6839\u6ca1\u8bb2\uff0c\u56e0\u6b64\uff0c\u6211\u5728\u8be2\u95ee ch \u8001\u5e08\u4ee5\u540e\uff0c\u5199\u4e0b\u4e86\u8fd9\u4e2a\u90e8\u5206\uff0c\u65e8\u5728\u8865\u5145 \\(k\\)-way merge \u4f7f\u7528 k \u9636 Fibonacci \u4f18\u5316\u7684\u65b9\u6cd5\u3002</p> <p>\u9996\u5148\uff0c\u505a\u4e00\u4e9b\u5f3a\u8c03\uff1a</p> <ol> <li>\u8be5\u65b9\u6cd5\u9648\u8ff0\u8fc7\u7a0b\u4e2d\uff0ck \u8def\u59cb\u7ec8\u76f4\u63a5\u5408\u5e76\u6210\u4e00\u8def\uff08\u5343\u4e07\u4e0d\u8981\u7528\u201citerative\u201d\u7684\u601d\u8def\u6765\u8003\u8651\uff0c\u5c31\u7b97 iterative\uff0c\u8fed\u4ee3\u5b8c\u4e86\u4e5f\u8fd8\u662f k \u8def\u5f52\u4e3a 1 \u8def\uff09\uff1b</li> <li>\u6211\u4eec\u7684\u76ee\u7684\u662f\u4f18\u5316\u6bcf\u4e00\u4e2a pass \u4e2d\u6bcf\u4e2a tape \u7684 \\(\\#run\\) \u4e0d\u4e00\u6837\u5e26\u6765\u7684\u6027\u80fd\u95ee\u9898\uff08\u4f8b\u5982\u5c34\u5c2c\u7684 \\(n\\) \u548c \\(n+1\\) \u5f52\uff0c\u4e0b\u4e00\u4e2a pass \u5c31\u5f97 \\(1\\) \u548c  \\(n\\) \u5f52\u4e86\uff09\uff1b</li> </ol> <p>\u5bf9\u4e8e\u7b2c \\(i\\) \u4e2a pass\uff0c\u6709 \\(k\\) \u4e2a tape\uff0c\u6211\u4eec\u8bb0\u6bcf\u4e00\u4e2a tape \u7684 \\(\\#run\\) \u4e3a \\(r_i\\)\uff0c\u5219\u6709\uff1a</p> <ul> <li>\\(\\max\\{r_i\\} = F^k_j\\);</li> <li>\\(\\min\\{r_i\\} = F^k_{j-1}\\);</li> </ul> <p>\u4e5f\u5c31\u662f\u8bf4\uff0c\u6bcf\u4e2a pass \u6700\u5927\u548c\u6700\u5c0f\u7684 \\(\\#run\\) \u5206\u522b\u6709 k \u9636 Fibonacci \u4e2d\u76f8\u90bb\u7684\u4e24\u9879\u3002</p> <p>\u8fd9\u91cc\u5206\u5f00\u7528 i \u548c j \u662f\u60f3\u8868\u8fbe\u8fd9\u4e2a\u5339\u914d\u5173\u7cfb\u4e0d\u91cd\u8981\uff0c\u91cd\u8981\u7684\u662f\u6700\u5927\u503c\u6700\u5c0f\u503c\u7531 Fibonacci \u76f8\u90bb\u9879\u6240\u786e\u5b9a\u3002</p> <p>\u90a3\u4e48\u5939\u5728\u6700\u5927\u548c\u6700\u5c0f\u7684\u4e2d\u95f4\u7684\u5176\u4ed6 \\(\\#run\\) \u8981\u5982\u4f55\u786e\u5b9a\u5462\uff1f\u9996\u5148\u6211\u4eec\u8fdb\u884c\u4e00\u6bb5\u63a8\u5bfc\uff1a</p> <p>\u5047\u8bbe \\(\\{r_i\\}\\) \u7ecf\u8fc7\u6392\u5e8f\uff0c\u5e76\u4e14\u521a\u597d\u80fd\u51d1\u4e0a\u6211\u4eec\u6240\u9700\u8981\u7684\u6570\u91cf\uff0c\u6709\uff1a</p> \\[ r_k &gt; r_{k-1} &gt; ... &gt; r_{2} &gt; r_{1} \\text{where } r_k = F^k_j \\text{ and } r_1 = F^k_{j-1} \\] <p>\u5728\u8fd9\u4e00\u4e2a pass \u4e2d\uff0c\u6211\u4eec\u5c06\u6240\u6709 tape \u7684\u524d \\(r1\\) \u4e2a run \u62ff\u51fa\u6765 merge\uff0c\u8fd9\u6837\uff0c\u9664\u4e86 \\(r_1\\) \u8fd9\u4e2a tape\uff0c\u5176\u4ed6 tape \u7684 \\(\\#run\\) \u90fd\u53d8\u4e3a \\(r_i-r_1\\)\u3002\u6b64\u65f6\u6709\u4e0d\u7b49\u5173\u7cfb\uff1a</p> \\[ r_1 &gt; r_k - r_1 &gt; r_{k-1} - r_1 &gt; ... &gt; r_{2} - r_1 \\] <p>\u8fd9\u91cc\u552f\u4e00\u9700\u8981\u8bf4\u660e\u7684\u5c31\u662f \\(r_1 &gt; r_k - r_1\\)\uff1a</p> proof of the relation \\[ \\begin{aligned}     &amp;\\begin{aligned}         \\because r_1          &amp;= F^k_{j-1} \\\\         &amp;= F^k_{j-2} + \\cdots + F^k_{j-k} + F^k_{j-k-1}     \\end{aligned}  &amp; (1)\\\\     &amp;\\begin{aligned}         \\text{and } r_k         &amp;= F^k_{j} \\\\         &amp;= F^k_{j-1} + F^k_{j-2} + \\cdots + F^k_{j-k}     \\end{aligned}  &amp; (2)\\\\     &amp;\\begin{aligned}         \\therefore r_k - r_1          &amp;= F^k_{j} - F^k_{j-1} \\quad \\text{ i.e. } (2) - (1)\\\\         &amp;= F^k_{j-2} + \\cdots + F^k_{j-k}     \\end{aligned}  &amp; (3)\\\\     &amp;\\begin{aligned}         \\therefore r_1 - (r_k - r_1)         &amp;= F^k_{j-k-1} &gt; 0 \\quad \\text{ i.e. } (1) - (3) \\\\     \\end{aligned} \\\\     &amp;\\begin{aligned}     \\therefore r_1 &gt; r_k - r_1     \\end{aligned} \\\\   \\end{aligned} \\] <p>\u5982\u679c\u6211\u4eec\u5c06\u73b0\u5728\u8fd9\u4e2a\u6392\u5e8f\u540e\u7684\u6570\u5217\u8bb0\u4e3a \\(\\{r_i'\\}\\)\uff0c\u5219\u6709\uff1a</p> \\[ \\left\\{ \\begin{aligned}     r_1' &amp;= r_2 - r_1 \\\\     r_2' &amp;= r_3 - r_1 \\\\     \\vdots \\\\     r_{k-1}' &amp;= r_k - r_1 \\\\     r_k' &amp;= r_1 \\end{aligned} \\right. \\] <p>\u6b64\u65f6\u6839\u636e\u6211\u4eec\u5173\u4e8e\u6700\u5927\u6700\u5c0f\u503c\u7684\u9648\u8ff0\uff0c\u53c8\u6709\uff1a</p> \\[ \\left\\{ \\begin{aligned}     r_1' &amp;= F^k_{j-2} \\\\     r_k' &amp;= F^k_{j-1} \\end{aligned} \\right. \\] <p>\u4e8e\u662f\u53ef\u4ee5\u63a8\u5f97\uff1a\\(r_2 = r_1 + F^k_{j-2} = F^k_{j-1} + F^k_{j-2}\\)\u3002\u5173\u4e8e \\(r_3, r_4\\)\uff0c\u4e5f\u662f\u4e00\u6837\u7684\u529e\u6cd5\uff0c\u5c06 \\(r_2\\) \u7684\u7ed3\u8bba\u8fc1\u79fb\u5230 \\(r_2'\\)\uff0c\u518d\u56de\u8fc7\u5934\u5f97\u5230 \\(r_3 = r_1 + r_2'= F^k_{j-1} + F^k_{j-2} + F^k_{j-3}\\)\uff0c\u4ee5\u6b64\u7c7b\u63a8\uff0c\u53ef\u4ee5\u5f97\u5230\u6700\u7ec8\u7ed3\u8bba\uff1a</p> \\[ \\left\\{ \\begin{aligned}     r_1 &amp;= F^k_{j-1} \\\\     r_2 &amp;= F^k_{j-1} + F^k_{j-2} \\\\     r_3 &amp;= F^k_{j-1} + F^k_{j-2} + F^k_{j-3} \\\\     \\vdots \\\\     r_k &amp;= F^k_{j-1} + F^k_{j-2} + ... + F^k_{j-k} = F^k_{j} \\end{aligned} \\right. \\] <p>\u601d\u8003\u9898</p> <p>\u53ef\u4ee5\u611f\u53d7\u601d\u8003\u4e00\u4e0b\u8fd9\u4e2a\u7279\u6027\uff08\u8003\u8651 2-way \u5373\u53ef\uff09\u4e0e\u9ec4\u91d1\u6bd4\u4f8b\u7684\u5173\u7cfb\uff01</p> <p>hint: \u5982\u4f55\u7406\u89e3 \\(\\frac{a_n}{a_{n-1}} \\approx \\frac{a_{n-1}}{a_n - a_{n-1}}\\) \u4e0e\u8fd9\u4e2a\u6027\u8d28\u7684\u5173\u7cfb\uff1f</p> <p>\u5f53\u7136\uff0c\u521a\u597d\u80fd\u51d1\u4e0a Fibonacci \u7684\u60c5\u51b5\u81ea\u7136\u662f\u5c11\u6570\uff0c\u5bf9\u4e8e\u65e0\u6cd5\u51d1\u4e0a Fibonacci \u7684\u60c5\u51b5\uff0c\u6211\u4eec\u53ef\u4ee5\u5c06\u591a\u4f59\u7684\u90e8\u5206\u5747\u5300\u7684\u5206\u5230\u8f83\u591a\u82e5\u5e72 tape \u4e0a\uff0c\u4ee5\u76f8\u5bf9\u7684\u5229\u7528 Fibonacci \u6570\u5217\u7684\u6027\u8d28\uff08\u8054\u7cfb\u601d\u8003\u9898\u7406\u89e3\uff09\u3002</p> <p>\u6ce8\u610f</p> <p>\u6216\u8bb8\u4f60\u5df2\u7ecf\u5f00\u59cb\u4ea7\u751f\u7591\u95ee\u4e86\uff0c\u5982\u679c\u8fd9\u6837\u6765\u505a\uff0c\u524d\u9762\u5bf9 \\(\\#pass\\) \u7684\u5206\u6790\u662f\u4e0d\u662f\u4e0d\u6210\u7acb\u4e86\u5462\uff1f</p> <p>\u6211\u60f3\u5e94\u8be5\u786e\u5b9e\u4e0d\u518d\u5b8c\u5168\u4e00\u6837\u4e86\uff0c\u4f46\u662f\u5e76\u4e0d\u5f71\u54cd\u6211\u4eec\u4e4b\u540e\u5229\u7528\u90a3\u4e2a\u7ed3\u8bba\u505a\u5b9a\u6027\u5206\u6790\uff0c\u6211\u4eec\u53ea\u9700\u8981\u77e5\u9053\uff0c\u91c7\u53d6 Fibonacci \u7b56\u7565\u6765\u4f18\u5316\u4f1a\u5bfc\u81f4 \\(\\#pass\\) \u589e\u591a\u5373\u53ef\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec15/#k-\u8def\u5185\u6392\u5e8f\u4f18\u5316","title":"k \u8def\u5185\u6392\u5e8f\u4f18\u5316","text":"<p>\u968f\u7740 \\(k\\) \u7684\u589e\u52a0\uff0c\u6211\u4eec\u4e0d\u80fd\u518d\u50cf\u4e24\u8def\u5f52\u5e76\u90a3\u6837\u76f4\u63a5\u8f93\u51fa\u8f83\u5c0f\u7684\u90a3\u4e2a\uff0c\u800c\u662f\u9700\u8981\u7ef4\u62a4\u6570\u636e\u7ed3\u6784\u6765\u603b\u662f\u8f93\u51fa k \u4e2a\u4e2d\u6700\u5c0f\u7684\u90a3\u4e2a\u2014\u2014\u6211\u4eec\u7528\u5806\u6765\u7ef4\u62a4\u6bcf\u4e00\u4e2a run \u5728\u5185\u5b58\u4e2d\u7684\u6570\u636e\u7684\u961f\u9996\u5143\u7d20\uff08\u540c\u65f6\u4e5f\u662f\u6700\u5c0f\u5143\u7d20\uff09\uff0c\u6bcf\u5f53\u5806\u9876\u5143\u7d20\u88ab\u8f93\u51fa\uff0c\u5c31\u9700\u8981\u4ece\u5bf9\u5e94\u7684 run \u4e2d\u8bfb\u5165\u4e0b\u4e00\u4e2a\u5143\u7d20\u3002</p> <p>\u6ce8\u610f</p> <p>\u9700\u8981\u6ce8\u610f\uff0c\u8fd9\u91cc\u7684\u5806\u662f\u989d\u5916\u7ef4\u62a4\u7684\uff0c\u800c\u6bcf\u6b21\u63a8\u5165\u5806\u4e2d\u7684\u5143\u7d20\u90fd\u662f\u4ece\u5bf9\u5e94\u7684 run \u7684 buffer \u4e2d\u62ff\u7684\uff0c\u800c\u4e0d\u662f\u6bcf\u6b21\u90fd\u4ece\u786c\u76d8\u4e2d\u62ff\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec15/#\u970d\u592b\u66fc\u6811\u4f18\u5316","title":"\u970d\u592b\u66fc\u6811\u4f18\u5316","text":"<p>\u5f53\u7136\uff0c\u6211\u4eec\u4e5f\u53ef\u4ee5\u4e0d\u4f7f\u7528\u76f4\u63a5 \\(k\\) \u8def\u5408\u5e76\uff0c\u800c\u662f\u91c7\u7528\u4e24\u4e24\u5f52\u5e76\u7684\u65b9\u6cd5\uff0c\u4e5f\u5c31\u662f wiki \u4e2d\u63d0\u5230\u7684\u8fed\u4ee3\u5f52\u5e76\uff08\u6ce8\u610f\uff0c\u8be5\u6761\u76ee\u4e2d\u63d0\u5230\u7684\u5f52\u5e76\u5e76\u6ca1\u6709\u8bf4\u660e\u662f\u5916\u6392\u5e8f\u80cc\u666f\uff0c\u4f46\u662f\u53ef\u4ee5\u8fc1\u79fb\uff09\u3002 </p> <p>\u5047\u8bbe\u6211\u4eec\u73b0\u5728\u6709\u82e5\u5e72\u4e2a run\uff0c\u5e76\u4e14\u6211\u4eec\u5c06\u8981\u8fdb\u884c\u4e24\u4e24\u5f52\u5e76\uff0c\u90a3\u4e48\u6211\u4eec\u53ef\u4ee5\u6839\u636e\u6bcf\u4e00\u4e2a run \u7684\u5927\u5c0f\uff0c\u6839\u636e\u970d\u592b\u66fc\u6811\u7684\u89c4\u5f8b\u6765\u8fdb\u884c\u5f52\u5e76\uff0c\u5373\u603b\u662f\u9009\u6700\u5c0f\u7684\u4e24\u4e2a\u8fdb\u884c\u5f52\u5e76\u3002</p>"},{"location":"cour_note/D2CX_AdvancedDataStructure/Lec15/#\u5e76\u884c\u4f18\u5316","title":"\u5e76\u884c\u4f18\u5316","text":"<p>\u8fd9\u91cc\u5e76\u884c\u7684\u76ee\u6807\u4e3b\u8981\u662f\u4f7f\u7b97\u6cd5\u652f\u6301\u6570\u636e\u7684\u8bfb-\u7528-\u5199\u7684\u6d41\u6c34\u7ebf\uff0c\u4e5f\u5c31\u662f\u8bf4\u6211\u4eec\u8981\u60f3\u529e\u6cd5\u8ba9\u8bfb\u4e0d\u963b\u585e\u7528\uff0c\u7528\u4e0d\u963b\u585e\u5199\u3002</p> <p>\u5148\u524d\u6211\u4eec\u9700\u8981\u5148\u8bfb\u5165\u6570\u636e\uff0c\u7136\u540e\u8fdb\u884c\u6392\u5e8f\uff0c\u6392\u5e8f\u5b8c\u4e86\u518d\u5199\u5165\u78c1\u76d8\uff0c\u817e\u51fa\u5185\u5b58\u7a7a\u95f4\u4ee5\u4f9b\u4e0b\u4e00\u6b21\u8bfb\u5165\u3002\u90a3\u4e3a\u4ec0\u4e48\u4f1a\u963b\u585e\u5462\uff1f\u56e0\u4e3a\u6211\u4eec\u6ca1\u6cd5\u8bfb\u4e00\u4e2a\u6b63\u5728\u5199\u7684\u6570\u636e\u5757\uff0c\u6240\u4ee5\u6211\u4eec\u53ea\u9700\u8981\u5728\u4e0d\u540c\u7684\u6570\u636e\u5757\u8bfb\u548c\u5199\u5c31\u884c\u4e86\u3002\u5bf9\u4e8e \\(k\\)-way \u4e2d\u7684\u6bcf\u4e00\u8def\uff0c\u6211\u4eec\u90fd\u63d0\u4f9b\u4e24\u4e2a input buffer\uff0c\u4e00\u4e2a\u7528\u4e8e\u5199\uff0c\u4e00\u4e2a\u7528\u4e8e\u6392\u5e8f\u3002\u5f53\u6392\u5e8f buffer \u7a7a\u4e86\u7684\u65f6\u5019\uff0c\u5c31\u548c\u8bfb\u6ee1\u4e86\u7684 input buffer \u4ea4\u6362\uff0c\u65e0\u7f1d\u8854\u63a5\u7ee7\u7eed\u8f93\u51fa\u3002\u4e8e\u6b64\u540c\u65f6\uff0c\u521a\u521a\u88ab\u4ea4\u6362\u8fc7\u53bb\u7684 buffer \u5219\u53ef\u7528\u4e8e\u7ee7\u7eed\u8bfb\u5165\u3002</p> <p>\u56e0\u6b64\uff0c\u5982\u679c\u6211\u4eec\u6267\u884c direct \\(k\\)-way merge\uff0c\u5c31\u9700\u8981 \\(2k\\) \u4e2a input buffer\uff08\u8fd9\u91cc\u5f3a\u8c03 direct \u662f\u56e0\u4e3a\uff0c\u5982\u679c\u4f7f\u7528 iterative \u7684\u8bdd\uff0cinput buffer \u53ea\u9700\u8981 4 \u4e2a\uff09\u3002</p> <p>\u800c\u5bf9\u4e8e\u8f93\u51fa\uff0c\u6211\u4eec\u53ea\u9700\u8981 2 \u4e2a output buffer \u4ea4\u66ff\u4f7f\u7528\u5373\u53ef\uff0c\u4e00\u4e2a\u7528\u6765\u63a5\u6536\u6765\u81ea\u6392\u5e8f\u7b97\u6cd5\u7684\u8f93\u51fa\uff0c\u4e00\u4e2a\u7528\u6765\u5c06\u6570\u636e\u5199\u5165\u78c1\u76d8\u3002</p> <p>\u4f46\u662f\uff0c\u5e76\u884c\u4f18\u5316\u7684\u7f3a\u70b9\u5c31\u662f\u5360\u636e\u4e86\u66f4\u591a\u7684\u5185\u5b58\u7a7a\u95f4\u2014\u2014\u539f\u5148 \\(k + 1\\) \u4e2a buffer \u5e73\u5206\u7684\u7528\u4e8e\u5904\u7406\u6570\u636e\u7684\u5185\u5b58\uff0c\u73b0\u5728\u9700\u8981\u88ab \\(2k + 2\\) \u4e2a buffer \u5e73\u5206\uff0c\u6240\u4ee5\u6bcf\u4e00\u4e2a buffer \u7684\u5927\u5c0f\u4f1a\u53d8\u5c0f\u3002\u8fdb\u800c\u5bfc\u81f4\u6bcf\u4e00\u6b21\u4ece disk \u4e2d\u8bfb\u53d6\u7684\u6570\u636e\u53d8\u5c11\uff0c\u6240\u4ee5\u8981\u8bfb\u5b8c\u6570\u636e\u6240\u9700\u8981\u7684\u8bfb\u53d6\u6b21\u6570\u5c31\u589e\u52a0\uff0c\u5373 seek \u6b21\u6570\u589e\u52a0\u3002</p>"},{"location":"cour_note/D2CX_ComputerOrganization/","title":"\ud83d\udd2e \u8ba1\u7b97\u673a\u7ec4\u6210 | Computer Organization","text":"<p> \u7ea6 57 \u4e2a\u5b57 </p> <p>\u7531\u4e8e\u7b14\u8bb0\u592a\u6d6a\u8d39\u65f6\u95f4\u4e86\uff0c\u6211\u5b66\u4e60\u8ba1\u7ec4\u4f7f\u7528\u7684\u662f xxjj \u7684\u7b14\u8bb0\uff1a</p> <p>https://xuan-insr.github.io/computer_organization/1_prelude/</p> <p>\u987a\u4fbf\u61d2\u5f97\u81ea\u5df1\u91cd\u65b0\u8c03\u6574\uff0c\u76f4\u63a5\u5728\u4ed6\u7684\u7b14\u8bb0\u4e0a\u4fee\u6539\u7136\u540e PR \u4e86\u3002</p>"},{"location":"cour_note/D2HJ_StanfordWriting/","title":"\ud83d\udd2e \u79d1\u5b66\u6587\u7ae0\u5199\u4f5c | Writing in the Sciences","text":"<p> \u7ea6 1331 \u4e2a\u5b57  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 4 \u5206\u949f</p> <ul> <li>\u5b98\u65b9\u7f51\u7ad9\uff1a\ud83d\udd17</li> <li>\u89c6\u9891\u94fe\u63a5\uff1a\ud83d\udd17</li> <li>\u53c2\u8003\u7b14\u8bb0\uff1a\ud83d\udd17</li> </ul> <p>\u5410\u69fd</p> <p>\u4e0d\u662f\u6211\u8bf4\uff0c\u6211\u611f\u89c9\u8fd9\u8bfe\u7684\u7ec4\u7ec7\u6ca1\u6709\u5f88\u6e05\u6670\u7684\u903b\u8f91\uff0c\u6216\u8005\u8bf4\u5b9e\u9645\u4e0a\u5b83\u5e76\u4e0d\u5c5e\u4e8e\u80fd\u591f\u7528\u6846\u67b6\u6027\u7684\u5185\u5bb9\u6982\u62ec\u7684\uff0c\u800c\u662f\u4e0d\u65ad\u7684\u628a\u7ec6\u8282\u5185\u5bb9\u4e22\u51fa\u6765\u5e76\u5728\u6848\u4f8b\u4e2d\u5206\u6790\uff0c\u6240\u4ee5\u611f\u89c9\u7b14\u8bb0\u5f88\u96be\u505a\u554a\uff0c\u7136\u540e\u611f\u89c9\u7b2c\u4e00\u5355\u5143\u7684\u5185\u5bb9\u662f\u5bf9\u6574\u4e2a\u8bfe\u7a0b\u7684\u5927\u81f4\u6897\u6982\uff0c\u6240\u4ee5\u8fd9\u91cc\u653e\u7684\u4e3b\u8981\u662f\u7b2c\u4e00\u7ae0\u7684\u5185\u5bb9\uff0c\u540e\u9762\u5982\u679c\u6709\u9047\u5230\u6211\u89c9\u5f97\u6709\u5fc5\u8981\u4e14\u65b9\u4fbf\u8bb0\u4e0b\u6765\u7684\u4e1c\u897f\u4f1a\u5fd8\u91cc\u9762\u4e22\uff0c\u4f46\u662f\u6211\u4e2a\u4eba\u611f\u89c9\u8fd9\u4efd\u7b14\u8bb0\u7684\u8d28\u91cf\u4e0d\u662f\u5f88\u9ad8\uff0c\u6548\u679c\u4e5f\u4e0d\u662f\u5f88\u597d\u2014\u2014\u5bf9\u4e8e\u66ff\u4ee3\u8fd9\u95e8\u8bfe\u6765\u8bf4\u3002</p> <p>\u6897\u6982</p> <p>\u79d1\u5b66\u6587\u732e\u662f\u4e3a\u4e86\u89c2\u70b9\u4ea4\u6d41\u5b58\u5728\u7684\uff0c\u800c\u201c\u6587\u7ae0\u201d\u53ea\u662f\u89c2\u70b9\u4ea4\u6d41\u8fc7\u7a0b\u4e2d\u7684\u4e00\u79cd\u627f\u8f7d\u5f62\u5f0f\u3002\u6211\u4eec\u8981\u7740\u91cd\u4e8e\u8ba9\u8bfb\u8005\u80fd\u4ee5\u66f4\u5c0f\u7684\u8d1f\u62c5\u7406\u89e3\u6587\u7ae0\u7684\u5185\u6db5\uff0c\u5373\u7528\u7b80\u660e\u627c\u8981\u7684\u3001\u8109\u7edc\u6e05\u6670\u7684\u6587\u5b57\uff0c\u8868\u8fbe\uff08\u6709\u53ef\u80fd\u6bd4\u8f83\u590d\u6742\u7684\uff09\u89c2\u70b9\u548c\u903b\u8f91\u3002</p> <p>\u6b64\u5916\uff0c\u6211\u4eec\u8fd8\u9700\u8981\u201c\u4e3a\u8bfb\u8005\u670d\u52a1\u201d\uff0c\u8003\u8651\u5230\u6587\u7ae0\u7684\u9605\u8bfb\u8282\u594f\uff0c\u5c3d\u53ef\u80fd\u8ba9\u6587\u7ae0\u80fd\u591f\u88ab\u884c\u4e91\u6d41\u6c34\u5730\u9605\u8bfb\u4e0b\u6765\uff0c\u800c\u975e\u78d5\u78d5\u7eca\u7eca\u6216\u53cd\u53cd\u590d\u590d\u3002</p> <p>\u4e00\u7bc7\u79d1\u5b66\u6587\u7ae0\u662f\u4e3a\u4e86\u4ea4\u6d41\u89c2\u70b9\u800c\u5b58\u5728\u7684\uff0c\u6240\u4ee5\u5b83\u5e94\u5f53\u80fd\u591f\u8ba9\u4eba \u9ad8\u6548 \u5730\u83b7\u53d6\u6838\u5fc3\u5185\u5bb9\uff0c\u6e05\u6670 \u5730\u641e\u6e05\u695a\u6587\u7ae0\u8bf4\u4e86\u4ec0\u4e48\uff0c\u5c24\u5176\u5728\u64b0\u5199\u6587\u7ae0\u521d\u7a3f\u7684\u65f6\u5019\uff0c\u8981\u5c24\u5176\u6ce8\u91cd\u8fd9\u4e9b\uff1b\u5728\u6b64\u57fa\u7840\u4e0a \u4f18\u96c5 \u7684\u6587\u98ce\u80fd\u8ba9\u6587\u7ae0\u66f4\u4e0a\u4e00\u5c42\u697c\uff0c\u800c\u8fd9\u4e9b\u901a\u5e38\u662f\u5728\u4fee\u6539\u4e0e\u6da6\u8272\u4e2d\u4f53\u73b0\u51fa\u6765\u7684\u3002</p> <p>\u800c\u4e3a\u4e86\u5b9e\u73b0\u300c\u9ad8\u6548\u300d\u548c\u300c\u6e05\u6670\u300d\uff0c\u4f60\u9996\u5148\u5fc5\u987b\u6e05\u695a\u81ea\u5df1\u5c06\u8981\u8868\u8fbe\u4ec0\u4e48\uff08Have something to say.\uff09\uff0c\u5e76\u4e14\u68b3\u7406\u6e05\u8fd9\u4e9b\u5185\u5bb9\u7684\u8109\u7edc\u548c\u903b\u8f91\u5173\u7cfb\uff08Logical thinking.\uff09\uff0c\u6b64\u5916\uff0c\u4e3a\u4e86\u8f85\u52a9\u6784\u5efa\u8d77\u4e00\u7bc7\u6587\u7ae0\uff0c\u4f60\u8fd8\u9700\u8981\u4e00\u4e9b\u5199\u4f5c\u5957\u8def\uff08A few simple, learnable rules of style.\uff09\u3002</p> <p>\u8fd9\u91cc\u6709\u4e00\u4e9b\u5176\u5b83\u4e60\u60ef\u80fd\u591f\u5e2e\u52a9\u4f60\u66f4\u597d\u5730\u5199\u4f5c\uff1a</p> <ol> <li>\u65e5\u5e38\u591a\u8bfb\u591a\u5199\u591a\u6a21\u4eff\uff0c\u4e0d\u4e00\u5b9a\u8981\u548c\u79d1\u5b66\u6587\u7ae0\u6709\u5173\uff1b</li> <li>\u6539\u6b63\u4e00\u4e9b\u5b66\u4e60\u8fc7\u7a0b\u4e2d\u517b\u6210\u7684\u574f\u7684\u201c\u5b66\u672f\u201d\u5199\u4f5c\u4e60\u60ef\uff0c\u8bb2\u8005\u79f0\u4e4b\u4e3a deprogramming step\uff1b</li> <li>\u52a8\u7b14\u4e4b\u524d\u5148\u5c1d\u8bd5\u7740\u7528\u8bed\u8a00\u6765\u8bb2\u8ff0\u6587\u7ae0\u5185\u5bb9\uff0c\u6bd4\u5982\u548c\u4f60\u7684\u670b\u53cb\u8c08\u8c08\uff1b</li> <li>\u5c1d\u8bd5\u8ba9\u6587\u7ae0\u53d8\u5f97\u6709\u5438\u5f15\u529b\uff1b</li> <li>\u8ba4\u8bc6\u5230\u5199\u4f5c\u4e0d\u9700\u8981\u7075\u611f\uff0c\u4e0d\u8981\u628a\u7075\u611f\u5f53\u4f5c\u501f\u53e3\uff1b</li> <li>\u8ba4\u8bc6\u5230\u5199\u4f5c\u672c\u8eab\u662f\u56f0\u96be\u7684\uff0c\u800c\u5927\u5bb6\u90fd\u4e00\u6837\uff1b</li> <li>\u575a\u6301\u53cd\u590d\u4fee\u6539\uff0c\u751a\u81f3\u662f\u5728\u5199\u521d\u7a3f\u7684\u65f6\u5019\uff0c\u4f18\u5148\u628a\u6587\u7ae0\u6210\u54c1\u5199\u51fa\u6765\uff0c\u518d\u4e0d\u538c\u5176\u70e6\u5730\u4fee\u7f2e\uff1b</li> <li>\u6740\u4f10\u679c\u65ad\uff0c\u4e0d\u8981\u6267\u7740\u4e8e\u5df2\u7ecf\u5199\u51fa\u6765\u7684\u4f46\u662f\u5b9e\u9645\u4e0a\u4e0d\u9700\u8981\u7684\u6587\u5b57\uff1b</li> <li>\u627e\u4e00\u4e2a\u597d\u7f16\u8f91\uff0cta \u4eec\u53ef\u80fd\u4f1a\u7ed9\u4f60\u597d\u7684\u610f\u89c1\u548c\u5efa\u8bae\uff1b</li> <li>\u53bb\u5192\u9669\uff0c\u52c7\u6562\u5730\u53bb\u7a81\u7834\u684e\u688f\uff1b</li> </ol> <p>\u5177\u4f53\u5230\u5199\u4f5c\u65f6\uff0c\u6211\u4eec\u8981\u5207\u5fcc\u53e5\u5b50\u6666\u6da9\u96be\u61c2\uff0c\u5728\u5199\u4f5c\u8fc7\u7a0b\u4e2d\u6211\u4eec\u53ef\u80fd\u65e0\u610f\u8bc6\u5730\u7528\u6666\u6da9\u590d\u6742\u7684\u8bed\u53e5\u63a9\u76d6\u6211\u4eec\u60f3\u8981\u8868\u8fbe\u7684\u5185\u5bb9\uff0c\u5176\u4e2d\u53ef\u80fd\u7684\u539f\u56e0\u6709\uff1a</p> <p>\u5c06\u8bb8\u591a\u52a8\u8bcd\u8f6c\u5316\u4e3a\u540d\u8bcd\u4f7f\u7528</p> <p>Verbs drive sentences along and nouns slow them down.</p> <p>bad eg</p> <p>Adoptive cell transfer (ACT) immunotherapy is based on the ex vivo selection of tumor-reactive lymphocytes, and their activation and numerical expression before reinfusion to the autologous tumor-bearing host.</p> <p>\u4f7f\u7528\u6a21\u7cca\u5bbd\u6cdb\u7684\u8bcd</p> <p>\u6a21\u7cca\u5bbd\u6cdb\u7684\u3001\u4e0d\u591f\u5177\u4f53\u7684\u3001\u4e0d\u80fd\u8ba9\u8bfb\u8005\u8111\u4e2d\u4ea7\u751f\u76f4\u63a5\u5370\u8c61\u7684\u8bcd\u4f1a\u8ba9\u8bfb\u8005\u611f\u5230\u56f0\u60d1\u3002</p> <p>\u4f7f\u7528\u4e0d\u5fc5\u8981\u7684\u7f29\u5199\u6216\u672f\u8bed</p> <p>\u9664\u975e\u662f\u4e00\u4e9b\u5e7f\u4e3a\u4eba\u77e5\u7684\u7f29\u5199\uff0c\u5426\u5219\u5f88\u53ef\u80fd\u4e3a\u8bfb\u8005\u5e26\u6765\u56f0\u6270\u3002\u5373\u4f7f\u4f60\u5728\u524d\u6587\u4e2d\u5df2\u7ecf\u4ecb\u7ecd\uff0c\u5b83\u4eec\u5f88\u53ef\u80fd\u9700\u8981\u56de\u8fc7\u5934\u6765\u67e5\u9605\u624d\u80fd\u201c\u8bb0\u8d77\u201d\u8fd9\u4e2a\u7f29\u5199\u7684\u542b\u4e49\u3002</p> <p>\u4f7f\u7528\u88ab\u52a8\u8bed\u6001</p> <p>\u8fdd\u53cd\u4e86\u60c5\u7eea\u4e0a\u7684 \u4e3b-\u8c13-\u5bbe \u7684\u987a\u5e8f\u3002\u5f53\u7136\u8981\u6309\u7167\u5b9e\u9645\u60c5\u51b5\u6765\u8bf4\uff0c\u5173\u952e\u662f\u8981\u907f\u514d\u4e0d\u5fc5\u8981\u7684\u8bed\u6cd5\u53d8\u5316\u3002</p> <p>\u4e3b\u8bed\u548c\u52a8\u8bcd\u592a\u9065\u8fdc</p> <p>\u8bfb\u8005\u603b\u662f\u5728\u671f\u5f85\u627e\u5230\u4e00\u53e5\u8bdd\u91cc\u7684\u201c\u52a8\u8bcd\u201d\uff0c\u800c\u5982\u679c\u8fd9\u4e2a\u201c\u52a8\u8bcd\u201d\u592a\u96be\u627e\uff0c\u5c06\u4f1a\u5f71\u54cd\u6574\u53e5\u8bdd\u7684\u9605\u8bfb\u6548\u7387\u3002</p> <p>\u6362\u53e5\u8bdd\u6765\u8bf4\uff0c\u4e0d\u7ba1\u4f60\u7684\u5185\u5bb9\u662f\u5426\u590d\u6742\uff0c\u627f\u8f7d\u8fd9\u4e9b\u5185\u5bb9\u7684\u8bed\u53e5\u90fd\u4e0d\u5e94\u5f53\u662f\u590d\u6742\u7684\u3002</p> <p>\u603b\u7684\u6765\u8bf4\uff0c\u6709\u8fd9\u4e48\u4e9b\u539f\u5219\uff1a</p> <ol> <li>\u5220\u51cf\u4e0d\u5fc5\u8981\u7684\u8bcd\u6c47\uff0c\u5bf9\u6b64\u4fdd\u6301 \u654f\u611f \u548c \u65e0\u60c5\uff0c\u4e0d\u8981\u6297\u62d2\u91cd\u6784\u5b57\u53e5\uff1b<ul> <li>\u4e0d\u5fc5\u8981\u7684\u8bcd\u6c47\uff0c\u6bd4\u5982\uff1a\u6ca1\u6709\u5b9e\u9645\u542b\u4e49\u7684\u8bcd\uff0c\u4e00\u4e9b\u53ea\u6709\u8bed\u6c14\u4f5c\u7528\u7684\u8bcd\u7b49\uff1b</li> <li>\u4e0d\u5fc5\u8981\u7684\u8bcd\u6c47\uff0c\u6bd4\u5982\uff1a\u6ca1\u6709\u610f\u4e49\u7684\u7f29\u5199\u548c\u672f\u8bed\uff1b</li> <li>\u4e0d\u5fc5\u8981\u7684\u8bcd\u6c47\uff0c\u6bd4\u5982\uff1a\u524d\u540e\u8bed\u4e49\u91cd\u590d\u7684\u8bcd\uff1b</li> <li>\u4e0d\u5fc5\u8981\u7684\u8bcd\u6c47\uff0c\u6bd4\u5982\uff1aadv. \u4eec\uff1b</li> </ul> </li> <li>\u66f4\u591a\u5730\u4f7f\u7528\u4e3b\u52a8\u8bed\u6001\uff08\u4e3b\u8c13\u5bbe\uff09\u800c\u975e\u88ab\u52a8\u8bed\u6001\uff1b</li> <li>\u56f4\u7ed5 \u52a8\u8bcd \u5199\u4f5c\uff1a\u4f7f\u7528\u5f3a\u52a8\u8bcd\uff0c\u907f\u514d\u5c06\u52a8\u8bcd\u53d8\u6210\u540d\u8bcd\uff0c\u5e76\u5c06\u52a8\u8bcd\u653e\u5728\u9192\u76ee\u7684\u4f4d\u7f6e\uff1b</li> <li>\u9ad8\u8003\u82f1\u8bed\u4f5c\u6587\u600e\u4e48\u5199\uff0c\u79d1\u5b66\u6587\u732e\u5c31\u4e0d\u8981\u600e\u4e48\u5199\uff1b</li> </ol> <p>\u51cf\u5c11\u6587\u7ae0\u4e2d\u7684\u6df7\u4e71\u6709\u5982\u4e0b\u65b9\u6cd5\uff1a</p> <p>\u8f6c\u5426\u5b9a\u4e3a\u80af\u5b9a</p> from to not honest dishonest not harmful safe not important unimportant do not have lack do not remember forget do not pay attention to ignore do not succeed fail <p>\u5220\u53bb\u8fc7\u5269\u7684 \"there are\" / \"there is\"</p> <p>\u5220\u53bb\u4e0d\u5fc5\u8981\u7684\u4ecb\u8bcd</p>"},{"location":"cour_note/D2QD_DigitalDesign/","title":"\ud83d\udd2e \u6570\u5b57\u903b\u8f91\u8bbe\u8ba1 | Digital Design","text":"<p> \u7ea6 385 \u4e2a\u5b57  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 1 \u5206\u949f</p> <p>\u6ce8\u610f\uff01</p> <p>\u672c\u7ad9\u90e8\u7f72\u5728 GitHub pages \u4e0a\uff0c\u6240\u4ee5\u53ef\u80fd\u4f1a\u51fa\u73b0\u5361\u987f\u60c5\u51b5\uff0c\u4f7f\u7528\u4ee3\u7406\u53ef\u4ee5\u6781\u5927\u4f18\u5316\u9605\u8bfb\u4f53\u9a8c\u3002</p> <p>\u8bfe\u7a0b\u4fe1\u606f</p> <ul> <li>\u6388\u8bfe\uff1a\u8521\u94ed</li> <li>\u667a\u4e91\u8bfe\u5802\u94fe\u63a5\uff1a\ud83d\udd17</li> <li>\u6559\u6750\uff1aLogic and Computer Design Fundamentals, Fifth Edition</li> <li>\u672c\u6587\u4e3b\u8981\u6765\u81ea\u4e8e\u6211\u5543\u6559\u6750\u65f6\u7684\u7b14\u8bb0\uff0c\u4f46\u5c0f\u7ed3\u5b89\u6392\u4e0d\u5b8c\u5168\u662f\u6309\u7167\u8bfe\u672c\u6765</li> <li>\u56e0\u4e3a\u6211\u7684\u5f3a\u8feb\u75c7\uff0c\u6211\u5f88\u7ea0\u7ed3\u5982\u4f55\u628a\u8bdd\u8bf4\u901a\u987a\u548c\u628a\u4e0a\u4e0b\u903b\u8f91\u5199\u51fa\u6765\uff0c\u6240\u4ee5\u6709\u4e9b\u53ef\u80fd\u4e00\u773c\u5c31\u770b\u51fa\u6765\u7684\u4e1c\u897f\u6211\u8fd8\u662f\u8981\u89e3\u91ca\u4e00\u5927\u5806\uff0c\u6240\u4ee5\u53ef\u80fd\u4f1a\u6bd4\u8f83\u5570\u55e6\u545c\u545c\u545c\uff0c\u5e0c\u671b\u5927\u5bb6\u6709\u4efb\u4f55\u610f\u89c1\u6216\u8005\u5efa\u8bae\u90fd\u5199\u5728\u8bc4\u8bba\u533a\u91cc\u8ba9\u6211\u77e5\u9053\uff01\u5e0c\u671b\u8fd9\u4efd\u8d44\u6599\u53ef\u4ee5\u7ed9\u4f60\u5e26\u6765\u5e2e\u52a9\uff01</li> </ul> <p>\u5f88\u663e\u7136\uff0c\u6211\u70c2\u5c3e\u4e86\uff0c\u7b2c\u4e94\u7ae0\u5185\u5bb9\u5f88\u7b80\u964b\uff0c\u7b2c\u4e03\u7ae0\u57fa\u672c\u6ca1\u5199\uff0c\u5b9e\u5728\u662f\u8003\u524d\u6765\u4e0d\u53ca\u5199\u5b8c\u4e86\u3002\u4f46\u662f\u6211\u53ef\u4ee5\u4fdd\u8bc1\u9664\u6b64\u4e4b\u5916\u7684\u5185\u5bb9\u6211\u90fd\u662f\u4ed4\u7ec6\u63a8\u6572\u540e\u624d\u5199\u51fa\u6765\u7684orz\u3002</p> <p>\u6b64\u5916\uff0c\u5bf9\u4e8e\u6211\u5df2\u7ecf\u5199\u4e86\u7684\u5185\u5bb9\u6709\u7591\u4e49\uff0c\u6216\u662f\u5e0c\u671b\u80fd\u8865\u5145\u6211\u6ca1\u5199\u7684\u5185\u5bb9\uff0c\u6b22\u8fce\u63d0\u4ea4 PR\uff01</p> <p>List</p> <p>\u8865\u5929\u65f6\u5019\u7684\u4e00\u70b9\u60f3\u6cd5\uff0c\u56e0\u4e3a\u8bfe\u672c\u6bcf\u4e00\u7ae0\u90fd\u6709\u4e00\u4e2a summary\uff0c\u6240\u4ee5\u5982\u679c\u8981\u770b\u4e66\u7684\u8bdd\u6216\u8bb8\u53ef\u4ee5\u5148\u770b\u90a3\u4e2a summary \u518d\u770b\u5177\u4f53\u7684\u3002</p> <ul> <li> Chap 1 Digital Systems and Information</li> <li> Chap 2 Combinational Logic Circuits</li> <li> Chap 3 Combinational Logic Design</li> <li> Chap 4 Sequential Circuits</li> <li> Chap 5 Digital Hardware Implementation \uff08\u7565\u7b80\u7565\uff09</li> <li> Chap 6 Registers &amp; Register Transfers</li> <li> Chap 7 Memory Basics \uff08\u6ca1\u5199\uff09</li> <li> Glossary</li> </ul>"},{"location":"cour_note/D2QD_DigitalDesign/Chap01/","title":"Chap 1 Digital Systems and Information","text":"<p> \u7ea6 2053 \u4e2a\u5b57  9 \u884c\u4ee3\u7801  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 7 \u5206\u949f</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap01/#\u4fe1\u606f\u8868\u8fbe--information-representation","title":"\u4fe1\u606f\u8868\u8fbe | Information Representation","text":"<p>\u73b0\u5b9e\u4e16\u754c\u4e2d\u7684\u4fe1\u606f\u5f80\u5f80\u662f \u8fde\u7eed(continuous) \u7684\uff0c\u4f46\u5728\u4eba\u9020\u7269\u7684\u4e16\u754c\u4e2d\uff0c\u5927\u90e8\u5206\u4fe1\u606f\u90fd\u662f \u79bb\u6563(discrete) \u7684\u3002</p> <p>\u5728\u7535\u5b50\u4fe1\u606f\u7cfb\u7edf\u4e2d\uff0c\u4fe1\u53f7\u5206\u4e3a \u6a21\u62df\u4fe1\u53f7(analog signal) \u548c \u6570\u5b57\u4fe1\u53f7(digital signal) \u4e24\u79cd\u3002\u5176\u4e2d\uff0c\u5728 \u6570\u5b57\u4fe1\u53f7(digital signal) \u4e2d\u53c8\u6709\u591a\u79cd\u8868\u793a\u65b9\u6cd5\uff0c\u5982\u4eca\u6211\u4eec\u6700\u5e38\u7528\u7684\u662f \u4e8c\u8fdb\u5236(binary)\u3002\u5bf9\u5e94\u5230\u7535\u8def\u5c42\u9762\uff0c\u6211\u4eec\u5e38\u5e38\u7528 \u9ad8\u7535\u4f4d(HIGH) \u548c \u4f4e\u7535\u4f4d(LOW) \u6765\u8868\u5f81 <code>1</code> \u548c <code>0</code>\u3002</p> <p></p> <p>\u503c\u5f97\u6ce8\u610f\u7684\u662f\uff0c\u5728\u8f93\u5165\u548c\u8f93\u51fa\u4e2d\uff0c\u9ad8\u4f4e\u7535\u4f4d\u7684\u63a5\u53d7\u8303\u56f4\u662f\u4e0d\u540c\u7684\u3002\u53ef\u4ee5\u53d1\u73b0\uff0c\u8f93\u5165\u7684\u5224\u5b9a\u8303\u56f4\u6bd4\u8f93\u51fa\u7684\u5224\u5b9a\u8303\u56f4\u5927\uff0c\u5373 \u5bbd\u8fdb\u4e25\u51fa\u3002\u5176\u76ee\u7684\u662f\u4e3a\u4e86\u8fdb\u4e00\u6b65\u63d0\u9ad8\u7535\u8def\u5728\u566a\u97f3\u7b49\u5f02\u5e38\u5f71\u54cd\u4e0b\u4e5f\u80fd\u6b63\u5e38\u8868\u73b0\u7684\u80fd\u529b\u3002</p> HIGH input LOW input HIGH output LOW output 0.6 ~ 1.1 -0.1 ~ 0.4 0.9 ~ 1.1 -0.1 ~ 0.1 <p>\u6216\u8bb8\u4f60\u4e5f\u5df2\u7ecf\u6ce8\u610f\u5230\u4e86\uff0c\u5728\u56fe\u4e2d\uff0cHIGH \u7684\u63a5\u53d7\u8303\u56f4\u548c LOW \u7684\u63a5\u53d7\u8303\u56f4\u4e4b\u95f4\u8fd8\u5b58\u5728\u4e00\u6bb5\u533a\u57df\u3002\u843d\u5728\u8fd9\u4e00\u90e8\u5206\u7684\u7535\u5e73\u662f \u672a\u5b9a\u4e49(undefined) \u7684\uff0c\u4e5f\u88ab\u79f0\u4e3a\u662f \u6d6e\u52a8(floating) \u7684\u3002\u5982\u679c\u8f93\u51fa\u7684\u7535\u5e73\u662f\u5728\u6d6e\u52a8\u533a\u95f4\u7684\uff0c\u90a3\u4e48\u5176\u8ba4\u5b9a\u503c\u5c06\u662f\u968f\u673a\u7684\u3002</p> <p>\u4e8b\u5b9e\u4e0a\uff0c\u5728\u4fe1\u606f\u7684\u5bf9\u5e94\u4e0a\uff0c\u867d\u7136\u5c06\u9ad8\u4f4e\u7535\u5e73\u540c HIGH/LOW \u8054\u7cfb\u662f\u5f88\u81ea\u7136\u7684\uff0c\u4f46\u662f\u5c06\u4ed6\u4eec\u540c true/false \u6216\u8005 1/0 \u8054\u7cfb\u5176\u5b9e\u5e76\u4e0d\u552f\u4e00\u3002\u4f46\u662f\u5728\u4e00\u822c\u60c5\u51b5\u4e0b\uff08\u6211\u4eec\u79f0\u4e4b\u4e3a positive logic\uff09\uff0c\u6211\u4eec\u90fd\u8ba4\u4e3a HIGH ~ true ~ 1\uff0c LOW ~ false ~ 0\u3002</p> <p>\u53ef\u4ee5\u53d1\u73b0\uff0c(b) \u56fe\u4e2d\u7684\u6a21\u62df\u4fe1\u53f7\u5728\u7ecf\u8fc7\u6211\u4eec\u7684\u5668\u4ef6\u540e\uff0c\u4f1a\u88ab\u8ba4\u4e3a\u662f (c) \u56fe\u6240\u793a\u7684\u4fe1\u53f7\u3002\u800c\u8fd9\u4e9b\u64cd\u4f5c\u5728\u786c\u4ef6\u5c42\u9762\uff0c\u6211\u4eec\u901a\u8fc7 \u6676\u4f53\u7ba1(transistors) \u6765\u5b9e\u73b0\u3002</p> <p>\u8fd9\u4e5f\u7275\u626f\u5230\u6211\u4eec\u4e3a\u4ec0\u4e48\u6700\u7ec8\u4f7f\u7528\u4e8c\u8fdb\u5236\u6765\u8868\u793a\u4fe1\u606f\u3002\u4e00\u65b9\u9762\u662f\u56e0\u4e3a\u4e8c\u503c\u5668\u4ef6\u6bd4\u8f83\u5e38\u89c1\uff0c\u4ea6\u5373\u8fd9\u91cc\u63d0\u5230\u7684\u6676\u4f53\u7ba1\uff1b\u53e6\u5916\u4e00\u65b9\u9762\u662f\u4f7f\u7528\u4e8c\u8fdb\u5236\u53ef\u4ee5\u964d\u4f4e\u7535\u8def\u6210\u672c\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap01/#\u8ba1\u7b97\u673a\u7cfb\u7edf\u8bbe\u8ba1\u4e2d\u7684\u62bd\u8c61\u5c42--abstraction-layers-in-computer-systems-design","title":"\u8ba1\u7b97\u673a\u7cfb\u7edf\u8bbe\u8ba1\u4e2d\u7684\u62bd\u8c61\u5c42 | Abstraction Layers in Computer Systems Design","text":"\u8d8a\u4e0a\u5c42\u62bd\u8c61\u7a0b\u5ea6\u8d8a\u9ad8 Algorithms Programing Languages Operating Systems Instruction Set Architecture Microarchitecture Register Transfers Logic Gates Transistor Circuits"},{"location":"cour_note/D2QD_DigitalDesign/Chap01/#\u6570\u5b57\u7cfb\u7edf--number-systems","title":"\u6570\u5b57\u7cfb\u7edf | Number Systems","text":"<p>\u9996\u5148\u9700\u8981\u6d89\u53ca\u7684\u95ee\u9898\u662f\u8fdb\u5236\u8f6c\u6362\u3002</p> <p>\u5bf9\u4e8e\u4e00\u4e2a \\(r\\) \u8fdb\u5236\u6570\uff0c\u5b83\u4e00\u822c\u88ab\u5199\u6210\u8fd9\u6837\uff1a</p> \\[ (A_{n-1}A_{n-2}...A_1A_0A_{-1}...A_{-(m-1)}A_{-m})_{r} \\] <p>\u800c\u5b83\u5bf9\u5e94\u7684\u5341\u8fdb\u5236\u771f\u503c\u4e3a\uff1a</p> \\[ \\begin{aligned} \\sum_{i=-m}^{n-1} A_ir^i\\;\\; =&amp;A_{n-1}r^{n-1}+A_{n-2}r^{n-2}+...\\\\ +&amp;A_{1}r^{1}+A_0r^0+A_{-1}r^{-1}+...\\\\ +&amp;A_{-(m-1)}r^{m-1}+A_{-m}r^{-m} \\end{aligned} \\] <p>\u8ba1\u7b97\u673a\u9886\u57df\u5e38\u89c1\u7684\u8fdb\u5236\u4e3b\u8981\u662f \u4e8c\u8fdb\u5236(binary)\uff0c\u516b\u8fdb\u5236(octal)\uff0c\u5341\u8fdb\u5236(decimal) \u548c \u5341\u516d\u8fdb\u5236(hexadecimal)\u3002</p> <p>\u5176\u4e2d\u4e8c\u3001\u516b\u3001\u5341\u516d\u8fdb\u5236\u4e4b\u95f4\u7684\u8f6c\u6362\u975e\u5e38\u7b80\u5355\uff0c\u5b58\u5728\u591a\u4f4d\u5230\u4e00\u4f4d\u4e4b\u95f4\u7684\u65e0\u540e\u6548\u6027\u6620\u5c04\uff0c\u4f8b\u5982\u4e8c\u8fdb\u5236\u8f6c\u6362\u5230\u5341\u516d\u8fdb\u5236\u53ea\u9700\u8981\u5c06\u4ece\u4f4e\u5230\u9ad8\u6bcf\u56db\u4f4d\u8f6c\u5316\u6210\u5341\u516d\u8fdb\u5236\u4e2d\u7684\u4e00\u4f4d\u5373\u53ef\u3002</p> <p>\u9700\u8981\u6ce8\u610f\uff0c\u7531\u4e8e\u4e8c\u8fdb\u5236\u548c\u5341\u8fdb\u5236\u5728\u96f6\u4f4d\u4e0a\u7684\u6743\u91cd\u76f8\u540c\uff0c\u8fd9\u610f\u5473\u7740\u5728\u6574\u6570\u90e8\u5206\uff0c\u4e8c\u8fdb\u5236\u548c\u5341\u8fdb\u5236\u662f\u53ef\u4ee5\u76f8\u4e92\u7cbe\u51c6\u8f6c\u5316\u7684\uff08\u5373\u6700\u5c0f\u7cbe\u5ea6\u662f\u4e00\u81f4\u7684\uff0c\u90fd\u662f 1\uff09\uff1b\u7136\u800c\u8be5\u6027\u8d28\u5728\u5c0f\u6570\u90e8\u5206\u5e76\u4e0d\u6210\u7acb\uff08\u56e0\u4e3a\u5c0f\u6570\u90e8\u5206\u4e0d\u5b58\u5728\u201c\u6700\u5c0f\u7cbe\u5ea6\u201d\u4e00\u8bf4\uff09\uff0c\u5373\u5341\u8fdb\u5236\u65e0\u6cd5\u7cbe\u51c6\u8f6c\u5316\u4e3a\u4e8c\u8fdb\u5236\uff0c\u4f46\u4e8c\u8fdb\u5236\u53ef\u4ee5\u8f6c\u5316\u4e3a\u5341\u8fdb\u5236\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap01/#\u7b97\u672f\u8fd0\u7b97--arithmetic-operations","title":"\u7b97\u672f\u8fd0\u7b97 | Arithmetic Operations","text":"<p>\u8fd9\u91cc\u6d89\u53ca\u7684\u4e3b\u8981\u662f \u52a0\u6cd5(Addition)\u3001\u51cf\u6cd5(Subtraction)\u3001\u4e58\u6cd5(Multiplication)\u3002</p> <p>\u6574\u4f53\u6d41\u7a0b\u548c\u5c0f\u5b66\u7ad6\u5f0f\u52a0\u6cd5\u662f\u4e00\u81f4\u7684\u3002</p> \u4e8c\u8fdb\u5236\u8fd0\u7b97 <p> </p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap01/#\u7f16\u7801--codes","title":"\u7f16\u7801 | Codes","text":"<p>\u4e8c\u8fdb\u5236\u7f16\u7801\u4e3b\u8981\u5206\u4e3a\u8fd9\u4e48\u51e0\u79cd\uff1a</p> <ul> <li>Numeric<ul> <li>\u5fc5\u987b\u8868\u8fbe\u4e00\u5b9a\u8303\u56f4\u5185\u7684\u6570\u5b57\uff1b</li> <li>\u80fd\u591f\u652f\u6301\u7b80\u5355\u4e14\u666e\u904d\u7684\u8ba1\u7b97\uff1b</li> <li>\u548c\u4e8c\u8fdb\u5236\u6570\u503c\u672c\u8eab\u6709\u8f83\u5927\u5173\u8054\uff1b</li> </ul> </li> <li>Non-numeric<ul> <li>\u76f8\u5bf9\u7075\u6d3b\uff0c\u56e0\u4e3a\u4e0d\u9700\u8981\u9002\u914d\u666e\u904d\u7684\u8fd0\u7b97\u6cd5\u5219\uff1b<ul> <li>\u7075\u6d3b\u6027\u6307\uff0c\u4fdd\u8bc1\u7f16\u7801\u6620\u5c04\u5173\u7cfb\u662f\u552f\u4e00\u7684\u7684\u60c5\u51b5\u4e0b\u90fd\u53ef\u4ee5\u79f0\u4e3a\u5408\u6cd5\u7f16\u7801\uff1b</li> </ul> </li> <li>\u548c\u4e8c\u8fdb\u5236\u6570\u503c\u672c\u8eab\u672a\u5fc5\u6709\u5173\u7cfb\uff1b</li> </ul> </li> </ul>"},{"location":"cour_note/D2QD_DigitalDesign/Chap01/#\u72ec\u70ed\u7801--\u72ec\u51b7\u7801","title":"\u72ec\u70ed\u7801 &amp; \u72ec\u51b7\u7801","text":"<p>\u72ec\u70ed\u7801(one-hot) \u8981\u6c42\u6bd4\u7279\u5411\u91cf\u4e2d\u53ea\u6709\u4e00\u4f4d\u662f <code>1</code>\uff1b\u5bf9\u5e94\u7684\u8fd8\u6709 \u72ec\u51b7\u7801(one-cold)\u3002</p> <p>\u4f7f\u7528\u8fd9\u79cd\u7f16\u7801\u7684\u597d\u5904\u662f\uff0c\u51b3\u5b9a\u6216\u6539\u53d8\u72b6\u6001\u673a\u76ee\u524d\u7684\u72b6\u6001\u7684\u6210\u672c\u76f8\u5bf9\u8f83\u4f4e\uff0c\u5bb9\u6613\u8bbe\u8ba1\u4e5f\u5bb9\u6613\u68c0\u6d4b\u975e\u6cd5\u884c\u4e3a\u7b49\u3002</p> <p>\u4f46\u662f\u76f8\u5bf9\u5e94\u7684\uff0c\u7f3a\u70b9\u662f\u4fe1\u606f\u8868\u793a\u7387\u8f83\u4f4e\uff0c\u975e\u6cd5\u72b6\u6001\u975e\u5e38\u591a\u800c\u6709\u6548\u72b6\u6001\u5f88\u5c11\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap01/#bcd-\u7801","title":"BCD \u7801","text":"<p>\u7531\u4e8e\u771f\u5b9e\u4e16\u754c\u4e2d\u5927\u90e8\u5206\u6570\u636e\u8868\u8ff0\u90fd\u662f\u4ee5\u5341\u8fdb\u5236\u5b9e\u73b0\u7684\uff0c\u6240\u4ee5\u6211\u4eec\u9700\u8981\u7814\u7a76\u5982\u4f55\u7528\u4e8c\u8fdb\u5236\u6765\u8868\u793a\u5341\u8fdb\u5236\u3002</p> <p>\u9996\u5148\uff0c\u4e00\u4f4d\u4e8c\u8fdb\u5236\u6570\u80fd\u5305\u542b\u7684\u4fe1\u606f\u662f 1bit\uff0c\u4e5f\u5c31\u662f\u4e00\u4e2a\u201c\u771f\u201d\u6216\u8005\u4e00\u4e2a\u201c\u5047\u201d\u3002\u6211\u4eec\u79f0\u4e00\u4e2a\u62e5\u6709 n \u4e2a\u5143\u7d20\u7684\u4e8c\u8fdb\u5236\u5411\u91cf\u4e3a\u4e00\u4e2a n\u4f4d\u4e8c\u8fdb\u5236\u7f16\u7801(n-bit binary code)\u3002\u4e00\u4e2a n \u4f4d\u4e8c\u8fdb\u5236\u6570\u62e5\u6709 \\(2^{n}\\) \u79cd\u53ef\u80fd\u7684\u7ec4\u5408\uff0c\u56e0\u800c\u53ef\u4ee5\u8868\u793a \\(2^n\\) \u79cd\u4fe1\u606f\u3002</p> <p>\u800c\u6211\u4eec\u9700\u8981\u8bbe\u8ba1\u7684\u7f16\u7801\u7cfb\u7edf\uff0c\u5c31\u662f\u5c06\u6211\u4eec\u9700\u8981\u7684\u4fe1\u606f\u6620\u5c04\u5230\u8fd9 \\(2^n\\) \u4e2a\u201c\u7a7a\u4f4d\u201d\u4e2d\u3002\u5f53\u7136\uff0c\u5f53\u6211\u4eec\u9700\u8981\u8868\u793a\u7684\u4fe1\u606f\u6570\u91cf\u5e76\u4e0d\u662f 2 \u7684\u5e42\u6b21\u65f6\u5019\uff0c\u4f1a\u51fa\u73b0\u4e00\u4e9b \u672a\u5206\u914d(unassigned) \u7684\u6bd4\u7279\u7ec4\u5408\u3002</p> <p>\u800c\u5728\u8fd9\u79cd\u7f16\u7801\u4e2d\uff0c\u6700\u5e38\u7528\u7684\u5c31\u662f BCD\u7801(binary-coded demical)\u3002\u5176\u6838\u5fc3\u601d\u8def\u5c31\u662f\uff0c\u5c06\u5341\u8fdb\u5236\u7684\u6bcf\u4e00\u4f4d \u5206\u522b \u7528 \u771f\u503c\u76f8\u7b49\u7684 4 \u4f4d\u4e8c\u8fdb\u5236 \u8868\u793a\uff0c\u5373 <code>0</code> ~ <code>9</code> \u5206\u522b\u7528 <code>0000</code> ~ <code>1001</code> \u8868\u793a\u3002</p> DecimalSymbol BCDDigit <code>0</code> <code>0000</code> <code>1</code> <code>0001</code> <code>2</code> <code>0010</code> <code>3</code> <code>0011</code> <code>4</code> <code>0100</code> <code>5</code> <code>0101</code> <code>6</code> <code>0110</code> <code>7</code> <code>0111</code> <code>8</code> <code>1000</code> <code>9</code> <code>1001</code> <p>eg</p> \\[ \\mathrm{ (185)_{10}\\;=\\;(0001\\;1000\\;0101)_{BCD}\\;=\\;(10111001)_2 } \\]"},{"location":"cour_note/D2QD_DigitalDesign/Chap01/#\u4f59\u4e09\u7801","title":"\u4f59\u4e09\u7801","text":"<p>\u4e00\u79cd BCD\u7801 \u7684\u6539\u8fdb\u662f \u4f59\u4e09\u7801(Excess3)\u3002\u5176\u6838\u5fc3\u601d\u8def\u662f\u5728 BCD\u7801\u7684\u57fa\u7840\u4e0a\uff0c\u589e\u52a0\u4e00\u4e2a\u5927\u5c0f\u4e3a 3 \u7684\u504f\u79fb\u91cf\u3002</p> DecimalSymbol Excess3Digit <code>0</code> <code>0011</code> <code>1</code> <code>0100</code> <code>2</code> <code>0101</code> <code>3</code> <code>0110</code> <code>4</code> <code>0111</code> <code>5</code> <code>1000</code> <code>6</code> <code>1001</code> <code>7</code> <code>1010</code> <code>8</code> <code>1011</code> <code>9</code> <code>1100</code> <p>\u4e3a\u4ec0\u4e48\u662f 3 \u5462\uff1f\u9996\u5148\u8fd9\u4e2a 3 \u6765\u81ea\u4e8e \\(\\frac{16-10}{2}\\)\uff0c\u4e5f\u5c31\u662f 8421 \u7801\u7684\u5bb9\u91cf\u51cf\u53bb\u6211\u4eec\u9700\u8981\u8868\u793a\u7684\u6570\u5b57\u6570\u91cf\uff0c\u518d\u9664\u4ee5\u4e8c\u3002\u8fd9\u6837\u7684\u597d\u5904\u662f\uff0c\u5341\u8fdb\u5236\u4e0b\u80fd\u8fdb\u4f4d\u7684\u4e24\u4e2a\u6570\uff0c\u5728\u4f59\u4e09\u7801\u4e0b\u76f8\u52a0\u4e5f\u521a\u597d\u8fdb\u4f4d\u3002</p> <p>\u4f46\u662f\u9700\u8981\u5f3a\u8c03\u7684\u4e00\u70b9\u662f\uff0c\u7f16\u7801\u548c\u6570\u503c\u662f\u5b58\u5728\u533a\u522b\u7684\uff0c\u867d\u7136\u6211\u4eec\u63d0\u5230\u4e86\u4f59\u4e09\u7801\u76f8\u52a0\uff0c\u4f46\u662f\u7f16\u7801\u505a\u8fd0\u7b97\u591a\u6570\u60c5\u51b5\u4e0b\u662f\u6ca1\u6709\u610f\u4e49\u7684\u3002\u201c\u8fd0\u7b97\u201d\u7684\u4e3b\u4f53\u66f4\u591a\u662f\u6570\u503c\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap01/#\u683c\u96f7\u7801","title":"\u683c\u96f7\u7801","text":"<p>\u6b64\u5916\uff0c\u8fd9\u91cc\u4e0d\u5f97\u4e0d\u63d0\u7684\u53e6\u5916\u4e00\u4e2a\u7f16\u7801\u662f \u683c\u96f7\u7801(Gray Codes)\u3002\u683c\u96f7\u7801\u7684\u7279\u5f81\uff0c\u4e5f\u662f\u4ed6\u7684\u4f18\u70b9\uff0c\u5c31\u662f\u76f8\u90bb\u7684\u4e24\u4e2a\u6570\u5728\u4e8c\u8fdb\u5236\u4e0b\u7684\u8868\u793a\u53ea\u5dee\u4e00\u4f4d\uff08\u5f53\u5728\u5360\u6ee1\u65f6\uff0c\u5bf9\u4e8e\u6574\u4e2a\u7f16\u7801\u5e8f\u5217\uff0c\u73af\u72b6\u6ee1\u8db3\u8be5\u6761\u4ef6\uff09\u3002</p> <p>\u6bd4\u5982\u6709\u5982\u4e0b\u5e94\u7528\uff1a</p> <p></p> <p>\u4ee5\u53ca\u5728\u8bb8\u591a\u72b6\u6001\u63a7\u5236\u4e2d\u90fd\u6709\u7740\u5e7f\u6cdb\u7684\u5e94\u7528\u3002</p> <p>\u4ece\u7b14\u8bd5\u505a\u9898\u89d2\u5ea6\u6765\u8bf4\uff0c\u683c\u96f7\u7801\u6700\u9ebb\u70e6\u7684\u5176\u5b9e\u662f\u4e0e\u5341\u8fdb\u5236\u6570\u7684\u8f6c\u6362\u3002\uff08\u6b64\u5904 @CSP-S2019-Day1-T1\uff09</p> <p>\u4e2a\u4eba\u8ba4\u4e3a\u6700\u597d\u505a\u7684\u505a\u6cd5\u5c31\u662f\uff0c\u5047\u8bbe\u6211\u4eec\u8981\u627e\u7684\u662f\u7b2c k \u4e2a\u683c\u96f7\u7801\uff0c\u5219\u5bf9\u5e94\u7684\u683c\u96f7\u7801\u4e3a\uff1a</p> \\[ k \\;\\;\\mathrm{XOR}\\;\\; (k&gt;&gt;1) \\]"},{"location":"cour_note/D2QD_DigitalDesign/Chap01/#ascii-\u7801","title":"ASCII \u7801","text":"<p>\u5b57\u7b26\u7f16\u7801\u6240\u4f7f\u7528\u7684\u4e00\u822c\u662f ASCII \u7f16\u7801\uff0c\u7531\u4e8e ASCII \u5df2\u7ecf\u662f\u8001\u751f\u5e38\u8c08\u4e86\uff0c\u6240\u4ee5\u8fd9\u91cc\u4e0d\u518d\u5c55\u5f00\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap01/#\u5947\u5076\u6821\u9a8c\u4f4d","title":"\u5947\u5076\u6821\u9a8c\u4f4d","text":"<p>\u4fe1\u9053\u7f16\u7801\u4e0e\u4fe1\u6e90\u7f16\u7801\uff1a</p> <p></p> <p>\u5728\u4fe1\u53f7\u4f20\u8f93\u8fc7\u7a0b\u4e2d\uff0c\u53ef\u80fd\u7531\u4e8e\u73af\u5883\u5e72\u6270\u7b49\u539f\u56e0\uff0c\u51fa\u73b0\u5404\u79cd\u4fe1\u53f7\u6296\u52a8\uff0c\u6240\u4ee5\u4e3a\u4e86\u4fdd\u8bc1\u6570\u636e\u7684\u53ef\u4fe1\u5ea6\uff0c\u6211\u4eec\u9700\u8981\u4e00\u4e2a\u9519\u8bef\u68c0\u6d4b\u673a\u5236\u3002</p> <p>\u4e00\u79cd\u5e38\u89c1\u7684\u65b9\u6cd5\u662f \u5197\u4f59(Redundancy)\uff0c\u5373\u52a0\u5165\u4e00\u4e9b\u989d\u5916\u7684\u4fe1\u606f\u7528\u4ee5\u6821\u9a8c\u3002</p> <pre><code>graph TD\nA[Error Detection Techniques]\nB[Single Parity Check]\nC[Cyclic Redundancy Check]\nD[Check Sum]\n\nA--&gt;B\nA--&gt;C\nA--&gt;D</code></pre> <p>\u5176\u4e2d\u4e00\u79cd\u505a\u6cd5\u662f\u5f15\u5165 \u5947\u5076\u6821\u9a8c\u4f4d(Parity Bit)\u3002\u5b83\u5206\u4e3a \u5947\u6821\u9a8c(Odd Parity) \u548c \u5076\u6821\u9a8c(Even Parity)\u3002\u5206\u522b\u901a\u8fc7\u5f15\u5165\u989d\u5916\u7684\u4e00\u4f4d\uff0c\u6765\u4fdd\u8bc1\u6574\u4e2a\u4fe1\u606f\u4e32\u4e2d <code>1</code> \u7684\u6570\u91cf\u662f\u5947\u6570/\u5076\u6570\u3002</p> <ul> <li>\u6bd4\u5982\uff0c\u5982\u679c\u6211\u4eec\u91c7\u7528\u5076\u6821\u9a8c\uff0c\u539f\u59cb\u4fe1\u606f\u4e3a <code>1101</code>\uff0c\u5176\u4e2d\u6709 3 \u4e2a <code>1</code>\uff0c\u8fd9\u65f6\u6211\u4eec\u5728\u540e\u9762\u518d\u52a0\u4e0a\u4e00\u4e2a <code>1</code>\uff0c\u4fdd\u8bc1\u4e86\u6574\u4e2a\u4fe1\u606f\u4e32\u4e2d\u6709\u5076\u6570\u4e2a <code>1</code>\uff1b\u6216\u8005\u5982\u679c\u539f\u59cb\u4fe1\u606f\u4e3a <code>1001</code>\uff0c\u5176\u4e2d\u6709 2 \u4e2a <code>1</code>\uff0c\u8fd9\u65f6\u6211\u4eec\u5219\u5728\u540e\u9762\u52a0\u4e00\u4e2a <code>0</code>\u3002\u6b64\u65f6\uff0c\u5982\u679c\u4f20\u8f93\u8fc7\u7a0b\u4e2d\u51fa\u73b0\u4e86\u95ee\u9898\uff0c\u90a3\u4e48 <code>1</code> \u7684\u6570\u91cf\u5f88\u53ef\u80fd\u53d8\u6210\u4e86\u4e00\u4e2a\u5947\u6570\uff0c\u6b64\u65f6\u6211\u4eec\u5c31\u77e5\u9053\uff0c\u8fd9\u4e2a\u4fe1\u606f\u662f\u4e0d\u5bf9\u7684\u3002</li> </ul>"},{"location":"cour_note/D2QD_DigitalDesign/Chap02/","title":"Chap 2 Combinational Logic Circuits","text":"<p> \u7ea6 8091 \u4e2a\u5b57  25 \u884c\u4ee3\u7801  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 27 \u5206\u949f</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap02/#\u903b\u8f91\u8fd0\u7b97","title":"\u903b\u8f91\u8fd0\u7b97","text":"<p>\u903b\u8f91\u8fd0\u7b97\u7684\u5bf9\u8c61\u662f\u5e03\u5c14\u53d8\u91cf\uff0c\u4e5f\u5c31\u662f 0/1 \u4e8c\u503c\u3002</p> <p>\u4e3b\u8981\u7684\u8fd0\u7b97\u5c31\u662f \u4e0e(AND)\uff0c\u6216(OR)\uff0c\u975e(NOT)\uff0c\u5f02\u6216(XOR)\uff0c\u4ee5\u53ca \u4e0e\u975e(NAND)\uff0c\u6216\u975e(NOR)\uff0c\u540c\u6216(XNOR)\u3002</p> <p>\u9ad8\u7ef4</p> <p>\u591a\u8f93\u5165\u7684\u5f02\u6216\u548c\u540c\u6216\u88ab\u79f0\u4e3a\u5947\u51fd\u6570\u548c\u5076\u51fd\u6570\u3002</p> <p>\u53ef\u4ee5\u7528\u5b83\u4eec\u6765\u5b9e\u73b0\u5947\u6821\u9a8c\u548c\u5076\u6821\u9a8c\u3002</p> <p>\u800c\u4e14\u89c2\u5bdf\u5176\u5361\u8bfa\u56fe\u7684\u5f62\u72b6\uff08\u68cb\u76d8\u5f62\uff09\uff0c\u53ef\u4ee5\u53d1\u73b0\uff0c\u5b83\u4eec\u662f\u5929\u7136\u4f18\u5316\u7684\uff0c\u5373\u4e0d\u53ef\u4f18\u5316\u7684\u3002</p> <p>\u8fd0\u7b97\u89c4\u5219\u633a\u7b80\u5355\u7684\uff0c\u5728\u6b64\u7565\u53bb\u3002</p> <p>\u6bd4\u8f83\u57fa\u7840\u7684\uff0c\u9700\u8981\u4e86\u89e3\u4e0e\u6216\u975e\u7684\u7b26\u53f7\u8868\u793a\u3002</p> <ul> <li><code>A</code> <code>AND</code> <code>B</code> \u53ef\u5199\u4f5c \\(A\\cdot B\\) \u6216\u8005 \\(AB\\)\uff1b</li> <li><code>A</code> <code>OR</code> <code>B</code> \u53ef\u5199\u4f5c \\(A+B\\)\uff1b</li> <li><code>NOT A</code> \u53ef\u5199\u4f5c \\(\\overline{A}\\)\uff1b</li> </ul> <p>\u7531\u6b64\u53ef\u4ee5\u8fdb\u884c\u4e00\u4e9b\u7ec4\u5408\uff0c\u4f8b\u5982\uff1a</p> <ul> <li><code>A</code> <code>NOR</code> <code>B</code> \u53ef\u5199\u4f5c \\(\\overline{A+B}\\)\uff1b</li> <li><code>A</code> <code>NAND</code> <code>B</code> \u53ef\u5199\u4f5c \\(\\overline{A\\cdot B}\\)\uff1b</li> </ul> <p>\u518d\u6b21\u8fd8\u9700\u8981\u63d0\u5230\u7684\u662f \u5fb7\u00b7\u6469\u6839\u5b9a\u5f8b(De Morgan's Laws)\uff0c\u5176\u8868\u8ff0\u4e3a\uff1a</p> <ul> <li>\\(\\overline{A+B} = \\overline{A}\\cdot\\overline{B}\\)\uff1b</li> <li>\\(\\overline{A\\cdot B} = \\overline{A}+\\overline{B}\\)\uff1b</li> </ul>"},{"location":"cour_note/D2QD_DigitalDesign/Chap02/#\u903b\u8f91\u95e8","title":"\u903b\u8f91\u95e8","text":"<p>\u903b\u8f91\u95e8\u662f\u5728\u786c\u4ef6\u5c42\u9762\u4e0a\u5b9e\u73b0\u5e03\u5c14\u4ee3\u6570\u7684\u903b\u8f91\u5355\u5143\u3002\u5176\u64cd\u4f5c\u5bf9\u8c61\u4e3a\u9ad8\u4f4e\u7535\u5e73\u3002</p> <p></p> <p>\u5982\u56fe\uff0c(a)\u4e2d\u7ed8\u5236\u4e86\u4e09\u4e2a\u5e38\u7528\u903b\u8f91\u95e8\u7684\u7b26\u53f7\uff1b(b)\u4e2d\u5219\u63cf\u8ff0\u4e86\u8fd9\u4e9b\u8fd0\u7b97\u5728 \u65f6\u5e8f\u56fe(timing diagram) \u4e2d\u7684\u72b6\u6001\uff1b(c)\u5219\u63cf\u8ff0\u4e86\u5728\u5ef6\u65f6\uff08\u89c1\u4e0b\uff09\u6548\u5e94\u4e0b\u7684\u65f6\u5e8f\u56fe\u3002</p> <p>\u8fd8\u6709\u4e00\u4e2a\u6ce8\u610f\u70b9\u662f\uff0c\u975e\u95e8\u5176\u5b9e\u66f4\u591a\u7684\u88ab\u79f0\u4e3a inverter\uff0c\u800c\u975e NOT\u3002</p> <p>\u4f46\u662f\u7531\u4e8e\u662f\u7269\u7406\u5c42\u9762\u7684\u5b9e\u73b0\uff0c\u6240\u4ee5\u4f1a\u6709\u4e00\u4e9b\u903b\u8f91\u8fd0\u7b97\u5c42\u9762\u4e0d\u4f1a\u51fa\u73b0\u7684\u95ee\u9898\uff0c\u6bd4\u5982 \u5ef6\u65f6(delay)\u3002</p> <p></p> <p>Source: https://en.wikipedia.org/wiki/Signal_propagation_delay#Electronics</p> <p>\u5ef6\u65f6\u7684\u957f\u77ed\u4e0e\u5f88\u591a\u56e0\u7d20\u6709\u5173\uff0c\u53d6\u51b3\u4e8e\u903b\u8f91\u95e8\u7684\u5b9e\u73b0\u6280\u672f\u3002\u800c\u4e14\u901a\u5e38\u6765\u8bf4\uff0c\u5bf9\u4e8e\u4e0d\u540c\u8fd0\u7b97\u53c2\u6570\uff0c\u5176\u5ef6\u65f6\u4e5f\u4f1a\u6709\u4e0d\u540c\u3002</p> <p>\u6b64\u5916\uff0c\u4e0e\u95e8\u548c\u6216\u95e8\u53ef\u80fd\u6709\u66f4\u591a\u7684\u8f93\u5165\u5f15\u811a\uff0c\u5982\u4e0b\uff1a</p> <p></p> <p>\u81f3\u6b64\uff0c\u7ed9\u51fa\u4e86 AND, OR, NOT \u4e09\u4e2a\u95e8\u7684\u7b26\u53f7\u8868\u793a\uff0c\u7c7b\u4f3c\u4e0a\u4e00\u5c0f\u8282\u63d0\u5230\u7684\u90a3\u6837\uff0c\u6211\u4eec\u4e5f\u53ef\u4ee5\u5229\u7528\u8fd9\u4e09\u4e2a\u57fa\u7840\u7684\u95e8\u7535\u8def\u6765\u6784\u6210\u5176\u4ed6\u7684\u95e8\u7535\u8def\uff08\u867d\u7136\u901a\u5e38\u6765\u8bf4\uff0c\u6211\u4eec\u53ef\u80fd\u662f\u901a\u8fc7 NAND + NOT \u6765\u5b9e\u73b0 AND \u7684\uff09\u3002</p> <p>\u4e8e\u662f\u53c8\u5f15\u7533\u51fa\u4e00\u4e2a\u6982\u5ff5\u2014\u2014\u901a\u7528\u95e8(Universal Gate)\u3002\u4e00\u4e2a\u529f\u80fd\u5b8c\u5168\u7684\uff0c\u80fd\u591f\u8868\u793a\u5176\u4ed6\u6240\u6709\u95e8\u7684\u903b\u8f91\u95e8\u88ab\u79f0\u4e3a\u901a\u7528\u95e8\uff0c\u5728\u6211\u4eec\u5b66\u8fc7\u7684\u903b\u8f91\u95e8\u4e2d\uff0cNAND \u548c NOR \u90fd\u662f\u901a\u7528\u95e8\u3002</p> <p>\u63a8\u8350\u9605\u8bfb</p> <ul> <li>Title: Universal Logic Gates</li> <li>URL: https://www.electronics-tutorials.ws/logic/universal-gates.html</li> </ul> <p>Universal Logic gates can be used to produce any other logic or Boolean function with the NAND and NOR gates being minimal</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap02/#\u5e03\u5c14\u4ee3\u6570","title":"\u5e03\u5c14\u4ee3\u6570","text":"<p>literal ~ \u5b57\u9762\u91cf\uff0c\u4e5f\u5c31\u662f\u201c\u53d8\u91cf\u201d\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap02/#\u8fd0\u7b97\u5f8b","title":"\u8fd0\u7b97\u5f8b","text":"<p>\u8fd9\u5f20\u56fe\u7247\u603b\u7ed3\u4e86\u5e03\u5c14\u8fd0\u7b97\u4e2d\u7684\u8fd0\u7b97\u5f8b\uff0c\u4e2a\u4eba\u611f\u89c9\u6700\u9700\u8981\u5f3a\u5316\u8bb0\u5fc6\u7684\u662f 15 \u6761\uff0c\u56e0\u4e3a\u5e03\u5c14\u4ee3\u6570\u501f\u7528\u4e86\u666e\u901a\u4ee3\u6570\u7684\u7b26\u53f7\uff0c\u4f46\u7b2c 15 \u6761\u5728\u666e\u901a\u4ee3\u6570\u4e2d\u5e76\u4e0d\u6210\u7acb\uff0c\u6240\u4ee5\u5bf9\u4e8e\u4e60\u60ef\u8fd9\u5957\u7b26\u53f7\u7684\u4eba\u6765\u8bf4\u53ef\u80fd\u4e0d\u592a straightfoward\u3002</p> <p>\u5728\u8bb0\u5fc6\u8fd9\u5957\u8fd0\u7b97\u89c4\u5f8b\u7684\u65f6\u5019\uff0c\u6211\u4e2a\u4eba\u7684\u4e00\u4e2a\u60f3\u6cd5\u662f\uff0c\u4e00\u5b9a\u8981\u5efa\u7acb \u4e0e \u548c \u6216 \u662f\u5bf9\u7b49\u7684\u89c2\u5ff5\u3002\u6211\u4eec\u4e60\u60ef\u7528\u201c\u771f\u201d\u53bb\u7406\u89e3\u8fd9\u4e24\u4e2a\u8fd0\u7b97\uff0c\u4f46\u662f\u5b9e\u9645\u4e0a\u5982\u679c\u4f60\u4ee5\u201c\u5047\u201d\u4e3a\u4e3b\u4f53\u53bb\u5206\u6790\u8fd9\u4e24\u4e2a\u8fd0\u7b97\uff0c\u4f1a\u53d1\u73b0\u548c\u201c\u771f\u201d\u662f\u5b8c\u5168\u5bf9\u79f0\u7684\u3002\u6362\u8a00\u4e4b\uff0c \u4e0e \u548c \u6216 \u662f\u5b8c\u5168\u5bf9\u79f0\u7684\u8fd0\u7b97\uff0c\u800c\u975e\u50cf\u4ed6\u4eec\u501f\u7528\u7684\u7b26\u53f7 \\(\\times\\) \u548c \\(+\\) \u90a3\u6837\u5b58\u5728\u975e\u5bf9\u79f0\u5173\u7cfb\u3002</p> <p>\u4f46\u662f\u8ba9\u8fd9\u4ef6\u4e8b\u53d8\u5f97\u53c8\u6ca1\u90a3\u4e48\u7b80\u5355\u7684\u4e8b\u60c5\u662f\uff0c\u867d\u7136 \u4e0e \u548c \u6216 \u662f\u5bf9\u7b49\u7684\uff0c\u4f46\u662f\u6211\u4eec\u5728\u501f\u7528\u666e\u901a\u4ee3\u6570\u7b26\u53f7\u4f53\u7cfb\u7684\u540c\u65f6\uff0c\u53c8\u4eba\u4e3a\u5730\u7ed9\u4ed6\u4eec\u6dfb\u52a0\u4e86\u4f18\u5148\u7ea7\uff08\u4f46\u662f\u8fd9\u4e5f\u662f\u5fc5\u8981\u7684\uff0c\u5426\u5219\u8868\u8fbe\u5f0f\u5c31\u4f1a\u5145\u6ee1\u62ec\u53f7\uff09\u3002</p> <p>\u4f18\u5148\u7ea7\u4ece\u9ad8\u5230\u4f4e\u4f9d\u6b21\u4e3a\uff1a</p> <ol> <li>\u62ec\u53f7 / ()\uff1b</li> <li>\u975e / NOT / \\(\\overline A\\)\uff1b</li> <li>\u4e0e / AND / \\(\\cdot\\)\uff1b</li> <li>\u6216 / OR / \\(+\\)\uff1b</li> </ol> <p>\u4e2a\u4eba\u611f\u89c9\uff0c\u8fd9\u4e00\u79cd\u601d\u8def\u5e76\u4e0d\u76f4\u89c9\uff0c\u5c24\u5176\u662f\u501f\u7528\u666e\u901a\u4ee3\u6570\u7684\u7b26\u53f7\u4f53\u7cfb\u4ee5\u540e\u66f4\u52a0\u6df7\u6dc6\uff0c\u6240\u4ee5\u53ef\u80fd\u9700\u8981\u4e00\u4e9b\u7ec3\u4e60\u6765\u6446\u8131\u8fd9\u4e9b\u201c\u523b\u677f\u5370\u8c61\u201d\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap02/#\u8fd0\u7b97\u5f8b\u63a8\u5e7f","title":"\u8fd0\u7b97\u5f8b\u63a8\u5e7f","text":"<p>\u9664\u6b64\u4e4b\u5916\uff0c\u4ece\u4e0a\u9762\u63d0\u5230\u7684\u8fd0\u7b97\u5f8b\u4e2d\u8fd8\u80fd\u63a8\u5e7f\u51fa\u5982\u4e0b\u51e0\u4e2a\u6a21\u578b\uff1a</p> <p></p> <p>\u5bf9\u6bd4\u524d\u4e09\u4e2a\u548c\u540e\u4e09\u4e2a\uff0c\u6211\u4eec\u518d\u6b21\u53d1\u73b0\uff0c\u4e0e \u548c \u6216 \u5728\u903b\u8f91\u4e0a\u662f\u5bf9\u79f0\u7684\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap02/#\u5bf9\u5076\u6cd5\u5219","title":"\u5bf9\u5076\u6cd5\u5219","text":"<p>\u5bf9\u5076\u6cd5\u5219(Duality Rule)\uff1a\u4e00\u4e2a\u8868\u8fbe\u5f0f\u7684 \u5bf9\u5076(dual) \u4e3a\uff0c\u5c06\u6240\u6709\u7684 \u4e0e \u548c \u6216 \u5bf9\u8c03\u5f97\u5230\u7684\u5f0f\u5b50\uff08\u6ce8\u610f\uff01\u9700\u8981\u4fdd\u8bc1\u53c2\u4e0e\u8fd0\u7b97\u7684\u7ed3\u6784\u4e0d\u80fd\u53d8\uff08\u662f\u201c\u5e26\u62ec\u53f7\u201d\u7684\u5b8f\u5c55\u5f00\uff09\uff0c\u6bd4\u5982 \u4e00\u822c\u60c5\u51b5\u4e0b \\(A\\cdot B\\) \u4f1a\u88ab\u5bf9\u5076\u4e3a \\((A+B)\\) \u4ee5\u4fdd\u8bc1\u8fd0\u7b97\u987a\u5e8f\uff09\u3002</p> <p>eg</p> <ul> <li>\\(X+XY\\) \u548c \\(X(X+Y)\\) \u5bf9\u5076\uff1b</li> <li>\\(X(Y+Z)\\) \u548c \\(X+YZ\\) \u5bf9\u5076\uff1b</li> </ul> <p>\u800c\u4e00\u822c\u60c5\u51b5\u4e0b\uff0c\u9664\u975e\u67d0\u4e2a\u8868\u8fbe\u5f0f\u662f \u81ea\u5bf9\u5076(self-dual) \u7684\uff0c\u90a3\u4e48\u5b83\u7684\u8868\u73b0\u90fd\u4e0e\u539f\u8868\u8fbe\u5f0f\u4e0d\u540c\u3002</p> <p>\u5bf9\u5076\u8868\u8fbe\u5f0f\u5177\u6709\u5982\u4e0b\u6027\u8d28\uff1a</p> <ul> <li>\u5982\u679c F \u7684\u5bf9\u5076\u662f G\uff0c\u90a3\u4e48 F \u4e5f\u662f G \u7684\u5bf9\u5076\uff0c\u5373\u5bf9\u5076\u5173\u7cfb\u662f\u5bf9\u6210\u7684\uff1b</li> <li>\u5982\u679c\u8868\u8fbe\u5f0f F \u548c G \u7b49\u4ef7\uff0c\u90a3\u4e48\u4ed6\u4eec\u7684\u5bf9\u5076\u4e5f\u7b49\u4ef7\uff1b</li> </ul>"},{"location":"cour_note/D2QD_DigitalDesign/Chap02/#\u4e92\u8865\u51fd\u6570","title":"\u4e92\u8865\u51fd\u6570","text":"<p>\u4e00\u4e2a \u51fd\u6570\u7684\u4e92\u8865(Complement of a Function) \u6307\u7684\u662f\uff0c\u5c06\u5b83\u7684 \u5bf9\u5076\u51fd\u6570 \u4e2d\u6bcf\u4e00\u4e2a \u53d8\u91cf \u90fd\u53d6\u53cd\u5f97\u5230\u7684\u51fd\u6570\uff0c\u800c\u8be5\u51fd\u6570\u6b63\u597d\u7b49\u4e8e\u539f\u51fd\u6570\u7684 \u975e\u3002</p> <p>eg</p> <ul> <li>\u539f\u51fd\u6570\uff1a\\(F=\\overline{A}B+C\\overline{B}\\)\uff1b</li> <li>\u5176\u5bf9\u5076\u51fd\u6570\uff1a\\(F=(\\overline{A}+B)(C+\\overline{B})\\)\uff1b</li> <li>\u5176\u4e92\u8865\u51fd\u6570\uff1a\\(\\overline{F}=(A+\\overline{B})(\\overline{C}+D)\\)\uff1b</li> </ul>"},{"location":"cour_note/D2QD_DigitalDesign/Chap02/#\u66ff\u4ee3\u6cd5\u5219","title":"\u66ff\u4ee3\u6cd5\u5219","text":"<p>\u66ff\u4ee3\u6cd5\u5219(Substitution Rules): \u5982\u679c\u5c06\u4e00\u4e2a\u7b49\u5f0f\u4e2d \u6240\u6709\u7684 \u67d0\u4e2a\u53d8\u91cf \u90fd\u66ff\u6362\u4e3a\u540c\u4e00\u4e2a\u8868\u8fbe\u5f0f\uff0c\u5219\u7b49\u5f0f\u4f9d\u7136\u6210\u7acb\u3002</p> <p>eg</p> <ul> <li>\u539f\u7b49\u5f0f\uff1a\\(X(Y+Z)=XY+XZ\\)\uff1b</li> <li>\u5982\u679c\u4f7f\u7528 \\(X+YZ\\) \u66ff\u6362\u6240\u6709\u7684 \\(X\\)\uff0c\u5219\uff1a</li> <li>\u4fee\u6539\u540e\u7684\u7b49\u5f0f \\((X+YZ)(Y+Z)=(X+YZ)Y+(X+YZ)Z\\) \u4f9d\u7136\u6210\u7acb\uff1b</li> </ul>"},{"location":"cour_note/D2QD_DigitalDesign/Chap02/#\u4e00\u81f4\u6027\u5b9a\u7406","title":"\u4e00\u81f4\u6027\u5b9a\u7406","text":"<p>\u5728\u7b80\u5316\u903b\u8f91\u8868\u8fbe\u5f0f\u7684\u65f6\u5019\uff0c\u4e00\u81f4\u6027\u5b9a\u7406(Consensus Theorem) \u4e5f\u5f88\u6709\u7528\uff1a</p> \\[ XY+\\overline{X}Z+YZ=XY+\\overline{X}Z \\] <p>\u5176\u8bc1\u660e\u7684\u7b2c\u4e00\u6b65\u662f\u8fd9\u6837\u7684\uff1a \\(XY+\\overline{X}Z+YZ=XY+\\overline{X}Z+(X+\\overline{X})YZ\\)\uff0c\u90a3\u540e\u9762\u5c31\u5f88\u7b80\u5355\u4e86\u3002\u672c\u8d28\u4e0a\u8fd9\u4e2a\u7b49\u5f0f\u662f\u5229\u7528\u4e86\u88c2\u9879\uff0c\u9700\u8981\u5c06\u5176\u4e2d\u6700\u672c\u8d28\u7684\u90e8\u5206\uff0c\u6700\u5c0f\u7684\u7c92\u5ea6\u7ed9\u88c2\u5f00\u6765\uff0c\u7136\u540e\u518d\u6162\u6162\u6d88\u6389\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap02/#\u6807\u51c6\u5f62\u5f0f\u4e0e\u89c4\u8303\u5f62\u5f0f","title":"\u6807\u51c6\u5f62\u5f0f\u4e0e\u89c4\u8303\u5f62\u5f0f","text":"<p>\u7531\u4e8e\u672c\u8d28\u4e0a\u76f8\u7b49\u7684\u5e03\u5c14\u8868\u8fbe\u5f0f\u5b9e\u9645\u4e0a\u6709\u5f88\u591a\u79cd\u5199\u6cd5\uff0c\u800c\u4e14\u968f\u7740\u53d8\u91cf\u8d8a\u6765\u8d8a\u590d\u6742\uff0c\u4ed6\u4eec\u4e4b\u95f4\u7684\u6bd4\u8f83\u4f1a\u5f88\u56f0\u96be\u3002\u6240\u4ee5\u6211\u4eec\u9700\u8981\u5b9a\u4e49\u4e00\u79cd\u5f62\u5f0f\uff0c\u4f7f\u5f97\u6240\u6709\u76f8\u540c\u7684\u8868\u8fbe\u5f0f\u90fd\u80fd\u6bd4\u8f83\u65b9\u4fbf\u7684\u201c\u5316\u7b80\u201d\u4e3a\u540c\u4e00\u4e2a\u5f62\u5f0f\uff0c\u540c\u65f6\u4e5f\u80fd\u8fa8\u522b\u51fa\u4e24\u4e2a\u8868\u8fbe\u5f0f\u662f\u4e0d\u540c\u7684\u3002\u8fd9\u5c31\u5f15\u5165\u4e86 \u6807\u51c6\u5f62\u5f0f(Standard Forms)\uff0c\u5305\u62ec SOP \u548c POS\uff1b\u4ee5\u53ca \u89c4\u8303\u5f62\u5f0f(Canonical Forms)\uff0c\u5206\u522b\u4e3a \u6700\u5c0f\u9879\u4e4b\u548c(Sum of Minterms, SOM) \u548c \u6700\u5927\u9879\u4e4b\u79ef(Product of Maxterms, POM)\u3002</p> <p>\u4e3a\u4e86\u65b9\u4fbf\u63cf\u8ff0\uff0c\u5728\u7ee7\u7eed\u4e4b\u524d\uff0c\u6211\u4eec\u5148\u7ed9\u51fa\u8fd9\u6837\u4e00\u5f20 \ud83c\udf30 \u771f\u503c\u8868\u3002</p> \ud83c\udf30 Index X Y Z Output 0 / <code>000</code> <code>0</code> <code>0</code> <code>0</code> <code>0</code> 1 / <code>001</code> <code>0</code> <code>0</code> <code>1</code> <code>0</code> 2 / <code>010</code> <code>0</code> <code>1</code> <code>0</code> <code>1</code> 3 / <code>011</code> <code>0</code> <code>1</code> <code>1</code> <code>0</code> 4 / <code>100</code> <code>1</code> <code>0</code> <code>0</code> <code>1</code> 5 / <code>101</code> <code>1</code> <code>0</code> <code>1</code> <code>1</code> 6 / <code>110</code> <code>1</code> <code>1</code> <code>0</code> <code>0</code> 7 / <code>111</code> <code>1</code> <code>1</code> <code>1</code> <code>1</code> <p>\u6570\u503c\u662f\u968f\u4fbf\u6413\u7684\uff0c\u8bf7\u7559\u610f\u4e3a\u4ec0\u4e48\u4e3a\u8981\u5728 Index \u7279\u5730\u5199\u51fa\u4e8c\u8fdb\u5236\u7684\u8868\u8ff0\u3002</p> <p>\u5728\u5f00\u59cb\u4e4b\u524d\uff0c\u6211\u9700\u8981\u5f3a\u8c03\uff0c\u6211\u4eec\u5f15\u5165 SOM \u548c POM \u7684\u76ee\u7684\u662f\u5bfb\u627e\u4e00\u79cd\u6bd4\u8f83\u5178\u578b\u7684 \u8868\u8fbe\uff0c\u4f7f\u5f97\u4ed6\u4eec\u80fd\u591f \u786e\u5b9a \u4e00\u5f20\u771f\u503c\u8868\u3002\u5373\uff0c\u77e5\u9053\u8fd9\u79cd \u8868\u8fbe \u6211\u4eec\u5c31\u8db3\u591f\u5199\u51fa\u8fd9\u5f20\u771f\u503c\u8868\uff0c\u53cd\u4e4b\u4ea6\u7136\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap02/#\u6700\u5c0f\u9879\u4e4b\u548c-som","title":"\u6700\u5c0f\u9879\u4e4b\u548c SOM","text":"<p>\u8bfe\u672c\u4e2d\u5bf9\u6700\u5c0f\u9879\u7684\u63cf\u8ff0\u662f\uff1a</p> <p>A product term in which all the variables appear exactly once, either complemented or uncomplemented, is called minterm. </p> <p>Its characteristic property is that it represents exactly one combination of binary variable values in the truth table.</p> <p>\u7528\u6211\u7684\u8bdd\u6765\u8bf4\uff0c\u6700\u5c0f\u9879\u4e4b\u548c\u5c31\u662f\u6311\u51fa\u771f\u503c\u8868\u4e2d\u6240\u6709\u7ed3\u679c\u662f <code>1</code> \u7684\u6700\u5c0f\u9879\uff08\u6bd4\u8f83\u6a21\u7cca\u4f46\u76f4\u89c2\uff0c\u6240\u4ee5\u8bf7\u5148\u56eb\u56f5\u541e\u67a3\uff0c\u6211\u5728\u201c\u8ffd\u52a0\u8bf4\u660e\u201d\u4f1a\u8fdb\u4e00\u6b65\u8bf4\u660e\uff09\u7136\u540e <code>OR</code> \u8d77\u6765\u3002\u663e\u7136\uff0c\u6700\u5c0f\u9879\u4e4b\u548c\u7684\u542b\u4e49\u5c31\u662f\uff0c\u4e00\u65e6\u5b57\u9762\u91cf\u53d6\u503c\u7684\u7ec4\u5408\u5339\u914d\u4e86\u8fd9\u51e0\u4e2a\u201c\u6700\u5c0f\u9879\u201d\u7684\u5176\u4e2d\u4e00\u9879\uff0c\u90a3\u4e48\u7ed3\u679c\u5c31\u662f <code>1</code>\uff0c\u7b26\u5408\u4e86 <code>OR</code> \u7684\u201c\u67091\u5f971\u201d\u7684\u89c4\u5219\u3002</p> <p>\u6211\u4eec\u4f7f\u7528\u7b26\u53f7 \\(m_{idx}\\) \u6765\u8868\u793a\u53d8\u91cf\u7ec4\u5408 \\(idx\\) \u662f\u4e00\u4e2a\u6700\u5c0f\u9879\uff0c\u5176\u4e2d \\(idx\\) \u8868\u793a\u63cf\u8ff0\u7684\u90a3\u4e00\u9879\u5728\u771f\u503c\u8868\u7684\u5e8f\u53f7\uff0c\u540c\u65f6\u8fd9\u4e2a\u4e0b\u6807\u7684\u4e8c\u8fdb\u5236\u4e5f\u80fd\u53cd\u6620\u51fa\u5b57\u9762\u91cf\u7684\u7ec4\u5408\u3002</p> <p>\u4f8b\u5982\uff0c\u5728 \ud83c\udf30 \u4e2d\uff0coutput \u4e3a <code>1</code> \u7684\u9879\u6709\uff1a<code>010</code> <code>100</code> <code>101</code> <code>111</code> \u8fd9\u56db\u9879\uff0c\u90a3\u4e48\u6211\u4eec\u9700\u8981\u6311\u51fa\u6765\u7684\u6700\u5c0f\u9879\u8868\u8fbe\u5c31\u5206\u522b\u662f \\(m_{2}=\\overline{X}Y\\overline{Z}, \\; m_{4}=X\\overline{Y}\\overline{Z}, \\; m_{5}=X\\overline{Y}Z, \\; m_{7}=XYZ\\)\uff0c\u8fd9\u4e9b\u53d8\u91cf\u8868\u8fbe\u5f0f\u90fd\u662f\u5f53\u4e14\u4ec5\u5f53\u53d8\u91cf\u7ec4\u5408\u4e3a\u5bf9\u5e94\u9879\u65f6\u624d\u4f1a\u53d6 <code>1</code> \u7684\u8868\u8fbe\u5f0f\uff0c\u53ef\u4ee5\u8ba4\u4e3a\uff0c\u8fd9\u5199\u8868\u8fbe\u5f0f\u552f\u4e00\u8868\u8fbe\u4e86\u8fd9\u4e9b\u771f\u503c\u8868\u4e2d\u7684 <code>1</code>\u3002</p> \u8ffd\u52a0\u8bf4\u660e\uff08\u7b80\u5355\uff0c\u4f46\u662f\u5efa\u8bae\u770b\u4e00\u770b\uff09 <p>\u6216\u8bb8\u60a8\u89c9\u5f97\u6700\u5c0f\u9879\u7684\u5f97\u5230\u975e\u5e38\u7684\u81ea\u7136\u4e14\u7b80\u5355\uff0c\u6211\u5efa\u8bae\u60a8\u4e5f\u5c1d\u8bd5\u7740\u770b\u4e00\u770b\u8ffd\u52a0\u8bf4\u660e\uff0c\u56e0\u4e3a\u8fd9\u5bf9\u7406\u89e3\u6700\u5927\u9879\u633a\u6709\u5e2e\u52a9\u7684\u3002</p> <p>\u90a3\u4e48\u4ec0\u4e48\u662f\u201c\u5217\u4e3e\u201d\u5462\uff1f\u8ba9\u6211\u4eec\u518d\u770b\u4e00\u773c\u4e0a\u9762\u5bf9\u6700\u5c0f\u9879\u4e4b\u548c\u7684\u63cf\u8ff0\uff1a\u201c\u4e00\u65e6\u5b57\u9762\u91cf\u53d6\u503c\u7684\u7ec4\u5408\u5339\u914d\u8fd9\u51e0\u4e2a\u2018\u6700\u5c0f\u9879\u2019\u7684\u5176\u4e2d\u4e00\u9879\uff0c\u90a3\u4e48\u7ed3\u679c\u5c31\u662f\u771f\u201d\uff0c\u8ffd\u672c\u6eaf\u6e90\uff0c\u5728\u6700\u5c0f\u9879\u4e2d\uff0c\u6211\u4eec\u5c31\u9700\u8981\u505a\u5230\u53ea\u6709\u5f53\u4e00\u4e2a\u7535\u8def\u7684\u72b6\u6001\u662f\u7279\u5b9a\u7ec4\u5408\u65f6\uff0c\u5176\u8fd4\u56de\u503c\u4e3a <code>1</code>\u3002</p> <p>\u5177\u4f53\u6765\u8bf4\uff0c\u6bd4\u5982\uff0c\u5bf9\u4e8e \ud83c\udf30 \u4e2d\u7684 \\(m_{5}=X\\overline{Y}Z\\)\uff0c\u4e5f\u53ef\u4ee5\u901a\u8fc7\u8fd9\u6837\u4e00\u79cd\u66f4\u5570\u55e6\u7684\u65b9\u5f0f\u8868\u8fbe\u51fa\u6765\u662f\u8fd9\u6837\u7684\uff1a</p> <pre><code>if(X == 1 &amp;&amp; Y == 0 &amp;&amp; Z == 1) {\nOutput = 1;\n} else {\nOutput = 0;\n}\n</code></pre> <p>\uff08\u5faa\u5e8f\u6e10\u8fdb\uff09\u6211\u4eec\u53ef\u4ee5\u5c06\u5b83\u53d8\u5316\u4e3a\u8fd9\u6837\uff1a</p> <pre><code>if(X == 1 &amp;&amp; (!Y) == 1 &amp;&amp; Z == 1) {\nOutput = 1;\n} else {\nOutput = 0;\n}\n</code></pre> <p>\u5982\u679c\u4f60\u719f\u6089\u201c\u538b\u884c\u201d\u6280\u5de7\uff0c\u90a3\u4e48\u8fd9\u4e00\u6bb5\u90fd\u53ef\u4ee5\u5199\u6210\uff1a</p> <pre><code>Output = (X == 1 &amp;&amp; (!Y) == 1 &amp;&amp; Z == 1);\n</code></pre> <p>\u800c\u8fd9\u4e2a\u903b\u8f91\u8868\u8fbe\u5f0f\uff0c\u5b9e\u9645\u4e0a\u5df2\u7ecf\u548c \\(m_5=X\\overline{Y}Z\\) \u4e00\u6a21\u4e00\u6837\u4e86\u3002</p> <p>\u5728\u8fd9\u91cc\u7ed9\u51fa\u4e00\u4e2a\u603b\u7ed3\u6027\u7684\u8868\u8ff0\uff1a\u6240\u8c13\u7684\u201c\u6311\u51fa\u201d\uff0c\u5c31\u662f\u5bf9\u4e8e\u9009\u5b9a\u7684\u4e00\u4e2a\u5b57\u9762\u91cf\u53d6\u503c\u7684\u7ec4\u5408\uff0c\u7ed9\u51fa\u4e00\u4e2a\u7279\u5b9a\u7684\u8868\u8fbe\u5f0f\uff0c\u4f7f\u5f97\u53ea\u6709\u8fd9\u79cd\u7ec4\u5408\u7684\u7ed3\u679c\u662f \\(f\\)\uff0c\u800c\u5bf9\u4e8e\u4efb\u4f55\u5176\u4ed6\u53d6\u503c\u7684\u7ec4\u5408\uff0c\u8be5\u8868\u8fbe\u5f0f\u7684\u7ed3\u679c\u90fd\u662f \\(\\overline{f}\\)\uff0c\u5373\u5b9e\u73b0\u4e86\u8be5\u8868\u8fbe\u5f0f\u80fd \u552f\u4e00\u8868\u8fbe \u8fd9\u4e2a\u53d6\u503c\u7ec4\u5408\u3002\uff08\u8fd9\u91cc\u4e4b\u6240\u4ee5\u5199\u7684\u662f \\(f\\) \u800c\u4e0d\u662f <code>1</code>\uff0c\u662f\u4e3a\u4e86\u7ed9\u4e4b\u540e\u5206\u6790 POM \u505a\u94fa\u57ab\uff0c\u5bf9\u4e8e POM\uff0c<code>0</code> \u624d\u662f\u552f\u4e00\u8868\u8fbe\u7684\u7279\u5f81\u7ed3\u679c\u3002\uff09</p> <p>\u81f3\u6b64\uff0c\u6211\u4eec\u5f97\u5230\u4e86 \ud83c\udf30 \u6240\u5bf9\u5e94\u7684 SOM\uff1a</p> \\[ \\begin{array}{l}     F(X,Y,Z)     &amp; = \\sum m(2,4,5,7) \\\\     &amp; = m_2+m_4+m_5+m_7 \\\\     &amp; = \\overline{X}Y\\overline{Z}+X\\overline{Y}\\,\\overline{Z}+X\\overline{Y}Z+XYZ \\end{array} \\] <p>\u518d\u6b21\u5f52\u7eb3\uff0c\u4f7f\u7528\u901a\u4fd7\u7684\u8bdd\u6765\u8bf4\uff0c\u6700\u5c0f\u9879\u4e4b\u548c\u66f4\u50cf\u662f\u201c\u679a\u4e3e\u4e86\u6240\u6709 <code>1</code> \u7684\u53ef\u80fd\u201d\uff0c\u53ea\u8981\u5339\u914d\u4e86\u8fd9\u4e2a\u201c\u548c\u201d\u4e2d\u7684\u67d0\u4e00\u9879\uff08\u4e8b\u5b9e\u4e0a\u4e0d\u505a\u5316\u7b80\u7684\u8bdd\u4f60\u4e5f\u53ea\u80fd\u6ee1\u8db3\u4e00\u9879\u7684\u503c\u53d6\u5230 <code>1</code>\uff09\uff0c\u8868\u8fbe\u5f0f\u7684\u503c\u5c31\u4f1a\u53d8\u6210 <code>1</code>\uff1b\u800c\u4e00\u4e2a\u90fd\u4e0d\u5339\u914d\u7684\uff0c\u81ea\u7136\u5c31\u53ea\u80fd\u5f97\u5230 <code>0</code>\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap02/#\u6700\u5927\u9879\u4e4b\u79ef-pom","title":"\u6700\u5927\u9879\u4e4b\u79ef POM","text":"<p>\u5c31\u50cf\u6211\u4e4b\u524d\u4e0d\u65ad\u4e0d\u65ad\u4e0d\u65ad\u5f3a\u8c03\u7684\uff0c\u6240\u8c13\u7684 <code>1</code> \u548c <code>0</code> \u90fd\u53ea\u662f\u4eba\u4e3a\u5b9a\u4e49\u7684\uff0c\u6446\u8131\u6f5c\u610f\u8bc6\u91cc\u5bf9\u8fd9\u4e24\u8005\u4e4b\u4e00\u7684\u503e\u5411\uff08\u4f8b\u5982\u6211\u672c\u4eba\u5c31\u4e00\u76f4\u5f88\u503e\u5411\u4e8e\u4ee5 <code>1</code> \u4e3a\u4e3b\u4f53\u7814\u7a76\u95ee\u9898\uff09\u4f1a\u5bf9\u7406\u89e3\u6700\u5927\u9879\u4e4b\u79ef\u548c\u903b\u8f91\u8868\u8fbe\u5f0f\u5316\u7b80\u5f88\u6709\u5e2e\u52a9\u3002</p> <p>\u800c\u6700\u5927\u9879\u4e4b\u79ef\u2014\u2014\u4ee5\u6211\u4e2a\u4eba\u7684\u611a\u89c1\u2014\u2014\u5c31\u662f\u4ee5 <code>0</code> \u4e3a\u4e3b\u4f53\u6765\u7814\u7a76\u771f\u503c\u8868\u7684\u7279\u5f81\u7684\u3002</p> <p>\u8bfe\u672c\u4e2d\u5bf9\u6700\u5927\u9879\u7684\u63cf\u8ff0\u662f\uff1a</p> <p>A sum term that contains all the variables in complemented or uncomplemented form is called a maxterm.</p> <p>\u4e0e\u6700\u5c0f\u9879\u5bf9\u6bd4\uff0c\u65e0\u975e\u662f\u628a \"product term\" \u6362\u6210\u4e86 \"sum term\"\uff0c\u4e5f\u5c31\u662f\u628a AND \u6362\u6210\u4e86 OR\u3002</p> <p>\u800c\u6700\u5927\u9879\u4e4b\u79ef\uff0c\u5c31\u662f\u6311\u51fa\u6240\u6709\u7ed3\u679c\u4e3a <code>0</code> \u7684\u6700\u5927\u9879\uff08\u201c\u6311\u51fa\u201d\u7684\u5b9a\u4e49\u6211\u5df2\u7ecf\u5728 SOM \u7684\u8ffd\u52a0\u8bf4\u660e\u4e2d\u7ed9\u51fa\uff0c\u5728 POM \u7684\u8ffd\u52a0\u8bf4\u660e\u4e2d\u6211\u8fd8\u4f1a\u518d\u4e00\u6b21\u63d0\u53ca\uff09\uff0c\u518d\u505a AND\u3002\u4ee5 <code>1</code> \u4e3a\u4e3b\u4f53\u63cf\u8ff0 AND \u662f\u201c\u90fd1\u51fa1\u201d\uff0c\u800c\u4ee5 <code>0</code> \u4e3a\u4e3b\u4f53\u63cf\u8ff0 AND \u5219\u662f\u201c\u67090\u51fa0\u201d\uff0c\u8fd9\u4e0e OR \u7684\u201c\u67091\u51fa1\u201d\u4e5f\u662f\u9ad8\u5ea6\u5bf9\u79f0\u7684\uff08\u53cd\u4e4b\u4ea6\u7136\uff09\u3002\u4e5f\u5c31\u662f\u8bf4\uff0c\u6700\u5927\u9879\u4e4b\u79ef\u7684\u542b\u4e49\u662f\uff0c\u5728\u6700\u5927\u9879\u4e4b\u79ef\u4e2d\uff0c\u53ea\u8981\u5b57\u9762\u91cf\u53d6\u503c\u7684\u7ec4\u5408\u5339\u914d\u8fd9\u51e0\u4e2a\u201c\u6700\u5927\u9879\u201d\u7684\u5176\u4e2d\u4e00\u9879\uff0c\u6574\u4e2a\u8868\u8fbe\u5f0f\u7684\u7ed3\u679c\u5c31\u4f1a\u53d8\u6210 <code>0</code>\u3002</p> <p>\u7c7b\u4f3c\u7684\uff0c\u6211\u4eec\u4f7f\u7528\u7b26\u53f7 \\(M_{idx}\\) \u6765\u8868\u793a\u53d8\u91cf\u7ec4\u5408 \\(idx\\) \u662f\u4e00\u4e2a\u6700\u5927\u9879\uff0c\u5176\u4e2d \\(idx\\) \u8868\u793a\u63cf\u8ff0\u7684\u90a3\u4e00\u9879\u5728\u771f\u503c\u8868\u7684\u5e8f\u53f7\uff0c\u540c\u65f6\u8fd9\u4e2a\u4e0b\u6807\u7684\u4e8c\u8fdb\u5236\u4e5f\u80fd\u53cd\u6620\u51fa\u5b57\u9762\u91cf\u7684\u7ec4\u5408\u3002</p> <p>\u4f8b\u5982\uff0c\u5728 \ud83c\udf30 \u4e2d\uff0coutput \u4e3a <code>0</code> \u7684\u9879\u6709\uff1a<code>000</code> <code>001</code> <code>011</code> <code>110</code> \u8fd9\u56db\u9879\uff0c\u90a3\u4e48\u6211\u4eec\u9700\u8981\u6311\u51fa\u6765\u7684\u6700\u5c0f\u9879\u8868\u8fbe\u5c31\u5206\u522b\u662f \\(M_{0}=X+Y+Z, \\; M_{1}=X+Y+\\overline{Z}, \\; M_{3}=X+\\overline{Y}+\\overline{Z}, \\; M_{6}=\\overline{X}+\\overline{Y}+Z\\)\u3002\u53ef\u4ee5\u68c0\u9a8c\uff0c\u53ea\u6709\u4ee3\u5165\u4ed6\u4eec\u5bf9\u5e94\u7684\u90a3\u4e00\u884c\u771f\u503c\u8868\u7ec4\u5408\u65f6\uff0c\u4ed6\u4eec\u624d\u4f1a\u5f97\u5230 <code>0</code>\u3002</p> \u8ffd\u52a0\u8bf4\u660e <p>\u540c\u6837\u7684\uff0c\u56de\u987e\u6700\u5927\u9879\u4e4b\u79ef\u7684\u63cf\u8ff0\uff1a\u201c\u5728\u6700\u5927\u9879\u4e4b\u79ef\u4e2d\uff0c\u53ea\u8981\u5b57\u9762\u91cf\u53d6\u503c\u7684\u7ec4\u5408\u5339\u914d\u8fd9\u51e0\u4e2a\u2018\u6700\u5927\u9879\u2019\u7684\u5176\u4e2d\u4e00\u9879\uff0c\u6574\u4e2a\u8868\u8fbe\u5f0f\u7684\u7ed3\u679c\u5c31\u4f1a\u53d8\u6210 <code>0</code>\u201d\u3002</p> <p>\u5177\u4f53\u6765\u8bf4\uff0c\u6bd4\u5982\uff0c\u5bf9\u4e8e \ud83c\udf30 \u4e2d\u7684 \\(M_6=\\overline{X}+\\overline{Y}+Z\\)\uff0c\u6211\u4eec\u53ef\u4ee5\u5982\u4e0b\u63cf\u8ff0\uff1a</p> <pre><code>if(X == 1 &amp;&amp; Y == 1 &amp;&amp; Z == 0){\nOutput = 0;\n} else {\nOutput = 1;\n}\n</code></pre> <p>\u56de\u987e\u6700\u5927\u9879\u7684\u76ee\u7684\u662f\u6ee1\u8db3\u8fd9\u4e2a\u5206\u652f\u6761\u4ef6\u7684\u60c5\u51b5\u4e0b\u8f93\u51fa <code>0</code>\uff0c\u4e5f\u5c31\u662f\u8bf4\u6211\u4eec\u9700\u8981\u8868\u8fbe <code>(X == 1 &amp;&amp; Y == 1 &amp;&amp; Z == 0)</code> \u8fd9\u4e2a\u903b\u8f91\u6761\u4ef6\u3002\u4f46\u7531\u4e8e\u6700\u5927\u9879\u7684\u5b9e\u73b0\u5f62\u5f0f\u662f <code>OR</code>\uff0c\u6240\u4ee5\u6211\u4eec\u9700\u8981\u5c06 <code>&amp;&amp;</code> \u7684\u5f0f\u5b50\u4ee5 <code>||</code> \u7684\u5f62\u5f0f\u8868\u8fbe\u3002</p> <p>\u5f53\u7136\uff0c\u4f60\u53ef\u4ee5\u9009\u62e9\u4f7f\u7528\u5404\u79cd\u8fd0\u7b97\u5f8b\u6765\u5316\u7b80\uff0c\u4f46\u662f\u4e0d\u59a8\u60f3\u4e00\u60f3 <code>AND</code> \u548c <code>OR</code> \u7684\u8fd0\u7b97\u7279\u5f81\uff0c\u524d\u8005\u662f\u201c\u67090\u51fa0\u201d\uff0c\u540e\u8005\u662f\u201c\u67091\u51fa1\u201d\u3002\u800c\u5bf9\u4e8e <code>AND</code> \u6765\u8bf4\uff0c\u60f3\u8981\u505a\u5230\u6761\u4ef6\u7b5b\u9009\uff0c\u5c31\u9700\u8981\u6bcf\u4e00\u4e2a\u6761\u4ef6\u90fd\u662f <code>1</code>\uff0c\u6700\u540e\u5982\u679c\u7b5b\u9009\u6210\u529f\u7ed3\u679c\u5c31\u662f <code>1</code>\uff1b\u5bf9\u4e8e <code>OR</code> \u6765\u8bf4\uff0c\u5c31\u662f\u6bcf\u4e00\u4e2a\u6761\u4ef6\u90fd\u662f <code>0</code>\uff0c\u5982\u679c \u7b5b\u9009\u6210\u529f \u7684\u7ed3\u679c\u5c31\u662f <code>0</code>\u3002\u4e5f\u5c31\u662f\u8bf4\u5bf9\u4e8e\u6216\uff0c\u6211\u4eec\u53ef\u4ee5\u8fd9\u6837\u8868\u793a\uff1a</p> <pre><code>if((X == 0 || Y == 0 || (!Z) == 0) == 0){\nOutput = 0;\n} else {\nOutput = 1;\n}\n</code></pre> <p>\u540c\u6837\u8fdb\u884c\u4e00\u4e0b\u538b\u884c\uff1a</p> <pre><code>// It might be too complex.\nOutput = !((X == 0 || Y == 0 || (!Z) == 0) == 0);\n// So we can simplify it.\nOutput = (X == 0 || Y == 0 || (!Z) == 0);\n</code></pre> <p>\u8fd9\u4e5f\u6b63\u5bf9\u5e94\u4e86 \\(M_6=\\overline{X}+\\overline{Y}+Z\\)\u3002</p> <p>\u518d\u6b21\u7ed9\u51fa\u8fd9\u4e2a\u603b\u7ed3\u6027\u7684\u8868\u8ff0\uff1a\u6240\u8c13\u7684\u201c\u6311\u51fa\u201d\uff0c\u5c31\u662f\u5bf9\u4e8e\u9009\u5b9a\u7684\u4e00\u4e2a\u5b57\u9762\u91cf\u53d6\u503c\u7684\u7ec4\u5408\uff0c\u7ed9\u51fa\u4e00\u4e2a\u7279\u5b9a\u7684\u8868\u8fbe\u5f0f\uff0c\u4f7f\u5f97\u53ea\u6709\u8fd9\u79cd\u7ec4\u5408\u7684\u7ed3\u679c\u662f \\(f\\)\uff0c\u800c\u5bf9\u4e8e\u4efb\u4f55\u5176\u4ed6\u53d6\u503c\u7684\u7ec4\u5408\uff0c\u8be5\u8868\u8fbe\u5f0f\u7684\u7ed3\u679c\u90fd\u662f \\(\\overline{f}\\)\uff0c\u5373\u5b9e\u73b0\u4e86\u8be5\u8868\u8fbe\u5f0f\u80fd \u552f\u4e00\u8868\u8fbe \u8fd9\u4e2a\u53d6\u503c\u7ec4\u5408\u3002</p> <p>\u81f3\u6b64\uff0c\u6211\u4eec\u5f97\u5230\u4e86 \ud83c\udf30 \u6240\u5bf9\u5e94\u7684 POM\uff1a</p> \\[     \\begin{aligned}     F(X,Y,Z)     &amp; = \\prod M(0,1,3,6) \\\\     &amp; = M_0M_1M_3M_6 \\\\     &amp; = (X+Y+Z)(X+Y+\\overline{Z})(X+\\overline{Y}+\\overline{Z})(\\overline{X}+\\overline{Y}+Z) \\end{aligned} \\] <p>\u540c\u6837\u518d\u6b21\u5f52\u7eb3\uff0c\u4f7f\u7528\u901a\u4fd7\u7684\u8bdd\u6765\u8bf4\uff0c\u6700\u5927\u9879\u4e4b\u79ef\u66f4\u50cf\u662f\u201c\u679a\u4e3e\u4e86\u6240\u6709 <code>0</code> \u7684\u53ef\u80fd\u201d\uff0c\u53ea\u8981\u5339\u914d\u4e86\u8fd9\u4e2a\u201c\u79ef\u201d\u4e2d\u7684\u67d0\u4e00\u9879\uff0c\u8868\u8fbe\u5f0f\u7684\u503c\u5c31\u4f1a\u53d8\u6210 <code>0</code>\uff1b\u800c\u4e00\u4e2a\u90fd\u4e0d\u5339\u914d\u7684\uff0c\u81ea\u7136\u5c31\u53ea\u80fd\u5f97\u5230 <code>1</code>\u3002</p> <p>\u4e0e\u6700\u5c0f\u9879\u76f8\u6bd4\uff0c\u4e00\u4e2a\u679a\u4e3e\u4e86\u6240\u6709\u7684 <code>1</code> \u7684\u53ef\u80fd\uff0c\u4e00\u4e2a\u679a\u4e3e\u4e86\u6240\u6709\u662f <code>0</code> \u7684\u53ef\u80fd\uff0c\u5bf9\u4e8e\u4e00\u4e2a\u4e8c\u503c\u8868\u8fbe\u5f0f\u6765\u8bf4\uff0c\u4e24\u79cd \u8868\u8fbe \u90fd\u662f\u5145\u8981\u7684\u3002</p> <p>\u6b64\u65f6\uff0c\u6211\u4eec\u8fd8\u80fd\u53d1\u73b0\uff1a</p> <p>\u4f8b\u5982\uff1a\\(M_5 = \\overline{X} + Y + \\overline{Z} = \\overline{ X\\overline{Y}Z } = \\overline{m}_5\\)</p> <p>\u5173\u4e8e\u8fd9\u4e2a\u53d1\u73b0\u7684\u66f4\u591a\u7684\u4f8b\u5b50\u548c\u8bf4\u660e\uff0c\u53ef\u4ee5\u770b\u4e0b\u9762\u7684\u7b2c\u4e00\u4e2a\u7ec3\u4e60\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap02/#\u7ec3\u4e60","title":"\u7ec3\u4e60","text":"<p>\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u5c06\u901a\u8fc7\u4e00\u4e9b\u4f8b\u5b50\u6765\u8fdb\u4e00\u6b65\u5f3a\u5316\u8fd9\u4e9b\u7406\u89e3\uff0c\u5e76\u4e14\u6316\u6398\u4e00\u4e9b\u795e\u5947\u7684\u7279\u6027\u3002</p> \u9898\u9762\u7b54\u6848 <p>\u8bf7\u5206\u522b\u5199\u51fa\u5982\u4e0b\u771f\u503c\u8868\u4e2d \\(F\\) \u548c \\(\\overline{F}\\) \u7684 SOM \u548c POM\u3002 </p> <p>\u7b54\u6848\uff1a   \\begin{array}{l}     \\overline{F}(X,Y,Z)     &amp; = \\sum m(1,3,4,6) \\\\     &amp; = \\overline{X}\\,\\overline{Y}Z + \\overline{X}YZ + X\\overline{Y}\\,\\overline{Z} + XY\\overline{Z} \\\\     &amp; = \\prod M(0,2,5,7) \\\\     &amp; = (X+Y+Z)(X+\\overline{Y}+Z)(\\overline{X}+Y+\\overline{Z})(\\overline{X}+\\overline{Y}+\\overline{Z}) \\end{array}  \u4e8e\u662f\u6211\u4eec\u53d1\u73b0\u4e00\u4ef6\u5f88\u6709\u610f\u601d\u7684\u4e8b\u60c5\uff0c\\(F\\) \u7684 SOM \u7684\u4e0b\u6807\u4e0e \\(\\overline{F}\\) \u7684 POM \u7684\u4e0b\u6807\u662f\u4e00\u6837\u7684\uff1b\u5f53\u7136\u5bf9\u4e8e \\(F\\) \u7684 POM \u548c \\(\\overline{F}\\) \u7684 SOM \u4e5f\u662f\u4e00\u6837\u7684\u3002\u8fd9\u53c8\u5370\u8bc1\u4e86\u5bf9\u79f0\u6027\u3002</p> <p>\u4e4b\u540e\u7684\u7ec3\u4e60\u7b49\u6211\u505a\u4e86\u518d\u6dfb\u52a0x \u5982\u679c\u505a\u4e86\u7684\u8bddx \ud83d\ude0b</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap02/#\u7535\u8def\u5b9e\u73b0\u4e0e\u4f18\u5316","title":"\u7535\u8def\u5b9e\u73b0\u4e0e\u4f18\u5316","text":"<p>\u5f15\u5165</p> <p>\u6211\u4eec\u5f53\u7136\u53ef\u4ee5\u76f4\u63a5\u901a\u8fc7\u6807\u51c6\u5f62\u5f0f\u6765\u5f97\u5230\u5bf9\u5e94\u7684\u7535\u8def\uff0c\u4f46\u662f\u5728\u5b9e\u9645\u60c5\u51b5\u4e2d\uff0c\u8fd9\u6837\u505a\u4f1a\u5bfc\u81f4\u6210\u672c\u8fc7\u9ad8\u4ee5\u53ca\u7535\u8def\u590d\u6742\uff08\u56e0\u4e3a\u95e8\u592a\u591a\u4e86\uff09\uff0c\u6240\u4ee5\u6211\u4eec\u9700\u8981\u5bf9\u7535\u8def\u8fdb\u884c\u4f18\u5316\u3002\u5728\u8fd9\u91cc\uff0c\u6211\u4eec\u4ecb\u7ecd\u901a\u8fc7 \u5361\u8bfa\u56fe(Karnaugh map) \u6765\u4f18\u5316\u903b\u8f91\u7535\u8def\u7684\u65b9\u6cd5\u3002</p> <p>\u4e0d\u8fc7\u518d\u5f00\u59cb\u201c\u4f18\u5316\u201d\u7684\u8bdd\u9898\u4e4b\u524d\uff0c\u6211\u4eec\u9700\u8981\u5b9a\u4e49\u4ec0\u4e48\u662f\u201c\u4f18\u201d\uff0c\u4e5f\u5c31\u662f\u7ed9\u51fa\u4e00\u4e2a\u7535\u8def\u6210\u672c\u7684\u8861\u91cf\u4f9d\u636e\uff0c\u5373 \u6210\u672c\u6807\u51c6(cost criteria)\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap02/#\u6210\u672c\u6807\u51c6","title":"\u6210\u672c\u6807\u51c6","text":"<p>\u5728\u6210\u672c\u6807\u51c6\u4e2d\uff0c\u6211\u4eec\u9700\u8981\u4ecb\u7ecd\u7684\u4e3b\u8981\u6709\u4e09\u79cd\u6807\u51c6\uff0c\u5206\u522b\u662f\uff1a</p> <ul> <li>\u6309\u7167\u5b57\u9762\u91cf\u5b57\u9762\u91cf\u8ba1(literal cost)\uff1a\\(L\\)</li> <li>\u6309\u95e8\u8f93\u5165\u8ba1\uff0c\u4e0d\u8ba1\u975e\u95e8(gate-input cost)\uff1a\\(G\\)</li> <li>\u6309\u95e8\u8f93\u5165\u8ba1\uff0c\u8ba1\u975e\u95e8(gate-input cost with NOTs)\uff1a\\(GN\\)</li> </ul>"},{"location":"cour_note/D2QD_DigitalDesign/Chap02/#\u6309\u7167\u5b57\u9762\u91cf\u5b57\u9762\u91cf\u8ba1","title":"\u6309\u7167\u5b57\u9762\u91cf\u5b57\u9762\u91cf\u8ba1","text":"<p>\u5f88\u76f4\u767d\uff0c\u5c31\u662f\u6309\u7167\u8868\u8fbe\u5f0f\u4e2d\u6709\u591a\u5c11\u5b57\u9762\u91cf\u6765\u8ba1\u7b97\uff0c\u4f8b\u5982\uff1a</p> <ul> <li>\\(F = BD + A\\overline{B}C + A\\overline{C}\\,\\overline{D}\\) \u4e2d \\(L = 8\\)\uff1b</li> <li>\\(F = ABC+\\overline{A}\\,\\overline{B}\\,\\overline{C}\\) \u4e2d \\(L = 6\\)\uff1b</li> <li>\\(F = (A+B+C)(\\overline{A}+\\overline{B} + \\overline{C})\\) \u4e2d \\(L = 6\\)\uff1b</li> </ul> <p>\u53ef\u4ee5\u60f3\u8c61\uff0c\u867d\u7136\u8fd9\u79cd\u8ba1\u7b97\u65b9\u6cd5\u975e\u5e38\u7684\u7b80\u5355\uff0c\u4f46\u662f\u611f\u89c9\u4e0d\u592a\u9760\u8c31\u3002\u6bd4\u5982\uff0c\u540e\u9762\u4e24\u4e2a\u4f8b\u5b50\uff0c\u867d\u7136\u4ed6\u4eec\u7684 literal cost \u662f\u4e00\u6837\u7684\uff0c\u4f46\u662f\u663e\u7136\u5f00\u9500\u4e0d\u592a\u4e00\u6837\uff08\u56e0\u4e3a\u4e00\u4e2a\u662f 3+3 \u4e00\u4e2a\u662f 2+2+2\uff09\u3002\u6240\u4ee5\u6211\u4eec\u9700\u8981\u4e00\u4e2a\u66f4\u5408\u9002\u7684\u8ba1\u7b97\u65b9\u6cd5\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap02/#\u6309\u95e8\u8f93\u5165\u8ba1","title":"\u6309\u95e8\u8f93\u5165\u8ba1","text":"<p>\u6309\u7167\u95e8\u8f93\u5165\u8ba1\u5c31\u662f\u6309\u7167\u903b\u8f91\u95e8\u8f93\u5165\u5f15\u811a\u7684\u603b\u4e2a\u6570\u6765\u8ba1\u7b97\uff0c\u8fd9\u91cc\u7684\u8f93\u5165\u5e76\u4e0d\u4ec5\u4ec5\u662f\u76f4\u63a5\u6765\u81ea\u4e8e\u5b57\u9762\u91cf\u8f93\u5165\u7684\u90a3\u4e9b\u5f15\u811a\uff0c\u4e5f\u5305\u62ec\u5b57\u9762\u91cf\u505a\u8fd0\u7b97\u540e\u5f97\u5230\u7684\u7ed3\u679c\u4f5c\u4e3a\u8f93\u5165\u4f20\u5165\u4e0b\u4e00\u7ea7\u903b\u8f91\u95e8\u7684\u5f15\u811a\u3002</p> <p>\u6ce8\u610f</p> <p>\u867d\u7136\u975e\u95e8\u4e5f\u662f\u95e8\uff0c\u4f46\u662f\u6211\u4eec\u901a\u5e38\u4e0d\u628a\u975e\u95e8\u76f4\u63a5\u8ba1\u5165 gate-input cost\uff0c\u6240\u4ee5\u63a5\u4e0b\u6765\u63d0\u5230\u7684\u201c\u8f93\u5165\u5f15\u811a\u201d\u9ed8\u8ba4\u662f\u4e0d\u5305\u542b\u975e\u95e8\u7684\u8f93\u5165\u5f15\u811a\u7684\u3002</p> <p></p> <p>\u4f8b\u5982\u8fd9\u5f20\u5bf9\u5e94\u8868\u8fbe\u5f0f \\(F = A+BC+\\overline{B}\\,\\overline{C}\\) \u7684\u56fe\u4e2d\uff1a</p> <ul> <li>\u7eff\u8272\u539f\u70b9\u8868\u793a\u4e00\u7ea7\u8f93\u5165\u5f15\u811a\uff1b</li> <li>\u84dd\u8272\u65b9\u70b9\u8868\u793a\u4e8c\u7ea7\u8f93\u5165\u5f15\u811a\uff1b</li> <li>\u9ed1\u8272\u4e09\u89d2\u8868\u793a\u975e\u95e8\u7684\u8f93\u5165\u5f15\u811a\uff1b</li> </ul> <p>\u4e5f\u5c31\u662f\u8bf4\uff0c\u8fd9\u91cc\u4e00\u5171\u6709 5 + 2 = 7 \u4e2a\u8f93\u5165\u5f15\u811a\uff0c\u4ee5\u53ca 2 \u4e2a\u975e\u95e8\u8f93\u5165\u5f15\u811a\u3002</p> <p>\u4ece\u8868\u8fbe\u5f0f\u6765\u770b\uff0c\u5b83\u53ef\u4ee5\u770b\u4f5c\u662f\u6bcf\u4e00\u5c42\u8fd0\u7b97\u7684\u53c2\u6570\u6570\u91cf\u6c42\u548c\uff0c\u4e0d\u8fc7\u6211\u4eec\u5ffd\u7565\u975e\u95e8\u3002</p> <p>\u4f8b\u5982\uff0c\u5f0f\u5b50 \\(F=AB+\\overline{B}C+C\\overline{D}\\) \u4e2d\uff0c\u6700\u9876\u5c42\u7684\u8fd0\u7b97\u662f\u4e00\u4e2a\u4e09\u8f93\u5165\u6216\u8fd0\u7b97\uff0c\u6240\u4ee5\u6709 3 \u4e2a\u8f93\u5165\uff1b\u63a5\u4e0b\u6765\u6709\u4e09\u4e2a\u4e8c\u8f93\u5165\u4e0e\u8fd0\u7b97\uff0c\u6240\u4ee5\u5404\u8ba1 2 \u4e2a\u8f93\u5165\uff0c\u4e00\u5171 2 * 3 = 6 \u4e2a\u8f93\u5165\uff0c\u4e00\u5171\u662f 9 \u4e2a\u8f93\u5165\u3002</p> <p>\u5f53\u7136\uff0c\u5b9e\u9645\u4e0a\u4ece\u5e95\u5c42\u5f80\u4e0a\u6570\u66f4\u65b9\u4fbf\uff1a</p> <ul> <li>A \u548c B \u5404\u81ea\u7b97\u4e00\u4e2a\uff0cAB \u6574\u4f53\u7b97\u4e00\u4e2a\uff0c\u4e00\u5171 3 \u4e2a\uff1b</li> <li>\u4e00\u5171\u6709\u4e09\u7ec4\u7c7b\u4f3c AB \u7684\u7ed3\u6784\uff0c\u6240\u4ee5\u4e00\u5171\u662f 3 * 3 = 9 \u4e2a\uff1b</li> <li>\u5373 \\(G=9\\)\uff1b</li> </ul> <p>\u603b\u4e4b\uff0c\u5c31\u662f\u7c7b\u4f3c\u4e8e\u5728\u505a\u7b97\u5f0f\u5316\u7b80\uff0c\u6bcf\u505a\u4e00\u6b21\u5316\u7b80\u90fd\u9700\u8981\u8ba1\u5165\u4e00\u6b21\u64cd\u4f5c\u6570\u7684\u6570\u91cf\u3002</p> <p>\u800c\u5bf9\u4e8e gate-input cost with NOTs\uff0c\u53ea\u8981\u518d\u989d\u5916\u8ba1\u5165\u975e\u95e8\u7684\u8f93\u5165\u5373\u53ef\u3002\u4f8b\u5982\u4e0a\u9762\u90a3\u4e2a\u5f0f\u5b50\uff1a</p> <ul> <li>\u53d1\u73b0\u6709\u4e24\u4e2a\u88ab\u975e\u4e86\u7684\u5b57\u9762\u91cf\uff0c\u6240\u4ee5\u8981\u989d\u5916\u8ba1 2 \u4e2a\uff0c\u4e00\u5171\u662f 11 \u4e2a\uff1b</li> <li>\u5373 \\(GN=11\\)\uff1b</li> </ul> <p>\u6ce8\u610f</p> <p>\u5982\u679c\u51fa\u73b0\u4e86\u6bd4\u5982 \\(F=\\overline{A}B+\\overline{A}C\\) \u7684\u60c5\u51b5\uff0c\u975e\u95e8\u53ea\u9700\u8981\u8ba1 1 \u4e2a\uff0c\u56e0\u4e3a\u6211\u4eec\u5b9e\u9645\u4e0a\u662f\u628a\u975e\u4e86\u4ee5\u540e\u7684\u4e1c\u897f\u5f53\u4f5c\u4e86\u4e00\u4e2a\u5b57\u9762\u91cf\u518d\u7528\u7684\uff0c\u5728\u5b9e\u9645\u7535\u8def\u4e2d\uff0c\u6211\u4eec\u53ea\u9700\u8981\u975e\u4e00\u6b21\uff0c\u4e4b\u540e\u53ea\u9700\u8981\u628a\u8fd9\u4e2a\u8f93\u51fa\u503c\u62ff\u8d70\u53bb\u7528\u5c31\u884c\u3002</p> <p>\u63a5\u4e0b\u6765\u653e\u51e0\u9053\u4f8b\u9898\u3002</p> \u9898\u9762\u7b54\u6848 <p>\u8ba1\u7b97 \\(F=ABC+\\overline{A}\\,\\overline{B}\\,\\overline{C}\\) \u7684 \\(L\\)\u3001\\(G\\)\u3001\\(GN\\)\u3002</p> <ul> <li>\\(L = 6\\)\uff1b</li> <li>\\(G = 8\\)\uff1b</li> <li>\\(GN = 11\\)\uff1b</li> </ul> \u9898\u9762\u7b54\u6848 <p>\u8ba1\u7b97 \\(F=(A+\\overline{C})(\\overline{B}+C)(\\overline{A}+B)\\) \u7684 \\(L\\)\u3001\\(G\\)\u3001\\(GN\\)\u3002</p> <ul> <li>\\(L = 6\\)\uff1b</li> <li>\\(G = 9\\)\uff1b</li> <li>\\(GN = 12\\)\uff1b</li> </ul> \u9898\u9762\u7b54\u6848 <p>\u8ba1\u7b97 \\(F=(A+\\overline{B})(A+D)(B+C+\\overline{D})(\\overline{B}+\\overline{C}+D)\\) \u7684 \\(L\\)\u3001\\(G\\)\u3001\\(GN\\)\u3002</p> <ul> <li>\\(L = 10\\)\uff1b</li> <li>\\(G = 14\\)\uff1b</li> <li>\\(GN = 17\\)\uff1b</li> </ul> <p>\u8fd9\u91cc\u9700\u8981\u6ce8\u610f\uff0c\u51fa\u73b0\u4e86\u91cd\u590d\u7684\u88ab\u975e\u4e86\u7684\u5b57\u9762\u91cf\uff0c\u4e0d\u8981\u91cd\u590d\u8ba1\u7b97\uff01</p> \u9898\u9762\u7b54\u6848 <p>\u8ba1\u7b97 \\(F=BD+A\\overline{B}C+A\\overline{B}\\,\\overline{D}+AB\\overline{C}\\) \u7684 \\(L\\)\u3001\\(G\\)\u3001\\(GN\\)\u3002</p> <ul> <li>\\(L = 11\\)\uff1b</li> <li>\\(G = 15\\)\uff1b</li> <li>\\(GN = 18\\)\uff1b</li> </ul> <p>\u8fd9\u91cc\u540c\u6837\u9700\u8981\u6ce8\u610f\uff0c\u51fa\u73b0\u4e86\u91cd\u590d\u7684\u88ab\u975e\u4e86\u7684\u5b57\u9762\u91cf\uff0c\u4e0d\u8981\u91cd\u590d\u8ba1\u7b97\uff01</p> \u9898\u9762\u7b54\u6848 <p>\u8ba1\u7b97 \\(F=\\overline{A}\\,\\overline{C}(B+\\overline{D})+AC(B+\\overline{D})\\) \u7684 \\(L\\)\u3001\\(G\\)\u3001\\(GN\\)\u3002</p> <ul> <li>\\(L = 8\\)\uff1b</li> <li>\\(G = 12\\)\uff1b</li> <li>\\(GN = 15\\)\uff1b</li> </ul> <p>\u8fd9\u91cc\u540c\u6837\u9700\u8981\u6ce8\u610f\uff0c\u51fa\u73b0\u4e86\u6bd4\u8f83\u590d\u6742\u7684\u903b\u8f91\u8fd0\u7b97\uff0c\u4ee5 \\(\\overline{A}\\,\\overline{C}(B+\\overline{D})\\) \u4e3a\u4f8b\uff0c\u81ea\u9876\u5411\u4e0b\u662f\uff1a\u24f5\u4e09\u8f93\u5165\u4e0e\u95e8\uff0c\u24f6\u4e8c\u8f93\u5165\u6216\u95e8\uff1b\u6240\u4ee5\u5e94\u8be5\u662f \\(1^{\\overline{A}} + 1^{\\overline{C}} + 1^{B} + 1^{\\overline{D}} + 1^{B+\\overline{D}} + 1^{\\overline{A}\\,\\overline{C}(B+\\overline{D})}\\)\uff0c\u5373 6\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap02/#\u5361\u8bfa\u56fe","title":"\u5361\u8bfa\u56fe","text":""},{"location":"cour_note/D2QD_DigitalDesign/Chap02/#\u5361\u8bfa\u56fe\u7684\u601d\u60f3","title":"\u5361\u8bfa\u56fe\u7684\u601d\u60f3","text":"<p>\u4f18\u5316\u903b\u8f91\u8868\u8fbe\u5f0f\u6700\u76f4\u767d\u7684\u601d\u60f3\u5c31\u662f\u51cf\u5c11\u95e8\u7535\u8def\uff0c\u4e5f\u5c31\u662f\u53bb\u51cf\u5c11 gate-input cost\u3002\u90a3\u4e48\u8981\u5982\u4f55\u505a\u5462\uff1f</p> <p>\u6211\u4eec\u8003\u8651\u5230\u903b\u8f91\u8fd0\u7b97\u5f8b\u4e2d\u7684\u8fd9\u4e2a\u63a8\u5e7f\uff1a\\(XY+X\\overline{Y}=X(Y+\\overline{Y})=X\\)\uff0c\u4e5f\u5c31\u662f\u8bf4\uff0c\u5982\u679c\u4e24\u4e2a\u6700\u5c0f\u9879\u53ea\u5dee\u4e00\u4e2a\u5b57\u9762\u91cf\u7684\u975e\uff0c\u90a3\u4e48\u4ed6\u4eec\u662f\u53ef\u4ee5\u5408\u5e76\u7684\uff1b\u5f53\u7136\uff0c\u5bf9\u79f0\u7684\uff0c\u6839\u636e\\((X+\\overline{Y})(X+Y)=X+Y\\overline{Y}=X\\)\uff0c\u6211\u4eec\u4e5f\u53ef\u4ee5\u5f97\u5230\u8fd9\u4e2a\u7ed3\u8bba\u5bf9\u6700\u5927\u9879\u4e5f\u6210\u7acb\u3002</p> <p>\u662f\u4e0d\u662f\u89c9\u5f97\u201c\u53ea\u5dee\u4e00\u4e2a\u201d\u5f88\u8033\u719f\uff1f\u662f\u7684\uff01\u6211\u4eec\u60f3\u5230\u4e86\u683c\u96f7\u7801\uff01\u5047\u8bbe\u6211\u4eec\u5c06 n \u4e2a\u5b57\u9762\u91cf\u6392\u5217\u6210\u4e00\u4e2a n bits \u7684\u5411\u91cf\uff0c\u90a3\u4e48\u53ea\u9700\u8981\u6309\u7167\u683c\u96f7\u7801\u6392\u5e8f\uff0c\u4e00\u65e6\u53d1\u73b0\u6709\u76f8\u90bb\u7684\u6700\u5c0f\u9879\uff0c\u6211\u4eec\u5c31\u53ef\u4ee5\u5408\u5e76\u4ed6\u4eec\u3002</p> <p>\u4f46\u8fd9\u8fd8\u4e0d\u591f\u5145\u5206\uff0c\u4f8b\u5982\u5728\u4e00\u4e2a\u6709\u4e09\u4e2a\u5b57\u9762\u91cf\u7684\u903b\u8f91\u8868\u8fbe\u5f0f\u4e2d\uff0c\u201c\u4e0e\u4e00\u4e2a\u8868\u8fbe\u5f0f\u76f8\u90bb\u201d\u7684\u8868\u8fbe\u5f0f\u5176\u5b9e\u6709\u4e09\u4e2a\uff0c\u4f46\u662f\u7528\u7ebf\u6027\u7684\u8868\u793a\u65b9\u6cd5\u53c8\u6ca1\u6cd5\u5f88\u597d\u7684\u8868\u793a\u8fd9\u4e00\u70b9\uff0c\u6240\u4ee5\u6211\u4eec\u60f3\u5230\u5c06\u5b83\u5199\u6210\u4e00\u5f20\u4e8c\u7ef4\u7684\u8868\uff0c\u5373\u5c06\u5b57\u9762\u91cf\u62c6\u6210\u4e24\u7ec4 bit \u5411\u91cf\uff0c\u5404\u81ea\u6309\u7167\u683c\u96f7\u7801\u6392\u5217\uff0c\u5f62\u6210\u4e00\u5f20\u4e8c\u7ef4\u8868\uff0c\u8fd9\u5c31\u662f \u5361\u8bfa\u56fe(Karnaugh Map)\uff0c\u4e5f\u53eb K-map\u3002</p> <p></p> <p>\u53ef\u4ee5\u53d1\u73b0\uff0c\u4efb\u610f\u4e24\u4e2a\u76f8\u90bb\u7684\u683c\u5b50\u90fd\u53ea\u5dee\u4e00\u4e2a\u5b57\u9762\u91cf\u7684\u975e\uff0c\u800c\u4e14\u662f\u5145\u8981\u7684\uff0c\u5373\u6240\u6709\u201c\u76f8\u90bb\u201d\u90fd\u53ef\u4ee5\u5728\u8fd9\u5f20\u56fe\u8868\u73b0\u51fa\u6765\u3002</p> <p>\u8bf4\u660e</p> <p>\u7531\u4e8e\u683c\u96f7\u7801\u7684\u6027\u8d28\u662f\u4e00\u4e2a\u5728\u201c\u6ee1\u201d\u72b6\u6001\u4e0b \u73af\u72b6\u6210\u7acb \u7684\u6027\u8d28\uff0c\u6240\u4ee5\u5361\u8bfa\u56fe\u4e5f\u9700\u8981\u7528\u201c\u73af\u72b6\u201d\u7684\u601d\u8def\u53bb\u770b\uff0c\u8fd9\u91cc\u53ef\u4ee5\u8054\u60f3\u4e00\u4e0b\u884c\u5217\u5f0f\u7684\u5f62\u8c61\u5316\u8ba1\u7b97\u65b9\u6cd5\uff0c\u5c06\u8fd9\u5f20\u8868\u5f53\u4f5c\u4e00\u4e2a\u65e0\u9650\u6269\u5c55\u7684\u8868\u683c\u3002</p> <p>\u601d\u8003\u9898</p> <p>\u5728\u8fd9\u91cc\uff0c\u4e5f\u53ef\u4ee5\u5c1d\u8bd5\u7740\u611f\u53d7\u4e00\u4e0b\u4e24\u4e2a\u5b57\u9762\u91cf\u7684\u60c5\u51b5\u4e0b\uff0c\u5373\u5b9e\u9645\u4e0a\u201c\u76f8\u90bb\u4e5f\u53ea\u67092\u4e2a\u201d\u7684\u60c5\u51b5\u4e0b\uff0c\u4e5f\u53ef\u4ee5\u4f7f\u7528\u201c4\u4e2a\u76f8\u90bb\u201d\u7684\u5361\u8bfa\u56fe\u3002\u4e8b\u5b9e\u4e0a\uff0c\u4e09\u4e2a\u5b57\u9762\u91cf\u4e5f\u53ea\u6709\u201c3\u4e2a\u76f8\u90bb\u201d\uff0c\u4f46\u662f\u4e3a\u4ec0\u4e48\u53ef\u4ee5\u7528\u660e\u660e\u6709\u201c4\u4e2a\u76f8\u90bb\u201d\u7684\u5361\u8bfa\u56fe\u6765\u5b9e\u73b0\u5462\uff1f</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap02/#\u5361\u8bfa\u56fe\u7684\u5c40\u9650\u6027","title":"\u5361\u8bfa\u56fe\u7684\u5c40\u9650\u6027","text":"<p>\u7136\u800c\uff0c\u4e0a\u9762\u7684\u8bf4\u6cd5\u5176\u5b9e\u5f88\u7275\u5f3a\u3002\u56e0\u4e3a\u4e00\u5f20\u4e8c\u7ef4\u8868\u4e2d\uff0c\u80fd\u4e0e\u4e00\u4e2a\u5143\u7d20\u76f8\u90bb\u7684\u5143\u7d20\u6700\u591a\u53ea\u6709\u56db\u4e2a\uff0c\u4e5f\u5c31\u662f\u8bf4\u6211\u4eec\u6491\u6b7b\u4e5f\u53ea\u80fd\u7528\u5361\u8bfa\u56fe\u8868\u793a 4 \u4e2a\u5b57\u9762\u91cf\u7684\u60c5\u51b5\uff08\u5f53\u7136\u66f4\u591a\u7684\u53d8\u91cf\u4e5f\u6709\u5904\u7406\u7684\u65b9\u6cd5\uff0c\u4f46\u662f\u591a\u5c11\u6709\u70b9\u9ebb\u70e6\u4e86\uff09\u3002\u56e0\u6b64\uff0c\u5b9e\u9645\u4e0a\u5361\u8bfa\u56fe\u53ea\u80fd\u7528\u4e8e\u5316\u7b80\u975e\u5e38\u7b80\u5355\u7684\u903b\u8f91\u8868\u8fbe\u5f0f\u3002</p> <p>cm \u8001\u5e08\u5982\u662f\u8bf4</p> <p>\u66f4\u591a\u60c5\u51b5\u4e0b\uff0c\u5361\u8bfa\u56fe\u5b9e\u9645\u4e0a\u53ea\u9002\u5408\u6211\u4eec\u505a\u9898\u3002\u4f46\u662f\u5176\u601d\u8def\u662f\u975e\u5e38\u6709\u610f\u601d\u7684\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap02/#\u5361\u8bfa\u56fe\u7684\u7ed3\u6784","title":"\u5361\u8bfa\u56fe\u7684\u7ed3\u6784","text":"<p>\u8fd9\u91cc\u6211\u4eec\u4ee5 3 \u5143\u7684\u903b\u8f91\u8868\u8fbe\u5f0f\u4e3a\u4f8b\uff0c2 \u5143\u548c 4 \u5143\u7684\u601d\u8def\u662f\u4e00\u6837\u7684\u3002</p> <p>\u540c\u6837\uff0c\u4e3e\u4e00\u4e2a \ud83c\udf30 \uff1a\\(F(X,Y,Z) = \\sum m(2,3,4,5)\\)</p> <p>\u9996\u5148\u6211\u4eec\u6309\u7167\u6bd4\u7279\u5411\u91cf\u7684\u5f62\u5f0f\u628a\u6700\u5c0f\u9879\u5199\u51fa\u6765\uff1a</p> \u503c X Y Z 2 0 1 0 3 0 1 1 4 1 0 0 5 1 0 1 <p>\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u6765\u7ed8\u5236\u5361\u8bfa\u56fe\uff0c\u6211\u4eec\u5c06 bit \u5411\u91cf <code>[x, y, z]</code> \u62c6\u6210 <code>[x]</code> \u548c <code>[y, z]</code> \u505a\u5982\u4e0b\u8868\u683c\uff1a</p> <code>yz</code> = <code>00</code> <code>yz</code> = <code>01</code> <code>yz</code> = <code>11</code> <code>yz</code> = <code>10</code> <code>x</code> = <code>0</code> 0 0 1 1 <code>x</code> = <code>1</code> 1 1 0 0 <p>\u53e6\u5916\u4e00\u79cd\u6807\u6ce8\u8868\u683c\u7684\u65b9\u5f0f\u662f\u8fd9\u6837\uff0c\u5b83\u53ef\u80fd\u66f4\u6e05\u6670\uff1a</p> <p></p> <p>\u4f46\u662f\u4ed6\u4eec\u7684\u672c\u8d28\u90fd\u662f\u683c\u96f7\u7801\u3002</p> <p>4 \u5143\u5b57\u9762\u91cf\u7684\u5361\u8bfa\u56fe\u5219\u957f\u8fd9\u4e2a\u6837\u5b50\uff1a</p> <p></p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap02/#\u4f7f\u7528\u5361\u8bfa\u56fe\u4f18\u5316","title":"\u4f7f\u7528\u5361\u8bfa\u56fe\u4f18\u5316","text":"<p>\u5df2\u7ecf\u8bb2\u4e86\u601d\u60f3\u548c\u5361\u8bfa\u56fe\u7684\u7ed3\u6784\uff0c\u90a3\u4e48\u5230\u5e95\u8981\u5982\u4f55\u5229\u7528\u5361\u8bfa\u56fe\u8fdb\u884c\u4f18\u5316\u5462\uff1f</p> <p>\u8ba9\u6211\u4eec\u56de\u987e\u4f18\u5316\u7684\u65b9\u6cd5\uff0c\u5373\u5408\u5e76\u76f8\u90bb\u4e24\u9879\uff0c\u4e5f\u5c31\u662f\u627e\u5230\u5361\u8bfa\u56fe\u4e2d\u76f8\u90bb\u7684\u90e8\u5206\u3002\u4f46\u662f\u8fd9\u4e0d\u591f\uff0c\u6211\u4eec\u8fd8\u8981\u601d\u8003\u662f\u4e0d\u662f\u80fd\u5408\u5e76\u5df2\u7ecf\u76f8\u90bb\u7684\u90e8\u5206\uff0c\u6bd4\u5982\uff1a</p> <p>\u6211\u4eec\u901a\u8fc7\u5361\u8bfa\u56fe\uff0c\u9996\u5148\u5408\u5e76\u4e86 \\(WXYZ\\) \u548c \\(WXY\\overline{Z}\\)\uff0c\\(WX\\overline{Y}Z\\) \u548c \\(WX\\overline{Y}\\,\\overline{Z}\\)\uff0c\u5206\u522b\u5f97\u5230\u4e86 \\(WXY\\) \u548c \\(WX\\overline{Y}\\)\uff0c\u663e\u7136\u8fd9\u4e24\u4e2a\u4e1c\u897f\u4e5f\u662f\u53ef\u4ee5\u5408\u5e76\u7684\uff1b\u800c\u5728\u5361\u8bfa\u56fe\u4e0a\uff0c\u8fd9\u8868\u73b0\u4e3a\u4e24\u4e2a\u76f8\u90bb\u7684 <code>1*2</code> \u7684\u77e9\u5f62\u3002</p> <p>\u603b\u800c\u8a00\u4e4b\uff0c\u8fd9\u79cd\u8fed\u4ee3\u5408\u5e76\u7684\u884c\u4e3a\u6700\u7ec8\u53ef\u4ee5\u5212\u5f52\u4e3a\u8fd9\u6837\u4e00\u4e2a\u884c\u4e3a\uff1a</p> <p>\u6211\u4eec\u5728\u5361\u8bfa\u56fe\u4e2d\u5bfb\u627e\u82e5\u5e72 \u6781\u5927 \u7684 2 \u5e42\u77e9\u5f62\uff0c\u5373\u5143\u7d20\u4e2a\u6570\u4e3a 2 \u7684\u5e42\u6b21\uff08\u81ea\u7136\u8fb9\u957f\u4e5f\u90fd\u4e3a 2 \u7684\u5e42\u6b21\uff09\u7684\u77e9\u5f62\uff0c\u800c\u6bcf\u4e00\u4e2a\u77e9\u5f62\u6240\u8986\u76d6\u7684\u5143\u7d20\u90fd\u5e94\u8be5\u662f \u6700\u5c0f\u9879/\u6700\u5927\u9879\uff08\u4e00\u822c\u90fd\u662f\u505a\u6700\u5c0f\u9879\uff09\u3002\u9700\u8981\u6ce8\u610f\uff0c\u201c\u5faa\u73af\u201d\u7684\u6027\u8d28\u4ecd\u7136\u6ee1\u8db3\uff0c\u5373\u7b2c\u4e00\u5217\u548c\u6700\u540e\u4e00\u5217\uff0c\u7b2c\u4e00\u884c\u548c\u6700\u540e\u4e00\u884c\u4e5f\u53ef\u4ee5\u8ba4\u4e3a\u662f\u76f8\u90bb\u7684\u3002</p> <p></p> <p></p> <p>\u4f8b\u5982\uff1a</p> <p></p> <p>\u4f8b\u5982\uff1a</p> <p></p> <p>\u518d\u4f8b\u5982\uff1a</p> <p></p> <p>\u90fd\u662f\u5408\u7406\u7684\u5361\u8bfa\u56fe\u5212\u5206\u3002</p> <p>\u5728\u5f97\u5230\u8fd9\u4e9b\u5212\u5206\u540e\uff0c\u6211\u4eec\u5c31\u53ef\u4ee5\u5f88\u65b9\u4fbf\u5730\u5c06\u8fd9\u4e9b\u9879\u62ce\u51fa\u6765\uff0c\u5199\u51fa\u5b83\u4eec\u7684\u8868\u8fbe\u5f0f\u3002</p> <p>\u800c\u81f3\u4e8e\u5982\u4f55\u62ce\u51fa\u6765\u2014\u2014\u4e0d\u96be\u53d1\u73b0\uff0c\u5982\u679c\u4e00\u4e2a\u65b9\u6846\u4e2d\uff0c\u67d0\u4e00\u4e2a\u5b57\u9762\u91cf\u7684\u503c\u65e2\u53ef\u4ee5\u662f <code>0</code>\uff0c\u53c8\u53ef\u4ee5\u662f <code>1</code> \u65f6\uff08\u8fd9\u91cc\u6307\u7684\u662f\u8f93\u5165\u7684\u503c\uff0c\u5e76\u975e\u8f93\u51fa\u7ed3\u679c\uff09\uff0c\u5728\u8fd9\u4e2a\u4f18\u5316\u9879\u7684\u7ed3\u679c\u4e2d\u5c31\u53ef\u4ee5\u4e0d\u7528\u5199\u51fa\u8fd9\u4e2a\u5b57\u9762\u91cf\uff1b\u53cd\u4e4b\uff0c\u5982\u679c\u8fd9\u4e2a\u5b57\u9762\u91cf \\(X\\) \u7684\u503c\u90fd\u662f <code>0</code>\uff0c\u5219\u7ed3\u679c\u4e2d\u4f1a\u5305\u542b \\(\\overline{X}\\)\uff0c\u5982\u679c\u90fd\u662f <code>1</code>\uff0c\u5219\u7ed3\u679c\u4e2d\u4f1a\u5305\u542b \\(X\\)\u3002</p> \u9898\u9762\u7b54\u6848 <p>\u5229\u7528\u5361\u8bfa\u56fe\u4f18\u5316 \\(F(X,Y,Z) = \\sum m(0,1,2,4,6,7)\\) \u7684\u7ed3\u679c\u3002</p> <p>\u753b\u51fa\u8fd9\u4e2a\u8868\u8fbe\u5f0f\u5bf9\u5e94\u7684\u5361\u8bfa\u56fe\uff1a</p> <p></p> <p>\u7136\u540e\u5212\u51fa\u5176\u4e2d\u7684\u6781\u5927\u6700\u5c0f\u9879\u4f18\u5316\u9879\uff1a</p> <p></p> <p>\u5199\u51fa\u6765\u662f\uff1a</p> <ul> <li>\u7eff\uff1a\\(x=0,\\;y=0,\\;z=0/1\\)<ul> <li>\u6240\u4ee5\u662f\uff1a\\(\\overline{X}\\,\\overline{Y}\\)\uff1b</li> </ul> </li> <li>\u84dd\uff1a\\(x=0/1,\\;y=0/1,\\;z=0\\)<ul> <li>\u6240\u4ee5\u662f\uff1a\\(\\overline{Z}\\)\uff1b</li> </ul> </li> <li>\u7ea2\uff1a\\(x=1,\\;y=1,\\;z=0/1\\)<ul> <li>\u6240\u4ee5\u662f\uff1a\\(XY\\)</li> </ul> </li> </ul> <p>\u7efc\u4e0a\u6240\u8ff0\uff0c\u4f18\u5316\u7ed3\u679c\u662f \\(F = \\overline{X}\\,\\overline{Y} + \\overline{Z} + XY\\)</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap02/#\u4e0d\u5b9a\u9879","title":"\u4e0d\u5b9a\u9879","text":"<p>\u63a8\u8350\u9605\u8bfb</p> <p>https://www.geeksforgeeks.org/dont-care-x-conditions-in-k-maps/</p> <p>\u4e0d\u5b9a\u9879(Don't Cares) \u6307\u7684\u662f\u9700\u8981\u5316\u7b80\u7684\u903b\u8f91\u51fd\u6570\u4e2d\uff0c\u6ca1\u6709\u7ed9\u51fa\u5b9a\u4e49\u7684\u51e0\u9879\uff0c\u5b83\u4eec\u53ef\u80fd\u662f\uff1a</p> <ul> <li>\u8f93\u5165\u7ec4\u5408\u4e0d\u4f1a\u51fa\u73b0\uff1b</li> <li>\u8f93\u5165\u7ec4\u5408\u7684\u8f93\u51fa\u4e0d\u88ab\u4f7f\u7528\uff1b</li> </ul> <p>\u5bf9\u4e8e\u8fd9\u79cd\u9879\uff0c\u5728\u5361\u8bfa\u56fe\u4e2d\u7528 X \u6765\u8868\u793a\uff0c\u5728\u6700\u5c0f\u9879\u4e4b\u548c\u4e2d\u7528 \\(\\sum d(...)\\) \u8868\u793a\u3002\u6211\u4eec\u53ef\u4ee5\u968f\u610f\u5b9a\u4e49\u5b83\u4eec\u7684\u8f93\u51fa\uff0c\u6b64\u65f6\u5c31\u53ef\u4ee5\u5229\u7528\u8fd9\u4e9b\u9879\u6765\u65b9\u4fbf\u6211\u4eec\u7684\u4f18\u5316\u2014\u2014\u5f53\u6211\u4eec\u753b\u51fa\u6765\u7684\u6781\u5927\u77e9\u9635\u8d8a\u5927\uff0c\u6210\u672c\u5c31\u8d8a\u4f4e\u3002</p> <p>\u4f8b\u5982\uff0c\u6211\u4eec\u5b9a\u4e49\u4e00\u4e2a\u51fd\u6570\uff0c\u5f53\u8f93\u5165\u7684 BCD \u7801\u8868\u793a\u7684\u6570\u5b57\u5927\u4e8e\u7b49\u4e8e 5 \u65f6\u8fd4\u56de <code>1</code>\uff0c\u5219\u5b83\u53ef\u4ee5\u901a\u8fc7\u8fd9\u6837\u7684\u5f62\u5f0f\u6765\u4f18\u5316\uff1a</p> <p></p> <p>\u6839\u636e\u7ed3\u679c\uff0c\u5199\u51fa\u4f18\u5316\u540e\u7684\u8868\u8fbe\u5f0f\u4e3a\uff1a\\(F(W,X,Y,Z) = W + XY + XZ\\)\u3002</p> <p>\u7531\u5361\u8bfa\u56fe\u5f97\u5230\u4e58\u79ef\u7ed3\u679c</p> <p>\u5c3d\u7ba1\u6211\u4eec\u4e0d\u505c\u5f3a\u8c03 \u4e0e \u548c \u6216 \u662f\u5bf9\u79f0\u7684\uff0c\u4f46\u662f\u4ecd\u7136\u6709\u5f88\u591a\u64cd\u4f5c\u662f\u9274\u4e8e\u6211\u4eec\u5bf9 <code>1</code> \u7684\u504f\u7231\u624d\u4f1a\u987a\u624b\u7684\uff08\u4f60\u4f1a\u53d1\u73b0\uff0c\u628a\u4e58\u9664\u6362\u6210\u6211\u4eec\u5b8c\u5168\u4e0d\u719f\u6089\u7684\u7b26\u53f7\uff0c\u4f60\u751a\u81f3\u53ef\u80fd\u65e0\u4ece\u4e0b\u624b\uff09\u3002</p> <p>\u6240\u4ee5\uff0c\u5728\u5361\u8bfa\u56fe\u7684\u95ee\u9898\u4e2d\uff0c\u5982\u679c\u8981\u5229\u7528\u5361\u8bfa\u56fe\u5f97\u5230 \\(F\\) \u4f18\u5316\u540e\u7684\u4e58\u79ef\u5f62\u5f0f\uff0c\u4e5f\u53ef\u4ee5\u5c06\u95ee\u9898\u8f6c\u5316\u4e3a\u6c42 \\(\\overline{F}\\) \u4f18\u5316\u540e\u7684\u548c\u5f62\u5f0f\uff0c\u7136\u540e\u518d\u5bf9\u5176\u53d6\u53cd\u8fc7\uff0c\u5229\u7528\u5fb7\u00b7\u6469\u6839\u5b9a\u5f8b\u6765\u5f97\u5230\u7ed3\u679c\u3002</p> <p>\u5177\u4f53\u6765\u8bf4\u5c31\u662f\u53cd\u8f6c K-map \u4e2d\u6240\u6709\u7684 <code>0</code> \u548c <code>1</code>\uff0c\u7136\u540e\u7740\u773c\u4e8e SOM \u8fdb\u884c\u4f18\u5316\uff0c\u6700\u540e\u518d\u5bf9\u7ed3\u679c\u53d6\u53cd\uff0c\u7528\u5fb7\u00b7\u6469\u6839\u5b9a\u5f8b\u6765\u5f97\u5230\u7ed3\u679c\u3002</p> eg <p></p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap02/#\u8574\u542b\u9879\u4e3b\u8574\u542b\u9879\u4e0e\u57fa\u672c\u4e3b\u8574\u542b\u9879","title":"\u8574\u542b\u9879\u3001\u4e3b\u8574\u542b\u9879\u4e0e\u57fa\u672c\u4e3b\u8574\u542b\u9879","text":"<p>\u8574\u542b\u9879(implicant) \u5206\u4e3a \u4e3b\u8574\u542b\u9879(prime implicant) \u548c \u57fa\u672c\u4e3b\u8574\u542b\u9879(essential prime implicant)\u3002</p> <ul> <li>\u5728\u5361\u8bfa\u56fe\u4e2d\uff0c\u4e00\u4e2a\u8574\u542b\u9879\u5c31\u662f\u4efb\u610f\u4e00\u4e2a\u5305\u542b \\(2^n\\) \u4e2a <code>1</code> \u7684\u5355\u5143\uff1b</li> <li>\u800c\u4e3b\u8574\u542b\u9879\u5219\u662f\u5728\u5361\u8bfa\u56fe\u4e2d\u7684 \u6781\u5927 \u8574\u542b\u9879\uff1b<ul> <li>\u5bf9\u4e8e\u5b58\u5728 Dont'cares \u7684 K-map\uff0c\u5982\u679c\u6211\u4eec\u5173\u6ce8\u7684\u662f <code>1</code>\uff0c\u90a3\u6211\u4eec\u79ef\u6781\u5730\u5c06\u4ed6\u4eec\u5f53\u4f5c <code>1</code> \u6765\u5904\u7406\uff0c\u53cd\u4e4b\u4ea6\u7136\uff1b</li> <li>\u4f46\u662f\u5355\u72ec\u7684 <code>X</code> \u4e0d\u4f1a\u88ab\u8ba4\u4e3a\u662f\u4e3b\u8574\u542b\u9879\uff1b</li> </ul> </li> <li>\u57fa\u672c\u4e3b\u8574\u542b\u9879\u662f\u5305\u542b \u53ea\u88ab\u5b83(\u57fa\u672c\u4e3b\u8574\u542b\u9879)\u8986\u76d6\u7684 <code>1</code> \u7684\u4e3b\u8574\u542b\u9879\uff1b</li> </ul> <p></p> <p>\u5982\u56fe\uff0c\u5de6\u4fa7\u7684\u4e24\u4e2a\u4e3b\u8574\u542b\u9879\u56e0\u4e3a\u5305\u62ec\u4e86 \u24f5 \u548c \u24f6 \u8fd9\u4e24\u4e2a\u552f\u4e00\u7684 <code>1</code>\uff0c\u6240\u4ee5\u662f\u57fa\u672c\u4e3b\u8574\u542b\u9879\uff1b</p> <p>\u800c\u53f3\u4fa7\u7684\u8574\u542b\u9879\u5219\u662f\u4e00\u4e2a\u5197\u4f59\u7684\u8574\u542b\u9879\uff1b</p> <p>\u6ce8\u610f</p> <p>\u5bf9\u4e8e\u4efb\u610f\u51fd\u6570\uff0c\u4e3b\u8574\u542b\u9879\u4e00\u5b9a\u5b58\u5728\uff0c\u4f46\u662f\u57fa\u672c\u4e3b\u8574\u542b\u9879\u4e0d\u4e00\u5b9a\u5b58\u5728\u3002</p> <p>\ud83e\udd14</p> <p>\u6b63\u56e0\u4e3a\u6709\u57fa\u672c\u4e3b\u8574\u542b\u9879\u7684\u5b58\u5728\uff0c\u5bf9\u4e8e\u4e00\u4e2a\u4efb\u610f\u51fd\u6570\uff0c\u4f18\u5316\u7684\u591a\u89e3\u7ed3\u679c\u603b\u6709\u4e00\u90e8\u5206\u662f\u4e0d\u53d8\u7684\uff08\u53ea\u4e0d\u8fc7\u6ca1\u6709\u57fa\u672c\u4e3b\u8574\u542b\u9879\u7684\u65f6\u5019\u8fd9\u90e8\u5206\u4e3a\u96f6\uff09\u3002</p> <p>\u9ea6\u514b\u62c9\u594e\u56e0\u7b97\u6cd5</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap02/#\u7ecf\u5178\u7ec4\u5408\u7535\u8def","title":"\u7ecf\u5178\u7ec4\u5408\u7535\u8def","text":"<p>\u5f15\u5165</p> <p>\u5728\u5b9e\u9645\u8bbe\u8ba1\u4e2d\uff0c\u6211\u4eec\u6709\u4e00\u4e9b\u73b0\u6210\u7684\u7ec4\u5408\u7535\u8def\u80fd\u591f\u4f7f\u7528\uff0c\u6765\u65b9\u4fbf\u6211\u4eec\u8bbe\u8ba1\u3002</p> <p>\u4e0d\u8fc7\u6211\u6ca1\u6709\u5168\u5199\u51fa\u6765\uff1b</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap02/#\u4e09\u6001\u95e8","title":"\u4e09\u6001\u95e8","text":"<p>\u4e09\u6001\u7f13\u51b2\u5668(3-State Buffer)</p> <p>\u9664\u4e86\u8f93\u5165\u548c\u8f93\u51fa\uff0c\u5b83\u8fd8\u6709\u4e00\u4e2a \u4f7f\u80fd\u7aef(enable) \u6765\u63a7\u5236\u8f93\u51fa\u3002</p> <p>\u6240\u8c13\u7684\u4e09\u6001\u6307\u7684\u662f\uff1a</p> <ul> <li>\u5f53\u4f7f\u80fd\u7aef\u4e3a <code>1</code>\uff0c\u4e14\u8f93\u5165\u4e3a <code>1</code> \u65f6\uff0c\u8f93\u51fa\u4e3a <code>1</code>\uff1b</li> <li>\u5f53\u4f7f\u80fd\u7aef\u4e3a <code>1</code>\uff0c\u4e14\u8f93\u5165\u4e3a <code>0</code> \u65f6\uff0c\u8f93\u51fa\u4e3a <code>0</code>\uff1b</li> <li>\u5f53\u4f7f\u80fd\u7aef\u4e3a <code>0</code>\uff0c\u8f93\u51fa\u4e3a <code>Hi-Z</code>/<code>Z</code>/<code>z</code>(\u6d6e\u52a8\uff0c\u9ad8\u963b\u6001)\uff1b</li> </ul> <p></p> <p>\u4f5c\u7528</p> <p>\u6211\u4eec\u53ef\u4ee5\u7528\u4e09\u6001\u95e8\u6765\u89e3\u51b3\u591a\u8def\u8f93\u51fa\u4e92\u8054\u7684\u95ee\u9898\u3002\u6b63\u5982\u5728 ICS \u7b14\u8bb0\u4e2d\u63d0\u5230\u7684\uff0c\u53ef\u4ee5\u8ba9\u591a\u4e2a\u8f93\u5165\u5728\u540c\u4e00\u65f6\u523b\u53ea\u6709\u4e00\u4e2a\u88ab\u8f93\u51fa\u5230\u603b\u7ebf\u4e2d\u2014\u2014\u5b9e\u73b0\u7684\u624b\u6bb5\u5c31\u662f\u901a\u8fc7\u7535\u8def\u6765\u4f7f\u540c\u4e00\u65f6\u523b\u53ea\u6709\u4e00\u4e2a\u4f7f\u80fd\u7aef\u4e3a <code>1</code>\u3002</p> <p>\u5728\u6570\u5b57\u903b\u8f91\u8bbe\u8ba1\u4e2d\uff0c\u4e09\u6001\u95e8\u5b9e\u73b0\u603b\u7ebf\u7684\u76f8\u5173\u77e5\u8bc6\u5c06\u5728 \u7b2c\u516d\u7ae0 \u63d0\u5230\u3002</p> <p>\u788e\u788e\u5ff5</p> <p>\u6240\u4ee5\u4ec0\u4e48\u662f\u300c\u9ad8\u963b\u6001\u300d\uff1f\u5b83\u8981\u5982\u4f55\u7406\u89e3\uff1f\u4ee5\u4e0b\u662f\u6211\u6839\u636e\u5b83\u7684\u5e94\u7528\u53cd\u63a8\u5f97\u5230\u7684\u7ed3\u8bba\uff1a</p> <p>\u9ad8\u963b\u6001\u540c\u5b83\u5b57\u9762\u610f\u601d\u76f8\u540c\uff0c\u6211\u4eec\u53ef\u4ee5\u5f53\u5b83\u6b64\u65f6\u662f\u65ad\u8def\uff0c\u800c\u9ad8\u963b\u6001\u91cd\u70b9\u8981\u4e0e\u4f4e\u7535\u5e73\u505a\u533a\u5206\uff1a\u5982\u679c\u73b0\u5728\u5b58\u5728\u4e00\u4e2a\u201c\u5bfc\u7ebf\u201d\uff0c\u5b83\u6709\u4e09\u4e2a\u7aef\uff0c\u5176\u4e2d\u6211\u4eec\u4eba\u4e3a\u5730\u8ba4\u4e3a\u5176\u4e2d\u4e24\u4e2a\u662f\u8f93\u5165\uff0c\u5206\u522b\u547d\u540d\u4e3a a \u548c b\uff0c\u53e6\u5916\u4e00\u4e2a\u8ba4\u4e3a\u662f\u8f93\u51fa\uff0c\u547d\u540d\u4e3a c\u3002</p> <p>\u6b64\u65f6\uff0c\u6211\u4eec\u662f\u4e0d\u5141\u8bb8 a \u548c b \u4e00\u4e2a\u4e3a\u9ad8\u7535\u5e73\uff0c\u4e00\u4e2a\u4e3a\u4f4e\u7535\u5e73\u7684\uff0c\u56e0\u4e3a\u6211\u4eec\u8fd9\u91cc\u4eba\u4e3a\u5b9a\u4e49\u7684\u8f93\u5165\u8f93\u51fa\u5e76\u4e0d\u5f71\u54cd\u7535\u6d41\u7684\u6d41\u52a8\u65b9\u5411\uff0c\u6240\u4ee5\u5f53 a \u4e3a <code>1</code>\uff0cb \u4e3a <code>0</code> \u65f6\uff0c\u7535\u6d41\u5f88\u53ef\u80fd\u4f1a\u53d8\u6210\u4ece a \u6d41\u5411 b\uff0c\u7535\u6e90\u53ef\u80fd\u76f4\u63a5\u63a5\u5730\uff0c\u8fd9\u662f\u6211\u4eec\u4e0d\u5e0c\u671b\u770b\u5230\u7684\uff0c\u8fd9\u4e5f\u662f\u4e3a\u4ec0\u4e48\u6211\u4eec\u9700\u8981\u4e00\u4e2a\u6216\u95e8\u6765\u5b9e\u73b0\u8fd9\u4e2a\u903b\u8f91\u884c\u4e3a\uff08\u6362\u8a00\u4e4b\uff0c\u8fd9\u79cd\u201c\u4e09\u7aef\u201d\u7535\u8def\u662f\u76f8\u5f53\u5371\u9669\u7684\uff0c\u4e0d\u8fc7\u5f53\u6211\u4eec\u4eba\u4e3a\u5b9a\u4e49\u591a\u4e2a\u8f93\u51fa\u65f6\uff0c\u4e00\u822c\u4f5c\u4e3a\u63a5\u6536\u7aef\u7684\u7535\u8def\u90fd\u6709\u4e8c\u6781\u7ba1\u9632\u6b62\u9006\u6d41\uff0c\u6240\u4ee5\u5355\u8f93\u5165\u591a\u8f93\u51fa\u662f\u5f88\u5e38\u89c1\u7684\uff09\u3002</p> <p>\u4ece\u66f4\u62bd\u8c61\u5730\u89d2\u5ea6\u6765\u7406\u89e3\uff0c\u4e00\u6839\u5bfc\u7ebf\u6700\u591a\u627f\u8f7d\u4e00\u4efd\u4fe1\u606f\uff0c\u7136\u800c\u6709\u4e24\u4e2a\u8f93\u5165\u4ecb\u5165\uff0c\u6b64\u65f6\u6211\u4eec\u53ea\u6709 <code>0</code>/<code>1</code> \u4e24\u6001\uff0c\u4e0d\u7ba1\u600e\u4e48\u6837\uff0c\u6211\u4eec\u90fd\u540c\u65f6\u62ff\u5230\u4e86\u6765\u81ea\u4e24\u4e2a\u8f93\u5165\u7684\u6570\u636e\uff0c\u800c\u5bf9\u4e8e\u53ea\u80fd\u627f\u8f7d\u4e00\u4efd\u4fe1\u606f\u7684\u5bfc\u7ebf\u6765\u8bf4\uff0c\u8fd9\u4e24\u4e2a\u4fe1\u606f\u51b2\u7a81\u4e86\u3002\u6240\u4ee5\u6211\u4eec\u9700\u8981 <code>MUX</code> \u6765\u9009\u62e9\u6211\u4eec\u9700\u8981\u7684\u5230\u5e95\u662f\u54ea\u4e2a\u4fe1\u606f\uff0c\u7136\u540e\u518d\u7ed9\u5bfc\u7ebf\u3002</p> <p>\u800c\u4e09\u6001\u95e8\uff0c\u5728\u9ad8\u4f4e\u7535\u5e73\u5916\u5f15\u5165\u4e86\u300c\u9ad8\u963b\u6001\u300d\uff0c\u5c31\u975e\u5e38\u5de7\u5999\u5730\u89e3\u51b3\u4e86\u8fd9\u4e2a\u300c\u591a\u8f93\u5165\u300d\u5371\u9669\u7684\u95ee\u9898\uff0c\u5f53\u6211\u4eec\u4e0d\u5e0c\u671b\u8fd9\u4e2a\u6570\u636e\u88ab\u8f93\u5165\u65f6\uff0c\u6211\u4eec\u76f4\u63a5\u628a\u5b83\u65ad\u5f00\uff0c\u7c7b\u4f3c\u4e8e\u76f4\u63a5\u628a\u5f00\u5173\u65ad\u5f00\uff0c\u53ea\u8981\u6211\u4eec\u8ba9\u5bfc\u7ebf\u7684\u82e5\u5e72\u8f93\u5165\u4e2d\u53ea\u6709\u4e00\u4e2a\u4e09\u6001\u95e8\u4e0d\u5728\u300c\u9ad8\u963b\u6001\u300d\uff0c\u5c31\u80fd\u591f\u4f18\u96c5\u5730\u5b9e\u73b0\u591a\u8def\u8f93\u51fa\u4e92\u8054\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap02/#\u590d\u6742\u95e8","title":"\u590d\u6742\u95e8","text":"<p>\u901a\u8fc7\u4e00\u4e9b\u57fa\u672c\u95e8\u7ec4\u5408\u51fa\u6765\u7684\u95e8\uff0c\u5b83\u4eec\u7684\u8868\u793a\u65b9\u6cd5\u5927\u81f4\u5982\u4e0b\uff1a</p> <p> </p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap03/","title":"Chap 3 Combinational Logic Design","text":"<p> \u7ea6 4261 \u4e2a\u5b57  7 \u884c\u4ee3\u7801  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 14 \u5206\u949f</p> <p>\u5f15\u5165</p> <p>\u6309\u7167\u529f\u80fd\uff0c\u903b\u8f91\u7535\u8def\u5206\u4e3a\u4e24\u7c7b\uff1a</p> <ul> <li>\u7ec4\u5408\u7535\u8def(Combinational Circuit)<ul> <li>\u62e5\u6709 m \u4e2a\u8f93\u5165\u548c n \u4e2a\u8f93\u51fa\uff0c\u5176\u4e2d\u5305\u542b\u4e86 \\(2^m\\) \u79cd\u8f93\u5165\u7ec4\u5408\uff0c\u4ee5\u53ca\u5bf9\u5e94\u7684 n \u4e2a\u4e0d\u540c\u7684\u51fd\u6570\uff1b</li> <li>\u6700\u5173\u952e\u7684\u662f\uff0c\u5b83\u7684 \u8f93\u51fa\u53ea\u4f9d\u8d56\u4e8e\u8fd9 m \u4e2a\u8f93\u5165\u7684\u7ec4\u5408\uff08\u4e0d\u5305\u542b\u56de\u8def\uff09\uff1b</li> </ul> </li> <li>\u65f6\u5e8f\u7535\u8def(Sequential Logic Cirtuit)<ul> <li>\u4e0e\u4e4b\u5bf9\u5e94\u7684\uff0c\u65f6\u5e8f\u7535\u8def\u5177\u6709\u8bb0\u5fc6\u529f\u80fd\uff0c\u5373\u5b83\u7684\u8f93\u51fa\u53ef\u80fd\u4f1a\u4f9d\u8d56\u4e4b\u524d\u7684\u7ed3\u679c\uff1b</li> </ul> </li> </ul> <p>\u800c\u672c\u7ae0\u5c06\u7740\u773c\u4e8e\u7ec4\u5408\u7535\u8def\u7684\u76f8\u5173\u5185\u5bb9\uff0c\u65f6\u5e8f\u7535\u8def\u7684\u76f8\u5173\u5185\u5bb9\u5c06\u5728 \u4e0b\u4e00\u7ae0 \u4ecb\u7ecd\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap03/#\u7ec4\u5408\u7535\u8def\u8bbe\u8ba1","title":"\u7ec4\u5408\u7535\u8def\u8bbe\u8ba1","text":"<p>\u8868\u793a\u903b\u8f91\u7684\u65b9\u6cd5</p> <ol> <li>\u771f\u503c\u8868(Truth Table)\uff1b</li> <li>\u5e03\u5c14\u51fd\u6570(Boolean Function)\uff1b</li> <li>\u5361\u8bfa\u56fe(Karnaugh Maps)\uff1b</li> <li>\u65f6\u5e8f\u56fe(Timing Diagram)\uff1b</li> <li>\u903b\u8f91\u7535\u8def\u56fe(Logic Circuit)\uff1b</li> </ol> <p>\u5176\u4e2d\uff0c\u4e0b\u5212\u7ebf\u7684\u65b9\u6cd5\u5728\u529f\u80fd\u786e\u5b9a\u7684\u60c5\u51b5\u4e0b\uff0c\u5176\u8868\u793a\u662f\u552f\u4e00\u7684\u3002</p> <p>\u800c\u6211\u4eec\u7684\u8bbe\u8ba1\uff0c\u5c31\u662f\u5728\u6ee1\u8db3\u529f\u80fd\u7684\u524d\u63d0\u4e0b\uff0c\u5c3d\u53ef\u80fd\u4f18\u5316\u548c\u627e\u5230\u6700\u597d\u7684\u8bbe\u8ba1\u3002</p> <p>\u800c\u4e3b\u8981\u7684\u8bbe\u8ba1\u8fc7\u7a0b\u5982\u4e0b\uff1a</p> <ol> <li>\u786e\u5b9a\u7cfb\u7edf\u7684\u884c\u4e3a\uff1b</li> <li>\u9610\u8ff0\u8f93\u5165\u548c\u8f93\u51fa\u4e4b\u95f4\u7684\u903b\u8f91\u5173\u7cfb\uff0c\u5e76\u7528\u771f\u503c\u8868\u6216\u903b\u8f91\u8868\u8fbe\u5f0f\u8868\u8fbe\u51fa\u6765\uff1b</li> <li>\u4f18\u5316\u903b\u8f91\u8868\u8fbe\u4ee5\u51cf\u5c11\u6210\u672c(\u6bd4\u5982\u4f7f\u7528\u5361\u8bfa\u56fe)\uff1b</li> <li>\u5c06\u4f18\u5316\u540e\u7684\u903b\u8f91\u8bbe\u8ba1\u5de5\u827a\u6620\u5c04\u5230\u786c\u4ef6\u5b9e\u73b0\u4e0a\uff1b</li> <li>\u9a8c\u8bc1\u6b63\u786e\u6027\uff08\u5728\u4eff\u771f\u73af\u5883\u4e2d\uff09\uff1b</li> </ol> <pre><code>graph LR;\n\nA[\"\u5b9e\u9645\u95ee\u9898\"] ===&gt; B[\"\u771f\u503c\u8868\"]\n\nB ==&gt;|\"\u5316\u7b80\"| C[\"\u6700\u7b80\u529f\u80fd\"] ===&gt;|\"\u5de5\u827a\u6620\u5c04\"| D[\"\u7f51\u8868\"]\n\nB ==&gt;|\"\u53d8\u6362\"| E[\"\u5408\u9002\u7684\u8868\u8fbe\u5f0f\"] ===&gt;|\"\u5de5\u827a\u6620\u5c04\"| D</code></pre>"},{"location":"cour_note/D2QD_DigitalDesign/Chap03/#\u5206\u5c42\u8bbe\u8ba1","title":"\u5206\u5c42\u8bbe\u8ba1","text":"<p>\u5206\u5c42\u8bbe\u8ba1\u5373\u5c06\u590d\u6742\u95ee\u9898\u6a21\u5757\u5316\u5206\u89e3\u4e3a\u82e5\u5e72\u5c42\u6b21\uff0c\u7136\u540e\u9010\u4e2a\u62bd\u8c61\u89e3\u51b3\u3002</p> <p>\u5176\u8bbe\u8ba1\u65b9\u6cd5\u5206\u4e3a \u81ea\u9876\u5411\u4e0b(Top-Down) \u548c \u81ea\u5e95\u5411\u4e0a(Bottom-Up)\u3002</p> <p>\u524d\u8005\u4ece\u9700\u6c42\u5f00\u59cb\uff0c\u81ea\u9876\u5411\u4e0b\u5206\u89e3\u529f\u80fd\u8bbe\u8ba1\uff1b\u540e\u8005\u6839\u636e\u73b0\u6709\u7684\u5143\u4ef6\u53bb\u7ec4\u5408\u6210\u76ee\u6807\u529f\u80fd\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap03/#\u96c6\u6210\u7535\u8def","title":"\u96c6\u6210\u7535\u8def","text":"<p>\u96c6\u6210\u7535\u8def(integrated circuits) \u53c8\u53eb \u82af\u7247(chip)\uff0c\u5206\u4e3a\u5982\u4e0b\u82e5\u5e72\u7b49\u7ea7\uff1a</p> <ul> <li>SSI(small-scale integrated) \u5185\u542b\u4e0d\u5230 10 \u4e2a gates\uff1b</li> <li>MSI(medium-scale integrated) \u5185\u542b 10 ~ 100 \u4e2a gates\uff1b</li> <li>LSI(large-scale integrated) \u5185\u542b \u6210\u767e\u4e0a\u5343 \u4e2a gates\uff1b</li> <li>VLSI(very large-scale integrated) \u5185\u542b \u6210\u5343\u4e0a\u4ebf \u4e2a gates\uff1b</li> </ul>"},{"location":"cour_note/D2QD_DigitalDesign/Chap03/#\u6280\u672f\u53c2\u6570","title":"\u6280\u672f\u53c2\u6570","text":"<p>\u95e8\u7684\u5b9e\u73b0\u4e3b\u8981\u901a\u8fc7\u8fd9\u4e9b\u53c2\u6570\u7279\u6027\u6765\u63cf\u8ff0\uff1a</p> Name Description Fan-in \u4e00\u4e2a\u95e8\u53ef\u7528\u7684\u8f93\u5165 Fan-out \u4e00\u4e2a\u6805\u6781\u8f93\u51fa\u9a71\u52a8\u7684\u6807\u51c6\u8d1f\u8f7d\u6570\u91cf Logic Levels \u88ab\u8ba4\u4e3a\u662f\u9ad8\u4f4e\u7535\u5e73\u7684\u8f93\u5165\u8f93\u51fa\u7535\u538b\u8303\u56f4 Noise Margin \u5bf9\u5916\u754c\u566a\u58f0\u7684\u5bb9\u5fcd\u80fd\u529b(\u5177\u4f53\u6765\u8bf4\u662f\u4e0d\u4f1a\u5bfc\u81f4\u884c\u4e3a\u5f02\u53d8\u7684\u6700\u5927\u566a\u58f0\u538b\u503c) Cost for a gate \u7ee7\u627f\u7535\u8def\u7684\u95e8\u6210\u672c Propagation Delay \u4fe1\u53f7\u6539\u53d8\u540e\u4ece\u8f93\u5165\u5230\u8f93\u51fa\u6240\u9700\u7684\u53d8\u5316\u65f6\u95f4 Power Dissipation \u7535\u6e90\u8f93\u51fa\u80fd\u8017\u548c\u95e8\u7684\u80fd\u8017"},{"location":"cour_note/D2QD_DigitalDesign/Chap03/#\u6247\u5165\u6247\u51fa","title":"\u6247\u5165\u6247\u51fa","text":"<p>\u6247\u5165\u63cf\u8ff0\u4e86\u4e00\u4e2a\u95e8\u80fd\u591f\u63a5\u53d7\u7684\u6700\u591a\u8f93\u5165\u91cf\uff0c\u5982\u4e00\u4e2a\u56db\u8f93\u5165\u4e0e\u975e\u95e8\u7684\u6247\u5165\u5c31\u662f 4\uff1b\u800c\u6247\u51fa\u63cf\u8ff0\u7684\u5219\u662f\u4e00\u4e2a\u95e8\u7684\u8f93\u51fa(\u6805\u6781\u8f93\u51fa)\u5728\u4e0d\u964d\u4f4e\u5de5\u4f5c\u6027\u80fd\u7684\u60c5\u51b5\u4e0b\u80fd\u591f\u8d1f\u8f7d\u591a\u5c11\u95e8\uff0c\u4f8b\u5982\u4e00\u4e2a\u975e\u95e8\u7684\u8f93\u51fa\u80fd\u591f\u540c\u65f6\u8d1f\u8f7d 4 \u4e2a\u975e\u95e8\u5e76\u4e14\u90fd\u80fd\u6b63\u5e38\u5de5\u4f5c\uff0c\u5219\u5176\u6247\u51fa\u4e3a 4\uff0c\u5176\u4e5f\u80fd\u901a\u8fc7\u6807\u51c6\u8d1f\u8f7d\u6765\u5b9a\u4e49\u3002</p> <p>\u6807\u51c6\u8d1f\u8f7d</p> <p>\u6240\u8c13\u7684\u6807\u51c6\u8d1f\u8f7d\uff0c\u662f\u8861\u91cf\u201c\u8d1f\u8f7d\u201d\u7684\u4e00\u4e2a\u201c\u5355\u4f4d\u781d\u7801\u201d\u3002\u5176\u5927\u5c0f\u7b49\u4e8e\u4e00\u4e2a\u975e\u95e8(\u9006\u53d8\u5668)\u8d21\u732e\u7684\u8d1f\u8f7d\u538b\u529b\u3002</p> <p>\u90a3\u4e48\u8981\u5982\u4f55\u8bc4\u4f30\u8d1f\u8f7d\u5462\uff1f\u9996\u5148\u6211\u4eec\u5f15\u5165 \u8fc7\u6e21\u65f6\u95f4(transition time)\uff1a</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap03/#\u8f6c\u6362\u65f6\u95f4","title":"\u8f6c\u6362\u65f6\u95f4","text":"<p>\u8f6c\u6362\u65f6\u95f4\u5206\u4e3a \\(\\mathrm{t_{LH}}\\)(rise time) \u548c \\(\\mathrm{t_{HL}}\\)(fall time) \u4e24\u4e2a\u90e8\u5206\u3002</p> <ul> <li>rise time \u7b49\u4e8e\u6805\u6781\u8f93\u51fa\u4ece \\(\\mathrm{V_{CC}}\\) \u7684 10% \u5347\u9ad8\u5230 90% \u6240\u9700\u8981\u7684\u65f6\u95f4\uff1b</li> <li>fall time \u7b49\u4e8e\u6805\u6781\u8f93\u51fa\u4ece \\(\\mathrm{V_{CC}}\\) \u7684 90% \u964d\u4f4e\u5230 10% \u6240\u9700\u8981\u7684\u65f6\u95f4\uff1b</li> </ul> <p>\u901a\u8fc7\u65f6\u5e8f\u56fe\u8868\u793a\u5c31\u662f\u8fd9\u6837\uff1a</p> <p></p> <p>\u968f\u7740\u8d1f\u8f7d\u589e\u52a0\uff0c\u8f6c\u6362\u65f6\u95f4\u4e5f\u4f1a\u589e\u52a0\uff08\u7ed9\u7535\u5bb9\u5145\u7535\u7684\u65f6\u95f4\u589e\u52a0\uff09\uff0c\u800c\u6247\u51fa\u5b9a\u4e49\u4e2d\u63d0\u5230\u7684\u201c\u6700\u5927\u8d1f\u8f7d\u201d\uff0c\u5c31\u662f\u6307\u5b83\u7684\u8f6c\u6362\u65f6\u95f4\u4e0d\u8d85\u8fc7\u5b83\u9884\u5b9a\u7684\u6700\u5927\u8f6c\u6362\u65f6\u95f4\u3002</p> <p></p> <p>\u4ece\u5de6\u5230\u53f3\u8868\u793a\u8d1f\u8f7d\u4e0d\u65ad\u589e\u52a0\u65f6\uff0crise time \u7684\u53d8\u5316\u8d8b\u52bf\u3002</p> <p>\u5b9e\u9645\u4e0a\uff0c\u7c7b\u4f3c\u7684\uff0c\u8d85\u51fa\u6247\u5165\u540e\uff0c\u95e8\u5bf9\u8f93\u5165\u7684\u53cd\u5e94\u5c31\u592a\u6162\u4e86\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap03/#\u4f20\u64ad\u5ef6\u8fdf","title":"\u4f20\u64ad\u5ef6\u8fdf","text":"<p>\u4f20\u64ad\u5ef6\u8fdf(propagation delay) \u8861\u91cf\u4e86\u95e8\u7684\u8f93\u5165\u53d8\u5316\u5bfc\u81f4\u8f93\u51fa\u53d8\u5316\u6240\u9700\u8981\u7684\u65f6\u95f4\u3002\u7531\u4e8e\u4ece\u4f4e\u7535\u5e73\u8f6c\u5316\u5230\u9ad8\u7535\u5e73\u548c\u9ad8\u7535\u5e73\u8f6c\u5316\u5230\u4f4e\u7535\u5e73\u6240\u9700\u8981\u7684\u65f6\u95f4\u4e0d\u4e00\u6837\uff0c\u6240\u4ee5\u4f20\u64ad\u5ef6\u8fdf\u540c\u6837\u6709\u4e24\u4e2a\u90e8\u5206\uff0c\u5206\u522b\u4f7f\u7528 \\(\\mathrm{t_{PHL}}\\) \u548c \\(\\mathrm{t_{PLH}} \u6765\u8868\u793a\\)\u3002</p> <p>\u66f4\u5177\u4f53\u7684\u6765\u8bf4\uff0c\u4f20\u64ad\u5ef6\u8fdf\u7684\u8ba1\u7b97\u65b9\u6cd5\u662f\u8f93\u5165\u548c\u8f93\u51fa\u7684\u53d8\u5316\u4e2d\u70b9\uff08\u5373\u53d8\u5316\u5230 \\(\\frac{1}{2}V_{CC}\\) \u65f6\uff09\u7684\u65f6\u95f4\u5dee\uff0c\u901a\u8fc7\u65f6\u5e8f\u56fe\u8868\u793a\u5c31\u662f\u8fd9\u6837\uff1a</p> <p></p> <p>\u6b64\u5916\uff0c\u6211\u4eec\u8fd8\u53ef\u4ee5\u5f15\u5165 \\(\\mathrm{ t_{pd} }\\) \u6765\u7edf\u4e00\u8868\u793a \\(\\mathrm{t_{PHL}}\\) \u548c \\(\\mathrm{t_{PLH}}\\)\u3002\u6570\u503c\u4e0a\uff0c\\(\\mathrm{ t_{pd} } = average(\\mathrm{t_{PHL}}, \\mathrm{t_{PLH}})\\) \u6216 \\(\\mathrm{ t_{pd} } = max(\\mathrm{t_{PHL}}, \\mathrm{t_{PLH}})\\)\u3002</p> \u9898\u9762\u7b54\u6848 <p>\u6839\u636e\u65f6\u5e8f\u56fe\uff0c\u5199\u51fa\u95e8\u7684\u4f20\u64ad\u5ef6\u8fdf\uff0c\u6b64\u5904 \\(\\mathrm{ t_{pd} } = average(\\mathrm{t_{PHL}}, \\mathrm{t_{PLH}})\\)\u3002</p> <p></p> <p></p> <p>Transition Time vs. Propagation Delay</p> <p>\u8f6c\u6362\u65f6\u95f4\u4e13\u6ce8\u4e8e\u8f93\u51fa\u7684\u53d8\u5316\uff0c\u800c\u4f20\u64ad\u5ef6\u8fdf\u5219\u5305\u542b\u4e86\u8f93\u5165\u7684\u53d8\u5316\u548c\u8f93\u51fa\u7684\u53d8\u5316\u6574\u4e2a\u8fc7\u7a0b\u3002</p> <p>\u4ece\u65f6\u5e8f\u56fe\u4e0a\u7684\u8868\u793a\u6765\u770b\uff0c\u8f6c\u6362\u65f6\u95f4\u53ea\u9700\u8981\u8f93\u51fa\u7684\u65f6\u5e8f\u56fe\u5373\u53ef\u8868\u793a\uff1b\u4f46\u4f20\u64ad\u5ef6\u8fdf\u5219\u662f\u901a\u8fc7\u6bd4\u8f83\u8f93\u5165\u548c\u8f93\u51fa\u7684\u504f\u5dee\u6765\u8868\u793a\u7684\u3002</p> <p></p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap03/#\u5ef6\u8fdf\u6a21\u578b","title":"\u5ef6\u8fdf\u6a21\u578b","text":"<p>\u4e3a\u4e86\u7814\u7a76\u4e3a\u4ec0\u4e48\u4f1a\u5b58\u5728\u95e8\u5ef6\u8fdf\uff0c\u523b\u753b\u95e8\u7684 \u56fa\u6709\u95e8\u5ef6\u8fdf(inherent gate delay)\uff0c\u6211\u4eec\u9700\u8981\u5bf9\u5176\u5efa\u6a21\uff0c\u5e38\u89c1\u7684 \u5ef6\u8fdf\u6a21\u578b(delay model) \u6709\u4ee5\u4e0b\u4e24\u79cd\uff1a</p> <ul> <li>\u4f20\u8f93\u5ef6\u8fdf(transport delay): \u8ba4\u4e3a\u8f93\u5165\u548c\u8f93\u51fa\u4e4b\u95f4\u7684\u5ef6\u8fdf\u662f\u4e00\u4e2a\u5b9a\u503c\u7684\uff1b</li> </ul> <p></p> <ul> <li>\u60ef\u6027\u5ef6\u8fdf(inertial delay): \u5f15\u5165\u4e86 \u62d2\u7edd\u65f6\u95f4(rejection time)\uff0c\u53ea\u6709\u5f53\u8f93\u5165\u8fbe\u5230\u4e00\u5b9a\u80fd\u91cf\u540e\uff0c\u624d\u4f1a\u51fa\u53d1\u6805\u6781\u8f93\u51fa\uff08\u5728\u8fd9\u79cd\u6a21\u578b\u4e0b\uff0c\u566a\u97f3\u7b49\u4f1a\u88ab\u8fc7\u6ee4\uff09\uff1b</li> </ul> <p></p> <p>\u5c06\u4e0d\u5b58\u5728\u5ef6\u8fdf\u7684\u6a21\u578b\u3001\u4f20\u8f93\u5ef6\u8fdf\u6a21\u578b\u548c\u60ef\u6027\u5ef6\u8fdf\u6a21\u578b\u505a\u6bd4\u8f83\u5730\u6765\u770b\uff0c\u5c31\u662f\u5982\u4e0b\u60c5\u51b5\uff1a</p> <p></p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap03/#\u5ef6\u8fdf\u4ee5\u53ca\u76f8\u5173\u95ee\u9898","title":"\u5ef6\u8fdf\u4ee5\u53ca\u76f8\u5173\u95ee\u9898","text":"<p>\u5f15\u5165</p> <p>\u7531\u4e8e\u5b9e\u9645\u7535\u8def\u4e2d\u5b9e\u73b0\u5ef6\u8fdf\uff0c\u6570\u5b66\u4e0a\u7684\u903b\u8f91\u8868\u8fbe\u5f0f\u4e0e\u5b9e\u9645\u7535\u8def\u60c5\u51b5\u4f1a\u5b58\u5728\u4e0d\u540c\u2014\u2014\u5373\u5b58\u5728\u82e5\u5e72\u6570\u5b66\u4e0a\u65e0\u6cd5\u76f4\u63a5\u89e3\u51b3\u7684\u95ee\u9898\u3002</p> <p>\u6240\u4ee5\u7814\u7a76\u5ef6\u8fdf\u662f\u975e\u5e38\u5fc5\u8981\u7684\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap03/#\u5ef6\u8fdf\u8ba1\u7b97","title":"\u5ef6\u8fdf\u8ba1\u7b97","text":"<p>\u8ba1\u7b97\u4e00\u4e2a\u7535\u8def\u7684\u5ef6\u8fdf\u65f6\uff0c\u6709\u4e24\u65b9\u9762\u9700\u8981\u8003\u8651\uff0c\u4e00\u65b9\u9762\u662f\u7535\u8def\u81ea\u8eab\u6240\u5bfc\u81f4\u7684\u4e00\u4e2a\u56fa\u5b9a\u5ef6\u8fdf\uff0c\u53e6\u5916\u4e00\u65b9\u9762\u5219\u662f\u7531\u4e8e\u4e0d\u540c\u7684\u8d1f\u8f7d\u5bfc\u81f4\u7684\u989d\u5916\u5ef6\u8fdf\u3002</p> <p></p> <p>\u5728\u8fd9\u4e2a\u4f8b\u5b50\u4e2d\uff0c0.07 \u4e3a\u56fa\u5b9a\u5ef6\u8fdf\uff0c0.021 \u4e3a\u4e00\u4e2a\u6807\u51c6\u8d1f\u8f7d\u5e26\u6765\u7684\u5ef6\u8fdf\u7cfb\u6570\uff0cSL(4.5 here) \u5219\u662f\u6807\u51c6\u5316\u7684\u8d1f\u8f7d\u91cf\u3002</p> <p>\u800c\u5177\u4f53\u7684\u8868\u8fbe\u5f0f\uff0c\u4f1a\u5728 Cell Library \u91cc\u5199\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap03/#\u5ef6\u8fdf\u5e26\u6765\u7684\u95ee\u9898","title":"\u5ef6\u8fdf\u5e26\u6765\u7684\u95ee\u9898","text":"<p>\u7531\u4e8e\u5b58\u5728\u5ef6\u8fdf\uff0c\u8bb8\u591a\u5728\u6570\u5b66\u610f\u4e49\u4e0a\u6ca1\u6709\u95ee\u9898\u7684\u903b\u8f91\u8868\u8fbe\u5f0f\u5728\u7535\u8def\u4e2d\u5c31\u5b58\u5728\u975e\u5e38\u5927\u7684\u95ee\u9898\u3002</p> <p>\u4f8b\u5982\uff0c\u4ece\u6570\u5b66\u89d2\u5ea6\u770b\uff0c\\(\\mathrm{Y=\\overline{A}A}\\) \u7684\u503c\u6052\u4e3a <code>0</code>\uff0c\u4f46\u662f\u5b9e\u9645\u4e0a\u7531\u4e8e\u5ef6\u8fdf\uff0c\u5176\u4eff\u771f\u6ce2\u5f62\u4e2d\u4f1a\u51fa\u73b0\u8fd9\u6837\u4e00\u4e2a \u6bdb\u523a(glitch)\uff0c\u800c\u8fd9\u5728\u5de5\u7a0b\u610f\u4e49\u4e0a\u6709\u5f88\u5927\u7684\u95ee\u9898\u3002</p> <p></p> \u66f4\u590d\u6742\u7684 \ud83c\udf30 <p>\u8ba9\u6211\u4eec\u5206\u6790\u4e0b\u9762\u8fd9\u4e2a\u4e8c\u8def\u9009\u62e9\u5668\uff0c\u5176\u529f\u80fd\u662f\u901a\u8fc7 S \u63a7\u5236\u8f93\u51fa\u8868\u8fbe\u7684\u662f A \u8fd8\u662f B\uff0c\u5728\u4f20\u8f93\u5ef6\u8fdf\u6a21\u578b\u4e0b\uff0c\u5176\u6ce2\u5f62\u5982\u4e0b\uff1a</p> <p></p> <p>\u53ef\u4ee5\u53d1\u73b0\uff0cY \u4e2d\u51fa\u73b0\u4e86\u610f\u6599\u4e4b\u5916\u7684\u6bdb\u523a\u3002</p> <p>\u800c\u8fd9\u4e2d\u6bdb\u523a\u53ef\u4ee5\u7528\u6dfb\u52a0\u5197\u4f59\u9879\u6765\u89e3\u51b3\uff1a</p> <p></p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap03/#\u6b63\u903b\u8f91\u548c\u8d1f\u903b\u8f91","title":"\u6b63\u903b\u8f91\u548c\u8d1f\u903b\u8f91","text":"<p>\u6b63\u903b\u8f91(positive logic) \u5c31\u662f <code>1</code> \u662f\u6709\u6548\u4fe1\u53f7\uff0c\u8d1f\u903b\u8f91(negative logic) \u5c31\u662f <code>0</code> \u662f\u6709\u6548\u4fe1\u53f7\u3002\u800c\u5728\u6b63\u903b\u8f91\u4e2d AND \u95e8\u7684\u4f5c\u7528\u5c31\u7b49\u6548\u4e8e\u8d1f\u903b\u8f91\u4e2d OR \u95e8\u7684\u4f5c\u7528\uff0c\u8fd9\u4e5f\u6b63\u662f\u6211\u5728\u524d\u9762\u51e0\u7ae0\u7684\u7b14\u8bb0\u4e2d\u63d0\u5230\u7684\u5bf9\u79f0\u3002</p> <p>\u800c\u6b63\u903b\u8f91\u7684\u7535\u8def\u7684\u7b26\u53f7\u4e00\u822c\u5c31\u662f\u6b63\u5e38\u7684\u903b\u8f91\u95e8\u7b26\u53f7\uff0c\u800c\u8d1f\u903b\u8f91\u7684\u903b\u8f91\u95e8\u7b26\u53f7\u5219\u53ef\u80fd\u6709\u5c0f\u4e09\u89d2\u6807\uff0c\u5373 \u6781\u6027\u6307\u793a\u5668(polarity indicator)\uff1a</p> <p></p> <p>\u5982\u56fe\uff0c\u5de6\u4fa7\u662f\u6b63\u903b\u8f91\u7535\u8def\u7684\u7b26\u53f7\uff0c\u53f3\u4fa7\u662f\u8d1f\u903b\u8f91\u7535\u8def\u7684\u7b26\u53f7\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap03/#\u5de5\u827a\u6620\u5c04","title":"\u5de5\u827a\u6620\u5c04","text":"<p>\u5de5\u827a\u6620\u5c04(technology mapping) \u662f\u6307\u5c06\u903b\u8f91\u56fe\u6216\u7f51\u8868\u8f6c\u5316\u4e3a\u53ef\u4ee5\u7528\u5de5\u827a\u5b9e\u73b0\u7684\u5fc3\u7684\u56fe\u6216\u7f51\u8868\u7684\u8fc7\u7a0b\u3002</p> <p>\u6709\u65f6\u6211\u4eec\u4f1a\u4f7f\u7528\u4e0e\u975e\u95e8\u548c\u975e\u95e8\u66ff\u6362\u4e0e\u95e8\u548c\u6216\u95e8(\u56e0\u4e3a\u7535\u8def\u5c42\u9762\uff0c\u4e0e\u95e8\u5b9e\u9645\u4e0a\u5c31\u662f\u901a\u8fc7\u4e0e\u975e\u95e8\u5b9e\u73b0\u7684)\uff0c\u7136\u540e\u4f1a\u53d1\u73b0\u6709\u4e00\u4e9b\u8fde\u7eed\u5bf9\u975e\u95e8\u53ef\u4ee5\u76f8\u4e92\u62b5\u6d88\uff0c\u4f8b\u5982\u4e0b\u9762\u7684\u60c5\u51b5\uff1a</p> <p></p> <p>\u84dd\u7eff\u8272\u5757\u4e2d\u5373\u4e3a\u88ab\u66ff\u6362\u540e\u7684\u5185\u5bb9\uff0c\u7136\u540e\u6211\u4eec\u53d1\u73b0\u51fa\u73b0\u4e86\u82e5\u5e72\u53ef\u4ee5\u62b5\u6d88\u7684\u975e\u95e8\u3002</p> <p>\u5f53\u7136\uff0c\u4e5f\u53ef\u4ee5\u901a\u8fc7\u6216\u975e\u95e8\u6765\u5b9e\u73b0\uff0c\u6bd4\u5982\u4e0b\u9762\u7684\u60c5\u51b5\uff1a</p> <p></p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap03/#\u9a8c\u8bc1\u6b63\u786e\u6027","title":"\u9a8c\u8bc1\u6b63\u786e\u6027","text":"<p>\u9a8c\u8bc1\u6b63\u786e\u6027(Verification)\u6307\u7684\u662f\u8bc1\u660e\u6700\u7ec8\u8bbe\u8ba1\u7684\u7535\u8def\u80fd\u591f\u5b9e\u73b0\u9884\u671f\u4ea7\u54c1\u89c4\u683c\uff08Specification\uff09\u3002 \u7b80\u5355\u7684\u4ea7\u54c1\u89c4\u683c\u53ef\u4ee5\u7528\u771f\u503c\u8868\u3001\u5e03\u5c14\u4ee3\u6570\u5f0f\u3001HDL \u4ee3\u7801\u7b49\u63cf\u8ff0\u3002</p> <p>\u6700\u57fa\u672c\u7684\u9a8c\u8bc1\u6b63\u786e\u6027\u65b9\u6cd5\u6709\uff1a</p> <ul> <li>\u4eba\u5de5\u903b\u8f91\u5206\u6790(Manual Logic Analysis)\uff1a<ul> <li>\u627e\u5230\u6700\u7ec8\u7535\u8def\u7684\u771f\u503c\u8868\u6216\u5e03\u5c14\u4ee3\u6570\u5f0f\uff0c\u5224\u65ad\u5176\u662f\u5426\u548c\u9884\u671f\u4ea7\u54c1\u89c4\u683c\u4e00\u81f4\uff1b</li> </ul> </li> <li>\u4eff\u771f(Simulation)\uff1a<ul> <li>\u5728\u4eff\u771f\u73af\u5883\u4e2d\uff0c\u4f7f\u7528\u5408\u9002\u7684\u6d4b\u8bd5\u8f93\u5165\uff08\u6fc0\u52b1\u4fe1\u53f7\uff09\u6765\u6d4b\u8bd5\u6700\u7ec8\u7535\u8def\uff08\u6216\u5176\u7f51\u8868\uff0c\u53ef\u80fd\u7f16\u5199\u4e3a HDL\uff09\uff0c\u901a\u8fc7\u89c2\u5bdf\u5176\u54cd\u5e94\u7ed3\u679c\u6765\u5224\u65ad\u662f\u5426\u5b9e\u73b0\u9884\u671f\u4ea7\u54c1\u89c4\u683c\uff1b</li> </ul> </li> </ul> <p>Why Simulate?</p> <p>\u6211\u4eec\u66fe\u5728\u6570\u903b\u5b9e\u9a8c\u4e2d\u9a8c\u8bc1\u8fc7\u4e8c\u8f93\u5165\u4e0e\u975e\u95e8\u7684\u6b63\u786e\u6027\uff0c\u90a3\u65f6\u6211\u4eec\u91c7\u7528\u4eba\u5de5\u903b\u8f91\u5206\u6790\uff0c\u901a\u8fc7\u6d4b\u8bd5\u786e\u5b9a\u4e86\u5f85\u6d4b\u95e8\u7684\u771f\u503c\u8868\uff0c\u5e76\u5c06\u5176\u4e0e\u6807\u51c6\u7684\u4e8c\u8f93\u5165\u4e0e\u975e\u95e8\u771f\u503c\u8868\u6bd4\u8f83\uff0c\u4ece\u800c\u5224\u65ad\u6211\u4eec\u7684\u4e8c\u8f93\u5165\u4e0e\u975e\u95e8\u662f\u5426\u6b63\u786e\u5b9e\u73b0\uff1b</p> <p>\u4f46\u5982\u679c\u6211\u4eec\u9700\u8981\u9a8c\u8bc1\u4e00\u4e2a\u4e00\u767e\u4e07\u8f93\u5165\u4e0e\u975e\u95e8\u7684\u6b63\u786e\u6027\u5462\uff1f\uff08\u4ec5\u7528\u4e8e\u4e3e\u4f8b\uff09</p> <p>\u6211\u4eec\u53d1\u73b0\uff0c\u5728\u73b0\u5b9e\u4e16\u754c\u4e2d\u4eba\u5de5\u6c42\u89e3\u8fd9\u4e2a\u7535\u8def\u7684\u771f\u503c\u8868\u6216\u5e03\u5c14\u4ee3\u6570\u5f0f\u662f\u4e0d\u53ef\u80fd\u7684\u3002\u8fd9\u65f6\u5019\u6211\u4eec\u53ef\u4ee5\u8bbe\u8ba1\u4e00\u7ec4\u5177\u6709\u4ee3\u8868\u6027\u7684\u8f93\u5165\uff08\u4ecd\u7136\u662f\u4e2a\u4e0d\u5c0f\u7684\u6570\u76ee\uff09\uff0c\u8ba9\u8ba1\u7b97\u673a\u5728\u4eff\u771f\u73af\u5883\u4e2d\u7528\u8fd9\u7ec4\u8f93\u5165\u53bb\u6d4b\u8bd5\u7535\u8def\uff0c\u5e76\u5c06\u6d4b\u8bd5\u7ed3\u679c\u4e0e\u9884\u671f\u7ed3\u679c\u8fdb\u884c\u5bf9\u6bd4\u3002\u6211\u4eec\u65e0\u6cd5\u786e\u4fdd\u9a8c\u8bc1\u662f\u5426\u5145\u5206\uff0c\u4f46\u81f3\u5c11\u8fd9\u662f\u5b9e\u8df5\u610f\u4e49\u4e0a\u8db3\u591f\u5145\u5206\u7684\u9a8c\u8bc1\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap03/#\u7ec4\u5408\u903b\u8f91","title":"\u7ec4\u5408\u903b\u8f91","text":""},{"location":"cour_note/D2QD_DigitalDesign/Chap03/#\u57fa\u672c\u903b\u8f91\u51fd\u6570","title":"\u57fa\u672c\u903b\u8f91\u51fd\u6570","text":"<ul> <li>\u5e38\u91cf\u51fd\u6570(Value-Fixing)\uff1a\\(F=0\\;\\;or\\;\\;F=1\\) | \u8f93\u51fa\u5b9a\u503c\uff1b</li> <li>\u4f20\u8f93\u51fd\u6570(Transferring)\uff1a\\(F=X\\) | \u76f4\u63a5\u8f93\u51fa\u8f93\u5165\u503c\uff1b</li> <li>\u9006\u53d8\u51fd\u6570(Inverting)\uff1a\\(F=\\overline{X}\\) | \u8f93\u51fa\u8f93\u5165\u7684\u76f8\u53cd\uff1b</li> <li>\u4f7f\u80fd\u51fd\u6570(Enabling)\uff1a\\(F=X\\cdot En \\;\\; or \\;\\; F = X + \\overline{En}\\) | \u901a\u8fc7\u4f7f\u80fd\u63a7\u5236\u8f93\u51fa\u662f\u5426\u53ef\u53d8\uff0c\u5206\u4e3a\u4e24\u79cd\uff0c\u6bd4\u5982\u4e0e\u7684\u5f62\u5f0f\u4e2d\uff0c\u53ea\u6709 \\(En\\) \u4e3a <code>1</code> \u65f6\uff0c\\(F\\) \u8868\u73b0\u4e3a \\(X\\) \u7684\u503c\uff1b\u53cd\u4e4b\u8f93\u51fa\u5fc5\u5b9a\u4e3a <code>0</code>\uff08\u6ce8\u610f\u533a\u5206\u5b83\u4e0e\u4e09\u6001\u95e8\u7684\u533a\u522b\uff0c\u9ad8\u963b\u6001 or \u5b9a\u503c\uff09\uff1b</li> </ul>"},{"location":"cour_note/D2QD_DigitalDesign/Chap03/#\u57fa\u672c\u529f\u80fd\u5757","title":"\u57fa\u672c\u529f\u80fd\u5757","text":"<ul> <li>\u8bd1\u7801\u5668(Decoder)</li> <li> <p>\u7f16\u7801\u5668(Encoder)</p> </li> <li> <p>\uff08\u4e09\u7aef\uff09\u591a\u8def\u590d\u7528\u5668(Multiplexer) <code>MUX</code></p> </li> <li>\uff08\u4e09\u7aef\uff09\u4fe1\u53f7\u5206\u914d\u5668(Demultiplexer) <code>DEMUX</code></li> </ul>"},{"location":"cour_note/D2QD_DigitalDesign/Chap03/#\u8bd1\u7801\u5668","title":"\u8bd1\u7801\u5668","text":"<p>\u7a77\u4e3e\u53ef\u80fd\u6027\uff0c\u7a20\u5bc6 -&gt; \u7a20\u5bc6/\u7a00\u758f</p> <p>\u4e3a\u4e86\u8282\u7701\u95e8\u8f93\u5165\u6210\u672c\uff0c\u6211\u4eec\u5e38\u5e38\u4f7f\u7528 \u5206\u7ea7 \u7684\u601d\u60f3\u6765\u6784\u9020\u591a\u8f93\u5165\u591a\u8bd1\u7801\u5668\u3002</p> <p>eg</p> <p></p> <p>\u7531\u4e8e\u5e95\u5c42\u7684\u7535\u8def\u80fd\u591f\u76f4\u63a5\u5b9e\u73b0\u7684\u8fd0\u7b97\u5341\u5206\u5c40\u9650\uff0c\u6240\u4ee5\u9700\u8981\u7528\u8bd1\u7801\u5668\u6765\u5b9e\u73b0\u4e00\u4e9b\u57fa\u7840\u8fd0\u7b97\uff0c\u4f8b\u5982\u52a0\u6cd5\u3002</p> <p>\u4e00\u4f4d\u52a0\u6cd5\u5668\u5c31\u53ef\u4ee5\u901a\u8fc7\u8bd1\u7801\u5668\u548c\u6216\u95e8\u5b9e\u73b0\uff0c\u6838\u5fc3\u5c31\u662f\u679a\u4e3e\u8f93\u5165\u7684\u5404\u79cd\u60c5\u51b5\uff0c\u7136\u540e\u7528\u6216\u95e8\u62fe\u53d6 sum \u548c carry \u7684\u6700\u5c0f\u9879\u3002</p> <p></p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap03/#\u7f16\u7801\u5668","title":"\u7f16\u7801\u5668","text":"<p>\u7a20\u5bc6/\u7a00\u758f -&gt; \u7a20\u5bc6</p> <p>\u5982\u4e0a\u5b9a\u4e49\u7684\u7f16\u7801\u5668\u6709\u4e00\u4e2a\u9650\u5236\uff0c\u5373\u4efb\u4f55\u65f6\u5019\u8f93\u5165\u53ea\u80fd\u6709\u4e00\u4e2a\u662f\u6d3b\u52a8\u7684\uff0c\u5373\u8f93\u5165\u662f one-hot \u7684\u3002</p> <p>\u4f18\u5148\u7f16\u7801\u5668</p> <p>\u4f18\u5148\u7f16\u7801\u5668\u80fd\u591f\u5b9e\u73b0\u4f18\u5148\u7ea7\u51fd\u6570\uff0c\u5b83\u4e0d\u8981\u6c42\u8f93\u5165\u662f one-hot \u7684\uff0c\u800c\u662f\u603b\u662f\u5173\u6ce8\u6709\u6548\u8f93\u5165\u4e2d\u4f18\u5148\u7ea7\u6700\u9ad8\u7684\u90a3\u4e00\u4e2a\u3002\u5373\u6bd4\u5982\u5f53\u4f18\u5148\u7ea7\u6700\u9ad8\u7684\u90a3\u4e00\u4f4d\u662f <code>1</code> \u65f6\uff0c\u5176\u5b83\u6240\u6709\u4f18\u5148\u7ea7\u4e0d\u5982\u5b83\u7684\u4f4d\u7f6e\u7684\u503c\u90fd\u662f\u6211\u4eec\u4e0d\u5173\u5fc3\u7684\u5185\u5bb9\u4e86\u3002</p> <p>\u4e2d\u65ad(interrupt)\u5224\u4f18\u5668</p> <p>\u4f18\u5148\u7f16\u7801\u5668\u7684\u4e00\u79cd\u5e94\u7528\u5c31\u662f\u4e2d\u65ad\u5224\u4f18\u5668\u3002</p> <p></p> <p>\u5176\u4e2d \\(V\\) \u8868\u793a\u8f93\u51fa\u662f\u5426\u6709\u6548\uff0c\u5728\u4e2d\u65ad\u5224\u4f18\u7cfb\u7edf\u4e2d\u5373\u8868\u793a\u662f\u5426\u6709\u4e2d\u65ad\u8bf7\u6c42\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap03/#\u591a\u8def\u590d\u7528\u5668","title":"\u591a\u8def\u590d\u7528\u5668","text":"<p>\u901a\u8fc7\u63a7\u5236\u7aef\u9009\u62e9\u8f93\u51fa\u7684\u662f\u82e5\u5e72\u8f93\u5165\u4e2d\u7684\u54ea\u4e00\u4e2a\u3002</p> <p>\u901a\u8fc7\u4e09\u6001\u95e8\u6765\u5b9e\u73b0 <code>MUX</code> \u80fd\u591f\u964d\u4f4e\u95e8\u8f93\u5165\u4ee3\u4ef7\u3002</p> eg <p></p> <p>\u5b8c\u5168\u4f7f\u7528\u4e09\u6001\u95e8\u6765\u5b9e\u73b0\u56db\u8f93\u5165 <code>MUX</code>\uff0c\u95e8\u8f93\u5165\u5927\u5927\u51cf\u5c11\u3002</p> <p><code>MUX</code> \u8fd8\u53ef\u4ee5 \u5b9e\u73b0\u4efb\u610f\u7684\u903b\u8f91\u51fd\u6570\uff1a</p> <ul> <li>\u5c06\u63a7\u5236\u7aef\u5f53\u4f5c\u8f93\u5165\uff0c\u539f\u6765\u7684\u8f93\u5165\u5f53\u4f5c\u7ed3\u679c\uff1b</li> <li>\u5373\u53ef\u4ee5\u5c06\u4e00\u4e2a\u56db\u8f93\u5165 <code>MUX</code> \u5f53\u4f5c\u4e00\u4e2a\u4e8c\u8f93\u5165\u7684\u51fd\u6570\uff1b</li> </ul> <p>\u6362\u53e5\u8bdd\u6765\u8bf4\uff0c\u5c31\u662f\u5c06\u539f\u6765\u7684\u63a7\u5236\u7aef\u5f53\u4f5c\u8f93\u5165\u7aef\uff0c\u5e76\u5728\u539f\u6765\u7684\u8f93\u5165\u7aef\u5199\u5165\u903b\u8f91\u51fd\u6570\u7684\u771f\u503c\u8868\uff0c\u4ee5\u5b9e\u73b0\u4efb\u610f\u903b\u8f91\u51fd\u6570\u3002</p> <p>\u6211\u4eec\u8fd8\u53ef\u4ee5\u901a\u8fc7\u628a\u4e00\u90e8\u5206\u7684\u8f93\u5165\u5f53\u4f5c\u5e38\u91cf\u7aef\u6765\u7b80\u5316\u5143\u4ef6\uff08\u964d\u7ef4\uff09\uff1a</p> <p></p> <p>\u89c2\u5bdf\u5176\u6700\u5c0f\u9879\uff0c\u4f7f\u5176\u8f93\u51fa\u6240\u6709\u6700\u5c0f\u9879\u3002\u4f46\u662f\u5728\u964d\u7ef4\u8fc7\u7a0b\u4e2d\u5e76\u4e0d\u9700\u8981\u5168\u90fd\u662f C\uff0c\u5982\u679c\u5361\u8bfa\u56fe\u4e2d\u5b58\u5728\u53cc <code>1</code> \u6216\u8005\u53cc <code>0</code>\uff0c\u4e5f\u53ef\u4ee5\u4ecd\u7136\u4f7f\u7528\u5e38\u91cf\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap03/#\u4fe1\u53f7\u5206\u914d\u5668","title":"\u4fe1\u53f7\u5206\u914d\u5668","text":"<p>\u7b80\u5199\u4e3a <code>DEMUX</code>\uff0c\u901a\u8fc7\u63a7\u5236\u7aef\u9009\u62e9\u8f93\u5165\u7ed9\u5230\u82e5\u5e72\u8f93\u51fa\u4e2d\u7684\u54ea\u4e00\u4e2a\u3002</p> <p></p> <p>\u540e\u7eed \ud83d\udc49 \u53ef\u91cd\u7f16\u7a0b\u6280\u672f</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap03/#\u7b97\u672f\u903b\u8f91\u7535\u8def","title":"\u7b97\u672f\u903b\u8f91\u7535\u8def","text":"<p>\u6211\u4eec\u4e3b\u8981\u8ba8\u8bba\u7684\u8ba1\u7b97\u4e3b\u8981\u5305\u62ec\u903b\u8f91\u8fd0\u7b97\u548c\u7b97\u672f\u8fd0\u7b97\uff0c\u524d\u8005\u7531\u4e8e\u53ef\u4ee5\u76f4\u63a5\u901a\u8fc7\u57fa\u672c\u95e8\u5f88\u65b9\u4fbf\u5b9e\u73b0\uff0c\u6240\u4ee5\u6211\u4eec\u4e0d\u8fc7\u591a\u8003\u8651\uff1b\u5728\u6b64\u4e3b\u8981\u4ecb\u7ecd\u7b97\u6570\u8fd0\u7b97\u3002\u5728\u8ba1\u7b97\u673a\u786c\u4ef6\u4e2d\uff0c\u627f\u62c5\u8ba1\u7b97\u5de5\u4f5c\u7684\u4e3b\u8981\u90e8\u4ef6\u4e3a <code>ALU</code>(Arithmetic Logical Unit)\u3002</p> <p>\u5f15\u5165</p> <p>\u5728\u4e4b\u524d #\u8bd1\u7801\u5668 \u548c #\u591a\u8def\u590d\u7528\u5668 \u7684\u90e8\u5206\u4e2d\u5df2\u7ecf\u4ecb\u7ecd\u8fc7\u4e00\u4e9b\u5b9e\u73b0 1 bit \u52a0\u6cd5\u5668\u7684\u65b9\u6cd5\uff0c\u63a5\u4e0b\u6765\u6211\u4eec\u5c31\u6765\u8be6\u7ec6\u770b\u770b\u52a0\u6cd5\u5668\u8fd9\u4e2a\u4e1c\u897f\u3002</p> <p>\u9996\u5148\u6211\u4eec\u9700\u8981\u4e86\u89e3\u52a0\u6cd5\u5668\u6700\u5e95\u5c42\u7684\u5355\u5143\uff0c\u5373\u5b9e\u73b0 1 bit \u8fd0\u7b97\u7684 \u534a\u52a0\u5668(half adder) \u548c \u5168\u52a0\u5668(full adder)\uff0c\u63a5\u4e0b\u6765\u9700\u8981\u5c06\u4ed6\u4eec\u7ec4\u5408\u5728\u4e00\u8d77\uff0c\u5b9e\u73b0 n bits \u7684\u52a0\u6cd5\u5668\uff0c\u5176\u4e2d\u4e3b\u8981\u4ecb\u7ecd \u884c\u6ce2\u52a0\u6cd5\u5668(binary ripple carry adder)\u3002\u6b64\u5916\uff0c\u57fa\u4e8e\u4e00\u4e9b\u7f16\u7801\u7684\u77e5\u8bc6\uff0c\u6211\u4eec\u8fd8\u53ef\u4ee5\u5c06\u5b83\u6539\u88c5\u6210\u52a0\u51cf\u6cd5\u5668\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap03/#\u534a\u52a0\u5668--\u5168\u52a0\u5668","title":"\u534a\u52a0\u5668 &amp; \u5168\u52a0\u5668","text":"<p>\u5bf9\u4e8e\u4e8c\u8fdb\u5236\u52a0\u6cd5\uff0c\u5176\u8f93\u51fa\u65e0\u7591\u6709\u5f53\u524d\u4f4d\u7684\u548c <code>S</code> \u548c\u8fdb\u4f4d <code>C</code>\uff0c\u800c\u8f93\u5165\u9664\u4e86\u4e24\u4e2a\u64cd\u4f5c\u6570 <code>X</code> \u548c <code>Y</code> \u4ee5\u5916\uff0c\u8fd8\u53ef\u80fd\u6709\u4e0a\u4e00\u4f4d\u7684\u8fdb\u4f4d <code>Z</code>(\u6216\u8005<code>C{n-1}</code>)\u3002\u800c\u5bf9\u4e8e\u4e00\u4e2a\u4e8c\u8fdb\u5236\u6570\u7684\u7b2c\u4e00\u4f4d\uff0c\u663e\u7136\u4e0d\u4f1a\u6709\u8fdb\u4f4d\uff0c\u6216\u8005\u8bf4 <code>Z=0</code>\uff0c\u6240\u4ee5\u6211\u4eec\u53ef\u4ee5\u5c06\u8fd9\u4e2a <code>Z</code> \u53bb\u6389\uff0c\u5373\u8f93\u5165\u53ea\u6709 <code>X</code> \u548c <code>Y</code>\uff0c\u8fd9\u5c31\u662f \u534a\u52a0\u5668(half adder)\uff1b\u663e\u7136\uff0c\u5bf9\u5e94\u7684\uff0c\u5982\u679c\u8f93\u5165\u4e2d\u6709\u4e0a\u4e00\u4f4d\u7684\u8fdb\u4f4d <code>Z</code>\uff0c\u5219\u79f0\u4e3a \u5168\u52a0\u5668(full adder)\u3002</p> \u534a\u52a0\u5668\u5168\u52a0\u5668 \u903b\u8f91\u8868\u8fbe\u5f0f\u771f\u503c\u8868\u7535\u8def\u56fe \\[ S=\\overline{X}Y+X\\overline{Y}=X\\oplus Y \\\\ C = XY \\] <p> </p> <p> </p> \u903b\u8f91\u8868\u8fbe\u5f0f\u771f\u503c\u8868\u5361\u8bfa\u56fe\u903b\u8f91\u8868\u8fbe\u5f0f with XOR \\[ S=\\overline{X}\\,\\overline{Y}Z + \\overline{X}Y\\overline{Z} + X\\overline{Y}\\,\\overline{Z} + XYZ \\\\ C = XY + XZ + YZ \\] <p> </p> <p> </p> \\[ S = (X\\oplus Y)\\oplus Z \\\\ C = XY + Z(X\\oplus Y) \\]"},{"location":"cour_note/D2QD_DigitalDesign/Chap03/#\u884c\u6ce2\u52a0\u6cd5\u5668","title":"\u884c\u6ce2\u52a0\u6cd5\u5668","text":"<p>\u884c\u6ce2\u52a0\u6cd5\u5668\u662f\u6734\u7d20\u7684 n bits \u52a0\u6cd5\u5668\u5b9e\u73b0\u3002\u5176\u6838\u5fc3\u601d\u60f3\u4e5f\u5c31\u662f\u6a21\u62df\u6211\u4eec\u4f7f\u7528\u201c\u7ad6\u5f0f\u201d\u6765\u8ba1\u7b97\u52a0\u6cd5\uff0c\u4ece\u4f4e\u4f4d\u5f00\u59cb\u9010\u4f4d\u8ba1\u7b97\uff0c\u5e76\u5c06\u8fdb\u4f4d\u7ed9\u5230\u4e0b\u4e00\u4f4d\u4f5c\u4e3a\u8f93\u5165\u3002</p> <p>\u5b9e\u9645\u4e0a\u65e0\u8bba\u662f\u53ea\u7528\u534a\u52a0\u5668\u6216\u662f\u53ea\u7528\u5168\u52a0\u5668\uff0c\u90fd\u53ef\u4ee5\u5b9e\u73b0\u884c\u6ce2\u52a0\u6cd5\u5668\uff0c\u4f46\u662f\u6b8a\u9014\u540c\u5f52\uff0c\u65e0\u975e\u662f\u901a\u8fc7\u5916\u90e8\u5668\u4ef6\u6765\u8fdb\u884c\u4e92\u76f8\u8f6c\u5316\u800c\u5df2\u3002\u5982\u679c\u53ea\u4f7f\u7528\u5168\u52a0\u5668\u6765\u5b9e\u73b0\uff0c\u5219\u4ee5 4 bits \u884c\u6ce2\u52a0\u6cd5\u5668\u4e3a\u4f8b\uff0c\u5176\u5927\u81f4\u903b\u8f91\u5982\u4e0b\uff1a</p> <p></p> <p>\u5176\u4e2d\uff0c\u5728\u52a0\u6cd5\u5668\u4e2d\uff0c\\(C_0\\) \u5fc5\u7136\u662f <code>0</code>\u3002</p> <p>\u52a0\u51cf\u6cd5\u5668\uff0c\u6216\u8005\u8bf4\u52a0\u6cd5\u5668\uff0c\u4e00\u822c\u60c5\u51b5\u4e0b\u5728 <code>ALU</code> \u4e2d\u662f\u6700\u5f71\u54cd\u6548\u7387\u7684\u90e8\u5206\uff0c\u800c\u4e14\u5982\u679c\u4f7f\u7528\u884c\u6ce2\u52a0\u6cd5\u5668\uff0c\u968f\u7740\u4f4d\u6570\u589e\u52a0\u6548\u7387\u4f1a\u8d8a\u6765\u8d8a\u6162\u3002</p> <p>\u6240\u4ee5\u4f1a\u6709\u7c7b\u4f3c\u4e8e\u8d85\u524d\u8fdb\u4f4d\u52a0\u6cd5\u5668\u4e4b\u7c7b\u7684\u4e1c\u897f\u6765\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\u3002</p> <p>\u66f4\u591a\u7684\u5185\u5bb9\u53ef\u4ee5\u770b xxjj \u7684\u8ba1\u7ec4\u7b14\u8bb0\u3002\uff08\u6570\u903b\u4e2d\u6700\u591a\u4e86\u89e3\u5230\u8d85\u524d\u8fdb\u4f4d\u52a0\u6cd5\u5668\u5373\u53ef\u3002\uff09</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap03/#\u4e8c\u8fdb\u5236\u51cf\u6cd5","title":"\u4e8c\u8fdb\u5236\u51cf\u6cd5","text":"<p>\u9996\u5148\uff0c\u5728\u5f00\u59cb\u4e8c\u8fdb\u5236\u51cf\u6cd5\u7684\u4ecb\u7ecd\u4e4b\u524d\uff0c\u4f60\u9700\u8981\u4e86\u89e3 \u8865\u7801(2's complement)\uff0c\u4e0d\u8fc7\u8fd9\u4e2a\u4e1c\u897f\u5b9e\u5728\u662f\u63d0\u8fc7\u592a\u591a\u6b21\u4e86\u6240\u4ee5\u6211\u4e0d\u6253\u7b97\u5728\u8fd9\u91cc\u518d\u5199\u4e00\u6b21\uff0c\u53ef\u4ee5\u67e5\u770b\u6211\u7684 C \u5c0f\u7b14\u8bb0\u7684\u8865\u7801\u5185\u5bb9\u3002</p> <p>\u7ed3\u5408\u8865\u7801\uff0c\u6211\u4eec\u518d\u6765\u89c2\u5bdf\u884c\u6ce2\u52a0\u6cd5\u5668\uff0c\u6211\u4eec\u9700\u8981\u5bf9\u51cf\u6570\u7684\u6bcf\u4e00\u4f4d\u53d6\u53cd\uff0c\u5e76\u5bf9\u6574\u4e2a\u6570\u52a0\u4e00\uff0c\u518d\u76f4\u63a5\u5c06\u5b83\u4eec\u76f8\u52a0\u5373\u53ef\uff0c\u5373\u5c06\u51cf\u6cd5\u8f6c\u5316\u4e3a\u8865\u7801\u4e0b\u7684\u52a0\u6cd5\u3002</p> <p></p> <p>\u5176\u4e2d\u52a0\u4e00\u8fd9\u4e00\u6b65\u6070\u597d\u53ef\u4ee5\u901a\u8fc7\u5728\u52a0\u6cd5\u5668\u4e2d\u5fc5\u5b9a\u4e3a <code>0</code> \u7684 \\(C_0\\) \u6765\u5b9e\u73b0\u3002\u6211\u4eec\u5728\u8f93\u5165\u4e2d\u6dfb\u52a0\u5f02\u6216\u95e8\u6765\u5b9e\u73b0\u53cd\u7801(1's complement)\uff0c\u518d\u7528 \\(C_0\\) \u5b9e\u73b0\u52a0\u4e00\uff0c\u4ece\u800c\u5f97\u5230\u8865\u7801(2's complement)\uff0c\u5c31\u6837\u5c31\u53ef\u4ee5\u5b9e\u73b0\u52a0\u51cf\u6cd5\u5668\u3002</p> <p></p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap03/#\u6709\u7b26\u53f7\u6570\u7684\u8868\u793a\u4e0e\u8ba1\u7b97","title":"\u6709\u7b26\u53f7\u6570\u7684\u8868\u793a\u4e0e\u8ba1\u7b97","text":"<ul> <li> TODO: \u8865\u5145\u8fd9\u91cc\u3002</li> </ul>"},{"location":"cour_note/D2QD_DigitalDesign/Chap04/","title":"Chap 4 Sequential Circuits","text":"<p> \u7ea6 5781 \u4e2a\u5b57  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 19 \u5206\u949f</p> <p>\u4e0a\u4e00\u7ae0\u8bb2\u7684\u662f\u7ec4\u5408\u7535\u8def\uff0c\u867d\u7136\u7ec4\u5408\u7535\u8def\u80fd\u591f\u5b9e\u73b0\u8bf8\u591a\u529f\u80fd\uff0c\u4f46\u662f\u5b83\u4f9d\u7136\u5b58\u5728\u4e00\u4e9b\u7684\u95ee\u9898\uff1a</p> <ol> <li>\u5bf9\u4e8e\u590d\u6742\u7684\u903b\u8f91\uff0c\u62bd\u8c61\u5c42\u7ea7\u591a\uff0c\u5bfc\u81f4\u786c\u4ef6\u5c42\u9762\u5f00\u9500\u5927\u3001\u8017\u65f6\u957f\uff0c\u4e00\u65b9\u9762\u63d0\u9ad8\u6210\u672c\uff0c\u4e00\u65b9\u9762\u964d\u4f4e\u6548\u7387\uff1b</li> <li>\u7ec4\u5408\u7535\u8def\u6ca1\u6cd5\u5b9e\u73b0\u4fe1\u606f\u7684\u5b58\u50a8\uff0c\u6240\u6709\u7684\u529f\u80fd\u6a21\u5757\u5bf9\u4e8e\u7279\u5b9a\u7684\u8f93\u5165\u7ed9\u51fa\u76f8\u540c\u7684\u8f93\u51fa\uff1b</li> </ol> <p>\u800c\u65f6\u5e8f\u7535\u8def\u5219\u62e5\u6709\u5b58\u50a8\u4fe1\u606f\u7684\u80fd\u529b\uff0c\u5bf9\u4e8e\u65f6\u5e8f\u7535\u8def\u6765\u8bf4\uff0c\u8f93\u51fa\u9664\u4e86\u4e0e\u8f93\u5165\u6709\u5173\uff08\u751a\u81f3\u53ef\u4ee5\u6ca1\u6709\u8f93\u5165\uff09\uff0c\u4e5f\u53ef\u4ee5\u4e0e\u81ea\u8eab \u72b6\u6001(state) \u6709\u5173\u3002</p> <p>\u65f6\u5e8f\u7535\u8def\u4e3b\u8981\u5206\u4e3a\u4e24\u7c7b\uff08\u4e3b\u8981\u5206\u7c7b\u4f9d\u636e\u662f\u8f93\u5165\u4fe1\u53f7\u7684\u65f6\u95f4\u548c\u5185\u90e8\u72b6\u6001\u6539\u53d8\u7684\u65f6\u95f4\uff09\uff1a\u540c\u6b65\u65f6\u5e8f\u7535\u8def(synchronous sequential circuit) \u548c \u5f02\u6b65\u65f6\u5e8f\u7535\u8def(asynchronous sequential circuit)\u3002</p> <p>The behavior of a synchronous sequential circuit can be defined from the knowledge of its signals at discrete instants of time. The behavior of an asynchronous sequential circuit depends upon the inputs at any instant of time and the order in continuous time in which the inputs change.</p> <p>\u4e00\u822c\u6765\u8bf4\uff0c\u5f02\u6b65\u7535\u8def\u7684\u8bbe\u8ba1\u76f8\u5bf9\u56f0\u96be\uff08\u884c\u4e3a\u4e0e\u95e8\u7684\u4f20\u64ad\u5ef6\u8fdf\u548c\u8f93\u5165\u4fe1\u53f7\u53d8\u5316\u7684\u65f6\u95f4\u5e8f\u5217\u5bc6\u5207\u76f8\u5173\uff09\uff0c\u4f46\u4ecd\u7136\u5341\u5206\u5fc5\u8981\uff0c\u6bd4\u5982\u89e6\u53d1\u5668\u5c31\u662f\u4ee5\u4e00\u90e8\u9501\u5b58\u5668\u4e3a\u6a21\u5757\u8bbe\u8ba1\u7684\uff1b\u800c\u540c\u6b65\u7535\u8def\u7684\u4f7f\u7528\u66f4\u52a0\u5e7f\u6cdb\uff0c\u901a\u5e38\u8fd9\u4e9b\u201c\u79bb\u6563\u7684\u65f6\u523b\u201d\u90fd\u662f\u7531 \u65f6\u949f\u53d1\u751f\u5668(clock generator) \u8fd9\u79cd\u65f6\u5e8f\u5668\u4ef6\u4ea7\u751f\u5468\u671f\u6027\u7684 \u65f6\u949f\u8109\u51b2(clock pulse) \u5e8f\u5217\u6765\u5b9e\u73b0\u7684\uff08\u8fd9\u79cd\u7535\u8def\u4e00\u822c\u88ab\u79f0\u4e3a \u949f\u63a7\u65f6\u5e8f\u7535\u8def(clocked sequential circuit)\uff0c\u7531\u4e8e\u8bbe\u8ba1\u76f8\u5bf9\u5bb9\u6613\uff0c\u9c81\u68d2\u6027\u5f3a\uff0c\u6240\u4ee5\u88ab\u5e7f\u6cdb\u5e94\u7528\uff09\u3002</p> <p>\u7f13\u51b2</p> <p>\u7f13\u51b2\u5668(buffer) \u4e00\u822c\u901a\u8fc7\u4e24\u4e2a\u975e\u95e8\u4e32\u8054\uff0c\u5e76\u5c06\u8f93\u5165\u8fde\u901a\u8f93\u51fa\u5b9e\u73b0\uff0c\u8fd9\u6837\u80fd\u591f\u5b9e\u73b0\u4fe1\u606f\u7684\u5b58\u50a8\uff0c\u7136\u800c\u65e0\u6cd5\u4fee\u6539\u3002\u800c\u9501\u5b58\u5668\u5c31\u662f\u5728\u7f13\u51b2\u5668\u7684\u57fa\u7840\u4e0a\uff0c\u5c06\u975e\u95e8\u66ff\u6362\u4e3a\u6216\u975e\u95e8\u6216\u4e0e\u975e\u95e8\u5b9e\u73b0\u7684\u3002</p> <p></p> <p>\u5176\u4e2d\uff0c\u4ece\u7ed9\u5b9a\u8f93\u5165\u5230\u66f4\u65b0\u8f93\u51fa\u6709\u4e00\u4e2a \\(t_G\\) \u7684\u5ef6\u65f6\u3002</p> <p>\u5f15\u5165</p> <p>\u663e\u7136\uff0c\u6839\u636e\u4e0a\u9762\u7684\u6982\u8ff0\uff0c\u65f6\u5e8f\u7535\u8def\u4e2d\u6700\u91cd\u8981\u7684\u5c31\u662f\u4fe1\u606f\u5b58\u50a8\u5143\u4ef6\u3002\u5f53\u8f93\u5165\u4fe1\u53f7\u4e0d\u53d1\u751f\u53d8\u5316\u65f6\uff08\u91cd\u70b9\u662f\u53d8\u5316\uff0c\u5373\u8f93\u5165\u548c\u5b58\u50a8\u4fe1\u606f\u672a\u5fc5\u5b58\u5728\u5bf9\u5e94\u5173\u7cfb\uff09\u5b58\u50a8\u5143\u4ef6\u5c31\u80fd\u591f\u4fdd\u6301\u5176\u5185\u90e8\u5b58\u50a8\u7684\u4e8c\u8fdb\u5236\u6570\u636e\u3002</p> <p>\u5b58\u50a8\u5143\u4ef6\u4e3b\u8981\u7531 \u9501\u5b58\u5668(latch) \u548c \u89e6\u53d1\u5668(flip-flop) \u4e24\u79cd\uff0c\u5176\u4e2d\u524d\u8005\u662f\u540e\u8005\u7684\u57fa\u7840\uff0c\u6216\u8005\u8bf4\u591a\u6570\u60c5\u51b5\u4e0b\u6211\u4eec\u4f7f\u7528\u540e\u8005\uff0c\u4f46\u540e\u8005\u7531\u524d\u8005\u6784\u6210\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap04/#\u9501\u5b58\u5668","title":"\u9501\u5b58\u5668","text":""},{"location":"cour_note/D2QD_DigitalDesign/Chap04/#sr--sr-\u9501\u5b58\u5668","title":"SR &amp; S'R' \u9501\u5b58\u5668","text":"<p>SR \u9501\u5b58\u5668\u548c S'R' \u9501\u5b58\u5668\u7684\u57fa\u672c\u539f\u7406\u662f\u4e00\u81f4\u7684\uff0c\u53ea\u4e0d\u8fc7\u524d\u8005\u7528\u7684\u662f\u6216\u975e\u95e8\uff0c\u540e\u8005\u7528\u7684\u662f\u4e0e\u975e\u95e8\u3002</p> <p>SR \u9501\u5b58\u5668\u548c S'R' \u9501\u5b58\u5668\u7684\u8f93\u5165\u90fd\u662f S(Set) \u548c R(Reset) \u4e24\u4e2a\u90e8\u5206\uff0c\u8f93\u51fa\u90fd\u662f Q \u548c Q' \u4e24\u4e2a\u90e8\u5206\u3002</p> <p>\u540d\u79f0\u4e0a \u7684\u5171\u540c\u70b9\u662f\uff0c\u5f53 S \u4e3a <code>1</code> \u65f6\uff0cQ \u90fd\u4f1a\u662f <code>1</code>\uff1b\u5bf9\u4e8e R \u548c Q' \u4e5f\u662f\u8fd9\u6837\uff0c\u53ea\u4e0d\u8fc7\u8981\u6ce8\u610f\uff0cS'R'\u9501\u5b58\u5668\u8f93\u5165\u7684\u5e76\u4e0d\u662f\u8fd9\u91cc\u6240\u8bf4\u7684 S\uff0c\u800c\u662f\u5c06 S' \u4f5c\u4e3a\u8f93\u5165\u3002</p> SR \u9501\u5b58\u5668S'R' \u9501\u5b58\u5668 <p> </p> <p> </p> <p>\u4e00\u4e2a\u8bb0\u5fc6\u65b9\u6cd5\u662f\uff0cSR \u7684\u95e8\u5143\u4ef6\u5bf9 <code>1</code> \u654f\u611f\uff0c\u6240\u4ee5\u662f \u6216\u975e\u95e8 \u7684\u5b9e\u73b0\uff1b\u800c S'R' \u7684\u95e8\u5143\u4ef6\u5bf9 <code>0</code> \u654f\u611f\uff0c\u6240\u4ee5\u662f \u4e0e\u975e\u95e8 \u7684\u5b9e\u73b0\u3002\u800c\u901a\u8fc7 \u300c\u5f53 S \u4e3a <code>1</code> \u65f6\uff0cQ \u90fd\u4f1a\u662f <code>1</code>\u300d\u53ef\u4ee5\u5f97\u5230 S\u3001R \u4e0e Q\u3001Q' \u7684\u4f4d\u7f6e\u3002</p> <p>\u4f46\u662f\u5b9e\u9645\u7684\u5b58\u50a8\u5143\u4ef6\u5e76\u4e0d\u662f\u5355\u7eaf\u7684 SR/S'R' Latches\uff0c\u6240\u4ee5\u5b83\u4eec\u5f53\u7136\u662f\u5b58\u5728\u95ee\u9898\u7684\u3002\u7531\u4e8e\u7535\u8def\u5b58\u5728\u5ef6\u65f6\uff0c\u6240\u4ee5 S \u548c R \u7684\u8f93\u5165\u5f88\u96be\u540c\u65f6\u5230\u8fbe\uff0c\u6240\u4ee5\u6211\u4eec\u53ef\u4ee5\u5728\u524d\u9762\u52a0\u4e00\u4e2a\u63a7\u5236\u7aef\uff0c\u5f53\u786e\u4fdd\u4e24\u4e2a\u8f93\u5165\u90fd\u5230\u4f4d\u7684\u65f6\u5019\u518d\u4f7f\u80fd\u3002</p> <p>\u4e8e\u662f\u6211\u4eec\u5f97\u5230\u4e86\uff0c\u5e26\u63a7\u5236\u8f93\u5165\u7684 SR \u9501\u5b58\u5668(SR Latch with Control Input)\uff08S'R'\u7565\uff09\uff1a</p> <p></p> <p>\u6ce8\u610f\uff01SR \u9501\u5b58\u5668\u901a\u8fc7 \u6216\u975e\u95e8 \u5b9e\u73b0\uff0c\u4f46\u5e26\u8f93\u5165\u63a7\u5236\u7684 SR \u9501\u5b58\u5668\u5219\u901a\u8fc7 \u4e0e\u975e\u95e8 \u5b9e\u73b0\uff01</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap04/#d-\u9501\u5b58\u5668","title":"D \u9501\u5b58\u5668","text":"<p>D \u9501\u5b58\u5668\u5b9e\u9645\u4e0a\u662f\u5e26\u63a7\u5236\u8f93\u5165\u7684 SR \u9501\u5b58\u5668\u7684\u6539\u8fdb\u3002\u5176\u4e2d\u6211\u4eec\u5173\u6ce8\u5230\uff0c\u867d\u7136 S \u548c R \u8d77\u4f5c\u7528\u7684\u6709\u4e09\u79cd\u72b6\u6001</p> <p>\u6211\u4eec\u5173\u6ce8\u5230\uff0c\u5373\u4f7f\u662f\u5e26\u63a7\u5236\u8f93\u5165\u7684 SR \u9501\u5b58\u5668\uff0c\u4e5f\u5b58\u5728\u4e00\u4e2a\u300cundefined\u300d\u72b6\u6001\uff0c\u800c\u8fd9\u662f\u6211\u4eec\u4e0d\u5e0c\u671b\u51fa\u73b0\u7684\uff0c\u4e8e\u662f\u6211\u4eec\u60f3\uff0c\u80fd\u4e0d\u80fd\u907f\u514d\u8fd9\u79cd\u60c5\u51b5\u7684\u53d1\u751f\u3002\u8fd9\u65f6\u5019\u6211\u4eec\u89c2\u5bdf\u5230\uff0c\u7531\u4e8e\u53ef\u4ee5\u901a\u8fc7 C \u6765\u63a7\u5236\u662f\u5426\u4fdd\u6301\uff0c\u6240\u4ee5\u53ef\u4ee5\u76f4\u63a5\u5f3a\u5236\u8981\u6c42 \\(S = \\overline R\\)\uff0c\u4e8e\u662f\u5c31\u907f\u514d\u4e86 undefined \u60c5\u51b5\u7684\u51fa\u73b0\uff0c\u8fd9\u5c31\u662f D \u9501\u5b58\u5668\u3002</p> <p></p> <p>\u53ea\u6709\u5f53 C \u4e3a <code>1</code> \u65f6\uff0cD \u9501\u5b58\u5668\u624d\u80fd\u5199\u5165\u6570\u636e\uff1b\u800c\u5f53 C \u4e3a <code>0</code> \u65f6\uff0cD \u9501\u5b58\u5668\u7684\u6570\u636e\u5c31\u4e0d\u4f1a\u53d8\u5316\u3002</p> <p>\u900f\u660e\u7684\u5371\u5bb3\uff1a\u7a7a\u7ffb</p> <p>\u5f53\u7136\uff0cD \u9501\u5b58\u5668\u4e5f\u5b58\u5728\u95ee\u9898\u3002\u5982\u679c\u6211\u95e8\u5c06 \\(\\overline Q\\) \u63a5\u5230 \\(D\\) \u4e0a\uff0c\u5c31\u4f1a\u53d1\u73b0 D \u9501\u5b58\u5668\u5c06\u4e0d\u505c\u7684\u53d8\u5316\u5176\u4e2d\u7684\u6570\u636e\uff0c\u51fa\u73b0 \u7a7a\u7ffb\uff0c\u5bfc\u81f4\u6211\u4eec\u65e0\u6cd5\u786e\u5b9a C \u7f6e <code>0</code> \u65f6 Q \u7684\u8f93\u51fa\u7a76\u7adf\u662f\u4ec0\u4e48\uff0c\u800c\u8fd9\u662f\u975e\u5e38\u5371\u9669\u7684\u3002</p> <p>\u8fd9\u4e3b\u8981\u662f\u56e0\u4e3a D \u9501\u5b58\u5668\u7684\u8f93\u5165\u548c\u8f93\u51fa\u90fd\u662f\u76f4\u63a5\u66b4\u9732\u51fa\u6765\u3001\u540c\u65f6\u5141\u8bb8\u53d8\u5316\u7684\uff08\u4e0d\u662f\u540c\u65f6\u53d8\u5316\uff0c\u662f\u6307\u5728 Input \u53ef\u4ee5\u53d8\u7684\u65f6\u5019 Output \u4e5f\u80fd\u53d8\uff09\uff0c\u5373 \u900f\u660e(transparent) \u7684\u3002\u8fd9\u5c31\u5bfc\u81f4\u4e86\u5728\u4e00\u4e2a\u65f6\u949f\u5468\u671f\u91cc\uff0c\u540c\u65f6\u5b58\u5728 \u53ef\u4ee5\u4e92\u76f8\u5f71\u54cd \u7684\u4e24\u4e2a\u4e1c\u897f\u3002\u8fd9\u4e5f\u662f\u89e6\u53d1\u5668\u6240\u89e3\u51b3\u7684\u95ee\u9898\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap04/#\u89e6\u53d1\u5668","title":"\u89e6\u53d1\u5668","text":"<p>\u4e3a\u4e86\u89e3\u51b3\u4e0a\u9762\u63d0\u5230\u7684\uff0c\u7531\u300c\u900f\u660e\u300d\u5f15\u53d1\u7684\u95ee\u9898\uff0c\u800c\u91c7\u7528\u89e6\u53d1\u5668\u7684\u8bbe\u8ba1\u3002\u901a\u8fc7\u7ec4\u5408\u4e24\u4e2a\u9501\u5b58\u5668\uff0c\u4e3b\u8981\u6709\u4e24\u79cd\u5b9e\u73b0\u65b9\u6cd5\uff1a</p> <ol> <li>\u5728\u6709\u8109\u51b2\uff08\u9ad8\u7535\u5e73\uff09\u65f6\uff0c\u4fee\u6539\u7b2c\u4e00\u4e2a\u9501\u5b58\u5668\u7684\u503c\uff0c\u4fdd\u6301\u7b2c\u4e8c\u4e2a\u9501\u5b58\u5668\u7684\u503c\uff1b\u5728\u6ca1\u6709\u8109\u51b2\uff08\u4f4e\u7535\u5e73\uff09\u65f6\u5019\u4fdd\u6301\u7b2c\u4e00\u4e2a\u9501\u5b58\u5668\u7684\u503c\uff0c\u4fee\u6539\u7b2c\u4e8c\u4e2a\u9501\u5b58\u5668\u7684\u503c\uff0c\u66f4\u65b0\u89e6\u53d1\u5668\u7684\u72b6\u6001\uff0c\u5373 \u4e3b\u4ece\u5f0f(master-slave)\u89e6\u53d1\u5668\uff1b</li> <li>\u4ec5\u5728\u65f6\u949f\u7684\u8fb9\u7f18\u89e6\u53d1\uff0c\u5373\u5728\u7279\u5b9a\u65f6\u523b\u4ec5\u63a5\u53d7\u4e00\u4e2a\u8f93\u5165\uff0c\u5373 \u8fb9\u6cbf\u89e6\u53d1\u5f0f(edge-triggered)\u89e6\u53d1\u5668\uff1b</li> </ol> <p>\u8fb9\u6cbf\u89e6\u53d1\u5f0f D \u89e6\u53d1\u5668\u662f\u76ee\u524d\u4f7f\u7528\u6700\u5e7f\u6cdb\u7684\u89e6\u53d1\u5668\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap04/#sr-\u4e3b\u4ece\u89e6\u53d1\u5668","title":"SR \u4e3b\u4ece\u89e6\u53d1\u5668","text":"<p>\u867d\u7136\u5b83\u53eb FF\uff0c\u4f46\u5b83\u5e76\u4e0d\u7b26\u5408 FF \u7684\u7279\u5f81\uff0c\u7136\u800c\u5206\u7c7b\u4e0a\u53c8\u5c5e\u4e8e pulse-triggered FF\u3002</p> <p>SR \u89e6\u53d1\u5668\u77e5\u6240\u4ee5\u662f\u6240\u8c13\u7684 pulse-triggered \u7684\uff0c\u662f\u56e0\u4e3a\u5728 S \u548c R \u8f93\u5165\u90fd\u4e3a <code>0</code> \u65f6\uff0c\u5982\u679c\u51fa\u73b0\u566a\u97f3\uff0c\u5c31\u4f1a\u5bfc\u81f4 Slave \u5199\u5165\u5f02\u5e38\u6570\u636e\u3002</p> <p>\u4f46\u662f\u6211\u4e2a\u4eba\u8ba4\u4e3a\u8fd9\u662f SR \u81ea\u8eab\u6709\u4e24\u4e2a\u4fdd\u6301\u6001\u5bfc\u81f4\u7684\u5f0a\u7aef\uff0c\u800c\u5728\u5b9e\u9645\u4f7f\u7528\u8fc7\u7a0b\u4e2d\u6211\u4eec\u5c31\u4e0d\u5e94\u8be5\u6709\u8f93\u5165\u4e3a S \u548c R \u90fd\u4e3a <code>0</code> \u7684\u60c5\u51b5\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap04/#\u8fb9\u6cbf\u89e6\u53d1\u5f0f\u89e6\u53d1\u5668","title":"\u8fb9\u6cbf\u89e6\u53d1\u5f0f\u89e6\u53d1\u5668","text":"<p>\u4e0a\u9762\u5df2\u7ecf\u8bf4\u8fc7\u4e86\uff0c\u8fb9\u6cbf\u89e6\u53d1\u5f0f\u89e6\u53d1\u5668\u4e3b\u8981\u5bf9\u8109\u51b2\u7684 \u4e0a\u5347\u6cbf \u6216 \u4e0b\u964d\u6cbf \u654f\u611f\u3002</p> <p>\u4e0b\u56fe\u4e3a\u6b63\u8fb9\u6cbf\u89e6\u53d1 D \u89e6\u53d1\u5668\u7684\u5927\u81f4\u539f\u7406\u56fe\u3002</p> <p></p> <p>\u5173\u6ce8\u4e0a\u5347\u6cbf\u524d\u540e\uff0c\u4e0a\u5347\u6cbf\u524d\u4e00\u523b\uff0c\u4e3b\u9501\u5b58\u5668\u53ef\u5199\uff0c\u4ece\u9501\u5b58\u5668\u53ea\u8bfb\uff1b\u4e0a\u5347\u6cbf\u540e\u4e00\u523b\uff0c\u4e3b\u9501\u5b58\u5668\u53ea\u8bfb\uff0c\u4ece\u9501\u5b58\u5668\u53ea\u5199\uff0c\u4e14\u5199\u5165\u7684\u662f\u4e3b\u9501\u5b58\u5668\u5b58\u50a8\u7684\u503c\u2014\u2014\u6362\u53e5\u8bdd\u6765\u8bf4\uff0c\u5b58\u7684\u662f\u4e0a\u5347\u6cbf\u524d\u4e00\u523b\u5199\u5165\u4e3b\u9501\u5b58\u5668\u7684\u5185\u5bb9\u3002</p> <p>\u9700\u8981\u6ce8\u610f\u7684\u4e00\u70b9\u662f\uff0cD \u89e6\u53d1\u5668\u6ca1\u6709\u300c\u4fdd\u6301\u300d\u6001\u3002\u5982\u679c\u8981\u4f7f D \u89e6\u53d1\u5668\u4fdd\u6301\uff0c\u53ef\u4ee5\u4f7f\u65f6\u949f\u8109\u51b2\u5931\u6548\u6216\u901a\u8fc7 <code>MUX</code> \u5c06\u8f93\u51fa\u63a5\u5230\u8f93\u5165\u5b9e\u73b0\u3002\u5176\u4e2d\u524d\u8005\u4e0d\u592a\u5e38\u7528\uff0c\u56e0\u4e3a\u53d7\u95e8\u63a7\u7684\u65f6\u949f\u8109\u51b2\u8fdb\u5165\u89e6\u53d1\u5668\u65f6\u6709\u5ef6\u8fdf\uff0c\u5373 \u65f6\u949f\u504f\u79fb(clock skew)</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap04/#\u6807\u51c6\u56fe\u5f62\u7b26\u53f7","title":"\u6807\u51c6\u56fe\u5f62\u7b26\u53f7","text":"<p>\u5e26\u5706\u5708\u8868\u793a\u8d1f\u903b\u8f91\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap04/#\u76f4\u63a5\u8f93\u5165","title":"\u76f4\u63a5\u8f93\u5165","text":"<p>\u8fd9\u4e9b\u76f4\u63a5\u8f93\u5165\u5f80\u5f80\u662f\u5f02\u6b65\u7684\uff0c\u4e00\u822c\u7528\u6765\u5f02\u6b65\u7f6e\u4f4d\uff08\u76f4\u63a5\u7f6e\u4f4d\u6216\u9884\u7f6e\uff09\u6216\u5f02\u6b65\u590d\u4f4d\uff08\u76f4\u63a5\u590d\u4f4d\u6216\u6e05\u96f6\uff09\u3002</p> <p>\u5bf9\u4e8e\u65f6\u5e8f\u7535\u8def\u6765\u8bf4\uff0c\u300c\u590d\u4f4d\u300d\u6216\u300c\u7f6e\u4f4d\u300d\u8fd9\u79cd\u8f93\u5165\u5e38\u5e38\u4f5c\u4e3a\u521d\u59cb\u5316\uff0c\u5373\u786e\u5b9a\u5404\u4e2a\u89e6\u53d1\u5668\u7684\u300c\u521d\u59cb\u72b6\u6001\u300d\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap04/#\u65f6\u5e8f\u7535\u8def\u5206\u6790","title":"\u65f6\u5e8f\u7535\u8def\u5206\u6790","text":"<p>\u4e3a\u4e86\u5206\u6790\u65f6\u5e8f\u7535\u8def\uff0c\u6211\u4eec\u9700\u8981\u4e00\u4e9b\u5de5\u5177\u6765\u8868\u793a\u65f6\u5e8f\u7535\u8def\u7684\u4e00\u4e9b\u7279\u5f81\u4e0e\u903b\u8f91\u3002\u89c2\u5bdf\u65f6\u5e8f\u7535\u8def\u548c\u7ec4\u5408\u7535\u8def\u7684\u533a\u522b\uff0c\u53d1\u73b0\u6700\u6838\u5fc3\u7684\u5c31\u662f\u903b\u8f91\u8fd0\u7b97\u8fc7\u7a0b\u4e2d\u51fa\u73b0\u4e86\u300c\u72b6\u6001\u300d\u53c2\u4e0e\u8fd0\u7b97\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u9700\u8981\u5728\u5404\u4e2a\u7ec4\u5408\u7535\u8def\u5206\u6790\u4e2d\u91c7\u7528\u7684\u8868\u793a\u65b9\u6cd5\u4e2d\uff0c\u6dfb\u52a0\u8868\u793a\u300c\u72b6\u6001\u300d\u7684\u4fe1\u606f\u3002</p> <p>\u9664\u6b64\u4e4b\u5916\uff0c\u5982\u679c\u53ea\u662f\u5355\u7eaf\u7684\u5c06\u300c\u72b6\u6001\u300d\u4f5c\u4e3a\u4e00\u4e2a\u65b0\u7684\u8f93\u5165\uff0c\u4f5c\u4e3a\u589e\u91cf\u6dfb\u52a0\u5230\u8868\u8fbe\u65b9\u5f0f\u4e2d\uff0c\u4f1a\u53d1\u73b0\u8fd9\u4e9b\u8868\u8ff0\u4f1a\u663e\u5f97\u5f88\u91cd\u3002\u6240\u4ee5\u6211\u4eec\u4e5f\u9700\u8981\u5bfb\u627e\u4e00\u79cd\u66f4\u597d\u7684\u529e\u6cd5\u6765\u8868\u8fbe\u65f6\u5e8f\u7535\u8def\u4e2d\u7684\u903b\u8f91\uff0c\u8fd9\u5c31\u662f\u300c\u72b6\u6001\u56fe\u300d\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap04/#\u89e6\u53d1\u5668\u7684\u8f93\u5165\u65b9\u7a0b","title":"\u89e6\u53d1\u5668\u7684\u8f93\u5165\u65b9\u7a0b","text":"<p>\u89e6\u53d1\u5668\u7684\u8f93\u5165\u65b9\u7a0b(flip-flop input equation) \u4e3b\u8981\u662f\u4e3a\u5176\u63d0\u4f9b\u4e00\u4e2a\u4ee3\u6570\u8868\u8fbe\u65b9\u5f0f\u3002\u5b83\u7684\u4e3b\u8981\u60f3\u6cd5\u662f\u24f5\u8868\u8fbe\u6bcf\u4e00\u4e2a\u89e6\u53d1\u5668\u7684\u8f93\u5165\u4e0e\u8f93\u51fa\u4e4b\u95f4\u7684\u5173\u7cfb\uff1b\u24f6\u8868\u8fbe\u6bcf\u4e00\u4e2a\u76f4\u63a5\u8f93\u51fa\u7684\u903b\u8f91\u8868\u8fbe\u5f0f\u3002\u5176\u4e2d\uff0c\u89e6\u53d1\u5668\u7684\u8f93\u51fa\u7b26\u53f7\u8868\u793a\u4e86\u5176\u7c7b\u578b\uff08\u5373\u7b26\u53f7\uff09\u4e0e\u8f93\u51fa\uff08\u5373\u4e0b\u6807\uff09\u3002</p> <p>\u5177\u4f53\u6765\u8bf4\uff0c\u4f8b\u5982\u4e0b\u9762\u8fd9\u4e2a\u7535\u8def\uff1a</p> <p></p> <p>\u53ef\u4ee5\u53d1\u73b0\uff0c\u5176\u4e2d\u5305\u542b\u4e24\u4e2a\u89e6\u53d1\u5668 \\(D_A\\) \u548c \\(D_B\\)\uff0c\u4ee5\u53ca\u4e00\u4e2a\u7ec4\u5408\u903b\u8f91\u8f93\u51fa \\(Y\\)\uff0c\u56e0\u800c\u53ef\u4ee5\u6839\u636e\u7535\u8def\u7684\u7279\u5f81\uff0c\u5f97\u5230\u4e0b\u9762\u8fd9\u51e0\u4e2a\u5f0f\u5b50\uff1a</p> \\[ \\begin{aligned}     D_A &amp; = AX + BX \\\\     D_B &amp; = \\overline{A}X \\\\     Y   &amp; = (A + B)\\overline{X} \\end{aligned} \\]"},{"location":"cour_note/D2QD_DigitalDesign/Chap04/#\u72b6\u6001\u8868","title":"\u72b6\u6001\u8868","text":"<p>\u5f53\u7136\uff0c\u65f6\u5e8f\u7535\u8def\u7684\u903b\u8f91\u6709\u65f6\u5019\u4e5f\u53ef\u4ee5\u901a\u8fc7\u72b6\u6001\u8868\u6765\u63cf\u8ff0\uff0c\u53ea\u4e0d\u8fc7\u4e0e\u7ec4\u5408\u7535\u8def\u7684 \u771f\u503c\u8868 \u4e0d\u540c\uff0c\u72b6\u6001\u8868(state table) \u6709\u56db\u680f\uff1a\u5f53\u524d\u72b6\u6001(present state)\u3001\u8f93\u5165(input)\u3001\u4e0b\u4e00\u72b6\u6001(next state)\u3001\u8f93\u51fa(output)\u3002\u5176\u542b\u4e49\u662f\u6bd4\u8f83\u663e\u7136\u7684\uff0c\u53ea\u4e0d\u8fc7\u9700\u8981\u901a\u8fc7\u7535\u8def\u56fe\u5f97\u5230\u72b6\u6001\u8868\uff0c\u9700\u8981\u9996\u5148\u5f97\u5230\u300c\u5f53\u524d\u72b6\u6001\u300d\u5411\u300c\u4e0b\u4e00\u72b6\u6001\u300d\u8f6c\u79fb\u7684\u65b9\u7a0b\uff0c\u5373\u5bf9\u4e8e\u67d0\u4e2a\u65f6\u523b \\(t\\) \u7684\u89e6\u53d1\u5668 \\(A\\) \u7684\u8f93\u51fa \\(A(t)\\)\uff0c\u9700\u8981\u5f97\u5230\u5b83\u4e0b\u4e00\u523b\u7684\u72b6\u6001 \\(A(t+1) = f(A(t), ...)\\)\u3002</p> <p>\u540c\u6837\u4ee5\u8fd9\u4e2a\u7535\u8def\u4e3a \ud83c\udf30\uff1a</p> <p></p> <p>\u9996\u5148\u6211\u4eec\u5bf9 \\(D_A\\) \u5f97\u5230\u8f6c\u79fb\u65b9\u7a0b\uff1a\\(A(t+1) = D_A = A(t)X + B(t)X\\)\uff0c\u53ef\u4ee5\u7b80\u5199\u4e3a \\(A(t+1) = D_A = AX+BX\\)\u3002\u7c7b\u4f3c\u5730\u4e5f\u80fd\u5f97\u5230 \\(B\\) \u7684\u8f6c\u79fb\u65b9\u7a0b\u3002</p> <p>\u4e8e\u662f\uff0c\u6839\u636e\u8fd9\u4e9b\u4fe1\u606f\uff0c\u6211\u4eec\u53ef\u4ee5\u5199\u51fa\u5b83\u7684\u72b6\u6001\u8868\uff1a</p> Present State<code>AB</code> Input<code>X</code> Next State<code>AB</code> Output<code>Y</code> <code>00</code> <code>0</code> <code>00</code> <code>0</code> <code>00</code> <code>1</code> <code>01</code> <code>0</code> <code>01</code> <code>0</code> <code>00</code> <code>1</code> <code>01</code> <code>1</code> <code>11</code> <code>0</code> <code>10</code> <code>0</code> <code>00</code> <code>1</code> <code>10</code> <code>1</code> <code>10</code> <code>0</code> <code>11</code> <code>0</code> <code>00</code> <code>1</code> <code>11</code> <code>1</code> <code>10</code> <code>0</code> <p>Mealy model circuit &amp; Moore model circuit</p> <p>\u5982\u679c\u8f93\u51fa\u65e2\u4f9d\u8d56\u4e8e\u5f53\u524d\u72b6\u6001\uff0c\u4e5f\u4f9d\u8d56\u4e8e\u8f93\u5165\u7684\u65f6\u5e8f\u7535\u8def\uff0c\u5219\u79f0\u4e3a \u7c73\u52d2\u578b\u7535\u8def(Mealy model circuit)\uff1b\u800c\u5982\u679c\u8f93\u51fa\u53ea\u4f9d\u8d56\u4e8e\u5f53\u524d\u72b6\u6001\uff0c\u5219\u79f0\u4e3a \u6469\u5c14\u578b\u7535\u8def(Moore model circuit)\u3002</p> <p>\u5728 \u72b6\u6001\u56fe \u4e2d\uff0c\u6211\u4eec\u8fd8\u5c06\u518d\u4e00\u6b21\u9047\u5230\u8fd9\u4e24\u4e2a\u4eba\u540d\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap04/#\u72b6\u6001\u56fe","title":"\u72b6\u6001\u56fe","text":"<p>\u53ef\u4ee5\u53d1\u73b0\uff0c\u72b6\u6001\u8868\u6bd4\u8f83\u6e05\u6670\u7684\u8868\u8fbe\u4e86\u4e0d\u540c\u7684\u72b6\u6001\u548c\u8f93\u5165\u5f97\u5230\u7684\u7ed3\u679c\uff0c\u4f46\u662f\u5bf9\u4e8e\u300c\u4e0d\u540c\u72b6\u6001\u4e4b\u95f4\u662f\u5982\u4f55\u8f6c\u6362\u7684\u300d\u8fd9\u4ef6\u4e8b\u7684\u63cf\u8ff0\u5e76\u4e0d\u6e05\u6670\u3002\u800c\u5bf9\u4e8e\u300c\u8054\u7cfb\u300d\u8fd9\u4ef6\u4e8b\uff0c\u6709\u5411\u56fe\u662f\u4e00\u4e2a\u975e\u5e38\u597d\u7684\u5f62\u5f0f\uff0c\u6240\u4ee5\u6211\u4eec\u5c06\u4ecb\u7ecd \u72b6\u6001\u56fe(state diagram)\u3002</p> <p>\u72b6\u6001\u56fe\u627f\u8f7d\u7684\u4fe1\u606f\u91cf\u548c\u72b6\u6001\u8868\u662f\u4e00\u6837\u7684\uff0c\u6240\u4ee5\u4e5f\u662f\u9700\u8981\u8868\u8fbe \u5f53\u524d\u72b6\u6001(present state)\u3001\u8f93\u5165(input)\u3001\u4e0b\u4e00\u72b6\u6001(next state)\u3001\u8f93\u51fa(output) \u8fd9\u56db\u4e2a\u4e1c\u897f\u3002\u53ea\u4e0d\u8fc7\u300c\u4e0b\u4e00\u72b6\u6001\u300d\u662f\u901a\u8fc7\u6709\u5411\u8fb9\u6765\u8868\u793a\u7684\u3002\u5f53\u524d\u72b6\u6001\u4f5c\u4e3a\u4e00\u4e2a node \u7684\u5c5e\u6027\uff1b\u800c\u8f93\u5165\u4f5c\u4e3a edge \u7684\u4e00\u4e2a\u5c5e\u6027\uff1b\u81f3\u4e8e\u8f93\u51fa\uff0c\u6839\u636e\u5b83\u662f\u653e\u5728 edge \u4e0a\u8fd8\u662f node \u4e0a\uff0c\u5206\u4e3a \u7c73\u52d2\u578b(Mealy) \u548c \u6469\u5c14\u578b(Moore) \u4e24\u79cd\u3002</p> <p>Mealy</p> <p>\u4f8b\u5982\uff0c\u8fd9\u662f\u4e00\u4e2a \u7c73\u52d2\u578b \u7684\u72b6\u6001\u56fe\uff0c\u4ee5\u53ca\u5bf9\u5e94\u7684\u72b6\u6001\u8868\u3002</p> <p></p> <p>\u56e0\u4e3a\u7c73\u52d2\u578b\u7535\u8def\u7684 \u8f93\u51fa\u4e0e\u5f53\u524d\u72b6\u6001\u548c\u8f93\u5165\u90fd\u6709\u5173\uff0c\u6240\u4ee5\u8f93\u51fa\u4f1a\u548c\u8f93\u5165\u653e\u5728\u4e00\u8d77\uff0c\u5373\u653e\u5728 edge \u91cc\u3002</p> <p>\u5bf9\u4e8e\u7c73\u52d2\u578b\uff0cnode \u5185\u7684\u4e8c\u8fdb\u5236\u4e3a present state \u4e2d\u7684 <code>AB</code>\uff1bedge \u4e0a\u5206\u522b\u4e3a input \u548c output\uff1a<code>X</code>/<code>Y</code>\uff1b\u6709\u5411\u8fb9\u8868\u8fbe\u4e86\u6bcf\u4e2a\u72b6\u6001\u5728\u7279\u5b9a\u8f93\u5165\u4e0b\u7684\u4e0b\u4e00\u4e2a\u72b6\u6001\u3002</p> <p>\u4f8b\u5982\uff0c\u5173\u6ce8 node <code>00</code>\uff0c\u5b83\u6709\u4e00\u6761\u81ea\u73af <code>0</code>/<code>0</code>\uff0c\u5bf9\u5e94 \u72b6\u6001\u8868 \u7684\u7b2c\u4e00\u884c\uff1b\u5b83\u6709\u4e00\u6761 edge <code>1</code>/<code>0</code> \u6307\u5411 node <code>01</code>\uff0c\u5bf9\u5e94 \u72b6\u6001\u8868\u7684\u7b2c\u4e8c\u884c\u3002</p> <p>\u5f53\u7136\uff0c\u7c73\u52d2\u578b\u662f\u6709 \u7f3a\u9677 \u7684\uff0c\u5728\u65f6\u5e8f\u7535\u8def\u8bbe\u8ba1\u4e4b\u540e\u7684\u6b65\u9aa4\u4e2d\uff0c\u6211\u4eec\u9700\u8981\u6839\u636e\u5b83\u6765\u5bf9\u6bcf\u4e00\u4e2a\u72b6\u6001\u8bbe\u8ba1\u8f93\u51fa\u65b9\u7a0b\u3002\u6b64\u65f6\u7531\u4e8e\u4e24\u4e2a\u8f93\u51fa\u5171\u4eab\u540c\u4e00\u4e2a\u76ee\u6807\u72b6\u6001\uff0c\u6240\u4ee5\u6211\u4eec\u9700\u8981\u5c06\u4e24\u4e2a\u8f93\u51fa\u7ed3\u5408\u5230\u540c\u4e00\u4e2a\u5f0f\u5b50\u4e2d\uff0c\u8fd9\u5c06\u63d0\u9ad8\u8bbe\u8ba1\u96be\u5ea6\u548c\u7ec4\u5408\u7535\u8def\u6210\u672c\u3002</p> <p>Moore</p> <p>\u800c\u4e0b\u9762\u662f\u4e00\u4e2a \u6469\u5c14\u578b \u7684\u72b6\u6001\u56fe\uff0c\u4ee5\u53ca\u5bf9\u5e94\u7684\u72b6\u6001\u8868\u3002</p> <p></p> <p>\u56e0\u4e3a\u6469\u5c14\u578b\u7535\u8def\u7684 \u8f93\u51fa\u53ea\u4e0e\u5f53\u524d\u72b6\u6001\u6709\u5173\uff0c\u6240\u4ee5\u8f93\u51fa\u4f1a\u548c\u5f53\u524d\u72b6\u6001\u653e\u5728\u4e00\u8d77\uff0c\u5373\u653e\u5728 node \u91cc\u3002</p> <p>\u5bf9\u4e8e\u6469\u5c14\u578b\uff0cnode \u5185\u7684\u4e8c\u8fdb\u5236\u8868\u793a present state \u548c output\uff1a<code>A</code>/<code>Z</code>\uff1bedge \u4e0a\u5217\u4e3e\u4e86\u8fd9\u79cd\u8f6c\u79fb\u53ef\u80fd\u7684 inputs\uff1a<code>XY</code>\u3002</p> <p>\u4f8b\u5982\uff0c\u5173\u6ce8 node <code>0</code>/<code>0</code>\uff0c\u5b83\u6709\u4e24\u6761\u81ea\u73af <code>00</code> \u548c <code>11</code>\uff0c\u5206\u522b\u5bf9\u5e94 \u72b6\u6001\u8868 \u7684\u7b2c\u4e00\u884c\u548c\u7b2c\u56db\u884c\uff1b\u5b83\u6709\u4e24\u6761 edge <code>01</code> \u548c <code>10</code> \u6307\u5411 node <code>1</code>/<code>1</code>\uff0c\u5bf9\u5e94 \u72b6\u6001\u8868 \u7684\u7b2c\u4e8c\u884c\u548c\u7b2c\u4e09\u884c\u3002</p> <p>\u6469\u5c14\u578b\u4e5f\u5b58\u5728 \u7f3a\u9677 \u7684\uff0c\u975e\u5e38\u663e\u7136\uff0c\u76f8\u6bd4\u4e8e\u7c73\u52d2\u578b\uff0c\u6469\u5c14\u578b\u9700\u8981\u66f4\u591a\u7684\u72b6\u6001\u3002</p> <p>\u6362\u53e5\u8bdd\u6765\u8bf4\uff0c\u7c73\u52d2\u578b\u503e\u5411\u4e8e\u8868\u8fbe\u300c\u5728\u7279\u5b9a\u72b6\u6001\u4e0b\uff0c\u7279\u5b9a\u8f93\u5165\u5c06\u5bfc\u81f4\u67d0\u79cd\u7ed3\u679c\uff0c\u4ee5\u53ca\u72b6\u6001\u8f6c\u79fb\u300d\uff1b\u800c\u6469\u5c14\u578b\u503e\u5411\u4e8e\u8868\u8fbe\u300c\u7279\u5b9a\u8f93\u5165\u5c06\u5bfc\u81f4\u67d0\u4e2a\u72b6\u6001\u5411\u53e6\u5916\u4e00\u4e2a\u72b6\u6001\u8f6c\u79fb\uff0c\u800c\u8f93\u51fa\u66f4\u50cf\u662f\u4e00\u79cd\u72b6\u6001\u7684\u7ed3\u679c\u300d\u3002</p> <p>\u72b6\u6001\u56fe\u8fd8\u6709\u8fdb\u9636\u5f62\u6001\uff0c\u4e4b\u540e\u4f1a\u63d0\u53ca\uff0c\u5c31\u662f \u72b6\u6001\u673a\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap04/#\u7b49\u4ef7\u72b6\u6001","title":"\u7b49\u4ef7\u72b6\u6001","text":"<p>\u6682\u7565</p> <p>\u5ef6\u65f6\u5206\u6790</p> <p>\u5ef6\u65f6\u5206\u6790\u662f\u4e00\u4e2a\u91cd\u96be\u70b9\uff0c\u5bf9\u4e8e\u65f6\u5e8f\u7535\u8def\u7684\u5ef6\u65f6\u5206\u6790\uff0c\u5c06\u5728\u4e4b\u540e\u5355\u72ec\u5f00\u4e00\u4e2a\u5c0f\u7ed3\u91cd\u70b9\u4ecb\u7ecd\u3002</p> <p>\u8bf7\u53c2\u8003 \u5ef6\u65f6\u5206\u6790\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap04/#\u65f6\u5e8f\u7535\u8def\u7684\u8bbe\u8ba1","title":"\u65f6\u5e8f\u7535\u8def\u7684\u8bbe\u8ba1","text":"<p>\u7c7b\u6bd4\u7ec4\u5408\u903b\u8f91\u7535\u8def\u901a\u8fc7\u771f\u503c\u8868\u8bbe\u8ba1\u7535\u8def\uff0c\uff08\u540c\u6b65\uff09\u65f6\u5e8f\u7535\u8def\u4e3b\u8981\u4f9d\u636e\u72b6\u6001\u8868\uff08\u6216\u7b49\u4ef7\u8868\u8fbe\uff0c\u5982\u72b6\u6001\u56fe\uff09\u6765\u8bbe\u8ba1\u7535\u8def\u3002\u5b9e\u9645\u8bbe\u8ba1\u4e2d\uff0c\u6211\u4eec\u9700\u8981\u8003\u8651\u89e6\u53d1\u5668\u4ee5\u53ca\u5176\u5b83\u7ec4\u5408\u7535\u8def\u7684\u9009\u62e9\u4e0e\u8bbe\u8ba1\uff1a</p> <ul> <li>\u89e6\u53d1\u5668\u7684\u6570\u91cf\u57fa\u672c\u53d6\u51b3\u4e8e\u6574\u4e2a\u9700\u6c42\u4e2d \u72b6\u6001 \u7684\u6570\u91cf\uff0c\\(n\\) \u4e2a\u89e6\u53d1\u5668\u80fd\u591f\u8868\u8fbe \\(2^n\\) \u4e2a\u4e8c\u8fdb\u5236\u72b6\u6001\uff1b</li> <li>\u7ec4\u5408\u7535\u8def\u7684\u4e3b\u8981\u8bbe\u8ba1\u56f4\u7ed5 \u89e6\u53d1\u5668 \u7684 \u8f93\u5165 \u548c \u8f93\u51fa \u5c55\u5f00\uff1b</li> </ul> <p>\u800c\u4e3b\u8981\u7684\u8bbe\u8ba1\u8fc7\u7a0b\u548c\u7ec4\u5408\u903b\u8f91\u7535\u8def\u7684\u8bbe\u8ba1\u662f\u7c7b\u4f3c\u7684\uff0c\u5982\u4e0b\uff1a</p> <ol> <li>\u786e\u5b9a\u7cfb\u7edf\u7684\u884c\u4e3a\uff1b<ol> <li>\u63cf\u8ff0\u7cfb\u7edf\u884c\u4e3a\u8fc7\u7a0b\u4e2d\uff0c\u8981\u6ce8\u610f\u72b6\u6001\u7684\u590d\u7528\uff08\u4e0d\u8fc7\u5e76\u975e\u72b6\u6001\u8d8a\u5c11\u6210\u672c\u5c31\u8d8a\u5c0f\uff0c\u8fd9\u91cc\u6709\u89e6\u53d1\u5668\u6570\u91cf\u548c\u7ec4\u5408\u903b\u8f91\u7535\u8def\u7684 trade-off\uff09\uff1b</li> <li>\u786e\u5b9a\u7535\u8def\u7684\u521d\u59cb\u72b6\u6001\uff08\u590d\u4f4d\u72b6\u6001(reset state)\uff0c\u901a\u8fc7\u7ed9\u5b9a\u590d\u4f4d(reset)\u4fe1\u53f7\u5b9e\u73b0\uff09\uff1b<ul> <li>\u590d\u4f4d\u4e00\u822c\u53ef\u4ee5\u662f\u5f02\u6b65\u7684\uff1b</li> </ul> </li> </ol> </li> <li>\u9610\u8ff0\u8f93\u5165\u548c\u8f93\u51fa\u4e4b\u95f4\u7684\u903b\u8f91\u5173\u7cfb\uff0c\u5e76\u7528\u771f\u503c\u8868\u6216\u903b\u8f91\u8868\u8fbe\u5f0f\u8868\u8fbe\u51fa\u6765\uff1b</li> <li>\u7ed9\u8bbe\u8ba1\u597d\u7684\u72b6\u6001\u7f16\u7801\u8d4b\u503c\uff0c\u5f97\u5230\u5177\u4f53\u7684\u72b6\u6001\u8868\uff1b<ol> <li>\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528 \u6309\u8ba1\u6570\u987a\u5e8f\u3001 \u6309\u683c\u96f7\u7801\u3001\u7528\u72ec\u70ed\u7801 \u6765\u7ed9\u72b6\u6001\u8d4b\u503c\uff0c\u66f4\u7cfb\u7edf\u7684\u65b9\u6cd5\u6bd4\u8f83\u590d\u6742\uff0c\u4e0d\u505a\u8ba8\u8bba\uff1b</li> <li>\u5176\u4e2d\u8fd8\u6709\u4e00\u79cd\u60c5\u51b5\u662f\u6240\u9700\u8981\u7684\u72b6\u6001\u4e0d\u80fd\u5b8c\u6574\u586b\u5145 \\(2^n\\) \u79cd\u60c5\u51b5\uff0c\u9700\u8981\u8bbe\u8ba1\u65e0\u6548\u72b6\u6001\uff0c\u8fd9\u79cd\u65f6\u5019\u53ef\u4ee5\u4e0d\u8003\u8651\u5b83\u4eec\uff1b</li> </ol> </li> <li>\u6839\u636e\u72b6\u6001\u8868\u786e\u5b9a\u4f7f\u7528\u7684\u89e6\u53d1\u5668\u53ca\u5176\u8f93\u5165\u65b9\u7a0b\uff1b</li> <li>\u6839\u636e\u72b6\u6001\u8868\u786e\u5b9a\u8f93\u51fa\u65b9\u7a0b\uff1b</li> <li>\u4f18\u5316\u8f93\u5165\u65b9\u7a0b\u548c\u8f93\u51fa\u65b9\u7a0b\uff1b</li> <li>\u5c06\u4f18\u5316\u540e\u7684\u903b\u8f91\u8bbe\u8ba1\u5de5\u827a\u6620\u5c04\u5230\u786c\u4ef6\u5b9e\u73b0\u4e0a\uff1b</li> <li>\u9a8c\u8bc1\u6b63\u786e\u6027\uff08\u5728\u4eff\u771f\u73af\u5883\u4e2d\uff09\uff1b<ul> <li>\u4e3b\u8981\u5c31\u662f\u770b\u80fd\u4e0d\u80fd\u590d\u73b0\u72b6\u6001\u56fe\uff1b</li> </ul> </li> </ol>"},{"location":"cour_note/D2QD_DigitalDesign/Chap04/#\u72b6\u6001\u673a","title":"\u72b6\u6001\u673a","text":"<p>\u5c3d\u7ba1\u5728\u5c0f\u89c4\u6a21\u7684\u8bbe\u8ba1\u4e2d\uff0c\u72b6\u6001\u56fe\u8868\u73b0\u826f\u597d\uff0c\u4f46\u662f\u968f\u7740\u8bbe\u8ba1\u7684\u7cfb\u7edf\u89c4\u6a21\u53d8\u5927\uff0c\u6211\u4eec\u9700\u8981\u4e00\u4e2a\u66f4\u52a0\u6cdb\u7528\u7684\u65b9\u5f0f\u6765\u8868\u8fbe\u7c7b\u4f3c\u7684\u65f6\u5e8f\u903b\u8f91\u3002</p> <p>\u4e8e\u662f\uff0c\u6211\u4eec\u5728\u72b6\u6001\u56fe\u7684\u57fa\u7840\u4e0a\u8fdb\u884c\u4fee\u6539\uff0c\u8bbe\u8ba1\u4e86 \u72b6\u6001\u673a(State-Machine Diagram) \u6765\u505a\u8fd9\u4ef6\u4e8b\u3002</p> <p>\u72b6\u6001\u673a\u6df7\u7528\u4e86\u7c73\u52d2\u578b\u548c\u6469\u5c14\u578b\u7684\u8f93\u51fa\u683c\u5f0f\uff0c\u4f18\u52a3\u5728 \u72b6\u6001\u56fe \u4e2d\u6709\u6240\u63d0\u53ca\u3002\u5e76\u4e14\uff0c\u6709\u9650\u56fe\u5c06\u72b6\u6001\u8f6c\u79fb\u65b9\u7a0b\u4e5f\u5199\u5165\uff0c\u603b\u4f53\u4e0a\u5bf9\u7535\u8def\u8bbe\u8ba1\u66f4\u53cb\u597d\u3002\u4e0b\u56fe\u662f\u72b6\u6001\u673a\u7684\u4e00\u4e2a\u201c\u8303\u5f0f\u201d\u3002</p> <p>Generic State Diagram Template</p> <p></p> <p>\u9996\u5148\u89e3\u91ca\u4e00\u4e0b\u8fd9\u4e2a\u201c\u8303\u5f0f\u201d\uff1a</p> <p>\u5177\u4f53\u89e3\u91ca\u72b6\u6001\u673a\u6709\u54ea\u4e9b\u5185\u5bb9\uff0c\u4ee5\u53ca\u5404\u4e2a\u90e8\u5206\u4e4b\u95f4\u7684\u903b\u8f91\u3002\u5173\u4e8e\u5404\u4e2a\u90e8\u5206\u51fa\u73b0\u7684\u4f4d\u7f6e\uff0c\u8bf7\u53c2\u8003 Template\u3002</p> <p>\u53e6\u5916\uff0c\u4e3a\u4e86\u7b80\u5316\u8bed\u53e5\uff0c\u4e0b\u9762\u7684\u8bf4\u6cd5\u7701\u7565\u4e86\u65f6\u949f\uff0c\u8bf7\u8bb0\u5f97\u8003\u8651\u3002</p> <p>\u72b6\u6001\u673a\u6a21\u578b\u4e3b\u8981\u6709\u4e09\u8981\u7d20\uff1a\u8f93\u5165\u6761\u4ef6(Input Conditions)\u3001\u72b6\u6001\u8f6c\u79fb(Transitions) \u548c \u8f93\u51fa\u884c\u4e3a(Output Actions)\u3002\u603b\u4f53\u6765\u8bf4\uff0c\u8f93\u5165\u6761\u4ef6\u544a\u8bc9\u6211\u4eec\u6574\u4e2a\u72b6\u6001\u673a\u8981\u5982\u4f55\u53d8\u5316\uff1b\u72b6\u6001\u8f6c\u79fb\u63cf\u8ff0\u4e86\u72b6\u6001\u673a\u7684\u5185\u90e8\u8f6c\u79fb\u884c\u4e3a\uff0c\u5373\u56fe\u8bba\u4e0a\u7684\u6709\u5411\u8054\u901a\u5173\u7cfb\uff1b\u8f93\u51fa\u884c\u4e3a\u63cf\u8ff0\u52a8\u6001\u53d8\u5316\u8fc7\u7a0b\u4e2d\u72b6\u6001\u673a\u7684\u5bf9\u5916\u8868\u8fbe\u3002\u5176\u4e2d\uff0c\u72b6\u6001\u8f6c\u79fb\u548c\u8f93\u51fa\u884c\u4e3a\u662f\u6211\u4eec\u9700\u8981\u5173\u6ce8\u7684\u72b6\u6001\u673a\u7684\u4e24\u4e2a\u7ef4\u5ea6\uff0c\u8f93\u5165\u6761\u4ef6\u662f\u6211\u4eec\u7528\u6765\u505a\u5b9e\u65f6\u5224\u65ad\u7684\u5916\u90e8\u4f9d\u636e\u3002</p> <p>\u300c\u8f93\u5165\u6761\u4ef6\u300d\u662f\u7531\u8f93\u5165\u53d8\u91cf\u5f62\u6210\u7684\u4e00\u4e2a\u5e03\u5c14\u65b9\u7a0b\uff0c\u5728\u6574\u4e2a\u72b6\u6001\u673a\u4e2d\uff0c\u8f93\u5165\u662f\u53d8\u5316\u7684\u201c\u56e0\u53d8\u91cf\u201d\uff0c\u6362\u53e5\u8bdd\u6765\u8bf4\uff0c\u65e0\u8bba\u662f\u72b6\u6001\u8f6c\u79fb\u8fd8\u662f\u8f93\u51fa\uff0c\u90fd\u53d6\u51b3\u4e8e\u8f93\u5165\u6761\u4ef6\u3002\u800c\u5bfc\u81f4\u7279\u5b9a\u884c\u4e3a\u7684\u8f93\u5165\u6761\u4ef6\u5219\u88ab\u5206\u7c7b\u4e3a \u8f6c\u79fb\u6761\u4ef6(Transition Condition, TC) \u548c \u8f93\u51fa\u6761\u4ef6(Output Condition, OC)\u3002</p> <p>\u300c\u72b6\u6001\u8f6c\u79fb\u300d\u5728\u56fe\u4e2d\u8868\u73b0\u4e3a\u6709\u5411\u8fb9\uff0c\u5f53 TC \u6210\u7acb\u65f6\uff0c\u72b6\u6001\u8f6c\u79fb\u53d1\u751f\uff1b\u6216\u8005\u5bf9\u4e8e\u65e0\u6761\u4ef6\u8f6c\u79fb\uff0c\u53ea\u8981\u5f97\u5230\u65f6\u949f\u8109\u51b2\u5c31\u4f1a\u8f6c\u79fb\u5230\u4e0b\u4e00\u4e2a\u72b6\u6001\u3002</p> <p>\u300c\u8f93\u51fa\u884c\u4e3a\u300d\u5728\u72b6\u6001\u673a\u4e2d\u6709\u56db\u79cd\u89e6\u53d1\u65b9\u6cd5\uff08\u5373\u56db\u79cd OC\uff09\uff1aMoore\u3001\u4e0d\u4f9d\u8d56\u8f6c\u79fb(Transition-condition Independent, TCI) Mealy\u3001\u4f9d\u8d56\u8f6c\u79fb(Transition-condition Dependent, TCD) Mealy \u548c \u4f9d\u8d56\u8f6c\u79fb\u548c\u8f93\u51fa\u6761\u4ef6(Transition and Output-condition Dependent, TOCD) Mealy\u3002\u6839\u636e\u5b57\u9762\u610f\u601d\u6765\u770b\uff1a</p> <ul> <li>Moore \u53ea\u4e0e\u72b6\u6001\u6709\u5173\uff0c\u6240\u4ee5\u5728\u56fe\u4e2d\u4ece\u72b6\u6001\u8282\u70b9\u5f15\u51fa\uff1b</li> <li>TCI Mealy \u4e0e\u72b6\u6001\u548c\u8f93\u51fa\u6761\u4ef6\u6709\u5173\uff0c\u6240\u4ee5\u5728\u56fe\u4e2d\u4ece\u72b6\u6001\u8282\u70b9\u5f15\u51fa\u5199\u5728 OC \u540e\u9762\uff08<code>OC</code>/<code>TCI OA</code>\uff09\uff1b</li> <li>TCD Mealy \u4e0e\u8f6c\u79fb\u6761\u4ef6\u6709\u5173\uff0c\u5f53\u8f6c\u79fb\u6210\u7acb\u7684\u65f6\u5019\u53d1\u751f Output Action\uff0c\u6240\u4ee5\u76f4\u63a5\u5199\u5728 TC \u540e\u9762\uff08<code>TC</code>/<code>TCD OA</code>\uff09\uff1b</li> <li>TOCD Mealy \u5728\u8f6c\u79fb\u53d1\u751f\u65f6\u5019\u624d\u53ef\u80fd\u6761\u4ef6\u6210\u7acb\uff0c\u5373\u5f53 TC \u548c OC \u90fd\u6210\u7acb\u65f6\u624d\u53d1\u751f Output Action\uff0c\u6240\u4ee5\u9700\u8981\u4ece TC \u5f15\u51fa OC\uff0c\u5e76\u8ddf\u5728 OC \u540e\u9762\uff08<code>TC</code>\u2014\u2014<code>OC</code>/<code>TOCD OA</code>\uff09\uff1b         - \u5982\u679c\u51fa\u73b0\u590d\u6570\u7684 TOCD OA\uff0c\u5219\u4f7f\u7528 <code>,</code> \u5206\u9694\uff1b</li> </ul> <p>In a given state, an output action occurs if: (a) it is unconditional (Moore), (b)  TCI and its output condition OC = 1, (c) TCD and its transition condition TD = 1, and (d) TOCD and its transition condition TC and output condition OC are both equal to 1, i.e, TC\u00b7OC = 1. Note that Moore and TCI output actions attached to a state, apply to all transitions from the state as well.</p> <p>\u56de\u5230\u8f93\u51fa\u884c\u4e3a\u672c\u8eab\uff0c\u5f53 OC \u6210\u7acb\u65f6\u8f93\u51fa\u884c\u4e3a\u53d1\u751f\uff0c\u4e00\u822c\u4f1a\u5c06\u8f93\u51fa\u53d8\u91cf\u6807\u51fa\uff0c\u5982\u679c\u5199\u7684\u662f NOT X\uff0c\u8868\u793a OC \u6210\u7acb\u65f6 X \u5e94\u4e3a <code>0</code>\uff1b\u5982\u679c\u5199\u7684\u662f X\uff0c\u5219\u8868\u793a OC \u6210\u7acb\u65f6 X \u4e3a <code>1</code>\u3002</p> <p>\u6ce8\u610f\u70b9</p> <p>\u6b64\u5916\uff0c\u8fd8\u6709\u4e00\u4e2a\u70b9\u9700\u8981\u8fa8\u6790\uff0c\u7531\u4e8e\u300cTransition\u300d\u8868\u793a\u7684\u662f\u201c\u4e0b\u4e00\u4e2a\u201d\u72b6\u6001\uff0c\u6240\u4ee5\u5bf9\u4e8e\u5f53\u524d\u65f6\u523b\uff0c\u5f53\u524d\u8282\u70b9\u7684\u8f93\u51fa\u548c\u51fa\u5ea6\u7684\u8f93\u51fa\u4e0d\u80fd\u51b2\u7a81\u3002\u4f8b\u5982\uff0c\u4e0b\u56fe\u56e0\u4e3a Moore \u8f93\u51fa\u884c\u4e3a\u7684 Z \u548c TC=AB \u90a3\u6761\u8fb9\u7684 Z' \u51b2\u7a81\uff0c\u6240\u4ee5\u975e\u6cd5\u3002</p> <p></p> <p>\u5f53\u7136\uff0c\u975e\u6cd5\u72b6\u6001\u673a\u5e76\u4e0d\u53ea\u6709\u8fd9\u4e00\u4e2a\u5224\u636e\u3002\u4e0d\u8fc7\u6838\u5fc3\u601d\u60f3\u5c31\u662f \u4e0d\u80fd\u6709\u6b67\u4e49\u6216\u51b2\u7a81\u4e14\u9700\u8981\u5145\u5206\uff0c\u66f4\u6570\u5b66\u7684\u8868\u8fbe\u662f\uff0c\u5fc5\u987b\u6ee1\u8db3\u5982\u4e0b\u4e24\u4e2a\u6761\u4ef6\uff1a</p> <p>1.\u975e\u4ea4\uff1a\u5bf9\u4e8e\u6bcf\u4e00\u4e2a\u72b6\u6001 \\(S_i\\)\uff0c\u5b83\u7684\u4efb\u610f\u4e24\u4e2a\u51fa\u5ea6 \\((T_{ij},T_{jk})\\) \u90fd\u4e0d\u80fd\u540c\u65f6\u6210\u7acb\uff0c\u5373\u5e94\u6709\uff1a</p> \\[ \\forall (T_{ij},T_{ik})\\;,\\;\\;T_{ij}\\cdot T_{ik} = 0 \\] <p>2.\u5145\u5206\uff1a\u5bf9\u4e8e\u6bcf\u4e00\u4e2a\u72b6\u6001 \\(S_i\\)\uff0c\u5b83\u7684\u6240\u6709\u51fa\u5ea6\u6761\u4ef6\u5e94\u8be5\u6db5\u76d6\u6240\u6709\u53ef\u80fd\uff0c\u5373\u5e94\u6709\uff1a</p> \\[ \\sum_{j}T_{ij} = 1 \\] <p>Tips: \u4e0a\u9762\u662f\u5bf9 Transition Condition \u7684\u7ea6\u675f\uff0c\u5c06 TC \u6362\u6210 OC \u4e5f\u9700\u8981\u6210\u7acb\u3002</p> \u7f29\u5199\u5bf9\u7167\u8868 \u7f29\u5199 \u542b\u4e49 \u6ce8\u91ca TC Transition Condition \u8f6c\u79fb\u6761\u4ef6\uff1a\u5bfc\u81f4 Transition \u7684 Input Condition OC Output Condition \u8f93\u51fa\u6761\u4ef6\uff1a\u5bfc\u81f4 Output Actions \u7684 Input Condition TCI Transition-condition Independent \u4e0d\u4f9d\u8d56\u8f6c\u79fb\uff1a\u53ea\u4e0e State \u6709\u5173\u7684 Output Actions TCD Transition-condition Dependent \u4f9d\u8d56\u8f6c\u79fb\uff1aTransition Condition \u6210\u7acb\u624d\u6709 Output Actions TOCD Transition and Output-condition Dependent \u4f9d\u8d56\u8f6c\u79fb\u548c\u8f93\u51fa\u65b9\u7a0b\uff1aTransition Condition \u548c Output Condition \u90fd\u6210\u7acb\u624d\u6709 Output Actions State Machine Diagram \ud83c\udf30 <p></p> <p>\u6ce8\u610f\uff0c\u56fe\u4e2d\u6709\u4e00\u4e2a\u9519\u8bef\uff08\u5927\u6982\uff09\uff0c\u53f3\u4fa7 \\(S_1\\) \u7684 OC \u5e94\u4e3a \\((\\overline{A}\\cdot\\overline{B})\\)\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap04/#\u5ef6\u65f6\u5206\u6790","title":"\u5ef6\u65f6\u5206\u6790","text":"<p>\u9996\u5148\uff0c\u81ea\u4e0a\u800c\u4e0b\u7684\u7ed9\u51fa\u89c2\u5ff5\uff0c\u65f6\u5e8f\u7535\u8def\u7684\u5ef6\u65f6\u5206\u6790\u6709\u4e24\u4e2a\u4e3b\u8981\u90e8\u5206\u548c\u4e00\u4e2a\u6b21\u8981\u90e8\u5206\uff1a</p> <ol> <li>\u7ec4\u5408\u7535\u8def\u5bfc\u81f4\u7684\u5ef6\u65f6\uff1b</li> <li>\u89e6\u53d1\u5668\u5bfc\u81f4\u7684\u5ef6\u65f6\uff1b</li> <li>\u7535\u8def\u7684\u677e\u5f1b\u65f6\u95f4\uff1b</li> </ol> <p>\u5e76\u4e14\u5f80\u5f80\u662f\u6839\u636e\u89e6\u53d1\u5668\u7684\u7c7b\u578b\uff0c\u8ba1\u7b97\u4e00\u4e2a\u65f6\u949f\u5468\u671f\u7684\u65f6\u95f4\u3002\u6700\u6838\u5fc3\u7684\u95ee\u9898\u5c31\u662f\u8ba1\u7b97\u7535\u8def\u80fd\u591f\u6b63\u5e38\u5de5\u4f5c\u7684\u6700\u77ed\u65f6\u949f\u5468\u671f\u3002\u63a5\u4e0b\u6765\uff0c\u81ea\u4e0b\u800c\u4e0a\u7684\u8fdb\u884c\u7ec6\u8282\u8865\u5145\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap04/#\u7ec4\u5408\u7535\u8def\u5ef6\u65f6","title":"\u7ec4\u5408\u7535\u8def\u5ef6\u65f6","text":"<p>\u8fd9\u4e00\u90e8\u5206\u7684\u8be6\u7ec6\u5185\u5bb9\u5df2\u7ecf\u5728 \u4e0a\u4e00\u7ae0 \u4ecb\u7ecd\u8fc7\u4e86\uff0c\u5728\u8fd9\u91cc\uff0c\u4e3a\u4e86\u7b80\u5316\u8ba1\u7b97\u8fc7\u7a0b\uff0c\u6211\u4eec\u5168\u90e8\u91c7\u7528 \\(t_{pd}\\)\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap04/#\u89e6\u53d1\u5668\u5ef6\u65f6","title":"\u89e6\u53d1\u5668\u5ef6\u65f6","text":"<p>\u89e6\u53d1\u5668\u5ef6\u65f6\u76f8\u6bd4\u7ec4\u5408\u7535\u8def\u5ef6\u65f6\u590d\u6742\u5f88\u591a\uff0c\u4e3b\u8981\u76ee\u7684\u662f\u4e3a\u4e86\u4fdd\u8bc1\u91c7\u6837\u3002\u4e5f\u5c31\u662f\u8bf4\u5b83\u7684\u201c\u5ef6\u65f6\u201d\u5e76\u4e0d\u4ec5\u4ec5\u662f\u56e0\u4e3a\u7535\u4fe1\u53f7\u4f20\u64ad\u7684\u5ef6\u8fdf\uff0c\u8fd8\u6709\u4e3a\u4e86\u4fdd\u8bc1\u4fe1\u53f7\u7a33\u5b9a\u8bbe\u8ba1\u7684\u4e00\u4e9b\u5185\u5bb9\u3002</p> <p>\u5927\u81f4\u6765\u8bf4\u6709\u4e09\u4e2a\u90e8\u5206\uff1a</p> <ul> <li>Setup Time\uff1a\u91c7\u6837\u8fb9\u7f18\u524d\u8f93\u5165\u4fe1\u53f7\u9700\u8981\u4fdd\u6301\u7a33\u5b9a\u7684\u65f6\u95f4\uff1b</li> <li>Hold Time\uff1a\u91c7\u6837\u8fb9\u7f18\u540e\u8f93\u5165\u4fe1\u53f7\u9700\u8981\u4fdd\u6301\u7a33\u5b9a\u7684\u65f6\u95f4\uff1b</li> <li>Propagation Time\uff1a\u89e6\u53d1\u5668\u7684\u91c7\u6837\u8fb9\u7f18\u5230\u8f93\u51fa\u7a33\u5b9a\u7684\u65f6\u95f4\uff08\u4f20\u64ad\u65f6\u95f4\uff09\uff1b</li> </ul> <p>\u4e00\u7bc7\u4ecb\u7ecd Setup Time \u548c Hold Time \u7684 \u6587\u7ae0\u3002</p> <p>\u6839\u636e\u89e6\u53d1\u5668\u7684\u7c7b\u578b\u4e0d\u540c\uff0c\u4e3b\u8981\u7684 Setup Time \u4e5f\u4e0d\u540c\uff1a</p> <p></p> <p>\u5176\u4e2d\u6bd4\u8f83\u91cd\u8981\u7684\u4e00\u4e9b\u70b9\u662f\uff1a</p> <ol> <li>\u8fd9\u51e0\u4e2a\u65f6\u95f4\u70b9\u8d77\u70b9/\u7ec8\u70b9\u90fd\u662f\u89e6\u53d1\u8fb9\u7f18\uff1b</li> <li>Propagation Time \u4e00\u5b9a\u957f\u4e8e Hold Time\uff0c\u56e0\u6b64\u5728\u8ba1\u7b97\u7535\u8def\u5ef6\u8fdf\u65f6\u53ea\u8003\u8651 Propagation Time\uff1b</li> <li>Pulse-trigger \u548c Edge-trigger \u5728\u8868\u73b0\u4e0a\u7684\u533a\u522b\u5728\u4e8e Setup Time\uff0c\u524d\u8005\u9700\u8981\u8986\u76d6\u6574\u4e2a pulse(<code>pos</code> or <code>neg</code>)\uff1b</li> </ol>"},{"location":"cour_note/D2QD_DigitalDesign/Chap04/#\u677e\u5f1b\u65f6\u95f4","title":"\u677e\u5f1b\u65f6\u95f4","text":"<p>\u5b9e\u9645\u4e0a\u8fd9\u5c31\u662f\u7ed9\u6574\u4e2a\u7535\u8def\u7684\u4e00\u4e2a\u201c\u5bb9\u5dee\u201d\u65f6\u95f4\uff0c\u7ed9\u5b9a\u4e00\u4e2a\u8bef\u5dee\uff0c\u4f46\u662f\u7531\u4e8e\u901a\u8fc7\u524d\u4e24\u8005\u8ba1\u7b97\u51fa\u6765\u7684\u662f\u6700\u77ed\u65f6\u95f4\uff0c\u6240\u4ee5\u677e\u5f1b\u65f6\u95f4\u5fc5\u5b9a\u975e\u8d1f\u3002\uff08\u4e0d\u80fd\u5012\u6263\uff01\uff09</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap04/#\u65f6\u5e8f\u7535\u8def\u5ef6\u65f6","title":"\u65f6\u5e8f\u7535\u8def\u5ef6\u65f6","text":"<p>\u65f6\u5e8f\u7535\u8def\u7684\u5ef6\u65f6\u8ba1\u7b97\u5b9e\u9645\u4e0a\u662f\u4e3a\u4e86\u8ba1\u7b97\u65f6\u5e8f\u7535\u8def\u8fd0\u4f5c\u7684\u6700\u5927\u9891\u7387\u4ee5\u8bbe\u8ba1\u65f6\u949f\u9891\u7387\u3002\u6240\u4ee5\u6211\u4eec\u9700\u8981\u7b97\u51fa\u7535\u8def\u80fd\u591f\u7a33\u5b9a\u5de5\u4f5c\u7684\u6700\u5c0f\u65f6\u949f\u671f\u3002</p> <p>\u5176\u8ba1\u7b97\u9075\u5faa\u4e00\u5b9a\u65b9\u6cd5\uff1a</p> <p></p> <p>\u56fe\u4e2d \\(t_{pd,FF}\\) \u6307\u89e6\u53d1\u5668\u7684 propagation time\uff0c\\(t_{COMB}\\) \u6307\u7ec4\u5408\u7535\u8def\u7684\u603b\u4f20\u64ad\u65f6\u95f4\uff08\u4e00\u822c\u60c5\u51b5\u4e0b \\(t_{COMB} = \\max{\\sum_i t_{pd,gate_i}}\\)\uff09\uff0c\\(t_{s}\\) \u6307\u89e6\u53d1\u5668\u7684 setup time\uff0c\\(t_{slack}\\) \u8868\u793a\u7535\u8def\u7684\u677e\u5f1b\u65f6\u95f4\u3002</p> <p>\uff08\u5047\uff09\u7ecf\u9a8c\u4e4b\u8c08</p> <p>\u4e00\u822c\u4ece\u4e00\u4e2a FF \u7684\u8f93\u51fa\u51fa\u53d1\u5230 FF \u7684\u8f93\u5165\u7ed3\u675f\u3002</p> <ul> <li> \u6211\u89c9\u5f97\u8fd9\u91cc\u5e94\u8be5\u662f\u9700\u8981\u6709\u4f8b\u9898\u7684\uff0c\u4f46\u662f\u6211\u73b0\u5728\u8fd8\u6ca1\u505a\u9898\uff0c\u6240\u4ee5\u505a\u4e86\u518d\u5199\u3002</li> </ul>"},{"location":"cour_note/D2QD_DigitalDesign/Chap05/","title":"Chap 5 Digital Hardware Implementation","text":"<p> \u7ea6 1303 \u4e2a\u5b57  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 4 \u5206\u949f</p> <p>\u6ce8\u610f</p> <p>\u672c\u7ae0\u8282\u5728\u8865\u5929\u4e2d\u5b8c\u6210\uff0c\u5185\u5bb9\u53ef\u80fd\u6bd4\u8f83\u7b80\u7565\u3002</p> <ul> <li> TODO: Finish this.</li> </ul>"},{"location":"cour_note/D2QD_DigitalDesign/Chap05/#\u53ef\u91cd\u7f16\u7a0b\u6280\u672f","title":"\u53ef\u91cd\u7f16\u7a0b\u6280\u672f","text":"<p>\u53ef\u91cd\u7f16\u7a0b\u6280\u672f(programmable implementation technologies)</p> <p>\u76f4\u63a5\u66f4\u6539\u7535\u8def\u6765\u4fee\u6539\u7535\u8def\u529f\u80fd\u88ab\u79f0\u4e3a\u786c\u7f16\u7a0b\uff0c\u800c\u53ef\u91cd\u53d8\u6210\u6280\u672f\u8ba9\u6211\u4eec\u80fd\u591f\u4e0d\u66f4\u6539\u786c\u4ef6\u5e03\u7ebf\u7684\u60c5\u51b5\u4e0b\uff0c\u5b9e\u73b0\u903b\u8f91\u529f\u80fd\u7684\u91cd\u65b0\u7f16\u8f91\u3002</p> <p>FPGA</p> <p>\u73b0\u573a\u53ef\u7f16\u7a0b\u903b\u8f91\u95e8\u9635\u5217(Field Programmable Gate Array, FPGA) - \u67e5\u627e\u8868(lookup table, LUT)</p> <p>\u7f16\u7a0b\u6280\u672f(programming technologies) \u5728\u786c\u4ef6\u5c42\u9762\u6709\u4e09\u79cd\u5b9e\u73b0\u624b\u6bb5\uff1a</p> <ul> <li>\u63a7\u5236\u8fde\u63a5\u6765\u5b9e\u73b0\uff08\u4e0d\u662f\u53ef\u91cd\u7f16\u7a0b\uff09\uff1b<ul> <li>Mask programing</li> <li>Fuse</li> <li>Anti-fuse</li> </ul> </li> <li>\u63a7\u5236\u95e8\u7ea7\u7535\u8def\u7535\u538b\uff1b<ul> <li>Single-bit storage element</li> <li>Stored charge on a floating gate<ul> <li>Erasable</li> <li>Electrically erasable</li> <li>Flash (as in Flash Memory) </li> </ul> </li> </ul> </li> <li>\u4f7f\u7528\u67e5\u627e\u8868(LUT)\uff1b<ul> <li>Storage elements for the function<ul> <li>\u6bd4\u5982\u4f7f\u7528\u4e00\u4e2a <code>MUX</code>\uff0c\u5e76\u5c06\u8f93\u5165\u7aef\u63a5\u5185\u5b58\uff0c\u901a\u8fc7\u4fee\u6539\u5185\u5b58\u7684\u503c\u6765\u4fee\u6539 <code>MUX</code> \u7684\u884c\u4e3a\uff0c\u8fdb\u800c\u5b9e\u73b0\u51fd\u6570\u91cd\u7f16\u7a0b</li> </ul> </li> </ul> </li> </ul> <p>\u8bfe\u7a0b\u4e2d\u4ecb\u7ecd\u7684\u53ef\u91cd\u7f16\u7a0b\u7684\u5668\u4ef6\u4e3b\u8981\u6709\u5982\u4e0b\u56db\u79cd\uff1a</p> <ul> <li>\u53ea\u8bfb\u5185\u5b58 Read Only Memory (ROM) </li> <li>\u53ef\u7f16\u7a0b\u9635\u5217\u903b\u8f91 Programmable Array Logic (PAL\u24c7)</li> <li>\u53ef\u7f16\u7a0b\u903b\u8f91\u9635\u5217 Programmable Logic Array (PLA)</li> <li>Complex Programmable Logic Device (CPLD) or Field-Programmable Gate Array(FPGA)</li> </ul> <p>\u524d\u4e09\u8005\u90fd\u53ea\u80fd\u91cd\u5199\u4e00\u6b21\uff0c\u5982\u4e0b\u662f\u5b83\u4eec\u7684\u91cd\u5199\u5185\u5bb9\uff1a</p> <p></p> <p>\u5f15\u5165</p> <p>\u7531\u4e8e\u4e4b\u540e\u51fa\u73b0\u7684\u7535\u8def\u56fe\u4f1a\u975e\u5e38\u5e9e\u5927\uff0c\u6240\u4ee5\u9700\u8981\u5f15\u5165\u4e00\u4e9b\u903b\u8f91\u7b26\u53f7\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap05/#\u903b\u8f91\u7b26\u53f7\u4ecb\u7ecd","title":"\u903b\u8f91\u7b26\u53f7\u4ecb\u7ecd","text":"<p>Buffer</p> <p></p> <p>\u7b80\u5316\u8868\u793a\u4e00\u4e2a\u53d8\u91cf\u7684\u81ea\u8eab\u548c\u5176\u975e\uff1b</p> <p>Wire connecting</p> <p>\u5728\u53ef\u7f16\u7a0b\u903b\u8f91\u7535\u8def\u4e2d\uff0c\u7ebf\u7684\u8fde\u63a5\u4e0d\u518d\u53ea\u6709\u5355\u7eaf\u7684\u8fde\u901a\u548c\u4e0d\u8fde\u901a\u7684\u5173\u7cfb\uff1a</p> <p>\u5bf9\u4e8e\u4e24\u6761\u76f8\u4ea4\u5bfc\u7ebf\uff1a</p> <ul> <li>\u5982\u679c\u6ca1\u6709\u7279\u6b8a\u7b26\u53f7\uff0c\u5219\u8868\u793a\u8fd9\u4e2a\u4ea4\u53c9\u70b9 is not connected \uff1b</li> </ul> <p></p> <ul> <li>\u5982\u679c\u6709\u4e00\u4e2a \u274c\uff0c\u5219\u8868\u793a\u8fd9\u4e2a\u4ea4\u53c9\u70b9 programmable\uff1b</li> </ul> <p></p> <ul> <li>\u5982\u679c\u53ea\u6709\u4e00\u4e2a\u52a0\u7c97\u7684\u70b9\uff0c\u5219\u8868\u793a\u8fd9\u4e2a\u4ea4\u53c9\u70b9 not programmable\uff1b</li> </ul> <p></p> <p>\u7279\u522b\u7684\uff0c\u5982\u679c\u4e00\u4e2a\u5143\u5668\u4ef6\u7684\u6240\u6709\u8f93\u5165\u90fd\u662f programmable\uff0c\u6211\u4eec\u4e5f\u53ef\u4ee5\u9009\u62e9\u628a\u8fd9\u4e2a \u274c \u753b\u5230\u903b\u8f91\u95e8\u4e0a\uff08\u5982\u4e0b\u56fe e \u548c f\uff09\u3002</p> <p></p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap05/#rom","title":"ROM","text":"<p>ROM \u7684\u57fa\u672c\u7ed3\u6784\u5982\u4e0b\uff1a</p> <p></p> <p>\u800c ROM \u7684\u5927\u5c0f\u5982\u4e0b\u8ba1\u7b97\uff08\u4ee5\u4e0a\u56fe\u4e3a\u4f8b\uff09\uff1a</p> \\[ \\begin{aligned}     ROM\\;\\;size\\;\\;&amp;=\\;\\;address\\;\\;width\\;\\;\\times\\;\\;word\\;\\;width&amp;\\\\                    &amp;=\\;\\;2^2\\;\\;\\times\\;\\;4\\;\\;=\\;\\;16\\;\\;bit&amp; \\end{aligned} \\] eg <p>\u66f4\u6e05\u6670\u7684\u8868\u793a\u5176\u5185\u90e8\u903b\u8f91\u7684\uff0c\u53ef\u4ee5\u5c06 ROM \u5199\u6210\u8fd9\u6837\uff1a</p> <p></p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap05/#pal","title":"PAL","text":"<p>\u53ef\u91cd\u7f16\u7a0b\u8f93\u5165\u7ec4\u5408\u6765\u5f97\u5230\u56fa\u5b9a\u8f93\u51fa\u3002</p> <p>\u5176\u5177\u6709\u4e00\u4e2a\u7f3a\u9677\u662f\uff0c\u56e0\u4e3a\u8868\u8fbe\u51fd\u6570\u7684\u65b9\u6cd5\u4e0d\u662f\u901a\u8fc7 SOM \u6216\u8005 POM \u7684\u5f62\u5f0f\uff0c\u6240\u4ee5\u4e0d\u4e00\u5b9a\u80fd\u591f\u5b8c\u5907\u8868\u8fbe\u51fd\u6570\u3002</p> <p>\u5728\u6b64\u57fa\u7840\u4e0a\u7684\u4e00\u4e2a\u6539\u8fdb\u662f\uff0c\u901a\u8fc7\u5c06\u4e00\u4e2a\u65e2\u6709\u7684 PAL \u8f93\u51fa\u5f53\u4f5c\u8f93\u5165\uff0c\u8f93\u5165\u5230\u53e6\u5916\u4e00\u4e2a\u51fd\u6570\u4e2d\uff0c\u6765\u5f25\u8865\u9879\u4e0d\u8db3\u7684\u95ee\u9898\u3002</p> eg <p></p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap05/#pla","title":"PLA","text":"<p>\u4e0e PAL \u7684\u533a\u522b\u5728\u4e8e\uff0c\u5728\u8f93\u51fa\u7684\u65f6\u5019\u4e5f\u80fd\u5bf9\u8f93\u51fa\u7ec4\u5408\u8fdb\u884c\u91cd\u7f16\u7a0b\u3002</p> <p>\u5176\u540c PAL \u4e00\u6837\u5177\u6709\u4e00\u4e2a\u7f3a\u9677\u662f\uff0c\u56e0\u4e3a\u8868\u8fbe\u51fd\u6570\u7684\u65b9\u6cd5\u4e0d\u662f\u901a\u8fc7 SOM \u6216\u8005 POM \u7684\u5f62\u5f0f\uff0c\u6240\u4ee5\u4e0d\u4e00\u5b9a\u80fd\u591f\u5b8c\u5907\u8868\u8fbe\u51fd\u6570\u3002</p> <p>\u5728\u57fa\u7840\u4e0a\u4e00\u4e2a\u6539\u8fdb\u662f\u5728\u8f93\u51fa\u7684\u65f6\u5019\u518d\u505a\u4e00\u6b21\u5f02\u6216\uff08\u4e0d\u7528\u975e\u95e8\u4f53\u73b0\u4e86\u53ef\u91cd\u7f16\u7a0b\u7684\u601d\u60f3\uff09\uff0c\u4ee5\u4ea7\u751f\u65b0\u7684\u9879\uff0c\u6765\u5f25\u8865\u9879\u4e0d\u8db3\u7684\u95ee\u9898\u3002</p> <p></p> <p>\u53ef\u4ee5\u53d1\u73b0\uff0c\u51fa\u73b0\u4e86\u65b0\u7684\u9879\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap05/#lookup-tables","title":"Lookup Tables","text":"<p>\u901a\u8fc7\u8ba9\u6570\u636e\u6e90\u63a5\u5185\u5b58\uff0c\u5e76\u901a\u8fc7\u4fee\u6539\u771f\u503c\u8868\u5185\u7684\u503c\uff0c\u5373\u4fee\u6539\u5185\u5b58\u91cc\u7684\u503c\uff0c\u6765\u5b9e\u73b0\u6570\u636e\u6e90\u7684\u53d8\u5316\uff0c\u6765\u6539\u53d8 <code>MUX</code> \u7684\u884c\u4e3a\u3002</p> <p>\u4f46\u662f\u5b9e\u9645\u5e94\u7528\u4e2d\uff0c\u51fd\u6570\u8f93\u5165\u7684\u6570\u91cf\u4f1a\u53d8\u5316\uff0c\u56e0\u6b64\u6211\u4eec\u9700\u8981\u901a\u8fc7\u7075\u6d3b\u7ec4\u5408\u7684\u65b9\u6cd5\uff08\u6bd4\u5982\u901a\u8fc7\u56db\u9009\u4e8c\u9009\u4e00\u7684\u65b9\u5f0f\uff0c\u7528\u4e09\u4e2a\u4e8c\u9009\u4e00\u7684 <code>MUX</code> \u6765\u5b9e\u73b0\u56db\u9009\u4e00\uff09\u6765\u5b9e\u73b0\u591a\u8f93\u5165\u3002</p> <p>\u5e38\u89c1\u7684 <code>LUT</code> \u5927\u5c0f\u4ee5 16bits \u6216 64bits \u7684 4 \u8f93\u5165\u6216 6 \u8f93\u5165\u4e3a\u4e3b\u3002</p> <p>\u7531\u4e8e <code>LUT</code> \u5b58\u7684\u672c\u8d28\u4e0a\u662f\u771f\u503c\u8868\uff0c\u6240\u4ee5\u5b83\u53ef\u4ee5\u5b9e\u73b0\u4efb\u610f\u8f93\u5165\u7b26\u5408\u8981\u6c42\u7684\u903b\u8f91\u51fd\u6570\u3002</p> <p>\u6240\u4ee5\uff0c\u95ee\u9898\u5c31\u53d8\u5316\u4e3a\u5982\u4f55\u7528\u8f83\u5c0f\u7684 <code>LUT</code> \u6765\u7ec4\u5408\u5b9e\u73b0\u590d\u6742\u7684\u903b\u8f91\u51fd\u6570\u3002</p> <p><code>LUT</code> \u7684\u57fa\u672c\u7ed3\u6784\u5982\u4e0b\uff1a</p> <p></p> <p><code>FPGA</code> \u7684\u57fa\u672c\u7ed3\u6784\u5982\u4e0b\uff1a</p> <p></p> <p>\u5176\u4e3b\u8981\u5206\u4e3a\u4e09\u4e2a\u7ec4\u6210\u90e8\u5206\uff1a</p> <ul> <li>CLB(Configurable Logic Block)<ul> <li>\u5927\u91cf\u5b58\u50a8 <code>LUT</code></li> </ul> </li> <li>SM(Switch Matrix)<ul> <li>\u53ef\u7f16\u7a0b\u7684\u4ea4\u6362\u77e9\u9635</li> </ul> </li> <li>IOB(Input &amp; Output Block)<ul> <li>\u53ef\u7f16\u7a0b\u7684\u8f93\u5165\u8f93\u51fa\u5355\u5143</li> </ul> </li> </ul>"},{"location":"cour_note/D2QD_DigitalDesign/Chap05/#clb","title":"CLB","text":"<p>CLB \u662f <code>FPGA</code> \u4e2d\u7684\u57fa\u7840\u903b\u8f91\u5355\u5143\u3002</p> <p></p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap05/#sm","title":"SM","text":"<p>\u901a\u8fc7\u76f8\u5f53\u590d\u6742\u7684\u7b97\u6cd5\uff0c <code>SM</code> \u4f1a\u6839\u636e\u76ee\u6807\u903b\u8f91\uff0c\u9009\u62e9\u94fe\u63a5\u4e0d\u540c\u7684 <code>CLB</code> \u4ee5\u5b9e\u73b0\u590d\u6742\u903b\u8f91\u3002</p> <p>\u5b83\u5177\u6709\u8fd9\u4e9b\u57fa\u672c\u5c5e\u6027\uff1a</p> <ol> <li>Flexibility: \u8bc4\u4f30\u4e00\u6761\u7ebf\u53ef\u4ee5\u8fde\u63a5\u5230\u591a\u5c11\u7ebf\uff1b</li> <li>Topology: \u54ea\u4e9b\u7ebf\u53ef\u4ee5\u88ab\u8fde\u63a5\u5230\uff1b</li> <li>Routability: \u6709\u591a\u5c11\u56de\u8def\u53ef\u4ee5\u88ab\u8def\u7531\uff1b</li> </ol> <p></p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap05/#iob","title":"IOB","text":"<p><code>IOB</code> \u7528\u6765\u5bf9\u5916\u90e8\u8bbe\u5907\u8fdb\u884c\u8fde\u63a5\uff0c\u7528\u6765\u63a7\u5236\u8f93\u5165\u548c\u8f93\u51fa\u3002</p> <p></p> eg for <code>FPGA</code> <p>\u901a\u8fc7 <code>FPGA</code> \u5b9e\u73b0 \\(f=x_1x_2+\\overline{x_2x_3}\\)\uff1a</p> <p>\u5206\u89e3\u95ee\u9898\uff1a\\(f_1 = x_1x_2,\\;\\;f_2=\\overline{x_2x_3},\\;\\;f=f_1+f_2\\)\u3002</p> <p></p> <p>\u5728\u8f6f\u4ef6\u5c42\u9762\u7f16\u7a0b\u5b8c\u540e\uff0c\u4f1a\u751f\u6210\u4f4d\u6d41\u6587\u4ef6(<code>bitfile</code>)\uff0c\u4e0b\u8f7d\u5230\u677f\u65f6\u4f1a\u66f4\u65b0 <code>FPGA</code> \u4e2d\u7684\u5185\u5bb9\u3002</p> <p>\u7ec4\u5408\u51fd\u6570\u7684\u5b9e\u73b0\u65b9\u6cd5</p> <p>\u5230\u76ee\u524d\u4e3a\u6b62\uff0c\u4e0d\u7ba1\u662f\u53ef\u91cd\u7f16\u7a0b\u8fd8\u662f\u4e0d\u53ef\u91cd\u7f16\u7a0b\uff0c\u90fd\u5df2\u7ecf\u4ecb\u7ecd\u4e86\u5f88\u591a\u65b9\u6cd5\uff0c\u8fd9\u91cc\u8fdb\u884c\u4e00\u6b21\u5c0f\u7ed3\uff1a</p> <ol> <li><code>Decoder</code>s &amp; <code>OR</code> gates<ul> <li>\u5c06\u8bd1\u7801\u51fa\u6765\u7684\u9700\u8981\u7684\u76ee\u6807\u7ec4\u5408\u90fd <code>OR</code> \u5728\u4e00\u8d77\uff1b</li> </ul> </li> <li><code>MUX</code>s<ul> <li>\u901a\u8fc7\u591a\u8def\u9009\u62e9\u5668\u5b9e\u73b0\u4efb\u610f\u903b\u8f91\u51fd\u6570\uff1b </li> </ul> </li> <li><code>ROM</code>s</li> <li><code>PAL</code>s</li> <li><code>PLA</code>s</li> <li><code>LUT</code>s</li> </ol>"},{"location":"cour_note/D2QD_DigitalDesign/Chap06/","title":"Chap 6 Registers &amp; Register Transfers","text":"<p> \u7ea6 6700 \u4e2a\u5b57  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 22 \u5206\u949f</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap06/#\u5bc4\u5b58\u5668","title":"\u5bc4\u5b58\u5668","text":"<p>\u5bc4\u5b58\u5668(registers)\u7c97\u7565\u7684\u6765\u8bf4\u5c31\u662f\u4e00\u5806\u89e6\u53d1\u5668\u4ee5\u53ca\u5bf9\u5e94\u7684\u72b6\u6001\u63a7\u5236\u7535\u8def\uff0c\u7528\u6765\u5b9e\u73b0\u591a\u4f4d\u6570\u636e\u7684\u5b58\u50a8\u7b49\u64cd\u4f5c\u3002</p> <p>\u5176\u4e2d\u6709\u4e00\u79cd\u7279\u6b8a\u7684\u5bc4\u5b58\u5668\u53eb\u8ba1\u6570\u5668(counter)\uff0c\u975e\u5e38\u76f4\u767d\u7684\uff0c\u5b83\u7684\u884c\u4e3a\u5c31\u662f\u968f\u7740\u65f6\u949f\u5468\u671f\u4e0d\u65ad\u5728\u56fa\u5b9a\u7684\u72b6\u6001\u5e8f\u5217\u4e2d\u5faa\u73af\u3002\u66f4\u5f62\u8c61\u7684\uff0c\u4e00\u822c\u662f\u5b9e\u73b0\u81ea\u52a8\u7684\u8ba1\u6570\u529f\u80fd\uff0c\u50cf\u7535\u5b50\u65f6\u949f\u90a3\u6837\u3002</p> <p>Registers are useful for storing and manipulating information; counters are employed in circuits that sequence and control operations in a digital system.</p> <p>\u5b9e\u73b0\u5bc4\u5b58\u5668\u4e00\u4e2a\u6700\u76f4\u767d\u7684\u60f3\u6cd5\u5c31\u662f\u516c\u7528\u63a7\u5236\u7ebf\u8def\u548c\u5206\u5217\u6570\u636e\u7ebf\u8def\u6765\u63a7\u5236\u591a\u4e2a\u89e6\u53d1\u5668\uff0c\u5982\u4e0b\u56fe\u662f\u4f7f\u7528 D <code>FF</code> \u5b9e\u73b0\u7684\u4e00\u4e2a 4-bit register\uff1a</p> <p></p> <p>\u6211\u4eec\u79f0\u65b0\u6570\u636e\u88ab\u5199\u5165\u5bc4\u5b58\u5668\u7684\u64cd\u4f5c\u4e3a\u8f7d\u5165(load)\uff0c\u800c\u5982\u679c\u8f7d\u5165\u64cd\u4f5c\u5728\u540c\u4e00\u4e2a\u65f6\u949f\u8109\u51b2\u4e2d\u5b8c\u6210\uff0c\u6211\u4eec\u79f0\u4e4b\u662f\u5e76\u884c(parallel)\u7684\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap06/#\u4fdd\u6301","title":"\u4fdd\u6301","text":"<p>\u4f46\u662f\u6211\u4eec\u53d1\u73b0\uff0c\u5982\u56fe\u7684\u5bc4\u5b58\u5668\u5728\u6bcf\u4e2a\u65f6\u949f\u90fd\u5141\u8bb8\u8f7d\u5165\uff0c\u6362\u53e5\u8bdd\u6765\u8bf4\u6bcf\u4e2a\u65f6\u949f\u5468\u671f\u90fd\u4f1a\u6539\u53d8\u4e3a\u8f93\u5165\u3002\u4f46\u662f\u6211\u4eec\u5e0c\u671b\u5373\u4f7f\u6211\u4eec\u4e0d\u7ba1\u5b83\u5b83\u4e5f\u80fd\u4fdd\u6301\u4e4b\u524d\u7684\u503c\uff0c\u4e3b\u8981\u6709\u4e24\u4e2a\u65b9\u6848\u3002</p> <p>\u65b9\u6848 A</p> <p>\u5176\u4e2d\u4e00\u4e2a\u505a\u6cd5\u662f\u9700\u8981\u9009\u62e9\u6027\u7684\u8ba9\u5b83\u8ddf\u968f\u65f6\u949f\u8109\u51b2\u5207\u6362\u72b6\u6001\u3002\u505a\u6cd5\u5c31\u662f\u5c06 Control \u4fe1\u53f7\u4fee\u6539\u4e3a \\(C = \\overline{Load} + Clock\\)\uff0c\u5982\u6b64\u800c\u6765\uff0c\u5f53 \\(Load = 0\\) \u65f6\uff0c\u59cb\u7ec8\u6709 \\(C = 0\\)\uff0c\u8109\u51b2\u6d88\u5931\uff0c\u5bc4\u5b58\u5668\u65e0\u6cd5\u88ab\u8f7d\u5165\u3002\u5982\u4e0b\u56fe\uff0c\u8fd9\u79cd\u6280\u672f\u53eb\u95e8\u63a7\u65f6\u949f(clock gating)\u3002</p> <p></p> <p>clock skew</p> <p>\u7136\u800c\uff0c\u5728\u95e8\u63a7\u65f6\u949f\u6280\u672f\u4e2d\uff0c\u7531\u4e8e\u6dfb\u52a0\u4e86\u4e00\u4e2a\u989d\u5916\u7684\u903b\u8f91\u95e8\uff0c\u65f6\u949f\u8109\u51b2\u5230\u8fbe Control \u7684\u65f6\u5019\u4f1a\u51fa\u73b0\u989d\u5916\u7684\u4f20\u64ad\u5ef6\u65f6\uff0c\u5373\u65f6\u949f\u504f\u79fb(clock skew)\u3002\u800c\u8fd9\u5fae\u5c0f\u7684\u5ef6\u65f6\u4f1a\u5bfc\u81f4\u5728\u6574\u4e2a\u540c\u6b65\u7cfb\u7edf\u4e2d\uff0c\u4e0d\u540c\u7ec4\u4ef6\u5f97\u5230\u7684\u65f6\u949f\u8109\u51b2\u6709\u504f\u5dee\uff0c\u800c\u8fd9\u662f\u6211\u4eec\u6240\u4e0d\u5e0c\u671b\u770b\u5230\u7684\u3002\u6240\u4ee5\u5728\u5b9e\u9645\u8bbe\u8ba1\u4e2d\uff0c\u6211\u4eec\u5e94\u5f53\u907f\u514d\u6216\u5c3d\u53ef\u80fd\u7f29\u5c0f\u65f6\u949f\u504f\u79fb\u3002</p> <p>\u65b9\u6848 B</p> <p>\u53e6\u5916\u4e00\u4e2a\u505a\u6cd5\u662f\uff0c\u5728\u4e0d\u5e0c\u671b\u5b83\u4fee\u6539\u7684\u65f6\u5019\uff0c\u4e0d\u65ad\u5c06\u5b83\u7684\u8f93\u5165\u8f7d\u5165\uff0c\u4e5f\u5c31\u662f\u4fdd\u6301\u4e0d\u53d8\u3002\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u4e00\u4e2a <code>MUX</code> \u6765\u5b9e\u73b0\u8fd9\u4e2a\u529f\u80fd\uff0c\u7528 <code>EN</code> \u4f7f\u80fd\u7aef\u6765\u9009\u62e9\u662f\u8f7d\u5165\u65b0\u503c\u8fd8\u662f\u4fdd\u6301\u4e4b\u524d\u7684\u503c\uff0c\u5982\u4e0b\u56fe\u3002</p> <p></p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap06/#\u5bc4\u5b58\u5668\u5355\u5143","title":"\u5bc4\u5b58\u5668\u5355\u5143","text":"<p>\u5c0f\u8282\u5bfc\u8bfb</p> <p>\u672c\u5c0f\u8282\u5728\u4e66\u672c\u4e2d\u7684\u4f4d\u7f6e\u9760\u540e\uff0c\u4f46\u662f\u8003\u8651\u5230\u5185\u5bb9\u7684\u8fde\u7eed\u6027\u6211\u51b3\u5b9a\u63d0\u524d\uff0c\u672c\u8282\u5185\u5bb9\u4f1a\u6d89\u53ca\u4e00\u4e9b\u4e4b\u540e\u7684\u5185\u5bb9\uff0c\u5b9e\u9645\u4e0a\u7684\u7edd\u5bf9\u6027\u77e5\u8bc6\u8f83\u5c11\uff0c\u53ef\u4ee5\u7c97\u770b\u8fc7\u7559\u4e0b\u5370\u8c61\u5373\u53ef\uff0c\u5927\u90e8\u5206\u77e5\u8bc6\u9700\u8981\u901a\u8fc7\u6848\u4f8b\u5206\u6790\u548c\u5b9e\u8df5\u83b7\u5f97\uff0c\u662f\u7c7b\u4f3c\u4e8e\u8bbe\u8ba1\u6307\u5bfc\u601d\u60f3\u7684\u5185\u5bb9\u3002</p> <p>\u5bc4\u5b58\u5668\u5355\u5143(Register Cell)\u662f\u5bc4\u5b58\u5668\u7684\u4e2a\u4f53\u5355\u5143\uff0c\u4e3b\u8981\u5305\u62ec\u4e00\u4e2a <code>FF</code> \u53ca\u5b9e\u73b0\u5176\u7ec4\u5408\u903b\u8f91\u7684\u7ec4\u5408\u7535\u8def\u3002</p> <p>A single-bit cell of an iterative combinational circuit, connected to a flip-flop that provides the output, forms a two-state sequential circuit called a register cell</p> <p>\u5bf9\u4e8e n bits \u7684\u5bc4\u5b58\u5668\u5355\u5143\uff0c\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u5b9e\u73b0\u5176 1 bit \u7684\u5bc4\u5b58\u5668\u5355\u5143\uff0c\u5e76\u590d\u5236 n \u4efd\u5b9e\u73b0\u3002</p> <p>\u8bbe\u8ba1\u5bc4\u5b58\u5668\u5355\u5143\u65f6\uff0c\u6211\u4eec\u9700\u8981\u5bf9\u5bc4\u5b58\u5668\u5355\u5143\u8fdb\u884c\u5b9a\u4e49\u3002\u800c\u6307\u5b9a(Specify)\u4e00\u4e2a\u5bc4\u5b58\u5668\u5355\u5143\u7684\u529f\u80fd\u7684\u4e3b\u8981\u6709\u8fd9\u4e9b\u65b9\u9762\uff1a</p> <ul> <li>\u5bc4\u5b58\u5668\u7684\u529f\u80fd\u51fd\u6570\uff1b<ul> <li>\u4e00\u822c\u6307\u5bc4\u5b58\u5668\u4f20\u8f93\uff1b</li> </ul> </li> <li>\u63a7\u5236\u4fe1\u53f7\u6784\u6210\uff1b<ul> <li>\u6709\u54ea\u4e9b\u63a7\u5236\u4fe1\u53f7\u3001\u662f\u5426\u7f16\u7801\u3001\u5982\u4f55\u51b3\u5b9a\u662f\u5426 Load \u7b49\uff1b</li> </ul> </li> <li>\u5bc4\u5b58\u5668\u7684\u8f93\u5165\u6570\u636e\uff1b<ul> <li>\u6709\u54ea\u4e9b\u8f93\u5165\u6570\u636e\u3001\u662f\u5426\u9700\u8981\u9884\u5148\u5904\u7406\u7b49\uff1b</li> </ul> </li> </ul> <p>\u5728\u5b9e\u9645\u5b9e\u73b0\u65f6\uff0c\u5206\u4e3a <code>MUX</code> \u5b9e\u73b0\u548c\u65f6\u5e8f\u903b\u8f91\u5b9e\u73b0\u4e24\u79cd\u65b9\u6cd5\u3002</p> <p>\u524d\u8005\u5c31\u662f#\u57fa\u4e8e Mux \u5b9e\u73b0\u4f20\u8f93\u4e2d\u5c06\u8981\u63d0\u5230\u7684\u90a3\u6837\uff0c\u5173\u4e8e\u4e0a\u9762\u54ea\u4e9b\u5185\u5bb9\u5728\u8be5\u5c0f\u8282\u4e2d\u7684\u4f53\u73b0\u5982\u4e0b\u56fe\uff1b</p> <p></p> <p>\u4e5f\u5c31\u662f\u901a\u8fc7\u5206\u522b\u5b9e\u73b0\u903b\u8f91\uff0c\u7136\u540e\u901a\u8fc7\u63a7\u5236\u4fe1\u53f7\u9009\u62e9\u6570\u636e\u8f93\u5165\u6765\u5b9e\u73b0\u3002</p> <p>\u800c\u540e\u8005\u6309\u7167\u65f6\u5e8f\u7535\u8def\u7684\u8bbe\u8ba1\u65b9\u6cd5\uff0c\u786e\u5b9a\u72b6\u6001\u56fe\u540e\u6839\u636e\u72b6\u6001\u53d8\u5316\u8bbe\u8ba1\u65f6\u5e8f\u7535\u8def\uff0c\u8bbe\u8ba1\u4f18\u5316\u51b3\u5b9a\u72b6\u6001\u8f6c\u79fb\u65b9\u7a0b\u5b9e\u73b0\uff0c\u5177\u4f53\u53ef\u4ee5\u53c2\u8003\u7b2c\u56db\u7ae0#\u65f6\u5e8f\u7535\u8def\u8bbe\u8ba1\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap06/#\u5bc4\u5b58\u5668\u4f20\u8f93","title":"\u5bc4\u5b58\u5668\u4f20\u8f93","text":"<p>\u8bf4\u660e</p> <p>\u628a transfer \u7ffb\u8bd1\u4e3a\u201c\u4f20\u8f93\u201d\u662f\u6211\u8111\u74dc\u4e00\u62cd\u7684\u884c\u4e3a\uff0c\u6211\u5e76\u4e0d\u77e5\u9053\u7ffb\u8bd1\u6210\u4ec0\u4e48\u6bd4\u8f83\u5408\u9002\uff0c\u5982\u679c\u8bfb\u8005\u6709\u66f4\u597d\u7684\u7ffb\u8bd1\uff0c\u8bf7\u544a\u8bc9\u6211\uff01</p> <p>\u4e00\u4e2a\u590d\u6742\u7cfb\u7edf\u9664\u4e86\u4fe1\u606f\u7684\u5b58\u50a8\u8fd8\u9700\u8981\u4fe1\u606f\u7684\u4f20\u8f93\u548c\u5904\u7406\uff0c\u6362\u53e5\u8bdd\u6765\u8bf4\uff0c\u4e3a\u4e86\u5b9e\u73b0\u7075\u6d3b\u3001\u590d\u6742\u7684\u8ba1\u7b97\uff0c\u6211\u4eec\u9700\u8981\u4fe1\u606f\u4e4b\u95f4\u80fd\u591f\u5e7f\u6cdb\u5730\u4ea4\u4e92\u3002\u5927\u90e8\u5206\u7535\u5b50\u7cfb\u7edf\u8bbe\u8ba1\u4e2d\uff0c\u90fd\u4f1a\u6709\u4e00\u4e2a\u63a7\u5236\u5355\u5143(Control Unit)\u6765\u8d1f\u8d23\u6307\u6325\uff08\u51b3\u5b9a\u6307\u4ee4\u7684\u5e8f\u5217\uff09\u6570\u636e\u901a\u8def(Datapath)\u8fdb\u884c\u6570\u636e\u5904\u7406\u3002</p> <p>Datapaths are defined by their registers and the operations performed on binary data stored in the registers.</p> <p>\u5bf9\u4e8e\u5bc4\u5b58\u5668\u81ea\u8eab\u800c\u8a00\uff0c\u5b83\u53ef\u80fd\u5b9e\u73b0 \u8f7d\u5165(load)\u3001\u6e05\u7a7a(clear)\u3001\u4f4d\u79fb(shift)\uff08\u5173\u4e8e\u8fd9\u91cc\u7684shift\u7684\u542b\u4e49\u6211\u5b58\u7591\uff09 \u548c \u8ba1\u6570(count) \u7b49\u3002\u6b64\u5916\uff0c\u5bf9\u4e8e\u90a3\u4e9b\u5bc4\u5b58\u5668\u4e2d\u7684\u6570\u636e\u8fdb\u884c\u79fb\u52a8\u4e86\u7684\u52a0\u5de5\uff0c\u88ab\u79f0\u4e3a\u5bc4\u5b58\u5668\u4f20\u8f93\u64cd\u4f5c(Register Transfer Operations)\uff0c\u5b83\u4eec\u4e3b\u8981\u5305\u542b\u8fd9\u4e09\u4e2a\u90e8\u5206\uff1a</p> <ol> <li>\u7cfb\u7edf\u4e2d\u7684\u5bc4\u5b58\u5668\u96c6\u5408\uff1b</li> <li>\u5bf9\u4e8e\u6570\u636e\u7684\u64cd\u4f5c\uff1b</li> <li>\u76d1\u7763\u64cd\u4f5c\u5e8f\u5217\u7684\u63a7\u5236\uff1b</li> </ol> <p>\u5176\u4e2d\uff0c\u6700\u57fa\u7840\u7684\u90a3\u90e8\u5206\u64cd\u4f5c\u88ab\u79f0\u4e3a\u5fae\u64cd\u4f5c(microoperation)\uff0c\u5b83\u4eec\u662f\u5b9e\u73b0\u590d\u6742\u64cd\u4f5c\u7684\u57fa\u7840\uff0c\u4f8b\u5982\u5c06 R1 \u7684\u6570\u636e\u8f7d\u5165 R2\uff0c\u5c06 R1 \u548c R2 \u76f8\u52a0\uff0c\u6216\u662f\u81ea\u589e R1 \u7b49\u3002\u5b83\u4eec\u901a\u5e38\u4ee5\u6bd4\u7279\u5411\u91cf\u4e3a\u8f7d\u4f53\u5e76\u884c\u5b9e\u73b0\u7684\u3002</p> <p>Note that:</p> <p>the term \u201cmicrooperation,\u201d as used here, does not refer to any particular way of producing the control signals: specifically, it does not imply that the control signals are generated by a control unit based on a technique called microprogramming.</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap06/#\u5bc4\u5b58\u5668\u4f20\u8f93\u64cd\u4f5c--\u5bc4\u5b58\u5668\u4f20\u8f93\u8bed\u8a00","title":"\u5bc4\u5b58\u5668\u4f20\u8f93\u64cd\u4f5c &amp; \u5bc4\u5b58\u5668\u4f20\u8f93\u8bed\u8a00","text":"<p>\u5bf9\u4e8e\u7b80\u5355\u7684\u65f6\u5e8f\u903b\u8f91\u7cfb\u7edf\uff0c\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528\u72b6\u6001\u673a\u7b49\u65b9\u5f0f\u6765\u63cf\u8ff0\u5b83\u4eec\u7684\u884c\u4e3a\uff0c\u4f46\u662f\u5bf9\u4e0e\u89c4\u6a21\u66f4\u5927\u7684\u7cfb\u7edf\u6765\u8bf4\uff0c\u8fd9\u662f\u4e00\u4ef6\u5f88\u75db\u82e6\u7684\u4e8b\u60c5\u3002\u6240\u4ee5\u6211\u4eec\u5f15\u5165\u4e86\u4e00\u79cd\u4e13\u6ce8\u4e8e\u884c\u4e3a\u903b\u8f91\u7684\u8bed\u8a00\u6765\u63cf\u8ff0\u5bc4\u5b58\u5668\u4f20\u8f93\u4e2d\u7684\u903b\u8f91\u884c\u4e3a\uff1a\u5bc4\u5b58\u5668\u4f20\u8f93\u8bed\u8a00(Register Transfer Language, RTL)\u3002</p> <p>\u901a\u5e38\u5177\u6709\u7279\u6b8a\u529f\u80fd\u7684\u5bc4\u5b58\u5668\u90fd\u4f1a\u7528\u5176\u540d\u79f0\u7f29\u5199\u5927\u5199\u8868\u793a\uff0c\u4f8b\u5982 AR(Address Register)\uff0cPC(Program Counter)\uff0cIR(Instruction Register) \u6216\u8005\u66f4\u666e\u901a\u7684 R2(Register 2)\u3002</p> <p>Little-endian &amp; Big-endian</p> <p>\u6211\u4eec\u6709\u65f6\u5019\u4e5f\u4f1a\u7528\u8fd9\u4e9b\u5f62\u5f0f\u6765\u56fe\u5f62\u5316\u7684\u8868\u793a\u5bc4\u5b58\u5668\uff1a</p> <p></p> <p>\u6b64\u5916\uff0c\u5e38\u89c1\u64cd\u4f5c\u7528 RTL \u8868\u793a\u65b9\u6cd5\u548c\u7b26\u53f7\u5982\u4e0b\uff1a</p> <p></p> <p></p> <p>\u9700\u8981\u989d\u5916\u8bf4\u660e\u7684\u662f\uff0c\u5982\u679c\u6211\u4eec\u60f3\u8868\u8fbe\u6761\u4ef6\u8bed\u53e5\uff0c\u4f8b\u5982\u6211\u4eec\u60f3\u8868\u8fbe\uff1a</p> \\[ if\\, (K_1 = 1) \\,then\\, (R2 \\leftarrow R1) \\] <p>\u5219\u53ef\u4ee5\u5199\u4e3a\uff1a</p> \\[ K_1 : R2 \\leftarrow R1 \\]"},{"location":"cour_note/D2QD_DigitalDesign/Chap06/#\u5bc4\u5b58\u5668\u4f20\u8f93\u7684\u5b9e\u73b0","title":"\u5bc4\u5b58\u5668\u4f20\u8f93\u7684\u5b9e\u73b0","text":"<p>\u5f15\u5165</p> <p>\u5982\u4f55\u5b9e\u73b0\u5bc4\u5b58\u5668\u6240\u5b58\u50a8\u7684\u6570\u636e\u4e4b\u95f4\u7684\u5904\u7406\u4e0e\u4ea4\u4e92\u662f\u672c\u7ae0\u8282\u7684\u6838\u5fc3\u547d\u9898\u3002\u5982\u679c\u8bf4\u5fae\u64cd\u4f5c\u5904\u7406\u7684\u662f\u6570\u636e\u4e4b\u95f4\u7684\u5904\u7406\uff0c\u90a3\u5bc4\u5b58\u5668\u4f20\u8f93\u5219\u7740\u773c\u4e8e\u6570\u636e\u4e4b\u95f4\u7684\u4ea4\u4e92\u3002</p> <p>\u6362\u53e5\u8bdd\u6765\u8bf4\uff0c\u5982\u4f55\u628a\u6570\u636e\u7ed9\u5230\u522b\u7684\u5bc4\u5b58\u5668\u3001\u5982\u4f55\u83b7\u53d6\u522b\u7684\u5bc4\u5b58\u5668\u7ed9\u5230\u7684\u6570\u636e\u3001\u5982\u4f55\u4f20\u8f93\u548c\u9009\u62e9\u8fd9\u4e9b\u6570\u636e\uff0c\u5c31\u662f\u672c\u5c0f\u8282\u8981\u89e3\u51b3\u7684\u95ee\u9898\u3002</p> <p>\u7279\u522b\u7684\uff0c\u5bc4\u5b58\u5668\u4f20\u8f93\u7684\u5b9e\u73b0\u53ef\u4ee5\u76f4\u63a5\u5b9e\u73b0\u8f6c\u79fb\u64cd\u4f5c\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap06/#\u57fa\u4e8e-mux-\u5b9e\u73b0\u4f20\u8f93","title":"\u57fa\u4e8e MUX \u5b9e\u73b0\u4f20\u8f93","text":"<p>\u5bf9\u4e8e\u4e00\u4e2a\u5355\u4e00\u5bc4\u5b58\u5668\uff0c\u5b83\u7684\u8f93\u5165\u53ef\u80fd\u6709\u591a\u79cd\u6765\u6e90\uff0c\u4f8b\u5982\u5176\u5b83\u5bc4\u5b58\u5668\uff0c\u53c8\u6216\u8005\u662f\u5176\u4ed6\u64cd\u4f5c\u7684\u7ed3\u679c\u3002\u603b\u800c\u8a00\u4e4b\uff0c\u5b83\u7684\u8f93\u5165\u5f88\u53ef\u80fd\u662f\u4e0d\u552f\u4e00\u7684\uff0c\u800c\u540c\u4e00\u65f6\u523b\u6211\u4eec\u53ea\u80fd\u63a5\u53d7\u4e00\u4e2a\u6765\u6e90\u7684\u8f93\u5165\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u9700\u8981\u4f7f\u7528 <code>MUX</code> \u6765\u5bf9\u8f93\u5165\u8fdb\u884c\u9009\u62e9\u3002</p> <p>\u4e00\u4e2a\u7b80\u5355 \ud83c\udf30 \u5982\u4e0b\uff1a</p> <p></p> <p>\u7528\u8bed\u8a00\u6765\u63cf\u8ff0\u8fd9\u4e2a\u603b\u4f53\u67b6\u6784\u5c31\u662f\uff0c\u6211\u4eec\u901a\u8fc7\u4e00\u7cfb\u5217 one-hot \u7f16\u7801\uff08\u4e0d\u786e\u5b9a\uff0c\u4e5f\u8bb8\u53ef\u80fd\u90fd\u4e3a\u96f6\uff1f\u6211\u611f\u89c9\u53d6\u51b3\u4e8e\u4fdd\u6301\u7684\u5b9e\u73b0\u3002\uff09\u6765\u8868\u793a\u9009\u62e9\u54ea\u4e2a\u8f93\u5165\u6e90\uff08\u4e0b\u56fe\u4e2d \\(K_0\\sim K_{n-1}\\)\uff09\uff0c\u518d\u901a\u8fc7 <code>Encoder</code> \u5c06\u5b83\u4eec\u7f16\u7801\u4f5c\u4e3a <code>MUX</code> \u7684\u8f93\u5165\u9009\u62e9\u4fe1\u53f7\uff08\u4e0b\u56fe\u4e2d \\(S_m \\sim S_0\\)\uff09\uff0c\u4ece\u591a\u4e2a\u8f93\u5165\u6e90\uff08\u4e0b\u56fe\u4e2d 0 \\sim k \\sim (n-1)$\uff09\u4e2d\u9009\u62e9\u5bf9\u5e94\u7684\u6e90\uff0c\u5e76\u8f93\u51fa\uff0c\u7ed9\u5230 R0\uff1b\u6b64\u5916\uff0c\u5c06\u9009\u62e9\u4fe1\u53f7\u90fd\u6216\u8d77\u6765\uff0c\u4f5c\u4e3a R0 \u7684 Load \u4fe1\u53f7\u8f93\u5165\u3002</p> <p></p> <p>\u5176\u4e2d <code>MUX</code> \u7684 \\(k \\sim (n-1)\\) \u5b9e\u73b0\u4e86\u8f6c\u79fb\u64cd\u4f5c\u3002</p> <p>\u5c0f\u7ed3</p> <p>\u6362\u53e5\u8bdd\u6765\u8bf4\uff0c<code>MUX</code> \u5b9e\u73b0\u4e3b\u8981\u7684\u5b9e\u73b0\u4e86\u591a\u5bf9\u4e00\u7684\u6570\u636e\u4f20\u8f93\u95ee\u9898\u3002\u5982\u679c\u6211\u4eec\u5355\u5355\u4f7f\u7528 <code>MUX</code> \u6765\u5b8c\u6210\u5bc4\u5b58\u5668\u4e4b\u95f4\u7684\u6570\u636e\u4ea4\u4e92\uff08\u5047\u8bbe\u6240\u6709\u5bc4\u5b58\u5668\u90fd\u80fd\u76f8\u4e92\u4f20\u8f93\u6570\u636e\uff09\uff0c\u90a3\u5c06\u8fd9\u4e2a\u6a21\u578b\uff08\u56fe\u4f8b\u5728\u4e0b\u4e00\u5c0f\u8282\uff09\u62bd\u8c61\u540e\uff0c\u6211\u4eec\u5f97\u5230\u7684\u5c06\u662f\u4e00\u5f20\u201c\u5b8c\u5168\u56fe\u201d\uff0c\u7136\u800c\u5b83\u8089\u773c\u53ef\u89c1\u7684\u5f00\u9500\u5927\u3002</p> <p>\u800c\u603b\u7ebf\u5219\u975e\u5e38\u5de7\u5999\u5730\u4f18\u5316\u4e86\u8fd9\u4e2a\u95ee\u9898\uff08\u5e76\u4e0d\u662f\u4e0a\u4f4d\u66ff\u4ee3\u5173\u7cfb\uff09\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap06/#\u57fa\u4e8e\u603b\u7ebf\u5b9e\u73b0\u4f20\u8f93","title":"\u57fa\u4e8e\u603b\u7ebf\u5b9e\u73b0\u4f20\u8f93","text":"<p>\u5728\u4e0a\u4e00\u5c0f\u8282\u7684\u5c0f\u7ed3\u4e2d\u6211\u4eec\u5df2\u7ecf\u63d0\u5230\u4e86 <code>MUX</code> \u5b9e\u73b0\u7684\u4f18\u52a3\uff0c\u4e5f\u63d0\u5230\u4e86\u603b\u7ebf(bus)\u4f20\u8f93\u7684\u4f18\u52bf\uff0c\u90a3\u4e48\u5b83\u5177\u4f53\u6765\u8bf4\u5176\u5b9e\u73b0\u65b9\u6cd5\u6709\u4e24\u79cd\u2014\u2014\u901a\u8fc7\u5171\u6709 <code>MUX</code> \u5b9e\u73b0\uff0c\u6216\u901a\u8fc7\u4e09\u6001\u95e8\u5b9e\u73b0\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap06/#\u5171\u6709-mux-\u5b9e\u73b0","title":"\u5171\u6709 MUX \u5b9e\u73b0","text":"<p>\u8ba9\u6211\u4eec\u4ee5\u4e09\u4e2a\u5bc4\u5b58\u5668\u7684\u6a21\u578b\u4e3a\u4f8b\uff0c\u5bf9\u6bd4\u901a\u8fc7\u4e13\u6709 <code>MUX</code> \u5b9e\u73b0\u548c\u901a\u8fc7\u5355\u4e00\u603b\u7ebf(single bus)\u5b9e\u73b0\u7684\u533a\u522b\uff1a</p> <p></p> <p>\u9996\u5148\u5bf9\u603b\u7ebf\u5b9e\u73b0\u8fdb\u884c\u8bf4\u660e\uff0c\u540c\u6837\u662f\u4f7f\u7528 <code>MUX</code>\uff0c\u4f46\u6b64\u65f6 <code>MUX</code> \u4e0d\u518d\u662f\u67d0\u4e2a\u5bc4\u5b58\u5668\u7684\u4e13\u6709\u903b\u8f91(dedicated logic)\uff0c\u800c\u662f\u4e09\u4e2a\u5bc4\u5b58\u5668\u5171\u540c\u4f7f\u7528\u7684\u5171\u6709\u903b\u8f91(shared logic)\u3002\u603b\u7ebf\u4e2d\u7684 <code>MUX</code> \u5728\u6240\u6709\u5bc4\u5b58\u5668\u7684\u8f93\u5165\u4e2d\u9009\u62e9\u5176\u4e2d\u4e00\u4e2a\uff0c\u5e76\u5c06\u5b83\u8f93\u51fa\uff0c\u7ed9\u5230\u6240\u6709\u5bc4\u5b58\u5668\uff1b\u800c\u603b\u7ebf\u901a\u8fc7\u63a7\u5236 Load \u4fe1\u53f7\u6765\u9009\u62e9\u8ba9\u54ea\u4e2a\uff08\u6216\u54ea\u4e9b\uff09\u5bc4\u5b58\u5668\u5f97\u5230\u8fd9\u4e2a\u4fe1\u53f7\u3002</p> <p>\u63a5\u4e0b\u6765\u8fdb\u884c\u5bf9\u6bd4\uff0c\u4ee5\u603b\u7ebf\u5b9e\u73b0\u4e3a\u4e3b\u4f53\uff0c\u4e0e <code>MUX</code> \u5b9e\u73b0\u5bf9\u6bd4\uff1a</p> <ul> <li>\u4f18\u52bf\uff1a<ul> <li>\u7535\u8def\u66f4\u7cbe\u7b80\uff0c\u6210\u672c\u66f4\u4f4e\uff0c\u968f\u7740\u5bc4\u5b58\u5668\u589e\u52a0\u8fd9\u4e2a\u7279\u70b9\u66f4\u52a0\u660e\u663e\uff1b</li> </ul> </li> <li>\u52a3\u52bf\uff1a<ul> <li>\u540c\u4e00\u65f6\u523b\u5185\u603b\u7ebf\u53ea\u80fd\u4f20\u8f93\u4e00\u4e2a\u6570\u636e\uff0c\u5373\u53ea\u6709\u4e00\u4e2a\u6570\u636e\u6e90(source)\uff1b<ul> <li>\u540c\u4e00\u65f6\u949f\u5468\u671f\u5185\u53ea\u6709\u4e00\u4e2a\u6570\u636e\u80fd\u4f20\u8f93\u5230\u522b\u7684\u5730\u65b9\uff0c\u4f8b\u5982\u4ea4\u6362\u64cd\u4f5c\u5c31\u9700\u8981\u81f3\u5c11\u4e24\u4e2a bus \u624d\u80fd\u5b9e\u73b0\uff1b</li> </ul> </li> </ul> </li> </ul> <p>\u800c\u56e0\u4e3a\u8fd9\u4e9b\u7279\u70b9\uff0c\u6211\u4eec\u9700\u8981\u8bc4\u4f30\u6211\u4eec\u7684\u9700\u6c42\uff0c\u9009\u62e9\u5408\u9002\u7684\u7ed3\u6784\u6765\u5b9e\u73b0\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap06/#\u4e09\u6001\u95e8\u5b9e\u73b0","title":"\u4e09\u6001\u95e8\u5b9e\u73b0","text":"<p>\u4e09\u6001\u95e8\u7684\u76f8\u5173\u5185\u5bb9\u5df2\u7ecf\u5728\u524d\u9762\u4ecb\u7ecd\uff0c\u4f20\u8f93\u95e8\u5728\u8fd9\u91cc\uff0c\u5173\u4e8e\u672c\u5c0f\u8282\u7684\u77e5\u8bc6\uff0c\u53ef\u4ee5\u91cd\u70b9\u5173\u6ce8#\u4e09\u6001\u95e8/\u788e\u788e\u5ff5\u3002</p> <p>\u800c\u5173\u4e8e\u603b\u7ebf\u7684\u5b9e\u73b0\uff0c\u5f15\u7528\u4e00\u53e5\u6211\u5728#\u4e09\u6001\u95e8/\u788e\u788e\u5ff5\u91cc\u5199\u7684\u8bdd\uff1a</p> <p>\u53ea\u8981\u6211\u4eec\u8ba9\u5bfc\u7ebf\u7684\u82e5\u5e72\u8f93\u5165\u4e2d\u53ea\u6709\u4e00\u4e2a\u4e09\u6001\u95e8\u4e0d\u5728\u300c\u9ad8\u963b\u6001\u300d\uff0c\u5c31\u80fd\u591f\u4f18\u96c5\u5730\u5b9e\u73b0\u591a\u8def\u8f93\u51fa\u4e92\u8054\u3002</p> <p>\u5b9e\u9645\u4e0a\uff0c\u6240\u8c13\u7684\u4e09\u6001\u95e8\u5b9e\u73b0\u539f\u7406\u4e0a\u548c <code>MUX</code> \u5b9e\u73b0\u65e0\u4e8c\uff0c\u53ea\u4e0d\u8fc7\u6211\u4eec\u662f\u901a\u8fc7\u4e09\u6001\u95e8\u6765\u5b9e\u73b0\u300c\u8def\u7531\u300d\u8fd9\u4e2a\u903b\u8f91\u800c\u5df2\uff0c\u4e5f\u5c31\u662f\u4e66\u4e0a\u6240\u8bf4\u7684\uff1a</p> <p>Three-state buffer outputs can be connected together to form a multiplexed output line.</p> <p>\u4e0e <code>MUX</code> \u5b9e\u73b0\u76f8\u5bf9\u6bd4\uff0c\u4e09\u6001\u95e8\u5b9e\u73b0\u65b9\u5f0f\u5982\u4e0b\uff1a</p> <p></p> <p>\u8fdb\u884c\u7b80\u5355\u8bf4\u660e\uff0c(c) \u4e2d\u5bf9\u4e09\u6001\u95e8\u7684\u8868\u793a\u8fdb\u884c\u4e86\u7b80\u5316\uff0c\u542b\u4e49\u53c2\u8003 (a)\u3002\u5b83\u60f3\u8868\u8fbe\u7684\u4e3b\u8981\u542b\u4e49\u662f\uff0c\u5f53 <code>EN</code> \u4e3a <code>1</code> \u65f6\uff0c\u8868\u793a\u8f93\u51fa\uff1b\u53cd\u4e4b\u8868\u793a\u8f93\u5165\uff08\u5f53\u7136\uff0c\u771f\u6b63\u51b3\u5b9a\u662f\u5426\u8bfb\u5165\u5bc4\u5b58\u5668\u7684\u8fd8\u662f <code>LD</code>\uff09\u3002</p> \u4e2a\u4eba\u7591\u60d1 <p>\u4e66\u4e2d\u7684\u8868\u8ff0\u662f\uff1a</p> <p>If the three-state buffers are enabled, then the lines are outputs; if the three-state buffers are disabled, then the lines can be inputs.</p> <p>\u4f46\u662f\u770b (a) \u7684\u8868\u8fbe\uff0c\u4e0d\u7ba1 <code>EN</code> \u662f\u4ec0\u4e48\uff0c\u5b83\u5e94\u5f53\u90fd\u6709\u8f93\u5165\u624d\u5bf9\uff0c\u771f\u6b63\u51b3\u5b9a\u662f\u5426\u8f93\u5165\u8fdb\u6765\u7684\u5e94\u8be5\u8fd8\u662f <code>LD</code>\uff1f</p> <p>\u5bf9\u6bd4\u6765\u770b\uff0c\u4e09\u6001\u95e8\u7684\u5b9e\u73b0\u5927\u5927\u964d\u4f4e\u4e86\u603b\u7ebf\u7684\u5b9e\u73b0\u6210\u672c\uff0c\u7cbe\u7b80\u4e86\u7535\u8def\u7684\u5b9e\u73b0\uff0c\u6240\u4ee5\u901a\u5e38\u6765\u8bf4\u66f4\u5e38\u7528\u3002</p> \u4e2a\u4eba\u60f3\u6cd5 <p>\u867d\u7136\u4e66\u4e2d\u8bf4\u4e09\u6001\u95e8\u7684\u63a5\u7ebf\u6bd4 <code>MUX</code> \u7684\u5c11\u4e86\u4e00\u534a\uff0c\u4f46\u6211\u89c9\u7684\u4e09\u6001\u95e8\u53ea\u662f\u628a\u7ebf\u5206\u5c94\u7684\u5730\u65b9\u79fb\u52a8\u5230\u4e86\u5bc4\u5b58\u5668\u9644\u8fd1\uff0c\u6362\u53e5\u8bdd\u6765\u8bf4\u4e0d\u5982\u8bf4\u662f\u8282\u7701\u4e86\u5bfc\u7ebf\u7684\u957f\u5ea6\u3002\u4f46\u662f\u968f\u7740\u8f93\u5165\u7684\u589e\u52a0\uff0c<code>MUX</code> \u7684\u7ed3\u6784\u4f1a\u8d8a\u6765\u8d8a\u590d\u6742\u4e14\u9700\u8981\u91cd\u65b0\u8bbe\u8ba1\uff0c\u4f46\u4e09\u6001\u95e8\u53ea\u9700\u8981\u91cf\u7684\u589e\u52a0\u5c31\u884c\u4e86\uff0c\u6240\u4ee5\u786e\u5b9e\u662f\u66f4\u52a0\u5438\u5f15\u4eba\u3002\uff08\u5f53\u7136\uff0c\u867d\u7136\u4e66\u4e2d\u6ca1\u8bf4\uff0c\u4f46\u662f\u6211\u89c9\u5f97 Enable \u5fc5\u987b at most one-hot\uff0c\u800c\u8fd9\u90e8\u5206\u7684\u903b\u8f91\u5bf9\u4e8e\u4e24\u4e2a\u5b9e\u73b0\u65b9\u6cd5\u6765\u8bf4\u662f\u4e00\u6837\u7684\uff09</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap06/#\u5fae\u64cd\u4f5c\u53ca\u5176\u5b9e\u73b0","title":"\u5fae\u64cd\u4f5c\u53ca\u5176\u5b9e\u73b0","text":"<p>A microoperation is an elementary operation performed on data stored in registers or in memory.</p> <p>\u5fae\u64cd\u4f5c\u4e00\u822c\u5206\u4e3a\u8fd9\u56db\u79cd\uff1a</p> <ol> <li>\u8f6c\u79fb\uff0ctransfer microoperations\uff0c\u5c06\u6570\u636e\u4ece\u4e00\u4e2a\u5bc4\u5b58\u5668\u8f6c\u79fb\u5230\u53e6\u5916\u4e00\u4e2a\u5bc4\u5b58\u5668\uff1b</li> <li>\u7b97\u672f\uff0carithmetic microoperations\uff0c\u5bf9\u6570\u636e\u7684\u7b97\u672f\u8fd0\u7b97\u64cd\u4f5c\uff1b</li> <li>\u903b\u8f91\uff0clogic microoperations\uff0c\u5bf9\u6570\u636e\u7684\u903b\u8f91\u8fd0\u7b97\u64cd\u4f5c\uff1b</li> <li>\u4f4d\u79fb\uff0cshift microoperations\uff0c\u5bf9\u6570\u636e\u7684\u4f4d\u79fb\u64cd\u4f5c\uff1b</li> </ol> <p>A given microoperation may be of more than one type. For example, a 1s complement operation is both an arithmetic microoperation and a logic microoperation.</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap06/#\u8f6c\u79fb","title":"\u8f6c\u79fb","text":"<p>\u4e0d\u6539\u53d8\u6570\u636e\u672c\u8eab\uff0c\u53ea\u662f\u4ece\u4e00\u4e2a\u5bc4\u5b58\u5668\u4e2d\u628a\u6570\u636e\u79fb\u52a8\u5230\u53e6\u5916\u4e00\u4e2a\u5bc4\u5b58\u5668\u3002</p> <p>\u5c06 R0 \u4e2d\u7684\u6570\u636e\u8f6c\u79fb\u5230 R1 \u4e2d\uff0c\u7528 RTL \u8868\u793a\u5c31\u662f \\(R0 \\leftarrow R1\\)\u3002</p> <p>\u8fd9\u4e00\u90e8\u5206\u7684\u5b9e\u73b0\u9014\u5f84\u5728\u5bc4\u5b58\u5668\u4f20\u8f93\u7684\u5b9e\u73b0\u5df2\u7ecf\u9610\u8ff0\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap06/#\u7b97\u672f","title":"\u7b97\u672f","text":"<p>Multiplication and division are not listed in Table 6-3. Multiplication can be represented by the symbol * and division by /. These two operations are not included in the basic set of arithmetic microoperations because they are assumed to be implemented by sequences of basic microoperations. However, multiplication can be considered as a microoperation if implemented by a combinational circuit. In such a case, the result is transferred into a destination register at the clock edge after all signals have propagated through the entire combinational circuit</p> <p>\u52a0\u51cf\u6cd5\u5668</p> <p>\u5c31\u50cf\u6211\u4eec\u4e4b\u524d\u5b66\u8fc7\u7684\uff0c\u7528\u52a0\u6cd5\u5668\u5b9e\u73b0\u52a0\u51cf\u6cd5\u5668\uff0c\u5728 RTL \u548c\u6a21\u5757\u903b\u8f91\u7535\u8def\u7684\u7ef4\u5ea6\u4e0b\uff0c\u53ef\u4ee5\u8fd9\u4e48\u8868\u793a\uff1a</p> \\[ \\begin{aligned}     &amp;\\overline{X}K_1:R_1\\leftarrow R_1 + R_2 \\\\     &amp;XK_1:R_1\\leftarrow R_1 + \\overline{R_2} + 1 \\end{aligned} \\] <p></p> <p>\u6ce8\u610f</p> <p>\u5bf9\u4e8e\u5982\u4e0a\u51fa\u73b0\u7684\u5f62\u5f0f\u5982\uff1a\\(condition: reg \\leftarrow options one regs\\) \u7684\u8868\u8fbe\u5f0f\uff0c<code>:</code> \u5de6\u4fa7\u51fa\u73b0\u7684 <code>+</code> \u8868\u793a\u6216\uff0c\u53f3\u4fa7\u7684\u5219\u8868\u793a\u52a0\uff08\u201c\u4e58\u201d\u4e5f\u662f\u8fd9\u6837\uff09\uff01</p> <p>\u76f8\u5bf9\u5e94\u7684\uff0c\u52a0\u51cf\u6cd5\u7684\u5b9e\u73b0\u53ef\u4ee5\u901a\u8fc7\u52a0\u51cf\u6cd5\u5668\u5b9e\u73b0\uff0c\u4e58\u6cd5\u53ef\u4ee5\u7528\u4f4d\u79fb\u64cd\u4f5c\u5b9e\u73b0\uff0c\u800c\u9664\u6cd5\u76f8\u5bf9\u590d\u6742\u3002</p> <p>\u4e58\u6cd5\u5b9e\u73b0\u7684\u5927\u81f4\u601d\u8def</p> <p>\u5047\u8bbe\u6211\u4eec\u9700\u8981\u8ba1\u7b97 \\(a \\cdot b\\)\uff0c\u4e14 \\(a\\)\uff0c\\(b\\) \u90fd\u662f\u6574\u6570\uff0c\u5219\u53ef\u4ee5\u5c06 \\(b\\) \u5199\u6210\u4e8c\u8fdb\u5236\u5f62\u5f0f \\((b_{n-1}b_{n-2}...b_1b_0)_2\\)\uff0c\u4e8e\u662f\uff1a</p> \\[ \\begin{aligned}     a \\cdot b &amp;= a \\cdot (b_{n-1}b_{n-2}...b_1b_0)_2 \\\\               &amp;= a \\cdot \\left[ (b_{n-1}0...00)_2 + \\cdot (0b_{n-2}...00)_2 + ... + \\cdot (00...b_10)_2 + \\cdot(00...0b_0)_2 \\right]\\\\               &amp;= a \\cdot \\sum_{i = 0} ^{n-1} b_i \\cdot 2^{i} \\\\               &amp;= \\left(a \\cdot \\sum_{i = 0} ^{n-1} b_i\\right) \\;\\mathrm{&lt;&lt;}\\; i \\;\\;\\; \\text{where \"&lt;&lt;\" means \"Shift Left\"} \\end{aligned} \\] <p>\u4e8e\u662f\u5c31\u53ef\u4ee5\u901a\u8fc7\u4f4d\u79fb\u7684\u76f8\u5173\u77e5\u8bc6\u6765\u5b9e\u73b0\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap06/#\u903b\u8f91","title":"\u903b\u8f91","text":"<p>\u903b\u8f91\u8fd0\u7b97\u7684\u5b9e\u73b0\u76f8\u6bd4\u7b97\u672f\u66f4\u52a0\u76f4\u63a5\uff0c\u56e0\u4e3a\u5927\u90e8\u5206\u903b\u8f91\u90fd\u53ef\u4ee5\u901a\u8fc7\u903b\u8f91\u95e8\u6765\u5b9e\u73b0\u3002</p> <p>\u800c\u627f\u62c5\u903b\u8f91\u548c\u7b97\u672f\u8fd0\u7b97\u7684\u786c\u4ef6\u6a21\u5757\uff0c\u4e00\u822c\u88ab\u79f0\u4e3aALU\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap06/#\u4f4d\u79fb","title":"\u4f4d\u79fb","text":"<p>\u4f4d\u79fb\u7684\u5b9e\u73b0\u901a\u8fc7\u4f4d\u79fb\u5bc4\u5b58\u5668(Shift Register, SHR)\u5b9e\u73b0\u3002</p> <p>\u5f15\u5165</p> <p>\u4f4d\u79fb\u64cd\u4f5c\u4ece\u672c\u8d28\u4e0a\u6765\u8bb2\uff0c\u662f\u901a\u8fc7\u89e6\u53d1\u5668\u968f\u7740\u65f6\u949f\u8109\u51b2\uff0c\u5c06\u4e32\u884c\u6570\u636e\u4e00\u4f4d\u4e00\u4f4d\u5730\u79fb\u52a8\u5b9e\u73b0\u7684\u3002\u4f46\u662f\u5982\u679c\u8bfb\u8005\u5c1a\u672a\u7406\u89e3\u5176\u5b9e\u73b0\u539f\u7406\uff0c\u9605\u8bfb\u4ee5\u4e0b\u5185\u5bb9\u521a\u5f00\u59cb\u53ef\u80fd\u4f1a\u89c9\u5f97\u6709\u4e9b\u83ab\u540d\u5176\u5999\uff0c\u4f46\u662f\u8bf7\u5148\u9605\u8bfb\u4e32\u884c\u5b9e\u73b0\u548c\u5e76\u884c\u5316\u7684\u5185\u5bb9\uff0c\u77e5\u9053\u5b83\u4eec\u7684\u884c\u4e3a\u540e\uff0c\u53ef\u4ee5\u5148\u6682\u65f6\u8df3\u8fc7\u53cc\u5411\u4f4d\u79fb\u5bc4\u5b58\u5668\uff0c\u518d\u6765\u770b\u672c\u8282\u672b\u5c3e\u7684\u603b\u7ed3\uff0c\u4e5f\u8bb8\u80fd\u591f\u8ba9\u60a8\u660e\u767d\u5b83\u7a76\u7adf\u662f\u600e\u4e48\u5b9e\u73b0\u7684\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap06/#\u4e32\u884c\u5b9e\u73b0","title":"\u4e32\u884c\u5b9e\u73b0","text":"<p>\u4f4d\u79fb\u64cd\u4f5c\u6700\u7b80\u5355\u7684\u5b9e\u73b0\u53ea\u9700\u8981\u4e0e\u8f93\u5165\u6570\u76f8\u540c\u4f4d\u6570\u7684\u89e6\u53d1\u5668\u5b9e\u73b0\u3002\u5b83\u7684\u57fa\u672c\u7ed3\u6784\u5982\u4e0b\uff1a</p> <p></p> <p>\u56db\u4e2a\u89e6\u53d1\u5668\u9996\u5c3e\u76f8\u8fde\uff0c\u6700\u524d\u9762\u4e32\u884c\u8f93\u5165(Serial Input, SI)\u6570\u636e\uff0c\u672b\u7aef\u5f97\u5230\u4e32\u884c\u8f93\u51fa(Serial Output, SO)\uff0c\u5728\u4e0d\u540c\u65f6\u949f\u5468\u671f\u7684\u504f\u5dee\u4e0b\uff0c\u8fde\u7eed\u8bfb\u5165\u7684 n bits \u5373\u4e3a\u4e0d\u540c\u4f4d\u6570\u4f4d\u79fb\u7684\u7ed3\u679c\u3002</p> <p>\u4e32\u884c\u4f4d\u79fb\u64cd\u4f5c\u5b9e\u73b0\u7684\u6a21\u62df\u89e3\u91ca</p> <p>\u5047\u8bbe\u73b0\u5728\u6211\u4eec\u6709 4 \u4e2a <code>FF</code> \u9996\u5c3e\u76f8\u8fde\uff0c\u73b0\u5728\u4e32\u884c\u8f93\u5165 <code>1001</code> \u8fd9 4bits \u7684\u6570\u636e\uff08\u5f53\u7136\uff0c\u5b8c\u5168\u8f93\u5165\u9700\u8981 4 \u4e2a\u65f6\u949f\u5468\u671f\uff09\u3002</p> <p>\u5047\u8bbe\u7b2c 1 \u4e2a\u5468\u671f\u7ed3\u675f\u540e\uff0c<code>1001</code> \u6700\u53f3\u4fa7\u7684 <code>1</code> \u88ab\u5b58\u5728\u4e86\u7b2c\u4e00\u4e2a FF\uff0c\u5219\uff1a</p> \u5468\u671f \u5f85\u8f93\u5165 FF1 FF2 FF3 FF4 SO 1 <code>100</code> <code>1</code> ? ? ? <code>1???</code> 2 <code>10</code> <code>0</code> <code>1</code> ? ? <code>01??</code> 3 <code>1</code> <code>0</code> <code>0</code> <code>1</code> ? <code>001?</code> 4 <code>1</code> <code>0</code> <code>0</code> <code>1</code> <code>1001</code> 5 ? <code>1</code> <code>0</code> <code>0</code> <code>?100</code> 6 ? ? <code>1</code> <code>0</code> <code>??10</code> 7 ? ? ? <code>1</code> <code>???1</code> <p>\u8fd9\u91cc\u7684 SO \u6307\u7684\u662f\u4ece\u5f53\u524d\u8f6e\u6b21\u5f00\u59cb\uff0c\u8bfb\u5165 4bits \u6570\u636e\u5f97\u5230\u7684\u4e32\u884c\u8f93\u51fa\u7ed3\u679c\uff0c\u8fd9\u91cc\u7684 4bits \u5f53\u7136\u662f\u5bf9\u5e94\u8f93\u5165\u7684 4bits\u3002</p> <p>\u53ef\u4ee5\u53d1\u73b0\uff0c\u5728\u7b2c\u56db\u8f6e\u524d\u540e\u7684\u7ed3\u679c\u5206\u522b\u662f\u5de6\u79fb\u548c\u53f3\u79fb\u7684\u7ed3\u679c\uff0c\u5f53\u7136\uff0c\u5982\u679c\u662f\u8981\u8003\u8651\u5177\u6709\u5b9e\u9645\u8ba1\u7b97\u4ef7\u503c\u7684\u4f4d\u79fb\uff0c\u6211\u4eec\u5f53\u7136\u9700\u8981\u586b\u5145 <code>?</code> \u7684\u503c\uff0c\u4e0d\u8fc7\u8fd9\u90fd\u662f\u5c0f\u4e8b\u60c5\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap06/#\u5e76\u884c\u5316","title":"\u5e76\u884c\u5316","text":"<p>\u5e76\u884c\u5316\u4e3b\u8981\u6709\u4e24\u4e2a\u65b9\u9762\uff0c\u5373\u5e76\u884c\u8f93\u51fa(parallel output)\u548c\u5e76\u884c\u8f7d\u5165(parallel load)\uff0c\u5206\u522b\u5bf9\u5e94\u7740 \u5728\u540c\u4e00\u4e2a\u65f6\u95f4\u5468\u671f\u5185\u5f97\u5230\u6bcf\u4e00\u4e2a <code>FF</code> \u7684\u7ed3\u679c\u548c\u5bf9\u6bcf\u4e00\u4e2a <code>FF</code> \u8f7d\u5165\u6570\u636e\u3002</p> <p>\u5e76\u884c\u8f93\u51fa\u7684\u5b9e\u73b0\u975e\u5e38\u7b80\u5355\uff0c\u53ea\u9700\u8981\u7ed9\u6bcf\u4e00\u4e2a <code>FF</code> \u7684\u8f93\u51fa\u5f15\u51fa\u4e00\u6761\u7ebf\u5c31\u884c\u4e86\uff0c\u5b83\u4e0e\u4e32\u884c\u8f93\u51fa\u53ef\u4ee5\u76f4\u63a5\u540c\u65f6\u5b58\u5728\uff1b\u800c\u5e76\u884c\u8f93\u5165\u5219\u4e0e\u4e32\u884c\u8f93\u5165\u51b2\u7a81\uff0c\u4e00\u6b21\u53ea\u80fd\u5b9e\u73b0\u5176\u4e2d\u4e00\u4e2a\uff0c\u6240\u4ee5\u9700\u8981\u4e00\u4e9b\u63a7\u5236\u7535\u8def\uff1a</p> <p></p> <p>\u770b\u8d77\u6765\u6709\u70b9\u590d\u6742\uff0c\u4f46\u662f\u5b9e\u9645\u4e0a\u903b\u8f91\u8fd8\u662f\u5f88\u6e05\u6670\u7684\u3002</p> <ul> <li>\u7eb5\u5411\u89c2\u5bdf\u53f3\u4fa7\u7684\u56db\u4e2a <code>FF</code>\uff0c\u53ef\u4ee5\u53d1\u73b0\u57fa\u672c\u4e0a\u5c31\u662f\u4e32\u884c\u4f4d\u79fb\u5b9e\u73b0\uff0c\u53ea\u4e0d\u8fc7\u5176\u8f93\u5165\u4e0d\u518d\u662f\u76f4\u63a5\u4ece\u4e0a\u4e00\u4e2a <code>FF</code> \u90a3\u8fb9\u62ff\u6765\u7684\uff1b</li> <li>\u56db\u4e2a <code>FF</code> \u7684\u8f93\u5165\u662f\u7c7b\u4f3c\u7684\uff0c\u6240\u4ee5\u6211\u4eec\u4ec5\u5173\u6ce8\u6700\u4e0a\u9762\u7684\u90a3\u4e09\u4e2a\u4e0e\u95e8\u548c\u4e00\u4e2a\u6216\u95e8\uff0c\u8868\u793a\u6570\u636e\u8f93\u5165\u6709\u4e09\u4e2a\u53ef\u80fd\u7684\u6765\u6e90\uff1b<ol> <li>\u7b2c\u4e00\u4e2a\u4e0e\u95e8\uff0c\\(F_i=Shift \\cdot SI\\)\uff08\u5bf9\u4e8e\u540e\u9762\u51e0\u4e2a <code>FF</code>\uff0c\u5219\u662f \\(F_i=Shift \\cdot FF_{i-1}\\)\uff09\uff0c\u53ef\u4ee5\u53d1\u73b0\uff0c\u6b64\u65f6\u7535\u8def\u7684\u884c\u4e3a\u4e0e\u4e32\u884c\u4f4d\u79fb\u5b9e\u73b0\u4e00\u81f4\uff1b<ul> <li>\u5373 \\(Shift\\) \u4e3a <code>1</code> \u65f6\uff0c<code>SHR</code> \u8868\u73b0\u4e3a\u300c\u6bcf\u4e2a\u5468\u671f\u6267\u884c\u4e00\u6b21\u4f4d\u79fb\u300d\uff1b</li> </ul> </li> <li>\u7b2c\u4e8c\u4e2a\u4e0e\u95e8\uff0c\\(F_i=\\overline{Shift} \\cdot Load \\cdot D_i\\)\uff0c\u6b64\u65f6\u7535\u8def\u7684\u884c\u4e3a\u662f\u4f7f\u7528\u6bd4\u7279\u5411\u91cf\u5bf9\u6bcf\u4e00\u4e2a <code>FF</code> \u8d4b\u503c\uff0c\u5373\u5e76\u884c\u8f7d\u5165\uff1b<ul> <li>\u5373 \\(\\overline{Shift} \\cdot Load\\) \u4e3a <code>1</code> \u65f6\uff0c<code>SHR</code> \u8868\u73b0\u4e3a\u300c\u5e76\u884c\u8f7d\u5165\u300d\uff1b</li> </ul> </li> <li>\u7b2c\u4e09\u4e2a\u4e0e\u95e8\uff0c\\(F_i=\\overline{Shift} \\cdot \\overline{Load} \\cdot Q_i\\)\uff0c\u6b64\u65f6\u7535\u8def\u7684\u884c\u4e3a\u662f\u4fdd\u6301\u4e0a\u4e00\u5468\u671f\u7684\u7ed3\u679c\uff1b<ul> <li>\u5373 \\(\\overline{Shift} \\cdot \\overline{Load}\\) \u4e3a <code>1</code> \u65f6\uff0c<code>SHR</code> \u8868\u73b0\u4e3a\u300c\u4fdd\u6301\u300d\uff1b</li> </ul> </li> </ol> </li> </ul> <p>\u603b\u548c\u6765\u8bf4\uff0c\u5c31\u662f\uff1a</p> \\[ \\begin{aligned}       Shift :&amp; Q\\leftarrow \\mathrm{sl}\\; Q \\\\          \\overline{Shift}\\cdot Load :&amp; Q\\leftarrow D \\\\          \\overline{Shift}\\cdot \\overline{Load} :&amp; Q\\leftarrow Q \\end{aligned} \\] <p></p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap06/#\u53cc\u5411\u4f4d\u79fb\u5bc4\u5b58\u5668","title":"\u53cc\u5411\u4f4d\u79fb\u5bc4\u5b58\u5668","text":"<p>\u4e0a\u9762\u4ecb\u7ecd\u7684\u4f4d\u79fb\u5bc4\u5b58\u5668\u968f\u7740\u65f6\u949f\u5468\u671f\u7684\u4f9b\u7ed9\uff0c\u53ea\u80fd\u4e0d\u53ef\u9006\u3001\u5355\u5411\u5730\u8fdb\u884c\u4f4d\u79fb\uff0c\u8fd9\u79cd\u4f4d\u79fb\u5bc4\u5b58\u5668\u79f0\u4e3a\u65e0\u5411\u4f4d\u79fb\u5bc4\u5b58\u5668(Unidirectional SHR)\uff1b\u5bf9\u5e94\u7684\uff0c\u5982\u679c\u80fd\u591f\u652f\u6301\u53ef\u63a7\u5236\u7684\u5de6\u79fb\u53f3\u79fb\uff0c\u5219\u88ab\u79f0\u4e3a\u53cc\u5411\u4f4d\u79fb\u5bc4\u5b58\u5668(Bidirectional SHR)\u3002</p> <p>\u5176\u884c\u4e3a\u5982\u4e0b\uff1a</p> \\[ \\begin{aligned}     \\overline{S_0} \\cdot \\overline{S_1} :&amp; Q \\leftarrow Q\\\\     S_0 \\cdot \\overline{S_1} :&amp; Q\\leftarrow\\mathrm{Sl}\\; Q \\\\     \\overline{S_0} \\cdot S_1 :&amp; Q\\leftarrow\\mathrm{Sr}\\; Q \\\\     S_0 \\cdot S_1:&amp; Q\\leftarrow D \\end{aligned} \\] <p>\u5176\u5355\u5143\u5b9e\u73b0\u5982\u4e0b\uff1a</p> <p></p> <p>\u5176\u672c\u8d28\u4e0a\u5c31\u662f\u6dfb\u52a0\u4e86\u4e00\u4e2a <code>MUX</code> \u6765\u9009\u62e9\u4e0b\u4e00\u4e2a\u65f6\u949f\u662f\u7ee7\u627f \\((i+1)\\)\u3001\\((i-1)\\)\u3001\\(D_i\\) \u8fd8\u662f \\(Q\\)\u3002</p> <p>\u7efc\u5408\u9610\u8ff0</p> <p>\u4ee3\u7801\u610f\u4e49\u4e0a\u7684\u4f4d\u79fb\u4e00\u822c\u6307\u7684\u662f\u4e00\u4e2a\u53cc\u76ee\u64cd\u4f5c\uff0c\u5373\u53ef\u4ee5\u6307\u5b9a\u4f4d\u79fb\u591a\u5c11\u4f4d\uff0c\u8fd9\u4e2a\u53c2\u6570\u88ab\u79f0\u4e3a\u4f4d\u79fb\u91cf(Shift Amount)\u3002</p> <p>\u4f46\u5728\u786c\u4ef6\u5c42\u9762\u7684\u5b9e\u73b0\u4e0a\uff0c\u8fd9\u4e2a\u591a\u5c11\u201c\u4f4d\u201d\u53ea\u80fd\u901a\u8fc7\u5faa\u73af\u548c\u5df2\u7ecf\u5b9e\u73b0\u7684\u3001\u6709\u9650\u79cd\u786e\u5b9a\u4f4d\u79fb\u91cf\u7684\u4f4d\u79fb\u5b9e\u73b0\uff0c\u5728\u6211\u4eec\u63d0\u5230\u7684\u5b9e\u73b0\u4e2d\uff0c\u6307\u7684\u5c31\u662f\u6211\u4eec\u786c\u4ef6\u53ea\u5b9e\u73b0\u300c\u4e00\u4f4d\u4f4d\u79fb\u300d\uff0c\u5e76\u901a\u8fc7\u5faa\u73af\u5b9e\u73b0\u300c\u4efb\u610f\u4f4d\u4f4d\u79fb\u300d\uff0c\u800c\u8fd9\u4e2a\u201c\u5faa\u73af\u201d\uff0c\u5c31\u662f\u5728\u65f6\u949f\u5468\u671f\u4e0b\uff0c<code>FF</code> \u4e0d\u65ad\u7ee7\u627f\u4e0a\u4e00\u4e2a <code>FF</code> \u7684\u503c\u6765\u5b9e\u73b0\u7684\u3002</p> <p>\u800c\u5e76\u884c\u4e0e\u4e32\u884c\u5b9e\u73b0\u65e0\u975e\u662f\u4f53\u73b0\u8fd9\u4e2a\u7279\u5f81\u7684\u4e24\u79cd\u5b9e\u73b0\u65b9\u6cd5\u800c\u5df2\u3002</p> \u5173\u4e8e\u5e76\u884c\u548c\u4e32\u884c <p>\u8fd9\u662f\u4e00\u4e2a\u9898\u5916\u8bdd\uff0c\u6211\u6682\u65f6\u4e0d\u77e5\u9053\u653e\u54ea\u91cc\uff0c\u521a\u597d\u8fd9\u91cc\u63d0\u5230\u4e86\u5c31\u5728\u8fd9\u91cc\u8bf4\u4e86\u3002</p> <p>\u5b9e\u9645\u4e0a\uff0c\u867d\u7136\u770b\u8d77\u6765\u5e76\u884c\u7684\u6548\u7387\u4f1a\u6bd4\u4e32\u884c\u9ad8\u5f88\u591a\uff0c\u4f46\u662f\u5b9e\u9645\u4e0a\u5f88\u591a\u9ad8\u901f\u4f20\u8f93\u8bbe\u5907\u6216\u534f\u8bae\u7528\u7684\u90fd\u662f\u4e32\u884c\u3002\u8fd9\u662f\u56e0\u4e3a\uff0c\u5e76\u884c\u5355\u6b21\u4f20\u8f93\u7ebf\u8def\u591a\uff0c\u7ebf\u8def\u4e4b\u95f4\u7684\u8ddd\u79bb\u5c0f\uff0c\u5e72\u6270\u5927\uff0c\u6240\u4ee5\u76f8\u5bf9\u6765\u8bf4\u6b63\u5e38\u5de5\u4f5c\u6240\u4e0b\u5bf9\u9891\u7387\u7684\u8981\u6c42\u66f4\u9ad8\uff1b\u800c\u4e32\u884c\u7531\u4e8e\u53ef\u4ee5\u4f7f\u7528\u66f4\u9ad8\u7684\u9891\u7387\u5de5\u4f5c\uff0c\u6240\u4ee5\u5728\u67d0\u4e9b\u60c5\u51b5\u4e0b\u6548\u7387\u66f4\u9ad8\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap06/#\u8ba1\u6570\u5668","title":"\u8ba1\u6570\u5668","text":"<p>\u8ba1\u6570\u5668(counter) \u662f\u4ec0\u4e48\uff0c\u5df2\u7ecf\u5728#\u5bc4\u5b58\u5668\u4e2d\u89e3\u91ca\u4e86\uff0c\u6839\u636e\u5b9e\u73b0\u539f\u7406\uff0c\u4e3b\u8981\u5206\u4e3a\u884c\u6ce2\u8ba1\u6570\u5668(Ripple Counter)\u548c\u540c\u6b65\u8ba1\u6570\u5668(Synchronous Counter)\u4e24\u79cd\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap06/#\u884c\u6ce2\u8ba1\u6570\u5668","title":"\u884c\u6ce2\u8ba1\u6570\u5668","text":"<p>\u884c\u6ce2\u8ba1\u6570\u5668\u7684\u4e3b\u8981\u601d\u60f3\u5c31\u662f\u5c06\u4e00\u4e2a\u4e0d\u65ad\u81ea\u53cd\u7684 <code>FF</code> \u7684\u8f93\u51fa\u76f4\u63a5\u6216\u95f4\u63a5\u4f5c\u4e3a\u4e0b\u4e00\u4e2a <code>FF</code> \u7684\u65f6\u949f\u8109\u51b2\u3002\u7531\u4e8e\u5f62\u6210\u4e00\u6b21\u8109\u51b2\u9700\u8981\u4e00\u5bf9 <code>0</code>&amp;<code>1</code>\uff0c\u6240\u4ee5\u524d\u4e00\u4e2a <code>FF</code> \u53d6\u53cd\u4e24\u6b21\u624d\u80fd\u5f15\u8d77\u4e0b\u4e00\u4e2a <code>FF</code> \u53d6\u53cd\u4e00\u6b21\uff0c\u5982\u679c\u4e0b\u4e00\u4e2a <code>FF</code> \u662f\u5728\u4e0a\u4e00\u4e2a <code>FF</code> \u7684\u8f93\u51fa\u4ece <code>1</code> \u53d8 <code>0</code> \u65f6\u89e6\u53d1\uff0c\u90a3\u4e24\u4e2a <code>FF</code> \u7684\u53d8\u5316\u521a\u597d\u5bf9\u5e94\u4e8e\u4e8c\u8fdb\u5236\u81ea\u589e\u7684\u8fdb\u4f4d\u89c4\u5f8b\uff1a<code>(0,0)</code>\uff0c<code>(0,1)</code>\uff0c<code>(1,0)</code>\uff0c<code>(1,1)</code>\uff0c<code>0,0</code>\uff0c...</p> <p>\u4e8e\u662f\uff0c\u4e00\u4e2a 4-Bit \u884c\u6ce2\u8ba1\u6570\u5668\u7684\u903b\u8f91\u56fe\u5c31\u5982\u4e0b\uff1a</p> <p></p> <ul> <li>\u4e0a\u56fe\u4e2d\uff0c\u4e0b\u4e00\u4e2a <code>FF</code> \u7684\u65f6\u949f\u6765\u81ea\u4e8e\u4e0a\u4e00\u4e2a <code>FF</code> \u7684\u8f93\u51fa\u53d6\u53cd\uff0c\u4e5f\u5c31\u662f\u5bf9\u4e8e\u4e0a\u5347\u6cbf\u89e6\u53d1\u7684 <code>FF</code> \u6765\u8bf4\uff0c\u4e0b\u4e00\u4e2a <code>FF</code> \u4f1a\u5728\u4e0a\u4e00\u4e2a <code>FF</code> \u7684\u8f93\u51fa\u4ece <code>1</code> \u5230 <code>0</code> \u65f6\u81ea\u53cd\uff0c\u6240\u4ee5\u662f\u6b63\u5411\u8ba1\u65f6(Upward Counting)\uff1b</li> <li>\u53cd\u4e4b\uff0c\u5982\u679c\u4e0b\u4e00\u4e2a <code>FF</code> \u7684\u65f6\u949f\u6765\u81ea\u4e8e\u4e0a\u4e00\u4e2a <code>FF</code> \u7684\u76f4\u63a5\u8f93\u51fa\uff0c\u4e5f\u5c31\u662f\u5bf9\u4e8e\u4e0a\u5347\u6cbf\u89e6\u53d1\u7684 <code>FF</code> \u6765\u8bf4\uff0c\u4e0b\u4e00\u4e2a <code>FF</code> \u4f1a\u5728\u4e0a\u4e00\u4e2a <code>FF</code> \u7684\u8f93\u51fa\u4ece <code>0</code> \u5230 <code>1</code> \u65f6\u81ea\u53cd\uff0c\u6240\u4ee5\u662f\u9006\u5411\u8f93\u51fa(Downward Counting)\uff1b</li> </ul> <p></p> <p>\u53ef\u4ee5\u53d1\u73b0\uff0c\u884c\u6ce2\u8ba1\u6570\u5668\u7684\u4f18\u70b9\u662f\u7535\u8def\u7b80\u5355\uff0c\u6210\u672c\u4f4e\uff1b\u4f46\u662f\u7f3a\u70b9\u4e5f\u5f88\u660e\u663e\uff0c\u65e2\u7136\u5b83\u4e0e\u540c\u6b65\u8ba1\u6570\u5668\u76f8\u533a\u5206\uff0c\u5c31\u8bf4\u660e\u5b83\u4e0d\u662f\u540c\u6b65\u7535\u8def\uff0c\u6bcf\u4e00\u4e2a <code>FF</code> \u90fd\u4f1a\u6709\u4f20\u64ad\u5ef6\u65f6\uff0c\u968f\u7740\u8ba1\u6570\u8303\u56f4\u589e\u5927\uff0c\u603b\u4f20\u64ad\u5ef6\u65f6\u4e5f\u4f1a\u589e\u52a0\uff0c\u800c\u4e3a\u4e86\u8ba9\u7535\u8def\u6b63\u5e38\u5de5\u4f5c\uff0c\u65f6\u949f\u9891\u7387\u4e5f\u8981\u56e0\u6b64\u4e0b\u964d\u3002</p> <p>\u7531\u4e8e\u8fd9\u4e9b\uff0c\u4e66\u4e0a\u5bf9\u884c\u6ce2\u8ba1\u6570\u5668\u7684\u8bc4\u4ef7\u662f\u591a\u6570\u60c5\u51b5\u4e0b\u884c\u6ce2\u52a0\u6cd5\u5668\u53ea\u4f1a\u5728\u4f4e\u529f\u8017\u7535\u8def\u4e2d\u88ab\u91c7\u7528\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap06/#\u540c\u6b65\u8ba1\u6570\u5668","title":"\u540c\u6b65\u8ba1\u6570\u5668","text":"<p>\u540c\u6b65\u8ba1\u6570\u5668\u4ece\u5b9e\u73b0\u81ea\u589e\u7684\u539f\u7406\u4e0a\u6765\u8bf4\uff0c\u548c\u884c\u6ce2\u8ba1\u6570\u5668\u4e5f\u662f\u7c7b\u4f3c\u7684\uff0c\u540c\u6837\u662f\u5728\u4e0a\u4e00\u4e2a <code>FF</code> \u5b8c\u6210\u4e00\u6b21\u7ffb\u8f6c\u7684\u65f6\u5019\u8ba9\u4e0b\u4e00\u4e2a <code>FF</code> \u53d8\u5316\u3002\u53ea\u4e0d\u8fc7\u540c\u6b65\u8ba1\u6570\u5668\u4e0d\u662f\u63a7\u5236\u65f6\u949f\uff0c\u800c\u662f\u63a7\u5236\u300c<code>FF</code> \u5185\u7684\u503c\u662f\u5426\u53d6\u53cd\u300d\u6765\u5b9e\u73b0\uff0c\u800c\u5b83\u662f\u901a\u8fc7\u5f02\u6216\u95e8\u6765\u5b9e\u73b0\u7684\u3002</p> <p>\u6211\u4eec\u77e5\u9053\uff0c\\(0 \\;\\mathrm{XOR}\\; X = X\\)\uff0c\u800c \\(1 \\;\\mathrm{XOR}\\; X = \\overline{X}\\)\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u53ef\u4ee5\u63a7\u5236 <code>XOR</code> \u7684\u67d0\u4e2a\u8f93\u5165\u662f <code>0</code> \u8fd8\u662f <code>1</code> \u6765\u5b9e\u73b0\u53d6\u53cd\u8fd8\u662f\u4fdd\u6301\u7684\u5207\u6362\u3002</p> <p>\u4e0d\u8fc7\u9700\u8981\u533a\u5206\u7684\u662f\uff0c\u884c\u6ce2\u8ba1\u6570\u5668\u662f\u5728\u4e0a\u4e00\u4e2a <code>FF</code> \u53d8\u5316\u5b8c\u624d\u5f71\u54cd\u4e0b\u4e00\u4e2a\u7684\uff0c\u6240\u4ee5\u662f <code>1</code> \u53d8 <code>0</code> \u65f6\u9700\u8981\u8fdb\u4f4d\uff1b\u800c\u540c\u6b65\u8ba1\u6570\u5668\u7684\u6240\u6709 <code>FF</code> \u662f\u4e00\u8d77\u53d8\u5316\u7684\uff0c\u6240\u4ee5\u53ea\u6709\u5728\u524d\u9762\u90fd\u662f <code>1</code> \u65f6\u5019\uff0c\u8868\u793a\u4e0b\u4e00\u523b\u5b83\u4eec\u90fd\u8981\u8fdb\u4f4d\u4e86\uff0c\u5f53\u524d <code>FF</code> \u624d\u8fdb\u4f4d\u3002</p> <p>\u4e5f\u5c31\u662f\u8bf4\uff0c\u884c\u6ce2\u8ba1\u6570\u5668\u662f\u5efa\u7acb\u5728\u524d\u4e00\u4e2a <code>FF</code> \u7684\u7ed3\u679c\u8fdb\u884c\u53d8\u5316\uff1b\u800c\u5e76\u884c\u52a0\u6cd5\u5668\u662f\u5efa\u7acb\u5728\u4e0a\u4e00\u523b\u6240\u6709\u5173\u8054 <code>FF</code> \u7684\u72b6\u6001\uff0c\u5bf9\u4e0b\u4e00\u72b6\u6001\u7684\u9884\u5224\u3002</p> <p>\u5728\u8fd9\u57fa\u7840\u4e0a\uff0c\u540c\u6b65\u8ba1\u6570\u5668\u7684\u81ea\u589e\u5668(incrementer)\u6709\u4e24\u79cd\u4e0d\u540c\u7684\u5b9e\u73b0\u65b9\u6cd5\uff1a</p> <p></p> <p>(b) \u7684\u84dd\u8272\u90e8\u5206\u66ff\u6362 (a) \u7684\u84dd\u6846\u90e8\u5206\u4e3a\u7b2c\u4e8c\u79cd\u3002\u4e24\u79cd\u5206\u522b\u4e3a \u95e8\u4e32\u884c\u5b9e\u73b0 \u548c \u95e8\u5e76\u884c\u5b9e\u73b0\u3002</p> <p>\u4e24\u79cd\u5b9e\u73b0\u5176\u5b9e\u539f\u7406\u90fd\u662f\u4e00\u6837\u7684\uff0c\u53ea\u4e0d\u8fc7\u95e8\u4e32\u884c\u727a\u7272\u67d0\u4e9b\u60c5\u51b5\u4e0b\u7684\u8fd0\u884c\u6548\u7387\uff0c\u8282\u7ea6\u4e86\u95e8\u6210\u672c\uff1b\u800c\u95e8\u5e76\u884c\u63d0\u9ad8x\u4e86\u95e8\u6210\u672c\uff0c\u51cf\u5c11\u4e86\u67d0\u4e9b\u60c5\u51b5\u4e0b\u7684\u95e8\u5ef6\u8fdf\u3002</p> <p>\u5f53\u7136\uff0c\u65e2\u7136\u4f7f\u7528\u7684\u662f\u81ea\u589e\u5668\uff0c\u90a3\u4e48\u5b9e\u73b0\u7684\u81ea\u7136\u5c31\u662f\u6b63\u5411\u8ba1\u6570\u5668\u3002\u4e3a\u4e86\u5b9e\u73b0\u9006\u5411\u8ba1\u6570\u5668\uff0c\u6211\u4eec\u5219\u9700\u8981\u5c06\u81ea\u589e\u5668\u6362\u4e3a\u81ea\u51cf\u5668\u3002\u505a\u6cd5\u53ea\u4e0d\u8fc7\u662f\u5c06\u5f02\u6216\u95e8\u7684\u63a7\u5236\u4fe1\u53f7\u53d6\u53cd\u3002</p> <p>\u5177\u4f53\u6765\u8bf4\uff0c\u8f93\u5165\u51fd\u6570\u53d8\u4e3a\uff1a</p> \\[ \\begin{aligned}     D_{A0} = &amp; Q_0 \\oplus EN \\\\     D_{A1} = &amp; Q_1 \\oplus \\left(         (Q_0 \\cdot \\overline{S} + \\overline{Q_0} \\cdot S) \\cdot EN     \\right) \\\\     D_{A2} = &amp; Q_2 \\oplus \\left(         (Q_0 \\cdot Q_1 \\cdot \\overline{S} + \\overline{Q_0} \\cdot \\overline{Q_1} \\cdot S) \\cdot EN     \\right) \\\\     D_{A3} = &amp; Q_3 \\oplus \\left(         (Q_0 \\cdot Q_1 \\cdot Q_2 \\cdot \\overline{S} + \\overline{Q_0} \\cdot \\overline{Q_1} \\cdot \\overline{Q_2} \\cdot S) \\cdot EN     \\right) \\end{aligned} \\] <p>\u4ece\u8fd9\u4e2a\u8868\u8fbe\u5f0f\u4e5f\u53ef\u4ee5\u7565\u5fae\u611f\u53d7\u5230\u95e8\u4e32\u884c\u548c\u95e8\u5e76\u884c\u7684\u533a\u522b\u7a76\u7adf\u5728\u54ea\u91cc\uff0c\u5b83\u4eec\u4f7f\u7528\u540c\u4e00\u4e2a\u8868\u8fbe\u5f0f\uff0c\u53ea\u4e0d\u8fc7\u7528\u4e0d\u540c\u7684\u65b9\u5f0f\u6765\u5b9e\u73b0\u591a\u4f4d <code>AND</code> \u8fd0\u7b97\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap06/#\u540c\u6b65\u8f7d\u5165","title":"\u540c\u6b65\u8f7d\u5165","text":"<p>\u8fd9\u91cc\u540c\u6b65\u8f7d\u5165\u7684\u542b\u4e49\u53ef\u4ee5\u540c\u4f4d\u79fb\u5bc4\u5b58\u5668\u7684\u5e76\u884c\u8f7d\u5165\u7c7b\u6bd4\uff0c\u5176\u4e3b\u8981\u76ee\u7684\u662f\u5c06\u8ba1\u6570\u5668\u7684\u5f53\u524d\u503c\u8bbe\u4e3a\u4e00\u4e2a\u6211\u4eec\u9700\u8981\u7684\u6570\u5b57\u3002</p> <p>\u4ee5\u95e8\u4e32\u884c\u5b9e\u73b0\u4e3a\u4f8b\uff0c\u6dfb\u52a0\u529f\u80fd\u63a7\u5236\u903b\u8f91\u540e\u7684\u8bbe\u8ba1\u5982\u4e0b\uff1a</p> <p></p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap06/#\u4efb\u610f\u8ba1\u6570\u5e8f\u5217","title":"\u4efb\u610f\u8ba1\u6570\u5e8f\u5217","text":"<p>\u73b0\u5728\u8ba9\u6211\u4eec\u56de\u5f52\u8ba1\u6570\u5668\u7684\u884c\u4e3a\uff1a\u968f\u7740\u65f6\u949f\u5468\u671f\u4e0d\u65ad\u5728\u56fa\u5b9a\u7684\u72b6\u6001\u5e8f\u5217\u4e2d\u5faa\u73af\u3002\u4e5f\u5c31\u662f\u8bf4\uff0c\u8fd9\u4e2a\u5e8f\u5217\u672a\u5fc5\u9700\u8981\u662f\u6574\u6570\u81ea\u589e\u81ea\u51cf\u5e8f\u5217\u3002\u800c\u5b9e\u73b0\u67d0\u4e00\u5e8f\u5217\u7684\u8ba1\u6570\u884c\u4e3a\uff0c\u5b9e\u9645\u4e0a\u53ea\u8981\u8bbe\u8ba1\u597d\u6709\u9650\u72b6\u6001\u548c\u72b6\u6001\u4e4b\u95f4\u7684\u8f6c\u79fb\u5373\u53ef\u3002</p> <p>\u5f53\u7136\uff0c\u8fd9\u4e2a\u8bdd\u9898\u592a\u8fc7\u5bbd\u6cdb\uff0c\u6211\u4eec\u5728\u8fd9\u91cc\u5177\u4f53\u8ba8\u8bba\u7684\u8fd8\u662f\u6574\u6570\u81ea\u589e\u5e8f\u5217\uff0c\u53ea\u4e0d\u8fc7\u9650\u5236\u4e86\u4e0a\u4e0b\u754c\u3002\u4e66\u4e0a\u63d0\u4f9b\u7684\u6848\u4f8b\u662f BCD \u7801\u7684\u5faa\u73af\u8ba1\u6570\uff0c\u90a3\u6211\u4eec\u4e5f\u8ddf\u7740\u8fd9\u4e2a\u6848\u4f8b\u6765\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap06/#bcd-\u7801\u5faa\u73af\u8ba1\u6570","title":"BCD \u7801\u5faa\u73af\u8ba1\u6570","text":"<p>\u9996\u5148\u6211\u4eec\u9700\u8981\u6839\u636e\u65f6\u5e8f\u7535\u8def\u7684\u8bbe\u8ba1\u89c4\u5219\uff0c\u641e\u6e05\u695a\u72b6\u6001\u5e8f\u5217\uff0c\u663e\u7136\uff0c\u6839\u636e BCD \u7801\u7684\u5b9a\u4e49\uff0c\u6211\u4eec\u53ef\u4ee5\u6bdb\u6bdb\u5730\u8ba4\u4e3a\u5b83\u662f\u4e0b\u786e\u754c\u4e3a <code>0</code>\uff0c\u4e0a\u786e\u754c\u4e3a <code>9</code> \u7684 4 \u6bd4\u7279\u6574\u6570\u5e8f\u5217\u3002\u6362\u53e5\u8bdd\u8bf4\uff0c\u6211\u4eec\u9700\u8981\u5b9e\u73b0\u4e00\u4e2a\u8ba1\u6570\u5230 <code>9</code> \u540e\u4e0b\u4e00\u4e2a\u72b6\u6001\u662f <code>0</code> \u7684 4 \u6bd4\u7279\u8ba1\u6570\u5668\u3002</p> <p>\u4e8e\u662f\u6211\u4eec\u53ef\u4ee5\u5f53\u8ba1\u6570\u5668\u7684\u8f93\u51fa\u4e3a <code>9</code> \u65f6\uff0c\u4e0b\u4e00\u5468\u671f\u8ba9\u8ba1\u6570\u5668\u8f7d\u5165 <code>0</code>\uff1a</p> <p></p> <p>\u6309\u7406\u6765\u8bf4\u8fd9\u91cc\u5e94\u8be5\u662f \\(Load = Q_0\\cdot\\overline{Q_1}\\cdot\\overline{Q_2}\\cdot Q_3\\)\uff0c\u4ee5\u5bf9\u5e94 <code>9D=1001B</code>\uff0c\u4f46\u662f\u7531\u4e8e\u81ea\u589e\u8fc7\u7a0b\u4e2d\uff0c<code>1001</code> \u662f\u7b2c\u4e00\u4e2a\u6ee1\u8db3 <code>1??1</code> \u7684\u7ec4\u5408\uff0c\u6240\u4ee5\u53ef\u4ee5\u76f4\u63a5\u7b80\u5316\u4e3a \\(Load = Q_0\\cdot Q_3\\)\u3002</p> <p>\u5982\u4e0a\u662f\u4fee\u6539\u4e0a\u786e\u754c\u7684\u65b9\u6cd5\uff0c\u800c\u4fee\u6539\u4e0b\u786e\u754c\u7684\u65b9\u6cd5\u5219\u662f\u4fee\u6539 \\(D_i\\) \u5e8f\u5217\uff0c\u4f8b\u5982\u4e0a\u56fe\u4e2d \\(D\\) \u63a5\u5730\uff0c\u6240\u4ee5\u4e0b\u786e\u754c\u662f <code>0000B</code>\u3002</p> <p>Mod N \u8ba1\u6570\u5668</p> <p>\u5b9e\u9645\u4e0a\uff0c\u6211\u4eec\u53ef\u4ee5\u628a BCD \u7801\u5faa\u73af\u8ba1\u6570\u5668\u770b\u4f5c\u662f\u7279\u6b8a\u7684 Mod N \u8ba1\u6570\u5668\uff0c\u5373 N = 10 \u7684 Mod N \u8ba1\u6570\u5668\u3002</p> <p>\u6216\u8bb8\u4f60\u4f1a\u60f3\uff0c\u5b9e\u73b0 Mod N \u8ba1\u6570\u5668\u80fd\u4e0d\u80fd\u5728\u6ee1\u8db3\u8f93\u51fa\u6761\u4ef6\u540e\u76f4\u63a5\u4f7f\u7528 <code>Clear</code> \u8f93\u5165\u3002\u4f46\u662f\u8bf7\u4e0d\u8981\u5fd8\u8bb0\u4e86\uff0c<code>Clear</code> \u4e5f\u597d\uff0c<code>Set</code> \u4e5f\u7f62\uff0c\u5b83\u4eec\u90fd\u662f\u5f02\u6b65\u64cd\u4f5c\u3002\u6211\u4eec\u6ca1\u6709\u5fc5\u8981\u4e5f\u4e0d\u5e94\u8be5\u4f7f\u7528\u5f02\u6b65\u64cd\u4f5c\uff0c\u6240\u4ee5\u6700\u597d\u7684\u505a\u6cd5\u8fd8\u662f\u4f7f\u7528 <code>Load</code>\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap06/#\u5bc4\u5b58\u5668\u4f20\u8f93\u7684\u63a7\u5236","title":"\u5bc4\u5b58\u5668\u4f20\u8f93\u7684\u63a7\u5236","text":"<p>\u672a\u5b8c\u6210</p> <p>Control Unit</p> <ul> <li>Programmable sys<ul> <li>instructions (usually stored in memory RAM/ROM)</li> <li>program counter</li> </ul> </li> <li> <p>Nonprogrammable sys</p> <ul> <li>focus on this</li> <li>State machine diagrams for Control Unit design.</li> </ul> </li> <li> <p>Write a detailed system specification.</p> </li> <li>Define all external data and control input signals, all external data, control, and status output signals, and the registers of the datapath and control unit.</li> <li>Find a state machine diagram for the system including the register transfers in the datapath and in the control unit.</li> <li>Define internal control and status signals. Use these signals to separate output conditions and actions, including register transfers, from the state diagram flow and represent them in tabular form.</li> <li>Draw a block diagram of the datapath including all control and status inputs and outputs. Draw a block diagram of the control unit if it includes register transfer hardware.</li> <li>Design any specialized register transfer logic in both the control and datapath.</li> <li>Design the control unit logic.</li> <li>Verify the correct operation of the combined datapath and control logic. If verification fails, debug the system and reverify it.</li> </ul> <p>\u91cd\u70b9\u770b\u4e66\u4e0a\u7684\u4f8b\u5b50\u3002</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap07/","title":"Chap 7 Memory Basics","text":"<p> \u7ea6 737 \u4e2a\u5b57  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 2 \u5206\u949f</p> <p>\u6846\u67b6</p> <ul> <li>Two types: RAM &amp; ROM<ul> <li>RAM ship consists of an array of RAM cells, decoders, write circuits, read circuits, output circuits</li> <li>RAM bit slice</li> <li>DRAM</li> <li>Error-detection and correction codes, often based on Hamming codes</li> </ul> </li> <li>R&amp;W operations have specific steps and associated timing parameters: access time &amp; write cycle time</li> <li>static(SRAM) or dynamic(DRAM), volatile or nonvolatile</li> </ul>"},{"location":"cour_note/D2QD_DigitalDesign/Chap07/#7-1-memory","title":"7-1 Memory","text":"<p>Two types of memories are used in various parts of a computer: random-access memory (RAM) and read-only memory (ROM). RAM accepts new information for storage to be available later for use. The process of storing new information in memory is referred to as a memory write operation. The process of transferring the stored information out of memory is referred to as a memory read operation. RAM can perform both the write and the read operations, whereas ROM, as introduced in Section 6-8, performs only read operations. RAM sizes may range from hundreds to billions of bits.</p> <p>Memory is a collection of binary storage cells together with associated circuits needed to transfer information into and out of the cells.</p>"},{"location":"cour_note/D2QD_DigitalDesign/Chap07/#7-2-ram","title":"7-2 RAM","text":"<p>Memory cells can be accessed to transfer information to or from any desired location, with the access taking the same time regardless of the location, hence the name random-access memory. In contrast,serial memory, such as is exhibited by a hard drive, takes different lengths of time to access information, depending on where the desired location is relative to the current physical position of the disk.</p> <p><code>word</code>: </p> <p>A word is an entity of bits that moves in and out of memory as a unit\u2014a group of 1s and 0s that represents a number, an instruction, one or more alphanumeric characters, or other binary-coded information.</p> <p>A group of eight bits is called a byte. </p> <p>Most computer memories use words that are multiples of eight bits in length. Thus, a 16-bit word contains two bytes, and a 32-bit word is made up of four bytes. The capacity of a memory unit is usually stated as the total number of bytes that it can store.</p> <p>Communication between a memory and its environment is achieved through data input and output lines, address selection lines, and control lines that specify the direction of transfer of information.</p> <p>Computer memory varies greatly in size. It is customary to refer to the number of words (or bytes) in memory with one of the letters K (kilo), M (mega), or G (giga). K is equal to 2^10, M to 2^20, and G to 2^30.</p> <p>A word in memory is selected by its binary address. When a word is read or written, the memory operates on all 16 bits as a single unit.</p> <p>The 1K * 16 memory of the figure has 10 bits in the address and 16 bits in each word. The number of address bits needed in memory is dependent on the total number of words that can be stored and is independent of the number of bits in each word. The number of bits in the address for a word is determined from the relationship 2^k &gt;= m, where m is the total number of words and k is the minimum number of address bits satisfying the relationship.</p> <p>The two operations that a random-access memory can perform are write and read. A write is a transfer into memory of a new word to be stored. A read is a transfer of a copy of a stored word out of memory.</p> <p>The steps that must be taken for a write are as follows:</p> <ol> <li>Apply the binary address of the desired word to the address lines.</li> <li>Apply the data bits that must be stored in memory to the data input lines.</li> <li>Activate the Write input.</li> </ol> <p>The memory unit will then take the bits from the data input lines and store them in the word specified by the address lines.The steps that must be taken for a read are as follows:</p> <ol> <li>Apply the binary address of the desired word to the address lines.</li> <li>Activate the Read input.</li> </ol> <p>The memory will then take the bits from the word that has been selected by the address and apply them to the data output lines. The contents of the selected word are not changed by reading them.</p> <p>...</p> <p>To avoid destroying data in other memory words, it is important that this change occur after the signals on the address lines have become fixed at the desired values. </p>"},{"location":"cour_note/D2QD_DigitalDesign/glossary/","title":"\u8bcd\u6c47\u8868","text":"<p> \u7ea6 1051 \u4e2a\u5b57  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 4 \u5206\u949f</p> <p>\ud83d\ude4f</p> <p>\u8bcd\u6c47\u8868\u662f cm \u8001\u5e08\u6574\u7406\u7684\uff0c\u8ba9\u6211\u4eec\u8bf4 \u8c22\u8c22 cm \uff01</p>"},{"location":"cour_note/D2QD_DigitalDesign/glossary/#1---ch11-7","title":"1)   Ch1.1-7","text":"<p>odometer\uff1a\u91cc\u7a0b\u8868\uff0c\u8ba1\u7a0b\u5668</p> <p>signal conditioning: \u4fe1\u53f7\u8c03\u7406\u3001\u4fe1\u53f7\u5904\u7406</p> <p>capacitor\uff1a\u7535\u5bb9\u5668\uff0ce.g., capacitor charge\uff0c\u7535\u5bb9\u5668\u5145\u7535</p> <p>radix\uff1a\u57fa\u6570(= base)</p> <p>radix point\uff1a\u5c0f\u6570\u70b9</p> <p>number = integer portion(\u6574\u6570\u90e8\u5206) + fraction portion(\u5c0f\u6570\u90e8\u5206)</p> <p>power series\uff1a\u5e42\u7ea7\u6570</p> <p>binary\uff1a\u4e8c\u8fdb\u5236\uff0coctal\uff1a\u516b\u8fdb\u5236\uff0cdecimal\uff1a\u5341\u8fdb\u5236\uff1bhexadecimal\uff1a\u5341\u516d\u8fdb\u5236</p> <p>augend\uff1a\u88ab\u52a0\u6570</p> <p>addend\uff1a\u52a0\u6570</p> <p>minuend: \u88ab\u51cf\u6570</p> <p>subtrahend\uff1a\u51cf\u6570</p> <p>padding\uff1a\u586b\u5145</p> <p>weighted code\uff1a\u6709\u6743\u7801</p> <p>arithmetic\uff1a\u7b97\u672f\u3001\u56db\u5219\u8fd0\u7b97</p> <p>significant digit\uff1a\u6709\u6548\u4f4d</p> <p>punched paper\uff1a\u6253\u5b54\u7eb8\u5e26</p> <p>parity\uff1a\u5947\u5076\u6821\u9a8c</p> <p>even\uff1a\u5076\u6570</p> <p>odd\uff1a\u5947\u6570</p> <p>source coding\uff1a\u4fe1\u6e90\u7f16\u7801</p> <p>channel coding\uff1a\u4fe1\u9053\u7f16\u7801</p> <p>optical Shaft Encoder\uff1a\u5149\u8f74\u7f16\u7801\u5668</p> <p>positional number system\uff1a\u6309\u4f4d\u8bb0\u6570\u5236</p>"},{"location":"cour_note/D2QD_DigitalDesign/glossary/#2---ch21-3","title":"2)   Ch2.1-3","text":"<p>notation: \u6807\u8bb0\u6cd5</p> <p>operator\uff1a\u8fd0\u7b97\u7b26\u3001\u7b97\u5b50\uff0ce.g., logical operator \u903b\u8f91\u8fd0\u7b97\u7b26</p> <p>operand\uff1a\u64cd\u4f5c\u6570</p> <p>identifier\uff1a\u6807\u8bc6\u7b26=designator\uff0ce.g., variable identifier\uff1a\u53d8\u91cf\u6807\u8bc6\u7b26</p> <p>overbar: ( \u00af )\u4e0a\u6a2a\u7ebf</p> <p>single quote mark (')\uff1a\u5355\u5f15\u53f7</p> <p>normally-closed switch\uff1a\u5e38\u95ed\u5f00\u5173,e.g. Normally-Open(NO), Normally-Closed(NC)</p> <p>magnetic field\uff1a\u78c1\u573a</p> <p>energizing coil\uff1a\u6fc0\u52b1\u7ebf\u5708</p> <p>relay\uff1a\u7ee7\u7535\u5668</p> <p>transistor: \u6676\u4f53\u7ba1\u3001\u4e09\u6781\u7ba1</p> <p>precedence\uff1a\u4f18\u5148\u6743\uff0ce.g., Boolean Operator Precedence</p> <p>parenthesis\uff1a\u62ec\u53f7\uff08\u5355\u6570\u5f62\u5f0fparenthesis\uff09</p> <p>leave out\uff1a\u9057\u6f0f, e.g., If the meaning is unambiguous, we leave out the symbol  \u201c\u00b7\u201d.</p> <p>idempotence: \u5e42\u7b49\u6027</p> <p>involution: \u4e58\u65b9</p> <p>dual\uff1a\u5bf9\u5076= duality\uff0ce.g., The dual of an algebraic expression is obtained by interchanging +  and \u00b7 and interchanging 0\u2019s and 1\u2019s.</p> <p>dual function\uff1a\u5bf9\u5076\u51fd\u6570</p> <p>complement function: \u8865\u51fd\u6570</p> <p>canonical form\uff1a\u89c4\u8303\u5f62\u5f0f</p> <p>standard form\uff1a\u6807\u51c6\u5f62\u5f0f</p> <p>designator\uff1a\u6807\u8bc6\u7b26= identifier\uff0ce.g., We drop the \u201cm\u201d designators\uff1a\u6211\u4eec\u5220\u9664\u4e86m\u53d8\u91cf\u6807\u8bc6\u7b26</p> <p>identity: \u540c\u4e00\u6027\uff1b\u4e00\u81f4\uff1b\u76f8\u7b49\uff1be.g., Prove the identity of each of the following Boolean  equations, using algebraic manipulation.</p> <p>indices\uff1aindex\u7684\u590d\u6570(=indexes) \u4e00\u822c\u5728\u6570\u5b66\uff0c\u91d1\u878d\u548c\u76f8\u5173\u9886\u57df\u4f7f\u7528</p> <p>subscript\uff1a\u4e0b\u6807</p>"},{"location":"cour_note/D2QD_DigitalDesign/glossary/#3---ch24-7","title":"3)   Ch2.4-7","text":"<p>Venn diagram\uff1a\u7ef4\u6069\u56fe</p> <p>Implicant\uff1a\u8574\u6db5\u9879\uff1b\u8574\u542b\u9879\uff1b\u9690\u542b\u6570</p> <p>Prime implicant: \u4e3b\u8574\u542b\u9879</p> <p>essential prime implicant\uff1a\u57fa\u672c\u7d20\u8574\u6db5; \u5b9e\u8d28\u672c\u539f\u8574\u6db5</p> <p>Don't cares: \u65e0\u5173\u6700\u5c0f\u9879</p> <p>degenerate: \u9000\u5316, e.g., A NAND gate with one input degenerates to an inverter.</p> <p>Hi-Impedance Outputs: \u9ad8\u963b\u6001\u8f93\u51fa</p>"},{"location":"cour_note/D2QD_DigitalDesign/glossary/#4---ch3-1-2","title":"4)   ch3. 1-2","text":"<p>rudimentary:\u57fa\u7840\u7684\uff1b\u57fa\u672c\u7684\uff1b\u672a\u5145\u5206\u53d1\u5c55\u7684\uff1b\u539f\u59cb\u7684</p> <p>die: \u88f8\u7247\u3001\u82af\u7247</p> <p>wafer\uff1a\u6676\u5706</p> <p>margin: \u8fb9\u7f18\u3001\u5dee\u989d\uff0ce.g., noise margin\uff0c\u566a\u58f0\u5bb9\u9650</p> <p>superimpose: v.\u4f7f\uff08\u7532\uff09\u53e0\u6620\u5728\uff08\u4e59\uff09\u4e0a\uff1b\u4f7f\u91cd\u53e0, e.g., Noise margin refers to the maximum external  noise voltage superimposed on a normal input value that will not cause an undesirable change  in the circuit output</p> <p>dissipation: n.\u6d88\u8017\uff1b\u653e\u8361\uff1b\u6d6a\u8d39\uff1be.g., power dissipation = power consumption</p> <p>propagation delay\uff1a\u4f20\u64ad\u5ef6\u8fdf</p> <p>transition time\uff1a\u8f6c\u6362\u65f6\u95f4</p> <p>transport delay\uff1a\u4f20\u8f93\u5ef6\u8fdf</p> <p>inertial delay\uff1a\u60ef\u6027\u5ef6\u8fdf</p> <p>full custom: \u5b8c\u5168\u5b9a\u5236</p> <p>fabrication: \u5236\u9020\u3001\u5236\u4f5c</p> <p>cell library\uff1a\u5143\u4ef6\u5e93</p> <p>schematic\uff1a\u539f\u7406\u56fe\uff0c\u7b80\u56fe</p>"},{"location":"cour_note/D2QD_DigitalDesign/glossary/#5---ch3-3-9","title":"5)   ch3. 3-9","text":"<p>decoder\uff1a\u8bd1\u7801\u5668</p> <p>encoder\uff1a\u7f16\u7801\u5668</p> <p>multiplexer\uff1a\u591a\u8def\u590d\u7528\u5668\uff0cMultiplexer means many into one.</p> <p>demultiplexer\uff1a\u4fe1\u53f7\u5206\u79bb\u5668\u3001\u591a\u8def\u5206\u914d\u5668\uff0cThe demultiplexer means one into many.</p> <p>anode: \u9633\u6781\uff0c\u6b63\u6781</p> <p>cathode: \u9634\u6781\uff0c\u8d1f\u6781</p>"},{"location":"cour_note/D2QD_DigitalDesign/glossary/#6---ch3-8-10","title":"6)   Ch3. 8-10","text":"<p>Iterative array\uff1a\u8fed\u4ee3\u9635\u5217</p> <p>Ripple Carry Adder\uff1a\u884c\u6ce2\u8fdb\u4f4d\u52a0\u6cd5\u5668</p> <p>Carry Look-ahead Adder: \u8d85\u524d\u8fdb\u4f4d\u52a0\u6cd5\u5668</p> <p>bit-wise: \u4ee5\u4f4d\u4e3a\u64cd\u4f5c\u5bf9\u8c61\u7684(wise\u662f\u65b9\u5f0f\u4e4b\u610f),\u5982bit-wise operators(\u4f4d\u8fd0\u7b97\u7b26), 2-input bit-wise  addition functional block</p>"},{"location":"cour_note/D2QD_DigitalDesign/glossary/#7---ch311-12","title":"7)   Ch3.11-12","text":"<p>1's Complement\uff1a\u53cd\u7801</p> <p>2's Complement\uff1a\u8865\u7801</p> <p>magnitude\uff1a\u6570\u503c</p> <p>Signed-Magnitude\uff1a\u7b26\u53f7\u2014\u6570\u503c\u8868\u793a\u6cd5</p> <p>Signed-Complement\uff1a\u7b26\u53f7\u2014\u8865\u7801\u8868\u793a\u6cd5</p> <p>contraction\uff1a(n.) \u6536\u7f29\u3001\u7d27\u7f29\uff1bcontract\uff1a(v.) \u6536\u7f29</p>"},{"location":"cour_note/D2QD_DigitalDesign/glossary/#8---ch5-2","title":"8)   Ch5. 2","text":"<p>fuse intact\uff1a\u7194\u4e1d\u4fdd\u7559</p> <p>fuse blown\uff1a\u7194\u4e1d\u7194\u65ad</p> <p>volatile\uff1a\u6613\u5931\u6027\u7684</p> <p>non-volatile\uff1a\u975e\u6613\u5931\u6027\u7684</p>"},{"location":"cour_note/D2QD_DigitalDesign/glossary/#9---ch4-1-4","title":"9)   Ch4. 1-4","text":"<p>tractable: (adj.) \u6613\u5904\u7406\u7684\uff1b\u6613\u9a7e\u9a6d\u7684</p> <p>oscillator: (n.) \u632f\u8361\u5668</p> <p>capacitors: (n.) \u7535\u5bb9\u5668</p> <p>inductor: (n.) \u7535\u611f\u5668</p> <p>latch\uff1a\u9501\u5b58\u5668</p> <p>flip-flop\uff1a\u89e6\u53d1\u5668</p> <p>metastable state\uff1a\u4e9a\u7a33\u6001</p> <p>alternating clock\uff1a\u4ea4\u66ff\u65f6\u949f</p> <p>disposable sampling = 1s catching\uff1a\u4e00\u6b21\u91c7\u6837</p> <p>setup time\uff1a\u5efa\u7acb\u65f6\u95f4</p> <p>hold time\uff1a\u4fdd\u6301\u65f6\u95f4</p> <p>pulse-triggering\uff1a\u8109\u51b2\u89e6\u53d1</p> <p>level triggering\uff1a\u7535\u5e73\u89e6\u53d1</p> <p>edge triggering\uff1a\u8fb9\u6cbf\u89e6\u53d1</p> <p>self-recovery capability\uff1a\u81ea\u6062\u590d\u80fd\u529b</p> <p>equivalent state\uff1a\u7b49\u4ef7\u72b6\u6001</p>"},{"location":"cour_note/D2QD_DigitalDesign/glossary/#10--ch6-1-5","title":"10)  Ch6. 1-5","text":"<p>register\uff1a\u5bc4\u5b58\u5668</p> <p>register transfer operation\uff1a\u5bc4\u5b58\u5668\u4f20\u8f93\u64cd\u4f5c</p> <p>microoperation\uff1a\u5fae\u64cd\u4f5c</p> <p>register transfer structure\uff1a\u5bc4\u5b58\u5668\u4f20\u8f93\u7ed3\u6784</p> <p>bus\uff1a\u603b\u7ebf</p> <p>lateral: (adj.) \u4fa7\u9762\u7684\uff1b\u6a2a\u5411\u7684\uff1b\u5411\u4fa7\u9762\u79fb\u52a8\u7684</p> <p>laterally: (adv.) \u4fa7\u9762\u5730\uff1b\u6a2a\u5411\u5730\uff1b\u5411\u4fa7\u9762\u79fb\u52a8\u5730</p> <p>serial gating\uff1a\u4e32\u884c\u95e8\u63a7</p> <p>parallel gating\uff1a\u5e76\u884c\u95e8\u63a7</p> <p>counter\uff1a\u8ba1\u6570\u5668</p> <p>data path\uff1a\u6570\u636e\u901a\u9053</p> <p>control unit\uff1a\u63a7\u5236\u5355\u5143</p>"},{"location":"cour_note/D2QD_DigitalDesign/glossary/#11--ch7-1-7","title":"11)  Ch7. 1-7","text":"<p>strobe\uff1a\u9009\u901a\uff1b\u9009\u901a\u8109\u51b2\uff1b\u95f8\u95e8</p> <p>SRAM\uff1a\u9759\u6001\u5185\u5b58</p> <p>DRAM\uff1a\u52a8\u6001\u5185\u5b58</p> <p>coincident selection\uff1a\u91cd\u5408\u9009\u62e9</p> <p>word extension\uff1a\u5b57\u6269\u5c55</p> <p>bit extension\uff1a\u4f4d\u6269\u5c55</p> <p>address multiplexing\uff1a\u5730\u5740\u590d\u7528\uff08\u6307DRAM\uff09</p> <p>refresh\uff1a\u5237\u65b0</p> <p>synchronous DRAM(SDRAM)\uff1a\u540c\u6b65DRAM</p> <p>burst read\uff1a\u7206\u53d1\u6a21\u5f0f\u8bfb\u53d6\u6570\u636e</p> <p>burst length\uff1a\u7206\u53d1\u6a21\u5f0f\u7684\u6570\u636e\u8bfb/\u5199\u957f\u5ea6</p> <p>memory bandwidth\uff1a\u5185\u5b58\u5e26\u5bbd</p>"},{"location":"cour_note/D2QD_Intro2CV/","title":"\ud83d\udc8e \u8ba1\u7b97\u673a\u89c6\u89c9\u5bfc\u8bba | Introduction to Computer Vision","text":"<p> \u7ea6 145 \u4e2a\u5b57 </p> <p>\u8bfe\u7a0b\u4fe1\u606f</p> <ul> <li>\u672c\u6587\u4e3a\u8bfe\u7a0b\u300a\u8ba1\u7b97\u673a\u89c6\u89c9\u5bfc\u8bba\u300b\u7684\u8bfe\u7a0b\u7b14\u8bb0\uff0c\u8bfe\u7a0b\u4e3b\u8981\u4ecb\u7ecd\u8ba1\u7b97\u673a\u89c6\u89c9\u7684\u57fa\u7840\u7406\u8bba\u548c\u57fa\u672c\u65b9\u6cd5\u3002</li> <li>\u667a\u4e91\u94fe\u63a5\uff1a\ud83d\udd17</li> <li>\u6388\u8bfe\uff1a\u5468\u6653\u5dcd</li> <li> <p>\u6559\u6750\uff1a\ud83d\udcd9 .</p> </li> <li> <p>\u63a8\u8350\u8d44\u6e90\uff1ahttps://paperswithcode.com/</p> </li> </ul> <p>List</p> <ul> <li> Lecture 1 | Introduction</li> <li> Lecture 2 | Image Formation</li> <li> Lecture 3 | Image Processing</li> <li> Lecture 4 | Model Fitting and Optimization</li> <li> Lecture 5 | Feature Matching and Motion Estimation</li> <li> Lecture 6 | Image Alignment and Stitching</li> <li> Lecture 7 | Structure From Motion</li> <li> Lecture 8 | Depth Estimation &amp; 3D Reconstruction</li> <li> Lecture 9 | Deep Learning</li> <li> Lecture 10 | Recognition</li> <li> Lecture 11 | 3D Deep Learning</li> <li> Lecture 12 | Computational Photography 1</li> <li> Lecture 13 | Computational Photography 2</li> </ul> <p>Lab</p> <ul> <li>Lab Code</li> </ul>"},{"location":"cour_note/D2QD_Intro2CV/Lec01/","title":"Lecture 1 | Introduction","text":"<p> \u7ea6 1737 \u4e2a\u5b57  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 6 \u5206\u949f</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec01/#cv-\u7684\u4e3b\u8981\u4efb\u52a1","title":"CV \u7684\u4e3b\u8981\u4efb\u52a1","text":"<ul> <li>\u4e09\u7ef4\u91cd\u5efa / Reconstruction</li> <li>\u56fe\u50cf\u7406\u89e3 / Understanding</li> <li>\u56fe\u50cf\u5408\u6210 / Synthesis</li> </ul>"},{"location":"cour_note/D2QD_Intro2CV/Lec01/#cv-\u7684\u5e94\u7528","title":"CV \u7684\u5e94\u7528","text":"Application Examples <ul> <li>Face Reconstruction and Recognition</li> <li>Face ID</li> <li>Vending Machine with Face Detection</li> <li>DeepFake</li> <li>Augmented reality</li> <li>Factory Automation</li> <li>Vision Inspection</li> <li>Optical Character Recognition(OCR)</li> <li>Video Surveillance</li> <li>Human Computer Interaction: Optical Mouse</li> <li>Human Computer Interaction: Motion Sensing Games</li> <li>Visual Effects (VFX)</li> <li>Digital Human</li> <li>VR Tour</li> <li>Visual Localization and Navigation</li> <li>Autonomous Navigation: Space Exploration</li> <li>Robot Perception</li> <li>Autonomous Driving</li> <li>Augmented Reality</li> <li>Free Viewpoint Video</li> <li>Medical Image Analysis</li> <li>......</li> </ul>"},{"location":"cour_note/D2QD_Intro2CV/Lec01/#\u5b66\u672f\u5708\u6982\u51b5","title":"\u5b66\u672f\u5708\u6982\u51b5","text":"<p>CV \u9886\u57df\u7684\u51e0\u4e2a\u9876\u4f1a</p> <ul> <li>CVPR (Computer Vision and Pattern Recognition)</li> <li>ICCV (International Conference on Computer Vision)</li> <li>ECCV (European Conference on Computer Vision)</li> </ul> <p>\u56fe\u5f62\u5b66\u76f8\u5173\u7684\u9876\u4f1a</p> <ul> <li>ACM SIGGRAPH</li> </ul>"},{"location":"cour_note/D2QD_Intro2CV/Lec01/#\u8bfe\u7a0b\u6982\u8ff0","title":"\u8bfe\u7a0b\u6982\u8ff0","text":"<ul> <li>\u8bfe\u7a0b\u76ee\u6807<ul> <li>\u5b66\u4e60\u8ba1\u7b97\u673a\u89c6\u89c9\u76f8\u5173\u7684\u77e5\u8bc6</li> <li>\u5b66\u4f1a\u300c\u7528\u6570\u5b66\u63cf\u8ff0\u4e0e\u89e3\u51b3\u95ee\u9898\u300d<ul> <li><code>Linear Algebra</code> / <code>Optimization</code> / <code>Geometry</code></li> </ul> </li> </ul> </li> <li> <p>\u8bfe\u7a0b\u8d44\u6e90</p> <ul> <li>\u6559\u6750\uff1ahttps://szeliski.org/Book/ </li> </ul> </li> <li> <p>\u8bfe\u7a0b\u8ba1\u5212</p> <ul> <li>Basics. (Lec.02 \u2013 Lec.04)</li> <li>Reconstruction. (Lec.05 \u2013 Lec.09) </li> <li>Understanding. (Lec.10 \u2013 Lec.12)</li> <li>Synthesis. (Lec. 13 \u2013 Lec.14)</li> </ul> </li> </ul> <p>Note</p> <ul> <li>\u4f5c\u4e3a\u540e\u7eed\u8bfe\u7a0b\u7684\u57fa\u7840\uff0c\u9700\u8981\u590d\u4e60\u7ebf\u6027\u4ee3\u6570\u7684\u76f8\u5173\u77e5\u8bc6\uff0c\u5b83\u5c06\u8d2f\u7a7f\u6574\u4e2a\u8bfe\u7a0b\uff1b</li> <li>\u9700\u8981\u719f\u6089\u6d89\u53ca\u7684\u8bcd\u6c47\uff0c\u4e4b\u540e\u4f1a\u82e5\u5e72\u6b21\u63d0\u5230\uff1b</li> </ul>"},{"location":"cour_note/D2QD_Intro2CV/Lec01/#\u7ebf\u4ee3\u590d\u4e60","title":"\u7ebf\u4ee3\u590d\u4e60","text":""},{"location":"cour_note/D2QD_Intro2CV/Lec01/#\u7ebf\u6027\u53d8\u6362","title":"\u7ebf\u6027\u53d8\u6362","text":"<p>\u9996\u5148\uff0c\u4e00\u4e2a\u77e9\u9635\u5de6\u4e58\u4e00\u4e2a\u5411\u91cf\uff1a</p> <ul> <li>\u4ee3\u6570\u4e0a\uff0c\u7ed3\u679c\u5411\u91cf\u7684\u6bcf\u4e00\u9879\u76f8\u5f53\u4e8e\u539f\u5411\u91cf\u7684\u4e00\u4e2a\u52a0\u6743\u6c42\u548c\uff1b</li> <li>\u51e0\u4f55\u4e0a\uff0c\u7ed3\u679c\u5411\u91cf\u76f8\u5f53\u4e8e\u539f\u5411\u91cf\u505a\u51e0\u4f55\u53d8\u6362\u5f97\u5230\u7684\u65b0\u5411\u91cf\uff1b</li> </ul> <p>\u5728\u8fd9\u79cd\u57fa\u7840\u4e0a\uff0c\u77e9\u9635\u4e58\u6cd5\u53ef\u4ee5\u8ba4\u4e3a\u662f\u4e00\u7cfb\u5217\u5411\u91cf\uff08\u53f3\u4fa7\u77e9\u9635\uff09\u7ecf\u8fc7\u540c\u4e00\u4e2a\u53d8\u6362\u5f97\u5230\u65b0\u7684\u4e00\u7cfb\u5217\u5411\u91cf\u3002</p> <ul> <li>\u90a3\u4e48\u53cd\u8fc7\u6765\u7684\uff0c\u6211\u4eec\u4e5f\u53ef\u4ee5\u901a\u8fc7\u89c2\u5bdf\u67d0\u4e9b\u70b9\u5728\u53d8\u6362\u540e\u7684\u4f4d\u7f6e\u6765\u611f\u53d7\u8fd9\u4e2a\u201c\u53d8\u6362\u201d\u7684\u5177\u4f53\u5185\u5bb9\uff1b</li> <li>\u66f4\u7279\u522b\u7684\uff0c\u6211\u4eec\u53ef\u4ee5\u53d1\u73b0\uff0c\u53d8\u6362\u77e9\u9635\uff08\u5de6\u4fa7\u77e9\u9635\uff09\u7684\u6bcf\u4e00\u5217\uff0c\u5c31\u76f8\u5f53\u4e8e\u5bf9\u5e94\u7684\u5355\u4f4d\u57fa\uff08\u4f8b\u5982\u7b2c \\(2\\) \u5217\u5bf9\u5e94 \\(\\vec{a}(0,1)\\) \u5411\u91cf\uff09\u7ecf\u8fc7\u8fd9\u4e2a\u53d8\u6362\uff08\u53f3\u4e58\u8fd9\u4e2a\u53d8\u6362\u77e9\u9635\uff09\u5f97\u5230\u7684\u7ed3\u679c\uff1b</li> </ul> <p>Tips</p> <p>\u5b9e\u9645\u4e0a\uff0c\u4ece\u5355\u4f4d\u77e9\u9635\u7684\u89d2\u5ea6\u4e5f\u53ef\u4ee5\u5f88\u597d\u7684\u7406\u89e3\u8fd9\u4ef6\u4e8b\uff1a</p> \\[ \\begin{bmatrix}     a &amp; b \\\\     c &amp; d \\end{bmatrix} \\begin{bmatrix}     1 &amp; 0 \\\\     0 &amp; 1 \\end{bmatrix} = \\begin{bmatrix}     a &amp; b \\\\     c &amp; d \\end{bmatrix} \\] <p>\u6211\u4eec\u6765\u8bd5\u7740\u8fd0\u7528\u4e0a\u9762\u7684\u6280\u5de7\u6c42\u4e00\u4e2a\u65cb\u8f6c\u53d8\u6362\u5bf9\u5e94\u7684\u53d8\u6362\u77e9\u9635\u3002</p> \u9898\u9762\u7b54\u6848 <p> \u5047\u8bbe\u8be5\u77e9\u9635\u8ba9\u76ee\u6807\u56fe\u5f62\u987a\u65f6\u9488\u65cb\u8f6c \\(\\theta\\) \uff0c\u5219\u5176\u8868\u8fbe\u5f0f\u4e3a\uff1f</p> <p></p> <p>\u6211\u4eec\u505a\u6b64\u5206\u6790\uff1a</p> <ul> <li>\u5bf9\u4e8e\u53c2\u8003\u70b9 \\((1,0)\\)\uff0c\u7ecf\u8fc7\u65cb\u8f6c\u540e\u4f4d\u7f6e\u53d8\u5316\u4e3a \\((\\cos\\theta,-\\sin\\theta)\\)\uff1b</li> <li>\u5bf9\u4e8e\u53c2\u8003\u70b9 \\((0,1)\\)\uff0c\u7ecf\u8fc7\u65cb\u8f6c\u540e\u4f4d\u7f6e\u53d8\u5316\u4e3a \\((\\sin\\theta,\\cos\\theta)\\)\uff1b</li> </ul> <p>\u56e0\u6b64\uff0c\u6839\u636e\u4e0a\u9762\u63d0\u5230\u7684\u6280\u5de7\uff0c\u65cb\u8f6c\u5bf9\u5e94\u7684\u53d8\u6362\u77e9\u9635\u4e3a\uff1a</p> \\[ R_{\\theta,clockwise} =  \\begin{bmatrix}     \\cos\\theta &amp; \\sin\\theta \\\\      -\\sin\\theta &amp; \\cos\\theta \\end{bmatrix} \\] <p>\u7279\u522b\u7684\uff0c\u5982\u679c\u662f\u9006\u65f6\u9488\uff0c\u7ed3\u679c\u5c31\u662f\uff1a</p> \\[ R_{\\theta,anti-clockwise} =  \\begin{bmatrix}     \\cos\\theta &amp; -\\sin\\theta \\\\      \\sin\\theta &amp; \\cos\\theta \\end{bmatrix} \\]"},{"location":"cour_note/D2QD_Intro2CV/Lec01/#\u4eff\u5c04\u53d8\u6362\u4e0e\u9f50\u6b21\u5750\u6807","title":"\u4eff\u5c04\u53d8\u6362\u4e0e\u9f50\u6b21\u5750\u6807","text":"<p>\u4eff\u5c04\u53d8\u6362(Affine Transformations) \u4e3b\u8981\u5305\u62ec\u4e24\u4e2a\u90e8\u5206\uff0c\u5373\u7ebf\u6027\u53d8\u6362\u548c\u5e73\u79fb\uff08\u6362\u8a00\u4e4b\uff0c\u4eff\u5c04\u53d8\u6362\u5e76\u4e0d\u662f\u7ebf\u6027\u53d8\u6362\uff09\uff0c\u5176\u6570\u5b66\u8868\u8ff0\u4e3a\uff1a</p> \\[ \\begin{bmatrix}      x' \\\\     y'  \\end{bmatrix} = \\begin{bmatrix}      a &amp; b \\\\      c &amp; d \\end{bmatrix}  \\begin{bmatrix}      x \\\\      y  \\end{bmatrix} + \\begin{bmatrix}      t_x \\\\      t_y  \\end{bmatrix} \\] <p>\u4e3a\u4e86\u8ba9\u4eff\u5c04\u53d8\u6362\u4e5f\u80fd\u5199\u6210 \\(a=Mb\\) \u7684\u5f62\u5f0f\u4ee5\u7b80\u5316\u8fd0\u7b97\uff0c\u6211\u4eec\u53ef\u4ee5\u7528 \\(n+1\\) \u7ef4\u5411\u91cf\u6765\u8868\u793a \\(n\\) \u7ef4\u70b9\uff0c\u5373\u4f7f\u7528\u9f50\u6b21\u5750\u6807(homogenous coordinates)\uff1a</p> \\[ \\begin{bmatrix}     x'\\\\     y'\\\\     1 \\end{bmatrix} \\cong \\begin{bmatrix}     a &amp; b &amp; t_x \\\\     c &amp; d &amp; t_y \\\\     0 &amp; 0 &amp; 1 \\end{bmatrix} \\begin{bmatrix}     x \\\\     y \\\\     1 \\end{bmatrix} \\] <p>\u4e3a\u4ec0\u4e48\u662f \u201c1\u201d</p> <p>\u8fd9\u91cc\u6211\u4eec\u4e0d\u7981\u629b\u51fa\u4e00\u4e2a\u7591\u95ee\uff0c\u4e3a\u4ec0\u4e48\u9f50\u6b21\u5750\u6807\u6dfb\u52a0\u7684\u7ef4\u5ea6\u4e2d\u8981\u586b\u5165 1 \u5462\uff1f\u5b83\u6709\u4ec0\u4e48\u542b\u4e49\u5417\uff1f\u5b83\u4e0d\u80fd\u662f 2 \u6216\u8005\u522b\u7684\u4ec0\u4e48\u4e1c\u897f\u5417\uff1f</p> <p>\u7b54\u6848\u662f\uff0c\u5b83\u53ef\u4ee5\u662f\u522b\u7684\u4e1c\u897f\uff0c\u6216\u8005\u8bf4\u6211\u4eec\u9700\u8981\u5bf9\u5b9a\u4e49\u8fdb\u884c\u4e00\u4e2a\u6269\u5c55\uff0c\u4ee5\u4f7f\u9f50\u6b21\u5750\u6807\u6709\u66f4\u5927\u7684\u7528\u5904\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec01/#\u9f50\u6b21\u5750\u6807\u7684\u6269\u5c55\u6027\u8d28","title":"\u9f50\u6b21\u5750\u6807\u7684\u6269\u5c55\u6027\u8d28","text":"<p>\u4f8b\u5982\uff0c\\((x,y)\\) \u5bf9\u5e94\u7684\u9f50\u6b21\u5750\u6807\u4e3a \\((x,y,1)\\)\uff0c\u5982\u679c\u4f60\u628a\u5b83\u60f3\u8c61\u6210\u4e09\u7ef4\u7a7a\u95f4\u4e2d\u7684\u70b9\uff0c\u4f1a\u53d1\u73b0\uff0c\u5982\u679c\u6539\u53d8 1 \u7684\u503c\uff0c\u5f97\u5230\u7684\u70b9\u7684\u8f68\u8ff9\u4f1a\u662f\u82e5\u5e72\u5f20\u5e73\u884c\u7684\u5e73\u9762\uff0c\u4e5f\u5c31\u662f\u8bf4\u4ed6\u4eec\u5728\u4e09\u7ef4\u7a7a\u95f4\u4e0b\u662f\u76f8\u4e92\u72ec\u7acb\u7684\u3002</p> <p>\u6b64\u65f6\uff0c\u6211\u4eec\u5c31\u53ef\u4ee5\u4eba\u4e3a\u7684\u5b9a\u4e49\u4e00\u4e2a\u6bcf\u4e00\u4e2a\u5e73\u9762\u5185\u7684\u70b9\u7684\u6620\u5c04\u5173\u7cfb\uff08\u6211\u4eec\u53ea\u8003\u8651\u7b2c\u4e00\u8c61\u9650\uff09\uff0c\u4ece\u539f\u70b9\u5f15\u4e00\u6761\u5c04\u7ebf\uff0c\u76f4\u7ebf\u4e0a\u4e0e\u6bcf\u4e00\u4e2a\u5e73\u9762\u7684\u4ea4\u70b9\u6211\u4eec\u90fd\u8ba4\u4e3a\u5bf9\u5e94\u7740\u4e8c\u7ef4\u5e73\u9762\u4e0a\u7684\u540c\u4e00\u70b9\u3002</p> <p></p> <p>\u6362\u53e5\u8bdd\u6765\u8bf4\uff0c\u6211\u4eec\u7528 \\(n+1\\) \u7ef4\u7a7a\u95f4\u4e2d \u4ece\u539f\u70b9\u53d1\u51fa\u7684\u4e00\u6761 \u5c04\u7ebf \u6765\u63cf\u8ff0 \\(n\\) \u7ef4\u7a7a\u95f4\u4e2d\u7684\u4e00\u4e2a\u70b9\u3002</p> <p>\u4e8e\u662f\u6211\u4eec\u53ef\u4ee5\u7528\u4e0b\u9762\u7684\u5f0f\u5b50\u6765\u6982\u62ec\u6269\u5c55\u5b9a\u4e49\uff1a</p> <ul> <li>\\(\\begin{bmatrix}x\\\\y\\\\k\\end{bmatrix}\\) \u7b49\u4ef7\u4e8e \\(\\begin{bmatrix}x/k\\\\y/k\\\\1\\end{bmatrix}\\)\uff0c\u5f53\u7136\uff0c\\(k\\not=0\\)\uff1b</li> </ul> <p>\u800c\u5f15\u5165\u8fd9\u79cd\u60f3\u6cd5\u540e\uff0c\u6211\u4eec\u5c31\u77e5\u9053\u4e3a\u4ec0\u4e48\u901a\u8fc7\u9f50\u6b21\u5750\u6807\u5316\u5c31\u80fd\u628a\u5e73\u79fb\u53d8\u6210\u7ebf\u6027\u53d8\u6362\u2014\u2014\u6211\u4eec\u53ef\u4ee5\u5c06 \\(n\\) \u7ef4\u70b9\u7684\u5e73\u79fb\u770b\u4f5c \\(n+1\\) \u7ef4\u5c04\u7ebf\u7684\u65cb\u8f6c\uff0c\u800c\u65cb\u8f6c\u663e\u7136\u662f\u4e00\u4e2a\u7ebf\u6027\u53d8\u6362\u3002</p> <p>\u800c\u5173\u4e8e\u8be5\u6027\u8d28\u7684\u5176\u4ed6\u5e94\u7528\uff0c\u53ef\u4ee5\u770b Lecture 2 \u7684\u7b2c\u4e8c\u5c0f\u8282\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec01/#\u9006\u53d8\u6362","title":"\u9006\u53d8\u6362","text":"<p>\u7ebf\u6027\u53d8\u6362 \\(T\\) \u7684\u9006\u53d8\u6362(Inverse Transform)\u5c31\u662f\u5176\u53d8\u6362\u77e9\u9635\u7684\u9006 \\(T^{-1}\\)\uff0c\u663e\u7136\uff0c\u5e76\u4e0d\u662f\u6240\u6709\u53d8\u6362\u90fd\u662f\u53ef\u9006\u7684\u3002</p> <p>\u5f62\u8c61\u5730\u7406\u89e3\uff0c\u4e00\u4e2a\u53d8\u6362\u77e9\u9635\u5982\u679c\u4e0d\u6ee1\u79e9\uff08\u4e0d\u53ef\u9006\uff09\uff0c\u90a3\u4e48\u5c31\u4f1a\u6709\u51e0\u4e2a\u57fa\u5728\u53d8\u6362\u4e2d\u5408\u5e76\uff0c\u6216\u8005\u8bf4\u591a\u4e2a\u70b9\u88ab\u6620\u5c04\u4e3a\u540c\u4e00\u4e2a\u70b9\uff0c\u5bfc\u81f4\u65e0\u6cd5\u8fd8\u539f\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec01/#\u884c\u5217\u5f0f\u7684\u51e0\u4f55\u542b\u4e49","title":"\u884c\u5217\u5f0f\u7684\u51e0\u4f55\u542b\u4e49","text":"<p>\u884c\u5217\u5f0f(Determinant) \u7684\u503c\u7b49\u4e8e\u8fd9\u4e2a\u65b9\u9635\u4e2d\u7684\u5411\u91cf\u5bf9\u5e94\u7684 \u5e73\u884c\u56fe\u5f62/\u51e0\u4f55\u4f53/... \u7684 \u9762\u79ef/\u4f53\u79ef/...</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec01/#\u7279\u5f81\u503c\u548c\u7279\u5f81\u5411\u91cf","title":"\u7279\u5f81\u503c\u548c\u7279\u5f81\u5411\u91cf","text":"<p>\u7279\u5f81\u5411\u91cf(eigenvector)\u548c\u7279\u5f81\u503c(eigenvalue)\u7684\u5b9a\u4e49\u5982\u4e0b\uff1a</p> <p>\u5bf9\u4e8e\u77e9\u9635 \\(A\\in R^{N\\times N}\\)\uff0c\u5982\u679c\u6709\u5411\u91cf \\(v\\in R^{N}\\) \u548c\u5b9e\u6570 \\(\\lambda \\not = 0\\)\uff0c\u6ee1\u8db3\uff1a</p> \\[ Av = \\lambda v \\] <p>\u5219\u79f0 \\(v\\) \u662f\u77e9\u9635 \\(A\\) \u7684\u7279\u5f81\u5411\u91cf\uff0c\u5bf9\u5e94\u7684\u7279\u5f81\u503c\u4e3a \\(\\lambda\\)\u3002</p> <p>\u4ece\u51e0\u4f55\u53d8\u6362\u7684\u89d2\u5ea6\u6765\u7406\u89e3\u8fd9\u4e2a\u5b9a\u4e49\u5f0f\uff0c\u53ef\u4ee5\u63cf\u8ff0\u4e3a\uff1a\u5411\u91cf \\(v\\) \u7ecf\u8fc7\u53d8\u6362 \\(A\\) \u5f97\u5230\u7684\u7ed3\u679c\uff0c\u7b49\u4e8e\u76f4\u63a5\u5bf9 \\(v\\) \u8fdb\u884c\u7f29\u653e\uff08\u800c\u6ca1\u6709\u6539\u53d8\u65b9\u5411\uff09\u3002</p> <p>\u5de5\u7a0b\u8ba1\u7b97\u65b9\u6cd5</p> <p>\u4ee4\u4eba\u60ca\u559c\u7684\u662f\uff0c\u6211\u4eec\u5728\u5b9e\u9645\u8fd0\u7528\u65f6\uff0c\u53ef\u4ee5\u76f4\u63a5\u4f7f\u7528\u6570\u5b66\u5e93\u4e2d\u7684\u7279\u5f81\u503c\u5206\u89e3(eigen decomposition)\u65b9\u6cd5\uff0c\u5176\u5927\u81f4\u4f1a\u505a\u8fd9\u6837\u4e00\u4ef6\u4e8b\uff1a</p> <p></p> <p>\u5c06\u77e9\u9635 \\(A\\) \u5206\u89e3\u4e3a \\(Q\\Lambda Q^{-1}\\)\uff0c\u5176\u4e2d \\(Q\\) \u4e2d\u7684\u6bcf\u4e00\u5217\u5373\u4e3a \\(A\\) \u7684\u7279\u5f81\u5411\u91cf\uff0c\u5bf9\u89d2\u9635 \\(\\Lambda\\) \u4e2d\u7684\u7b2c \\(i\\) \u9879\u5c31\u662f\u7b2c \\(i\\) \u4e2a\u7279\u5f81\u5411\u91cf\u7684\u7279\u5f81\u503c\u3002</p> <p>\u7279\u5f81\u503c\u4e0e\u7279\u5f81\u5411\u91cf\u7684\u5e94\u7528\uff1a\u4e3b\u6210\u5206\u5206\u6790(principal component analysis)</p> <p></p> <p>\u4e3b\u6210\u5206(principal component)\u7b49\u4e8e\u534f\u65b9\u5dee\u77e9\u9635\u7684 \u7279\u5f81\u503c\u6700\u5927\u7684 \u90a3\u4e2a\u7279\u5f81\u5411\u91cf\u3002</p> <ul> <li>\u5982\u56fe\uff0c\u6211\u4eec\u8981\u4ece\u56fe\u4e2d\u627e\u5230\u4e00\u4e2a\u65b9\u5411\uff0c\u4f7f\u5f97\u6240\u6709\u6570\u636e\u70b9\u5728\u8fd9\u4e2a\u65b9\u5411\u4e0a\u7684\u6295\u5f71\uff0c\u65b9\u5dee\u6700\u5927\uff08\u6362\u8a00\u4e4b\uff0c\u627e\u5230\u8fd9\u4e9b\u6570\u636e\u7684\u4e00\u4e2a\u201c\u65b9\u5411\u201d\uff09\uff1b</li> <li>\u8bb0\u6240\u6709\u6570\u636e\u70b9\u4e3a \\(A\\)\uff0c\u5219 \\(A^{T}A\\) \u4e3a\u534f\u65b9\u5dee\u77e9\u9635(covariance matrix)\uff0c\u5176\u7279\u5f81\u5411\u91cf\u4e2d\uff0c\u7279\u5f81\u503c\u6700\u5927\u7684\u90a3\u4e2a\uff0c\u5c31\u662f\u8fd9\u7ec4\u6570\u636e\u7684\u4e3b\u6210\u5206\uff1b</li> </ul>"},{"location":"cour_note/D2QD_Intro2CV/Lec02/","title":"Lecture 2 | Image Formation","text":"<p> \u7ea6 3769 \u4e2a\u5b57  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 13 \u5206\u949f</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec02/#\u76f8\u673a\u4e0e\u5149\u5b66\u539f\u7406","title":"\u76f8\u673a\u4e0e\u5149\u5b66\u539f\u7406","text":""},{"location":"cour_note/D2QD_Intro2CV/Lec02/#\u5c0f\u5b54\u6210\u50cf","title":"\u5c0f\u5b54\u6210\u50cf","text":"<p>\u5982\u679c\u6211\u4eec\u76f4\u63a5\u62ff\u4e00\u5757\u5e73\u9762\u6765\u8bb0\u5f55\u81ea\u7136\u754c\u7684\u5149\u4fe1\u606f\uff0c\u4e0d\u96be\u53d1\u73b0\uff0c\u7531\u4e8e\u5149\u7ebf\u662f\u5411\u56db\u9762\u516b\u65b9\u4f20\u64ad\u7684\uff0c\u6240\u4ee5\u63a5\u6536\u5230\u7684\u4fe1\u606f\u4e5f\u4e71\u4e03\u516b\u7cdf\uff0c\u6240\u4ee5\u6211\u4eec\u9700\u8981\u901a\u8fc7\u4e00\u4e2a\u5c0f\u5b54\uff0c\u4e5f\u5c31\u662f\u5982\u4eca\u7684\u5149\u5708(aperture)\u6765\u5bf9\u5149\u7ebf\u8fdb\u884c\u4e00\u4e2a\u8fc7\u6ee4\u3002\u8fd9\u5c31\u662f\u65e9\u671f\u9488\u5b54\u6444\u50cf\u673a(pinhole camera)\u7684\u539f\u7406\u3002</p> <p> </p> <p>\u8fd9\u4e5f\u5c31\u662f\u6211\u4eec\u5f88\u65e9\u5c31\u5b66\u8fc7\u7684\uff0c\u5c0f\u5b54\u6210\u50cf\u539f\u7406\u3002\u800c\u5149\u5708\u8d8a\u5c0f\uff0c\u6210\u50cf\u4e5f\u4f1a\u8d8a\u6765\u8d8a\u6e05\u695a\uff0c\u4f46\u4e5f\u4e0d\u80fd\u592a\u5c0f\uff0c\u5426\u5219\u4f1a\u5bfc\u81f4\u4eae\u5ea6\u4e0d\u8db3\u751a\u81f3\u884d\u5c04\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec02/#\u900f\u955c","title":"\u900f\u955c","text":"<p>\u51f8\u900f\u955c\u5177\u6709\u6c47\u805a\u5149\u7ebf\u7684\u4f5c\u7528\uff0c\u5728\u6ee1\u8db3\u7279\u5b9a\u5149\u5b66\u51e0\u4f55\u5173\u7cfb\u7684\u524d\u63d0\u4e0b\u5177\u6709\u548c\u5c0f\u5b54\u6210\u50cf\u7c7b\u4f3c\u7684\u6548\u679c\uff0c\u4f46\u662f\u80fd\u591f\u6c47\u805a\u66f4\u591a\u7684\u5149\u7ebf\u3002</p> <p></p> <p>Source: https://fpcv.cs.columbia.edu/</p> <p>\u5bf9\u4e8e\u8584\u51f8\u900f\u955c\uff0c\u6709\u9ad8\u65af\u6210\u50cf\u516c\u5f0f\uff1a</p> \\[ \\frac{1}{i} + \\frac{1}{o} = \\frac{1}{f} \\] <p>\u5176\u4e2d \\(i\\) \u4e3a\u50cf\u8ddd(img dis)\uff0c\\(o\\) \u4e3a\u7269\u8ddd(obj dis)\uff0c\\(f\\) \u4e3a\u7126\u8ddd(focal len)\u3002</p> <p>\u800c\u5bf9\u4e8e\u5e73\u884c\u5149\uff0c\u6216\u8005\u8bf4 \\(o\\to +\\infty\\) \u65f6\uff0c\u5c31\u4f1a\u6709 \\(i=f\\)\u3002\u901a\u8fc7\u8fd9\u79cd\u65b9\u6cd5\uff0c\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u6d4b\u91cf\u5e73\u884c\u5149\u900f\u8fc7\u51f8\u900f\u955c\u6c47\u805a\u7684\u4f4d\u7f6e\u6765\u6d4b\u91cf\u7126\u8ddd\u3002</p> <p>\u540c\u65f6\u518d\u5f15\u5165\u4e00\u4e2a\u653e\u5927\u7387(Magnification)\uff1a\\(m=\\frac{h_i}{h_o}=\\frac{i}{o}\\)\u3002</p> <p></p> <p>Source: https://fpcv.cs.columbia.edu/</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec02/#\u89c6\u91ce-fovfield-of-view","title":"\u89c6\u91ce FoV(field of view)","text":"<p>\u7126\u8ddd\u548c\u5e95\u7247\u7684\u7ebf\u5ea6\u5171\u540c\u51b3\u5b9a\u4e86 FoV \u7684\u5927\u5c0f\u3002</p> <p></p> <p>Source: https://snapsnapsnap.photos/</p> <p>\u53ef\u4ee5\u53d1\u73b0\uff0c\u7126\u8ddd\u7684\u5927\u5c0f\u4f1a\u5f71\u54cd\u89c6\u91ce\u7684\u5927\u5c0f\u548c\u653e\u5927\u7387\u7684\u5927\u5c0f\u3002</p> <p>50mm/46\u00b0 \u4e0e\u4eba\u7684\u89c6\u91ce\u76f8\u8fd1\uff0c\u56e0\u6b64\u5b83\u88ab\u79f0\u4e3a\u6807\u51c6\u955c\u5934(standard lens).</p> <p>\u6b64\u5916\uff0c\u5373\u4f7f\u5728\u753b\u9762\u4e2d\u4fdd\u8bc1\u4e00\u4e2a\u7269\u4f53\u7684\u5927\u5c0f\u4e0d\u53d8\uff0c\u9009\u7528\u4e0d\u540c\u7684\u7126\u8ddd\u4e5f\u4f1a\u5bfc\u81f4\u753b\u9762\u7684\u53d8\u5316\u2014\u2014\u80cc\u666f\u7684\u5927\u5c0f\uff0c\u901a\u8fc7\u4e0b\u9762\u8fd9\u5f20\u56fe\u7684\u4e09\u4e2a\u753b\u9762\u6211\u4eec\u53ef\u4ee5\u5f88\u6e05\u6670\u7684\u611f\u53d7\u5230\u8fd9\u4e00\u70b9\u3002</p> <p></p> <p>\u6b64\u5916\uff0c\u4f20\u611f\u5668\u7684\u5927\u5c0f\uff0c\u6216\u8005\u8bf4\u5e95\u7247\u7684\u5927\u5c0f\uff0c\u4e5f\u4f1a\u5f71\u54cd FoV\u3002\u800c\u4e14\u4e00\u822c\u6765\u8bf4\uff0c\u8d8a\u5927\u7684\u5e95\u7247\u80fd\u591f\u63d0\u4f9b\u66f4\u9ad8\u7684\u5206\u8fa8\u7387\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec02/#f-\u6570","title":"F \u6570","text":"<p>F \u6570(F-Number)\u7528\u6765\u63cf\u8ff0\u5149\u5708\u7684\u76f8\u5bf9\u5927\u5c0f\uff0c\u5176\u5b9a\u4e49\u5f0f\u4e3a \\(N=\\frac{f}{D}\\)\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec02/#\u5bf9\u7126","title":"\u5bf9\u7126","text":"<p>Source: https://fpcv.cs.columbia.edu/</p> <p>\u7531\u76f8\u4f3c\u4e09\u89d2\u5f62\uff0c\u6ca1\u6709\u5bf9\u4e0a\u7126\u800c\u5f62\u6210\u7684\u5149\u6591(Blur Circle)\u7684\u8ba1\u7b97\u516c\u5f0f\u4e3a\uff1a</p> \\[ \\begin{align}     &amp;\\because \\frac{b}{D}=frac{|i'-i|}{i'} \\\\     &amp;\\therefore b = \\frac{D}{i'}|i'-i|\\;,\\;\\;\\;b \\propto D \\propto \\frac{1}{N} \\end{align} \\] <p>\u800c\u5bf9\u7126\uff0c\u5c31\u662f\u5c06\u5931\u7126\u7684\u5185\u5bb9\u91cd\u65b0\u6c47\u805a\u5230\u5e95\u7247\u4e0a\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec02/#\u666f\u6df1-dof","title":"\u666f\u6df1 DoF","text":"<p>\u6839\u636e\u4e0a\u4e00\u5c0f\u8282\u5f97\u5230\u7684\u7ed3\u8bba\uff0c\u7406\u8bba\u4e0a\u6211\u4eec\u597d\u50cf\u53ea\u6709\u6e05\u6670\u6210\u50cf\u4e00\u4e2a\u7279\u5b9a\u5e73\u9762\u4e0a\u7684\u5185\u5bb9\uff0c\u4f46\u662f\u5b9e\u9645\u4e0a\u76f8\u673a\u4e0a\u4f1a\u6709\u4e00\u6bb5\u8ddd\u79bb\u4e0a\u7684\u5185\u5bb9\u90fd\u662f\u6e05\u6670\u7684\uff0c\u8fd9\u6bb5\u8ddd\u79bb\u5c31\u662f\u666f\u6df1 DoF(Depth of Field)\u3002\u800c\u4e4b\u6240\u4ee5\u6709\u666f\u6df1\uff0c\u662f\u56e0\u4e3a\u5e95\u7247\u7684\u611f\u5149\u5143\u4ef6\u662f\u6709\u6781\u9650\u7684\uff0c\u5f53\u5149\u6591\u5c0f\u96e8\u8fd9\u4e2a\u6781\u9650\u65f6\uff0c\u62cd\u6444\u51fa\u6765\u7684\u5c31\u4ecd\u7136\u662f\u6e05\u6670\u7684\u3002</p> <p>\u800c\u666f\u6df1\u7684\u5927\u5c0f\u53ef\u4ee5\u8fd9\u4e48\u8ba1\u7b97\uff1a</p> <p></p> <p>\u6211\u4eec\u53ef\u4ee5\u53d1\u73b0\uff0c\u666f\u6df1\u7684\u5927\u5c0f \u5927\u81f4\u4e0e \u5149\u5708\u5927\u5c0f\u3001\u7269\u50cf \u6b63\u76f8\u5173\uff0c\u4e0e \u7126\u8ddd \u8d1f\u76f8\u5173\u3002</p> <p>\u5f15\u8a00</p> <p>\u7531\u4e8e\u6211\u4eec\u8003\u8651\u7684\u662f\u6210\u50cf\u95ee\u9898\uff0c\u6240\u4ee5\u66f4\u591a\u7684\u662f\u5728\u63cf\u8ff0\u4e09\u7ef4\u771f\u5b9e\u4fe1\u606f\u4e0e\u4e8c\u7ef4\u5e73\u9762\u4fe1\u606f\u4e4b\u95f4\u7684\u4e92\u76f8\u8868\u8fbe\u3002</p> <p>\u800c\u8fd9\u79cd\u201c\u63cf\u8ff0\u201d\u9700\u8981\u57fa\u4e8e\u4e00\u4e2a\u6295\u5f71\u6a21\u578b\u3002\u6216\u8005\u8bf4\u8bf4\u4e00\u79cd\u6620\u5c04\u5173\u7cfb\uff0c\u7b80\u5355\u6765\u8bf4\u5c31\u597d\u50cf\u201c\u70b9\u5149\u6e90\u6295\u5f71\u201d\u548c\u201c\u5e73\u884c\u5149\u6e90\u6295\u5f71\u201d\u3002</p> <p>\u4f46\u662f\u9700\u8981\u6ce8\u610f\uff0c\u65e0\u8bba\u662f\u54ea\u4e00\u79cd\u6a21\u578b\uff0c\u7531\u4e8e\u6211\u4eec\u5c06\u4e09\u7ef4\u4fe1\u606f\u901a\u8fc7\u4e0d\u53ef\u9006\u7684\u7ebf\u6027\u53d8\u6362\u538b\u7f29\u5230\u4e86\u4e8c\u7ef4\u4fe1\u606f\uff0c\u6240\u4ee5\u4e00\u5b9a\u662f\u5b58\u5728\u4fe1\u606f\u7f3a\u5931\u7684\u3002\u901a\u5e38\u6765\u8bf4\uff0c\u6307\u7684\u662f\u6df1\u5ea6\u7f3a\u5931\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec02/#\u900f\u89c6\u6295\u5f71","title":"\u900f\u89c6\u6295\u5f71","text":"<p>\u5982\u56fe\u662f 3D \u5750\u6807\u901a\u8fc7\u900f\u89c6\u6295\u5f71\u5230 2D \u5750\u6807\u5230\u793a\u610f\u56fe\u3002\u5176\u4e2d \\(x,y,Z\\) \u7528\u6765\u63cf\u8ff0\u7a7a\u95f4\u5750\u6807\u4fe1\u606f\uff0c\u65b9\u4fbf\u8d77\u89c1\uff0c\u6211\u4eec\u7528\u4ed6\u4eec\u8868\u793a\u76f8\u5bf9\u4e8e\u76f8\u673a\u4e2d\u5fc3(camera center)\u7684\u6b63\u4ea4\u5750\u6807\uff0c\u5176\u4e2d \\(Z\\) \u548c\u5149\u8f74(optical axis)\u65b9\u5411\u76f8\u540c\uff0c\u6211\u4eec\u4e5f\u53ef\u4ee5\u79f0\u4e4b\u4e3a\u6df1\u5ea6\u3002</p> <p>\u540c\u65f6\uff0c\u5149\u8f74\u5e94\u5f53\u5782\u76f4\u4e8e\u6210\u50cf\u5e73\u9762\uff0c\u800c\u5149\u8f74\u4e0e\u6210\u50cf\u5e73\u9762\u7684\u4ea4\u70b9\u4e3a\u56fe\u50cf\u4e2d\u5fc3(img center)\u3002</p> <p>\u53ef\u4ee5\u53d1\u73b0\uff0c\\(P\\) \u4e0e \\(p\\) \u7684\u5173\u7cfb\u5982\u4e0b\uff1a</p> \\[ p =  \\begin{bmatrix}     u \\\\     v \\end{bmatrix} = \\begin{bmatrix}     \\frac{f}{Z}\\cdot x \\\\     \\frac{f}{Z}\\cdot y \\end{bmatrix} \\] <p>\u90a3\u6709\u6ca1\u6709\u529e\u6cd5\u5c06 \\(p\\) \u548c \\(P\\) \u901a\u8fc7\u7ebf\u6027\u53d8\u5316\u653e\u5728\u540c\u4e00\u4e2a\u7b49\u5f0f\u91cc\u5462\uff1f</p> <p>\u6362\u53e5\u8bdd\u6765\u8bf4\uff0c\u6709\u6ca1\u6709\u529e\u6cd5\u4f7f\u5f97\u5982\u4e0b\u7b49\u5f0f\u6210\u7acb\uff1f</p> \\[ A \\begin{bmatrix}     x \\\\     y \\\\     z \\end{bmatrix} \\overset{?}= \\begin{bmatrix}     \\frac{f}{Z}\\cdot x \\\\     \\frac{f}{Z}\\cdot y \\end{bmatrix} \\] <p>\u5f88\u53ef\u60dc\uff0c\u7531\u4e8e\u5f0f\u5b50\u4e2d\u51fa\u73b0\u4e86 \\(\\frac{1}{Z}\\)\uff0c\u5373\u9664\u6cd5\uff0c\u5b83\u5e76\u4e0d\u662f\u4e2a\u7ebf\u6027\u53d8\u6362\u3002\u6240\u4ee5\u5373\u4f7f\u6211\u4eec\u6269\u5c55 \\(p\\) \u548c \\(P\\) \u7684\u7ef4\u5ea6\u6211\u4eec\u6ca1\u6cd5\u76f4\u63a5\u5c06\u5b83\u53d8\u6210\u7ebf\u6027\u53d8\u6362\u3002</p> <p>\u4f46\u662f\u4f60\u4e5f\u770b\u5230\u4e86\uff0c\u6211\u7528\u7684\u8bcd\u662f\u201c\u76f4\u63a5\u201d\uff0c\u6240\u4ee5\u6211\u4eec\u63a5\u4e0b\u6765\u53ef\u4ee5\uff1a</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec02/#\u5e94\u7528\u9f50\u6b21\u5750\u6807","title":"\u5e94\u7528\u9f50\u6b21\u5750\u6807","text":"<p>\u8ba9\u6211\u4eec\u56de\u987e\u9f50\u6b21\u5750\u6807\u7684 \u6269\u5c55\u6027\u8d28\uff0c\u5c06\u5b83\u5e94\u7528\u4e8e\u6b64\u5f0f\uff1a</p> \\[ \\begin{bmatrix}     \\frac{f}{Z}\\cdot x \\\\     \\frac{f}{Z}\\cdot y \\\\     1 \\end{bmatrix} \\cong \\begin{bmatrix}     f \\cdot x \\\\     f \\cdot y \\\\     Z \\end{bmatrix} \\] <p>\u4e8e\u662f\u6211\u4eec\u53d1\u73b0\uff0c\u867d\u7136\u6211\u4eec\u6ca1\u6cd5\u627e\u5230 \\(A\\) \u4f7f\u5f97\uff1a</p> \\[ A \\begin{bmatrix}     x \\\\     y \\\\     Z \\\\     1 \\end{bmatrix} \\overset{?}= \\begin{bmatrix}     \\frac{f}{Z}\\cdot x \\\\     \\frac{f}{Z}\\cdot y \\\\     1 \\end{bmatrix} \\] <p>\u6210\u7acb\uff0c\u4f46\u662f\u6211\u4eec\u53ef\u4ee5\u627e\u5230 \\(A=\\begin{bmatrix}f &amp; 0 &amp; 0 &amp; 0 \\\\ 0 &amp; f &amp; 0 &amp; 0 \\\\ 0 &amp; 0 &amp; 1 &amp; 0\\end{bmatrix}\\) \u4f7f\u5f97\uff1a</p> \\[ \\begin{bmatrix}     f &amp; 0 &amp; 0 &amp; 0 \\\\      0 &amp; f &amp; 0 &amp; 0 \\\\      0 &amp; 0 &amp; 1 &amp; 0 \\end{bmatrix} \\begin{bmatrix}     x \\\\     y \\\\     Z \\\\     1 \\end{bmatrix} = \\begin{bmatrix}     f \\cdot x \\\\     f \\cdot y \\\\     Z \\end{bmatrix} \\cong \\begin{bmatrix}     \\frac{f}{Z}\\cdot x \\\\     \\frac{f}{Z}\\cdot y \\\\     1 \\end{bmatrix} \\] <p>\u4e8e\u662f\uff0c\u6211\u4eec\u5c31\u6210\u529f\u7684\u901a\u8fc7\u7ebf\u6027\u53d8\u6362\u5c06 \\(P\\) \u548c \\(p\\) \u7edf\u4e00\u4e86\u8d77\u6765\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec02/#\u53ef\u89c6\u5316\u8868\u793a","title":"\u53ef\u89c6\u5316\u8868\u793a","text":"<p>\u6211\u4eec\u53ef\u4ee5\u53d1\u73b0\uff0c\u5c0f\u5b54\u6210\u50cf\u7684\u6a21\u578b\u89c6\u56fe\u5176\u5b9e\u8fd8\u662f\u6bd4\u8f83\u9ebb\u70e6\u7684\u3002\u73b0\u5728\u6211\u4eec\u628a\u8fd9\u4e2a\u5b9a\u89d2\u76f8\u4f3c\u5bf9\u6298\uff0c\u53d8\u6210 A \u5b57\u578b\u76f8\u4f3c\u6765\u8868\u793a\u8fd9\u4e2a\u6a21\u578b\uff0c\u4ee5\u7b80\u5316\u4e0d\u5fc5\u8981\u7684\u4fe1\u606f\uff0c\u540c\u65f6\u4e5f\u80fd\u66f4\u6e05\u6670\u5730\u8868\u793a\u900f\u89c6\u5173\u7cfb\u3002</p> <p>\u89c4\u5b9a\u6211\u4eec\u8ba8\u8bba\u7684\u95ee\u9898\u4e2d\u7269\u8ddd\u603b\u662f\u5927\u4e8e\u50cf\u8ddd\uff0c\u5219\u53ef\u4ee5\u5c06\u50cf\u8868\u793a\u4e3a\u76f8\u673a\u4e2d\u5fc3\u5230\u7269\u4f53\u7684\u653e\u5c04\u8fde\u7ebf\u4e2d\u7684\u622a\u9762\u3002</p> <p>\u5b83\u6bd4\u8f83\u597d\u5730\u8868\u8fbe\u4e86\u900f\u89c6\u5173\u7cfb\uff0c\u5373 \u76f8\u673a\u4e2d\u5fc3 \u7269\u70b9B \u50cf\u70b9B' \u59cb\u7ec8\u5171\u7ebf\u3002\u8fd9\u4e5f\u662f\u5728\u4e4b\u540e\u7684\u5185\u5bb9\u4e2d\u66f4\u52a0\u5e38\u89c1\u7684\u53ef\u89c6\u5316\u8868\u73b0\u65b9\u6cd5\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec02/#\u4fe1\u606f\u7f3a\u5931","title":"\u4fe1\u606f\u7f3a\u5931","text":"<p>\u7531\u4e8e\u5728\u900f\u89c6\u6295\u5f71\u7cfb\u7edf\u4e2d\uff0c\u7269\u4f53\u7684\u771f\u5b9e\u7ebf\u5ea6\u5927\u5c0f\u4e0e\u56fe\u50cf\u7ebf\u5ea6\u5927\u5c0f\u7684\u6bd4\u4f8b\u7531\u6df1\u5ea6\u51b3\u5b9a\uff0c\u4f46\u6df1\u5ea6\u53c8\u4e0d\u80fd\u76f4\u63a5\u4ece\u56fe\u4e2d\u83b7\u53d6\uff0c\u6240\u4ee5\u6709\u65f6\u5019\u6211\u4eec\u65e0\u6cd5\u6bd4\u8f83\u56fe\u50cf\u4e2d\u4e24\u4e2a\u7269\u4f53\u7684\u771f\u5b9e\u7ebf\u5ea6\u5dee\u3002\u6362\u53e5\u8bdd\u6765\u8bf4\uff0c\u957f\u5ea6\u4fe1\u606f\u548c\u89d2\u5ea6\u4fe1\u606f\u662f\u4e22\u5931\u7684\u3002</p> <p>\uff08\u591a\u6570\u60c5\u51b5\u4e0b\uff0c\u6211\u4eec\u9700\u8981\u4ee5\u4e00\u4e9b\u4e1c\u897f\u6765\u505a\u53c2\u8003\u7cfb\uff0c\u5224\u65ad A \u548c B \u7684\u6df1\u5ea6\u4fe1\u606f\uff0c\u518d\u5206\u6790\u4ed6\u4eec\u7684\u5b9e\u9645\u7ebf\u5ea6\u5927\u5c0f\u5173\u7cfb\u3002\uff09</p> <p>\u7136\u800c\u4ecd\u7136\u6709\u4e9b\u6027\u8d28\u662f\u4fdd\u7559\u7684\uff0c\u4f8b\u5982\u76f4\u7ebf\u4ecd\u7136\u662f\u76f4\u7ebf\uff0c\u4f46\u662f\u5b9e\u9645\u4e0a\uff0c\u5982\u679c\u4f60\u80fd\u60f3\u8c61\u7684\u8bdd\uff0c\u867d\u7136\u76f4\u7ebf\u4ecd\u7136\u662f\u76f4\u7ebf\uff0c\u4f46\u662f\u5b83\u7684\u201c\u7ebf\u5bc6\u5ea6\u201d\u4e0d\u4e00\u6837\u4e86\u3002</p> <p>\u6240\u4ee5\uff0c\u5982\u679c\u662f\u66f2\u7ebf\uff0c\u5b83\u867d\u7136\u4e0d\u4f1a\u53d8\u6210\u6298\u7ebf\uff0c\u4f46\u662f\u7279\u5f81\u53ef\u80fd\u5df2\u7ecf\u53d8\u4e86\uff0c\u6bd4\u5982\u5706\u662f\u4f1a\u626d\u66f2\u7684\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec02/#\u706d\u70b9\u4e0e\u706d\u7ebf","title":"\u706d\u70b9\u4e0e\u706d\u7ebf","text":"<p>\u5728\u900f\u89c6\u4e2d\u4e00\u4e2a\u5f88\u6709\u610f\u601d\u7684\u73b0\u8c61\u662f\u706d\u70b9(vanishing point)\u548c\u706d\u7ebf(vanishing line)\u3002</p> <p></p> <p>\u53ef\u4ee5\u53d1\u73b0\uff0c\u5728\u56fe\u50cf\u4e2d\u4e00\u6761\u4e0d\u65ad\u884d\u751f\u7684\u76f4\u7ebf\uff0c\u5728\u50cf\u4e2d\u6700\u7ec8\u4f1a\u7ec8\u7ed3\u4e8e\u4e00\u4e2a\u70b9\uff0c\u8fd9\u4e2a\u70b9\u5c31\u662f\u201c\u706d\u70b9\u201d\u3002\u51e0\u4f55\u4e0a\uff0c\u706d\u70b9\u4e0e\u76f8\u673a\u4e2d\u5fc3\u7684\u8fde\u7ebf\u5e94\u5f53\u5e73\u884c\u4e8e\u8be5\u76f4\u7ebf\u3002</p> <p>\u800c\u73b0\u5b9e\u4e2d\u76f8\u4e92\u5e73\u884c\u7684\u4e24\u6761\u76f4\u7ebf\uff0c\u6700\u7ec8\u4f1a\u5728\u56fe\u50cf\u4e2d\u7ec8\u6b62\u4e8e\u540c\u4e00\u4e2a\u706d\u70b9\u3002</p> <p>\u706d\u70b9\u672a\u5fc5\u5728\u56fe\u50cf\u4e2d\uff0c\u751a\u81f3\u53ef\u80fd\u65e0\u9650\u8fdc\u3002</p> <p> </p> <p></p> <p>\u521a\u624d\u63d0\u5230\uff0c\u5e73\u884c\u7ebf\u5171\u4eab\u706d\u70b9\u8fd9\u610f\u5473\u7740\u6709\u591a\u5c11\u7ec4\u5e73\u884c\u7ebf\u5c31\u6709\u591a\u5c11\u706d\u70b9\u3002</p> <p>\u5982\u679c\u6211\u4eec\u5c06\u4e00\u4e2a\u5e73\u9762\u50cf\u68cb\u76d8\u90a3\u6837\uff0c\u5212\u51fa\u4e24\u7ec4\u5e73\u884c\u7ebf\uff0c\u90a3\u4e48\u5c31\u4f1a\u5f97\u5230\u4e24\u4e2a\u706d\u70b9\uff0c\u5982\u56fe\u4e2d\u7684 \\(v_1\\) \u548c \\(v_2\\)\u3002\u8fd9\u610f\u5473\u7740\uff0c\u5bf9\u4e8e\u4e00\u4e2a\u5e73\u9762\uff0c\u6211\u4eec\u53ef\u4ee5\u4ece\u4e2d\u53d6\u51fa\u65e0\u6570\u7ec4\u5e73\u884c\u7ebf\uff0c\u56e0\u800c\u65e0\u9650\u5927\u7684\u5e73\u9762\u4f1a\u4ea7\u751f\u65e0\u6570\u591a\u7684\u706d\u70b9\uff0c\u800c\u8fd9\u4e9b\u706d\u70b9\u8fde\u6210\u7ebf\u5c31\u6210\u4e86\u201c\u706d\u7ebf\u201d\u3002\u5e38\u89c1\u7684\u706d\u7ebf\u5c31\u6bd4\u5982\u7167\u7247\u4e0a\u7684\u6d77\u5929\u754c\u7ebf\u3002</p> <p>\u56e0\u6b64\uff0c\u5982\u679c\u8bf4\u706d\u70b9\u8c61\u5f81\u4e86\u4e00\u7ec4\u5e73\u884c\u7ebf\uff0c\u90a3\u706d\u7ebf\u5c31\u662f\u8c61\u5f81\u4e86\u4e00\u5757\u5e73\u9762\u3002\u800c\u6211\u4eec\u5c31\u53ef\u4ee5\u901a\u8fc7\u770b\u5e73\u9762\u4e0a\u7684\u5185\u5bb9\u51fa\u73b0\u5728\u706d\u7ebf\u4ee5\u4e0a\u8fd8\u662f\u706d\u7ebf\u4e00\u4e0b\uff0c\u6765\u5224\u65ad\u5e73\u9762\u5728\u6211\u4eec\u7684\u76f8\u673a\u4e2d\u5fc3\u4ee5\u4e0b\u8fd8\u662f\u4ee5\u4e0a\uff08\u53ef\u4ee5\u601d\u8003\u4e00\u4e0b\u4e3a\u4ec0\u4e48\uff09\u3002</p> <p>Interesting Try</p> \u9898\u9762\u7b54\u6848 <p>\u89c2\u5bdf\u5982\u4e0b\u56fe\u7247\uff0c\u5224\u65ad \ud83e\ude82(\u8df3\u4f1e\u8005) \u5728 \ud83d\udcf7 \u4ee5\u4e0a\u8fd8\u662f\u4ee5\u4e0b\uff0c\u5e76\u9610\u660e\u7406\u7531\u3002</p> <p></p> <p>\u663e\u7136\uff0c\ud83e\ude82(\u8df3\u4f1e\u8005) \u5728 \ud83d\udcf7 \u4ee5\u4e0b\uff08\u4f1e\u5728\u4ee5\u4e0a\uff09\uff0c\u4f9d\u636e\u662f \u4eba \u5728 \u5929\u9645\u7ebf \u4ee5\u4e0b\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec02/#\u900f\u89c6\u7578\u53d8","title":"\u900f\u89c6\u7578\u53d8","text":"<p>\u5728\u62cd\u6444\u8f83\u5927\u7684\u7269\u4f53\u65f6\uff0c\u6bd4\u5982\u5efa\u7b51\u7269\uff0c\u5982\u679c\u5efa\u7b51\u7269\u7684\u5899\u9762\u6ca1\u6709\u548c\u5e95\u7247\u5e73\u884c\uff0c\u5219\u4f1a\u51fa\u73b0\u900f\u89c6\u7578\u53d8\u3002</p> <p>\u5728\u5efa\u7b51\u62cd\u6444\u65b9\u9762\uff0c\u6211\u4eec\u7684\u89e3\u51b3\u529e\u6cd5\u662f\u4e0b\u79fb\u4f20\u611f\u5668\uff0c\u4f7f\u5e95\u7247\u4e2d\u5fc3\u5728\u5149\u8f74\u4ea4\u70b9\u4ee5\u4e0b\uff0c\u8fd9\u79cd\u955c\u5934\u79f0\u4e3a\u79fb\u8f74\u955c\u5934\u3002</p> <p>\u53e6\u5916\u4e00\u79cd\u900f\u89c6\u7578\u53d8\u4f53\u73b0\u5728\u66f2\u7ebf\u7684\u5f62\u53d8\u4e0a\uff0c\u4e5f\u5c31\u662f\u6211\u4eec\u5e38\u611f\u53d7\u5230\u7684\uff0c\u7ad9\u5728\u8fb9\u4e0a\u7684\u4eba\u8138\u603b\u662f\u66f4\u5927\u4e00\u70b9\u3002\u800c\u8fd9\u79cd\u7578\u53d8\u5728\u65ad\u955c\u5934\u4e0b\u66f4\u5e38\u89c1\uff0c\u6240\u4ee5\u4eba\u50cf\u66f4\u591a\u7528\u7684\u662f\u957f\u7126\u955c\u5934\uff08\u5176\u4e00\u539f\u56e0\uff0c\u5176\u4ed6\u7684\u8fd8\u6709 FoV \u5c0f\u6240\u4ee5\u80cc\u666f\u66f4\u5e72\u51c0\u7b49\uff09\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec02/#\u6795\u578b\u7578\u53d8\u548c\u6876\u578b\u7578\u53d8","title":"\u6795\u578b\u7578\u53d8\u548c\u6876\u578b\u7578\u53d8","text":"\\[ \\begin{align} r^2 &amp; = {x'}_n^2 + {y'}_n^2 \\\\ {x'}_d &amp; = {x'}_n(1 + \\kappa_1 r^2 + \\kappa_2 r^4) \\\\ {y'}_d &amp; = {y'}_n(1 + \\kappa_1 r^2 + \\kappa_2 r^4) \\\\ \\end{align} \\] <p>\u800c\u8fd9\u79cd\u7167\u7247\u7684\u7ea0\u6b63\u529e\u6cd5\u5c31\u662f\u5bfb\u627e\u7167\u7247\u4e2d\u7684\u683c\u70b9\uff0c\u7136\u540e\u901a\u8fc7\u6570\u5b66\u65b9\u6cd5\u6765\u8fd8\u539f\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec02/#\u6b63\u4ea4\u6295\u5f71","title":"\u6b63\u4ea4\u6295\u5f71","text":"<p>\u6b63\u4ea4\u6295\u5f71\u7684\u542b\u4e49\u5c31\u662f\uff0c\u76f4\u63a5\u62b9\u6389\u6df1\u5ea6\u4fe1\u606f\uff0c\u4e09\u7ef4\u70b9 \\(P\\) \u5230\u4e8c\u7ef4\u70b9 \\(p\\) \u7684\u6620\u5c04\u89c4\u5219\u5982\u4e0b\uff1a</p> \\[ \\begin{bmatrix}     1 &amp; 0 &amp; 0 \\\\     0 &amp; 1 &amp; 0  \\end{bmatrix} \\begin{bmatrix}     x \\\\     y \\\\     z \\end{bmatrix} = \\begin{bmatrix}     x \\\\     y  \\end{bmatrix} \\] <p>\u4e5f\u5c31\u662f\u5e73\u884c\u5149\u6e90\u6295\u5f71\u3002</p> <p>\u8fd9\u79cd\u6295\u5f71\u53ef\u80fd\u4e0d\u592a\u62df\u771f\uff0c\u4f46\u662f\u5728\u67d0\u4e9b\u4e0d\u8981\u6c42\u7cbe\u5ea6\u7684\u60c5\u51b5\u4e0b\u6211\u4eec\u603b\u662f\u4e50\u4e8e\u4f7f\u7528\u7684\u3002</p> <p>\u8fd9\u6837\u8bf4\u53ef\u80fd\u6bd4\u8f83\u62bd\u8c61\uff0c\u4f46\u662f\u5b83\u5176\u5b9e\u5f88\u5e38\u89c1\uff0c\u6bd4\u5982\u5728\u4e00\u4e9b\u4ee5\u201c\u4e0a\u5e1d\u89c6\u89d2\u201d\u5c55\u5f00\u7684\u6e38\u620f\u4e2d\uff0c\u4f8b\u5982\u201c\u5f00\u7f57\u6e38\u620f\u201d\u3001\u201c\u6a21\u62df\u90fd\u5e02\u201d\u8fd9\u79cd\uff0c\u91c7\u7528\u7684\u57fa\u672c\u90fd\u662f\u8fd9\u79cd\u6295\u5f71\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec02/#\u5feb\u95e8shutter","title":"\u5feb\u95e8(Shutter)","text":"<ul> <li>\u66dd\u5149\u65f6\u95f4(shutter speed)</li> <li>\u957f\u66dd\u5149\u65f6\u95f4\u62cd\u6444\u95ea\u7535\u7b49\uff1b</li> <li>\u6eda\u52a8\u5feb\u95e8\u6548\u5e94(rolling shutter effect)</li> <li>\u7528\u6eda\u52a8\u5feb\u95e8\u62cd\u6444\u4f8b\u5982\u98ce\u6247\u65f6\uff0c\u4f1a\u51fa\u73b0\u4e00\u4e9b\u56fe\u50cf\u53d8\u5f62\uff1b</li> </ul>"},{"location":"cour_note/D2QD_Intro2CV/Lec02/#\u5149\u5ea6\u56fe\u50cf\u751f\u6210\u4e0e\u7740\u8272","title":"\u5149\u5ea6\u56fe\u50cf\u751f\u6210\u4e0e\u7740\u8272","text":"<p>\u5149\u5ea6\u56fe\u50cf\u751f\u6210\u8003\u8651\u7684\u4e3b\u8981\u662f\u5149\u5f3a\u548c\u989c\u8272\u4e24\u4e2a\u65b9\u9762\u7684\u95ee\u9898\u3002</p> <p>\u786c\u4ef6\u4e0a\uff0c\u5b83\u4eec\u90fd\u901a\u8fc7\u56fe\u50cf\u4f20\u611f\u5668(img sensor)\u5b9e\u73b0\u3002</p> <ul> <li>\u4e3b\u8981\u5206\u4e3a CMOS(Complimentary Metal-Oxide Semiconductor) \u548c CCD(Charge Coupled Device) \u4e24\u79cd\uff0c\u533a\u522b\u5728\u4e8e Electron to Voltage Conversion \u662f\u5426\u516c\u7528\uff1b</li> </ul> <p>\u5f15\u5165</p> <p>\u7740\u8272(shading)\u4e2d\u6240\u8bf4\u7684\u5149\u5f3a\uff0c\u4e3b\u8981\u6709\u4e24\u4e2a\u65b9\u9762\uff1a\u4e00\u65b9\u9762\u4e0e\u8ddd\u79bb\u5149\u6e90\u7684\u8ddd\u79bb\u6709\u5173\uff0c\u7406\u60f3\u60c5\u51b5\u4e0b\u7b26\u5408\u5e73\u65b9\u53cd\u6bd4\u5b9a\u5f8b\uff0c\u8fd9\u79cd\u7279\u5f81\u6211\u4eec\u79f0\u4e4b\u4e3a Light Falloff\uff1b\u53e6\u4e00\u65b9\u9762\u5b9e\u9645\u4e0a\u662f\u9700\u8981\u6211\u4eec\u8ba1\u7b97\u5149\u7684\u53cd\u5c04\u884c\u4e3a\u3002</p> <p>\u7406\u8bba\u4e0a\uff0c\u6211\u4eec\u4f1a\u9700\u8981\u53cc\u5411\u53cd\u5c04\u5206\u5e03\u51fd\u6570 BRDF(Bidirectional Reflectance Distribution Function)\u6765\u8ba1\u7b97\uff0cBRDF \u7684\u8f93\u5165\u5927\u81f4\u53ef\u4ee5\u5206\u4e3a\u5982\u4e0b\u51e0\u4e2a\uff1a</p> <ul> <li>\u89c2\u6d4b\u89d2\u5ea6(viewer direction)\uff1a\\(\\vec v\\)</li> <li>\u8868\u9762\u6cd5\u5411\u91cf(surface normal)\uff1a\\(\\vec n\\)</li> <li>\u5165\u5c04\u5149\u65b9\u5411(light direction)\uff1a \\(\\vec l\\)</li> <li>\u663e\u7136\uff0c\u5bf9\u4e8e\u6bcf\u4e00\u6761\u5149\u7ebf\u90fd\u9700\u8981\u7ed9\u51fa\uff1b</li> <li>\u8868\u9762\u6750\u8d28(surface parameters)</li> </ul> <p>\u53ef\u4ee5\u53d1\u73b0\uff0c\u9700\u8981\u5efa\u7acb\u8fd9\u6837\u4e00\u4e2a\u6a21\u578b\u662f\u5f88\u56f0\u96be\u7684\uff0c\u4e14\u8fd9\u4e2a\u6a21\u578b\u4e0d\u5e38\u7528\uff0c\u800c\u4e14\u8ba1\u7b97\u8d77\u6765\u6bd4\u8f83\u9ebb\u70e6\u3002</p> <p>\u53cd\u5c04\u4e3b\u8981\u53ef\u4ee5\u5f52\u7eb3\u4e3a\u4e24\u79cd\u7b80\u5355\u6a21\u578b\u548c\u4e00\u79cd\u6df7\u5408\u6a21\u578b\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec02/#\u6f2b\u53cd\u5c04","title":"\u6f2b\u53cd\u5c04","text":"<p>\u6f2b\u53cd\u5c04(diffuse reflection) \u53c8\u53eb \u6717\u4f2f\u53cd\u5c04(Lambertian reflection)\uff0c\u662f\u8868\u73b0\u5728\u7c97\u7cd9\u8868\u9762\u4e0a\u7684\u53cd\u5c04\u7279\u5f81\uff0c\u56e0\u4e3a\u6211\u4eec\u9ed8\u8ba4\u5b83\u5411\u56db\u9762\u516b\u65b9\u53cd\u5c04\u7684\u5149\u5f3a\u90fd\u4e00\u6837\uff0c\u6240\u4ee5\u5b83\u7684\u8ba1\u7b97\u76f8\u5bf9\u6bd4\u8f83\u7b80\u5355\uff08Shading independent of view direction\uff09\uff1a</p> \\[ L_d = k_d \\cdot \\frac{I}{r^2} \\cdot \\max(0,n\\cdot l) \\] <p>\u5bf9\u6210\u5206\u505a\u89e3\u91ca\uff1a</p> <ul> <li>\\(L_d\\) \u4e3a\u6f2b\u53cd\u5c04\u5149\u5f3a(diffusely reflected light)\uff1b</li> <li>\\(k_d\\) \u4e3a\u6f2b\u53d1\u5c04\u7cfb\u6570(diffuse coefficient)\uff0c\u5982\u989c\u8272\uff1b</li> <li>\\(\\frac{I}{r^2}\\) \u4e3a \u5230\u8fbe\u7740\u8272\u70b9\u7684\u5149\u5f3a\uff1b</li> <li>\\(\\max(0,n \\cdot l)\\) \u4e3a \u7740\u8272\u70b9\u5438\u6536\u7684\u5149\u5f3a\uff1b</li> </ul> \u5982\u4f55\u7406\u89e3\u5149\u5f3a\u5ea6\u4e0e\u89d2\u5ea6\u7684\u5173\u7cfb <p>\u4e00\u5f00\u59cb\u6ca1\u4ed4\u7ec6\u60f3\u7684\u65f6\u5019\u8fd8\u89c9\u5f97\u5f88\u81ea\u7136\uff0c\u4f46\u662f\u4ed4\u7ec6\u4e00\u60f3\u4e3a\u4ec0\u4e48\u80fd\u8fd9\u6837\u8868\u8ff0\uff1f\u4e8e\u662f\u548c\u540c\u5b66\u63a2\u8ba8\u4e86\u4e00\u4e0b\uff0c\u611f\u89c9\u4e00\u4e2a\u53ef\u4ee5\u63a5\u53d7\u7684\u89e3\u91ca\u662f\u8fd9\u6837\u7684\uff1a</p> <p>\u9996\u5148\uff0c\u8fd9\u91cc\u4e0e\u5176\u8bf4\u4e0e\u89d2\u5ea6\u76f8\u5173\uff0c\u4e0d\u5982\u8bf4\u4e0e\u5355\u4f4d\u9762\u79ef\u53d7\u5230\u7684\u5149\u7167\u5f3a\u5ea6\u6709\u5173\u3002\u6362\u53e5\u8bdd\u6765\u8bf4\uff0c\u5bf9\u4e8e\u540c\u4e00\u675f\u5149\uff0c\u503e\u659c\u7684\u9762\u4e0a\u4f1a\u6709\u66f4\u5927\u7684\u9762\u79ef\u88ab\u7167\u5c04\u5230\uff0c\u5747\u644a\u4e0b\u6765\u5355\u4f4d\u9762\u79ef\u4e0a\u7684\u5149\u5f3a\u5ea6\u5c31\u5c0f\uff0c\u6216\u8bb8\u53ef\u4ee5\u5c06\u5b83\u7406\u89e3\u6210\u7c7b\u4f3c\u4e8e\u201c\u5bc6\u5ea6\u201d\u7684\u6982\u5ff5\u3002</p> <p>\u5e26\u7740\u8fd9\u6837\u7684\u60f3\u6cd5\uff0c\u518d\u6765\u770b\u8fd9\u5f20\u56fe\uff0c\u5c31\u6bd4\u8f83\u6e05\u6670\u4e86\u3002</p> <p></p> <p>Source: https://sites.cs.ucsb.edu/~lingqi/teaching/games101.html</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec02/#\u9ad8\u5149\u53cd\u5c04","title":"\u9ad8\u5149\u53cd\u5c04","text":"<p>\u9ad8\u5149\u53cd\u5c04(specular reflection) \u7c7b\u4f3c\u6211\u4eec\u8ba4\u77e5\u4e2d\u7684\u955c\u9762\u53cd\u5c04\uff0c\u5b83\u7684\u7279\u5f81\u662f\u57fa\u672c\u7b26\u5408\u955c\u53cd\u5c04\u7684\u89c4\u5f8b\u3002</p> <p>\u5728\u9ad8\u5149\u53cd\u5c04\u4e2d\uff0c\u6211\u4eec\u9700\u8981\u5b9a\u4e49\u534a\u7a0b\u5411\u91cf(half vec)\\(\\vec h = bisector(\\vec v,\\vec l) = \\frac{\\vec v + \\vec l}{||\\vec v + \\vec l||}\\) </p> <p>\u5f53 \\(\\vec h\\) \u4e0e \\(\\vec n\\) \u975e\u5e38\u63a5\u8fd1\u65f6\uff0c\u5373 \\(\\alpha = &lt;\\vec n, \\vec h&gt;\\) \u5f88\u5c0f\u65f6\uff0c\u6211\u4eec\u79f0\u4e4b\u7b26\u5408\u9ad8\u5149\u53cd\u5c04\u3002</p> <p>\u9ad8\u5149\u53cd\u5c04\u7684\u5f3a\u5ea6\u516c\u5f0f\u5927\u81f4\u5982\u4e0b\uff1a</p> \\[ L_s = k_s \\cdot \\frac{I}{r^2} \\cdot \\max(0, \\cos\\alpha)^p=k_s \\cdot \\frac{I}{r^2} \\cdot \\max(0, \\vec n \\cdot \\vec h)^p \\] <p>\u5bf9\u6210\u5206\u505a\u89e3\u91ca\uff1a</p> <ul> <li>\\(L_s\\) \u4e3a\u9ad8\u5149\u53cd\u5c04\u5149\u5f3a(specularly reflected light)\uff1b</li> <li>\\(k_s\\) \u4e3a\u9ad8\u5149\u53d1\u5c04\u7cfb\u6570(specular coefficient)\uff1b</li> </ul> <p>\u5206\u6790\u53ef\u5f97\uff0c\\(p\\) \u8d8a\u5927\uff0c\u9ad8\u5149\u8d8a\u96c6\u4e2d\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec02/#blinn-phong-\u53cd\u5c04","title":"Blinn-Phong \u53cd\u5c04","text":"<p>Blinn-Phong \u53cd\u5c04\u6a21\u578b(Blinn-Phong Reflection Model)\u53ef\u4ee5\u8bf4\u96c6\u5408\u4e86\u524d\u4e24\u8005\uff0c\u6b64\u5916\u8fd8\u5f15\u5165\u4e86\u73af\u5883\u5149(ambient part)\u3002</p> \\[ L_a=k_aI_a \\] <p>Blinn-Phong \u53cd\u5c04\u6a21\u578b\u7684\u5927\u81f4\u6210\u5206\u5982\u4e0b\uff1a</p> <p></p> \\[ \\begin{align} L &amp; = L_a + L_d + L_s \\\\ &amp; = k_aI_a + k_d \\cdot \\frac{I}{r^2} \\cdot \\max(0,n\\cdot l) + k_s \\cdot \\frac{I}{r^2} \\cdot \\max(0, \\vec n \\cdot \\vec h)^p \\end{align} \\]"},{"location":"cour_note/D2QD_Intro2CV/Lec02/#\u989c\u8272","title":"\u989c\u8272","text":"<p>\u4e3a\u4e86\u63cf\u8ff0\u989c\u8272\uff0c\u6211\u4eec\u9700\u8981\u5b9a\u4e49\u8272\u5f69\u7a7a\u95f4(color spaces)\uff0c\u5e38\u89c1\u7684\u6709 RGB \u548c HSV \u7b49\uff0c\u5bf9\u76f8\u673a\u6765\u8bf4\u6211\u4eec\u66f4\u5e38\u7528\u7684\u662f RGB\u3002</p> in py <p>\u5728\u7b97\u6cd5\u4e2d\uff0c\u6211\u4eec\u7528\u77e9\u9635\u6765\u5b58\u50a8\u56fe\u50cf\u4fe1\u606f\uff0c\u5176\u4e2d\u5de6\u4e0a\u89d2\u7684\u5143\u7d20\u5750\u6807\u4e3a <code>(0, 0, :)</code>\uff0c\u5176\u4e2d\u7b2c\u4e09\u7ef4\u7528\u6765\u6307\u5b9a\u989c\u8272\u901a\u9053(channel)\uff0c\u6240\u4ee5\u7b2c i \u884c j \u5217\u7684\u50cf\u7d20\u70b9\u8868\u793a\u4e3a <code>(i-1, j-1, :)</code>\uff1b</p> <p>\u5728\u786c\u4ef6\u4e0a\uff0c\u989c\u8272\u4f20\u611f\u4e3b\u8981\u901a\u8fc7\u62dc\u5c14\u6ee4\u955c(Bayer filter)\u5b9e\u73b0\u3002\u4e5f\u5c31\u662f\u901a\u8fc7\u5728\u4f20\u611f\u5668\u524d\u5b89\u88c5\u4e00\u4e2a\u5355\u8272\u6ee4\u955c\uff0c\u6765\u63a5\u6536\u5355\u4e00\u8272\u5149\u3002\u5e38\u89c1\u7684\u505a\u6cd5\u662f\u4ee5\u7530\u5b57\u683c\u7684\u56db\u4e2a\u4f20\u611f\u5668\u4e3a\u5355\u4f4d\uff0c\u5206\u914d <code>R*1</code> <code>G*2</code> <code>B*1</code> \u7684\u6ee4\u955c\u3002</p> <p></p> <p>Source: https://en.wikipedia.org/wiki/Bayer_filter</p> <p>\u53ef\u4ee5\u53d1\u73b0\uff0c\u7eff\u8272\u7684\u6ee4\u955c\u66f4\u591a\uff0c\u56e0\u4e3a\u592a\u9633\u5149\u4e2d\u7eff\u8272\u6ce2\u6bb5\u66f4\u591a\uff0c\u4e8e\u662f\u4eba\u773c\u5bf9\u7eff\u8272\u66f4\u654f\u611f\u3002</p> <p>\u663e\u7136\uff0c\u8fd9\u6837\u5f97\u5230\u7684\u56fe\u7247\u9700\u8981\u8fdb\u884c\u63d2\u503c\u624d\u80fd\u5f97\u5230\u6700\u7ec8\u56fe\u7247\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec03/","title":"Lecture 3 | Image Processing","text":"<p> \u7ea6 5940 \u4e2a\u5b57  3 \u884c\u4ee3\u7801  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 20 \u5206\u949f</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec03/#\u57fa\u672c\u64cd\u4f5c","title":"\u57fa\u672c\u64cd\u4f5c","text":"<p>\u5bf9\u56fe\u50cf\u7684\u57fa\u672c\u64cd\u4f5c\u5373\u5728\u56fe\u50cf\u7f16\u8f91\u8f6f\u4ef6\u4e2d\u5e38\u89c1\u7684\u90a3\u4e48\u51e0\u79cd\uff0c\u7a0d\u540e\u6211\u4eec\u5c06\u4f1a\u7b80\u5355\u4ecb\u7ecd\u8fd9\u51e0\u79cd\u64cd\u4f5c\u662f\u5982\u4f55\u5b9e\u73b0\u7684\u3002</p> <p>\u4e0d\u8fc7\u5728\u6b64\u4e4b\u524d\uff0c\u6211\u4eec\u9700\u8981\u5148\u4ecb\u7ecd\u4e00\u4e2a\u5de5\u5177\u2014\u2014\u5377\u79ef(convolution)\uff0c\u4e4b\u540e\u4e00\u4e9b\u64cd\u4f5c\u90fd\u4f9d\u8d56\u4e8e\u6b64\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec03/#\u5377\u79ef","title":"\u5377\u79ef","text":"<p>\u6570\u5b66\u4e0a\u5bf9\u5377\u79ef(convolution)\u7ed9\u51fa\u7684\u5b9a\u4e49\u662f\uff1a</p> \\[ (f*g)(x)=\\int_{-\\infty}^{\\infty} f(y)g(x-y)\\mathrm{d}y \\] <p>\u7b2c\u4e00\u6b21\u63a5\u89e6\u8fd9\u4e2a\u5f0f\u5b50\u7684\u65f6\u5019\u6211\u4e2a\u4eba\u611f\u89c9\u662f\u4e00\u5934\u96fe\u6c34\u7684\u3002\u4f46\u662f\uff0c\u63a5\u4e0b\u6765\u8ba9\u6211\u4eec\u4ece\u4e00\u4e2a\u66f4\u76f4\u89c2\u7684\u89d2\u5ea6\u6765\u7406\u89e3\u4e00\u4e0b\u8fd9\u4e2a\u5f0f\u5b50\uff1a</p> <p>\u4e00\u8a00\u4ee5\u853d\u4e4b\uff1a\\((f*g)(x)\\) \u662f \\(g(x)\\) \u5728\u6ee4\u6ce2\u89c4\u5219 \\(f(y)\\) \u4e0b\u7684\u52a0\u6743\u5747\u503c\u51fd\u6570\u3002</p> <ul> <li>\u6211\u4eec\u4e00\u822c\u79f0 \\(f(y)\\) \u4e3a\u6ee4\u6ce2\u5668(filter)\uff0c\u8fd9\u662f\u56e0\u4e3a\u6211\u4eec\u672c\u8d28\u4e0a\u662f\u5728\u6c42 \\(g(x)\\) \u5728\u8fd9\u4e2a\u6ee4\u6ce2\u89c4\u5219\u4e0b\u52a0\u6743\u6c42\u5747\u503c\u751f\u6210\u7684\u65b0\u51fd\u6570\u3002</li> <li>\u6240\u4ee5\uff0c\\(f(y)\\) \u4e00\u822c\u662f\u6839\u636e\u9700\u6c42\u800c\u51b3\u5b9a\u7684\u4e00\u4e9b\u7279\u6b8a\u51fd\u6570\uff0c\u6bd4\u5982\u9ad8\u65af\u51fd\u6570\u3001\u7279\u5b9a\u533a\u95f4\u5185\u7684\u5e38\u51fd\u6570\u7b49\u3002</li> </ul> <p>\u9996\u5148\uff0c\u6211\u4eec\u5148\u6765\u4ece\u4e00\u7ef4\u79bb\u6563\u7684\u89d2\u5ea6\u6765\u7406\u89e3\u5377\u79ef\uff0c\u5373\uff1a</p> \\[ (f*a)_i = \\sum_{j=-m}^{m} f_j * a_{i+j}  \\] <p>\u5f53\u7136\uff0c\u4e0a\u9762\u53ef\u80fd\u51fa\u73b0 \\(f_{-1}\\) \u8fd9\u79cd\u9b3c\u755c\u7684\u4e1c\u897f\uff0c\u4f46\u662f\u5b9e\u9645\u4e0a\u8fd9\u91cc\u7684 \\(f\\) \u6570\u5217\u786e\u5b9e\u662f\u5b9a\u4e49\u5728\u6574\u4e2a\u6574\u6570\u8f74\u4e0a\u7684\uff08\u5f53\u7136\u4e0b\u6807\u5565\u7684\u662f\u65e0\u6240\u8c13\u7684\uff0c\u7ec8\u70b9\u5173\u6ce8\u4e0b\u9762\u7684\u6a21\u62df\u8fc7\u7a0b\uff09</p> <p>\u6bd4\u5982\uff0c\u6211\u4eec\u6709\u539f\u59cb\u6570\u5217 \\(a_n\\) \u548c\u6ee4\u6ce2\u5668\u6570\u5217 \\(f_m\\) \u5982\u4e0b\uff1a</p> \\(a_n\\) 2 4 2 6 2 \\(f_m\\) 1 2 1 \\(f_m\\) \u7684\u201c\u4e2d\u5fc3\u201d \u2b06\ufe0f <p>\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u6765\u624b\u52a8\u6a21\u62df\u4e00\u4e0b\u5377\u79ef\u8fc7\u7a0b\uff1a</p> \u5377\u79ef\u8fc7\u7a0b \\(a_n\\) 2 4 2 6 2 \u6b63\u5728\u88ab\u5377\u7684\u6570 \u2b06\ufe0f \u2b06\ufe0f\u2b06\ufe0f \u2b06\ufe0f \\(f_m\\) 1 2 1 0 0 \\(f_m\\) \u7684\u201c\u4e2d\u5fc3\u201d \u2b06\ufe0f \u5377\u79ef\u7684\u8fc7\u7a0b \\(1\\times2+2\\times4+1\\times2\\) \u5377\u51fa\u6765\u7684\u7ed3\u679c - \\(12\\) \\(a_n\\) 2 4 2 6 2 \u6b63\u5728\u88ab\u5377\u7684\u6570 \u2b06\ufe0f \u2b06\ufe0f\u2b06\ufe0f \u2b06\ufe0f \\(f_m\\) 0 1 2 1 0 \\(f_m\\) \u7684\u201c\u4e2d\u5fc3\u201d \u2b06\ufe0f \u5377\u79ef\u7684\u8fc7\u7a0b \\(1\\times4+2\\times2+1\\times6\\) \u5377\u51fa\u6765\u7684\u7ed3\u679c - \\(12\\) \\(14\\) \\(a_n\\) 2 4 2 6 2 \u6b63\u5728\u88ab\u5377\u7684\u6570 \u2b06\ufe0f \u2b06\ufe0f\u2b06\ufe0f \u2b06\ufe0f \\(f_m\\) 0 0 1 2 1 \\(f_m\\) \u7684\u201c\u4e2d\u5fc3\u201d \u2b06\ufe0f \u5377\u79ef\u7684\u8fc7\u7a0b \\(1\\times2+2\\times6+1\\times2\\) \u5377\u51fa\u6765\u7684\u7ed3\u679c - \\(12\\) \\(14\\) \\(16\\) - <p>\u53ef\u4ee5\u53d1\u73b0\uff0c\u5982\u679c \\(f_m\\) \u6bcf\u4e00\u9879\u90fd\u9664\u4ee5 4\uff0c\u90a3\u5b9e\u9645\u4e0a\u8fd9\u4e2a\u8fc7\u7a0b\u5c31\u662f\u5728\u6c42\u6bcf\u4e00\u9879\u4e0e\u76f8\u90bb\u4e24\u9879\u7684\u52a0\u6743\u5e73\u5747\uff08\u4e2d\u5fc3\u6743\u91cd\u66f4\u5927\uff09\u3002</p> <p>\u73b0\u5728\uff0c\u4ece\u79bb\u6563\u4f1a\u5230\u8fde\u7eed\u7684\u60c5\u51b5\uff0c\u6211\u4eec\u4ecb\u7ecd\u6700\u7ecf\u5178\u7684\u4e00\u4e2a\u5377\u79ef\u5e94\u7528\u2014\u2014\"box function\"\uff0c\u5176\u4f5c\u4e3a\u6ee4\u6ce2\u5668\u65f6\u5b9a\u4e49\u5982\u4e0b\uff1a</p> <p></p> \\[ f(x) =  \\left\\{     \\begin{array}{}         1 &amp;|x| \\leq 0.5\\\\         0 &amp;otherwise     \\end{array} \\right. \\] <p>\u800c\u5c06\u5b83\u5e26\u5165\u5377\u79ef\u7684\u8868\u8fbe\u5f0f\uff0c\u5f97\u5230\u7684\u7ed3\u679c\u5c31\u662f\uff1a</p> \\[ (f*g)(x)=\\int_{-0.5}^{0.5}g(x-y)\\mathrm{d}y \\] <p>\u90a3\u5b9e\u9645\u4e0a\uff0c\u8fd9\u5c31\u662f\u5728\u6c42\u51fd\u6570\u5728\u5bbd\u5ea6\u4e3a 1 \u7684\u8303\u56f4\u5185\u7684\u5747\u503c\u3002</p> <p>\u73b0\u5728\uff0c\u6211\u4eec\u5c06\u5b83\u8fdb\u884c\u4e00\u70b9\u6269\u5c55\uff0c\u6765\u5230\u4e8c\u7ef4\uff0c\u5219\u53ef\u4ee5\u5c06\u79bb\u6563\u7684\u5377\u79ef\u8fc7\u7a0b\u7528\u8fd9\u6837\u4e00\u4e2a gif \u6765\u8868\u793a\uff1a</p> <p> </p> <ul> <li>Wiki \u4e2d\u6709\u66f4\u9177\u7684\u52a8\u56fe\uff1a\ud83d\udd17</li> </ul> <p>\u601d\u8003</p> <p>\u53ef\u4ee5\u53d1\u73b0\uff0c\u5728\u4e8c\u7ef4\u5377\u79ef\u7684\u8fc7\u7a0b\u4e2d\uff0c\u6211\u4eec\u5377\u51fa\u6765\u7684\u4e1c\u897f\u8981\u6bd4\u539f\u59cb\u56fe\u50cf\u5c0f\u3002\u800c\u5176\u4e2d\u4e00\u79cd\u89e3\u51b3\u7684\u65b9\u6cd5\u662f padding\u3002\u5728\u6b64\u4e0d\u505a\u8fc7\u591a\u4ecb\u7ecd\u3002</p> <p>\u5178\u578b\u6ee4\u6ce2\u5668</p> <p>\u5176\u4ed6\u5178\u578b\u7684\u6ee4\u6ce2\u5668\u53ef\u80fd\u5c06\u5728\u4e4b\u540e\u4ecb\u7ecd\uff0c\u8fd9\u91cc\u7b80\u5355\u63d0\u51e0\u4e2a\uff1a</p> <ul> <li>\u9ad8\u65af\u6ee4\u6ce2\u5668(\u4e2d\u5fc3\u6743\u91cd\u5927)</li> <li>\u9510\u5316\u6ee4\u6ce2\u5668</li> <li>\u8fb9\u7f18\u68c0\u6d4b\u6ee4\u6ce2\u5668</li> <li>\u53ef\u5206\u79bb\u6ee4\u6ce2\u5668</li> <li>\u53cc\u8fb9\u6ee4\u6ce2\u5668</li> <li>\u2026\u2026</li> </ul>"},{"location":"cour_note/D2QD_Intro2CV/Lec03/#\u589e\u52a0\u5bf9\u6bd4\u5ea6","title":"\u589e\u52a0\u5bf9\u6bd4\u5ea6","text":"<p>\u589e\u52a0\u5bf9\u6bd4\u5ea6(increase contrast)\u5373\u8ba9\u753b\u9762\u4e2d\u7684\u989c\u8272\u5411\u4e24\u4e2a\u6781\u7aef\u504f\u79fb\uff0c\u901a\u4fd7\u6765\u8bf4\u5c31\u662f\u9ed1\u7684\u66f4\u9ed1\uff0c\u767d\u7684\u66f4\u767d\u3002</p> <p>\u4f53\u611f\u4e0a\u8ba9\u4e00\u5f20\u96fe\u8499\u8499\u7684\u7167\u7247\u53d8\u5f97\u66f4\u52a0\u9ed1\u767d\u5206\u660e\u3002</p> <p>\u4e0a\u9762\u4e5f\u8bf4\u4e86\uff0c\u662f\u5c06\u8272\u5f69\u5411\u4e24\u4e2a\u6781\u7aef\u504f\u79fb\uff0c\u5b9e\u9645\u4e0a\u5c31\u662f\u8bb2\u539f\u6765\u7684\u989c\u8272\u8fdb\u884c\u4e00\u4e2a\u6620\u5c04\uff0c\u4ee4 \\(color'(x,y) = f[color(x,y)]\\)\u3002</p> <p>\u90a3\u4e48\u4e00\u822c\u6765\u8bf4\uff0c\u6211\u4eec\u91c7\u7528S \u66f2\u7ebf(S curve)\u6765\u8fdb\u884c\u8fd9\u4e2a\u6620\u5c04\uff0c\u4e5f\u5c31\u662f\u5c06\u539f\u672c\u5747\u5300\u5206\u5e03\u7684\u70b9\u6309\u7167 S \u66f2\u7ebf\u8fdb\u884c\u62c9\u4f38\u548c\u538b\u7f29\uff0c\u8fd9\u6837\uff0c\u767d\u7684\u4f1a\u66f4\u767d\uff0c\u9ed1\u7684\u5c31\u4f1a\u66f4\u9ed1\u3002</p> <p> </p> <p>\u56fe\u4e2d\u6a2a\u5750\u6807\u8868\u793a\u539f\u6765\u7684\u989c\u8272\uff0c\u7eb5\u5750\u6807\u8868\u793a\u6620\u5c04\u540e\u7684\u989c\u8272\uff0c\u53ef\u4ee5\u53d1\u73b0\u9ed1\u8272\u90e8\u5206\u7684\u989c\u8272\u90fd\u5411\u9ed1\u8272\u504f\u79fb\uff0c\u767d\u8272\u90e8\u5206\u4ea6\u7136\u3002</p> <p>\u800c\u5177\u4f53\u4f7f\u7528\u7684\u66f2\u7ebf\uff0c\u5219\u9700\u8981\u6839\u636e\u9700\u6c42\u8fdb\u884c\u8c03\u6574\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec03/#\u53cd\u8272","title":"\u53cd\u8272","text":"<p>\u987e\u540d\u601d\u4e49\uff0c\u56fe\u50cf\u53d6\u53cd\u8272(image invert)\u5c31\u662f\u5c06\u989c\u8272\u53d6\u53cd\uff0c\u9ed1\u53d8\u767d\uff0c\u767d\u53d8\u9ed1\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec03/#\u8fb9\u7f18\u63d0\u53d6","title":"\u8fb9\u7f18\u63d0\u53d6","text":"<p>\u8fb9\u7f18\u63d0\u53d6 Edge detection</p> <p>\u5f15\u5165</p> <p>\u6a21\u7cca(blur) \u548c \u9510\u5316(sharpen) \u662f\u4e24\u4e2a\u5bf9\u5e94\u7684\u6982\u5ff5\uff0c\u5b9e\u73b0\u7684\u624b\u6bb5\u4e5f\u975e\u5e38\u7c7b\u4f3c\u3002</p> <p>\u4f7f\u7528\u5bf9\u6bd4</p> <ul> <li>\u4ece\u5e94\u7528\u6765\u8bb2\uff0c\u6a21\u7cca\u53ef\u4ee5\u7528\u6765\u505a\u4e00\u4e9b\u964d\u566a\u7684\u5de5\u4f5c\uff0c\u4e5f\u53ef\u4ee5\u7ed9\u56fe\u7247\u8425\u9020\u51fa\u4e00\u79cd\u5149\u6ed1\u7684\u8d28\u611f\uff1b</li> <li>\u800c\u9510\u5316\u53ef\u4ee5\u4e00\u5b9a\u7a0b\u5ea6\u4e0a\u589e\u52a0\u56fe\u7247\u7684\u6e05\u6670\u5ea6\u3002</li> </ul>"},{"location":"cour_note/D2QD_Intro2CV/Lec03/#\u6a21\u7cca","title":"\u6a21\u7cca","text":"<p>\u6240\u8c13\u7684\u6a21\u7cca(blur)\uff0c\u50cf\u662f\u5c06\u67d0\u4e2a\u4f4d\u7f6e\u7684\u50cf\u7d20\u548c\u5468\u56f4\u6df7\u5408\u8d77\u6765\uff0c\u66f4\u6570\u5b66\u7684\u8868\u8ff0\u6765\u8bf4\uff0c\u9700\u8981\u4e0e\u5468\u56f4\u8fdb\u884c\u52a0\u6743\u6c42\u5e73\u5747\uff0c\u6ca1\u9519\uff0c\u6211\u4eec\u9700\u8981\u4f7f\u7528\u5377\u79ef\u6765\u5b9e\u73b0\u3002</p> <p></p> <p>Source: Stanford CS248, Winter 202</p> <p>\u4f8b\u5982\uff0c\u5047\u8bbe\u6211\u4eec\u7528\u8fd9\u6837\u4e00\u4e2a\u4e8c\u7ef4\u6ee4\u6ce2\u5668\u5bf9\u4e00\u5f20\u56fe\u50cf\u8fdb\u884c\u5377\u79ef\uff1a</p> \\[ \\begin{bmatrix}     \\frac{1}{9} &amp; \\frac{1}{9} &amp; \\frac{1}{9} \\\\     \\frac{1}{9} &amp; \\frac{1}{9} &amp; \\frac{1}{9} \\\\     \\frac{1}{9} &amp; \\frac{1}{9} &amp; \\frac{1}{9} \\end{bmatrix} \\] <p>\u90a3\u4e48\u65b0\u5f97\u5230\u7684\u56fe\u7247\u4e2d\u7684\u50cf\u7d20\u5c06\u4f1a\u7b49\u4e8e\u539f\u56fe\u7247\u8fd9\u4e2a\u50cf\u7d20\u5468\u56f4\u7684 8 \u4e2a\u50cf\u7d20\u548c\u5b83\u6c42\u5e73\u5747\u5f97\u5230\u7684\u989c\u8272\u3002</p> <p>\u518d\u6bd4\u5982\uff0c\u6ee4\u6ce2\u5668\u4f7f\u7528\u9ad8\u65af\u51fd\u6570\u7684\u9ad8\u65af\u6a21\u7cca\uff1a</p> \\[ f(i,j)=\\frac{1}{2\\pi \\sigma^2}e^{-\\frac{i^2+j^2}{2\\sigma^2}} \\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\; \\begin{bmatrix}     0.075 &amp; 0.124 &amp; 0.075 \\\\     0.124 &amp; 0.204 &amp; 0.124 \\\\     0.075 &amp; 0.124 &amp; 0.075 \\end{bmatrix} \\] <p>\u9ad8\u65af\u6a21\u7cca\u4f1a\u66f4\u52a0\u6ce8\u91cd\u4e2d\u5fc3\u7684\u6743\u91cd\uff0c\u6240\u4ee5\u6a21\u7cca\u8d77\u6765\u76f8\u5bf9\u6765\u8bf4\u66f4\u80fd\u4fdd\u6301\u56fe\u7247\u539f\u6765\u7684\u7279\u5f81\u4e00\u70b9\u3002</p> <p>\u66f4\u4f18\u79c0\u7684\u4e00\u79cd\u6a21\u7cca</p> <p>\u4e00\u79cd\u66f4\u6709\u7528\u7684\u6a21\u7cca\u662f\uff0c\u63d0\u53d6\u8fb9\u7f18\u540e\u7684\u6a21\u7cca\uff0c\u5373\u6a21\u7cca\u8fc7\u7a0b\u4e2d\u4e0d\u5f71\u54cd\u8fb9\u7f18\uff0c\u6bd4\u5982\u4eba\u8138\u8fb9\u7f18\u6a21\u7cca\uff0c\u53ea\u5f71\u54cd\u8138\u800c\u4e0d\u5f71\u54cd\u5176\u4ed6\u90e8\u5206\u3002</p> <p>\u5177\u4f53\u5b9e\u73b0\u6211\u4eec\u5c06\u5728 \u518d\u770b\u6ee4\u6ce2\u5668 \u4e2d\u7684 \u53cc\u8fb9\u6ee4\u6ce2\u5668\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec03/#\u9510\u5316","title":"\u9510\u5316","text":"<p>\u6211\u4eec\u6ce8\u610f\u5230\uff0c\u6a21\u7cca\u4e2d\u7684\u6ee4\u6ce2\u5668\u57fa\u672c\u4e0a\u6bcf\u4e00\u4e2a\u5143\u7d20\u90fd\u662f\u975e\u8d1f\u6570\uff0c\u610f\u601d\u662f\u5377\u79ef\u7ed3\u679c\u4e2d\u4f1a\u4fdd\u7559\u4e00\u90e8\u5206\u8fd9\u4e9b\u50cf\u7d20\u7684\u7279\u5f81\u3002</p> <p>\u90a3\u5982\u679c\u6211\u4eec\u628a\u5176\u4e2d\u4e00\u90e8\u5206\u6539\u6210\u8d1f\u6570\u5462\uff1f\u90a3\u5c31\u8bf4\u660e\u5377\u79ef\u7ed3\u679c\u4e2d\u4f1a\u51cf\u53bb\u8fd9\u90e8\u5206\u7684\u7279\u5f81\u3002\u4e5f\u5c31\u662f\u8bf4\uff0c\u5982\u679c\u6743\u503c\u4e3a\u8d1f\u6570\u7684\u50cf\u7d20\u548c\u6743\u503c\u4e3a\u6b63\u6570\u7684\u50cf\u7d20\u5f88\u50cf\uff0c\u90a3\u4e48\u8fd9\u4e2a\u7279\u5f81\u5c31\u4f1a\u88ab\u524a\u5f31\uff1b\u53cd\u8fc7\u6765\u8bf4\uff0c\u5982\u679c\u6743\u503c\u4e3a\u8d1f\u6570\u7684\u50cf\u7d20\u548c\u6743\u503c\u4e3a\u6b63\u6570\u7684\u50cf\u7d20\u51e0\u4e4e\u76f8\u53cd\uff0c\u90a3\u4e48\u6743\u503c\u4e3a\u6b63\u6570\u7684\u50cf\u7d20\u7684\u7279\u5f81\u5c31\u4f1a\u88ab\u52a0\u5f3a\u3002</p> <p>\u6211\u4eec\u8003\u8651\u8fd9\u6837\u4e00\u4e2a\u7279\u6b8a\u4f8b\u5b50\uff1a</p> \\[ \\begin{bmatrix}     0 &amp; -1 &amp; 0 \\\\     -1 &amp; 5 &amp; -1 \\\\     0 &amp; -1 &amp; 0 \\end{bmatrix} \\] <p>\u5982\u679c\u8fb9\u7f18\u7684\u70b9\u548c\u77e9\u9635\u4e2d\u5fc3\u7684\u70b9\u4e0d\u4e00\u6837\uff0c\u5219\u77e9\u9635\u4e2d\u5fc3\u7684\u70b9\u7684\u7279\u5f81\u4f1a\u88ab\u5f3a\u8c03\uff0c\u5373\u4f1a\u653e\u5927\u76f8\u90bb\u70b9\u7684\u533a\u522b\uff0c\u8fd9\u5c31\u662f\u9510\u5316(sharpen)\u7684\u539f\u7406\u3002</p> <p></p> <p>Source: Stanford CS248, Winter 202</p> <p>\u6a21\u7cca\u4e0e\u9510\u5316\u7684\u8054\u7cfb</p> <ul> <li>\u5982\u679c\u5b9a\u4e49\u539f\u672c\u7684\u56fe\u50cf\u4e3a \\(I\\)\uff0c\u6a21\u7cca\u540e\u7684\u56fe\u50cf\u4e3a \\(I_b\\)</li> <li>\u5b9a\u4e49\u56fe\u50cf\u4e2d\u7684\u9ad8\u9891(high frequencies)\u4e3a I_h = I - I_b\uff1b</li> <li>\u5219\u9510\u5316\u7684\u56fe\u50cf \\(I_s = I + I_h\\)\uff1b</li> <li>\u5373\u6709 \\(2I = I_s + I_h\\)\uff0c\u53ef\u4ee5\u53d1\u73b0\uff0c\u53c8\u4e00\u4e2a\u7c7b\u4f3c\u4e8e\u4e92\u8865\u7684\u5173\u7cfb\uff1b</li> <li>\u800c\u8fd9\u91cc\u7684\u9ad8\u9891\u53ef\u4ee5\u7406\u89e3\u4e3a\u56fe\u50cf\u4e2d\u53d8\u5316\u6bd4\u8f83\u660e\u663e\u7684\u5730\u65b9\uff1b</li> </ul> <p> </p> <p> </p>"},{"location":"cour_note/D2QD_Intro2CV/Lec03/#\u518d\u770b\u6ee4\u6ce2\u5668","title":"\u518d\u770b\u6ee4\u6ce2\u5668","text":"<p>\u4e0a\u9762\u6211\u4eec\u5df2\u7ecf\u63d0\u5230\u4e86\u7528\u4e8e\u6a21\u7cca\u7684\u6ee4\u6ce2\u5668\uff08\u6bd4\u5982\u9ad8\u65af\u6ee4\u6ce2\u5668\uff09\uff0c\u7528\u4e8e\u9510\u5316\u7684\u6ee4\u6ce2\u5668\uff0c\u63a5\u4e0b\u6765\u8ba9\u6211\u4eec\u770b\u770b\u5176\u4ed6\u7684\u6ee4\u6ce2\u5668\u7684\u76f8\u5173\u5185\u5bb9\uff1a</p> \u6c34\u5e73/\u5782\u76f4\u68af\u5ea6\u63d0\u53d6 <p></p> <ul> <li>Extracts horizontal gradients</li> </ul> \\[ \\begin{bmatrix}     -1 &amp; 0 &amp; 1 \\\\     -2 &amp; 0 &amp; 2 \\\\     -1 &amp; 0 &amp; 1 \\end{bmatrix} \\] <ul> <li>Extracts vertical gradients</li> </ul> \\[ \\begin{bmatrix}     -1 &amp; -2 &amp; -1 \\\\     0 &amp; 0 &amp; 0 \\\\     1 &amp; 2 &amp; 1 \\end{bmatrix} \\] \u53ef\u5206\u79bb\u6ee4\u6ce2\u5668 <ul> <li>Separable filter\uff0c\u53ef\u4ee5\u7528\u8fd9\u79cd\u65b9\u5f0f\u6765\u964d\u4f4e\u8ba1\u7b97\u91cf\uff1b  </li> <li>\u53ea\u8981\u8868\u8fbe\u5f0f\u53ef\u4ee5\u5199\u6210\u4e24\u4e2a\u51fd\u6570\u76f8\u4e58\uff0c\u90a3\u57fa\u672c\u662f separable \u7684;<ul> <li>\u6bd4\u5982\u9ad8\u65af\u77e9\u9635\u5c31\u53ef\u4ee5\u62c6\u6210\u8fd9\u6837\uff1a</li> <li>\\(f(i,j)=\\frac{1}{2\\pi \\sigma^2}e^{-\\frac{i^2+j^2}{2\\sigma^2}}=\\frac{1}{2\\pi \\sigma^2}e^{-\\frac{i^2}{2\\sigma^2}}\\cdot e^{-\\frac{j^2}{2\\sigma^2}}\\)</li> </ul> </li> </ul> \u53cc\u8fb9\u6ee4\u6ce2\u5668 <ul> <li> <p>\u53cc\u8fb9\u6ee4\u6ce2\u5668 Bilateral filter</p> <ul> <li>\u5728\u6ee4\u6ce2\u65f6\uff0c\u6bcf\u4e00\u4e2a\u70b9\u7684\u6743\u91cd\u4e0e \u76ee\u6807\u70b9 \u4e0e \u4e2d\u5fc3\u70b9\u7684\u76f8\u4f3c\u7a0b\u5ea6\u6709\u5173;</li> </ul> </li> <li> <p> TODO: \u66f4\u8be6\u7ec6\u5730\u8bb2\u8fd9\u91cc</p> </li> </ul> <p></p> <p>\u5f15\u5165</p> <p>\u56fe\u50cf\u91c7\u6837(sampling)\u5206\u4e3a\u5411\u4e0a\u91c7\u6837(up-sampling)\u548c\u5411\u4e0b\u91c7\u6837(down-sampling)\u4e24\u79cd\u3002</p> <p>\u66f4\u901a\u4fd7\u7684\u6765\u8bf4\uff0c\u5c31\u662f\u5728\u4fdd\u6301\u56fe\u50cf\u7279\u5f81\u7684\u60c5\u51b5\u4e0b\u5bf9\u56fe\u7247\u8fdb\u884c\u7f29\u653e\u3002\u663e\u7136\uff0c\u5728\u7f29\u653e\u56fe\u50cf\u65f6\uff0c\u4f1a\u51fa\u73b0\u50cf\u7d20\u6570\u91cf\u7684\u53d8\u5316\uff0c\u90a3\u8981\u5982\u4f55\u6dfb\u52a0\u50cf\u7d20\u3001\u5982\u4f55\u51cf\u5c11\u50cf\u7d20\uff0c\u5c31\u662f\u56fe\u50cf\u91c7\u6837\u8003\u8651\u7684\u4e8b\u60c5\u3002</p> <p>\u6b64\u5916\uff0c\u5c06\u4e24\u8005\u7ed3\u5408\uff0c\u8fd8\u4f1a\u6709\u4f8b\u5982\u6539\u53d8\u56fe\u7247\u957f\u5bbd\u6bd4\uff0c\u8fdb\u884c\u62c9\u4f38\u8fd9\u79cd\u95ee\u9898\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec03/#\u7f29\u5c0f\u56fe\u7247\u5411\u4e0b\u91c7\u6837","title":"\u7f29\u5c0f\u56fe\u7247\uff1a\u5411\u4e0b\u91c7\u6837","text":"<p>\u5411\u4e0b\u91c7\u6837\u4e5f\u5c31\u662f\u8ba9\u56fe\u7247\u53d8\u5c0f\uff0c\u8fd9\u91cc\u4e3b\u8981\u9700\u8981\u8003\u8651\u7684\u95ee\u9898\u662f\u5982\u4f55\u7f29\u5c0f\u56fe\u7247\uff0c\u5982\u4f55\u907f\u514d\u51fa\u73b0\u4fe1\u53f7\u8d70\u6837\u7684\u95ee\u9898\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec03/#\u4fe1\u53f7\u8d70\u6837","title":"\u4fe1\u53f7\u8d70\u6837","text":"<p>\u8bf4\u5230\u8ba9\u56fe\u50cf\u53d8\u5c0f\uff0c\u6700\u7b80\u5355\u7684\u4e00\u4e2a\u60f3\u6cd5\u5c31\u662f\u2014\u2014\u6bd4\u5982\uff0c\u8ba9\u56fe\u7247\u7684\u7ebf\u5ea6\u7f29\u5c0f\u4e00\u534a\uff0c\u53ef\u4ee5\u6bcf\u56db\u4e2a\u683c\u5b50\u5c31\u91c7\u4e00\u4e2a\u683c\u5b50\u7684\u6837\u672c\u3002</p> <p></p> <p>\u800c\u8fd9\u79cd\u7c97\u66b4\u7684\u505a\u6cd5\u5219\u6709\u53ef\u80fd\u5bfc\u81f4\uff1a</p> <p>-\u6469\u5c14\u7eb9(Moir\u00e9 Patterns)\u3002 -\u9a6c\u8f66\u8f6e\u9519\u89c9(Wagon Wheel Illusion) - ...</p> <p>\u800c\u8fd9\u4e9b\u7531\u91c7\u6837\u5bfc\u81f4\u7684\u95ee\u9898\uff0c\u6211\u4eec\u79f0\u4e4b\u4e3a\u4fe1\u53f7\u8d70\u6837(aliasing)\u3002</p> <p>\u4ece\u672c\u8d28\u4e0a\u6765\u8bf4\uff0c\u4fe1\u53f7\u8d70\u6837\u7684\u53d1\u751f\uff0c\u662f\u56e0\u4e3a\u91c7\u6837\u9891\u7387\u8ddf\u4e0d\u4e0a\u56fe\u50cf\u9891\u7387\u5bfc\u81f4\u7684\u3002</p> <p>Signals are changing too fast but sampled too slow.</p> <p>\u5982\u4f55\u7406\u89e3\u8fd9\u91cc\u7684\u201c\u9891\u7387\u201d</p> <p>\u5728\u4e4b\u540e\u7684\u90e8\u5206\u4e2d\uff0c\u6211\u4eec\u4f1a\u7ed9\u51fa\u8fd9\u91cc\u7684\u201c\u9891\u7387\u201d\u7684\u6765\u6e90\u3002</p> <p>\u4f46\u662f\u4e00\u4e2a\u66f4\u76f4\u89c2\uff0c\u66f4\u6a21\u7cca\u7684\u770b\u6cd5\u662f\uff1a\u5982\u679c\u4e00\u4e2a\u56fe\u50cf\u7684\u67d0\u4e2a\u90e8\u5206\u53d8\u5316\u8d8a\u5267\u70c8\uff0c\u4e00\u822c\u6765\u8bf4\u5176\u9891\u7387\u5c31\u4f1a\u8f83\u5927\u3002\u6bd4\u5982\u56fe\u50cf\u4e2d\u6709\u4e00\u4e2a\u975e\u5e38\u5206\u660e\u7684\u8fb9\u754c\uff0c\u90a3\u4e48\u5b83\u7684\u9891\u7387\u4e00\u822c\u4e0d\u4f1a\u4f4e\u3002</p> <p>\u800c\u8fd9\u91cc\u7684\u201c\u91c7\u6837\u9891\u7387\u201d\u8861\u91cf\u4e86\u4fe1\u53f7\u53d8\u5316\u7684\u9891\u7387\u3002</p> <p>\u6bd4\u5982\uff0c\u5982\u679c\u5bf9\u4e00\u4e2a\u6b63\u5f26\u6ce2\u8fdb\u884c\u91c7\u6837\uff0c\u5373\u4ece\u4e00\u4e2a\u8fde\u7eed\u7684\u6b63\u5f26\u6a21\u62df\u4fe1\u53f7\u4e2d\u9009\u53d6\u82e5\u5e72\u70b9\uff0c\u53ef\u4ee5\u53d1\u73b0\uff0c\u4e0d\u540c\u91c7\u6837\u9891\u7387\u548c\u4e0d\u540c\u7684\u56fe\u50cf\u9891\u7387\u7684\u9009\u53d6\u65b9\u6848\u4f1a\u4ea7\u751f\u4e0d\u540c\u7684\u7ed3\u679c\uff1a</p> <p></p> <p>\u53ef\u4ee5\u53d1\u73b0\uff0c\u5bf9\u4e8e\u4e0a\u9762\u7684\u51e0\u4e2a\u51fd\u6570\uff0c\u91c7\u6837\u9891\u7387\u548c\u539f\u51fd\u6570\u7684\u9891\u7387\u5339\u914d\u8f83\u597d\uff0c\u6240\u4ee5\u91c7\u6837\u5f97\u5230\u7684\u70b9\u57fa\u672c\u80fd\u53cd\u6620\u51fa\u539f\u6765\u56fe\u5f62\u7684\u7279\u5f81\uff1b\u4f46\u662f\u5bf9\u4e8e\u6bd4\u8f83\u4e0b\u9762\u7684\u51e0\u4e2a\u66f2\u7ebf\uff0c\u91c7\u6837\u5c31\u4e0d\u662f\u5f88\u7406\u60f3\u4e86\u3002</p> <p>\u6bd4\u8f83\u76f4\u89c2\u7684\u4e00\u4e2a\u60f3\u6cd5\u662f\uff0c\u8fc7\u6162\u70b9\u91c7\u6837\u9891\u7387\u4f1a\u5bfc\u81f4\u4fe1\u606f\u4e22\u5931\uff0c\u751a\u81f3\u662f\u8868\u73b0\u51fa\u5176\u5b83\u9891\u7387\u7684\u4fe1\u53f7\u7684\u7279\u5f81\uff0c\u8fd9\u4e9b\u4e0d\u6b63\u5e38\u7684\u884c\u4e3a\u5c31\u5bfc\u81f4\u4e86\u4fe1\u53f7\u8d70\u6837\u3002</p> <p>\u8fd9\u4e2a\u201c\u9891\u7387\u201d\u548c\u56fe\u50cf\u6709\u4ec0\u4e48\u5173\u7cfb\uff1f</p> <p>\u9996\u5148\u6211\u4eec\u77e5\u9053\uff0c\u8981\u5411\u6709\u201c\u9891\u7387\u201d\u8fd9\u4e2a\u5c5e\u6027\uff0c\u8868\u8fbe\u5f0f\u6216\u8005\u8bf4\u51fd\u6570\u9700\u8981\u662f\u5468\u671f\u6027\u7684\u3002\u7136\u800c\u201c\u5468\u671f\u6027\u201d\u5bf9\u4e8e\u4efb\u610f\u51fd\u6570\u6765\u8bf4\u53ef\u80fd\u662f\u4e00\u4e2a\u8f83\u4e3a\u82db\u523b\u7684\u6761\u4ef6\u3002</p> <p>\u6b64\u65f6\u5c31\u8f6e\u5230\u5085\u7acb\u53f6\u53d8\u6362\u767b\u573a\u4e86\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec03/#fourier-\u53d8\u6362","title":"Fourier \u53d8\u6362","text":"<p>\u6700\u7b80\u5355\u76f4\u767d\u5730\u7406\u89e3\u5085\u7acb\u53f6\u53d8\u6362(Fourier Transform)\uff0c\u5b9e\u9645\u4e0a\u5c31\u662f\u5c06\u4efb\u610f\u53ef\u4ee5\u8fdb\u884c\u5085\u7acb\u53f6\u53d8\u6362\u7684\u51fd\u6570\uff0c\u53d8\u5316\u4e3a\u4e00\u4e2a\u6b63\u5f26\u3001\u4f59\u5f26\u51fd\u6570\u7ea7\u6570\u7684\u5f62\u5f0f\u3002</p> <p>\u4f8b\u5982\u6700\u7ecf\u5178\u7684\uff0c\u4f7f\u7528\u4e0d\u540c\u9891\u7387\u7684\u6b63\u5f26\u6ce2\u6765\u62df\u5408\u4e00\u4e2a\u65b9\u6ce2\u3002</p> <p>\u8fd9\u91cc\u5f15\u6d41\u4e00\u4e2a xg \u7684\u89c6\u9891\uff1ahttps://www.bilibili.com/video/BV1Y7411W73U/</p> <p>\u6b64\u65f6\u4f60\u53ef\u80fd\u4f1a\u95ee\uff0c\u6b63\u4f59\u5f26\u51fd\u6570\u7684\u7ea7\u6570\u4e5f\u4e0d\u4fdd\u8bc1\u6709\u5468\u671f\u554a\uff0c\u4f46\u662f\u8bf7\u6ce8\u610f\uff0c\u6211\u4eec\u7684\u76ee\u7684\u5e76\u4e0d\u662f\u627e\u5230\u4e00\u4e2a\u5468\u671f\uff0c\u800c\u662f\u80fd\u591f\u4f7f\u7528\u9891\u7387\u6765\u8868\u8fbe\u8fd9\u4e2a\u51fd\u6570\u7684\u67d0\u4e9b\u7279\u5f81\u3002</p> <p>\u6211\u4eec\u77e5\u9053\uff0c\u6b63\u4f59\u5f26\u51fd\u6570\u662f\u5177\u6709\u5468\u671f\u6027\u7684\uff0c\u90a3\u4e48\u6211\u4eec\u5c31\u53ef\u4ee5\u7528\u8fd9\u4e2a\u7ea7\u6570\u4e2d\u7684\u6b63\u4f59\u5f26\u51fd\u6570\u7684\u9891\u7387\u6765\u8868\u8fbe\u8fd9\u4e2a\u51fd\u6570\u3002</p> <p></p> <p>\u4e0b\u9762\u8fd9\u5f20\u56fe\u7247\u5c31\u662f\u7f16\u7801\u540e\u7684\u9891\u8c31\u3002</p> <p>\u800c\u5728\u6b27\u62c9\u516c\u5f0f \\(e^{i\\theta} = \\cos\\theta + i\\sin\\theta\\) \u7684\u7edf\u4e00\u4e0b\uff0cFourier \u53d8\u6362\u53ef\u4ee5\u8868\u793a\u4e3a\uff1a</p> \\[ F(u) = \\int^{\\infty}_{-\\infty} f(x) e^{-i2\\pi ux} \\rm{d} x \\\\ f(x) = \\int^{\\infty}_{-\\infty} F(u) e^{i2\\pi ux} \\rm{d} u \\\\ \\text{ where 'x' refers to space, 'u' refers to frequency} \\] <p>\u901a\u8fc7\u8fd9\u79cd\u5f62\u5f0f\uff0c\u6211\u4eec\u5b9e\u73b0\u4e86 spatial domain \u548c frequency domain \u4e4b\u95f4\u7684\u7edf\u4e00\u3002</p> <pre><code>graph LR;\nA([\"spatial domain\"]) ==&gt;|\"Fourier transform\"| B([\"frequency domain\"])\nB ===&gt;|\"Inverse transform\"| A</code></pre> <p>\u5c1d\u8bd5\u4f7f\u7528\u5377\u79ef\u7684\u89d2\u5ea6\u6765\u770b\u5085\u7acb\u53f6\u53d8\u6362</p> <p>\u89c2\u5bdf\u5f0f\u5b50 \\(F(u) = \\int^{\\infty}_{-\\infty} f(x) e^{-i2\\pi ux} \\rm{d} x\\)\uff0c\u662f\u4e0d\u662f\u80fd\u5c06\u5b83\u770b\u4f5c\u4e00\u4e2a\u5377\u79ef\u5f0f\u5462\uff1f</p> <ul> <li> TODO: \u5177\u4f53\u89e3\u91ca\u6682\u65f6\u5495\u5495\u5495\u3002</li> </ul> <p>\u4e00\u4e2a\u6709\u610f\u601d\u7684\u6027\u8d28</p> <p>\u800c\u4f7f\u7528 Fourier \u7684\u53e6\u5916\u4e00\u4e2a\u597d\u5904\u662f\uff0c\u5b83\u4e3a\u6211\u4eec\u5e26\u6765\u4e86\u8fd9\u6837\u4e00\u4e2a\u6570\u5b66\u6027\u8d28\uff1a</p> Spatial Domain Frequency Domain \\(g(x) = f(x) * h(x)\\)  Convolution \\(\\leftrightarrow\\) \\(G(u) = F(u)H(u)\\)  Multiplication g(x)=f(x)h(x)  Multiplication \\(\\leftrightarrow\\) \\(G(u) = F(u) * H(u)\\)  Convolution <p>\u5177\u4f53\u6765\u8bf4\uff0c\u4f8b\u5982\uff1a</p> <p>\u6211\u4eec\u5bf9\u4e00\u4e2a\u56fe\u50cf\u8fdb\u884c\u6a21\u7cca\u5904\u7406\uff0c\u5373\u5c06\u56fe\u50cf\u4e0e Blur Kernel \u8fdb\u884c\u5377\u79ef\uff0c\u5c31\u7b49\u6548\u4e8e\u5c06\u8fd9\u4e24\u4e2a\u77e9\u9635\u5728\u9891\u7387\u57df\u4e2d\u76f8\u4e58\u3002</p> <p></p> <p>\u800c\u4f20\u7edf\u56fe\u50cf\u538b\u7f29\uff0c\u5bf9\u5e94\u5230\u9891\u7387\u57df\u4e0a\uff0c\u5c31\u662f\u5c06\u4ed6\u4eec\u7684\u4e8c\u7ef4\u9891\u8c31\u4e2d\u7684\u9ad8\u9891\u4e22\u6389\u3002</p> <p>\u90a3\u4e48\u5f97\u5230 Fourier \u53d8\u6362\u8fd9\u4e2a\u5de5\u5177\u4ee5\u540e\uff0c\u6211\u4eec\u5c31\u53ef\u4ee5\u5c06\u8f83\u96be\u5904\u7406\u7684\u50cf\u7d20\u4fe1\u606f\u8f6c\u5316\u4e3a\u9891\u7387\u4fe1\u606f\u3002</p> <p>\u5982\u4e0b\u56fe\uff0c\u5c06\u4e00\u5f20\u56fe\u7247\u4fe1\u606f\u7f16\u7801\u4e3a\u4e86\u9891\u8c31\u7684\u5f62\u5f0f\u3002\u7531\u4e8e\u8fd9\u91cc\u7684\u9891\u8c31\u662f\u4e8c\u7ef4\u7684\uff0c\u6240\u4ee5\u4f7f\u7528\u4e00\u5f20\u7070\u5ea6\u56fe\u8868\u73b0\u51fa\u6765\u3002</p> <p></p> <ul> <li> TODO: \u9700\u8981\u66f4\u8be6\u7ec6\u7684\u89e3\u91ca</li> </ul> <p>\u597d\uff0c\u6709\u4e86\u8fd9\u4e9b\u94fa\u57ab\uff0c\u6211\u4eec\u5728\u56de\u5934\u6765\u8bb2\u91c7\u6837\uff0c\u8fd9\u6b21\u6211\u4eec\u5c06\u5c1d\u8bd5\u7740\u540c\u65f6\u4ece Spatial domain \u548c Frequency domain \u7684\u89d2\u5ea6\u6765\u770b\u5f85\u95ee\u9898\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec03/#\u91c7\u6837","title":"\u91c7\u6837","text":"<p>\u9996\u5148\uff0c\u6211\u4eec\u4ece\u5b57\u9762\u610f\u601d\u4e0a\u548c\u76ee\u7684\u4e0a\u6765\u7406\u89e3\u4e00\u4e0b\u91c7\u6837\u3002</p> <p>wiki \u4e0a\u5bf9\u91c7\u6837\u7684\u5b9a\u4e49\u662f\u8fd9\u6837\u7684\uff1a</p> <p>\u5728\u4fe1\u53f7\u5904\u7406\u9886\u57df\uff0c\u91c7\u6837\u662f\u5c06\u4fe1\u53f7\u4ece\u8fde\u7eed\u65f6\u95f4\u57df\u4e0a\u7684\u6a21\u62df\u4fe1\u53f7\u8f6c\u6362\u5230\u79bb\u6563\u65f6\u95f4\u57df\u4e0a\u7684\u79bb\u6563\u4fe1\u53f7\u7684\u8fc7\u7a0b\u3002</p> <p>\u663e\u7136\uff0c\u6211\u4eec\u8fd9\u91cc\u91c7\u6837\u7684\u5b9a\u4e49\u548c\u8fd9\u91cc\u7684\u5b9a\u4e49\u5e76\u4e0d\u4e00\u6837\u3002\u4e0e\u4e4b\u4e0d\u540c\u7684\u662f\uff0c\u6211\u4eec\u9700\u8981\u4ece\u539f\u59cb\u7684\uff0c\u8fd1\u4f3c\u8fde\u7eed\u7684\u56fe\u7247\u4e2d\u63d0\u53d6\u51fa\u5177\u6709\u7279\u5f81\u7684\u4e00\u4e9b\u540c\u6837\u662f\u79bb\u6563\u7684\u7684\u4fe1\u606f\uff0c\u4ee5\u6b64\u6765\u5b9e\u73b0\u6211\u4eec\u5c06\u56fe\u7247\u8fdb\u884c\u653e\u5927\u7f29\u5c0f\u53d8\u6362\u7684\u76ee\u7684\u3002</p> <p>\u5173\u4e8e\u91c7\u6837\u66f4\u6570\u5b66\u7684\u5b9a\u4e49\uff0c\u5c31\u662f\u4f7f\u7528\uff08\u68b3\u5f62\uff09\u8109\u51b2\u51fd\u6570(Dirac comb function)\u53bb\u4e58\u88ab\u91c7\u6837\u7684\u51fd\u6570\u3002</p> <ul> <li>\u8109\u51b2\u51fd\u6570\u7ecf\u8fc7 Fourier \u53d8\u6362\u540e\u4ecd\u7136\u662f\u68b3\u5f62\u7684\u3002</li> </ul> <p></p> <ul> <li>\u901a\u8fc7\u8109\u51b2\u51fd\u6570\uff0c\u6211\u4eec\u5c06\u7279\u5b9a\u9891\u7387\u7684\u5185\u5bb9\u7ed9\u8fc7\u6ee4\u4e0b\u6765\uff0c\u5c06\u4e00\u4e2a\u201c\u8fde\u7eed\u201d\u7684\u5185\u5bb9\u91c7\u6837\u4e3a\u4e86\u4e00\u4e2a\u201c\u79bb\u6563\u201d\u7684\u5185\u5bb9\u3002</li> </ul> <p></p> <p>\u53d6\u51b3\u4e8e\u8109\u51b2\u51fd\u6570\u7684\u9891\u7387\uff0c\u91c7\u6837\u53c8\u88ab\u5206\u4e3a\u5bc6\u96c6\u91c7\u6837(Dense sampling)\u548c\u7a00\u758f\u91c7\u6837(Sparse sampling)\uff0c\u4e5f\u5c31\u5206\u522b\u5bf9\u5e94\u7740\u4e4b\u524d\u63d0\u5230\u7684\uff0c\u91c7\u6837\u9891\u7387\u8f83\u9ad8\u548c\u91c7\u6837\u9891\u7387\u8f83\u4f4e\u7684\u60c5\u51b5\u3002</p> <p>\u800c\u7a00\u758f\u91c7\u6837\u5bfc\u81f4\u7684\u4fe1\u53f7\u8d70\u6837\u95ee\u9898\uff0c\u5c31\u662f\u91c7\u6837\u7ed3\u679c\u518d\u9891\u7387\u57df\u4e2d\u51fa\u73b0\u4e86\u4ea4\u96c6\u3002</p> <ul> <li> TODO: \u7406\u89e3\u5e76\u89e3\u91ca\u8fd9\u4e00\u70b9\u3002</li> </ul>"},{"location":"cour_note/D2QD_Intro2CV/Lec03/#\u51cf\u5c11\u8d70\u6837","title":"\u51cf\u5c11\u8d70\u6837","text":"<p>\u65e2\u7136\u641e\u6e05\u695a\u4e86\u8d70\u6837\u662f\u5982\u4f55\u4ea7\u751f\u7684\uff0c\u90a3\u63a5\u4e0b\u6765\u6211\u4eec\u5c31\u9700\u8981\u8003\u8651\u5982\u4f55\u51cf\u5c11\u4fe1\u53f7\u8d70\u6837\u3002</p> <p>\u603b\u4f53\u6765\u8bf4\uff0c\u6709\u8fd9\u4e48\u4e24\u79cd\u9009\u62e9\uff1a</p> <ol> <li>\u63d0\u9ad8\u91c7\u6837\u9891\u7387\uff1b</li> <li>\u5148\u8fc7\u6ee4\u9ad8\u9891\u518d\u91c7\u6837\uff1b</li> </ol> <p>\u9996\u5148\u6211\u4eec\u56de\u987e\u77e5\u9053\uff0c\u8d70\u6837\u662f\u7531\u4e8e\u91c7\u6837\u9891\u7387\u4f4e\u4e8e\u56fe\u50cf\u9ad8\u9891\u5bfc\u81f4\u7684\uff0c\u90a3\u4e48\u6211\u4eec\u53ea\u9700\u8981\u63d0\u9ad8\u91c7\u6837\u9891\u7387\u5c31\u80fd\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\u4e86\u3002</p> <p>\u800c\u5177\u4f53\u9700\u8981\u63d0\u9ad8\u5230\u591a\u5c11\u5462\uff1f\u5c31\u9700\u8981\u5948\u594e\u65af\u91c7\u6837\u5b9a\u7406(Nyquies-Shannon Theorem)\u3002</p> <p>\u5948\u594e\u65af\u91c7\u6837\u5b9a\u7406</p> <p>\u5f53\u7136\uff0c\u4e3a\u4e86\u8de8\u8fc7\u4e00\u4e2a\u66f4\u9ad8\u7684\u95e8\u69db\u6211\u4eec\u4e5f\u4e0d\u4e00\u5b9a\u9700\u8981\u589e\u957f\u81ea\u5df1\u7684\u817f\u3002\u5728\u80fd\u591f\u63a5\u53d7\u7684\u60c5\u51b5\u4e0b\uff0c\u6211\u4eec\u4e5f\u53ef\u4ee5\u9009\u62e9\u964d\u4f4e\u95e8\u69db\u2014\u2014\u5373\uff0c\u5148\u5c06\u9ad8\u9891\u6ee4\u6ce2\uff0c\u518d\u8fdb\u884c\u91c7\u6837\u3002</p> <p>\u66f4\u5f62\u8c61\u5730\u6765\u8bf4\uff0c\u5728\u9891\u7387\u57df\u4e2d\u53bb\u6389\u4ea4\u96c6\u7684\u624b\u6bb5\u4e3a\uff1a</p> <p></p> <p>\u90a3\u4e48\u8981\u5982\u4f55\u5b9e\u73b0\u5462\uff1f</p> <p>\u56de\u987e\u6211\u4eec\u4e00\u5f00\u59cb\u7ed9\u51fa\u7684\uff0c\u5173\u4e8e\u9891\u7387\u7684\u4e00\u4e2a\u6a21\u7cca\u7684\u7406\u89e3\uff0c\u201c\u5982\u679c\u4e00\u4e2a\u56fe\u50cf\u7684\u67d0\u4e2a\u90e8\u5206\u53d8\u5316\u8d8a\u5267\u70c8\uff0c\u4e00\u822c\u6765\u8bf4\u5176\u9891\u7387\u5c31\u4f1a\u8f83\u5927\u201d\u3002\u6362\u53e5\u8bdd\u6765\u8bf4\uff0c\u8981\u6d88\u53bb\u8fd9\u4e2a\u9ad8\u9891\uff0c\u6211\u4eec\u5c31\u9700\u8981\u8ba9\u62b9\u53bb\u8fd9\u4e9b\u201c\u53d8\u5316\u5267\u70c8\u201d\u7684\u6210\u5206\u3002\u518d\u63a5\u5730\u6c14\u4e00\u70b9\uff0c\u5c31\u662f\u6211\u4eec\u9700\u8981\u5c06\u8fd9\u4e9b\u68f1\u89d2\u62b9\u5f00\u2014\u2014\u6240\u4ee5\u4e00\u79cd\u624b\u6bb5\u5c31\u662f\u8fdb\u884c\u6a21\u7cca\u3002</p> \u4e00\u4e2a\u76f4\u89c2\u7684 \ud83c\udf30 <p>\u6211\u4eec\u4ee5\u5bf9\u4e00\u4e2a\u4e09\u89d2\u5f62\u91c7\u6837\u4e3a\u4f8b\uff0c\u8bf4\u660e\u5982\u4f55\u6ee4\u9ad8\u9891\uff1a</p> <p></p> <p>\u53ef\u4ee5\u53d1\u73b0\uff0c\u76f4\u63a5\u91c7\u6837\u4f1a\u5bfc\u81f4\u7ed3\u679c\u4e0d\u592a\u7406\u60f3\u63a5\u4e0b\u6765\u6211\u4eec\u5728\u91c7\u6837\u4e4b\u524d\u8fdb\u884c\u4e00\u6b21\u6a21\u7cca\u64cd\u4f5c\uff1a</p> <p></p> <p>\u5b83\u5c06\u8d85\u8fc7\u5948\u594e\u65af\u9891\u7387\u7684\u90e8\u5206\u6ee4\u6ce2\u540e\uff0c\u660e\u663e\u53d1\u73b0\u91c7\u6837\u4fdd\u7559\u7684\u539f\u672c\u56fe\u50cf\u7684\u7279\u5f81\u66f4\u591a\u4e86\u3002</p> <p>\u800c\u8fd9\u91cc\u5c31\u4ea7\u751f\u4e86\u4e00\u4e2a\u6bd4\u8f83\u8d34\u8fd1\u65e5\u5e38\u751f\u6d3b\u7684\u8bcd\uff0c\u53eb\u6297\u952f\u9f7f(anti-aliasing)\uff0c\u6216\u8005\u8bf4\u53cd\u8d70\u6837\u3002</p> <p></p>"},{"location":"cour_note/D2QD_Intro2CV/Lec03/#\u5948\u594e\u65af\u91c7\u6837\u5b9a\u7406","title":"\u5948\u594e\u65af\u91c7\u6837\u5b9a\u7406","text":"<p>\u9996\u5148\u89c4\u5b9a\u9891\u5e26\u9650\u5236\u4fe1\u53f7(band-limited signal) \\(f_0\\) \u662f\u56fe\u50cf\u9891\u7387\u7684\u4e00\u4e2a\u4e0a\u754c\uff1b\u5219\u5948\u594e\u65af\u91c7\u6837\u5b9a\u7406\u6307\u51fa\uff0c\u5982\u679c\u91c7\u6837\u9891\u7387\u5927\u4e8e \\(2f_0\\)\uff0c\u5219\u8be5\u91c7\u6837\u5f97\u5230\u7684\u7ed3\u679c\u53ef\u4ee5\u5b8c\u7f8e\u8868\u5f81\u539f\u51fd\u6570\u7684\u7279\u5f81\uff0c\u5373 \"perfectly reconstruct\"\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec03/#\u653e\u5927\u56fe\u7247\u5411\u4e0a\u91c7\u6837--\u63d2\u503c","title":"\u653e\u5927\u56fe\u7247\uff1a\u5411\u4e0a\u91c7\u6837 / \u63d2\u503c","text":"<p>\u56fe\u50cf\u653e\u5927(image magnification)\u662f\u56fe\u50cf\u7f29\u5c0f\u7684\u9006\u53d8\u6362(\u5e9f\u8bdd)\uff0c\u4f46\u662f\u5b9e\u9645\u4e0a\u5e76\u4e0d\u80fd\u4e25\u683c\u5730\u8bf4\u662f\u9006\u53d8\u6362\uff0c\u56e0\u4e3a\u56fe\u50cf\u7f29\u5c0f\u4e0e\u56fe\u50cf\u653e\u5927\u90fd\u662f\u4e0d\u53ef\u9006\u7684\u2014\u2014\u5373\uff0c\u56fe\u7247\u7f29\u5c0f\u5fc5\u7136\u5e26\u5566\u50cf\u7d20\u635f\u5931\uff0c\u56fe\u50cf\u653e\u5927\u5fc5\u7136\u5e26\u6765\u4e00\u4e9b\u901a\u8fc7\u8ba1\u7b97\u5f97\u5230\u7684\u8fd1\u4f3c\u50cf\u7d20\uff0c\u800c\u8fd9\u4e9b\u50cf\u7d20\u5728\u53d8\u6362\u5f97\u5230\u7684\u7ed3\u679c\u56fe\u50cf\u4e2d\u4e0e\u539f\u672c\u50cf\u7d20\u662f\u65e0\u6cd5\u533a\u5206\u7684\u3002</p> <p>\u90a3\u4e48\uff0c\u5355\u5c31\u56fe\u50cf\u653e\u5927\u6765\u8bf4\uff0c\u6211\u4eec\u5c31\u9700\u8981\u6839\u636e\u5df2\u6709\u7684\u50cf\u7d20\uff0c\u8fdb\u884c\u4e00\u4e9b\u63d2\u503c(interpolation)\u64cd\u4f5c\uff0c\u4ee5\u751f\u6210\u90a3\u4e9b\u653e\u5927\u8fc7\u7a0b\u4e2d\u65b0\u51fa\u73b0\u7684\u50cf\u7d20\u3002</p> <p>\u6211\u4eec\u4ece\u5bf9\u4e00\u4e2a\u4e00\u5143\u4e00\u7ef4\u51fd\u6570\u63d2\u503c\u7684\u89d2\u5ea6\u6765\u770b\u8fd9\u4e2a\u95ee\u9898\uff0c\u5373\u628a\u8fd9\u4e2a\u95ee\u9898\u62bd\u8c61\u4e3a\u5728\u91c7\u6837\u5f53\u4e2d\u63d2\u5165\u70b9\u7684\u95ee\u9898\u3002\u4f8b\u5982\uff0c\u6211\u4eec\u73b0\u5728\u6709\u4e00\u4e2a\u6765\u81ea\u4e8e\u6b63\u5f26\u51fd\u6570\u7684\u91c7\u6837\uff0c\u73b0\u5728\u6211\u4eec\u5e0c\u671b\u5728 \\(x\\in(x_i,x_{i+1})\\) \u4e2d\u63d2\u5165\u4e00\u4e2a\u70b9 \\((x_{ip}, y_{ip})\\) \u4f7f\u5f97\u5b83\u5c3d\u53ef\u80fd\u7b26\u5408\u539f\u672c\u7684\u6b63\u5f26\u51fd\u6570\u2014\u2014\u53c8\u6216\u8005\u8bf4\uff0c\u4f7f\u5f97\u5b83\u770b\u8d77\u6765\u5c3d\u53ef\u80fd\u5408\u7406\u3002</p> <p>\u800c\u8fd9\u4e2a\u95ee\u9898\uff0c\u6211\u4eec\u518d\u8fdb\u4e00\u6b65\u5730\u601d\u8003\uff0c\u5b9e\u9645\u4e0a\u5c31\u662f\u5229\u7528\u73b0\u6709\u7684\u70b9\u53bb\u62df\u5408\u4e00\u4e2a\u65b0\u7684\u51fd\u6570\uff0c\u7136\u540e\u518d\u7528\u8fd9\u4e2a\u51fd\u6570\u4e0a\u53d6\u7684\u70b9\u4f5c\u4e3a\u63d2\u5165\u7684\u70b9\u3002</p> <p>\u90a3\u4e48\u6bd4\u8f83\u5e38\u89c1\u7684\u201c\u62df\u5408\u201d\u65b9\u6cd5\u6709\u8fd9\u4e48\u51e0\u79cd\uff1a</p> <p>1.\u6700\u8fd1\u63d2\u503c(nearest-neighbor interpolation)\uff1b 2.\u7ebf\u6027\u63d2\u503c(linear interpolation)\uff1b 3.(3\u6b21)\u591a\u9879\u5f0f\u63d2\u503c(cubic interpolation)\uff1b</p> <p>\u63a5\u4e0b\u6765\u6211\u4eec\u4e00\u4e00\u4ecb\u7ecd\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec03/#\u6700\u8fd1\u63d2\u503c","title":"\u6700\u8fd1\u63d2\u503c","text":"<p>\u6240\u8c13\u7684\u6700\u8fd1\u63d2\u503c(nearest-neighbor interpolation)\uff0c\u5b9e\u9645\u4e0a\u4e0e KNN \u7684 K=1 \u7684\u7279\u6b8a\u60c5\u51b5\u3002\u5373\uff0c\\(y(x) = y(x_{\\mathop{argmin}(|x-x_i|)})\\)\u3002\u8bf4\u4eba\u8bdd\u5c31\u662f\u6a2a\u5750\u6807\u79bb\u54ea\u4e2a\u8fd1\uff0c\u5c31\u548c\u54ea\u4e2a\u4e00\u6837\u3002</p> <p></p> <p>\u5176\u4e2d\u7ea2\u8272\u4e3a\u539f\u6709\u7684\u91c7\u6837\u70b9\uff0c\u84dd\u8272\u4e3a\u6211\u4eec\u7684\u6240\u6709\u63d2\u503c\u6784\u6210\u7684\u66f2\u7ebf\u3002</p> <p>\u89c2\u5bdf\u8fd9\u6761\u84dd\u8272\u66f2\u7ebf\uff0c\u4e0d\u96be\u53d1\u73b0\uff0c\u5b83\u5177\u6709\u8fd9\u51e0\u4e2a\u7279\u5f81\uff1a</p> <ul> <li>\u4e0d\u8fde\u7eed\uff08\u5177\u4f53\u6765\u8bf4\u5c31\u662f\u5728\u6bcf\u4e24\u4e2a\u91c7\u6837\u70b9\u7684\u4e2d\u95f4\uff0c\u4f1a\u51fa\u73b0\u65ad\u70b9\uff09\uff1b</li> <li>\u4e0d\u5149\u6ed1\uff08\u65ad\u70b9\u5904\u65e0\u6cd5\u6c42\u5bfc\uff09\uff1b</li> </ul> <p>\u800c\u4e14\u62cd\u8111\u74dc\u60f3\u60f3\u4e5f\u80fd\u611f\u53d7\u5230\uff0c\u8fd9\u79cd\u63d2\u503c\u7684\u65b9\u6cd5\u5e76\u4e0d\u4f18\u96c5\u2014\u2014\u4e00\u5f20\u56fe\u7247\u653e\u5927\u540e\u4e00\u4e2a\u50cf\u7d20\u7684\u989c\u8272\u53d6\u51b3\u4e8e\u6700\u8fd1\u7684\u91c7\u6837\u50cf\u7d20\u989c\u8272\u2014\u2014\u5728\u591a\u6570\u60c5\u51b5\u4e0b\uff0c\u6211\u4eec\u5e76\u4e0d\u5e0c\u671b\u6709\u8fd9\u6837\u7684\u7ed3\u679c\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec03/#\u7ebf\u6027\u63d2\u503c","title":"\u7ebf\u6027\u63d2\u503c","text":"<p>\u7ebf\u6027\u63d2\u503c(linear interpolation)\u5c31\u662f\u76f4\u63a5\u505a\u8fde\u7ebf\uff0c\u5c06\u76f8\u90bb\u7684\u70b9\u4e24\u4e24\u7528\u76f4\u7ebf\u8fde\u8d77\u6765\uff0c\u7ed8\u5236\u51fa\u4e00\u4e2a\u6298\u7ebf\u56fe\u3002</p> <p></p> <p>\u5176\u4e2d\u7ea2\u8272\u4e3a\u539f\u6709\u7684\u91c7\u6837\u70b9\uff0c\u84dd\u8272\u4e3a\u6211\u4eec\u7684\u6240\u6709\u63d2\u503c\u6784\u6210\u7684\u66f2\u7ebf\u3002</p> <p>\u53ef\u4ee5\u53d1\u73b0\uff0c\u76f8\u6bd4\u4e8e\u6700\u8fd1\u63d2\u503c\uff0c\u7ebf\u6027\u63d2\u503c\u5bf9\u539f\u51fd\u6570\u7684\u62df\u5408\u6027\u76f8\u5bf9\u6765\u8bf4\u597d\u4e86\u5f88\u591a\uff0c\u800c\u4e14\u53d8\u5f97\u8fde\u7eed\u4e86\uff0c\u89c2\u5bdf\u84dd\u8272\u66f2\u7ebf\uff0c\u53d1\u73b0\u6709\u8fd9\u4e48\u51e0\u4e2a\u7279\u5f81\uff1a</p> <ul> <li>\u8fde\u7eed\uff1b</li> <li>\u4e0d\u5149\u6ed1\uff08\u5728\u91c7\u6837\u70b9\u51fd\u6570\u4f1a\u51fa\u73b0\u7a81\u53d8\uff0c\u65e0\u6cd5\u6c42\u5bfc\uff09\uff1b</li> </ul> <p>\u4e8e\u662f\u6211\u4eec\u7ee7\u7eed\u6539\u8fdb\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec03/#3\u6b21\u591a\u9879\u5f0f\u63d2\u503c","title":"(3\u6b21)\u591a\u9879\u5f0f\u63d2\u503c","text":"<p>\u987e\u540d\u601d\u4e49\uff0c(3\u6b21)\u591a\u9879\u5f0f\u63d2\u503c(cubic interpolation)\u5c31\u662f\u4f7f\u7528\u591a\u9879\u5f0f\u51fd\u6570\u6bb5\u6765\u62df\u5408\u91c7\u6837\u533a\u95f4\u3002</p> <p>\u8fd9\u91cc\u9700\u8981\u505a\u4e00\u4e2a\u8fa8\u6790\uff1a\u5e76\u4e0d\u662f\u7528\u4e00\u4e2a\u591a\u9879\u5f0f\u6765\u62df\u5408\u6240\u6709\u7684\u91c7\u6837\u70b9\uff0c\u800c\u662f\u7528\u591a\u9879\u5f0f\u6765\u62df\u5408\u4e00\u5bf9\u91c7\u6837\u70b9\uff0c\u5373\u4e00\u4e2a interval\u3002</p> <p></p> <p>\u5176\u4e2d\u7ea2\u8272\u4e3a\u539f\u6709\u7684\u91c7\u6837\u70b9\uff0c\u84dd\u8272\u4e3a\u6211\u4eec\u7684\u6240\u6709\u63d2\u503c\u6784\u6210\u7684\u66f2\u7ebf\u3002</p> <p>\u5176\u4e2d\uff0c\u6bcf\u4e00\u6bb5 interval \u7684\u84dd\u8272\u7ebf\u6761\u90fd\u7b26\u5408 \\(f_i(x) = a_ix^3 + b_ix^2 + c_ix + d_i, x \\in [x_i, x_{i+1}]\\)\uff1b\u5e76\u4e14\u6211\u4eec\u4fdd\u8bc1\u5728\u91c7\u6837\u70b9\u5904\u5b83\u4eec\u90fd\u662f\u5149\u6ed1\u7684\uff0c\u5373\u4fdd\u8bc1 \\(\\forall i, \\frac{\\mathrm{d}f_i(x_{i+1})}{\\mathrm{d} x} = \\frac{\\mathrm{d}f_{i+1}(x_{i+1})}{\\mathrm{d} x}\\)</p> <p>\u4e8e\u662f\uff0c\u5b83\u81ea\u7136\u5c31\u5177\u6709\u4ee5\u4e0b\u6027\u8d28\uff1a</p> <ol> <li>\u8fde\u7eed\uff1b</li> <li>\u5149\u6ed1\uff1b</li> </ol> <p>\u66f4\u5177\u4f53\u7684</p> <p>\u521a\u624d\u8bb2\u7684\u90fd\u662f\u4ece\u4e00\u7ef4\u51fd\u6570\u7684\u89d2\u5ea6\u6765\u601d\u8003\u63d2\u503c\uff0c\u73b0\u5728\u6211\u4eec\u6765\u4ecb\u7ecd\u4e00\u4e9b\u5728\u4e8c\u7ef4\u5c42\u9762\u505a\u63d2\u503c\u7684\u6848\u4f8b\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec03/#\u53cc\u7ebf\u6027\u63d2\u503c","title":"\u53cc\u7ebf\u6027\u63d2\u503c","text":"<p>\u53cc\u7ebf\u6027\u63d2\u503c(bilinear interpolation)\u5c31\u662f\u5728\u4e8c\u7ef4\u5e73\u9762\u5185\u505a\u7ebf\u6027\u63d2\u503c\uff0c\u601d\u8def\u975e\u5e38\u7b80\u5355\u3002</p> <p></p> <p>\u5982\u56fe\uff0c\u6211\u4eec\u5e0c\u671b\u5728\u7ea2\u70b9\u5904\u8fdb\u884c\u63d2\u503c\uff0c\u90a3\u4e48\u6211\u4eec\u5c31\u4f1a\u9009\u53d6\u4e0e\u4e4b\u76f8\u90bb\u7684\u56db\u4e2a\u70b9\uff0c\\(u_{ij},\\;\\; i,j\\in \\{0,1\\}\\)\uff0c\u518d\u6839\u636e\u8fd9\u4e2a\u70b9\u5728\u8fd9\u4e2a\u77e9\u9635\u4e2d\u7684\u4f4d\u7f6e\u8fdb\u884c\u6c42\u503c\u3002</p> \u5177\u4f53\u8ba1\u7b97\u65b9\u6cd5 <p> </p>"},{"location":"cour_note/D2QD_Intro2CV/Lec03/#\u53cc3\u6b21\u591a\u9879\u5f0f\u63d2\u503c","title":"\u53cc(3\u6b21)\u591a\u9879\u5f0f\u63d2\u503c","text":"<p>wiki \ud83d\udd17</p> <p>\u53cc(3\u6b21)\u591a\u9879\u5f0f\u63d2\u503c(bicubic interpolation)\u5373\u5728\u4e8c\u7ef4\u5e73\u9762\u505a(3\u6b21)\u591a\u9879\u5f0f\u63d2\u503c\uff0c\u5b9e\u73b0\u601d\u8def\u4e0e\u53cc\u7ebf\u6027\u63d2\u503c\u662f\u7c7b\u4f3c\u7684\u3002</p> \\[ p(x,y) = \\sum_{i=0}^{3}\\sum_{j=0}^{3}a_{i,j}x^iy^j \\] <p>What's '4' means here?</p> <p>\u8d85\u5206\u8fa8\u7387</p> <p>\u5728\u5f97\u5230\u8fd9\u4e9b\u63d2\u503c\u7b56\u7565\u540e\uff0c\u6211\u4eec\u5c31\u53ef\u4ee5\u5f15\u51fa\u8d85\u5206\u8fa8\u7387(Super-Resolution)\u8fd9\u4e2a\u6982\u5ff5\uff0c\u5373\u901a\u8fc7\u63d2\u503c\uff0c\u6211\u4eec\u5c06\u4e00\u5f20\u56fe\u7247\u7684\u5206\u8fa8\u7387\u63d0\u9ad8\uff0c\u5f97\u5230\u8d85\u8fc7\u539f\u6709\u56fe\u7247\u5206\u8fa8\u7387\u7684\u4e00\u5f20\u56fe\u7247\u3002</p> <p>\u4f8b\u5982\uff0c\u901a\u8fc7\u4e0b\u9762\u8fd9\u4e2a\u5bf9\u6bd4\uff0c\u6211\u4eec\u4f1a\u53d1\u73b0\uff0c\u591a\u9879\u5f0f\u63d2\u503c\u7684\u8868\u73b0\u6bd4\u7ebf\u6027\u63d2\u503c\u7684\u8868\u73b0\u597d\u4e0d\u5c11\u3002</p> <p></p>"},{"location":"cour_note/D2QD_Intro2CV/Lec03/#\u6539\u53d8\u56fe\u50cf\u957f\u5bbd\u6bd4","title":"\u6539\u53d8\u56fe\u50cf\u957f\u5bbd\u6bd4","text":"<p>\u6539\u53d8\u56fe\u50cf\u957f\u5bbd\u6bd4(aspect ratio)\u8fd9\u4ef6\u4e8b\u8c8c\u4f3c\u53ef\u4ee5\u76f4\u63a5\u901a\u8fc7\u5355\u7ef4\u5ea6\u4e0a\u8fdb\u884c\u7f29\u653e\u6765\u5b9e\u73b0\uff08\u8fdb\u884c\u4e00\u7ef4\u63d2\u503cor\u91c7\u6837\uff09\uff0c\u4f46\u662f\u662f\u5426\u5b58\u5728\u522b\u7684\u65b9\u6cd5\uff0c\u4e0d\u5927\u5e45\u6539\u53d8\u6574\u4f53\u56fe\u50cf\u5f62\u72b6\u7684\u60c5\u51b5\u4e0b\uff0c\u5b9e\u73b0\u8be5\u5f7c\u5cb8\u957f\u5bbd\u6bd4\u5462\uff1f</p> <p>\u5b9e\u9645\u4e0a\uff0c\u6709\u4e00\u4e2a\u505a\u6cd5\u5c31\u662f\u5077\u5077\u5220\u6389\u51e0\u884c/\u51e0\u5217\u50cf\u7d20\uff0c\u5bf9\u4eba\u773c\u6765\u8bf4\u8fd9\u8c8c\u4f3c\u662f\u96be\u4ee5\u5bdf\u89c9\u7684\u3002</p> <p>\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u6765\u505a\u4e00\u4e9b\u6539\u8fdb\uff0c\u6211\u4eec\u8fd9\u6b21\u4e0d\u662f\u66b4\u529b\u7684\u5220\u9664\u4e00\u884c\u6216\u4e00\u5217\uff0c\u800c\u662f\u6709\u9009\u62e9\u6027\u7684\uff0c\u5728\u6bcf\u4e00\u884c\u91cc\u5220\u9664\u51e0\u4e2a\u50cf\u7d20\u3002\u4e3a\u4e86\u4fdd\u8bc1\u56fe\u50cf\u4e0d\u9519\u4f4d\uff0c\u6211\u4eec\u5e0c\u671b\u8fd9\u4e9b\u9009\u4e2d\u7684\u50cf\u7d20\u53ef\u4ee5\u88ab\u770b\u4f5c\u56fe\u50cf\u4e0a\u7684\u201c\u88c2\u7f1d\u201d\uff0c\u5373\u4e00\u6761\u5f2f\u5f2f\u66f2\u66f2\u7684\u66f2\u7ebf\u3002</p> <p></p> <p>\u8fd9\u79cd\u505a\u6cd5\u53ebseam carving\uff0c\u6211\u4eec\u9700\u8981\u627e\u5230\u6bd4\u8f83\u4e0d\u91cd\u8981\u7684\u4e00\u8fde\u4e32\u8fde\u7eed\u50cf\u7d20\u3002\u800c\u8fd9\u91cc\u7684\u201c\u4e0d\u91cd\u8981\u201d\uff0c\u6307\u7684\u5c31\u662f\u90a3\u4e9b\u53d8\u5316\u4e0d\u90a3\u4e48\u5267\u70c8\u7684\u50cf\u7d20\uff0c\u5373\u4e0e\u5468\u56f4\u5341\u5206\u76f8\u8fd1\u7684\u70b9\u3002</p> <p>\u66f4\u6570\u5b66\u7684\u8868\u8ff0\u662f\uff1a</p> <ul> <li>\u6211\u4eec\u5b9a\u4e49edge energy\\(E(I) = \\big|\\frac{\\partial I}{\\partial x}\\big| + \\big| \\frac{\\partial I}{\\partial y} \\big|\\)\uff1b</li> <li>\u627e\u5230\u4ece\u9876\u5230\u5e95\u7684\u4e00\u6761\u8054\u901a\uff08\u5c31\u662f\u4e0b\u4e00\u4e2a\u70b9\u80af\u5b9a\u4e0e\u4e0a\u4e00\u4e2a\u70b9\u76f8\u90bb\u6216\u8005\u5171\u540c\u9876\u70b9\uff09\u8def\u5f84\uff0c\u4f7f\u5f97 edge energy \u6700\u5c0f\uff1b</li> <li>\u7136\u540e\u5c06\u8fd9\u6761\u8def\u5f84\u4ece\u56fe\u7247\u4e2d\u5220\u9664\uff0c\u5c31\u597d\u50cf\u5c06\u8fd9\u4e2a\u88c2\u7f1d\u4e24\u8fb9\u62fc\u8d77\u6765\uff1b</li> </ul> <p>\u800c\u81f3\u4e8e\u5bfb\u627e\u6700\u77ed\u8def\u7684\u7b97\u6cd5\uff0c\u5219\u662f\u4e2a dp \u95ee\u9898\uff0c\u5728\u8fd9\u91cc\u5c31\u4e0d\u5c55\u5f00\u4e86\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec04/","title":"Lecture 4 | Model Fitting and Optimization","text":"<p> \u7ea6 4135 \u4e2a\u5b57  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 14 \u5206\u949f</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec04/#\u4f18\u5316","title":"\u4f18\u5316","text":"<p>\u9996\u5148\u6211\u4eec\u6765\u5b9a\u4e49\u4e00\u4e2a\u4f18\u5316(Optimization)\u95ee\u9898\u7684\u6a21\u578b\uff1a</p> <p>\u4f18\u5316\u95ee\u9898\u7684\u6a21\u578b</p> <p>\u8bbe\u76ee\u6807\u51fd\u6570\\(f_0(\\vec x)\\) \u6ee1\u8db3\u7ea6\u675f\u6761\u4ef6\uff1a</p> \\[ \\left\\{ \\begin{aligned}     f_i(\\vec x) &amp;\\leq 0,  &amp;i = 1,...,m &amp; \\text{inequality constraint functions} \\\\     g_i(\\vec x) &amp;= 0,  &amp;i = 1,...,p &amp; \\text{equality constraint functions}&amp; \\end{aligned} \\right. \\] <p>\u6c42 \\(\\vec x\\in \\mathrm{R}^n\\) \uff0c\u4f7f \\(f_0(\\vec{x})\\) \u6700\u5c0f\uff08\u5373\u6700\u4f18\uff09\u3002</p> <p>\u5f88\u663e\u7136\uff0c\u8fd9\u548c\u6211\u4eec\u9ad8\u4e2d\u63a5\u89e6\u7684\u7ebf\u6027\u89c4\u5212\u5f88\u50cf\uff0c\u5b9e\u9645\u4e0a\u7ebf\u6027\u89c4\u5212\u5c31\u662f\u5176\u4e2d\u4e00\u79cd\u4f18\u5316\u95ee\u9898\u3002</p> <p>\u800c\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u9700\u8981\u5c1d\u8bd5\u5c06\u4e00\u4e9b\u590d\u6742\u95ee\u9898\u8f6c\u5316\u4e3a\u4f18\u5316\u95ee\u9898\uff0c\u5373\u6839\u636e\u95ee\u9898\uff0c\u5199\u51fa\u76ee\u6807\u51fd\u6570\u548c\u7ea6\u675f\u6761\u4ef6\uff0c\u5e76\u901a\u8fc7\u4e00\u4e9b\u65b9\u6cd5\u6765\u5f97\u5230\u6211\u4eec\u9700\u8981\u7684 \\(\\vec x\\)\u3002</p> <p>\ud83c\udf30 \u56fe\u50cf\u53bb\u6a21\u7cca\u95ee\u9898</p> <p>\u5728\u8fd9\u4e2a \ud83c\udf30 \u4e2d\uff0c\u6211\u4eec\u5df2\u77e5\u6a21\u7cca\u56fe\u50cf \\(Y\\) \u548c\u6a21\u7cca\u6ee4\u6ce2\u5668(\u5377\u79ef\u6838) \\(F\\)\uff0c\u9700\u8981\u901a\u8fc7\u4f18\u5316\u7684\u65b9\u6cd5\u6765\u6c42\u5377\u79ef\u8fd0\u7b97\u4e4b\u524d\u7684\u6e05\u6670\u56fe\u50cf \\(X\\)\u3002</p> <p>\u8fdb\u4e00\u6b65\u6765\u8bf4\uff0c\u5c31\u662f\u627e\u5230\u6e05\u6670\u7684\u56fe\u50cf \\(X\\)\uff0c\u4f7f\u5f97\u5b83\u505a\u6a21\u7cca\u5904\u7406\u540e\u4e0e\u5df2\u77e5\u7684\u6a21\u7cca\u56fe\u50cf \\(Y\\) \u5dee\u522b\u5c3d\u53ef\u80fd\u5c0f\uff0c\u4e8e\u662f\u95ee\u9898\u8f6c\u5316\u4e3a\uff1a</p> <ul> <li>\u76ee\u6807\u51fd\u6570\u4e3a \\(\\min\\limits_{X} || Y - F * X ||^2_2\\) \u7684\u4f18\u5316\u95ee\u9898\u3002</li> </ul>"},{"location":"cour_note/D2QD_Intro2CV/Lec04/#\u6a21\u578b\u62df\u5408","title":"\u6a21\u578b\u62df\u5408","text":"<p>\u4e3a\u4e86\u7814\u7a76\u5206\u6790\u5b9e\u9645\u95ee\u9898\uff0c\u6211\u4eec\u9700\u8981\u5bf9\u95ee\u9898\u8fdb\u884c\u4e00\u4e2a\u5efa\u6a21\uff0c\u66f4\u5177\u4f53\u7684\u6765\u8bf4\u5c31\u662f\u6839\u636e\u5b9e\u9645\u60c5\u51b5\uff0c\u5bfb\u627e\u6570\u636e\u4e4b\u95f4\u7684\u5173\u7cfb\uff0c\u5e76\u5efa\u7acb\u6570\u5b66\u6a21\u578b\u3002</p> <p>\u4e00\u4e2a\u6570\u5b66\u6a21\u578b(model)\u63cf\u8ff0\u95ee\u9898\u4e2d\u8f93\u5165\u548c\u8f93\u51fa\u7684\u5173\u7cfb\uff0c\u4f8b\u5982\uff1a\u7ebf\u6027\u6a21\u578b(linear model) \\(b = a^T x\\) \u5c31\u63cf\u8ff0\u4e86\u8f93\u5165(input) \\(a\\) \u548c\u8f93\u51fa(output) \\(b\\) \u5173\u4e8e\u6a21\u578b\u53c2\u6570(model parameter) \\(x\\) \u7684\u5173\u7cfb\u3002</p> <p>\u800c\u5b9e\u9645\u7684\u7ed3\u679c\u5f88\u96be\u4e25\u683c\u6ee1\u8db3\u6570\u5b66\u6a21\u578b\uff0c\u8fd9\u662f\u7531\u591a\u65b9\u539f\u56e0\u5bfc\u81f4\u7684\uff0c\u6240\u4ee5\u6211\u4eec\u5f80\u5f80\u505a\u7684\u662f\u5bf9\u5b9e\u9645\u60c5\u51b5\u8fdb\u884c\u6a21\u578b\u62df\u5408(model fitting)\u3002</p> <p>\u66f4\u5177\u4f53\u7684\u6765\u8bf4\uff0c\u6211\u4eec\u53ef\u80fd\u5df2\u7ecf\u6709\u4e00\u4e2a\u5148\u9a8c\u7684\u5047\u8bbe\uff0c\u5373\u6570\u636e\u7b26\u5408\u54ea\u79cd\u6a21\u578b\uff0c\u63a5\u4e0b\u6765\u6839\u636e\u6570\u636e\u6765\u5206\u6790\u5f97\u5230\u5408\u9002\u7684 model parameters\uff0c\u800c\u8fd9\u4e2a\u6b65\u9aa4\u4e5f\u5e38\u5e38\u88ab\u79f0\u4e3a learning\u3002</p> <p>\u4e00\u79cd\u6bd4\u8f83\u7ecf\u5178\u7684\u903c\u8fd1\u65b9\u6cd5\uff08\u6700\u5c0f\u4e8c\u4e58\u6cd5\uff09\u662f\u6c42\u4f7f\u5747\u65b9\u8bef\u5dee(mean square error, MSE)\u6700\u5c0f\u7684 model parameters\uff1a</p> <p>\\(\\hat{x} = \\mathop{\\arg \\min\\limits_x} \\sum\\limits_i(b_i - a_i^Tx)^2\\)</p> <p>\u800c\u5982\u679c\u6211\u4eec\u5047\u8bbe\u6570\u636e\u4e2d\u7684\u566a\u58f0\u662f\u9ad8\u65af\u5206\u5e03\u7684\uff08\u5b9e\u9645\u4e0a\u5927\u90e8\u5206\u566a\u58f0\u5728\u57fa\u6570\u8db3\u591f\u5927\u7684\u60c5\u51b5\u4e0b\u90fd\u53ef\u4ee5\u770b\u4f5c\u4e3a\u9ad8\u65af\u5206\u5e03\u7684\uff09\uff0c\u90a3\u4e48\u53ef\u4ee5\u4e0e\u7edf\u8ba1\u5b66\u7684\u6781\u5927\u4f3c\u7136\u4f30\u8ba1(maximum likelihood estimation, MLE)\u76f8\u7edf\u4e00.</p> <p>MSE vs. MLE</p> <p>MSE vs MLE for linear regression</p> <p>\u5177\u4f53\u6765\u8bf4\uff0c\\(b_i = a_i^T x + n, \\;\\; n \\sim G(0,\\sigma)\\)\uff0c\u800c\u5bf9\u4e8e\u7ed9\u5b9a\u7684 \\(x\\)\uff0c\u5176\u4f3c\u7136(likehood)\\(P[(a_i,b_i)|x] = P[b_i-a_i^Tx] \\propto \\exp \\left( - \\frac{(b_i-a_i^Tx)^2}{2\\sigma^2} \\right)\\)\uff0c\u8868\u793a\u5728 model parameter \u4e3a \\(x\\) \u7684\u60c5\u51b5\u4e0b\uff0c\u6570\u636e\u7b26\u5408 \\((a_i,b_i)\\) \u7684\u53ef\u80fd\u6027\u3002</p> Maximum Likelihood Estimation <p> If the data points are independent,</p> \\[ \\begin{aligned} P[(a_1, b_1)(a_2, b_2)\\dots|x] &amp; = \\prod\\limits_iP[(a_i, b_i)|x] = \\prod\\limits_i P[b_i - a_i^T x] \\\\ &amp; \\propto \\exp\\left(-\\frac{\\sum_i(b_i - a_i^Tx)^2}{2\\sigma^2}\\right) = \\exp\\left(-\\frac{||Ax-b||^2_2}{2\\sigma^2}\\right) \\end{aligned} \\] <p>That is, maximize the likelihood to find the best \\(x\\).</p> \\[ \\begin{aligned} \\hat x &amp;= \\mathop{\\arg \\max\\limits_x} P[(a_1, b_1)(a_2, b_2)\\dots|x] \\\\ &amp;= \\mathop{\\arg \\max\\limits_x} \\exp\\left(-\\frac{||Ax-b||^2_2}{2\\sigma^2}\\right)  = \\mathop{\\arg \\min\\limits_x}||Ax - b||_2^2 \\end{aligned} \\] <p>MSE = MLE with Gaussian noise assumption</p> <p>\u9700\u8981\u8865\u6570\u5b66\u77e5\u8bc6\uff0c\u5b8c\u5584\u8fd9\u90e8\u5206\u5185\u5bb9</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec04/#\u6570\u503c\u65b9\u6cd5","title":"\u6570\u503c\u65b9\u6cd5","text":"<p>\u4e0a\u4e00\u5c0f\u8282\u4ecb\u7ecd\u4e86\u5982\u4f55\u5bf9\u5b9e\u9645\u95ee\u9898\u8fdb\u884c\u6570\u5b66\u5efa\u6a21\uff0c\u63a5\u4e0b\u6765\u9700\u8981\u4ecb\u7ecd\u7684\u662f\u5982\u4f55\u6c42\u89e3\u6570\u5b66\u6a21\u578b\u3002</p> <p>\u6211\u4eec\u77e5\u9053\uff0c\u5bf9\u4e8e\u4e00\u4e9b\u6bd4\u8f83\u7b80\u5355\u7684\u6a21\u578b\uff0c\u6211\u4eec\u53ef\u4ee5\u76f4\u63a5\u6c42\u5176\u89e3\u6790\u89e3(analytical solution)\uff0c\u6bd4\u5982\u4f7f\u7528\u6c42\u5bfc\u7b49\u65b9\u6cd5\u3002</p> <p>\ud83c\udf30</p> <p>\u4ee5\u521a\u624d\u7684\u7ebf\u6027 MSE \u4e3a\u4f8b\uff0c\\(\\hat{x} = \\mathop{\\arg \\min\\limits_x} \\sum\\limits_i(b_i - a_i^Tx)^2\\) \u7b49\u6548\u4e8e\u6c42\u89e3\u7b49\u5f0f \\(A^TAx=A^Tb\\)\u3002</p> <p>\u7136\u800c\uff0c\u5b9e\u9645\u60c5\u51b5\u662f\u5927\u90e8\u5206\u95ee\u9898\u8fc7\u4e8e\u590d\u6742\uff0c\u6211\u4eec\u6ca1\u6cd5\u76f4\u63a5\u6c42\u5176\u89e3\u6790\u89e3\uff0c\u6240\u4ee5\u6211\u4eec\u9700\u8981\u91c7\u7528\u4e00\u4e9b\u5373\u91c7\u7528\u4e00\u4e9b\u6570\u503c\u65b9\u6cd5(numerical methods)\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec04/#\u68af\u5ea6\u4e0b\u964d","title":"\u68af\u5ea6\u4e0b\u964d","text":"<p>\u7531\u4e8e\u76f8\u5173\u9886\u57df\u7684\u201c\u51fd\u6570\u201d\u7b49\u57fa\u672c\u4e0a\u90fd\u662f\u9ad8\u7ef4\u7684\uff0c\u6240\u4ee5\u6211\u4eec\u4e00\u822c\u4f7f\u7528\u4e8c\u7ef4\u51fd\u6570\u56fe\u50cf\u7684\u65b9\u6cd5\u6765\u5f62\u8c61\u8868\u793a\u51fd\u6570\uff0c\u5373\u4f7f\u7528\u201c\u7b49\u9ad8\u7ebf\u201d\u7684\u5f62\u5f0f\u6765\u53ef\u89c6\u5316\u51fd\u6570\u3002</p> <p>\u867d\u7136\u6ca1\u6cd5\u76f4\u63a5\u6c42\u89e3\u6790\u89e3\uff0c\u4f46\u662f\u4e00\u822c\u51fd\u6570\u90fd\u5177\u6709\u4e00\u4e9b\u5c40\u90e8\u6027\u8d28\uff0c\u4f8b\u5982\u6781\u503c\u70b9\u4e34\u57df\u7684\u68af\u5ea6\u90fd\u6307\u5411\u6781\u503c\u70b9\u3002\u6a21\u7cca\u5730\u6765\u8bf4\uff0c\u53ea\u8981\u6211\u4eec\u968f\u7740\u201c\u68af\u5ea6\u201d\u53bb\u201c\u4e0b\u964d\u201d\uff0c\u5c31\u6709\u53ef\u80fd\u627e\u5230\u6781\u503c\u70b9\uff0c\u8fd9\u5c31\u662f\u901a\u8fc7\u68af\u5ea6\u4e0b\u964d(gradient descent)\u7684\u65b9\u6cd5\u6765\u89e3\u51b3\u4f18\u5316\u95ee\u9898\u3002</p> <p>\u7b80\u5355\u63cf\u8ff0\u68af\u5ea6\u4e0b\u964d\u7684\u8fc7\u7a0b\uff1a</p> <ol> <li>\u521d\u59cb\u5316\u8d77\u70b9\u5750\u6807 x\uff1b</li> <li>\u76f4\u5230 x \u6536\u655b\u5230\u6211\u4eec\u6ee1\u610f\u7684\u7a0b\u5ea6\u4e4b\u524d\uff1a<ol> <li>\u8ba1\u7b97\u4e0b\u964d\u65b9\u5411 p\uff1b</li> <li>\u51b3\u5b9a\u4e0b\u964d\u6b65\u957f \u237a\uff1b</li> <li>\u66f4\u65b0 x = x + \u237ap\uff1b</li> </ol> </li> </ol> <p> </p> <p>Sourece: https://commons.wikimedia.org/w/index.php?curid=2283984</p> <p>\u5176\u4e2d\u6709\u4e09\u4ef6\u4e8b\u9700\u8981\u7279\u6b8a\u8bf4\u660e\uff1a</p> <ul> <li>\u5982\u4f55\u786e\u5b9a\u4e0b\u964d\u65b9\u5411 \\(\\vec p\\)</li> <li>\u5982\u4f55\u786e\u5b9a\u4e0b\u964d\u6b65\u957f</li> <li>\u5168\u5c40\u6700\u4f18\u548c\u5c40\u90e8\u6700\u4f18</li> </ul>"},{"location":"cour_note/D2QD_Intro2CV/Lec04/#\u786e\u5b9a\u4e0b\u964d\u65b9\u5411","title":"\u786e\u5b9a\u4e0b\u964d\u65b9\u5411","text":"<p>\u5bf9\u4e8e\u6211\u4eec\u4ee5\u524d\u63a5\u89e6\u8fc7\u7684\u51fd\u6570\uff0c\u5373\u5f62\u5f0f\u76f8\u5bf9\u7b80\u5355\u7684\u51fd\u6570\uff0c\u6211\u4eec\u5f53\u7136\u53ef\u4ee5\u76f4\u63a5\u6c42\u5176\u68af\u5ea6\u5f97\u5230\u4e0b\u964d\u65b9\u5411\u3002\u7136\u800c\u5b9e\u9645\u95ee\u9898\u4e2d\u7684\u51fd\u6570\u53ef\u80fd\u975e\u5e38\u590d\u6742\uff0c\u6216\u68af\u5ea6\u89e3\u6790\u5f0f\u5f88\u96be\u5f97\u5230\u3002\u8fd9\u65f6\u5019\u6211\u4eec\u5c31\u53ea\u80fd\u9000\u800c\u6c42\u5176\u6b21\uff0c\u6c42\u5176\u201c\u8fd1\u4f3c\u201d\u68af\u5ea6\u65b9\u5411\u3002\u6362\u53e5\u8bdd\u6765\u8bf4\uff0c\u6211\u4eec\u5e0c\u671b\u80fd\u591f\u627e\u5230\u4e00\u4e2a\u548c\u539f\u51fd\u6570\u5728\u5c40\u90e8\u548c\u8be5\u51fd\u6570\u5f88\u50cf\u7684\u62df\u5408\u51fd\u6570\uff0c\u5e76\u4e14\u7528\u8fd9\u4e2a\u62df\u5408\u51fd\u6570\u7684\u68af\u5ea6\u65b9\u5411\u6765\u51b3\u5b9a\u68af\u5ea6\u4e0b\u964d\u7684\u65b9\u5411\u3002</p> <p>\u4e8e\u662f\u6211\u4eec\u60f3\u5230\u6cf0\u52d2\u5c55\u5f00\uff0c\u5b83\u5c06\u51fd\u6570\u5c55\u5f00\u4e3a\u591a\u9879\u5f0f\uff0c\u800c\u591a\u9879\u5f0f\u7684\u68af\u5ea6\u662f\u76f8\u5bf9\u5bb9\u6613\u5f97\u5230\u7684\u3002</p> <p>\u5176\u4e2d\u6bd4\u8f83\u5e38\u7528\u7684\u662f\uff1a</p> <ul> <li>first-order approximation: \\(F(x_k + \\Delta x) \\approx F(x_k) + J_F \\Delta x\\)</li> <li>second-order approximation: \\(F(x_k + \\Delta x) \\approx F(x_k) + J_F\\Delta x + \\frac{1}{2}\\Delta x^T H_F \\Delta x\\)</li> </ul> <p>\u5176\u4e2d \\(J_F\\) \u662f\u96c5\u5404\u6bd4\u77e9\u9635\uff0c\u53ef\u4ee5\u7406\u89e3\u4e3a\u591a\u7ef4\u5411\u91cf\u51fd\u6570\u7684\u5bfc\u6570\uff1b\\(H_F\\) \u662f\u6d77\u68ee\u77e9\u9635\uff0c\u53ef\u4ee5\u7406\u89e3\u4e3a\u591a\u4f4d\u5411\u91cf\u51fd\u6570\u7684\u4e8c\u9636\u5bfc\u6570\u3002</p> <p>\u63a5\u4e0b\u6765\u4ee5 first-order approximation \u4e3a\u4f8b\u7ee7\u7eed\u5206\u6790\u3002</p> <p>\u89c2\u5bdf \\(F(x_k + \\Delta x) \\approx F(x_k) + J_F \\Delta x\\)\uff0c\u53d1\u73b0\u5f53 \\(J_F\\Delta x &lt; 0\\) \u65f6\uff0c \\(F(x_0 + \\Delta x)\\) \u5927\u6982\u7387\u6bd4 \\(F(x_0)\\) \u5c0f\uff0c\u5373\u201c\u4e0b\u964d\u201d\uff0c\u6240\u4ee5\u5728 first-order approximation \u7684\u60c5\u51b5\u4e0b\uff0c\u4e00\u822c\u9009\u62e9\u65b9\u5411 \\(\\vec p = -J_F^T\\)\uff0c\u4e8e\u662f\u4f4d\u79fb\u91cf \\(movement = -J_F \\cdot J_F^T \\cdot step\\)\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec04/#\u786e\u5b9a\u4e0b\u964d\u6b65\u957f","title":"\u786e\u5b9a\u4e0b\u964d\u6b65\u957f","text":"<p>\u5373\u4f7f\u4f46\u4ece\u4e0b\u964d\u901f\u7387\u6765\u8003\u8651\uff0c\u6b65\u957f\u592a\u957f\u6216\u592a\u5c0f\u4e5f\u90fd\u6709\u660e\u663e\u7684\u95ee\u9898\uff1a</p> <p> </p> <p>\u6240\u4ee5\u6b65\u957f\u7684\u9009\u62e9\u5bf9\u4e0b\u964d\u901f\u7387\u7684\u5341\u5206\u5173\u952e\u3002</p> <p>\u4e3a\u4e86\u4e13\u6ce8\u4e8e\u6b65\u957f\u7684\u9009\u62e9\uff0c\u6211\u4eec\u8bb0 \\(\\phi(\\alpha) = F(x+\\alpha h),\\;\\;\\text{where x and h fixed}, x\\geq 0\\)\u3002\u73b0\u5728\u6211\u4eec\u5e0c\u671b\u627e\u5230\u4e00\u4e2a\u80fd\u8ba9 \\(\\phi(\\alpha)\\) \u5c3d\u53ef\u80fd\u5c0f\u4e8e \\(\\phi(0)\\) \u7684 \\(\\alpha\\)\u3002\u63a5\u4e0b\u6765\u6211\u4eec\u4ecb\u7ecd Backtracking Algorithm\uff1a</p> <ol> <li>\u521d\u59cb\u5316 \\(\\alpha\\) \u4e3a\u4e00\u4e2a\u6bd4\u8f83\u5927\u7684\u503c\uff1b</li> <li>\u4e0d\u65ad\u51cf\u5c0f \\(\\alpha\\) \u76f4\u5230 \\(\\phi(\\alpha) \\leq \\phi(0) + \\gamma\\phi'(0)\\alpha\\)\uff1b<ul> <li>\u5176\u4e2d \\(\\gamma\\in(0,1)\\) \u662f\u4e00\u4e2a\u56fa\u5b9a\u7684\u53c2\u6570\uff1b</li> </ul> </li> </ol> <p> </p> <p>\u6362\u53e5\u8bdd\u8bf4\u5c31\u662f\uff0c\u7b26\u5408\u9884\u671f\u7684\u6700\u5927\u6b65\u957f\uff0c\u8fd9\u4e2a\u201c\u9884\u671f\u201d\uff0c\u5c31\u662f\u901a\u8fc7 \\(\\gamma\\) \u4f53\u73b0\u7684\u3002\u56fe\u4e2d\u7ea2\u8272\u865a\u7ebf\u548c\u9ed1\u8272\u7ec6\u7ebf\u5206\u522b\u662f \\(\\gamma\\) \u53d6\u8fb9\u754c\u503c\u65f6\u7684\u60c5\u51b5\uff0c\u800c\u7ea2\u8272\u5b9e\u7ebf\u5219\u8868\u793a\u6211\u4eec\u7684\u9884\u671f\u968f \\(\\alpha\\) \u7684\u53d8\u5316\u3002</p> <p>\u4e0a\u9762\u4f7f\u7528 first-order approximation \u4e3a\u4f8b\u4ecb\u7ecd\u7684\u8fd9\u5957\u65b9\u6cd5\u5c31\u662f\u6700\u901f\u68af\u5ea6\u4e0b\u964d\u6cd5(steepest descent method)\u3002</p> <p>\u6700\u901f\u68af\u5ea6\u4e0b\u964d\u6cd5</p> <p>\\(\\vec p = -J_F^T\\)\uff1b</p> <ul> <li>\u4f18\u70b9<ul> <li>\u5bb9\u6613\u5b9e\u73b0\uff1b</li> <li>\u5728\u8ddd\u79bb\u76ee\u6807\u70b9\u8f83\u8fdc\u65f6\u8868\u73b0\u826f\u597d\uff1b</li> </ul> </li> <li>\u7f3a\u70b9<ul> <li>\u5728\u76ee\u6807\u70b9\u9644\u8fd1\u6536\u655b\u6bd4\u8f83\u6162\uff1b</li> <li>\u6d6a\u8d39\u4e86\u5927\u91cf\u7b97\u529b\uff1b</li> </ul> </li> </ul> <p>\u8fd9\u662f\u56e0\u4e3a\uff0c\u6700\u901f\u68af\u5ea6\u4e0b\u964d\u6cd5\u4e3b\u8981\u91c7\u7528\u7684\u662f first-order approximation\uff0c\u6ca1\u6709\u4f53\u73b0\u66f2\u7387\u7279\u5f81\u3002</p> <p>\u56e0\u800c\u4e00\u79cd\u5f88\u81ea\u7136\u7684\u6539\u8fdb\u65b9\u6cd5\u5c31\u662f\u4f7f\u7528 second-order approximation\uff0c\u5373\u725b\u987f\u6cd5(Newton Method)\u3002</p> <p>\u725b\u987f\u6cd5</p> <p>\\(F(x_k + \\Delta x) \\approx F(x_k) + J_F\\Delta x + \\frac{1}{2}\\Delta x^T H_F \\Delta x\\)</p> <p>\u5bf9\u5b83\u6c42\u5bfc\u5f97\u5230 \\(\\frac{\\partial F}{\\partial \\Delta x} = J_F^T+H_F\\Delta x = 0\\)\u3002</p> <p>\u6240\u4ee5\u5f97\u5230\u65b9\u5411\u4e3a \\(\\vec p = \\Delta x =  -H_F^{-1}J_F^T\\)</p> <ul> <li>\u4f18\u70b9<ul> <li>\u5728\u76ee\u6807\u70b9\u9644\u8fd1\u4e0b\u964d\u901f\u5ea6\u76f8\u5bf9\u66f4\u5feb\uff1b</li> </ul> </li> <li>\u7f3a\u70b9<ul> <li>Hessian matrix \u7684\u8ba1\u7b97\u9700\u8981\u76f8\u5f53\u7b97\u529b\uff0c\u751a\u81f3\u6709\u65f6\u5019\u65e0\u6cd5\u8ba1\u7b97\uff1b</li> </ul> </li> </ul> <p>\u7531\u6b64\u53d1\u73b0\uff0c\u725b\u987f\u6cd5\u7684\u8868\u73b0\u4f1a\u597d\u5f88\u591a\uff0c\u5982\u679c\u80fd\u591f\u907f\u514d\u8ba1\u7b97\u9ed1\u585e\u77e9\u9635\uff0c\u5c31\u53ef\u4ee5\u8fdb\u4e00\u6b65\u63d0\u9ad8\u725b\u987f\u6cd5\u7684\u6548\u679c\uff0c\u4e8e\u662f\u5c31\u51fa\u73b0\u4e86\u9ad8\u65af\u725b\u987f\u6cd5(Gauss-Newton method)\u3002</p> <p>\u9ad8\u65af\u725b\u987f\u6cd5</p> <p>\u5bf9\u4e8e\u89e3\u51b3\u6700\u5c0f\u4e8c\u4e58\u6cd5 \\(\\hat x = \\mathop{\\arg \\min\\limits_x} ||R(x)||^2_2\\) \u7684\u95ee\u9898\u8868\u73b0\u975e\u5e38\u597d\u3002</p> <p>\u5bf9\u4e8e\u8fd9\u7c7b\u95ee\u9898\uff0c\u9ad8\u65af\u725b\u987f\u6cd5\u4f7f\u7528 \\(J_R^TJ_R\\) \u6765\u8fd1\u4f3c\u4ee3\u66ff \\(H_F\\)\uff0c\u5f97\u5230\u4e0b\u964d\u65b9\u5411\u4e3a \\(\\vec p = -(J_R^TJ_R)^{-1}J_R^T,\\;\\;\\text{where }J_R\\text{ is the Jacobian of }R(x)\\)\u3002</p> <ul> <li>\u4f18\u70b9<ul> <li>\u4e0d\u9700\u8981\u8ba1\u7b97 Hessian matrix\uff0c\u53ea\u9700\u8981\u8ba1\u7b97 Jacobian matrix\uff1b</li> </ul> </li> <li>\u7f3a\u70b9<ul> <li>\u7531\u4e8e \\(J_R^TJ_R\\) \u4e0d\u6b63\u5b9a\uff0c\u6240\u4ee5\u672a\u5fc5\u53ef\u9006\uff0c\u9ad8\u65af\u725b\u987f\u6cd5\u6210\u7acb\u7684\u524d\u63d0\u662f\u5176\u53ef\u9006\uff1b</li> <li>\u5f53\u7136\uff0c\u53ef\u4ee5\u4f7f\u7528 Levenberg-Marquardt \u7b97\u6cd5\uff08LM \u7b97\u6cd5\uff09\uff0c\u5373\u5c06 \\(J_R^TJ_R\\) \u4fee\u6b63\u4e3a \\(J_R^TJ_R + \\lambda I\\) \u4ee5\u4fdd\u8bc1\u6b63\u5b9a\uff1b</li> </ul> </li> </ul> Levenberg-Marquardt <p>Wiki: \ud83d\udd17</p> \\[ \\Delta x = -(J_R^TJ_R+\\lambda I)^{-1}J_R^TR(x_k) \\] <ul> <li>The effect of \\(\\lambda\\):<ul> <li>\\(\\lambda \\to \\infty\\): Gradient descent, and stepsize is small;</li> <li>\\(\\lambda \\to 0\\): Gauss-Newton step;</li> </ul> </li> <li>How to determine \\(\\lambda\\):<ul> <li>Update in every iteration;</li> <li>When decreases obviously, \\(\\lambda\\uparrow\\);</li> <li>When doesn't decrease obviously, \\(\\lambda\\downarrow\\);</li> </ul> </li> </ul> <p>\u7b80\u5355\u6765\u8bf4\uff0cLM \u5c31\u662f\u7efc\u5408\u4e86\u6700\u901f\u68af\u5ea6\u4e0b\u964d\u6cd5\u548c\u725b\u987f\u6cd5\u7684\u4f18\u70b9\uff0c\u5728\u8fdc\u79bb\u76ee\u6807\u70b9\u7684\u65f6\u5019\u4f7f\u7528\u6700\u901f\u68af\u5ea6\u4e0b\u964d\u6cd5\uff0c\u4fdd\u8bc1\u542f\u52a8\u901f\u5ea6\u5feb\uff1b\u5728\u9760\u8fd1\u76ee\u6807\u70b9\u7684\u65f6\u5019\u4f7f\u7528\u725b\u987f\u6cd5\uff0c\u4fdd\u8bc1\u6536\u655b\u901f\u5ea6\u8db3\u591f\u5feb\uff1b\u5e76\u4e14\u4fdd\u8bc1 \\(J_R^TJ_R+\\lambda I\\) \u6b63\u5b9a\uff0c\u6240\u4ee5\u59cb\u7ec8\u80fd\u591f\u4f7f\u725b\u987f\u6cd5\u6210\u7acb\u3002</p> <p>\u5e26\u7ea6\u675f\u7684\u4f18\u5316\u95ee\u9898</p> <p>\u5bf9\u4e8e\u5e26\u7ea6\u675f\u7684\u4f18\u5316\u95ee\u9898(constrained optimization)\uff0c\u5219\u9700\u8981\u6839\u636e\u5b9e\u9645\u95ee\u9898\u6c42\u89e3\u3002</p> <ul> <li>\u6211\u4eec\u53ef\u80fd\u53ef\u4ee5\u8f6c\u5316\u95ee\u9898\uff0c\u4f7f\u7528\u66f4\u7b80\u5355\u7684\u8868\u8fbe\u5f0f\u53bb\u62df\u5408\u539f\u6765\u7684\u8868\u8fbe\u5f0f\uff0c\u6765\u6c42\u89e3\uff1b</li> <li>\u5176\u4e2d\uff0c\uff08\u51f9\uff09\u51f8\u51fd\u6570\u662f\u4e00\u5b9a\u80fd\u627e\u5230\u6700\u4f18\u89e3\u7684\uff0c\u6211\u4eec\u79f0\u8fd9\u79cd\u95ee\u9898\u4e3a\u51f8\u4f18\u5316\u95ee\u9898(Convex optimization)</li> </ul> <p>\u63a8\u8350\u540c\u540d\u8bfb\u7269\uff1ahttps://web.stanford.edu/class/ee364a</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec04/#\u5168\u5c40\u6700\u4f18\u548c\u5c40\u90e8\u6700\u4f18","title":"\u5168\u5c40\u6700\u4f18\u548c\u5c40\u90e8\u6700\u4f18","text":"<p>\u5206\u591a\u4e2a batch \u6765\u5904\u7406\uff0c\u5927\u91cf\u6492\u70b9\uff0c\u7136\u540e\u6bd4\u8f83\u6bcf\u4e00\u4e2a batch \u7684\u7ed3\u679c\uff0c\u6700\u7ec8\u53d6\u6700\u597d\u7684\u4e00\u4e2a\u5373\u53ef\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec04/#\u9c81\u68d2\u4f30\u8ba1","title":"\u9c81\u68d2\u4f30\u8ba1","text":"<p>\u9c81\u68d2\u4f30\u8ba1(robust estimation)\u662f\u5bf9\u4ece\u5404\u79cd\u6982\u7387\u5206\u5e03\uff08\u5c24\u5176\u662f\u975e\u6b63\u6001\u5206\u5e03\uff09\u4e2d\u63d0\u53d6\u7684\u6570\u636e\u5177\u6709\u826f\u597d\u6027\u80fd\u7684\u7edf\u8ba1\u3002</p> <p>\u5728\u62df\u5408\u6a21\u578b\u4e2d\uff0c\u96be\u514d\u51fa\u73b0\u4e00\u4e9b\u4e0d\u7b26\u5408\u9884\u671f\u7684\u70b9\uff0c\u800c\u5b83\u4eec\u4f1a\u5bf9\u62df\u5408\u7ed3\u679c\u4ea7\u751f\u6216\u591a\u6216\u5c0f\u7684\u5f71\u54cd\uff0c\u800c\u5982\u4f55\u6743\u8861\u8fd9\u4e9b\u566a\u58f0\u4e0e\u771f\u6b63\u6709\u7528\u7684\u6570\u636e\u70b9\u4e4b\u95f4\u7684\u5173\u7cfb\uff0c\u5c31\u662f\u9c81\u68d2\u4f30\u8ba1\u7684\u8bfe\u9898\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec04/#\u5185\u70b9--\u5916\u70b9","title":"\u5185\u70b9 &amp; \u5916\u70b9","text":"<p>\u9996\u5148\u6211\u4eec\u5bf9\u6570\u636e\u70b9\u8fdb\u884c\u5206\u7c7b\uff1a</p> <ul> <li>\u5185\u70b9(inlier)\uff1a\u7b26\u5408\u6211\u4eec\u9884\u671f\u7684\u6a21\u578b\u62df\u5408\u7684\u70b9\uff1b</li> <li>\u5916\u70b9(outlier)\uff1a\u5b8c\u5168\u4e0d\u7b26\u5408\u6211\u4eec\u9884\u671f\u6a21\u578b\u7684\u70b9\uff0c\u53c8\u53eb\u79bb\u7fa4\uff1b</li> </ul> <p></p> <p>\u5916\u70b9\u7684\u5f71\u54cd</p> <p>\u7531\u4e8e\u5916\u70b9\u504f\u79bb\u5f88\u5927\uff0c\u800c\u6700\u5c0f\u4e8c\u4e58\u6cd5\u4e2d\u5b58\u5728\u5e73\u65b9\u64cd\u4f5c\uff0c\u6240\u4ee5\u6700\u5c0f\u4e8c\u4e58\u6cd5\u62df\u5408\u53d7\u8fd9\u4e9b\u5916\u70b9\u5f71\u54cd\u5f88\u5927\uff1a</p> <p></p>"},{"location":"cour_note/D2QD_Intro2CV/Lec04/#\u4e0d\u540c\u7684\u635f\u5931\u51fd\u6570","title":"\u4e0d\u540c\u7684\u635f\u5931\u51fd\u6570","text":"<p>\u4e8e\u662f\u6211\u4eec\u8003\u8651\uff0c\u53ef\u4ee5\u66f4\u6362\u62df\u5408\u7684\u635f\u5931\u51fd\u6570\uff0c\u6765\u51cf\u5c0f\u5927\u504f\u5dee\u70b9\u5e26\u6765\u7684\u5f71\u54cd\uff0c\u6bd4\u5982\u4f7f\u7528 L1 loss(\u5373\u6c42\u7edd\u5bf9\u503c)\u3002\u4e0d\u8fc7\u66f4\u597d\u7684\u662f\u4e00\u79cd\u9009\u62e9\u53eb huber loss\uff0c\u5b83\u5728\u8ddd\u79bb\u8fdc\u70b9\u8f83\u8fdc\u7684\u65f6\u5019\u6bd4\u8f83\u63a5\u8fd1 L1 loss\u3002</p> L1 &amp; L2 &amp; Huber <ul> <li>L1 loss \u5373\u76f4\u63a5\u5bf9\u504f\u5dee\u53d6\u7edd\u5bf9\u503c\uff0c\u5176\u516c\u5f0f\u4e3a \\(L_1 = |f(x)-Y|\\)\uff0c\u5176\u6700\u5927\u7684\u95ee\u9898\u5c31\u662f\u5728\u62d0\u70b9\u5904\u4e0d\u5149\u6ed1\uff0c\u5373\u4e0d\u53ef\u5bfc\uff0c\u800c\u4e14\u5176\u6536\u655b\u53ef\u80fd\u8fc7\u5feb\uff1b</li> <li>L2 loss \u5373\u5c06\u504f\u5dee\u53d6\u5e73\u65b9\uff0c\u5373 \\(L_2 = |f(x)-Y|^2\\)\uff0cL2 loss \u5728\u62d0\u70b9\u5904\u5219\u662f\u5149\u6ed1\u53ef\u5bfc\u7684\uff0c\u4e14\u6536\u655b\u76f8\u5bf9\u7a33\u5b9a\u5149\u6ed1\uff0c\u4f46\u662f\u4e14\u5728\u67d0\u4e9b\u65f6\u5019\u5177\u6709\u6bd4\u8f83\u597d\u7684\u51e0\u4f55\u610f\u4e49\uff0c\u4f46\u662f\u5bf9\u4e8e\u504f\u5dee\u8f83\u5927\u7684\u70b9\u66f4\u654f\u611f\uff1b</li> <li>Huber loss \u53c8\u53eb smooth L1 loss\uff0c\u5373\u4f7f\u7528\u5206\u6bb5\u51fd\u6570\uff0c\u5728\u62d0\u70b9\u9644\u8fd1\u4f7f\u7528 L2 loss\uff0c\u5728\u8fdc\u7aef\u4f7f\u7528 L1 loss\uff1b</li> </ul> <p></p> <ul> <li>\u76f8\u5173\u6587\u7ae0\uff1ahttps://zhuanlan.zhihu.com/p/48426076</li> </ul>"},{"location":"cour_note/D2QD_Intro2CV/Lec04/#\u968f\u673a\u62bd\u6837\u4e00\u81f4","title":"\u968f\u673a\u62bd\u6837\u4e00\u81f4","text":"<p>\u968f\u673a\u62bd\u6837\u4e00\u81f4(random sample consensus, RANSAC)\u91c7\u7528\u8fed\u4ee3\u7684\u65b9\u5f0f\u4ece\u5305\u542b\u5916\u70b9\u7684\u6570\u636e\u4e2d\u4f30\u8ba1\u6570\u5b66\u6a21\u578b\u53c2\u6570\uff0c\u662f\u4e00\u4e2a\u5bf9\u4e8e\u5b58\u5728\u660e\u663e\u5916\u70b9\u7684\u6570\u636e\u975e\u5e38\u6709\u6548\u7684\u65b9\u6cd5\u3002</p> <p>RANSAC procedure</p> <ol> <li>\u9996\u5148\u968f\u673a\u627e\u4e24\u4e2a\u70b9\u62df\u5408\u4e00\u6761\u76f4\u7ebf\uff0c\u7136\u540e\u68c0\u67e5\u6709\u591a\u5c11\u70b9\u7b26\u5408\u8fd9\u6761\u76f4\u7ebf\uff0c\u5e76\u5bf9\u5176\u8fdb\u884c vote\uff1b</li> <li>\u91cd\u590d\u8fd9\u4e2a\u6b65\u9aa4\uff0c\u6700\u540e\u9009\u62e9\u7968\u6570\u6700\u9ad8\u7684\u62df\u5408\uff1b</li> </ol> <p></p> <p>\u7531 outlier \u62df\u5408\u51fa\u6765\u7684\u76f4\u7ebf\u4e00\u822c votes \u6bd4\u8f83\u5c11\uff0c\u56e0\u4e3a outlier \u4e4b\u95f4\u5f88\u96be\u4e00\u81f4\uff1b\u4f46\u662finlier\u4e4b\u95f4\u5bb9\u6613\u4e00\u81f4\uff0c\u56e0\u800c\u5f97\u5206\u5f80\u5f80\u66f4\u9ad8\uff0c\u4e8e\u662f\u5c06\u5b83\u4eec\u533a\u5206\u5f00\u6765\u3002\u8fd9\u4e0d\u5c31\u662f Voting Tree (\u9003</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec04/#\u75c5\u6001\u95ee\u9898","title":"\u75c5\u6001\u95ee\u9898","text":"<p>\u5982\u679c\u4e00\u4e2a\u95ee\u9898\u7684\u89e3\u4e0d\u552f\u4e00\uff0c\u90a3\u4e48\u8fd9\u4e2a\u95ee\u9898\u662f\u4e00\u4e2a\u75c5\u6001\u95ee\u9898(ill-posed problem)\u3002\u7279\u522b\u7684\uff0c\u5728\u7ebf\u6027\u95ee\u9898\u4e2d\uff0c\u4e00\u4e2a\u7ebf\u6027\u65b9\u7a0b\uff08\u7ec4\uff09\u7684\u89e3\u5982\u679c\u4e0d\u552f\u4e00\uff08\u4e0d\u6ee1\u79e9\uff09\uff0c\u5219\u540c\u6837\u662f\u4e00\u4e2a\u75c5\u6001\u95ee\u9898\u3002</p> <p>\u5f53\u7136\uff0c\u5bf9\u4e8e\u7ebf\u6027\u65b9\u7a0b\u7ec4\uff0c\u6839\u636e\u7ebf\u6027\u4ee3\u6570\u7684\u77e5\u8bc6\uff0c\u6211\u4eec\u53ef\u4ee5\u589e\u52a0\u65b9\u7a0b\uff0c\u5373\u589e\u52a0\u7ea6\u675f\u3002\u800c\u8fd9\u79cd\u7ea6\u675f\u4e00\u822c\u6765\u81ea\u4e8e\u5bf9\u53d8\u91cf\u7684\u5148\u9a8c\u7ea6\u675f\uff0c\u6bd4\u5982\uff1a</p> <p>L2 regularization</p> <p>L2 norm: \\(||x||_2 = \\sum_i x_i^2\\);</p> <p>L2 regularization: \\(\\min\\limits x ||Ax-b||^2_2\\;\\;s.t. ||x||_2 \\leq 1\\);</p> <p> </p> <p>\u901a\u8fc7\u8ba9\u9009\u62e9\u7684\u89e3\u5c3d\u53ef\u80fd\u63a5\u8fd1\u539f\u70b9\uff0c\u800c\u8ba9\u6211\u4eec\u6ca1\u6709\u7528\u7684\u89e3\u7684\u7ef4\u5ea6\u5c3d\u53ef\u80fd\u63a5\u8fd1 0\uff0c\u4ee5\u51cf\u5c0f\u6ca1\u7528\u7684\u53d8\u91cf\u7684\u5f71\u54cd\uff0c\u6291\u5236\u5197\u4f59\u53d8\u91cf\u3002</p> <p>L1 regularization</p> <p>L1 norm: \\(||x||_1=\\sum_i|x_i|\\);</p> <p>L1 regularization: \\(\\min\\limits x ||Ax-b||^2_2\\;\\;s.t. ||x||_1 \\leq 1\\)</p> <p> </p> <p>L1 \u53ef\u89c6\u5316\u4e2d\u53ef\u4ee5\u53d1\u73b0\uff0c\u5750\u6807\u8f74\u4e0a\u6bd4\u8f83\u5bb9\u6613\u6293\u4f4f\u89e3\uff0c\u6b64\u65f6\u610f\u5473\u7740\u6709\u4e9b\u53d8\u91cf(\u7ef4\u5ea6)\u662f 0\uff0c\u6362\u53e5\u8bdd\u6765\u8bf4\u80fd\u8ba9\u89e3\u53d8\u5f97\u201c\u7a00\u758f(sparse)\u201d\uff0c\u5373\u5728\u7ef4\u5ea6\u4e0a\u7684\u5206\u5e03\u53ea\u6bd4\u8f83\u96c6\u4e2d\u4e8e\u4e2a\u522b\u9879\u3002</p> <p>\u4e0d\u8fc7\uff0c\u5c06\u4ed6\u4eec\u4f5c\u4e3a\u7ea6\u675f\u6761\u4ef6\u53c2\u4e0e\u6c42\u89e3\uff0c\u4e0d\u5982\u76f4\u63a5\u52a0\u8fdb\u53bb\u4f5c\u4e3a\u4e00\u4e2a\u9879\uff0c\u5176\u6548\u679c\u662f\u7b49\u4ef7\u7684\uff1a</p> \\[ \\begin{matrix}     \\text{L2 regularization:}               &amp; | &amp; \\text{or L1 regularization:}\\\\     \\min_{x}||Ax-b||^2_2+\\lambda ||x||_2^2  &amp; | &amp; \\min_{x}||Ax-b||^2_2+\\lambda ||x||_1\\\\     s.t. ||x||_2 \\leq 1                     &amp; | &amp; s.t. ||x||_1 \\leq 1 \\\\ \\end{matrix} \\]"},{"location":"cour_note/D2QD_Intro2CV/Lec04/#\u8fc7\u62df\u5408\u548c\u6b20\u62df\u5408","title":"\u8fc7\u62df\u5408\u548c\u6b20\u62df\u5408","text":"<p>\u5728\u8fd9\u4e2a\u8fc7\u7a0b\u4e2d\uff0c\u4e5f\u8981\u5c0f\u5fc3\u8fc7\u62df\u5408(overfitting)\u548c\u6b20\u62df\u5408(underfitting)\uff0c\u5b83\u4eec\u7684\u542b\u4e49\u975e\u5e38\u76f4\u767d\uff1a</p> <p></p>"},{"location":"cour_note/D2QD_Intro2CV/Lec04/#\u63d2\u503c","title":"\u63d2\u503c","text":"<p>\u63d2\u503c(interpolation)\u5176\u5b9e\u5df2\u7ecf\u5728 lec 3 \u7684\u7b14\u8bb0 \u91cc\u63d0\u5230\u8fc7\u4e86\u3002</p> <p>\u8fd9\u91cc\u5148\u7565\u8fc7\u3002</p> <ul> <li> TODO: \u518d\u7ec6\u8bf4\u3002</li> </ul> sketch <p>\u7ebf\u6027\u62df\u5408\u3001\u4e8c\u6b21\u6837\u6761\u63d2\u503c\uff08\u6bcf\u4e00\u6bb5\u90fd\u662f\u4e00\u4e2a\u4e8c\u6b21\u51fd\u6570\uff09\u3001\u4e09\u6b21\u6837\u6761\u63d2\u503c\uff08\u4e00\u9636\u5bfc\u4e8c\u9636\u5bfc\u8fde\u7eed\uff0c\u4f46\u6700\u7ec8\u662f\u4e2a\u75c5\u6001\u95ee\u9898\uff0c\u9700\u8981\u989d\u5916\u518d\u7ea6\u675f\u8d77\u70b9\u548c\u7ec8\u70b9\u4e8c\u9636\u5bfc\u4e3a\u96f6\u6216\u8005\u9650\u5b9a\u7ed9\u5b9a\u659c\u7387\u7b49\uff0c\u5c31\u9700\u8981\u4fe9\u989d\u5916\u7ea6\u675f\u6761\u4ef6\uff09\u3001</p> <p>\u4e0a\u9762\u662f\u8fde\u7eed\u4f18\u5316\u95ee\u9898\uff0c\u4e0b\u9762\u662f\u79bb\u6563\u4f18\u5316\u95ee\u9898</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec04/#\u56fe\u5272--\u9a6c\u53ef\u592b\u968f\u673a\u573a","title":"\u56fe\u5272 &amp; \u9a6c\u53ef\u592b\u968f\u673a\u573a","text":""},{"location":"cour_note/D2QD_Intro2CV/Lec04/#\u56fe\u50cf\u6807\u7b7e\u95ee\u9898","title":"\u56fe\u50cf\u6807\u7b7e\u95ee\u9898","text":"<p>\u56fe\u50cf\u6807\u7b7e\u95ee\u9898(image labeling problems)\u5373\u901a\u8fc7\u56fe\u7247\u4fe1\u606f\u7ed9\u6bcf\u4e00\u4e2a\u50cf\u7d20\u5206\u914d\u6807\u7b7e\uff0c\u5b9e\u9645\u4e0a\u5c31\u662f\u4e00\u4e2a\u5bf9\u56fe\u50cf\u5185\u5bb9\u7684\u5206\u7c7b\u548c\u8bc6\u522b\u95ee\u9898\u3002</p> <p></p> <p>\u5176\u4e2d\u4e00\u4e2a\u6bd4\u8f83\u5f3a\u7684\u5148\u9a8c(prior)\u662f\uff1a\u76f8\u90bb\u4e14\u76f8\u4f3c\u7684\u50cf\u7d20\u5e94\u5f53\u62e5\u6709\u76f8\u540c\u7684\u6807\u7b7e\u3002</p> <p>\u800c\u56fe\u5272\u548c\u9a6c\u53ef\u592b\u968f\u673a\u573a\u53ef\u4ee5\u5efa\u6a21\u8fd9\u79cd\u5148\u9a8c\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec04/#\u56fe\u5272","title":"\u56fe\u5272","text":"<p>\u56fe\u5272(Graphcut)\u7684\u6838\u5fc3\u601d\u60f3\u662f\uff0c\u628a\u4e00\u5f20\u56fe\u7247\u7684\u6bcf\u4e00\u4e2a\u50cf\u7d20\u770b\u4f5c\u4e00\u4e2a graph \u4e2d\u7684 vertex\uff0c\u5e76\u5728\u50cf\u7d20\u4e4b\u95f4\u5efa edge\uff0c\u5e76\u5c06 weight \u5b9a\u4e49\u4e3a\u4e24\u50cf\u7d20\u4e4b\u95f4\u7684\u76f8\u4f3c\u6027\u6216\u5173\u8054\u6027(affinity or similarity)\u3002</p> <p>measuring affinity</p> <p>\u6bd4\u5982\uff0c\u6211\u4eec\u53ef\u4ee5\u8fd9\u6837\u8861\u91cf\u50cf\u7d20\u7684\u76f8\u4f3c\u6027\uff1a</p> <ul> <li>\u8bbe \\(f\\) \u8868\u793a\u989c\u8272\uff1b</li> <li>\u50cf\u7d20\u5dee\u5f02(dissimilarity)\u4e3a \\(s(f_i,f_j)=\\sqrt{\\sum_k(f_{ik},f_{jk})^2}\\)\uff1b</li> <li>\u5219\u76f8\u4f3c\u6027(affinity)\u6743\u91cd\u4e3a\uff1a\\(w(i,j) = A(f_i,f_j) = e^{\\frac{-1}{2\\sigma^2}s(f_i,f_j)}\\)\uff1b</li> </ul> <p>\u518d\u63a5\u4e0b\u6765\uff0c\u901a\u8fc7\u8fd9\u6837\u7684\u65b9\u5f0f\u5c06\u56fe\u7247\u5efa\u6210\u56fe\u540e\uff0c\u5c31\u53ef\u4ee5\u628a\u95ee\u9898\u8f6c\u5316\u4e3a\u56fe\u5272\u95ee\u9898\uff0c\u6211\u4eec\u5c06\u5c0f\u6743\u7684\u8fb9\u5220\u53bb\uff0c\u6700\u7ec8\u4f1a\u5f62\u6210\u82e5\u5e72\u8fde\u901a\u5206\u91cf\uff0c\u800c\u8fd9\u4e9b\u8fde\u901a\u5206\u91cf\u90a3\u7684\u70b9\u5219\u88ab\u89c6\u4e3a\u4e00\u4e2a\u201c\u5206\u5272\u201d\u3002</p> <p>\u5177\u4f53\u6765\u8bf4\uff0c\u56fe\u5272\u7684\u4ee3\u4ef7\u4e3a\u65ad\u7684\u8fb9\u6743\u4e4b\u6743\u91cd\u548c \\(cut(V_A,V_B)= \\sum_{u\\in V_A, v\\in V_B} w(u,v)\\)\uff0c\u800c\u6211\u4eec\u9700\u8981\u627e\u4ee3\u4ef7\u5c3d\u53ef\u80fd\u5c0f\u7684\uff0c\u6ee1\u8db3\u6211\u4eec\u8981\u6c42\u7684\u56fe\u5272\u3002\u5f53\u7136\uff0c\u8fd9\u4e2a\u95ee\u9898\u4e5f\u7b49\u6548\u4e8e\u6700\u5927\u6d41\u95ee\u9898\uff1b</p> <p>Problem with min-cut</p> <p>Bias to cut small, isolated segments.</p> <p></p> <p>\u7531\u4e8e min-cut \u7684\u8fd9\u4e2a\u95ee\u9898\uff0c\u6211\u4eec\u8fd8\u9700\u8981\u8861\u91cf\u8fd9\u4e2a\u5b50\u96c6\u662f\u5426\u8db3\u591f\u7a20\u5bc6\uff0c\u6240\u4ee5\u6211\u4eec\u503e\u5411\u4e8e\u4f7f\u7528 normalized-cut\u3002</p> \\[ assoc(V_A,V) = \\sum_{u\\in V_A, v\\in V} w(u,v) \\\\ NCut(V_A,V_B) = \\frac{cut(V_A,V_B)}{assoc(V_A,V)} + \\frac{cut(V_A,V_B)}{assoc(V_B,V)} \\] <ul> <li>NP-Complete</li> <li>Approximate solution by eigenvalue decomposition</li> </ul>"},{"location":"cour_note/D2QD_Intro2CV/Lec04/#\u9a6c\u53ef\u592b\u968f\u673a\u573a","title":"\u9a6c\u53ef\u592b\u968f\u673a\u573a","text":"<p>\u9a6c\u53ef\u592b\u968f\u673a\u573a(Markov Random Field, MRF)\u662f\u4e00\u79cd\u66f4\u901a\u7528\u7684\u89e3\u51b3\u65b9\u6848\uff0c\u53ef\u60dc\u6211\u7b2c\u4e00\u6b21\u6ca1\u542c\u61c2\uff0c\u7b49\u6211\u542c\u61c2\u4e86\u518d\u6765\u8865\u5145\u8fd9\u91cc\u7684\u5185\u5bb9\u3002</p> sketch <p>Markov chains</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec05/","title":"Lecture 5 | Feature Matching and Motion Estimation","text":"<p> \u7ea6 3966 \u4e2a\u5b57  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 13 \u5206\u949f</p> <p>\u6ce8\u610f</p> <p>\u672c\u6587\u5c1a\u672a\u5b8c\u5168\u6574\u7406\u597d\uff01</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec05/#\u56fe\u50cf\u7279\u5f81\u5339\u914d","title":"\u56fe\u50cf\u7279\u5f81\u5339\u914d","text":"<p>\u672c\u8282\u7684\u8bfe\u9898\u662f\u7279\u5f81\u5339\u914d(feature matching)\uff0c\u5177\u4f53\u6765\u8bf4\u662f\u627e\u5230\u4e24\u5f20\u56fe\u50cf\u4e2d\u53ef\u80fd\u6307\u4ee3\u540c\u4e00\u5ba2\u4f53\u7684\u90e8\u5206\uff0c\u5173\u952e\u5728\u4e8e\u627e\u5230\u56fe\u7247\u4e4b\u95f4\u70b9\u548c\u70b9\u7684\u5339\u914d\u5173\u7cfb\u3002\u8be5\u95ee\u9898\u662f\u5f88\u591a\u95ee\u9898\u7684\u57fa\u77f3\uff0c\u4f8b\u5982\uff1a</p> applications <ul> <li>Image alignment / Panoramas</li> <li>3D reconstruction</li> <li>Motion tracking</li> <li>Object recognition</li> <li>Indexing &amp; database retrieval</li> <li>Robot navigation</li> <li>...</li> </ul> <p>\u5934\u8111\u98ce\u66b4</p> <p>\u7a76\u5176\u6839\u672c\uff0c\u7279\u5f81\u5339\u914d\u201c\u8054\u901a\u201d\u4e86\u4e24\u5f20\u56fe\u7247\uff0c\u4f7f\u5b83\u4eec\u539f\u672c\u5b64\u7acb\u8868\u8fbe\u7684\u4fe1\u606f\u8fde\u7ed3\u8d77\u6765\u3002</p> <p>\u7b80\u5355\u7684\u5e94\u7528\u5982\u56fe\u50cf\u62fc\u63a5\uff0c\u518d\u5f80\u540e\uff0c\u6211\u4eec\u4f1a\u53d1\u73b0\u4e09\u7ef4\u91cd\u5efa\u4e2d\u4e5f\u4f1a\u5e94\u7528\u5230\u7279\u5f81\u5339\u914d\u5230\u76f8\u5173\u5185\u5bb9\u3002</p> <p>\u6982\u62ec\u4f20\u7edf\u7279\u5f81\u5339\u914d\u4e3b\u8981\u73af\u8282\uff0c\u5927\u6982\u53ef\u4ee5\u5206\u4e3a\u5982\u4e0b\u4e09\u6b65\uff1a</p> <ol> <li>\u68c0\u6d4b(detection): \u627e\u5230\u5173\u952e\u70b9(interest points)\uff0c\u5373\u53ef\u80fd\u4f1a\u88ab\u5339\u914d\u7684\u201c\u7279\u5f81\u70b9\u201d\uff1b</li> <li>\u8868\u8fbe(description): \u63d0\u53d6\u6bcf\u4e2a\u5173\u952e\u70b9\u5468\u56f4\u7684\u5411\u91cf\u7279\u5f81\u63cf\u8ff0\u7b26(feature descriptor)\uff0c\u5373\u5c06\u201c\u7279\u5f81\u201d\u6570\u636e\u5316\uff1b</li> <li>\u5339\u914d(matching): \u51b3\u5b9a\u4e24\u4e2a\u89c6\u89d2\u4e0b\u7279\u5f81\u63cf\u8ff0\u7b26\u7684\u5173\u8054\u5e76\u5339\u914d\uff0c\u5373\u6784\u5efa\u201c\u7279\u5f81\u201d\u4e4b\u95f4\u7684\u5339\u914d\u5173\u7cfb\uff1b</li> </ol>"},{"location":"cour_note/D2QD_Intro2CV/Lec05/#\u5173\u952e\u70b9\u68c0\u6d4b","title":"\u5173\u952e\u70b9\u68c0\u6d4b","text":"<p>\u63a8\u8350\u9605\u8bfb</p> <p>\u3010\u8ba1\u7b97\u673a\u89c6\u89c9\u30112. \u7279\u5f81\u70b9\u68c0\u6d4b\uff1aHarris, SIFT, SURF, ORB</p> <p>\u68c0\u6d4b(detection)\u7684\u9996\u8981\u95ee\u9898\u662f\u5982\u4f55\u9009\u62e9\u5173\u952e\u70b9(interest points/feature points)\uff0c\u6216\u8005\u8bf4\uff0c\u4e00\u4e2a\u70b9\u4ec0\u4e48\u60c5\u51b5\u4e0b\u4f1a\u88ab\u8ba4\u4e3a\u662f\u4e00\u4e2a\u7279\u5f81\u70b9\u3002</p> <p>\u603b\u4f53\u6765\u8bf4\uff0c\u5173\u952e\u70b9\u9700\u8981\u7531\u8fd9\u4e48\u4e24\u4e2a\u7279\u5f81\uff1a</p> <ol> <li>\u72ec\u7279\u6027(uniqueness)\uff0c\u5373\u8fd9\u4e2a\u70b9\u9700\u8981\u80fd\u591f\u8868\u5f81\u4e00\u5b9a\u7279\u6027\uff1b</li> <li>\u5bf9\u4e8e\u53d8\u6362\u4e0d\u654f\u611f\uff0c\u5373\u5bf9\u4e8e\u4e00\u4e2a\u5ba2\u89c2\u4e0a\u7684\u5173\u952e\u70b9\uff0c\u5373\u4f7f\u56fe\u7247\u88ab\u65cb\u8f6c\u3001\u538b\u7f29\u3001\u9002\u5f53\u7684\u626d\u66f2\uff0c\u5b83\u90fd\u5e94\u5f53\uff08\u5c3d\u53ef\u80fd\u5730\uff09\u88ab\u8bc6\u522b\u4e3a\u5173\u952e\u70b9\uff1b</li> </ol> <p>\u5173\u952e\u70b9</p> <p>\u867d\u7136\u8bf4\u662f\u5173\u952e\u201c\u70b9\u201d\uff0c\u4f46\u662f\u5b9e\u9645\u4e0a\u6307\u7684\u662f\u4e00\u5c0f\u5757\u533a\u57df\u3002\u65e2\u7136\u4f5c\u4e3a\u4e00\u4e2a\u80fd\u8868\u8fbe\u5c40\u90e8\u7279\u5f81\u7684\u70b9\uff0c\u5b83\u5fc5\u7136\u9700\u8981\u56ca\u62ec\u4e00\u5b9a\u8303\u56f4\u5185\u7684\u4fe1\u606f\u3002</p> <p>\u9996\u5148\u6211\u4eec\u8ba8\u8bba\u5982\u4f55\u8861\u91cf\u4e00\u4e2a\u70b9\u7684\u72ec\u7279\u6027(uniqueness)\uff0c\u672c\u6587\u4f1a\u4ecb\u7ecd\u4e24\u79cd\u68c0\u6d4b\u5668\uff1a</p> <ol> <li>\u7740\u773c\u4e8e\u56fe\u50cf\u7684\u89d2\u70b9 - Harris corner detector\uff1b</li> <li>\u7740\u773c\u4e8e\u56fe\u50cf\u7684\u6591\u70b9 - Blob detector(LoG or DoG)\uff1b</li> </ol>"},{"location":"cour_note/D2QD_Intro2CV/Lec05/#\u89d2\u70b9\u68c0\u6d4b","title":"\u89d2\u70b9\u68c0\u6d4b","text":"<p>\u63a8\u8350\u9605\u8bfb</p> <p>Harris Corners @ 16-385 Computer Vision (Kris Kitani) @ Carnegie Mellon University</p> <p>\u89d2\u70b9\u68c0\u6d4b\u7684\u57fa\u672c\u601d\u8def\u662f\uff0c\u6211\u4eec\u79f0\u67d0\u4e2a\u70b9\u6bd4\u8f83\u72ec\u7279\u65f6\uff0c\u5b83\u76f8\u5bf9\u4e8e\u5468\u56f4\u4e00\u5b9a\u53c8\u4e00\u4e9b\u201c\u4e0d\u540c\u201d\u7684\u5730\u65b9\u3002\u6216\u8005\u8bf4\u5b58\u5728\u4e00\u4e9b\u9ad8\u9891\u7279\u5f81\uff0c\u800c\u4e14\u8fd9\u79cd\u9ad8\u9891\u7279\u5f81\u4e0d\u4f1a\u5404\u5411\u540c\u6027\u6216\u8005\u8bf4\u51e0\u4e2a\u5411\u540c\u6027\u3002</p> <p>\u5728\u6a21\u5f0f\u5316\u7684\u63cf\u8ff0\u8fd9\u4e2a\u601d\u8def\u5c31\u662f\uff1a</p> <p>Local measures of uniqueness(rough):</p> <p>\u6211\u4eec\u4ee5\u7a97\u53e3\u7684\u5f62\u5f0f\u5bf9\u76ee\u6807\u70b9\u53ca\u5176\u90bb\u57df\u8fdb\u884c\u91c7\u6837\uff0c\u5f53\u65e0\u8bba\u5f80\u54ea\u4e2a\u65b9\u5411\u79fb\u52a8\u7a97\u53e3\uff0c\u91c7\u6837\u7ed3\u679c\u90fd\u4f1a\u4ea7\u751f\u8f83\u5927\u53d8\u5316\u65f6\uff0c\u6211\u4eec\u5c31\u8ba4\u4e3a\u8fd9\u4e2a\u70b9\u72ec\u7279\u6027\u5f3a\u3002</p> <p></p> Flag Edge Corner \u65e0\u8bba\u5411\u54ea\u4e2a\u65b9\u5411\u79fb\u52a8\uff0c\u90fd\u4e0d\u4f1a\u6709\u592a\u5927\u53d8\u5316 \u5f53\u6cbf\u7740\u201cEdge\u201d\u7684\u65b9\u5411\u79fb\u52a8\u65f6\uff0c\u4e0d\u592a\u6709\u53d8\u5316 \u65e0\u8bba\u5411\u54ea\u4e2a\u65b9\u5411\u79fb\u52a8\uff0c\u90fd\u4f1a\u5bfc\u81f4\u8f83\u5927\u7684\u53d8\u5316 <p>\u4e0d\u8fc7\u8fd9\u4ecd\u7136\u662f\u4e00\u4e2a\u76f8\u5bf9\u6a21\u7cca\u7684\u5b9a\u4e49\uff0c\u4e3a\u4e86\u5bf9\u5176\u8fdb\u884c\u5efa\u6a21\uff0c\u6211\u4eec\u8fdb\u4e00\u6b65\u5730\u5bf9\u4e0a\u9762\u63d0\u5230\u7684\u201c\u53d8\u5316\u5e45\u5ea6\u201d\u8d4b\u4e88\u6570\u5b66\u542b\u4e49\uff1a</p> <p>Local measures of uniqueness(detail):</p> <p>\u6240\u8c13\u53d8\u5316\u5927\uff0c\u5b9e\u9645\u4e0a\u6307\u7684\u662f\u76f8\u540c\u7684\u5355\u4f4d\u957f\u5ea6\u91cc\uff0c\u8272\u5f69\u503c\u7684\u5dee\u66f4\u5927\uff0c\u4e3a\u4ec0\u4e48\u6211\u4eec\u4e0d\u7528\u68af\u5ea6\u6765\u8861\u91cf\u5462\uff1f\u5173\u6ce8\u533a\u57df\u5185\u7684\u68af\u5ea6\u5206\u5e03\uff1a</p> <p></p> <p>\u6839\u636e\u68af\u5ea6\u7684\u5206\u5e03\uff0c\u6211\u4eec\u53ef\u4ee5\u5927\u81f4\u89c2\u5bdf\u5230\u56fe\u5f62\u7684\u7279\u5f81\uff0c\uff0c\u5305\u62ec\u5b58\u5728\u591a\u5c11\u4e2a Edge \u4ee5\u53ca\u8fd9\u4e9b Edge \u7684\u65b9\u5411\u3002</p> <p>\u4e0d\u8fc7\u7eaf\u7cb9\u6839\u636e\u68af\u5ea6\u6765\u5bfb\u627e\u89d2\u70b9\u6709\u65f6\u5019\u53ef\u80fd\u4f1a\u6536\u5230\u566a\u58f0\u7684\u5f71\u54cd\uff0c\u8fdb\u4e00\u6b65\u7684\uff0c\u6211\u4eec\u53ef\u4ee5\u7528\u4e3b\u6210\u5206\u5206\u6790(Principle Component Analysis)\u6765\u4f18\u5316\u8fd9\u4e2a\u8fc7\u7a0b\u3002\u3002</p> <p>Principle Component Analysis</p> <p>\u2460 Subtract off the mean for each data point.</p> <p></p> <p>\u2461 Compute the covariance matrix at each point.</p> \\[ H = \\sum_{(u,v)}w(u,v) \\begin{bmatrix}     I_x^2 &amp; I_xI_y \\\\     I_xI_y &amp; I_y^2 \\end{bmatrix} \\text{           where  }  I_x = \\frac{\\partial f}{\\partial x}, I_y = \\frac{\\partial y}{\\partial y} \\] <p>\\(w(u,v)\\) \u4e00\u822c\u662f\u9ad8\u65af\u6743\u91cd\u3002</p> <p>\u2462 Compute eigenvalues.</p> \\[ H = \\begin{bmatrix}     a &amp; b \\\\     c &amp; d \\end{bmatrix} \\;\\;\\;\\; \\lambda_{\\pm} = \\frac{1}{2}\\left(     (a+d) \\pm \\sqrt{4bc + (a-d)^2}    \\right) \\] error function approximation <p>Carnegie Mellon University \u7684 slides P18  \u5f00\u59cb\u8fd8\u63d0\u5230\u4e86\u4e0d\u540c\u4f4d\u79fb\u4e0b\u7684\u8bef\u5dee\u51fd\u6570\uff0c\u5e76\u7ed9\u51fa\u4e86\u4e09\u79cd\u60c5\u51b5\u4e0b\u8bef\u5dee\u51fd\u6570\u7684\u70ed\u529b\u56fe\u3002</p> <p></p> <p>\u2463 Components are the eigenvectors ranked by the eigenvalues.</p> <p>\u5728\u672c\u8282\u7684\u8bed\u5883\u4e0b\uff0c\u5f62\u8c61\u5730\u53d9\u8ff0\u4e3b\u6210\u5206\u5206\u6790\u5f97\u5230\u7684\u7ed3\u679c\u5c31\u662f\uff1a\u7b2c\u4e00\u4e2a\u4e3b\u6210\u5206\u6307\u5411\u65b9\u5dee\u6700\u5927\u7684\u65b9\u5411\uff0c\u7b2c\u4e8c\u4e2a\u4e3b\u6210\u5206\u6307\u5411\u5782\u76f4\u4e8e\u7b2c\u4e00\u4e2a\u4e3b\u6210\u5206\u7684\u65b9\u5411\uff0c\u5b83\u4eec\u7684\u5927\u5c0f\u5219\u4e0e\u8fd9\u4e9b\u65b9\u5dee\u6b63\u76f8\u5173\u3002</p> <p>\u5bf9\u4e8e\u4e0a\u9762\u7684\u4e09\u79cd\u60c5\u51b5\uff0c\u5b83\u4eec\u505a\u4e3b\u6210\u5206\u5206\u6790\u540e\u5f97\u5230\u7684\u7ed3\u679c\u662f\uff1a</p> <p></p> <p>\u53ef\u4ee5\u53d1\u73b0\uff0c\u7b2c\u4e09\u4e2a\u60c5\u51b5\u7684\u4e24\u4e2a\u7279\u5f81\u503c\u90fd\u5f88\u5927\u3002</p> <p>\u6211\u4eec\u901a\u8fc7\u5224\u65ad\u4e24\u4e2a\u7279\u5f81\u503c\u7684\u5927\u5c0f\u5173\u7cfb\u60c5\u51b5\u6765\u5224\u65ad\u4e00\u4e2a\u533a\u57df\u662f\u5426\u5305\u542b\u4e00\u4e2a\u89d2(corner)\u3001\u8fb9(edge)\u6216\u5e73\u9762(flat)\uff0c\u53ef\u4ee5\u5c06\u4ed6\u4eec\u653e\u5230\u4e00\u4e2a\u76f4\u65b9\u56fe\u4e2d\uff0c\u6839\u636e\u4e24\u4e2a\u7279\u5f81\u503c\u5f62\u6210\u7684\u70b9\u5bf9\u5728\u6574\u4e2a\u8c61\u9650\u4e2d\u51fa\u73b0\u7684\u4f4d\u7f6e\u6765\u5224\u65ad\u89d2\u70b9\u60c5\u51b5\uff1a</p> <p></p> <p>Figure from Carnegie Mellon University's slides. Corner detection.</p> <p>\u4e3a\u4e86\u80fd\u591f\u91cf\u5316\u5730\u8868\u8fbe\u4e0a\u9762\u8fd9\u5f20\u56fe\u7684\u5206\u7c7b\u89c4\u5219\uff0c\u6211\u4eec\u5f15\u5165\u54c8\u91cc\u65af\u7b97\u5b50(Harris operator):</p> \\[ f = \\frac{\\lambda_1\\lambda_2}{\\lambda_1+\\lambda_2} = \\frac{determinant(H)}{trace(H)} \\] <p>\u8fd9\u91cc\u7684\u4e00\u4e2a\u7279\u6027\u662f\uff0c\u5bf9\u4e8e\u4e8c\u7ef4\u77e9\u9635\u6765\u8bf4\uff0c\u6211\u4eec\u5b9e\u9645\u4e0a\u5e76\u4e0d\u9700\u8981\u6309\u7167\u4e4b\u524d\u7684\u6b65\u9aa4\uff0c\u8fdb\u884c\u4e3b\u6210\u5206\u5206\u6790\u4ee5\u540e\u518d\u5f97\u5230\uff0c\u800c\u662f\u53ef\u4ee5\u76f4\u63a5\u901a\u8fc7\u8fd9\u4e2a\u516c\u5f0f\u5f97\u5230\u3002</p> <p>\u800c\u8fd9\u4e2a \\(f\\) \u5c31\u53eb\u505a corner response\u3002</p> reminder \\[ det\\left(\\begin{bmatrix}     a &amp; b\\\\     c &amp; d \\end{bmatrix}\\right) = ad-bc \\;\\;\\;\\;\\; trace\\left(\\begin{bmatrix}     a &amp; b\\\\     c &amp; d \\end{bmatrix}\\right) = a+d \\] <p>\u5982\u4e0a\u8fd9\u5957\u65b9\u6cd5\u5c31\u662fHarris corner detector\u7684\u5b9e\u73b0\u3002</p> <p>\u5f52\u7eb3\u4e00\u4e0b\uff0c\u5176\u6b65\u9aa4\u5c31\u662f\uff1a</p> <p>Harris detector </p> <ol> <li>\u6c42\u5bfc | Compute derivatives at each pixel.</li> <li>\u534f\u65b9\u5dee\u77e9\u9635 | Compute covariance matrix \\(H\\) in a Gaussian window around each pixel.</li> <li>\u54cd\u5e94\u51fd\u6570 | Compute corner response function \\(f\\).</li> <li>\u9608\u503c\u8fc7\u6ee4 | Threshold \\(f\\).</li> <li>\u975e\u6781\u5927\u503c\u6291\u5236 | Find local maxima of response function (nonmaximum suppression).</li> </ol> <p>\u66f4\u8be6\u7ec6\u7684\u8bf4\u660e\u53ef\u4ee5\u53c2\u8003 wiki \u4e0a\u7684\u8bf4\u660e\uff1aHarris corner detector\u3002</p> <ul> <li>C.Harris and M.Stephens. \u201cA Combined Corner and Edge Detector.\u201d Proceedings of the 4th Alvey Vision Conference: pages 147\u2014151, 1988.</li> </ul> <p>\u53e6\u4e00\u4e2a\u5173\u952e\u95ee\u9898\u662f\uff0c\u901a\u8fc7\u8fd9\u4e2a\u65b9\u6cd5\u5f97\u5230\u7684\u5173\u952e\u70b9\uff0c\u5177\u6709\u5bf9\u53d8\u6362\u4e0d\u654f\u611f\u6027\u5417\uff1f</p> <p>\u5bf9\u6b64\uff0c\u7ed3\u8bba\u662f\uff1a</p> <ol> <li>Partially invariant to affine intensity change.</li> <li>Corner response is invariant w.r.t. translation.</li> <li>Corner response is invariant w.r.t. image rotation.</li> <li>Corner response is NOT invariant to scaling.</li> </ol> <p>\u5bf9\u5c3a\u5ea6\u53d8\u5316\u654f\u611f\u7684\u89e3\u51b3\u65b9\u6848</p> <p>\u9488\u5bf9\u7ed3\u8bba 4\uff0c\u7531\u4e8e Harris detector \u5bf9\u5c3a\u5ea6\u53d8\u5316\u654f\u611f\uff0c\u6240\u4ee5\u6211\u4eec\u5728\u4f7f\u7528\u8fd9\u4e2a\u65b9\u6cd5\u7684\u8fc7\u7a0b\u4e2d\u9700\u8981\u6ce8\u610f\u5c3a\u5ea6\uff0c\u5373\u7a97\u53e3\u7684\u5927\u5c0f\u9009\u5b9a\u3002</p> <p> </p> <p>\u4e00\u79cd\u8bbe\u60f3\u7684\u65b9\u6848\u662f\uff0c\u4e0d\u65ad\u5c1d\u8bd5\u4e0d\u540c\u7684 window size\uff0c\u7136\u540e\u53d6\u5f97 response \u66f2\u7ebf\uff0c\u5047\u8bbe response \u7684\u5927\u5c0f\u53ea\u4e0e scale \u6709\u5173\uff0c\u5219\u66f2\u7ebf\u90fd\u5e94\u8be5\u662f\u5355\u5cf0\u7684\uff0c\u800c\u53d6\u51fa\u8fd9\u4e2a\u5cf0\u503c\uff08\u7279\u5f81\u6700\u660e\u663e\u7684\u65f6\u5019\uff09\uff0c\u5c31\u53ef\u4ee5\u5f53\u4ed6\u4e3a\u5bf9\u5e94\u7684 scale \u4ee5\u53ca\u5bf9\u5e94\u7684 response\u3002</p> <p>\u4e0d\u8fc7\u4e00\u822c\u5b9e\u9645\u7684\u505a\u6cd5\u662f\u56fa\u5b9a\u7a97\u53e3\u5927\u5c0f\uff0c\u800c\u6539\u53d8\u56fe\u7247\u7684\u5927\u5c0f\uff0c\u518d\u5728\u5f97\u5230\u7684\u56fe\u50cf\u91d1\u5b57\u5854\u4e0a\u8fdb\u884c\u8fd9\u4e2a\u65b9\u6cd5\u7684\u8ba1\u7b97\uff0c\u5373\u5bf9\u4e0d\u540c\u5206\u8fa8\u7387\u7684\u56fe\u7247\u4e0a\u5206\u522b\u8fdb\u884c\u54c8\u91cc\u65af\u68c0\u6d4b\u3002\uff08\u76f8\u5f53\u4e8e\u7ed9\u56fe\u7247\u589e\u52a0\u4e86\u4e00\u4e2a\u7ef4\u5ea6\uff0c\u672c\u8d28\u4e0a\u548c\u4e0a\u9762\u7684\u65b9\u6cd5\u662f\u4e00\u6837\u7684\uff0c\u53ea\u4e0d\u8fc7\u7528\u4e86\u4e00\u4e2a\u66f4\u5408\u7406\u7684\u5b9e\u73b0\u89d2\u5ea6\u3002\uff09</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec05/#\u6591\u70b9\u68c0\u6d4b","title":"\u6591\u70b9\u68c0\u6d4b","text":"<p>\u9664\u4e86\u89d2\u70b9\uff0c\u6591\u70b9(blob)\u4e5f\u662f\u4e00\u4e2a\u6bd4\u8f83\u597d\u7684\u7279\u6027\uff0c\u975e\u5e38\u9002\u5408\u4f5c\u4e3a\u5173\u952e\u70b9\u3002</p> <p>\u800c\u6591\u70b9\u7684\u5bfb\u627e\u6211\u4eec\u5219\u53ef\u4ee5\u5229\u7528\u6ee4\u6ce2\u5668\u6765\u5b9e\u73b0\uff0c\u8ba9\u6211\u4eec\u56de\u987e\u7b2c\u4e09\u7ae0\u8fb9\u7f18\u63d0\u53d6\u7684\u76f8\u5173\u5185\u5bb9\uff0c\u6211\u4eec\u53ef\u4ee5\u5229\u7528\u7c7b\u4f3c\u7684\u505a\u6cd5\uff0c\u4f7f\u7528\u4e00\u4e2a\u4e2d\u95f4\u8d1f\u56db\u5468\u6b63\u7684\u6ee4\u6ce2\u5668\u6765\u63d0\u53d6\u6591\u70b9\u3002</p> <p>\u901a\u5e38\u6765\u8bf4\uff0c\u6211\u4eec\u4f7f\u7528 Gaussian \u6ee4\u6ce2\u5668\u7684 Laplacian\uff0c\u5373 Laplacian of Gaussian Filter(LoG)\uff0c\u6765\u4f5c\u4e3a\u6ee4\u6ce2\u5668\u548c\u56fe\u50cf\u8fdb\u884c\u5377\u79ef\u3002</p> <p>\ud83d\udc49 Laplacian \u7b97\u5b50</p> <p></p> <p>\u5b9e\u9645\u4e0a\u4e5f\u7b49\u6548\u4e8e\u5148\u5bf9\u56fe\u7247\u4f5c\u9ad8\u65af\u6a21\u7cca\uff08\u51cf\u5c0f\u566a\u58f0\u5f71\u54cd\uff09\uff0c\u518d\u8ba1\u7b97\u5176\u62c9\u666e\u62c9\u65af\u7b97\u5b50\uff0c\u5373\uff1a</p> \\[ \\nabla^2(f*g) = f * \\nabla^2 g \\] <p>\u5176\u4e2d\uff0cLoG \u7684 scale \u662f\u901a\u8fc7\u9ad8\u65af\u51fd\u6570\u7684 \\(\\sigma\\) \u63a7\u5236\u7684\uff0c\u4e5f\u540c\u6837\u901a\u8fc7\u50cf\u7d20\u91d1\u5b57\u5854\u6765\u5b9e\u73b0\u3002</p> <p></p> <p>\u53c8\u6216\u8005\u53ef\u4ee5\u4f7f\u7528 Difference of Gaussian(DoG)\uff0c\u5373\u5c06 Laplacian of Gaussian Filter \u66ff\u6362\u4e3a\u4e00\u4e2a\u7531\u4e24\u4e2a\u9ad8\u65af\u51fd\u6570\u505a\u5dee\u5f97\u5230\u7684 Filter\uff0c\u76f8\u5bf9\u6765\u8bf4\u6548\u7387\u66f4\u9ad8\u3002</p> <p></p> <p></p>"},{"location":"cour_note/D2QD_Intro2CV/Lec05/#\u5173\u952e\u70b9\u8868\u8fbe","title":"\u5173\u952e\u70b9\u8868\u8fbe","text":"<p>\u9009\u5b9a\u5173\u952e\u70b9\u540e\uff0c\u6211\u4eec\u9700\u8981\u8003\u8651\u5982\u4f55\u63cf\u8ff0\u548c\u8868\u8fbe\u8fd9\u4e9b\u70b9\uff0c\u4ee5\u4f7f\u5bf9\u5e94\u5bf9\u5173\u952e\u70b9\u8868\u8fbe\u76f8\u8fd1\uff0c\u800c\u4e0d\u76f8\u5173\u5bf9\u5173\u952e\u70b9\u8868\u8fbe\u76f8\u8fdc\u3002</p> <p>\u4e00\u79cd\u6734\u7d20\u7684\u601d\u60f3\u662f\u5c06\u7a97\u53e3\u5185\u7684\u50cf\u7d20\u4f5c\u4e3a\u4e00\u4e2a\u7279\u6027\u5411\u91cf(feature vector)\u8fdb\u884c\u6bd4\u8f83\uff0c\u4f46\u662f\u8fd9\u6837\u505a\u5bf9\u504f\u79fb\u7684\u8bef\u5dee\u8fc7\u4e8e\u654f\u611f\u3002\u4e5f\u5c31\u662f\u8bf4\uff0c\u4e5f\u8bb8\u4e24\u5f20\u56fe\u7247\u5f88\u50cf\uff0c\u4f46\u662f\u56e0\u4e3a\u4e00\u70b9\u4f4d\u79fb\u8bef\u5dee\uff0c\u5bfc\u81f4\u5411\u91cf\u521a\u597d\u9519\u5f00\uff0c\u5bfc\u81f4\u7ed3\u679c\u663e\u793a\u4e24\u4e2a\u70b9\u5dee\u522b\u5f88\u5927\u3002\u8fd9\u662f\u56e0\u4e3a\u8fd9\u79cd\u505a\u6cd5\u5bf9\u50cf\u7d20\u70b9\u5728\u7a97\u53e3\u4e2d\u7684\u4f4d\u7f6e\u5f88\u654f\u611f\uff0c\u4f46\u662f\u663e\u7136\u4f4d\u7f6e\u5e76\u4e0d\u662f\u5173\u952e\u70b9\u7684\u7279\u5f81\u4e4b\u6240\u5728\u3002</p> <p> </p> <p>\u53e6\u5916\u66f4\u597d\u7684\u505a\u6cd5\u662f\u5c3a\u5ea6\u4e0d\u53d8\u7684\u7279\u5f81\u53d8\u6362(Scale Invariant Feature Transform, SIFT) descriptor\uff0c\u4e0d\u518d\u4f7f\u7528\u50cf\u7d20\u503c\uff0c\u800c\u662f\u4f7f\u7528\u533a\u57df\u4e2d\u7684\u68af\u5ea6\u7684\u5206\u5e03\u4f5c\u4e3a\u4e00\u4e2a\u63cf\u8ff0\uff0c\u53ef\u4ee5\u8868\u793a\u4e3a\u4e00\u5f20 \\([0,2\\pi)\\) \u7684\uff0c\u5faa\u73af\u7684\u76f4\u65b9\u56fe\u3002\u6b64\u65f6\u5c0f\u7684\u5e73\u79fb\u548c\u7f29\u653e\u90fd\u4e0d\u4f1a\u5bf9\u5b83\u4ea7\u751f\u5f88\u5927\u5f71\u54cd\uff0c\u800c\u65cb\u8f6c\u53ea\u4f1a\u5bfc\u81f4\u76f4\u65b9\u56fe\u7684\u5faa\u73af\u5e73\u79fb\u2014\u2014\u4e0d\u8fc7\u8fd9\u79cd\u5faa\u73af\u5e73\u79fb\u662f\u5f88\u597d\u5904\u7406\u7684\uff0c\u6bd4\u5982\u6211\u4eec\u53ef\u4ee5\u9009\u4e2d\u6700\u5927\u7684\u5206\u91cf\u4f5c\u4e3a\u53c2\u8003\uff0c\u5e76\u5c06\u6574\u4e2a\u76f4\u65b9\u56fe\u5e73\u79fb\u5bf9\u9f50\u3002\u76f8\u6bd4\u76f4\u63a5\u5c06\u50cf\u7d20\u8f6c\u5316\u4e3a\u7279\u5f81\u5411\u91cf SIFT \u9c81\u68d2\u6027\u66f4\u9ad8\u3002</p> <p></p> <p>\u5b8c\u6574\u7684 SIFT \u662f\u5305\u62ec\u300c\u68c0\u6d4b\u300d\u6b65\u9aa4\u7684\u3002</p> <p>Other detectors and descriptors:</p> <ul> <li>HOG: Histogram of oriented gradients<ul> <li>Dalal &amp; Triggs, 2005 </li> </ul> </li> <li>SURF: Speeded Up Robust Features<ul> <li>Herbert Bay, Andreas Ess, Tinne Tuytelaars, Luc Van Gool, \"SURF: Speeded Up Robust Features\", Computer Vision and Image Understanding (CVIU), Vol. 110, No. 3, pp. 346--359, 2008 </li> </ul> </li> <li>FAST (corner detector)<ul> <li>Rosten. Machine Learning for High-speed Corner Detection, 2006. </li> </ul> </li> <li>ORB: an efficient alternative to SIFT or SURF<ul> <li>Ethan Rublee, Vincent Rabaud, Kurt Konolige, Gary R. Bradski: ORB: An efficient alternative to SIFT or SURF. ICCV 2011 </li> </ul> </li> <li>Fast Retina Key- point (FREAK)<ul> <li>A. Alahi, R. Ortiz, and P. Vandergheynst. FREAK: Fast Retina Keypoint. In IEEE Conference on Computer Vision and Pattern Recognition, 2012. CVPR 2012 Open Source Award Winner.</li> </ul> </li> </ul>"},{"location":"cour_note/D2QD_Intro2CV/Lec05/#\u5173\u952e\u70b9\u5339\u914d","title":"\u5173\u952e\u70b9\u5339\u914d","text":"<p>\u6240\u8c13\u7684\u5339\u914d(matching)\u5c31\u662f\u5b57\u9762\u4e0a\u7684\u5c06\u4e24\u5f20\u56fe\u4e2d\u5bf9\u5e94\u7684\u70b9\u5efa\u7acb\u8d77\u5339\u914d\u5173\u7cfb\u3002\u800c\u8bc4\u4f30\u65b9\u6cd5\u5c31\u662f\u5bfb\u627e\u300c\u8ddd\u79bb\u300d\u6700\u63a5\u8fd1\u7684\u70b9\u3002</p> <p>\u800c\u8fd9\u91cc\u7684\u300c\u8ddd\u79bb\u51fd\u6570\u300d\u662f\u7528\u6765\u8861\u91cf\u4e24\u4e2a\u5173\u952e\u70b9\u7684\u8868\u8fbe\u7684\u5dee\u5f02\u7684\u51fd\u6570\uff0c\u4e00\u822c\u4f7f\u7528 L2 distance\uff0c\u5373 \\(||f_1 - f_2||\\)\u3002</p> <p>\u91cd\u590d\u6027\u7eb9\u7406</p> <p>\u7136\u800c\u9700\u8981\u7279\u522b\u6ce8\u610f\u70b9\u4e00\u4e2a\u95ee\u9898\u662f\uff0c\u5f88\u6709\u53ef\u80fd\u51fa\u73b0\u67d0\u4e2a\u7279\u5f81\u56fe\u6848\u91cd\u590d\u51fa\u73b0\u7684\u60c5\u51b5\uff0c\u8fd9\u7c7b\u95ee\u9898\u53eb\u505a\u91cd\u590d\u6027\u7eb9\u7406\u95ee\u9898\u3002</p> <p>\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\u53ef\u80fd\u6709\u5f88\u591a\u5173\u952e\u70b9\u80fd\u548c\u8fd9\u4e2a\u5173\u952e\u70b9\u5b9e\u73b0\u5339\u914d\uff08\u8868\u8fbe\u76f8\u8fd1\uff09\uff0c\u8fd9\u4e2a\u65f6\u5019\u6211\u4eec\u5c31\u9700\u8981\u7528 Ratio score = \\(\\frac{ ||f_1 - f_2|| }{ ||f_1 - f_2'|| }\\)\uff0c\u6bd4\u8f83\u6700\u63a5\u8fd1\u7684\u4e24\u79cd\u5339\u914d\u3002</p> <p>\u5982\u679c Ratio score \u63a5\u8fd1 1\uff0c\u8bf4\u660e \\(f_1, F_2,f_2'\\) \u7684\u8868\u8fbe\u90fd\u5f88\u63a5\u8fd1\uff0c\u8fd9\u4e2a\u5339\u914d\u5e76\u4e0d\u53ef\u9760\uff0c\u53ea\u80fd\u4e22\u6389\u8fd9\u4e2a\u5173\u952e\u70b9\u3002</p> <p>\u5728\u4f20\u7edf CV \u6280\u672f\u4e2d\uff0c\u6211\u4eec\u5f88\u96be\u5904\u7406\u8fd9\u4e00\u7c7b\u91cd\u590d\u6027\u7eb9\u7406\u7684\u95ee\u9898\uff0c\u6240\u4ee5\u9047\u5230\u8fd9\u79cd\u96be\u4ee5\u5bfb\u627e\u5339\u914d\u5173\u7cfb\u7684\u60c5\u51b5\uff0c\u6211\u4eec\u53ea\u80fd\u9009\u62e9\u4e0d\u5339\u914d\u5b83\u4eec\u3002</p> <p>\u6b64\u5916\uff0c\u4e3a\u4e86\u589e\u52a0\u5339\u914d\u7684\u51c6\u786e\u6027\uff0c\u6211\u4eec\u8fd8\u6709\u4e00\u4e2a\u5224\u5b9a\u89c4\u5219\uff1a\u4e24\u70b9\u76f8\u4e92\u6700\u76f8\u4f3c\uff0c\u5219\u8be5\u5339\u914d\u5341\u5206\u53ef\u4fe1\u3002\uff08\u5728 I2 \u4e2d\u4f60\u6700\u50cf\u6211\uff0c\u5728 I1 \u4e2d\u6211\u6700\u50cf\u4f60\uff09</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec05/#\u8fd0\u52a8\u4f30\u8ba1","title":"\u8fd0\u52a8\u4f30\u8ba1","text":"<p>\u5148\u524d\uff0c\u6211\u4eec\u7740\u773c\u4e8e\u5355\u5f20\u56fe\u7247\uff0c\u6216\u8005\u8bf4\u51e0\u5f20\u56fe\u7247\uff0c\u4ecd\u7136\u662f\u4ee5\u4e00\u4e2a\u9759\u6001\u7684\u89c6\u89d2\u6765\u89c2\u5bdf\u56fe\u50cf\u3002</p> <p>\u800c\u5f53\u6211\u4eec\u628a\u7814\u7a76\u5bf9\u8c61\u4ece\u56fe\u7247\u6539\u53d8\u4e3a\u89c6\u9891\u6216\u8005\u8bf4\u56fe\u7247\u5e8f\u5217\u7684\u65f6\u5019\uff0c\u56fe\u7247\u5c31\u88ab\u8d4b\u4e88\u4e86\u8fd0\u52a8\u7684\u5c5e\u6027\uff0c\u800c\u8fd9\u5c31\u5f15\u51fa\u4e86\u8fd0\u52a8\u4f30\u8ba1(motion estimation)\u95ee\u9898\u3002</p> <p>\u9996\u5148\uff0c\u8fd0\u52a8\u6309\u7167\u6210\u56e0\u4e3b\u8981\u53ef\u4ee5\u5206\u4e3a\u76f8\u673a\u8fd0\u52a8\u548c\u573a\u666f\u8fd0\u52a8\u4e24\u4e2a\u7ef4\u5ea6\u3002</p> \u76f8\u673a\u8fd0\u52a8 \u573a\u666f\u8fd0\u52a8 eg (\u5149\u7ebf\u53d8\u5316\u7b49\u5f71\u54cd\u89c6\u9891\u6bcf\u4e00\u5e27\u7684\u5185\u5bb9\u5b58\u5728\u5149\u5f71\u5dee\u5f02\u7b49) \u9759\u666f\u201c\u8fd0\u955c\u201d \u76d1\u63a7\u5f55\u50cf \u4f53\u80b2\u8d5b\u4e8b\u955c\u5934\u8ddf\u8e2a <p>\u800c\u9488\u5bf9\u8fd0\u52a8\u4f30\u8ba1\u95ee\u9898\uff0c\u6709\u8fd9\u4e48\u51e0\u79cd\u89e3\u51b3\u7684\u89c6\u89d2\uff1a</p> <ul> <li>\u7279\u5f81\u8ddf\u8e2a\uff0c\u5728\u6bcf\u4e00\u5e27\u4e2d\u8fdb\u884c\u5173\u952e\u70b9\u5339\u914d\uff0c\u4ee5\u8ddf\u8e2a\u7279\u5b9a\u5173\u952e\u70b9\u7684\u53d8\u5316\u2014\u2014\u8fd9\u4e00\u7c7b\u65b9\u6cd5\u5f97\u5230\u7684\u7ed3\u679c\u76f8\u5bf9\u7a00\u758f\uff0c\u6bd5\u7adf\u5173\u952e\u70b9\u603b\u662f\u5c11\u7684\uff1b</li> <li>\u5149\u6d41(optical flow)\u6280\u672f\uff0c\u901a\u8fc7\u5bf9\u76f8\u90bb\u5e27\u7684\u50cf\u7d20\u8fdb\u884c\u5339\u914d\uff0c\u4ee5\u8ddf\u8e2a\u50cf\u7d20\u7684\u53d8\u5316\u2014\u2014\u8fd9\u4e00\u7c7b\u65b9\u6cd5\u5f97\u5230\u7684\u7ed3\u679c\u76f8\u5bf9\u5bc6\u96c6\uff1b</li> </ul> <p>\u800c\u4e24\u4e2a\u89c6\u89d2\u90fd\u53ef\u4ee5\u4f7f\u7528 Lucas-Kanade method \u89e3\u51b3\u3002</p> <p>\u9996\u5148\uff0c\u6211\u4eec\u9700\u8981\u7ed9\u8fd0\u52a8\u4f30\u8ba1(motion estimation)\u95ee\u9898\u4e00\u4e2a\u66f4\u660e\u786e\u7684\u5b9a\u4e49\uff1a</p> <p>motion estimation</p> <p>Wiki: https://en.wikipedia.org/wiki/Motion_estimation</p> <p>\u8fd0\u52a8\u4f30\u8ba1\u662f\u6307\u4ece\u4e00\u4e2a 2D \u56fe\u50cf\u5230\u53e6\u4e00\u4e2a 2D \u56fe\u50cf\u7684\u8f6c\u6362\u4e2d\u786e\u5b9a\u63cf\u8ff0\u8fd0\u52a8\u7684\u8fd0\u52a8\u77e2\u91cf\u7684\u8fc7\u7a0b\uff0c\u901a\u5e38\u662f\u4ece\u89c6\u9891\u5e8f\u5217\u4e2d\u76f8\u90bb\u7684\u5e27\u4e2d\u63d0\u53d6\u3002</p> <p>\u5047\u8bbe\u6211\u4eec\u6709\u5339\u914d\u70b9 \\(P(x,y,t)\\) \u548c \\(P(x+u, y+v, t+1)\\)\uff0c\u5219\u8fd0\u52a8\u4f30\u8ba1\u5219\u662f\u6c42\u89e3 \\((u,v)\\) \u7684\u8fc7\u7a0b\u3002</p> <p>\u4e0d\u540c\u4e8e\u5173\u952e\u70b9\u7684\u5339\u914d\uff0c\u8fd0\u52a8\u4f30\u8ba1\u66f4\u4fa7\u91cd\u4e8e\u5bf9\u5173\u952e\u70b9\u7684\u65f6\u5e8f\u5173\u7cfb\u7684\u5339\u914d\u4e0e\u63cf\u8ff0\u3002</p> <p>\u800c\u6211\u4eec\u4e4b\u540e\u7684\u63a2\u8ba8\uff0c\u90fd\u9700\u8981\u57fa\u4e8e LK \u5047\u8bbe\u5c55\u5f00\uff1a</p> <p>Key Asumptions of Lucas-Kanade</p> <ol> <li>[Small motion] \u76f8\u90bb\u5e27\uff0c\u5339\u914d\u70b9\u7684\u8fd0\u52a8\u8ddd\u79bb\u5c0f\uff1b</li> <li>[Brightness constancy] \u76f8\u90bb\u5e27\uff0c\u70b9\u7684\u4eae\u5ea6\u503e\u5411\u4e8e\u4e0d\u53d8\uff0c\u5373\u53d8\u5316\u5fae\u5c0f\uff1b</li> <li>[Spatial coherence] \u76f8\u90bb\u7684\u70b9\u503e\u5411\u4e8e\u8fd0\u52a8\u76f8\u4f3c\uff1b</li> </ol> <p>\u63a5\u4e0b\u6765\uff0c\u57fa\u4e8e LK \u5047\u8bbe\uff0c\u6211\u4eec\u6765\u7814\u7a76\u8fd0\u52a8\u4f30\u8ba1\u95ee\u9898\u7684\u6c42\u89e3\u3002</p> <p>\u9996\u5148\uff0c\u6211\u4eec\u5c06\u7b2c\u4e8c\u6761\u5047\u8bbe\u8868\u8fbe\u5f0f\u5316\uff0c\u5373\u6709\uff1a</p> \\[ I(x,y,t) = I(x+u, y+v, t+1) \\] <p>\u4e3a\u4e86\u6c42\u89e3 \\(u\\) \u548c \\(v\\)\uff0cLK Method \u5bf9\u5176\u4f5c\u6cf0\u52d2\u5c55\u5f00\uff1a</p> \\[ I(x+u,y+v,t+1) \\approx I(x,y,t) + I_x\\cdot u + I_y \\cdot v + I_t \\] <p>\u79fb\u9879\uff1a</p> \\[ I(x+u,y+v,t+1) - I(x,y,t) = I_x\\cdot u + I_y \\cdot v + I_t \\] <p>\u6839\u636e\u5047\u8bbe 2\uff0c\u5f97\u5230\uff1a</p> \\[ I_x\\cdot u + I_y \\cdot v + I_t \\approx 0 \\] <p>\u5373\uff1a</p> \\[ \\nabla I \\cdot \\begin{bmatrix}     u &amp; v \\end{bmatrix}^T + I_t = 0 \\] <p>\u4e8e\u662f\u6211\u4eec\u5f97\u5230\u4e86\u5173\u4e8e \\(u\\) \u548c \\(v\\) \u7684\u4e00\u4e2a\u8f83\u7b80\u5355\u7684\u7b49\u5f0f\u3002</p> <p>\u7136\u800c\u6211\u4eec\u53ea\u6709\u4e00\u4e2a\u7b49\u5f0f\uff0c\u4f46\u9700\u8981\u6c42\u89e3\u7684\u672a\u77e5\u5143 \\(u\\) \u548c \\(v\\) \u6709\u4e24\u4e2a\u3002</p> <p>\u4e8e\u662f\u6211\u4eec\u5f15\u5165\u4e86\u5047\u8bbe 3\uff0c\u5373\u76f8\u90bb\u7684\u70b9\u503e\u5411\u4e8e\u8fd0\u52a8\u76f8\u4f3c\u3002</p> <p>\u4e8e\u662f\u6211\u4eec\u53ef\u4ee5\u628a\u7a97\u53e3\u5185\u7684\u50cf\u7d20\u90fd\u5e26\u5165\u4e0a\u9762\u90a3\u4e2a\u7b49\u5f0f\uff0c\u5c1d\u8bd5\u6765\u6c42\u89e3\uff08\u5927\u81f4\u90fd\u76f8\u4f3c\u7684\uff09\\(u\\) \u548c \\(v\\)\u3002\u6b64\u65f6\u6211\u4eec\u7684\u65b9\u7a0b\u6570\u91cf\u5c31\u975e\u5e38\u5145\u88d5\u4e86\u3002\u6b64\u65f6\u6211\u4eec\u53ef\u4ee5\u5c06\u95ee\u9898\u8f6c\u5316\u4e3a\u4f18\u5316\u95ee\u9898\u3002</p> \\[ Ad=b \\rightarrow \\min\\limits_d ||Ad-b||^2 \\] <p>Least squares solution(\u524d\u9762\u63d0\u5230\u8fc7\u7684\u6700\u5c0f\u4e8c\u4e58\u6cd5\u7684\u8fd1\u4f3c\u89e3) for d given by \\((A^TA)d = A^Tb\\).</p> <p>\u800c\u8fd9\u4e2a\u89e3\u662f\u5426\u5b58\u5728\u7684\u6761\u4ef6\u662f\uff1a</p> \\[ \\underbrace{     \\begin{bmatrix}         \\sum I_x I_x &amp; \\sum \\sum I_x I_x \\\\         \\sum I_x I_y &amp; \\sum I_y I_y     \\end{bmatrix} }_{A^T A} \\begin{bmatrix}     u \\\\     v \\end{bmatrix} = \\underbrace{     \\begin{bmatrix}         \\sum I_x I_t \\\\         \\sum I_y I_t     \\end{bmatrix} }_{A^T b} \\] <p>\u5728\u8be5\u5f0f\u4e2d\uff0c\\(A^TA\\) \u9700\u8981\u662f\u53ef\u9006\u7684\uff0c\u5e76\u4e14\u5b83\u7684\u4e24\u4e2a\u7279\u5f81\u503c\u90fd\u4e0d\u80fd\u592a\u5c0f\u3002\u4e5f\u5c31\u8be5\u70b9\u80fd\u591f\u88ab Harris corner detector \u68c0\u6d4b\u5230\u70b9\u89d2\u70b9\uff01</p> <p>\u56e0\u6b64\uff0c\u5018\u82e5\u4f7f\u7528 LK \u65b9\u6cd5\uff0c\u6211\u4eec\u9700\u8981\u4fdd\u8bc1 \\(A^TA\\) \u53ef\u9006\uff0c\u4e14\u56fe\u50cf\u4e2d\u4e0d\u80fd\u6709\u592a\u591a\u566a\u70b9\u3002</p> <p>\u6b64\u5916\uff0c\u5173\u4e8e\u5bf9\u5047\u8bbe 1 \u7684\u7ea6\u675f\uff0c\u539f\u5219\u4e0a\u4e24\u5e27\u4e4b\u95f4\u7684\u8fd0\u52a8\u5dee\u8ddd\u5e94\u8be5\u5c0f\u4e8e\u4e00\u4e2a\u50cf\u7d20\uff0c\u7136\u800c\u8fd9\u4e2a\u6761\u4ef6\u975e\u5e38\u82db\u523b\u3002\u6240\u4ee5\u6211\u4eec\u7684\u53ef\u4ee5\u5148\u5bf9\u56fe\u7247\u8fdb\u884c\u6a21\u7cca/\u7f29\u5c0f\u5904\u7406\uff0c\u50cf\u7d20\u8db3\u591f\u201c\u5927\u201d\u4e4b\u540e\u5c31\u53ef\u4ee5\u6ee1\u8db3\u8fd9\u4e2a\u5047\u8bbe 1\u3002\u7136\u800c\u5728\u8fd9\u4e2a\u8fc7\u7a0b\u4e2d\u4f1a\u4e22\u5931\u5f88\u591a\u4fe1\u606f\uff0c\u6240\u4ee5\u53ea\u6839\u636e\u8fd9\u4e2a\u6761\u4ef6\u6765\u8ba1\u7b97\u4e5f\u4e0d\u884c\uff0c\u6240\u4ee5\u6211\u4eec\u53ef\u4ee5\u5728\u50cf\u7d20\u91d1\u5b57\u5854\u4e0a\u8fdb\u884c\u9010\u5c42\u6b21\u4f30\u8ba1\uff0c\u518d\u4e0d\u65ad\u7ec6\u5316\u7684\u505a\u6cd5\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec06/","title":"Lecture 6 | Image Alignment and Stitching","text":"<p> \u7ea6 1320 \u4e2a\u5b57  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 4 \u5206\u949f</p> <p>\u6ce8\u610f</p> <p>\u672c\u6587\u5c1a\u672a\u5b8c\u5168\u6574\u7406\u597d\uff01</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec06/#\u56fe\u50cf\u62fc\u63a5","title":"\u56fe\u50cf\u62fc\u63a5","text":"<p>\u6240\u8c13\u7684\u56fe\u50cf\u62fc\u63a5\uff0c\u6a21\u5f0f\u4e0a\u5c31\u662f\u5bfb\u627e\u82e5\u5e72\u56fe\u7247\u7684\u5171\u540c\u90e8\u5206\uff0c\u5e76\u5c06\u753b\u9762\u5185\u5bb9\u8fdb\u884c\u62fc\u63a5\u548c\u5ef6\u5c55\uff0c\u5176\u672c\u8d28\u662f\u6c42\u89e3\u56fe\u50cf\u4e4b\u95f4\u7684\u53d8\u6362\u5173\u7cfb\uff0c\u4e5f\u5c31\u662f\u4e00\u4e2a\u6a21\u5f0f\u62df\u5408\u7684\u95ee\u9898\u3002\u5e94\u7528\u4e0a\u6bd4\u5982 \u5168\u666f\u56fe(panorama) \u6216 360\u00b0VR\u7b49\u3002</p> <p>\u6295\u5f71\u5e73\u9762/\u66f2\u9762</p> <p>\u5e38\u89c1\u7684\u56fe\u50cf\u62fc\u63a5\u6709\u6bd4\u5982\u5c06\u5e73\u884c\u7684\u666f\u8c61\u5728\u5e73\u9762\u4e0a\u6295\u5f71\u548c\u62fc\u63a5\uff0c\u4e5f\u6709\u5c06\u6c34\u5e73\u73af\u7ed5\u7684\u7684\u666f\u8c61\u5728\u67f1\u9762\u4e0a\u6295\u5f71\u548c\u62fc\u63a5\u7b49\u3002\u533a\u522b\u5728\u4e8e\u9700\u8981\u5bf9\u56fe\u50cf\u5185\u5bb9\u7684\u8868\u8fbe\u8fdb\u884c\u4e00\u4e2a\u201c\u53d8\u6362\u201d\uff0c\u4f46\u5b9e\u9645\u53d8\u5316\u65b9\u6cd5\u4e0d\u4f1a\u6709\u5927\u533a\u522b\uff0c\u4ecd\u7136\u662f\u5148\u68c0\u6d4b\u76f8\u540c\u90e8\u5206\u518d\u6c42\u89e3\u53d8\u6362\u5173\u7cfb\u3002</p> <p>\u5728\u8fd9\u91cc\u9700\u8981\u505a\u7684\u4e00\u4e2a\u7279\u522b\u8bf4\u660e\u662f\uff0c\u5728\u4e4b\u540e\u8be6\u7ec6\u4ecb\u7ecd\u201c\u53d8\u6362\u201d\u7684\u8fc7\u7a0b\u4e2d\uff0c\u6211\u4eec\u4f1a\u89e3\u91ca\u4e3a\u4ec0\u4e48\u624b\u673a\u62cd\u6444\u5e7f\u89d2\u7167\u7247\u65f6\uff0c\u4f1a\u8981\u6c42\u62cd\u6444\u8005\u53ea\u505a\u89c6\u89d2\u53d8\u5316\u800c\u4e0d\u505a\u4f4d\u79fb\u3002</p> <p>\u8fc7\u7a0b\u6982\u8ff0</p> <p>\u6211\u4eec\u8fd9\u91cc\u8003\u8651\u7684\u56fe\u50cf\u62fc\u63a5\u95ee\u9898\uff0c\u66f4\u591a\u6307\u7684\u662f\u4e24\u5f20\u56fe\u7247\u62e5\u6709\u5171\u540c\u523b\u753b\u76ee\u6807\u7684\u60c5\u51b5\u4e0b\u8fdb\u884c\u62fc\u63a5\uff0c\u5373\u4e24\u5f20\u7167\u7247\u5b58\u5728\u4ea4\u96c6\u3002</p> <p>\u9996\u5148\uff0c\u6211\u4eec\u901a\u8fc7\u56fe\u50cf\u7279\u5f81\u5339\u914d\u76f8\u5173\u6280\u672f\uff0c\u627e\u5230\u8fd9\u4e24\u5f20\u56fe\u7247\u7684\u5171\u540c\u90e8\u5206\uff0c\u63a5\u4e0b\u6765\u901a\u8fc7\u8f6c\u5316\u4e3a\u4f18\u5316\u95ee\u9898\uff0c\u6c42\u89e3\u8fd9\u4e9b\u5171\u540c\u90e8\u5206\u5982\u4f55\u5b9e\u73b0\u8f6c\u5316\uff08\u76f8\u5f53\u4e8e\u5728\u505a\u201c\u5bf9\u9f50\u201d\uff09\u3002</p> <ul> <li>\u56fe\u50cf\u62fc\u63a5\u7684\u4e24\u4e2a\u65b9\u9762\uff1a<ul> <li>\u5c06\u4e24\u5f20\u56fe\u7247\u5bf9\u9f50\uff0c\u627e\u5230\u91cd\u5408\u7684\u90e8\u5206 image warping (change shape of image)<ul> <li>\u4e00\u822c\u6765\u8bf4\u662f \u53c2\u6570\u5316parametric \u6216\u8005\u8bf4 \u5168\u5c40global \u7684 warping\uff0c\u7531\u4e00\u4e2a\u542b\u6709\u53c2\u6570\u7684\u65b9\u7a0b\u51b3\u5b9a\uff1a\\(p' = T(p)\\)\uff1b<ul> <li></li> <li>translation / affine / projective</li> <li> </li> <li>\u9664\u4e86\u80fd\u591f\u7528\u4eff\u5c04\u53d8\u6362\u63cf\u8ff0\u7684\u53d8\u6362\uff0c\u8fd8\u6709\u6295\u5f71\u53d8\u6362(Projective Transformation)\uff0c\u6216\u8005\u8bf4\u5355\u5e94\u53d8\u6362(Homography)\uff0c\u5b83\u65e0\u6cd5\u7528\u4eff\u5c04\u53d8\u6362\u63cf\u8ff0\u3002<ul> <li>\u5355\u5e94\u77e9\u9635\u5728\u5e73\u9762\u56fe\u5f62\u4e2d\u4e5f\u662f\u4e00\u4e2a 3*3 \u7684\u77e9\u9635\uff0c\u4f46\u662f\u6ca1\u6709\u5fc5\u987b\u4e3a 0 \u7684\u5143\u7d20\u7ea6\u675f\uff08\u533a\u522b\u4e8e\u9f50\u6b21\u5750\u6807\uff09\uff1a</li> <li>\\(\\begin{bmatrix}x'_i \\\\ y'_i \\\\ 1 \\end{bmatrix} \\cong \\begin{bmatrix} h_{00} &amp; h_{01} &amp; h_{02} \\\\ h_{10} &amp; h_{11} &amp; h_{12} \\\\ h_{20} &amp; h_{21} &amp; h_{22} \\end{bmatrix}\\begin{bmatrix}x_i \\\\ y_i \\\\ 1\\end{bmatrix}\\)\uff0c\u7531\u4e8e \\(h_{22}\\) \u5b9e\u9645\u4e0a\u53ef\u4ee5\u662f\u4efb\u610f\u5b9e\u6570\uff0c\u6240\u4ee5\u5b9e\u9645\u4e0a\u7684\u81ea\u7531\u5ea6\u4e3a 8\uff0c\u6240\u4ee5\u4e3a\u4e86\u8ba9\u89e3\u5177\u6709\u552f\u4e00\u6027\uff0c\u6211\u4eec\u7ea6\u675f \\(||\\begin{bmatrix}h_{00} &amp; h_{01} &amp; ... &amp; h_{21} &amp; h_{22}\\end{bmatrix}||_2 = 1\\)\uff0c\u8fd9\u6837\u5c31\u80fd\u4fdd\u8bc1\u81ea\u7531\u5ea6\u4e3a 8 \u4e14\u5bf9\u5e94\u7684\u89e3\u552f\u4e00\uff1b</li> <li>\u5b9e\u9645\u4e0a\uff0c\u53ef\u4ee5\u7406\u89e3\u4e3a\u5b83\u662f\u5728\u4e09\u7ef4\u7a7a\u95f4\u4e0b\uff0c\u76f8\u673a\u4e0d\u5e73\u79fb\u53ea\u65cb\u8f6c\u7684\u4e00\u4e2a\u89c6\u89d2\u53d8\u5316\uff0c\u5373 change projection plane\uff1b<ul> <li>\u5982\u679c\u76f8\u673a\u5e73\u79fb\u4e14\u65cb\u8f6c\uff0c\u90a3\u60c5\u51b5\u975e\u5e38\u590d\u6742\uff0c\u751a\u81f3\u4e0d\u4e00\u5b9a\u5177\u6709\u70b9\u70b9\u5bf9\u5e94\u5173\u7cfb\uff1b</li> <li>\u4f46\u662f\u6709\u4e00\u4e2a\u7279\u6b8a\u60c5\u51b5\uff0c\u5c31\u662f\u6211\u89c2\u6d4b\u5230\u573a\u666f\u672c\u8eab\u5c31\u662f\u5e73\u9762\uff08\u6216\u8005\u7279\u522b\u8fdc\u7684\u666f\u89c2\uff09\uff0c\u573a\u666f\u4e0d\u5b58\u5728\u906e\u6321\uff0c\u8fd9\u4e2a\u65f6\u5019\u4e5f\u53ef\u4ee5\u4f7f\u7528 homography\uff1b</li> <li>\u5982\u4e0a\u5c31\u662f\u4e3a\u4ec0\u4e48\u624b\u673a\u62cd\u6444\u5168\u666f\u7167\u7247\u65f6\u8981\u6c42\u4e0d\u8981\u79fb\u52a8\u53ea\u8f6c\u52a8\u76f8\u673a</li> </ul> </li> <li>\u5982\u4e0a\u53d8\u6362\u90fd\u6709\u9006\u53d8\u6362\uff1b</li> <li>\u5b9e\u9645\u64cd\u4f5c\u8fc7\u7a0b\u4e2d\uff0c\u6211\u4eec\u4f7f\u7528\u9006\u53d8\u6362\uff08\u6b63\u5411\u53d8\u6362\u7684\u8bdd\u50cf\u7d20\u4f4d\u7f6e\u53ef\u80fd\u4e0d\u5bf9\uff09\uff0c\u5373\u5bf9\u4e8e\u6bcf\u4e00\u4e2a\u9700\u8981\u627e\u7684\u50cf\u7d20\u70b9\uff0c\u6211\u4eec\u53bb\u627e\u53d8\u6362\u524d\u7684\u5750\u6807\uff0c\u5e76\u6839\u636e\u8fd9\u4e2a\u5750\u6807\u6765\u8fdb\u884c\u63d2\u503c\uff0c\u4e00\u822c\u4f7f\u7528\u53cc\u7ebf\u6027\u63d2\u503c\uff1b</li> </ul> </li> </ul> </li> </ul> </li> <li>\u8ba1\u7b97\u5982\u4f55\u5bf9\u9f50\u5408\u5e76\u8fd9\u4e24\u4e2a\u56fe\u7247 image stitching<ul> <li>\u5373\u7ed9\u5b9a\u4e24\u5f20\u56fe\u50cf\uff0c\u5982\u4f55\u8ba1\u7b97\u4e0a\u4e00\u6b65\u63d0\u5230\u7684 T\uff1b</li> <li>\u6b65\u9aa4\uff1a<ol> <li>image matching(each match gives an equation);</li> <li>solve T from the obtained matches;</li> </ol> </li> <li>\u4f8b\u5982\uff0c\u5bf9\u4e8e afine transformations\uff0c\u6709\u516d\u4e2a\u81ea\u7531\u5ea6\uff0c\u9700\u8981\u516d\u4e2a\u65b9\u7a0b\u4e09\u5bf9\u5339\u914d\u5173\u7cfb\uff08\u6bcf\u4e00\u5bf9\u5339\u914d\u5173\u7cfb\u63d0\u4f9b\u4e24\u4e2a\u65b9\u7a0b\uff0c\u5206\u522b\u662f\u5173\u4e8e x \u548c\u5173\u4e8e y \u7684\uff09\uff1b<ul> <li>\u5b83\u4eec\u5177\u6709\u77e9\u9635\u5f62\u5f0f\uff1a \uff08\u6284\u9ea6\u54e5\u7b14\u8bb0\uff09</li> <li>\u5b9e\u9645\u8fc7\u7a0b\u4e2d\u6211\u4eec\u5e76\u4e0d\u4f1a\u76f4\u63a5\u53bb\u201c\u89e3\u65b9\u7a0b\u201d\uff0c\u800c\u662f\u53bb\u505a\u4e00\u4e2a\u201c\u5c3d\u91cf\u76f8\u7b49\u201d\u7684\u4e00\u4e2a\u6700\u5c0f\u4e8c\u4e58\u95ee\u9898\uff0c\u8fd9\u4e2a\u95ee\u9898\u7684\u89e3\u6709\u4e00\u4e2a\u89e3\u6790\u89e3\uff1a\\(t = (A^TA)^{-1}A^Tb\\)\uff1b</li> </ul> </li> <li>\u518d\u4f8b\u5982\u5bf9\u4e8e homography\uff0c\u6709\u516b\u4e2a\u81ea\u7531\u5ea6\u5c31\u9700\u8981\u516b\u4e2a\u65b9\u7a0b\u56db\u5bf9\u5339\u914d\u5173\u7cfb\uff1b</li> <li>\u5bf9\u4e8e\u4f18\u5316\u95ee\u9898\uff1a\\(\\mathop{min}_h ||Ah||^2 \\;\\;\\; s.t. ||h|| = 1\\)\uff0c\u5176\u89e3 \\(\\hat{h}\\) \u4e3a \\(A_TA\\) \u7279\u5f81\u503c\u6700\u5c0f\u7684\u7279\u5f81\u5411\u91cf\uff1b</li> <li>\u6b64\u5916\uff0c\u8fd8\u8981\u5173\u6ce8\u5982\u4f55\u5904\u7406 outliers\uff1a\u4f7f\u7528 RANSAC\uff1b <ul> <li>\u5373\uff0c\u5229\u7528\u5c0f\u90e8\u5206\u5339\u914d\u5173\u7cfb\u8ba1\u7b97\u51fa T\uff0c\u7136\u540e\u62ff\u53bb\u68c0\u9a8c\u5176\u4ed6\u7684\u5339\u914d\u5173\u7cfb\uff1b </li> </ul> </li> </ul> </li> <li>\u7136\u800c\u4e0a\u9762\u8fd9\u4e9b\u505a\u6cd5\u90fd\u662f\u5c06\u56fe\u7247\u6295\u5f71\u5230\u4e00\u4e2a\u5e73\u9762\u4e0a\uff0c\u4e5f\u5c31\u662f\u8bf4\u5c06\u56fe\u50cf\u62fc\u63a5\u4e3a\u4e00\u4e2a\u66f4\u5927\u90fd\u5e73\u9762\u56fe\u50cf\uff1b\u4f46\u662f\u5728\u5168\u666f\u8fd9\u79cd\u6848\u4f8b\u4e2d\uff0c\u8fd9\u4e48\u505a\u4f1a\u8ba9\u8fb9\u7f18\u62c9\u4f38\u8d8a\u6765\u6108\u660e\u663e\uff08\u8fd1\u5927\u8fdc\u5c0f\uff09\uff0c\u6240\u4ee5\u5bf9\u4e8e\u8fd9\u79cd\u6848\u4f8b\uff0c\u6211\u4eec\u8981\u5148\u5c06\u5b83\u6295\u5c04\u5230\u67f1\u9762\u4e0a\uff0c\u7136\u540e\u5728\u67f1\u9762\u4e0a\u8fdb\u884c\u62fc\u63a5\uff0cTODO:\u516c\u5f0f\u8bb0\u5f97\u6284\u4e0a\u6765\uff1b</li> <li>\u8fd8\u6709\u4e00\u4e2a\u95ee\u9898\u662f\u8bef\u5dee\u7d2f\u79ef\uff0c\u5bfc\u81f4\u6f02\u79fb(drift)\uff0c\u89e3\u51b3\u529e\u6cd5\u5c31\u662f\u6700\u540e\u4e00\u5f20\u548c\u7b2c\u4e00\u5f20\u4e4b\u95f4\u4e5f\u8ba1\u7b97\u4e00\u6b21 T \u6765\u8fdb\u884c\u7ea6\u675f\uff0c\u8fd9\u79cd\u60f3\u6cd5\u53eb\u56de\u8def\u95ed\u5408\uff1b </li> </ul> </li> </ul> <p>\u62fc\u63a5\u8fc7\u7a0b\u4e2d\u4f1a\u51fa\u73b0\u8fb9\u754c\uff0c\u800c\u8fd9\u4e2a\u8fb9\u754c\u6211\u4eec\u662f\u53ef\u4ee5\u4eba\u4e3a\u9009\u62e9\u7684\uff0c\u6bd4\u5982\u6211\u4eec\u53ef\u4ee5\u9009\u62e9\u8ba9\u5b83\u5dee\u8ddd\u6700\u5c0f\u7684\u5730\u65b9\u6210\u4e3a\u8fb9\u754c\uff0c\u53c8\u6216\u8005\u662f\u4e00\u4e2a\u56fe\u5272\u95ee\u9898\uff1b</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec07/","title":"Lecture 7 | Structure From Motion","text":"<p> \u7ea6 8658 \u4e2a\u5b57  14 \u884c\u4ee3\u7801  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 29 \u5206\u949f</p> <p>\u524d\u8a00</p> <p>\u4e2a\u4eba\u611f\u89c9\u8fd9\u4e00\u7ae0\u7684\u5185\u5bb9\u867d\u7136\u8109\u7edc\u6e05\u6670\uff0c\u4f46\u662f\u9700\u8981\u4e0d\u65ad\u5f15\u5165\u65b0\u7684\u5185\u5bb9\uff0c\u5982\u679c\u76f4\u63a5\u91c7\u7528\u201c\u7528\u5230\u4ec0\u4e48\u8bb2\u4ec0\u4e48\u201d\u7684\u987a\u5e8f\u9610\u8ff0\uff0c\u53ef\u80fd\u4f1a\u6709\u4e9b\u6742\u4e71\uff0c\u4e0d\u65b9\u4fbf\u77e5\u8bc6\u7d22\u5f15\u548c\u590d\u4e60\uff0c\u6240\u4ee5\u6211\u5927\u81f4\u6309\u7167\u62d3\u6251\u6392\u5e8f\u7684\u987a\u5e8f\u6392\u5217\u5185\u5bb9\uff0c\u503e\u5411\u4e8e\u5b8c\u6574\u5730\u4ecb\u7ecd\u4e00\u4e0b\u524d\u7f6e\uff0c\u518d\u5f15\u5165\u4e4b\u540e\u7684\u5185\u5bb9\u5e76\u9636\u6bb5\u6027\u5c0f\u7ed3\uff0c\u53ef\u80fd\u770b\u8d77\u6765\u6bd4\u8f83\u5510\u7a81\uff0c\u4f46\u662f\u5927\u6982\u5bf9\u56de\u5934\u67e5\u77e5\u8bc6\u70b9\u6bd4\u8f83\u65b9\u4fbf\u3002</p> <p>\u8bf4\u660e</p> <p>\u672c\u6587\u4e2d\u63d0\u5230\u7684\u6240\u6709\u7684\u300c\u6210\u50cf\u5e73\u9762\u300d\u6307\u7684\u90fd\u662f\u6211\u4eec\u7684\u7b80\u5316\u51e0\u4f55\u6a21\u578b\u4e2d\u7684\u865a\u62df\u6210\u50cf\u5e73\u9762\uff0c\u5e76\u4e0d\u662f\u7269\u7406\u610f\u4e49\u4e0a\u5c0f\u5b54\u6210\u50cf\u6240\u5728\u7684\u90a3\u4e2a\u6210\u53cd\u5411\u5012\u7acb\u50cf\u7684\u5e73\u9762\uff01</p> <p>\u8fd0\u52a8\u63a8\u65ad\u7ed3\u6784(Structure from Motion, SfM)\u7528\u4e8e\u4f30\u8ba1\u4e8c\u7ef4\u56fe\u50cf\u4e2d\u7684\u4e09\u7ef4\u7ed3\u6784\uff0c\u901a\u8fc7\u76f8\u673a\u8fd0\u52a8\uff08\u5e73\u79fb\u3001\u65cb\u8f6c\uff09\u5f15\u8d77\u7684\u753b\u9762\u53d8\u5316\u6765\u8ba1\u7b97\u5176\u53cd\u5e94\u7684 3D \u7ed3\u6784\u3002</p> <p>\u5728\u673a\u5668\u4eba\u9886\u57df\uff0c\u4e00\u4e2a\u76f8\u5173\u7684\u9886\u57df\u662f \u540c\u65f6\u5b9a\u4f4d\u4e0e\u5730\u56fe\u6784\u5efa(Simultaneous Localization and Mapping, SLAM)\u3002</p> <p>\u4e09\u4e2a\u5173\u952e\u95ee\u9898</p> <ol> <li>\u5982\u4f55\u63cf\u8ff0\u76f8\u673a\u7684\u6295\u5f71\u884c\u4e3a\uff0c\u4e5f\u5c31\u662f\u76f8\u673a\u6a21\u578b\u7684\u76f8\u5173\u5185\u5bb9\uff0c\u672c\u5c0f\u7ed3\u6307\u900f\u89c6\u6a21\u578b\uff1b</li> <li>\u5982\u4f55\u901a\u8fc7\u56fe\u50cf\u6c42\u89e3\u76f8\u673a\u53c2\u6570\uff0c\u8fd9\u4e2a\u8fc7\u7a0b\u88ab\u79f0\u4e3a\u76f8\u673a\u6807\u5b9a(Camera Calibration)\uff0c\u4ee5\u53ca\u5982\u4f55\u6c42\u89e3\u76f8\u673a\u7684\u7a7a\u95f4\u4f4d\u7f6e\u4e0e\u671d\u5411\uff0c\u8fd9\u4e2a\u8fc7\u7a0b\u88ab\u79f0\u4e3a\u4f4d\u7f6e\u4f30\u8ba1(Pose Estimation)\uff1b</li> <li>\u5982\u4f55\u5229\u7528\u82e5\u5e72\u89c6\u89d2\u8fdb\u884c\u91cd\u5efa\uff1b</li> </ol> <p>\u5176\u4e2d\uff0c\u7b2c\u4e00\u4e2a\u547d\u9898\u7684\u5185\u5bb9\u5df2\u7ecf\u5728\u7b2c\u4e8c\u8bb2\u4e2d\u6d89\u53ca\uff0c\u6240\u4ee5\u4e0d\u518d\u5c55\u5f00\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec07/#\u76f8\u673a\u6807\u5b9a\u4e0e\u4f4d\u7f6e\u4f30\u8ba1","title":"\u76f8\u673a\u6807\u5b9a\u4e0e\u4f4d\u7f6e\u4f30\u8ba1","text":"<p>\u76f8\u673a\u6807\u5b9a(Camera Calibration)\u5373\u6c42\u89e3\u76f8\u673a\u7528\u6765\u63cf\u8ff0\u76f8\u673a\u6a21\u578b\u7684\u81ea\u8eab\u53c2\u6570\uff0c\u6362\u53e5\u8bdd\u6765\u8bf4\u5c31\u662f\u6c42\u89e3\u76f8\u673a\u7684\u5185\u53c2(Intrinsic Parameters)\uff1b\u800c\u4f4d\u7f6e\u4f30\u8ba1(Pose Estimation)\u6c42\u89e3\u76f8\u673a\u7684\u7a7a\u95f4\u4f4d\u7f6e\u4ee5\u53ca\u671d\u5411\uff0c\u4e0e\u5185\u53c2\u76f8\u5bf9\u5e94\u7684\uff0c\u5c31\u662f\u6c42\u89e3\u76f8\u673a\u7684\u5916\u53c2(Extrinsic Parameters)\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec07/#\u6210\u50cf\u8fc7\u7a0b\u7684\u5efa\u6a21","title":"\u6210\u50cf\u8fc7\u7a0b\u7684\u5efa\u6a21","text":"<p>\u89c6\u89c9\u5b9a\u4f4d\u95ee\u9898</p> <p>\u9996\u5148\uff0c\u4e3a\u4e86\u5c55\u5f00\u4e4b\u540e\u7684\u5185\u5bb9\uff0c\u6211\u4eec\u9700\u8981\u5b9a\u4e49\u89c6\u89c9\u5b9a\u4f4d\u95ee\u9898(Visual Localization Problem)\uff1a\u7ed9\u5b9a\u4e00\u4e2a\u5df2\u77e5\u7684\u4e09\u7ef4\u6a21\u578b\uff0c\u4ece\u67d0\u4e2a\u4f4d\u7f6e\u5bf9\u5176\u8fdb\u884c\u62cd\u6444\uff0c\u6c42\u89e3\u62cd\u6444\u4f4d\u7f6e\u548c\u89c6\u89d2\u3002</p> <p>\u800c\u4e3a\u4e86\u5c55\u5f00\u89c6\u89c9\u5b9a\u4f4d\u95ee\u9898\uff0c\u6211\u4eec\u9996\u5148\u9700\u8981\u5bf9\u76f8\u673a\u6210\u50cf\u8fd9\u4e2a\u8fc7\u7a0b\u8fdb\u884c\u4e00\u4e2a\u6570\u5b66\u5efa\u6a21\u2014\u2014\u66f4\u8be6\u7ec6\u7684\u6765\u8bf4\uff0c\u662f\u5efa\u6a21\u4e00\u4e2a\u7a7a\u95f4 3D \u70b9\u4e0e\u76f8\u673a\u4e0a\u7279\u5b9a\u50cf\u7d20\u533a\u57df\u7684\u8f6c\u5316\u5173\u7cfb\u3002</p> <p>\u9996\u5148\u8ba9\u6211\u4eec\u56de\u987e\u4e00\u4e0b\u6295\u5f71\u6a21\u578b\u7684\u53ef\u89c6\u5316\u8868\u793a\u4e2d\u7684\u76f8\u5173\u5185\u5bb9\uff1a</p> <p>\u56de\u987e</p> <p></p> <p>\u6211\u4eec\u53ef\u4ee5\u53d1\u73b0\uff0c\u5c0f\u5b54\u6210\u50cf\u7684\u6a21\u578b\u89c6\u56fe\u5176\u5b9e\u8fd8\u662f\u6bd4\u8f83\u9ebb\u70e6\u7684\u3002\u73b0\u5728\u6211\u4eec\u628a\u8fd9\u4e2a\u5b9a\u89d2\u76f8\u4f3c\u5bf9\u6298\uff0c\u53d8\u6210 A \u5b57\u578b\u76f8\u4f3c\u6765\u8868\u793a\u8fd9\u4e2a\u6a21\u578b\uff0c\u4ee5\u7b80\u5316\u4e0d\u5fc5\u8981\u7684\u4fe1\u606f\uff0c\u540c\u65f6\u4e5f\u80fd\u66f4\u6e05\u6670\u5730\u8868\u793a\u900f\u89c6\u5173\u7cfb\u3002</p> <p>\u89c4\u5b9a\u6211\u4eec\u8ba8\u8bba\u7684\u95ee\u9898\u4e2d\u7269\u8ddd\u603b\u662f\u5927\u4e8e\u50cf\u8ddd\uff0c\u5219\u53ef\u4ee5\u5c06\u50cf\u8868\u793a\u4e3a\u76f8\u673a\u4e2d\u5fc3\u5230\u7269\u4f53\u7684\u653e\u5c04\u8fde\u7ebf\u4e2d\u7684\u622a\u9762\u3002</p> <p>\u5b83\u6bd4\u8f83\u597d\u5730\u8868\u8fbe\u4e86\u900f\u89c6\u5173\u7cfb\uff0c\u5373 \u76f8\u673a\u4e2d\u5fc3 \u7269\u70b9B \u50cf\u70b9B' \u59cb\u7ec8\u5171\u7ebf\u3002\u8fd9\u4e5f\u662f\u5728\u4e4b\u540e\u7684\u5185\u5bb9\u4e2d\u66f4\u52a0\u5e38\u89c1\u7684\u53ef\u89c6\u5316\u8868\u73b0\u65b9\u6cd5\u3002</p> <p>\u5b83\u63d0\u4f9b\u4e86\u4e00\u79cd\u5c06\u76f8\u673a\u6a21\u578b\u6210\u50cf\u539f\u7406\u53ef\u89c6\u5316\u7684\u65b9\u6cd5\uff0c\u63a5\u4e0b\u6765\u6211\u4eec\u5c06\u5b83\u653e\u5230 3D \u7a7a\u95f4\u4e2d\uff1a</p> <p></p> <p>\u8fd9\u5f20\u56fe\u5927\u81f4\u63cf\u8ff0\u4e86\uff1a\u5728\u7279\u5b9a\u4f4d\u7f6e\u6709\u7740\u7279\u5b9a\u671d\u5411\u7684\u76f8\u673a\u6a21\u578b\u5982\u4f55\u62cd\u5230\u5df2\u77e5 3D \u666f\u8c61\u7684\u7279\u5b9a\u753b\u9762\uff0c\u4f46\u9700\u8981\u6ce8\u610f\u7684\u662f\uff0c\u8fd9\u91cc\u7684\u300cPicture\u300d\u4ee3\u8868\u7684\u662f Image Plane\uff0c\u4e5f\u5c31\u662f\u6210\u50cf\u5e73\u9762\uff0c\u6b64\u65f6\u300c\u5750\u6807\u300d\u7684\u5355\u4f4d\u662f\u957f\u5ea6\uff0c\u5982\u6beb\u7c73\u2014\u2014\u4e0e\u4ee5\u300c\u50cf\u7d20\u300d\u4e3a\u57fa\u672c\u5355\u5143\u7684\u201c\u56fe\u7247\u201d\u6709\u4e00\u5b9a\u533a\u522b\u3002</p> <p>\u4e5f\u5c31\u662f\u8bf4\uff0c\u4ece 3D \u4e2d\u7684\u67d0\u4e00\u4e2a\u70b9\uff0c\u5230\u56fe\u7247\u4e0a\u7684\u67d0\u5757\u50cf\u7d20\u533a\u57df\uff0c\u6709\u5927\u81f4\u5982\u4e0b\u51e0\u4e2a\u9636\u6bb5\uff1a</p> <pre><code>graph LR\n    A[3D \u666f\u8c61] --&gt; B[2D \u6210\u50cf\u5e73\u9762] --&gt; C[\u50cf\u7d20\u56fe\u50cf];</code></pre> <p>\u4e0d\u8fc7\u9700\u8981\u6ce8\u610f\u7684\u4e00\u70b9\u662f\uff0c\u6211\u4eec\u5728\u76f8\u673a\u6a21\u578b\u4e2d\u4ecb\u7ecd\u7684\u4e00\u7cfb\u5217\u5efa\u6a21\uff0c\u662f\u5efa\u7acb\u5728\u4ee5\u76f8\u673a\u4e3a\u53c2\u8003\u7cfb\u7684\u60c5\u51b5\u4e0b\u7684\uff0c\u800c\u5728\u89c6\u89c9\u5b9a\u4f4d\u95ee\u9898\u4e2d\uff0c\u6211\u4eec\u62e5\u6709\u7684 3D \u666f\u8c61\u4fe1\u606f\u80af\u5b9a\u4e0d\u662f\u901a\u8fc7\u76f8\u673a\u5750\u6807(Camera Coordinates)\u6765\u8868\u793a\u7684\uff0c\u800c\u662f\u7528\u4e16\u754c\u5750\u6807(World Coordinates)\uff0c\u663e\u7136\uff0c\u8fd9\u91cc\u53ea\u5305\u62ec\u5e73\u79fb\u548c\u65cb\u8f6c\uff0c\u4e5f\u5c31\u662f\u7ecf\u8fc7\u4e00\u6b21\u4eff\u5c04\u53d8\u6362\u3002</p> <p>\u6211\u4eec\u5bf9\u4e0a\u9762\u90a3\u4e2a\u6d41\u7a0b\u56fe\u7684\u7ed3\u679c\u8fdb\u884c\u4e00\u4e2a\u6539\u8fdb\uff1a</p> <pre><code>graph LR\n    A[\"(\u4e16\u754c\u5750\u6807) 3D \u666f\u8c61\"] --&gt; B[\"(\u76f8\u673a\u5750\u6807) 3D \u666f\u8c61\"] --&gt; C[\"(\u6210\u50cf\u5e73\u9762) 2D \u6620\u5c04\"] --&gt; D[\"(\u4f20\u611f\u5668\u5e73\u9762) \u50cf\u7d20\u56fe\u50cf\"];</code></pre>"},{"location":"cour_note/D2QD_Intro2CV/Lec07/#\u4e16\u754c\u5750\u6807-to-\u76f8\u673a\u5750\u6807","title":"\u4e16\u754c\u5750\u6807 to \u76f8\u673a\u5750\u6807","text":"<p>\u4e3a\u4e86\u5b9e\u73b0\u4e16\u754c\u5750\u6807\u5411\u76f8\u673a\u5750\u6807\u7684\u8f6c\u6362\uff0c\u6211\u4eec\u9700\u8981\u77e5\u9053\u76f8\u673a\u5750\u6807\u5728\u4e16\u754c\u5750\u6807\u4e2d\u7684\u65b9\u5411\u4e0e\u4f4d\u7f6e\uff0c\u4e0d\u96be\u53d1\u73b0\uff0c\u5b9e\u9645\u4e0a\u8fd9\u5c31\u8981\u6c42\u6211\u4eec\u77e5\u9053\u76f8\u673a\u7684\u5916\u53c2\u3002</p> <p></p> <p>\u66f4\u8fdb\u4e00\u6b65\u7684\uff0c\u5b9e\u9645\u4e0a\u6211\u4eec\u5c31\u662f\u5bfb\u627e\u4e00\u79cd\u53d8\u6362\uff0c\u80fd\u591f\u5b9e\u73b0\u4e16\u754c\u5750\u6807\u7cfb\u4e0b\u7684\u5750\u6807\u5411\u76f8\u673a\u5750\u6807\u7cfb\u4e0b\u5750\u6807\u7684\u8f6c\u6362\uff1a</p> \\[ \\underbrace{\\;\\mathbf{x}_w = \\begin{bmatrix}     x_w \\\\     y_w \\\\     z_w \\end{bmatrix}\\;}_{\\text{World Coordinates}} \\xrightarrow{\\text{Rotation \\&amp; Movement}} \\underbrace{\\;\\mathbf{x}_c = \\begin{bmatrix}     x_c \\\\     y_c \\\\     z_c \\end{bmatrix}\\;}_{\\text{Camera Coordinates}} \\] <p>\u6211\u4eec\u5b9a\u4e49\u5916\u53c2 \\((R,\\mathbf{c}_w)\\)\uff0c\u5206\u522b\u4ee3\u8868\u300c\u4ece\u4e16\u754c\u5750\u6807\u5411\u76f8\u673a\u5750\u6807\u7684\u65cb\u8f6c\u77e9\u9635\u300d\u548c\u300c\u5728\u4e16\u754c\u5750\u6807\u7cfb\u4e0b\u7684\u76f8\u673a\u7684\u4e2d\u5fc3\u5750\u6807\u300d\uff0c\u5219\u53d8\u6362\u540e\u7684\u5750\u6807\u5373\u4e3a\uff1a</p> \\[ \\mathbf{x}_c = R(\\mathbf{x}_w - \\mathbf{c}_w) = R \\mathbf{x}_w - R \\mathbf{c}_w = R \\mathbf{x}_w + \\mathbf{t},\\ \\ \\text{ where } \\mathbf{t} = -R \\mathbf{c}_w \\\\ \\text{i.e.} \\;\\; \\mathbf{x}_c = \\begin{bmatrix} x_c \\\\ y_c \\\\ z_c \\end{bmatrix} = \\begin{bmatrix}     r_{11} &amp; r_{12} &amp; r_{13} \\\\     r_{21} &amp; r_{22} &amp; r_{23} \\\\     r_{31} &amp; r_{32} &amp; r_{33} \\\\ \\end{bmatrix} \\begin{bmatrix}     x_w \\\\ y_w \\\\ z_w \\end{bmatrix} + \\begin{bmatrix}     t_x \\\\ t_y \\\\ t_z \\end{bmatrix} \\] <ul> <li>\u8bf4\u660e\uff1a<ol> <li>\\((\\mathbf{x}_w - \\mathbf{c}_w)\\) \u53ef\u4ee5\u7406\u89e3\u4e3a\u4ece\u76f8\u673a\u4e2d\u5fc3\u6307\u5411\u76ee\u6807\u70b9\u7684\u4e00\u4e2a\u5411\u91cf\uff1b</li> <li>\u65cb\u8f6c\u77e9\u9635 \\(R\\) \u5355\u4f4d\u6b63\u4ea4\uff1b </li> </ol> </li> </ul> <p>\u5f53\u7136\uff0c\u6211\u4eec\u53ef\u4ee5\u5c06\u5b83\u4f7f\u7528\u9f50\u6b21\u5750\u6807\u7edf\u4e00\uff1a</p> \\[ \\mathbf{\\tilde x}_c = \\begin{bmatrix} x_c \\\\ y_c \\\\ z_c \\\\ 1\\end{bmatrix} = \\underbrace{\\begin{bmatrix}     r_{11} &amp; r_{12} &amp; r_{13} &amp; t_x \\\\     r_{21} &amp; r_{22} &amp; r_{23} &amp; t_y\\\\     r_{31} &amp; r_{32} &amp; r_{33} &amp; t_z\\\\     0 &amp; 0 &amp; 0 &amp; 1 \\end{bmatrix}}_{\\text{Extrinsic Matrix}} \\begin{bmatrix}     x_w \\\\ y_w \\\\ z_w \\\\ 1 \\end{bmatrix} \\] <p>\u5916\u53c2\u77e9\u9635</p> <p>\u5176\u4e2d\uff0c\u65b0\u5f97\u5230\u7684\u8fd9\u4e2a 44 \u7684\u77e9\u9635\u5c31\u88ab\u79f0\u4e3a\u5916\u53c2\u77e9\u9635(Extrinsic Matrix)*\uff0c\u4e5f\u88ab\u5199\u4f5c\uff1a</p> \\[ M_{ext} = \\begin{bmatrix}     R_{3\\times 3} &amp; \\mathbf{t} \\\\     \\mathbf{0}_{1\\times 3} &amp; 1 \\end{bmatrix} = \\begin{bmatrix}     r_{11} &amp; r_{12} &amp; r_{13} &amp; t_x \\\\     r_{21} &amp; r_{22} &amp; r_{23} &amp; t_y\\\\     r_{31} &amp; r_{32} &amp; r_{33} &amp; t_z\\\\     0 &amp; 0 &amp; 0 &amp; 1 \\end{bmatrix} \\\\ or \\\\ M_{ext} = \\begin{bmatrix}     R_{3\\times 3} &amp; \\mathbf{t} \\\\ \\end{bmatrix} = \\begin{bmatrix}     r_{11} &amp; r_{12} &amp; r_{13} &amp; t_x \\\\     r_{21} &amp; r_{22} &amp; r_{23} &amp; t_y\\\\     r_{31} &amp; r_{32} &amp; r_{33} &amp; t_z\\\\ \\end{bmatrix} \\]"},{"location":"cour_note/D2QD_Intro2CV/Lec07/#\u76f8\u673a\u5750\u6807-to-\u6210\u50cf\u5e73\u9762","title":"\u76f8\u673a\u5750\u6807 to \u6210\u50cf\u5e73\u9762","text":"<p>\u5b9e\u9645\u4e0a\u8fd9\u4e00\u6b65\u5c31\u662f\u6211\u4eec\u5728\u76f8\u673a\u6a21\u578b\u4ecb\u7ecd\u8fc7\u7684\u5185\u5bb9\uff0c\u6211\u4eec\u5728\u4e0a\u4e00\u6b65\u5df2\u7ecf\u505a\u597d\u4e86\u9f50\u6b21\u5750\u6807\u7684\u94fa\u57ab\uff0c\u6240\u4ee5\u8fd9\u4e00\u6b65\u683c\u5916\u7b80\u5355\u3002</p> \\[ \\begin{bmatrix}     \\mathbf{x}_{i_{1 \\times 2}} \\\\ 1 \\end{bmatrix} \\cong \\begin{bmatrix}     f &amp; 0 &amp; 0 &amp; 0 \\\\     0 &amp; f &amp; 0 &amp; 0 \\\\     0 &amp; 0 &amp; 1 &amp; 0 \\end{bmatrix} \\begin{bmatrix}     x_c \\\\     y_c \\\\     z_c \\\\     1 \\end{bmatrix} \\] <p>\u6ce8\u610f</p> <p>\u8fd9\u91cc 3*4 \u7684\u77e9\u9635\u8fd8\u4e0d\u662f\u5185\u53c2\u77e9\u9635\uff01</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec07/#\u6210\u50cf\u5e73\u9762-to-\u4f20\u611f\u5668\u5e73\u9762","title":"\u6210\u50cf\u5e73\u9762 to \u4f20\u611f\u5668\u5e73\u9762","text":"<p>\u4e4b\u524d\u8bf4\u8fc7\uff0c\u6210\u50cf\u5e73\u9762\u4e0a\u7684\u5185\u5bb9\u548c\u4f20\u611f\u5668\u5e73\u9762\u4e0a\u7684\u5185\u5bb9\u6700\u5927\u7684\u4e0d\u540c\u5c31\u662f\u8ba1\u91cf\u5355\u4f4d\u4e0d\u540c\uff0c\u6240\u4ee5\u6211\u4eec\u9700\u8981\u5c06\u957f\u5ea6\u4fe1\u606f\u8f6c\u5316\u4e3a\u50cf\u7d20\u4fe1\u606f\uff1b\u6b64\u5916\uff0c\u4e2d\u5fc3\u5750\u6807\u4e5f\u9700\u8981\u53d8\u6362\u3002</p> <p>\u5047\u8bbe \\(m_x\\) \u548c \\(m_y\\) \u5206\u522b\u662f\u5355\u4f4d\u957f\u5ea6\u4e0a\u7684\u50cf\u7d20\u5bc6\u5ea6\uff08\u4ee5 px/mm \u4e3a\u4f8b\uff09\uff0c\\((c_x,c_y)\\) \u5206\u522b\u662f\u5728\u6210\u50cf\u5e73\u9762\u4e0b\u4f20\u611f\u5668\u5e73\u9762\u7684\u4e2d\u5fc3\u5750\u6807\uff0c\u5219\uff1a</p> \\[ \\left\\{     \\begin{aligned}         u &amp;= m_x \\cdot x_i + c_x\\\\         v &amp;= m_y \\cdot y_i + c_y     \\end{aligned} \\right. \\] <p>\u5e26\u5165\u4e0a\u4e00\u8282\u7684\u7ed3\u679c\uff0c\u5f97\u5230\uff08\u6ce8\u610f\uff0c\u8fd9\u91cc\u7684\u201c\u9f50\u6b21\u5750\u6807\u201d\u662f\u4e0a\u4e00\u8282\u5e26\u6765\u7684\uff0c\u8fd9\u4e00\u8282\u7684\u8ba1\u7b97\u5e76\u4e0d\u9700\u8981\u9f50\u6b21\u5750\u6807\uff09\uff1a</p> \\[ \\begin{bmatrix}     u \\\\     v \\\\     1 \\end{bmatrix} = ... \\cong \\begin{bmatrix}     u' \\\\     v' \\\\     z_c \\end{bmatrix} = \\underbrace{{\\begin{bmatrix}     m_x f &amp; 0 &amp; c_x &amp; 0 \\\\     0 &amp; m_y f &amp; c_y &amp; 0 \\\\     0 &amp; 0 &amp; 1 &amp; 0 \\end{bmatrix}}}_{\\text{Intrinsic Matrix}} \\begin{bmatrix}     x_c \\\\     y_c \\\\     z_c \\\\     1 \\end{bmatrix} \\] <p>\u5185\u53c2\u77e9\u9635</p> <p>\u8fd9\u91cc\u5f97\u5230\u7684\uff0c\u5305\u542b \\(f\\) \u548c \\(m\\) \u7684\u77e9\u9635\u624d\u662f\u5185\u53c2\u77e9\u9635(Intrinsic Matrix)\uff0c\u4e5f\u88ab\u5199\u4f5c\uff1a</p> \\[ M_{int} =  \\begin{bmatrix}     m_x f &amp; 0 &amp; c_x &amp; 0 \\\\     0 &amp; m_y f &amp; c_y &amp; 0 \\\\     0 &amp; 0 &amp; 1 &amp; 0 \\end{bmatrix} \\\\ or \\\\ K =  \\begin{bmatrix}     m_x f &amp; 0 &amp; c_x \\\\     0 &amp; m_y f &amp; c_y \\\\     0 &amp; 0 &amp; 1 \\end{bmatrix} \\]"},{"location":"cour_note/D2QD_Intro2CV/Lec07/#\u5185\u53c2\u77e9\u9635\u5916\u53c2\u77e9\u9635\u4e0e\u6295\u5f71\u77e9\u9635","title":"\u5185\u53c2\u77e9\u9635\u3001\u5916\u53c2\u77e9\u9635\u4e0e\u6295\u5f71\u77e9\u9635","text":"<p>\u7b80\u5355\u603b\u7ed3\u4e0a\u9762\u51e0\u4e2a\u6b65\u9aa4\u4e0e\u5185\u53c2\u5916\u53c2\u77e9\u9635\u7684\u5173\u7cfb\uff0c\u5c31\u662f\u4e0b\u9762\u8fd9\u5f20\u6d41\u7a0b\u56fe\uff1a</p> <pre><code>graph LR\n    subgraph EM[\"Using Extrinsic Matrix\"]\n        A[\"Coordinate Transformation\"]\n    end\n    subgraph IM[\"Using Intrinsic Matrix\"]\n        B[\"Perspective Projection\"]\n        C[\"Image Plane to Image Sensor Mapping\"]\n    end\n    A ---&gt; B\n    B ---&gt; C</code></pre>"},{"location":"cour_note/D2QD_Intro2CV/Lec07/#\u5185\u53c2\u77e9\u9635","title":"\u5185\u53c2\u77e9\u9635","text":"<p>\u6211\u4eec\u5728\u4e0a\u9762\u63d0\u5230\u7684\u5185\u53c2\u77e9\u9635\u957f\u8fd9\u6837\uff1a</p> \\[ M_{int} =  \\begin{bmatrix}     m_x f &amp; 0 &amp; c_x &amp; 0 \\\\     0 &amp; m_y f &amp; c_y &amp; 0 \\\\     0 &amp; 0 &amp; 1 &amp; 0 \\end{bmatrix} \\\\ or \\\\ K =  \\begin{bmatrix}     m_x f &amp; 0 &amp; c_x \\\\     0 &amp; m_y f &amp; c_y \\\\     0 &amp; 0 &amp; 1 \\end{bmatrix} \\] <p>\u5176\u4e2d\u4e3b\u8981\u6709 4 \u4e2a\u81ea\u7531\u5ea6\uff1a\\(m_x f\\)\u3001\\(m_y f\\)\u3001\\(c_x\\)\u3001\\(c_y\\)\u3002</p> <p>\u7136\u800c\u5b9e\u9645\u4e0a\u672a\u5fc5\u5982\u6b64\uff0c\u7531\u4e8e\u7578\u53d8\u7b49\u53ef\u80fd\u5b58\u5728\u7684\u539f\u56e0\uff0c\u5b9e\u9645\u7684\u5185\u53c2\u77e9\u9635\uff0c\u6216\u8005\u662f\u6c42\u89e3\u51fa\u6765\u7684\u5185\u53c2\u77e9\u9635\u5e76\u4e0d\u4e00\u5b9a\u5f62\u5982\u6b64\uff0c\u6211\u4eec\u5728\u540e\u9762\u4f1a\u63d0\u5230\uff0c\u7531\u4e8e\u67d0\u4e9b\u6027\u8d28\u5206\u89e3\u51fa\u6765\u7684\u5185\u53c2\u77e9\u9635\uff0c\u66f4\u591a\u7684\u662f\u4e00\u4e2a\u53f3\u4e0a\u4e09\u89d2\u9635\uff0c\u5373\u7b2c\u4e00\u884c\u7b2c\u4e8c\u5217\u7684\u5143\u7d20\u672a\u5fc5\u4e3a\u96f6\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec07/#\u5916\u53c2\u77e9\u9635","title":"\u5916\u53c2\u77e9\u9635","text":"<p>\u6211\u4eec\u5728\u4e0a\u9762\u63d0\u5230\u7684\u5916\u53c2\u77e9\u9635\u957f\u8fd9\u6837\uff1a</p> \\[ M_{ext} = \\begin{bmatrix}     R_{3\\times 3} &amp; \\mathbf{t} \\\\     \\mathbf{0}_{1\\times 3} &amp; 1 \\end{bmatrix} = \\begin{bmatrix}     r_{11} &amp; r_{12} &amp; r_{13} &amp; t_x \\\\     r_{21} &amp; r_{22} &amp; r_{23} &amp; t_y\\\\     r_{31} &amp; r_{32} &amp; r_{33} &amp; t_z\\\\     0 &amp; 0 &amp; 0 &amp; 1 \\end{bmatrix} \\\\ or \\\\ M_{ext} = \\begin{bmatrix}     R_{3\\times 3} &amp; \\mathbf{t} \\\\ \\end{bmatrix} = \\begin{bmatrix}     r_{11} &amp; r_{12} &amp; r_{13} &amp; t_x \\\\     r_{21} &amp; r_{22} &amp; r_{23} &amp; t_y\\\\     r_{31} &amp; r_{32} &amp; r_{33} &amp; t_z\\\\ \\end{bmatrix} \\] <p>\u5176\u4e2d\u4e3b\u8981\u6709 12 \u4e2a\u81ea\u7531\u5ea6\uff0c\u5305\u542b\u4e86\u65cb\u8f6c\u77e9\u9635 \\(R\\) \u548c\u65cb\u8f6c\u540e\u7684\u4f4d\u79fb\u5411\u91cf \\(\\mathbf{t}\\)\u3002</p> <p>\u7c7b\u4f3c\u4e8e\u4e0a\u4e00\u8282\u63d0\u5230\u7684\u65cb\u8f6c\u77e9\u9635\uff0c\u8fd9\u91cc\u7684\u65cb\u8f6c\u77e9\u9635\u540c\u6837\u62e5\u6709 \u6b63\u4ea4 \u548c \\(||R||_2^2 = 1\\) \u7684\u6027\u8d28\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec07/#\u6295\u5f71\u77e9\u9635","title":"\u6295\u5f71\u77e9\u9635","text":"<p>\u603b\u7ed3\u5e94\u7528\u4e24\u4e2a\u77e9\u9635\u7684\u4e24\u4e2a\u9636\u6bb5\uff1a</p> <p>Camera to Pixel: Intrinsic Matrix</p> \\[ \\mathbf{\\tilde{u}} = M_{int} \\mathbf{\\tilde{x}}_c \\;\\;\\;\\;i.e.\\;\\;\\;\\; \\begin{bmatrix}     u' \\\\ v' \\\\ z_c \\end{bmatrix} = \\begin{bmatrix}     f_x &amp; 0 &amp; c_x &amp; 0 \\\\     0 &amp; f_y &amp; c_y &amp; 0 \\\\     0 &amp; 0 &amp; 1 &amp; 0 \\end{bmatrix} \\begin{bmatrix}     x_c \\\\     y_c \\\\     z_c \\\\     1 \\end{bmatrix} \\] <p>World to Camera: Extrinsic Matrix</p> \\[ \\mathbf{\\tilde{x}}_c = M_{ext} \\mathbf{\\tilde{x}}_w \\;\\;\\;\\;i.e.\\;\\;\\;\\; \\begin{bmatrix} x_c \\\\ y_c \\\\ z_c \\\\ 1\\end{bmatrix} = \\begin{bmatrix}     r_{11} &amp; r_{12} &amp; r_{13} &amp; t_x \\\\     r_{21} &amp; r_{22} &amp; r_{23} &amp; t_y\\\\     r_{31} &amp; r_{32} &amp; r_{33} &amp; t_z\\\\     0 &amp; 0 &amp; 0 &amp; 1 \\end{bmatrix} \\begin{bmatrix}     x_w \\\\ y_w \\\\ z_w \\\\ 1 \\end{bmatrix} \\] <p>\u800c\u5c06\u5b83\u4eec\u7ed3\u5408\uff0c\u6211\u4eec\u5c31\u5f97\u5230\u4e86\u5b8c\u6574\u7684\u6295\u5f71\u77e9\u9635(Projection Matrix)\\(P\\)\uff1a</p> \\[ \\mathbf{\\tilde u} = M_{int}M_{ext} \\mathbf{\\tilde x}_w = P \\mathbf{\\tilde x} \\;\\;\\;\\; i.e. \\;\\;\\;\\; \\begin{bmatrix}     u \\\\ v \\\\ 1 \\end{bmatrix} \\cong \\begin{bmatrix}     u' \\\\ v' \\\\ z_c \\end{bmatrix} = \\underbrace{\\begin{bmatrix}     p_{11} &amp; p_{12} &amp; p_{13} &amp; p_{14} \\\\     p_{21} &amp; p_{22} &amp; p_{23} &amp; p_{24} \\\\     p_{31} &amp; p_{32} &amp; p_{33} &amp; p_{34} \\end{bmatrix}}_{\\text{Projection Matrix } P} \\begin{bmatrix}     x_w \\\\     y_w \\\\     z_w \\\\     1 \\end{bmatrix} \\]"},{"location":"cour_note/D2QD_Intro2CV/Lec07/#\u76f8\u673a\u6807\u5b9a\u4e0e\u4f4d\u7f6e\u4f30\u8ba1_1","title":"\u76f8\u673a\u6807\u5b9a\u4e0e\u4f4d\u7f6e\u4f30\u8ba1","text":"<p>\u6839\u636e\u6295\u5f71\u77e9\u9635\u6211\u4eec\u5f97\u5230\u4e86\u50cf\u7d20\u70b9\u4e0e 3D \u666f\u7269\u4e16\u754c\u5750\u6807\u7684\u8f6c\u5316\u5173\u7cfb\uff0c\u800c\u76f8\u673a\u6807\u5b9a\u4e0e\u4f4d\u7f6e\u4f30\u8ba1\u5c31\u662f\u5229\u7528\u8fd9\u4e2a\u5173\u7cfb\u5f0f\u6c42\u89e3\u6295\u5f71\u77e9\u9635\u3002\u6240\u4ee5\u8fd9\u5c31\u8981\u6c42\u6211\u4eec\u540c\u65f6\u77e5\u9053\u82e5\u5e72\u70b9\u7684\u50cf\u7d20\u70b9\u4f4d\u7f6e\u548c 3D \u666f\u7269\u4e16\u754c\u5750\u6807\uff0c\u4e00\u822c\u6765\u8bf4\u76f8\u673a\u6807\u5b9a\u4e0e\u4f4d\u7f6e\u4f30\u8ba1\u662f\u8fd9\u4e48\u5b9e\u73b0\u7684\uff1a</p> <p>\u6b65\u9aa4\u4e00</p> <p></p> <p>\u7ed9\u5b9a\u4e00\u4e2a\u51e0\u4f55\u7279\u6027\u5df2\u77e5\u7684\u6807\u5b9a\u677f\uff0c\u4eba\u4e3a\u5b9a\u4e49\u5176\u4e16\u754c\u5750\u6807\u7cfb\u3002</p> <p>\u7531\u4e8e\u5750\u6807\u90fd\u662f\u7531\u6211\u4eec\u4eba\u4e3a\u7ed9\u5b9a\u7684\uff0c\u6240\u4ee5\u6211\u4eec\u53ef\u4ee5\u6309\u7167\u5c3d\u53ef\u80fd\u65b9\u4fbf\u7684\u539f\u5219\u8fdb\u884c\u89c4\u5212\u3002\u6b64\u5916\uff0c\u4e3a\u4e86\u65b9\u4fbf\u4e4b\u540e\u7684\u8ba1\u7b97\uff0c\u6807\u5b9a\u677f\u7684\u5185\u5bb9\u4e00\u822c\u662f\u7b80\u5355\u660e\u4e86\u7684\u3002</p> <p>\u4f8b\u5982\u56fe\u4e2d\uff0c\u5b9a\u4e49\u4e16\u754c\u5750\u6807\u7cfb\u540e\uff0c\u6bcf\u4e00\u683c\u7684\u8fb9\u957f\u4e3a 5cm\uff0c\u6240\u4ee5\u7d2b\u8272\u70b9\u7684\u5750\u6807\u4e3a \\((0, 15, 20) cm\\)\u3002</p> <p>\u6b65\u9aa4\u4e8c</p> <p>\u5bfb\u627e\u7279\u5b9a\u5173\u952e\u70b9\u7684\u5bf9\u5e94\u5173\u7cfb\uff0c\u4e5f\u5c31\u662f\u505a\u7279\u5f81\u5339\u914d\uff0c\u5373\u82e5\u5e72\u70b9\u5bf9\uff0c\u6bcf\u4e00\u4e2a\u70b9\u5bf9\u90fd\u662f\u4e00\u4e2a 3D \u70b9\u548c\u4e00\u4e2a 2D \u70b9\u7684\u5bf9\u5e94\u3002</p> <p>\u9700\u8981\u8bf4\u660e\u7684\u4e00\u70b9\u662f\uff0c\u6211\u4eec\u5df2\u77e5\u7684\u7279\u5f81\u5339\u914d\u662f\u5efa\u7acb\u5728\u4e24\u5f20\u4e8c\u7ef4\u56fe\u7247\u4e0a\u7684\uff0c\u800c\u73b0\u5728\u8981\u505a\u7684\u662f 3D \u5230 2D \u7684\u5339\u914d\u3002\u4e00\u79cd\u60f3\u6cd5\u662f\uff0c\u6211\u4eec\u53ef\u4ee5\u5c06 3D \u666f\u8c61\u6309\u7167\u6211\u4eec\u5e0c\u671b\u7684\u65b9\u6cd5\u6620\u5c04\u4e3a 2D \u666f\u8c61\uff0c\u4f8b\u5982\u5728\u8fd9\u4e2a\u95ee\u9898\u4e2d\u6211\u4eec\u53ef\u4ee5\u76f4\u63a5\u62ff\u8fd9\u4e2a\u6807\u5b9a\u677f\u7684 zy \u5e73\u9762\u6765\u8fdb\u884c\u7279\u5f81\u5339\u914d\u3002</p> <p></p> <p>\u6b65\u9aa4\u4e09</p> <p>\u6839\u636e\u521a\u521a\u5f97\u5230\u7684\u82e5\u5e72\u5bf9\u5174\u8da3\u70b9\uff0c\u5efa\u7acb\u65b9\u7a0b\uff0c\u6c42\u89e3\u6295\u5f71\u77e9\u9635\u3002</p> <p>\u6bcf\u4e00\u5bf9\u5173\u952e\u70b9\u53ef\u4ee5\u5206\u522b\u6839\u636e \\(u\\) \u548c \\(v\\) \u5efa\u7acb\u4e24\u4e2a\u7b49\u5f0f\uff1a</p> \\[ \\underbrace{\\begin{bmatrix}     u^{(i)} \\\\     v^{(i)} \\\\     1 \\end{bmatrix}}_{known} =  \\underbrace{\\begin{bmatrix}     p_{11} &amp; p_{12} &amp; p_{13} &amp; p_{14} \\\\     p_{21} &amp; p_{22} &amp; p_{23} &amp; p_{24} \\\\     p_{31} &amp; p_{32} &amp; p_{33} &amp; p_{34} \\end{bmatrix}}_{unknown} \\underbrace{\\begin{bmatrix}     x_w^{(i)} \\\\     y_w^{(i)} \\\\     z_w^{(i)} \\\\     1 \\end{bmatrix}}_{known} \\\\ i.e. \\;\\;\\;\\; \\left\\{ \\begin{aligned}     u^{(i)} &amp;= \\frac{p_{11}x_w^{(i)} + p_{12}y_w^{(i)} + p_{13}z_w^{(i)} + p_{14}}{p_{31}x_w^{(i)} + p_{32}y_w^{(i)} + p_{33}z_w^{(i)} + p_{34}} \\\\     v^{(i)} &amp;= \\frac{p_{21}x_w^{(i)} + p_{22}y_w^{(i)} + p_{23}z_w^{(i)} + p_{24}}{p_{31}x_w^{(i)} + p_{32}y_w^{(i)} + p_{33}z_w^{(i)} + p_{34}} \\end{aligned} \\right. \\] <p>\u7531\u4e8e\u6295\u5f71\u77e9\u9635\u6709 12 \u4e2a\u81ea\u7531\u5ea6\uff0c\u6240\u4ee5\u81f3\u5c11\u9700\u8981 6 \u5bf9\u5173\u952e\u70b9 12 \u4e2a\u7b49\u5f0f\u3002</p> <p>\u6b65\u9aa4\u56db</p> <p>\u5c06\u82e5\u5e72\u65b9\u7a0b\u91cd\u65b0\u6392\u5217\u4e3a\u77e9\u9635\u5f62\u5f0f\uff0c\u65b9\u4fbf\u4e4b\u540e\u7684\u8ba1\u7b97\u3002</p> <p>\u5c06\u6b65\u9aa4\u4e09\u5f97\u5230\u7684\u5f0f\u5b50\u540c\u5206\u79fb\u9879\uff0c\u5f62\u6210 \\(f(...) = 0\\) \u7684\u5f62\u5f0f\uff0c\u518d\u5c06 12 \u4e2a\u5f0f\u5b50\u7ed3\u5408\u5728\u4e00\u8d77\u5c31\u5f97\u5230\u4e86\u4e0b\u9762\u8fd9\u4e2a\u5e9e\u5927\u7684\u77e9\u9635\u65b9\u7a0b\uff1a</p> \\[ \\begin{bmatrix}     x_w^{(1)} &amp; y_w^{(1)} &amp; z_w^{(1)} &amp; 1 &amp; 0 &amp; 0 &amp; 0 &amp; 0 &amp; -u_1x_w^{(1)} &amp; -u_1y_w^{(1)} &amp; -u_1z_w^{(1)} &amp; -u_1 \\\\     0 &amp; 0 &amp; 0 &amp; 0 &amp;  x_w^{(1)} &amp; y_w^{(1)} &amp; z_w^{(1)} &amp; 1 &amp; -v_1x_w^{(1)} &amp; -v_1y_w^{(1)} &amp; -v_1z_w^{(1)} &amp; -v_1 \\\\     \\vdots &amp; \\vdots &amp; \\vdots &amp; \\vdots &amp; \\vdots &amp; \\vdots &amp; \\vdots &amp; \\vdots &amp; \\vdots &amp; \\vdots &amp; \\vdots &amp; \\vdots \\\\      x_w^{(i)} &amp; y_w^{(i)} &amp; z_w^{(i)} &amp; 1 &amp; 0 &amp; 0 &amp; 0 &amp; 0 &amp; -u_ix_w^{(i)} &amp; -u_iy_w^{(i)} &amp; -u_iz_w^{(i)} &amp; -u_i \\\\     0 &amp; 0 &amp; 0 &amp; 0 &amp;  x_w^{(i)} &amp; y_w^{(i)} &amp; z_w^{(i)} &amp; 1 &amp; -v_ix_w^{(i)} &amp; -v_iy_w^{(i)} &amp; -v_iz_w^{(i)} &amp; -v_i \\\\     \\vdots &amp; \\vdots &amp; \\vdots &amp; \\vdots &amp; \\vdots &amp; \\vdots &amp; \\vdots &amp; \\vdots &amp; \\vdots &amp; \\vdots &amp; \\vdots &amp; \\vdots \\\\      x_w^{(n)} &amp; y_w^{(n)} &amp; z_w^{(n)} &amp; 1 &amp; 0 &amp; 0 &amp; 0 &amp; 0 &amp; -u_nx_w^{(n)} &amp; -u_ny_w^{(n)} &amp; -u_nz_w^{(n)} &amp; -u_n \\\\     0 &amp; 0 &amp; 0 &amp; 0 &amp;  x_w^{(n)} &amp; y_w^{(n)} &amp; z_w^{(n)} &amp; 1 &amp; -v_nx_w^{(n)} &amp; -v_ny_w^{(n)} &amp; -v_nz_w^{(n)} &amp; -v_n \\\\ \\end{bmatrix} \\begin{bmatrix}     p_{11} \\\\ p_{12} \\\\ p_{13} \\\\ p_{14} \\\\     p_{21} \\\\ p_{22} \\\\ p_{23} \\\\ p_{24} \\\\     p_{31} \\\\ p_{32} \\\\ p_{33} \\\\ p_{34} \\end{bmatrix} = \\begin{bmatrix}     0 \\\\ 0 \\\\ 0 \\\\ 0 \\\\     0 \\\\ 0 \\\\ 0 \\\\ 0 \\\\     0 \\\\ 0 \\\\ 0 \\\\ 0 \\end{bmatrix} \\] <p>\u6211\u4eec\u5c06\u5176\u7b80\u5199\uff0c\u4e5f\u5c31\u662f \\(A\\mathbf{p} = 0\\)\u3002</p> <p>\u6b65\u9aa4\u4e94</p> <p>\u6c42\u89e3 \\(A\\mathbf{p} = 0\\) \u5f97\u5230 \\(\\mathbf{p}\\)\u3002</p> <p>\u7c7b\u4f3c\u4e8e\u4e0a\u4e00\u8282\u7684\u64cd\u4f5c\uff0c\u8fd9\u91cc\u5f97\u5230\u7684 \\(mathbf{p}\\) \u4e5f\u6709\u591a\u79cd\u53ef\u80fd\uff0c\u6240\u4ee5\u6211\u4eec\u8981\u5bf9\u5b83\u8fdb\u884c\u7ea6\u675f\uff0c\u4e00\u822c\u6709\u4e24\u79cd\u9009\u62e9\uff1a</p> <ul> <li>\u4ee4 \\(p_{34} = 1\\)\uff1b</li> <li>\u4ee4 \\(||p|| = 1\\)\uff1b</li> </ul> <p>\u4e00\u822c\u6211\u4eec\u9009\u62e9\u540e\u8005\uff0c\u4e5f\u5c31\u662f\u8ba9 \\(mathbf{p}\\) \u7684\u957f\u5ea6\u4e3a 1\uff0c\u6b64\u65f6\u81ea\u7531\u5ea6\u524a\u51cf\u4e3a 11\uff0c\u4ecd\u7136\u9700\u8981\u516d\u5bf9\u5173\u952e\u70b9\u3002</p> <p>\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u5c06\u6c42\u89e3\u65b9\u7a0b \\(A\\mathbf{p} = 0\\) \u8f6c\u5316\u4e3a \\(\\mathop{minimize} \\limits_\\mathbf{p} ||A\\mathbf{p}||^2 \\;\\; \\text{ such that } ||\\mathbf{p}||^2 = 1\\) \u7684\u4f18\u5316\u95ee\u9898\uff0c\u7531\u4e8e\u548c\u4e4b\u524d\u7684\u4e00\u6837\uff0c\u6240\u4ee5\u4e0d\u518d\u8d58\u8ff0\u3002</p> <p>\u5206\u89e3\u6295\u5f71\u77e9\u9635</p> <p>\u6839\u636e\u6295\u5f71\u77e9\u9635\u7684\u76f8\u5173\u5185\u5bb9\u6211\u4eec\u77e5\u9053\uff1a  </p> <p>\u901a\u5e38\u6765\u8bf4\uff0c\u5c06\u4e00\u4e2a\u77e9\u9635\u5206\u89e3\u4e3a\u4e24\u4e2a\u7279\u5b9a\u77e9\u9635\u662f\u4e0d\u73b0\u5b9e\u7684\uff0c\u4f46\u662f\u6b64\u5904\u7684\u5185\u53c2\u77e9\u9635\u7684\u5b50\u5f0f\u5177\u6709\u201c\u4e0a\u4e09\u89d2\u9635\u201d\u8fd9\u4e2a\u6027\u8d28\uff0c\u5916\u53c2\u77e9\u9635\u4e2d\u65cb\u8f6c\u77e9\u9635\u5b50\u5f0f\u5177\u6709\u201c\u6b63\u4ea4\u201d\u8fd9\u4e2a\u6027\u8d28\uff0c\u800c\u4e14\u89c2\u5bdf 0 \u7684\u5206\u5e03\uff0c\u6211\u4eec\u53d1\u73b0 \\([p_{11} \\sim p_{33}]\\) \u7531 \\(KR\\) \u5f97\u5230\u3002\u6240\u4ee5\u6211\u4eec\u6070\u597d\u53ef\u4ee5\u4f7f\u7528QR \u5206\u89e3\u6765\u5b9e\u73b0\uff1a</p> \\[ \\begin{bmatrix}     p_{11} &amp; p_{12} &amp; p_{13} \\\\     p_{21} &amp; p_{22} &amp; p_{23} \\\\     p_{31} &amp; p_{32} &amp; p_{33} \\end{bmatrix} = \\begin{bmatrix}     f_x &amp; 0 &amp; c_x \\\\     0 &amp; f_y &amp; c_y \\\\     0 &amp; 0 &amp; 1 \\end{bmatrix} \\begin{bmatrix}     r_{11} &amp; r_{12} &amp; r_{13} \\\\     r_{21} &amp; r_{22} &amp; r_{23} \\\\     r_{31} &amp; r_{32} &amp; r_{33} \\\\ \\end{bmatrix} = KR \\] <p>\u9700\u8981\u6ce8\u610f\u7684\u662f\uff0c\u4f7f\u7528 QR \u5206\u89e3\u5f97\u5230\u7684\u4e09\u89d2\u9635\u5e76\u4e0d\u4e00\u5b9a\u5177\u6709\u7b2c\u4e00\u884c\u7b2c\u4e8c\u5217\u5143\u7d20\u4e3a 0 \u7684\u6027\u8d28\u3002</p> <p>\u6b64\u65f6\uff0c\u6211\u4eec\u5df2\u7ecf\u77e5\u9053\u4e86\u9664\u4e86 \\(t_x,t_y,t_z\\) \u4ee5\u5916\u7684\u6240\u6709\u672a\u77e5\u5143\u4e86\uff0c\u6240\u4ee5\u5f53\u7136\u53ef\u4ee5\u56de\u8fc7\u6765\u7ee7\u7eed\u6c42\u5b83\u4eec\u3002</p> \\[ \\because \\begin{bmatrix}     p_{14} \\\\ p_{24} \\\\ p_{34} \\end{bmatrix} = \\begin{bmatrix}     f_x &amp; 0 &amp; c_x \\\\     0 &amp; f_y &amp; c_y \\\\     0 &amp; 0 &amp; 1 \\end{bmatrix} \\begin{bmatrix}     t_x \\\\ t_y \\\\ t_z \\end{bmatrix} = K \\mathbf{t} \\\\ \\therefore \\mathbf{t} = K^{-1}  \\begin{bmatrix}     p_{14} \\\\ p_{24} \\\\ p_{34} \\end{bmatrix} \\] <p>\u6ce8\u610f</p> <p>\u9700\u8981\u7279\u522b\u6ce8\u610f\u7684\u4e00\u70b9\u662f\uff0c\u5728\u6211\u4eec\u4e0a\u9762\u6d89\u53ca\u7684\u8ba8\u8bba\u4e2d\uff0c\u6211\u4eec\u90fd\u6ca1\u6709\u8003\u8651\u7578\u53d8\u5e26\u6765\u7684\u5f71\u54cd\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec07/#\u591a\u70b9\u900f\u89c6\u6210\u50cf\u95ee\u9898","title":"\u591a\u70b9\u900f\u89c6\u6210\u50cf\u95ee\u9898","text":"<p>\u591a\u70b9\u900f\u89c6\u6210\u50cf\u95ee\u9898(Perspective-n-Point Problem)\uff0c\u5373 PnP \u95ee\u9898\uff0c\u6307\u7684\u662f\u5df2\u77e5\u5185\u53c2\u6c42\u5916\u53c2\u7684\u89c6\u89c9\u5b9a\u4f4d\u95ee\u9898\u3002</p> <p>\u5e38\u89c1\u7684\u89e3\u51b3\u65b9\u6848\u6709\u5982\u4e0b\u51e0\u79cd\u3002</p> <p>DLT Direct Linear Transform</p> <p>\u4e5f\u5c31\u662f\u4e0a\u9762\u63d0\u5230\u7684\u505a\u6cd5\u3002</p> <p>P3P</p> <p>\u81f3\u5c11\u9700\u8981 3 \u7ec4\u5bf9\u5e94\u5173\u7cfb\u624d\u80fd\u6c42\u89e3\u76f8\u673a\u4f4d\u7f6e\uff0c\u6b64\u5916\uff0c\u6211\u4eec\u8fd8\u9700\u8981\u4e00\u4e2a\u989d\u5916\u7684\u70b9\u6765\u4fdd\u8bc1\u7b54\u6848\u7684\u552f\u4e00\u6027\uff08\u5426\u5219\u4e00\u822c\u6765\u8bf4\u4f1a\u6709\u56db\u4e2a\u89e3\uff09</p> <p>\u5176\u4e3b\u8981\u601d\u8def\u662f\u6839\u636e\u56fe\u50cf\uff0c\u4f7f\u7528\u4f59\u5f26\u5b9a\u5f8b\u8fdb\u884c\u6c42\u89e3\u3002</p> <p>\u61d2\u5f97\u5199\u4e86\uff0c\u76f4\u63a5\u8d34\u9ea6\u54e5\u7684\u7b14\u8bb0\u4e86\uff01</p> <p>PnP</p> <p>n &gt; 3 \u7684\u60c5\u51b5\u7684\u505a\u6cd5\u3002</p> <p>\u8f6c\u5316\u4e3a\u4f18\u5316\u95ee\u9898\uff0c\u6c42\u89e3\u7406\u8bba\u548c\u5b9e\u9645\u7684\u70b9\u8bef\u5dee\u2014\u2014\u91cd\u6295\u5f71\u8bef\u5dee(reprojection error)\u6700\u5c0f\u65f6\u7684\u5916\u53c2\uff0c\u6ce8\u610f\u5c06\u9f50\u6b21\u5750\u6807\u8f6c\u5316\u4e3a\u4e8c\u7ef4\u5750\u6807\u3002</p> <p>Initialized by P3P, optimized by Gauss-Newton\u3002</p> <p>\u61d2\u5f97\u5199\u4e86\uff0c\u76f4\u63a5\u8d34\u9ea6\u54e5\u7684\u7b14\u8bb0\u4e86\uff01</p> <p>EPnP</p> <p>\u76ee\u524d\u6700\u53d7\u6b22\u8fce\u7684\u505a\u6cd5\uff0cO(N) \u5341\u5206\u9ad8\u6548\u4e5f\u5341\u5206\u51c6\u786e\uff0c\u5927\u6982\u662f\u7528\u56db\u4e2a\u63a7\u5236\u70b9\u8868\u793a\u5176\u4ed6\u70b9\u3002</p> <p>\u61d2\u5f97\u5199\u4e86\uff0c\u76f4\u63a5\u8d34\u9ea6\u54e5\u7684\u7b14\u8bb0\u4e86\uff01</p> <p>\u8bf4\u660e</p> <p>\u672c\u8282\u63a5\u4e0b\u6765\u7684\u5185\u5bb9\uff0c\u8bb2\u7684\u662f\u5982\u4f55\u4e09\u7ef4\u91cd\u5efa\u5f97\u5230\u7a00\u758f\u7684\u70b9\u4e91\uff0c\u800c\u5982\u4f55\u5f97\u5230\u7a20\u5bc6\u7684\u4e09\u7ef4\u91cd\u5efa\uff0c\u5c06\u6210\u4e3a\u4e0b\u4e00\u8282\u7684\u91cd\u70b9\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec07/#\u53cc\u76ee\u4e09\u7ef4\u91cd\u5efa","title":"\u53cc\u76ee\u4e09\u7ef4\u91cd\u5efa","text":"<p>\u53cc\u76ee\u89c6\u89c9(Stereo Vision)\uff1a\u5df2\u77e5\u4e24\u4e2a\u76f8\u673a\u7684\u5185\u53c2\uff0c\u6839\u636e\u4e24\u5f20\u56fe\u50cf\u6c42\u89e3\u4e24\u4e2a\u76f8\u673a\u7684\u5916\u53c2\u548c\u76ee\u6807\u7684 3D \u7ed3\u6784\u3002</p> <p></p>"},{"location":"cour_note/D2QD_Intro2CV/Lec07/#\u5bf9\u6781\u51e0\u4f55","title":"\u5bf9\u6781\u51e0\u4f55","text":"<p>\u5728\u524d\u4e00\u8282\u6211\u4eec\u4ecb\u7ecd\u4e86\u5982\u4f55\u5728\u300c3D \u666f\u8c61\u6a21\u578b\u5df2\u77e5\u300d\u7684\u60c5\u51b5\u4e0b\uff0c\u5bf9\u76f8\u673a\u8fdb\u884c\u6807\u5b9a\u6216\u8fdb\u884c\u672a\u77e5\u4f30\u8ba1\uff0c\u4f46\u6211\u4eec\u4ecd\u7136\u4e0d\u77e5\u9053\u5982\u4f55\u4ece 2D \u56fe\u7247\u4e2d\u91cd\u5efa\u51fa 3D \u6a21\u578b\u3002</p> <p>\u8ba9\u6211\u4eec\u8003\u8651\u53cc\u76ee\u4e09\u7ef4\u91cd\u5efa\u4e2d\u7684\u60c5\u5f62\u2014\u2014\u4e24\u4e2a\u76f8\u673a\u4e0b\u4e0d\u540c\u666f\u8c61\u4e4b\u95f4\u663e\u7136\u662f\u5b58\u5728\u4e00\u5b9a\u7684\u51e0\u4f55\u5173\u7cfb\u7684\uff0c\u800c\u5bf9\u6781\u51e0\u4f55(Epipolar Geometry)\u7740\u773c\u4e8e\u4e0b\u9762\u8fd9\u4e09\u4e2a\u76ee\u6807\u4e4b\u95f4\u7684\u51e0\u4f55\u5173\u7cfb\uff1a\u4e24\u4e2a\u76f8\u673a\u4e2d\u5fc3 \\(O_L\\) \u548c \\(O_R\\)\uff0c\u4ee5\u53ca\u666f\u7269\u4e2d\u7684\u67d0\u4e2a\u7a7a\u95f4\u70b9 \\(X\\)\uff08\u6216\u8005 \\(P\\)\uff09\u3002</p> <p>WIKI page</p> <p>https://en.wikipedia.org/wiki/Epipolar_geometry</p> <p></p> <p>Epipolar geometry is the geometry of stereo vision. When two cameras view a 3D scene from two distinct positions, there are a number of geometric relations between the 3D points and their projections onto the 2D images that lead to constraints between the image points. These relations are derived based on the assumption that the cameras can be approximated by the pinhole camera model.</p> <p>\u5bf9\u6781\u51e0\u4f55\u662f\u7acb\u4f53\u89c6\u89c9\u7684\u51e0\u4f55\u5b66\u3002\u5f53\u4e24\u4e2a\u6444\u50cf\u673a\u4ece\u4e24\u4e2a\u4e0d\u540c\u7684\u4f4d\u7f6e\u67e5\u770b 3D \u573a\u666f\u65f6\uff0c3D \u70b9\u4e0e\u5b83\u4eec\u5728 2D \u56fe\u50cf\u4e0a\u7684\u6295\u5f71\u4e4b\u95f4\u5b58\u5728\u8bb8\u591a\u51e0\u4f55\u5173\u7cfb\uff0c\u5bfc\u81f4\u56fe\u50cf\u70b9\u4e4b\u95f4\u5b58\u5728\u7ea6\u675f\u3002\u8fd9\u4e9b\u5173\u7cfb\u662f\u57fa\u4e8e\u76f8\u673a\u53ef\u4ee5\u7528\u9488\u5b54\u76f8\u673a\u6a21\u578b\u8fd1\u4f3c\u7684\u5047\u8bbe\u5bfc\u51fa\u7684\u3002</p> <p>\u2014\u2014Wiki</p> <p>\u9996\u5148\uff0c\u6211\u4eec\u9700\u8981\u4ecb\u7ecd\u5bf9\u6781\u51e0\u4f55\u4e2d\u7684\u51e0\u4e2a\u6982\u5ff5\uff0c\u6211\u4eec\u5c06\u501f\u52a9\u4e0a\u56fe\u8fdb\u884c\u8bf4\u660e\u3002</p> <p>\u57fa\u7ebf</p> <p>\u57fa\u7ebf(Baseline)\u662f\u4e24\u4e2a\u76f8\u673a\u4e2d\u5fc3\u7684\u8fde\u7ebf\uff0c\u5373 \\(OO'\\)\u3002</p> <p>\u5bf9\u6781\u70b9</p> <p>\u5bf9\u6781\u70b9(Epipole)\u6307\u7684\u662f\uff1a\u5176\u4e2d\u4e00\u4e2a\u76f8\u673a\u7684\u76f8\u673a\u4e2d\u5fc3\u5728 \u53e6\u5916\u4e00\u4e2a\u76f8\u673a\u7684\u6210\u50cf\u5e73\u9762\u4e0a\u7684\u6295\u5f71\u70b9\uff0c\u5373 \\(e_l\\) \u548c \\(e_r\\)\uff0c\u4e14\u4ed6\u4eec\u5728\u65e2\u5b9a\u7684\u5177\u4f53\u53cc\u76ee\u6a21\u578b\u4e0b\u662f\u552f\u4e00\u7684\u3002</p> <p>\u5bf9\u6781\u9762</p> <p>\u5bf9\u6781\u9762(Epipolar Plane)\u6307\u7684\u662f\u4e24\u4e2a\u76f8\u673a\u4e2d\u5fc3 \\(O_L\\) \u548c \\(O_R\\)\uff0c\u4ee5\u53ca\u666f\u7269\u4e2d\u7684\u67d0\u4e2a\u7a7a\u95f4\u70b9 \\(X\\) \u8fd9\u4e09\u4e2a\u70b9\u6240\u786e\u5b9a\u7684\u7a7a\u95f4\u5e73\u9762\u3002</p> <p>\u5176\u4e2d\u6709\u4e00\u4e2a\u6027\u8d28\uff0c\u5bf9\u6781\u9762\u603b\u662f\u7ecf\u8fc7\u76f8\u673a\u4e2d\u5fc3\u8fde\u7ebf \\(O_L O_R\\)\uff0c\u6240\u4ee5\u5bf9\u4e8e\u67d0\u4e2a\u666f\u7269\u4e2d\u7684\u70b9 \\(X_i\\)\uff0c\u5176\u5bf9\u6781\u9762\u90fd\u662f\u552f\u4e00\u7684\u3002\uff08\u663e\u7136\uff0c\u53cd\u8fc7\u6765\u4e0d\u6210\u7acb\u3002\uff09</p> <p>\u5bf9\u6781\u7ebf</p> <p>\u5bf9\u6781\u7ebf(Epipolar Line)\u662f\u5173\u4e8e\u52a8\u70b9 \\(X\\) \u6765\u8bf4\u7684\uff0c\u4f53\u73b0\u4e3a\u5bf9\u6781\u9762\u4e0e\u6210\u50cf\u5e73\u9762\u7684\u4ea4\u7ebf\u3002</p> <p>\u5047\u8bbe\u6211\u4eec\u53ea\u77e5\u9053 \\(X_L\\) \u800c\u4e0d\u77e5\u9053 \\(X_R\\)\uff0c\u90a3\u4e48 \\(X\\) \u53ef\u80fd\u5728 \\(O_L X_L\\) \u8fd9\u6761\u7ebf\u4e0a\u7684\u4efb\u4e00\u70b9\uff1b\u800c\u8fd9\u6761\u7ebf\u5728 \\(R\\) \u5e73\u9762\u4e0a\u7684\u6295\u5f71\u5c31\u662f\u4e00\u6761\u5bf9\u6781\u7ebf\uff0c\u5b83\u7684\u542b\u4e49\u662f\u53ef\u80fd\u7684 \\(X_R\\) \u7684\u8f68\u8ff9\u3002</p> <p>\u6b64\u5916\uff0c\u5bf9\u6781\u7ebf\u6709\u4e00\u4e2a\u6027\u8d28\uff1a\u5bf9\u6781\u7ebf\u5fc5\u5b9a\u7ecf\u8fc7\u5bf9\u6781\u70b9\uff0c\u800c\u7ecf\u8fc7\u5bf9\u6781\u70b9\u7684\u4efb\u610f\u4e00\u6761\u76f4\u7ebf\uff08\u5f53\u7136\u5f97\u5728\u6210\u50cf\u5e73\u9762\u4e0a\uff09\u90fd\u53ef\u4ee5\u662f\u5bf9\u6781\u7ebf\u3002</p> <p>\ud83d\udc49 WIKI\u3002</p> <p>\u5176\u4ed6\u8bf4\u660e</p> <p>\u56fe\u4e2d\u8fd8\u9700\u8981\u989d\u5916\u89e3\u91ca\u7684\u5c31\u662f \\(X_L\\) \u548c \\(X_R\\)\uff0c\u5b83\u4eec\u5206\u522b\u662f\u666f\u7269\u4e2d\u7684\u67d0\u4e2a\u7a7a\u95f4\u70b9 \\(X\\) \u5728\u4e24\u4e2a\u6210\u50cf\u5e73\u9762\u4e0a\u7684\u50cf\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec07/#\u6781\u7ebf\u7ea6\u675f","title":"\u6781\u7ebf\u7ea6\u675f","text":"<p>\u73b0\u5728\u6211\u4eec\u5173\u6ce8\u5bf9\u6781\u9762\uff0c\u7740\u773c\u4e8e\u89e3\u51b3\u4e0b\u9762\u8fd9\u6837\u4e00\u4e2a\u95ee\u9898\u3002</p> <p></p> <p>\u5176\u4e2d\u4e24\u4fa7\u7684\u76f8\u673a\u7406\u6240\u5f53\u7136\u7684\u90fd\u62e5\u6709\u81ea\u5df1\u7684\u5750\u6807\u7cfb\uff0c\u73b0\u5728\u6211\u4eec\u5bfb\u627e\u4e00\u79cd\u53d8\u6362\uff0c\u4f7f\u5f97\uff1a\\(\\mathbf{x}_l = R\\mathbf{x}_r + \\mathbf{t}\\)\uff0c\u5176\u4e2d \\(\\mathbf{t} = \\overrightarrow{O_r O_l}\\)\uff08\u56fe\u4e2d\u8c8c\u4f3c\u6807\u9519\u4e86\u65b9\u5411\uff09\uff0c\\(\\mathbf{x}_l = \\overrightarrow{O_l P}\\) \u800c \\(\\mathbf{x}_r = \\overrightarrow{O_r P}\\) \u3002</p> <p>\u4e0b\u9762\u5f00\u59cb \u53d8\u9b54\u6cd5 \u8fdb\u884c\u4e00\u4e9b\u53d8\u5316\uff1a</p> \u5f62\u5f0f \u2461 \u63a8\u7406\u8fc7\u7a0b <p>\u9996\u5148\uff0c\u5728\u540c\u4e00\u4e2a\uff08\u4efb\u4f55\u4e00\u4e2a\uff09\u7b1b\u5361\u5c14\u5750\u6807\u7cfb\u4e2d\uff0c\u90fd\u6709 \\(\\mathbf{x}_l \\cdot (\\mathbf{t} \\times \\mathbf{x}_l) = 0\\)\u3002</p> <p>\u5177\u4f53\u6765\u8bf4\uff0c\\(\\mathbf{t}\\) \u548c \\(\\mathbf{x}_l\\) \u90fd\u662f\u5bf9\u6781\u9762\u5185\u7684\u4e24\u4e2a\u4e0d\u5e73\u884c\uff08\u6211\u4eec\u5047\u5b9a\u8fd9\u4e00\u70b9\u6052\u6210\u7acb\uff09\u7684\u5411\u91cf\uff0c\u90a3\u4e48 \\(\\mathbf{t} \\times \\mathbf{x}_l\\) \u7684\u7ed3\u679c\u5fc5\u7136\u662f\u4e00\u4e2a\u5782\u76f4\u4e8e\u5bf9\u6781\u9762\u7684\u5411\u91cf\u3002\u800c\u8fd9\u4e2a\u5411\u91cf\u5fc5\u7136\u5782\u76f4\u4e8e\u5bf9\u6781\u9762\u4e0a\u4efb\u610f\u4e00\u4e2a\u5411\u91cf\uff0c\u6240\u4ee5\u4e0a\u5f0f\u7ed3\u679c\u4e3a \\(0\\)\u3002\u800c\u5c06\u8fd9\u4e2a\u5f0f\u5b50\u5199\u6210\u77e9\u9635\u5411\u91cf\u8fd0\u7b97\u7684\u5f62\u5f0f\uff0c\u5c31\u662f\uff1a</p> \\[ \\begin{bmatrix}     x_l &amp; y_l &amp; z_l \\end{bmatrix} \\left( \\begin{bmatrix}     0    &amp; -t_z &amp; t_y  \\\\     t_z  &amp; 0    &amp; -t_x \\\\     -t_y &amp; t_x  &amp; 0 \\end{bmatrix} \\begin{bmatrix}     x_l \\\\     y_l \\\\     z_l \\end{bmatrix} \\right) = 0 \\;\\;\\;\\;\\;\\left( 1 \\right) \\] <p>\u7c7b\u4f3c\u7684\uff0c\u6211\u4eec\u5c06 \\(\\mathbf{x}_l = R\\mathbf{x}_r + \\mathbf{t}\\) \u4e5f\u5199\u6210\u77e9\u9635\u548c\u5411\u91cf\u8fd0\u7b97\u7684\u5f62\u5f0f\uff1a</p> \\[ \\begin{bmatrix}     x_l \\\\     y_l \\\\     z_l         \\end{bmatrix} = \\begin{bmatrix}     r_{11} &amp; r_{12} &amp; r_{13} \\\\     r_{21} &amp; r_{22} &amp; r_{23} \\\\     r_{31} &amp; r_{32} &amp; r_{33} \\end{bmatrix} \\begin{bmatrix}     x_r \\\\     y_r \\\\     z_r \\end{bmatrix} + \\begin{bmatrix}     t_x \\\\     t_y \\\\     t_z \\end{bmatrix} \\;\\;\\;\\;\\;\\left( 2 \\right) \\] <p>\u6211\u4eec\u5c06 \\((2)\\) \u5f0f\u5e26\u5165 \\((1)\\) \u5f0f\uff0c\u5f97\u5230\uff1a</p> \\[ \\begin{bmatrix}     x_l &amp; y_l &amp; z_l \\end{bmatrix} \\begin{bmatrix}     0    &amp; -t_z &amp; t_y  \\\\     t_z  &amp; 0    &amp; -t_x \\\\     -t_y &amp; t_x  &amp; 0 \\end{bmatrix} \\left( \\begin{bmatrix}     r_{11} &amp; r_{12} &amp; r_{13} \\\\     r_{21} &amp; r_{22} &amp; r_{23} \\\\     r_{31} &amp; r_{32} &amp; r_{33} \\end{bmatrix} \\begin{bmatrix}     x_r \\\\     y_r \\\\     z_r \\end{bmatrix} + \\begin{bmatrix}     t_x \\\\     t_y \\\\     t_z \\end{bmatrix}     \\right) = 0 \\] <p>\u7a0d\u4f5c\u53d8\u5316\uff08\u628a\u542b \\(t\\) \u7684\u65b9\u9635\u62ff\u5230\u62ec\u53f7\u91cc\u9762\uff09\uff1a</p> \\[ \\begin{bmatrix}     x_l &amp; y_l &amp; z_l \\end{bmatrix} \\left( \\begin{bmatrix}     0    &amp; -t_z &amp; t_y  \\\\     t_z  &amp; 0    &amp; -t_x \\\\     -t_y &amp; t_x  &amp; 0 \\end{bmatrix} \\begin{bmatrix}     r_{11} &amp; r_{12} &amp; r_{13} \\\\     r_{21} &amp; r_{22} &amp; r_{23} \\\\     r_{31} &amp; r_{32} &amp; r_{33} \\end{bmatrix} \\begin{bmatrix}     x_r \\\\     y_r \\\\     z_r \\end{bmatrix} + \\underbrace{     \\begin{bmatrix}         0    &amp; -t_z &amp; t_y  \\\\         t_z  &amp; 0    &amp; -t_x \\\\         -t_y &amp; t_x  &amp; 0     \\end{bmatrix}     \\begin{bmatrix}         t_x \\\\         t_y \\\\         t_z     \\end{bmatrix} }_{\\mathbf{t} \\times \\mathbf{t} = 0} \\right) = 0 \\] <p>\u6211\u4eec\u5f00\u5fc3\u7684\u53d1\u73b0\u91cc\u9762\u51fa\u6765\u4e86\u4e00\u4e2a \\(0\\)\uff0c\u628a\u5b83\u6458\u6389\u4ee5\u540e\u5c31\u53d8\u6210\u4e86\uff1a</p> \\[ \\begin{bmatrix}     x_l &amp; y_l &amp; z_l \\end{bmatrix} \\underbrace{     \\begin{bmatrix}         0    &amp; -t_z &amp; t_y  \\\\         t_z  &amp; 0    &amp; -t_x \\\\         -t_y &amp; t_x  &amp; 0     \\end{bmatrix}     \\begin{bmatrix}         r_{11} &amp; r_{12} &amp; r_{13} \\\\         r_{21} &amp; r_{22} &amp; r_{23} \\\\         r_{31} &amp; r_{32} &amp; r_{33}     \\end{bmatrix} }_{\\text{Essential Matrix E}} \\begin{bmatrix}     x_r \\\\     y_r \\\\     z_r \\end{bmatrix} = 0 \\] <p>\u4e5f\u5c31\u662f\u8bf4\uff0c\u6211\u4eec\u5c06\u6c42\u89e3\u8fd9\u4e2a\u95ee\u9898\uff1a</p> <p>\u5f62\u5f0f \u2460\uff1a\u5bfb\u627e\u4e00\u79cd\u53d8\u6362\uff0c\u4f7f\u5f97\uff1a\\(\\mathbf{x}_l = R\\mathbf{x}_r + \\mathbf{t}\\)\uff0c\u5176\u4e2d \\(\\mathbf{t} = \\overrightarrow{O_r O_l}\\)\uff1b</p> <p>\u5229\u7528\u5bf9\u6781\u51e0\u4f55\u7684\u76f8\u5173\u5185\u5bb9\uff0c\u8f6c\u6362\u4e3a\u4e86\uff1a</p> <p>\u5f62\u5f0f \u2461\uff1a\u6c42\u89e3 \\(E\\) \u4f7f\u5f97 \\(\\mathbf{x}_l^T E \\mathbf{x}_r = 0\\)\uff0c\u5176\u4e2d \\(E = T_{\\times}R\\)\uff0c\u5176\u4e2d \\(T\\) \u662f \\(\\mathbf{t}\\) \u7684\u77e9\u9635\u5f62\u5f0f\uff1b</p> <p>\u7136\u800c\u6211\u4eec\u5e76\u4e0d\u77e5\u9053 \\(\\mathbf{x}_l\\) \u548c \\(\\mathbf{x}_r\\)\uff0c\u6240\u4ee5\u8fd8\u9700\u8981\u8fdb\u4e00\u6b65\u53d8\u5316\u3002</p> \u5f62\u5f0f \u2462 \u63a8\u7406\u8fc7\u7a0b <p>\u6839\u636e\u900f\u89c6\u6295\u5f71\u7684\u76f8\u5173\u5185\u5bb9\uff0c\u6211\u4eec\u53ef\u4ee5\u5f97\u5230\uff1a</p> \\[ \\small \\begin{aligned}     \\text{Left Camera} &amp;&amp; \\text{Right Camera}     \\\\     z_l      \\begin{bmatrix}     u_l \\\\ v_l \\\\ 1     \\end{bmatrix}     &amp; =     \\underbrace{     \\begin{bmatrix}     f_x^{(l)} &amp; 0 &amp; o_x^{(l)} \\\\     0 &amp; f_y^{(l)} &amp; o_y^{(l)} \\\\     0 &amp; 0 &amp; 1     \\end{bmatrix}     }_{K_l}     \\begin{bmatrix}     x_l \\\\ y_l \\\\ z_l     \\end{bmatrix}     &amp;     z_r      \\begin{bmatrix}     u_r \\\\ v_r \\\\ 1     \\end{bmatrix}     &amp;=     \\underbrace{     \\begin{bmatrix}     f_x^{(r)} &amp; 0 &amp; o_x^{(r)} \\\\     0 &amp; f_y^{(r)} &amp; o_y^{(r)} \\\\     0 &amp; 0 &amp; 1     \\end{bmatrix}     }_{K_r}     \\begin{bmatrix}     x_r \\\\ y_r \\\\ z_r     \\end{bmatrix}     \\\\     \\mathbf{x}_l^T &amp;=     \\begin{bmatrix}     u_l &amp; v_l &amp; 1     \\end{bmatrix}     z_l (K_l^{-1})^T     &amp; \\mathbf{x}_r &amp;=      K_r^{-1} z_r     \\begin{bmatrix}     u_r \\\\ v_r \\\\ 1     \\end{bmatrix} \\end{aligned} \\] <p>\u5c06\u4e0a\u5f0f\u5e26\u5165\u5230\u5f62\u5f0f \u2461 \u5f97\u5230\uff1a</p> \\[ \\begin{bmatrix}     x_l &amp; y_l &amp; z_l \\end{bmatrix} \\begin{bmatrix}     e_{11} &amp; e_{12} &amp; e_{13} \\\\     e_{21} &amp; e_{22} &amp; e_{23} \\\\     e_{31} &amp; e_{32} &amp; e_{33} \\end{bmatrix} \\begin{bmatrix}     x_r \\\\     y_r \\\\     z_r \\end{bmatrix} = 0 \\] <p>\u5c31\u53d8\u6210\u4e86\uff1a</p> \\[ \\begin{bmatrix}     u_l &amp; v_l &amp; 1 \\end{bmatrix} z_l (K_l^{-1})^T \\begin{bmatrix}     e_{11} &amp; e_{12} &amp; e_{13} \\\\     e_{21} &amp; e_{22} &amp; e_{23} \\\\     e_{31} &amp; e_{32} &amp; e_{33} \\end{bmatrix} K_r^{-1} z_r \\begin{bmatrix}     u_r \\\\ v_r \\\\ 1 \\end{bmatrix} = 0 \\] <p>\u8fd9\u65f6\uff0c\u6211\u4eec\u53d1\u73b0\uff0c\\(\\mathbf{u}_l\\) \u548c \\(\\mathbf{u}_r\\) \u7ec8\u4e8e\u662f\u6211\u4eec\u5df2\u77e5\u7684\u4e1c\u897f\u4e86\uff0c\u8fd9\u4e0b\u6211\u4eec\u53ef\u4ee5\u6c42\u89e3\u57fa\u672c\u77e9\u9635 \\(F\\)\uff0c\u800c\u7531\u4e8e\u4e24\u4e2a\u76f8\u673a\u7684\u5185\u53c2\u77e9\u9635\u4e5f\u662f\u5df2\u77e5\u7684\uff0c\u6240\u4ee5\u6211\u4eec\u8fd8\u53ef\u4ee5\u5012\u8fc7\u6765\u63a5\u7740\u5f97\u5230\u672c\u5f81\u77e9\u9635 \\(E\\)\uff0c\u6700\u540e\u901a\u8fc7 SV \u5206\u89e3\u5f97\u5230\u6211\u4eec\u60f3\u8981\u7684 \\(R\\) \u548c \\(\\mathbf{t}\\)\u3002</p> <p>\u5177\u4f53\u6765\u8bf4\uff0c\u6c42\u89e3\u57fa\u672c\u77e9\u9635\u3001\u672c\u5f81\u77e9\u9635\u3001\u5750\u6807\u53d8\u6362\u7684\u6b65\u9aa4\u5982\u4e0b\uff1a</p> \u6c42\u89e3\u6b65\u9aa4 <p>\u5bf9\u4e8e\u5173\u952e\u70b9 \\(i\\)\uff0c\u6211\u4eec\u9700\u8981\u6c42\u89e3\uff1a</p> \\[ \\begin{bmatrix}     u_l^{(i)} &amp; v_l^{(i)} &amp; 1 \\end{bmatrix} \\begin{bmatrix}     f_{11} &amp; f_{12} &amp; f_{13} \\\\     f_{21} &amp; f_{22} &amp; f_{23} \\\\     f_{31} &amp; f_{32} &amp; f_{33} \\end{bmatrix} \\begin{bmatrix}     u_r^{(i)} \\\\ v_r^{(i)} \\\\ 1 \\end{bmatrix} = 0 \\] <p>\u5c06\u5176\u5c55\u5f00\uff1a</p> \\[ \\left( f_{11} u_r^{(i)} + f_{12} v_r^{(i)} + f_13 \\right) u_l^{(i)} + \\left( f_{21} u_r^{(i)} + f_{22} v_r^{(i)} + f_23 \\right) v_l^{(i)} + f_{31} u_r^{(i)} + f_{32} v_r^{(i)} + f_33 = 0. \\] <p>\u63a5\u4e0b\u6765\u5c06\u6240\u6709\u7684 \\(m\\) \u7ec4\u65b9\u7a0b\u5408\u518d\u540c\u4e00\u4e2a\u77e9\u9635\u91cc\uff08\u6211\u4eec\u81f3\u5c11\u9700\u8981\u989d\u5916\u7684 8 \u4e2a\u65b9\u7a0b\uff0c\u4e4b\u540e\u4f1a\u8bf4\uff09\uff1a</p> \\[ \\underbrace{     \\begin{bmatrix}         u_l^{(1)}u_r^{(1)} &amp; u_l^{(1)}v_r^{(1)} &amp; u_l^{(1)} &amp; v_l^{(1)}u_r^{(1)} &amp; v_l^{(1)}v_r^{(1)} &amp; v_l^{(1)} &amp; u_r^{(1)} &amp; v_r^{(1)} &amp; 1 \\\\         \\vdots &amp; \\vdots &amp; \\vdots &amp; \\vdots &amp; \\vdots &amp; \\vdots &amp; \\vdots &amp; \\vdots &amp; \\vdots \\\\          u_l^{(i)}u_r^{(i)} &amp; u_l^{(i)}v_r^{(i)} &amp; u_l^{(i)} &amp; v_l^{(i)}u_r^{(i)} &amp; v_l^{(i)}v_r^{(i)} &amp; v_l^{(i)} &amp; u_r^{(i)} &amp; v_r^{(i)} &amp; 1 \\\\         \\vdots &amp; \\vdots &amp; \\vdots &amp; \\vdots &amp; \\vdots &amp; \\vdots &amp; \\vdots &amp; \\vdots &amp; \\vdots \\\\          u_l^{(m)}u_r^{(m)} &amp; u_l^{(m)}v_r^{(m)} &amp; u_l^{(m)} &amp; v_l^{(m)}u_r^{(m)} &amp; v_l^{(m)}v_r^{(m)} &amp; v_l^{(m)} &amp; u_r^{(m)} &amp; v_r^{(m)} &amp; 1 \\\\     \\end{bmatrix} }_{A: \\text{ Known }} \\underbrace{     \\begin{bmatrix}         f_{11} \\\\ f_{12} \\\\ f_{13} \\\\         f_{21} \\\\ f_{22} \\\\ f_{23} \\\\         f_{31} \\\\ f_{32} \\\\ f_{33} \\\\     \\end{bmatrix} }_{\\mathbf{f}: \\text{ Unknown }} = \\begin{bmatrix}     0 \\\\ 0 \\\\ 0 \\\\ 0 \\\\ 0 \\\\ 0 \\\\ 0 \\\\ 0 \\\\ 0 \\end{bmatrix} \\\\ \\text{i.e.} \\;\\;\\;\\; A\\mathbf{f}=0 \\] <p>\u5f53\u7136\uff0c\u50cf\u4e4b\u524d\u4e00\u6837\uff0c\u7531\u4e8e\u8fd9\u4e2a\u65b9\u7a0b\u53ef\u4ee5\u89e3\u51fa \\(k\\mathbf{f}, \\forall k\\in \\text{Z}\\)\uff0c\u6240\u4ee5\u6211\u4eec\u9700\u8981\u7ed9 \\(\\mathbf{f}\\) \u4e00\u4e2a\u7ea6\u675f\uff0c\u5728\u8fd9\u91cc\u6211\u4eec\u53d6 \\(||\\mathbf{f}||^2 = 1\\)\uff0c\u4e8e\u662f\u95ee\u9898\u5c31\u53c8\u53d8\u6210\u4e86\uff1a</p> \\[ \\mathop{minimize} \\limits_{\\mathbf{f}} ||A\\mathbf{f}||^2 \\text{ such that } ||\\mathbf{f}||^2 = 1 \\] <p>\u4e3a\u4e86\u6c42\u89e3 \\(F\\) \u4e2d\u7684 9 \u4e2a\u672a\u77e5\u6570\uff0c\u6211\u4eec\u5df2\u7ecf\u6709\u4e00\u4e2a\u786e\u5b9a\u7684\u7ea6\u675f\u65b9\u7a0b\u662f \\(||\\mathbf{f}||^2 = 1\\)\uff0c\u6240\u4ee5\u8fd8\u9700\u8981\u989d\u5916 8 \u4e2a\u65b9\u7a0b\u3002</p> <p>\u6c42\u89e3\u5f97\u5230 \\(F\\) \u4ee5\u540e\uff0c\u6839\u636e \\(E = K_l^T F K_r\\) \u5f97\u5230 \\(E\\)\u3002</p> <p>\u524d\u9762\u4e5f\u5df2\u7ecf\u8bf4\u8fc7\uff0c\u5bf9 \\(E\\) \u8fdb\u884c SV \u5206\u89e3\u5c31\u53ef\u4ee5\u5f97\u5230 \\(R\\) \u548c \\(T_{\\times}\\)\uff0c\u5bf9 \\(T_{\\times}\\) \u91cd\u6392\u5217\u5c31\u5f97\u5230\u4e86 \\(\\mathbf{t}\\)\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec07/#\u672c\u5f81\u77e9\u9635","title":"\u672c\u5f81\u77e9\u9635","text":"<p>\u66f4\u8fdb\u4e00\u6b65\u5316\u7b80\uff0c\u6211\u4eec\u53ef\u4ee5\u628a\u4e2d\u95f4\u4e24\u4e2a\u77e9\u9635\u5408\u8d77\u6765\uff0c\u5f97\u5230\u672c\u5f81\u77e9\u9635(Essential Matrix)\\(E\\)\uff1a</p> \\[ E=T_{\\times}R= \\begin{bmatrix}     e_{11} &amp; e_{12} &amp; e_{13} \\\\     e_{21} &amp; e_{22} &amp; e_{23} \\\\     e_{31} &amp; e_{32} &amp; e_{33} \\end{bmatrix} \\] <p>\u4e8e\u662f\u6211\u4eec\u5c31\u5f97\u5230\uff1a</p> \\[ \\begin{bmatrix}     x_l &amp; y_l &amp; z_l \\end{bmatrix} \\begin{bmatrix}     e_{11} &amp; e_{12} &amp; e_{13} \\\\     e_{21} &amp; e_{22} &amp; e_{23} \\\\     e_{31} &amp; e_{32} &amp; e_{33} \\end{bmatrix} \\begin{bmatrix}     x_r \\\\     y_r \\\\     z_r \\end{bmatrix} = 0 \\;\\;\\;\\text{i.e.} \\;\\;\\; \\mathbf{x}_l^T E \\mathbf{x}_r = 0 \\] <p>\u672c\u5f81\u77e9\u9635\u7684\u6027\u8d28</p> <p>\u7531\u4e8e Essential Matrix \u7684\u5b9a\u4e49\u5177\u6709\u5982\u4e0b\u7279\u5f81\uff1a</p> <p></p> <p>\\(T_{\\times}\\) \u53cd\u5bf9\u79f0(Skew-Symmetric)\uff0c\\(R\\) \u6b63\u4ea4(Orthonormal)\u3002</p> <p>\u6240\u4ee5\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528\u5947\u5f02\u503c\u5206\u89e3(Singular Value Decomposition)\u6216\u8005\u8bf4 SV \u5206\u89e3\u6765\u53bb\u8026\u5408\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec07/#\u57fa\u672c\u77e9\u9635","title":"\u57fa\u672c\u77e9\u9635","text":"<p>\u6211\u4eec\u53ef\u4ee5\u5c06\u5e38\u6570 \\(z_l\\) \u548c \\(z_r\\) \u7ea6\u6389\uff0c\u5e76\u4e14\u5408\u5e76\u4e2d\u95f4\u7684\u4e09\u4e2a\u77e9\u9635\uff0c\u5f97\u5230\uff1a</p> \\[ \\begin{bmatrix}     u_l &amp; v_l &amp; 1 \\end{bmatrix} \\underbrace{     (K_l^{-1})^T     \\begin{bmatrix}         e_{11} &amp; e_{12} &amp; e_{13} \\\\         e_{21} &amp; e_{22} &amp; e_{23} \\\\         e_{31} &amp; e_{32} &amp; e_{33}     \\end{bmatrix}     K_r^{-1} }_{\\text{Fundamental Matrix F}} \\begin{bmatrix}     u_r \\\\ v_r \\\\ 1 \\end{bmatrix} = 0 \\] <p>\u4e8e\u662f\u5f97\u5230\u4e86\u57fa\u672c\u77e9\u9635(Fundamental Matrix)\\(F\\)\uff1a</p> \\[ F = (K_l^{-1})^T E K_r^{-1}    = (K_l^{-1})^T      \\begin{bmatrix}         e_{11} &amp; e_{12} &amp; e_{13} \\\\         e_{21} &amp; e_{22} &amp; e_{23} \\\\         e_{31} &amp; e_{32} &amp; e_{33}     \\end{bmatrix}     K_r^{-1}   = \\begin{bmatrix}         f_{11} &amp; f_{12} &amp; f_{13} \\\\         f_{21} &amp; f_{22} &amp; f_{23} \\\\         f_{31} &amp; f_{32} &amp; f_{33}     \\end{bmatrix} \\] <p>\u8fd9\u5c31\u662f\u6211\u4eec\u7684\u5f62\u5f0f \u2462\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec07/#\u4e09\u89d2\u6d4b\u91cf","title":"\u4e09\u89d2\u6d4b\u91cf","text":"<p>\u6211\u4eec\u77e5\u9053\uff0c\u5982\u679c\u5047\u8bbe\u6570\u636e\u90fd\u662f\u51c6\u786e\u7684\uff0c\u90a3\u4e48 \\(O_l X_l\\) \u548c \\(O_r X_r\\) \u5e94\u5f53\u76f8\u4ea4\u4e8e\u7a7a\u95f4\u70b9 \\(X\\)\u3002\u800c\u4e09\u89d2\u6d4b\u91cf\u63cf\u8ff0\u7684\u5c31\u662f\u5982\u4f55\u901a\u8fc7\u8fd9\u6837\u4e00\u4e2a\u8fc7\u7a0b\u5f97\u5230\u7a7a\u95f4\u70b9 \\(X\\)\u3002</p> <p>\u6211\u4eec\u5728 \u6781\u7ebf\u7ea6\u675f \u91cc\u5df2\u7ecf\u77e5\u9053\u4e86 \\(\\mathbf{x}_l\\) \u548c \\(\\mathbf{x}_r\\) \u7684\u53d8\u6362\u5173\u7cfb\uff0c\u4e5f\u5c31\u662f\u8bf4\u6211\u4eec\u73b0\u5728\u5df2\u7ecf\u6709\u4e86 \\(O_l X_l\\) \u548c \\(O_r X_r\\) \u7684\u65b9\u7a0b\u4e86\u3002\u90a3\u4e48\u5e94\u5f53\u80fd\u591f\u89e3\u51fa\u8fd9\u4e2a \\(X\\)\uff0c\u4e0d\u8fc7\u7531\u4e8e\u5b9e\u9645\u6570\u636e\u6709\u8bef\u5dee\uff0c\u6240\u4ee5\u6211\u4eec\u53ef\u80fd\u53ea\u80fd\u901a\u8fc7\u4f18\u5316\u7684\u65b9\u6cd5\u5f97\u5230\u8fd1\u4f3c\u89e3\u3002</p> <p>\u5177\u4f53\u7684\u63a8\u7406\u6b65\u9aa4\u5982\u4e0b\uff1a</p> \u6c42\u89e3\u6b65\u9aa4 <p>\u9996\u5148\u6211\u4eec\u4f7f\u7528\u9f50\u6b21\u5750\u6807\u6539\u5199\u53d8\u6362\u65b9\u7a0b\uff0c\u5e76\u6700\u7ec8\u5199\u6210\u5173\u4e8e \\(\\mathbf{u}\\) \u7684\u5f62\u5f0f   \\begin{aligned}     \\text{Left Camera}     \\\\     \\because     \\begin{bmatrix}         u_l \\\\ v_l \\\\ 1     \\end{bmatrix}     &amp;=     \\begin{bmatrix}         f_x^{(l)} &amp; 0 &amp; o_x^{(l)} &amp; 0 \\\\         0 &amp; f_y^{(l)} &amp; o_y^{(l)} &amp; 0 \\\\         0 &amp; 0 &amp; 1 &amp; 0     \\end{bmatrix}     \\begin{bmatrix}         x_l \\\\ y_l \\\\ z_l \\\\ 1     \\end{bmatrix}     ,\\ \\      \\begin{bmatrix}         x_l \\\\ y_l \\\\ z_l \\\\ 1     \\end{bmatrix}     =     \\begin{bmatrix}         r_{11} &amp; r_{12} &amp; r_{13} &amp; t_x \\\\         r_{21} &amp; r_{22} &amp; r_{23} &amp; t_y \\\\         r_{31} &amp; r_{32} &amp; r_{33} &amp; t_z \\\\         0 &amp; 0 &amp; 0 &amp; 1     \\end{bmatrix}     \\begin{bmatrix}         x_r \\\\ y_r \\\\ z_r \\\\ 1     \\end{bmatrix}     \\\\     \\therefore     \\begin{bmatrix}         u_l \\\\ v_l \\\\ 1     \\end{bmatrix}     &amp;=     \\begin{bmatrix}         f_x^{(l)} &amp; 0 &amp; o_x^{(l)} &amp; 0 \\\\         0 &amp; f_y^{(l)} &amp; o_y^{(l)} &amp; 0 \\\\         0 &amp; 0 &amp; 1 &amp; 0     \\end{bmatrix}     \\begin{bmatrix}         r_{11} &amp; r_{12} &amp; r_{13} &amp; t_x \\\\         r_{21} &amp; r_{22} &amp; r_{23} &amp; t_y \\\\         r_{31} &amp; r_{32} &amp; r_{33} &amp; t_z \\\\         0 &amp; 0 &amp; 0 &amp; 1     \\end{bmatrix}     \\begin{bmatrix}         x_r \\\\ y_r \\\\ z_r \\\\ 1     \\end{bmatrix}     \\\\     \\text{i.e. } \\mathbf{\\tilde u}_l &amp;=      P_l \\mathbf{\\tilde x}_r     \\\\     \\text{Right Camera}     \\\\     \\begin{bmatrix}         u_r \\\\ v_r \\\\ 1     \\end{bmatrix}     &amp;=     \\begin{bmatrix}         f_x^{(r)} &amp; 0 &amp; o_x^{(r)} &amp; 0 \\\\         0 &amp; f_y^{(r)} &amp; o_y^{(r)} &amp; 0 \\\\         0 &amp; 0 &amp; 1 &amp; 0     \\end{bmatrix}     \\begin{bmatrix}         x_r \\\\ y_r \\\\ z_r \\\\ 1     \\end{bmatrix}     \\\\     \\text{i.e. } \\mathbf{\\tilde u}_r &amp;=      M_{int_r} \\mathbf{\\tilde x}_r \\end{aligned}  </p> <p>\u7a0d\u4f5c\u603b\u7ed3\uff0c\u5c31\u662f\u5f97\u5230\u4e86\u4e0b\u9762\u8fd9\u4e24\u4e2a\u5173\u7cfb\uff1a</p> \\[ \\mathbf{\\tilde u}_l = P_l \\mathbf{\\tilde x}_r \\\\ \\begin{bmatrix}     u_r \\\\ v_r \\\\ 1 \\end{bmatrix} = \\begin{bmatrix}     m_{11} &amp; m_{12} &amp; m_{13} &amp; m_{14} \\\\     m_{21} &amp; m_{22} &amp; m_{23} &amp; m_{24} \\\\     m_{31} &amp; m_{32} &amp; m_{33} &amp; m_{34} \\\\ \\end{bmatrix} \\begin{bmatrix}     x_r \\\\ y_r \\\\ z_r \\\\ 1 \\end{bmatrix} \\\\ \\\\ \\mathbf{\\tilde u}_l = M_{int_r} \\mathbf{\\tilde x}_r \\\\ \\begin{bmatrix} u_l \\\\ v_l \\\\ 1 \\end{bmatrix} = \\begin{bmatrix} p_{11} &amp; p_{12} &amp; p_{13} &amp; p_{14} \\\\ p_{21} &amp; p_{22} &amp; p_{23} &amp; p_{24} \\\\ p_{31} &amp; p_{32} &amp; p_{33} &amp; p_{34} \\\\ \\end{bmatrix} \\begin{bmatrix} x_r \\\\ y_r \\\\ z_r \\\\ 1 \\end{bmatrix} \\] <p>\u6211\u4eec\u53d1\u73b0\uff0c\u9664\u4e86 \\(\\mathbf{x}_r\\) \u7684\u90e8\u5206\u90fd\u662f\u5df2\u77e5\u7684\uff0c\u6b64\u65f6\u6211\u4eec\u5c31\u53ef\u4ee5\u300c\u8054\u7acb\u300d\u8fd9\u4e24\u4e2a\u65b9\u7a0b\uff0c\u5c06\u4ed6\u4eec\u91cd\u6392\u5217\u4e3a\u5982\u4e0b\u5f62\u5f0f\uff1a</p> \\[ \\underbrace{ \\begin{bmatrix}     u_r m_{31} - m_{11} &amp; u_r m_{32} - m_{12} &amp; u_r m_{33} - m_{13} \\\\      v_r m_{31} - m_{21} &amp; v_r m_{32} - m_{22} &amp; v_r m_{33} - m_{23} \\\\      u_l p_{31} - p_{11} &amp; u_l p_{32} - p_{12} &amp; u_l p_{33} - p_{13} \\\\       v_l p_{31} - p_{21} &amp; v_l p_{32} - p_{22} &amp; v_l p_{33} - p_{23} \\end{bmatrix} }_{A_{4\\times 3}} \\underbrace{ \\begin{bmatrix}     x_r \\\\ y_r \\\\ z_r \\end{bmatrix} }_{\\mathbf{x}_r} = \\underbrace{ \\begin{bmatrix}     m_{14} - m_{34} \\\\     m_{24} - m_{34} \\\\       p_{14} - p_{34} \\\\      p_{24} - p_{34} \\end{bmatrix} }_{\\mathbf{b}} \\] <p>\u6211\u4eec\u5df2\u77e5 \\(A_{4 \\times 3}\\) \u548c \\(\\mathbf{b}\\)\uff0c\u9700\u8981\u6c42 \\(\\mathbf{x}_r\\)\u3002</p> <p>\u6211\u4eec\u4e4b\u524d\u5df2\u7ecf\u63d0\u5230\uff0c\u7531\u4e8e\u5b9e\u9645\u6570\u636e\u5b58\u5728\u8bef\u5dee\uff0c\u6240\u4ee5\u6211\u4eec\u6ca1\u53d1\u76f4\u63a5\u6c42\u5176\u89e3\u6790\u89e3\uff0c\u800c\u662f\u53ef\u4ee5\u4f7f\u7528\u6700\u5c0f\u4e8c\u4e58\u7684\u7ed3\u8bba\uff0c\u5f97\u5230\uff1a</p> \\[ \\mathbf{x}_r = (A^TA)^{-1}A^T\\mathbf{b} \\] <p>\u8fd8\u6709\u4e00\u79cd\u6539\u8fdb\uff0c\u5c31\u662f\u5c06\u5b83\u8f6c\u5316\u6210\u6700\u5c0f\u5316\u518d\u6295\u5f71\u8bef\u5dee(Reprojection Error)\u7684\u4f18\u5316\u95ee\u9898\u3002</p> <p>\u6362\u53e5\u8bdd\u6765\u8bf4\uff0c\u5c31\u662f\u6c42\u4e00\u4e2a \\(X\\) \u4f7f\u5f97\u5b83\u5728\u4e24\u4e2a\u6210\u50cf\u5e73\u9762\u4e0a\u7684\u6295\u5f71\u548c\u5b9e\u9645\u7684\u6295\u5f71\u4e4b\u95f4\u7684\u8bef\u5dee\u6700\u5c0f\u3002</p> <p></p> <p>\u5b9a\u4e49\u518d\u6295\u5f71\u8bef\u5dee\u4e3a\uff1a</p> \\[ cost(P) = dist(\\mathbf{u}_l, \\cap{\\mathbf{u}_l})^2 + dist(\\mathbf{u}_r, \\cap{\\mathbf{u}_r})^2 \\]"},{"location":"cour_note/D2QD_Intro2CV/Lec07/#\u5177\u4f53\u6b65\u9aa4","title":"\u5177\u4f53\u6b65\u9aa4","text":"<p>\u524d\u63d0</p> <p>\u4e24\u4e2a\u76f8\u673a\u7684\u5185\u53c2\u77e9\u9635\\(K\\) \u5df2\u77e5\u3002</p> <p>\u8fd9\u610f\u5473\u7740\u6211\u4eec\u53ef\u4ee5\u6839\u636e\u8fd9\u4e9b\u53c2\u6570\u5c06\u76f8\u673a\u6210\u50cf\u53ef\u89c6\u5316\uff0c\u5982\u4e0b\u56fe\u3002</p> <p>\u5176\u4e2d\u4e0b\u6807\u4e3a \\(l\\) \u7684\u8868\u793a\u5de6\u4fa7\u76f8\u673a\u7684\u76f8\u5173\u5173\u952e\u70b9\uff0c\u4e0b\u6807\u4e3a \\(r\\) \u7684\u8868\u793a\u53f3\u4fa7\u76f8\u673a\u7684\u76f8\u5173\u5173\u952e\u70b9\u3002</p> <p></p> <p>\u6b65\u9aa4\u4e00</p> <p>\u5bf9\u4e24\u5f20\u56fe\u7247\u8fdb\u884c \u5173\u952e\u70b9\u5339\u914d\uff0c\u627e\u5230\u81f3\u5c11 8 \u5bf9\u5339\u914d\u7279\u5f81\u3002</p> <p>\u300c\u4e3a\u4ec0\u4e48\u9700\u8981 8 \u5bf9\u300d\u8fd9\u4e2a\u95ee\u9898\u6211\u4eec\u5728 #\u6781\u7ebf\u7ea6\u675f/\u6c42\u89e3\u8fc7\u7a0b \u4e2d\u5df2\u7ecf\u8bf4\u660e\u3002</p> <p></p> <p>\u6b65\u9aa4\u4e8c</p> <p>\u6309\u7167 #\u6781\u7ebf\u7ea6\u675f/\u6c42\u89e3\u8fc7\u7a0b \u63d0\u5230\u7684\u6b65\u9aa4\uff0c\u6c42\u89e3\u4e24\u4e2a\u76f8\u673a\u5750\u6807\u7684\u53d8\u6362\u53c2\u6570 \\(R\\) \u548c \\(\\mathbf{t}\\)\u3002</p> <p>\u6b65\u9aa4\u4e09</p> <p>\u63a5\u4e0b\u6765\u5bf9\u4e8e\u6bcf\u4e00\u5bf9\u5339\u914d\u7684\u5173\u952e\u70b9\uff0c\u6309\u7167 #\u4e09\u89d2\u6d4b\u91cf \u63d0\u5230\u7684\u65b9\u6cd5\uff0c\u6c42\u89e3\u7a7a\u95f4\u70b9 \\(X_i\\)\u3002</p> <p>\u4e8e\u662f\u6211\u4eec\u5c31\u5f97\u5230\u4e86\u6240\u6709\u5339\u914d\u7684\u5173\u952e\u70b9\u8ba1\u7b97\u5f97\u5230\u7684\u7a7a\u95f4\u70b9\uff0c\u6700\u7ec8\u5f97\u5230\u4e00\u4efd\u7a00\u758f\u7684\u7a7a\u95f4\u70b9\u4e91\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec07/#\u591a\u76ee\u4e09\u7ef4\u91cd\u5efa","title":"\u591a\u76ee\u4e09\u7ef4\u91cd\u5efa","text":"<p>Sequential SfM\uff1a</p> <ol> <li>\u4ece\u5176\u4e2d\u4e24\u5f20\u5f00\u59cb\uff0c\u5bf9\u573a\u666f\u8fdb\u884c\u91cd\u5efa</li> <li>\u4e4b\u540e\u4e0d\u65ad\u62ff\u51fa\u65b0\u7684\u56fe\u50cf\uff0c\u6839\u636e\u5df2\u77e5\u8ba1\u7b97 camera pose\uff0c\u518d\u8fdb\u4e00\u6b65\u4f18\u5316\u4e4b\u524d\u91cd\u5efa\u51fa\u6765\u7684 3D \u70b9\uff0c\u4ee5\u53ca\u589e\u52a0\u4e00\u4e9b\u65b0\u7684\u70b9</li> <li>\u4f7f\u7528\u96c6\u675f\u4f18\u5316\u8fdb\u4e00\u6b65\u4f18\u5316\u548c\u8c03\u6574</li> </ol>"},{"location":"cour_note/D2QD_Intro2CV/Lec07/#\u96c6\u675f\u4f18\u5316","title":"\u96c6\u675f\u4f18\u5316","text":"<p>\u96c6\u675f\u4f18\u5316(Bundle Adjustment)\u4e5f\u5c31\u662f\u5728\u591a\u76ee\u60c5\u51b5\u4e0b\uff0c\u5bf9\u4e8e\u6240\u6709\u70b9\u7684 \u518d\u6295\u5f71\u8bef\u5dee \u4f18\u5316\u95ee\u9898\uff1a</p> <p></p> \\[ \\mathop{minimize} \\limits_\\mathbf{P} E(P_{proj}, \\mathbf{P}) = \\sum^m_{i=1}\\sum^n_{j=1} dist(u_j^{(i)}, P_{proj}^{(i)}\\mathbf{P}_j)^2 \\] <p>\u5176\u6c42\u89e3\u53ef\u4ee5\u4f7f\u7528 LM algorithm\u3002</p> <p>A modern SfM system: COLMAP</p> <ul> <li>GitHub Repo: https://github.com/colmap/colmap</li> </ul> <p>COLMAP is a general-purpose Structure-from-Motion (SfM) and Multi-View Stereo (MVS) pipeline with a graphical and command-line interface. It offers a wide range of features for reconstruction of ordered and unordered image collections. </p> <p></p>"},{"location":"cour_note/D2QD_Intro2CV/Lec08/","title":"Lecture 8 | Depth Estimation &amp; 3D Reconstruction","text":"<p> \u7ea6 5007 \u4e2a\u5b57  6 \u884c\u4ee3\u7801  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 17 \u5206\u949f</p> <p>\u6ce8\u610f</p> <p>\u672c\u6587\u5c1a\u672a\u5b8c\u5168\u6574\u7406\u597d\uff01</p> <p>\u5f15\u5165</p> <p>\u5728 \u4e0a\u4e00\u7ae0 \u4e2d\uff0c\u6211\u4eec\u5df2\u7ecf\u4ecb\u7ecd\u4e86\u5982\u4f55\u91cd\u5efa\u5f97\u5230\u5173\u952e\u70b9\u7684\u70b9\u4e91\uff0c\u4f46\u662f\u6b64\u65f6\u6211\u4eec\u5f97\u5230\u7684\u53ea\u662f\u4e00\u4e2a\u7a00\u758f\u7684\u70b9\u4e91\uff0c\u800c\u672c\u7ae0\u9700\u8981\u89e3\u51b3\u7684\u95ee\u9898\u5c31\u662f\u5982\u4f55\u201c\u7a20\u5bc6\u201d\u5730\u8fdb\u884c\u91cd\u5efa\u3002</p> <p>\u800c\u5728\u7a20\u5bc6\u91cd\u5efa\u8fc7\u7a0b\u4e2d\uff0c\u6211\u4eec\u4e0d\u80fd\u5355\u5355\u7740\u773c\u4e8e\u5173\u952e\u70b9\uff0c\u800c\u662f\u8981\u5e7f\u6cdb\u5730\u9762\u5411\u56fe\u50cf\u4e2d\u7684\u6240\u6709\u50cf\u7d20\uff0c\u800c\u5176\u4e2d\u6700\u91cd\u8981\u7684\u4e00\u4e2a\u6280\u672f\u5c31\u662f\u6df1\u5ea6\u4f30\u8ba1(Depth Estimation)\u3002</p> <p>\u300c\u6df1\u5ea6\u300d\u8fd9\u4e2a\u6982\u5ff5\u548c\u5b83\u7684\u5b57\u9762\u610f\u601d\u51e0\u4e4e\u4e00\u6837\uff0c\u800c\u5728\u300c\u6df1\u5ea6\u4f30\u8ba1\u300d\u4e2d\uff0c\u6211\u4eec\u9700\u8981\u505a\u7684\u662f\u5bf9\u4e8e\u7ed9\u5b9a\u7684\u56fe\u50cf\uff0c\u6807\u8bb0\u6bcf\u4e00\u4e2a\u50cf\u7d20\u7684\u6df1\u5ea6\u3002\u800c\u5c06\u5176\u53ef\u89c6\u5316\uff0c\u5c31\u662f\u6df1\u5ea6\u56fe\u3002</p> <p></p> <p>\u53ea\u4e0d\u8fc7\u6709\u65f6\u5019\u6df1\u5ea6\u6307\u7684\u662f\u7a7a\u95f4\u70b9\u5230\u76f8\u673a\u4e2d\u95f4\u6216\u8005\u76f8\u673a\u5e73\u9762\u7684\u8ddd\u79bb\uff0c\u4e5f\u6709\u7684\u65f6\u5019\u6307\u7684\u662f\u67d0\u4e2a\u7a7a\u95f4\u5750\u6807\u8f74\u5411\u7684\u6df1\u5ea6\uff0c\u5177\u4f53\u5e94\u5f53\u6839\u636e\u5b9e\u9645\u60c5\u51b5\u6765\u3002</p> <p>\u6309\u7167\u6df1\u5ea6\u611f\u77e5\u7684\u624b\u6bb5\u5206\u7c7b\uff0c\u6709\u4e3b\u52a8\u6df1\u5ea6\u63a2\u6d4b\u65b9\u6cd5(Active depth sensing)\u548c\u88ab\u52a8\u6df1\u5ea6\u63a2\u6d4b\u65b9\u6cd5(Passive depth sensing)\u4e24\u79cd\uff0c\u5176\u4e2d\u6211\u4eec\u5c06\u8981\u5c55\u5f00\u7684\u89c6\u89c9\u65b9\u6cd5\u90fd\u662f\u88ab\u52a8\u63a2\u6d4b\u65b9\u6cd5\u3002</p> <p>\u4e3b\u52a8\u63a2\u6d4b\u65b9\u6cd5 / \u975e\u89c6\u89c9\u65b9\u6cd5</p> <ul> <li>LiDAR</li> <li>Structured light</li> <li>Active stereo</li> </ul> <p>\u88ab\u52a8\u63a2\u6d4b\u65b9\u6cd5 / \u89c6\u89c9\u65b9\u6cd5</p> <ul> <li>Stereo</li> <li>Multi-view stereo</li> <li>Monocular</li> </ul> <p>\u903b\u8f91\u94fe\uff1a</p> <p>(\u53cc\u76ee\u89c6\u89c9 -&gt; \u6df1\u5ea6\u611f\u77e5) =&gt; ((\u53cc\u89c6\u89d2\u5339\u914d\u70b9 + \u89c6\u5dee -&gt; \u6df1\u5ea6) + (\u5bf9\u6240\u6709\u50cf\u7d20\u8fdb\u884c\u5339\u914d)) =&gt; \u6781\u7ebf\u4e0a\u5bfb\u627e\u5339\u914d\u70b9</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec08/#\u7acb\u4f53\u89c6\u89c9","title":"\u7acb\u4f53\u89c6\u89c9","text":"<p>\u6211\u4eec\u5df2\u7ecf\u6709\u4e86\u7a00\u758f\u91cd\u5efa\u7684\u65b9\u6cd5\uff0c\u60f3\u8981\u5f97\u5230\u7a20\u5bc6\u91cd\u5efa\u7684\u65b9\u6cd5\uff0c\u4e00\u4e2a\u6700\u66b4\u529b\u7684\u65b9\u6cd5\u5c31\u662f\u5c1d\u8bd5\u7740\u53bb\u5339\u914d\u6240\u6709\u50cf\u7d20\uff0c\u5f53\u7136\u8fd9\u770b\u8d77\u6765\u65f6\u95f4\u5f00\u9500\u975e\u5e38\u5927\u3002\u4f46\u662f\u6bcb\u5eb8\u7f6e\u7591\u7684\u662f\uff0c\u5728\u76ee\u524d\u8fd8\u6ca1\u6709\u4ecb\u5165\u4eba\u5de5\u667a\u80fd\u6280\u672f\u7684\u60c5\u51b5\u4e0b\uff0c\u6211\u4eec\u4ecd\u7136\u9700\u8981\u50cf\u7d20\u7684\u5339\u914d\u5173\u7cfb\u3002</p> <p>\u4ee5\u53ca\u8fd8\u6709\u4e00\u4e2a\u9700\u8981\u89e3\u51b3\u7684\u95ee\u9898\u5c31\u662f\uff0c\u5982\u4f55\u5f97\u5230\u5339\u914d\u70b9\u7684\u6df1\u5ea6\u4fe1\u606f\u3002</p> <p>\u6240\u4ee5\u603b\u7ed3\u4e0b\u6765\uff0c\u6709\u4e24\u4e2a\u95ee\u9898\u9700\u8981\u89e3\u51b3\uff1a</p> <ul> <li> \u5982\u4f55\u9ad8\u6548\u5730\u5f97\u5230\u5339\u914d\u5173\u7cfb\uff1b</li> <li> \u5982\u4f55\u6839\u636e\u5339\u914d\u70b9\u8ba1\u7b97\u70b9\u6df1\u5ea6\uff1b</li> </ul> <p>\u7531\u4e8e\u5339\u914d\u4e2d\u4f1a\u6709\u90e8\u5206\u4f18\u5316\u5185\u5bb9\u6d89\u53ca\u5230\u6df1\u5ea6\u8ba1\u7b97\u7684\u5185\u5bb9\uff0c\u6240\u4ee5\u6211\u60f3\u5148\u4ece\u6df1\u5ea6\u8ba1\u7b97\u5f00\u59cb\u8bb2\uff0c\u4e5f\u5c31\u662f\u4ece\u89c6\u5dee\u5f00\u59cb\u8bb2\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec08/#\u89c6\u5dee","title":"\u89c6\u5dee","text":"<p>\u9996\u5148\uff0c\u6211\u4eec\u90fd\u77e5\u9053\u4eba\u7684\u53cc\u773c\u8d4b\u4e88\u4e86\u4eba\u7c7b\u89c6\u89c9\u4e0a\u6df1\u5ea6\u611f\u77e5\u7684\u80fd\u529b\uff0c\u4e5f\u5c31\u662f\u7acb\u4f53\u89c6\u89c9(stereo vision)\u3002\u4e00\u4e2a\u6bd4\u8f83\u5bb6\u55bb\u6237\u6653\u7684\u5b9e\u9a8c\u5c31\u662f\u5355\u773c\u7a7f\u9488\u4f1a\u53d8\u5f97\u5341\u5206\u56f0\u96be\u3002</p> <p>\u5728\u5355\u76ee\u89c6\u89c9\u4e0b\uff0c\u4f53\u73b0\u8fdc\u8fd1\u6700\u7b80\u5355\u7684\u539f\u7406\u63cf\u8ff0\u5c31\u662f\u300c\u8fd1\u5927\u8fdc\u5c0f\u300d\uff0c\u800c\u5728\u52a8\u6001\u7684\u60c5\u51b5\u4e0b\uff0c\u8fd9\u4e5f\u4f53\u73b0\u5728\u79fb\u52a8\u76f8\u540c\u7684\u8ddd\u79bb\uff0c\u8fd1\u5904\u7684\u7269\u4f53\u79fb\u52a8\u66f4\u660e\u663e\uff0c\u800c\u8fdc\u5904\u7684\u66f4\u4e0d\u660e\u663e\u3002\u7136\u800c\u8fd9\u4e2a\u4fe1\u606f\u548c\u5355\u7eaf\u7684\u201c\u5927\u5c0f\u201d\u4fe1\u606f\u662f\u53ef\u4ee5\u6df7\u6dc6\u7684\uff0c\u6216\u8005\u8bf4\u5728\u201c\u5927\u5c0f\u201d\u53d8\u5316\u4e0d\u660e\u663e\u7684\u60c5\u51b5\u4e0b\uff0c\u8fd9\u4e2a\u4fe1\u606f\u662f\u5f88\u96be\u88ab\u8bc6\u522b\u51fa\u6765\u7684\u3002</p> <p>\u800c\u5728\u53cc\u76ee\u89c6\u89c9\u4e0b\uff0c\u6211\u4eec\u6709\u6709\u4e00\u4e2a\u66f4\u8fd1\u4e00\u6b65\u7684\u539f\u7406\uff0c\u4e5f\u5c31\u662f\u89c6\u5dee(disparity)\uff0c\u901a\u8fc7\u89c6\u5dee\uff0c\u6211\u4eec\u53ef\u4ee5\u66f4\u7cbe\u786e\u5730\u611f\u53d7\u5230\u201c\u8ddd\u79bb\u201d\uff08\u5b9e\u9645\u4e0a\u4e5f\u662f\u5bf9\u6781\u51e0\u4f55\u90a3\u4e00\u5957\uff09\uff0c\u63a5\u4e0b\u6765\u9610\u8ff0\u5176\u539f\u7406\u3002</p> <p>\u9996\u5148\uff0c\u6211\u4eec\u7ed8\u5236\u4e00\u4e2a\u7b80\u5355\u7684\u6a21\u578b\uff1a</p> <p>\u5728\u8fd9\u4e2a\u6a21\u578b\u4e2d\uff0c\u6211\u4eec\u5047\u8bbe\u4e24\u4e2a\u56fe\u50cf\u4e2d\u7684\u5339\u914d\u70b9\u7b26\u5408\u4e4b\u540e\u4f1a\u5728\u7acb\u4f53\u5339\u914d\u4e00\u8282\u91cc\u63d0\u5230\u7684\u6700\u7b80\u60c5\u51b5(simplest case)\uff0c\u4f46\u662f\u53ef\u4ee5\u4e0d\u7528\u7ba1\u8fd9\u4e2a\u6700\u7b80\u60c5\u51b5\u662f\u4ec0\u4e48\uff0c\u76f4\u63a5\u5f53\u4f5c\u8fd9\u662f\u4e00\u4e2a\u4fef\u89c6\u89c6\u89d2\u4e0b\u7684\u7b80\u5316\uff0c\u76f4\u63a5\u770b\u4e0b\u9762\u7684\u6a21\u578b\u5373\u53ef\u3002</p> <p></p> <p>\u8fd9\u56fe\u6211\u753b\u4e86\u81f3\u5c11\u534a\u5c0f\u65f6 T^T\uff08\u5f3a\u8feb\u75c7\u306e\u6028\u5ff5\uff09</p> <p>(1) \u4e2d OL \u548c OR \u5206\u522b\u662f\u4e24\u76f8\u673a\u4e2d\u5fc3\uff0c\u6de1\u84dd\u8272\u7ebf\u6761\u8868\u793a\u6210\u50cf\u5e73\u9762\uff0cXL \u548c XR \u5206\u522b\u8868\u793a\u5b9e\u9645\u70b9 X \u5728\u6210\u50cf\u5e73\u9762\u4e0a\u7684\u6295\u5f71\uff0c\u6a59\u8272\u7ebf\u6761\u8868\u793a\u4ed6\u4eec\u7684\u6a2a\u5411\u5750\u6807\uff08\u5047\u8bbe\u4ed6\u4eec\u90fd\u5728\u540c\u4e00\u6c34\u5e73\u7ebf\u4e0a\uff09\uff0cz \u8868\u793a\u5b9e\u9645\u70b9 X \u5230\u57fa\u7ebf\u7684\u8ddd\u79bb\uff0c\u8fd9\u91cc\u6211\u4eec\u6682\u4e14\u79f0\u4e4b\u4e3a\u201c\u6df1\u5ea6\u201d\uff08\u53cd\u6b63\u4e0d\u7ba1\u600e\u4e48\u5b9a\u4e49\u6df1\u5ea6\uff0c\u6709 z \u90fd\u80fd\u7b97\uff09\u3002</p> <p>(2) \u4e2d\u6211\u753b\u56fe\u7684\u65f6\u5019\u5fd8\u8bb0\u533a\u5206\u4e24\u4e2a XR \u4e86\uff0c\u6240\u4ee5\u5173\u4e8e (2) \u56fe\u4e2d\u7684 XR \u4e00\u5f8b\u6307\u5de6\u8fb9\u90a3\u4e2a XR\u3002</p> <p>\u6211\u4eec\u5c06 OR \u7684\u6210\u50cf\u6a21\u578b\u5e73\u79fb\u5230\u5de6\u4fa7\uff0c\u5373\u56fe (2)\uff0c\u53d1\u73b0\u6a59\u8272\u7684\u4e09\u89d2\u5f62\u548c\u7ea2\u8272\u7684\u4e09\u89d2\u5f62\u76f8\u4f3c\uff1a\\(\\Delta O X_L X_R \\cong \\Delta X O_L O_R\\) \uff08\u6ce8\u610f\uff0c\u5b9e\u9645\u60c5\u51b5\u4e0d\u4e00\u5b9a\u7b49\u8170\uff01\uff09</p> <p>\u4e8e\u662f\u6211\u4eec\u5f97\u5230\uff0c\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff1a</p> \\[ \\frac{\\overline{X_L X_R}}{f} = \\frac{\\overline{O_L O_R}}{z} \\\\ \\text{ i.e. }\\; disparity = \\Delta{\\mathbf{x}} = |\\mathbf{x}_l - \\mathbf{x}_r| = |x_l - x_r| = \\frac{B \\cdot f}{z} \\\\ \\text{where }B\\text{ is the length of baseline} \\\\ \\text{ i.e. }\\; z = \\frac{B \\cdot f}{|x_l-x_r|} \\] <p>\u63d0\u793a</p> <p>\u867d\u7136\u662f\u4e2a\u7b80\u5316\u60c5\u51b5\uff0c\u4f46\u662f\u5728\u6700\u7b80\u60c5\u51b5(simplest case)\u4e0b\u662f\u53ef\u4ee5\u76f4\u63a5\u632a\u7528\u7ed3\u8bba\u7684\uff0c\u7a0d\u540e\u6211\u4f1a\u63d0\u9192\u56de\u987e\u8fd9\u4e00\u8282\u6765\u7406\u89e3\u8fd9\u4e00\u70b9\uff0c\u6240\u4ee5\u5b89\u5fc3\u987a\u7740\u8bfb\u4e0b\u53bb\u5373\u53ef\u3002</p> <p>\u81f3\u6b64\uff0c\u6211\u4eec\u5728\u672c\u8282\u5f00\u5934\u63d0\u5230\u7684\u4e24\u4e2a\u95ee\u9898\uff0c\u5df2\u7ecf\u89e3\u51b3\u4e00\u4e2a\u4e86\u3002</p> <ul> <li> \u5982\u4f55\u9ad8\u6548\u5730\u5f97\u5230\u5339\u914d\u5173\u7cfb\uff1b</li> <li> \u5982\u4f55\u6839\u636e\u5339\u914d\u70b9\u8ba1\u7b97\u70b9\u6df1\u5ea6\uff1b</li> </ul>"},{"location":"cour_note/D2QD_Intro2CV/Lec08/#\u7acb\u4f53\u5339\u914d","title":"\u7acb\u4f53\u5339\u914d","text":"<p>\u9996\u5148\u6211\u4eec\u505a\u4e00\u4e2a\u5047\u8bbe\uff0c\u4e5f\u5c31\u662f\u5728\u5339\u914d\u8fc7\u7a0b\u4e2d\uff0c\u6211\u4eec\u7684\u4e24\u4e2a view \u7684\u8ddd\u79bb\u76f8\u5dee\u4e0d\u5927\uff0c\u4e5f\u5c31\u662f\u8bf4\u5c40\u90e8\u7279\u5f81\u4ecd\u7136\u662f\u76f8\u4f3c\u7684\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec08/#\u641c\u7d22","title":"\u641c\u7d22","text":"<p>\u7acb\u4f53\u5339\u914d(Stereo Matching)\u7684\u539f\u7406\u5c31\u662f\uff0c\u9009\u5b9a\u7b2c\u4e00\u4e2a\u56fe\u50cf\u5185\u7684\u67d0\u4e00\u70b9\uff0c\u7136\u540e\u53bb\u53e6\u5916\u4e00\u5f20\u56fe\u50cf\u5bf9\u5e94\u7684\u5bf9\u6781\u7ebf\u4e0a\u641c\u7d22\u627e\u5230\u80fd\u591f\u548c\u5b83\u5339\u914d\u7684\u70b9\u3002\u6ca1\u9519\uff0c\u6211\u4eec\u53ea\u9700\u8981\u5728\u4e00\u6761\u76f4\u7ebf\u4e0a\u641c\u7d22\u627e\u5230\u5339\u914d\u7684\u70b9\u5373\u53ef\uff0c\u8fd9\u5927\u5927\u4f18\u5316\u4e86\u590d\u6742\u5ea6\u3002\u800c\u5b83\u7684\u6839\u636e\u6070\u597d\u5c31\u662f\u5bf9\u6781\u7ebf\u7684\u5b9a\u4e49\u3002</p> <p>\ud83d\udc49 \u56de\u987e\u5bf9\u6781\u51e0\u4f55\uff01</p> <p>\u6ca1\u9519\uff0c\u6211\u4eec\u73b0\u5728\u5df2\u77e5\u4e86 \\(X_L\\)\uff08\u7531\u6211\u4eec\u9009\u5b9a\u7684\uff09\uff0c\u90a3\u4e48 \\(X_R\\) \u7684\u8f68\u8ff9\u4fbf\u662f\u5bf9\u6781\u7ebf\uff0c\u4e8e\u662f\u6211\u4eec\u53ea\u9700\u8981\u5148\u627e\u5230\u6211\u4eec\u9009\u5b9a\u7684 \\(X_L\\) \u5728\u53e6\u5916\u4e00\u5f20\u56fe\u50cf\u4e0a\u5bf9\u5e94\u7684\u5bf9\u6781\u7ebf\uff0c\u7136\u540e\u518d\u5728\u8fd9\u6761\u7ebf\u4e0a\u641c\u7d22\u7279\u5f81\u4e0e \\(X_L\\) \u6700\u5339\u914d\u7684\u90a3\u4e2a\u70b9\u5373\u53ef\u3002\uff08\u8fd9\u91cc\u6211\u4eec\u4e5f\u6ca1\u6709\u5fc5\u8981\u4f7f\u7528 SIFT\uff0c\u76f4\u63a5\u505a\u5dee\u5c31\u591f\u4e86\uff09</p> <p>\u4f46\u662f\u8bdd\u53c8\u8bf4\u56de\u6765\uff0c\u8ba1\u7b97\u5bf9\u6781\u7ebf\u8fd9\u4ef6\u4e8b\u4e5f\u5e76\u975e\u5341\u5206\u7b80\u5355\uff0c\u5982\u679c\u5bf9\u4e8e\u6bcf\u4e2a\u70b9\u6211\u4eec\u90fd\u9700\u8981\u53bb\u8ba1\u7b97\u5bf9\u6781\u7ebf\uff0c\u90a3\u4e48\u5c06\u5e26\u6765\u4e0d\u5c0f\u7684\u5e38\u6570\uff0c\u800c\u4e14\u7531\u4e8e\u8fd9\u4ef6\u4e8b\u6ca1\u6cd5\u201c\u6574\u4f53\u5730\u9884\u5904\u7406\u201d\uff0c\u6240\u4ee5\u6211\u4eec\u8fd8\u9700\u8981\u4f18\u5316\u8fd9\u4ef6\u4e8b\u3002</p> <p>\u6700\u7b80\u60c5\u51b5</p> <p>\u9996\u5148\u8003\u8651\u6700\u7b80\u60c5\u51b5(simplest case)\u8fd9\u4e2a\u7279\u6b8a\u60c5\u51b5\uff1a</p> <p></p> <ol> <li>\u4e24\u4e2a\u76f8\u673a\u7684\u7126\u8ddd\u76f8\u540c\uff1b</li> <li>\u76f8\u673a\u4f4d\u7f6e\u5728\u540c\u4e00\u6c34\u5e73\u9762\u4e0a\uff0c\u5373\u9ad8\u5ea6\u76f8\u540c\uff1b</li> <li>\u4e24\u4e2a\u6210\u50cf\u5e73\u9762\u548c\u57fa\u7ebf\uff0c\u4e09\u8005\u76f8\u4e92\u5e73\u884c\uff0c\u6216\u8005\u8bf4\u4e24\u4e2a\u6210\u50cf\u5e73\u9762\u5171\u9762\uff08\u6b64\u65f6\u5bf9\u6781\u70b9\u4e0d\u5b58\u5728\uff09\uff1b</li> </ol> <p>\u6b64\u65f6\uff0c\u5bf9\u6781\u7ebf\u4e5f\u6c34\u5e73\uff0c\u800c\u4e14\u4e24\u6761\u5bf9\u6781\u7ebf\u4e5f\u5171\u7ebf\uff08\u53ef\u4ee5\u601d\u8003\u4e00\u4e0b\u4e3a\u4ec0\u4e48\uff09\u3002</p> <p>\u6362\u53e5\u8bdd\u6765\u8bf4\uff0c\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u5f53\u6211\u4eec\u9009\u5b9a\u5de6\u56fe\u4e2d\u7684\u67d0\u4e2a\u70b9 \\(X_L\\)\uff0c\u90a3\u4e48 \\(X_R\\) \u7684\u5019\u9009\u4f4d\u7f6e\u5c31\u5728\u53f3\u56fe\u4e2d\u540c\u4e00\u9ad8\u5ea6\u7684\u90a3\u6761\u6c34\u5e73\u7ebf\u4e0a\u3002</p> <p></p> <p>\u90a3\u4e48\u5982\u4f55\u89e3\u51b3\u8fd9\u79cd\u60c5\u51b5\u4ee5\u5916\u7684\u60c5\u51b5\u5462\uff1f\u65e2\u7136\u6211\u90fd\u8fd9\u4e48\u6392\u4e86\uff0c\u90a3\u89e3\u51b3\u529e\u6cd5\u81ea\u7136\u5c31\u662f\u8f6c\u5316\u4e3a\u6700\u7b80\u60c5\u51b5\u6765\u505a\u4e86\u3002</p> <p>\u8f6c\u5316\u601d\u60f3</p> <p>\u53c8\u662f\u4e00\u4e2a\u7a81\u7136\u7684\u60f3\u6cd5\uff0c\u5f88\u591a\u65f6\u5019\u6211\u4eec\u6216\u8bb8\u53ef\u4ee5\u4e0d\u4ece\u6574\u4f53\u53bb\u601d\u8003\uff0c\u800c\u662f\u5148\u89e3\u51b3\u4e00\u4e2a\u6700\u7b80\u60c5\u51b5\uff0c\u518d\u8f6c\u5316\u95ee\u9898\u3002</p> <p>\u4e00\u822c\u60c5\u51b5</p> <p></p> <p>\u8fd9\u4e2a\u95ee\u9898\u88ab\u79f0\u4e3a\u7acb\u4f53\u5f71\u50cf\u77eb\u6b63\uff0c\u8fd9\u91cc\u5e76\u4e0d\u5c55\u5f00\uff0c\u53ef\u4ee5\u53c2\u8003\u8fd9\u7bc7\u6587\u7ae0\uff1a</p> <p>C. Loop and Z. Zhang. Computing Rectifying Homographies for Stereo Vision. IEEE Conf. Computer Vision and Pattern Recognition, 1999.</p> <p></p> <p>\u56de\u987e</p> <p>\u76f8\u4fe1\u73b0\u5728\u4f60\u5bf9\u201c\u6700\u7b80\u60c5\u51b5\u201d\u5df2\u7ecf\u6709\u66f4\u6df1\u523b\u7684\u7406\u89e3\u4e86\uff0c\u4e0d\u59a8\u56de\u8fc7\u5934\u53bb\u7406\u89e3\u4e00\u4e0b\u4e3a\u4ec0\u4e48\u6211\u4eec\u4e4b\u524d\u63d0\u5230\u7684\u90a3\u4e2a\u7b80\u5316\u7684\u89c6\u5dee\u6a21\u578b\u53ef\u4ee5\u76f4\u63a5\u632a\u7528\u7ed3\u8bba\uff1f</p> <p>\ud83d\udc49 \u89c6\u5dee</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec08/#\u5339\u914d","title":"\u5339\u914d","text":"<p>\u6240\u8c13\u7684\u5bfb\u627e\u5339\u914d\uff0c\u5c31\u662f\u5728\u5145\u65a5\u7740\u5019\u9009\u70b9\u7684\u5bf9\u6781\u7ebf\u4e0a\u641c\u7d22\u5339\u914d\u6700\u597d\u7684\u4e00\u4e2a\u70b9\uff0c\u6216\u8005\u8bf4\u5dee\u5f02\u6700\u5c0f\u7684\u4e00\u4e2a\u70b9\u3002</p> <p>\u5e38\u89c1\u7684\u5dee\u5f02\u8861\u91cf\u65b9\u6cd5\u6709\u8fd9\u4e48\u51e0\u79cd\uff1a</p> <p>SSD: Sum of Squared Differences</p> \\[ diff = \\sum_{x,y} |W_1(x,y) - W_2(x,2)|^2 \\] <p>SAD: Sum of Absolute Differences</p> \\[ diff = \\sum_{x,y} |W_1(x,y) - W_2(x,y)| \\] <p>ZNCC: Zero-mean Normalized Cross Correlation</p> \\[ diff = \\frac{(W_1(x,y)-\\overline{W_1})(W_2(x,y)-\\overline{W_2})}{\\sigma_{W_1}\\sigma_{W_2}} \\\\ \\text{where  } \\overline{W_i} = \\frac{1}{n}\\sum_{x,y} W_i \\;\\;\\; \\sigma_{W_i} = \\sqrt{\\frac{1}{n}\\sum_{x,y}(W_i-\\overline{W_i})^2} \\] <p>\u5176\u4e2d\uff0cZNCC \u76f8\u6bd4\u5176\u4ed6\u65b9\u6cd5\uff0c\u4f18\u8d8a\u6027\u5728\u4e8e\u5b83\u5bf9\u56fe\u50cf\u6574\u4f53\u7684\u5149\u5f3a\u5ea6\u4e0d\u654f\u611f\uff0c\u56e0\u4e3a\u6211\u4eec\u53ef\u4ee5\u53d1\u73b0\uff0c\\(W_i\\) \u5728\u53c2\u4e0e\u8ba1\u7b97\u524d\u90fd\u51cf\u53bb\u4e86 \\(\\overline{W_i}\\)\uff0c\u6240\u4ee5\u6d88\u9664\u4e86\u56fe\u50cf\u6574\u4f53\u4eae\u5ea6\u5e26\u6765\u7684\u5f71\u54cd\u3002</p> \u4e2a\u4eba\u7591\u60d1 <p>\u8fd9\u91cc\u6240\u8c13\u7684\u201c\u6d88\u9664\u4eae\u5ea6\u5f71\u54cd\u201d\uff0c\u662f\u5426\u662f\u5bf9\u4e8e multi-view \u7684\u60c5\u51b5\u6765\u8bf4\u7684\uff1f\u56e0\u4e3a\u5982\u679c\u53ea\u6709\u4e24\u5f20\u56fe\u7247\uff0c\u4e14\u4eae\u5ea6\u5dee\u8ddd\u6574\u4f53\u6052\u5b9a\u7684\u8bdd\uff0c\u867d\u7136\u8ba1\u7b97\u51fa\u6765\u7684 diff \u4f1a\u504f\u5927\uff0c\u4f46\u662f\u6574\u4f53\u4e0a\u7684\u5927\u5c0f\u5173\u7cfb\u597d\u50cf\u4e5f\u6ca1\u6709\u53d8\u5316\uff1f\u6211\u6ca1\u6709\u60f3\u6e05\u695a\u8fd9\u4e00\u70b9\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec08/#\u5339\u914d\u7684\u6539\u8fdb","title":"\u5339\u914d\u7684\u6539\u8fdb","text":"<p>\u7136\u800c\uff0c\u5339\u914d\u8fc7\u7a0b\u4e2d\u8fd8\u6709\u4e00\u4e2a\u989d\u5916\u7684\u95ee\u9898\u9700\u8981\u89e3\u51b3\u3002</p> <p>\u7a97\u53e3\u641c\u7d22\u7684\u5f0a\u7aef</p> <p>\u7a97\u53e3\u641c\u7d22\u7684\u6548\u679c\u5b9e\u9645\u4e0a\u5e38\u5e38\u4e0d\u5c3d\u5982\u4eba\u610f\uff0c\u6709\u4e00\u79cd\u57fa\u4e8e\u56fe\u5272\u7684\u505a\u6cd5\uff0c\u6548\u679c\u76f8\u5bf9\u7a0d\u597d\u3002</p> <p>\u8fd9\u91cc\u6240\u8bf4\u7684\u7a97\u53e3\uff0c\u6307\u7684\u662f\u5728\u5339\u914d\u641c\u7d22\u8fc7\u7a0b\u4e2d\uff0c\u7528\u6765\u6bd4\u8f83\u76f8\u4f3c\u5ea6\u7684\u7a97\u53e3\u5927\u5c0f\u3002</p> <p></p> <p>\ud83d\udc49 Boykov et al., Fast Approximate Energy Minimization via Graph Cuts, International Conference on Computer Vision 1999.</p> <p>\u8fd8\u6709\u53e6\u5916\u4e00\u4e2a\u601d\u8def\uff0c\u90a3\u5c31\u662f\u8f6c\u5316\u4e3a\u4f18\u5316\u95ee\u9898\uff0c\u5982\u679c\u8bf4\u539f\u6765\u7684\u76ee\u6807\u51fd\u6570\u662f\u4e24\u70b9\u7684\u5339\u914d\u7a0b\u5ea6\uff0c\u90a3\u4e48\u73b0\u5728\u7684\u76ee\u6807\u51fd\u6570\u53ef\u4ee5\u662f\u5339\u914d\u7a0b\u5ea6\u548c\u5e73\u6ed1\u7a0b\u5ea6\u7684\u52a0\u6743\u548c\uff1a</p> <p></p> \\[ \\begin{aligned}     E(d) = E_d(d) + \\lambda E_s(s) \\\\     \\text{match cost:   } &amp; E_d(d) = \\sum_{(x,y)\\in I} C(x,y,d(x,y)) \\;\\;\\; \\text{e.g., SSD, SAD, ZNCC} \\\\     \\text{smoothness cost:   } &amp; E_s(d) = \\sum_{(p,q) \\in \\varepsilon} V(d_p, d_q) \\;\\;\\; \\text{where } \\varepsilon \\text{ is the set of neighboring pixels } \\end{aligned} \\] <p>\u5176\u4e2d\uff0c\\(V(d_p,d_q)\\) \u4e00\u822c\u6709\u4e24\u79cd\u9009\u62e9\uff1a</p> \\[ \\begin{aligned} \\begin{aligned}     \\text{L_1 Distance: } \\\\     V(d_p, d_q) &amp;= |d_p - d_q| \\end{aligned} &amp; &amp; \\begin{aligned}     \\text{Potts Model: } \\\\     V(d_p, d_q) &amp;=          \\left\\{             \\begin{array}{*}                 0 &amp; \\text{ if } d_p = d_q \\\\                 1 &amp; \\text{ if } d_p \\not = d_q             \\end{array}         \\right. \\end{aligned} \\end{aligned} \\] <p></p> <p>\u7279\u522b\u7684\uff0c\u5982\u679c\u6d89\u53ca\u7684\u662f\u4e00\u4e2a\u7ebf\u6027\u7684\u626b\u63cf\uff0c\u4e5f\u5c31\u662f\u5f53 \\(\\varepsilon\\) \u4e2d\u53ea\u542b\u6709\u5de6\u53f3\u4e24\u4fa7\u7684\u70b9\uff0c\u90a3\u4e48\u8fd9\u4e2a\u95ee\u9898\u53ef\u4ee5\u7528 DP \u89e3\u51b3\u3002\u800c\u8fd9\u79cd\u65b9\u5f0f\u4f18\u5316\u51fa\u6765\u7684\u56fe\u7247\u6548\u679c\u662f\u8fd9\u6837\u7684\uff1a</p> <p></p> <p>\u7136\u800c\uff0c\u5982\u679c\u4e0d\u6ee1\u8db3\u7ebf\u6027\u626b\u63cf\u8fd9\u4e2a\u6761\u4ef6\u7684\u8bdd\uff0c\u8fd9\u4e2a\u95ee\u9898\u5c31\u53d8\u6210\u4e86\u4e00\u4e2a NP-hard \u95ee\u9898\uff0c\u4e0d\u8fc7\u53ef\u4ee5\u7528\u56fe\u5272\u6c42\u8fd1\u4f3c\u89e3\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec08/#\u7efc\u5408","title":"\u7efc\u5408","text":"<p>\u81f3\u6b64\uff0c\u6211\u4eec\u5728\u672c\u8282\u5f00\u5934\u63d0\u5230\u7684\u4e24\u4e2a\u95ee\u9898\uff0c\u5df2\u7ecf\u5168\u90e8\u89e3\u51b3\u4e86\u3002</p> <ul> <li> \u5982\u4f55\u9ad8\u6548\u5730\u5f97\u5230\u5339\u914d\u5173\u7cfb\uff1b</li> <li> \u5982\u4f55\u6839\u636e\u5339\u914d\u70b9\u8ba1\u7b97\u70b9\u6df1\u5ea6\uff1b</li> </ul> <p>\u4e8e\u662f\u53cc\u76ee\u91cd\u5efa\u7684\u5927\u81f4\u6d41\u7a0b\u5982\u4e0b\u2014\u2014\u9996\u5148\u6211\u4eec\u5bf9\u76f8\u673a\u8fdb\u884c\u6807\u5b9a\uff0c\u83b7\u5f97\u76f8\u673a\u7684\u5185\u53c2\uff1b\u63a5\u4e0b\u6765\u901a\u8fc7\u7acb\u4f53\u5f71\u50cf\u77eb\u6b63\u6280\u672f\uff0c\u5c06\u4e24\u5f20\u56fe\u7247\u8f6c\u5316\u4e3a\u6700\u7b80\u60c5\u51b5\uff1b\u7136\u540e\u518d\u5bf9\u6bcf\u4e00\u4e2a\u50cf\u7d20\u8fdb\u884c\u5339\u914d\uff0c\u53ea\u9700\u8981\u5728\u540c\u9ad8\u5ea6\u7684\u5bf9\u6781\u7ebf\u4e0a\u641c\u7d22\u5339\u914d\u5c40\u90e8\u7279\u5f81\u6700\u76f8\u4f3c\u7684\u53e6\u5916\u4e00\u4e2a\u70b9\u5373\u53ef\uff1b\u63a5\u7740\u518d\u6839\u636e\u5339\u914d\u70b9\u7684\u5173\u7cfb\u8fdb\u884c\u6df1\u5ea6\u4f30\u8ba1\u5373\u53ef\u3002</p> <pre><code>graph LR;\n    A --&gt; B --&gt; C --&gt; D\n    A[\"Calibrate Cameras\"]\n    B[\"Rectify Images\"]\n    C[\"Compute Disparity\"]\n    D[\"Estimate Depth\"]</code></pre> \u5f15\u8d77\u8bef\u5dee\u7684\u53ef\u80fd\u56e0\u7d20 <p>\u8bfe\u7a0b\u5185\u8fd9\u4e2a\u5217\u8868\u5176\u5b9e\u662f\u7ed9\u5927\u4f5c\u4e1a\u7684\u63d0\u793a\uff0c\u4e2a\u4eba\u8ba4\u4e3a\u4e5f\u6709\u52a9\u4e8e\u68b3\u7406\u6574\u4e2a\u6d41\u7a0b\u3002</p> <ul> <li>Camera calibration errors</li> <li>Poor image resolution</li> <li>Occlusions</li> <li>Violations of brightness constancy (specular reflections)</li> <li>Large motions</li> <li>Textureless regions</li> </ul> <p>\u4e0b\u9762\u8be6\u7ec6\u8bf4\u660e\u51e0\u4e2a\u56e0\u7d20\u5bf9\u7ed3\u679c\u7684\u5f71\u54cd\u3002</p> <p>\u7a97\u53e3\u5927\u5c0f\u7684\u9009\u62e9\u5bf9\u7ed3\u679c\u7684\u5f71\u54cd</p> <p>\u5f53\u6211\u4eec\u4f7f\u7528\u7a97\u53e3\u641c\u7d22\u65f6\uff0c\u7a97\u53e3\u5927\u5c0f\u7684\u9009\u62e9\u4ecd\u7136\u662f\u4e2a\u96be\u9898\u2014\u2014\u7a97\u53e3\u8d8a\u5c0f\uff0c\u5f80\u5f80\u7ed3\u679c\u7684\u7ec6\u8282\u4f1a\u66f4\u591a\uff0c\u76f8\u5bf9\u7684\u566a\u58f0\u4e5f\u66f4\u591a\uff0c\u56fe\u7247\u770b\u8d77\u6765\u5c31\u5f88\u4e71\uff1b\u800c\u7a97\u53e3\u8d8a\u5927\uff0c\u5f80\u5f80\u566a\u58f0\u66f4\u5c11\u3001\u66f4\u5e73\u6ed1\uff0c\u4f46\u662f\u7ec6\u8282\u4e5f\u66f4\u5c11\uff0c\u4e5f\u5c31\u662f\u8bf4\uff0c\u8fd9\u91cc\u6709\u4e00\u4e2a\u5e73\u6ed1\u5ea6\u548c\u7cbe\u786e\u5ea6\u7684 trade off\u3002</p> <p></p> <p>W \u8868\u793a\u7a97\u53e3\u5927\u5c0f\u3002</p> <p>\u57fa\u7ebf\u5927\u5c0f\u7684\u9009\u62e9\u5bf9\u7ed3\u679c\u7684\u5f71\u54cd</p> <ul> <li>\u5982\u679c\u57fa\u7ebf\u9009\u62e9\u8fc7\u5927\uff0c\u90a3\u4e48\u4e24\u5f20\u56fe\u7247\u4e4b\u95f4\u7684\u5185\u5bb9\u5dee\u522b\u5c31\u4f1a\u8f83\u5927\uff0c\u5728\u641c\u7d22\u8fc7\u7a0b\u4e2d\u5c31\u66f4\u96be\u627e\u5230\u80fd\u591f\u5339\u914d\u7684\u70b9\uff0c\u6b64\u5916\uff0c\u6a2a\u5411\u7684\u8bef\u5dee\u4e5f\u4f1a\u589e\u5927\uff0c\u7406\u7531\u53ef\u4ee5\u53c2\u8003\u4e0b\u9762\u8fd9\u5f20\u56fe\u7684\u539f\u7406\uff1b</li> <li>\u800c\u5982\u679c\u57fa\u7ebf\u9009\u62e9\u8fc7\u5c0f\uff0c\u5219\u70b9\u7684\u6df1\u5ea6\u8bef\u5dee\u5c31\u4f1a\u5f88\u5927\uff0c\u5177\u4f53\u539f\u56e0\u53ef\u4ee5\u53c2\u8003\u4e0b\u9762\u8fd9\u5f20\u56fe\u2014\u2014\u5355\u4e00\u50cf\u7d20\u5bf9\u5e94\u7684\u5019\u9009\u70b9\u533a\u57df\u66f4\u6df1\uff0c\u610f\u5473\u7740\u5f53\u524d\u70b9\u53ef\u80fd\u662f\u8fd9\u4e00\u83f1\u5f62\u91cc\u7684\u4efb\u4f55\u70b9\uff1b</li> </ul> <p></p> <p>\u8c28\u8bb0\u6211\u53c8\u56e0\u4e3a\u753b\u56fe\u6d6a\u8d39\u534a\u4e2a\u5c0f\u65f6\u3002</p> <p>\u4e0a\u9762\u7684\u5185\u5bb9\u7ed3\u675f\u540e\uff0c\u5176\u5b9e\u8fd8\u6709\u4e00\u4e2a\u9057\u7559\u4e0b\u6765\u95ee\u9898\uff0c\u8bfb\u8005\u53ef\u4ee5\u5148\u601d\u8003\u4e00\u4e0b\u76ee\u524d\u8fd9\u4e2a\u6d41\u7a0b\u6709\u4ec0\u4e48\u95ee\u9898\uff0c\u518d\u6253\u5f00\u4e0b\u9762\u7684\u63d0\u793a\u6846\u3002</p> \u4e00\u4e2a\u5c1a\u672a\u88ab\u89e3\u51b3\u7684\u95ee\u9898 <p>\u8ba9\u6211\u4eec\u56de\u5230\u7b2c\u4e94\u7ae0\u7684\u5173\u952e\u70b9\u5339\u914d\u2014\u2014\u4e3a\u4ec0\u4e48\u6211\u4eec\u53ea\u627e\u5173\u952e\u70b9\uff1f</p> <p>\u6211\u4e2a\u4eba\u7684\u60f3\u6cd5\u662f\uff0c\u9996\u5148\uff0c\u5173\u952e\u70b9\u80fd\u591f\u4e00\u5b9a\u7a0b\u5ea6\u4e0a\u8868\u8fbe\u4e00\u4e2a\u7269\u4f53\u7684\u7279\u5f81\uff0c\u6216\u8005\u8bf4\u5b83\u662f\u52fe\u52d2\u4e00\u4e2a\u7269\u4f53\u975e\u5e38\u91cd\u8981\u7684\u4e00\u4e2a\u90e8\u5206\uff1b\u8fd8\u6709\u4e00\u4e2a\u539f\u56e0\u662f\uff0c\u5173\u952e\u70b9\u7279\u5f81\u660e\u663e\uff0c\u5176\u8868\u8fbe\u5177\u6709\u4e00\u5b9a\u7684\u72ec\u7279\u6027\uff08\u4e5f\u5c31\u662f\u5173\u952e\u70b9\u7684\u72ec\u7279\u6027(uniqueness)\uff09\u3002</p> <p>\u800c\u73b0\u5728\u6211\u4eec\u505a\u5339\u914d\u7684\u5185\u5bb9\u662f\u4efb\u610f\u7684\u3001\u5e7f\u6cdb\u7684\uff0c\u4f8b\u5982\u6211\u4eec\u73b0\u5728\u5728\u505a\u5339\u914d\u7684\u5f88\u53ef\u80fd\u662f\u4e00\u9762\u767d\u5899\u4e0a\u7684\u67d0\u4e00\u4e2a\u70b9\uff08\u5c31\u662f\u4e0a\u9762\u63d0\u5230\u8fc7\u7684 textureless regions\uff09\uff0c\u8fd9\u6837\u7684\u70b9\u53c8\u8981\u5982\u4f55\u627e\u5230\u5b83\u7684\u5339\u914d\u70b9\u5462\uff1f</p> <p>\u7b54\u6848\u5c31\u662f\uff0c\u6211\u4eec\u53ef\u4ee5\u7528\u7ed3\u6784\u5149\u6765\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\u3002</p> \u7ed3\u6784\u5149 <p>\u6211\u4eec\u518d\u68b3\u7406\u4e00\u4e0b\u95ee\u9898\u7684\u8981\u70b9\uff0c\u5c31\u4ee5\u767d\u5899\u4e3a\u4f8b\u5b50\uff0c\u5b83\u96be\u4ee5\u8fdb\u884c\u5339\u914d\u662f\u56e0\u4e3a\u5b83\u7f3a\u5c11\u7279\u5f81\u3001\u7f3a\u5c11\u7eb9\u7406\uff0c\u800c\u6211\u4eec\u7684\u76ee\u6807\u662f\u5bf9\u5176\u7ed3\u6784\u8fdb\u884c\u91cd\u5efa\u2014\u2014\u90a3\u4e48\u4e00\u4e2a\u60f3\u6cd5\u5c31\u662f\u6211\u4eec\u624b\u52a8\u7ed9\u4ed6\u300c\u4e0a\u7eb9\u7406\u300d\uff0c\u5f53\u7136\u5e76\u4e0d\u662f\u6307\u753b\u4e0a\u53bb\uff0c\u800c\u662f\u4f7f\u7528\u7ed3\u6784\u5149\uff1a</p> <p></p> <p>\u4e8e\u662f\u6211\u4eec\u7684\u56fe\u50cf\u5c31\u6709\u4e86\u7eb9\u7406\uff0c\u62e5\u6709\u4e86\u201c\u7279\u5f81\u201d\u3002</p> <p>\u4e2a\u4eba\u60f3\u6cd5</p> <p>\u6211\u5f53\u65f6\u770b\u5230\u8fd9\u4e2a idea \u7684\u65f6\u5019\uff0c\u611f\u89c9\u5f88\u523a\u6fc0\uff0c\u4f46\u662f\u53c8\u89c9\u5f97\u8fd9\u7834\u574f\u4e86\u666f\u8c61\u672c\u6765\u7684\u7eb9\u7406\uff0c\u4f46\u662f\u8f6c\u5ff5\u4e00\u60f3\uff0c\u662f\u4e0d\u662f\u4f1a\u62cd\u4e24\u5f20\uff0c\u4e00\u5f20\u7528\u6765\u4e0a\u8272\uff0c\u4e00\u5f20\u7528\u6765\u5efa\u6a21\uff1f\u6211\u6682\u65f6\u8fd8\u4e0d\u77e5\u9053\uff0c\u7ebf\u653e\u4e2a\u731c\u60f3\u5728\u8fd9\u91cc\u3002</p> <p>\u4e0d\u8fc7\u6b64\u65f6\u53c8\u6709\u4e00\u4e2a\u5f15\u7533\u51fa\u6765\u7684\u70b9\uff0c\u5c31\u662f\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u5176\u5b9e\u53ef\u4ee5\u51cf\u5c11\u4e00\u4e2a\u76f8\u673a\u3002</p> <p></p> <p>\u8fd9\u662f\u56e0\u4e3a\uff0c\u5047\u8bbe\u6211\u4eec\u628a camera 2 \u653e\u5728\u4e0e projector \u4e00\u6837\u7684\u4f4d\u7f6e\uff0c\u6b64\u65f6 camera 2 \u6536\u5230\u7684\u56fe\u50cf\u5e94\u5f53\u548c projector \u5c04\u51fa\u53bb\u7684\u662f\u4e00\u6837\u7684\uff0c\u6216\u8005\u8bf4\u662f\u7c7b\u4f3c\u7684\u3002</p> <p>\u5982\u4f55\u89e3\u91ca\uff1f</p> <p>\u8bf4\u5b9e\u8bdd\u6211\u8fd8\u662f\u4e0d\u592a\u80fd\u7406\u89e3\u8fd9\u4e00\u70b9\u3002\u5982\u679c\u8981\u6211\u5f3a\u884c\u7406\u89e3\u7684\u8bdd\uff0c\u6211\u89c9\u5f97\u5927\u6982\u662f\u53c8\u8fd9\u4e48\u4e24\u70b9\uff0c\u7b2c\u4e00\u70b9\u662f\u88ab\u7ed3\u6784\u5149\u7167\u5c04\u7684\u4e1c\u897f\u5bf9\u7ed3\u6784\u5149\u7684\u53cd\u5c04\u4ee5\u6f2b\u53cd\u5c04\u4e3a\u4e3b\uff0c\u800c\u4e14\u6240\u8c13\u7684\u201c\u4e00\u6837\u201d\u4e5f\u53ea\u662f\u7d2f\u6b7b\uff0c\u5e76\u4e0d\u80fd\u5305\u62ec\u9634\u5f71\u5173\u7cfb\u7b49\uff0c\u6240\u4ee5\u5bf9\u8fd9\u4e2a\u7ed3\u8bba\u7684\u6b63\u786e\u4e0e\u5426\u6211\u8868\u793a\u6000\u7591\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec08/#\u591a\u89c6\u89d2","title":"\u591a\u89c6\u89d2","text":"<p>\u591a\u89c6\u89d2\u7acb\u4f53(Multi-view Stereo, MVS)\u91cd\u5efa\uff0c\u987e\u540d\u601d\u4e49\u5c31\u662f\u5229\u7528\u66f4\u591a\u7684\u89c6\u89d2\u6765\u8fdb\u884c\u91cd\u5efa\uff0c\u76f8\u6bd4\u4e8e\u524d\u9762\u63d0\u5230\u7684\u53cc\u76ee\u6a21\u578b\uff0c\u5b83\u6709\u66f4\u5f3a\u7684\u7ea6\u675f\u3001\u80fd\u5728\u591a\u4e2a\u5019\u9009\u4e2d\u9009\u62e9\u6700\u5408\u9002\u7684\u65b9\u6848\uff0c\u4ee5\u53ca\u80fd\u5f97\u5230\u66f4\u5b8c\u6574\u7684 3D</p> <p>\u6211\u4eec\u5728\u53cc\u76ee\u5339\u914d\u4e2d\uff0c\u9996\u5148\u5bfb\u627e\u80fd\u591f\u5339\u914d\u7684\u70b9\u5bf9\u518d\u505a\u63a5\u4e0b\u6765\u7684\u4e8b\u60c5\uff0c\u4f46\u662f\u5728\u591a\u89c6\u89d2\u4e2d\uff0c\u627e\u5230\u300c\u5339\u914d\u7684\u4e00\u7cfb\u5217\u70b9\u300d\u662f\u6bd4\u8f83\u56f0\u96be\u4e14\u8017\u65f6\u7684\uff0c\u56e0\u4e3a n \u4e2a\u70b9\u6709 \\(C_n^2\\) \u5bf9\u5339\u914d\u5173\u7cfb\u3002\u6240\u4ee5\u6211\u4eec\u8981\u53d8\u6362\u601d\u8def\uff0c\u6211\u4eec\u9700\u8981\u4ee5\u67d0\u4e00\u4e2a\u89c6\u89d2\u4e3a\u57fa\u7840\uff0c\u5e76\u679a\u4e3e\u8fd9\u4e2a\u70b9\u7684\u6df1\u5ea6\uff0c\u8ba1\u7b97\u91cd\u6295\u5f71\u8bef\u5dee\uff0c\u627e\u5230\u4f7f\u91cd\u6295\u5f71\u8bef\u5dee\u6700\u4f18\u79c0\u7684\u90a3\u4e2a\u6df1\u5ea6\u4f5c\u4e3a\u8fd9\u4e2a\u70b9\u7684\u6df1\u5ea6\uff08\u800c\u4e0d\u662f\u5728\u6bcf\u4e00\u4e2a\u5bf9\u6781\u7ebf\u4e0a\u627e\uff0c\u53ef\u4ee5\u601d\u8003\u4e3a\u4ec0\u4e48\uff09\u3002</p> <p>\u4e2a\u4eba\u7591\u95ee</p> <p>\u8bdd\u8bf4\u8fd9\u4e2a\u91cd\u6295\u5f71\u8bef\u5dee\u6307\u7684\u662f\u4ec0\u4e48\u554a\uff0c\u662f\u9700\u8981\u5148\u7b97\u597d\u5339\u914d\u70b9\u7136\u540e L2 \u8ddd\u79bb\u7684\u8bef\u5dee\u8fd8\u662f\u76f8\u4f3c\u5ea6\u7684\u8bef\u5dee\uff1f\u5982\u679c\u662f\u76f8\u4f3c\u5ea6\u7684\u8bef\u5dee\uff0c\u90a3\u600e\u4e48\u89e3\u51b3\u5f62\u53d8\uff1f</p> <ul> <li>multi-view stereo  MVS<ul> <li>\u5177\u4f53\u505a\u6cd5\u662f<ul> <li>\u53ef\u4ee5\u4f7f\u7528 Plane-Sweep<ul> <li>\u5bf9\u4e8e\u6bcf\u4e00\u4e2a\u5176\u4ed6\u89c6\u89d2\uff0c\u6784\u9020\u4e00\u4e2a\u5173\u4e8e x-y-z \u7684\u4e09\u7ef4\u8868\uff0c\u80fd\u591f\u67e5\u8be2\u5bf9\u4e8e\u53c2\u8003\u56fe\u7247<code>[x][y]</code>\u5904\u7684\u50cf\u7d20\uff0c\u5982\u679c\u5904\u4e8e\u6df1\u5ea6<code>[z]</code>\u65f6\u7684\u60c5\u51b5</li> <li>\u5229\u7528\u4e24\u6b21\u6295\u5f71\uff0c\u5148\u5728\u201cA\u201d\u5b57\u91cc\u76f8\u4f3c\u5230\u8fdc\u5904\uff0c\u7136\u540e\u518d\u659c\u7740\u6295\u5f71\u5230\u6bcf\u4e2a\u89c6\u89d2\u91cc</li> <li>\u6bcf\u4e00\u5c42\u5c42\u626b\u8fc7\u53bb</li> <li><ul> <li>\u5728\u4e0a\u56fe\u6570\u7ec4\u91cc\u627e\u6bcf\u4e00\u4e2a<code>[x][y]</code>\u91cc\u8868\u73b0\u6700\u597d\u7684<code>[z]</code>\u4f5c\u4e3a\u90a3\u4e2a\u50cf\u7d20\u7684\u6df1\u5ea6\u3002</li> </ul> </li> <li>\u7136\u800c\u8fd9\u4e2a\u505a\u6cd5\u8fd8\u662f\u4e0d\u592a\u9ad8\u6548\uff0c\u4e00\u4e2a\u66f4\u9ad8\u6548\u7684\u505a\u6cd5\uff0c\u662f PatchMatch\u3002<ul> <li>\u968f\u5373\u521d\u59cb\u5316\uff0c\u603b\u6709\u51e0\u4e2a\u662f\u63a5\u8fd1\u6700\u4f18\u89e3\u7684</li> <li>\u5bf9\u4e8e\u8fd9\u4e9b\u6bd4\u8f83\u4f18\u7684\u89e3\uff0c\u5b83\u9644\u8fd1\u7684\u50cf\u7d20\u7b54\u6848\u5728\u8fd9\u4e2a\u7b54\u6848\u7684\u9644\u8fd1\u5bfb\u627e\uff08\u4f20\u64ad\uff09\uff0c\u7136\u540e\u518d\u5728\u5c0f\u8303\u56f4\u5185\u8fdb\u4e00\u6b65\u4f18\u5316\uff08\u641c\u7d22\uff09</li> </ul> </li> </ul> </li> </ul> </li> </ul> </li> </ul>"},{"location":"cour_note/D2QD_Intro2CV/Lec08/#3d-reconstruction","title":"3D reconstruction","text":"<p>\u5177\u4f53\u6765\u8bf4\uff0c3D \u91cd\u5efa\u5305\u62ec\u8fd9\u4e48\u4e09\u4e2a\u6b65\u9aa4\uff1a</p> <ol> <li>\u6df1\u5ea6\u8ba1\u7b97</li> <li>\u6df1\u5ea6 -&gt; 3D\u7f51\u683c\u8868\u9762</li> <li>\u7eb9\u7406\u586b\u5145</li> </ol>"},{"location":"cour_note/D2QD_Intro2CV/Lec08/#3d-representations","title":"3D representations","text":"<p>\u8865\u5145\u56fe\u7247</p> <ul> <li>\u70b9\u4e91 point cloud</li> <li>\u4f53\u7d20\uff083d\u50cf\u7d20\uff09occupancy</li> <li>signed distance function (SDF)<ul> <li>\u5927\u5c0f\u8ddd\u79bb\u8868\u9762\u7684\u8ddd\u79bb\uff0c\u5185\u90e8\u4e3a\u8d1f\uff0c\u5916\u90e8\u4e3a\u6b63</li> <li>Truncated Signed Distance Function \u622a\u65adSDF\uff0c\u5373\u4ecd\u548c\u5927\u4e8e 1 \u90fd\u8bb0\u4e3a 1\uff0c\u5c0f\u4e8e -1 \u7684\u8bb0\u4e3a -1</li> </ul> </li> <li>\u7f51\u683c mesh\uff08\u6bd4\u8f83\u5e38\u7528\uff09</li> </ul>"},{"location":"cour_note/D2QD_Intro2CV/Lec08/#3d-surface-reconstruction","title":"3D surface reconstruction","text":"<ol> <li>\u6df1\u5ea6 -&gt; \u4f53\u7d20\u8868\u793a</li> <li>\u4f53\u7d20\u8868\u793a -&gt; \u4e09\u7ef4\u7f51\u683c</li> </ol>"},{"location":"cour_note/D2QD_Intro2CV/Lec08/#\u6df1\u5ea6---\u4f53\u7d20\u8868\u793a","title":"\u6df1\u5ea6 -&gt; \u4f53\u7d20\u8868\u793a","text":"<p>\u5e38\u7528\u65b9\u6cd5\uff1a</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec08/#depth-fusion-depth-maps-to-tsdf","title":"Depth Fusion \uff08depth maps to TSDF\uff09","text":"<p>\u3010\u5bf9\u4e8e\u56fe\u4e2d\u3011\uff1a</p> <ul> <li>\u53ef\u4ee5\u8ba1\u7b97\u6bcf\u4e00\u4e2a\u4f53\u7d20\u5230\u76f8\u673a\u4e2d\u5fc3\u7684\u8ddd\u79bb \\(d_p\\)</li> <li>\u6839\u636e\u5c0f\u5b54\u6210\u50cf\u89c4\u5219\uff0c\u53ef\u4ee5\u5f97\u5230\u4e0e\u5f53\u524d\u4f53\u7d20\u6240\u5bf9\u5e94\u7684\u50cf\u7d20\uff0c\u8bb0\u5bf9\u5e94\u7684\u50cf\u7d20\u7684\u6df1\u5ea6\u4e3a \\(D_k(u)\\)</li> <li>\u5219\u8be5\u4f53\u7d20\u7684 TSDF \u503c\u622a\u65ad\u524d\u4e3a \\(D_k(u) - d_p\\)</li> <li>\u5728\u591a\u56fe\u60c5\u51b5\u4e0b\uff0c\u6bcf\u4e00\u5f20\u56fe\u7684\u7ed3\u679c\u505a\u52a0\u6743\u8ba1\u7b97</li> </ul> <p>\u601d\u8def</p> <p>\u4e4b\u524d\u4e5f\u6709\u7c7b\u4f3c\u7684\u5185\u5bb9\u3002\u4e00\u4e2a\u603b\u7ed3\u6027\u7684\u60f3\u6cd5\u662f\uff0c\u5f53\u4f60\u9700\u8981\u628a\u300c\u5206\u8fa8\u7387\u300d\u4f4e\u7684\u4e1c\u897f\u6295\u5f71\u5230\u300c\u5206\u8fa8\u7387\u300d\u9ad8\u5230\u5730\u65b9\u53bb\u65f6\uff0c\u5e94\u5f53\u679a\u4e3e\u300c\u5206\u8fa8\u7387\u300d\u9ad8\u7684\u90a3\u4e00\u4fa7\u7684\u5355\u5143\uff0c\u7136\u540e\u5229\u7528\u300c\u5206\u8fa8\u7387\u300d\u4f4e\u7684\u8fd9\u4e00\u4fa7\u53bb\u8ba1\u7b97\uff0c\u800c\u4e0d\u662f\u4ece\u4f4e\u5230\u9ad8\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec08/#poisson-reconstruction-depth-maps-to-occupancy-volume","title":"Poisson reconstruction \uff08depth maps to occupancy volume\uff09","text":"<p>\u67cf\u677e\u91cd\u5efa</p> <ul> <li>\u6df1\u5ea6\u56fe -&gt; \u5e26\u6cd5\u5411\u91cf\u7684\u70b9\u4e91<ul> <li>Oriented points \u90a3\u91cc\u7684\u7bad\u5934\u662f\u8868\u9762\u6cd5\u5411\u91cf\uff08\u6df1\u5ea6\u7684\u68af\u5ea6\uff09</li> </ul> </li> <li>\u7528\u4f18\u5316\u7684\u65b9\u5f0f\u6c42\u89e3 indicator function \uff08\u5927\u6982\u5c31\u662f\u6700\u7ec8\u7ed3\u679c\u7684\u90a3\u4e2a\u7269\u4f53\u7684\u8868\u9762\u53d1\u5411\u91cf\u51fd\u6570\uff09<ul> <li>\u8fd9\u91cc\u6709\u4e00\u4e2a\u70b9\u5c31\u662f\uff0c\u4f53\u7d20\u7684\u66f2\u9762\u662f\u95ed\u5408\u7684\uff0c\u6240\u4ee5\u4f1a\u6709\u5185\u5916\u4e4b\u5206\uff0c\u5185\u90e8\u5b9e\u5fc3\u5916\u90e8\u7a7a\u5fc3\uff0c\u6240\u4ee5 indicator function \u5c31\u662f\u60f3\u540c\u65f6\u8868\u8fbe \u8868\u9762 \u548c \u5185\u5916 \u4e24\u4ef6\u4e8b\u3002</li> </ul> </li> </ul>"},{"location":"cour_note/D2QD_Intro2CV/Lec08/#\u4f53\u7d20\u8868\u793a---\u4e09\u7ef4\u7f51\u683c","title":"\u4f53\u7d20\u8868\u793a -&gt; \u4e09\u7ef4\u7f51\u683c","text":"<p>\u5e38\u7528\u65b9\u6cd5\uff1a</p> <p>Marching cubes</p> <ul> <li>\u4ee5 2D \u4e3a\u4f8b\uff0c\u5982\u679c\u4e00\u4e2a\u300c\u8fb9\u300d\u7684\u4e24\u8fb9\uff0c\u9ed1\u767d\u4e0d\u4e00\u81f4\uff08\u9ed1\u8868\u793a\u5916\u90e8\uff0c\u767d\u8868\u793a\u5185\u90e8\uff09\uff0c\u5219\u8bf4\u660e\u8fd9\u91cc\u5b58\u5728\u4e00\u4e2a\u8fb9\u754c\uff0c\u4e8e\u662f\u6807\u4e00\u4e2a\u70b9\uff0c\u7136\u540e\u5c06\u6240\u6709\u7684\u8fd9\u6837\u7684\u70b9\u6309\u7167\u7279\u5b9a\u987a\u5e8f\u8fde\u63a5\u8d77\u6765\uff0c\u5c31\u5f97\u5230\u7684\u4e86\u8fb9\u754c\u3002</li> <li>\u5177\u4f53\u6807\u5728\u8fb9\u754c\u7684\u54ea\u4e2a\u4f4d\u7f6e\uff0c\u5982\u679c\u662f SDF \u7684\u8bdd\u53ef\u4ee5\u8ba1\u7b97\u77e5\u9053\uff0c\u5426\u5219\u53ef\u80fd\u53ea\u80fd\u5728\u4e2d\u95f4\u4e86</li> <li> <p>\u4f46\u662f\u9700\u8981\u6ce8\u610f\u4e00\u4e2a\u683c\u5b50\u5982\u679c\u6709\u591a\u4e2a\u70b9\u7684\u65f6\u5019\u600e\u4e48\u8fde\u7684\u95ee\u9898\uff0c\u6709\u4e00\u4e2a\u8868\u53ef\u4ee5\u67e5\uff0c\u6491\u6b7b\u4e5f\u5c31 2^4=16 \u79cd\u60c5\u51b5</p> </li> <li> <p>\u5728 3D \u60c5\u51b5\u4e0b\uff0c\u5c31\u662f\u5728\u7acb\u65b9\u4f53\u91cc\u8fde\u63a5\u4e09\u4e2a\u70b9\u5f62\u6210\u4e09\u89d2\u9762\uff0c\u7136\u540e\u4e5f\u6709\u4e00\u4e2a\u8868\u53ef\u4ee5\u67e5\uff0c\u6491\u6b7b\u4e5f\u5c31 2^8=256 \u79cd\u60c5\u51b5\u3002</p> </li> </ul> <p></p>"},{"location":"cour_note/D2QD_Intro2CV/Lec08/#texture-mapping","title":"Texture mapping","text":"<p>\u5c55\u5f00 get \u7eb9\u7406\u56fe\uff08\u4e8c\u7ef4\u5750\u6807\u80fd\u591f\u5bf9\u5e94\u4e00\u4e2a\u7f51\u683c\u9762\uff09 using \u53c2\u6570\u5316</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec09/","title":"Lecture 9 | Deep Learning","text":"<p> \u7ea6 1839 \u4e2a\u5b57  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 6 \u5206\u949f</p> <p>\u6ce8\u610f</p> <p>\u672c\u6587\u5c1a\u672a\u5b8c\u5168\u6574\u7406\u597d\uff01</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec09/#\u673a\u5668\u5b66\u4e60\u6982\u8ff0","title":"\u673a\u5668\u5b66\u4e60\u6982\u8ff0","text":"<p>\u8bf4\u660e</p> <p>\u672c\u8bfe\u7a0b\u4e0d\u4f1a\u8be6\u7ec6\u4ecb\u7ecd\u5173\u4e8e\u673a\u5668\u5b66\u4e60\u7684\u6240\u6709\u77e5\u8bc6\uff0c\u4f46\u4ecd\u7136\u5bf9\u57fa\u7840\u6982\u5ff5\u6709\u6240\u8981\u6c42\uff0c\u6240\u4ee5\u5728\u6b64\u4ec5\u505a\u6982\u5ff5\u6027\u5bf9\u7b80\u4ecb\u3002</p> <p>\u673a\u5668\u5b66\u4e60(Machine Learning, ML) \u7c97\u7565\u7684\u6765\u8bf4\u5c31\u662f\u901a\u8fc7\u5bf9\u5927\u91cf\u6570\u636e\u8fdb\u884c\u5b66\u4e60\uff0c\u5728\u4e00\u5b9a\u89c4\u5219\u4e0b\u751f\u6210\u7a0b\u5e8f\uff0c\u5bf9\u4e8e\u673a\u5668\u5b66\u4e60\u6765\u8bf4\uff0c\u5b66\u4e60\u51fa\u6765\u7684\u8fd9\u4e2a\u201c\u7a0b\u5e8f\u201d\u7ed3\u679c\u662f\u6a21\u578b(model)\u3002</p> <p>\u800c\u5982\u679c\u7528\u6765\u5b66\u4e60\u7684\u662f\u88ab\u6807\u6ce8\u8fc7\u7684\u6570\u636e(labeled data)\uff0c\u5219\u79f0\u4e4b\u4e3a(\u6709)\u76d1\u7763(\u7684)\u5b66\u4e60(supervised learning)\u3002</p> <p>\u65e0\u8bba\u662f\u673a\u5668\u5b66\u4e60\u6280\u672f\u8fd8\u662f\u4f20\u7edf\u7684\u7f16\u7a0b\u6280\u672f\uff0c\u90fd\u662f\u4e3a\u4e86\u89e3\u51b3\u67d0\u4e2a\u95ee\u9898\u800c\u5b58\u5728\u7684\u3002\u800c\u89e3\u51b3\u4e00\u4e2a\u590d\u6742\u95ee\u9898\u2014\u2014\u6b63\u5982\u6211\u4eec\u4e4b\u524d\u5f3a\u8c03\u7684\u2014\u2014\u9700\u8981\u5bf9\u95ee\u9898\u8fdb\u884c\u62bd\u8c61\u5efa\u6a21\u3002\u800c\u4e00\u4e2a\u673a\u5668\u5b66\u4e60\u5b66\u4e60\u51fa\u6765\u7684\u6a21\u578b(model)\u53ef\u4ee5\u88ab\u89c6\u4f5c\u4e00\u4e2a\u5173\u4e8e\u8f93\u5165\u548c\u8f93\u51fa\u7684\u63cf\u8ff0\uff1a</p> \\[ \\text{Input } X \\rightarrow f_w \\rightarrow \\text{Output } Y \\] <p>\u800c\u6839\u636e\u8fd9\u91cc\u63d0\u5230\u7684\u201c\u8f93\u51fa\u201d\u7684\u4e0d\u540c\uff0c\u6309\u7167\u8fde\u7eed\u4e0e\u79bb\u6563\uff0c\u6211\u4eec\u5c06\u6240\u89e3\u51b3\u7684\u95ee\u9898\u533a\u5206\u4e3a\u56de\u5f52(regression)\u95ee\u9898\uff08\u7ed3\u679c \\(y\\) \u662f\u8fde\u7eed\u7684\u6570\u503c\uff09\u548c\u5206\u7c7b(classification)\u95ee\u9898\uff08\u7ed3\u679c \\(y\\) \u662f\u79bb\u6563\u7684\u6807\u7b7e\uff09\uff0c</p> <p>\u66f4\u5177\u9898\u7684\u6765\u8bf4\uff0c\u4e00\u822c\u673a\u5668\u5b66\u4e60\u7684 pipeline \u662f\u8fd9\u6837\u7684\uff1a</p> <ol> <li>\u5bf9\u95ee\u9898\u8fdb\u884c\u5b9a\u4e49\uff1b</li> <li>\u6536\u96c6\uff08\u548c\u5904\u7406\uff09\u7528\u6765\u5b66\u4e60\u7684\u6570\u636e\u96c6\uff1b</li> <li>\u5bf9\u95ee\u9898\u5efa\u6a21\uff0c\u5e76\u8bbe\u8ba1\u6a21\u578b\uff1b<ul> <li>\u62bd\u8c61\u5730\u6765\u8bf4\u662f\u51b3\u5b9a\u8f93\u5165\u8f93\u51fa\u7684\u5173\u8054\u5f62\u5f0f\uff1b</li> </ul> </li> <li>\u6a21\u578b\u8bad\u7ec3\uff1b<ul> <li>\u8bbe\u8ba1\u635f\u5931\u51fd\u6570\u6765\u8bc4\u4f30\u6a21\u578b\u7684\u6548\u679c\uff1b</li> <li>\u7528\u4f18\u5316\u6280\u672f\u6c42\u89e3\u4f7f\u6a21\u578b\u6548\u679c\u6700\u597d\u7684\u53c2\u6570\uff1b</li> </ul> </li> <li>\u6a21\u578b\u6d4b\u8bd5\uff1b<ul> <li>\u4e5f\u5c31\u662f\u7528\u6d4b\u8bd5\u6570\u636e\u96c6\u6d4b\u8bd5\u5b83\u7684\u8868\u73b0\uff1b</li> </ul> </li> </ol>"},{"location":"cour_note/D2QD_Intro2CV/Lec09/#\u7ebf\u6027\u5206\u7c7b\u5668","title":"\u7ebf\u6027\u5206\u7c7b\u5668","text":"<p>\u7ebf\u6027\u5206\u7c7b\u5668(Linear Classifier)\u6700\u65e9\u53eb\u611f\u77e5\u673a(Perceptron)\uff0c\u5b83\u662f ML \u4e2d\u4e00\u4e2a\u6700\u7b80\u5355\u4e5f\u662f\u6700\u57fa\u672c\u7684\u6784\u6210\u3002</p> \\[ y = f(x, W) = W x + b \\\\ \\begin{aligned}   &amp; \\text{where } x \\text{ means inputs, such as image, } \\\\   &amp; y \\text{ means outputs, such as the class of the object, } \\\\   &amp; \\text{and } W \\text{ is the parameters matrix.} \\end{aligned} \\] <p>\u53ef\u4ee5\u53d1\u73b0\uff0c\u5176\u6570\u5b66\u63cf\u8ff0\u5c31\u89e3\u91ca\u4e86\u5b83\u4e3a\u4ec0\u4e48\u53eb\u300c\u7ebf\u6027\u300d\u5206\u7c7b\u5668\u3002</p> <p>\u66f4\u8be6\u7ec6\u7684\u89e3\u91ca\u4e0d\u5728\u8fd9\u91cc\u5c55\u5f00\uff0c\u53ef\u4ee5\u67e5\u770b cs231n \u7b14\u8bb0\u7684\u76f8\u5173\u4ecb\u7ecd</p> <p>\u4f55\u65f6\u8f93\u51fa\u6bd4\u8f83\u5927\uff1f</p> <p>\u8f93\u51fa\u5927\uff0c\u6216\u8005\u8bf4\u5bf9\u4e8e\u67d0\u884c\u5927\uff0c\u6362\u53e5\u8bdd\u6765\u8bf4\u5c31\u662f\u5206\u7c7b\u5230\u8fd9\u4e00\u884c\u7684\u53ef\u80fd\u6027\u66f4\u5927\uff0c\u4e00\u822c\u662f \\(x\\) \u4e0e \\(W\\) \u7684\u5bf9\u5e94\u884c\u76f8\u4f3c\u65f6\u3002</p> <p>\u8fd9\u91cc\u6709\u4e00\u4e2a\u7279\u6b8a\u7684\u6982\u5ff5\u662f\u51b3\u7b56\u8fb9\u754c(Decision Boundary)\uff1a</p> <ul> <li>\\(w^Tx+b = 0\\)</li> <li>It's a line in 2D, a plane in 3D or hyperplane ...</li> </ul> <p></p>"},{"location":"cour_note/D2QD_Intro2CV/Lec09/#training","title":"Training","text":"<p>\u5982\u4f55\u627e\u5230\u6700\u4f73\u7684\u53c2\u6570\uff1f</p> <ul> <li>loss function</li> <li>optimization problem</li> </ul> <p>\u6700\u5c0f\u4e8c\u4e58\u6cd5\u7684\u7f3a\u70b9</p> <ul> <li>\u5bb9\u6613\u6536\u5230\u566a\u58f0\u5f71\u54cd</li> <li>\u5bf9\u4e8e classifier \u7684\u95ee\u9898\uff0c\u5f88\u96be\u7528\u201c\u505a\u5dee\u201d\u6765\u63cf\u8ff0\u5f97\u5206\u4e0e\u7c7b\u522b\u7684\u5173\u7cfb\u2014\u2014\u8ba9\u4ed6\u4ece\u4efb\u610f\u6570\u6620\u5c04\u5230\u4e00\u4e2a <code>[0,1]</code>\uff0csigmoid\uff0c\u53ef\u4ee5\u7406\u89e3\u6210\u201c\u6982\u7387\u201d\u3002i.e. softmax operator: \\(.....\\)</li> </ul> <p>\u8bc4\u4ef7\u4e24\u4e2a\u6982\u7387\u5206\u5e03\u662f\u5426\u76f8\u4f3c\uff0c\u5e38\u7528\u7684\u662f\u4ea4\u53c9\u5dee\uff0ccross entropy as loss function</p> \\[ S \\sim S(y) \\\\ D(S,L) = -\\sum_i L_i \\log S_i \\]"},{"location":"cour_note/D2QD_Intro2CV/Lec09/#neural-networks","title":"Neural Networks","text":"<p>\u7ebf\u6027\u5206\u7c7b\u6700\u65e9\u53eb\u611f\u77e5\u673a\uff0cperceptron</p> <p>\u7136\u800c\u6709\u4e9b\u5206\u7c7b\u53ef\u80fd\u662f\u975e\u7ebf\u6027\u7684\uff0c\u5982\u56fe</p> <p></p> <p>\u8fd9\u79cd\u65f6\u5019\u6211\u4eec\u53ef\u80fd\u4f1a\u4f7f\u7528\u4e00\u4e2a\u51fd\u6570\u5c06\u5b83\u4e0e\u7ebf\u6027\u5206\u7c7b\u6620\u5c04\u8d77\u6765\uff0c\u8fd9\u79cd\u51fd\u6570\u4e00\u822c\u53eb\u6fc0\u6d3b\u51fd\u6570 activation functions</p> <ul> <li>ReLU</li> <li>Sigmoid</li> </ul> <p>\u591a\u7c7b\u522b\u8868\u793a</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec09/#\u591a\u5c42\u611f\u77e5\u673a-multi-layer-perceptron","title":"\u591a\u5c42\u611f\u77e5\u673a Multi-layer perceptron","text":"\\[ \\sigma \\text{ is a nonlinear transform.} f(x) = \\sigma(w^T x + b) \\] <p>hidden layers</p> <p>\u5982\u679c\u6ca1\u6709\u975e\u7ebf\u6027\u6fc0\u6d3b\u51fd\u6570\uff0c\u6700\u540e\u7b49\u4ef7\u4e8e\u4e00\u4e2a\u5355\u5c42\u7ebf\u6027\u611f\u77e5\u673a</p> <p>Neural Networks</p> <p>\u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc Deep Neural Networks \u5c42\u6570\u591a =&gt; </p> <ul> <li>\u8868\u8fbe\u80fd\u529b \u2b06\ufe0f</li> <li>\u53c2\u6570 \u2b06\ufe0f</li> <li>\u8bad\u7ec3\u6570\u636e \u2b06\ufe0f \u6210\u672c \u2b06\ufe0f </li> <li>\u4f18\u5316\u95ee\u9898\u6c42\u89e3\u96be\u5ea6 \u2b06\ufe0f</li> </ul> <p>\u5168\u8fde\u5c42 Fully connected layer </p> <ul> <li>\u5355\u5c42\u53c2\u6570\u91cf\u5de8\u5927\uff08W \u5927\uff09</li> </ul>"},{"location":"cour_note/D2QD_Intro2CV/Lec09/#convolution-neural-networks","title":"Convolution Neural Networks","text":"<p>What is CNN? What is convolution? Layer Types: 1. Convolutional layer 2. Pooling layer 3. Fully-connected layer</p> <p></p> <p>\u5728 CV \u4e2d\uff0c\u6709\u65f6\u5019\u56fe\u50cf\u7684\u5c40\u90e8\u7279\u5f81\u5c31\u591f\u6211\u4eec\u8fdb\u884c\u5206\u7c7b\u3002\u8fd9\u610f\u5473\u7740\u6211\u4eec\u53ef\u80fd\u4e0d\u9700\u8981\u8ba9\u7f51\u7edc\u8fde\u4e0a\u6240\u6709\u7684\u90e8\u5206\u3002</p> <p>1 \u4e2a\u7f51\u7edc -&gt; 3 \u4e2a\u7f51\u7edc\uff0cwith weight sharing\uff0c\u56e0\u4e3a 3 \u4e2a\u7f51\u7edc\u90fd\u662f\u7528\u6765\u8bc6\u522b\u540c\u6837\u7684\u4e1c\u897f\u7684\uff0c\u6216\u8005\u8bf4\u529f\u80fd\u76f8\u540c\u3002</p> \\[ y = \\sigma(x \\otimes w + b) \\] <p>padding &amp; pooling &amp; stride</p> <p>\u597d\u5904\u662f\u53c2\u6570\u6bd4\u5168\u8fde\u5c42\u5c11\u5f88\u591a</p> <p>\u611f\u53d7\u91ce Receptive fields</p> <ul> <li>\u5c42\u6570\u8d8a\u591a\uff0c\u4e00\u822c\u8d8a\u5927</li> <li> P69</li> </ul>"},{"location":"cour_note/D2QD_Intro2CV/Lec09/#\u6c60\u5316\u5c42","title":"\u6c60\u5316\u5c42","text":"<p>\u628a\u4e0d\u540c\u5730\u996d\u7684\u7ed3\u679c\u7ed3\u5408\u5728\u4e00\u8d77\uff0c\u5c06\u54cd\u5e94\u56fe\u7684\u591a\u4e2a\u7ed3\u679c\u5408\u5e76\u4e3a\u540c\u4e00\u4e2a</p> <p>CNN \u4e00\u822c\u8fc7\u7a0b </p> <p> P71</p> <p>CNN \u7ecf\u5178\u7f51\u7edc\uff1aAlexNet, VGG, </p> <p>\u4e0d\u540c channel \u5355\u72ec\u505a ----&gt; Batch Normalization</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec09/#training-neural-networks","title":"Training Neural Networks","text":"<p>\u867d\u7136\u6211\u4eec\u6ca1\u6cd5\u627e\u5230\u4e00\u4e2a\u975e\u5e38\u597d\u7684\u65b9\u6cd5\u8bbe\u8ba1\u4e00\u4e2a\u201c\u6700\u4f73\u201d\u7684\u7f51\u7edc\uff0c\u4f46\u662f\u5982\u4f55\u5bfb\u627e\u5176\u4e2d\u6700\u597d\u7684\u53c2\u6570\u5219\u662f\u6709\u4e00\u7cfb\u5217\u4e25\u683c\u7684\u65b9\u6cd5\u3002</p> <p>loss function</p> <ul> <li>classification: cross-entropy</li> <li>regression: L2 loss</li> </ul> <p>optimization</p> <p>\u6700\u5c0f\u5316 loss function\uff0c\u4f7f\u7528\u5404\u79cd\u68af\u5ea6\u4e0b\u964d</p> <p>This training method is called \u540e\u5411/\u53cd\u5411\u4f20\u64ad back-propagation</p> \\[ \\mathbf{w}^{t+1} = \\mathbf{w}^t - \\eta_t\\frac{\\partial L}{\\partial \\mathbf{w}}\\mathbf{w}^t  \\] <p>\u6c42\u68af\u5ea6-\u300b\u590d\u5408\u51fd\u6570\u6c42\u5bfc-\u300b\u94fe\u5f0f\u6cd5\u5219</p> <p>\u5bf9\u4e8e\u73b0\u5728\u7684\u6df1\u5ea6\u5b66\u4e60\u5de5\u5177\u6765\u8bf4\uff0c\u53cd\u5411\u4f20\u64ad\u4e0e\u6c42\u5bfc\u7b49\u8fc7\u7a0b\u90fd\u53ef\u4ee5\u81ea\u52a8\u5b9e\u73b0\uff0c\u4e5f\u5c31\u662f\u8bf4\u6211\u4eec\u53ea\u9700\u8981\u8bbe\u8ba1\u597d\u7f51\u7edc\u7ed3\u6784\u548c loss function \u5373\u53ef\uff0c\u800c\u4f18\u5316\u90e8\u5206\u5219\u53ef\u4ee5\u901a\u8fc7\u5de5\u5177\u5b9e\u73b0\u3002</p> <p>\u968f\u673a\u68af\u5ea6\u4e0b\u964d\uff0c\u968f\u673a\u7684\u91c7\u6837\u4e00\u90e8\u5206\u70b9\uff0c\\(\\Omega\\) @P86\uff0c</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec09/#architecture--hyper-parameters","title":"Architecture &amp; hyper-parameters","text":"<p>\u65e0\u6cd5\u901a\u8fc7\u90a3\u4e9b\u80fd\u591f\u81ea\u52a8\u8ba1\u7b97\u7684\u6743\u91cd\uff0c\u6d89\u53ca\u5230\u7f51\u7edc\u8bbe\u8ba1\u7684\u4e00\u4e9b\u5185\u5bb9\u7684\u4e00\u4e9b\u53c2\u6570\uff0c\u6210\u4e3a\u8d85\u53c2\u6570 hyper-parameters\u3002</p> <p>\u65b9\u6cd5\uff1a\u8bd5\uff08\u5f53\u7136\u4e0d\u662f\u7528\u624b\u8bd5x\uff09\uff01</p> <p>How to prevent overfitting? \u2022 Cross validation and early stop \u2022 Regularization or dropout \u2022 Data augmentation</p> <p>\u5982\u4f55\u8bc4\u4ef7\u7ed3\u679c\u201c\u597d\u201d\u8fd8\u662f\u201c\u4e0d\u597d\u201d\uff1f</p> <p>\u5982\u4f55\u5206\u5272\u6570\u636e\u96c6\uff1f(cross validation: train &amp; validation &amp; test)</p> <p>Data split idea * 3</p> <p> P89\uff08cs231n also\uff09</p> <p>\u4e00\u79cd\u8fdd\u548c\u611f\uff0cvalidation \u53c2\u4e0e\u81ea\u52a8\u53cd\u9988\uff0ctest \u96be\u9053\u4e0d\u7b97\u4e00\u79cd\u4eba\u4e3a\u53cd\u9988\u5417\uff1f</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec09/#\u6b63\u5219\u5316","title":"\u6b63\u5219\u5316","text":"<p>\u589e\u52a0\u7ea6\u675f\u4ee5\u51cf\u5c11 over fit </p>"},{"location":"cour_note/D2QD_Intro2CV/Lec09/#dropout","title":"Dropout","text":"<p>\u8bad\u7ec3\u65f6\u5ffd\u7565\u4e00\u90e8\u5206\u54cd\u5e94\uff0c\u6d4b\u8bd5\u7684\u65f6\u5019\u4ecd\u7136\u4f7f\u7528</p> <p>\u65ed\u5b9d\uff1aDropout\u8bf4\u7684\u7b80\u5355\u4e00\u70b9\u5c31\u662f\uff1a\u6211\u4eec\u5728\u524d\u5411\u4f20\u64ad\u7684\u65f6\u5019\uff0c\u8ba9\u67d0\u4e2a\u795e\u7ecf\u5143\u7684\u6fc0\u6d3b\u503c\u4ee5\u4e00\u5b9a\u7684\u6982\u7387p\u505c\u6b62\u5de5\u4f5c\uff0c\u8fd9\u6837\u53ef\u4ee5\u4f7f\u6a21\u578b\u6cdb\u5316\u6027\u66f4\u5f3a\uff0c\u56e0\u4e3a\u5b83\u4e0d\u4f1a\u592a\u4f9d\u8d56\u67d0\u4e9b\u5c40\u90e8\u7684\u7279\u5f81\u3002</p> <p>\u7edf\u8ba1\u4e0a\u7b49\u6548\u4e8e L2</p> <p>\u6211\uff1a\u56e0\u4e3a\u6bcf\u4e2a\u70b9\u90fd\u6709\u53ef\u80fd\u6982\u7387\u6027\u5931\u6548\uff0c\u6cdb\u5316\u6027\u66f4\u5f3a\uff0c\u8fd9\u4e5f\u8981\u6c42\u67d0\u4e00\u4e2a\u7279\u5f81\u7684contributes\u4f1a\u88ab\u201c\u5206\u644a\u201d\u5f00\u6765\uff0c\u6240\u4ee5\u6548\u679c\u4e0a\u6709\u70b9\u50cfL2\u7684\u90a3\u79cd\u8ba9\u6743\u91cd\u66f4\u5c0f</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec09/#\u6570\u636e\u589e\u5e7f-data-augmentation","title":"\u6570\u636e\u589e\u5e7f Data augmentation","text":"<p>overfit \u53ca\u6570\u636e\u592a\u5c11\u8bad\u7ec3\u592a\u591a\uff0c\u6240\u4ee5\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u5bf9\u5df2\u6709\u6570\u636e\u53d8\u6362\u6765\u201c\u9020\u201d\u4e00\u4e9b\u6570\u636e\u51fa\u6765\uff0c\u6bd4\u5982\u7ffb\u8f6c\u3001\u62c9\u4f38\u2026\u2026</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec09/#batch-normalization","title":"Batch Normalization","text":"<p>\u5bf9\u591a\u4e2a channel \u5bf9\u7ed3\u679c\u8fdb\u884c\u5f52\u4e00\u5316\u64cd\u4f5c</p> <p>Reduce internal covariate shift\uff0c\u4ee5\u51cf\u5c11 channal \u4e4b\u95f4\u7684\u53d1\u6563\u6027\uff0c\u66f4\u7a33\u5b9a\u66f4\u6536\u655b</p> <p>For more: https://web.eecs.umich.edu/~justincj/teaching/eecs498/FA2020/</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec09/#deep-learning-frameworks","title":"Deep Learning Frameworks","text":"<ul> <li>Caffe \u8001\u4e1c\u897f</li> <li>TF \u5f00\u53d1\u8005\u66f4\u559c\u6b22</li> <li>PyTorch \u7814\u7a76\u8005\u66f4\u559c\u6b22</li> </ul>"},{"location":"cour_note/D2QD_Intro2CV/Lec09/#network-architectures","title":"Network Architectures","text":"<p>\u65e9\u671f\u4e0d\u53d7\u6b22\u8fce\uff1a\u6548\u679c\u5dee &amp; \u53ef\u63a5\u53d7\u6027\u5dee</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec09/#resnet","title":"ResNet","text":"<p>\u5047\u8bbe\u6570\u636e\u91cf\u591f\u5927\uff0c\u662f\u4e0d\u662f\u5c42\u6570\u8d8a\u591a\u8d8a\u597d\uff1f</p> <ul> <li>\u96be\u8bad\u7ec3\uff0c\u201c\u68af\u5ea6\u6d88\u5931\u201d\uff0c\u5c42\u6570\u592a\u591a\u4ee5\u540e\uff0c\u5230\u540e\u9762\u68af\u5ea6\u5c31\u5f88\u5c0f\u4e86\uff0c\u4e0b\u964d\u4e0d\u4e0b\u53bb\u4e86</li> <li>\u4f46\u662f\u4e3a\u4ec0\u4e48\u4f1a\u53d8\u5dee\u5462\uff1f</li> <li>\u5982\u4f55\u8bbe\u8ba1\u589e\u52a0\u5c42\u6570\u800c\u81f3\u5c11\u4e0d\u53d8\u5dee\u5462\uff1f<ul> <li>ResNet: \\(H(x) = F(x) + x\\)</li> <li>\u6b8b\u5dee\u5b66\u4e60 residual learning</li> </ul> </li> </ul>"},{"location":"cour_note/D2QD_Intro2CV/Lec09/#densenet","title":"DenseNet","text":"<p>\u66f4\u52a0\u7a20\u5bc6\u7684\u94fe\u63a5\uff0c\u672c\u5c42\u53d6\u51b3\u4e8e\u524d\u9762\u6240\u6709\u5c42</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec09/#mobilenets","title":"MobileNets","text":"<p>\u901f\u5ea6\u5feb</p> <p>NAS: Neural Architecture Search \u81ea\u52a8\u5316\u7f51\u7edc\u7ed3\u6784\u8bbe\u8ba1\uff0clearning to learn</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec09/#why-deep-learning-is-powerful","title":"why deep learning is powerful?","text":"<p>End-to-end learning\uff0c\u7aef\u5230\u7aef\u5b66\u4e60</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec10/","title":"Lecture 10 | Recognition","text":"<p> \u7ea6 1509 \u4e2a\u5b57  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 5 \u5206\u949f</p> <p>\u6ce8\u610f</p> <p>\u672c\u6587\u5c1a\u672a\u5b8c\u5168\u6574\u7406\u597d\uff01</p> <p>\u4e8c\u7ef4\u56fe\u50cf\u8bc6\u522b(Recognition)\u4e0b\u6709\u5f88\u591a\u4efb\u52a1\uff0c\u4e3b\u8981\u5206\u4e3a\u8fd9\u4e48\u51e0\u79cd\uff1a</p> <ul> <li>\u5206\u7c7b Classification</li> <li>\u8bed\u4e49\u5206\u5272 Semantic segmentation</li> <li>\u5bf9\u8c61\u68c0\u6d4b Object detection</li> <li>\u5b9e\u4f8b\u5206\u5272 Instance segmentation</li> </ul>"},{"location":"cour_note/D2QD_Intro2CV/Lec10/#semantic-segmentation","title":"Semantic segmentation","text":"<p>\u6bcf\u4e2a\u50cf\u7d20\u5c5e\u4e8e\u54ea\u4e2a\u7c7b\u522b\u8fd9\u79cd\u4fe1\u606f\u53eb\u8bed\u4e49\u4fe1\u606f\u3002</p> <ul> <li>\u8f93\u5165\uff1a\u56fe\u7247</li> <li>\u8f93\u51fa\uff1a\u6bcf\u4e2a\u50cf\u7d20\u7684\u7c7b\u522b\u6807\u7b7e\uff0c\u4e0d\u9700\u8981\u533a\u5206\u540c\u4e00\u7c7b\u522b\u7684\u4e0d\u540c\u5b9e\u4f8b</li> </ul> <p>\u6700\u6734\u7d20\u7684\u505a\u6cd5\u662f sliding window\uff0c\u53d6\u51fa\u4e00\u4e2a window \u653e\u8fdb\u5206\u7c7b\u673a\u5f97\u5230\u7ed3\u679c\uff0c\u4f46\u662f\u663e\u7136\u7531\u4e8e window \u5305\u542b\u7684\u4fe1\u606f\u592a\u5c11\uff0c\u800c\u4e14\u6548\u7387\u592a\u4f4e\uff0c\u8fd9\u4e2a\u65b9\u6cd5\u975e\u5e38 naive\u3002</p> <p>\u73b0\u5728\u6807\u51c6\u7684\u505a\u6cd5\u662f\u5168\u5377\u79ef\u7f51\u7edc(Fully Convolutional Network)</p> <ul> <li>Loss function: Per-pixel cross-entropy</li> </ul> <p>\u5c40\u9650\u6027\uff1a</p> <ul> <li>Receptive field is linear in number of conv layers</li> <li>Convolution on high resolution is expensive\uff08\u8017\u65f6\uff09</li> </ul> <p>\u6539\u8fdb\uff1a</p> <ul> <li>Downsampling: pooling, strided conv</li> </ul> <p>\u4f46\u662f\u7531\u4e8e\u6211\u4eec\u6700\u540e\u5e0c\u671b\u5f97\u5230\u7684\u662f\u4e00\u4e2a\u548c\u539f\u56fe\u4e00\u6837\u5927\u7684\u4e1c\u897f\uff0c\u6240\u4ee5\u6709\u5411\u4e0b\u91c7\u6837\u5c31\u80af\u5b9a\u4f1a\u6709\u5411\u4e0a\u91c7\u6837\uff08\u56de\u5fc6\uff1a\u63d2\u503c\uff09\u3002</p> <p>\u56fe\u50cf\u5411\u4e0a\u91c7\u6837\u4ee5\u540e\u53d8\u5927\u4ee5\u540e\u53c8\u5377\u79ef\uff0c\u8fd9\u4e2aTransposed convolution</p> <p> ppt P13</p> <p>\u4f46\u662f\u5f88\u663e\u7136\uff0c\u5728\u53d8\u5c0f\u53d8\u5927\u7684\u8fc7\u7a0b\u4e2d\u80af\u5b9a\u6709\u4fe1\u606f\u635f\u5931\u3002\u6240\u4ee5\u73b0\u5728\u4e00\u4e2a\u6bd4\u8f83\u6d41\u884c\u7684\u505a\u6cd5\u662f U-Net\uff0c\u4e5f\u5c31\u662f\u5927\u91cf\u5e94\u7528 skip-connection\u3002</p> <p> ppt P14 https://web.eecs.umich.edu/~justincj/teaching/eecs498/FA2020/</p> <p>DeepLab P15</p> <p>\u8003\u8651\u76f8\u90bb\u50cf\u7d20\u4e4b\u95f4\u7684\u5173\u8054\u6027\uff0c\u4f7f\u7528 CRF(Conditional random field) \u4f18\u5316 P16</p> <p>\u9a6c\u53ef\u592b\u968f\u673a\u573a\uff1f</p> <p>Unary potential: \u4f53\u73b0\u81ea\u5df1\u7684\u7279\u6027</p> <p>Pairwise potential: \u4f53\u73b0\u5173\u8054\u6027</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec10/#\u8861\u91cf\u6307\u6807-evaluation-metric-per-pixel-intersection-over-union-iou","title":"\u8861\u91cf\u6307\u6807 Evaluation metric: Per-pixel Intersection-over-union (IoU)","text":"<p>\\(IoU=\\frac{     \\text{Ground truth \u548c prediction \u7684\u4ea4\u96c6\u9762\u79ef} }{     \\text{Ground truth \u548c prediction \u7684\u5e76\u96c6\u9762\u79ef} }\\)  P19</p> <p>mIoU \u6307\u7684\u662f\u5206\u51fa\u6765\u7684\u4e0d\u540c\u7c7b\u522b\u7684 mean IoU</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec10/#object-detection","title":"Object detection","text":"<p>Bounding box (bbox)</p> <ul> <li>Class label</li> <li>Location (x,y)</li> <li> <p>Size (w,h)</p> </li> <li> <p>\u8f93\u5165\uff1a\u56fe\u50cf</p> </li> <li>\u8f93\u51fa\uff1a\u4e00\u5806 bounding box</li> </ul> <p>\u90a3\u4e48\u5982\u4f55\u5b9e\u73b0\u5462\uff1f\u6211\u4eec\u5148\u5047\u8bbe\u4e00\u5171\u53ea\u6709 1 \u4e2a\u5bf9\u8c61\uff0c\u90a3\u4e48\u6b64\u65f6\u548c\u5206\u7c7b\u4efb\u52a1\u662f\u975e\u5e38\u63a5\u8fd1\u7684\uff0c\u53ea\u9700\u8981\u518d\u989d\u5916\u6c42\u89e3\u4e00\u4e2a\u7a97\u53e3\u4f4d\u7f6e\u5373\u53ef\u3002</p> <p>\u90a3\u4e48\u591a\u4e2a\u7a97\u53e3\u5462\uff1f</p> <p>\u89e3\u51b3\u529e\u6cd5\u8fd8\u662f\u6ed1\u52a8\u7a97\u53e3\uff0c\u53ea\u4e0d\u8fc7\u4e0d\u540c\u4e4b\u524d\u7684\uff0c\u6211\u4eec\u73b0\u5728\u91c7\u7528\u7684\u65b9\u6cd5\u57fa\u672c\u4e0a\u4e5f\u662f\u57fa\u4e8e\u6ed1\u52a8\u7a97\u53e3\u5c55\u5f00\u7684\u3002\u800c\u5728\u8fd9\u79cd\u8bed\u5883\u4e0b\uff0c\u8fd9\u6837\u7684\u4e00\u4e2a\u6ed1\u52a8\u7a97\u53e3\u88ab\u79f0\u4e3a\u4e00\u4e2a\u63d0\u8bae(proposal)\u3002</p> <p>\u4f46\u662f\u663e\u7136\uff0c\u4f7f\u7528\u6700\u6734\u7d20\u7684\u6ed1\u52a8\u7a97\u53e3\u4f1a\u5bfc\u81f4\u201c\u63d0\u8bae\u201d\u8fc7\u591a\uff0c\u5bfc\u81f4\u6548\u7387\u592a\u4f4e\u3002\u6240\u4ee5\u6211\u4eec\u8981\u4f18\u5316\u8fd9\u4e2a\u8fc7\u7a0b\u3002</p> <p>\u4e00\u822c\u8fd9\u4e9b\u4f18\u5316\u7684\u65b9\u6cd5\u90fd\u662f\u542f\u53d1\u5f0f(heuristics)\u7684\u505a\u6cd5\uff0c\u4f8b\u5982 over-segmentation\uff0c </p> <p>\u800c\u8fd9\u7c7b\u65b9\u6cd5\u5c31\u662f R-CNN (region proposal &amp; CNN) P36</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec10/#evaluation-metric","title":"Evaluation metric","text":"<p>\u5bf9\u4e8e\u5355\u4e2a\u7269\u4f53\uff0c\u4ecd\u7136\u662f IoU</p> <p>P39</p> <p>\u4e3a\u4e86\u8bc4\u4ef7\u9884\u6d4b\u7ed3\u679c\u7684\u6b63\u786e\u6027\uff0c\u6211\u4eec\u9700\u8981\u4e3a\u5b83\u8bbe\u7f6e\u4e00\u4e2a\u9608\u503c\u3002</p> <p>\u800c\u5bf9\u4e8e\u591a\u4e2a\u7269\u4f53\uff0c\u5219\u4e0d\u90a3\u4e48\u7b80\u5355\uff1aP42</p> <p>\uff08\u56de\u5fc6\u7edf\u8ba1\u5b66\u5185\u5bb9\uff09</p> <p>positive: \u80af\u5b9a\u7684\u5047\u8bbe P</p> <p>negative: \u5426\u5b9a\u7684\u5047\u8bbe N</p> <p>true: \u5047\u8bbe\u662f\u6210\u7acb\u7684 T</p> <p>false: \u5047\u8bbe\u662f\u9519\u8bef\u7684 F</p> <p>\u6211\u4eec\u901a\u8fc7\u4e0b\u9762\u4e24\u4e2a\u6807\u51c6\u6765\u8054\u5408\u5224\u65ad\u6548\u679c\u3002</p> <p>\u7cbe\u5ea6 Precision = TP/(TP+FP)\uff1a\u63cf\u8ff0\u7ed9\u5b9a\u7684 bbox \u91cc\u6709\u591a\u5c11\u662f\u6b63\u786e\u7684</p> <p>\u53ec\u56de\u7387 Recall = TP/(TP+FN)\uff1a\u63cf\u8ff0\u6240\u6709\u5bf9\u8c61\u4e2d\uff0c\u88ab\u6211\u4eec\u8bc6\u522b\u51fa\u6765\u7684\u6709\u591a\u5c11</p> <p>\u4e00\u822c\u6765\u8bf4\uff0c\u8fd9\u4fe9\u4e1c\u897f\u6709\u4e00\u4e2a trade-off\u3002\uff08\u6982\u7edf\u91cc\u5e94\u8be5\u6709\u7c7b\u4f3c\u7684\u5185\u5bb9\uff09</p> <p>https://en.wikipedia.org/wiki/Precision_and_recall</p> <p>\u800c\u6700\u7ec8\u7684\u8861\u91cf\u65b9\u6cd5\uff0c\u662f Mean Average Precision (mAP)\u3002</p> <ol> <li>Run object detector on all test images</li> <li>For each category, compute Average Precision </li> <li>(AP) = area under Precision vs Recall Curves</li> </ol> <p>PPT p52</p> <p>\u5148\u505a\u6240\u6709\u7c7b\u522b\u7684 AP\uff0c\u7136\u540e\u53d6\u5e73\u5747\u5c31\u662f mAP</p> <p>mAP@threshold = ...</p> <p>COCOmAP = average(mAP@threshold_i), for i \\in {0.5, 0.55, 0.6, \u2026, 0.95}</p> <p>Non-Max Suppression</p> <p>\u5bf9\u4e8e\u540c\u4e00\u4e2a\u5bf9\u8c61\uff0c\u6211\u6709\u53ef\u80fd\u8bc6\u522b\u51fa\u597d\u51e0\u4e2a\u8bc6\u522b\u540c\u4e00\u4e2a\u7269\u4f53\u7684 bbox\uff0c\u6240\u4ee5\u6211\u53ef\u4ee5\u8003\u8651\u8bbe\u8ba1\u4e00\u79cd\u7b97\u6cd5\u51cf\u5c11\u8fd9\u79cd\u8bc6\u522b\u3002</p> <p>\u7b80\u5355\u6765\u8bf4\uff0c\u505a\u6cd5\u5c31\u662f\u627e score \u6700\u5927\u7684\uff0c\u7136\u540e\u770b\u5176\u4ed6 bbox \u548c\u8fd9\u4e2a bbox \u7684 IoU\uff0c\u5927\u4e8e\u4e00\u5b9a\u6743\u91cd\u65f6\uff0c\u8ba4\u4e3a\u5b83\u4eec\u662f\u4e00\u81f4\u7684\uff0c\u5c31\u53ef\u4ee5\u628a\u8f83\u5c0f\u7684\u90a3\u4e2a\u5220\u6389\u4e86\u3002 </p> <p>Fast R-CNN</p> <p>RoI pool \uff08\u6ca1\u542c\u61c2\uff0c\u6574\u7406\u7684\u65f6\u5019\u518d\u4ed4\u7ec6\u5b66\u4e00\u4e0b\uff09</p> <p>Faster R-CNN</p> <p>\u7528\u7f51\u7edc\uff08Region Proposal Network, RPN\uff09\u751f\u6210\u63d0\u8bae\u9009\u6846\uff0c</p> <p>\u951a\u70b9 anchor\uff1a</p> <p>\u5728\u8ba1\u7b97\u673a\u89c6\u89c9\u4e2d\uff0c\u951a\u70b9\u662f\u7528\u4e8e\u76ee\u6807\u68c0\u6d4b\u7684\u9884\u5b9a\u4e49\u6846\u6216\u611f\u5174\u8da3\u533a\u57df\u3002\u951a\u70b9\u80fd\u591f\u5e2e\u52a9\u5377\u79ef\u795e\u7ecf\u7f51\u7edc\u8bc6\u522b\u56fe\u50cf\u4e2d\u5b58\u5728\u7684\u7269\u4f53\u53ca\u5176\u4f4d\u7f6e\uff0c\u4ece\u800c\u63d0\u9ad8\u76ee\u6807\u68c0\u6d4b\u7684\u51c6\u786e\u6027\u3002\u951a\u70b9\u901a\u5e38\u7531\u4e00\u7ec4\u9884\u5b9a\u4e49\u7684\u957f\u5bbd\u6bd4\u548c\u5c3a\u5ea6\u5b9a\u4e49\uff0c\u8fd9\u4e9b\u56e0\u7d20\u51b3\u5b9a\u4e86\u5b83\u4eec\u7684\u5927\u5c0f\u548c\u5f62\u72b6\u3002\u5728\u8bad\u7ec3\u671f\u95f4\uff0cCNN\u5b66\u4e60\u9884\u6d4b\u76f8\u5bf9\u4e8e\u8fd9\u4e9b\u951a\u70b9\u7684\u7269\u4f53\u7684\u4f4d\u7f6e\u548c\u5927\u5c0f\u3002\u4f7f\u7528\u951a\u70b9\u53ef\u4ee5\u68c0\u6d4b\u4e0d\u540c\u5927\u5c0f\u548c\u5bbd\u9ad8\u6bd4\u7684\u7269\u4f53\uff0c\u5e76\u6709\u52a9\u4e8e\u63d0\u9ad8\u76ee\u6807\u68c0\u6d4b\u5728\u590d\u6742\u573a\u666f\u4e0b\u7684\u51c6\u786e\u6027\u3002----chatGPT</p> <p>RPN \u7684\u5927\u81f4\u601d\u8def\u662f\uff0c\u628a\u751f\u6210\u9009\u6846\u95ee\u9898\u8f6c\u5316\u4e3a\u6253\u5206\u95ee\u9898\uff0c\u5177\u4f53\u6765\u8bf4\u662f\u7ed9\u6bcf\u4e2a\u50cf\u7d20\u6253\u5728\u8be5\u4f4d\u7f6e\u6709\u4e00\u4e2a\u7279\u5b9a size \u7684\u6846\u7684\u53ef\u80fd\u6027\u7684\u5206\u3002</p> <p>\u4e8c\u9636\u6bb5\u5bf9\u8c61\u68c0\u6d4b\u7b26 two-stage object detector</p> <ol> <li></li> <li></li> </ol> <p> P76 \u5404\u79cd\u65b9\u6cd5\u7684\u6548\u679c\u6392\u5e8f\u3002</p> <p>\u4e00\u79cd\u5bf9 two-stage object detector \u7684\u6539\u8fdb\u662f single-stage object detector\uff0c\u5927\u6982\u5c31\u662f\u5728\u505a RPN \u7684\u540c\u65f6\u53bb\u9884\u6d4b\u8fd9\u4e2a\u6846\u6807\u8bb0\u7684\u662f\u67d0\u4e2a\u7c7b\u522b\u7684\u6982\u7387\u3002</p> <p>single-stage \u7684\u4ee3\u8868\u6027\u5de5\u4f5c\uff1aYOLO</p> <p>two-stage v.s. single-stage</p> <ul> <li>Two-stage is generally more accurate \uff08\u6570\u636e\u91cf\u8db3\u591f\u5927\uff09</li> <li>Single-stage is faster</li> </ul> <p>\u4f46\u662f\u6211\u4eec\u4e0a\u9762\u7684\u5de5\u4f5c\u90fd\u6ca1\u8003\u8651\u5c3a\u5ea6\u53d8\u5316\uff0cFeature pyramid network \u5728\u8fd9\u65b9\u9762\u63d0\u51fa\u4e86\u89e3\u51b3\u65b9\u6848\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec10/#instance-segmentation","title":"Instance segmentation","text":"<p>Faster R-CNN + additional head</p> <p>Mask R-CNN</p> <p>Deep snake</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec10/#panoptic-segmentation","title":"Panoptic segmentation","text":"<p>Microsoft COCO dataset</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec10/#human-pose-estimation","title":"Human pose estimation","text":"<p>keypoints</p> <p>represent joint location as the heatmap // hourglass networks</p> <p>Top-down: - Detect humans and detect keypoints in each bbox - Example: Mask R-CNN - \u6700\u5927\u7684\u95ee\u9898\u8fd8\u662f\u6162</p> <p>Bottom-up: - Detect keypoints and group keypoints to form humans - Example: OpenPose \u5148\u627e kpts\uff0c\u518d\u5229\u7528 Affinity Fields \u628a\u5c5e\u4e8e\u4e00\u4e2a\u4eba\u7684 kpts \u5408\u5728\u4e00\u8d77\u3002</p> <p>Top-down is generally more accurate Bottom-up is faster\uff0c\u800c\u4e14\u5728\u906e\u6321\u60c5\u51b5\u4e0b\u4e5f\u6709\u5b83\u7684\u4f18\u52bf</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec10/#optical-flow","title":"Optical flow","text":"<p>\u5149\u6d41</p> <p>video classification</p> <p>\u4e00\u4e2a\u505a\u6cd5\u662f\u628a\u89c6\u9891\u5f53\u4f5c\u4e00\u4e2a 3d \u56fe\u50cf\u53bb\u505a\uff0c\u5373 3D CNN\u3002\u4f46\u662f\u6570\u636e\u7ef4\u5ea6\u975e\u5e38\u5927\u3002</p> <p>Temporal action localization</p> <p>Spatial-temporal detection</p> <p>\u505a\u6cd5\u4e5f\u53ef\u4ee5\u5f53\u4f5c\u4e00\u4e2a 3D \u7684 R-CNN \u53bb\u505a\u3002</p> <p>Multi-object tracking</p> <p>\u5bf9\u6bcf\u4e00\u5e27\u505a\u7269\u4f53\u68c0\u6d4b\uff0c\u7136\u540e\u5728\u6bcf\u4e00\u5e27\u4e4b\u95f4\u505a\u5173\u8054\u5339\u914d\u3002</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec11/","title":"Lecture 11 | 3D Deep Learning","text":"<p> \u7ea6 385 \u4e2a\u5b57  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 1 \u5206\u949f</p> <p>\u6ce8\u610f</p> <p>\u672c\u6587\u5c1a\u672a\u5b8c\u5168\u6574\u7406\u597d\uff01</p> <p>Deep Learning for 3D reconstruction</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec11/#feature-matching","title":"Feature matching","text":"<p>recap: SfM // Colmap</p> <p>use deep learning to improve feature matching</p> <p>\u4f20\u7edf\u65b9\u6cd5\u7684\u7f3a\u70b9\u5c31\u662f\u56e0\u4e3a\u8fd9\u4e9b\u65b9\u6cd5\u90fd\u662f handcrafted \u7684\u3002\u6240\u4ee5\u6211\u4eec\u5e0c\u671b\u80fd\u591f\u7528 deep learning \u6765\u589e\u5f3a\u6548\u679c\u3002</p> <p></p> <p>example: SuperPoint\u3001SuperGlue</p> <ul> <li>CNN-base descriptor \u597d\u6709\u610f\u601d\uff01</li> </ul> <p>\u63cf\u8ff0\u503c\uff1a</p> <ol> <li>contrastive loss</li> <li>triplet loss</li> </ol> <p>\u5b9e\u9645\u4e0a\u672c\u8d28\u7c7b\u4f3c\uff0c\u6548\u679c\u76f8\u8fd1</p> <p>\u4e3b\u6d41\u7528 MVS \u6765\u751f\u6210\u8bad\u7ec3\u6570\u636e</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec11/#object-pose-estimation","title":"Object Pose Estimation","text":"<p>\u672c\u8d28\u4e0a\u662f\u5728\u8ba8\u8bba\u7269\u4f53\u5728\u91cd\u5efa\u7a7a\u95f4\u4e2d\u7684\u5750\u6807\u7cfb\u548c\u76f8\u673a\u7a7a\u95f4\u4e2d\u7684\u5750\u6807\u7cfb\u7684\u53d8\u6362\u5173\u7cfb\u3002</p> <p>PnP</p> <p>\u53ef\u662f\u96be\u5c31\u96be\u5728\uff0c\u5982\u4f55\u5bfb\u627e 3D-2D \u7684\u5173\u7cfb\u5462\uff1f</p> <p>\u4e00\u4e2a idea \u662f\uff0c\u9996\u5148\u5f97\u5230\u4e00\u4e2a\u8f83\u597d\u7684\u91cd\u5efa\uff0c\u7136\u540e\u57fa\u4e8e\u8fd9\u4e2a\u91cd\u5efa\u6a21\u578b\uff0c\u6211\u4eec\u5c31\u53ef\u4ee5\u4ece\u522b\u7684\u601d\u8def\u6765\u770b\u8fd9\u4ef6\u4e8b\u3002</p> <p>pose refinement methods</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec11/#human-pose-estimation","title":"Human Pose Estimation","text":"<p>(Markerless) MoCap</p> <p>Monocular 3D Human Pose Estimation (eg. Vnet)</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec11/#depth-estimation","title":"Depth Estimation","text":"<p>MVSNet</p> <p>MVS</p> <p>\u79bb\u6563\u8868\u793a\u3001\u9690\u5f0f\u8868\u793a\uff08\u7528\u4e00\u4e2a\u7f51\u7edc\u6765\u8868\u793a\u4e00\u4e2a\u51fd\u6570 Implicit Neural Representations\uff0c\u4ee3\u8868\uff1aNeRF\uff09</p> <p>Replacing density field in NeRF by SDF: NeuS</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec11/#single-image-to-3d","title":"Single Image to 3D","text":""},{"location":"cour_note/D2QD_Intro2CV/Lec11/#deep-learning-for-3d-understanding","title":"Deep learning for 3D understanding","text":"<p>\u8ba1\u7b97\u5f00\u9500\u5f88\u5927</p> <p>\u8fd1\u51e0\u5e74\u63d0\u51fa\u7684\u89e3\u51b3\u65b9\u6848\uff1aSparse ConvNets</p> <p>Octree \u516b\u53c9\u6811\uff0c\u7a7a\u95f4\u5212\u5206</p> <p>\u7a00\u758f\u5377\u79ef\uff0c\u53ea\u6709\u6709\u503c\u7684\u5730\u65b9\u8fdb\u884c\u5377\u79ef</p> <p>\u7531\u4e8e\u5377\u79ef\u7b49\u64cd\u4f5c\u662f\u5efa\u7acb\u5728\u7f51\u683c\u4e0a\u7684\uff0c\u800c\u70b9\u4e91\u5e76\u4e0d\u5b9a\u4e49\u5728\u7f51\u683c\u4e0a\uff0c\u6240\u4ee5\u5bf9\u70b9\u4e91\u8fdb\u884c\u5377\u79ef\u5219\u9700\u8981\u4e00\u4e9b\u5176\u4ed6\u65b9\u6cd5\u3002</p> <p>\u4e00\u4e2a\u76f8\u5173\u5de5\u4f5c\u662f PointNet\uff0c\u4e13\u95e8\u7528\u5728\u5bf9\u70b9\u4e91\u4e0a\u3002\u8fd8\u6709 PointNet++</p> <p>3D Semantic Segmentation</p> <p>3D Object Detection</p> <p>3D Instance Segmentation</p> <p>PointRCNN</p> <p>Frustum PointNets</p> <p>\u6570\u636e\u96c6\uff1aShapeNet, PartNet,SceneNet , ScanNet</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec12/","title":"Lecture 12 | Computational Photography 1","text":"<p> \u7ea6 253 \u4e2a\u5b57  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 1 \u5206\u949f</p> <p>\u6ce8\u610f</p> <p>\u672c\u6587\u5c1a\u672a\u5b8c\u5168\u6574\u7406\u597d\uff01</p> What's \u8ba1\u7b97\u6444\u5f71\uff1f <p>...</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec12/#high-dynamic-range-imaging-hdr","title":"High Dynamic Range Imaging (HDR)","text":"<p>\u6211\u4eec\u5e0c\u671b\u4eae\u7684\u548c\u6697\u7684\u5730\u65b9\u7ec6\u8282\u90fd\u5f88\u4e30\u5bcc</p> <p>\u66dd\u5149 exposure = Gain\u589e\u76ca * Irradiance\u8f90\u7167\u5ea6 * Time\u66dd\u5149\u65f6\u95f4</p> <p>\u5206\u522b\u53d6\u51b3\u4e8e\u2026\u2026</p> <ul> <li>\u5feb\u95e8</li> <li>\u5149\u5708</li> <li>ISO \u611f\u5149\u5ea6<ul> <li>\u9ad8\uff1a\u66f4\u4eae\u3001\u66f4\u591a\u566a\u58f0</li> </ul> </li> </ul> <p>Dynamic range</p> <p>The ratio between the largest and smallest values of a certain quantity </p> <p>HRD: \u4e0d\u540c\u4eae\u5ea6\u90fd\u62cd\u4e00\u4e9b\uff0c\u7136\u540e\u5408\u6210</p> <p>12 to 8 -&gt; tone mapping</p> <p>Gamma compression</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec12/#deblurring","title":"Deblurring","text":"<p>\u6a21\u7cca\u7684\u4e24\u4e2a\u4e3b\u8981\u539f\u56e0\uff1adefocus and motion blur</p> <p>blurred image = clear image * blur kernel</p> <p>deblurring = deconvolution</p> <ul> <li>Non-blind image deconvolution, NBID</li> <li>Blind image deconvolution, BID</li> </ul> <p>inverse filter</p> <p>wiener filter</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec12/#colorization","title":"Colorization","text":"<p>\u6700\u5173\u952e\u7684\u95ee\u9898\u662f\uff0c\u5982\u4f55\u51b3\u5b9a\u4e0a\u7684\u989c\u8272</p> <p>\u4e3b\u8981\u6709\u4e24\u7c7b\u65b9\u6cd5\uff1a</p> <ol> <li>sample-based colorization</li> <li>interactive colorization</li> </ol>"},{"location":"cour_note/D2QD_Intro2CV/Lec12/#sample-based","title":"Sample-based","text":"<p>...</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec12/#interactive","title":"Interactive","text":"<p>...</p> <p>\u5bf9\u4e8e\u89c6\u9891</p> <p>Colorful Image Colorization</p> <p>GAN (Generative Adversarial Network)</p> <ul> <li>\u4e24\u4e2a\u4e00\u8d77\u8bad\u7ec3\uff0cmin-max problem  </li> <li>GAN \u5f88\u96be\u6536\u655b\uff0c\u4e0d\u597d\u8c03</li> <li>adversarial loss</li> </ul>"},{"location":"cour_note/D2QD_Intro2CV/Lec12/#more-image-synthesis-tasks","title":"more Image synthesis tasks","text":"<ul> <li>image to image translation<ul> <li>pix2pix gan</li> </ul> </li> <li>style transfer</li> <li>text-to-photo</li> <li>image dehazing</li> <li>customized gaming</li> </ul> <p>GAN \u7684\u6539\u8fdb\uff1aCycle-GAN\uff0c\u89e3\u51b3\u4e86\u7f3a\u5c11\u6210\u5bf9\u7684\u8bad\u7ec3\u6570\u636e\u7684\u95ee\u9898</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec12/#super-resolution","title":"Super Resolution","text":"<p>up sampling</p> <p>bi-cubic</p> <p>super resolution using GAN</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec13/","title":"Lecture 13 | Computational Photography 2","text":"<p> \u7ea6 90 \u4e2a\u5b57 </p> <p>\u6ce8\u610f</p> <p>\u672c\u6587\u5c1a\u672a\u5b8c\u5168\u6574\u7406\u597d\uff01</p>"},{"location":"cour_note/D2QD_Intro2CV/Lec13/#image-based-rendering","title":"Image-based Rendering","text":"<p>rendering: from 3D models to images.</p> <p>Image-based Rendering: images -&gt; 3D Models -&gt; novel views.</p> <p>representations:</p> <ul> <li>Textured Mesh (surface-based representations)</li> <li>Light Fields and Lumigraphs<ul> <li>\u727a\u7272\u4e86\u4e00\u4e2a\u65b9\u5411\uff0c\u51cf\u5c11\u4e86\u4e00\u4e2a\u7eac\u5ea6</li> <li>\u53ea\u80fd\u5185\u91c7\u6837</li> </ul> </li> <li>Depth Warping</li> <li>Multi-plane Images (MPI) (volume-based representations)<ul> <li>rgba x multi planes</li> <li>Neural Volumes</li> </ul> </li> <li>Neural Radiance Fields</li> </ul> <p>surface-based representations</p> <ul> <li>a</li> <li>da</li> </ul> <p>volume-based representations</p> <ul> <li>a</li> <li>da</li> </ul> <p>\u81ea\u7531\u89c6\u70b9\u89c6\u9891</p>"},{"location":"cour_note/D3QD_OperatingSystem/","title":"\ud83d\udc8e \u64cd\u4f5c\u7cfb\u7edf | Operating System","text":"<p> \u7ea6 243 \u4e2a\u5b57  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 1 \u5206\u949f</p> <p>\u8bfe\u7a0b\u4fe1\u606f</p> <ul> <li>\u667a\u4e91\u94fe\u63a5\uff1a\ud83d\udd17</li> <li>\u6388\u8bfe\uff1a\u5b63\u6c5f\u6c11</li> <li>\u8bfe\u672c\uff1aOperating System Concepts (10th edition)</li> </ul> <p>\u5206\u6570\u6784\u6210</p> <ul> <li>[50%] \u5e73\u65f6\u6210\u7ee9<ul> <li>[5%] HOMEWORK</li> <li>[5%] Quiz / \u70b9\u540d</li> <li>[20%] Lab \u62a5\u544a\uff08\u6bcf 5 \u884c\u4ee3\u7801\u9700\u8981\u6ce8\u91ca\uff0c\u9700\u8981\u6709\u5fc3\u5f97\u4e0e\u95ee\u9898\u8ba8\u8bba\uff0c\u5360 20%\uff09</li> <li>[20%] Lab \u9a8c\u6536</li> <li>[6%] Bonus<ul> <li>[4%] Lab 7</li> <li>[2%] \u8bfe\u5802\u56de\u7b54\u95ee\u9898\uff0c0.5/\u6b21</li> </ul> </li> </ul> </li> <li>[50%] \u671f\u672b\u6210\u7ee9\uff08\u5141\u8bb8\u643a\u5e26 3 \u5f20 A4\uff0c\u5141\u8bb8\u6253\u5370\uff09</li> </ul> <p>\u7b14\u8bb0\u53c2\u8003</p> <p>\u672c\u8bfe\u7a0b\u7684\u7b14\u8bb0\u4e3b\u8981\u53c2\u8003\u4e86\u5982\u4e0b\u8d44\u6599\uff1a</p> <ul> <li>Operating System Concepts (10th edition)</li> <li>2024 \u64cd\u4f5c\u7cfb\u7edf\u8003\u7814\u590d\u4e60\u6307\u5bfc\uff08\u738b\u9053\uff09\uff08\u540e\u5f03\u7528\uff09</li> <li>\u54b8\u9c7c\u6684\u7684\u64cd\u4f5c\u7cfb\u7edf\u7b14\u8bb0</li> </ul> <p>list</p> <ul> <li> Unit 0: \u603b\u89c8 | Overview</li> <li> Unit 1: \u8fdb\u7a0b\u7ba1\u7406 | Process Management</li> <li> Unit 2: \u540c\u6b65 | Synchronization<ul> <li> Part 1: \u540c\u6b65\u5de5\u5177 | Synchronization Tools</li> <li> Part 2: \u7ecf\u5178\u540c\u6b65\u4f8b\u5b50 | Synchronization Problems Examples</li> <li> Part 3: \u6b7b\u9501 | Deadlocks</li> </ul> </li> <li> Unit 3: \u5185\u5b58\u7ba1\u7406 | Memory Management<ul> <li> Part 1: \u4e3b\u5b58 | Main Memory</li> <li> Part 2: \u865a\u62df\u5185\u5b58 | Virtual Memory</li> </ul> </li> <li> Unit 4: \u5b58\u50a8\u7ba1\u7406 | Storage Management</li> <li> Unit 5: \u6587\u4ef6\u7cfb\u7edf | File System</li> </ul>"},{"location":"cour_note/D3QD_OperatingSystem/Unit0-brief/","title":"[\u6559\u5b66\u7248] Unit 0: \u603b\u89c8 | Overview","text":"<p> \u7ea6 3594 \u4e2a\u5b57  23 \u884c\u4ee3\u7801  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 12 \u5206\u949f</p> \u4e24\u4e2a\u4efb\u52a1 <ol> <li>\u5bf9\u64cd\u4f5c\u7cfb\u7edf\u8fdb\u884c\u4e00\u4e2a\u8f83\u4e3a\u62bd\u8c61\u7684\u4ecb\u7ecd\uff0c\u540c\u65f6\u5efa\u7acb\u8d77\u6574\u95e8\u8bfe\u7a0b\u7684\u6846\u67b6\uff0c\u65b9\u4fbf\u8bfb\u8005\u5728\u4e4b\u540e\u7684\u5b66\u4e60\u8fc7\u7a0b\u4e2d\u80fd\u6709\u4e00\u4e2a\u6bd4\u8f83\u603b\u4f53\u7684\u8ba4\u8bc6\uff0c\u80fd\u5e26\u7740\u76ee\u7684\u53bb\u5b66\u4e60\u5177\u4f53\u7684\u77e5\u8bc6\uff1b</li> <li>\u4ecb\u7ecd\u4e00\u4e9b\u6bd4\u8f83\u57fa\u7840\u7684\u5185\u5bb9\uff0c\u6216\u662f\u4e00\u4e9b\u6bd4\u8f83\u7410\u788e\u3001\u4ec5\u9700\u4e86\u89e3\u7684\u5185\u5bb9\uff1b</li> </ol> \u201c\u5b9a\u4e49\u4e0d\u5b58\u5728\u4e86\u201d <ul> <li>\u5f88\u591a\u6982\u5ff5\u90fd\u5f88\u96be\u754c\u5b9a\u4e00\u4e2a\u660e\u786e\u7684\u754c\u9650\u3002</li> </ul> \u64cd\u4f5c\u7cfb\u7edf\u6982\u8ff0 \u4f55\u4e3a\u64cd\u4f5c\u7cfb\u7edf \u2460 \u4ece\u804c\u80fd\u4e0a\u770b <p></p> <ul> <li> <p>\u4e00\u4e2a\u8bcd\u6982\u62ec\uff1a\u8d44\u6e90\u7ba1\u7406\u7cfb\u7edf\uff1b</p> </li> <li> <p>\u81ea\u4e0a\u800c\u4e0b\uff1b</p> </li> <li>\u81ea\u4e0b\u800c\u4e0a\uff1b</li> </ul> <p>\u8d44\u6e90\uff1aCPU\u3001\u5185\u5b58\u3001\u8bbe\u5907\u2026\u2026\u2026</p> <ul> <li>\u4e4b\u540e\u5c06\u56f4\u7ed5\u8981\u5982\u4f55\u7ef4\u62a4\u548c\u64cd\u4f5c\u5404\u79cd\u8d44\u6e90\u800c\u5c55\u5f00\u7684\u3002</li> </ul> \u2461 \u4ece\u5b58\u5728\u4e0a\u770b <ul> <li>\u4e00\u4e2a\u8bcd\u6982\u62ec\uff1a\u4e0d\u505c\u8fd0\u884c\u7684\uff0c\u7528\u6765\u8dd1\u8f6f\u4ef6\u7684\u8f6f\u4ef6\u7a0b\u5e8f\uff08\u53cd\u5e94\u4e86\u64cd\u4f5c\u7cfb\u7edf\u4e3a\u4f55\u8bde\u751f\uff09\uff1b</li> </ul> <p>\u5185\u6838(kernel)\u2014\u2014\u81ea\u8ba1\u7b97\u673a\u5f00\u673a\u540e\u5c31\u4e0d\u505c\u5728\u8fd0\u884c\uff08\u6211\u4eec\u5b66\u7684\u57fa\u672c\u90fd\u662f kernel \u7684\u4e1c\u897f\uff09\u3002</p> \u603b\u7ed3 <p>The common functions of controlling and allocating resources are then brought together into one piece of software: the operating system. --Operating System Concepts (10th edition)</p> \u5982\u4f55\u8bc4\u4ef7\u64cd\u4f5c\u7cfb\u7edf <ul> <li>\u53ef\u9760\u6027\u548c\u5b89\u5168\u6027\uff1b</li> <li>\u6613\u7528\u6027\uff1b</li> <li>\u9ad8\u6548\u6027\uff1b</li> <li>\u516c\u5e73\u6027\uff1b</li> <li>\u53ef\u6269\u5c55\u6027\uff0c\u6613\u7ef4\u62a4\u6027\uff1b</li> <li>...</li> </ul> <p>\u6ce8\u610f</p> <p>\u4e0a\u8ff0\u89c2\u70b9\u5e76\u4e0d\u5168\u9762\u4e5f\u4e0d\u4e00\u5b9a\u5b8c\u5168\u6b63\u786e\uff0c\u6709\u4e00\u5927\u90e8\u5206\u90fd\u662f\u6211\u7684\u4e2a\u4eba\u7406\u89e3\uff0c\u8bf7\u8bfb\u8005\u8fa8\u8bc1\u5730\u770b\u5f85\uff0c\u5982\u679c\u6709\u9519\u8bef\u8bf7\u52a1\u5fc5\u544a\u8bc9\u6211\uff01</p> \u64cd\u4f5c\u7cfb\u7edf\u7684\u6574\u4f53\u8bbe\u8ba1 \u8ba1\u7b97\u673a\u7cfb\u7edf\u67b6\u6784 \u6982\u5ff5\u8fa8\u6790 <p> \u540d\u8bcd \u5b9a\u4f4d CPU \u6267\u884c\u6307\u4ee4\u7684\u786c\u4ef6 Core CPU \u7684\u57fa\u7840\u8ba1\u7b97\u5355\u5143 Multi-core \u4e00\u4e2a CPU \u4e0a\u6709\u591a\u4e2a core Processor \u5305\u542b\u4e00\u4e2a\u6216\u591a\u4e2a CPU \u7684\u82af\u7247 Multi-processor \u591a\u4e2a processor </p> <p>\u6839\u636e\u5904\u7406\u5668\u7684\u6570\u91cf\u548c\u7ec4\u7ec7\u5f62\u5f0f\uff0c\u6211\u4eec\u8fd9\u91cc\u4ecb\u7ecd\u4e09\u79cd\u8ba1\u7b97\u673a\u7cfb\u7edf\u67b6\u6784\uff1a\u5355\u5904\u7406\u5668\u7cfb\u7edf\u3001\u591a\u5904\u7406\u5668\u7cfb\u7edf\u3001\u96c6\u7fa4\u7cfb\u7edf\u3002</p> \u2460 \u5355\u5904\u7406\u5668\u7cfb\u7edf(Single-Processor System) <p>\u6709\u4e14\u4ec5\u6709\u4e00\u4e2a\u901a\u7528\u5904\u7406\u5668(general-purpose processor)\uff0c\u5e76\u4e14\u8fd9\u4e2a processor \u53ea\u6709\u4e00\u4e2a\u6838(core)\u3002</p> <p>\u53ef\u4ee5\u6709\u82e5\u5e72\u4e13\u7528\u5904\u7406\u5668(special-purpose processor)\uff0c\u7528\u6765\u6267\u884c\u4e00\u4e9b\u7279\u5b9a\u7684\u6307\u4ee4\uff0c\u800c\u8fd9\u4e9b\u4e13\u7528\u5904\u7406\u5668\u5e76\u4e0d\u8fd0\u884c\u7ebf\u7a0b\u3002</p> \u2461 \u591a\u5904\u7406\u5668\u7cfb\u7edf(Multiprocessor System) <p>\u591a\u5904\u7406\u5668\u7cfb\u7edf\u662f\u6307\u6709\u591a\u4e2a\u5355\u6838\u901a\u7528\u5904\u7406\u5668\u7684\u7cfb\u7edf\uff0c\u8fd9\u4e9b\u5904\u7406\u5668\u5171\u4eab\u4e00\u5757\u4e3b\u5185\u5b58\uff0c\u5b83\u4eec\u901a\u8fc7\u603b\u7ebf\u6216\u4ea4\u6362\u7f51\u7edc\u8fde\u63a5\u5728\u4e00\u8d77\u3002</p> <ul> <li>\u589e\u52a0\u541e\u5410\u91cf(throughput)\uff0c\u4f46\u662f\u8fd9\u4e2a\u589e\u52a0\u5e76\u4e0d\u662f\u7ebf\u6027\u7684\uff1b</li> </ul> \u2462 \u96c6\u7fa4\u7cfb\u7edf(Cluster System) <p> </p> <ul> <li>\u5197\u4f59 -&gt; \u9ad8\u53ef\u7528\uff1b</li> <li>\u5e76\u884c -&gt; \u9ad8\u6027\u80fd\uff1b</li> <li>\u8282\u70b9(node)\u901a\u8fc7\u9ad8\u901f\u901a\u4fe1\u7f51\u7edc\u4e92\u76f8\u8fde\u63a5\u5f62\u6210\uff1b</li> <li>\u5206\u5bf9\u79f0\u548c\u4e0d\u5bf9\u79f0\u4e24\u79cd\uff1b</li> </ul> \u64cd\u4f5c\u7cfb\u7edf\u7684\u4efb\u52a1\u6267\u884c\u8bbe\u8ba1 <p>\u64cd\u4f5c\u7cfb\u7edf\u88ab\u7528\u6765\u300c\u81ea\u52a8\u5316\u201c\u8ba9\u8ba1\u7b97\u673a\u5b8c\u6210\u4e00\u7cfb\u5217\u7279\u5b9a\u4efb\u52a1\u201d\u300d\u7684\uff0c\u968f\u7740\u9700\u6c42\u4e0d\u65ad\u590d\u6742\uff0c\u4f7f\u7528\u7684\u6280\u672f\u4e5f\u4e0d\u65ad\u53d1\u5c55\u3002</p> \u2460 \u6279\u5904\u7406\u7cfb\u7edf\u9636\u6bb5 \u80cc\u666f 1 <p>\u4eba\u5de5\u901f\u5ea6\u4e25\u91cd\u9650\u5236\u4e86\u8ba1\u7b97\u673a\u7684\u5de5\u4f5c\u6548\u7387\u3002</p> \u2776 \u5355\u9053\u6279\u5904\u7406\u9636\u6bb5 <p>\u4e24\u4e2a\u5173\u952e\u8bcd\uff1a\u201c\u6279\u5904\u7406\u201d\u548c\u201c\u5355\u9053\u201d\u3002</p> <p>\u201c\u6279\u5904\u7406\u201d\u6307\u7684\u662f\uff0c\u7cfb\u7edf\u6267\u884c\u7684\u4efb\u52a1\u662f\u6210\u6279\u7684\uff0c\u82e5\u5e72\u4efb\u52a1\u88ab\u4f5c\u4e3a\u4e00\u6574\u6279\u4ea4\u4ed8\u7ed9\u64cd\u4f5c\u7cfb\u7edf\u3002\u5728\u5177\u4f53\u6267\u884c\u8fc7\u7a0b\u4e2d\uff0c\u64cd\u4f5c\u7cfb\u7edf\u81ea\u52a8\u6309\u987a\u5e8f\u4e32\u884c(serial)\u6267\u884c\u8fd9\u4e9b\u4efb\u52a1\u3002</p> <p>\u800c\u201c\u5355\u9053\u201d\u6307\u7684\u662f\uff0c\u4e00\u6bb5\u65f6\u95f4\u5185\u5185\u5b58\u4e2d\u53ea\u6709\u4e00\u9053\u7a0b\u5e8f\u5728\u8fd0\u884c\uff0c\u7cfb\u7edf\u53ea\u5904\u7406\u4e00\u9879\u4efb\u52a1\uff0c\u5728\u8fd9\u4e2a\u4efb\u52a1\u7ed3\u675f\u4e4b\u524d\uff0c\u4e0d\u4f1a\u5207\u6362\u5230\u5176\u4ed6\u4efb\u52a1\u3002</p> \u80cc\u666f 2 <ul> <li>\u89e3\u51b3\u4e86\u80cc\u666f 1\uff1a\u51cf\u5c11\u4e86\u4eba\u5de5\u64cd\u4f5c\u901f\u5ea6\u5bf9\u64cd\u4f5c\u7cfb\u7edf\u7684\u5f71\u54cd\uff1b</li> <li>\u4ea7\u751f\u4e86\u80cc\u666f 2\uff1aCPU \u5229\u7528\u7387\u4f4e\uff1b</li> </ul> \u2777 \u591a\u9053\u6279\u5904\u7406\u9636\u6bb5 <p>\u5173\u952e\u8bcd\uff1a\u201c\u591a\u9053(Multiprogramming)\u201d\uff0c\u5373\u4e00\u6bb5\u65f6\u95f4\u5185\u5185\u5b58\u4e2d\u540c\u65f6\u5b58\u5728\u591a\u4e2a\u8fdb\u7a0b\u3002</p> <p>\u4e0d\u8ba9 CPU \u95f2\u4e0b\u6765 -&gt; \u8ba9\u5b83\u5148\u53bb\u505a\u4e0b\u4e00\u4ef6\u4e8b\u3002</p> <p>\u5b8f\u89c2\u5e76\u53d1\uff0c\u5fae\u89c2\u4e32\u884c\u3002\uff08\u533a\u5206\u5e76\u53d1\u548c\u5e76\u884c\uff01\uff09</p> <p>\u6211\u4eec\u53ef\u4ee5\u7528\u7518\u7279\u56fe\u6765\u53ef\u89c6\u5316\u591a\u9053\u6279\u5904\u7406\u7cfb\u7edf\u7684\u7b56\u7565\uff08\u4e00\u79cd\u5e38\u89c1\u7684\u9898\u578b\uff09\u3002\u4ee5\u4e0b\u9762\u7684\u9898\u76ee\u4e3a\u4f8b\uff0c\u6211\u4eec\u6765\u5b9e\u8df5\u4e00\u4e0b\u3002</p> \ud83c\udf30 \u9898\u9762\u89e3\u6790 <p>\u73b0\u5728\u6709\u4e24\u4e2a\u7a0b\u5e8f A \u548c B\uff0c\u4ee5\u53ca\u4e24\u4e2a\u5206\u522b\u72ec\u7acb\u7684\u8bbe\u5907 X \u548c Y\uff0c\u4e14\u6211\u4eec\u53ea\u6709\u4e00\u4e2a CPU\uff1a</p> <ul> <li>A \u9700\u8981\u987a\u5e8f\u4f7f\u7528\u5982\u4e0b\u8d44\u6e90\uff1aCPU:10s, X:5s, CPU:5s, Y:10s, CPU:10s</li> <li>B \u9700\u8981\u987a\u5e8f\u4f7f\u7528\u5982\u4e0b\u8d44\u6e90\uff1aX:10s, CPU 10s, Y:5s, CPU:5s, Y:10s </li> </ul> <p>\u8bf7\u8ba8\u8bba\uff1a</p> <ol> <li>\u5728\u5355\u9053\u7a0b\u5e8f\u73af\u5883\u4e0b\u5148\u6267\u884c A \u518d\u6267\u884c B\uff0cCPU \u7684\u5229\u7528\u7387\u662f\u591a\u5c11\uff1f</li> <li>\u5728\u591a\u9053\u7a0b\u5e8f\u73af\u5883\u4e0b\uff0cCPU \u7684\u5229\u7528\u7387\u662f\u591a\u5c11\uff1f\u8bf7\u7ed9\u51fa\u7518\u7279\u56fe\u3002</li> </ol> <p>\u5728\u5355\u9053\u7a0b\u5e8f\u4e0b\u6267\u884c\uff0c\u5373\u6309\u987a\u5e8f\u6267\u884c A \u548c B\uff0cCPU \u7684\u5229\u7528\u7387\u5373\u5b9e\u9645 CPU \u4f7f\u7528\u65f6\u95f4\u9664\u4ee5\u5b8c\u6210\u4efb\u52a1\u7684\u603b\u65f6\u95f4\uff0c\u56e0\u6b64\uff1a</p> \\[ U = \\frac{(10+5+10)+(10+5)}{(10+5+5+10+10)+(10+10+5+5+10)} = \\frac{40}{80} = 50\\% \\] <p>\u800c\u5728\u591a\u9053\u7a0b\u5e8f\u73af\u5883\u4e0b\uff0c\u6211\u4eec\u5f97\u5230\u5982\u4e0b\u7518\u7279\u56fe\uff1a</p> <pre><code>gantt\n    title Multiprogramming\n    dateFormat ss\n    axisFormat %S\n\n    section Program A\n    CPU :a,  00,  10\n    X   :b,  10,  15\n    CPU :c,  20,  25\n    Y   :d,  25,  35\n    CPU :e,  35,  45\n\n    section Program B\n    X   :g,  00,  10\n    CPU :h,  10,  20\n    Y   :i,  20,  25\n    CPU :j,  25,  30\n    Y   :k,  35,  45</code></pre> <p>\u7531\u4e8e Mermaid \u7684\u9650\u5236\uff0c\u6211\u73b0\u5728\u662f\u628a\u6bcf\u4e2a\u7a0b\u5e8f\u7684\u4efb\u52a1\u9519\u5f00\u753b\u7684\uff0c\u5b9e\u9645\u4e0a\u505a\u9898\u7684\u65f6\u5019\u53ef\u4ee5\u76f4\u63a5\u753b\u6210\u4e24\u884c\u3002</p> <p>\u8981\u70b9\u5c31\u662f\u7eb5\u5411\u4e0d\u80fd\u540c\u65f6\u51fa\u73b0\u540c\u4e00\u4e2a\u8d44\u6e90\uff0c\u4f8b\u5982 18s \u65f6\u4e0d\u80fd A \u548c B \u90fd\u7528 CPU\uff0c\u6240\u4ee5 A \u9700\u8981\u7b49 B \u7528\u5b8c CPU \u518d\u4f7f\u7528\u3002</p> <p>\u73b0\u5728\u6211\u4eec\u518d\u6765\u7edf\u8ba1 CPU \u7684\u5229\u7528\u7387\uff1a</p> \\[ U = \\frac{10+10+5+5+10}{45} = \\frac{40}{45} = 88.89\\% \\] <p>\u7531\u4e8e\u5f15\u5165\u4e86\u591a\u9053\u6280\u672f\uff0c\u7cfb\u7edf\u590d\u6742\u7a0b\u5ea6\u4e0a\u5347\u3002</p> \u80cc\u666f 3 <ul> <li>\u89e3\u51b3\u4e86\u80cc\u666f 2\uff1a\u63d0\u9ad8\u4e86 CPU \u5229\u7528\u7387\uff1b</li> <li>\u4ea7\u751f\u4e86\u80cc\u666f 3\uff1a\u4ea4\u4e92\u6027\u5dee\uff1b</li> </ul> <p>\uff08\u5047\u8bbe\u6211\u4eec\u5ffd\u7565\u5173\u4e8e\u5c4f\u5e55\u663e\u793a\u7684 I/O\uff09\u8bd5\u60f3\uff0c\u4f60\u5e0c\u671b\u5728\u8dd1\u7a0b\u5e8f\u7684\u65f6\u5019\u653e\u4e00\u4e2a\u89c6\u9891\uff0c\u4f46\u662f\u7531\u4e8e\u4f60\u7684\u7a0b\u5e8f\u8fd8\u6ca1\u8dd1\u5b8c\uff0c\u4f60\u7684\u89c6\u9891\u5c31\u6ca1\u6cd5\u64ad\u653e\uff0c\u7a81\u7136\u4f60\u7684\u7a0b\u5e8f\u53d1\u751f\u4e86\u4e00\u6b21 I/O\uff0cCPU \u8f6c\u800c\u64ad\u653e\u5df2\u7ecf\u5b8c\u6210 I/O \u540e\u7684\u90a3\u90e8\u5206\u89c6\u9891\uff0c\u4f46\u662f\u8fd9\u4e2a\u65f6\u5019\u4f60\u7684\u7a0b\u5e8f I/O \u5f88\u5feb\u4e5f\u5b8c\u6210\u4e86\uff0c\u5374\u9700\u8981\u7b49\u5f85\u7f13\u5b58\u4e2d\u7684\u89c6\u9891\u653e\u5b8c\u624d\u80fd\u7ee7\u7eed\u6267\u884c\uff0c\u8fd9\u79cd\u7528\u6237\u4f53\u9a8c\u51e0\u4e4e\u65e0\u6cd5\u63a5\u53d7\u3002</p> <ul> <li>\u5bf9\u4e8e\u7528\u6237\u6765\u8bf4\uff0c\u6700\u597d\u80fd\u540c\u65f6\u5b9e\u73b0\u4f53\u611f\u4e0a\u7684\u5e76\u884c\uff0c\u4e5f\u5c31\u662f\u51e0\u4ef6\u4e8b\u60c5\u81f3\u5c11\u770b\u8d77\u6765\u8981\u50cf\u662f\u540c\u65f6\u53d1\uff1b</li> </ul> \u2461 \u5206\u65f6\u7cfb\u7edf\u9636\u6bb5 <ul> <li>\u5206\u65f6\u7cfb\u7edf(Time Sharing Systems)\u662f\u591a\u4efb\u52a1(Multitasking)\u7684\u4e00\u4e2a\u5177\u4f53\u5b9e\u73b0\uff1b</li> <li> <p>Multitasking \u662f Multiprogramming \u7684\u4e00\u4e2a\u903b\u8f91\u6269\u5c55\uff1b</p> <ul> <li>Multitasking \u4e5f\u662f Multiprogramming \u7684\u4e00\u79cd\uff0c\u5b83\u7b26\u5408\u5185\u5b58\u4e2d\u6709\u591a\u4e2a\u8fdb\u7a0b\uff0c\u4e00\u6bb5\u65f6\u95f4\u5185\u6709\u591a\u4e2a\u4efb\u52a1\u4e00\u8d77\u6267\u884c\u7684\u7279\u70b9\uff1b</li> </ul> </li> <li> <p>\u5206\u65f6\u7cfb\u7edf\u901a\u8fc7\u9891\u7e41\u5730\u5728\u591a\u4e2a\u8fdb\u7a0b\u95f4\u5207\u6362\u6765\u8fd1\u4f3c\u5b9e\u73b0\u5e76\u884c\uff08\u4ecd\u7136\u4e0d\u662f\u771f\u6b63\u7684\u5e76\u884c\uff09\uff1b</p> <ul> <li>\u65f6\u95f4\u7247(time slice)\uff1b</li> </ul> </li> </ul> <p>\u300a\u5341\u4e07\u4e2a\u51b7\u7b11\u8bdd\u300b\u7684 4:09 - 4:48\u3002</p> <p>\u5206\u65f6\u7528\u6237\u5141\u8bb8\u591a\u4e2a\u7528\u6237\u540c\u65f6\u4f7f\u7528\u540c\u4e00\u53f0\u8ba1\u7b97\u673a\uff0c\u6240\u6709\u4efb\u52a1\u4e4b\u95f4\u4e92\u76f8\u72ec\u7acb\uff0c\u4e92\u4e0d\u5e72\u6270\u3001\u4e92\u4e0d\u963b\u585e\uff0c\u56e0\u6b64\u4efb\u52a1\u7684\u6700\u957f\u5468\u8f6c\u65f6\u95f4\u51cf\u5c11\uff0c\u7528\u6237\u7684\u64cd\u4f5c\u4e5f\u4f1a\u88ab\u53ca\u65f6\u54cd\u5e94\uff0c\u5b9e\u73b0\u4e86\u66f4\u65b9\u4fbf\u8fdb\u884c\u4eba\u673a\u5bf9\u8bdd\u3002</p> \u64cd\u4f5c\u7cfb\u7edf\u7684\u7ed3\u6784\u8bbe\u8ba1 <p>\u968f\u7740\u64cd\u4f5c\u7cfb\u7edf\u7684\u529f\u80fd\u4e0d\u65ad\u6269\u5c55\u3001\u4f53\u91cf\u9010\u6e10\u53d8\u5927\uff0c\u6574\u4e2a\u64cd\u4f5c\u7cfb\u7edf\u8f6f\u4ef6\u7684\u7ed3\u6784\u8bbe\u8ba1\u5c31\u8d8a\u53d1\u91cd\u8981\u4e86\u3002</p> <p></p> \u5b8f\u5185\u6838 <p>\u5b8f\u5185\u6838(Monolithic-Kernels)\u4e5f\u53eb\u5355\u5185\u6838\u6216\u5927\u5185\u6838\u3002</p> <p>\u4f18\u52bf\uff1a\u64cd\u4f5c\u7cfb\u7edf\u6548\u7387\u6781\u9ad8\u3002</p> <p>\u52a3\u52bf\uff1a\u5927\u91cf\u590d\u6742\u7684\u529f\u80fd\u4e92\u76f8\u8026\u5408 -&gt; \u7ef4\u62a4\u56f0\u96be\u3001\u4e00\u635f\u5177\u635f\uff1b</p> <p> </p> \u5206\u5c42\u8bbe\u8ba1 <p>\u5206\u5c42\u8bbe\u8ba1(layer approach)\u7684\u6838\u5fc3\u601d\u60f3\u662f\u5c06\u7cfb\u7edf\u5206\u4e3a\u82e5\u5e72\u5c42\uff0c\u5e95\u5c42\u4e3a\u786c\u4ef6\uff0c\u9876\u5c42\u4e3a\u7528\u6237\u63a5\u53e3\uff0c\u7b2c \\(i\\) \u5c42\u53ea\u8c03\u7528 \\(i-1\\) \u5c42\u63d0\u4f9b\u7684\u63a5\u53e3\u3002</p> <p>\u7406\u60f3\uff1a\u4f4e\u8026\u5408\uff0c\u9636\u6bb5\u6027\u5f00\u53d1\u3002</p> <p>\u73b0\u5b9e\uff1a\u6548\u7387\u4f4e\u3001\u96be\u8bbe\u8ba1\u3002</p> <p></p> \u5fae\u5185\u6838 <p>\u5fae\u5185\u6838(Micro-Kernels)\u4e3b\u5f20\u5c06\u4e0d\u662f\u5fc5\u8981\u7684\u4e1c\u897f\u90fd\u4ece\u5185\u6838\u91cc\u62ff\u51fa\u53bb\uff0c\u653e\u5230\u7528\u6237\u7a7a\u95f4\uff0c\u4ee5\u7528\u6237\u6001\u6267\u884c\u3002</p> <p>\u6574\u4f53\u5f62\u6210\u4e00\u79cd\u5fae\u5185\u6838-\u670d\u52a1\u5668\u7684\u7ed3\u6784\uff0c\u6b64\u65f6\u5185\u6838\u53ea\u63d0\u4f9b\u901a\u8baf\u3001\u5185\u5b58\u7ba1\u7406\u3001\u8fdb\u7a0b\u7ba1\u7406\u7b49\u57fa\u672c\u529f\u80fd\uff0c\u4e5f\u53ea\u6709\u8fd9\u4e9b\u90e8\u5206\u76f4\u63a5\u8fd0\u884c\u5728\u5185\u6838\u6001\uff0c\u4f5c\u4e3a\u670d\u52a1\u5668\u7684\u5176\u5b83\u529f\u80fd\u90e8\u4ef6\u5219\u901a\u8fc7\u6d88\u606f\u4f20\u9012\u673a\u5236\u4e0e\u5185\u6838\u4e92\u52a8\u3002</p> <p>\u4f18\u52bf\uff1a\u89c4\u6a21\u51cf\u5c0f,\u8026\u5408\u964d\u4f4e -&gt; \u66f4\u65b9\u4fbf\u7ef4\u62a4\uff0c\u53ef\u9760\u6027\u589e\u52a0\u3002</p> <p>\u52a3\u52bf\uff1a\u6548\u7387\u4f4e\u3002</p> <p> </p> \u6a21\u5757\u5316\u8bbe\u8ba1 <p>\u6a21\u5757\u5316\u8bbe\u8ba1(Modules Approach)\u6307\u5c06\u64cd\u4f5c\u7cfb\u7edf\u5212\u5206\u4e3a\u82e5\u5e72\u5206\u7acb\u6a21\u5757\uff0c\u5e76\u89c4\u5b9a\u6a21\u5757\u4e4b\u95f4\u7684\u63a5\u53e3\uff0c\u751a\u81f3\u5355\u4e2a\u6a21\u5757\u4e0b\u4e5f\u53ef\u80fd\u662f\u7531\u591a\u4e2a\u6a21\u5757\u901a\u8fc7\u540c\u6837\u7684\u65b9\u5f0f\u7ec4\u7ec7\u800c\u6210\u7684\u3002\u8fd9\u79cd\u8bbe\u8ba1\u65b9\u6cd5\u4e5f\u88ab\u79f0\u4e3a\u6a21\u5757-\u63a5\u53e3\u6cd5\u3002</p> <p>\u8fa8\u6790</p> <p>\u6a21\u5757\u5316\u7684\u8bbe\u8ba1\u4e0e\u5fae\u5185\u6838\u662f\u4e0d\u540c\u7684\uff0c\u9700\u8981\u6ce8\u610f\u533a\u5206\u3002\u5fae\u5185\u6838\u8bbe\u8ba1\u4ecd\u7136\u662f\u6709\u4e2d\u5fc3\uff08\u5fae\u5185\u6838\uff09\u7684\uff0c\u4f46\u662f\u6a21\u5757\u5316\u8bbe\u8ba1\u6574\u4f53\u662f\u5206\u5c42\u7f51\u72b6\u7684\u3002</p> <p>\u7406\u60f3\uff1a\u4f4e\u8026\u5408 -&gt; \u5e76\u884c\u5f00\u53d1\uff0c\u597d\u7ef4\u62a4\u3002</p> <p>\u73b0\u5b9e\uff1a\u8bbe\u8ba1\u5341\u5206\u56f0\u96be\uff0c\u96be\u4ee5\u9012\u8fdb\u5f0f\u5f00\u53d1\u3002</p> \u6df7\u5408\u7cfb\u7edf <p>\u6df7\u5408\u7cfb\u7edf(Hybrid Systems)\u662f\u6307\u5c06\u5b8f\u5185\u6838\u548c\u5fae\u5185\u6838\u7684\u8bbe\u8ba1\u601d\u8def\u7ed3\u5408\u8d77\u6765\uff0c\u8fd9\u79cd\u8bbe\u8ba1\u6a21\u5f0f\u66f4\u73b0\u4ee3\uff0c\u4e5f\u662f\u76ee\u524d\u4e3b\u6d41\u7684\u64cd\u4f5c\u7cfb\u7edf\u7684\u6a21\u5f0f\u3002</p> \u64cd\u4f5c\u7cfb\u7edf\u7684\u8fd0\u884c\u539f\u7406 \u4e2d\u65ad <ul> <li>\u903b\u8f91\u4e0a\u7684\u8f6e\u8be2\u4e0d\u5408\u7406\uff1b</li> <li>\u5b9e\u73b0\u4e0a\u7528\u201c\u786c\u4ef6\u8f6e\u8be2\u201d\u6765\u5b9e\u73b0\u4e2d\u65ad\uff1b</li> </ul> <p>\u4e2d\u65ad\u5411\u91cf\u8868</p> <p>\u7531\u4e8e\u4e2d\u65ad\u88ab\u5e7f\u6cdb\u4f7f\u7528\uff0c\u64cd\u4f5c\u7cfb\u7edf\u9700\u8981\u9891\u7e41\u7684\u5904\u7406\u5404\u79cd\u4e2d\u65ad\uff0c\u5904\u7406\u6bcf\u4e00\u79cd\u4e2d\u65ad\u90fd\u9700\u8981\u4e00\u4e2a\u7279\u5b9a\u7684\u65b9\u6cd5\uff0c\u56e0\u6b64\uff0c\u4e00\u79cd\u5feb\u901f\u5b9a\u4f4d\u4e2d\u65ad\u5904\u7406\u65b9\u6cd5\u7684\u624b\u6bb5\u5c31\u663e\u5f97\u5c24\u4e3a\u91cd\u8981\u3002</p> <p>\u4e2d\u65ad\u5411\u91cf\u8868(Interrupt Vector Table)\u901a\u8fc7\u4e2d\u65ad\u53f7\u6765\u7d22\u5f15\u4e2d\u65ad\u5904\u7406\u65b9\u6cd5\uff0c\u5b9e\u73b0\u4e86\u4e00\u79cd\u201c\u968f\u673a\u8bbf\u95ee\u201d\uff0c\u5927\u5927\u52a0\u901f\u4e86\u4e2d\u65ad\u5904\u7406\u7684\u901f\u5ea6\u3002</p> <ul> <li>\u5916\u4e2d\u65ad\uff08CPU \u5916\u4ea7\u751f\uff09\uff1b</li> <li>\u5185\u4e2d\u65ad\uff08CPU \u5185\u4ea7\u751f\uff09\u3002</li> </ul> <p>\u7406\u60f3\u60c5\u51b5\u4e0b\uff0c\u6211\u4eec\u5e0c\u671b\u4e2d\u65ad\u4e00\u65e6\u53d1\u751f\u5c31\u7acb\u523b\u88ab\u89e3\u51b3\uff0c\u4f46\u662f\u4e2d\u65ad\u5904\u7406\u4e5f\u540c\u6837\u9700\u8981\u8d44\u6e90\uff0c\u8fd9\u610f\u5473\u7740\u4e2d\u65ad\u4e5f\u6709\u53ef\u80fd\u4ea7\u751f\u51b2\u7a81\u3002\u4e8e\u662f\uff0c\u6211\u4eec\u9700\u8981\u4e00\u7cfb\u5217\u673a\u5236\u6765\u89e3\u51b3\u8fd9\u4e9b\u95ee\u9898\u3002</p> <ol> <li>\u5206\u7ea7\u673a\u5236\uff1b</li> <li>\u5c4f\u853d\u673a\u5236\uff1b</li> </ol> <p>\u4e00\u79cd\u6bd4\u8f83\u666e\u901a\u7684\u8bbe\u8ba1\uff1a\u51c6\u5907 maskable interrupt-request line \u548c non-maskable interrupt-request line \u4e24\u6761\u4e2d\u65ad\u8bf7\u6c42\u7ebf\uff0c\u524d\u8005\u7528\u4e8e\u53ef\u5c4f\u853d\u7684\u4e2d\u65ad\uff0c\u540e\u8005\u7528\u4e8e\u4e0d\u53ef\u5c4f\u853d\u7684\u4e2d\u65ad\u3002</p> <p>\u9700\u8981\u6ce8\u610f\uff0c\u64cd\u4f5c\u7cfb\u7edf\u53d1\u73b0\u4e2d\u65ad\u540e\u5e76\u4e0d\u662f\u4e8c\u8bdd\u4e0d\u8bf4\u9a6c\u4e0a\u53bb\u5904\u7406\u4e2d\u65ad\u7684\uff0c\u4e3a\u4e86\u4fdd\u8bc1\u4e2d\u65ad\u5904\u7406\u5b8c\u6210\u540e\u4ecd\u80fd\u7ee7\u7eed\u5f53\u524d\u4efb\u52a1\uff0c\u64cd\u4f5c\u7cfb\u7edf\u9700\u8981\u4fdd\u5b58\u5f53\u524d\u4efb\u52a1\u7684\u72b6\u6001\uff08\u4e0a\u4e0b\u6587\uff09\uff0c\u4ee5\u4fbf\u5b8c\u6210\u4e2d\u65ad\u5904\u7406\u540e\u6062\u590d\u5f53\u524d\u4efb\u52a1\u7684\u72b6\u6001\u3002</p> \u8ba1\u65f6\u5668 <p>\u8ba1\u65f6\u5668(timer)\uff1a\u56fa\u5b9a\u9891\u7387\u7684\u65f6\u949f + \u8ba1\u6570\u5668\u3002</p> <ul> <li>\u65f6\u95f4\u7247\u7684\u957f\u5ea6\uff1b</li> <li>\u907f\u514d\u8fdb\u7a0b\u5360\u7528\u7cfb\u7edf\u8d44\u6e90\u8fc7\u4e45\uff1b</li> <li>...</li> </ul> \u7279\u6743\u6a21\u5f0f \u9694\u79bb <p>\u64cd\u4f5c\u7cfb\u7edf\u7684\u67d0\u4e9b\u64cd\u4f5c\u662f\u5371\u9669\u7684\uff0c\u6709\u53ef\u80fd\u5a01\u80c1\u5230\u81ea\u8eab\u6b63\u5e38\u8fd0\u4f5c\u7684\uff08\u5982\u4e0e\u786c\u4ef6\u76f4\u63a5\u76f8\u5173\u7684\u884c\u4e3a\u3001\u63a7\u5236 CPU \u8fd0\u884c\u89c4\u5219\u7684\u884c\u4e3a\u7b49\uff09\uff0c\u800c\u8fd9\u4e9b\u64cd\u4f5c\u4e0d\u5e94\u5f53\u88ab\u7528\u6237\u7a0b\u5e8f\u76f4\u63a5\u6267\u884c\u3002</p> <p>\u4e00\u79cd\u7b80\u5355\u7684\u601d\u8def\u662f\uff0c\u6211\u4eec\u5212\u5206\u5e38\u89c4\u64cd\u4f5c\u548c\u5371\u9669\u64cd\u4f5c\uff0c\u5141\u8bb8\u7528\u6237\u7a0b\u5e8f\u6267\u884c\u5e38\u89c4\u64cd\u4f5c\uff0c\u800c\u5371\u9669\u64cd\u4f5c\u5219\u9700\u8981\u59d4\u6258\u4e13\u4e1a\u4eba\u58eb\u4ee3\u4e3a\u6267\u884c\u3002\u800c\u8fd9\u5c31\u662f\u7279\u6743\u6a21\u5f0f(Privileged Mode)\u7684\u57fa\u672c\u601d\u8def\u3002</p> <p>\u5de5\u4e1a\u4e0a\u7684\u7279\u6743\u6a21\u5f0f\u53ef\u80fd\u4f1a\u6709\u591a\u79cd\u590d\u6742\u7684\u5b9e\u73b0\u5f62\u5f0f\uff0c\u4f46\u662f\u6211\u4eec\u8fd9\u91cc\u53ea\u8bb2\u6700\u7b80\u5355\u7684\u4e00\u79cd\uff0c\u5373\u53cc\u6a21\u5f0f(Dual-Mode)\u3002</p> <p>\u53cc\u6a21\u5f0f\u4e0b\uff0cCPU \u6709\u4e24\u79cd\u8fd0\u884c\u6a21\u5f0f\uff0c\u4e00\u79cd\u662f\u7528\u6237\u6001(User Mode)\uff08\u76ee\u6001\uff09\uff0c\u4e00\u79cd\u662f\u5185\u6838\u6001(Kernel Mode)\uff08\u7ba1\u6001\uff0c\u6838\u5fc3\u6001\uff09\u3002</p> <p>\u540c\u65f6\uff0c\u6211\u4eec\u5c06\u90a3\u4e9b\u201c\u5371\u9669\u201d\u7684\u6307\u4ee4\u79f0\u4e3a\u7279\u6743\u6307\u4ee4(privileged instruction)\uff0c\u4f8b\u5982 I/O \u63a7\u5236\uff0c\u8ba1\u65f6\u5668\u7ba1\u7406\uff0c\u4e2d\u65ad\u7ba1\u7406\u7b49\u3002\u8fd9\u4e9b\u6307\u4ee4\u53ea\u80fd\u5728\u5185\u6838\u6001\u4e0b\u6267\u884c\uff0c\u800c\u7528\u6237\u6001\u4e0b\u6267\u884c\u8fd9\u4e9b\u6307\u4ee4\u65f6\u4f1a\u8ba4\u4e3a\u8fd9\u6761\u6307\u4ee4\u4e0d\u5b58\u5728\u3002</p> \u95ee\u9898\u5c1a\u672a\u89e3\u51b3 <p>\u73b0\u5728\u6211\u4eec\u5c06\u5371\u9669\u64cd\u4f5c\u548c\u76f8\u5bf9\u5b89\u5168\u7684\u64cd\u4f5c\u9694\u79bb\u5f00\u6765\u4e86\uff0c\u4f46\u662f\u8fd9\u5e76\u4e0d\u610f\u5473\u7740\u7528\u6237\u7a0b\u5e8f\u5c31\u4e0d\u9700\u8981\u4f7f\u7528\u90a3\u4e9b\u5371\u9669\u64cd\u4f5c\u4e86\uff0c\u5355\u7eaf\u7684\u9694\u79bb\u5e76\u4e0d\u80fd\u89e3\u51b3\u95ee\u9898\uff0c\u7528\u6237\u7a0b\u5e8f\u4ecd\u7136\u5b58\u5728\u9700\u8981\u4f7f\u7528\u7279\u6743\u6307\u4ee4\u7684\u9700\u6c42\u3002</p> \u9694\u79bb\u800c\u975e\u9694\u7edd <p>\u8fd9\u4e9b\u9700\u6c42\u5f80\u5f80\u662f\u53ef\u4ee5\u88ab\u62bd\u8c61\u7684\u3001\u88ab\u5c01\u88c5\u7684\u3002</p> <ul> <li>\u5b9e\u73b0\u65b9\u6cd5\uff1a\u8ba9\u6e21\u63a7\u5236\u6743\u3002</li> </ul> <p>\u800c\u90a3\u4e48\u5728\u5177\u4f53\u5b9e\u73b0\u4e0a\uff0c\u8fd9\u4e00\u6b65\u662f\u901a\u8fc7 trap \u5b9e\u73b0\u7684\u3002</p> <p>  Transition from user to kernel mode. </p> \u7cfb\u7edf\u8c03\u7528 <p>  Examples of W&amp;U system calls. </p> <p>\u7cfb\u7edf\u8c03\u7528(System Call)\u662f\u7cfb\u7edf\u5411\u7528\u6237\u7a0b\u5e8f\u63d0\u4f9b\u670d\u52a1\u7684\u4e00\u4e2a\u63a5\u53e3\uff0c\u5b83\u4eec\u7ecf\u5e38\u4ee5 C/C++ \u51fd\u6570\u7684\u5f62\u5f0f\u5b58\u5728\uff0c\u5bf9\u4e8e\u67d0\u4e9b\u6bd4\u8f83\u63a5\u8fd1\u5e95\u5c42\u7684\u4efb\u52a1\uff0c\u4e5f\u53ef\u80fd\u662f\u901a\u8fc7\u6c47\u7f16\u7f16\u5199\u7684\u3002</p> <p>\u4f46\u8bf4\u5230\u5e95\uff0c\u7cfb\u7edf\u8c03\u7528\u8fd8\u662f\u76f8\u5bf9\u5e95\u5c42\u7684\u8bbe\u8ba1\uff0c\u901a\u5e38\u7684\u5f00\u53d1\u5e76\u4e0d\u57fa\u4e8e\u5982\u6b64\u5e95\u5c42\u7684\u8bbe\u8ba1\u5c55\u5f00\u3002\u66f4\u5e38\u89c1\u7684\u662f\u5229\u7528\u5404\u79cd\u62bd\u8c61\u5c42\u7ea7\u66f4\u9ad8\u7684 Application Programming Interface, API \u8fdb\u884c\u5f00\u53d1\u3002</p> <p>API \u7531\u201c\u73af\u5883\u201d\u63d0\u4f9b\uff0c\u4e5f\u5c31\u662f\u6211\u4eec\u6240\u8bf4\u7684\u8fd0\u884c\u65f6\u73af\u5883(run-time environment, RTE)\u3002</p> \u601d\u8003\u9898 \u9898\u9762\u89e3\u6790 <p>\u8fa8\u6790\u5e93\u51fd\u6570\u4e0e\u7cfb\u7edf\u8c03\u7528\uff1f</p> <p>\u5e93\u51fd\u6570\u8fd0\u884c\u5728\u7528\u6237\u7a7a\u95f4\u800c\u7cfb\u7edf\u8c03\u7528\u8fd0\u884c\u5728\u5185\u6838\u7a7a\u95f4\u3002\u5927\u90e8\u5206\u5e93\u51fd\u6570\u53ef\u80fd\u4f7f\u7528\u7cfb\u7edf\u8c03\u7528\u6765\u5b9e\u73b0\u76ee\u7684\u3002</p> \u94fe\u63a5\u5668\u548c\u88c5\u8f7d\u5668 <p>  The role of the linker and loader. </p> <p>\u8bf4\u4e86\u8fd9\u4e48\u591a\uff0c\u90a3\u4e48\u64cd\u4f5c\u7cfb\u7edf\u5230\u5e95\u662f\u5982\u4f55\u6267\u884c\u4e00\u4e2a\u7a0b\u5e8f\u7684\u5462\uff1f\u4ee5 C \u4e3a\u4f8b\uff0c\u4e00\u4e2a\u5199\u5b8c\u7684\u4ee3\u7801\u9700\u8981\u7ecf\u8fc7\u7f16\u8bd1\u3001\u94fe\u63a5\u3001\u88c5\u8f7d\u4e09\u4e2a\u6b65\u9aa4\uff0c\u624d\u80fd\u6210\u4e3a\u4e00\u4e2a\u5728\u5185\u5b58\u4e2d\u7684\uff0c\u53ef\u4ee5\u88ab\u6267\u884c\u7684\u7a0b\u5e8f\u3002</p> <ol> <li>\u7f16\u8bd1\u5668\u9996\u5148\u5c06\u82e5\u5e72 <code>.c</code> \u6e90\u6587\u4ef6\u7f16\u8bd1\u4e3a\u82e5\u5e72 <code>.o</code> \u6587\u4ef6\uff08\u8fd9\u91cc\u5408\u5e76\u4e86\u9884\u5904\u7406\u3001\u7f16\u8bd1\u3001\u6c47\u7f16\u6b65\u9aa4\uff09\uff0c\u8fd9\u4e9b <code>.o</code> \u6587\u4ef6\u88ab\u79f0\u4e3a\u53ef\u91cd\u5b9a\u4f4d\u76ee\u6807\u6587\u4ef6(relocatable object file)\uff0c\u5176\u5b58\u5728\u5f62\u5f0f\u4e3a\u673a\u5668\u7801\uff1b</li> <li>\u968f\u540e\u94fe\u63a5\u5668\u5c06\u82e5\u5e72 <code>.o</code> \u6587\u4ef6\u8fde\u5e26\u6240\u9700\u8981\u7684\u4e00\u4e9b\u5e93\u6587\u4ef6\uff08\u5982 <code>.a</code> \u6587\u4ef6\uff09\u94fe\u63a5\u4e3a\u4e00\u4e2a\u53ef\u6267\u884c\u76ee\u6807\u6587\u4ef6(executable object file)\uff1b</li> </ol> <p>\u7279\u522b\u7684\uff0c\u94fe\u63a5\u5206\u4e3a\u9759\u6001\u94fe\u63a5\u548c\u52a8\u6001\u94fe\u63a5\u4e24\u79cd\u3002\u9759\u6001\u94fe\u63a5\u5c06\u5e93\u6587\u4ef6\u7684\u4ee3\u7801\u76f4\u63a5\u5408\u5e76\u8fdb\u5165\u6700\u7ec8\u7684\u53ef\u6267\u884c\u6587\u4ef6\uff0c\u800c\u52a8\u6001\u94fe\u63a5\u4ec5\u4ec5\u5c06\u5e93\u6587\u4ef6\u7684\u5f15\u7528\u4fe1\u606f\u5199\u5165\u6700\u7ec8\u7684\u53ef\u6267\u884c\u6587\u4ef6\uff0c\u800c\u5728\u7a0b\u5e8f\u8fd0\u884c\u65f6\u518d\u53bb\u5bfb\u627e\u8fd9\u4e9b\u5e93\u6587\u4ef6\u3002</p> <pre><code>gcc -E main.c -o main.i # pre-process\ngcc -S main.i -o main.s # compile to assembly code\ngcc -c main.s -o main.o # assemble to object file\ngcc main.o -o main      # link\n./main                  # (load and) execute\n</code></pre> <p>  \u53ef\u4ee5\u53d1\u73b0\uff0c\u52a8\u6001\u94fe\u63a5\u5f97\u5230\u7684\u53ef\u6267\u884c\u6587\u4ef6\u6bd4\u9759\u6001\u94fe\u63a5\u5f97\u5230\u7684\u53ef\u6267\u884c\u6587\u4ef6\u8981\u5c0f\u4e0d\u5c11\u3002 </p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit0/","title":"Unit 0: \u603b\u89c8 | Overview","text":"<p> \u7ea6 8917 \u4e2a\u5b57  23 \u884c\u4ee3\u7801  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 30 \u5206\u949f</p> <p>\u5bfc\u8bed</p> <p>\u672c\u5355\u5143\u4e3b\u8981\u6709\u4e24\u4e2a\u4efb\u52a1\uff1a</p> <ol> <li>\u5bf9\u64cd\u4f5c\u7cfb\u7edf\u8fdb\u884c\u4e00\u4e2a\u8f83\u4e3a\u62bd\u8c61\u7684\u4ecb\u7ecd\uff0c\u540c\u65f6\u5efa\u7acb\u8d77\u6574\u95e8\u8bfe\u7a0b\u7684\u6846\u67b6\uff0c\u65b9\u4fbf\u8bfb\u8005\u5728\u4e4b\u540e\u7684\u5b66\u4e60\u8fc7\u7a0b\u4e2d\u80fd\u6709\u4e00\u4e2a\u6bd4\u8f83\u603b\u4f53\u7684\u8ba4\u8bc6\uff0c\u80fd\u5e26\u7740\u76ee\u7684\u53bb\u5b66\u4e60\u5177\u4f53\u7684\u77e5\u8bc6\uff1b</li> <li>\u4ecb\u7ecd\u4e00\u4e9b\u6bd4\u8f83\u57fa\u7840\u7684\u5185\u5bb9\uff0c\u6216\u662f\u4e00\u4e9b\u6bd4\u8f83\u7410\u788e\u3001\u4ec5\u9700\u4e86\u89e3\u7684\u5185\u5bb9\uff1b</li> </ol> <p>\u7531\u4e8e\u8bfe\u672c\u7684 Overview \u5199\u5f97\u975e\u5e38\u4e00\u8a00\u96be\u5c3d\uff0c\u6240\u4ee5\u6211\u5728\u5543\u5b8c\u540e\u8fdb\u884c\u4e86\u4e00\u4e9b\u6574\u7406\uff0c\u4f60\u53ef\u4ee5\u5728\u8fd9\u91cc\u627e\u5230\u6211\u6574\u7406\u8fc7\u7a0b\u4e2d\u5b8c\u6210\u7684\u601d\u7ef4\u5bfc\u56fe\uff0c\u4e0d\u8fc7\u8fd9\u4e2a\u601d\u7ef4\u5bfc\u56fe\u66f4\u591a\u7684\u662f\u63d0\u4f9b\u6846\u67b6\u6027\u7684\u8ba4\u77e5\uff0c\u5177\u4f53\u5230\u6bcf\u4e2a\u53f6\u5b50\u8282\u70b9\u7684\u5185\u5bb9\u5efa\u8bae\u8fd8\u662f\u4ee5\u672c\u6587\u4e3a\u4e3b\u3002\u6b64\u5916\uff0c\u672c\u6587\u5f88\u591a\u89c2\u70b9\u5177\u6709\u6bd4\u8f83\u5f3a\u70c8\u7684\u4e2a\u4eba\u7406\u89e3\u8272\u5f69\uff0c\u5982\u679c\u4f60\u5bf9\u5176\u4e2d\u7684\u8bba\u65ad\u62b1\u6709\u5f02\u8bae\uff0c\u6b22\u8fce\u8ba8\u8bba\uff01</p> <p>\u5728\u6b63\u5f0f\u5f00\u59cb\u6838\u5fc3\u5185\u5bb9\u7684\u5b66\u4e60\u4e4b\u524d\uff0c\u6211\u60f3\u5148\u505a\u4e00\u70b9\u8bf4\u660e\uff0c\u4e5f\u7b97\u662f\u4e00\u70b9\u5173\u4e8e\u5b66\u4e60\u64cd\u4f5c\u7cfb\u7edf\u7684\u7ecf\u9a8c\u4e4b\u8c08\u3002</p> <p>\u201c\u5b9a\u4e49\u4e0d\u5b58\u5728\u4e86\u201d</p> <p>\u533a\u522b\u4e8e\u81ea\u7136\u79d1\u5b66\u7684\u7814\u7a76\u5bf9\u8c61\uff0c\u64cd\u4f5c\u7cfb\u7edf\u4f5c\u4e3a\u4e00\u4e2a\u5f7b\u5f7b\u5e95\u5e95\u7684\u4eba\u9020\u7269\uff0c\u5176\u5f88\u591a\u6982\u5ff5\u90fd\u5f88\u96be\u754c\u5b9a\u4e00\u4e2a\u660e\u786e\u7684\u754c\u9650\uff0c\u8fd9\u4e5f\u6b63\u662f\u6211\u5728\u5b66\u4e60\u64cd\u4f5c\u7cfb\u7edf\u7684\u8fc7\u7a0b\u4e2d\u9047\u5230\u7684\u6700\u9996\u8981\u7684\u95ee\u9898\u3002\u6211\u4f1a\u5c3d\u529b\u7ed9\u51fa\u6211\u8ba4\u4e3a\u66f4\u7cbe\u786e\u7684\u5b9a\u4e49\uff0c\u4f46\u8fd9\u4e2a\u95ee\u9898\u4ecd\u7136\u5b58\u5728\uff0c\u6240\u4ee5\u6211\u4eec\u5c3d\u91cf\u53ea\u56f4\u7ed5\u5b9a\u4e49\u7684\u4e2d\u5fc3\u8fdb\u884c\u5b66\u4e60\u3002</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit0/#\u64cd\u4f5c\u7cfb\u7edf\u6982\u8ff0","title":"\u64cd\u4f5c\u7cfb\u7edf\u6982\u8ff0","text":"<p>\u672c\u8282\u4e3b\u8981\u5c06\u64cd\u4f5c\u7cfb\u7edf\u5f53\u4f5c\u4e00\u4e2a\u4e0d\u53ef\u62c6\u5206\u7684\u5355\u4f4d\uff0c\u6765\u8ba8\u8bba\u4ec0\u4e48\u662f\u64cd\u4f5c\u7cfb\u7edf\u3002</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit0/#\u4f55\u4e3a\u64cd\u4f5c\u7cfb\u7edf","title":"\u4f55\u4e3a\u64cd\u4f5c\u7cfb\u7edf","text":"<p>\u6574\u95e8\u8bfe\u7a0b\u6211\u4eec\u9700\u8981\u89e3\u51b3\u7684\u7b2c\u4e00\u4e2a\u95ee\u9898\uff0c\u663e\u7136\u662f\u4ec0\u4e48\u662f\u64cd\u4f5c\u7cfb\u7edf(Operating System, OS)\u3002\u63a5\u4e0b\u6765\u6211\u5c06\u4ece\u4e24\u4e2a\u65b9\u9762\u7b80\u8ff0\u4f55\u4e3a\u64cd\u4f5c\u7cfb\u7edf\u3002</p> \u2460 \u4ece\u804c\u80fd\u4e0a\u770b <p></p> <p>\u4ece\u5176\u804c\u80fd\u4e0a\u770b\uff0c\u6211\u8ba4\u4e3a\u64cd\u4f5c\u7cfb\u7edf\u662f\u4e00\u4e2a\u8d44\u6e90\u7ba1\u7406\u7cfb\u7edf\u3002</p> <p>\u53f3\u56fe\u63cf\u8ff0\u4e86\u8ba1\u7b97\u673a\u7cfb\u7edf\u7684\u62bd\u8c61\u5c42\u7ea7\uff1a\u81ea\u4e0a\u800c\u4e0b\uff0c\u7528\u6237\u901a\u8fc7\u5e94\u7528\u7a0b\u5e8f\u89e3\u51b3\u95ee\u9898\uff0c\u5e94\u7528\u7a0b\u5e8f\u5411\u64cd\u4f5c\u7cfb\u7edf\u8bf7\u6c42\u8ba1\u7b97\u673a\u8d44\u6e90\uff1b\u81ea\u4e0b\u800c\u4e0a\uff0c\u8ba1\u7b97\u673a\u786c\u4ef6\u4e3a\u8f6f\u4ef6\uff08\u5305\u62ec OS\uff09\u63d0\u4f9b\u4e86\u7269\u8d28\u57fa\u7840\uff0c\u672c\u8d28\u4e0a\uff0c\u786c\u4ef6\u63d0\u4f9b\u4e86\u8ba1\u7b97\u673a\u8d44\u6e90\u3002</p> <p>\u64cd\u4f5c\u7cfb\u7edf\u4f5c\u4e3a\u4e2d\u95f4\u5c42\uff0c\u5411\u4e0a\u4e3a\u7528\u6237\u7a0b\u5e8f\u5206\u914d\u6613\u7528\u7684\u8d44\u6e90\uff0c\u5411\u4e0b\u76f4\u63a5\u64cd\u4f5c\u786c\u4ef6\u8d44\u6e90\u7684\uff0c\u5728\u8fd9\u4e2a\u8fc7\u7a0b\u4e2d\uff0c\u64cd\u4f5c\u7cfb\u7edf\u8fd8\u9700\u8981\u516c\u5e73\u3001\u9ad8\u6548\u5730\u89e3\u51b3\u8d44\u6e90\u4e4b\u95f4\u7684\u51b2\u7a81\u95ee\u9898\u7b49\u7b49\u3002</p> <p>\u5b83\u5c31\u597d\u50cf\u836f\u623f\u67dc\u53f0\uff0c\u5404\u79cd\u836f\u54c1\u5c31\u597d\u50cf\u8ba1\u7b97\u673a\u8d44\u6e90\uff0c\u75c5\u4eba\u63d0\u4f9b\u5904\u65b9\uff0c\u67dc\u53f0\u6536\u5230\u8bf7\u6c42\uff08\u7cfb\u7edf\u8c03\u7528\uff09\u540e\u5904\u7406\u8bf7\u6c42\uff0c\u5e76\u5343\u8f9b\u4e07\u82e6\uff08\u5177\u4f53\u4f1a\u9047\u5230\u4ec0\u4e48\u95ee\u9898\u6211\u4eec\u4f1a\u5728\u4e4b\u540e\u7684\u5185\u5bb9\u4e2d\u5b66\u5230\uff09\u66ff\u4f60\u51c6\u5907\u597d\u4f60\u9700\u8981\u7684\u8d44\u6e90\uff0c\u5b8c\u6210\u4f60\u7684\u8bf7\u6c42\u3002</p> <p>\u5177\u4f53\u6765\u8bf4\uff0c\u64cd\u4f5c\u7cfb\u7edf\u7ba1\u7406\u7684\u8d44\u6e90\u6709\u8fd9\u4e9b\uff1a\u2460 CPU\uff0c\u7531\u4e8e CPU \u7684\u4e00\u4e2a\u6838(core)\u5728\u7279\u5b9a\u65f6\u523b\u53ea\u80fd\u5904\u7406\u4e00\u4ef6\u4e8b\uff0c\u6240\u4ee5\u201cCPU \u80fd\u591f\u4e3a\u6211\u6240\u7528\u201d\u662f\u4e00\u4e2a\u975e\u5e38\u91cd\u8981\u7684\u8d44\u6e90\uff1b\u2461 \u5185\u5b58\uff0c\u6267\u884c\u7a0b\u5e8f\u79bb\u4e0d\u5f00\u5185\u5b58\uff0c\u7528\u6237\u7a0b\u5e8f\u81ea\u7136\u4e5f\u9700\u8981\u5360\u7528\u4e00\u5b9a\u7684\u5185\u5b58\u6765\u89e3\u51b3\u95ee\u9898\uff1b\u2462 I/O \u8bbe\u5907\uff0c\u6253\u5370\u673a\u4e0d\u80fd\u540c\u65f6\u6253\u5370\u6bdb\u6982\u5386\u5e74\u5377\u548c\u8f6c\u4e13\u4e1a\u7533\u8bf7\u8868\uff1b\u2463\u2026\u2026</p> <p>\u7c97\u7565\u7684\u6765\u8bf4\uff0c\u672c\u8bfe\u7a0b\u4e4b\u540e\u7684\u5185\u5bb9\u57fa\u672c\u4e0a\u90fd\u662f\u56f4\u7ed5\u8981\u5982\u4f55\u7ef4\u62a4\u548c\u64cd\u4f5c\u5404\u79cd\u8d44\u6e90\u800c\u5c55\u5f00\u7684\u3002</p> \u2461 \u4ece\u5b58\u5728\u4e0a\u770b <p>\u4ece\u5176\u5b58\u5728\u6765\u770b\uff0c\u64cd\u4f5c\u7cfb\u7edf\u672c\u8d28\u4e0a\u8fd8\u662f\u4e00\u4e2a\u8f6f\u4ef6\u7a0b\u5e8f\uff0c\u662f\u4e00\u4e2a\u4e0d\u505c\u8fd0\u884c\u7740\u7684\uff0c\u7528\u6765\u6267\u884c\u7528\u6237\u7a0b\u5e8f\u7684\u8f6f\u4ef6\u3002\u8fd9\u4e2a\u89d2\u5ea6\u7684\u672c\u8d28\u540c\u65f6\u53cd\u5e94\u4e86\u64cd\u4f5c\u7cfb\u7edf\u6700\u521d\u5b58\u5728\u7684\u76ee\u7684\uff0c\u4e3a\u4e86\u63d0\u9ad8\u8ba1\u7b97\u673a\u8d44\u6e90\u7684\u5229\u7528\u6548\u7387\uff0c\u6211\u4eec\u9700\u8981\u4e00\u4e2a\u7a0b\u5e8f\u6765\u81ea\u52a8\u5316\u201c\u8ba9\u8ba1\u7b97\u673a\u5b8c\u6210\u4e00\u7cfb\u5217\u7279\u5b9a\u4efb\u52a1\u201d\u8fd9\u4ef6\u4e8b\uff0c\u800c\u4e3a\u4e86\u5b9e\u73b0\u8fd9\u4e2a\u81ea\u52a8\u5316\uff0c\u8fd9\u4e2a\u7a0b\u5e8f\u4e5f\u9700\u8981\u6210\u4e3a\u8ba1\u7b97\u673a\u786c\u4ef6\u7684\u201c\u4ee3\u7406\u4eba\u201d\uff0c\u638c\u63e1\u786c\u4ef6\u7684\u6240\u6709\u8d44\u6e90\uff0c\u5e76\u4e14\u8fd9\u4e2a\u201c\u4ee3\u7406\u4eba\u201d\u8fd8\u5f97\u60f3\u65b9\u6cd5\u8ba9\u81ea\u5df1\u597d\u597d\u201c\u6d3b\u7740\u201d\u3002</p> <p>\u64cd\u4f5c\u7cfb\u7edf\u4e2d\u6700\u57fa\u7840\u6700\u4e2d\u592e\u7684\u90e8\u5206\u662f\u5185\u6838(kernel)\uff0c\u8981\u7ed9\u51fa kernel \u7684\u7cbe\u786e\u5b9a\u4e49\u5f88\u96be\uff0c\u8fd9\u4e0e\u64cd\u4f5c\u7cfb\u7edf\u8bbe\u8ba1\u7684\u7ed3\u6784\u6709\u5173\uff08\u53c2\u8003\u5b8f\u5185\u6838\u548c\u5fae\u5185\u6838\uff09\uff0c\u5b83\u6700\u660e\u663e\u7684\u4e00\u4e2a\u7279\u70b9\u5c31\u662f\u81ea\u8ba1\u7b97\u673a\u5f00\u673a\u540e\u5c31\u4e0d\u505c\u5728\u8fd0\u884c\u3002OS \u548c kernel \u7684\u5173\u7cfb\u5c31\u597d\u50cf\u7b14\u8bb0\u672c\u7535\u8111\u548c\u5b83\u7684\u4e3b\u677f\uff0c\u5982\u679c\u5c06 OS \u4e2d\u7684\u5176\u4ed6\u90e8\u5206\u9664\u53bb\uff0ckernel \u4ecd\u7136\u81ea\u6d3d\uff0c\u4ecd\u7136\u5177\u5907\u5b83\u5e94\u6709\u7684\u5185\u5728\u7684\u529f\u80fd\uff0c\u6bd4\u5982\u5b83\u4ecd\u7136\u5177\u5907\u5bf9\u8d44\u6e90\u8fdb\u884c\u8c03\u5ea6\u7684\u80fd\u529b\uff0c\u53ea\u4e0d\u8fc7\u5b83\u53ef\u80fd\u62ff\u4e0d\u5230\u80fd\u8ba9\u5b83\u8c03\u5ea6\u7684\u8d44\u6e90\u3002\u6211\u5728\u8fd9\u91cc\u907f\u514d\u8c08\u5230 OS \u548c kernel \u7684\u533a\u522b\uff0c\u56e0\u4e3a\u8fd9\u5b9e\u5728\u96be\u4ee5\u8bf4\u6e05\uff0c\u751a\u81f3\u5728\u4e4b\u540e\u7684\u5185\u5bb9\u4e2d\uff0c\u6211\u90fd\u4f1a\u7528 OS \u6765\u4ee3\u66ff kernel \u7684\u6982\u5ff5\u3002</p> <p>\u81f3\u6b64\uff0c\u6211\u4eec\u4ece\u4e24\u4e2a\u65b9\u9762\u4e86\u89e3\u4e86\u4ec0\u4e48\u662f\u64cd\u4f5c\u7cfb\u7edf\uff0c\u73b0\u5728\u7528\u4e00\u53e5\u8bfe\u672c\u4e0a\u7684\u8bdd\u6765\u505a\u603b\u7ed3\u3002</p> <p>The common functions of controlling and allocating resources are then brought together into one piece of software: the operating system. --Operating System Concepts (10th edition)</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit0/#\u64cd\u4f5c\u7cfb\u7edf\u7684\u8bbe\u8ba1\u76ee\u6807","title":"\u64cd\u4f5c\u7cfb\u7edf\u7684\u8bbe\u8ba1\u76ee\u6807","text":"<p>\u73b0\u5728\u6211\u4eec\u77e5\u9053\u64cd\u4f5c\u7cfb\u7edf\u662f\u4ec0\u4e48\u4e1c\u897f\u4e86\uff0c\u90a3\u4e48\u5728\u6b64\u57fa\u7840\u4e0a\u6211\u4eec\u6316\u6398\u4e00\u4e0b\uff0c\u600e\u6837\u624d\u7b97\u4e00\u4e2a\u597d\u7684\u64cd\u4f5c\u7cfb\u7edf\uff0c\u4e5f\u5c31\u662f\u64cd\u4f5c\u7cfb\u7edf\u7684\u53d1\u5c55\u65b9\u5411\uff0c\u800c\u5728\u8fd9\u4e2a\u8fc7\u7a0b\u4e2d\uff0c\u6211\u4e5f\u4f1a\u7b80\u5355\u63d0\u53ca\u4e00\u4e9b\u6211\u4eec\u4e4b\u540e\u4f1a\u8bbe\u8ba1\u7684\u5185\u5bb9\uff0c\u4ee5\u4f9b\u53c2\u8003\u3002</p> <p>\u9996\u5148\uff0c\u64cd\u4f5c\u7cfb\u7edf\u672c\u8eab\u9700\u8981\u6709\u8f83\u597d\u7684\u53ef\u9760\u6027\u548c\u5b89\u5168\u6027\uff0c\u4e5f\u5c31\u662f\u6211\u4eec\u4e4b\u524d\u63d0\u5230\u7684\uff0c\u8fd9\u4e2a\u201c\u4ee3\u7406\u4eba\u201d\u8981\u5c3d\u53ef\u80fd\u8ba9\u81ea\u5df1\u597d\u597d\u201c\u6d3b\u7740\u201d\u3002\u4e00\u65b9\u9762\u5b83\u9700\u8981\u6709\u826f\u597d\u7684\u5f02\u5e38\u5904\u7406\u673a\u5236\uff08\u901a\u8fc7#\u4e2d\u65ad\u673a\u5236\u5b9e\u73b0\uff09\uff0c\u8fd9\u4e2a\u201c\u4ee3\u7406\u4eba\u201d\u9700\u8981\u6709\u5f3a\u5065\u7684\u4f53\u9b44\uff0c\u4e0d\u80fd\u4e00\u522e\u98ce\u5b83\u5c31\u75c5\u5012\u4e86\uff1b\u53e6\u4e00\u65b9\u9762\u5b83\u9700\u8981\u6709\u6743\u9650\u7ba1\u7406\u7cfb\u7edf\uff08#\u7279\u6743\u6a21\u5f0f\uff09\uff0c\u4ee5\u5c4f\u853d\u6765\u81ea\u7528\u6237\u7a0b\u5e8f\u7684\u5371\u9669\u884c\u4e3a\uff0c\u7528\u6237\u53ef\u4ee5\u5411\u201c\u67dc\u53f0\u201d\u7d22\u53d6\u6297\u751f\u7d20\uff0c\u4f46\u662f\u7528\u6237\u7d22\u53d6\u5e93\u623f\u94a5\u5319\u65f6\uff0c\u5408\u683c\u7684\u201c\u67dc\u53f0\u201d\u663e\u7136\u4e0d\u80fd\u7b54\u5e94\u8fd9\u4e2a\u8bf7\u6c42\u3002</p> <p>\u5176\u6b21\uff0c\u64cd\u4f5c\u7cfb\u7edf\u9700\u8981\u6709\u8f83\u597d\u7684\u6613\u7528\u6027\uff0c\u5b83\u9700\u8981\u5411\u7528\u6237\u63d0\u4f9b\u7b80\u4fbf\u7684\u670d\u52a1\u4ee5\u8bf7\u6c42\u7cfb\u7edf\u8d44\u6e90\uff0c\u6bd5\u7adf\u64cd\u4f5c\u7cfb\u7edf\u7684\u76ee\u7684\u4e4b\u4e00\u5c31\u662f\u65b9\u4fbf\u7528\u6237\u4f7f\u7528\u7cfb\u7edf\u8d44\u6e90\u2014\u2014\u8fd9\u610f\u5473\u7740\u6211\u4eec\u7684\u201c\u4ee3\u7406\u4eba\u201d\u5f97\u662f\u4e2a\u597d\u4ea4\u6d41\u7684\u4eba\uff0c\u800c\u7528\u6237\u7a0b\u5e8f\u8c03\u7528\u64cd\u4f5c\u7cfb\u7edf\u8d44\u6e90\u7684\u9014\u5f84\u662f\u7cfb\u7edf\u8c03\u7528\u3002</p> <p>\u5bbd\u6cdb\u4e00\u70b9\u6765\u8bb2\uff0c\u64cd\u4f5c\u7cfb\u7edf\u4e3a\u6211\u4eec\u63d0\u4f9b\u4e86\u547d\u4ee4\u63a5\u53e3\u548c\u7a0b\u5e8f\u63a5\u53e3\uff0c\u6709\u4e9b\u5730\u65b9\u4e5f\u4f1a\u63d0\u5230\u56fe\u5f62\u7528\u6237\u63a5\u53e3(Graphical User Interface, GUI)\uff0c\u4ee5\u53ca\u547d\u4ee4\u884c\u63a5\u53e3(Command Line Interface, CLI)\uff0c\u4f46\u662f\u6211\u4e2a\u4eba\u4e0d\u662f\u5f88\u559c\u6b22\u8fd9\u4e2a\u5206\u7c7b\u3002</p> <p>\u5f53\u7136\uff0c\u64cd\u4f5c\u7cfb\u7edf\u9700\u8981\u662f\u9ad8\u6548\u7684\uff0c\u4ece\u6700\u65e9\u7684\u6279\u5904\u7406\u7cfb\u7edf\u5230\u73b0\u5728\u7684\u5206\u65f6\u7cfb\u7edf\uff08#\u64cd\u4f5c\u7cfb\u7edf\u7684\u4efb\u52a1\u6267\u884c\u8bbe\u8ba1\uff09\uff0cCPU \u7684\u5229\u7528\u7387\u5728\u4e0d\u65ad\u63d0\u5347\uff0c\u5468\u8f6c\u65f6\u95f4\u4e5f\u5728\u4e0d\u65ad\u7f29\u77ed\uff0c\u5982\u4eca\u7684\u64cd\u4f5c\u7cfb\u7edf\u901a\u8fc7\u5206\u65f6\u6280\u672f\u4e5f\u5b9e\u73b0\u4e86\u4f53\u611f\u4e0a\u7684\u5e76\u884c\uff0c\u63d0\u9ad8\u6548\u7387\u7684\u540c\u65f6\u4e5f\u63d0\u9ad8\u4e86\u7528\u6237\u4f53\u9a8c\u3002</p> <p>\u8fd8\u6709\u4e00\u70b9\u4e0d\u5bb9\u5ffd\u89c6\u7684\u662f\u64cd\u4f5c\u7cfb\u7edf\u7684\uff08\u4e00\u5b9a\u7a0b\u5ea6\u4e0a\u7684\uff09\u516c\u5e73\u6027\uff0c\u5728 Unit 1: \u8fdb\u7a0b\u7ba1\u7406\u4e2d\u6211\u4eec\u4f1a\u4e86\u89e3\u5230\uff0c\u591a\u8fdb\u7a0b\u8bed\u5883\u4e0b\u6709\u5927\u91cf\u7684\u51b2\u7a81\u95ee\u9898\u9700\u8981\u89e3\u51b3\uff0c\u800c\u6211\u4eec\u5728\u5904\u7406\u8fd9\u4e9b\u51b2\u7a81\u95ee\u9898\u7684\u65f6\u5019\uff0c\u53ef\u80fd\u4f1a\u51fa\u73b0\u9965\u997f(Starvation)\uff08\u5177\u4f53\u662f\u4ec0\u4e48\u8bf7\u53c2\u8003\u4e0b\u4e00\u5355\u5143\uff09\uff0c\u800c\u64cd\u4f5c\u7cfb\u7edf\u8981\u505a\u7684\u5c31\u662f\u907f\u514d\u9965\u997f\u7684\u51fa\u73b0\uff0c\u5c31\u597d\u50cf\u7e41\u5fd9\u65f6\u6bb5\u7684\u7535\u68af\uff0c\u6211\u4eec\u4e0d\u80fd\u56e0\u4e3a\u4e8c\u697c\u6d41\u91cf\u5f88\u5927\u5c31\u4e0d\u7ba1\u4e09\u697c\u4ee5\u4e0a\u7684\u4eba\u3002</p> <p>\u4e0a\u8ff0\u76ee\u6807\u5927\u591a\u662f\u9488\u5bf9\u4f7f\u7528\u8005\u800c\u8a00\u7684\uff0c\u90a3\u4e48\u5bf9\u4e8e\u5f00\u53d1\u8005\u6765\u8bf4\uff0c\u64cd\u4f5c\u7cfb\u7edf\u7684\u53ef\u6269\u5c55\u6027\u3001\u6613\u7ef4\u62a4\u6027\u7b49\u4e5f\u662f\u975e\u5e38\u91cd\u8981\u7684\u3002\u4e0d\u540c\u7684\u8bbe\u8ba1\u601d\u8def\u9020\u5c31\u4e86\u4e0d\u540c\u7684\u64cd\u4f5c\u7cfb\u7edf\u7ed3\u6784\uff0c\u5404\u79cd\u8bbe\u8ba1\u4e5f\u5404\u81ea\u6709\u5404\u81ea\u7684\u4e3b\u6218\u573a\uff0c\u5173\u4e8e\u8fd9\u4e9b\u5185\u5bb9\uff0c\u6211\u4eec\u4f1a\u5728#\u64cd\u4f5c\u7cfb\u7edf\u7684\u7ed3\u6784\u8bbe\u8ba1\u8fd9\u4e00\u90e8\u5206\u66f4\u8be6\u7ec6\u5730\u4ecb\u7ecd\u3002</p> <p>\u8fd8\u6709\u8bb8\u591a\uff0c\u4f8b\u5982\u64cd\u4f5c\u7cfb\u7edf\u7684\u8bbe\u8ba1\u8981\u5c3d\u53ef\u80fd\u5229\u7528\u786c\u4ef6\u8d44\u6e90\u7b49\uff0c\u4f46\u5e76\u4e0d\u662f\u6211\u4eec\u5728\u672c\u8282\u60f3\u8981\u8ba8\u8bba\u7684\u91cd\u70b9\uff0c\u6240\u6709\u5c31\u63a0\u8fc7\u4e86\u3002\u4e0a\u8ff0\u89c2\u70b9\u5e76\u4e0d\u5168\u9762\u4e5f\u4e0d\u4e00\u5b9a\u5b8c\u5168\u6b63\u786e\uff0c\u6709\u4e00\u5927\u90e8\u5206\u90fd\u662f\u6211\u7684\u4e2a\u4eba\u7406\u89e3\uff0c\u8bf7\u8bfb\u8005\u8fa8\u8bc1\u5730\u770b\u5f85\uff0c\u5982\u679c\u6709\u9519\u8bef\u8bf7\u52a1\u5fc5\u544a\u8bc9\u6211\uff01</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit0/#\u64cd\u4f5c\u7cfb\u7edf\u7684\u6574\u4f53\u8bbe\u8ba1","title":"\u64cd\u4f5c\u7cfb\u7edf\u7684\u6574\u4f53\u8bbe\u8ba1","text":"<p>\u672c\u8282\u4e3b\u8981\u5c31\u4e00\u4e9b\u5173\u4e8e\u64cd\u4f5c\u7cfb\u7edf\u6574\u4f53\u8bbe\u8ba1\u7684\u95ee\u9898\u505a\u4e00\u4e9b\u8ba8\u8bba\uff0c\u4ece\u4e00\u4e2a\u76f8\u5bf9\u6bd4\u8f83\u9ad8\u7684\u89d2\u5ea6\u8c08\u4e00\u8c08\u4e00\u4e9b\u9876\u5c42\u8bbe\u8ba1\u3002</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit0/#\u8ba1\u7b97\u673a\u7cfb\u7edf\u67b6\u6784","title":"\u8ba1\u7b97\u673a\u7cfb\u7edf\u67b6\u6784","text":"<p>\u867d\u7136\u64cd\u4f5c\u7cfb\u7edf\u672c\u8eab\u662f\u8f6f\u4ef6\uff0c\u4f46\u662f\u5b83\u6bd5\u7adf\u662f\u4e0e\u786c\u4ef6\u7d27\u5bc6\u5173\u8054\u7684\uff0c\u6240\u4ee5\u6211\u4eec\u8fd8\u662f\u4f1a\u6d89\u53ca\u5230\u4e00\u4e9b\u5173\u4e8e\u786c\u4ef6\u7684\u5185\u5bb9\uff0c\u8fd9\u91cc\u7b80\u5355\u6d89\u53ca\u4e00\u4e9b\u5173\u4e8e\u8ba1\u7b97\u673a\u7cfb\u7edf\u67b6\u6784\u7684\u5185\u5bb9\u3002</p> \u6982\u5ff5\u8fa8\u6790 <p> \u540d\u8bcd \u5b9a\u4f4d CPU \u6267\u884c\u6307\u4ee4\u7684\u786c\u4ef6 Core CPU \u7684\u57fa\u7840\u8ba1\u7b97\u5355\u5143 Multi-core \u4e00\u4e2a CPU \u4e0a\u6709\u591a\u4e2a core Processor \u5305\u542b\u4e00\u4e2a\u6216\u591a\u4e2a CPU \u7684\u82af\u7247 Multi-processor \u591a\u4e2a processor </p> <p>\u6839\u636e\u5904\u7406\u5668\u7684\u6570\u91cf\u548c\u7ec4\u7ec7\u5f62\u5f0f\uff0c\u6211\u4eec\u8fd9\u91cc\u4ecb\u7ecd\u4e09\u79cd\u8ba1\u7b97\u673a\u7cfb\u7edf\u67b6\u6784\uff1a\u5355\u5904\u7406\u5668\u7cfb\u7edf\u3001\u591a\u5904\u7406\u5668\u7cfb\u7edf\u3001\u96c6\u7fa4\u7cfb\u7edf\u3002</p> \u2460 \u5355\u5904\u7406\u5668\u7cfb\u7edf(Single-Processor System) <p>\u4e66\u4e2d\u7ed9\u51fa\u7684\u5173\u4e8e\u5355\u5904\u7406\u5668\u7cfb\u7edf\u7684\u5b9a\u4e49\u662f\uff0c\u6709\u4e14\u4ec5\u6709\u4e00\u4e2a\u901a\u7528\u5904\u7406\u5668(general-purpose processor)\uff0c\u5e76\u4e14\u8fd9\u4e2a processor \u53ea\u6709\u4e00\u4e2a\u6838(core)\u3002\u4f46\u5b83\u53ef\u4ee5\u6709\u82e5\u5e72\u4e13\u7528\u5904\u7406\u5668(special-purpose processor)\uff0c\u7528\u6765\u6267\u884c\u4e00\u4e9b\u7279\u5b9a\u7684\u6307\u4ee4\uff0c\u800c\u8fd9\u4e9b\u4e13\u7528\u5904\u7406\u5668\u5e76\u4e0d\u8fd0\u884c\u7ebf\u7a0b\u3002</p> \u2461 \u591a\u5904\u7406\u5668\u7cfb\u7edf(Multiprocessor System) <p>\u591a\u5904\u7406\u5668\u7cfb\u7edf\u662f\u6307\u6709\u591a\u4e2a\u5355\u6838\u901a\u7528\u5904\u7406\u5668\u7684\u7cfb\u7edf\uff0c\u8fd9\u4e9b\u5904\u7406\u5668\u5171\u4eab\u4e00\u5757\u4e3b\u5185\u5b58\uff0c\u5b83\u4eec\u901a\u8fc7\u603b\u7ebf\u6216\u4ea4\u6362\u7f51\u7edc\u8fde\u63a5\u5728\u4e00\u8d77\u3002</p> <p>\u663e\u800c\u6613\u89c1\u7684\u662f\uff0c\u589e\u52a0\u4e86\u5904\u7406\u5668\u7684\u6570\u91cf\u80fd\u591f\u589e\u52a0\u541e\u5410\u91cf(throughput)\uff0c\u5373\u5355\u4f4d\u65f6\u95f4\u5185\u5904\u7406\u7684\u4efb\u52a1\u6570\u91cf\uff0c\u4f46\u662f\u8fd9\u4e2a\u589e\u52a0\u5e76\u4e0d\u662f\u7ebf\u6027\u7684\uff0c\u56e0\u4e3a\u5904\u7406\u5668\u4e4b\u95f4\u7684\u901a\u4fe1\u4e5f\u9700\u8981\u65f6\u95f4\uff0c\u800c\u4e14\u8fd8\u4f1a\u6709\u4e00\u4e9b\u989d\u5916\u7684\u5f00\u9500\u3002</p> \u76f8\u5173\u9605\u8bfb <ul> <li>\u5bf9\u79f0\u591a\u5904\u7406 | SMP\uff1b</li> <li>\u975e\u4e00\u81f4\u5185\u5b58\u8bbf\u95ee | NUMA\uff1b</li> </ul> <p>\u4f46\u662f multi-core \u7684\u8bbe\u8ba1\u5728\u901f\u5ea6\u548c\u6548\u80fd\u4e0a\u90fd\u66f4\u80dc\u4e00\u7b79\uff0c\u56e0\u4e3a on-chip \u7684\u901a\u4fe1\u6bd4 between-chip \u7684\u901a\u4fe1\u66f4\u5feb\uff0c\u800c\u4e14\u66f4\u7701\u7535\u3002</p> \u2462 \u96c6\u7fa4\u7cfb\u7edf(Cluster System) <p> </p> <p>\u96c6\u7fa4\u7cfb\u7edf\u901a\u8fc7\u5197\u4f59\u5b9e\u73b0\u9ad8\u53ef\u7528\u670d\u52a1\uff0c\u901a\u8fc7\u5e76\u884c\u5b9e\u73b0\u9ad8\u6027\u80fd\u8ba1\u7b97\uff0c\u5b83\u662f\u7531\u591a\u4e2a\u5404\u81ea\u72ec\u7acb\u7684\u8ba1\u7b97\u673a\u7cfb\u7edf\u4f5c\u4e3a\u8282\u70b9(node)\uff0c\u901a\u8fc7\u9ad8\u901f\u901a\u4fe1\u7f51\u7edc\u4e92\u76f8\u8fde\u63a5\u5f62\u6210\u7684\u3002</p> <p>\u96c6\u7fa4\u4e5f\u5206\u5bf9\u79f0\u548c\u4e0d\u5bf9\u79f0\u4e24\u79cd\uff0c\u5bf9\u79f0\u96c6\u7fa4\u7684\u5404\u4e2a\u8282\u70b9\u4e92\u76f8\u76d1\u7763\uff0c\u800c\u4e0d\u5bf9\u79f0\u7684\u96c6\u7fa4\u5219\u5b58\u5728\u4e00\u79cd\u7c7b\u4f3c\u201c\u66ff\u8865\u201d\u7684\u4e1c\u897f\uff0c\u7531\u201c\u66ff\u8865\u201d\u53bb\u76d1\u7763\u5de5\u4f5c\u4e2d\u7684\u8282\u70b9\uff0c\u5f53\u5de5\u4f5c\u4e2d\u7684\u8282\u70b9\u51fa\u73b0\u4e86\u95ee\u9898\uff0c\u5c31\u7531\u201c\u66ff\u8865\u201d\u6765\u63a5\u66ff\u5b83\u7684\u5de5\u4f5c\u3002</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit0/#\u64cd\u4f5c\u7cfb\u7edf\u7684\u4efb\u52a1\u6267\u884c\u8bbe\u8ba1","title":"\u64cd\u4f5c\u7cfb\u7edf\u7684\u4efb\u52a1\u6267\u884c\u8bbe\u8ba1","text":"<p>\u524d\u9762\u6211\u4eec\u8bf4\u8fc7\uff0c\u64cd\u4f5c\u7cfb\u7edf\u88ab\u7528\u6765\u300c\u81ea\u52a8\u5316\u201c\u8ba9\u8ba1\u7b97\u673a\u5b8c\u6210\u4e00\u7cfb\u5217\u7279\u5b9a\u4efb\u52a1\u201d\u300d\u7684\u3002\u4e00\u5f00\u59cb\u8fd9\u4ef6\u4e8b\u6bd4\u8f83\u7b80\u5355\uff0c\u53ea\u9700\u8981\u50cf\u961f\u5217\u4e00\u6837\uff0c\u4e00\u4e2a\u4e00\u4e2a\u7684\u6267\u884c\u5c31\u884c\uff0c\u4f46\u662f\u6162\u6162\u7684\u968f\u7740\u8ba1\u7b97\u673a\u5e94\u7528\u8303\u56f4\u7684\u6269\u5927\u4ee5\u53ca\u5404\u79cd\u9700\u6c42\u7684\u51fa\u73b0\uff0c\u8fd9\u79cd\u8bbe\u8ba1\u5c31\u4e0d\u592a\u5408\u7406\u4e86\u3002\u6309\u7167\u53d1\u5c55\u9636\u6bb5\u6f14\u8fdb\uff0c\u6211\u4eec\u5212\u5206\u51fa\u4e24\u4e2a\u9636\u6bb5\u4e09\u4e2a\u8bbe\u8ba1\uff1a\u5355\u9053\u6279\u5904\u7406\u7cfb\u7edf(Batch Processing System)\u3001\u591a\u9053\u6279\u5904\u7406\u7cfb\u7edf(Multiprogramming Batch Processing System)\u548c\u5206\u65f6\u7cfb\u7edf(Time Sharing Systems)\u3002</p> <p></p> \u2460 \u6279\u5904\u7406\u7cfb\u7edf\u9636\u6bb5 <p>\u6700\u65e9\u64cd\u4f5c\u7cfb\u7edf\u6267\u884c\u4efb\u52a1\u90fd\u9700\u8981\u4eba\u5de5\u624b\u52a8\u5e72\u9884\uff0c\u4f46\u662f\u8ba1\u7b97\u673a\u6267\u884c\u4efb\u52a1\u7684\u901f\u5ea6\u4e0e\u4eba\u5de5\u5e72\u9884\u7684\u901f\u5ea6\u76f8\u5dee\u592a\u5927\uff0c\u6362\u53e5\u8bdd\u6765\u8bf4\u4eba\u5de5\u901f\u5ea6\u4e25\u91cd\u9650\u5236\u4e86\u8ba1\u7b97\u673a\u7684\u5de5\u4f5c\u6548\u7387\uff0c\u4e8e\u662f\u64cd\u4f5c\u7cfb\u7edf\u5f00\u59cb\u51fa\u73b0\uff0c\u5176\u4e2d\u4e00\u4e2a\u6bd4\u8f83\u539f\u59cb\u7684\u5b9e\u73b0\u5c31\u662f\u6279\u5904\u7406\u7cfb\u7edf\u3002\uff08\u4f46\u4e0d\u662f\u6700\u65e9\uff0c\u4e4b\u524d\u8fd8\u6709\u8131\u673a\u5904\u7406\u4e4b\u7c7b\u7684\u4e1c\u897f\u3002\uff09</p> \u2776 \u5355\u9053\u6279\u5904\u7406\u9636\u6bb5 <p>\u6309\u7167\u64cd\u4f5c\u7cfb\u7edf\u53d1\u5c55\u8fdb\u7a0b\uff0c\u6211\u4eec\u9996\u5148\u4ecb\u7ecd\u5355\u9053\u6279\u5904\u7406\u7cfb\u7edf(Batch Processing)\u3002</p> <p>\u5355\u9053\u6279\u5904\u7406\u7cfb\u7edf\u6709\u4e24\u4e2a\u5173\u952e\u8bcd\uff0c\u201c\u6279\u5904\u7406\u201d\u548c\u201c\u5355\u9053\u201d\u3002</p> <p>\u201c\u6279\u5904\u7406\u201d\u6307\u7684\u662f\uff0c\u7cfb\u7edf\u6267\u884c\u7684\u4efb\u52a1\u662f\u6210\u6279\u7684\uff0c\u82e5\u5e72\u4efb\u52a1\u88ab\u4f5c\u4e3a\u4e00\u6574\u6279\u4ea4\u4ed8\u7ed9\u64cd\u4f5c\u7cfb\u7edf\u3002\u5728\u5177\u4f53\u6267\u884c\u8fc7\u7a0b\u4e2d\uff0c\u64cd\u4f5c\u7cfb\u7edf\u81ea\u52a8\u6309\u987a\u5e8f\u4e32\u884c(serial)\u6267\u884c\u8fd9\u4e9b\u4efb\u52a1\u3002</p> <p>\u800c\u201c\u5355\u9053\u201d\u6307\u7684\u662f\uff0c\u4e00\u6bb5\u65f6\u95f4\u5185\u5185\u5b58\u4e2d\u53ea\u6709\u4e00\u9053\u7a0b\u5e8f\u5728\u8fd0\u884c\uff0c\u7cfb\u7edf\u53ea\u5904\u7406\u4e00\u9879\u4efb\u52a1\uff0c\u5728\u8fd9\u4e2a\u4efb\u52a1\u7ed3\u675f\u4e4b\u524d\uff0c\u4e0d\u4f1a\u5207\u6362\u5230\u5176\u4ed6\u4efb\u52a1\u3002</p> <p>\u5355\u9053\u6279\u5904\u7406\u7cfb\u7edf\u521d\u6b65\u5b9e\u73b0\u4e86\u4e00\u79cd\u201c\u81ea\u52a8\u5316\u201d\uff0c\u6781\u5927\u51cf\u5c11\u4e86\u4eba\u5de5\u64cd\u4f5c\u901f\u5ea6\u5bf9\u64cd\u4f5c\u7cfb\u7edf\u7684\u5f71\u54cd\u3002\u4f46\u5b83\u5b58\u5728\u4e00\u4e2a\u975e\u5e38\u660e\u663e\u7684\u95ee\u9898\uff1a\u7531\u4e8e\u5f53\u524d\u4efb\u52a1\u7ed3\u675f\u4e4b\u524d\u4e0d\u4f1a\u5207\u6362\u5230\u5176\u5b83\u4efb\u52a1\uff0c\u6240\u4ee5\u5f53\u5f53\u524d\u4efb\u52a1\u51fa\u73b0 I/O \u8bf7\u6c42\u65f6\uff0cCPU \u5c31\u9700\u8981\u7b49\u5f85 I/O \u5b8c\u6210\u3002\u6211\u4eec\u77e5\u9053 I/O \u64cd\u4f5c\u662f\u975e\u5e38\u8017\u65f6\u7684\uff0c\u66f4\u4e25\u91cd\u7684\u662f\u4f8b\u5982\u7b49\u5f85\u952e\u76d8\u8f93\u5165\u8fd9\u79cd\u9700\u8981\u4eba\u5de5\u53c2\u4e0e\u7684 I/O\uff0c\u5355\u9053\u6279\u5904\u7406\u7cfb\u7edf\u4ecd\u7136\u6ca1\u6cd5\u907f\u514d\u8fd9\u79cd\u4eba\u5de5\u64cd\u4f5c\u5bf9\u8ba1\u7b97\u673a\u6267\u884c\u6548\u7387\u7684\u5f71\u54cd\uff0c\u8fd9\u5c31\u5bfc\u81f4 CPU \u4f1a\u957f\u65f6\u95f4\u5904\u4e8e\u7a7a\u95f2\u72b6\u6001\uff0c\u800c\u8ba9 CPU \u957f\u65f6\u95f4\u7a7a\u95f2\u8fd9\u4ef6\u4e8b\uff0c\u662f\u4e0d\u88ab\u63a5\u53d7\u7684\u3002</p> \u2777 \u591a\u9053\u6279\u5904\u7406\u9636\u6bb5 <p>\u56e0\u6b64\uff0c\u4e3a\u4e86\u4e0d\u8ba9 CPU \u95f2\u4e0b\u6765\uff0c\u4e00\u4e2a\u7b26\u5408\u76f4\u89c9\u7684\u60f3\u6cd5\u5c31\u662f\u8ba9\u5b83\u5148\u53bb\u505a\u4e0b\u4e00\u4ef6\u4e8b\uff0c\u5c31\u597d\u50cf\u4ed3\u5e93\u6b63\u5728\u6536\u96c6\u4e0a\u4e00\u4e2a\u75c5\u4eba\u6240\u9700\u8981\u7684\u836f\u54c1\u7684\u65f6\u5019\uff0c\u67dc\u53f0\u53ef\u4ee5\u5148\u53bb\u5904\u7406\u4e0b\u4e00\u4e2a\u75c5\u4eba\u7684\u8bf7\u6c42\u3002\u591a\u9053\u6279\u5904\u7406\u7cfb\u7edf(Multiprogramming Batch Processing System)\u5e94\u8fd0\u800c\u751f\u3002</p> <p>\u4ece\u540d\u5b57\u4e0a\u6765\u770b\uff0c\u591a\u9053\u6279\u5904\u7406\u7cfb\u7edf\u5389\u5bb3\u5728\u8fd9\u4e2a\u201c\u591a\u9053(Multiprogramming)\u201d\uff0c\u5373\u4e00\u6bb5\u65f6\u95f4\u5185\u5185\u5b58\u4e2d\u540c\u65f6\u5b58\u5728\u591a\u4e2a\u8fdb\u7a0b\u3002</p> <p>\u5177\u4f53\u6765\u8bf4\uff0c\u5728\u591a\u9053\u6279\u5904\u7406\u7cfb\u7edf\u4e2d\uff0c\u5f53\u524d\u4efb\u52a1\u53d1\u751f IO \u8bf7\u6c42\u65f6\uff0cCPU \u8f6c\u800c\u53bb\u6267\u884c\u5176\u5b83\u4efb\u52a1\uff0c\u4ee5\u6b64\u6765\u5b9e\u73b0\u5c3d\u91cf\u8ba9 CPU \u59cb\u7ec8\u5728\u5de5\u4f5c\u72b6\u6001\u3002\u56e0\u6b64\uff0c\u5b8f\u89c2\u4e0a\u6765\u770b\uff0c\u591a\u9053\u6279\u5904\u7406\u7cfb\u7edf\u5728\u4e00\u6bb5\u65f6\u95f4\u5185\u540c\u65f6\u6267\u884c\u82e5\u5e72\u4efb\u52a1\uff08\u5728\u4efb\u52a1 A \u5b8c\u6210\u4e4b\u524d\u4efb\u52a1 B \u4e5f\u53ef\u80fd\u5f00\u59cb\u4e86\uff09\uff0c\u6211\u4eec\u79f0\u4e4b\u4e3a\u5e76\u53d1(concurrency)\uff08\u6ce8\u610f\uff0c\u5e76\u53d1\u4e0e\u5e76\u884c\u7684\u6982\u5ff5\u5e76\u4e0d\u4e00\u81f41\uff09\uff1b\u4f46\u5728\u5fae\u89c2\u4e0a\uff0c\u591a\u9053\u6279\u5904\u7406\u7cfb\u7edf\u4ecd\u7136\u662f\u987a\u5e8f\u4e32\u884c\u7684\uff0c\u53ea\u4e0d\u8fc7\u533a\u522b\u4e8e\u5355\u9053\u6279\u5904\u7406\u7cfb\u7edf\u4ee5\u5b8c\u6574\u7684\u4efb\u52a1\u4f5c\u4e3a\u4efb\u52a1\u5355\u5143\uff0c\u591a\u9053\u6279\u5904\u7406\u7cfb\u7edf\u662f\u5c06\u5b8c\u6574\u4efb\u52a1\u6309\u7167 I/O \u7684\u53d1\u751f\u505a\u5212\u5206\uff0c\u4ee5\u8fd9\u4e9b\u5212\u5206\u540e\u7684\u90e8\u5206\u4efb\u52a1\u4f5c\u4e3a\u4efb\u52a1\u5355\u5143\u8fdb\u884c\u987a\u5e8f\u4e32\u884c(serial)\u3002</p> <p>\u6211\u4eec\u53ef\u4ee5\u7528\u7518\u7279\u56fe\u6765\u53ef\u89c6\u5316\u591a\u9053\u6279\u5904\u7406\u7cfb\u7edf\u7684\u7b56\u7565\uff08\u4e00\u79cd\u5e38\u89c1\u7684\u9898\u578b\uff09\u3002\u4ee5\u4e0b\u9762\u7684\u9898\u76ee\u4e3a\u4f8b\uff0c\u6211\u4eec\u6765\u5b9e\u8df5\u4e00\u4e0b\u3002</p> \ud83c\udf30 \u9898\u9762\u89e3\u6790 <p>\u73b0\u5728\u6709\u4e24\u4e2a\u7a0b\u5e8f A \u548c B\uff0c\u4ee5\u53ca\u4e24\u4e2a\u5206\u522b\u72ec\u7acb\u7684\u8bbe\u5907 X \u548c Y\uff0c\u4e14\u6211\u4eec\u53ea\u6709\u4e00\u4e2a CPU\uff1a</p> <ul> <li>A \u9700\u8981\u987a\u5e8f\u4f7f\u7528\u5982\u4e0b\u8d44\u6e90\uff1aCPU:10s, X:5s, CPU:5s, Y:10s, CPU:10s</li> <li>B \u9700\u8981\u987a\u5e8f\u4f7f\u7528\u5982\u4e0b\u8d44\u6e90\uff1aX:10s, CPU 10s, Y:5s, CPU:5s, Y:10s </li> </ul> <p>\u8bf7\u8ba8\u8bba\uff1a</p> <ol> <li>\u5728\u5355\u9053\u7a0b\u5e8f\u73af\u5883\u4e0b\u5148\u6267\u884c A \u518d\u6267\u884c B\uff0cCPU \u7684\u5229\u7528\u7387\u662f\u591a\u5c11\uff1f</li> <li>\u5728\u591a\u9053\u7a0b\u5e8f\u73af\u5883\u4e0b\uff0cCPU \u7684\u5229\u7528\u7387\u662f\u591a\u5c11\uff1f\u8bf7\u7ed9\u51fa\u7518\u7279\u56fe\u3002</li> </ol> <p>\u5728\u5355\u9053\u7a0b\u5e8f\u4e0b\u6267\u884c\uff0c\u5373\u6309\u987a\u5e8f\u6267\u884c A \u548c B\uff0cCPU \u7684\u5229\u7528\u7387\u5373\u5b9e\u9645 CPU \u4f7f\u7528\u65f6\u95f4\u9664\u4ee5\u5b8c\u6210\u4efb\u52a1\u7684\u603b\u65f6\u95f4\uff0c\u56e0\u6b64\uff1a</p> \\[ U = \\frac{(10+5+10)+(10+5)}{(10+5+5+10+10)+(10+10+5+5+10)} = \\frac{40}{80} = 50\\% \\] <p>\u800c\u5728\u591a\u9053\u7a0b\u5e8f\u73af\u5883\u4e0b\uff0c\u6211\u4eec\u5f97\u5230\u5982\u4e0b\u7518\u7279\u56fe\uff1a</p> <pre><code>gantt\n    title Multiprogramming\n    dateFormat ss\n    axisFormat %S\n\n    section Program A\n    CPU :a,  00,  10\n    X   :b,  10,  15\n    CPU :c,  20,  25\n    Y   :d,  25,  35\n    CPU :e,  35,  45\n\n    section Program B\n    X   :g,  00,  10\n    CPU :h,  10,  20\n    Y   :i,  20,  25\n    CPU :j,  25,  30\n    Y   :k,  35,  45</code></pre> <p>\u7531\u4e8e Mermaid \u7684\u9650\u5236\uff0c\u6211\u73b0\u5728\u662f\u628a\u6bcf\u4e2a\u7a0b\u5e8f\u7684\u4efb\u52a1\u9519\u5f00\u753b\u7684\uff0c\u5b9e\u9645\u4e0a\u505a\u9898\u7684\u65f6\u5019\u53ef\u4ee5\u76f4\u63a5\u753b\u6210\u4e24\u884c\u3002</p> <p>\u8981\u70b9\u5c31\u662f\u7eb5\u5411\u4e0d\u80fd\u540c\u65f6\u51fa\u73b0\u540c\u4e00\u4e2a\u8d44\u6e90\uff0c\u4f8b\u5982 18s \u65f6\u4e0d\u80fd A \u548c B \u90fd\u7528 CPU\uff0c\u6240\u4ee5 A \u9700\u8981\u7b49 B \u7528\u5b8c CPU \u518d\u4f7f\u7528\u3002</p> <p>\u73b0\u5728\u6211\u4eec\u518d\u6765\u7edf\u8ba1 CPU \u7684\u5229\u7528\u7387\uff1a</p> \\[ U = \\frac{10+10+5+5+10}{45} = \\frac{40}{45} = 88.89\\% \\] <p>\u901a\u8fc7\u8fd9\u9053\u9898\u6211\u4eec\u4e5f\u53ef\u4ee5\u53d1\u73b0\uff0c\u591a\u9053\u7a0b\u5e8f\u8bbe\u8ba1\u6280\u672f\u5bf9 CPU \u5229\u7528\u7387\u7684\u63d0\u5347\u6709\u591a\u9ad8\uff0c\u540c\u65f6\u4e5f\u53ef\u4ee5\u4ece\u8ba1\u7b97\u8fc7\u7a0b\u4e2d\u7684\u5206\u6bcd\u770b\u51fa\u5176\u5bf9\u7a0b\u5e8f\u541e\u5410\u91cf\u7684\u63d0\u5347\u6709\u591a\u9ad8\u3002</p> <p>\u591a\u9053\u6279\u5904\u7406\u89e3\u51b3\u4e86\u5355\u9053\u6279\u5904\u7406\u7cfb\u7edf\u53ef\u80fd\u8ba9 CPU \u95f2\u7f6e\u4e0b\u6765\u7684\u95ee\u9898\uff08\u5f53\u7136\u524d\u63d0\u662f\u6709\u4efb\u52a1\u8ba9\u5b83\u505a\uff09\uff0c\u63d0\u9ad8\u4e86 CPU \u7b49\u8d44\u6e90\u7684\u5229\u7528\u7387\uff0c\u589e\u52a0\u4e86\u541e\u5410\u91cf\uff0c\u4f46\u662f\u7531\u4e8e\u6d89\u53ca\u5230\u4e86\u8fdb\u7a0b\u7684\u5207\u6362\u95ee\u9898\uff0c\u6240\u4ee5\u5b9e\u9645\u5b9e\u73b0\u4f1a\u590d\u6742\u5f88\u591a\u3002\u5177\u4f53\u7684\u5185\u5bb9\u6211\u4eec\u4f1a\u5728 Unit 1: \u8fdb\u7a0b\u7ba1\u7406 \u4e2d\u8be6\u7ec6\u4ecb\u7ecd\u3002</p> <p>\u4f46\u662f\u65e0\u8bba\u5355\u9053\u8fd8\u662f\u591a\u9053\uff0c\u6279\u5904\u7406\u7cfb\u7edf\u5e76\u4e0d\u9002\u5408\u4f5c\u4e3a\u73b0\u4ee3\u8ba1\u7b97\u673a\u7cfb\u7edf\uff0c\u5176\u4e2d\u4e00\u4e2a\u6700\u5927\u7684\u95ee\u9898\u5c31\u662f\u5b83\u7684\u4ea4\u4e92\u6027\u975e\u5e38\u5dee\u3002\u7528\u6237\u7ed9\u5b9a\u4e00\u5b9a\u6279\u6b21\u7684\u4efb\u52a1\uff0c\u7136\u540e\u7cfb\u7edf\u4f1a\u81ea\u52a8\u8c03\u6574\u8fd9\u4e00\u6279\u4efb\u52a1\u7684\u6267\u884c\u987a\u5e8f\uff0c\u6700\u7ec8\u5b8c\u6210\u8fd9\u6279\u4efb\u52a1\uff0c\u7136\u800c\u5728\u8fd9\u6bb5\u65f6\u95f4\u91cc\uff0c\u7528\u6237\u5c31\u6ca1\u6cd5\u518d\u7528\u8ba1\u7b97\u673a\u505a\u5176\u5b83\u4e8b\u60c5\u4e86\uff0c\u540c\u65f6\u4f60\u4e5f\u6ca1\u6cd5\u63a7\u5236\u6b63\u5728\u6267\u884c\u7684\u4efb\u52a1\uff0c\u8fd9\u5bf9\u73b0\u4ee3\u8ba1\u7b97\u673a\u6765\u8bf4\u662f\u4e0d\u53ef\u60f3\u8c61\u7684\u3002</p> <p>\uff08\u5047\u8bbe\u6211\u4eec\u5ffd\u7565\u5173\u4e8e\u5c4f\u5e55\u663e\u793a\u7684 I/O\uff09\u8bd5\u60f3\uff0c\u4f60\u5e0c\u671b\u5728\u8dd1\u7a0b\u5e8f\u7684\u65f6\u5019\u653e\u4e00\u4e2a\u89c6\u9891\uff0c\u4f46\u662f\u7531\u4e8e\u4f60\u7684\u7a0b\u5e8f\u8fd8\u6ca1\u8dd1\u5b8c\uff0c\u4f60\u7684\u89c6\u9891\u5c31\u6ca1\u6cd5\u64ad\u653e\uff0c\u7a81\u7136\u4f60\u7684\u7a0b\u5e8f\u53d1\u751f\u4e86\u4e00\u6b21 I/O\uff0cCPU \u8f6c\u800c\u64ad\u653e\u5df2\u7ecf\u5b8c\u6210 I/O \u540e\u7684\u90a3\u90e8\u5206\u89c6\u9891\uff0c\u4f46\u662f\u8fd9\u4e2a\u65f6\u5019\u4f60\u7684\u7a0b\u5e8f I/O \u5f88\u5feb\u4e5f\u5b8c\u6210\u4e86\uff0c\u5374\u9700\u8981\u7b49\u5f85\u7f13\u5b58\u4e2d\u7684\u89c6\u9891\u653e\u5b8c\u624d\u80fd\u7ee7\u7eed\u6267\u884c\uff0c\u8fd9\u79cd\u7528\u6237\u4f53\u9a8c\u51e0\u4e4e\u65e0\u6cd5\u63a5\u53d7\u3002</p> <p>\u5bf9\u4e8e\u7528\u6237\u6765\u8bf4\uff0c\u6700\u597d\u80fd\u540c\u65f6\u5b9e\u73b0\u4f53\u611f\u4e0a\u7684\u5e76\u884c\uff0c\u4e5f\u5c31\u662f\u51e0\u4ef6\u4e8b\u60c5\u81f3\u5c11\u770b\u8d77\u6765\u8981\u50cf\u662f\u540c\u65f6\u53d1\u751f\u7684\uff0c\u4e8e\u662f\u51fa\u73b0\u4e86\u5206\u65f6\u7cfb\u7edf(Time Sharing Systems)\u3002</p> <p></p> \u2461 \u5206\u65f6\u7cfb\u7edf\u9636\u6bb5 <p>\u5206\u65f6\u7cfb\u7edf(Time Sharing Systems)\u662f\u591a\u4efb\u52a1(Multitasking)\u7684\u4e00\u4e2a\u5177\u4f53\u5b9e\u73b0\uff0c\u800c Multitasking \u662f Multiprogramming \u7684\u4e00\u4e2a\u903b\u8f91\u6269\u5c55\uff0c\u5373 Multitasking \u4e5f\u662f Multiprogramming \u7684\u4e00\u79cd\uff0c\u5b83\u7b26\u5408\u5185\u5b58\u4e2d\u6709\u591a\u4e2a\u8fdb\u7a0b\uff0c\u4e00\u6bb5\u65f6\u95f4\u5185\u6709\u591a\u4e2a\u4efb\u52a1\u4e00\u8d77\u6267\u884c\u7684\u7279\u70b9\u3002</p> <p>\u5206\u65f6\u7cfb\u7edf\u901a\u8fc7\u9891\u7e41\u5730\u5728\u591a\u4e2a\u8fdb\u7a0b\u95f4\u5207\u6362\u6765\u8fd1\u4f3c\u5b9e\u73b0\u5e76\u884c\uff08\u5e76\u4e0d\u662f\u771f\u6b63\u610f\u4e49\u4e0a\u7684\u5e76\u884c\uff0c\u771f\u6b63\u610f\u4e49\u4e0a\u7684\u5e76\u884c\u9700\u8981\u901a\u8fc7\u591a\u6838/\u591a\u5904\u7406\u5668\u5b9e\u73b0\uff09\u3002\u5177\u4f53\u6765\u8bf4\u662f\u6309\u7167\u65f6\u95f4\u7247(time slice)\uff0c\u8f6e\u6d41\u5c06 CPU \u5206\u914d\u7ed9\u5404\u4e2a\u8fdb\u7a0b\uff0c\u8fd9\u6837\u53ea\u8981\u65f6\u95f4\u7247\u8db3\u591f\u77ed\uff0c\u7528\u6237\u4f53\u611f\u4e0a\u5c31\u50cf\u662f\u591a\u4e2a\u4efb\u52a1\u5e76\u884c\u6267\u884c\u3002</p> <p>\u611f\u89c9\u6bd4\u8f83\u50cf\u300a\u5341\u4e07\u4e2a\u51b7\u7b11\u8bdd\u300b\u8d85\u4eba\u8fd9\u4e00\u96c6\u7684 4:09 - 4:48\u3002</p> <p>\u5206\u65f6\u7528\u6237\u5141\u8bb8\u591a\u4e2a\u7528\u6237\u540c\u65f6\u4f7f\u7528\u540c\u4e00\u53f0\u8ba1\u7b97\u673a\uff0c\u6240\u6709\u4efb\u52a1\u4e4b\u95f4\u4e92\u76f8\u72ec\u7acb\uff0c\u4e92\u4e0d\u5e72\u6270\u3001\u4e92\u4e0d\u963b\u585e\uff0c\u56e0\u6b64\u4efb\u52a1\u7684\u6700\u957f\u5468\u8f6c\u65f6\u95f4\u51cf\u5c11\uff0c\u7528\u6237\u7684\u64cd\u4f5c\u4e5f\u4f1a\u88ab\u53ca\u65f6\u54cd\u5e94\uff0c\u5b9e\u73b0\u4e86\u66f4\u65b9\u4fbf\u8fdb\u884c\u4eba\u673a\u5bf9\u8bdd\u3002</p> \u76f8\u5173\u9605\u8bfb <p>\u5173\u4e8e\u8fd9\u4e09\u4e2a\u6280\u672f\u7684\u8bf4\u660e\u4e5f\u53ef\u4ee5\u770b\u770b xyx \u662f\u600e\u4e48\u5199\u7684\uff1a\ud83d\udd17</p> <p>\u9664\u4e86\u8fd9\u51e0\u79cd\u7cfb\u7edf\u5916\uff0c\u738b\u9053\u91cc\u4e5f\u63d0\u5230\u4e86\u8fd9\u4e9b\u7cfb\u7edf\uff1a</p> <ul> <li>\u5b9e\u65f6\u7cfb\u7edf(Real-time System)\uff1a\u5728\u7279\u5b9a\u65f6\u95f4\uff08\u53ef\u80fd\u6bd4\u65f6\u95f4\u7247\u8fd8\u5c0f\uff09\u5185\u5b8c\u6210\u7279\u5b9a\u4efb\u52a1\u7684\u7cfb\u7edf\uff0c\u4f8b\u5982\u822a\u7a7a\u822a\u5929\u7cfb\u7edf\u3001\u6838\u53cd\u5e94\u5806\u63a7\u5236\u7cfb\u7edf\u7b49\uff1b</li> <li>\u5206\u5e03\u5f0f\u7cfb\u7edf(Distributed System)\uff1a\u7531\u591a\u53f0\u8ba1\u7b97\u673a\u7ec4\u6210\u7684\u7cfb\u7edf\uff0c\u8fd9\u4e9b\u8ba1\u7b97\u673a\u901a\u8fc7\u901a\u4fe1\u4ea4\u6362\u4fe1\u606f\uff0c\u5171\u540c\u5b8c\u6210\u4e00\u4e2a\u4efb\u52a1\uff0c\u4f8b\u5982\u4e91\u8ba1\u7b97\u3001\u5927\u578b\u7f51\u7ad9\u7b49\uff1b</li> </ul> <p>\u591a\u9053\u6280\u672f\u51fa\u73b0\u4e4b\u540e\uff0c\u867d\u7136\u8ba1\u7b97\u673a\u7684\u8868\u73b0\u4e0d\u65ad\u63d0\u5347\uff0c\u4f46\u662f\u591a\u9053\u6280\u672f\u672c\u8eab\u7684\u6280\u672f\u7279\u70b9\uff0c\u5404\u4e2a\u8fdb\u7a0b\u5728\u672a\u5b8c\u6210\u7684\u60c5\u51b5\u4e0b\u9700\u8981\u4e92\u76f8\u5207\u6362\uff0c\u4e00\u7cfb\u5217\u95ee\u9898\u63a5\u8e35\u800c\u6765\uff0c\u8fd9\u4e9b\u90fd\u662f\u6211\u4eec\u5728\u4e4b\u540e\u7684\u5355\u5143\u91cc\u8be6\u7ec6\u8ba8\u8bba\u7684\u5185\u5bb9\u3002</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit0/#\u64cd\u4f5c\u7cfb\u7edf\u7684\u7ed3\u6784\u8bbe\u8ba1","title":"\u64cd\u4f5c\u7cfb\u7edf\u7684\u7ed3\u6784\u8bbe\u8ba1","text":"<p>\u968f\u7740\u64cd\u4f5c\u7cfb\u7edf\u7684\u529f\u80fd\u4e0d\u65ad\u6269\u5c55\u3001\u4f53\u91cf\u9010\u6e10\u53d8\u5927\uff0c\u6574\u4e2a\u64cd\u4f5c\u7cfb\u7edf\u8f6f\u4ef6\u7684\u7ed3\u6784\u8bbe\u8ba1\u5c31\u8d8a\u53d1\u91cd\u8981\u4e86\u3002\u63a5\u4e0b\u6765\u6211\u4eec\u4ecb\u7ecd\u82e5\u5e72\u8bbe\u8ba1\u601d\u8def\u3002</p> <p></p> \u5b8f\u5185\u6838 <p> </p> <p>\u5b8f\u5185\u6838(Monolithic-Kernels)\u4e5f\u53eb\u5355\u5185\u6838\u6216\u5927\u5185\u6838\uff0c\u5b83\u7684\u6838\u5fc3\u601d\u60f3\u5341\u5206\u7b80\u5355\u7c97\u66b4\uff0c\u5c06\u6240\u6709\u4e3b\u8981\u529f\u80fd\u90fd\u7d27\u5bc6\u8026\u5408\u5728\u4e00\u8d77\u4f5c\u4e3a\u4e00\u4e2a\u5b8c\u6574\u7684\u6574\u4f53\u3002</p> <p>\u5b8f\u5185\u6838\u5e26\u6765\u7684\u597d\u5904\u662f\u64cd\u4f5c\u7cfb\u7edf\u6548\u7387\u6781\u9ad8\uff0c\u4ece\u64cd\u4f5c\u7cfb\u7edf\u7684\u53d1\u5c55\u5386\u7a0b\u6765\u770b\uff0c\u4e3b\u6d41\u64cd\u4f5c\u7cfb\u7edf\u90fd\u662f\u4ece\u5b8f\u5185\u6838\u53d1\u5c55\u8fc7\u6765\u7684\uff08\u4e0d\u8fc7\u5982\u4eca\u7684\u4e3b\u6d41\u64cd\u4f5c\u7cfb\u7edf\u66f4\u504f\u5411\u6df7\u5408\u7cfb\u7edf\uff09\u3002</p> <p>\u4f46\u662f\u5b8f\u5185\u6838\u7684\u7f3a\u70b9\u4e5f\u662f\u5341\u5206\u660e\u663e\u7684\uff0c\u5927\u91cf\u590d\u6742\u7684\u529f\u80fd\u4e92\u76f8\u8026\u5408\uff0c\u5bfc\u81f4\u64cd\u4f5c\u7cfb\u7edf\u7684\u7ef4\u62a4\u5341\u5206\u56f0\u96be\uff1b\u4e0d\u4ec5\u5982\u6b64\uff0c\u4e00\u65e6\u67d0\u4e2a\u90e8\u5206\u51fa\u73b0\u4e86\u4e25\u91cd\u95ee\u9898\uff0c\u6574\u4e2a\u7cfb\u7edf\u90fd\u4f1a\u53d7\u5230\u5f71\u54cd\uff0c\u5728\u8fd9\u65b9\u9762\uff0c\u5b8f\u5185\u6838\u7684\u8868\u73b0\u90fd\u4e0d\u5982\u5fae\u5185\u6838\u3002</p> \u5206\u5c42\u8bbe\u8ba1 <p>\u5206\u5c42\u8bbe\u8ba1(layer approach)\u7684\u6838\u5fc3\u601d\u60f3\u662f\u5c06\u7cfb\u7edf\u5206\u4e3a\u82e5\u5e72\u5c42\uff0c\u5e95\u5c42\u4e3a\u786c\u4ef6\uff0c\u9876\u5c42\u4e3a\u7528\u6237\u63a5\u53e3\uff0c\u7b2c \\(i\\) \u5c42\u53ea\u8c03\u7528 \\(i-1\\) \u5c42\u63d0\u4f9b\u7684\u63a5\u53e3\u3002\u6bcf\u4e00\u5c42\u90fd\u5b9e\u73b0\u826f\u597d\u7684\u5c01\u88c5\uff0c\u4e8e\u662f\u5f00\u53d1\u8fc7\u7a0b\u4e2d\u53ea\u9700\u8981\u9010\u6b65\u5b9e\u73b0\u5e76\u8c03\u8bd5\u9a8c\u8bc1\u6bcf\u4e00\u5c42\uff0c\u518d\u9010\u7ea7\u5411\u4e0a\u5f00\u53d1\u5373\u53ef\uff1b\u5728\u7ef4\u62a4\u6216\u6269\u5c55\u8fc7\u7a0b\u4e2d\uff0c\u53ea\u8981\u4fee\u6539\u6bcf\u4e00\u5c42\u7684\u5185\u90e8\u5b9e\u73b0\uff0c\u800c\u4e0d\u9700\u8981\u4fee\u6539\u5176\u5b83\u5c42\u7684\u4ee3\u7801\uff0c\u8fd9\u6837\u5c31\u5927\u5927\u964d\u4f4e\u4e86\u5f00\u53d1\u548c\u7ef4\u62a4\u7684\u96be\u5ea6\u3002</p> <p>\u7136\u800c\uff0c\u7531\u4e8e\u6bcf\u6b21\u6267\u884c\u4e00\u4e2a\u529f\u80fd\u90fd\u9700\u8981\u4e0a\u4e0b\u8de8\u8d8a\u591a\u5c42\uff0c\u53d1\u751f\u591a\u6b21\u63a5\u53e3\u8c03\u7528\uff0c\u5206\u5c42\u8bbe\u8ba1\u4e0b\u7684\u7cfb\u7edf\u6548\u7387\u5f80\u5f80\u90fd\u53d7\u5230\u9650\u5236\uff1b\u4e0d\u4ec5\u5982\u6b64\uff0c\u8981\u60f3\u771f\u6b63\u610f\u4e49\u4e0a\u5b9e\u73b0\u826f\u597d\u7684\u5206\u5c42\u8bbe\u8ba1\uff0c\u5c31\u9700\u8981\u5bf9\u5404\u5c42\u6709\u826f\u597d\u7684\u5b9a\u4e49\uff0c\u8fd9\u4e2a\u8bbe\u8ba1\u96be\u5ea6\u662f\u4e0d\u5c0f\u7684\u3002</p> <p></p> \u5fae\u5185\u6838 <p> </p> <p>\u5fae\u5185\u6838(Micro-Kernels)\u7684\u8bbe\u8ba1\u601d\u8def\u4e0e\u5b8f\u5185\u6838\u76f8\u53cd\uff0c\u4e3b\u5f20\u5c06\u4e0d\u662f\u5fc5\u8981\u7684\u4e1c\u897f\u90fd\u4ece\u5185\u6838\u91cc\u62ff\u51fa\u53bb\uff0c\u653e\u5230\u7528\u6237\u7a7a\u95f4\uff0c\u4ee5\u7528\u6237\u6001\u6267\u884c\u3002\u6574\u4f53\u5f62\u6210\u4e00\u79cd\u5fae\u5185\u6838-\u670d\u52a1\u5668\u7684\u7ed3\u6784\uff0c\u6b64\u65f6\u5185\u6838\u53ea\u63d0\u4f9b\u901a\u8baf\u3001\u5185\u5b58\u7ba1\u7406\u3001\u8fdb\u7a0b\u7ba1\u7406\u7b49\u57fa\u672c\u529f\u80fd\uff0c\u4e5f\u53ea\u6709\u8fd9\u4e9b\u90e8\u5206\u76f4\u63a5\u8fd0\u884c\u5728\u5185\u6838\u6001\uff0c\u4f5c\u4e3a\u670d\u52a1\u5668\u7684\u5176\u5b83\u529f\u80fd\u90e8\u4ef6\u5219\u901a\u8fc7\u6d88\u606f\u4f20\u9012\u673a\u5236\u4e0e\u5185\u6838\u4e92\u52a8\u3002</p> <p>\u7531\u4e8e\u5185\u6838\u53ea\u63d0\u4f9b\u6700\u57fa\u672c\u7684\u529f\u80fd\uff0c\u6240\u4ee5\u5185\u6838\u7684\u4f53\u79ef\u4f1a\u5927\u5927\u51cf\u5c0f\uff0c\u5185\u6838\u7684\u7ef4\u62a4\u548c\u6269\u5c55\u4e5f\u4f1a\u53d8\u5f97\u66f4\u52a0\u5bb9\u6613\uff0c\u5fae\u5185\u6838-\u670d\u52a1\u5668\u7684\u7ed3\u6784\u4e5f\u4f7f\u529f\u80fd\u6269\u5c55\u66f4\u52a0\u5bb9\u6613\uff1b\u53e6\u5916\uff0c\u7531\u4e8e\u5185\u6838\u53ea\u63d0\u4f9b\u6700\u57fa\u672c\u7684\u529f\u80fd\uff0c\u6240\u4ee5\u5185\u6838\u7684\u6548\u7387\u4e5f\u4f1a\u5927\u5927\u63d0\u5347\uff1b\u4e0d\u4ec5\u5982\u6b64\uff0c\u7531\u4e8e\u5404\u4e2a\u529f\u80fd\u4e4b\u95f4\u7684\u8026\u5408\u964d\u4f4e\uff0c\u4e14\u90fd\u8fd0\u884c\u5728\u7528\u6237\u6001\uff0c\u529f\u80fd\u4e4b\u95f4\u4ec5\u4f7f\u7528\u901a\u4fe1\u5efa\u7acb\u94fe\u63a5\uff0c\u5373\u4f7f\u67d0\u4e2a\u529f\u80fd\u90e8\u4ef6\u51fa\u73b0\u95ee\u9898\uff0c\u4e5f\u4e0d\u4f1a\u5bfc\u81f4\u6574\u4e2a\u7cfb\u7edf\u5d29\u6e83\uff0c\u76f8\u6bd4\u4e8e\u5b8f\u5185\u6838\uff0c\u7cfb\u7edf\u53ef\u9760\u6027\u5927\u5927\u63d0\u5347\u3002</p> \u6a21\u5757\u5316\u8bbe\u8ba1 <p>\u6a21\u5757\u5316\u8bbe\u8ba1(Modules Approach)\u6307\u5c06\u64cd\u4f5c\u7cfb\u7edf\u5212\u5206\u4e3a\u82e5\u5e72\u5206\u7acb\u6a21\u5757\uff0c\u5e76\u89c4\u5b9a\u6a21\u5757\u4e4b\u95f4\u7684\u63a5\u53e3\uff0c\u751a\u81f3\u5355\u4e2a\u6a21\u5757\u4e0b\u4e5f\u53ef\u80fd\u662f\u7531\u591a\u4e2a\u6a21\u5757\u901a\u8fc7\u540c\u6837\u7684\u65b9\u5f0f\u7ec4\u7ec7\u800c\u6210\u7684\u3002\u8fd9\u79cd\u8bbe\u8ba1\u65b9\u6cd5\u4e5f\u88ab\u79f0\u4e3a\u6a21\u5757-\u63a5\u53e3\u6cd5\u3002</p> <p>\u6a21\u5757\u5316\u7684\u8bbe\u8ba1\u4e0e\u5fae\u5185\u6838\u662f\u4e0d\u540c\u7684\uff0c\u9700\u8981\u6ce8\u610f\u533a\u5206\u3002\u5fae\u5185\u6838\u8bbe\u8ba1\u4ecd\u7136\u662f\u6709\u4e2d\u5fc3\uff08\u5fae\u5185\u6838\uff09\u7684\uff0c\u4f46\u662f\u6a21\u5757\u5316\u8bbe\u8ba1\u6574\u4f53\u662f\u5206\u5c42\u7f51\u72b6\u7684\u3002</p> <p>\u7406\u60f3\u7684\u6a21\u5757\u5316\u8bbe\u8ba1\u4f1a\u8ba9\u7cfb\u7edf\u8bbe\u8ba1\u53ef\u4ee5\u591a\u7ebf\u5e76\u884c\uff0c\u53ea\u9700\u8981\u4e8b\u5148\u5546\u91cf\u597d\u63a5\u53e3\uff0c\u5404\u4e2a\u5de5\u7a0b\u5e08\u5c31\u53ef\u4ee5\u72ec\u7acb\u5730\u5b9e\u73b0\u3001\u586b\u5145\u6a21\u5757\u5185\u5bb9\uff1b\u9ad8\u5185\u805a\u4f4e\u8026\u5408\u7684\u8bbe\u8ba1\u4e5f\u80fd\u8ba9\u7cfb\u7edf\u7684\u7ef4\u62a4\u548c\u6269\u5c55\u53d8\u5f97\u66f4\u52a0\u5bb9\u6613\u3002</p> <p>\u7136\u800c\u6a21\u5757\u5316\u7684\u8bbe\u8ba1\u5341\u5206\u56f0\u96be\uff0c\u6a21\u5757\u5316\u7684\u8bbe\u8ba1\u5e76\u6ca1\u6709\u4e00\u4e2a\u6e05\u6670\u7684\u5355\u5411\u4f9d\u8d56\u5173\u7cfb\uff0c\u56e0\u6b64\u65e0\u6cd5\u9012\u8fdb\u5f0f\u7684\u63a8\u8fdb\u4efb\u52a1\uff0c\u6574\u4e2a\u5f00\u53d1\u8fc7\u7a0b\u5c31\u597d\u50cf\u59cb\u7ec8\u60ac\u5728\u534a\u7a7a\uff1b\u9664\u6b64\u4e4b\u5916\uff0c\u5982\u4f55\u8bbe\u8ba1\u63a5\u53e3\u4f7f\u5f97\u6240\u6709\u9700\u6c42\u90fd\u80fd\u88ab\u5f88\u597d\u6ee1\u8db3\u4e5f\u662f\u4e2a\u96be\u4ee5\u89e3\u51b3\u7684\u95ee\u9898\u3002</p> \u6df7\u5408\u7cfb\u7edf <p>\u6df7\u5408\u7cfb\u7edf(Hybrid Systems)\u662f\u6307\u5c06\u5b8f\u5185\u6838\u548c\u5fae\u5185\u6838\u7684\u8bbe\u8ba1\u601d\u8def\u7ed3\u5408\u8d77\u6765\uff0c\u8fd9\u79cd\u8bbe\u8ba1\u6a21\u5f0f\u66f4\u73b0\u4ee3\uff0c\u4e5f\u662f\u76ee\u524d\u4e3b\u6d41\u7684\u64cd\u4f5c\u7cfb\u7edf\u7684\u6a21\u5f0f\u3002</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit0/#\u64cd\u4f5c\u7cfb\u7edf\u7684\u8fd0\u884c\u539f\u7406","title":"\u64cd\u4f5c\u7cfb\u7edf\u7684\u8fd0\u884c\u539f\u7406","text":"<p>\u672c\u8282\u6211\u4eec\u6df1\u5165\u5230\u64cd\u4f5c\u7cfb\u7edf\u7684\u4e00\u4e9b\u5177\u4f53\u8fd0\u884c\u8fc7\u7a0b\uff0c\u63a2\u7a76\u4e00\u4e9b\u6b65\u9aa4\u7684\u5177\u4f53\u5b9e\u73b0\u3002</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit0/#\u4e2d\u65ad","title":"\u4e2d\u65ad","text":"<p>\u4e2d\u65ad\uff08\u5e7f\u4e49\uff09\u662f\u8d2f\u7a7f\u73b0\u4ee3\u64cd\u4f5c\u7cfb\u7edf\u7684\u4e00\u4e2a\u91cd\u8981\u6280\u672f\uff0c\u5b83\u4f7f\u5f97\u201c\u8ba1\u5212\u4e4b\u5916\u201d\u7684\u4e8b\u60c5\u53ef\u4ee5\u53ca\u65f6\u7684\u88ab\u544a\u77e5\u5e76\u5904\u7406\u3002\u4f8b\u5982\uff0c\u7a0b\u5e8f\u7a81\u7136\u51fa\u73b0\u4e86\u81f4\u547d\u9519\u8bef\uff0c\u8fd9\u65f6\u64cd\u4f5c\u7cfb\u7edf\u5e94\u8be5\u53ca\u65f6\u5bdf\u89c9\u5e76\u5904\u7406\uff1b\u53c8\u6bd4\u5982\uff0c\u7528\u6237\u5728\u547d\u4ee4\u884c\u8f93\u5165\u4e86\u6307\u4ee4\uff0c\u6309\u4e0b\u4e86\u56de\u8f66\uff0c\u64cd\u4f5c\u7cfb\u7edf\u5e94\u5f53\u5bdf\u89c9\u5230 I/O \u5df2\u7ecf\u51c6\u5907\u597d\u4e86\u3002\u4f46\u662f\u6211\u4eec\u4e0d\u5e94\u5f53\u8ba9\u64cd\u4f5c\u7cfb\u7edf\u4e0d\u538c\u5176\u70e6\u5730\u8be2\u95ee\u4f60\u6709\u6ca1\u6709\u53d1\u751f\u9519\u8bef\uff0c\u53c8\u6216\u8005\u8fd9\u4e2a I/O \u662f\u5426\u5c31\u7eea\uff0c\u8fd9\u5f88\u4e0d\u5408\u7406\u3002</p> <p>\u4e5f\u5c31\u662f\u8bf4\uff0c\u6211\u4eec\u4e0d\u5e94\u5f53\u8ba9\u64cd\u4f5c\u7cfb\u7edf\u4e8b\u65e0\u5de8\u7ec6\u5730\u53bb\u8d1f\u8d23\u68c0\u67e5\u610f\u5916\u662f\u5426\u53d1\u751f\uff0c\u800c\u662f\u5e94\u5f53\u63d0\u4f9b\u4e00\u4e2a\u4e0a\u62a5\u610f\u5916\u7684\u63a5\u53e3\uff0c\u8ba9\u4ea7\u751f\u610f\u5916\u7684\u4eba\u81ea\u884c\u4e0a\u62a5\u8fd9\u4e9b\u610f\u5916\u3002\u5728\u5177\u4f53\u786c\u4ef6\u7684\u5b9e\u73b0\u4e0a\uff0c\u4f1a\u6709\u4e24\u6761\u4e13\u95e8\u8868\u793a\u4e2d\u65ad\u4fe1\u53f7\u7684\u7ebf\uff08\u7a0d\u5019\u4f1a\u5728\u4e2d\u65ad\u5c4f\u853d\u4e2d\u8bb2\u5230\uff09\uff0cCPU \u4f1a\u5728\u6bcf\u4e00\u6761\u6307\u4ee4\u7ed3\u675f\u540e\u68c0\u6d4b\u662f\u5426\u6709\u4e2d\u65ad\u53d1\u751f\uff0c\u800c\u5728\u8f6f\u4ef6\u4e0a\u5c31\u4f53\u73b0\u4e3a\u6bcf\u5f53\u6709\u4e2d\u65ad\u53d1\u751f\u65f6\uff0c\u64cd\u4f5c\u7cfb\u7edf\u5c31\u9700\u8981\u53bb\u5904\u7406\u3002\u7531\u4e8e\u4e2d\u65ad\u7684\u5f3a\u5927\u7279\u6027\uff0c\u4ece\u6700\u65e9\u4ec5\u7684\u5904\u7406\u786c\u4ef6\u72b6\u6001\uff0c\u5230\u5904\u7406\u8f6f\u4ef6\u9519\u8bef\u548c\u4f5c\u4e3a\u4e00\u79cd\u7c7b\u4f3c\u51fd\u6570\u7684\u624b\u6bb5\uff0c\u4e2d\u65ad\u7684\u5e94\u7528\u8303\u56f4\u8d8a\u6765\u8d8a\u5e7f\uff0c\u5b83\u7684\u6982\u5ff5\u968f\u7740\u5e94\u7528\u8303\u56f4\u4e5f\u4e0d\u65ad\u6269\u5927\u3002</p> <p>\u4e2d\u65ad\u5411\u91cf\u8868</p> <p>\u7531\u4e8e\u4e2d\u65ad\u88ab\u5e7f\u6cdb\u4f7f\u7528\uff0c\u64cd\u4f5c\u7cfb\u7edf\u9700\u8981\u9891\u7e41\u7684\u5904\u7406\u5404\u79cd\u4e2d\u65ad\uff0c\u5904\u7406\u6bcf\u4e00\u79cd\u4e2d\u65ad\u90fd\u9700\u8981\u4e00\u4e2a\u7279\u5b9a\u7684\u65b9\u6cd5\uff0c\u56e0\u6b64\uff0c\u4e00\u79cd\u5feb\u901f\u5b9a\u4f4d\u4e2d\u65ad\u5904\u7406\u65b9\u6cd5\u7684\u624b\u6bb5\u5c31\u663e\u5f97\u5c24\u4e3a\u91cd\u8981\u3002</p> <p>\u4e2d\u65ad\u5411\u91cf\u8868(Interrupt Vector Table)\u901a\u8fc7\u4e2d\u65ad\u53f7\u6765\u7d22\u5f15\u4e2d\u65ad\u5904\u7406\u65b9\u6cd5\uff0c\u5b9e\u73b0\u4e86\u4e00\u79cd\u201c\u968f\u673a\u8bbf\u95ee\u201d\uff0c\u5927\u5927\u52a0\u901f\u4e86\u4e2d\u65ad\u5904\u7406\u7684\u901f\u5ea6\u3002</p> <p>\u6839\u636e\u4e2d\u65ad\u662f\u5426\u7531\u7a0b\u5e8f\u4ea7\u751f\uff0c\u4e2d\u65ad\u53ef\u4ee5\u5206\u4e3a\u5916\u4e2d\u65ad\uff08\u72ed\u4e49\u7684\u4e2d\u65ad\uff0c\u7531\u786c\u4ef6\u4ea7\u751f\uff09\u548c\u5185\u4e2d\u65ad\uff08\u5f02\u5e38...\uff0c\u4e3b\u8981\u7531\u7a0b\u5e8f\u4ea7\u751f\uff09\u3002\u8fd9\u91cc\u6709\u5f88\u591a\u6982\u5ff5\uff1ainstruction, exception, trap, abort, ...\uff0c\u8fd9\u90e8\u5206\u533a\u5206\u8bf7\u5927\u5bb6\u81ea\u884c\u5bfb\u627e\u8d44\u6599\u53c2\u8003\uff0c\u6211\u5728\u8fd9\u91cc\u653e\u51e0\u4e2a\u53c2\u8003\u94fe\u63a5\u3002</p> \u76f8\u5173\u9605\u8bfb <ul> <li>Difference between TRAP and exceptions | StackOverflow</li> <li>Difference between Interrupt and Exception | GeeksForGeeks</li> </ul> <p>\u7406\u60f3\u60c5\u51b5\u4e0b\uff0c\u6211\u4eec\u5e0c\u671b\u4e2d\u65ad\u4e00\u65e6\u53d1\u751f\u5c31\u7acb\u523b\u88ab\u89e3\u51b3\uff0c\u4f46\u662f\u4e2d\u65ad\u5904\u7406\u4e5f\u540c\u6837\u9700\u8981\u8d44\u6e90\uff0c\u8fd9\u610f\u5473\u7740\u4e2d\u65ad\u4e5f\u6709\u53ef\u80fd\u4ea7\u751f\u51b2\u7a81\u3002\u4e8e\u662f\uff0c\u6211\u4eec\u9700\u8981\u4e00\u7cfb\u5217\u673a\u5236\u6765\u89e3\u51b3\u8fd9\u4e9b\u95ee\u9898\u3002</p> <ol> <li>\u663e\u7136\uff0c\u4e2d\u65ad\u4e4b\u95f4\u4ea6\u6709\u533a\u522b\uff0c\u6709\u7684\u7a0b\u5e8f\u53d1\u751f\u4e86\u201c\u81f4\u547d\u9519\u8bef\u201d\u8fd9\u4ef6\u4e8b\uff0c\u663e\u7136\u6bd4\u6253\u5370\u673a\u5c31\u7eea\u66f4\u91cd\u8981\uff0c\u56e0\u6b64\uff0c\u4e2d\u65ad\u9700\u8981\u5206\u7ea7\u673a\u5236\uff0c\u4ee5\u533a\u5206\u4e2d\u65ad\u7684\u4f18\u5148\u7ea7\uff0c\u8fd9\u6837\u5c31\u53ef\u4ee5\u5728\u5904\u7406\u4e2d\u65ad\u65f6\uff0c\u4f18\u5148\u5904\u7406\u4f18\u5148\u7ea7\u9ad8\u7684\u4e2d\u65ad\uff1b</li> <li>\u4e2d\u65ad\u5e76\u4e0d\u662f\u968f\u65f6\u968f\u5730\u90fd\u80fd\u53d1\u751f\u7684\uff0c\u201c\u4ee3\u7406\u4eba\u201d\u5728\u8d70\u72ec\u6728\u6865\u65f6\u4e0d\u5e94\u5f53\u6682\u505c\u53bb\u5904\u7406\u836f\u54c1\u7f3a\u8d27\u7684\u95ee\u9898\uff0c\u5bf9\u4e8e\u64cd\u4f5c\u7cfb\u7edf\u6765\u8bf4\uff0c\u6709\u8bb8\u591a\u539f\u5b50\u6027\u7684\u884c\u4e3a\u662f\u4e0d\u53ef\u88ab\u4e2d\u65ad\u7684\uff0c\u4e5f\u6709\u4e00\u4e9b\u91cd\u8981\u7684\u4efb\u52a1\u662f\u4e0d\u5e94\u5f53\u88ab\u666e\u901a\u7684\u4e2d\u65ad\u6253\u6270\u7684\uff0c\u8fd9\u5c31\u6d89\u53ca\u5230\u4e2d\u65ad\u5c4f\u853d\u95ee\u9898\uff1b</li> </ol> <p>\u5b58\u7591</p> <p>\u8fd9\u5c31\u9700\u8981\u6211\u4eec\u8c08\u5230\u4e2d\u65ad\u7684\u786c\u4ef6\u8bbe\u8ba1\uff0c\u4e00\u79cd\u6bd4\u8f83\u666e\u901a\u7684\u8bbe\u8ba1\u662f\uff0c\u51c6\u5907 maskable interrupt-request line \u548c non-maskable interrupt-request line \u4e24\u6761\u4e2d\u65ad\u8bf7\u6c42\u7ebf\uff0c\u524d\u8005\u7528\u4e8e\u53ef\u5c4f\u853d\u7684\u4e2d\u65ad\uff0c\u540e\u8005\u7528\u4e8e\u4e0d\u53ef\u5c4f\u853d\u7684\u4e2d\u65ad\uff0c\u64cd\u4f5c\u7cfb\u7edf\u5728\u6bcf\u4e2a\u6307\u4ee4\u540e\u68c0\u67e5\u8fd9\u4e2d\u65ad\u7ebf\u4e0a\u662f\u5426\u6709\u4e2d\u65ad\u8bf7\u6c42\uff0c\u800c\u5982\u679c\u6b64\u65f6\u64cd\u4f5c\u7cfb\u7edf\u5c4f\u853d\u4e86\u4e2d\u65ad\uff0c\u90a3\u4e48\u5c31\u4e0d\u4f1a\u68c0\u67e5 maskable interrupt-request line \u4e0a\u7684\u4e2d\u65ad\u8bf7\u6c42\u3002</p> <p>\u9700\u8981\u6ce8\u610f\uff0c\u64cd\u4f5c\u7cfb\u7edf\u53d1\u73b0\u4e2d\u65ad\u540e\u5e76\u4e0d\u662f\u4e8c\u8bdd\u4e0d\u8bf4\u9a6c\u4e0a\u53bb\u5904\u7406\u4e2d\u65ad\u7684\uff0c\u4e3a\u4e86\u4fdd\u8bc1\u4e2d\u65ad\u5904\u7406\u5b8c\u6210\u540e\u4ecd\u80fd\u7ee7\u7eed\u5f53\u524d\u4efb\u52a1\uff0c\u64cd\u4f5c\u7cfb\u7edf\u9700\u8981\u4fdd\u5b58\u5f53\u524d\u4efb\u52a1\u7684\u72b6\u6001\uff0c\u4ee5\u4fbf\u5b8c\u6210\u4e2d\u65ad\u5904\u7406\u540e\u6062\u590d\u5f53\u524d\u4efb\u52a1\u7684\u72b6\u6001\u3002</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit0/#\u8ba1\u65f6\u5668","title":"\u8ba1\u65f6\u5668","text":"<p>\u867d\u7136\u770b\u8d77\u6765\u5f88\u4e0d\u8d77\u773c\uff0c\u4f46\u8ba1\u65f6\u5668(timer)\u5728\u64cd\u4f5c\u7cfb\u7edf\u4e2d\u662f\u4e00\u4e2a\u975e\u5e38\u91cd\u8981\u7684\u4e1c\u897f\u3002\u8ba1\u65f6\u5668\u9700\u8981\u4e00\u4e2a\u56fa\u5b9a\u9891\u7387\u7684\u65f6\u949f\u4ee5\u53ca\u4e00\u4e2a\u8ba1\u6570\u5668\uff0c\u5728\u6bcf\u4e2a\u65f6\u949f\u5468\u671f\u4ee4\u8ba1\u6570\u5668\u51cf 1\uff0c\u5f53\u8ba1\u6570\u5668\u5f52\u96f6\u65f6\u4ea7\u751f\u4e2d\u65ad\uff0c\u544a\u8bc9\u64cd\u4f5c\u7cfb\u7edf\u5b9a\u7684\u65f6\u5df2\u7ecf\u5230\u4e86\u3002</p> <p>\u5b83\u7684\u529f\u80fd\u867d\u7136\u57fa\u7840\u4f46\u662f\u5341\u5206\u91cd\u8981\uff0c\u4f8b\u5982\u5206\u65f6\u7cfb\u7edf\u4e2d\u5c31\u9700\u8981\u8ba1\u6570\u5668\u6765\u63a7\u5236\u65f6\u95f4\u7247\u7684\u957f\u5ea6\uff0c\u53c8\u6bd4\u5982\u64cd\u4f5c\u7cfb\u7edf\u9700\u8981\u5b9a\u671f\u68c0\u67e5\u5185\u5b58\u4e2d\u7684\u8fdb\u7a0b\uff0c\u4ee5\u9632\u6b62\u8fdb\u7a0b\u4e00\u76f4\u5360\u7528\u7cfb\u7edf\u8d44\u6e90\uff0c\u8fd9\u4e9b\u90fd\u9700\u8981\u8ba1\u65f6\u5668\u7684\u5e2e\u52a9\u3002</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit0/#\u7279\u6743\u6a21\u5f0f","title":"\u7279\u6743\u6a21\u5f0f","text":"<p>\u6211\u4eec\u524d\u9762\u8bf4\u8fc7\uff0c\u64cd\u4f5c\u7cfb\u7edf\u7684\u67d0\u4e9b\u64cd\u4f5c\u662f\u5371\u9669\u7684\uff0c\u6709\u53ef\u80fd\u5a01\u80c1\u5230\u81ea\u8eab\u6b63\u5e38\u8fd0\u4f5c\u7684\uff08\u5982\u4e0e\u786c\u4ef6\u76f4\u63a5\u76f8\u5173\u7684\u884c\u4e3a\u3001\u63a7\u5236 CPU \u8fd0\u884c\u89c4\u5219\u7684\u884c\u4e3a\u7b49\uff09\uff0c\u800c\u8fd9\u4e9b\u64cd\u4f5c\u4e0d\u5e94\u5f53\u88ab\u7528\u6237\u7a0b\u5e8f\u76f4\u63a5\u6267\u884c\u3002\u4e00\u79cd\u7b80\u5355\u7684\u601d\u8def\u662f\uff0c\u6211\u4eec\u5212\u5206\u5e38\u89c4\u64cd\u4f5c\u548c\u5371\u9669\u64cd\u4f5c\uff0c\u5141\u8bb8\u7528\u6237\u7a0b\u5e8f\u6267\u884c\u5e38\u89c4\u64cd\u4f5c\uff0c\u800c\u5371\u9669\u64cd\u4f5c\u5219\u9700\u8981\u59d4\u6258\u4e13\u4e1a\u4eba\u58eb\u4ee3\u4e3a\u6267\u884c\u3002\u800c\u8fd9\u5c31\u662f\u7279\u6743\u6a21\u5f0f(Privileged Mode)\u7684\u57fa\u672c\u601d\u8def\u3002</p> <p>\u5de5\u4e1a\u4e0a\u7684\u7279\u6743\u6a21\u5f0f\u53ef\u80fd\u4f1a\u6709\u591a\u79cd\u590d\u6742\u7684\u5b9e\u73b0\u5f62\u5f0f\uff0c\u4f46\u662f\u6211\u4eec\u8fd9\u91cc\u53ea\u8bb2\u6700\u7b80\u5355\u7684\u4e00\u79cd\uff0c\u5373\u53cc\u6a21\u5f0f(Dual-Mode)\u3002\u53cc\u6a21\u5f0f\u4e0b\uff0cCPU \u6709\u4e24\u79cd\u8fd0\u884c\u6a21\u5f0f\uff0c\u4e00\u79cd\u662f\u7528\u6237\u6001(User Mode)\uff08\u76ee\u6001\uff09\uff0c\u4e00\u79cd\u662f\u5185\u6838\u6001(Kernel Mode)\uff08\u7ba1\u6001\uff0c\u6838\u5fc3\u6001\uff09\u3002Mode Bit \u4e3a 0\uff0c\u8868\u793a CPU \u5de5\u4f5c\u5728\u5185\u6838\u6001\uff0cMode Bit \u4e3a 1 \u65f6\uff0cCPU \u5de5\u4f5c\u5728\u7528\u6237\u6001\u3002</p> <p>\u540c\u65f6\uff0c\u6211\u4eec\u5c06\u90a3\u4e9b\u201c\u5371\u9669\u201d\u7684\u6307\u4ee4\u79f0\u4e3a\u7279\u6743\u6307\u4ee4(privileged instruction)\uff0c\u4f8b\u5982 I/O \u63a7\u5236\uff0c\u8ba1\u65f6\u5668\u7ba1\u7406\uff0c\u4e2d\u65ad\u7ba1\u7406\u7b49\u3002\u8fd9\u4e9b\u6307\u4ee4\u53ea\u80fd\u5728\u5185\u6838\u6001\u4e0b\u6267\u884c\uff0c\u800c\u7528\u6237\u6001\u4e0b\u6267\u884c\u8fd9\u4e9b\u6307\u4ee4\u65f6\u4f1a\u8ba4\u4e3a\u8fd9\u6761\u6307\u4ee4\u4e0d\u5b58\u5728\u3002</p> <p>\u95ee\u9898\u5c1a\u672a\u89e3\u51b3</p> <p>\u73b0\u5728\u6211\u4eec\u5c06\u5371\u9669\u64cd\u4f5c\u548c\u76f8\u5bf9\u5b89\u5168\u7684\u64cd\u4f5c\u9694\u79bb\u5f00\u6765\u4e86\uff0c\u4f46\u662f\u8fd9\u5e76\u4e0d\u610f\u5473\u7740\u7528\u6237\u7a0b\u5e8f\u5c31\u4e0d\u9700\u8981\u4f7f\u7528\u90a3\u4e9b\u5371\u9669\u64cd\u4f5c\u4e86\uff0c\u5355\u7eaf\u7684\u9694\u79bb\u5e76\u4e0d\u80fd\u89e3\u51b3\u95ee\u9898\uff0c\u7528\u6237\u7a0b\u5e8f\u4ecd\u7136\u5b58\u5728\u9700\u8981\u4f7f\u7528\u7279\u6743\u6307\u4ee4\u7684\u9700\u6c42\u3002</p> <p>\u8fd9\u4e9b\u9700\u6c42\u5f80\u5f80\u662f\u53ef\u4ee5\u88ab\u62bd\u8c61\u7684\u3001\u88ab\u5c01\u88c5\u7684\u3002\u5c31\u597d\u50cf\u300c\u201c\u7528\u6237\u201d\u5411\u201c\u67dc\u53f0\u201d\u7d22\u8981\u5e93\u623f\u94a5\u5319\uff0c\u4ee5\u4fbf ta \u80fd\u53bb\u5e93\u623f\u62ff\u7f3a\u8d27\u7684\u8d27\u7269\u300d\u8fd9\u4ef6\u4e8b\u662f\u4e0d\u5408\u7406\u7684\uff0c\u6211\u4eec\u65e0\u6cd5\u63a7\u5236\u201c\u7528\u6237\u201d\u5b9e\u9645\u62ff\u201c\u94a5\u5319\u201d\u505a\u4e86\u4ec0\u4e48\uff0c\u800c\u201c\u94a5\u5319\u201d\u7684\u6ee5\u7528\u53c8\u4f1a\u5bfc\u81f4\u201c\u67dc\u53f0\u201d\u9677\u5165\u5371\u9669\u4e2d\uff1b\u4f46\u662f\u300c\u201c\u7528\u6237\u201d\u8bf7\u6c42\u201c\u67dc\u53f0\u201d\u53bb\u5e93\u623f\u62ff ta \u9700\u8981\u7684\u8d27\u7269\u300d\u662f\u5408\u7406\u7684\u3002</p> <p>\u53cd\u8fc7\u6765\u8bb2\uff0c\u867d\u7136\u300c\u201c\u7528\u6237\u201d\u8bf7\u6c42\u201c\u67dc\u53f0\u201d\u53bb\u5e93\u623f\u62ff ta \u9700\u8981\u7684\u8d27\u7269\u300d\u8fd9\u4e2a\u4efb\u52a1\u5fc5\u987b\u4f7f\u7528\u5e93\u623f\u201c\u94a5\u5319\u201d\u624d\u80fd\u8fdb\u884c\uff0c\u4f46\u662f\u65e0\u8bba\u5982\u4f55\u8fd9\u4e2a\u201c\u94a5\u5319\u201d\u4e5f\u53ea\u4f1a\u88ab\u201c\u67dc\u53f0\u201d\u7528\u6765\u83b7\u53d6\u5e93\u623f\u91cc\u7684\u7279\u5b9a\u8d27\u7269\uff0c\u800c\u4e0d\u4f1a\u53d1\u751f\u8bf8\u5982\u201c\u7528\u6237\u201d\u5e26\u7740\u5341\u516b\u8f66\u9762\u5305\u4eba\u628a\u5e93\u623f\u6d17\u52ab\u4e00\u7a7a\u7684\u60c5\u51b5\u3002</p> <p>\u64cd\u4f5c\u7cfb\u7edf\u53ea\u9700\u8981\u5c01\u88c5\u597d\u4e00\u7cfb\u5217\u7c7b\u4f3c\u8fd9\u79cd\u7684\u9700\u6c42-\u7ed3\u679c\u7684\u5904\u7406\u65b9\u6848\uff0c\u8ba9\u7528\u6237\u5728\u6709\u9700\u8981\u7684\u65f6\u5019\u8ba9\u64cd\u4f5c\u7cfb\u7edf\u6267\u884c\u8fd9\u4e9b\u65b9\u6848\uff0c\u5728\u6267\u884c\u5f53\u524d\u4efb\u52a1\u7684\u65f6\u5019\u5c06\u63a7\u5236\u6743\u8ba9\u6e21\u7ed9\u64cd\u4f5c\u7cfb\u7edf\uff0c\u64cd\u4f5c\u7cfb\u7edf\u5b8c\u6210\u540e\u518d\u8fd8\u56de\u63a7\u5236\u6743\uff0c\u5c31\u53ef\u4ee5\u5b9e\u73b0\u5c06\u7279\u6743\u6307\u4ee4\u9694\u79bb\u5728\u5185\u6838\u6001\uff0c\u540c\u65f6\u7528\u6237\u7a0b\u5e8f\u4e5f\u80fd\u5b8c\u6210\u9700\u6c42\u3002</p> <p>\u800c\u90a3\u4e48\u5728\u5177\u4f53\u5b9e\u73b0\u4e0a\uff0c\u8fd9\u4e00\u6b65\u662f\u901a\u8fc7 trap \u5b9e\u73b0\u7684\u3002</p> <p> Transition from user to kernel mode.</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit0/#\u7cfb\u7edf\u8c03\u7528","title":"\u7cfb\u7edf\u8c03\u7528","text":"<p>  Examples of W&amp;U system calls. </p> <p>\u7cfb\u7edf\u8c03\u7528(System Call)\u662f\u7cfb\u7edf\u5411\u7528\u6237\u7a0b\u5e8f\u63d0\u4f9b\u670d\u52a1\u7684\u4e00\u4e2a\u63a5\u53e3\uff0c\u5b83\u4eec\u7ecf\u5e38\u4ee5 C/C++ \u51fd\u6570\u7684\u5f62\u5f0f\u5b58\u5728\uff0c\u5bf9\u4e8e\u67d0\u4e9b\u6bd4\u8f83\u63a5\u8fd1\u5e95\u5c42\u7684\u4efb\u52a1\uff0c\u4e5f\u53ef\u80fd\u662f\u901a\u8fc7\u6c47\u7f16\u7f16\u5199\u7684\u3002</p> <p>\u4f46\u8bf4\u5230\u5e95\uff0c\u7cfb\u7edf\u8c03\u7528\u8fd8\u662f\u76f8\u5bf9\u5e95\u5c42\u7684\u8bbe\u8ba1\uff0c\u901a\u5e38\u7684\u5f00\u53d1\u5e76\u4e0d\u57fa\u4e8e\u5982\u6b64\u5e95\u5c42\u7684\u8bbe\u8ba1\u5c55\u5f00\u3002\u66f4\u5e38\u89c1\u7684\u662f\u5229\u7528\u5404\u79cd\u62bd\u8c61\u5c42\u7ea7\u66f4\u9ad8\u7684 Application Programming Interface, API \u8fdb\u884c\u5f00\u53d1\u3002</p> <p>API \u662f\u4e00\u4e2a\u975e\u5e38\u5e38\u89c1\u7684\u6982\u5ff5\uff0c\u5728\u6211\u770b\u6765\u7cfb\u7edf\u8c03\u7528\u672c\u8eab\u4e5f\u662f\u4e00\u79cd API\u3002API \u7684\u6838\u5fc3\u601d\u60f3\u662f\u8ba9\u8c03\u7528\u8005\u53ea\u9700\u8981\u77e5\u9053\u5982\u4f55\u4e0e\u88ab\u8c03\u7528\u8005\u4ea4\u6d41\u4ee5\u5b9e\u73b0\u76ee\u7684\uff0c\u800c\u4e0d\u9700\u8981\u5173\u5fc3\u5176\u5177\u4f53\u5b9e\u73b0\u3002\u8fd9\u540c\u65f6\u4e5f\u6697\u793a\u7740\uff0c\u53ea\u8981 API \u4e00\u81f4\uff0c\u540c\u6837\u7684\u7a0b\u5e8f\u5728\u4e0d\u540c\u7684\u5e73\u53f0\u4e0a\u4e5f\u80fd\u76f4\u63a5\u7f16\u8bd1\u540e\u8fd0\u884c\u3002</p> <p>\u663e\u7136\uff0cAPI \u4e0e\u7f16\u7a0b\u8bed\u8a00\u5f80\u5f80\u662f\u5f3a\u76f8\u5173\u7684\uff0c\u7279\u5b9a\u7f16\u7a0b\u8bed\u8a00\u5728\u64cd\u4f5c\u7cfb\u7edf\u4e0a\u8fd0\u884c\u4e5f\u662f\u9700\u8981\u4e00\u5b9a\u7684\u201c\u73af\u5883\u201d\u7684\uff0c\u4e5f\u5c31\u662f\u6211\u4eec\u6240\u8bf4\u7684\u8fd0\u884c\u65f6\u73af\u5883(run-time environment, RTE)\u3002RTE \u901a\u5e38\u5305\u62ec\u4e86\u7f16\u8bd1\u5668(compilers)\u3001\u89e3\u91ca\u5668(interpreters)\u3001\u5e93(libraries)\u548c\u88c5\u8f7d\u5668(loaders)\u7b49\uff0c\u5b83\u4eec\u5171\u540c\u7ec4\u6210\u4e86\u4e00\u4e2a\u5b8c\u6574\u7684\u8fd0\u884c\u65f6\u73af\u5883\u3002</p> \u76f8\u5173\u9605\u8bfb <ul> <li>ABI | Wiki</li> <li>Difference between API and ABI | StackOverflow</li> </ul> \u601d\u8003\u9898 \u9898\u9762\u89e3\u6790 <p>\u8fa8\u6790\u5e93\u51fd\u6570\u4e0e\u7cfb\u7edf\u8c03\u7528\uff1f</p> <p>\u5e93\u51fd\u6570\u8fd0\u884c\u5728\u7528\u6237\u7a7a\u95f4\u800c\u7cfb\u7edf\u8c03\u7528\u8fd0\u884c\u5728\u5185\u6838\u7a7a\u95f4\u3002\u5927\u90e8\u5206\u5e93\u51fd\u6570\u53ef\u80fd\u4f7f\u7528\u7cfb\u7edf\u8c03\u7528\u6765\u5b9e\u73b0\u76ee\u7684\u3002</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit0/#\u94fe\u63a5\u5668\u548c\u88c5\u8f7d\u5668","title":"\u94fe\u63a5\u5668\u548c\u88c5\u8f7d\u5668","text":"<p>  The role of the linker and loader. </p> <p>\u8bf4\u4e86\u8fd9\u4e48\u591a\uff0c\u90a3\u4e48\u64cd\u4f5c\u7cfb\u7edf\u5230\u5e95\u662f\u5982\u4f55\u6267\u884c\u4e00\u4e2a\u7a0b\u5e8f\u7684\u5462\uff1f\u4ee5 C \u4e3a\u4f8b\uff0c\u4e00\u4e2a\u5199\u5b8c\u7684\u4ee3\u7801\u9700\u8981\u7ecf\u8fc7\u7f16\u8bd1\u3001\u94fe\u63a5\u3001\u88c5\u8f7d\u4e09\u4e2a\u6b65\u9aa4\uff0c\u624d\u80fd\u6210\u4e3a\u4e00\u4e2a\u5728\u5185\u5b58\u4e2d\u7684\uff0c\u53ef\u4ee5\u88ab\u6267\u884c\u7684\u7a0b\u5e8f\u3002</p> <p>\u7b80\u5355\u6765\u8bf4\uff0c\u7f16\u8bd1\u5668\u9996\u5148\u5c06\u82e5\u5e72 <code>.c</code> \u6e90\u6587\u4ef6\u7f16\u8bd1\u4e3a\u82e5\u5e72 <code>.o</code> \u6587\u4ef6\uff08\u8fd9\u91cc\u5408\u5e76\u4e86\u9884\u5904\u7406\u3001\u7f16\u8bd1\u3001\u6c47\u7f16\u6b65\u9aa4\uff09\uff0c\u8fd9\u4e9b <code>.o</code> \u6587\u4ef6\u88ab\u79f0\u4e3a\u53ef\u91cd\u5b9a\u4f4d\u76ee\u6807\u6587\u4ef6(relocatable object file)\uff0c\u5176\u5b58\u5728\u5f62\u5f0f\u4e3a\u673a\u5668\u7801\uff1b\u968f\u540e\u94fe\u63a5\u5668\u5c06\u82e5\u5e72 <code>.o</code> \u6587\u4ef6\u8fde\u5e26\u6240\u9700\u8981\u7684\u4e00\u4e9b\u5e93\u6587\u4ef6\uff08\u5982 <code>.a</code> \u6587\u4ef6\uff09\u94fe\u63a5\u4e3a\u4e00\u4e2a\u53ef\u6267\u884c\u76ee\u6807\u6587\u4ef6(executable object file)\u3002</p> <p>\u7279\u522b\u7684\uff0c\u94fe\u63a5\u5206\u4e3a\u9759\u6001\u94fe\u63a5\u548c\u52a8\u6001\u94fe\u63a5\u4e24\u79cd\u3002\u9759\u6001\u94fe\u63a5\u5c06\u5e93\u6587\u4ef6\u7684\u4ee3\u7801\u76f4\u63a5\u5408\u5e76\u8fdb\u5165\u6700\u7ec8\u7684\u53ef\u6267\u884c\u6587\u4ef6\uff0c\u800c\u52a8\u6001\u94fe\u63a5\u4ec5\u4ec5\u5c06\u5e93\u6587\u4ef6\u7684\u5f15\u7528\u4fe1\u606f\u5199\u5165\u6700\u7ec8\u7684\u53ef\u6267\u884c\u6587\u4ef6\uff0c\u800c\u5728\u7a0b\u5e8f\u8fd0\u884c\u65f6\u518d\u53bb\u5bfb\u627e\u8fd9\u4e9b\u5e93\u6587\u4ef6\u3002</p> <pre><code>gcc -E main.c -o main.i # pre-process\ngcc -S main.i -o main.s # compile to assembly code\ngcc -c main.s -o main.o # assemble to object file\ngcc main.o -o main      # link\n./main                  # (load and) execute\n</code></pre> \u4e00\u4e9b\u64cd\u4f5c <ul> <li>\u4f7f\u7528 <code>gcc -static ...</code> \u6765\u6307\u5b9a\u4f7f\u7528\u9759\u6001\u94fe\u63a5\uff1b</li> <li>\u4f7f\u7528 <code>ldd &lt;file&gt;</code> \u6765\u67e5\u770b\u6587\u4ef6\u94fe\u63a5\u4e86\u54ea\u4e9b\u5e93\uff1b</li> </ul> <p>  \u53ef\u4ee5\u53d1\u73b0\uff0c\u52a8\u6001\u94fe\u63a5\u5f97\u5230\u7684\u53ef\u6267\u884c\u6587\u4ef6\u6bd4\u9759\u6001\u94fe\u63a5\u5f97\u5230\u7684\u53ef\u6267\u884c\u6587\u4ef6\u8981\u5c0f\u4e0d\u5c11\u3002</p> <ol> <li> <p>\u5e76\u53d1\u662f\u6307\u4e24\u4e2a\u6216\u591a\u4e2a\u4e8b\u4ef6\u5728\u540c\u4e00\u65f6\u95f4\u95f4\u9694\u5185\u53d1\u751f\uff0c\u800c\u5e76\u884c\u662f\u6307\u4e24\u4e2a\u6216\u591a\u4e2a\u4e8b\u4ef6\u5728\u540c\u4e00\u65f6\u523b\u53d1\u751f\u3002\u903b\u8f91\u4e0a\uff0c\u5e76\u884c\u662f\u5e76\u53d1\u7684\u5b50\u96c6\u3002\u00a0\u21a9</p> </li> </ol>"},{"location":"cour_note/D3QD_OperatingSystem/Unit1/","title":"Unit 1: \u8fdb\u7a0b\u7ba1\u7406 | Process Management","text":"<p> \u7ea6 6600 \u4e2a\u5b57  78 \u884c\u4ee3\u7801  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 23 \u5206\u949f</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit1/#\u8fdb\u7a0b","title":"\u8fdb\u7a0b","text":"<p>\u4e00\u6bb5\u672c\u8d28\u4e0a\u7a0b\u5e8f\u662f\u9759\u6001\u7684\u3001\u5b58\u50a8\u5728\u786c\u76d8\u4e0a\u7684\u6307\u4ee4\u6570\u636e\uff0c\u800c\u5f53\u5b83\u9644\u5e26\u8fd0\u884c\u7a0b\u5e8f\u6240\u9700\u8981\u7684\u5fc5\u8981\u4fe1\u606f\u8fdb\u5165\u5185\u5b58\uff0c\u5f97\u5230\u76f8\u5173\u8d44\u6e90\u540e\uff0c\u5b83\u6210\u4e3a\u4e00\u4e2a\u52a8\u6001\u7684\u3001\u4e0e\u8ba1\u7b97\u673a\u8d44\u6e90\u4e92\u52a8\u7684\u5b9e\u4f53\uff0c\u8fd9\u4e2a\u5b9e\u4f53\u5c31\u662f\u8fdb\u7a0b(process)\u3002</p> <p>\u8fdb\u7a0b\u662f\u662f\u64cd\u4f5c\u7cfb\u7edf\u8fdb\u884c\u8d44\u6e90\u5206\u914d\u548c\u8c03\u5ea6\u7684\u4e00\u4e2a\u72ec\u7acb\u5355\u4f4d\uff0c\u5b83\u4ee5\u7279\u5b9a\u5f62\u5f0f\u5b58\u5728\u4e8e\u5185\u5b58\u4e2d\uff0c\u5177\u6709\u4e00\u5b9a\u7684\u5c01\u95ed\u6027\uff0c\u662f\u591a\u9053\u6280\u672f\u7684\u91cd\u8981\u57fa\u7840\u3002</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit1/#\u8fdb\u7a0b\u7684\u5f62\u5f0f","title":"\u8fdb\u7a0b\u7684\u5f62\u5f0f","text":"<p>\u524d\u9762\u6211\u4eec\u63d0\u5230\uff0c\u8fdb\u7a0b\u52a8\u6001\u5730\u5b58\u5728\u4e8e\u5185\u5b58\u4e2d\uff0c\u56e0\u6b64\u9664\u4e86\u547d\u4ee4\u4ee5\u5916\uff0c\u8fd8\u5305\u62ec\u5176\u8fd0\u884c\u65f6\u7684\u52a8\u6001\u4fe1\u606f\u3002\u62bd\u8c61\u6765\u8bf4\uff0c\u4e3b\u8981\u5305\u542b\u8fd9\u4e09\u4e2a\u7ef4\u5ea6\uff1a\u2460 \u7528\u6765\u8dd1\u7684\u4ee3\u7801\uff1b\u2461 \u8dd1\u7684\u8fc7\u7a0b\u4e2d\uff0c\u4e0d\u65ad\u4f1a\u88ab\u66f4\u65b0\u7684\u6570\u636e\uff1b\u2462 \u7528\u6765\u7ef4\u62a4\u3001\u63a7\u5236\u8fdb\u7a0b\u7684\u63a7\u5236\u4fe1\u606f\u3002</p> <p>\u8fdb\u7a0b\u5728\u5185\u5b58\u4e2d\u5b58\u5728\u9700\u8981\u4e00\u5757\u865a\u62df\u7684\u5730\u5740\u7a7a\u95f4\u4ee5\u5b58\u50a8\u4e0a\u8ff0\u8fd9\u4e9b\u5185\u5bb9\u3002\u5176\u5305\u542b\u4e24\u4e2a\u90e8\u5206\uff0c\u5373\u865a\u62df\u5730\u5740\u7a7a\u95f4\u4e2d\u7684\u7528\u6237\u90e8\u5206\u548c\u865a\u62df\u5730\u5740\u7a7a\u95f4\u7684\u5185\u6838\u90e8\u5206\u3002</p> <p>\u4e0b\u56fe\u662f\u8fdb\u7a0b\u5728\u865a\u62df\u5730\u5740\u7a7a\u95f4\u4e2d\u7528\u6237\u90e8\u5206\u7684\u7ec4\u6210\uff1a</p> <p>\u7528\u6237\u90e8\u5206</p> <p> </p> <ul> <li>Text section:<ul> <li>\u5b58\u50a8\u4ee3\u7801\uff1b</li> </ul> </li> <li>Data section:<ul> <li>\u5b58\u50a8\u4ee3\u7801\u4e2d\u7684\u5168\u5c40\u53d8\u91cf\u3001\u9759\u6001\u53d8\u91cf\uff1b</li> </ul> </li> <li>Heap section:<ul> <li>\u5e38\u8bf4\u7684\u201c\u5806\u201d\uff0c\u88ab\u52a8\u6001\u5206\u914d\u7684\u5185\u5b58\uff1b</li> </ul> </li> <li>Stack section:<ul> <li>\u5e38\u8bf4\u7684\u201c\u6808\u201d\uff0c\u5b58\u50a8\u4e00\u4e9b\u6682\u65f6\u6027\u7684\u6570\u636e\uff0c\u5982\u51fd\u6570\u4f20\u53c2\u3001\u8fd4\u56de\u503c\u3001\u5c40\u90e8\u53d8\u91cf\u7b49\uff1b</li> </ul> </li> </ul> <p>\u53ef\u4ee5\u53d1\u73b0\uff0cText \u548c Data \u90e8\u5206\u6240\u9700\u8981\u7684\u7a7a\u95f4\u5728\u4e00\u5f00\u59cb\u5c31\u88ab\u786e\u5b9a\uff0c\u800c Heap \u548c Stack \u90fd\u53ef\u80fd\u52a8\u6001\u7684\u6269\u5c55\u548c\u6536\u7f29\u3002\u89c2\u5bdf\u53f3\u56fe\uff0cHeap \u548c Stack \u662f\u76f8\u5411\u6269\u5c55\u7684\uff0c\u4e8e\u662f\u6574\u4e00\u5757\u7684\u5927\u5c0f\u80fd\u591f\u56fa\u5b9a\u4e0b\u6765\uff0c\u800c\u5728\u5185\u90e8\u8fdb\u884c\u6709\u9650\u5236\u7684\u52a8\u6001\u5206\u914d\u3002\u5f53\u7136\uff0cHeap \u548c Stack \u7684\u533a\u57df\u5e76\u4e0d\u4f1a\u4ea4\u53c9\u3002</p> memory layout of a C program <p></p> <p>\u4e4b\u6240\u4ee5\u628a\u6709\u521d\u59cb\u503c\u7684\u9759\u6001\u53d8\u91cf\u548c\u6ca1\u521d\u59cb\u503c\u7684\u9759\u6001\u53d8\u91cf\u5206\u5f00\u6765\uff0c\u662f\u56e0\u4e3a\u6211\u4eec\u53ef\u4ee5\u5728\u4e00\u5f00\u59cb\u53ea\u5b58\u50a8\u6ca1\u521d\u59cb\u503c\u7684\u9759\u6001\u53d8\u91cf\u7684\u5927\u5c0f\uff0c\u800c\u5728\u771f\u6b63\u7b2c\u4e00\u6b21\u8bbf\u95ee\u7684\u65f6\u5019\u624d\u5206\u914d\u5185\u5b58\uff0c\u4ee5\u6b64\u6765\u5b9e\u73b0\u51cf\u5c11\u5185\u5b58\u5360\u7528\u3002</p> <p>\u901a\u5e38\u6765\u8bf4\uff0c\u672a\u521d\u59cb\u5316\u7684\u9759\u6001\u53d8\u91cf\u4e00\u822c\u90fd\u88ab\u653e\u5728 <code>.bss</code> \u6bb5\uff0c\u800c\u5728\u88ab\u521d\u59cb\u5316\u7684\u65f6\u5019\u79fb\u52a8\u5230 <code>.data</code> \u6bb5\u30021</p> <p>\u800c\u653e\u5728\u5185\u6838\u90e8\u5206\u7684\u5185\u5bb9\uff0c\u5219\u66f4\u4fa7\u91cd\u4e8e\u8fdb\u7a0b\u7684\u63a7\u5236\u4fe1\u606f\uff0c\u5177\u4f53\u6765\u8bf4\u5c31\u662f\u8fdb\u7a0b\u63a7\u5236\u5757(Process Control Block, PCB)\u3002</p> <p>\u5185\u6838\u90e8\u5206</p> <p>\u8fdb\u7a0b\u63a7\u5236\u5757(Process Control Block, PCB)\u662f\u64cd\u4f5c\u7cfb\u7edf\u4e2d\u7528\u6765\u63cf\u8ff0\u8fdb\u7a0b\u7684\u4e00\u79cd\u6570\u636e\u7ed3\u6784\uff0c\u5b83\u5305\u542b\u4e86\u8fdb\u7a0b\u7684\u6240\u6709\u4fe1\u606f\uff0c\u662f\u64cd\u4f5c\u7cfb\u7edf\u4e2d\u6700\u91cd\u8981\u7684\u6570\u636e\u7ed3\u6784\u4e4b\u4e00\u3002\u53ef\u4ee5\u8bf4\uff0cPCB \u662f\u8fdb\u7a0b\u5b58\u5728\u7684\u552f\u4e00\u6807\u5fd7\u3002</p> <p>\u901a\u5e38\u6765\u8bf4\uff0cPCB \u53ef\u80fd\u5305\u542b\u8fd9\u4e9b\u5185\u5bb9\uff1a</p> <p> </p> <ul> <li>Process state:<ul> <li>\u8fdb\u7a0b\u7684\u72b6\u6001\uff1b</li> </ul> </li> <li>Program counter:<ul> <li>\u6807\u8bc6\u8be5\u8fdb\u7a0b\u8dd1\u5230\u4e86\u54ea\u91cc\uff0c\u7531\u4e8e\u8fdb\u7a0b\u662f\u52a8\u6001\u7684\uff0c\u6bcf\u4e00\u88ab\u5207\u6362\u90fd\u9700\u8981\u4fdd\u8bc1\u4e0b\u4e00\u6b21\u80fd\u65e0\u7f1d\u8854\u63a5\u4e4b\u524d\u7684\u8fdb\u5ea6\uff0c\u6240\u4ee5\u9700\u8981\u5b58\u50a8\u6bcf\u6b21\u7684\u5de5\u4f5c\u72b6\u6001\uff1b</li> </ul> </li> <li>CPU registers:<ul> <li>\u4fdd\u5b58\u8fdb\u7a0b\u76f8\u5173\u7684\u5bc4\u5b58\u5668\u4fe1\u606f\uff1b</li> </ul> </li> <li>CPU-scheduling information:<ul> <li>CPU \u8c03\u5ea6\u53c2\u8003\u7684\u4fe1\u606f\uff0c\u5305\u62ec\u4f18\u5148\u7ea7\u3001\u8c03\u5ea6\u961f\u5217\u7684\u6307\u9488\u3001\u8c03\u5ea6\u53c2\u6570\u7b49\uff1b</li> </ul> </li> <li>Memory-management information:<ul> <li>\u5305\u62ec\u9875\u8868\u3001\u6bb5\u8868\u7b49\u4fe1\u606f\uff0c\u5177\u4f53\u4e0e\u5b9e\u73b0\u7684\u5185\u5b58\u7cfb\u7edf\u6709\u5173\uff1b</li> </ul> </li> <li>Accounting information\uff1a<ul> <li>\u4e00\u4e9b\u5173\u4e8e\u8fdb\u7a0b\u7684\u52a8\u6001\u6570\u636e\u7684\u7edf\u8ba1\u548c\u8bb0\u5f55\uff0c\u6bd4\u5982\u603b\u5171\u5df2\u7ecf\u8dd1\u4e86\u591a\u4e45\u3001\u65f6\u95f4\u9650\u5236\u3001\u8fdb\u7a0b\u53f7\u7b49\uff1b</li> </ul> </li> <li>I/O status information:<ul> <li>\u88ab\u5206\u914d\u7ed9\u8fdb\u7a0b\u7684 I/O \u8bbe\u5907\u5217\u8868\u3001\u6253\u5f00\u7684\u6587\u4ef6\u5217\u8868\u7b49\uff1b</li> </ul> </li> </ul> <p>\u4e24\u4e2a\u90e8\u5206\u5728\u903b\u8f91\u4e0a\u7684\u5173\u7cfb\u662f\uff0c\u7528\u6237\u90e8\u5206\u5212\u5206\u5e76\u5b9e\u9645\u5b58\u50a8\u8fdb\u7a0b\u6240\u9700\u8981\u7684\u6570\u636e\u8d44\u6e90\uff08\u5305\u62ec\u7a0b\u5e8f\u8fd0\u884c\u7684\u4ee3\u7801\uff09\uff0c\u800c\u5185\u6838\u90e8\u5206\u5b58\u50a8\u8fdb\u7a0b\u7684\u5143\u6570\u636e\uff0c\u5305\u62ec\u63a7\u5236\u4fe1\u606f\u4e0e\u7528\u6237\u90e8\u5206\u4e2d\u5404\u4e2a\u90e8\u5206\u5185\u5b58\u7684\u5206\u914d\u548c\u4f7f\u7528\u60c5\u51b5\u3002</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit1/#\u8fdb\u7a0b\u7684\u72b6\u6001","title":"\u8fdb\u7a0b\u7684\u72b6\u6001","text":"<p>\u5728\u5355\u673a\u8bed\u5883\u4e0b\uff0c\u8fdb\u7a0b\u8c03\u5ea6\u4e00\u4e2a\u6bd4\u8f83\u6838\u5fc3\u7684\u90e8\u5206\u5c31\u662f\u5c06 CPU \u8d44\u6e90\u7ed9\u54ea\u4e2a\u4efb\u52a1\u7528\u3002\u800c\u5e76\u4e0d\u662f\u4efb\u4f55\u8fdb\u7a0b\u5728\u4efb\u4f55\u65f6\u523b\u90fd\u53ef\u4ee5\u76f4\u63a5\u83b7\u5f97 CPU \u8d44\u6e90\u5e76\u76f4\u63a5\u5f00\u59cb\u4f7f\u7528\u7684\uff0c\u56e0\u6b64\u6211\u4eec\u9700\u8981\u5bf9\u8fdb\u7a0b\u7684\u72b6\u6001\u8fdb\u884c\u5efa\u6a21\u3002</p> <p> </p> <ul> <li><code>new</code>:<ul> <li>\u8fdb\u7a0b\u6b63\u5728\u521b\u5efa\u8fc7\u7a0b\u4e2d\uff0c\u5305\u62ec\u7533\u8bf7 PCB\uff0c\u5206\u914d\u521d\u59cb\u8d44\u6e90\u7b49\uff1b</li> </ul> </li> <li><code>running</code>:<ul> <li>\u8fdb\u7a0b\u6b63\u5728\u8fd0\u884c\uff0c\u5373\u6b63\u5728\u4f7f\u7528 CPU \u8d44\u6e90\uff1b</li> <li>\u6709\u51e0\u4e2a\u6838\u5c31\u6700\u591a\u6709\u51e0\u4e2a\u8fdb\u7a0b\u5904\u4e8e <code>running</code> \u72b6\u6001\uff1b</li> </ul> </li> <li><code>ready</code>:<ul> <li>\u8fdb\u7a0b\u5df2\u7ecf\u51c6\u5907\u597d\u4e86\uff0c\u53ea\u5dee CPU \u8d44\u6e90\uff0c\u4e00\u65e6\u6709 CPU \u8d44\u6e90\u5f85\u5206\u914d\uff0c\u5c31\u4f1a\u6709\u5c31\u7eea\u6001\u7684\u8fdb\u7a0b\u53d8\u4e3a\u8fd0\u884c\u6001\uff1b</li> <li>\u5982\u679c\u6709\u8fdb\u7a0b\u5904\u4e8e\u5c31\u7eea\u6001\uff0c\u5c31\u4e00\u5b9a\u6709\u8fdb\u7a0b\u5904\u4e8e\u8fd0\u884c\u6001\uff1b</li> <li>CPU \u8c03\u5ea6\u5b9e\u9645\u4e0a\u6307\u7684\u5c31\u662f\u82e5\u5e72\u8fdb\u7a0b\u5728\u5c31\u7eea\u6001\u548c\u8fd0\u884c\u6001\u4e4b\u95f4\u7684\u5207\u6362\uff1b</li> </ul> </li> <li><code>waiting</code>:<ul> <li>\u8fdb\u7a0b\u6b63\u5728\u7b49\u5f85\u67d0\u4e2a\u4e8b\u4ef6\u7684\u53d1\u751f\uff0c\u6bd4\u5982\u7b49\u5f85 I/O \u5b8c\u6210\u3001\u7b49\u5f85\u67d0\u4e2a\u4fe1\u53f7\u91cf\u7b49\uff1b</li> <li>\u6b64\u65f6\u5373\u4f7f\u6709\u7a7a\u4f59\u7684 CPU \u8d44\u6e90\uff0c\u8be5\u8fdb\u7a0b\u4e5f\u65e0\u6cd5\u7ee7\u7eed\uff1b</li> <li>\u4e00\u822c\u8fdb\u7a0b\u4ece\u8fd0\u884c\u6001\u8fdb\u5165\u963b\u585e\u6001\u662f\u4e3b\u52a8\u7684\uff0c\u79bb\u5f00\u963b\u585e\u6001\u8fdb\u5165\u5c31\u7eea\u6001\u662f\u88ab\u52a8\u7684\uff1b</li> </ul> </li> <li><code>terminated</code>:<ul> <li>\u8fdb\u7a0b\u56e0\u4e3a\u67d0\u4e9b\u539f\u56e0\u7ec8\u6b62\uff0c\u7ed3\u675f\u8fd0\u884c\uff0c\u9700\u8981\u91ca\u653e\u8d44\u6e90\uff1b</li> </ul> </li> </ul> <p>\u8fdb\u7a0b\u5728\u5c31\u7eea\u6001\u9700\u8981\u7b49\u5f85 CPU \u8d44\u6e90\u7684\u6d3e\u53d1(dispatch)\uff0c\u63a5\u53d7\u8c03\u5ea6\uff1b\u5728\u963b\u585e\u6001\u9700\u8981\u7b49\u5f85\u5bf9\u5e94\u7684 I/O \u5b8c\u6210\u6216\u4e8b\u4ef6\u5b8c\u6210\uff0c\u56e0\u800c\u5b58\u5728\u4e00\u79cd\u7ed3\u6784\u9700\u8981\u53bb\u7ef4\u62a4\u8fd9\u4e9b\u201c\u76f8\u5bf9\u9759\u6b62\u201d\u7684\u8fdb\u7a0b\u3002\u901a\u5e38\u4f7f\u7528\u5c31\u7eea\u961f\u5217(ready queue)\u548c\u7b49\u5f85\u961f\u5217(wait queue)\u6765\u5b9e\u73b0\uff0c\u5176\u57fa\u672c\u7ed3\u6784\u5982\u4e0b\uff1a</p> <p></p> <p>\u5b9e\u9645\u5b9e\u73b0\u4e2d\uff0c\u7531\u4e8e\u7b49\u5f85\u7684 I/O \u6216\u4e8b\u4ef6\u4e0d\u540c\uff0c\u53ef\u80fd\u7ef4\u62a4\u591a\u4e2a\u7b49\u5f85\u961f\u5217\uff0c\u4e8e\u662f\u5b9e\u9645\u8fc7\u7a0b\u4e2d\u7684\u60c5\u51b5\u53ef\u80fd\u5982\u4e0b\uff1a</p> <p></p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit1/#\u8fdb\u7a0b\u7ba1\u7406","title":"\u8fdb\u7a0b\u7ba1\u7406","text":"<p>\u73b0\u5728\u6211\u4eec\u5df2\u7ecf\u8ba8\u8bba\u4e86\u8fdb\u7a0b\u7684\u5f62\u5f0f\u548c\u4e00\u4e2a\u4e2a\u79bb\u6563\u7684\u72b6\u6001\uff0c\u73b0\u5728\u6211\u4eec\u6765\u8bb2\u8bb2\u8fdb\u7a0b\u5728\u51e0\u4e2a\u9636\u6bb5\u7684\u52a8\u6001\u8fc7\u7a0b\u3002</p> <p>\u7528\u6237\u8fdb\u7a0b\u5728\u64cd\u4f5c\u7cfb\u7edf\u4e2d\uff0c\u603b\u4f53\u4e0a\u6765\u8bb2\u9075\u5faa\u4e00\u4e2a\u6811\u72b6\u7684\u7ec4\u7ec7\u5f62\u5f0f\uff0c\u6bcf\u4e00\u4e2a\u8fdb\u7a0b\u90fd\u6709\u4e00\u4e2a\u552f\u4e00\u6807\u8bc6\u7b26\u8fdb\u7a0b\u53f7\uff08\u901a\u5e38\u88ab\u79f0\u4e3a pid\uff0c\u4f46\u5728\u7279\u5b9a\u8bed\u5883\u4e0b\u53ef\u80fd\u6709\u4e0d\u540c\u7684\u542b\u4e49\uff09\u3002\u5982\u4e0b\u56fe\u662f Linux \u7684\u4e00\u4e2a\u8fdb\u7a0b\u6811\u3002</p> <p></p> <p>\u4f60\u4e5f\u53ef\u4ee5\u5728 Linux \u4e2d\u4f7f\u7528 <code>pstree</code> \u6765\u67e5\u770b\u8fdb\u7a0b\u6811\u3002 \u8a00\u4e0b\u4e4b\u610f\u5c31\u662f\u8fdb\u7a0b\u4e4b\u95f4\u5b58\u5728\u4e00\u79cd\u7236\u5b50\u5173\u7cfb\uff0c\u5373 child \u8fdb\u7a0b\u662f\u7531 parent \u8fdb\u7a0b\u521b\u5efa\u7684\uff0c\u56e0\u6b64\u8fdb\u7a0b\u9664\u4e86\u81ea\u5df1\u7684 <code>pid</code> \u8fd8\u6709 <code>ppid</code> \u6765\u6807\u8bc6\u5b83\u7684 parent \u8fdb\u7a0b\u3002</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit1/#\u8fdb\u7a0b\u7684\u521b\u5efa","title":"\u8fdb\u7a0b\u7684\u521b\u5efa","text":"<p>child \u8fdb\u7a0b\u7684\u8d44\u6e90\u53ef\u80fd\u76f4\u63a5\u6765\u81ea\u64cd\u4f5c\u7cfb\u7edf\u7684\u5206\u914d\uff0c\u4e5f\u53ef\u80fd\u6765\u81ea parent \u8fdb\u7a0b\u7684\u5206\u914d\uff0c\u9650\u5236\u4f7f\u7528\u540e\u8005\u7684\u597d\u5904\u662f\u80fd\u591f\u907f\u514d\u56e0\u4e3a\u521b\u5efa\u592a\u591a\u5b50\u8fdb\u7a0b\u800c\u5bfc\u81f4\u8d44\u6e90\u4e0d\u591f\u7528\u3002\u7279\u522b\u7684\uff0c\u6211\u4eec\u89c2\u5bdf\u5230\u8fd9\u68f5\u6811\u7684\u6839\u662f <code>systemd</code>\uff0c\u5386\u53f2\u4e0a\u4e5f\u66fe\u53eb\u8fc7 <code>init</code>\uff0c\u5b83\u662f\u64cd\u4f5c\u7cfb\u7edf\u542f\u52a8\u540e\u8fd0\u884c\u7684\u7b2c\u4e00\u4e2a\u7528\u6237\u8fdb\u7a0b\uff0c\u81f3\u5c11\u5728 Linux \u4e2d\uff0c\u5b83\u7684 <code>pid</code> \u88ab\u5206\u914d\u4e3a 1\uff0c\u800c\u5b83\u7684 <code>ppid</code> \u662f 0\uff0c\u53ef\u4ee5\u7406\u89e3\u4e3a\u8fd9\u4e2a\u8fdb\u7a0b\u7684 parent \u662f scheduler \u800c\u975e\u4e00\u4e2a\u8fdb\u7a0b2\u3002</p> <p>\u5728 Linux \u4e2d\uff0c\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528 <code>fork</code> \u6765\u521b\u5efa\u4e00\u4e2a child \u8fdb\u7a0b\uff0c\u5728\u8fd9\u91cc\u5148\u5f15\u5165\u5982\u4f55\u5b9e\u73b0\u662f\u4e3a\u4e86\u5f15\u5165\u4e00\u4e2a\u53ef\u4ee5\u501f\u6765\u63cf\u8ff0\u8fc7\u7a0b\u7684\u8bed\u8a00\uff0c\u6211\u4eec\u4ee5\u4e0b\u9762\u7684 C \u7a0b\u5e8f\u4e3a\u4f8b\u5c55\u5f00\u4e4b\u540e\u7684\u8ba8\u8bba\u3002</p> <pre><code>#include &lt;stdio.h&gt;\n#include &lt;unistd.h&gt;\n#include &lt;sys/wait.h&gt;\n#include &lt;sys/types.h&gt;\n\nint main() {\nprintf(\"A process starts!\\n\");\n\npid_t pid;\npid = fork();\nif (pid &lt; 0) {\nprintf(\"Fork failed!\\n\");\n} else if (pid == 0) {\n// sleep(1);\nprintf(\"pid is zero, so it's child process!\\n\");\n} else {\n// wait(NULL);\n// sleep(1);\nprintf(\"pid is nonzero thus it's parent process!\\n\");\n}\n}\n</code></pre> <p>\u7b2c 10 \u884c\u9ad8\u4eae\u7684 <code>fork()</code> \u8bed\u53e5\u521b\u5efa\u4e86\u4e00\u4e2a\u8fdb\u7a0b\uff0c\u8be5\u8fdb\u7a0b\u53ea\u6709\u8fdb\u7a0b\u53f7\u4e0e parent \u8fdb\u7a0b\u4e0d\u4e00\u6837\uff0c\u540c\u65f6\u901a\u8fc7\u68c0\u67e5\u8fd4\u56de\u503c <code>pid</code> \u6765\u5224\u65ad\u5c5e\u4e8e parent \u8fd8\u662f child\u3002</p> <p>\u5982\u679c\u7b2c 18 \u884c\u4ecd\u7136\u88ab\u6ce8\u91ca\uff0c\u90a3\u4e48 parent \u8fdb\u7a0b\u8bf6 child \u8fdb\u7a0b\u5c06\u5e76\u53d1\u6267\u884c\uff0c\u5373\u5b8c\u6210 <code>fork()</code> \u540e\u4e24\u4e2a\u8fdb\u7a0b\u90fd\u4ece 11 \u884c\u5f00\u59cb\u7ee7\u7eed\u5411\u4e0b\u5e76\u53d1\u7684\u6267\u884c\uff0c\u4e92\u4e0d\u963b\u585e\uff1b\u5982\u679c 18 \u884c\u7684\u6ce8\u91ca\u88ab\u53d6\u6d88\uff0c\u90a3\u4e48 parent \u8fdb\u7a0b\u5c06\u7b49\u5f85 child \u8fdb\u7a0b\u7ed3\u675f\u540e\u518d\u7ee7\u7eed\u3002\u8bfb\u8005\u53ef\u4ee5\u5c1d\u8bd5\u6392\u5217\u7ec4\u5408\u4e24\u4e2a\u6ce8\u91ca\u6765\u89c2\u5bdf\u7a0b\u5e8f\u8fd0\u884c\u7684\u7ed3\u679c\u4f1a\u5982\u4f55\u53d8\u5316\u3002</p> <p>\u903b\u8f91\u4e0a\u521b\u5efa\u7684\u65b0\u8fdb\u7a0b\u6709\u4e24\u79cd\u60c5\u51b5\uff1a</p> <ol> <li>\u590d\u5236 parent \u8fdb\u7a0b\u7684\u4ee3\u7801\u6570\u636e\uff1b</li> <li>\u8f7d\u5165\u65b0\u7684\u7a0b\u5e8f\u5e76\u7ee7\u7eed\u6267\u884c\uff1b</li> </ol> <p>\u800c\u5b9e\u9645\u5728 Linux \u4e2d\uff0c\u7b2c\u4e00\u79cd\u901a\u8fc7 <code>fork()</code> \u5b9e\u73b0\uff0c\u7b2c\u4e8c\u79cd\u901a\u8fc7 <code>fork()</code> \u540e <code>execXX()</code> \u5b9e\u73b0\uff0c<code>execXX()</code> \u4f1a\u8986\u76d6\u90a3\u4e2a\u8fdb\u7a0b\u7684\u5730\u5740\u7a7a\u95f4\uff0c\u4ee5\u5b9e\u73b0\u6267\u884c\u5176\u4ed6\u7a0b\u5e8f\u30023 4</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit1/#\u8fdb\u7a0b\u7684\u7ec8\u6b62","title":"\u8fdb\u7a0b\u7684\u7ec8\u6b62","text":"<p>\u5f53\u8fdb\u7a0b\u8c03\u7528 <code>exit()</code> \u8fd9\u4e2a\u7cfb\u7edf\u8c03\u7528\u65f6\uff0c\u8fd9\u4e2a\u8fdb\u7a0b\u5c06\u88ab\u7ec8\u6b62\uff0c\u8fd9\u610f\u5473\u7740\u8fd9\u4e2a\u8fdb\u7a0b\u5c06\u4e0d\u518d\u6267\u884c\uff0c\u5176\u8d44\u6e90\u5c06\u88ab\u91ca\u653e\uff0c\u540c\u65f6\u2014\u2014\u8fd4\u56de\u72b6\u6001\u503c\uff0c\u800c\u8fd9\u4e2a\u72b6\u6001\u503c\u5c06\u88ab parent \u8fdb\u7a0b\u7684 <code>wait()</code> \u63a5\u6536\u3002\u7279\u522b\u7684\uff0c\u5982\u679c parent \u8fdb\u7a0b\u5c1a\u672a\u8c03\u7528 <code>wait()</code>\uff0c\u5219\u8fd9\u4e2a child \u8fdb\u7a0b\u8fd8\u4e0d\u4f1a\u5b8c\u5168\u6d88\u5931\uff0c\u56e0\u4e3a\u8981\u8fd4\u56de\u7684\u4e1c\u897f\u8fd8\u6ca1\u8fd4\u56de\uff0c\u8fd9\u79cd\u903b\u8f91\u4e0a\u5df2\u7ecf\u7ec8\u6b62\uff0c\u4f46\u4ecd\u7136\u5360\u6709\u4e00\u90e8\u5206\u8d44\u6e90\uff0c\u7b49\u5f85 parent \u8fdb\u7a0b\u8c03\u7528 <code>wait()</code> \u7684\u8fdb\u7a0b\uff0c\u6211\u4eec\u79f0\u4e4b\u4e3a\u50f5\u5c38\u8fdb\u7a0b(zombie)\u3002\u4e00\u4e2a\u8fdb\u7a0b\u53d8\u6210\u50f5\u5c38\u8fdb\u7a0b\u662f\u5f88\u666e\u901a\u7684\uff0c\u5173\u952e\u5728\u4e8e\uff0c\u5982\u679c parent \u8fdb\u7a0b\u4e0d\u8c03\u7528 <code>wait()</code>\uff0c\u90a3\u7b49 parent \u7ec8\u6b62\u540e\uff0c\u8fd9\u4e2a\u50f5\u5c38\u8fdb\u7a0b\u53ef\u80fd\u4ecd\u7136\u4e00\u76f4\u5b58\u5728\uff0c\u6b64\u65f6\u8fd9\u4e2a\u50f5\u5c38\u8fdb\u7a0b\u540c\u65f6\u662f\u4e00\u4e2a\u5b64\u513f\u8fdb\u7a0b(orphan)\u2014\u2014\u5373\u6ca1\u6709 parent \u8fdb\u7a0b\u7684\u8fdb\u7a0b\uff0c\u8fd9\u663e\u7136\u662f\u4e0d\u5408\u7406\u7684\uff0cUNIX \u7684\u89e3\u51b3\u529e\u6cd5\u662f\uff0c\u8ba9\u6240\u6709\u5b64\u513f\u8fdb\u7a0b\u90fd\u6210\u4e3a <code>init</code>/<code>systemd</code> \u7684 child \u8fdb\u7a0b\uff0c\u7531 <code>init</code>/<code>systemd</code> \u6765 <code>wait()</code> \u5b83\u4eec\u3002</p> <p>\u5728\u67d0\u4e9b\u7cfb\u7edf\u91cc\uff0c\u64cd\u4f5c\u7cfb\u7edf\u901a\u8fc7\u7ea7\u8054\u7ec8\u6b62(cascading termination)\u6765\u907f\u514d\u5b64\u513f\u8fdb\u7a0b\u7684\u51fa\u73b0\uff0c\u5373\u5f53\u4e00\u4e2a\u8fdb\u7a0b\u88ab\u7ec8\u6b62\u65f6\uff0c\u5b83\u7684 child \u4e5f\u5e94\u5f53\u88ab\u9012\u5f52\u5730\u7ec8\u6b62\u3002</p> daemon <p>\u5b88\u62a4\u8fdb\u7a0b\u662f\u4e00\u79cd\u7279\u6b8a\u7684\u8fdb\u7a0b\uff0c\u5b83\u4eec\u5728\u201c\u540e\u53f0\u201d\u957f\u671f\u8fd0\u884c\uff0c\u4f8b\u5982\u67d0\u4e9b\u6570\u636e\u5e93\u670d\u52a1\u3001\u53cd\u4ee3\u7406\u670d\u52a1\u7b49\uff0c\u800c\u975e\u50cf\u666e\u901a\u7684\u7528\u6237\u7a0b\u5e8f\u4e00\u6837\u4f9d\u8d56\u4e8e\u7528\u6237\u4ea4\u4e92\u3002</p> <p>\u4e3a\u4e86\u5b9e\u73b0\u201c\u957f\u671f\u8fd0\u884c\u201d\uff0c\u6211\u4eec\u9700\u8981\u8ba9\u5b83\u4ee5 <code>init</code>/<code>systemd</code> \u4e3a parent\uff0c\u56e0\u4e3a\u4efb\u4f55\u5176\u5b83\u8fdb\u7a0b\u90fd\u6709\u53ef\u80fd\u5728\u64cd\u4f5c\u7cfb\u7edf\u8fd0\u884c\u7684\u65f6\u5019\u7ec8\u6b62\u3002</p> <p>\u90a3\u4e48\u4e00\u79cd\u529e\u6cd5\u5c31\u662f\u6211\u4eec\u9012\u5f52\u5730 <code>fork()</code> \u4e24\u6b21\uff0c\u7136\u540e\u7ec8\u6b62\u7b2c\u4e00\u4e2a\u8fdb\u7a0b\uff0c\u5373\u7ec8\u6b62\u7b2c\u4e8c\u4e2a\u8fdb\u7a0b\u7684 parent\uff0c\u8fd9\u6837\u5b83\u5c31\u80fd\u6210\u4e3a\u4e00\u4e2a\u5b64\u513f\u8fdb\u7a0b\uff0c\u8fdb\u800c\u88ab <code>init</code>/<code>systemd</code> \u63a5\u7ba1\u3002</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit1/#\u8fdb\u7a0b\u95f4\u901a\u4fe1","title":"\u8fdb\u7a0b\u95f4\u901a\u4fe1","text":"<p>\u5982\u679c\u4e00\u4e2a\u8fdb\u7a0b\u53d7\u5230\u5176\u5b83\u8fdb\u7a0b\u7684\u5f71\u54cd\uff0c\u6216\u4f1a\u5f71\u54cd\u5176\u5b83\u8fdb\u7a0b\uff0c\u90a3\u4e48\u6211\u4eec\u79f0\u4e4b\u4e3a\u534f\u4f5c\u8fdb\u7a0b(cooperation process)\uff0c\u800c\u8fdb\u7a0b\u95f4\u901a\u4fe1(Inter-Process Communication, IPC)\u652f\u6301\u4e86\u8fdb\u7a0b\u534f\u4f5c\uff0c\u4ee5\u5b9e\u73b0\u8fdb\u7a0b\u95f4\u7684\u6570\u636e\u4ea4\u6362\u3002</p> <ul> <li>\u4fe1\u53f7\u91cf(semaphores)\uff1b</li> <li>\u5171\u4eab\u5185\u5b58(shared memory)\uff1a<ul> <li>\u66f4\u5feb\uff0c\u9700\u8981\u7528\u5230 sys call \u7684\u5730\u65b9\u53ea\u6709\u5efa\u7acb\u5171\u4eab\u5185\u5b58\u7684\u65f6\u5019\u7528\u7684\u5230\u3002</li> </ul> </li> <li>\u6d88\u606f\u4f20\u9012(message passing)\uff1a<ul> <li>\u5728\u5206\u5e03\u5f0f\u7cfb\u7edf\u4e2d\u66f4\u5bb9\u6613\u5b9e\u73b0\uff0c\u5bf9\u4e8e\u5c11\u91cf\u6570\u636e\u901a\u4fe1\u5f88\u6709\u7528\uff08\u56e0\u4e3a\u4e0d\u9700\u8981\u5904\u7406\u51b2\u7a81\u95ee\u9898\uff09\u3002</li> </ul> </li> <li>\u6587\u4ef6 / \u7ba1\u9053(pipe)\uff1a<ul> <li>\u7ba1\u9053\u672c\u8d28\u4e0a\u4e5f\u662f\u4e00\u79cd\u6587\u4ef6\uff0c\u4f46\u4e00\u4e2a\u7ba1\u9053\u53ea\u652f\u6301\u5355\u5411\u4f20\u8f93\uff0c\u5373\u53ea\u80fd A \u5199 B \u8bfb\uff0c\u5982\u679c\u8981\u5b9e\u73b0\u53cc\u5411\u9700\u8981\u4e24\u4e2a\u7ba1\u9053\u3002</li> </ul> </li> </ul> <p> Communications models. (a) Shared memory. (b) Message passing.</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit1/#\u8fdb\u7a0b\u8c03\u5ea6","title":"\u8fdb\u7a0b\u8c03\u5ea6","text":"<p>\u591a\u9053\u6280\u672f\u5f15\u5165\u540e\uff0c\u5185\u5b58\u4e2d\u540c\u65f6\u5b58\u5728\u591a\u4e2a\u8fdb\u7a0b\uff0c\u8fdb\u7a0b\u7684\u6570\u91cf\u6211\u4eec\u79f0\u4e4b\u4e3a\u591a\u9053\u7684\u5ea6(degree of multiprogramming)\u3002\u4e00\u6bb5\u65f6\u95f4\u5185\u82e5\u5e72\u8fdb\u7a0b\u5e76\u53d1\u6267\u884c\uff0c\u56e0\u6b64\u8c03\u5ea6\u95ee\u9898(scheduling)\u2014\u2014CPU scheduler \u5c06\u51b3\u5b9a\u5728\u4f55\u65f6\u5c06 CPU \u8d44\u6e90\u5206\u914d\u7ed9\u54ea\u4e00\u4e2a\u5c31\u7eea\u8fdb\u7a0b\uff0c\u4f7f\u4e4b\u8fdb\u5165\u8fd0\u884c\u6001\u2014\u2014\u8fd9\u4e2a\u95ee\u9898\u5c31\u5f88\u91cd\u8981\u4e86\u3002\u603b\u4f53\u6765\u8bb2\uff0c\u6211\u4eec\u9700\u8981\u5b9e\u73b0\u4e00\u4e2a\u9ad8\u6548\u3001\u516c\u5e73\u7684\u7684\u8c03\u5ea6\uff0c\u4ee5\u6b64\u4fdd\u8bc1 CPU \u5229\u7528\u7387\u8db3\u591f\u9ad8\uff0c\u540c\u65f6\u53c8\u4fdd\u8bc1\u8ba1\u7b97\u673a\u529f\u80fd\u6b63\u5e38\u8fd0\u4f5c\u3002</p> <p> Diagram of process state.</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit1/#\u8c03\u5ea6\u7684\u65f6\u673a","title":"\u8c03\u5ea6\u7684\u65f6\u673a","text":"<p>\u6211\u4eec\u518d\u6b21\u5ba1\u89c6\u8fdb\u7a0b\u72b6\u6001\u7684 FSM\uff0c\u53d1\u73b0\u6240\u6709\u72b6\u6001\u90fd\u662f\u56f4\u7ed5\u7740 <code>ready</code>/<code>running</code> \u5c55\u5f00\u7684\uff0c\u800c CPU \u5177\u4f53\u8d44\u6e90\u5206\u914d\u7684\u8fc7\u7a0b\u4e5f\u6b63\u662f\u901a\u8fc7\u8fd9\u4e24\u4e2a\u72b6\u6001\u7684\u8f6c\u5316\u4f53\u73b0\u7684\u3002\u800c \u2776 \u5f53\u8fd0\u884c\u6001\u7684\u8fdb\u7a0b\u7531\u4e8e\u67d0\u4e9b\u539f\u56e0\u9700\u8981\u4e3b\u52a8\u79bb\u5f00\u8fd0\u884c\u6001\u65f6\uff0c\u6216 \u2777 \u5f53\u5c31\u7eea\u6001\u7684\u67d0\u4e2a\u8fdb\u7a0b\u9700\u8981\u7acb\u523b\u5f97\u5230 CPU \u8d44\u6e90\u65f6\uff0cscheduler \u4f1a\u8fdb\u884c\u8c03\u5ea6\u3002\u4e0a\u9762\u8fd9\u53e5\u8bdd\u53cd\u5e94\u5728\u3000FSM \u4e0a\uff0c\u5c31\u662f \u2776 \u8fdb\u7a0b\u4ece\u8fd0\u884c\u6001\u8f6c\u5316\u4e3a\u5176\u5b83\u72b6\u6001\uff0c\u5373\u7bad\u5934\u4ece <code>running</code> \u51fa\u53d1\u5411\u5916\uff1b\u2777 \u8fdb\u7a0b\u4ece\u5176\u5b83\u72b6\u6001\u8f6c\u5316\u4e3a\u5c31\u7eea\u6001\uff0c\u5373\u7bad\u5934\u4ece\u5916\u6307\u5411 <code>ready</code>\uff0c\u8fd9\u91cc\u5176\u5b9e\u8fd8\u6697\u542b\u4e86\u4e00\u4e2a <code>ready</code> \u6307\u5411 <code>ready</code> \u7684\u7bad\u5934\uff0c\u5728\u4f8b\u5982 priority aging \u7684\u60c5\u51b5\u4e0b\uff0c<code>ready</code> \u4e2d\u53ef\u80fd\u7a81\u7136\u6709\u4e00\u4e2a\u4f18\u5148\u7ea7\u8db3\u591f\u5927\u4e86\u5c31\u4f1a\u53d1\u751f\u62a2\u5360\u5f0f\u8c03\u5ea6\u3002\u4e0a\u9762\u63cf\u8ff0\u7684\u8fd9\u4e24\u79cd\u65f6\u673a\u4e0b\u4ea7\u751f\u7684\u8c03\u5ea6\uff0c\u5c31\u5206\u522b\u5b9a\u4e49\u4e3a\u975e\u62a2\u5360\u5f0f\u8c03\u5ea6(non-preemptive scheduling)\u548c\u62a2\u5360\u5f0f\u8c03\u5ea6(preemptive scheduling)\u3002</p> <p> Diagram of process state.</p> <p>\u4e24\u8005\u672c\u8d28\u4e0a\u7684\u533a\u522b\u5c31\u662f\uff0c\u975e\u62a2\u5360\u5f0f\u8c03\u5ea6\u662f\u7531\u5df2\u7ecf\u62e5\u6709\u8d44\u6e90\u7684\u8fdb\u7a0b\u4e3b\u52a8\u91ca\u653e CPU \u8d44\u6e90\u5f15\u8d77\u7684\uff0c\u800c\u62a2\u5360\u5f0f\u8c03\u5ea6\u5219\u662f\u4e0d\u5360\u6709\u8d44\u6e90\u7684\u8fdb\u7a0b\u7d22\u53d6 CPU \u8d44\u6e90\u6210\u529f\u5f15\u8d77\u7684\u3002</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit1/#\u8c03\u5ea6\u7684\u8fc7\u7a0b","title":"\u8c03\u5ea6\u7684\u8fc7\u7a0b","text":"<p>\u7531 CPU scheduler \u9009\u62e9\u54ea\u4e00\u4e2a\u5c31\u7eea\u6001\u7684\u5c06\u8981\u88ab\u6267\u884c\u540e\uff0c\u7531 dispatcher \u6765\u5b8c\u6210\u5177\u4f53\u7684\u5207\u6362\u5de5\u4f5c\u5305\u62ec\uff1a</p> <ol> <li>\u5728\u4e24\u4e2a\u8fdb\u7a0b\u95f4\u8fdb\u884c\u4e0a\u4e0b\u6587\u5207\u6362\uff1b</li> <li>\u5207\u6362\u5230\u7528\u6237\u6001\uff1b</li> <li>\u8df3\u8f6c\u5230\u7528\u6237\u7a0b\u5e8f\u4e2d\u5408\u9002\u7684\u4f4d\u7f6e\u4ee5\u7ee7\u7eed\u8fdb\u7a0b\u6267\u884c\uff1b</li> </ol> <p>\u800c\u4ece dispatcher \u505c\u6b62\u4e0a\u4e00\u4e2a\u8fd0\u884c\u65f6\u7684\u8fdb\u7a0b\uff0c\u5b8c\u6210\u4e0a\u4e0b\u6587\u5207\u6362\uff0c\u5e76\u542f\u52a8\u4e0b\u4e00\u4e2a\u8fdb\u7a0b\u7684\u5ef6\u65f6\uff0c\u79f0\u4e3a dispatch latency\u3002</p> <p></p> <p>\u4e0a\u4e0b\u6587\u5207\u6362</p> <p>\u5207\u6362\u8fdb\u7a0b\u7684\u65f6\u5019\u9700\u8981\u4fdd\u5b58\u201c\u73b0\u573a\u201d\uff0c\u5e76\u5728\u4e0b\u4e00\u6b21\u62ff\u51fa\u8fd9\u4e2a\u8fdb\u7a0b\u51c6\u5907\u6267\u884c\u4e4b\u524d\u6062\u590d\u201c\u73b0\u573a\u201d\uff0c\u4ee5\u6b64\u6765\u4fdd\u8bc1\u8fdb\u7a0b\u6267\u884c\u7684\u4e00\u81f4\u6027\u3002\u8fd9\u91cc\u63d0\u5230\u7684\u201c\u73b0\u573a\u201d\u88ab\u79f0\u4e3a\u4e0a\u4e0b\u6587(context)\uff0c\u8868\u793a\u4e00\u79cd\u201c\u8bed\u5883\u201d\uff1b\u800c\u4fdd\u62a4-\u6062\u590d\u7684\u8fc7\u7a0b\uff0c\u5c31\u662f\u4e0a\u9762\u63d0\u5230\u7684\u4e0a\u4e0b\u6587\u5207\u6362(context switch)\u3002</p> <p>\u5176\u4e2d\uff0c\u4e0a\u4e0b\u6587\u53ef\u80fd\u5305\u62ec \u2460 CPU \u5bc4\u5b58\u5668\u4e2d\u7684\u503c\uff0c\u2461 \u8fdb\u7a0b\u72b6\u6001\uff0c\u2462 \u5185\u5b58\u7684\u7ba1\u7406\u4fe1\u606f\u7b49\u3002</p> <p>\u4e0a\u4e0b\u6587\u5207\u6362\u7684\u76f8\u5173\u5185\u5bb9\u5728 Lab2 \u91cc\u6709\u6240\u6d89\u53ca\uff0c\u9700\u8981\u5b9e\u73b0\u4e00\u4e2a\u7b80\u5355\u7684\u4e0a\u4e0b\u6587\u5207\u6362\u3002</p> <p> (a) Diagram showing context switch from process to process. (b) Role of dispatcher.</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit1/#\u8c03\u5ea6\u7b97\u6cd5","title":"\u8c03\u5ea6\u7b97\u6cd5","text":"<p>\u5728\u8ba8\u8bba\u6709\u54ea\u4e9b\u8c03\u5ea6\u7b97\u6cd5\u4e4b\u524d\uff0c\u6211\u4eec\u9996\u5148\u9700\u8981\u77e5\u9053\u600e\u6837\u7b97\u4e00\u4e2a\u597d\u7684\u8c03\u5ea6\u7b97\u6cd5\u3002\u7c7b\u4f3c\u4e8e\u64cd\u4f5c\u7cfb\u7edf\u7684\u8bc4\u4ef7\uff0c\u8c03\u5ea6\u7b97\u6cd5\u7684\u8bc4\u4ef7\u6807\u51c6\u4e5f\u4e0d\u662f\u5355\u4e00\u7684\uff1b\u5bf9\u5e94\u7684\uff0c\u4e0d\u540c\u8c03\u5ea6\u7b97\u6cd5\u6709\u5404\u81ea\u7684\u4f18\u7f3a\u70b9\uff0c\u9700\u8981\u6839\u636e\u5b9e\u9645\u60c5\u51b5\u548c\u9700\u6c42\u6709\u6240\u9009\u62e9\u3002\u901a\u5e38\u6765\u8bf4\u6709\u8fd9\u4e9b\u8c03\u5ea6\u7b97\u6cd5\u7684\u6307\u6807(scheduling criteria)\uff1a</p> <ul> <li>CPU \u4f7f\u7528\u7387(CPU utilization)\uff1a<ul> <li>CPU \u4f7f\u7528\u65f6\u95f4 / \u603b\u65f6\u95f4\uff0c\u4ece CPU \u662f\u5426\u8db3\u591f\u5fd9\u788c\u6765\u770b\u786c\u4ef6\u6027\u80fd\u662f\u5426\u5145\u5206\u53d1\u6325\uff1b</li> </ul> </li> <li>\u541e\u5410\u91cf(throughput)\uff1a<ul> <li>\u5355\u4f4d\u65f6\u95f4\u5185\u5b8c\u6210\u7684\u8fdb\u7a0b\u6570\uff0c\u4ece\u7ed3\u679c\u6765\u770b\u4efb\u52a1\u5b8c\u6210\u662f\u5426\u8db3\u591f\u9ad8\u6548\uff1b</li> </ul> </li> <li>\u5468\u8f6c\u65f6\u95f4(turnaround time)\uff1a<ul> <li>\u4ece\u8fdb\u7a0b\u5f00\u59cb\u5efa\u7acb\u5230\u8fdb\u7a0b\u5b8c\u6210\u7684\u65f6\u95f4\uff0c\u5373\u5305\u62ec\u7b49\u5f85\u8fdb\u5165\u5185\u5b58\u3001\u5728\u5404\u79cd queue \u4e2d\u7684\u7b49\u5f85\u65f6\u95f4\u3001\u5728 CPU \u4e2d\u7684\u8fd0\u884c\u65f6\u95f4\u3001I/O \u65f6\u95f4\u7b49\uff0c\u901a\u8fc7\u89c2\u5bdf\u6700\u5927\u5468\u8f6c\u65f6\u95f4\uff0c\u80fd\u53cd\u5e94\u8c03\u5ea6\u7684\u6548\u7387\u548c\u201c\u516c\u5e73\u6027\u201d\uff1b</li> </ul> </li> <li>\u7b49\u5f85\u65f6\u95f4(waiting time)\uff1a<ul> <li>\u8fdb\u7a0b\u5728 ready queue \u4e2d\u7b49\u5f85\u7684\u65f6\u95f4\u7684\u603b\u548c\uff0c\u7531\u4e8e\u4efb\u52a1\u6240\u9700\u8981\u7684 CPU \u65f6\u95f4\u3001I/O \u65f6\u95f4\u4e0d\u53d7\u8c03\u5ea6\u7b97\u6cd5\u5f71\u54cd\uff0c\u6240\u4ee5\u629b\u5f00\u8fd9\u4e9b\u53ea\u770b\u5728 ready queue \u4e2d\u7684\u7b49\u5f85\u65f6\u95f4\uff0c\u80fd\u53cd\u5e94\u8c03\u5ea6\u7b97\u6cd5\u7684\u6548\u7387\uff1b</li> <li>\u5bb9\u6613\u53d1\u73b0\uff0c\u7b49\u5f85\u65f6\u95f4 = \u5468\u8f6c\u65f6\u95f4 - \u8fd0\u884c\u65f6\u95f4\uff1b</li> </ul> </li> <li>\u54cd\u5e94\u65f6\u95f4(response time)\uff1a<ul> <li>\u8fdb\u7a0b\u4ece\u53d1\u51fa\u8bf7\u6c42\u5230\u7b2c\u4e00\u6b21\u54cd\u5e94\u7684\u65f6\u95f4\uff0c\u80fd\u53cd\u5e94\u4ea4\u4e92\u5f0f\u7cfb\u7edf\u4e2d\u8c03\u5ea6\u7b97\u6cd5\u7684\u201c\u53ca\u65f6\u6027\u201d\uff1b</li> </ul> </li> </ul> <p>\u4e0a\u9762\u4e94\u4e2a\u524d\u4e24\u4e2a\u8d8a\u5927\u8d8a\u597d\uff0c\u540e\u4e09\u4e2a\u8d8a\u5c0f\u8d8a\u597d\u3002</p> <p>\u63a5\u4e0b\u6765\u6211\u4eec\u5f00\u59cb\u4ecb\u7ecd\u5404\u79cd\u8c03\u5ea6\u7b97\u6cd5\uff0c\u9700\u8981\u6ce8\u610f\u7684\u662f\uff0c\u5982\u4e0b\u8c03\u5ea6\u7b97\u6cd5\u4e2d\u5b58\u5728\u4e00\u4e9b\u7406\u60f3\u5316\u7684\u5efa\u6a21\uff08\u4f8b\u5982\u5047\u8bbe\u6211\u4eec\u77e5\u9053\u8fdb\u7a0b\u9700\u8981\u4f7f\u7528\u591a\u4e45 CPU\uff09\uff0c\u800c\u6211\u4eec\u91cd\u70b9\u9700\u8981\u638c\u63e1\u5b83\u7684\u601d\u8def\uff0c\u505a\u5230\u80fd\u753b\u7518\u7279\u56fe\u3001\u80fd\u7b97\u65f6\u95f4\u3002\u6b64\u5916\uff0c\u8fd9\u91cc\u6211\u4eec\u4ee5\u201c\u591a\u9053\u201d\u4e3a\u8bed\u5883\uff0c\u5373\u5982\u679c\u4e0d\u662f\u7279\u522b\u8bf4\u660e\uff0c\u4e0d\u8003\u8651\u5206\u65f6\u6280\u672f\u3002</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit1/#\u7b97\u6cd5--first-come-first-serve-fcfs","title":"\u7b97\u6cd5 | First-Come, First-Serve (FCFS)","text":"<p>FCFS \u662f\u6700\u57fa\u672c\u7684\u975e\u62a2\u5360\u5f0f\u8c03\u5ea6\u65b9\u6cd5\u5c31\u662f\u6309\u7167\u8fdb\u7a0b\u5148\u6765\u540e\u5230\u7684\u987a\u5e8f\u8fdb\u884c\u8c03\u5ea6\uff0c\u53ef\u4ee5\u5f88\u7b80\u5355\u5730\u901a\u8fc7\u4e00\u4e2a FIFO \u7684\u961f\u5217\u5b9e\u73b0\u3002FCFS \u6700\u5927\u7684\u4f18\u70b9\u5c31\u662f\u5b9e\u73b0\u7b80\u5355\u3002</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit1/#\u7b97\u6cd5--shortest-job-first-sjf--shortest-remaining-time-first-srtf","title":"\u7b97\u6cd5 | Shortest-Job-First (SJF) / Shortest-Remaining-Time-First (SRTF)","text":"<p>SJF \u7684\u601d\u8def\u662f\uff0c\u5f53\u6709\u591a\u4e2a\u8fdb\u7a0b\u5904\u4e8e\u5c31\u7eea\u6001\u65f6\uff0c\u9009\u62e9\u9700\u8981\u8fd0\u884c\u65f6\u95f4\u6700\u77ed\u7684\u8fdb\u7a0b\u5148\u8fd0\u884c\u3002\u8fd9\u79cd\u7b97\u6cd5\u7684\u4f18\u70b9\u662f\uff0c\u80fd\u591f\u4fdd\u8bc1\u5e73\u5747\u7b49\u5f85\u65f6\u95f4\u6700\u5c0f\uff1b\u4f46\u662f\u7f3a\u70b9\u662f\uff0c\u5982\u679c\u6709\u4e00\u4e2a\u8fdb\u7a0b\u9700\u8981\u8fd0\u884c\u65f6\u95f4\u5f88\u957f\uff0c\u90a3\u4e48\u5b83\u53ef\u80fd\u4f1a\u4e00\u76f4\u88ab\u63a8\u8fdf\uff0c\u4ece\u800c\u5bfc\u81f4\u201c\u9965\u997f\u201d\u73b0\u8c61\uff0c\u6b64\u5916\uff0c\u6211\u4eec\u5e76\u4e0d\u77e5\u9053\u8fdb\u7a0b\u8fd0\u884c\u65f6\u95f4\u6709\u591a\u4e45\u3002</p> \ud83c\udf30 \u9898\u9762\u89e3\u6790 <p>\u73b0\u5728\u6709\u4e09\u4e2a\u8fdb\u7a0b\uff0c\u5b83\u4eec\u5c06\u8981\u6267\u884c\u7684\u65f6\u95f4\u5206\u522b\u5982\u4e0b\uff1a</p> <ul> <li>P1: 24</li> <li>P2: 3</li> <li>P3: 3</li> </ul> <p>\u73b0\u5728\u5b83\u4eec\u6309\u7167\u987a\u5e8f\u8fdb\u5165 ready queue\uff0c\u8bf7\u5206\u522b\u8ba1\u7b97 FCFS \u4e0b\u548c SJF \u4e0b\u7684\u5e73\u5747\u7b49\u5f85\u65f6\u95f4\u3002</p> <p>\u9996\u5148\u770b FCFS\uff0c\u5373\u6309\u7167\u987a\u5e8f\u6267\u884c\uff0c\u753b\u51fa\u7518\u7279\u56fe\uff1a</p> <pre><code>gantt\n    title FCFS\n    dateFormat ss\n    axisFormat %S\n\n    section processes\n    P1: a, 00, 24\n    P2: b, 24, 27\n    P3: c, 27, 30</code></pre> <p>\u4e8e\u662f\u5e73\u5747\u7b49\u5f85\u65f6\u95f4\u4e3a \\((0 + 24 + 27) / 3 = 17\\)\u3002</p> <p>\u73b0\u5728\u6309\u7167 SJF \u6765\uff0c\u987a\u5e8f\u53d8\u4e3a P2 \u548c P3 \u5148\u6267\u884c\uff1a</p> <pre><code>gantt\n    title SJF\n    dateFormat ss\n    axisFormat %S\n\n    section processes\n    P2: a, 00, 03\n    P3: b, 03, 06\n    P1: c, 06, 30</code></pre> <p>\u4e8e\u662f\u5e73\u5747\u7b49\u5f85\u65f6\u95f4\u4e3a \\((0 + 3 + 6) / 3 = 3\\)\u3002</p> <p>\u53ef\u4ee5\u53d1\u73b0\uff0c\u4f7f\u7528 SJF \u4ee5\u540e\u5bf9\u4e8e\u8fd9\u79cd\u524d\u9762\u653e\u4e86\u4e2a\u5927\u4efb\u52a1\u7684\u60c5\u51b5\u5e73\u5747\u7b49\u5f85\u65f6\u95f4\u5927\u5927\u51cf\u5c11\u3002</p> <p>\u8fd9\u79cd\u505a\u6cd5\u53c8\u88ab\u79f0\u4e3a Shortest-Next-CPU-Burst\uff0c\u5b83\u662f\u4e00\u79cd\u975e\u62a2\u5360\u5f0f\u8c03\u5ea6\u7b97\u6cd5\uff0c\u4f46\u5047\u8bbe\u6211\u4eec\u5728\u6267\u884c\u4e00\u4e2a\u8fdb\u7a0b\u7684\u8fc7\u7a0b\u4e2d\uff0c\u6709\u4e00\u4e2a\u65b0\u7684\u8fdb\u7a0b\u52a0\u5165\u4e86 ready queue\uff0c\u800c\u4e14\u8fd9\u4e2a\u8fdb\u7a0b\u7684\u6267\u884c\u65f6\u95f4\u6bd4\u6b63\u5728\u8fd0\u884c\u7684\u8fdb\u7a0b\u7684\u5269\u4f59\u65f6\u95f4\u8fd8\u8981\u77ed\uff0c\u6211\u4eec\u4ecd\u7136\u9700\u8981\u7ee7\u7eed\u6267\u884c\u5b8c\u5f53\u524d\u7684\u8fdb\u7a0b\u624d\u884c\u2014\u2014\u56e0\u4e3a\u5b83\u662f\u975e\u62a2\u5360\u5f0f\u7684\u3002\u800c\u663e\u7136\u8fd9\u4e2a\u8fc7\u7a0b\u662f\u53ef\u4ee5\u901a\u8fc7\u62a2\u5360\u5f0f\u8c03\u5ea6\u6765\u4f18\u5316\u7684\uff0c\u4e8e\u662f\u6211\u4eec\u5f15\u5165\u4e86 Shortest-Remaining-Time-First (SRTF)\uff0c\u5176\u8868\u8ff0\u662f\uff1a\u603b\u662f\u6267\u884c\u5269\u4f59\u8fd0\u884c\u65f6\u95f4\u6700\u77ed\u7684\u8fdb\u7a0b\u3002\u5176\u4f18\u7f3a\u70b9\u4e0e SJF \u4e00\u81f4\u3002</p> <p>\u6211\u4eec\u53ea\u9700\u8981\u8003\u8651\u6240\u6709\u62a2\u5360\u5f0f\u8c03\u5ea6\u548c\u975e\u62a2\u5360\u5f0f\u8c03\u5ea6\u65f6\u673a\uff0c\u5e76\u9009\u62e9\u6b64\u65f6\u7684\u5269\u4f59\u8fd0\u884c\u65f6\u95f4\u6700\u77ed\u7684\u8fdb\u7a0b\u8fdb\u884c\u8c03\u5ea6\u5373\u53ef\u3002</p> <p>\u5982\u4f55\u5f97\u5230\u5269\u4f59\u65f6\u95f4</p> <p>\u6211\u4eec\u77e5\u9053\uff0c\u4e00\u4e2a\u7a0b\u5e8f\u8fd0\u884c\u6240\u9700\u8981\u7684\u65f6\u95f4\u662f\u4e00\u4e2a\u65e0\u6cd5\u5728\u8fd0\u884c\u7ed3\u675f\u524d\u5f97\u5230\u7684\u6570\u636e\uff0c\u56e0\u6b64\u4f7f\u7528\u8fd9\u4e2a\u4e1c\u897f\u8fdb\u884c\u8c03\u5ea6\u5c31\u663e\u5f97\u5341\u5206\u4e0d\u5408\u7406\u3002\u4f46\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u9884\u6d4b\u7684\u65b9\u6cd5\u4f30\u8ba1\u8fd0\u884c\u7684\u5269\u4f59\u65f6\u95f4\uff0c\u4f46\u662f\u65e2\u7136\u662f\u9884\u6d4b\u5c31\u4f1a\u6709\u4e0d\u51c6\u786e\uff0c\u6240\u4ee5 SJF/SRTF \u5e76\u4e0d\u80fd\u5b9e\u73b0\u7406\u8bba\u4e0a\u5e73\u5747\u7b49\u5f85\u65f6\u95f4\u6700\u4f18\u3002\u81f3\u4e8e\u5982\u4f55\u9884\u6d4b\uff0c\u4e66\u4e0a\u63d0\u4f9b\u4e86\u4e00\u4e2a\u53eb exponential average \u7684\u65b9\u6cd5\uff0c\u6211\u4eec\u5728\u8fd9\u91cc\u4e0d\u5c55\u5f00\u3002</p> \ud83c\udf30 \u9898\u9762\u89e3\u6790 <p>\u73b0\u5728\u6709\u4e09\u4e2a\u8fdb\u7a0b\uff0c\u5b83\u4eec\u5c06\u8981\u6267\u884c\u7684\u65f6\u95f4\u5206\u522b\u5982\u4e0b\uff1a</p> <ul> <li>P1: 8</li> <li>P2: 4</li> <li>P3: 9</li> <li>P4: 5</li> </ul> <p>\u5b83\u4eec\u5230\u8fbe ready queue \u7684\u65f6\u95f4\u5206\u522b\u5982\u4e0b\uff1a</p> <ul> <li>P1: 0</li> <li>P2: 1</li> <li>P3: 2</li> <li>P4: 3</li> </ul> <p>\u8bf7\u5206\u522b\u8ba1\u7b97 SJF \u4e0b\u548c SRTF \u4e0b\u7684\u5e73\u5747\u7b49\u5f85\u65f6\u95f4\u3002</p> <p>\u5bf9\u4e8e SJF \u6765\u8bf4\uff0c\u5728\u7b2c 0 \u65f6\u523b\uff0c\u53ea\u6709 P1 \u53ef\u7528\uff0c\u6240\u4ee5\u53ea\u80fd\u6267\u884c P1\uff1bP1 \u6267\u884c\u7ed3\u675f\u540e\u6240\u6709\u5176\u5b83\u8fdb\u7a0b\u90fd\u53ef\u7528\u4e86\uff0c\u6b64\u65f6\u6309\u7167\u6b63\u5e38\u7684 SJF \u5373\u53ef\u5f97\u5230\u7ed3\u679c\u3002</p> <pre><code>gantt\n    title SJF\n    dateFormat ss\n    axisFormat %S\n\n    section P1\n    run: a, 00, 08\n\n    section P2\n    ready: b, 01, 08\n    run: e, 08, 12\n\n    section P3\n    ready: c, 02, 17\n    run: 17, 26\n\n    section P4\n    ready: d, 03, 12\n    run: f, 12, 17</code></pre> <p>\u6b64\u65f6\u5e73\u5747\u7b49\u5f85\u65f6\u95f4\u4e3a \\((0 + 7 + 15 + 9) / 4 = 7.75\\)\u3002</p> <p>\u5bf9\u4e8e SRFT \u6765\u8bf4\uff0c\u540c\u6837\u4ece P1 \u5f00\u59cb\u6267\u884c\uff0c\u4f46\u662f\u7b2c\u4e00\u79d2 P2 \u8fdb\u5165\uff0c\u53d1\u73b0\u6b64\u65f6 P1 \u8fd8\u5269\u4e0b 7\uff0c\u800c P2 \u53ea\u9700\u8981 4\uff0c\u4e8e\u662f P2 \u9700\u8981\u62a2\u5360 P1 \u7684\u8d44\u6e90\uff1b\u4e4b\u540e\u7684\u8fc7\u7a0b\u7c7b\u4f3c</p> <pre><code>gantt\n    dateFormat ss\n    axisFormat %S\n\n    section P1\n    run: a, 00, 01\n    ready(rest 7): e, 01, 10\n    run: g, 10, 17\n\n    section P2\n    run: b, 01, 05\n\n    section P3\n    ready(rest 9): c, 02, 17\n    run: h, 17, 26\n\n    section P4\n    ready(rest 5): d, 03, 05\n    run: f, 05, 10</code></pre> <p>\u6b64\u65f6\u5e73\u5747\u7b49\u5f85\u65f6\u95f4\u4e3a \\(((0+9) + 0 + 15 + 2) / 4 = 6.5\\)\u3002</p> <p>\u53ef\u4ee5\u53d1\u73b0 SRTF \u80fd\u591f\u63d0\u5347 SJF \u7684\u6548\u7387\u3002</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit1/#\u7b97\u6cd5--round-robin-rr","title":"\u7b97\u6cd5 | Round-Robin (RR)","text":"<p>RR \u8c03\u5ea6\u5c31\u662f\u4f7f\u7528\u5206\u65f6\u6280\u672f\u540e\u7684 FCFS \u8c03\u5ea6\uff0c\u56e0\u6b64\u5b83\u4e5f\u662f\u975e\u62a2\u5360\u5f0f\u7684\u3002\u6bcf\u4e00\u4e2a\u8fdb\u7a0b\u6700\u591a\u8fde\u7eed\u6267\u884c\u4e00\u4e2a\u65f6\u95f4\u7247\u7684\u957f\u5ea6\uff0c\u5b8c\u6210\u540e\u88ab\u63d2\u5165\u5230 FIFO ready queue \u7684\u672b\u5c3e\uff0c\u5e76\u53d6\u51fa FIFO ready queue \u7684\u961f\u9996\u8fdb\u884c\u6267\u884c\u3002</p> <p>\u6211\u4eec\u4e4b\u524d\u63d0\u5230\u5206\u65f6\u7684\u65f6\u5019\u4e5f\u8bf4\u8fc7\uff0c\u5206\u65f6\u6280\u672f\u901a\u8fc7\u4f18\u5316\u54cd\u5e94\u65f6\u95f4\u89e3\u51b3\u4e86\u7528\u6237\u4ea4\u4e92\u95ee\u9898\uff0cRR \u8c03\u5ea6\u867d\u7136\u76f8\u6bd4 SJF \u6709\u4e86\u66f4\u957f\u7684\u7b49\u5f85\u65f6\u95f4\uff0c\u4f46\u662f\u6709\u4e86\u66f4\u77ed\u7684\u54cd\u5e94\u65f6\u95f4\uff0c\u800c\u5b9e\u9645\u76f4\u63a5\u5f71\u54cd\u7528\u6237\u4ea4\u4e92\u95ee\u9898\u7684\u5e94\u8be5\u662f\u54cd\u5e94\u65f6\u95f4\u3002</p> <p>\u4e00\u4e2a\u9700\u8981\u6ce8\u610f\u7684\u662f\uff0cRR \u8c03\u5ea6\u6709\u4e00\u4e2a\u201c\u8d85\u53c2\u6570\u201d\uff0c\u5373\u65f6\u95f4\u7247\u7684\u957f\u5ea6\u3002\u7406\u8bba\u4e0a\uff0c\u65f6\u95f4\u7247\u7ea6\u77ed\uff0c\u54cd\u5e94\u65f6\u95f4\u8d8a\u77ed\uff1b\u4f46\u66f4\u77ed\u7684\u65f6\u95f4\u7247\u5c06\u5e26\u6765\u66f4\u9891\u7e41\u7684\u8fdb\u7a0b\u5207\u6362\uff0c\u4ece\u800c\u5e26\u6765\u66f4\u591a\u7684 dispatch latency\u3002</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit1/#\u7b97\u6cd5--priority-scheduling","title":"\u7b97\u6cd5 | Priority Scheduling","text":"<p>\u4f18\u5148\u7ea7\u8c03\u5ea6\u7684\u601d\u8def\u662f\uff0c\u6bcf\u4e2a\u8fdb\u7a0b\u90fd\u6709\u4e00\u4e2a\u4f18\u5148\u7ea7\uff0c\u5f53\u6709\u591a\u4e2a\u8fdb\u7a0b\u5904\u4e8e\u5c31\u7eea\u6001\u65f6\uff0c\u9009\u62e9\u4f18\u5148\u7ea7\u6700\u9ad8\u7684\u8fdb\u7a0b\u5148\u8fd0\u884c\u3002\u8fd9\u79cd\u7b97\u6cd5\u7684\u4f18\u70b9\u662f\uff0c\u80fd\u591f\u4fdd\u8bc1\u4f18\u5148\u7ea7\u9ad8\u7684\u8fdb\u7a0b\u4f18\u5148\u8fd0\u884c\uff1b\u4f46\u662f\u7f3a\u70b9\u662f\uff0c\u5982\u679c\u6709\u4e00\u4e2a\u8fdb\u7a0b\u7684\u4f18\u5148\u7ea7\u5f88\u9ad8\uff0c\u90a3\u4e48\u5b83\u53ef\u80fd\u4f1a\u4e00\u76f4\u88ab\u63a8\u8fdf\uff0c\u4ece\u800c\u5bfc\u81f4\u201c\u9965\u997f\u201d\u73b0\u8c61\u3002</p> <p>\u4f60\u53ef\u80fd\u53d1\u73b0\u4e86\uff0c\u5982\u679c\u628a\u4e0a\u9762\u8fd9\u53e5\u8bdd\u7684\u201c\u4f18\u5148\u7ea7\u6700\u9ad8\u201d\u6539\u6210\u201c\u8fd0\u884c\u65f6\u95f4\u6700\u77ed\u201d/\u201c\u5269\u4f59\u8fd0\u884c\u65f6\u95f4\u6700\u77ed\u201d\uff0c\u90a3\u5c31\u548c SJF/SRTF \u4e00\u6a21\u4e00\u6837\u4e86\uff0cSJF/SRTF \u5b9e\u9645\u4e0a\u5c31\u662f\u4f18\u5148\u7ea7\u8c03\u5ea6\u7684\u4e00\u4e2a\u7279\u4f8b\uff0c\u56e0\u800c\u4f18\u5148\u7ea7\u8c03\u5ea6\u5f53\u7136\u662f\u53ef\u4ee5\u5b9e\u73b0\u62a2\u5360\u5f0f\u548c\u975e\u62a2\u5360\u5f0f\u4e24\u79cd\u7684\u3002</p> <p>\u6b64\u5916\uff0c\u4f18\u5148\u7ea7\u7684\u5206\u914d\u53ef\u4ee5\u6839\u636e\u4f7f\u7528\u9700\u6c42\u8fdb\u884c\u8bbe\u8ba1\uff0c\u5b83\u53ef\u80fd\u662f\u4e00\u4e9b\u6d4b\u91cf\u6570\u636e\uff0c\u4e5f\u53ef\u80fd\u5177\u6709\u4e00\u4e9b\u88ab\u8d4b\u4e88\u7684\u610f\u4e49\uff0c\u751a\u81f3\u53ef\u4ee5\u662f\u4e00\u4e9b\u590d\u5408\u7684\u503c\uff1b\u4f18\u5148\u7ea7\u4e5f\u5e76\u4e0d\u4e00\u5b9a\u662f\u9759\u6001\u7684\uff0c\u5148\u524d\u6211\u4eec\u63d0\u5230\u8fc7\u7684\u9965\u997f\u95ee\u9898\uff0c\u5c31\u53ef\u4ee5\u901a\u8fc7\u52a8\u6001\u7684\u4f18\u5148\u7ea7\u6765\u89e3\u51b3\uff1a\u4f18\u5148\u7ea7\u968f\u7740\u7b49\u5f85\u65f6\u95f4\u589e\u52a0\u4e0d\u65ad\u589e\u957f\uff0c\u7b49\u5f85\u8fc7\u4e45\u7684\u4efb\u52a1\u5c31\u4f1a\u88ab\u8d4b\u4e88\u8f83\u9ad8\u7684\u4f18\u5148\u7ea7\uff0c\u4ee5\u6b64\u907f\u514d\u9965\u997f\u7684\u53d1\u751f\uff0c\u8fd9\u79cd\u7b56\u7565\u53eb priority aging\u3002</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit1/#\u8bbe\u8ba1--multilevel-queue-scheduling","title":"\u8bbe\u8ba1 | Multilevel Queue Scheduling","text":"<p>\u65e2\u7136\u8c03\u5ea6\u7b97\u6cd5\u591a\u79cd\u591a\u6837\uff0c\u4ed6\u4eec\u9002\u914d\u4e0d\u540c\u7684\u9700\u6c42\uff0c\u90a3\u80fd\u5426\u53ea\u5728\u7279\u5b9a\u60c5\u51b5\u4e0b\u4f7f\u7528\u7279\u5b9a\u7b97\u6cd5\u5462\uff1f\u7b54\u6848\u662f\u80af\u5b9a\u7684\uff0c\u6211\u4eec\u53ef\u4ee5\u5c06 ready queue \u5206\u6210\u591a\u4e2a\u961f\u5217\uff0c\u6bcf\u4e2a\u961f\u5217\u4f7f\u7528\u4e0d\u540c\u7684\u8c03\u5ea6\u7b97\u6cd5\uff0c\u7136\u540e\u518d\u8fdb\u884c\u961f\u5217\u95f4\u8c03\u5ea6\uff0c\u8fd9\u79cd\u65b9\u6cd5\u88ab\u79f0\u4e3a\u591a\u7ea7\u961f\u5217\u8c03\u5ea6(multilevel queue scheduling)\u3002</p> <p>\ud83c\udf30</p> <p>\u4e00\u4e2a\u64cd\u4f5c\u7cfb\u7edf\u6309\u7167\u4f18\u5148\u7ea7\u5148\u540e\uff0c\u53ef\u80fd\u6709\u8fd9\u4e48\u4e9b\u961f\u5217\uff1a</p> <ol> <li>Real-time processes</li> <li>System processes</li> <li>Interactive processes</li> <li>Batch processes</li> </ol> <p>\u5b83\u4eec\u7684\u4f18\u5148\u7ea7\u968f\u7740 1 -&gt; 4 \u9012\u51cf\uff0c\u800c\u5f53\u4f18\u5148\u7ea7\u66f4\u9ad8\u7684\u961f\u5217\u4e2d\u5b58\u5728\u4efb\u52a1\u65f6\uff0c\u4f18\u5148\u7ea7\u4f4e\u7684\u961f\u5217\u4fbf\u4e0d\u4f1a\u53c2\u4e0e\u8c03\u5ea6\u3002\u4e0d\u4ec5\u5982\u6b64\uff0c\u9ad8\u4f18\u5148\u7ea7\u7684\u961f\u5217\u4e2d\u51fa\u73b0\u65b0\u7684\u4efb\u52a1\u65f6\uff0c\u4e5f\u4f1a\u62a2\u5360\u6b63\u5728\u8fd0\u884c\u7684\u4f4e\u4f18\u5148\u7ea7\u961f\u5217\u7684\u4efb\u52a1\u3002</p> <p>\ud83c\udf30</p> <p>\u53c8\u6bd4\u5982\uff0c\u4e00\u4e2a\u64cd\u4f5c\u7cfb\u7edf\u53ef\u80fd\u5206\u524d\u53f0(foreground)\u7a0b\u5e8f\u961f\u5217\u548c\u540e\u53f0(background)\u7a0b\u5e8f\u961f\u5217\uff0c\u800c\u6211\u4eec\u4f7f\u7528\u65f6\u95f4\u7247\u6765\u8fdb\u884c\u961f\u5217\u95f4\u8c03\u5ea6\uff0c\u4f46\u524d\u53f0\u5360\u7528 80% \u7684\u65f6\u95f4\uff0c\u800c\u540e\u53f0\u5360\u7528 20% \u7684\u65f6\u95f4\u3002</p> <p>\u800c\u5728\u961f\u5217\u5185\u90e8\uff0c\u6211\u4eec\u4e5f\u53ef\u4ee5\u6839\u636e\u9700\u6c42\u4f7f\u7528\u4e0d\u540c\u7684\u961f\u5217\u5185\u8c03\u5ea6\u7b97\u6cd5\u3002\u5728\u8fd9\u4e2a\u4f8b\u5b50\u4e2d\uff0c\u7531\u4e8e\u524d\u53f0\u7a0b\u5e8f\u5f80\u5f80\u8981\u6c42\u66f4\u597d\u7684\u54cd\u5e94\u65f6\u95f4\u8868\u73b0\uff0c\u6240\u4ee5\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528 RR \u8c03\u5ea6\uff1b\u800c\u5728\u540e\u53f0\u4f7f\u7528 FCFS \u8c03\u5ea6\u3002</p> <p>Windows XP Scheduling</p> <ul> <li>windows-xp-scheduling</li> </ul>"},{"location":"cour_note/D3QD_OperatingSystem/Unit1/#\u8bbe\u8ba1--multilevel-feedback-queue-scheduling","title":"\u8bbe\u8ba1 | Multilevel Feedback Queue Scheduling","text":"<p>\u66f4\u8fdb\u4e00\u6b65\uff0cMultilevel Feedback Queue Scheduling \u5728 Multilevel Queue Scheduling \u7684\u57fa\u7840\u4e0a\uff0c\u5141\u8bb8\u8fdb\u7a0b\u5728\u961f\u5217\u95f4\u8f6c\u79fb\uff0c\u4ee5\u6b64\u5b9e\u73b0\u66f4\u7075\u6d3b\u66f4\u79d1\u5b66\u7684\u8c03\u5ea6\u3002\u4f8b\u5982\uff0c\u4e00\u4e2a\u8fdb\u7a0b\u5982\u679c\u4f7f\u7528\u4e86\u8fc7\u957f\u7684 CPU \u65f6\u95f4\uff0c\u5b83\u53ef\u80fd\u88ab\u79fb\u52a8\u5230\u4f18\u5148\u7ea7\u66f4\u4f4e\u7684\u961f\u5217\uff1b\u76f8\u53cd\uff0c\u5982\u679c\u4e00\u4e2a\u8fdb\u7a0b\u7b49\u5f85\u4e86\u592a\u4e45\uff0c\u5b83\u53ef\u80fd\u88ab\u79fb\u52a8\u5230\u4f18\u5148\u7ea7\u66f4\u9ad8\u7684\u961f\u5217\u3002</p> <p>\u5f53\u7136\uff0c\u76f8\u5bf9\u5e94\u7684\uff0c\u7b97\u6cd5\u590d\u6742\u5ea6\u4e5f\u4f1a\u63d0\u9ad8\u4e0d\u5c11\u3002</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit1/#\u7ebf\u7a0b","title":"\u7ebf\u7a0b","text":"<p>\u7ebf\u7a0b\u662f\u4e00\u79cd\u8f7b\u91cf\u7ea7\u7684\u8fdb\u7a0b\uff0c\u5b83\u5728\u8fdb\u7a0b\u7684\u57fa\u7840\u4e0a\u8fdb\u884c\u5212\u5206\uff0c\u662f\u8fdb\u7a0b\u5185\u7684\u4e00\u4e2a\u53ef\u8c03\u5ea6\u7684\u6267\u884c\u5355\u5143\uff0c\u4ee5\u51cf\u5c0f\u8fdb\u7a0b folk \u548c\u5207\u6362\u7684\u5f00\u9500\u4e3a\u76ee\u7684\u3002</p> <p>\u540c\u4e00\u8fdb\u7a0b\u7684\u82e5\u5e72\u7ebf\u7a0b\u5171\u4eab\u4ee3\u7801\u3001\u6570\u636e\u7b49\u201c\u76f8\u5bf9\u9759\u6001\u201d\u7684\u8d44\u6e90\uff0c\u800c\u5404\u81ea\u7ef4\u62a4\u5bc4\u5b58\u5668\u3001\u6808\u3001PC \u7b49\u201c\u76f8\u5bf9\u52a8\u6001\u201d\u7684\u8d44\u6e90\uff1b\u6216\u8005\u8bf4\u7ebf\u7a0b\u53ea\u62e5\u6709\u4e00\u4e9b\u8fd0\u884c\u4e2d\u5fc5\u4e0d\u53ef\u7701\u7684\u8d44\u6e90\uff0c\u800c\u6240\u6709\u5176\u5b83\u8d44\u6e90\u90fd\u5c5e\u4e8e\u8fdb\u7a0b\uff0c\u7ebf\u7a0b\u4e0e\u8fdb\u7a0b\u4e2d\u7684\u5176\u5b83\u7ebf\u7a0b\u5171\u4eab\u8fd9\u4e9b\u8d44\u6e90\uff0c\u4ee5\u6b64\u6765\u51cf\u5c11\u8fdb\u7a0b\u521b\u5efa\u8fc7\u7a0b\u4e2d\u590d\u5236\u4ee3\u7801\u6bb5\u7b49\u8d44\u6e90\u65f6\u5e26\u6765\u7684\u4e0d\u5c0f\u5f00\u9500\u3002</p> <p></p> <p>\u7ebf\u7a0b\u5929\u751f\u548c\u540c\u4e00\u8fdb\u7a0b\u5185\u7684\u5176\u5b83\u7ebf\u7a0b\u5171\u4eab\u8d44\u6e90\uff0c\u56e0\u6b64\u540c\u8fdb\u7a0b\u5185\u7ebf\u7a0b\u5929\u751f\u5c31\u6709\u7ebf\u7a0b\u95f4\u901a\u4fe1\u7684\u80fd\u529b\u3002\u540c\u65f6\uff0c\u7531\u4e8e\u5c06\u8fdb\u7a0b\u8fdb\u884c\u4e86\u518d\u5212\u5206\uff0c\u4e00\u65b9\u9762\u5728\u786c\u4ef6\u652f\u6301\u7684\u60c5\u51b5\u4e0b\u80fd\u66f4\u597d\u5730\u9002\u914d\u5e76\u884c\uff0c\u53e6\u4e00\u65b9\u9762\u4e5f\u80fd\uff08\u4ee3\u4ef7\u66f4\u5c0f\u5730\uff09\u8ba9\u4efb\u52a1\u7684\u7c92\u5ea6\u53d8\u5c0f\uff0c\u6b64\u65f6\u53ef\u4ee5\u5c06\u6574\u4e2a\u8fdb\u7a0b\u7684\u963b\u585e\u8f6c\u79fb\u5230\u5355\u4e2a\u7ebf\u7a0b\u7684\u963b\u585e\u4e0a\uff0c\u8fdb\u4e00\u6b65\u51cf\u5c11\u54cd\u5e94\u65f6\u95f4\u3002</p> <p>\u5f53\u7136\uff0c\u7531\u4e8e\u8fd9\u91cc\u5b58\u5728\u4e00\u4e2a\u90e8\u5206\u6574\u4f53\u7684\u5173\u7cfb\uff0c\u5373\u5b58\u5728\u4e00\u4e2a\u201c\u5c06\u82e5\u5e72\u9e21\u86cb\u653e\u5728\u540c\u4e00\u4e2a\u7bee\u5b50\u91cc\u201d\u7684\u95ee\u9898\uff0c\u867d\u7136\u5c06\u82e5\u5e72\u4efb\u52a1\u90fd\u653e\u5230\u4e00\u4e2a\u8fdb\u7a0b\u7684\u591a\u7ebf\u7a0b\u53ef\u4ee5\u63d0\u9ad8\u6548\u7387\uff0c\u4f46\u662f\u4e00\u65e6\u201c\u7bee\u5b50\u201d\u574f\u4e86\uff0c\u90a3\u6240\u6709\u201c\u9e21\u86cb\u201d\u90fd\u65e0\u6cd5\u5e78\u514d\uff1b\u5176\u6b21\uff0c\u867d\u7136\u5929\u7136\u7684\u5171\u4eab\u5c5e\u6027\u8ba9\u7ebf\u7a0b\u80fd\u66f4\u65b9\u4fbf\u5730\u8fdb\u884c\u7ebf\u7a0b\u95f4\u901a\u4fe1\uff0c\u4f46\u4e5f\u5e26\u6765\u4e86\u5185\u5b58\u4fdd\u62a4\u7684\u95ee\u9898\u3002</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit1/#\u591a\u7ebf\u7a0b\u6a21\u578b","title":"\u591a\u7ebf\u7a0b\u6a21\u578b","text":"<p>\u6309\u7167\u7ebf\u7a0b\u5212\u5206\u7684\u5b9e\u73b0\u4f4d\u7f6e\uff0c\u591a\u7ebf\u7a0b\u6a21\u578b\u5206\u4e3a\u7528\u6237\u7ea7\u591a\u7ebf\u7a0b(user threads)\u548c\u5185\u6838\u7ea7\u591a\u7ebf\u7a0b(kernel threads)\u3002</p> <p>\u7528\u6237\u7ea7\u591a\u7ebf\u7a0b\u5728\u7528\u6237\u7a7a\u95f4\u5b9e\u73b0\u591a\u7ebf\u7a0b\uff0c\u5373\u4f7f\u7528\u7ebf\u7a0b\u5e93(thread library)\u5229\u7528\u5355\u4e2a\u8fdb\u7a0b\u7684\u8d44\u6e90\uff0c\u5728\u7528\u6237\u7a7a\u95f4\u7ef4\u62a4\u591a\u4e2a\u7ebf\u7a0b\uff1b\u800c\u5185\u6838\u7ea7\u591a\u7ebf\u7a0b\u5219\u662f\u7531\u5185\u6838\u652f\u6301\u591a\u7ebf\u7a0b\u64cd\u4f5c\u3002\u4e24\u8005\u5404\u6709\u4f18\u7f3a\u70b9\uff1a</p> <ul> <li>\u7528\u6237\u7ea7\u591a\u7ebf\u7a0b &gt; \u5185\u6838\u7ea7\u591a\u7ebf\u7a0b<ul> <li>\u7528\u6237\u7ea7\u591a\u7ebf\u7a0b\u4e0d\u9700\u8981\u5185\u6838\u652f\u6301\u591a\u7ebf\u7a0b\uff0c\u4e0d\u9700\u8981\u8fdb\u5165\u5185\u6838\u6001\u5b9e\u73b0\u591a\u7ebf\u7a0b\uff0c\u4e5f\u4e0d\u9700\u8981\u5360\u7528\u7ebf\u7a0b ID\uff0c\u56e0\u6b64\u7406\u8bba\u4e0a\u53ef\u4ee5\u6bd4\u5185\u6838\u7ea7\u652f\u6301\u66f4\u591a\u7684\u7ebf\u7a0b\u6570\uff1b</li> <li>\u7531\u4e8e\u5176\u5212\u5206\u662f\u9488\u5bf9\u8fdb\u7a0b\u7684\uff0c\u800c\u4e0d\u540c\u8fdb\u7a0b\u4e4b\u95f4\u7684\u7ebf\u7a0b\u5b9e\u73b0\u6ca1\u6709\u76f4\u63a5\u5173\u7cfb\uff0c\u800c\u4e14\u7531\u4e8e\u662f\u5728\u7528\u6237\u7a7a\u95f4\u5b9e\u73b0\u7b97\u6cd5\uff0c\u6240\u4ee5\u80fd\u591f\u66f4\u5bb9\u6613\u7684\u5bf9\u5355\u4e2a\u8fdb\u7a0b\u5185\u7684\u591a\u4e2a\u7ebf\u7a0b\u7684\u8c03\u5ea6\u7b97\u6cd5\u8fdb\u884c\u81ea\u5b9a\u4e49\uff1b</li> </ul> </li> <li>\u7528\u6237\u7ea7\u591a\u7ebf\u7a0b &lt; \u5185\u6838\u7ea7\u591a\u7ebf\u7a0b<ul> <li>\u7531\u4e8e\u5bf9\u5185\u6838\u6765\u8bf4\uff0c\u7528\u6237\u7ea7\u591a\u7ebf\u7a0b\u4ecd\u7136\u662f\u4e00\u4e2a\u666e\u901a\u7684\u8fdb\u7a0b\uff0c\u6240\u4ee5\u5f53\u7528\u6237\u7ea7\u7684\u7ebf\u7a0b\u51fa\u73b0\u963b\u585e\u65f6\uff0c\u5185\u6838\u4f1a\u8ba4\u4e3a\u6574\u4e2a\u8fdb\u7a0b\u90fd\u88ab\u963b\u585e\uff1b\u5185\u6838\u7ea7\u7ebf\u7a0b\u7531\u4e8e\u662f\u5185\u6838\u5b9e\u73b0\uff0c\u6240\u4ee5\u5355\u7ebf\u7a0b\u7684\u963b\u585e\u5e76\u4e0d\u4f1a\u5bfc\u81f4\u6574\u4e2a\u8fdb\u7a0b\u963b\u585e\uff1b</li> <li>\u5728\u591a\u6838\u7684\u60c5\u51b5\u4e0b\uff0c\u7528\u6237\u7ea7\u591a\u7ebf\u7a0b\u6ca1\u6cd5\u5229\u7528\u591a\u6838\u8fdb\u884c\u7ebf\u7a0b\u5e76\u884c\uff1b\u663e\u7136\u5185\u6838\u591a\u7ea7\u7ebf\u7a0b\u662f\u505a\u5f97\u5230\u8fd9\u4e00\u70b9\u7684\uff1b</li> </ul> </li> </ul> <p>\u9700\u8981\u6ce8\u610f\u7684\u662f\uff0c\u7528\u6237\u7ea7\u591a\u7ebf\u7a0b\u548c\u5185\u6838\u7ea7\u591a\u7ebf\u7a0b\u5e76\u4e0d\u51b2\u7a81\uff0c\u56e0\u800c\u6392\u5217\u7ec4\u5408\u540e\u5f97\u5230\u591a\u7ebf\u7a0b\u4e3b\u8981\u6709\u5982\u4e0b\u4e09\u79cd\u6a21\u578b\uff1a</p> <p> (a) Many-to-many model. (b) One-to-one model. (c) Many-to-one model.</p> <p>Linux \u7ebf\u7a0b</p> <ul> <li>Linux \u7ebf\u7a0b</li> </ul> <ol> <li> <p>Where memory will be allocated to \"Uninitialized Static variable\" upon initialization? \u21a9</p> </li> <li> <p>What process is the parent of the init process in Linux? \u21a9</p> </li> <li> <p>Linux CreateProcess? \u21a9</p> </li> <li> <p>Differences between fork and exec? \u21a9</p> </li> </ol>"},{"location":"cour_note/D3QD_OperatingSystem/Unit2-Part1/","title":"U2 Part 1: \u540c\u6b65\u5de5\u5177 | Synchronization Tools","text":"<p> \u7ea6 7937 \u4e2a\u5b57  215 \u884c\u4ee3\u7801  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 29 \u5206\u949f</p> <p>\u5f15\u5165</p> <p>\u9996\u5148\u6211\u4eec\u7b80\u5355\u63cf\u8ff0\u4ec0\u4e48\u662f\u540c\u6b65\u95ee\u9898\uff0c\u8bfb\u8005\u53ef\u4ee5\u62b1\u7740\u5bf9\u4e0b\u9762\u8fd9\u6bb5\u8bdd\u7684\u7591\u95ee\u53bb\u9605\u8bfb\u63a5\u4e0b\u6765\u7684\u5185\u5bb9\u3002</p> <p>\u4e0d\u5fc5\u5c1d\u8bd5\u7acb\u523b\u7406\u89e3\u8fd9\u6bb5\u8bdd\uff0c\u6211\u5e0c\u671b\u8bfb\u8005\u80fd\u591f\u5728\u770b\u7684\u8fc7\u7a0b\u4e2d\u4ee5\u4e0b\u9762\u8fd9\u6bb5\u8bdd\u4e3a\u4e3b\u7ebf\uff0c\u731c\u6d4b\u63a5\u4e0b\u6765\u5c06\u8981\u5c55\u5f00\u7684\u5185\u5bb9\uff0c\u53bb\u53d1\u73b0\u95ee\u9898\u3001\u601d\u8003\u89e3\u51b3\u529e\u6cd5\u3002</p> <p>\u5728\u652f\u6301\u5e76\u53d1\u751a\u81f3\u5e76\u884c\u7684\u7cfb\u7edf\u4e2d\uff0c\u867d\u7136\u8fdb\u7a0b\u4e4b\u95f4\u76f8\u5bf9\u9694\u79bb\uff0c\u5728\u4e00\u822c\u60c5\u51b5\u4e0b\u4e92\u4e0d\u76f4\u63a5\u5e72\u6270\uff0c\u81ea\u987e\u81ea\u8dd1\u2014\u2014\u5373\u662f\u5f02\u6b65\u7684\uff1b\u4f46\u7531\u4e8e\u5404\u4e9b\u539f\u56e0\uff08\u4f8b\u5982\u90fd\u9700\u8981\u5bf9\u4e00\u5171\u4eab\u8d44\u6e90\u7684\u4fee\u6539\uff09\uff0c\u8fdb\u7a0b\u4e4b\u95f4\u7684\u6267\u884c\u9700\u8981\u4e92\u76f8\u5236\u7ea6\uff0c\u9075\u5faa\u7279\u5b9a\u7684\u5148\u540e\u987a\u5e8f\uff0c\u56e0\u6b64\u8fdb\u7a0b\u9700\u8981\u901a\u8fc7\u67d0\u4e9b\u624b\u6bb5\uff0c\u8ba9\u534f\u4f5c\u8fdb\u7a0b\u80fd\u591f\u76f4\u63a5\u6216\u95f4\u63a5\u4e86\u89e3\u5230\u5176\u5b83\u76f8\u5173\u8fdb\u7a0b\u7684\u72b6\u6001\uff0c\u4ee5\u5b9e\u73b0\u5bf9\u5f53\u524d\u8fdb\u7a0b\u6267\u884c\u7684\u63a7\u5236\uff0c\u6700\u7ec8\u5728\u5b8f\u89c2\u4e0a\u5b9e\u73b0\u540c\u6b65\u63a7\u5236\u3002</p> <p>\u800c\u4e0a\u9762\u63d0\u5230\u7684\u201c\u5404\u79cd\u539f\u56e0\u201d\u548c\u201c\u67d0\u4e9b\u624b\u6bb5\u201d\uff0c\u5c31\u662f\u6211\u4eec\u7a0d\u540e\u5c06\u8ba8\u8bba\u7684\u4e1c\u897f\uff0c\u5176\u4e2d\uff0c\u8fd9\u91cc\u7684\u201c\u67d0\u4e9b\u624b\u6bb5\u201d\uff0c\u5c31\u662f\u6307\u6211\u4eec\u7684\u5404\u79cd\u540c\u6b65\u5de5\u5177\u3002</p> <p>\u9700\u8981\u6ce8\u610f\u7684\u662f\uff0c\u540c\u6b65\u5e76\u4e0d\u662f\u67d0\u79cd\u4e2d\u592e\u8c03\u63a7\u673a\u5236\uff0c\u800c\u66f4\u50cf\u662f\u4e00\u79cd\u201c\u534f\u8bae\u201d\uff0c\u5f53\u5404\u4e2a\u8fdb\u7a0b\u53d1\u73b0\u6709\u522b\u7684\u8fdb\u7a0b\u4e0e\u81ea\u5df1\u4ea7\u751f\u7ade\u4e89\u65f6\uff0c\u5e94\u5f53\u6709\u67d0\u79cd\u624b\u6bb5\u5141\u8bb8\u5b83\u4eec\u8fbe\u6210\u534f\u5546\uff0c\u4ee5\u51b3\u5b9a\u8c01\u5148\u8c01\u540e\u3002</p> <p>\u6211\u4eec\u6309\u7167\u95ee\u9898\u7684\u590d\u6742\u7a0b\u5ea6\uff0c\u7531\u6d45\u5165\u6df1\u5730\u8ba8\u8bba\u8fd9\u4e9b\u4e1c\u897f\u3002</p> <p>\u8bed\u5883\u95ee\u9898</p> <p>\u4e00\u4e2a\u6bd4\u8f83\u5c34\u5c2c\u7684\u95ee\u9898\u662f\uff0c\u4e66\u672c\u4e0a\u4ee5\u534f\u4f5c\u8fdb\u7a0b\u7684\u8bed\u5883\u4e3a\u5f00\u7bc7\uff0c\u4f46\u63a5\u4e0b\u6765\u8bb2\u7684\u6709\u4e9b\u5185\u5bb9\u662f\u4ee5\u7ebf\u7a0b\u540c\u6b65\u4e3a\u8bed\u5883\uff08\u5bf9\u4e8e\u8fd9\u4e2a\u95ee\u9898\u6211\u5df2\u7ecf\u653e\u5f03\u53bb\u68b3\u7406\u548c\u7ea0\u6b63\u4e66\u4e2d\u7684\u63aa\u8f9e\u4e86\uff0c\u7d2f\u4e86\uff09\uff0c\u5982\u679c\u5728\u7528\u8bcd\u4e0a\u90fd\u533a\u5206\u7ebf\u7a0b\u548c\u8fdb\u7a0b\uff0c\u90a3\u4e48\u4f1a\u53d8\u5f97\u5f88\u7e41\u6742\uff0c\u6240\u4ee5\u6211\u63a5\u4e0b\u6765\u4e00\u5f8b\u7528\u8fdb\u7a0b\u8868\u793a\uff0c\u4f46\u8bfb\u8005\u5fc3\u4e2d\u5e94\u5f53\u5bf9\u8fd9\u4e2a\u8bed\u5883\u66f4\u9002\u4e8e\u7ebf\u7a0b\u8fd8\u662f\u8fdb\u7a0b\u6709\u6240\u611f\u53d7\u3002</p> <p>\u5173\u4e8e\u8fd9\u4e9b\u65b9\u6cd5\u66f4\u9002\u5408\u5728 process \u8fd8\u662f thread \u4e0a\u88ab\u5e94\u7528\uff0c\u53ef\u4ee5\u770b\u8fd9\u4e2a\u3002</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit2-Part1/#\u7ade\u6001\u6761\u4ef6","title":"\u7ade\u6001\u6761\u4ef6","text":"<p>Links</p> <ul> <li>Race Condition | Wikipedia</li> </ul> <p>\u6211\u4eec\u9700\u8981\u610f\u8bc6\u5230\uff0c\u6211\u4eec\u65e0\u6cd5\u4e00\u6b65\u5230\u4f4d\u5730\u3001in-place \u5730\u53bb\u4fee\u6539\u4e00\u4e2a\u5185\u5b58\u4e2d\u7684\u6570\u636e\uff0c\u6362\u8a00\u4e4b\uff0c\u8981\u60f3\u4fee\u6539 <code>mem[x]</code>\uff0c\u6211\u4eec\u9700\u8981\u4e09\u4e2a\u6b65\u9aa4\uff1a</p> <ol> <li><code>reg</code> &lt;- <code>mem[x]</code>\uff1b</li> <li><code>reg</code> &lt;- update(<code>reg</code>)\uff1b</li> <li><code>mem[x]</code> &lt;- <code>reg</code>\uff1b</li> </ol> <p>\u800c\u5982\u679c\u73b0\u5728\u4e0d\u6b62\u4e00\u4e2a\u8fdb\u7a0b\u5728\u4fee\u6539 <code>mem[x]</code>\uff0c\u4f8b\u5982\u4e0b\u9762\u8fd9\u4e2a\u4f8b\u5b50\uff1a</p> <pre><code>\u250c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u252c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2510\n\u2502 process A    \u2502 process B    \u2502 mem[x] = 1 (initial)\n\u251c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u253c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2524\n\u2502 t0 &lt;- mem[x] \u2502 t0 &lt;- mem[x] \u2502 mem[x] = 1\n\u2502 t0 &lt;- t0 + 1 \u2502 t0 &lt;- t0 + 1 \u2502\n\u2502 mem[x] &lt;- t0 \u2502 t0 &lt;- t0 + 1 \u2502 mem[x] = 2, B's t0 is out of date\n\u2502              \u2502 mem[x] &lt;- t0 \u2502 mem[x] = 3, 2 is overwritten\n\u2514\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2534\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2518\n</code></pre> <p>\u5b83\u4eec\u90fd\u60f3\u8981\u66f4\u65b0 <code>mem[x]</code>\uff0c\u53c8\u597d\u5de7\u4e0d\u5de7\u7684\u5b83\u4eec\u51e0\u4e4e\u540c\u65f6\u53d1\u751f\u8bfb\u53d6\u4e86 <code>mem[x]</code>\uff0c\u90a3\u4e48\u5c31\u4f1a\u51fa\u73b0\u95ee\u9898\uff1a\u4e24\u4e2a\u8fdb\u7a0b\u540c\u65f6\u8bfb\u53d6 <code>mem[x]</code>\uff0c\u7136\u540e\u5404\u81ea\u8ba1\u7b97\u66f4\u65b0\u540e\u7684\u503c\uff0c\u7136\u540e\u5404\u81ea\u5199\u56de <code>mem[x]</code>\uff0c\u7406\u60f3\u60c5\u51b5\u4e0b\uff0c\u6700\u7ec8\u7684 <code>mem[x]</code> \u4f1a\u6bd4\u539f\u6765\u5927 3\uff0c\u4f46\u73b0\u5728\u7684 <code>mem[x]</code> \u53ea\u6bd4\u539f\u6765\u5927 2\uff0c\u5176\u4e2d process A \u5bf9\u5b83\u7684\u4fee\u6539\u5728\u7b2c 7 \u884c\u88ab\u8986\u76d6\u4e86\u3002</p> <p>\u7a76\u5176\u6839\u672c\uff0c\u7531\u4e8e\u5982\u4eca\u6211\u4eec\u5904\u5728\u5e76\u53d1\u8bed\u5883\u4e0b\uff0c\u6240\u4ee5\u4f1a\u51fa\u73b0\u82e5\u5e72\u7528\u6237\u540c\u65f6\u6301\u6709\u4e00\u4efd\u6570\u636e\u8d44\u6e90\u7684\u60c5\u51b5\uff08\u4e3a\u4e86\u53d1\u6325\u5e76\u53d1\u7684\u4f18\u52bf\uff0c\u6211\u4eec\u4e5f\u5e94\u5f53\u5c3d\u53ef\u80fd\u7684\u6ee1\u8db3\u8fd9\u79cd\u9700\u6c42\uff09\uff0c\u903b\u8f91\u4e0a\u6570\u636e\u4fee\u6539\u8fc7\u7a0b\u5e94\u5f53\u662f\u7b26\u53f7\u7684\u3001\u77ac\u95f4\u7684\u3001\u7acb\u5373\u751f\u6548\u7684\uff0c\u4f46\u5b9e\u9645\u4e0a\u6211\u4eec\u5bf9\u6570\u636e\u7684\u64cd\u4f5c\u662f\u6570\u503c\u7684\u3001\u9700\u8981\u4e00\u6bb5\u65f6\u95f4\u6765\u5b8c\u6210\u7684\u3002\u5728\u8fd9\u79cd\uff08\u540e\u8005\uff09\u8bed\u5883\u4e0b\uff0c\u5982\u679c\u6211\u4eec\u65e0\u6cd5\u4fdd\u8bc1\u8bfb\u5165\u6570\u503c\u5b8c\u6210\u5230\u5199\u5165\u6570\u503c\u5b8c\u6210\u7684\u8fc7\u7a0b\u4e2d\uff0c<code>mem[x]</code> \u4fdd\u6301\u4e0d\u53d8\uff0c\u90a3\u4e48\u8be5\u64cd\u4f5c\u5b9e\u9645\u4e0a\u662f\u4f7f\u7528\u8fc7\u65f6\u6570\u636e\u8fdb\u884c\u8ba1\u7b97\u3002</p> <pre><code>\u250c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u252c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2510\n\u2502 process A    \u2502 process B    \u2502 mem[x] = 1 (initial)\n\u251c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u253c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2524\n\u2502 t0 &lt;- mem[x] \u2502 t0 &lt;- mem[x] \u2502 mem[x] = 1\n\u2502 t0 &lt;- t0 + 1 \u2502 t0 &lt;- t0 + 1 \u2502\n\u2502 mem[x] &lt;- t0 \u2502 t0 &lt;- t0 + 1 \u2502 mem[x] = 2, B's t0 is out of date\n\u2502              \u2502 mem[x] &lt;- t0 \u2502 mem[x] = 3, 2 is overwritten\n\u2514\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2534\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2518\n</code></pre> <p>\u53ef\u4ee5\u53d1\u73b0\uff0c\u7b2c\u516d\u884c\u7684 <code>t0</code> \u4ecd\u7136\u5728\u7528\u66f4\u65b0\u4e4b\u524d\u7684 <code>mem[x]</code> \u505a\u8ba1\u7b97\uff0c\u56e0\u800c\u53ef\u4ee5\u8ba4\u4e3a\u6b64\u65f6 process B \u4e2d\u7684 <code>t0</code> \u53c2\u4e0e\u8fd0\u7b97\u7684\u3001\u6697\u542b\u7684 <code>mem[x]</code> \u7684\u6570\u636e\u5df2\u7ecf\u8fc7\u65f6\u3002</p> <p>race condition</p> <p>\u7c7b\u4f3c\u8fd9\u79cd\u7684\uff0c\u7531\u4e24\u4e2a\u4fe1\u53f7\u4ea7\u751f\u7ade\u4e89\uff0c\u5176\u7ade\u4e89\u60c5\u51b5\u5f71\u54cd\u6700\u7ec8\u7ed3\u679c\u7684\u60c5\u51b5\uff0c\u88ab\u79f0\u4e3a\u7ade\u6001\u6761\u4ef6(race condition)\u3002\u5728\u4e0a\u9762\u8fd9\u4e2a\u4f8b\u5b50\u4e2d\uff0c\u8c01\u540e\u6267\u884c\uff0c\u6700\u7ec8\u7ed3\u679c\u5c31\u662f\u8c01\u7684\u8f93\u51fa\uff0c\u800c\u53e6\u4e00\u4e2a\u7528\u6237\u7684\u8f93\u51fa\u5219\u4f1a\u88ab\u8986\u76d6\u3002</p> <p>\u9700\u8981\u6ce8\u610f\u7684\u662f\uff0c\u8fd9\u91cc\u7684\u91cd\u70b9\u5e76\u4e0d\u662f\u201c\u5982\u4f55\u63a7\u5236\u7ade\u4e89\u7ed3\u679c\u201d\uff0c\u56e0\u4e3a\u65e0\u8bba\u7ade\u4e89\u7ed3\u679c\u5982\u4f55\uff08\u751a\u81f3\u8c01\u8d62\u4e86\u7ed3\u679c\u53ef\u80fd\u90fd\u4e00\u6837\uff09\uff0c\u53ea\u8981\u8fd9\u79cd\u201c\u7ade\u4e89\u201d\u51fa\u73b0\uff0c\u90a3\u4e48\u6700\u7ec8\u7ed3\u679c\u5c31\u6709\u53ef\u80fd\u4e0d\u7b26\u5408\u9884\u671f\u7684\u3002 \u771f\u6b63\u7684\u91cd\u70b9\u5e94\u8be5\u662f\u5982\u4f55\u907f\u514d\u8fd9\u79cd\u7ade\u4e89\u7684\u51fa\u73b0\u3002</p> <p>\u5c31\u6bd4\u5982\u4e0a\u9762\u7684\u4f8b\u5b50\uff0c\u65e0\u8bba\u6700\u7ec8 <code>mem[x]</code> \u662f 3 \u8fd8\u662f 2 \u90fd\u4e0d\u5bf9\uff0c\u7406\u60f3\u60c5\u51b5\u4e0b\u5e94\u8be5\u662f 4\u2014\u2014\u65e0\u8bba\u662f\u5148\u8fdb\u884c <code>+1</code> \u8fd8\u662f\u5148\u8fdb\u884c <code>+2</code>\u3002</p> <p>\u6ce8\u610f</p> <p>\u867d\u7136\u4e0a\u9762\u7684\u4f8b\u5b50\u4e2d\u6211\u4eec\u6a21\u62df\u7684\u4e24\u4e2a\u7a0b\u5e8f\u662f\u6309\u7167\u76f8\u540c\u901f\u5ea6\uff0c\u4e00\u884c\u4e00\u4e2a\u6307\u4ee4\u6267\u884c\u7684\uff0c\u4f46\u662f\u6211\u4eec\u5728\u5e76\u884c\u8bed\u5883\u4e0b\u5bf9\u6240\u6709\u8fdb\u7a0b\u6267\u884c\u7684\u901f\u5ea6\u4e0d\u5e94\u5f53\u6709\u6240\u5047\u8bbe\uff0c\u5373\u8fdb\u7a0b A \u4e0d\u77e5\u9053\u8fdb\u7a0b B \u7684\u901f\u5ea6\u3002</p> <p>\u4e0d\u4ec5\u5982\u6b64\uff0c\u6211\u4eec\u4e5f\u5e76\u4e0d\u4e00\u5b9a\u8981\u5728\u5e76\u884c\u8bed\u5883\u4e0b\u8ba8\u8bba\u8fd9\u4e2a\u95ee\u9898\uff0c\u5728\u591a\u9053\u8bed\u5883\u4e0b\u8fd9\u4e2a\u95ee\u9898\u90fd\u4f1a\u51fa\u73b0\uff0c\u4f8b\u5982\uff1a</p> <pre><code>\u250c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2510     \u250c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2510\n\u2502 process A    \u2502     \u2502 process B    \u2502 mem[x] = 1 (initial)\n\u251c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2524     \u251c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2524\n\u2502              \u2502     \u2502 t0 &lt;- mem[x] \u2502 mem[x] = 1\n\u2502 t0 &lt;- mem[x] \u2502\u25c4\u2500\u2500\u2500\u2500\u2524 &lt;ctx switch&gt; \u2502 mem[x] = 1\n\u2502 t0 &lt;- t0 + 1 \u2502     \u2502              \u2502\n\u2502 mem[x] &lt;- t0 \u2502     \u2502              \u2502 mem[x] = 2, B's t0 is out of date\n\u2502 &lt;ctx switch&gt; \u251c\u2500\u2500\u2500\u2500\u25ba\u2502 t0 &lt;- t0 + 1 \u2502\n\u2502              \u2502     \u2502 t0 &lt;- t0 + 1 \u2502 \n\u2502              \u2502     \u2502 mem[x] &lt;- t0 \u2502 mem[x] = 3, 2 is overwritten\n\u2514\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2518     \u2514\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2518\n</code></pre> <p>\u95ee\u9898\u4f9d\u65e7\u3002</p> <p>\u6839\u636e\u4e0a\u9762\u8fd9\u4e2a\u5177\u4f53\u7684\u4f8b\u5b50\uff0c\u6211\u4eec\u53d1\u73b0\uff0c\u5982\u679c\u9700\u8981\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\uff0c\u6211\u4eec\u6709\u4e24\u79cd\u9009\u62e9\uff1a</p> <ol> <li>\u8fdb\u884c\u7b26\u53f7\u7684\u8fd0\u7b97\u800c\u975e\u6570\u503c\u7684\u8fd0\u7b97\uff0c\u8fd9\u6837\u8f93\u5165\u7684\u53d8\u5316\u80fd\u5728\u4efb\u610f\u65f6\u523b\u53cd\u6620\u5728\u8f93\u51fa\u4e0a\uff0c\u8fd9\u6837\u65f6\u65f6\u523b\u523b\u90fd\u662f\u201c\u6700\u65b0\u201d\uff0c\u800c\u4e0d\u4f1a\u51fa\u73b0\u201c\u8fc7\u65f6\u201d\uff1b</li> <li>\u4fdd\u8bc1\u8bfb\u5165\u6570\u503c\u5b8c\u6210\u5230\u5199\u5165\u6570\u503c\u5b8c\u6210\u7684\u8fc7\u7a0b\u4e2d\uff0c<code>mem[x]</code> \u4fdd\u6301\u4e0d\u53d8\uff0c\u5373\u4e24\u4e2a\u53ef\u80fd\u7ade\u4e89\u7684\u64cd\u4f5c\uff0c\u5728\u65f6\u95f4\u4e0a\u4e0d\u5e94\u8be5\u6709\u4ea4\u96c6\uff1b</li> </ol> <p>\u663e\u7136\uff0c\u6211\u4eec\u5e94\u5f53\u9009\u62e9\u7b2c\u4e8c\u79cd\u3002</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit2-Part1/#the-critical-section-problem","title":"The Critical-Section Problem","text":"<p>\u4e3a\u4e86\u66f4\u597d\u5730\u5c55\u5f00\uff0c\u6211\u4eec\u5bf9\u4e0a\u9762\u7684\u8fd9\u79cd\u60c5\u51b5\u8fdb\u884c\u5efa\u6a21\uff0c\u5e76\u7ed9\u51fa\u89e3\u51b3 race condition \u95ee\u9898\u7684\u65b9\u6cd5\u9700\u8981\u6ee1\u8db3\u7684\u8303\u5f0f\uff1a</p> <p>\u6211\u4eec\u5e94\u5f53\u4fdd\u8bc1\u5728\u4e00\u4e2a\u8fdb\u7a0b\u5728\u4fee\u6539 <code>mem[x]</code> \u7684\u65f6\u5019\uff0c\u5176\u5b83\u8fdb\u7a0b\u4e0d\u5e94\u8be5\u8bfb\u53d6 <code>mem[x]</code>\uff08\u81f3\u5c11\u4e0d\u5e94\u4ee5\u4fee\u6539 <code>mem[x]</code> \u4e3a\u76ee\u7684\u6765\u8bfb\u53d6\uff09\uff0c\u76f4\u5230\u8fd9\u4e2a\u8fdb\u7a0b\u5b8c\u6210\u4e86\u5bf9 <code>mem[x]</code> \u7684\u4fee\u6539\u3002\u6362\u53e5\u8bdd\u6765\u8bf4\uff0c<code>mem[x]</code> \u8fd9\u4e2a\u5171\u4eab\u8d44\u6e90\u5e94\u5f53\u53ea\u80fd\u88ab\u4e00\u4e2a\u7528\u6237\u6301\u6709\uff0c\u6211\u4eec\u79f0\u8fd9\u79cd\u53ea\u80fd\u88ab\u81f3\u591a\u4e00\u4e2a\u7528\u6237\u5360\u6709\u7684\u8d44\u6e90\u4e3a\u4e34\u754c\u8d44\u6e90\u3002\u800c\u7a0b\u5e8f\u4e2d\u8bbf\u95ee\u4e34\u754c\u8d44\u6e90\u7684\u4ee3\u7801\u6bb5\uff0c\u6211\u4eec\u79f0\u4e4b\u4e3a\u4e34\u754c\u533a\u6bb5(critical section, CS)\ud83d\udd17\u3002</p> <p>\u90a3\u4e48\uff0c\u5bf9\u4e8e\u4e4b\u524d\u63d0\u5230\u8fc7\u7684\u4f8b\u5b50\uff0c\u6211\u4eec\u62ff\u51fa\u6765\u5bf9\u6bd4\u6a21\u62df\u7684\u90e8\u5206\u5c31\u662f critical section\u3002</p> <p>\u800c CS \u95ee\u9898\uff0c\u6307\u7684\u5c31\u662f\u5982\u4f55\u4fdd\u8bc1\u6700\u591a\u53ea\u6709\u4e00\u4e2a\u7528\u6237\u5728\u6267\u884c\u4e34\u754c\u533a\u6bb5\u7684\u4ee3\u78011\u3002</p> <p>\u56f4\u7ed5\u4e34\u754c\u533a\u6bb5\uff0c\u6211\u4eec\u5b9a\u4e49\u80fd\u591f\u89e3\u51b3 CS \u95ee\u9898\u7684\u4ee3\u7801\u5e94\u5f53\u80fd\u591f\u505a\u5982\u4e0b\u5212\u5206\uff1a</p> <pre><code>\u250c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2510\n\u2502  Entry Section      \u2502 &lt;-- ask for &amp; wait for permission to enter CS\n\u251c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2524\n\u2502  Critical Section   \u2502 &lt;-- codes manipulating critical resources\n\u251c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2524\n\u2502  Exit Section       \u2502 &lt;-- release the critical resources\n\u251c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2524\n\u2502  Remainder Section  \u2502 &lt;-- other codes\n\u2514\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2518\n</code></pre> <p>\u8fdb\u7a0b\u9700\u8981\u5728 entry section \u5224\u65ad\u662f\u5426\u80fd\u591f\u8fdb\u5165 critical section\uff0c\u5373\u7d22\u53d6\u4e34\u754c\u8d44\u6e90\uff0c\u5982\u679c\u4e0d\u884c\u5219\u7b49\u5f85\uff1b\u800c\u5728\u8fdb\u5165 critical section \u540e\uff0c\u8fdb\u7a0b\u9700\u8981\u5728 exit section \u91ca\u653e\u4e34\u754c\u8d44\u6e90\uff1b\u7136\u540e\u8131\u79bb CS \u95ee\u9898\u7684\u8bed\u5883\uff0c\u8fdb\u5165 remainder section \u7ee7\u7eed\u6267\u884c\u3002</p> <p>Brainstorming</p> <p>\u6574\u4e2a\u8fc7\u7a0b\u6709\u70b9\u50cf\u8c03\u5ea6\uff0c\u7b49\u5f85\u4e34\u754c\u8d44\u6e90\u7684\u8fc7\u7a0b\u5c31\u597d\u50cf ready \u6001\u7b49\u5f85\u8c03\u5ea6\u8fc7\u7a0b\u4e2d\u7684 CPU \u8d44\u6e90\uff08CPU \u4e5f\u53ef\u4ee5\u8ba4\u4e3a\u662f\u4e00\u79cd\u4e34\u754c\u8d44\u6e90\uff0c\u53ea\u4e0d\u8fc7\u5b83\u4e0d\u662f\u7531\u8fdb\u7a0b\u4e3b\u52a8\u5904\u7406\u548c\u7d22\u53d6\uff09\u3002</p> <p>\u65e2\u7136\u5982\u6b64\u6211\u4eec\u53ef\u4ee5\u8fc1\u79fb\u201c\u72b6\u6001\u201d\u8fd9\u4e2a\u6982\u5ff5\u3002\u6211\u4eec\u53ea\u5173\u5fc3\u76f4\u63a5\u4e0e CS \u95ee\u9898\u6709\u5173\u7684\u72b6\u6001\uff0c\u6240\u4ee5\u6211\u5728\u8fd9\u91cc\u5b9a\u4e49\uff1a\u5c31\u7eea\u3001\u4e34\u754c\u3001\u65e0\u5173\u4e09\u4e2a\u72b6\u6001\u3002</p> <ol> <li>\u5c31\u7eea\u6001\uff1a\u8fdb\u7a0b\u968f\u65f6\u51c6\u5907\u597d\u8fdb\u5165 critical section\uff0c\u60f3\u8981\u6301\u6709\u4e34\u754c\u8d44\u6e90\uff1b</li> <li>\u4e34\u754c\u6001\uff1a\u8fdb\u7a0b\u6b63\u5728\u6267\u884c critical section\uff0c\u6301\u6709\u4e34\u754c\u8d44\u6e90\uff0c\u6216\u8fdb\u7a0b\u6267\u884c\u5b8c critical section\uff0c\u6267\u884c exit section \u6b63\u5728\u91ca\u653e\u6301\u6709\u7684\u4e34\u754c\u8d44\u6e90\u4e2d\uff1b</li> <li>\u65e0\u5173\u6001\uff1a\u4e0d\u5904\u4e8e\u5c31\u7eea\u6001\u4e5f\u4e0d\u5904\u4e8e\u4e34\u754c\u6001\uff0c\u4e0d\u60f3\u8981\u6301\u6709\u4e34\u754c\u8d44\u6e90\uff0c\u6216\u662f\u4f7f\u7528\u5b8c\u5df2\u7ecf\u91ca\u653e\uff1b</li> </ol> <p>\u6839\u636e\u6211\u4eec\u5148\u524d\u7ed9\u51fa\u7684\uff0c\u89e3\u6cd5\u9700\u8981\u6ee1\u8db3\u7684\u6027\u8d28\u4e2d\u7684 mutual exclusion\uff0c\u4e0d\u80fd\u540c\u65f6\u6709\u591a\u4e2a\u8fdb\u7a0b\u5904\u4e8e\u4e34\u754c\u6001\uff0c\u4f46\u662f\u53ef\u4ee5\u6709\u82e5\u5e72\u8fdb\u7a0b\u5904\u4e8e\u5c31\u7eea\u6001\uff0c\u800c\u65e0\u5173\u6001\u5219\u8868\u793a\u4e0d\u4f1a\u4ea7\u751f\u7ade\u4e89\uff0c\u548c\u8c03\u5ea6\u8fc7\u7a0b\u5341\u5206\u76f8\u4f3c\u3002</p> <p>\u8fd9\u4e9b\u5b9a\u4e49\u5c06\u4f1a\u5728\u6211\u4eec\u4e4b\u540e\u7684\u63a2\u7d22\u4e2d\u8d77\u4f5c\u7528\u3002</p> <p>\u540c\u65f6\uff0c\u6211\u4eec\u8981\u6c42\u89e3\u51b3\u65b9\u6848\u9700\u8981\u6ee1\u8db3\u5982\u4e0b\u6027\u8d28\uff1a</p> <p></p> <p>requirements for solution to CS problem</p> <ol> <li>\u4e34\u754c\u4e92\u65a5(mutual exclusion)\uff1a\u64cd\u4f5c\u540c\u4e00\u4e34\u754c\u8d44\u6e90\u7684\u4e34\u754c\u533a\u6bb5\u5e94\u5f53\u4e92\u76f8\u6392\u65a5\uff1b<ul> <li>\u5982\u679c\u8fdb\u7a0b \\(P_i\\) \u6b63\u5728\u6267\u884c\u5176 critical section\uff0c\u90a3\u4e48\u4e0d\u5e94\u5f53\u6709\u5176\u4ed6\u8fdb\u7a0b\u5904\u4e8e\uff08\u64cd\u4f5c\u540c\u4e00\u4e34\u754c\u8d44\u6e90\u7684\uff09critical section\uff1b</li> </ul> </li> <li>\u9009\u62e9\u65f6\u95f4\u6709\u9650(progress)\uff1a\u9009\u62e9\u4e0b\u4e00\u4e2a\u8fdb\u5165 critical section \u7684\u64cd\u4f5c\u5e94\u5f53\u53ea\u6709\u5904\u4e8e entry/critical/exit section \u7684\u8fdb\u7a0b\u53c2\u4e0e\uff0c\u4e14\u8be5\u9009\u62e9\u5e94\u5f53\u5728\u6709\u9650\u65f6\u95f4\u5185\u88ab\u6267\u884c\uff1b</li> <li>\u7b49\u5f85\u65f6\u95f4\u6709\u9650(bounded waiting)\uff1a\u8fdb\u7a0b\u7b49\u5f85\u88ab\u5141\u8bb8\u8fdb\u5165 critical section \u7684\u65f6\u95f4\u5e94\u5f53\u662f\u6709\u9650\u7684\uff1b</li> </ol> <p>\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u4ee5\u8ba8\u8bba CS \u95ee\u9898\u662f\u5982\u4f55\u89e3\u51b3\u7684\u4e3a\u4e3b\u7ebf\uff0c\u63a2\u7d22\u5982\u4f55\u89e3\u51b3 race condition\u3002</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit2-Part1/#for-kernel-code","title":"For Kernel Code","text":"<p>\u7531\u4e8e kernel code \u4e0b\u7684 CS \u95ee\u9898\u89e3\u51b3\u8f83\u4e3a\u6e05\u6670\u76f4\u63a5\uff0c\u6240\u4ee5\u5148\u884c\u4ecb\u7ecd\u3002</p> <p>For Kernel Code</p> <p>\u5728 kernel code \u4e2d\u4e5f\u666e\u904d\u5b58\u5728\u7740 race condition \u7684\u95ee\u9898\uff0c\u4f8b\u5982\uff1a</p> <p>  Race condition when assigning a pid. </p> <p>\u4e0a\u4f8b\u4e2d \\(P_0\\) \u548c \\(P_1\\) \u540c\u65f6\u8bbf\u95ee\u4e86 <code>next_available_pid</code> \u8fd9\u4e2a\u4e34\u754c\u8d44\u6e90\uff0c\u4ea7\u751f\u7ade\u4e89\uff0c\u5bfc\u81f4\u6700\u540e\u6709\u4e24\u4e2a\u8fdb\u7a0b\u4f7f\u7528\u4e86\u540c\u4e00\u4e2a <code>pid</code>\u3002</p> <p>\u6b32\u89e3\u51b3 kernel code \u4e2d\u7684 CS \u95ee\u9898\uff0c\u6211\u4eec\u53ef\u4ee5\u4fdd\u8bc1\u53ea\u6709\u4e00\u4e2a\u8fdb\u7a0b\u53ef\u4ee5\u8fd0\u884c\u5728 kernel mode\uff0c\u8fd9\u6837\u5c31\u53ef\u4ee5\u4fdd\u8bc1\u5728 kernel code \u4e2d\u8bbf\u95ee\u4e34\u754c\u8d44\u6e90\u7684\u884c\u4e3a\uff0c\u4ece\u800c\u89e3\u51b3 CS \u95ee\u9898\u3002</p> <p>\u5bf9\u4e8e\u5355\u5904\u7406\u5668\u6765\u8bf4\uff0c\u6211\u4eec\u53ea\u9700\u8981\u5728 kernel code \u4e2d\u7981\u6b62\u4e2d\u65ad\uff0c\u5c31\u53ef\u4ee5\u4fdd\u8bc1\u53ea\u6709\u4e00\u4e2a\u8fdb\u7a0b\u53ef\u4ee5\u8fd0\u884c\u5728 kernel mode\uff1b\u800c\u5bf9\u4e8e\u591a\u5904\u7406\u5668\u6765\u8bf4\uff0c\u8fd9\u79cd\u65b9\u6cd5\u5c31\u4e0d\u90a3\u4e48\u5408\u9002\u4e86\u2014\u2014\u6211\u4eec\u9700\u8981\u540c\u65f6\u544a\u8bc9\u591a\u4e2a\u5904\u7406\u5668\u4e2d\u65ad\u88ab\u7981\u6b62\uff0c\u800c\u8fd9\u4e2a\u8fc7\u7a0b\u4e2d\u7684\u65f6\u5ef6\u4ecd\u7136\u4f1a\u4ea7\u751f\u95ee\u9898\uff1b\u4e0d\u4ec5\u5982\u6b64\uff0c\u8fd9\u4e2a\u65b9\u6cd5\u4e5f\u4f1a\u5e26\u6765\u989d\u5916\u7684\u5f00\u9500\u3002\u5728\u591a\u5904\u7406\u5668\u8bed\u5883\u4e0b\uff0c\u6211\u4eec\u9700\u8981\u5b9e\u73b0\u62a2\u5360\u5f0f\u5185\u6838(preemptive kernels)\u548c\u975e\u62a2\u5360\u5f0f\u5185\u6838(non-preemptive kernels)\uff0c\u5173\u952e\u662f\u540e\u8005\u5b9e\u73b0\u4e86\u4e00\u6bb5\u65f6\u95f4\u5185\u53ea\u6709\u4e00\u4e2a\u8fdb\u7a0b\u53ef\u4ee5\u8fd0\u884c\u5728 kernel mode2\u3002</p> <p>\u63a5\u4e0b\u6765\u6211\u4eec\u63a2\u7d22\u66f4\u4e3a\u901a\u7528\u7684\u89e3\u51b3\u65b9\u6848\u3002</p> <p>\u8bf4\u660e</p> <p>\u4e3a\u4e86\u7b80\u5316\u8bf4\u660e\u4ee3\u7801\uff0c\u6211\u4eec\u7528\u5168\u5927\u5199\u6765\u8868\u793a\u4e00\u4e2a\u5171\u4eab\u8d44\u6e90\uff0c\u4f8b\u5982 <code>READY</code>\uff0c\u5b83\u80fd\u591f\u88ab\u82e5\u5e72\u8fdb\u7a0b\u8bbf\u95ee\u3002\u5b9e\u9645\u4e0a\u8fd9\u4e2a\u529f\u80fd\u5e94\u5f53\u7531\u64cd\u4f5c\u7cfb\u7edf\u63d0\u4f9b\uff0c\u5e76\u4e0d\u662f\u6211\u4eec\u5173\u6ce8\u7684\u91cd\u70b9\u3002</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit2-Part1/#petersons-algorithm","title":"Peterson\u2019s Algorithm","text":"<p>Links</p> <ul> <li>Peterson's algorithm | Wikipedia</li> </ul> <p>Peterson's algorithm \u662f\u5bf9\u53ea\u6709\u4e24\u4e2a\u8fdb\u7a0b\u53c2\u4e0e\u7684\u540c\u6b65\u95ee\u9898\u7684\u4e00\u4e2a\u89e3\u6cd5\uff0c\u5177\u6709\u4e00\u5b9a\u7684\u5c40\u9650\u6027\uff0c\u4f46\u5176\u8bbe\u8ba1\u76f8\u5bf9\u7b80\u5355\uff0c\u6240\u4ee5\u5148\u884c\u7ed9\u51fa\u3002\u5728\u672c\u8282\u4e2d\uff0c\u6211\u4eec\u5047\u8bbe \\(P_0\\) \u548c \\(P_1\\) \u662f\u53c2\u4e0e\u540c\u6b65\u95ee\u9898\u8ba8\u8bba\u7684\u4e24\u4e2a\u8fdb\u7a0b\u3002</p> <p>\u57fa\u4e8e Peterson's algorithm \u5bf9\u591a\u8fdb\u7a0b\u60c5\u51b5\u7684\u6269\u5c55\u88ab\u79f0\u4e3a filter algorithm\uff0c\u4f46 filter algorithm \u4e0d\u6ee1\u8db3 bounded waiting time \u7684\u6761\u4ef6\uff0c\u8bfb\u8005\u6709\u5174\u8da3\u53ef\u4ee5\u81ea\u884c\u4e86\u89e3\u3002</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit2-Part1/#\u7b97\u6cd5\u63cf\u8ff0","title":"\u7b97\u6cd5\u63cf\u8ff0","text":"<p>\u4e3a\u4e86\u4fdd\u8bc1\u5904\u4e8e\u4e34\u754c\u6001\u7684\u8fdb\u7a0b\u81f3\u591a\u53ea\u6709\u4e00\u4e2a\uff0c\u6211\u4eec\u5e94\u5f53\u5728\u8fdb\u7a0b\u5904\u4e8e\u5c31\u7eea\u6001\u65f6\uff0c\u786e\u8ba4\u6ca1\u6709\u5176\u4ed6\u8fdb\u7a0b\u5904\u4e8e\u4e34\u754c\u6001\u540e\u518d\u8fdb\u5165\u3002\u5176\u4e2d\u6700\u91cd\u8981\u7684\u4e00\u4ef6\u4e8b\u5c31\u662f\uff0c\u5f53\u6211\u4eec\u5904\u5728 \\(P_0\\) \u65f6\uff0c\u6211\u4eec\u5982\u4f55\u77e5\u9053 \\(P_1\\) \u662f\u5426\u6b63\u5904\u4e8e\u4e34\u754c\u6001\u5462\uff1fPeterson\u2019s Algorithm \u901a\u8fc7\u5982\u4e0b\u65b9\u5f0f\u5b9e\u73b0\u4e86\u8fd9\u4ef6\u4e8b\uff1a</p> <pre><code>// `i` is 0 or 1, indicating current pid, while `j` is another pid.\nprocess(i) {\nj = 1 - i;\n\nREADY[i] = true;                    // \u2510\nTURN = j;                           // \u2502\nwhile (READY[j] &amp;&amp; TURN == j) {}    // \u251c entry section\n// i.e. wait until:             // \u2502\n//  (1) j exits,                // \u2502\n//  (2) j is slower, so it      // \u2502\n//      should run now.         // \u2518\n\n/* operate critical resources */    // - critical section\n\nREADY[i] = false;                   // - exit section\n\n/* other things */                  // - remainder section\n}\n</code></pre> <p>\u9996\u5148\uff0c\u6211\u4eec\u8bf4\u660e entry section \u6ca1\u6709\u4e34\u754c\u8d44\u6e90\u3002<code>READY</code> \u662f\u4e00\u4e2a\u5171\u4eab\u7684\u6570\u7ec4\uff0c\u6bcf\u4e2a\u8fdb\u7a0b\u53ea\u4fee\u6539\u4e0e\u81ea\u5df1\u4e00\u4e00\u5bf9\u5e94\u7684 element\uff0c\u6240\u4ee5\u672c\u8d28\u4e0a <code>READY</code> \u4e0d\u4f1a\u51fa\u73b0 race condition\uff0c\u56e0\u800c\u4e5f\u4e0d\u662f\u4e34\u754c\u8d44\u6e90\u3002\u800c <code>TURN</code>\uff0c\u6211\u4eec\u8fd9\u91cc\u53ea\u5bf9 <code>TURN</code> \u8fdb\u884c\u5199\u7684\u64cd\u4f5c\uff0c\u4f46\u662f P1 \u548c P2 \u8c01\u5148\u8dd1\u5230\u8fd9\u4e00\u884c\u4f1a\u51b3\u5b9a <code>TURN</code> \u6700\u540e\u7684\u503c\uff0c\u6240\u4ee5\u5b9e\u9645\u4e0a\u8fd9\u91cc\u6709 race condition\u3002</p> <p>\u4f46\u8fd9\u5c31\u662f Peterson\u2019s Algorithm \u5de7\u5999\u7684\u5730\u65b9\uff0cPeterson's \u5229\u7528 race condition \u8fd9\u4e2a\u201c\u540e\u8986\u76d6\u524d\u201d\u7684\u6027\u8d28\uff0c\u5b9e\u73b0\u4e86\u6807\u8bb0\u4e86\u8fd9\u4e24\u4e2a\u8fdb\u7a0b\u7684\u5148\u6765\u540e\u5230\u7684\u6548\u679c\u3002\u6211\u4eec\u90fd\u5411\u8fd9\u4e2a <code>TURN</code> \u5199\u4e00\u4e2a\u4e92\u5f02\u7684\u503c\uff08\u6bd4\u5982\u81ea\u5df1\u7684 id\uff0c\u6216\u8005\u5bf9\u65b9\u7684 id\uff09\uff0c\u7b49\u5927\u5bb6\u90fd\u5199\u597d\u540e\u6211\u4eec\u770b\u770b\u8fd9\u4e2a\u503c\u6700\u7ec8\u662f\u8c01\u5199\u7684\uff0c\u4e8e\u662f\u5c31\u77e5\u9053\u8c01\u540e\u5230\u3002</p> <p>\u5229\u7528\u8fd9\u4e2a\u539f\u7406\uff0cPeterson's \u8fd9\u91cc\u505a\u4e86\u4e00\u4e2a\u201c\u975e\u5e38\u6709\u4e2d\u56fd\u4eba\u6c14\u8d28\u201d\u7684\u4e8b\u60c5\uff1a\\(P_0\\) \u548c \\(P_1\\) \u4e0a\u516c\u4ea4\u8f66\u540e\u540c\u65f6\u770b\u4e0a\u4e86\u4e00\u4e2a\u5ea7\u4f4d\uff0c\\(P_0\\) \u8bf4\uff1a\u201c\u4f60\u5750\u5427\u3002\u201d\uff0c \\(P_1\\) \u81ea\u7136\u4e5f\u8981\u5ba2\u6c14\u4e00\u4e0b\uff0c\u8bf4\uff1a\u201c\u8fd8\u662f\u4f60\u5750\u5427\uff01\u201d\u3002\u73b0\u5728\u4e24\u8fb9\u90fd\u5ba2\u6c14\u8fc7\u4e86\uff0c\\(P_0\\) \u5c31\u53ef\u4ee5\u5fc3\u5b89\u7406\u5f97\u5730\u5750\u4e0b\u4e86\u3002\u5bf9\u4e0a\u8ff0\u8fc7\u7a0b\uff0c\u6211\u4eec\u7ed9\u51fa \\(P_0\\) \u83b7\u5f97\u6905\u5b50\u7684\u51c6\u786e\u6761\u4ef6\u6709\uff1a</p> <ol> <li>\\(P_0\\) \u60f3\u5750\u4e0b\uff0c\\(P_1\\) \u4e5f\u60f3\u5750\u4e0b\uff0c\u5426\u5219\u5c31\u6ca1\u6709\u51b2\u7a81\u4e86\uff1b</li> <li>\\(P_0\\) \u53d1\u73b0 \\(P_1\\) \u5728\u5ba2\u6c14\uff0c\u4f46 \\(P_0\\) \u5df2\u7ecf\u5ba2\u6c14\u8fc7\u4e86\uff1b</li> </ol> <p>\u5bf9\u5e94\u5230\u4e0a\u9762\u7ed9\u51fa\u7684\u4ee3\u7801\u91cc\uff0c\u8fd9\u4e2a\u6761\u4ef6\u53ef\u4ee5\u7ffb\u8bd1\u4e3a\uff1a</p> <ol> <li><code>READY[0]</code> = <code>READY[1]</code> = <code>true</code>\uff1b</li> <li><code>TURN</code> \u2260 <code>j</code>\uff0c\u4f46\u6b64\u524d \\(P_i\\) \u5df2\u7ecf\u6267\u884c\u8fc7 <code>TURN &lt;- j</code>\uff1b</li> </ol> <p>\u8bf7\u8bfb\u8005\u4ed4\u7ec6\u601d\u8003\u4e0a\u9762\u7684\u8fc7\u7a0b\uff0c\u5e76\u9002\u5f53\u8fdb\u884c\u5168\u9762\u7684\u6a21\u62df\u4ee5\u7406\u89e3 Peterson's \u662f\u5982\u4f55\u5de5\u4f5c\u7684\u3002</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit2-Part1/#\u6027\u8d28\u8bc1\u660e","title":"\u6027\u8d28\u8bc1\u660e","text":"<p>\u73b0\u5728\u6211\u4eec\u9700\u8981\u8bc1\u660e\u8fd9\u4e2a\u7b97\u6cd5\u6ee1\u8db3\u6027\u8d28\u3002</p> <p>\u6211\u7684\u8bc1\u660e\u6bd4\u8f83\u8be6\u7ec6\u548c\u5570\u55e6\uff0c\u4f46\u6211\u8ba4\u4e3a\u5b8c\u6574\u5730\u6a21\u62df\u66f4\u52a0\u6709\u5229\u4e8e\u76f4\u89c9\u7406\u89e3\uff0c\u5982\u679c\u4f60\u60f3\u8981\u66f4\u7b80\u6d01\u7684\u8bc1\u660e\uff0c\u53ef\u4ee5\u53c2\u8003 xyx \u7684\u7b14\u8bb0\u3002</p> mutual exclusion <pre><code>// `i` is 0 or 1, indicating current pid, while `j` is another pid.\nprocess(i) {\nj = 1 - i;\n\nREADY[i] = true;                    // \u2510\nTURN = j;                           // \u2502\nwhile (READY[j] &amp;&amp; TURN == j) {}    // \u251c entry section\n// i.e. wait until:             // \u2502\n//  (1) j exits,                // \u2502\n//  (2) j is slower, so it      // \u2502\n//      should run now.         // \u2518\n\n/* operate critical resources */    // - critical section\n\nREADY[i] = false;                   // - exit section\n\n/* other things */                  // - remainder section\n}\n</code></pre> <p>lemma</p> <p>\u5982\u679c\u6b64\u65f6 i \u548c j \u540c\u5904\u4e8e\u7b2c 7 \u884c\uff0c\u90a3\u4e48\u663e\u7136\uff1a</p> <ol> <li>\u4e24\u4e2a\u8fdb\u7a0b\u90fd\u60f3\u8981\u8fdb\u5165 critical section\uff0c\u5373 <code>READY[i]</code> \u548c <code>READY[j]</code> \u90fd\u4e3a <code>true</code>\uff1b</li> <li><code>TURN</code> \u7684\u503c\u4e0d\u518d\u4f1a\u88ab\u66f4\u6539\uff1b</li> <li>\u4e24\u4e2a\u8fdb\u7a0b\u90fd\u5c1a\u672a\u8fdb\u5165 critical section\uff1b</li> </ol> <p>\u7531\u4e8e <code>TURN</code> \u5fc5\u5b9a\u4e5f\u53ea\u80fd\u4e3a i \u6216 j\uff0c\u6240\u4ee5 i \u548c j \u5fc5\u7136\u6709\u4e14\u4ec5\u6709\u4e00\u4e2a\u8fdb\u7a0b\u63a5\u4e0b\u6765\u4f1a break loop \u5e76\u8fdb\u5165 critical section\uff0c\u5728\u5b83\u7ed3\u675f\u4e4b\u524d\uff0c\u5373\u5728 <code>READY[?]</code> \u88ab\u6539\u53d8\u4e4b\u524d\uff0c\u8be5\u6761\u4ef6\u6301\u7eed\u6210\u7acb\u3002</p> <p>\u56e0\u6b64\u6211\u4eec\u5f97\u5230\u4e00\u4e2a\u7ed3\u8bba\uff1a\u5982\u679c\u6b64\u65f6 i \u548c j \u540c\u5904\u4e8e\u7b2c\u4e03\u884c\uff0c\u90a3\u4e48\u4ece\u8be5\u65f6\u523b\u5f00\u59cb\uff0c\u5230\u4e24\u4e2a\u8fdb\u7a0b\u90fd\u79bb\u5f00 critical section \u4e3a\u6b62\uff0c\u4e92\u65a5\u6027\u8d28\u90fd\u6210\u7acb\u3002</p> <p>\u73b0\u5728\u6211\u4eec\u8003\u8651 i \u5df2\u7ecf\u5148\u884c\u8fd0\u884c\u5230\u7b2c 7 \u884c\uff0c\u800c j \u8fd8\u6ca1\u8fd0\u884c\u5230\u7b2c 7 \u884c\uff1a</p> <p>Situation 1</p> <p>\u5982\u679c j \u8fd8\u6ca1\u8fdb\u5165\u7b2c 5 \u884c\uff0c\u90a3\u4e48 <code>READY[j]</code> \u4e3a <code>false</code>\uff0c\u6b64\u65f6\u6ca1\u6709\u7ade\u4e89\uff0ci \u53ef\u4ee5\u76f4\u63a5\u8fdb\u5165\u4e34\u754c\u6001\u3002\u5e76\u4e14 j \u4e4b\u540e\u8fd0\u884c\u5230\u7b2c 7 \u884c\u65f6\uff0c<code>TURN == &lt;another&gt;</code> \u59cb\u7ec8\u6210\u7acb\u3002\u6240\u4ee5 j \u4f55\u65f6\u8fdb\u5165 critical section \u5b8c\u5168\u53d6\u51b3\u4e8e <code>READY[j]</code>\uff0c\u5373 j \u4f55\u65f6\u79bb\u5f00 critical section\u3002</p> <p>\u663e\u7136\uff0c\u6b64\u65f6\u6ee1\u8db3\u4e92\u65a5\u6027\u8d28\u3002</p> <p>Situation 2</p> <p>\u5982\u679c j \u5df2\u7ecf\u8fd0\u884c\u5b8c\u7b2c 5 \u884c\uff0c\u8fd8\u6ca1\u6267\u884c\u7b2c 6 \u884c\uff0c\u90a3\u4e48\u5bf9\u4e8e i \u6765\u8bf4\uff0c<code>(READY[j] &amp;&amp; TURN == j)</code> \u4e3a <code>true</code>\uff0c\u6b64\u65f6 i \u5c06\u7b49\u5f85 j\uff0c\u8fdb\u5165 Situation 3\u3002</p> <p>\u4e5f\u5c31\u662f\u8bf4\uff0c\u8981\u4e48 i \u548c j \u4e0d\u7ade\u4e89\uff0c\u8981\u4e48\u4e24\u8005\u90fd\u8fd0\u884c\u5230\u7b2c 7 \u884c\u540e\u624d\u4f1a\u6709\u8fdb\u7a0b\u8fdb\u5165 critical section</p> <p>\u8fd9\u5c31\u597d\u50cf\u4e24\u8005\u5728\u7b2c 6 \u884c\u6bd4\u8c01\u5148\u4e3e\u624b\uff0c\u7136\u540e\u7b49\u4e24\u8005\u90fd\u4e3e\u8fc7\u624b\uff08\u90fd\u8dd1\u5b8c\u7b2c 6 \u884c\uff0c\u5230\u8fbe\u7b2c 7 \u884c\uff09\u540e\uff0c\u518d\u5224\u65ad\u8c01\u8fdb\u5165 critical section\uff0c\u800c\u8fdb\u5165\u7b2c 7 \u884c\u4ee5\u540e\u6240\u6709\u7684\u5224\u65ad\u6761\u4ef6\u90fd\u662f\u76f8\u5bf9\u9759\u6b62\u7684\u3001\u4e0d\u4f1a\u518d\u88ab\u4fee\u6539\u7684\uff0c\u56e0\u800c\u907f\u514d\u751a\u81f3\u5229\u7528\u4e86 race condition \u5bf9 selection \u7684\u5f71\u54cd\uff0c\u4fdd\u8bc1\u4e86\u4e92\u65a5\u7684\u6027\u8d28\u3002</p> progress <p>\u8fd9\u6761\u6027\u8d28\u7684\u6210\u7acb\u6bd4\u8f83\u7b26\u5408\u76f4\u89c9\uff0c\u552f\u4e00\u9700\u8981\u8bf4\u660e\u7684\u5c31\u662f\u4e0d\u4f1a\u51fa\u73b0\u4e24\u4e2a\u8fdb\u7a0b\u540c\u65f6\u5728 <code>while ()</code> \u88ab\u963b\u585e\u4f4f\u7684\u60c5\u51b5\u3002\u4f46\u662f\u8fd9\u70b9\u975e\u5e38\u663e\u7136\uff0c<code>TURN == i &amp;&amp; TURN == j</code> \u5fc5\u7136\u662f false\uff0c\u6240\u4ee5\u4e24\u4e2a\u5faa\u73af\u603b\u6709\u4e00\u4e2a\u4f1a\u88ab break\u3002</p> bounded waiting time <p>\u5728 Peterson's \u4e2d\uff0c\u7b49\u5f85\u65f6\u95f4\u4e3b\u8981\u6307\u8fd9\u90e8\u5206\u7684\u8fd0\u884c\u65f6\u95f4\uff0c\u5c24\u5176\u6307\u7b2c\u4e03\u884c\u7684 <code>while</code> \u5faa\u73af\u3002</p> <pre><code>// `i` is 0 or 1, indicating current pid, while `j` is another pid.\nprocess(i) {\nj = 1 - i;\n\nREADY[i] = true;                    // \u2510\nTURN = j;                           // \u2502\nwhile (READY[j] &amp;&amp; TURN == j) {}    // \u251c entry section\n// i.e. wait until:             // \u2502\n//  (1) j exits,                // \u2502\n//  (2) j is slower, so it      // \u2502\n//      should run now.         // \u2518\n\n/* operate critical resources */    // - critical section\n\nREADY[i] = false;                   // - exit section\n\n/* other things */                  // - remainder section\n}\n</code></pre> <p>\u6211\u4eec\u53ef\u4ee5\u53d1\u73b0\uff0c\u4e0d\u65ad\u5faa\u73af\u7684\u6761\u4ef6\u662f\uff1a<code>READY[j] &amp;&amp; TURN == j</code>\uff0c\u5982\u679c\u8be5\u5faa\u73af\u4e00\u5f00\u59cb\u5c31\u4e0d\u6210\u7acb\uff0c\u90a3\u4e48\u663e\u7136\u662f\u7b26\u5408 bounded waiting time \u7684\uff0c\u6240\u4ee5\u6211\u4eec\u8003\u8651\u8fd9\u4e2a\u6761\u4ef6\u6700\u591a\u80fd\u6301\u7eed\u591a\u4e45\u3002</p> <p>A. <code>READY[j]</code> \u4e3a <code>true</code></p> <p>\u8fd9\u9700\u8981 process j \u5df2\u7ecf\u8fd0\u884c\u8fc7\u7b2c 5 \u884c\uff0c\u5e76\u4e14\u8fd8\u6ca1\u8fd0\u884c\u7b2c 15 \u884c\uff0c\u5373 process j \u4e5f\u60f3\u8981\u8fdb\u5165\u4e34\u754c\u6001\u3002</p> <p>\u8fd9\u4e00\u6761\u662f\u5728\u5224\u65ad\u662f\u5426\u6709\u51b2\u7a81\u5b58\u5728\uff0c\u5982\u73b0\u5728\u53ea\u6709 process i \u60f3\u8981\u8fdb\u5165\u4e34\u754c\u6001\uff0c\u90a3\u65e0\u9700\u7b49\u5f85\u76f4\u63a5\u8fdb\u5165\u5373\u53ef\u3002\u901a\u8fc7\u6539\u53d8\u8fd9\u4e2a\u6761\u4ef6\u800c\u8fdb\u5165\u4e34\u754c\u6001\u6709\u4e24\u79cd\u53ef\u80fd\uff1a</p> <ol> <li>\u4e00\u5f00\u59cb\u51b2\u7a81\u5c31\u4e0d\u5b58\u5728\uff1b</li> <li>process j \u521a\u79bb\u5f00\u4e34\u754c\u6001\uff0c\u91ca\u653e\u4e86\u4e34\u754c\u8d44\u6e90\uff1b</li> </ol> <p>B. <code>TURN == j</code> \u4e3a <code>true</code></p> <p>\u6709\u4e24\u79cd\u53ef\u80fd\uff1a</p> <ol> <li>process j \u8fd8\u6ca1\u8fd0\u884c\u7b2c 6 \u884c\uff1b</li> <li>process j \u5728 process i \u4e4b\u524d\u5c31\u8fd0\u884c\u4e86\u7b2c 6 \u884c\uff1b</li> </ol> <p>\u5bf9\u4e8e\u7b2c\u4e00\u79cd\u60c5\u51b5\uff0c\u7531\u4e8e A. \u6210\u7acb\u540e\u624d\u4f1a\u5224\u65ad\u8fd9\u6761\uff0c\u6240\u4ee5 process j \u7684\u72b6\u6001\u5176\u5b9e\u662f\u521a\u8fd0\u884c\u5b8c\u7b2c 5 \u884c\u8fd8\u6ca1\u8fd0\u884c\u5b8c\u7b2c 6 \u884c\uff0c\u663e\u7136\u8fd9\u4e2a\u65f6\u95f4\u662f\u6709\u754c\u7684\u3002</p> <p>\u800c\u5bf9\u4e8e\u7b2c\u4e8c\u79cd\u60c5\u51b5\uff0c\u8bf4\u660e i \u662f\u540e\u6765\u8005\uff0cj \u5df2\u7ecf\u5ba2\u6c14\u8fc7\u4e00\u6b21\u4e86\uff0c\u6240\u4ee5\u5e94\u5f53\u8ba9 j \u8fd0\u884c\uff0ci \u7b49\u5f85 j \u79bb\u5f00\u4e34\u754c\u6001\u91ca\u653e\u8d44\u6e90\uff0c\u6b64\u65f6\u901a\u8fc7 A.2. \u6765\u8fdb\u5165\u4e34\u754c\u6001\u3002\u800c process j \u64cd\u4f5c\u4e34\u754c\u8d44\u6e90\u7684\u65f6\u95f4\u4e5f\u5e94\u5f53\u6709\u9650\u7684\u3002</p> <p>\u7efc\u4e0a\u6240\u8ff0\uff0cwaiting time \u7684\u6700\u5927\u503c\u57fa\u672c\u4e0a\u53d6\u81ea\uff1a</p> <ol> <li>process j \u6267\u884c\u7b2c 6 \u884c\u7684\u65f6\u95f4\uff1b</li> <li>process j \u64cd\u4f5c\u4e34\u754c\u8d44\u6e90\u7684\u65f6\u95f4\uff1b</li> </ol> <p>\u901a\u8fc7\u4e4b\u524d\u7684\u8bba\u8ff0\u6211\u4eec\u77e5\u9053\uff0c\u8fd9\u4e24\u4e2a\u90fd\u662f\u6709\u754c\u7684\uff0c\u4e8e\u662f\u8be5\u6027\u8d28\u5f97\u8bc1\u3002</p> <p>Oops!</p> <p>\u4f46\u662f\uff0cPeterson's \u5b9e\u9645\u4e0a\u65e0\u6cd5\u9002\u7528\u4e8e\u73b0\u4ee3\u8ba1\u7b97\u673a\u4e2d\u3002\u4e0a\u8ff0\u505a\u6cd5\u6709\u4e00\u4e2a\u5173\u952e\uff0c\u4e5f\u662f\u6211\u4eec\u5728\u8bc1\u660e\u8fc7\u7a0b\u4e2d\u4e00\u76f4\u9ed8\u8ba4\u6210\u7acb\u7684\u4e8b\u60c5\uff1a\u8fdb\u7a0b\u603b\u662f\u5148\u6267\u884c <code>READY[i] = true;</code>\uff0c\u7136\u540e\u624d\u4f1a\u6267\u884c <code>TURN = j;</code>\uff0c\u5373\u5148\u8fdb\u5165\u5c31\u7eea\u6001\uff0c\u518d\u7d22\u53d6\u4e34\u754c\u8d44\u6e90\uff0c\u8fd9\u770b\u8d77\u6765\u662f\u4e2a\u975e\u5e38\u5408\u7406\u7684\u6761\u4ef6\u3002\u4f46\u5728\u73b0\u4ee3\u8ba1\u7b97\u673a\u4e2d\uff0c\u7f16\u8bd1\u5668\u53ef\u80fd\u4f1a\u901a\u8fc7\u91cd\u6392\u5217\u90e8\u5206\u8bed\u53e5\u6765\u66f4\u597d\u5730\u5229\u7528 CPU \u8d44\u6e90\uff08\u53c2\u8003\u8ba1\u7ec4\u7684\u5404\u79cd\u7ade\u4e89\uff09\u3002\u800c\u5bf9\u7f16\u8bd1\u5668\u6765\u8bf4\uff0c\u8fd9\u4e24\u4e2a\u64cd\u4f5c\uff08\u5c31\u7eea\u548c\u8bf7\u6c42\uff09\u5e76\u6ca1\u6709\u64cd\u4f5c\u76f8\u540c\u5185\u5bb9\uff0c\u56e0\u800c\u4ea4\u6362\u987a\u5e8f\u662f\u4e0d\u4f1a\u5f71\u54cd\u7ed3\u679c\u7684\uff0c\u6240\u4ee5\u53ef\u80fd\u88ab\u7f16\u8bd1\u5668\u4ea4\u6362\u3002\u800c\u8fd9\u5c31\u6709\u53ef\u80fd\u5bfc\u81f4\u51fa\u73b0\u95ee\u9898\uff0c\u4f8b\u5982\uff1a</p> <p>  The effects of instruction reordering in Peterson\u2019s solution. </p> <p>\u5728\u68d5\u8272\u6807\u8bb0\u65f6\u523b\uff0cprocess 1 \u8fdb\u884c <code>while</code> \u5faa\u73af\u5224\u65ad\uff0c\u53d1\u73b0 <code>READY[0]</code> \u4e3a <code>false</code>\uff0c\u4f46\u6b64\u65f6 <code>TURN</code> \u6307\u5411\u5bf9\u65b9\uff0c\u6240\u4ee5\u6309\u7167\u6211\u4eec\u5148\u524d\u7684\u5206\u6790\uff0c\u6b64\u65f6 process 1 \u4f1a\u8ba4\u4e3a process 0 \u662f\u5df2\u7ecf\u8fd0\u884c\u5b8c critical section\uff0c\u5df2\u7ecf\u91ca\u653e\u4e86\u4e34\u754c\u8d44\u6e90\uff0c\u6240\u4ee5\u8fdb\u5165\u4e34\u754c\u6001\uff1b\u7136\u800c\uff0c\u5728\u7eff\u8272\u6807\u8bb0\u65f6\u523b\uff0c\u5bf9\u4e8e process 0\uff0c\u6b64\u65f6 <code>TURN</code> \u6307\u5411\u81ea\u5df1\uff0cprocess 1 \u8fd8\u6ca1\u8fd0\u884c\u5b8c\u6240\u4ee5 <code>READY[1]</code> \u8fd8\u662f <code>true</code>\uff0c\u6839\u636e\u6211\u4eec\u4e4b\u524d\u7684\u5206\u6790\uff0c\u6b64\u65f6 process 0 \u4f1a\u8ba4\u4e3a process 1 \u5728\u7b49\u5f85\u81ea\u5df1\uff0c\u6240\u4ee5\u4e5f\u8fdb\u5165\u4e86\u4e34\u754c\u6001\u3002\u4e8e\u662f\uff0c\u4e24\u4e2a\u8fdb\u7a0b\u540c\u65f6\u8fdb\u5165\u4e86\u4e34\u754c\u6001\uff0c\u8fdd\u53cd\u4e86 mutual exclusion \u7684\u6027\u8d28\u3002</p> <p>\u6240\u4ee5\uff0c\u5b9e\u9645\u4e0a Peterson's Algorithm \u4ecd\u7136\u6ca1\u6709\u89e3\u51b3\u95ee\u9898\u3002</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit2-Part1/#memory-barriers","title":"Memory Barriers","text":"<p>\u8be5\u65b9\u6cd5\u5b9e\u9645\u4e0a\u662f\u5bf9\u8f6f\u4ef6\u65b9\u6cd5\u7684\u8865\u8db3\u3002\u6211\u4eec\u5148\u524d\u63d0\u5230\uff0cPeterson's Algorithm \u5931\u6548\u7684\u539f\u56e0\u662f\u7f16\u8bd1\u5668\u4f1a\u6839\u636e\u9700\u6c42\u91cd\u6392\u5217\u4e00\u4e9b\u5185\u5b58\u64cd\u4f5c\uff0c\u800c memory barriers \u4fdd\u8bc1 barrier \u4e4b\u524d\u7684 S/L \u6307\u4ee4\u5fc5\u987b\u5728 barrier \u4e4b\u540e\u7684 S/L \u6307\u4ee4\u4e4b\u524d\u5b8c\u6210\uff0c\u4f7f\u6211\u4eec\u80fd\u591f\u4e3b\u52a8\u7981\u6b62\u7f16\u8bd1\u5668\u505a\u8fd9\u79cd\u91cd\u6392\u3002</p> <pre><code>// `i` is 0 or 1, indicating current pid, while `j` is another pid.\nprocess(i) {\nj = 1 - i;\n\nREADY[i] = true;                    // \u2510\nmemory_barrier();                   // \u2502\nTURN = j;                           // \u2502\nwhile (READY[j] &amp;&amp; TURN == j) {}    // \u251c entry section\n// i.e. wait until:             // \u2502\n//  (1) j exits,                // \u2502\n//  (2) j is slower, so it      // \u2502\n//      should run now.         // \u2518\n\n/* operate critical resources */    // - critical section\n\nREADY[i] = false;                   // - exit section\n\n/* other things */                  // - remainder section\n}\n</code></pre> <p>Memory Model</p> <p>\u4e0d\u540c\u7684\u8ba1\u7b97\u673a\u67b6\u6784\u53ef\u80fd\u4f1a\u5bf9\u7528\u6237\u7a0b\u5e8f\u64cd\u4f5c\u5185\u5b58\u7684\u4fdd\u8bc1\u6709\u6240\u4e0d\u540c\uff0c\u8fd9\u79cd\u4fdd\u8bc1\u88ab\u79f0\u4e3a memory model\u3002\u6211\u4eec\u53ef\u4ee5\u5c06\u5b83\u5206\u4e3a\u4e24\u5927\u7c7b\uff1a</p> <ol> <li>\u5f3a\u6709\u5e8f(strongly ordered)\uff1a\u8fdb\u7a0b\u5bf9\u5185\u5b58\u505a\u7684\u4fee\u6539\u7acb\u523b\u5bf9\u5176\u5b83\u5904\u7406\u5668\u53ef\u89c1\uff1b</li> <li>\u5f31\u6709\u5e8f(weakly ordered)\uff1a\u8fdb\u7a0b\u5bf9\u5185\u5b58\u505a\u7684\u4fee\u6539\u4e0d\u7acb\u523b\u5bf9\u5176\u5b83\u5904\u7406\u5668\u53ef\u89c1\uff1b</li> </ol> <p>\u6211\u4eec\u77e5\u9053\uff0c\u4e3a\u4e86\u63d0\u9ad8\u5185\u5b58\u64cd\u4f5c\u7684\u6548\u7387\uff0c\u6211\u4eec\u5f15\u5165\u4e86 cache\uff0c\u5728\u591a\u5904\u7406\u5668\u60c5\u51b5\u4e0b\uff0ccache \u673a\u5236\u7684\u5b58\u5728\u53ef\u80fd\u5bfc\u81f4\u8fdb\u7a0b A \u5bf9\u5185\u5b58\u7684\u5199\u65e0\u6cd5\u5bf9\u8fdb\u7a0b B \u7acb\u523b\u53ef\u89c1\uff0c\u8fd9\u5c31\u662f\u5f31\u6709\u5e8f\u7684\u4e00\u79cd\u4f53\u73b0\u3002</p> <p>\u8fd9\u90e8\u5206\u6211\u6ca1\u6709\u5b8c\u5168\u641e\u6e05\u695a\uff0c\u4e66\u672c\u7684\u903b\u8f91\u975e\u5e38\u7684\u8be1\u5f02\uff1a\u4e66\u672c\u8ba4\u4e3a memory barrier \u662f\u5f31\u6709\u5e8f\u95ee\u9898\u7684\u89e3\u51b3\u65b9\u6848\uff0c\u4f46\u662f\u6211\u59cb\u7ec8\u6ca1\u660e\u767d\u5b83\u4eec\u4e4b\u95f4\u7684\u903b\u8f91\u5728\u54ea\u91cc\uff0c\u4ee5\u53ca\u201c\u6709\u5e8f\u201d\u548c\u201c\u7acb\u523b\u53ef\u89c1\u201d\u7684\u6839\u672c\u8054\u7cfb\u5728\u54ea\u91cc\u3002\u8fd9\u91cc\u4e00\u5b9a\u662f\u5b58\u5728\u4e0d\u6e05\u695a\u7684\u5730\u65b9\u7684\u3002\u4f46\u662f\u8fd9\u90e8\u5206\u770b\u8d77\u6765\u4e0d\u662f\u5f88\u91cd\u8981\uff0c\u6240\u4ee5\u6211\u5c31\u5148\u653e\u7740\u4e0d\u7ba1\u4e86\u3002</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit2-Part1/#hardware-instructions","title":"Hardware Instructions","text":"<p>\u8ba8\u8bba Peterson's Algorithm \u540e\u6211\u4eec\u5e94\u5f53\u610f\u8bc6\u5230\uff0c\u540c\u6b65\u95ee\u9898\u7684\u51fa\u73b0\u662f \u2776 \u786c\u4ef6\u64cd\u4f5c\u6570\u636e\u9700\u8981\u65f6\u95f4\uff0c\u4e0e \u2777 \u6570\u636e\u5177\u6709\u5171\u4eab\u6027\u7684\u4e0d\u534f\u8c03\uff0c\u6240\u4ee5\u672c\u8d28\u4e0a\u662f\u786c\u4ef6\u4ea7\u751f\u7684\u95ee\u9898\u3002\u56e0\u800c\uff0c\u8981\u60f3\u66f4\u597d\u7684\u89e3\u51b3\u95ee\u9898\uff0c\u6211\u4eec\u8fd8\u662f\u5e94\u5f53\u4ece\u786c\u4ef6\u51fa\u53d1\u3002\u6211\u4eec\u5728\u8fd9\u91cc\u5f15\u5165\u539f\u5b50\u6027(atomic)\u8fd9\u4e2a\u6982\u5ff5\uff0c\u5b83\u7684\u57fa\u672c\u903b\u8f91\u662f\u8ba9\u201c\u9700\u8981\u65f6\u95f4\u7684\uff0c\u5bf9\u6570\u636e\u7684\u64cd\u4f5c\u201d\uff0c\u53d8\u6210\u4e00\u4e2a\u201c\u5728\u65f6\u95f4\u4e0a\u4e0d\u53ef\u5206\u5272\u3001\u4e0d\u53ef\u88ab\u6253\u65ad\u7684\uff0c\u5373\u539f\u5b50\u6027\u7684\u64cd\u4f5c\u201d\u3002\u4e0d\u540c\u786c\u4ef6\u53ef\u80fd\u63d0\u4f9b\u4e0d\u540c\u7684\u539f\u5b50\u6027\u64cd\u4f5c\uff0c\u6211\u4eec\u8fd9\u91cc\u5c06\u5b83\u4eec\u62bd\u8c61\u4e3a <code>test_and_set()</code> \u548c <code>compare_and_swap()</code> \u4e24\u7c7b\u6765\u4ecb\u7ecd\u3002</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit2-Part1/#test_and_set","title":"<code>test_and_set()</code>","text":"<p>Links</p> <ul> <li>Wikipedia</li> </ul> <pre><code>&lt;atomic&gt; test_and_set(bool * target) {\nbool ret = *target;\n*target = true;\nreturn ret;\n}\n</code></pre> <p>\u8be5\u6307\u4ee4\u7684\u529f\u80fd\u5c31\u7c7b\u4f3c\u4e0a\u9762\u8fd9\u6bb5\u4ee3\u7801\uff1a\u5c06\u76ee\u6807\u8bbe\u4e3a <code>true</code>\uff0c\u540c\u65f6\u8fd4\u56de\u5176\u65e7\u503c\u3002\u4f46\u9664\u6b64\u4e4b\u5916\uff0c\u8fd9\u4e2a\u6307\u4ee4\u9700\u8981\u4fdd\u8bc1\u539f\u5b50\u6027\uff0c\u5373\u5982\u679c\u6709\u82e5\u5e72 <code>test_and_set()</code> \u540c\u65f6\u53d1\u751f\uff0c\u90a3\u4e48\u65e0\u8bba\u5e76\u53d1\u8fd8\u662f\u5e76\u884c\uff0c\u5b83\u4eec\u90fd\u5e94\u5f53\u4e00\u4e2a\u4e00\u4e2a\u5730\u6267\u884c\uff0c\u800c\u4e0d\u80fd\u4ea7\u751f\u65f6\u95f4\u4e0a\u7684\u4ea4\u96c6\u3002</p> <p>\u53ef\u4ee5\u53d1\u73b0\uff0c\u8fd9\u79cd atomic \u7684\u64cd\u4f5c\u5929\u7136\u4fdd\u8bc1\u4e86 mutual exclusion\uff0c\u56e0\u800c\u5bf9\u4e8e\u5b9e\u73b0\u4e86 <code>test_and_set()</code> \u7684\u673a\u5668\uff0c\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528 <code>test_and_set()</code> \u6765\u89e3\u51b3 CS \u95ee\u9898\u3002</p> <pre><code>process(i) {\nwhile ( test_and_set(&amp;LOCK) ) {}    // - entry section\n/* operate critical resources */    // - critical section\n\nLOCK = false;                       // - exit section\n\n/* other things */                  // - remainder section\n}\n</code></pre> <p>\u5728\u7b2c 3 \u884c\uff0c\u5faa\u73af\u7b49\u5f85\u7684\u6761\u4ef6\u53d8\u4e3a <code>test_and_set(&amp;LOCK)</code>\uff0c\u5982\u679c <code>LOCK</code> \u7684\u65e7\u503c\u662f <code>false</code>\uff0c\u5219\u53ef\u4ee5\u7ee7\u7eed\uff0c\u5e76\u4e14\u6b64\u65f6 <code>LOCK</code> \u7684\u503c\u88ab\u539f\u5b50\u6027\u5730\u4fee\u6539\u4e3a <code>true</code>\uff1b\u800c\u5982\u679c <code>LOCK</code> \u7684\u65e7\u503c\u662f <code>true</code>\uff0c\u90a3\u4e48\u5b83\u7ecf\u8fc7 <code>test_and_set(&amp;LOCK)</code> \u540e\u7684\u503c\u4ecd\u7136\u662f <code>true</code>\uff0c\u4e14\u9700\u8981\u7b49\u5f85\uff0c\u76f4\u5230\uff1a\u5c06 <code>LOCK</code> \u6539\u6210 <code>true</code> \u7684\u90a3\u4e2a\u8fdb\u7a0b\u5728 exit section \u5c06 <code>LOCK</code> \u6539\u56de <code>false</code>\uff0c\u5373\u91ca\u653e\u9501\u3002</p> <p>\u4f46\u662f\u8bf7\u6ce8\u610f\uff0c\u4e0e\u6211\u4eec\u8ba8\u8bba Peterson's Algorithm \u65f6\u7684\u8bed\u5883\u4e0d\u540c\uff0c\u6211\u4eec\u73b0\u5728\u4e0d\u518d\u5047\u8bbe\u53c2\u4e0e\u7ade\u4e89\u7684\u8fdb\u7a0b\u53ea\u6709\u4e24\u4e2a\uff08\u8fd9\u662f Peterson's \u7684\u5c40\u9650\u6027\u4e4b\u4e00\uff09\u3002\u5728\u8fd9\u4e2a\u8bed\u5883\u4e0b\uff0c\u6211\u4eec\u518d\u6765\u8003\u8651\u5b83\u662f\u5426\u6ee1\u8db3\u4e09\u6761\u6027\u8d28\u3002</p> <p>mutual exclusion</p> <p>\u7531\u4e8e <code>test_and_set()</code> \u662f\u539f\u5b50\u6027\u7684\uff0c\u6240\u4ee5\u540c\u65f6\u6267\u884c\u7684\u4e00\u7cfb\u5217 <code>test_and_set()</code> \u4e2d\uff0c\u53ea\u6709\u4e00\u4e2a\u80fd\u8fd4\u56de <code>false</code>\uff0c\u5373\u53ea\u6709\u4e00\u4e2a\u80fd\u901a\u8fc7\u9501\uff0c\u56e0\u800c\u5929\u751f\u6ee1\u8db3\u4e86 mutual exclusion\u3002</p> <p>progress</p> <p>\u4ee3\u7801\u4e2d\u5bf9 <code>LOCK</code> \u7684\u4fee\u6539\u64cd\u4f5c\u662f\u95ed\u5408\u7684\uff0c\u5373\u8fdb\u5165 critical section \u4f1a\u5bfc\u81f4 <code>LOCK</code> \u53d8\u4e3a <code>false</code>\uff0c\u4f46\u79bb\u5f00 critical section \u5fc5\u5b9a\u5bfc\u81f4 <code>LOCK</code> \u53d8\u4e3a true\u3002\u56e0\u6b64\uff0c\u53ea\u8981\u6ca1\u6709\u8fdb\u7a0b\u5904\u4e8e critical section\uff0c\u90a3\u4e48 <code>LOCK</code> \u5fc5\u5b9a\u4e3a <code>false</code>\uff0c\u5219\u4e00\u5b9a\u6709\u5c31\u7eea\u7684\u8fdb\u7a0b\u80fd\u591f\u8fdb\u5165 critical section\uff0c\u800c\u8fd0\u884c critical section \u7684\u65f6\u95f4\u662f\u6709\u9650\u7684\uff0c\u56e0\u6b64 <code>LOCK</code> \u53c8\u4e00\u5b9a\u4f1a\u5728\u6709\u9650\u65f6\u95f4\u5185\u53d8\u4e3a <code>false</code>\uff0c\u4ece\u800c\u6ee1\u8db3 progress\u3002</p> <p>bounded waiting time</p> <p>\u5982\u679c\u53ea\u6709\u4e24\u4e2a\u8fdb\u7a0b\u53c2\u4e0e\u7ade\u4e89\uff0c\u90a3\u4e48\u901a\u8fc7\u7c7b\u4f3c\u8bc1\u660e progress \u7684\u8fc7\u7a0b\u53ef\u4ee5\u5f97\u5230 bounded waiting time \u662f\u53ef\u4ee5\u6210\u7acb\u7684\u3002A \u79bb\u5f00\u4e34\u754c\u6001\u540e\u5904\u4e8e\u5c31\u7eea\u6001\u7b49\u5f85\u7684 B \u7acb\u523b\u5c31\u80fd\u8fdb\u5165 critical section\uff0c\u5373\u53ea\u6709\u4e24\u4e2a\u4eba\u6392\u961f\u662f\u4e0d\u4f1a\u88ab\u63d2\u961f\u7684\u3002</p> <p>\u4f46\u5728\u53c2\u4e0e\u7ade\u4e89\u7684\u8fdb\u7a0b\u53d8\u591a\u4ee5\u540e\uff0c\u5c31\u5f88\u6709\u53ef\u80fd\u51fa\u73b0\u7c7b\u4f3c\u4e8e\u8c03\u5ea6\u4e2d\u201c\u9965\u997f\u201d\u7684\u73b0\u8c61\uff1a</p> <pre><code>    \u250c\u2500\u2500\u2500\u2500\u2510      \u250c\u2500\u2500\u2500\u2500\u2510      \u250c\u2500\u2500\u2500\u2500\u2510      \u250c\u2500\u2500\u2500\u2500\u2510      \nP0  \u2502 CS \u2502   \u2500\u2500\u2500\u2524 CS \u2502   \u2500\u2500\u2500\u2524 CS \u2502   \u2500\u2500\u2500\u2524 CS \u2502   \u2500\u2500\u2500 \u00b7\u00b7\u00b7\n    \u2514\u2500\u2500\u2500\u2500\u2518      \u2514\u2500\u2500\u2500\u2500\u2518      \u2514\u2500\u2500\u2500\u2500\u2518      \u2514\u2500\u2500\u2500\u2500\u2518      \n          \u250c\u2500\u2500\u2500\u2500\u2510      \u250c\u2500\u2500\u2500\u2500\u2510      \u250c\u2500\u2500\u2500\u2500\u2510      \u250c\u2500\u2500\u2500\u2500\u2510\nP1  \u2500\u2500\u2500\u2500\u2500\u2500\u2524 CS \u2502   \u2500\u2500\u2500\u2524 CS \u2502   \u2500\u2500\u2500\u2524 CS \u2502   \u2500\u2500\u2500\u2524 CS \u2502 \u00b7\u00b7\u00b7\n          \u2514\u2500\u2500\u2500\u2500\u2518      \u2514\u2500\u2500\u2500\u2500\u2518      \u2514\u2500\u2500\u2500\u2500\u2518      \u2514\u2500\u2500\u2500\u2500\u2518\n\nP2  \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 \u00b7\u00b7\u00b7\n</code></pre> <p>\u53ef\u4ee5\u53d1\u73b0\uff0c\u7531\u4e8e <code>P0</code> \u548c <code>P1</code> \u603b\u662f\u8f6e\u6d41\u83b7\u5f97\u9501\uff0c\u5bfc\u81f4 <code>P2</code> \u59cb\u7ec8\u5904\u4e8e\u5c31\u7eea\u6001\u7b49\u5f85\u9501\uff0c\u56e0\u800c\u5bf9\u4e8e <code>P2</code> \u6765\u8bf4 waiting time \u5c31\u4e0d\u518d\u6709\u9650\u4e86\u3002</p> <p>\u7cdf\u4e86\uff0c\u770b\u8d77\u6765\u5f88\u9177\u7684\u4e00\u4e2a\u65b9\u6cd5\u8c8c\u4f3c\u4e0d\u80fd\u6ee1\u8db3 CS \u89e3\u6cd5\u7684\u6027\u8d28\uff0c\u4f46\u4ed4\u7ec6\u5206\u6790\uff0c\u8fd9\u662f\u7531\u4e8e\u9501\u7684\u5206\u914d\u673a\u5236\u662f\u4e0d\u53ef\u63a7\u7684\u2014\u2014\u5728\u4e00\u4e2a\u9501\u88ab\u91ca\u653e\u540e\uff0c\u63a5\u4e0b\u6765\u5c06\u62ff\u5230\u9501\u7684\u8fdb\u7a0b\u5e94\u5f53\u662f\u63a5\u4e0b\u6765\u7b2c\u4e00\u4e2a\u5b9e\u9645\u6267\u884c <code>test_and_set()</code> \u7684\u8fdb\u7a0b\uff0c\u7136\u800c\u7531\u4e8e \u2776 \u6211\u4eec\u5bf9\u6bcf\u4e2a\u8fdb\u7a0b\u7684\u8fd0\u884c\u901f\u5ea6\uff0c\u4e0d\u5e94\u5f53\u6709\u5047\u8bbe\uff0c\u2777 \u6211\u4eec\u5bf9\u540c\u65f6\u4ea7\u751f\u7684 <code>test_and_set()</code> \u5c06\u6309\u4f55\u987a\u5e8f\u88ab\u5904\u7406\uff0c\u4e0d\u5e94\u5f53\u6709\u5047\u8bbe\uff0c\u6240\u4ee5\u6211\u4eec\u5fc5\u987b\u624b\u52a8\u7528\u67d0\u79cd\u65b9\u6cd5\u6765\u5b9e\u73b0\u8fd9\u79cd\u201c\u9501\u7684\u8c03\u5ea6\u201d\uff1a</p> <pre><code>// `i` is process id in [0, n), where `n` is the count of related process. \nprocess(i) {\nWAITING[i] = true;                                  // \u2510\nwhile ( WAITING[i] &amp;&amp; test_and_set(&amp;LOCK) ) {}      // \u251c entry sec.\n// \u2502\nWAITING[i] = false;                                 // \u2518\n\n/* operate critical resources */                    // - critical sec.\n\n// i.e. find next waiting process j                 // \u2510\nj = (i + 1) % n;                                    // \u2502\nwhile (i != j &amp;&amp; !WAITING[j]) {                     // \u251c exit sec.\nj = (i + 1) % n;                                // \u2502\n}                                                   // \u2502\n// release j's LOCK or release whole LOCK           // \u2502\nif (i == j)     LOCK = false;                       // \u2502\nelse            WAITING[j] = false;                 // \u2518\n\n/* other things */                                  // - remainder sec.\n}\n</code></pre> <p>\u6211\u4eec\u5f15\u5165\u4e86\u4e00\u4e2a <code>WAITING[]</code> \u6570\u7ec4\u6765\u8f85\u52a9 <code>LOCK</code> \u7ec6\u5316\u9501\u7684\u7c92\u5ea6\uff0c\u6b64\u65f6 <code>LOCK</code> \u8868\u793a\u7684\u201c\u662f\u5426\u5b58\u5728\u7ade\u4e89\u201d\uff0c\u800c <code>WAITING[]</code> \u5219\u6807\u8bc6\u4e86\u6240\u6709\u6b63\u5728\u7b49\u5f85\u7684\u8fdb\u7a0b\u3002\u533a\u522b\u4e8e\u4e4b\u524d\u76f4\u63a5\u91ca\u653e\u6574\u4e2a\u9501\uff0c\u8ba9\u5269\u4e0b\u7684\u8fdb\u7a0b\u53bb\u201c\u62fc\u624b\u901f\u201d\uff0c\u6211\u4eec\u8fd9\u6b21\u7531\u91ca\u653e\u9501\u7684\u8fdb\u7a0b\u6765\u9009\u62e9\u4e0b\u4e00\u4e2a\u8fdb\u5165 critical section \u7684\u662f\u8c01\u3002</p> <p>\u5728 11-14 \u884c\uff0c\u901a\u8fc7\u4e00\u4e2a\u5faa\u73af\u627e\u5230\u4e0b\u4e00\u4e2a <code>WAITING[j]</code> \u4e3a <code>true</code> \u7684 j\uff0c\u2776 \u5982\u679c\u627e\u5230\u4e86\u8fd9\u4e2a j\uff0c\u90a3\u4e48\u5c31\u5c06 <code>WAITING[j]</code> \u8bbe\u4e3a <code>false</code>\uff0819 \u884c\uff09\uff0c\u8fd9\u6837 j \u9a6c\u4e0a\u5c31\u4f1a\u5728\u7b2c 4 \u884c break\uff0c\u8fdb\u5165 critical section\uff1b\u2777 \u800c\u5982\u679c\u627e\u4e0d\u5230\u8fd9\u4e2a j\uff0c\u5373\u627e\u4e86\u4e00\u5708\u53c8\u627e\u56de\u4e86 i\uff0c\u90a3\u4e48\u8bf4\u660e i \u662f\u6700\u540e\u4e00\u4e2a\u4e86\uff0c\u6240\u4ee5\u53ef\u4ee5\u76f4\u63a5\u91ca\u653e\u6574\u4e2a\u9501\uff0817 \u884c\uff09\u3002</p> <p>\u901a\u8fc7\u4f7f\u7528\u8fd9\u79cd\u65b9\u6cd5\uff0c\u6211\u4eec\u4fdd\u8bc1\u4e86\u7b49\u5f85\u4e2d\u7684\u8fdb\u7a0b\u6700\u591a\u53ea\u9700\u8981\u7b49\u5f85 n-1 \u4e2a\u8fdb\u7a0b\u8fd0\u884c\u5b8c critical section\uff08\u7c7b\u4f3c\u4e8e\u5b9e\u73b0\u4e86\u201cFCFS\u201d\uff09\u3002</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit2-Part1/#compare_and_swap","title":"<code>compare_and_swap()</code>","text":"<p>Links</p> <ul> <li>Wikipedia</li> </ul> <p><code>compare_and_swap()</code> \u4e5f\u88ab\u7b80\u5199\u4e3a CAS \u6307\u4ee4\uff0c\u5b83\u7684\u529f\u80fd\u5982\u4e0b\uff1a</p> <pre><code>&lt;atomic&gt; compare_and_swap(int * target, int expected, int new_val) {\nint ret = *target;\n\n// *target = (*target == expected) ? new_val : *target;\nif (*target == expected) {\n*target = new_val;\n}\n\nreturn ret;\n}\n</code></pre> <p>CAS \u63a5\u53d7\u4e09\u4e2a\u503c\uff1a</p> <ol> <li><code>target</code> \u5f85\u4fee\u6539\u7684\u6570\u636e\u7684\u5730\u5740\uff1b</li> <li><code>expected</code> \u9884\u671f\u4e2d\u5f85\u4fee\u6539\u7684\u6570\u636e\u7684\u65e7\u503c\uff1b</li> <li><code>new_val</code> \u5e0c\u671b\u5c06\u6570\u636e\u4fee\u6539\u4e3a\u7684\u65b0\u503c\uff1b</li> </ol> <p>\u800c\u5f53\u4e14\u4ec5\u5f53 <code>*target</code> \u7b26\u5408\u9884\u671f\uff0c\u4e0e <code>expected</code> \u76f8\u540c\u65f6\u5019\uff0c\u624d\u4f1a\u5c06\u5b83\u6539\u4e3a <code>new_val</code>\u3002\u540c\u6837\uff0cCAS \u4e5f\u5e94\u5f53\u4fdd\u8bc1\u539f\u5b50\u6027\uff0c\u5373\u82e5\u5e72 CAS \u540c\u65f6\u53d1\u751f\u65f6\uff0c\u4e5f\u5e94\u5f53\u4e00\u4e2a\u4e00\u4e2a\u7684\u6267\u884c\uff0c\u800c\u4e0d\u80fd\u5b58\u5728\u65f6\u95f4\u4e0a\u7684\u4ea4\u96c6\u3002</p> <p>\u6211\u4eec\u6ce8\u610f\u5230\uff0c\u5b9e\u9645\u4e0a <code>test_and_set(target)</code> \u5c31\u662f <code>compare_and_swap(target, false, true)</code>\uff0c\u56e0\u800c\u5b9e\u9645\u4e0a CAS \u89e3\u51b3 CS \u95ee\u9898\u7684\u65b9\u6cd5\u4ee5\u53ca\u95ee\u9898\u548c\u4e0a\u4e00\u8282\u7684\u5185\u5bb9\u6ca1\u4ec0\u4e48\u5dee\u522b\u3002</p> <p>\u4f46\u662f\u6211\u4eec\u53d1\u73b0\uff0c<code>compare_and_swap()</code> \u76f8\u6bd4\u4e8e <code>test_and_set()</code>\uff0c\u663e\u7136\u6709\u66f4\u5927\u7684\u64cd\u4f5c\u7a7a\u95f4\uff0c\u4e5f\u66f4\u6cdb\u7528\uff0c\u8003\u8651\u5230 CAS \u6307\u4ee4\u81ea\u8eab\u5df2\u7ecf\u80fd\u591f\u652f\u6301\u539f\u5b50\u6027\u7684\u4fee\u6539\u503c\uff0c\u6211\u4eec\u8003\u8651\u80fd\u5426\u8df3\u51fa CS \u95ee\u9898\u7684\u8303\u5f0f\u6765\u8003\u8651\u95ee\u9898\u3002</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit2-Part1/#atomic-variables","title":"Atomic Variables","text":"<p>\u539f\u5b50\u53d8\u91cf(atomic variables)\u662f\u4e00\u79cd\u7528\u539f\u5b50\u6027\u64cd\u4f5c\u7ef4\u62a4\u7684\u53d8\u91cf\u3002\u6211\u4eec\u6240\u6709\u5bf9\u539f\u5b50\u53d8\u91cf\u7684\u64cd\u4f5c\u53ef\u4ee5\u901a\u8fc7 CAS \u6765\u5b9e\u73b0\uff0c\u4f8b\u5982\u81ea\u589e\u64cd\u4f5c\uff1a</p> <pre><code>increment(atomic_int * v) {\nint tmp;\ndo {\ntmp = *v;\n} while ( tmp != compare_and_swap(v, tmp, tmp+1) );\n}\n</code></pre> <p>\u4f7f\u7528 atomic variables \u540e\u5b9e\u9645\u4e0a\u5c31\u4e0d\u592a\u7b26\u5408 CS \u95ee\u9898\u7684\u6a21\u578b\u4e86\uff0c\u53ef\u4ee5\u53d1\u73b0\uff0c\u8fd9\u91cc\u5e76\u4e0d\u518d\u9700\u8981\u7ef4\u62a4\u7c7b\u4f3c <code>LOCK</code> \u7684\u4e1c\u897f\uff0c\u800c\u662f\u4ee5 <code>*target</code> \u662f\u5426\u7b26\u5408 <code>expected</code> \u7684\u9884\u8bbe\u6765\u5224\u65ad\u662f\u5426\u6709\u7ade\u4e89\u51fa\u73b0\uff0c\u4f5c\u4e3a\u4e00\u4e2a\u540c\u6b65\u5de5\u5177\uff0c\u6211\u4eec\u53ef\u4ee5\u76f4\u63a5\u4f7f\u7528\u8fd9\u79cd\u5c01\u88c5\u540e\u7684\u539f\u5b50\u6027\u64cd\u4f5c\u6765\u89e3\u51b3 race condition\uff0c\u800c\u4e0d\u9700\u8981\u518d\u533a\u5206 entry section \u6216\u662f critical section \u7b49\u3002</p> <p>\u4e66\u672c\u4e0a\u7279\u5730\u63d0\u5230\uff0c\u5728\u4f8b\u5982 producer&amp;consumer \u7684\u6a21\u578b\u4e2d\uff0c\u4f7f\u7528 atomic variables \u7ef4\u62a4 count \u5e76\u4e0d\u80fd\u89e3\u51b3 race condition\uff0c\u4f46\u6211\u8ba4\u4e3a\u8fd9\u79cd\u8ba8\u8bba\u662f\u6709\u5931\u504f\u9887\u7684\uff0c\u6240\u8c13\u7684\u201c\u539f\u5b50\u6027\u201d\u5e94\u8be5\u5305\u62ec\u6240\u6709\u64cd\u4f5c\u4e34\u754c\u8d44\u6e90\u7684\u90e8\u5206\uff0c\u4e66\u4e2d\u53ea\u7ef4\u62a4 count \u4e0d\u7ef4\u62a4 buffer \u7684\u5047\u8bbe\u6211\u89c9\u5f97\u5bf9\u4e8e atomic \u8fd9\u4e2a\u6982\u5ff5\u6765\u8bf4\u5b9e\u5728\u4e0d\u591f\u516c\u5e73\u3002\u6240\u4ee5\u6211\u5728\u8fd9\u91cc\u5c31\u4e0d\u7740\u91cd\u8bf4\u660e\u8fd9\u4e2a\u95ee\u9898\u3002</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit2-Part1/#mutex-locks","title":"Mutex Locks","text":"<p>\u7531\u6b64\u6211\u4eec\u5df2\u7ecf\u5f97\u5230\u4e86\u80fd\u5728\u786c\u4ef6\u5c42\u9762\u89e3\u51b3 race condition \u95ee\u9898\u7684\u6839\u6e90\u7684\u5de5\u5177\u4e86\uff0c\u4f46\u662f\u4e3a\u4e86\u80fd\u8ba9\u7528\u6237\u7a0b\u5e8f\u4e5f\u80fd\u66f4\u597d\u7684\u4f7f\u7528\uff0c\u6211\u4eec\u9700\u8981\u5c06\u5b83\u505a\u4e00\u6b21\u8f6f\u4ef6\u5c42\u9762\u7684\u5c01\u88c5\u3002\u4e8e\u662f\uff0c\u6211\u4eec\u8bbe\u8ba1\u4e86\u4e92\u65a5\u9501(mutex locks)\u8fd9\u4e2a\u4e1c\u897f\u3002</p> <p>\u5229\u7528\u4e92\u65a5\u9501\u907f\u514d race condition \u7684\u57fa\u672c\u601d\u8def\u4ecd\u7136\u662f\u57fa\u4e8e CS \u95ee\u9898\u7684\u5efa\u6a21\uff0c\u4f46\u5b83\u66f4\u5177\u4f53\u5730\u8ba4\u4e3a\u5728 entry section \u5c31\u8be5\u53bb\u7d22\u53d6\u4e92\u65a5\u9501\uff0c\u800c\u5728 exit section \u5c31\u5e94\u8be5\u53bb\u91ca\u653e\u4e92\u65a5\u9501\uff0c\u5373\uff1a</p> <pre><code>\u250c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2510\n\u2502  Acquire Lock       \u2502\n\u251c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2524\n\u2502  Critical Section   \u2502 &lt;-- codes manipulating critical resources\n\u251c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2524\n\u2502  Release Lock       \u2502\n\u251c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2524\n\u2502  Remainder Section  \u2502 &lt;-- other codes\n\u2514\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2518\n</code></pre> <p>\u56de\u987e\u6211\u4eec\u5728\u4ecb\u7ecd <code>test_and_set()</code> \u90e8\u5206\u7ed9\u51fa\u7684\u8fd9\u6bb5\u4ee3\u7801\uff1a</p> <pre><code>process(i) {\nwhile ( test_and_set(&amp;LOCK) ) {}    // - entry section\n/* operate critical resources */    // - critical section\n\nLOCK = false;                       // - exit section\n/* other things */                  // - remainder section\n}\n</code></pre> <p>\u6211\u4eec\u53ea\u9700\u8981\u5c06\u9ad8\u4eae\u7684\u8fd9\u4e24\u884c\u5c01\u88c5\u8d77\u6765\uff0c\u5c31\u5b9e\u73b0\u4e86 acquire LOCK \u548c release LOCK\u3002</p> <pre><code>// `available` means whether the `LOCK` is free, or whether the related resources is available\nacquire() {\nwhile ( !compare_and_swap(&amp;available, true, false) ) {}\n}\n\nrelease() {\navailable = true;\n}\n</code></pre> <p>\u4f60\u53ef\u80fd\u6ce8\u610f\u5230\u4e86\uff0c\u6211\u4eec\u5728 <code>test_and_set()</code> \u8ba8\u8bba\u4e0a\u9762\u90a3\u6bb5\u4ee3\u7801\u7684\u65f6\u5019\uff0c\u8ba8\u8bba\u8fc7\u5b83\u65e0\u6cd5\u6ee1\u8db3 bounded waiting time \u7684\u95ee\u9898\uff0c\u90a3\u65e2\u7136\u5982\u6b64\u6211\u4eec\u4e3a\u4ec0\u4e48\u4e0d\u628a <code>WAITING[]</code> \u4e5f\u4e00\u8d77\u5c01\u8fdb\u53bb\u5462\uff1f</p> <p>\u8fd9\u662f\u56e0\u4e3a\u4e66\u4e0a\u76f4\u63a5\u5ffd\u7565\u4e86\u8fd9\u4e2a\u95ee\u9898\uff0c\u76f4\u5230\u5728\u4e4b\u540e\u8bb2 semaphores \u7684\u65f6\u5019\u624d\u60f3\u8d77\u6765\uff0c\u4f46 semaphores \u548c mutex lock \u53c8\u662f\u4e24\u4e2a\u8def\u5b50\uff0c\u6211\u4e5f\u4e0d\u77e5\u9053\u5b83\u5230\u5e95\u60f3\u8bf4\u660e\u4ec0\u4e48\u95ee\u9898\u3002\u4f46\u662f\u65e2\u7136\u5b83\u73b0\u5728\u5ffd\u7565\u4e86\uff0c\u6211\u4eec\u5c31\u5148\u4e0d\u7ba1\u5b83\uff0c\u4f46\u662f\u6211\u5e0c\u671b\u8bfb\u8005\u80fd\u610f\u8bc6\u5230\u8fd9\u4e2a\u95ee\u9898\u662f\u5b58\u5728\u7684\u3002</p> <p>\u7ecf\u8fc7\u8fd9\u4e48\u957f\u7684\u94fa\u57ab\uff0c\u6211\u4eec\u73b0\u5728\u80fd\u591f\u4fdd\u8bc1\u7684\u4e00\u4ef6\u4e8b\u662f\uff0c\u6211\u4eec\u7ec8\u4e8e\u5f97\u5230\u4e86\u4e00\u4e2a\u8f6f\u4ef6\u5c42\u9762\u7684\u3001\u80fd\u591f\u907f\u514d race condition \u7684\u540c\u6b65\u5de5\u5177\u3002\u90a3\u4e48\u5b9e\u73b0\u57fa\u672c\u9700\u6c42\u4ee5\u540e\u6211\u4eec\u5c31\u5f00\u59cb\u8003\u8651\u80fd\u4e0d\u80fd\u4f18\u5316\u5b83\u3002</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit2-Part1/#\u5fd9\u7b49\u5f85","title":"\u5fd9\u7b49\u5f85","text":"<p>\u5982\u679c\u8bfb\u8005\u5bf9\u4ee3\u7801\u6709\u6bd4\u8f83\u654f\u611f\u7684\u55c5\u89c9\uff0c\u90a3\u53ef\u80fd\u770b\u8fd9\u51e0\u5343\u4e2a\u5b57\u5230\u73b0\u5728\uff0c\u4f60\u5df2\u7ecf\u4e3a\u6570\u4e0d\u6e05\u7684 <code>while()</code> \u63d0\u5fc3\u540a\u80c6\u8fc7\u5341\u591a\u6b21\u4e86\u3002\u6ca1\u9519\uff0c\u867d\u7136\u6211\u4eec\u901a\u8fc7\u903b\u8f91\u4fdd\u8bc1\u8fd9\u91cc\u4e0d\u4f1a\u51fa\u73b0\u6b7b\u5faa\u73af\uff0c\u4f46\u5bf9\u4e8e\u7b49\u5f85\u4e2d\u7684 process\uff0c\u786e\u5b9e\u8981\u5728\u6570\u4e0d\u5c3d\u7684 <code>while</code> loop \u4e2d\u6d6a\u8d39 CPU\uff0c\u6211\u4eec\u79f0\u8fd9\u79cd\u7b49\u5f85\u9501\u91ca\u653e\u7684\u884c\u4e3a\u4e3a\u5fd9\u7b49\u5f85(busy waiting)\uff0c\u5176\u4e2d\u201c\u5fd9\u201d\u6307\u7684\u5c31\u662f\u5728\u7b49\u5f85\u8fc7\u7a0b\u4e2d\u4ecd\u7136\u5360\u7528 CPU \u8d44\u6e90\u3002\u800c\u8fd9\u79cd\u4f7f\u7528\u5fd9\u7b49\u5f85\u7684\u4e92\u65a5\u9501\uff0c\u4e5f\u88ab\u79f0\u4e3a\u81ea\u65cb\u9501(spinLOCK)\u3002</p> <p>\u6211\u4eec\u5f15\u5165\u4e24\u4e2a\u8bcd\u6765\u66f4\u51c6\u786e\u7684\u63cf\u8ff0\u8fd9\u4ef6\u4e8b\uff1a</p> <p>Lock Contention</p> <p>\u5982\u679c\u4e00\u4e2a\u7528\u6237\u8bd5\u56fe\u7d22\u53d6\u67d0\u4e2a\u9501\u65f6\uff0c\u5982\u679c\u8fd9\u4e2a\u9501\u4e0d\u662f available \u7684\uff0c\u8fd9\u5c31\u610f\u5473\u7740\u6709\u7528\u6237\u6b63\u5728\u4f7f\u7528\u8fd9\u4e2a\u9501\uff0c\u800c\u5f53\u524d\u7528\u6237\u9700\u8981\u7b49\u5f85\u8fd9\u4e2a\u9501\u91cd\u65b0\u53ef\u7528\uff0c\u6b64\u65f6\u6211\u4eec\u79f0\u8fd9\u4e2a\u9501\u662f\u88ab\u4e89\u62a2\u7684(contended)\uff1b\u53cd\u4e4b\uff0c\u5982\u679c\u4e0d\u5b58\u5728\u4e89\u62a2\uff0c\u6211\u4eec\u5c31\u79f0\u4e4b\u4e3a\u4e0d\u88ab\u4e89\u62a2\u7684(uncontended)\u3002</p> <p>\u5982\u679c\u73b0\u5728\u6709\u597d\u591a\u7528\u6237\u90fd\u5728\u4e89\u62a2\u4e00\u4e2a\u9501\uff0c\u6211\u4eec\u79f0\u4e4b\u4e3a high contention\uff1b\u53cd\u4e4b\u5982\u679c\u53ea\u6709\u96f6\u661f\u51e0\u4e2a\u7528\u6237\u5728\u4e89\u62a2\u8fd9\u4e2a\u9501\uff0c\u6211\u4eec\u79f0\u4e4b\u4e3a low contention\u3002</p> <p>\u5982\u679c\u5ef6\u7528 spinLOCK\uff0c\u90a3\u4e48\u4e0d\u96be\u5f97\u5230\u7ed3\u8bba\uff1ahigh contention \u4f1a\u5bfc\u81f4\u4e25\u91cd\u7684\u6027\u80fd\u95ee\u9898\uff0c\u56e0\u4e3a\u603b\u662f\u4f1a\u6709\u5927\u91cf\u5f97\u4e0d\u5230\u9501\u7684\u7528\u6237\u5904\u4e8e busy waiting \u4e2d\u3002</p> <p>\u65e2\u7136\u5b83\u4eec\u90fd\u662f\u5728\u505a\u65e0\u610f\u4e49\u7684\u7b49\u5f85\uff0c\u90a3\u6211\u4eec\u4e3a\u4ec0\u4e48\u4e0d\u5728\u8fd9\u4e2a\u65f6\u5019\u628a\u8d44\u6e90\u8ba9\u7ed9\u6709\u9700\u8981\u7684\u4eba\u5462\uff1f</p> <p>\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u6682\u65f6\u5730\u5207\u6362\u8fdb\u7a0b\uff0c\u8ba9\u8fd9\u4e9b\u5904\u4e8e\u7b49\u5f85\u7684\u7528\u6237\u6682\u65f6\u4f11\u7720\uff0c\u7b49\u65f6\u673a\u5230\u6765\u518d\u5524\u9192\u5b83\u4eec\uff0c\u6b64\u65f6\u5c31\u9700\u8981\u7cfb\u7edf\u8c03\u7528\u7684\u4ecb\u51653\u3002\u800c\u5177\u4f53\u7684\u65b9\u6cd5\u6211\u4eec\u5728\u4e0b\u4e00\u8282\u7684\u907f\u514d\u5fd9\u7b49\u5f85\u4e2d\u4ecb\u7ecd\u3002</p> <p>\u4f46\u662f\u8bf7\u6ce8\u610f\uff0c\u6211\u4eec\u5728\u8fd9\u91cc\u9700\u8981\u4fdd\u6301\u5ba2\u89c2\uff1aspinLOCK \u5728\u7279\u5b9a\u60c5\u51b5\u4e0b\u662f\u6709\u597d\u5904\u7684\uff0c\u5728\u7b49\u5f85\u65f6\u95f4\u5e76\u4e0d\u957f\u7684\u60c5\u51b5\u4e0b\uff0c\u76f8\u6bd4\u4e8e\u62e5\u6709\u9501\u7684\u7528\u6237\u91ca\u653e\u9501\uff0c\u8fdb\u884c\u8c03\u5ea6\u9501\u9700\u8981\u7684 context switch \u7684\u5f00\u9500\u53ef\u80fd\u663e\u5f97\u8f83\u5927\uff0c\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\u6211\u4eec\u8fd8\u6ca1\u6765\u5f97\u53ca\u628a\u8d44\u6e90\u8ba9\u7ed9\u522b\u4eba\u9501\u5c31\u597d\u4e86\uff0c\u90a3\u4e48\u8fd9\u79cd\u8d44\u6e90\u8f6c\u8ba9\u8fd8\u4e0d\u5982\u4e0d\u8f6c\u3002\u800c\u4e8b\u5b9e\u4e0a\uff0c\u5728\u7279\u5b9a\u60c5\u51b5\u4e0b\uff0c\u81ea\u65cb\u9501\u4e5f\u786e\u5b9e\u662f\u4e00\u4e9b\u591a\u6838\u7cfb\u7edf\u7684\u9996\u9009\u3002</p> <p>\u4e0d\u8fc7\u5728\u8bb8\u591a\u8bed\u5883\u91cc mutex \u548c spinLOCK \u662f\u533a\u5206\u5f00\u6765\u7684\u4e24\u4e2a\u6982\u5ff5\uff0c\u5177\u4f53\u4f7f\u7528\u54ea\u4e2a\u5219\u9700\u8981\u9002\u65f6\u5224\u65ad4\u3002</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit2-Part1/#semaphores","title":"Semaphores","text":"<p>Links</p> <ul> <li>Wikipedia</li> </ul> <p>Mutex LOCK \u4e3a\u7528\u6237\u7a0b\u5e8f\u63d0\u4f9b\u4e86\u7c7b\u4f3c\u4e8e\u201c\u623f\u95f4\u7533\u8bf7\u201d\u7684\u529f\u80fd\uff0c\u9501\u7ade\u4e89\u5c31\u597d\u50cf\u5927\u5bb6\u62a2\u623f\u95f4\u7684\u4f7f\u7528\u6743\u3002\u800c\u4fe1\u53f7\u91cf(semaphores)\u5219\u662f\u7c7b\u4f3c\u4e8e\u6211\u4eec\u4e4b\u524d\u63d0\u5230\u8fc7\u7684 atomic variables\uff0c\u901a\u8fc7\u63d0\u4f9b\u6807\u51c6\u5316\u7684\u539f\u5b50\u6027\u64cd\u4f5c\uff0c\u6765\u7ef4\u62a4\u4e00\u4e9b\u53d8\u91cf\uff0c\u53ea\u4e0d\u8fc7\u5b83\u989d\u5916\u5bf9\u53d8\u91cf\u7684\u503c\u6709\u4e00\u5b9a\u7684\u7ea6\u675f\u3002</p> <p>\uff08\u8bf4\u5b9e\u8bdd\u6211\u611f\u89c9\u8fd9\u4fe9\u4e1c\u897f\u672c\u8d28\u4e0a\u771f\u6ca1\u5565\u533a\u522b\u2026\u2026\uff09</p> <p>Semaphores \u53ea\u63d0\u4f9b\u4e24\u4e2a\u6807\u51c6\u5316\u7684\u63a5\u53e3\uff1a<code>wait()</code>\uff08\u6216<code>P()</code>\uff09 \u548c <code>signal()</code>\uff08\u6216<code>V()</code>\uff09\uff0c\u5b83\u4eec\u7684\u529f\u80fd\u5982\u4e0b\uff1a</p> <pre><code>&lt;atomic&gt; wait(reference S) {\nwhile (S &lt;= 0) {} // busy wait here\nS--;\n}\n\n&lt;atomic&gt; signal(reference S) {\nS++;\n}\n</code></pre> <p>\u663e\u7136\uff0c\u8fd9\u4e24\u4e2a\u64cd\u4f5c\u7684\u5b9e\u73b0\u4e5f\u5e94\u5f53\u4fdd\u8bc1\u662f atomic \u7684\u3002</p> <p>\u533a\u522b\u4e8e\u666e\u901a\u7684 atomic variables\uff0csemaphores \u591a\u4e86\u5728\u7b2c 2 \u884c\u7684 busy wait\uff0c\u8fd9\u6697\u542b\u4e86\u4e00\u79cd\u201c\u6709\u9650\u201d\u7684\u6982\u5ff5\uff0c\u5373\u4fdd\u8bc1 \\(0 \\leq S\\)\u3002\u5728\u5b9e\u9645\u4f7f\u7528\u4e2d\uff0csemaphores \u5206\u4e3a counting semaphore \u548c binary semaphore\uff0c\u524d\u8005\u7684\u529f\u80fd\u5982\u4e0a\uff0c\u540e\u8005\u53ea\u4e0d\u8fc7\u662f\u989d\u5916\u8981\u6c42 \\(0 \\leq S \\leq 1\\)\uff0c\u4fee\u6539 loop \u7684\u6761\u4ef6\u5373\u53ef\u3002</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit2-Part1/#\u4f7f\u7528","title":"\u4f7f\u7528","text":"<p>\u4f8b\u5982\uff0c\u6211\u4eec\u53ef\u4ee5\u7528\u5982\u4e0b\u65b9\u5f0f\uff0c\u4fdd\u8bc1 <code>P0()</code> \u4e2d\u7684 section A \u5fc5\u987b\u5728 <code>P1()</code> \u7684 section B \u4e4b\u524d\u5b8c\u6210\uff1a</p> <pre><code>semaphore S = 0;\n\nP0() {\n/* Section A */\nsignal(S);\n}\n\nP1() {\nwait(S);\n/* Section B */\n}\n</code></pre> <p>\u4e0a\u9762\u7684\u4f8b\u5b50\u975e\u5e38\u5f62\u8c61\u5730\u5c55\u793a\u4e86\u4fe1\u53f7\u91cf\u662f\u5982\u4f55\u53d1\u6325\u4f5c\u7528\u7684\uff0c\u5f53\u7136\uff0c\u4e0a\u9762\u53ea\u5c55\u793a\u4e86\u7c7b\u4f3c\u8fdb\u7a0b\u95f4\u901a\u8baf\u7684\u529f\u80fd\uff0c\u4e0b\u9762\u8fd9\u4e2a\u5f62\u5f0f\u5219\u66f4\u63a5\u8fd1\u6211\u4eec\u4e0a\u6587\u4e2d\u8ba8\u8bba\u7684\u60c5\u51b5\uff0c\u5373\u5b9e\u73b0\u4e86\u4e92\u65a5\uff1a</p> <pre><code>// `i` is process id and S is the semaphores\nprocess(i) {\nwait(S);    // i.e. release the 'LOCK'\n\n/* critical section */\n\nsignal(S);  // only one process can pass this line at once\n}\n</code></pre>"},{"location":"cour_note/D3QD_OperatingSystem/Unit2-Part1/#\u907f\u514d\u5fd9\u7b49\u5f85","title":"\u907f\u514d\u5fd9\u7b49\u5f85","text":"<p>\u6211\u4eec\u5728 mutex \u4e2d\u63d0\u51fa\u5fd9\u7b49\u5f85\u7684\u65f6\u5019\u5c31\u5df2\u7ecf\u63d0\u5230\u8fc7\uff0c\u53ef\u4ee5\u901a\u8fc7\u300c\u5728\u7b49\u5f85\u7684\u65f6\u5019\u8ba9\u8fdb\u7a0b\u4f11\u7720\uff0c\u7b49\u65f6\u673a\u5408\u9002\u7684\u65f6\u5019\u518d\u5524\u9192\u300d\u7684\u65b9\u5f0f\uff0c\u6765\u51cf\u5c0f\u8f83\u957f\u7684\u5fd9\u7b49\u5f85\u5f15\u8d77\u7684\u6027\u80fd\u964d\u4f4e\u3002\u800c\u4e3a\u4e86\u5b9e\u73b0\u8fd9\u4e00\u70b9\uff0c\u6211\u4eec\u9700\u8981\u6269\u5c55 semaphores \u7684\u5185\u5bb9\uff0c\u5f15\u5165\u4e00\u4e2a\u94fe\u8868\u6765\u7ef4\u62a4\u7b49\u5f85\u4e2d\u7684\u8fdb\u7a0b\u3002</p> <pre><code>struct semaphore {\nvalue;\nwaiting_list;\n};\n\n&lt;atomic&gt; wait(reference S) {\nS-&gt;value--;\nif (S-&gt;value &lt; 0) {\nS-&gt;waiting_list.push(current process);\nsleep();\n}\n}\n\n&lt;atomic&gt; signal(reference S) {\nS-&gt;value++;\nif (S-&gt;value &lt;= 0) {\np = S-&gt;waiting_list.pop();\nwakeup(p);\n}\n}\n</code></pre> <p>\u76f8\u6bd4\u4e8e\u4e4b\u524d\u7684\u903b\u8f91\uff0c\u73b0\u5728\u7684\u903b\u8f91\u7a0d\u5fae\u6709\u70b9\u53d8\u5316\uff0c\u8bf7\u8bfb\u8005\u5c1d\u8bd5\u72ec\u7acb\u5206\u6790\u5176\u4e2d\u7684\u5965\u79d8\u3002\u8fd9\u91cc\u662f\u4e00\u4e9b\u63d0\u793a\uff1a</p> <p>\u601d\u8003\u9898</p> <ol> <li>\u73b0\u5728\u5df2\u7ecf\u6ca1\u6709 <code>while</code> \u4e86\uff0c\u53ea\u4f59\u4e0b <code>if</code>\uff0c\u73b0\u5728\u662f\u5982\u4f55\u4fdd\u8bc1\u7b49\u5f85\u4e2d\u7684\u8fdb\u7a0b\u80fd\u591f\u88ab\u53ca\u65f6\u5524\u9192\uff1f</li> <li><code>wait</code> \u539f\u5148\u662f\u5148\u7b49\u5f85\u518d\u4fee\u6539\uff0c\u73b0\u5728\u662f\u5148\u4fee\u6539\u3001\u518d\u7b49\u5f85\uff0c\u8fd9\u5bf9\u6574\u4f53\u903b\u8f91\u6709\u4f55\u5f71\u54cd\uff1f</li> <li><code>signal</code> \u4e2d\u7684\u6761\u4ef6\u8bed\u53e5\uff0c\u4e3a\u4f55\u662f <code>S-&gt;value &lt;= 0</code>\uff1f\u8fd9\u4e2a\u6761\u4ef6\u4e3a false \u65f6\u610f\u5473\u7740\u4ec0\u4e48\uff1f<ul> <li>\u8003\u8651\u5728 high contention \u7684\u60c5\u51b5\u4e0b\uff0c\u8d44\u6e90\u603b\u662f\u4e00\u51fa\u73b0\u5c31\u88ab\u62a2\u7a7a\u3002</li> </ul> </li> </ol> <ol> <li> <p>The Critical Section Problem \u21a9</p> </li> <li> <p>\u4e66\u672c\u4e2d\u5bf9 preemptive kernels \u548c non-preemptive kernels \u7684\u5b9a\u4e49\u5e76\u4e0d\u51c6\u786e\uff0c\u4e24\u8005\u6700\u672c\u8d28\u7684\u533a\u522b\u662f\u540e\u8005\u5b9e\u73b0\u4e86 Giant Lock\u3002\u540c\u65f6\u8bfb\u8005\u53ef\u4ee5\u53c2\u8003\u8fd9\u4e2a\u94fe\u63a5\uff1aWhat was the reason of the non-preemptivity of older Linux kernels? \u21a9</p> </li> <li> <p>Mutex access and system call \u21a9</p> </li> <li> <p>When should one use a spinLOCK instead of mutex? \u2b50\ufe0f\u00a0\u21a9</p> </li> </ol>"},{"location":"cour_note/D3QD_OperatingSystem/Unit2-Part2/","title":"U2 Part 2: \u540c\u6b65\u95ee\u9898\u4f8b\u5b50 | Synchronization Problems Examples","text":"<p> \u7ea6 1568 \u4e2a\u5b57  51 \u884c\u4ee3\u7801  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 6 \u5206\u949f</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit2-Part2/#the-bounded-buffer-problem","title":"The Bounded-Buffer Problem","text":""},{"location":"cour_note/D3QD_OperatingSystem/Unit2-Part2/#\u95ee\u9898\u80cc\u666f","title":"\u95ee\u9898\u80cc\u666f","text":"<ul> <li>\ud83d\udd17 Wiki</li> </ul> <p>The Bounded-Buffer Problem \u53c8\u79f0 The Producer\u2013Consumer Problem\uff0c\u5728\u8be5\u95ee\u9898\u4e2d\uff0c\u6709\u4e24\u4e2a\u89d2\u8272\uff0cproducer \u548c consumer\uff1aproducer \u4f1a\u4ea7\u751f item \u5b58\u653e\u5230 buffer \u4e2d\uff0c\u800c consumer \u53ef\u4ee5\u5c06\u6570\u636e\u4ece buffer \u4e2d\u53d6\u51fa item\u3002\u5982\u679c\u6211\u4eec\u7528 \\(n = \\# items\\) \u6765\u63cf\u8ff0 buffer \u7684\u72b6\u6001\uff0c\u90a3\u4e48\u95ee\u9898\u5c06\u62bd\u8c61\u4e3a\uff1a</p> <pre><code>void produce() {\n/* something */\n++n;\n/* something */\n}\n\nvoid consume() {\n/* something */\n--n;\n/* something */\n}\n</code></pre> <p>\u540c\u65f6\uff0c\u6211\u4eec\u9700\u8981\u4fdd\u8bc1 \\(0 \\leq n \\leq n_{max}\\)\uff0c\u6240\u4ee5\u6211\u4eec\u9700\u8981\u5728 \\(n = 0\\) \u65f6\uff0c\u8ba9 consumer \u7b49\u5f85 \\(n &gt; 0\\) \u518d <code>consume()</code>\uff1b\u5bf9\u5e94\u7684\uff0c\u5728 \\(n = \\leq n_{max}\\) \u65f6\u5019\uff0c\u8ba9 producer \u7b49\u5f85 \\(n &lt; n_{max}\\) \u518d <code>produce()</code>\u3002\u4f46\u8fd9\u5e76\u4e0d\u662f\u6211\u4eec\u5728\u672c\u5355\u5143\u63d0\u53ca\u5b83\u7684\u91cd\u70b9\uff0c\u6240\u4ee5\u6211\u4eec\u5728\u8fd9\u91cc\u8ba4\u4e3a\u5b83\u4eec\u5728 <code>/* something */</code> \u4e2d\u3002</p> <p>\u5b9e\u9645\u7684 The Bounded-Buffer Problem \u4e2d\u8fd8\u6709\u4e00\u4e9b\u5176\u5b83\u7ec6\u8282\uff0c\u4f46\u662f\u8fd9\u91cc\u6211\u4eec\u5c06\u6574\u4e2a\u95ee\u9898\u62bd\u8c61\u4e3a\u6211\u4eec\u9700\u8981\u7684\u6a21\u6837\uff0c\u8bf7\u4e0d\u8981\u8ba4\u4e3a\u4e0a\u9762\u7684\u4ee3\u7801\u5c31\u662f The Bounded-Buffer Problem \u7684\u5168\u90e8\u3002</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit2-Part2/#\u95ee\u9898\u63cf\u8ff0","title":"\u95ee\u9898\u63cf\u8ff0","text":"<p>\u8003\u8651\u5728\u5e76\u884c\u8bed\u5883\u4e0b\uff0c<code>produce()</code> \u548c <code>consume()</code> \u540c\u65f6\u53d1\u751f\uff0c\u7531\u4e8e <code>++n</code> \u548c <code>--n</code> \u8fd9\u4e9b\u64cd\u4f5c\u672c\u8d28\u4e0a\u662f\u6570\u503c\u7684\u3001\u9700\u8981\u4e00\u6bb5\u65f6\u95f4\u6765\u5b8c\u6210\u7684\uff0c\u6240\u4ee5\u5bb9\u6613\u51fa\u73b0 race condition\u95ee\u9898\u3002</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit2-Part2/#\u89e3\u51b3---semaphores","title":"\u89e3\u51b3 - semaphores","text":"<p>\u6211\u4eec\u4f7f\u7528\u4fe1\u53f7\u91cf\u6765\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\uff0c\u9700\u8981\u5b9a\u4e49\u4e09\u4e2a\u4fe1\u53f7\u91cf\uff1a</p> <pre><code>// suppose the capacity of the buffer is n\nsemaphore mutex = 1;\nsemaphore empty = n;\nsemaphore full  = 0;\n</code></pre> <p>\u903b\u8f91\u4e0a\u6211\u4eec\u8981\u6c42 <code>empty + full == n</code> \u59cb\u7ec8\u6210\u7acb\uff0c\u4f46\u662f\u5728\u5b9e\u9645\u8fd0\u884c\u8fc7\u7a0b\u4e2d\u53ef\u80fd\u4f1a\u4ea7\u751f\u4e00\u5b9a\u8bef\u5dee\uff08\u8003\u8651\u67d0\u4e2a\u539f\u8bed\u8fd8\u6ca1\u5f7b\u5e95\u6267\u884c\u5b8c\uff09\u3002\u800c\u6211\u4eec\u8fd9\u91cc\u4e4b\u6240\u4ee5\u8981\u4f7f\u7528\u4e24\u4e2a\u4fe1\u53f7\u91cf\u6765\u7ef4\u62a4\u4e00\u4e2a buffer \u7684\u5360\u7528\u72b6\u6001\uff0c\u662f\u56e0\u4e3a\u4fe1\u53f7\u91cf\u7684\u201c\u6709\u754c\u201d\u662f\u901a\u8fc7 0 \u7ef4\u62a4\u7684\uff0c\u4e5f\u5c31\u662f\u53ea\u6709\u5728\u201c\u51cf\u5c11\u201d\u7684\u65f6\u5019\u624d\u80fd\u7ef4\u62a4\uff1b\u800c\u6211\u4eec\u7684\u8981\u6c42\u662f\uff0cbuffer \u7684\u4e0a\u4e0b\u754c\u90fd\u6709\u754c\uff0c\u6240\u4ee5\u6211\u4eec\u9700\u8981\u4e24\u4e2a\u4fe1\u53f7\u91cf\u5206\u522b\u6765\u7ef4\u62a4\u4e24\u4e2a\u8fb9\u754c\u3002</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit2-Part2/#the-readerswriters-problem","title":"The Readers\u2013Writers Problem","text":""},{"location":"cour_note/D3QD_OperatingSystem/Unit2-Part2/#\u95ee\u9898\u80cc\u666f--\u95ee\u9898\u63cf\u8ff0","title":"\u95ee\u9898\u80cc\u666f &amp; \u95ee\u9898\u63cf\u8ff0","text":"<ul> <li>\ud83d\udd17 Wiki</li> </ul> <p>\u8be5\u95ee\u9898\u62bd\u8c61\u81ea\u6570\u636e\u5e93\u7684\u4f7f\u7528\u3002\u7528\u6237\u4f7f\u7528\u6570\u636e\u5e93\u4fee\u6539\u6570\u636e\uff08<code>UPDATE</code>\uff09\uff0c\u672c\u8d28\u4e0a\u4e5f\u662f\u6709\u4e09\u4e2a\u6b65\u9aa4\uff1a</p> <ol> <li>[READ] \u4ece\u6570\u636e\u5e93\u4e2d\u68c0\u7d22\u3001\u8bfb\u53d6\u6570\u636e\uff1b</li> <li>\u6570\u636e\u7ecf\u8fc7\u4e1a\u52a1\u903b\u8f91\u7684\u5904\u7406\uff0c\u5f97\u5230\u65b0\u503c\uff1b</li> <li>[WRITE] \u5c06\u65b0\u503c\u5199\u56de\u6570\u636e\u5e93\uff1b</li> </ol> <p>\u8fd9\u4e2a\u6b65\u9aa4\u4e0e\u6211\u4eec\u4fee\u6539 <code>mem[x]</code> \u7684\u8fc7\u7a0b\u9ad8\u5ea6\u76f8\u4f3c\uff0c\u56e0\u6b64\u9047\u5230\u7684\u95ee\u9898\u4e5f\u662f\u7c7b\u4f3c\u7684\u3002</p> <p>\u51b2\u7a81\u4e3b\u8981\u4f53\u73b0\u5728\u4e24\u79cd\u60c5\u51b5\uff1a</p> <ul> <li>reader \u548c writer \u7684\u51b2\u7a81\uff1b</li> <li>writer \u548c writer \u7684\u51b2\u7a81\uff1b</li> </ul> <p>\u663e\u7136\uff0creader \u548c reader \u4e0d\u4f1a\u6709\u51b2\u7a81\u3002</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit2-Part2/#\u89e3\u51b3---semaphores_1","title":"\u89e3\u51b3 - semaphores","text":"<p>\u6709\u4e24\u79cd\u79cd\u6734\u7d20\u7684\u89e3\u51b3\u529e\u6cd5\uff1a\u24f5 writer \u603b\u662f\u7b49\u5f85 reader\uff0c\u24f6 reader \u603b\u662f\u7b49\u5f85 writer\u3002\u4f46\u662f\u8fd9\u4e24\u79cd\u89e3\u51b3\u529e\u6cd5\u90fd\u4e0d\u662f\u5f88\u597d\uff0c\u56e0\u4e3a \u24f5 \u4f1a\u5bfc\u81f4 writer \u9965\u997f\uff0c\u24f6 \u4f1a\u5bfc\u81f4 reader \u9965\u997f\u3002</p> <p>\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u7ed9\u51fa\u6b63\u5f0f\u7684\u89e3\u51b3\u65b9\u6cd5\uff0c\u5f15\u5165\u4e24\u4e2a\u4fe1\u53f7\u91cf\u548c\u4e00\u4e2a\u5171\u4eab\u53d8\u91cf\uff1a</p> <pre><code>semaphores rw_mutex   = 1;\nsemaphores mutex      = 1;\nint        read_count = 0;\n</code></pre> <p>\u8003\u8651\u5230 reader \u548c reader \u4e0d\u4f1a\u51b2\u7a81\uff0c\u6240\u4ee5 readers \u4e4b\u95f4\u4e0d\u5e94\u8be5\u4e92\u65a5\u3002\u800c\u6211\u4eec\u9700\u8981\u4fdd\u8bc1\u7684\u662f\uff1a\u5355\u4e2a writer \u548c\u82e5\u5e72 readers \u4e4b\u95f4\u4e92\u65a5\uff0c\u5355\u4e2a writer \u548c\u5355\u4e2a writer \u4e4b\u95f4\u4e92\u65a5\u3002\u800c <code>rw_mutex</code> \u5c31\u662f\u7528\u4e8e\u63a7\u5236\u8fd9\u79cd\u4e92\u65a5\u3002</p> writer's code<pre><code>writer() {\nwait(rw_mutex);\n\n/* critical section */\nsignal(rw_mutex);\n}\n</code></pre> <p>\u4f46\u6b64\u65f6\u5982\u4f55\u4fdd\u8bc1 readers \u4e4b\u95f4\u4e0d\u4f1a\u4e92\u65a5\u5462\uff1f\u9996\u5148\uff0c\u5f53\u7b2c\u4e00\u4e2a reader \u8bd5\u56fe\u8fdb\u5165\u4e34\u754c\u6bb5\u65f6\uff0c\u5b83\u5e94\u5f53\u83b7\u53d6\u4e00\u4e2a <code>rw_mutex</code>\uff0c\u4ee5\u963b\u6b62\u5176\u5b83 writer \u8fdb\u5165\u4e34\u754c\u6bb5\u3002\u800c\u5bf9\u4e8e\u4e4b\u540e\u7684 reader \u6765\u8bf4\uff0c\u5982\u679c\u76ee\u524d\u83b7\u53d6\u9501\u7684\u662f\u4e00\u4e2a reader\uff0c\u90a3\u4e48\u5b83\u53ef\u4ee5\u76f4\u63a5\u8fdb\u5165\u4e34\u754c\u6bb5\uff1b\u5982\u679c\u76ee\u524d\u83b7\u53d6\u9501\u7684\u662f\u4e00\u4e2a writer\uff0c\u90a3\u4e48\u5b9e\u9645\u4e0a\u5b83\u624d\u662f\u7b2c\u4e00\u4e2a reader\u3002\u6362\u53e5\u8bdd\u6765\u8bf4\uff0c\u5bf9\u4e8e\u62ff <code>rw_mutex</code> \u6765\u8bf4\uff0c\u6211\u4eec\u53ea\u9700\u8981\u5224\u65ad\u5f53\u524d\u6709\u6ca1\u6709 reader \u6b63\u5728\u4eab\u7528\u4e34\u754c\u8d44\u6e90\u5373\u53ef\uff1b\u800c\u5bf9\u4e8e\u653e <code>rw_mutex</code> \u6765\u8bf4\uff0c\u6211\u4eec\u9700\u8981\u5224\u65ad\u5f53\u524d\u662f\u4e0d\u662f\u6700\u540e\u4e00\u4e2a reader\uff0c\u6240\u4ee5\u5b9e\u9645\u4e0a\u6211\u4eec\u9700\u8981\u7ef4\u62a4\u4e00\u4e2a\u8ba1\u6570\u5668 <code>read_count</code>\uff0c\u800c\u7531\u4e8e\u8fd9\u4e2a\u8ba1\u6570\u5668\u662f\u4e2a\u666e\u901a\u7684\u5171\u4eab\u53d8\u91cf\uff0c\u800c\u4e14\u8fd9\u4e2a\u8ba1\u6570\u5668\u672c\u8eab\u4e5f\u662f\u4e2a\u4e34\u754c\u8d44\u6e90\uff0c\u6240\u4ee5\u6211\u4eec\u8fd8\u9700\u8981\u4e00\u4e2a <code>mutex</code> \u6765\u7ef4\u62a4\u5b83\u3002</p> <p>\u6240\u4ee5\uff0c\u5b9e\u9645\u4e0a reader \u7684\u4ee3\u7801\u4e2d\u542b\u6709 3 \u4e2a\u4e34\u754c\u6bb5\uff0c\u5206\u522b\u662f\uff1a\u8ba1\u6570\u5668\u589e\u3001\u8bfb\u53d6\u4e34\u754c\u8d44\u6e90\u3001\u8ba1\u6570\u5668\u51cf\u3002</p> reader's code<pre><code>reader() {\nwait(mutex);            //   \u2510\nread_count++;           //   \u251c obtain `mutex` to increase\nif (read_count == 1) {  //   \u2502 `read_count`\nwait(rw_mutex);     // \u2510 \u2502\n}                       // \u2502 \u2502\nsignal(mutex);          // \u2502 \u2518\n// \u251c\u2500\u2500 readers share `rw_mutex` to\n/* critical section */  // \u2502   read critical resource\n// \u2502\nwait(mutex);            // \u2502 \u2510\nread_count--;           // \u2502 \u251c obtain `mutex` to decrease\nif (read_count == 0) {  // \u2502 \u2502 `read_count`\nsignal(rw_mutex);   // \u2518 \u2502\n}                       //   \u2502\nsignal(mutex);          //   \u2518\n}\n</code></pre> <p>\u903b\u8f91\u4e0a\uff0c\u91ca\u653e <code>rw_mutex</code> \u7684 reader \u4e0d\u9700\u8981\u662f\u7533\u8bf7 <code>rw_mutex</code> \u7684 reader\uff0c\u8fd9\u4e5f\u5370\u8bc1\u4e86\u8fd9\u4e2a\u9501\u7ef4\u62a4\u7684\u662f\u6574\u4e2a readers \u7fa4\u4f53\u7684\u5b58\u5728\u4e0e\u5426\uff0c\u800c\u4e0d\u662f\u201c\u67d0\u4e2a reader\u201d\u7684\u5b58\u5728\u4e0e\u5426\u3002</p> <p>\u4e3a\u4ec0\u4e48 <code>read_count</code> \u4e0d\u4f7f\u7528\u4fe1\u53f7\u91cf\uff1f</p> <p>\u6211\u4eec\u89c2\u5bdf\u5bf9 <code>read_count</code> \u7684\u64cd\u4f5c\uff0c\u4e00\u5171\u6709\u4e09\u7c7b\uff1a</p> <ol> <li><code>read_count++</code>\uff1b</li> <li><code>read_count--</code>\uff1b</li> <li><code>read_count == k</code>\uff1b</li> </ol> <p>\u5e76\u4e14 <code>read_count &gt;= 0</code> \u5e94\u5f53\u59cb\u7ec8\u6210\u7acb\uff0c\u6240\u4ee5\u5149\u770b\u524d\u4e24\u7c7b\uff0c\u5176\u5b9e\u5f88\u9002\u5408\u76f4\u63a5\u4f5c\u4e3a\u4fe1\u53f7\u91cf\u6765\u7ef4\u62a4\u3002\u4f46\u662f\u6211\u4eec\u65e0\u6cd5\u5bf9\u4fe1\u53f7\u91cf\u8fdb\u884c\u6bd4\u8f83\u64cd\u4f5c\uff0c\u6240\u4ee5\u6211\u4eec\u662f\u7528 <code>mutex</code> \u7ef4\u62a4\u4e86 <code>read_count</code>\uff0c\u53ef\u4ee5\u53d1\u73b0\uff0c\u6240\u6709\u5bf9 <code>read_count</code> \u7684\u64cd\u4f5c\u90fd\u662f\u5728 <code>mutex</code> \u7684\u4fdd\u62a4\u4e0b\u8fdb\u884c\u7684\u3002\u6362\u53e5\u8bdd\u6765\u8bf4\uff0c\u5176\u5b9e <code>read_count</code> \u548c <code>mutex</code> \u4e00\u8d77\u6784\u6210\u4e86\u4e00\u4e2a\u539f\u5b50\u53d8\u91cf\u3002</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit2-Part2/#the-dining-philosophers-problem","title":"The Dining Philosophers Problem","text":""},{"location":"cour_note/D3QD_OperatingSystem/Unit2-Part2/#\u95ee\u9898\u80cc\u666f--\u95ee\u9898\u63cf\u8ff0_1","title":"\u95ee\u9898\u80cc\u666f &amp; \u95ee\u9898\u63cf\u8ff0","text":"<ul> <li>\ud83d\udd17 Wiki</li> </ul> <p>\u5728\u8fd9\u4e2a\u95ee\u9898\u4e2d\uff0c\u6709\u4e94\u4e2a\u54f2\u5b66\u5bb6\uff0cta \u4eec\u56f4\u5750\u5728\u4e00\u5f20\u5706\u684c\u65c1\uff0c\u6bcf\u4e2a\u54f2\u5b66\u5bb6\u9762\u524d\u90fd\u6709\u4e00\u7897\u7c73\u996d\uff0c\u800c ta \u4eec\u4e24\u4e24\u4e4b\u95f4\u5206\u522b\u6709\u4e00\u6839\u7b77\u5b50\u3002</p> <p> </p> <p>\u6bcf\u5e27\u54f2\u5b66\u5bb6\u90fd\u80fd\u9009\u62e9\u6267\u884c\u4ee5\u4e0b\u4e24\u4e2a\u884c\u4e3a\u4e4b\u4e00\uff1a</p> <ol> <li>\u601d\u8003\uff1b</li> <li>\u62ff\u7b77\u5b50\uff1b</li> </ol> <p>\u54f2\u5b66\u5bb6\u5982\u679c\u60f3\u8981\u5e72\u996d\u5c31\u5fc5\u987b\u6709\u4e24\u6839\u7b77\u5b50\uff0cta \u540c\u65f6 \u62ff\u8d77 ta \u5de6\u53f3\u4fa7\u7b77\u5b50\u65f6\uff0c\u624d\u80fd\u5e72\u996d\u3002\u663e\u7136\uff0c\u4e24\u4e2a\u54f2\u5b66\u5bb6\u4e0d\u80fd\u540c\u65f6\u62ff\u8d77\u540c\u4e00\u6839\u7b77\u5b50\uff1b\u5e72\u5b8c\u996d\u54f2\u5b66\u5bb6\u4f1a\u653e\u4e0b\u7b77\u5b50\u3002\u5047\u8bbe\u54f2\u5b66\u5bb6\u4eec\u90fd\u4e0d\u5acc\u810f\u3002</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit2-Part2/#\u89e3\u51b3---semaphores_2","title":"\u89e3\u51b3 - semaphores","text":"<p>\u663e\u7136\uff0c\u6211\u4eec\u53ef\u4ee5\u7528\u4fe1\u53f7\u91cf\u6765\u7ef4\u62a4\u4e00\u4e2a\u7b77\u5b50\u662f\u5426\u53ef\u7528\uff0c\u5c31\u53ef\u4ee5\u5f97\u5230\u4e0b\u9762\uff08\u6709\u95ee\u9898\u7684\uff09\u89e3\u6cd5\uff1a</p> <pre><code>process() {\nwait(chopstick[i]);\nwait(chopstick[ (i+1) % 5 ]); // i.e. the next chopstick\n\n/* eat rice */\n\nsignal(chopstick[i]);\nsignal(chopstick[ (i+1) % 5 ]);\n}\n</code></pre> <p>\u4e0a\u8ff0\u65b9\u6848\u5b58\u5728\u95ee\u9898\uff01</p> <p>\u8003\u8651\u8fd9\u79cd\u60c5\u51b5\uff1a\u6240\u6709\u54f2\u5b66\u5bb6\u5728\u7b2c\u4e00\u5e27\u90fd\u60f3\u8981\u5e72\u996d\uff0c\u6b64\u65f6\u5b83\u4eec\u540c\u65f6\u8fd0\u884c\u5b8c\u4e86\u7b2c 2 \u884c\uff08\u4f8b\u5982\uff0c\u540c\u65f6\u62ff\u8d77\u4e86\u53f3\u624b\u8fb9\u7684\u7b77\u5b50\uff09\uff0c\u8fd9\u65f6\u6211\u4eec\u53d1\u73b0\uff0c\u6240\u6709\u7b77\u5b50\u90fd\u88ab\u5360\u6709\uff0c\u6ca1\u6709\u4efb\u4f55\u4e00\u4e2a\u4eba\u80fd\u7b49\u5230\u4e0b\u4e00\u4e2a\u7b77\u5b50\uff0c\u6b64\u65f6\uff0c\u54f2\u5b66\u5bb6\u4eec\u53d1\u751f\u4e86\u6b7b\u9501\u3002</p> <p>\u5bf9\u4e8e\u8fd9\u4e2a\u6b7b\u9501\uff0c\u4e66\u4e2d\u7ed9\u51fa\u4e86\u4e09\u79cd\u89e3\u51b3\u65b9\u6848\uff1a</p> <ol> <li>\u5141\u8bb8\u6700\u591a 4 \u4f4d\u54f2\u5b66\u5bb6\u540c\u65f6\u83b7\u53d6\u7b77\u5b50\uff1b</li> <li>\u54f2\u5b66\u5bb6\u5fc5\u987b\u540c\u65f6\u83b7\u53d6\u4e24\u4e2a\u7b77\u5b50\uff0c\u800c\u4e0d\u80fd\u6293\u4e00\u652f\u7b49\u4e00\u652f\uff1b<ul> <li>\u4e3a\u4e86\u5b9e\u73b0\u8fd9\u4e00\u70b9\uff0c\u201c\u6293\u7b77\u5b50\u201d\u8fd9\u4ef6\u4e8b\u5e94\u5f53\u5728\u4e00\u4e2a\u4e34\u754c\u6bb5\u4e2d\u5b8c\u6210\uff1b</li> </ul> </li> <li>\u5947\u6570\u54f2\u5b66\u5bb6\u5148\u62ff\u5de6\u624b\u7684\u7b77\u5b50\uff0c\u5076\u6570\u54f2\u5b66\u5bb6\u5148\u62ff\u53f3\u624b\u7684\u7b77\u5b50\uff0c\u8fd9\u6837\u4e0d\u4f1a\u4ea7\u751f\u5faa\u73af\u7b49\u5f85\uff1b</li> </ol>"},{"location":"cour_note/D3QD_OperatingSystem/Unit2-Part2/#\u89e3\u51b3---monitors","title":"\u89e3\u51b3 - monitors","text":"<ul> <li> TODO: \u4e0d\u662f\u5f88\u91cd\u8981</li> </ul>"},{"location":"cour_note/D3QD_OperatingSystem/Unit2-Part3/","title":"U2 Part 3: \u6b7b\u9501 | Deadlocks","text":"<p> \u7ea6 5215 \u4e2a\u5b57  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 17 \u5206\u949f</p> <p>\u5f15\u5165</p> <p>\u6b7b\u9501\u95ee\u9898\u5e7f\u6cdb\u5b58\u5728\u4e8e\u8ba1\u7b97\u673a\u8f6f\u4ef6\u7cfb\u7edf\u4e2d\uff0c\u800c\u6211\u4eec\u672c\u8282\u53ea\u8ba8\u8bba\u64cd\u4f5c\u7cfb\u7edf\u4e2d\u7684\u6b7b\u9501\u95ee\u9898\u3002</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit2-Part3/#\u6b7b\u9501\u5efa\u6a21","title":"\u6b7b\u9501\u5efa\u6a21","text":"<p>\u6211\u4eec\u5728\u4e0a\u4e00\u8282\u4e2d\u5df2\u7ecf\u63d0\u5230\u4e86\u4e00\u4e2a\u6b7b\u9501\u60c5\u51b5\u3002\u672c\u8282\u6211\u4eec\u4e13\u6ce8\u4e8e\u5982\u4f55\u89e3\u51b3\u64cd\u4f5c\u7cfb\u7edf\u4e2d\u7684\u6b7b\u9501(deadlock)\u95ee\u9898\u3002</p> <p>deadlock</p> <p>A deadlock is a situation in which every process in a set of processes is waiting for an event that can be caused only by another process in the set.</p> <p>\u5373\u5b58\u5728\u4e00\u4e2a\u8fdb\u7a0b/\u7ebf\u7a0b\u7684\u96c6\u5408\uff0c\u5b83\u4eec\u4e92\u76f8\u7b49\u5f85\u5bf9\u65b9\u6301\u6709\u7684\u8d44\u6e90\u3002</p> <p>\u4e0e\u4e4b\u5bf9\u5e94\u7684\uff0c\u5176\u5b9e\u8fd8\u6709\u4e00\u4e2a\u53eb\u6d3b\u9501(livelock)1\u7684\u4e1c\u897f\u3002</p> <p>\u6b7b\u9501\u4ea7\u751f\u4e8e\u8d44\u6e90\u7684\u4f7f\u7528\u8fc7\u7a0b\uff0c\u800c\u4e14\u901a\u5e38\u53ea\u5728\u7279\u5b9a\u60c5\u51b5\u4e0b\u624d\u4f1a\u53d1\u751f\uff0c\u800c\u6b63\u662f\u56e0\u4e3a\u8fd9\u79cd\u4e0d\u786e\u5b9a\u6027\uff0c\u6b7b\u9501\u95ee\u9898\u624d\u5f02\u5e38\u68d8\u624b\u3002\u4e3a\u4e86\u89e3\u51b3\u6b7b\u9501\uff0c\u6211\u4eec\u9996\u5148\u9700\u8981\u7406\u89e3\u6b7b\u9501\u4ea7\u751f\u7684\u539f\u56e0\uff0c\u4ee5\u65b9\u4fbf\u5bf9\u5b83\u8fdb\u884c\u5efa\u6a21\uff0c\u8fdb\u800c\u66f4\u597d\u5730\u63cf\u8ff0\u6b7b\u9501\u3002</p> <p>\u4ece\u8d44\u6e90\u4f7f\u7528\u7684\u89d2\u5ea6\u6765\u770b\uff0c\u6211\u4eec\u53ef\u4ee5\u5c06\u7cfb\u7edf\u7684\u884c\u4e3a\u5206\u6210\u4e09\u4e2a\u90e8\u5206\uff1a</p> <ol> <li>\u7533\u8bf7\u8d44\u6e90\uff1b</li> <li>\u4f7f\u7528\u8d44\u6e90\uff1b</li> <li>\u91ca\u653e\u8d44\u6e90\uff1b</li> </ol> <p>\u5176\u4e2d\uff0c\u7533\u8bf7\u8d44\u6e90\u548c\u91ca\u653e\u8d44\u6e90\u901a\u5e38\u901a\u8fc7\u4e0d\u540c\u7684\u7cfb\u7edf\u8c03\u7528\u5b9e\u73b0\u3002\u800c\u90e8\u5206\u8d44\u6e90\u662f\u6709\u9650\u4e14\u4e92\u65a5\u7684\uff0c\u56e0\u800c\u5982\u679c\u5728\u7f3a\u4e4f\u8d44\u6e90\u7684\u60c5\u51b5\u4e0b\uff0c\u8fdb\u7a0b/\u7ebf\u7a0b\u4ecd\u7136\u60f3\u8981\u7533\u8bf7\u8d44\u6e90\uff0c\u5c31\u53ea\u80fd\u9677\u5165\u7b49\u5f85\u3002\u800c\u6b63\u5728\u7b49\u5f85\u7684\u8d44\u6e90\u4e5f\u53ef\u80fd\u6301\u6709\u4e00\u4e9b\u8d44\u6e90\uff0c\u4e00\u65e6\u6070\u597d\u51fa\u73b0\u4e86\u4e92\u76f8\u7b49\u5f85\u7684\u60c5\u51b5\uff0c\u5c31\u4f1a\u51fa\u73b0\u6b7b\u9501\u3002\u4f8b\u5982\uff0c\u4e92\u65a5\u9501\u548c\u4fe1\u53f7\u91cf\u8fd9\u4e9b\u4e1c\u897f\u5c31\u662f\u6b7b\u9501\u4ea7\u751f\u7684\u4e00\u5927\u91cd\u8981\u6765\u6e90\u3002</p> <p>\u8ba1\u7b97\u673a\u8d44\u6e90\u5206\u4e3a\u5f88\u591a\u7c7b\uff0c\u6bcf\u4e00\u7c7b\u4e2d\u53ef\u80fd\u6709\u82e5\u5e72\u5e73\u7b49\u7684\u201c\u5b9e\u4f8b(instance)\u201d\u3002\u5bf9\u4e8e\u4e00\u4e2a\u5408\u7406\u7684\u201c\u8d44\u6e90\u5206\u7c7b\u201d\u6765\u8bf4\uff0c\u4e00\u4e2a\u8fdb\u7a0b/\u7ebf\u7a0b\u9700\u8981\u67d0\u79cd\u8d44\u6e90\u65f6\u5019\uff0c\u8fd9\u4e2a\u8d44\u6e90\u7c7b\u522b\u4e2d\u7684\u4efb\u610f\u7a7a\u95f2\u5b9e\u4f8b\u90fd\u5e94\u5f53\u53ef\u4ee5\u88ab\u7528\u4e8e\u6ee1\u8db3\u8fd9\u4e2a\u8fdb\u7a0b/\u7ebf\u7a0b\u7684\u9700\u6c42\u3002</p> <p>\u5bfc\u8bfb</p> <p>\u4e0b\u9762\u4e24\u4e2a\u90e8\u5206\u5e76\u4e0d\u4f1a\u5f88\u5feb\u5c31\u88ab\u7528\u5230\uff0c\u5c24\u5176\u662f\u5b89\u5168\u72b6\u6001\u4e0e\u4e0d\u5b89\u5168\u72b6\u6001\u662f\u88ab\u6211\u63d0\u524d\u653e\u5230\u8fd9\u91cc\u6765\u7684\uff0c\u8bfb\u8005\u53ef\u4ee5\u81ea\u884c\u8003\u8651\u662f\u76f4\u63a5\u987a\u5e8f\u9605\u8bfb\uff0c\u8fd8\u662f\u6682\u65f6\u8df3\u8fc7\uff08\u4e4b\u540e\u7528\u5230\u7684\u65f6\u5019\u6211\u4f1a\u7ed9\u51fa\u8df3\u56de\u94fe\u63a5\uff09\u3002</p> <p>\u6211\u4e2a\u4eba\u8ba4\u4e3a\u7ed3\u6784\u4e0a\u8fd9\u6837\u5b89\u6392\u66f4\u6e05\u6670\uff0c\u4f46\u8003\u8651\u5230\u4e24\u4e2a\u5185\u5bb9\u5b58\u5728\u4e00\u5b9a\u95f4\u9694\uff0c\u6240\u4ee5\u5f80\u540e\u653e\u7f6e\u4e5f\u6709\u5f80\u540e\u653e\u7f6e\u7684\u9053\u7406\u3002</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit2-Part3/#\u8d44\u6e90\u5206\u914d\u56fe","title":"\u8d44\u6e90\u5206\u914d\u56fe","text":"<p>\u6839\u636e\u4e0a\u9762\u7684\u63cf\u8ff0\uff0c\u6211\u4eec\u53ef\u4ee5\u77e5\u9053\uff0c\u5efa\u6a21\u6b7b\u9501\u53ef\u4ee5\u4ece\u8ba8\u8bba\u8fdb\u7a0b/\u7ebf\u7a0b\u4e0e\u8d44\u6e90\u7684\u6c42\u53d6\u5173\u7cfb\u5165\u624b\u3002\u6211\u4eec\u53ef\u4ee5\u7528\u8d44\u6e90\u5206\u914d\u56fe(resource-allocation graph)\u6765\u63cf\u8ff0\u8fd9\u4ef6\u4e8b\u3002</p> <p>\u9759\u6001</p> <p>\u8d44\u6e90\u5206\u914d\u56fe\u662f\u4e00\u79cd\u6709\u4e24\u7c7b\u8282\u70b9\u7684\u6709\u5411\u56fe\uff0c\u6211\u4eec\u7528\u5706\u8282\u70b9 \\(T_i\\) \u8868\u793a\u8fdb\u7a0b/\u7ebf\u7a0b\uff0c\u7528\u65b9\u8282\u70b9 \\(R_j\\) \u8868\u793a\u8d44\u6e90\uff0c\u65b9\u8282\u70b9\u4e2d\u7684\u5b9e\u5fc3\u70b9\u8868\u793a\u4e00\u4e2a\u8d44\u6e90\u7c7b\u522b\u7684\u4e00\u4e2a\u5b9e\u4f8b\u3002\u540c\u65f6\uff0c\u6211\u4eec\u79f0\u4ece\u8fdb\u7a0b/\u7ebf\u7a0b\u6307\u5411\u8d44\u6e90\u7c7b\u522b\u7684\u6709\u5411\u8fb9\u4e3a\u8bf7\u6c42\u8fb9(request edge)\uff0c\u8868\u793a\u8fdb\u7a0b/\u7ebf\u7a0b \\(T_i\\) \u6b63\u5728\u7b49\u5f85\u8fd9\u79cd\u8d44\u6e90\uff1b\u79f0\u4ece\u8d44\u6e90\u5b9e\u4f8b\u6307\u5411\u8fdb\u7a0b/\u7ebf\u7a0b\u7684\u6709\u5411\u8fb9\u4e3a\u5206\u914d\u8fb9(allocation edge)\uff0c\u8868\u793a\u8d44\u6e90 \\(R_j\\) \u88ab\u5206\u914d\u7ed9\u8fdb\u7a0b/\u7ebf\u7a0b \\(T_i\\)\uff0c\u5373\u76ee\u524d\u8fdb\u7a0b/\u7ebf\u7a0b \\(T_i\\) \u6301\u6709\u4e00\u4e2a\uff08\u4e00\u6761\u8fb9\u8868\u793a\u4e00\u4e2a\uff09\u8d44\u6e90 \\(R_j\\) \u7684\u5b9e\u4f8b\uff0c\u4f8b\u5982\u4e0b\u56fe\uff1a</p> <p>      Resource allocation graph. </p> <ul> <li>\u5f53\u8d44\u6e90\u5206\u914d\u56fe\u4e2d\u4e0d\u5b58\u5728\u73af\u65f6\uff0c\u8bf4\u660e\u4e0d\u4f1a\u51fa\u73b0\u6b7b\u9501\u72b6\u6001\uff1b</li> <li>\u5f53\u8d44\u6e90\u5206\u914d\u56fe\u4e2d\u5b58\u5728\u73af\u65f6\uff0c\u7cfb\u7edf\u53ef\u80fd\u5904\u4e8e\u6b7b\u9501\u72b6\u6001\uff0c\u4e5f\u53ef\u80fd\u4e0d\u5904\u4e8e\u6b7b\u9501\u72b6\u6001\uff1b<ul> <li>\u7279\u4f8b\uff1a\u5982\u679c\u4e0e\u73af\u76f8\u5173\u7684\u8282\u70b9\u90fd\u53ea\u6709\u4e00\u4e2a\u5b9e\u4f8b\u65f6\u5019\uff0c\u7cfb\u7edf\u5904\u4e8e\u6b7b\u9501\u72b6\u6001\uff1b</li> </ul> </li> </ul> <p>\u6362\u53e5\u8bdd\u6765\u8bf4\uff0c\u8d44\u6e90\u5206\u914d\u56fe\u4e2d\u5b58\u5728\u73af\uff0c\u662f\u7cfb\u7edf\u5904\u4e8e\u6b7b\u9501\u72b6\u6001\u7684\u5fc5\u8981\u6761\u4ef6\u3002</p> <p>\u52a8\u6001</p> <ul> <li>\u8fdb\u7a0b/\u7ebf\u7a0b\u7533\u8bf7\u67d0\u4e2a\u8d44\u6e90\u65f6\uff0c\u5728\u56fe\u4e2d\u6dfb\u52a0\u4e00\u6761\u5bf9\u5e94\u7684 request edge\uff1b</li> <li>\u5f53\u8d44\u6e90\u7d22\u53d6\u6210\u529f\u65f6\uff0c\u8fd9\u6761 request edge \u88ab\u66ff\u6362\u4e3a allocation edge\uff1b</li> <li>\u5f53\u8fdb\u7a0b\u91ca\u653e\u8fd9\u4e2a\u8d44\u6e90\u65f6\uff0c\u5219\u9700\u8981\u5c06\u8be5 allocation edge \u6d88\u9664\uff1b</li> </ul> <p>\u5728\u4e4b\u540e\u7684\u5185\u5bb9\u4e2d\uff0c\u6211\u4eec\u8fd8\u5c06\u770b\u5230\u4e00\u4e9b\u8d44\u6e90\u5206\u914d\u56fe\u7684\u53d8\u4f53\uff1a\u5f15\u5165 claim edge \u7684\u8d44\u6e90\u5206\u914d\u56fe\u7b97\u6cd5\u4ee5\u53ca\u53ea\u4fdd\u7559\u8fdb\u7a0b/\u7ebf\u7a0b\u7b49\u5f85\u5173\u7cfb\u7684 wait for graph\u3002</p> <p>\u7531\u4e8e\u552f\u4e00\u5b9e\u4f8b\u8fd9\u4e2a\u6027\u8d28\u88ab\u7834\u574f\u540e\uff0c\u6b7b\u9501\u5728\u8d44\u6e90\u5206\u914d\u56fe\u4e0a\u4e0d\u518d\u90a3\u4e48\u76f4\u89c2\u4e86\uff0c\u6240\u4ee5\u6211\u4eec\u9700\u8981\u5f15\u5165\u65b0\u7684\u5de5\u5177\u6765\u63cf\u8ff0\u6b7b\u9501\u3002</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit2-Part3/#\u5b89\u5168\u72b6\u6001\u4e0e\u4e0d\u5b89\u5168\u72b6\u6001","title":"\u5b89\u5168\u72b6\u6001\u4e0e\u4e0d\u5b89\u5168\u72b6\u6001","text":"<p>\u8be5\u90e8\u5206\u5185\u5bb9\u88ab\u4e66\u672c\u5b89\u6392\u5728\u6b7b\u9501\u907f\u514d\u4e2d\uff0c\u88ab\u6211\u63d0\u524d\uff0c\u53ef\u4ee5\u8003\u8651\u4e0d\u76f4\u63a5\u6df1\u5165\u800c\u662f\u7b49\u4e4b\u540e\u9047\u5230\u4e86\u518d\u770b\u3002</p> <p>\u5b89\u5168\u72b6\u6001(safe state)\u6307\u5b58\u5728\u5b89\u5168\u5e8f\u5217(safe sequence)\u7684\u72b6\u6001\uff0c\u7cfb\u7edf\u6309\u7167 safe sequence \u7684\u987a\u5e8f\u6267\u884c\u8fdb\u7a0b/\u7ebf\u7a0b\u548c\u5206\u914d\u8d44\u6e90\uff0c\u5c31\u4e0d\u4f1a\u51fa\u73b0\u6b7b\u9501\uff1b\u76f8\u5bf9\u5e94\u7684\uff0c\u4e0d\u662f\u5b89\u5168\u72b6\u6001\u7684\u72b6\u6001\u79f0\u4e3a\u4e0d\u5b89\u5168\u72b6\u6001(unsafe state)\u3002\u5177\u4f53\u6765\u8bf4\uff0csafe sequence \u7684\u5b9a\u4e49\u5982\u4e0b\uff1a</p> <p>safe sequence</p> <p>\u9996\u5148 high level \u5730\u8bb2\u4e00\u4e0b safe sequence \u7684\u601d\u8def\uff0csafe sequence \u4e2d\u7684\u6bcf\u4e00\u9879 \\(T_i\\) \u6240\u9700\u8981\u7684\u8d44\u6e90\uff0c\u90fd\u80fd\u901a\u8fc7\u73b0\u6709\u8d44\u6e90\u6216\u5176\u4e4b\u524d\u7684\u8fdb\u7a0b/\u7ebf\u7a0b \\(\\forall j &lt; i T_{j}\\) \u6267\u884c\u5b8c\u6bd5\u91ca\u653e\u7684\u8d44\u6e90\u6765\u6ee1\u8db3\u3002</p> <p>\u5177\u4f53\u6765\u8bf4\uff0c\u5bf9\u4e8e safe sequence \\(&lt;T_1, T_2, \\dots, T_n&gt;\\)\uff0c\u6211\u4eec\u5b9a\u4e49\u6bcf\u4e00\u9879\u8fd8\u9700\u8981\u7684 \\(R_j\\) \u8d44\u6e90\u4e3a \\(need_{i,j}\\)\u3001\u5df2\u7ecf\u88ab\u5206\u914d\u7684 \\(R_j\\) \u8d44\u6e90\u4e3a \\(allocated_{i,j}\\)\uff0c\u4ee5\u53ca\u8d44\u6e90 \\(R_j\\) \u4e2d\u8fd8\u7a7a\u95f2\u7684\u8d44\u6e90\u7684\u91cf \\(available_{j}\\)\uff0c\u5219\u5e94\u5f53\u6709\uff1a</p> \\[ \\begin{aligned}     \\forall i \\in \\{1, 2, \\dots, n\\},\\quad     \\forall j \\in \\{1, 2, \\dots, m\\}, \\\\     available_{j} + \\sum_{k=1}^{i-1} allocated_{k,j} \\geq need_{i,j} \\end{aligned} \\] <p>\u5bf9\u4e8e\u7b2c \\(i\\) \u4e2a\u8fdb\u7a0b/\u7ebf\u7a0b\u6765\u8bf4\uff0c\u5b9e\u9645\u8fd0\u884c\u65f6\u7684\u7a7a\u95f2\u8d44\u6e90\u53ef\u80fd\u6765\u81ea\u4e8e \\(allocated_{k,j}\\)\uff0c\u4f46\u8fd9\u91cc\u662f\u7528\u6765\u505a\u5224\u65ad\u7684\uff0c\u5e76\u4e0d\u662f\u4e00\u4e2a\u5728\u7ebf\u7684\u8ba1\u7b97\u8fc7\u7a0b\uff0c\u6240\u4ee5\u7528 \\(available_{j} + \\sum_{k=1}^{i-1} allocated_{k,j}\\) \u8fd9\u4e2a\u5f0f\u5b50\u6765\u7ef4\u62a4\u6b64\u65f6 \\(T_i\\) \u7684\u6700\u5927\u53ef\u7528\u8d44\u6e90\u3002</p> <p>\u601d\u8003\u5982\u4f55\u5bfb\u627e\u4e00\u4e2a safe sequence</p> <p>\u8fd9\u4e2a\u95ee\u9898\u6211\u4eec\u5728\u4e4b\u540e\u6b7b\u9501\u68c0\u6d4b\u7684\u90e8\u5206\u4f1a\u7ed9\u51fa\u7b54\u6848\uff0c\u4f46\u4e0d\u59a8\u7b80\u5355\u601d\u8003\u4e00\u4e0b\u600e\u6837\u5bfb\u627e\u4e00\u4e2a safe sequence \u5462\uff1f\u80fd\u5426\u8d2a\u5fc3\u5730\u6765\u6c42\u7b97\u8fd9\u6837\u4e00\u4e2a\u5e8f\u5217\u5462\uff1f</p> <p>\u4f46\u662f\uff0csafe state \u662f\u4e00\u4e2a\u76f8\u5bf9\u8f83\u5f3a\u7684\u7ea6\u675f\uff0c\u4e0d\u5b89\u5168\u72b6\u6001\u4e0d\u4ee3\u8868\u6b7b\u9501\u4e00\u5b9a\u4f1a\u53d1\u751f\uff0c\u7528\u97e6\u6069\u56fe\u6765\u8868\u793a\u5b83\u4eec\u7684\u5173\u7cfb\u5c31\u662f\uff1a</p> <p> </p> <p>\u5982\u679c\u6211\u4eec\u80fd\u4fdd\u8bc1\u7cfb\u7edf\u53ea\u8fd0\u884c\u5728 safe state\uff0c\u4e5f\u5c31\u80fd\u5145\u5206\u5730\u907f\u514d\u6b7b\u9501\u7684\u53d1\u751f\u3002</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit2-Part3/#\u6b7b\u9501\u7684\u6761\u4ef6","title":"\u6b7b\u9501\u7684\u6761\u4ef6","text":"<p>\u8981\u60f3\u6b7b\u9501\u51fa\u73b0\uff0c\u4e0b\u9762\u56db\u4e2a\u6761\u4ef6\u5fc5\u987b\u540c\u65f6\u6ee1\u8db3\uff1a</p> <ol> <li>\u4e92\u65a5(mutual exclusion)\uff1a\u6b7b\u9501\u4e2d\u81f3\u5c11\u6709\u4e00\u4e2a\u8d44\u6e90\u5fc5\u987b\u662f\u975e\u5171\u4eab\u7684\uff0c\u5373\u4e00\u6b21\u53ea\u80fd\u88ab\u4e00\u4e2a\u8fdb\u7a0b/\u7ebf\u7a0b\u4f7f\u7528\uff1b<ul> <li>\u6b63\u56e0\u4e3a\u4e92\u65a5\u8d44\u6e90\u65e0\u6cd5\u88ab\u540c\u65f6\u4f7f\u7528\uff0c\u6240\u4ee5\u9700\u8981\u8d44\u6e90\u7684\u8fdb\u7a0b/\u7ebf\u7a0b\u9700\u8981\u7b49\u5f85\u6301\u6709\u76ee\u6807\u8d44\u6e90\u7684\u8fdb\u7a0b/\u7ebf\u7a0b\u91ca\u653e\u8be5\u8d44\u6e90\u4ee5\u540e\u624d\u80fd\u4f7f\u7528\u76ee\u6807\u8d44\u6e90\uff1b</li> </ul> </li> <li>\u6301\u6709\u5e76\u7b49\u5f85(hold &amp; wait)\uff1a\u6b7b\u9501\u4e2d\u7684\u8fdb\u7a0b/\u7ebf\u7a0b\u5728\u7b49\u5f85\u8d44\u6e90\u7684\u540c\u65f6\uff0c\u4e5f\u5fc5\u987b\u6301\u6709\u81f3\u5c11\u4e00\u4e2a\u8d44\u6e90\uff1b<ul> <li>\u4e3a\u4e86\u4fc3\u6210\u5faa\u73af\u7b49\u5f85\uff0c\u4e00\u4e2a\u7b49\u5f85\u5176\u5b83\u8d44\u6e90\uff08\u6709\u51fa\u8fb9\uff09\u7684\u8fdb\u7a0b/\u7ebf\u7a0b\u5fc5\u987b\u6301\u6709\u81f3\u5c11\u4e00\u4e2a\u8d44\u6e90\uff0c\u8fd9\u6837\u624d\u80fd\u8ba9\u5176\u5b83\u8d44\u6e90\u4e5f\u7b49\u5f85\u5b83\uff08\u6709\u5165\u8fb9\uff09\uff1b</li> <li>\u8bf4\u767d\u4e86\u5c31\u662f\uff1a\u6301\u6709\u5bfc\u81f4\u53ef\u80fd\u88ab\u7b49\u5f85\uff0c\u7b49\u5f85\u5c31\u662f\u7b49\u5f85\uff0c\u800c\u4e00\u65e6\u4e00\u4e2a\u8282\u70b9\u65e2\u7b49\u5f85\u53c8\u88ab\u7b49\u5f85\uff0c\u5c31\u6709\u53ef\u80fd\u4fc3\u6210\u5faa\u73af\u7b49\u5f85</li> </ul> </li> <li>\u975e\u62a2\u5360(no preemption)\uff1a\u6b7b\u9501\u4e2d\u7684\u8fdb\u7a0b/\u7ebf\u7a0b\u53ea\u80fd\u5728\u4f7f\u7528\u5b8c\u8d44\u6e90\u540e\u4e3b\u52a8\u91ca\u653e\u8d44\u6e90\uff0c\u5176\u6301\u6709\u7684\u8d44\u6e90\u65e0\u6cd5\u88ab\u5176\u5b83\u8fdb\u7a0b/\u7ebf\u7a0b\u62a2\u5360\uff1b<ul> <li>\u4e3a\u4e86\u4fdd\u8bc1\u7b49\u5f85\u5173\u7cfb\u4e0d\u4f1a\u88ab\u5f3a\u884c\u7834\u574f\uff1b</li> </ul> </li> <li>\u5faa\u73af\u7b49\u5f85(circular wait)\uff1a\u6b7b\u9501\u4e2d\u7684\u8fdb\u7a0b\u5b58\u5728\u73af\u72b6\u7684\u7b49\u5f85\u8d44\u6e90\u5173\u7cfb\uff0c\u5373 wait for graph \u4e2d\u5b58\u5728\u73af\uff1b<ul> <li>\u903b\u8f91\u4e0a\u5bfc\u81f4\u6b7b\u9501\u51fa\u73b0\u7684\u76f4\u63a5\u539f\u56e0\uff0c\u4e92\u76f8\u7b49\u5f85\u5bfc\u81f4\u6ca1\u6709\u8d44\u6e90\u4f1a\u88ab\u91ca\u653e\uff0c\u5bfc\u81f4\u6b7b\u9501\u72b6\u6001\u65e0\u6cd5\u88ab\u6253\u7834\uff1b</li> </ul> </li> </ol> <p>\u53ef\u4ee5\u53d1\u73b0\uff0c\u8fd9\u56db\u4e2a\u5173\u7cfb\u5e76\u4e0d\u5b8c\u5168\u72ec\u7acb\u3002</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit2-Part3/#\u6b7b\u9501\u7684\u5904\u7406","title":"\u6b7b\u9501\u7684\u5904\u7406","text":"<p>\u5f88\u5bb9\u6613\u8ba4\u8bc6\u5230\uff0c\u6b7b\u9501\u7684\u5371\u5bb3\u662f\u5de8\u5927\u7684\uff0c\u90a3\u4e48\u5982\u4f55\u5904\u7406\u64cd\u4f5c\u7cfb\u7edf\u4e2d\u7684\u6b7b\u9501\u95ee\u9898\u5462\uff1f\u4e3b\u8981\u6709\u8fd9\u4e48\u51e0\u4e2a\u601d\u8def\uff1a</p> <ol> <li>\u4e0d\u505a\u989d\u5916\u5904\u7406\uff0c\u8981\u6c42\u7a0b\u5e8f\u5458\u4fdd\u8bc1\u903b\u8f91\u4e0a\u4e0d\u4f1a\u51fa\u73b0\u6b7b\u9501\uff1b</li> <li>\u6b7b\u9501\u9884\u9632(deadlock prevention)\uff1a\u4f7f\u7528\u67d0\u79cd\u89c4\u8303\u6216\u534f\u8bae\u6765\u4fdd\u8bc1\u6b7b\u9501\u4e0d\u4f1a\u51fa\u73b0\uff1b</li> <li>\u6b7b\u9501\u907f\u514d(deadlock avoidance)\uff1a\u7981\u6b62\u53ef\u80fd\u4ea7\u751f\u6b7b\u9501\u7684\u884c\u4e3a\u7684\u53d1\u751f\uff1b<ul> <li>\u4e0e 2. \u7684\u6700\u4e3b\u8981\u7684\u533a\u522b\u662f\uff0c2. \u5728\u89c4\u8303\u4e0b\u7684\u6240\u6709\u884c\u4e3a\u90fd\u4e0d\u4f1a\u51fa\u73b0\u6b7b\u9501\u95ee\u9898\uff1b\u800c 3. \u5219\u662f\u4e0d\u7ea6\u675f\u884c\u4e3a\uff0c\u4f46\u662f\u7981\u6b62\u53ef\u80fd\u4ea7\u751f\u6b7b\u9501\u7684\u884c\u4e3a\u6267\u884c\uff0c\u5728\u7a0d\u5019\u4ecb\u7ecd\u5177\u4f53\u5185\u5bb9\u540e\u4f1a\u66f4\u5bb9\u6613\u7406\u89e3\uff1b</li> </ul> </li> <li>\u6b7b\u9501\u68c0\u6d4b(deadlock detection)\u548c\u6b7b\u9501\u89e3\u9664(deadlock recovery)\u5141\u8bb8\u6b7b\u9501\u7684\u51fa\u73b0\uff0c\u4f46\u662f\u5f53\u68c0\u6d4b\u5230\u6b7b\u9501\u65f6\uff0c\u9700\u8981\u53bb\u6d88\u9664\u6b7b\u9501\u95ee\u9898\uff1b</li> </ol> <p>\u4e8b\u5b9e\u4e0a\uff0c\u5728\u4e3b\u6d41\u64cd\u4f5c\u7cfb\u7edf\u4e2d\uff0c\u4e00\u822c\u9009\u62e9\u4f7f\u7528\u7b2c\u4e00\u79cd\uff0c\u5373\u5c06\u95ee\u9898\u4ea4\u7ed9\u5f00\u53d1\u8005\u53bb\u89e3\u51b3\u3002</p> <p>\u63a5\u4e0b\u6765\u6211\u4eec\u6765\u4ecb\u7ecd\u4e0a\u9762\u63d0\u5230\u7684\u540e\u4e09\u4e2a\u65b9\u6cd5\u4e2d\u7684\u56db\u5757\u5185\u5bb9\u3002\u5176\u4e2d\u6709\u90e8\u5206\u5185\u5bb9\u6709\u8f83\u5927\u4ea4\u96c6\uff0c\u5b83\u4eec\u53ef\u80fd\u5c5e\u4e8e\u540c\u4e00\u7eb2\u9886\u4e0b\u5728\u4e0d\u540c\u65f6\u523b\u505a\u7684\u5904\u7406\u3002</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit2-Part3/#\u6b7b\u9501\u9884\u9632","title":"\u6b7b\u9501\u9884\u9632","text":"<p>\u6b7b\u9501\u9884\u9632(deadlock prevention)\u7684\u6838\u5fc3\u601d\u8def\u662f\u7834\u574f\u6b7b\u9501\u4ea7\u751f\u7684\u5fc5\u8981\u6761\u4ef6\u3002\u7531\u4e8e\u300c\u8981\u60f3\u6b7b\u9501\u51fa\u73b0\uff0c\u56db\u4e2a\u6761\u4ef6\u5fc5\u987b\u540c\u65f6\u6ee1\u8db3\u300d\uff0c\u6240\u4ee5\u6211\u4eec\u5982\u679c\u80fd\u4fdd\u8bc1\u56db\u4e2a\u6761\u4ef6\u4e2d\u67d0\u4e00\u4e2a\u4e00\u76f4\u4e0d\u6210\u7acb\uff0c\u90a3\u4e48\u6b7b\u9501\u5c06\u6c38\u8fdc\u4e0d\u4f1a\u4ea7\u751f\uff0c\u800c\u65e2\u7136\u6b7b\u9501\u4e0d\u4f1a\u4ea7\u751f\uff0c\u90a3\u4e5f\u5c31\u4e0d\u9700\u8981\u53bb\u5904\u7406\u6b7b\u9501\u95ee\u9898\u3002\u63a5\u4e0b\u6765\u6211\u4eec\u5bf9\u56db\u4e2a\u5fc5\u8981\u6761\u4ef6\u9010\u4e00\u5206\u6790\uff1a</p> <ol> <li>\u7834\u574f\u4e92\u65a5(mutual exclusion)\uff1a<ul> <li>\u8fd9\u4e2a\u6761\u4ef6\u51e0\u4e4e\u662f\u65e0\u6cd5\u7834\u574f\u7684\uff0c\u5f88\u591a\u8d44\u6e90\u5929\u7136\u662f\u4e92\u65a5\u7684\uff1b</li> <li>\u6709\u4e9b\u8d44\u6599\u91cc\u4e5f\u6709\u5199\u4e00\u4e9b\u65b9\u6cd5\u6765\u7834\u574f\u8fd9\u4e2a\u6761\u4ef62\uff0c\u4f46\u662f\u6211\u611f\u89c9\u8fd8\u662f\u6709\u5c40\u9650\u6027\u7684\uff0c\u53cd\u6b63\u4e66\u672c\u91cc\u8bf4\u7684\u662f\u6ca1\u6cd5\u7834\u574f\uff1b</li> </ul> </li> <li>\u7834\u574f\u6301\u6709\u5e76\u7b49\u5f85(hold &amp; wait)\uff1a<ul> <li>\u5728\u6211\u4eec\u524d\u9762\u7684\u5206\u6790\u4e2d\u77e5\u9053\uff1a\u300c\u6301\u6709\u5bfc\u81f4\u53ef\u80fd\u88ab\u7b49\u5f85\uff0c\u7b49\u5f85\u5c31\u662f\u7b49\u5f85\uff0c\u800c\u4e00\u65e6\u4e00\u4e2a\u8282\u70b9\u65e2\u7b49\u5f85\u53c8\u88ab\u7b49\u5f85\uff0c\u5c31\u6709\u53ef\u80fd\u4fc3\u6210\u5faa\u73af\u7b49\u5f85\u300d\uff1b</li> <li>\u4f46\u662f\uff0c\u5982\u679c\u6211\u4eec\u53ea\u5141\u8bb8\u4e00\u4e2a\u8282\u70b9\u53ea\u80fd\u5728\u201c\u88ab\u7b49\u5f85\u201d\u548c\u201c\u7b49\u5f85\u201d\u4e2d\u4e8c\u9009\u4e00\uff0c\u4e5f\u5c31\u662f\u8bf4\u8ba9\u4e00\u4e2a\u7ebf\u7a0b/\u8fdb\u7a0b\u4e00\u65e6\u7533\u8bf7\u8d44\u6e90\u5c31\u4e00\u6b21\u6027\u83b7\u53d6\u6240\u6709\u8d44\u6e90\uff0c\u5982\u679c\u6ca1\u6cd5\u4e00\u6b21\u6027\u83b7\u53d6\u6240\u6709\u8d44\u6e90\u5c31\u91ca\u653e\u5df2\u7ecf\u7533\u8bf7\u5230\u7684\u8d44\u6e90\uff0c\u901a\u8fc7\u8fd9\u79cd\u65b9\u6cd5\u907f\u514d\u4e86\u5faa\u73af\u7b49\u5f85\u7684\u4ea7\u751f\uff1b</li> </ul> </li> <li>\u7834\u574f\u975e\u62a2\u5360(no preemption)\uff1a<ul> <li>\u901a\u8fc7\u5141\u8bb8\u8fdb\u7a0b/\u7ebf\u7a0b\u5f3a\u884c\u62a2\u5360\u53e6\u5916\u4e00\u4e2a\u8fdb\u7a0b/\u7ebf\u7a0b\u6301\u6709\u7684\u8d44\u6e90\uff0c\u53ef\u4ee5\u7834\u574f\u88ab\u52a8\u7684\u7b49\u5f85\u5173\u7cfb\uff0c\u4ece\u800c\u907f\u514d\u6b7b\u9501\uff1b</li> <li>\u4f46\u662f\u548c\u4e92\u65a5\u5176\u5b9e\u662f\u7c7b\u4f3c\u7684\uff0c\u975e\u62a2\u5360\u4e5f\u5177\u6709\u4e00\u5b9a\u7684\u5929\u7136\u6027\uff0c\u5f3a\u884c\u62a2\u5360\u4e00\u90e8\u5206\u8d44\u6e90\u53ef\u80fd\u5bfc\u81f4\u8fdb\u884c\u5230\u4e00\u534a\u7684\u4efb\u52a1\u5931\u8d25\uff0c\u751a\u81f3\u4e00\u4e9b\u66f4\u4e25\u91cd\u7684\u540e\u679c\uff0c\u6240\u4ee5\u8fd9\u5e76\u4e0d\u662f\u4e00\u4e2a\u5f88\u597d\u7684\u529e\u6cd5\uff1b</li> <li>\u800c\u4e14\uff0c\u5141\u8bb8\u201c\u62a2\u5360\u201d\u4e5f\u4f1a\u5e26\u6765\u9965\u997f\u95ee\u9898\uff0c\u603b\u4f53\u6765\u8bf4\u96be\u4ee5\u5b9e\u73b0\u800c\u4e14\u6548\u7387\u4e0d\u9ad8\uff1b</li> </ul> </li> <li>\u7834\u574f\u5faa\u73af\u7b49\u5f85(circular wait)\uff1a<ul> <li>\u901a\u8fc7\u7ed9\u8d44\u6e90\u7f16\u53f7\uff0c\u89c4\u5b9a\u8fdb\u7a0b/\u7ebf\u7a0b\u53ea\u80fd\u6309\u7279\u5b9a\u7684\u987a\u5e8f\u7533\u8bf7\u8d44\u6e90\uff0c\u5c31\u4e0d\u4f1a\u51fa\u73b0\u5faa\u73af\u7b49\u5f85\u7684\u60c5\u51b5\uff1b</li> <li>\u7531\u4e8e\u8fdb\u7a0b/\u7ebf\u7a0b\u53ea\u80fd\u6309\u7167\u7279\u5b9a\u987a\u5e8f\u7533\u8bf7\u8d44\u6e90\uff0c\u800c\u8d44\u6e90\u7684\u7533\u8bf7\u5e94\u5f53\u662f\u4e2a\u52a8\u6001\u7684\u8fc7\u7a0b\uff0c\u6240\u4ee5\u53ef\u80fd\u4f1a\u51fa\u73b0\u300c\u8fdb\u7a0b\u5927\u534a\u90e8\u5206\u53ea\u9700\u8981\u7528\u5230 \\(R_3\\)\uff0c\u4f46\u662f\u7531\u4e8e\u6700\u540e\u9700\u8981\u7528\u4e00\u4e0b \\(R_1\\)\uff0c\u6240\u4ee5\u5fc5\u987b\u5148\u7533\u8bf7 \\(R_1\\) \u518d\u7533\u8bf7 \\(R_3\\)\uff0c\u5bfc\u81f4\u8fc7\u7a0b\u4e2d \\(R_1\\) \u4e00\u76f4\u88ab\u6301\u6709\u4f46\u4e00\u76f4\u672a\u88ab\u4f7f\u7528\u300d\u7684\u60c5\u51b5\uff0c\u6548\u7387\u582a\u5fe7\uff1b</li> <li>\u4e3a\u4e86\u89e3\u51b3\u4e0a\u9762\u8fd9\u4e2a\u95ee\u9898\uff0c\u53ef\u4ee5\u5c1d\u8bd5\u5728\u8bbe\u8ba1\u7f16\u53f7\u65f6\u5c06\u8d44\u6e90\u4f7f\u7528\u7684\u5e38\u89c4\u987a\u5e8f\u7b49\u56e0\u7d20\u7eb3\u5165\u8003\u8651\uff0c\u4f46\u7cbe\u5fc3\u8bbe\u8ba1\u7684\u8d44\u6e90\u5e8f\u53f7\u9047\u5230\u65e0\u7a77\u65e0\u5c3d\u7684\u8d44\u6e90\u7c7b\u578b\u65f6\uff0c\u53c8\u5f53\u5982\u4f55\u5462\uff1f\u7531\u4e8e\u9700\u8981\u5927\u91cf\u8bbe\u8ba1\uff0c\u6240\u4ee5\u5e26\u6765\u4e86\u8d44\u6e90\u7684\u6269\u5c55\u6027\u8f83\u5dee\u7684\u95ee\u9898\uff1b</li> </ul> </li> </ol>"},{"location":"cour_note/D3QD_OperatingSystem/Unit2-Part3/#\u6b7b\u9501\u907f\u514d","title":"\u6b7b\u9501\u907f\u514d","text":"<p>\u6b7b\u9501\u907f\u514d(deadlock avoidance)\u901a\u8fc7\u963b\u6b62\u53ef\u80fd\u8ba9\u7cfb\u7edf\u8fdb\u5165\u6b7b\u9501\u72b6\u6001\u7684\u884c\u4e3a\uff0c\u6765\u89e3\u51b3\u6b7b\u9501\u95ee\u9898\u3002\u5373\uff1a\u5982\u679c\u8fd9\u4e48\u505a\u53ef\u80fd\u5bfc\u81f4\u6b7b\u9501\uff0c\u90a3\u6211\u5c31\u4e0d\u8fd9\u4e48\u505a\uff0c\u4ee5\u6b64\u6765\u907f\u514d\u6b7b\u9501\u3002</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit2-Part3/#\u8d44\u6e90\u5206\u914d\u56fe\u7b97\u6cd5","title":"\u8d44\u6e90\u5206\u914d\u56fe\u7b97\u6cd5","text":"<p>\u524d\u7f6e\uff1a\u8d44\u6e90\u5206\u914d\u56fe\uff01</p> <p>\u8d44\u6e90\u5206\u914d\u56fe\u7b97\u6cd5\u8f83\u4e3a\u76f4\u63a5\uff0c\u5b83\u4e0e\u5b89\u5168\u72b6\u6001\u7684\u6982\u5ff5\u65e0\u5173\uff0c\u76f4\u63a5\u68c0\u6d4b\u67d0\u79cd\u5206\u914d\u662f\u5426\u4f1a\u5bfc\u81f4\u6b7b\u9501\u53d1\u751f\uff0c\u5982\u679c\u8be5\u5206\u914d\u4f1a\u5bfc\u81f4\u6b7b\u9501\u53d1\u751f\uff0c\u5219\u4e0d\u8fdb\u884c\u8be5\u5206\u914d\u3002\u4f46\u662f\u9700\u8981\u6ce8\u610f\uff0c\u8be5\u7b97\u6cd5\u53ea\u9002\u7528\u4e8e\u6bcf\u4e2a\u8d44\u6e90\u7c7b\u522b\u4e2d\u90fd\u53ea\u6709\u4e00\u4e2a\u5b9e\u4f8b\u7684\u60c5\u51b5\u3002\uff08\u56e0\u4e3a\u5b83\u4ee5\u8d44\u6e90\u5206\u914d\u56fe\u4e2d\u7684\u90a3\u4e2a\u7279\u4f8b\u4e3a\u539f\u7406\uff01\uff09</p> <p>\u6211\u4eec\u4e4b\u524d\u5df2\u7ecf\u5f15\u5165\u4e86\u8d44\u6e90\u5206\u914d\u56fe\u8fd9\u4e2a\u5de5\u5177\uff0c\u73b0\u5728\u6211\u4eec\u8981\u5728\u8d44\u6e90\u5206\u914d\u56fe\u7684\u57fa\u7840\u4e0a\uff0c\u5f15\u5165\u4e00\u6761\u8bc9\u6c42\u8fb9(claim edge)\uff0c\u7528\u865a\u7ebf\u8868\u793a\uff0c\u5b83\u4ece\u8fdb\u7a0b/\u7ebf\u7a0b \\(T_i\\) \u6307\u5411\u8d44\u6e90 \\(R_j\\)\uff0c\u8868\u793a\u8fdb\u7a0b/\u7ebf\u7a0b \\(T_i\\) \u4f1a\u5728\u672a\u6765\u7533\u8bf7\u8d44\u6e90 \\(R_j\\)\u3002</p> <p>\u4e8e\u662f\uff0c\u5728\u52a8\u6001\u8fc7\u7a0b\u4e2d\uff0c\u8d44\u6e90\u5206\u914d\u56fe\u6309\u7167\u5982\u4e0b\u89c4\u5219\u53cd\u5e94\u5206\u914d\u8fc7\u7a0b\uff1a</p> <ol> <li>\u8fdb\u7a0b/\u7ebf\u7a0b \\(T_i\\) \u88ab\u6dfb\u52a0\u5230\u8d44\u6e90\u5206\u914d\u56fe\u4e2d\u65f6\u5019\uff0c\u9700\u8981\u8fde\u597d\u6240\u6709\u76f8\u5173\u7684 claim edge\uff1b<ul> <li> <p>\u8981\u6c42\u6700\u521d\u5c31\u77e5\u9053\u9700\u8981\u7684\u6240\u6709\u8d44\u6e90\uff0c\u8fd9\u4e5f\u6784\u6210\u8fd9\u7c7b\u65b9\u6cd5\u7684\u4e00\u4e2a\u5c40\u9650\u6027\uff1b</p> </li> </ul> </li> <li>\u8fdb\u7a0b/\u7ebf\u7a0b \\(T_i\\) \u7533\u8bf7\u8d44\u6e90 \\(R_j\\) \u65f6\u5019\uff0c\u5982\u679c\u8fd9\u6761\u8fb9\u53d8\u4e3a assignment edge \u4e0d\u4f1a\u5bfc\u81f4\u6210\u73af\uff0c\u5219\u5c06 claim edge \u8f6c\u5316\u4e3a\u4e00\u6761 request edge \\(T_i \\rightarrow R_j\\)\uff1b<ul> <li> <p>\u8bf7\u6ce8\u610f\uff0c\u8fd9\u91cc\u9700\u8981\u5224\u65ad\u7684\u662f assignment edge\uff0c\u800c\u8f6c\u5316\u7684\u662f request edge\uff1b</p> </li> </ul> </li> <li>\u8fdb\u7a0b/\u7ebf\u7a0b \\(T_i\\) \u83b7\u5f97\u8d44\u6e90 \\(R_j\\) \u65f6\u5019\uff0c\u5c06 request edge \u8f6c\u5316\u4e3a\u4e00\u6761 allocation edge \\(R_j \\rightarrow T_i\\)\uff1b</li> <li>\u8fdb\u7a0b/\u7ebf\u7a0b \\(T_i\\) \u91ca\u653e\u8d44\u6e90 \\(R_j\\) \u65f6\u5019\uff0c\u5c06 allocation edge \u5220\u53bb\uff1b</li> </ol> <p>\u6211\u4eec\u5728\u4e0a\u9762\u4e5f\u8bf4\u4e86\uff1a\u300c\u8be5\u7b97\u6cd5\u53ea\u9002\u7528\u4e8e\u6bcf\u4e2a\u8d44\u6e90\u7c7b\u522b\u4e2d\u90fd\u53ea\u6709\u4e00\u4e2a\u5b9e\u4f8b\u7684\u60c5\u51b5\u300d\uff0c\u90a3\u4e48\u5982\u4f55\u89e3\u9664\u8fd9\u4e2a\u9650\u5236\u5462\uff1f\u8be5\u95ee\u9898\u6211\u4eec\u65e9\u5728\u8d44\u6e90\u5206\u914d\u56fe\u5c0f\u8282\u5c31\u5df2\u7ecf\u8ba8\u8bba\uff0c\u6211\u4eec\u4f7f\u7528\u5b89\u5168\u72b6\u6001\u4e0e\u4e0d\u5b89\u5168\u72b6\u6001\u6765\u63cf\u8ff0\u4e00\u4e2a\u7ea6\u675f\u8f83\u5f3a\u7684\u3001\u4e0d\u4f1a\u4ea7\u751f\u6b7b\u9501\u7684\u72b6\u6001\u3002</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit2-Part3/#\u94f6\u884c\u5bb6\u7b97\u6cd5","title":"\u94f6\u884c\u5bb6\u7b97\u6cd5","text":"<p>\u524d\u7f6e\uff1a\u5b89\u5168\u72b6\u6001\u4e0e\u4e0d\u5b89\u5168\u72b6\u6001\uff01</p> <p>\u94f6\u884c\u5bb6\u7b97\u6cd5(Banker's algorithm)\u5f25\u8865\u4e86\u8d44\u6e90\u5206\u914d\u56fe\u7b97\u6cd5\u53ea\u9002\u7528\u4e8e\u6bcf\u4e2a\u8d44\u6e90\u7c7b\u522b\u4e2d\u90fd\u53ea\u6709\u4e00\u4e2a\u5b9e\u4f8b\u7684\u60c5\u51b5\u7684\u7f3a\u9677\uff0c\u5b83\u652f\u6301\u6bcf\u4e2a\u8d44\u6e90\u7c7b\u522b\u4e0d\u6b62\u4e00\u4e2a\u7684\u60c5\u51b5\uff0c\u4f46\u662f\u6548\u7387\u4e0d\u5982\u5206\u914d\u56fe\u7b97\u6cd5\u3002\u7c7b\u4f3c\u4e8e\u8d44\u6e90\u5206\u914d\u56fe\u7b97\u6cd5\u9700\u8981\u5728\u6700\u5f00\u59cb\u7ed9\u51fa\u6240\u6709 claim edge\uff0c\u94f6\u884c\u5bb6\u7b97\u6cd5\u8981\u6c42\u6ca1\u4e2a\u8fdb\u7a0b/\u7ebf\u7a0b\u7ed9\u51fa\u6267\u884c\u8fc7\u7a0b\u4e2d\u6240\u9700\u8981\u7684\u5404\u7c7b\u8d44\u6e90\u7684\u6700\u5927\u91cf\uff0c\u540c\u65f6\u7ef4\u62a4\u4e00\u4e9b\u6570\u636e\u4ee5\u52a8\u6001\u5730\u8ba1\u7b97\u5b89\u5168\u72b6\u6001\u3002High level \u5730\u6765\u8bb2\uff0c\u5c31\u662f\u9700\u8981\u52a8\u6001\u5730\u68c0\u6d4b\u67d0\u4e2a\u8d44\u6e90\u7533\u8bf7\u662f\u5426\u4f1a\u5bfc\u81f4\u7cfb\u7edf\u8fdb\u5165\u4e0d\u5b89\u5168\u72b6\u6001\uff0c\u5982\u679c\u4f1a\u5bfc\u81f4\u7cfb\u7edf\u8fdb\u5165\u4e0d\u5b89\u5168\u72b6\u6001\uff0c\u5219\u7b49\u5f85\u8d44\u6e90\u8db3\u591f\u518d\u5206\u914d\u3002</p> <p>\u66f4\u5177\u4f53\u7684\u6765\u8bf4\uff0c\u9700\u8981\u7ef4\u62a4\u8fd9\u4e9b\u4e1c\u897f\uff08\u5047\u8bbe\u95ee\u9898\u4e2d\u6709 n \u4e2a\u8fdb\u7a0b/\u7ebf\u7a0b\u548c m \u79cd\u8d44\u6e90\uff09\uff1a</p> <p>data structure</p> <ul> <li><code>Available[m]</code>: number of available resources of each type.</li> <li><code>Max[n][m]</code>: maximum demand of each thread.</li> <li><code>Allocation[n][m]</code>: number of resources of each type currently allocated to each thread.</li> <li><code>Need[n][m]</code>: remaining resource need of each thread.<ul> <li><code>Need[i][j] = Max[i][j] - Allocation[i][j]</code> always holds true.</li> <li> <p>\u6240\u4ee5\u903b\u8f91\u4e0a\u8fd9\u4e2a\u5f0f\u5b50\u5e94\u5f53\u662f\u5197\u4f59\u7684\uff0c\u4f46\u662f\u53d6\u540d\u6709\u5229\u4e8e\u4e4b\u540e\u7684\u6d41\u7a0b\u9610\u8ff0\uff0c\u6240\u4ee5\u6211\u5728\u8fd9\u91cc\u4fdd\u7559\uff1b</p> </li> </ul> </li> </ul> <p>\u94f6\u884c\u5bb6\u7b97\u6cd5\u5206\u4e3a\u4e24\u4e2a\u90e8\u5206\uff0c\u5206\u522b\u662f\u5b89\u5168\u7b97\u6cd5(safety algorithm)\u548c\u8d44\u6e90\u8bf7\u6c42\u7b97\u6cd5(resource request algorithm)\u3002\u524d\u8005\u68c0\u6d4b\u5f53\u524d\u72b6\u6001\u662f\u5426\u5904\u4e8e\u4e0d\u5b89\u5168\u72b6\u6001\uff0c\u540e\u8005\u4ee5\u524d\u8005\u4e3a\u57fa\u7840\uff0c\u5224\u65ad\u662f\u5426\u5141\u8bb8\u5f53\u524d\u8d44\u6e90\u8bf7\u6c42\u53d1\u751f\u3002</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit2-Part3/#\u5b89\u5168\u7b97\u6cd5","title":"\u5b89\u5168\u7b97\u6cd5","text":"<p>\u5b89\u5168\u7b97\u6cd5\u901a\u8fc7\u5bfb\u627e\u662f\u5426\u5b58\u5728\u4e00\u4e2a\u5b89\u5168\u5e8f\u5217\u6765\u5224\u65ad\u5f53\u524d\u72b6\u6001\u662f\u5426\u5904\u4e8e\u5b89\u5168\u72b6\u6001\u3002\u5148\u524d\u5728\u5b89\u5168\u72b6\u6001\u4e0e\u4e0d\u5b89\u5168\u72b6\u6001\u4e00\u8282\u4e2d\u6211\u7559\u4e0b\u8fc7\u4e00\u4e2a\u95ee\u9898\uff1a\u300c\u80fd\u5426\u8d2a\u5fc3\u5730\u6765\u6c42\u7b97\u8fd9\u6837\u4e00\u4e2a\u5e8f\u5217\u5462\u300d\uff0c\u7b54\u6848\u662f\u53ef\u4ee5\uff0c\u6211\u4eec\u4ee5\u4e00\u79cd\u8fd1\u4f3c\u8d2a\u5fc3\u5730\u7b56\u7565\u53bb\u6a21\u62df\u5b89\u5168\u5e8f\u5217\u7684\u8d44\u6e90\u5206\u914d\u8fc7\u7a0b\uff0c\u5c31\u53ef\u4ee5\u5224\u65ad\u662f\u5426\u5b58\u5728\u5b89\u5168\u7b56\u7565\u3002</p> <p>\u56e0\u4e3a\u5bf9\u4e8e\u6240\u6709\u53ef\u4ee5\u4f5c\u4e3a\u5b89\u5168\u72b6\u6001\u4e0b\u4e00\u9879\u7684 \\(T_{i_k}\\)\uff0c\u7531\u4e8e\u6267\u884c\u5b83\u4eec\u540e\uff0c\u7b49\u5230\u8fdb\u7a0b/\u7ebf\u7a0b\u8fd0\u884c\u7ed3\u675f\uff0c\u4f59\u4e0b\u7684\u8d44\u6e90\u53ea\u4f1a\u66f4\u591a\u4e0d\u4f1a\u66f4\u5c11\uff08\u5bf9\u6bd4\u8fd0\u884c\u524d\u540e\uff0c\u4f1a\u591a\u51fa\u6765\u539f\u672c\u5206\u914d\u7ed9\u8fd9\u4e9b\u8fdb\u7a0b/\u7ebf\u7a0b\u7684\u90a3\u4e9b\u8d44\u6e90\uff09\uff0c\u56e0\u800c\u53ea\u8981\u7b26\u5408\u6761\u4ef6\uff0c\u5c31\u53ef\u4ee5\u4f5c\u4e3a\u4e0b\u4e00\u9879\uff0c\u6b65\u6b65\u53ef\u884c\u6700\u7ec8\u4e5f\u53ef\u884c\u3002</p> <p>\u8bf7\u4ed4\u7ec6\u601d\u8003\u8fd9\u4e2a\u8fc7\u7a0b\u7684\u5408\u7406\u6027\uff0c\u5c24\u5176\u662f\u6211\u4e3a\u4ec0\u4e48\u5728\u8fd9\u91cc\u63d0\u5230\u4e86\u201c\u8d2a\u5fc3\u201d\uff0c\u6211\u611f\u89c9\u6211\u67e5\u5230\u7684\u8d44\u6599\u51e0\u4e4e\u90fd\u5ffd\u7565\u4e86\u8fd9\u4e2a\u95ee\u9898\u3002</p> <p>\u5177\u4f53\u6765\u8bf4\uff0c\u5b89\u5168\u7b97\u6cd5\u7684\u6b65\u9aa4\u5982\u4e0b\uff1a</p> <p>algorithm</p> <ol> <li>\u521d\u59cb\u5316\uff1a</li> <li><code>Work[m]</code> &lt;- <code>Available[m]</code>\uff0c<code>Work[m]</code> \u8868\u793a\u5f53\u524d\u72b6\u6001\u7684\u5269\u4f59\u8d44\u6e90\u91cf\uff1b</li> <li><code>Finish[n]</code> &lt;- <code>false</code>\uff0c\u8868\u793a\u6240\u6709\u8fdb\u7a0b/\u7ebf\u7a0b\u90fd\u8fd8\u6ca1\u8fd0\u884c\uff1b</li> <li>\u627e\u5230\u4e00\u4e2a <code>i</code> \u4f7f\u5f97\uff1a</li> <li><code>(Finish[i] == false) &amp;&amp; (Need[i] &lt;= Work)</code>\uff08\u6ce8\u610f\uff0c\u7b2c\u4e8c\u4e2a term \u662f vector \u6bd4\u8f83\uff0c\u8981\u6c42\u6bcf\u4e00\u9879\u90fd\u6ee1\u8db3\uff09\uff0c\u6ee1\u8db3\u8be5\u6761\u4ef6\u8868\u793a\u8be5\u8fdb\u7a0b/\u7ebf\u7a0b\u6240\u9700\u8981\u7684\u8d44\u6e90\u53ef\u4ee5\u88ab\u6ee1\u8db3\uff1b</li> <li>\u5982\u679c\u6ca1\u6709\u8fd9\u4e2a <code>i</code>\uff0c\u5219 goto 3.\uff1b</li> <li>\u5982\u679c\u6709\u8fd9\u4e2a <code>i</code>\uff0c\u5219\u66f4\u65b0\u72b6\u6001\uff1a         - <code>Finish[i]</code> &lt;- <code>true</code>\uff0c\u8868\u793a\u8be5\u8fdb\u7a0b/\u7ebf\u7a0b\u6267\u884c\u5b8c\u6bd5\uff1b         - <code>Work</code> &lt;- <code>Work + Allocation[i]</code>\uff0c\u8868\u793a\u8fdb\u7a0b/\u7ebf\u7a0b\u6267\u884c\u5b8c\u6bd5\u540e\u91ca\u653e\u8d44\u6e90\uff1b         - repeat 2.\uff1b</li> <li>\u5982\u679c\u6240\u6709\u8fdb\u7a0b/\u7ebf\u7a0b\u90fd\u6ee1\u8db3 <code>Finish[i] == true</code>\uff0c\u5219\u7cfb\u7edf\u5904\u4e8e\u5b89\u5168\u72b6\u6001\uff0c\u5426\u5219\u7cfb\u7edf\u5904\u4e8e\u4e0d\u5b89\u5168\u72b6\u6001\uff1b</li> </ol>"},{"location":"cour_note/D3QD_OperatingSystem/Unit2-Part3/#\u8d44\u6e90\u8bf7\u6c42\u7b97\u6cd5","title":"\u8d44\u6e90\u8bf7\u6c42\u7b97\u6cd5","text":"<p>\u6709\u4e86\u5b89\u5168\u7b97\u6cd5\u4f5c\u4e3a\u57fa\u7840\uff0c\u6211\u4eec\u5c31\u53ef\u4ee5\u5728\u5b83\u7684\u57fa\u7840\u4e0a\uff0c\u5224\u65ad\u67d0\u4e2a\u8d44\u6e90\u8bf7\u6c42\u662f\u5426\u4f1a\u5bfc\u81f4\u7cfb\u7edf\u8fdb\u5165\u4e0d\u5b89\u5168\u72b6\u6001\uff0c\u8fdb\u800c\u5f97\u5230\u5b8c\u6574\u7684\u94f6\u884c\u5bb6\u7b97\u6cd5\u4e86\u3002</p> <p>\u5b89\u5168\u7b97\u6cd5\u901a\u8fc7\u6a21\u62df\u7684\u65b9\u5f0f\u5224\u65ad\u4e00\u4e2a\u72b6\u6001\u662f\u4e0d\u662f\u5b89\u5168\u72b6\u6001\uff0c\u800c\u8d44\u6e90\u8bf7\u6c42\u7b97\u6cd5\u5219\u662f\u8d1f\u8d23\u7ef4\u62a4\u8fd9\u4e2a\u201c\u72b6\u6001\u201d\uff0c\u5e76\u6839\u636e\u5b89\u5168\u7b97\u6cd5\u8fd4\u56de\u7684\u7ed3\u679c\u6765\u5224\u65ad\u67d0\u4e2a\u8bf7\u6c42\u662f\u5426\u5e94\u5f53\u88ab\u63a5\u53d7\u3002</p> <p>\u5177\u4f53\u6765\u8bf4\uff0c\u8d44\u6e90\u8bf7\u6c42\u7b97\u6cd5\u7684\u6b65\u9aa4\u5982\u4e0b\uff1a</p> <p>algorithm</p> <ol> <li>\u7528 <code>Request[n][m]</code> \u6765\u7ef4\u62a4\u8fdb\u7a0b/\u7ebf\u7a0b\u60f3\u8981\u8bf7\u6c42\u7684\u8d44\u6e90\u7684\u6570\u91cf\uff1b</li> <li>\u5728\u6bcf\u4e2a\u8bf7\u6c42\u4e2d\uff0c\u5982\u679c <code>Request[i] &lt;= Need[i]</code>\uff08\u6ce8\u610f\u5411\u91cf\u6bd4\u8f83\uff09\uff0c\u5219\u7ee7\u7eed\uff1b\u5426\u5219\u629b\u51fa\u5f02\u5e38\uff0c\u56e0\u4e3a\u6b64\u65f6\u5b83\u8bf7\u6c42\u7684\u91cf\u8d85\u8fc7\u4e86\u5b83\u9884\u671f\u9700\u8981\u7684\u8d44\u6e90\u7684\u6700\u5927\u91cf\uff1b</li> <li>\u5982\u679c <code>Request[i] &lt;= Available</code>\uff0c\u8bf4\u660e\u8d44\u6e90\u8db3\u591f\uff0c\u7ee7\u7eed\uff1b\u5426\u5219\uff0c\u8fdb\u7a0b/\u7ebf\u7a0b\u5fc5\u987b\u7b49\u5f85\u8db3\u591f\u7684\u8d44\u6e90\uff1b</li> <li>\u5047\u8bbe\u7cfb\u7edf\u5206\u914d\u4e86\u8d44\u6e90\uff0c\u5219\u9700\u8981\u66f4\u65b0\u6a21\u62df\u72b6\u6001\uff08\u6b64\u65f6\u8d44\u6e90\u8fd8\u672a\u5b9e\u9645\u5206\u914d\uff01\u53ea\u662f\u4e3a\u4e86\u4ece\u6570\u503c\u4e0a\u6d4b\u8bd5\u662f\u5426\u5b89\u5168\u800c\u4e34\u65f6\u6784\u9020\u7684\u865a\u62df\u5c40\u9762\uff01\uff09\uff1a<ul> <li><code>Available</code> &lt;- <code>Available - Request[i]</code>\uff0c\u5373\u6a21\u62df\u5269\u4f59\u8d44\u6e90\u91cf\uff1b</li> <li><code>Allocation[i]</code> &lt;- <code>Allocation[i] + Request[i]</code>\uff0c\u5373\u6a21\u62df\u5206\u914d\u5f97\u5230\u7684\u8d44\u6e90\uff1b</li> <li><code>Need[i]</code> &lt;- <code>Need[i]</code> - <code>Request[i]</code>\uff0c\u5373\u6a21\u62df\u9884\u671f\u9700\u6c42\u91cf\uff1b</li> </ul> </li> <li>\u4f7f\u7528\u5b89\u5168\u7b97\u6cd5\u5224\u65ad\uff1a<ul> <li>\u5982\u679c\u5f53\u524d\u72b6\u6001\u662f\u5b89\u5168\u7684\uff0c\u5219\u8bf7\u6c42\u88ab\u63a5\u53d7\uff1b</li> <li>\u5982\u679c\u5f53\u524d\u72b6\u6001\u662f\u4e0d\u5b89\u5168\u7684\uff0c\u8bf7\u6c42\u4e0d\u88ab\u5141\u8bb8\uff0c\u540c\u65f6\u9700\u8981\u5c06\u8fd9\u4e9b\u77e9\u9635\u56de\u6eda\u5230\u6a21\u62df\u4e4b\u524d\u7684\u72b6\u60013\uff1b</li> </ul> </li> </ol> <p>limitations</p> <p>Like the other algorithms, the Banker's algorithm has some limitations when implemented. </p> <p>Specifically, it needs to know how much of each resource a process could possibly request. In most systems, this information is unavailable, making it impossible to implement the Banker's algorithm. </p> <p>Also, it is unrealistic to assume that the number of processes is static since in most systems the number of processes varies dynamically. </p> <p>Moreover, the requirement that a process will eventually release all its resources (when the process terminates) is sufficient for the correctness of the algorithm, however it is not sufficient for a practical system. Waiting for hours (or even days) for resources to be released is usually not acceptable.</p> <p>From Banker's algorithm | Wikipedia.</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit2-Part3/#\u6b7b\u9501\u68c0\u6d4b","title":"\u6b7b\u9501\u68c0\u6d4b","text":"<p>\u6b7b\u9501\u68c0\u6d4b(deadlock detection)\u548c\u6b7b\u9501\u89e3\u9664(deadlock recovery)\u642d\u914d\u4f7f\u7528\uff0c\u5176\u6838\u5fc3\u601d\u8def\u662f\u4e0d\u5bf9\u8d44\u6e90\u8bf7\u6c42\u505a\u8fc7\u591a\u7ea6\u675f\uff0c\u800c\u662f\u5728\u68c0\u6d4b\u5230\u7cfb\u7edf\u4e2d\u5b58\u5728\u6b7b\u9501\u65f6\uff0c\u53bb\u5904\u7406\u6b7b\u9501\u3002\u5176\u4e2d\u7684\u7b2c\u4e00\u6b65\u5c31\u662f\u68c0\u6d4b\u5230\u6b7b\u9501\u3002</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit2-Part3/#\u9762\u5411\u5355\u5b9e\u4f8b\u8d44\u6e90","title":"\u9762\u5411\u5355\u5b9e\u4f8b\u8d44\u6e90","text":"<p>\u7b49\u5f85\u56fe(wait-for graph)\u662f\u8d44\u6e90\u5206\u914d\u56fe\u7684\u5316\u7b80\uff0c\u8be5\u7b97\u6cd5\u53ea\u80fd\u89e3\u51b3\u6bcf\u4e2a\u8d44\u6e90\u7c7b\u522b\u4e2d\u53ea\u6709\u4e00\u4e2a\u5b9e\u4f8b\u7684\u60c5\u51b5\u3002</p> <p>\u5728\u8d44\u6e90\u5206\u914d\u56fe\u4e00\u8282\u4e2d\u6211\u4eec\u77e5\u9053\uff0c\u5bf9\u4e8e\u6bcf\u4e2a\u8d44\u6e90\u7c7b\u522b\u4e2d\u53ea\u6709\u4e00\u4e2a\u5b9e\u4f8b\u7684\u60c5\u51b5\uff0c\u53ea\u8981\u6709\u73af\u5c31\u4f1a\u6709\u6b7b\u9501\uff0c\u800c\u53ea\u8981\u80fd\u68c0\u6d4b\u8fd9\u4e2a\u73af\uff0c\u5c31\u80fd\u68c0\u6d4b\u6b7b\u9501\u3002\u800c\u5b9e\u9645\u7684\u8d44\u6e90\u5206\u914d\u56fe\u4e2d\u8d44\u6e90\u548c\u8fdb\u7a0b/\u7ebf\u7a0b\u7684\u8282\u70b9\u4ece\u662f\u6210\u5bf9\u51fa\u73b0\u5728\u73af\u4e2d\uff0c\u800c wait-for graph \u5219\u662f\u6293\u4f4f\u4e3b\u8981\u77db\u76fe\uff0c\u53ea\u4fdd\u7559\u8fdb\u7a0b/\u7ebf\u7a0b\u7684\u8282\u70b9\uff08\u8bf7\u8bfb\u8005\u601d\u8003\u4e3a\u4ec0\u4e48\u53ef\u4ee5\u8fd9\u6837\uff09\u4ee5\u51cf\u5c0f\u70b9\u7684\u6570\u91cf\uff0c\u63d0\u9ad8\u6548\u7387\u3002</p> <p>\u6211\u4eec\u5c06\u8d44\u6e90\u5206\u914d\u56fe\u4e00\u8282\u4e2d\u7684\u8d44\u6e90\u5206\u914d\u56fe\u6539\u4e3a\u7b49\u5f85\u56fe\uff0c\u5373\u4e3a\uff1a</p> <pre><code>&lt;center&gt; ![](img/26.png) &lt;/center&gt;\nWait-for graph.\n</code></pre> <p>\u901a\u8fc7\u52a8\u6001\u5730\u7ef4\u62a4\u8fd9\u4e2a wait-for graph \u548c\u5b9a\u671f\u8c03\u7528\u4e00\u4e2a\u73af\u68c0\u6d4b\u7b97\u6cd5\uff0c\u6765\u5b9e\u73b0\u6b7b\u9501\u68c0\u6d4b\u3002</p> <p>\u663e\u800c\u6613\u89c1\u7684\uff0c\u5c31\u7b97\u629b\u5f00\u5b83\u53ea\u652f\u6301\u6bcf\u4e2a\u8d44\u6e90\u7c7b\u522b\u4ec5\u80fd\u6709\u4e00\u4e2a\u5b9e\u4f8b\u7684\u7f3a\u70b9\uff0c\u9891\u7e41\u5730\u7ef4\u62a4\u56fe\u548c\u5b9a\u671f\u8c03\u7528\u73af\u68c0\u6d4b\u7b97\u6cd5\uff0c\u90fd\u4f1a\u5e26\u6765\u8f83\u5927\u7684\u5f00\u9500\u3002\u6240\u4ee5\uff0c\u8be5\u65b9\u6cd5\u5176\u5b9e\u8868\u73b0\u5e76\u4e0d\u7406\u60f3\u3002</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit2-Part3/#\u9762\u5411\u591a\u5b9e\u4f8b\u8d44\u6e90","title":"\u9762\u5411\u591a\u5b9e\u4f8b\u8d44\u6e90","text":"<p>\u4ece\u5355\u5b9e\u4f8b\u5411\u591a\u5b9e\u4f8b\u7684\u8fc1\u79fb\u601d\u8def\u548c\u6b7b\u9501\u907f\u514d\u4e2d\u4f7f\u7528\u7684\u8fc1\u79fb\u601d\u8def\u662f\u7c7b\u4f3c\u7684\uff0c\u4f7f\u7528\u5b89\u5168\u72b6\u6001\u6765\u5224\u65ad\u800c\u975e\u627e\u73af\u3002\u56e0\u800c\u8fd9\u4e2a\u7b97\u6cd5\u7684\u5b9e\u73b0\u548c\u94f6\u884c\u5bb6\u7b97\u6cd5\u7684\u5b9e\u73b0\u4e5f\u662f\u7c7b\u4f3c\u7684\uff08\u4f46\u662f\u6709\u4e00\u5b9a\u533a\u522b\uff0c\u53c2\u8003\u4e66\u672c P339\uff09\uff0cjjm \u8868\u793a\u4e00\u822c\u53ea\u8003\u94f6\u884c\u5bb6\u7b97\u6cd5\uff0c\u6240\u4ee5\u6211\u5728\u8fd9\u91cc\u4e5f\u4e0d\u8bb2\u8fd9\u4e2a\u7b97\u6cd5\u4e86\u3002</p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit2-Part3/#\u6b7b\u9501\u89e3\u9664","title":"\u6b7b\u9501\u89e3\u9664","text":"<p>\u6b7b\u9501\u89e3\u9664(deadlock recovery)\u867d\u7136\u662f \"recovery\"\uff0c\u4f46\u662f\u5b9e\u9645\u4e0a\u662f\u7834\u574f\u6b7b\u9501\u800c\u5e76\u6ca1\u6709\u6062\u590d\u5230\u4e00\u4e2a\u6b7b\u9501\u4e0d\u5b58\u5728\u7684\u72b6\u6001\uff0c\u6240\u4ee5\u7ffb\u8bd1\u4e3a\u89e3\u9664\u3002\u5bf9\u4e8e\u5df2\u7ecf\u4ea7\u751f\u7684\u6b7b\u9501\uff0c\u81f3\u5c11\u5f97\u6b7b\u4e00\u4e2a\uff0c\u6211\u4eec\u9700\u8981\u4f5c\u51fa\u51b3\u65ad\u3002\u4e66\u672c\u4e2d\u63d0\u5230\u4e86\u7ec8\u6b62\u548c\u8d44\u6e90\u62a2\u5360\u4e24\u79cd\u65b9\u6cd5\uff0c\u4f46\u6211\u8ba4\u4e3a\u672c\u8d28\u4e0a\u662f\u4e00\u6837\u7684\uff0c\u6240\u4ee5\u5e76\u5217\u5730\u7ed9\u51fa\uff1a</p> <ol> <li>\u90fd\u522b\u6d3b\uff0c\u6740\u6b7b\u6240\u6709\u6b7b\u9501\u4e2d\u7684\u8fdb\u7a0b/\u7ebf\u7a0b\uff1b<ul> <li>\u5f00\u9500\u5f88\u5927\uff0c\u56e0\u4e3a\u6240\u6709\u8fd9\u4e9b\u5de5\u4f5c\u90fd\u76f8\u5f53\u4e8e\u767d\u8d39\u4e86\uff0c\u800c\u4e14\u5e76\u4e0d\u662f\u968f\u968f\u4fbf\u4fbf\u5c31\u80fd\u6740\u7684\uff1b</li> </ul> </li> <li>\u4e00\u4e2a\u4e00\u4e2a\u6740\uff0c\u6740\u5230\u6ca1\u6709\u6b7b\u9501\uff1b<ul> <li>\u4ee5\u7279\u5b9a\u987a\u5e8f\u6740\u8fd9\u4e9b\u8fdb\u7a0b\uff0c\u53ef\u4ee5\u4f18\u5316\u8868\u73b0\uff0c\u4f8b\u5982\u6309\u7167\u4f18\u5148\u7ea7\u4ece\u4f4e\u5230\u9ad8\u6740\uff1b </li> </ul> </li> <li>\u7559\u6d3b\u547d\uff0c\u4f46\u662f\u9700\u8981\u56de\u6eda\u90e8\u5206\u8fdb\u7a0b\uff0c\u5f3a\u884c\u62a2\u5360\u5360\u6709\u7684\u8d44\u6e90\uff1b<ul> <li>\u5f88\u96be\u754c\u5b9a\u5e94\u8be5\u56de\u6eda\u5230\u54ea\u91cc\uff0c\u56de\u6eda\u4e5f\u96be\u5b9e\u73b0\uff0c\u4e3a\u4e86\u56de\u6eda\u4e5f\u9700\u8981\u5b58\u50a8\u66f4\u591a\u7684\u4fe1\u606f\uff0c\u5f00\u9500\u5f88\u5927\uff1b</li> <li>\u53c8\u770b\u5230\u62a2\u5360\u8fd9\u4e24\u4e2a\u5b57\uff0c\u6240\u4ee5\u8fd9\u91cc\u4e5f\u4f1a\u6709\u9965\u997f\u95ee\u9898\uff0c\u89e3\u51b3\u65b9\u6cd5\u4e5f\u548c\u4e4b\u524d\u4e00\u6837\uff0c\u901a\u8fc7\u8003\u8651\u4f18\u5148\u7ea7\uff0c\u5e76\u5c06\u88ab\u62a2\u5360\uff08\u88ab\u8feb\u56de\u6eda\uff09\u7684\u6b21\u6570\u7eb3\u5165\u4f18\u5148\u7ea7\u7684\u8003\u8651\u8303\u7574\u3002</li> </ul> </li> </ol> <ol> <li> <p>What's the difference between deadlock and livelock? \u21a9</p> </li> <li> <p>Deadlock Prevention \u4e00\u6587\u4e2d\u63d0\u5230\u4e86\u4f7f\u7528\u5047\u8131\u673a(spooling)\u7684\u65b9\u6cd5\u6765\u89e3\u9664\u6253\u5370\u673a\u8d44\u6e90\u7684\u4e92\u65a5\u6027\u3002\u00a0\u21a9</p> </li> <li> <p>Banker's Algorithm in Operating System (OS) \u4e00\u6587\u4e2d\u63d0\u5230\u4e86\u8981\u6062\u590d\u77e9\u9635\u72b6\u6001\uff0c\u4e66\u4e0a\u8c8c\u4f3c\u6ca1\u5199\u8fd9\u4e2a\u3002\u00a0\u21a9</p> </li> </ol>"},{"location":"cour_note/D3QD_OperatingSystem/Unit3-Part1/","title":"U3 Part 1: \u4e3b\u5b58 | Main Memory [\u672a\u5b8c\u6210]","text":"<p> \u7ea6 10 \u4e2a\u5b57 </p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit3-Part2/","title":"U3 Part 2: \u865a\u62df\u5185\u5b58 | Virtual Memory [\u672a\u5b8c\u6210]","text":"<p> \u7ea6 12 \u4e2a\u5b57 </p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit4/","title":"Unit 4: \u5b58\u50a8\u7ba1\u7406 | Storage Management [\u672a\u5b8c\u6210]","text":"<p> \u7ea6 11 \u4e2a\u5b57 </p>"},{"location":"cour_note/D3QD_OperatingSystem/Unit5/","title":"Unit 5: \u6587\u4ef6\u7cfb\u7edf | File System [\u672a\u5b8c\u6210]","text":"<p> \u7ea6 11 \u4e2a\u5b57 </p>"},{"location":"others/","title":"\u6249\u9875","text":"<p> \u7ea6 21 \u4e2a\u5b57 </p> <p> \u300e\u305d\u306e\u6642\u3092\u5f85\u3064\u3088\u300f      \u6211\u4e0d\u80fd\u4e00\u76f4\u5728\u4f60\u8eab\u8fb9\u5e2e\u52a9\u4f60\u3002  \u2014\u2014\u67e5\u7406\u00b7\u5e03\u6717  </p>"},{"location":"others/tools/","title":"\u5de5\u5177\u6536\u96c6","text":"<p> \u7ea6 46 \u4e2a\u5b57 </p> <ul> <li> <p>\u7ed8\u56fe</p> <ul> <li>\u77e2\u91cf\u56fe\u7ed8\u5236\u8bed\u8a00 Graphviz</li> <li>\u5728\u7ebf\u77e2\u91cf\u56fe\u7ed8\u5236 draw.io</li> <li>\u5728\u7ebf\u56fe\u8bba\u4f5c\u56fe</li> <li>\u5728\u7ebf\u624b\u5199\u98ce\u4f5c\u56fe Excalidraw</li> </ul> </li> <li> <p>\u547d\u4ee4\u884c\u8f85\u52a9</p> <ul> <li>ffmpeg \u6307\u4ee4\u751f\u6210</li> </ul> </li> </ul>"},{"location":"others/reveal-md2Slides/","title":"\u4f7f\u7528 reveal-md \u6765\u5199 Slides","text":"<p> \u7ea6 4169 \u4e2a\u5b57  151 \u884c\u4ee3\u7801  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 16 \u5206\u949f</p> <p>\u524d\u8a00</p> <ul> <li>\u672c\u6587\u9762\u5411 \u8ba4\u4e3a PPT \u5e76\u4e0d\u9ad8\u6548\uff0c\u4f46\u540c\u65f6\u53c8\u786e\u5b9e\u9700\u8981\u4e00\u79cd\u300c\u6f14\u793a\u300d\u9014\u5f84 \u7684\u504f\u6280\u672f\u4eba\u5458\uff1b</li> <li>\u867d\u7136\u5de5\u5177\u57fa\u4e8e\u524d\u7aef\u6280\u672f\u6808\uff0c\u4f46\u524d\u7aef\u77e5\u8bc6\u4ec5\u51b3\u5b9a\u5de5\u5177\u4f7f\u7528\u4e0a\u9650\uff0c\u5b8c\u5168\u53ef\u4ee5\u505a\u5230\u65e0\u524d\u7aef\u57fa\u7840\u8fdb\u884c\u57fa\u7840\u4f7f\u7528\uff1b</li> <li>\u6211\u5e76\u6ca1\u6709\u5c1d\u8bd5\u8fc7\u8131\u79bb\u547d\u4ee4\u884c\u6765\u5b9e\u73b0\u8fd9\u4e9b\uff0c\u4f46\u662f\u6211\u89c9\u5f97\u5927\u6982\u201c\u504f\u6280\u672f\u201d\u4eba\u5458\u4e0d\u5e94\u5f53\u4e0d\u4f1a\u4f7f\u7528\u547d\u4ee4\u884c\uff0c\u81f3\u5c11\u4f60\u8981\u77e5\u9053\u5728\u54ea\u91cc\u80fd\u8fd0\u884c\u547d\u4ee4\uff1b\u6b64\u5916\uff0c\u60a8\u9700\u8981\u786e\u4fdd\u60a8\u7684\u547d\u4ee4\u884c\u73af\u5883\u80fd\u591f\u4f7f\u7528 npm\uff1b</li> </ul>"},{"location":"others/reveal-md2Slides/#\u7b80\u4ecb","title":"\u7b80\u4ecb","text":"<p><code>reveal-md</code> \u662f <code>reveal.js</code> \u7684\u4e00\u4e2a\u6269\u5c55\u5de5\u5177\uff0c\u7c7b\u4f3c\u4e8e\u4e00\u4e2a\u9884\u7f16\u8bd1\u5de5\u5177\u3002\u5229\u7528 <code>reveal-md</code>\uff0c\u4f60\u53ef\u4ee5\u901a\u8fc7\u7f16\u5199\u4e00\u4e2a <code>Markdown</code> \u6587\u4ef6\u6765\u5feb\u901f\u7b80\u4fbf\u5730\u751f\u6210\u4e00\u4e2a\u57fa\u4e8e\u7f51\u9875\u7684 Slides\uff0c\u4f60\u4e5f\u53ef\u4ee5\u5c06\u5b83\u5bfc\u51fa\u4e3a\u9759\u6001\u8d44\u6e90\u5e76\u90e8\u7f72\u5728\u7c7b\u4f3c github pages \u7b49\u5e73\u53f0\u6765\u5206\u4eab\u9759\u6001\u9875\u9762\u3002</p> <ul> <li><code>reveal.js</code> \u7684\u5b98\u65b9 demo\uff1a\ud83d\udd17</li> <li>\u6211\u81ea\u5df1\u5199\u7684\u4e00\u4e2a project\uff1a\ud83d\udd17</li> <li><code>reveal-md</code> \u7684 github repo\uff1a\ud83d\udd17</li> </ul>"},{"location":"others/reveal-md2Slides/#\u4e3a\u4ec0\u4e48\u6211\u4e0d\u7528-ppt-\u548c\u8bed\u96c0\u6587\u6863\u6f14\u793a\u6a21\u5f0f","title":"\u4e3a\u4ec0\u4e48\u6211\u4e0d\u7528 PPT \u548c\u8bed\u96c0\u201c\u6587\u6863\u6f14\u793a\u6a21\u5f0f\u201d","text":"<p>\u5728\u8fd9\u7bc7\u6587\u7ae0\u548c\u8bed\u5883\u4e2d\uff0c\u6211\u60f3\u5927\u6982\u5c06\u300c\u6f14\u793a\u300d\u6240\u4f7f\u7528\u7684\u5f62\u5f0f\u5206\u4e3a\u4e09\u79cd\uff1a</p> <ul> <li>PPT \u7b49\u56fe\u5f62\u5316\u7684\u300c\u6f14\u793a\u300d\u6587\u6863\u5236\u4f5c\u5e73\u53f0\uff1b</li> <li>\u4f7f\u7528<code>Beamer</code>\u3001<code>reveal.js</code>\u3001<code>nodeppt</code>\u7b49\u5de5\u5177\uff0c\u4f7f\u7528\u4ee3\u7801\u7f16\u5199\u300c\u6f14\u793a\u300d\u6587\u6863\uff1b</li> <li>\u8bed\u96c0\u7684\u300c\u6587\u6863\u6f14\u793a\u6a21\u5f0f\u300d\uff1b</li> </ul> <p>\u6070\u597d\uff0c\u8bed\u96c0\u63a8\u51fa\u6f14\u793a\u6587\u7a3f\u7684\u65f6\u5019\u6709\u8bf4\u660e\u4e3a\u4ec0\u4e48\u4ed6\u4eec\u8981\u5f00\u53d1\u8fd9\u6837\u4e00\u4e2a\u4e1c\u897f\u3002</p> <p>\u518d\u89c1PPT\uff0c\u4f60\u597d\u201c\u6587\u6863\u6f14\u793a\u6a21\u5f0f\u201d</p> <p>\u6211\u975e\u5e38\u8d5e\u540c\u8fd9\u7bc7\u6587\u7ae0\u4e2d\u5bf9\u4e8e PPT \u7684\u53d9\u8ff0\uff0c\u6211\u4e5f\u5f88\u8ba8\u538c PPT \uff0c\u5b83\u786e\u5b9e\u53ef\u4ee5\u505a\u5f88\u591a\u4e8b\uff0c\u4f46\u662f\u5bf9\u6211\u6765\u8bf4\u6ca1\u5fc5\u8981\uff0c\u6211\u4e5f\u7528\u4e0d\u5230\u3002\u800c\u4e14\u8eab\u4e3a\u7834\u5199\u4ee3\u7801\u7684\uff0c\u6211\u5bf9\u90a3\u79cd\u6240\u8c13\u7684\u9ad8\u7ea7\u611f\u5e76\u6ca1\u6709\u4ec0\u4e48\u611f\u89c9\u3002\u800c\u4e14 PPT \u6709\u4e00\u4e2a\u81f4\u547d\u7684\u7f3a\u70b9\u5c31\u662f\u5b83\u7684\u5206\u4eab\u975e\u5e38\u4e0d\u65b9\u4fbf\uff0c\u4f60\u5fc5\u987b\u8981\u901a\u8fc7\u300c\u6587\u4ef6\u300d\u6765\u4f20\u9012\u4f60\u7684\u6750\u6599\uff0c\u800c\u4e14\u8fd8\u6536\u5230\u5c55\u793a\u8bbe\u5907\u7684\u73af\u5883\u9650\u5236\uff0c\u800c\u5176\u4ed6\u4e24\u79cd\u65b9\u6cd5\u90fd\u53ef\u4ee5\u5f88\u65b9\u4fbf\u7684\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\u3002</p> <p>\u56de\u5230\u300c\u6587\u6863\u6f14\u793a\u6a21\u5f0f\u300d\uff0c\u8bda\u7136\uff0c\u5728\u67d0\u4e9b\u7279\u5b9a\u7684\u65f6\u95f4\uff0c\u6587\u6863\u6f14\u793a\u786e\u5b9e\u80fd\u4fbf\u6377\u7684\u89e3\u51b3\u8bb8\u591a\u95ee\u9898\uff0c\u4f46\u662f\u6211\u4e0d\u89c9\u5f97\u76ee\u524d\u7684\u6587\u7a3f\u6f14\u793a\u80fd\u6210\u4e3a Slides \u7684\u66ff\u4ee3\u54c1\u3002\u5b83\u786e\u5b9e\u4fbf\u6377\u4e14\u9ad8\u6548\uff0c\u4f46\u662f\u5e76\u4e0d\u597d\u770b\uff0c\u4e5f\u5e76\u4e0d\u6e05\u6670\u2014\u2014\u800c\u4e14\u8bf4\u56de\u6765\uff0c\u5176\u5b9e\u4e5f\u4e0d\u65b9\u4fbf\uff08\u4e3a\u4ec0\u4e48\u6211\u4e4b\u540e\u4f1a\u8bb2\uff09\u3002 \u7b80\u5355\u8bb2\u4e86\u4e00\u4e0b\u6211\u5bf9\u5176\u4ed6\u4e24\u79cd\u9014\u5f84\u7684\u770b\u6cd5\uff0c\u5173\u4e8e\u901a\u8fc7\u4ee3\u7801\u9014\u5f84\u7f16\u5199\u300c\u6f14\u793a\u300d\u6587\u6863\u6211\u5f53\u7136\u4e5f\u6709\u8bdd\u8bf4\uff0c\u4f46\u662f\u6211\u60f3\u628a\u4ed6\u4eec\u653e\u5728\u540e\u9762\u3002</p> <p>\u63a5\u4e0b\u6765\uff0c\u6211\u60f3\u4ece\u300c\u4f7f\u7528\u4f53\u9a8c\u300d\u7684\u89d2\u5ea6\u6765\u8bc4\u4ef7\u4e00\u4e0b\u4e0a\u9762\u5df2\u7ecf\u63d0\u8fc7\u7684\u4e24\u4e2a\u9014\u5f84\u3002</p> <p>\u5728\u6211\u770b\u6765\uff0cPPT \u4e4b\u6240\u4ee5\u7d2f\u8d58\u4e14\u4f4e\u6548\uff0c\u662f\u56e0\u4e3a\u5927\u90e8\u5206\u4eba\u6d6a\u8d39\u65f6\u95f4\u5728\u4e8e\u4e0e\u6838\u5fc3\u5185\u5bb9\u5e76\u4e0d\u76f4\u63a5\u76f8\u5173\u7684\u7f8e\u5de5\u4e0a\u3002\u800c\u4ece\u5de5\u4f5c\u6d41\u7a0b\u4e0a\u6765\u8bb2\uff0c\u9664\u975e\u6211\u7cbe\u901a PPT \u4e14\u6709\u65f6\u95f4\uff0c\u5426\u5219\u6211\u4e0d\u4f1a\u4eb2\u81ea\u53bb\u505a PPT\uff0c\u800c\u662f\u548c\u7f8e\u5de5\u5bf9\u63a5\uff0c\u8ba9\u4ed6\u4eec\u6765\u505a\u3002\u53ef\u8fd9\u6837\u4e00\u6765\u95ee\u9898\u5c31\u51fa\u73b0\u4e86\uff0c\u201c\u5bf9\u63a5\u201d\u8fd9\u4ef6\u4e8b\u672a\u5fc5\u6bd4\u505a PPT \u8f7b\u677e\u3002\u53c8\u6216\u8005\u6211\u8fd9\u4e2a PPT \u662f\u6211\u81ea\u5df1\u9700\u8981\u7684\uff0c\u90a3\u6211\u5c31\u5f97\u786c\u7740\u5934\u76ae\u82b1\u8d39\u65f6\u95f4\u53bb\u94bb\u7814\u5982\u4f55\u505a\u4e00\u4e2a\u597d\u770b\u7684 PPT\uff0c\u7ed3\u679c\u6d6a\u8d39\u5927\u628a\u65f6\u95f4\u505a\u51fa\u6765\u7684\u53ef\u80fd\u8fd8\u662f\u4e2a\u8fde\u6cb9\u817b\u90fd\u8bf4\u4e0d\u4e0a\u7684\u4e1c\u897f\u3002</p> <p>\u800c\u56de\u5230\u8bed\u96c0\u7684\u300c\u6587\u6863\u6f14\u793a\u6a21\u5f0f\u300d\uff0c\u8bf4\u6765\u53ef\u7b11\uff0c\u6211\u5199\u8fd9\u4e00\u884c\u7684\u65f6\u5019\u5c31\u53c8\u51fa\u4e86 bug\u3002\u8bda\u7136\u300c\u6587\u6863\u6f14\u793a\u6a21\u5f0f\u300d\u662f\u4e00\u4e2a\u5f88\u597d\u7684 Idea\uff0c\u4f46\u662f\u8bed\u96c0\u81ea\u8eab\u5927\u5927\u5c0f\u5c0f\u7684\u95ee\u9898\u5230\u5904\u90fd\u662f\uff0c\u672c\u6765\u4f5c\u4e3a\u4e00\u4e2a\u6548\u7387\u5de5\u5177\u5374\u603b\u662f\u5728\u610f\u6599\u4e4b\u5916\u7684\u5730\u65b9\u9047\u5230\u5f88\u7cdf\u5fc3\u7684 Bug \uff0c\u8fd9\u7740\u5b9e\u5f88\u5f71\u54cd\u6548\u7387\uff08\u5173\u4e8e\u8fd9\u65b9\u9762\u7684\u5410\u69fd\u6211\u5c31\u4e0d\u653e\u5728\u8fd9\u91cc\u8bf4\u4e86\uff0c\u4ee5\u9632\u504f\u9898\uff09\u3002</p> <p>\u5728\u8fd9\u6837\u4e00\u4e2a\u57fa\u7840\u4e0b\uff0c\u51fa\u73b0\u4e86\u95ee\u9898\u4f46\u662f\u6211\u4eec\u65e0\u6cd5\uff0c\u6216\u8005\u8bf4\u5feb\u901f\u6392\u67e5\uff0c\u6216\u8005\u8bf4\u662f\u9000\u800c\u6c42\u5176\u6b21\u5bfb\u627e\u522b\u7684\u5b9e\u73b0\u529e\u6cd5\uff0c\u90fd\u662f\u4e0d\u65b9\u4fbf\u7684\u3002\u6362\u53e5\u8bdd\u6765\u8bf4\u5c31\u662f\u8fd9\u4e2a\u529f\u80fd\u81ea\u8eab\u7684\u7a33\u5b9a\u6027\u5c31\u4e0d\u80fd\u4fdd\u8bc1\uff0c\u800c\u5176\u5b9e\u73b0\u5bf9\u4f7f\u7528\u8005\u6765\u8bf4\u4e5f\u5e76\u4e0d\u8db3\u591f\u7b80\u5355\u900f\u660e\uff0c\u5bfc\u81f4\u4f7f\u7528\u8d77\u6765\u4f1a\u9700\u8981\u627f\u62c5\u5f88\u591a\u4e0d\u786e\u5b9a\u7684\u98ce\u9669\u3002\uff08\u987a\u4fbf\u5410\u69fd\u4e00\u53e5\uff0c\u4f7f\u7528\u8bed\u96c0\u7684\u8fd9\u4e00\u5e74\u6211\u4f53\u611f\u4e0a\u5f71\u54cd\u4f53\u9a8c\u7684 Bug \u662f\u8d8a\u6765\u8d8a\u591a\u4e86\u2026\u2026\uff09</p>"},{"location":"others/reveal-md2Slides/#\u4e3a\u4ec0\u4e48\u6211\u7528-reveal","title":"\u4e3a\u4ec0\u4e48\u6211\u7528 reveal*","text":"<p>\u90a3\u4e48\uff0c\u901a\u8fc7\u4ee3\u7801\u6765\u5236\u4f5c\u300c\u6f14\u793a\u300d\u6750\u6599\u53c8\u600e\u4e48\u6837\u5462\uff1f\u9996\u5148\u662f <code>Beamer</code>\uff0c\u5927\u6982\u4e5f\u662f\u6700\u6709\u540d\u7684\uff0c\u5176\u57fa\u4e8e \\(\\LaTeX\\) \u5b9e\u73b0\uff0c\u5176\u5728\u6392\u7248\u4e0a\u7684\u53ef\u63a7\u6027\u4e0d\u8a00\u800c\u55bb\uff0c\u4f46\u662f\u5199\u8fc7\u7684\u4eba\u90fd\u77e5\u9053 \\(\\LaTeX\\) \u5199\u8d77\u6765\u591a\u8d39\u5fc3\uff1b\u800creveal.js \u4ee5\u53ca nodeppt \u662f\u6211\u627e\u5230\u8fc7\u7684\u4e24\u4e2a\u6bd4\u8f83\u6ee1\u610f\u7684\uff0c\u901a\u8fc7\u4ee3\u7801\u6765\u5199 Slides \u7684\u5de5\u5177\u3002\u6211\u5e76\u4e0d\u6253\u7b97\u5728\u8fd9\u91cc\u628a\u4ed6\u4eec\u4e24\u4e2a\u90fd\u8be6\u7ec6\u7684\u4ecb\u7ecd\u4e00\u904d\uff0c\u4f46\u662f\u6211\u5e0c\u671b\u7b80\u5355\u8868\u8fbe\u4e00\u4e0b\u6211\u5bf9\u8fd9\u4e24\u4e2a\u4e1c\u897f\u7684\u770b\u6cd5\u3002</p> <p>\u9996\u5148\uff0c\u5728\u6211\u7684\u7406\u89e3\u4e2d\uff0c<code>nodeppt</code> \u5bf9\u7f8e\u5316\u662f\u6bd4 <code>reveal.js</code> \u8981\u597d\u4e00\u4e9b\u7684\uff0c\u5373\uff0c\u629b\u5f00\u82b1\u8d39\u5728\u91cc\u9762\u7684\u65f6\u95f4\u4e0d\u8bf4\uff0c\u5c31\u7ed3\u679c\u800c\u8a00\uff0c\u4f7f\u7528 <code>nodeppt</code> \u4f1a\u6bd4 <code>reveal.js</code> \u597d\u770b\u4e00\u4e9b\uff0c\u6392\u7248\u66f4\u81ea\u7531\u4e00\u4e9b\u3002\u4f46\u662f\u4ece\u300c\u6548\u7387\u300d\u6765\u8bf4\uff0c\u6211\u503e\u5411\u4e8e <code>reveal.js</code>\u3002 \u7406\u7531\u5f88\u7b80\u5355\uff0c<code>reveal.js</code> \u7684\u5206\u9875\u903b\u8f91\u6df1\u5f97\u6211\u5fc3\uff1a</p> <p></p> <p>\u6211\u81ea\u5df1\u5199\u7684\u67d0\u4e2a Slides \u7684\u7ed3\u6784\u901f\u89c8</p> <p>\u53ef\u4ee5\u53d1\u73b0\uff0c\u9875\u9762\u6709\u7eb5\u5411\u548c\u6a2a\u5411\u4e24\u4e2a\u6269\u5c55\u65b9\u5411\uff0c\u8fd9\u975e\u5e38\u7b26\u5408\u5c42\u6b21\u5316\u7684\u601d\u7ef4\u903b\u8f91\uff0c\u4e5f\u5f88\u7b26\u5408\u6587\u6863\u7684\u7f16\u5199\u903b\u8f91\uff0c\u5e76\u4e14\u603b\u4f53\u800c\u8a00 \u6ca1\u6709\u4ec0\u4e48\u82b1\u91cc\u80e1\u54e8\u4f46\u662f\u6ca1\u5565\u7528\u7684\u4e1c\u897f\uff0c\u5177\u6709\u4e00\u79cd\u5965\u5361\u59c6\u5243\u5200\u7684\u7f8e\u611f\u3002\u7136\u800c\u8fd9\u5e76\u4e0d\u610f\u5473\u7740\u5b83\u7684\u7f8e\u5de5\u4e0a\u9650\u5f88\u4f4e\uff0c\u6070\u6070\u76f8\u53cd\uff0c\u4e0d\u4ec5 <code>reveal.js</code> \u7684\u5185\u7f6e\u52a8\u753b\u548c\u98ce\u683c\u5c31\u5f88\u8212\u9002\uff0c\u800c\u4e14\u65e0\u8bba\u662f <code>reveal.js</code> \u8fd8\u662f <code>nodeppt</code>\uff0c\u4ed6\u4eec\u7684\u672c\u8d28\u90fd\u662f\u9759\u6001\u7f51\u9875\uff0c\u4f60\u5927\u53ef\u4ee5\u7528\u4f60\u7684\u524d\u7aef\u6280\u80fd\u6765\u7f8e\u5316\u5b83\u2014\u2014\u5f53\u7136\uff0c \u5bf9\u6211\u6765\u8bf4\u8fd9\u4e9b\u4e1c\u897f\u5c31\u6ca1\u5565\u5fc5\u8981\u4e86\u3002 \u4ee5\u4e0a\u90fd\u662f\u5173\u4e8e\u6548\u679c\u7684\u53d9\u8ff0\uff0c\u90a3\u5b83\u662f\u5426\u771f\u7684\u5199\u8d77\u6765\u5f88\u65b9\u4fbf\u5462\uff1f\u5176\u5b9e\u6211\u611f\u89c9\u539f\u751f\u7684 <code>reveal.js</code> \u5199\u8d77\u6765\u5e76\u4e0d\u65b9\u4fbf\uff0c\u6211\u4e00\u5f00\u59cb\u751a\u81f3\u4e0d\u77e5\u9053\u8981\u5982\u4f55\u521b\u5efa\u4e00\u4e2a\u65b0\u7684\u6587\u6863\u3002\u4f46\u662f\u6211\u540e\u6765\u53d1\u73b0\u4e86<code>[reveal-md](https://github.com/webpro/reveal-md)</code>\u8fd9\u4e2a\u5de5\u5177\u3002\u5229\u7528<code>reveal-md</code>\uff0c\u4f60\u53ef\u4ee5\u771f\u6b63\u610f\u4e49\u4e0a\u7684\u5b9e\u73b0\u4f7f\u7528<code>markdown</code>\u8bed\u6cd5\u6765\u5199\u4e00\u4e2a Slides\u3002</p>"},{"location":"others/reveal-md2Slides/#\u5b89\u88c5\u4e0e\u6f14\u793a","title":"\u5b89\u88c5\u4e0e\u6f14\u793a","text":"<p>\u786e\u4fdd\u60a8\u7684<code>[npm](https://www.npmjs.com/)</code>\u80fd\u591f\u6b63\u5e38\u4f7f\u7528\uff0c\u63a5\u4e0b\u6765\u5b89\u88c5<code>reveal-md</code>\u4f60\u53ea\u9700\u8981\u4f7f\u7528\u5982\u4e0b\u547d\u4ee4\u5373\u53ef\u3002</p> <pre><code>npm install -g reveal-md\n</code></pre> <p></p> <p>\u5b89\u88c5\u5b8c\u6210\u540e\uff0c\u4f60\u5c31\u53ef\u4ee5\u5c06 <code>reveal-md</code> \u5f53\u4f5c\u4e00\u4e2a console app \u6765\u4f7f\u7528\uff0c\u8f93\u5165 <code>reveal-md --help</code> \u6765\u67e5\u770b\u547d\u4ee4\u8be6\u7ec6\u7684\u4f7f\u7528\u65b9\u6cd5\u3002</p> help list <pre><code>Puppeteer unavailable, unable to create featured slide image for OpenGraph metadata.\nPuppeteer unavailable, unable to generate PDF file.\nUsage: cli &lt;slides.md&gt; [options]\n\nSee https://github.com/webpro/reveal-md for more details.\n\nOptions:\n  -V, --version                               output the version number\n      --title &lt;title&gt;                         Title of the presentation\n  -s, --separator &lt;separator&gt;                 Slide separator [default: 3 dashes (---) surrounded by two blank lines]\n-S, --vertical-separator &lt;separator&gt;        Vertical slide separator [default: 4 dashes (----) surrounded by two blank lines]\n-t, --theme &lt;theme&gt;                         Theme [default: black]\n--highlight-theme &lt;theme&gt;               Highlight theme [default: zenburn]\n--css &lt;files&gt;                           CSS files to inject into the page\n      --scripts &lt;files&gt;                       Scripts to inject into the page\n      --assets-dir &lt;dirname&gt;                  Defines assets directory name [default: _assets]\n--preprocessor &lt;script&gt;                 Markdown preprocessor script\n      --template &lt;filename&gt;                   Template file for reveal.js\n      --listing-template &lt;filename&gt;           Template file for listing\n      --glob &lt;pattern&gt;                        Glob pattern to select markdown files for listing and conversion [default: **/*.md]\n--print [filename]                      Print to PDF file\n      --static [dir]                          Export static html to directory [_static]. Incompatible with --print.\n      --static-dirs &lt;dirs&gt;                    Extra directories to copy into static directory. Only used in conjunction with --static.\n  -w, --watch                                 Watch for changes in markdown file and livereload presentation\n      --disable-auto-open                     Disable auto-opening your web browser\n      --host &lt;host&gt;                           Host [default: localhost]\n--port &lt;port&gt;                           Port [default: 1948]\n--featured-slide &lt;num&gt;                  Capture snapshot from this slide (numbering starts from 1) and use it as og:image for static build. Defaults to first slide. Only used with --static.\n      --absolute-url &lt;url&gt;                    Define url used for hosting static build. This is included in OpenGraph metadata. Only used with --static.\n      --print-size                            Paper size to use in exported PDF files\n      --puppeteer-launch-args &lt;args&gt;          Customize how Puppeteer launches Chromium. The arguments are specified as a space separated list (for example --puppeteer-launch-args=\"--no-sandbox --disable-dev-shm-usage\"). Needed for some CI setups.\n      --puppeteer-chromium-executable &lt;path&gt;  Customize which Chromium executable puppeteer will launch. Allows to use a globally installed version of Chromium.\n  -h, --help                                  output usage information\n</code></pre> <p>\u5728\u6211\u81ea\u5df1\u7684\u4f7f\u7528\u8fc7\u7a0b\u4e2d\uff0c\u6211\u8ba4\u4e3a\u6bd4\u8f83\u6838\u5fc3\u7684\u4e24\u6761\u547d\u4ee4\u5982\u4e0b\uff1a</p> <pre><code>## \u6700\u57fa\u7840\u7684\u547d\u4ee4\uff0c\u6839\u636e Markdown \u6587\u4ef6\u5728\u672c\u5730 1948 \u7aef\u53e3\u751f\u6210 Slides \u670d\u52a1\u3002\n$ reveal-md your-md-file.md\n\n## \u4e3a\u4e86\u5b9e\u73b0\u5728\u7ebf\u90e8\u7f72\uff0c\u9700\u8981\u5bfc\u51fa\u4e3a\u9759\u6001\u8d44\u6e90\u3002\n$ reveal-md your-md-file.md --static your-static-dir\n</code></pre> <p>\u4e5f\u5c31\u662f\u8bf4\uff0c\u4f60\u53ea\u9700\u8981\u7f16\u5199\u4e00\u4e2amd\u6587\u4ef6\uff0c\u5e76\u4f7f\u7528\u8fd9\u4e9b\u6307\u4ee4\u5c31\u80fd\u751f\u6210 reveal.js Slides\u3002 \u63a5\u4e0b\u6765\u4ee5\u5b98\u65b9 demo \u4e3a\u4f8b\u4ecb\u7ecd\u4e00\u4e0b\u4f7f\u7528\u3002\u8fd0\u884c\u6307\u4ee4\u4ee5\u540e\u4f1a\u5728 1948 \u7aef\u53e3\u542f\u52a8\u670d\u52a1\uff0c\u4e00\u822c\u4f1a\u76f4\u63a5\u901a\u8fc7\u6d4f\u89c8\u5668\u6253\u5f00\u3002 \u5728 PC \u7aef\u53e3\uff1a</p> <ul> <li>\u901a\u8fc7\u70b9\u51fb/ \u7a7a\u683c\u6765\u9009\u62e9\u4e0b\u4e00\u9875\uff0c\u4f7f\u7528 <code>h/\u2190</code> <code>j/\u2193</code> <code>k/\u2191</code> <code>l/\u2192</code> \u6216\u8005\u70b9\u51fb\u53f3\u4e0b\u89d2\u7684\u65b9\u5411\u76d8\u6765\u8fdb\u884c\u4e0a\u4e0b\u5de6\u53f3\u5207\u6362\uff0c\u76f4\u63a5\u70b9\u51fb\u9875\u9762\u5e95\u90e8\u7684\u8fdb\u5ea6\u6761\u4e5f\u53ef\u4ee5\u5b9e\u73b0\u9875\u9762\u8df3\u8f6c\u3002</li> </ul> <p></p> <ul> <li>\u6309\u4e0b <code>f</code> \u6765\u5168\u5c4f\u663e\u793a\uff0c\u6309\u4e0b <code>Esc</code> \u6216\u8005 <code>f</code> \u9000\u51fa\u3002</li> </ul> \u6309 <code>f</code> \u4e4b\u524d\u3002 \u5168\u5c4f\u663e\u793a\u3002 <ul> <li>\u6309\u4e0b<code>s</code>\u8fdb\u5165\u6f14\u8bb2\u8005\u6a21\u5f0f\uff0c\u4e5f\u5c31\u662f\u518d\u591a\u8df3\u51fa\u6765\u4e00\u4e2a\u5f39\u7a97\uff0c\u5728\u5b9e\u9645\u4f7f\u7528\u4e2d\u53ef\u4ee5\u5728\u6295\u5f71\u4eea\u91cc\u653e\u5168\u5c4f\uff0c\u5728\u81ea\u5df1\u7535\u8111\u4e0a\u5c55\u793a\u8fd9\u4e2a\u7a97\u53e3\u3002\u4fee\u6539\u53f3\u4e0a\u89d2\u7684 Layout \u53ef\u4ee5\u4fee\u6539\u663e\u793a\u6a21\u5f0f\u3002<code>Notes</code> \u7684\u5185\u5bb9\u4f1a\u5728\u540e\u9762\u4ecb\u7ecd\uff0c\u7c7b\u4f3c\u4e8e PPT \u7684\u5907\u6ce8\u3002</li> </ul> <p></p> <ul> <li>\u6309\u4e0b<code>o</code>\u8fdb\u5165\u603b\u89c8\u89c6\u56fe\uff0c\u53ef\u4ee5\u5229\u7528\u65b9\u5411\u952e\u8fdb\u884c\u79fb\u52a8\uff0c\u56de\u8f66\u6216\u70b9\u51fb\u8fdb\u884c\u9009\u62e9\u3002\u9700\u8981\u6ce8\u610f\uff0c\u8fd9\u91cc\u663e\u793a\u7684\u5185\u5bb9\u548c\u5b9e\u9645\u5c55\u793a\u7684\u9875\u9762\u5185\u5bb9\u5728\u5e03\u5c40\u4e0a\u5b58\u5728\u5dee\u5f02\u3002</li> </ul> <p></p> <ul> <li>\u6309\u4e0b<code>v</code>\u6216<code>.</code>\u9ed1\u5c4f\u3002</li> </ul> <p>\u800c\u5728\u79fb\u52a8\u7aef\uff08\u6bd4\u5982\u8bbf\u95ee\u67d0\u4e2a\u5b9e\u4f8b\u7684\u5728\u7ebf\u90e8\u7f72\u65f6\uff09\uff0c\u57fa\u672c\u7684\u70b9\u51fb\u64cd\u4f5c\u662f\u4e00\u6837\u7684\uff0c\u6b64\u5916\uff0c\u5e26\u6709\u65b9\u5411\u7684\u6ed1\u52a8\u53ef\u4ee5\u5bf9\u5e94\u65b9\u5411\u952e\u529f\u80fd\u3002</p> <p></p>"},{"location":"others/reveal-md2Slides/#\u6587\u6863\u7f16\u5199","title":"\u6587\u6863\u7f16\u5199","text":"<p>\u5728\u8fd9\u90e8\u5206\uff0c\u6211\u5e76\u4e0d\u6253\u7b97\u6309\u7167\u6a21\u5757\u5316\u3001\u7cfb\u7edf\u5316\u7684\u6d41\u7a0b\u6765\u7f16\u5199\u6559\u7a0b\uff0c\u8fd9\u4e9b\u4f60\u5728\u5b98\u65b9\u6587\u6863\u4e2d\u90fd\u80fd\u627e\u5230\u2014\u2014\u6211\u5e76\u4e0d\u89c9\u5f97\u201c\u5b57\u5178\u201d\u662f\u4e00\u4e2a\u5f88\u597d\u7684\u5b66\u4e60\u9014\u5f84\uff0c\u5c31\u50cf\u6211\u4eec\u4e00\u822c\u4e0d\u5efa\u8bae\u7528\u300aC++ Primer\u300b\u5165\u95e8 C++\uff0c\u66f4\u4e0d\u4f1a\u5efa\u8bae\u5916\u56fd\u53cb\u4eba\u901a\u8fc7\u300a\u65b0\u534e\u5b57\u5178\u300b\u6765\u5b66\u4e60\u6c49\u8bed\u3002 \u6211\u5c06\u6309\u7167\u6211\u5bf9\u8fd9\u4e2a\u5de5\u5177\u7684\u7406\u89e3\uff0c\u6309\u7167\u7531\u6d45\u5165\u6df1\uff0c\u6309\u7167\u5fc5\u8981\u7a0b\u5ea6\u6765\u4ecb\u7ecd\u5185\u5bb9\u3002\u5b83\u53ef\u80fd\u770b\u8d77\u6765\u4f1a\u53c8\u4e9b\u6df7\u4e71\uff0c\u4f46\u662f\u6211\u89c9\u5f97\u5b83\u662f\u7b26\u5408\u5b9e\u8df5\u987a\u5e8f\u7684\uff0c\u5982\u679c\u8ba9\u4f60\u89c9\u5f97\u770b\u8d77\u6765\u5f88\u8d39\u52b2\uff0c\u53ef\u4ee5\u642d\u914d\u5b98\u65b9\u6587\u6863\u6765\u4f7f\u7528\uff0c\u6216\u8005\u76f4\u63a5\u544a\u8bc9\u6211\u3002 \u6b64\u5916\uff0c\u5176\u4e2d\u53ef\u80fd\u4e0d\u4f1a\u6d89\u53ca\u4e00\u90e8\u5206\u6211\u4e2a\u4eba\u4e0d\u592a\u559c\u6b22\u7684\u4e1c\u897f\uff0c\u6bd4\u5982\u540c\u6837\u53ef\u4ee5\u901a\u8fc7\u914d\u7f6e\u6587\u4ef6\u548c\u547d\u4ee4\u53c2\u6570\u7684\u884c\u4e3a\uff0c\u6211\u4f1a\u9009\u62e9\u53ea\u4ecb\u7ecd\u914d\u7f6e\u6587\u4ef6\u7684\u65b9\u6848\u3002\u5982\u679c\u4f60\u5bf9\u53e6\u5916\u4e00\u79cd\u65b9\u6848\u611f\u5174\u8da3\uff0c\u53ef\u4ee5\u8be6\u7ec6\u9605\u8bfb\u6587\u6863\u6216\u8005\u5e2e\u52a9\u83dc\u5355\u3002\u6b64\u5916\uff0c\u672c\u6587\u7ae0\u4e5f\u4e0d\u4f1a\u6d89\u53ca <code>reveal-md</code> \u7684\u6240\u6709\u5185\u5bb9\uff0c\u800c\u66f4\u591a\u7684\u662f\u4e00\u4e2a\u629b\u7816\u5f15\u7389\u6216\u8005\u8bf4\u57fa\u7840\u4f7f\u7528\u7684\u6559\u7a0b\u3002\u90e8\u5206\u9700\u6c42\u53ef\u80fd\u662f\u9762\u5411\u7279\u6b8a\u7528\u6237\u7fa4\u4f53\u7684\uff0c\u8fd8\u662f\u90a3\u53e5\u8bdd\uff0c\u5982\u679c\u6709\u5174\u8da3\u53ef\u4ee5\u67e5\u770b\u5b98\u65b9\u6587\u6863\u3002</p>"},{"location":"others/reveal-md2Slides/#\u5206\u9875","title":"\u5206\u9875","text":"<p>\u9996\u5148\uff0c\u5982\u679c\u4f60\u7528\u4e00\u4e2a\u518d\u666e\u901a\u4e0d\u8fc7\u7684 Markdown \u6587\u4ef6\u6765\u521b\u5efa Slides\uff0c\u6bd4\u5982\uff1a</p> <pre><code>## Part 1\n\n### Part 1.1\n\n- Orderred List\n- Next Line\n\n1. Numberred List\n2. Next Line\n\n### Part 1.2\n\n{code block here}\n\n### Part 1.3\n\n&gt; Everthings seems ok!\n</code></pre> <p>\u90a3\u4e48\u8fd0\u884c\u4ee5\u540e\u6211\u4eec\u4f1a\u5f97\u5230\u8fd9\u6837\u4e00\u4e2a\u9875\u9762\uff1a</p> <p></p> <p>\u53ef\u4ee5\u53d1\u73b0\uff0c\u5b83\u5e76\u4e0d\u50cf\u6211\u4eec\u60f3\u7684\u90a3\u6837\uff0c\u5411\u6a2a\u5411\u548c\u7eb5\u5411\u6269\u5c55\u3002\u4f46\u662f\u8fd9\u6070\u597d\u8bf4\u660e\u6240\u6709\u4e1c\u897f\u90fd\u662f\u53ef\u63a7\u7684\uff0c\u800c\u4e0d\u662f\u83ab\u540d\u5176\u5999\u7684\u6839\u636e\u67d0\u4e2a\u6807\u9898\u5c31\u81ea\u52a8\u6362\u6389\uff0c\u8fdb\u800c\u5bfc\u81f4\u4e00\u7cfb\u5217\u8be1\u5f02\u7684\u95ee\u9898\u3002</p> <p>\u5728 reveal-md \u4e2d\uff0c\u6709\u4e24\u79cd separator \u548c vertical separator \u4e24\u79cd\uff0c\u987e\u540d\u601d\u4e49\uff0c\u5206\u522b\u5bf9\u5e94\u7740\u5de6\u53f3\u5206\u9875\u548c\u4e0a\u4e0b\u5206\u9875\u3002\u9ed8\u8ba4\u60c5\u51b5\u4e0b\uff0cseparator \u662f <code>\\n---\\n</code>\uff0c\u800c vertical separator \u662f <code>\\n----\\n</code>\u3002\u6240\u4ee5\u7a0d\u5fae\u5bf9\u4e0a\u9762\u7684\u6587\u6863\u8fdb\u884c\u4e00\u4e9b\u4fee\u6539\uff1a</p> <pre><code>### Part 1\n\n---\n\n#### Part 1.1\n\n- Orderred List\n- Next Line\n\n1. Numberred List\n2. Next Line\n\n----\n\n#### Part 1.2\n\n{code block here}\n\n----\n\n#### Part 1.3\n\n&gt; Everthings seems ok!\n</code></pre> <p>\u518d\u6b21\u8fd0\u884c\u5c31\u80fd\u53d1\u73b0\u6211\u4eec\u7684 Slides \u5df2\u7ecf\u6709\u4e86\u4e8c\u7ef4\u7684\u5c42\u7ea7\u7ed3\u6784\uff1a</p> <p></p> <p>\u867d\u7136\u8fd9\u91cc\u7684\u9884\u89c8\u56fe\u91cc\u770b\u8d77\u6765\u6392\u7248\u5f88\u4e11\uff0c\u4f46\u662f\u5b9e\u9645\u5c55\u793a\u7684\u65f6\u5019\u90fd\u662f\u9ed8\u8ba4\u5c45\u4e2d\uff0c\u4e0d\u559c\u6b22\u7684\u8bdd\u53ef\u4ee5\u6539\u76f8\u5173\u8bbe\u7f6e\u6216\u8005\u7528 html \u6807\u7b7e\u4fee\u6539\u3002</p> <p>\u90a3\u4e48\u5176\u5b9e\u5230\u6b64\u4e3a\u6b62\uff0c\u4f60\u5df2\u7ecf\u80fd\u591f\u901a\u8fc7<code>reveal-md</code>\u6765\u5b9e\u73b0\u975e\u5e38\u5feb\u901f\u7684 Slides \u7f16\u5199\u4e86\u3002\u4f46\u662f\u4e3a\u4e86\u5b9a\u5236\u4e3b\u9898\uff0c\u6216\u8005\u662f\u4f7f\u7528\u4e00\u4e9b\u66f4\u9ad8\u7ea7\u7684\u4e1c\u897f\uff0c\u6211\u4eec\u8fd8\u9700\u8981\u4ecb\u7ecd\u4e00\u4e9b\u522b\u7684\u4e1c\u897f\uff0c\u5305\u62ec\u5bf9\u67d0\u4e9b\u4e1c\u897f\u7684\u81ea\u5b9a\u4e49\u3001\u67d0\u4e9b\u6a21\u5757\u7684\u6269\u5c55\u529f\u80fd\u3001\u4e0e\u539f\u751f<code>reveal.js</code>\u8bed\u6cd5\u7684\u6df7\u7528\u3002 \u5728\u6b63\u5f0f\u8fdb\u5165\u4e0b\u4e00\u4e2a\u90e8\u5206\u4e4b\u524d\uff0c\u6211\u60f3\u8865\u5145\u4ecb\u7ecd\u4e00\u4e0b\u5982\u4f55\u4fee\u6539\u9ed8\u8ba4\u7684 separator\uff1a \u6709\u4e24\u79cd\u65b9\u6848\u80fd\u5b9e\u73b0 seperator \u7684\u81ea\u5b9a\u4e49\uff0c\u4e00\u79cd\u662f\u901a\u8fc7\u5728\u547d\u4ee4\u884c\u4e2d\u7684\u9644\u52a0\u53c2\u6570\u5b9e\u73b0\uff0c\u53e6\u4e00\u79cd\u5219\u662f\u5728<code>md</code>\u6587\u4ef6\u5f00\u5934\u5199\u597d\u914d\u7f6e\u6587\u4ef6\u5b9e\u73b0\u3002</p> <p></p> <pre><code>---\nseparator: &lt;!--s--&gt;\nverticalSeparator: &lt;!--v--&gt;\n---\n</code></pre> <ul> <li>\u8fd9\u91cc\u5c06 <code>&lt;!--s--&gt;</code> \u8bbe\u4e3a separator\uff0c\u5c06 <code>&lt;!--v--&gt;</code> \u8bbe\u4e3a vertical separator\u3002</li> <li>\u8fd9\u4e00\u90e8\u5206\u5185\u5bb9\u9700\u8981\u653e\u5728 <code>md</code> \u6587\u4ef6\u7684\u5f00\u5934\uff0c\u4e4b\u540e\u4f1a\u8be6\u7ec6\u4ecb\u7ecd\u3002</li> </ul> <p>\u8fd9\u91cc\u6211\u624d\u7528\u7b2c\u4e8c\u79cd\u65b9\u6848\u6765\u6539\u88c5\u6211\u4eec\u7684 <code>md</code> \u6587\u4ef6\u73b0\u5728\u5f97\u5230\uff1a</p> <pre><code>---\nseparator: &lt;!--s--&gt;\nverticalSeparator: &lt;!--v--&gt;\n---\n\n### Part 1\n\n&lt;!--s--&gt;\n\n#### Part 1.1\n\n- Orderred List\n- Next Line\n\n1. Numberred List\n2. Next Line\n\n&lt;!--v--&gt;\n\n#### Part 1.2\n\n{code block here}\n\n&lt;!--v--&gt;\n\n#### Part 1.3\n\n&gt; Everthings seems ok!\n</code></pre> <p>\u800c\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u9664\u4e86\u5f00\u5934\u914d\u7f6e\u6587\u4ef6\u7684\u90e8\u5206\uff0c\u5176\u4ed6\u7684 <code>---</code> \u5219\u4f1a\u88ab\u8ba4\u4e3a\u662f <code>md</code> \u7684\u8bed\u6cd5\uff0c\u6e32\u67d3\u4e3a\u6b63\u5e38\u7684\u5206\u5272\u7ebf\u3002</p>"},{"location":"others/reveal-md2Slides/#\u4ee3\u7801\u6846","title":"\u4ee3\u7801\u6846","text":"<p>\u9996\u5148\uff0c\u5728 <code>reveal-md</code> \u4e2d\u4f7f\u7528\u4ee3\u7801\u6846\u548c\u5728 <code>markdown</code> \u4e2d\u4f7f\u7528\u662f\u4e00\u6837\u7684\uff0c\u53ea\u4e0d\u8fc7 <code>reveal.js</code> \u5bf9\u4ee3\u7801\u6846\u6709\u66f4\u591a\u7684\u652f\u6301\uff0c\u800c <code>reveal-md</code> \u5c06\u8fd9\u79cd\u652f\u6301\u878d\u5408\u8fdb\u4e86 <code>markdown</code> \u7684\u8bed\u6cd5\u3002\u6211\u5728\u8fd9\u91cc\u4e3b\u8981\u60f3\u4ecb\u7ecd\u7684\u662f\u4ee3\u7801\u6846\u9ad8\u4eae\u884c\u52a8\u753b\u3002</p> <p>\u4e0d\u77e5\u9053\u4f60\u6709\u6ca1\u6709\u9047\u5230\u8fc7\u8fd9\u79cd\u60c5\u51b5\uff0c\u6211\u4eec\u9700\u8981\u8d34\u51fa\u4e00\u6bb5\u4ee3\u7801\uff0c\u4f46\u662f\u6709\u4e9b\u90e8\u5206\u5e76\u4e0d\u662f\u91cd\u70b9\uff0c\u4f46\u662f\u4e0d\u653e\u4e0a\u53bb\u53c8\u89c9\u5f97\u602a\u602a\u7684\uff1b\u53c8\u6216\u8005\u4f60\u7684\u4ee3\u7801\u91cc\u6709\u591a\u4e2a\u91cd\u70b9\uff0c\u4f60\u9700\u8981\u5728\u5c55\u793a\u65f6\u624b\u52a8\u544a\u8bc9\u5927\u5bb6\u54ea\u91cc\u662f\u91cd\u70b9\uff1f<code>reveal*</code> \u53ef\u4ee5\u505a\u5230\u6309\u884c\u9ad8\u4eae\u4ee3\u7801\uff0c\u5e76\u4e14\u80fd\u591f\u5b9e\u73b0\u52a8\u753b\u3002\u8fd9\u4e48\u8bf4\u6709\u70b9\u62bd\u8c61\uff0c\u53ef\u4ee5\u4f53\u9a8c\u4e00\u4e0b\u8fd9\u4e00\u9875 Slide\u3002</p> \u53ef\u4ee5\u53d1\u73b0\uff0c\u4e0d\u4ec5\u9ad8\u4eae\u4e86\uff0c\u800c\u4e14\u8fd8\u6709\u81ea\u52a8\u6eda\u52a8\u5230\u4e2d\u5fc3\u3002 <p>\u90a3\u4e48\u8981\u5982\u4f55\u5b9e\u73b0\u5462\uff1f\u6211\u4eec\u77e5\u9053\uff0c\u5728<code>Markdown</code>\u4e2d\u4f7f\u7528\u4ee3\u7801\u6846\u7684\u8bed\u6cd5\u5982\u4e0b\uff1a</p> <pre><code>- \u524d\u9762\u7684\u6570\u5b57\u662f\u4e3a\u4e86\u6807\u8bb0\u5b83\u4eec\u5c5e\u4e8e\u4ee3\u7801\u6846\u7684\u7b2c\u51e0\u884c\u800c\u5199\u7684\uff0c\u5b9e\u9645\u4e0d\u9700\u8981\u5199\u8fd9\u4e9b\u6570\u5b57\uff08\u5e9f\u8bdd\uff09\n- \u53cd\u659c\u6760\u662f\u4e3a\u4e86\u9632\u6b62md\u6e32\u67d3\u9519\u8bef\uff0c\u5b9e\u9645\u4e0a\u4e0d\u9700\u8981\u52a0\n\n\\```cpp\n1       #include &lt;iostream&gt;\n2       int main(){\n3           std::cout &lt;&lt; \"Hello World!\\n\";\n4       return 0;\n5       }\n\\```\n</code></pre> <p>\u90a3\u4e48\uff0c\u4e3a\u4e86\u5b9e\u73b0\u9ad8\u4eae\uff0c\u6211\u4eec\u53ea\u9700\u8981\u5728\u8bed\u8a00\u540e\u9762\u52a0\u4e0a\u4e00\u4e2a\u65b9\u62ec\u53f7 <code>[...]</code> \u6765\u6807\u8bb0\u9ad8\u4eae\u884c\u5373\u53ef\uff0c\u6bd4\u5982 <code>[2-5]</code> \u5c31\u662f\u6807\u8bb0 2\uff5e5 \u884c\uff0c\u4e5f\u5c31\u662f\u6574\u4e2a <code>main()</code> \u51fd\u6570\u3002\u6b64\u5916\uff0c\u4f60\u8fd8\u53ef\u4ee5\u7528<code>|</code>\u6765\u5206\u9694\u591a\u4e2a\u9ad8\u4eae\u5757\uff0c\u6765\u5b9e\u73b0\u52a8\u753b\u7684\u6548\u679c\uff0c\u4f8b\u5982 <code>[1|2-5]</code> \u5c31\u662f\u5148\u9ad8\u4eae\u9884\u7f16\u8bd1\uff0c\u518d\u9ad8\u4eae <code>main()</code> \u51fd\u6570\u3002</p> <pre><code>---\nseparator: &lt;!--s--&gt;\nverticalSeparator: &lt;!--v--&gt;\n---\n\n### Part 1\n\n&lt;!--s--&gt;\n\n#### Part 1.1\n\n- Orderred List\n- Next Line\n\n1. Numberred List\n2. Next Line\n\n&lt;!--v--&gt;\n\n#### Part 1.2\n\n\\```cpp[1|2-5]\n#include &lt;iostream&gt;\nint main(){\n    std::cout &lt;&lt; \"Hello World!\\n\";\n    return 0;\n}\n\\```\n\n&lt;!--v--&gt;\n\n#### Part 1.3\n\n&gt; Everthings seems ok!\n</code></pre>"},{"location":"others/reveal-md2Slides/#\u683c\u5f0f\u652f\u6301","title":"\u683c\u5f0f\u652f\u6301","text":"<p>\u5728\u6587\u672c\u683c\u5f0f\u6392\u7248\u65b9\u9762\uff0c<code>Markdown</code> \u7684\u539f\u751f\u8bed\u6cd5\u90fd\u662f\u652f\u6301\u7684\uff0c\u6b64\u5916\u4f60\u5f53\u7136\u4e5f\u53ef\u4ee5\u4f7f\u7528 <code>html</code> \u6807\u7b7e\u6765\u7f16\u8f91\u4f60\u7684\u6587\u5b57\uff0c\u4f8b\u5982\u4fee\u6539\u989c\u8272\u3001\u8bbe\u7f6e\u5c45\u4e2d/\u9760\u5de6/\u9760\u53f3\u3001\u4fee\u6539\u5927\u5c0f\u2026\u2026 \u4f8b\u5982\uff0c\u4e0a\u9762\u5c55\u793a\u7684\u90a3\u5f20\u5c55\u793a\u4ee3\u7801\u9ad8\u4eae\u7684 Slide \u7684\u521d\u59cb\u4ee3\u7801\u5982\u4e0b\uff1a</p> <pre><code>### \u8f93\u51fa\u6d41\n\n\\```c[1-19|13-16]\n#ifndef __C_NEWBIE_HELPER__\n#define __C_NEWBIE_HELPER__\n/****************************************************\n * C Newbie Helper 1.0                              *\n * ------------------------------------------------ *\n * Github Repository Address:                       *\n * - https://github.com/IsshikiHugh/C-Newbie-Helper *\n ****************************************************/\n/*** Config Part ************************************/\n// MODE 0 : Logs will be write to 'CNH_log.txt' file.\n// MODE 1 : Logs will be print to console (colorful for normal terminal).\n// MODE 2 : Logs will be print to console (colorless but fine for CMD).\n#define CNH_MODE 2\n...\n\\```\n\n&lt;font size=\"6\"&gt;\n\n- \u5982\u679c\u4f60\u5bf9\u547d\u4ee4\u884c&lt;font color=\"orange\"&gt;\u6beb\u65e0\u4e86\u89e3&lt;/font&gt;\uff0c\u90a3\u4e48\u8bf7\u68c0\u67e5 &lt;font color=\"cyan\"&gt;CNH_MODE&lt;/font&gt; \u88ab\u8bbe\u7f6e\u4e3a &lt;font color=\"cyan\"&gt;2&lt;/font&gt; \uff1b\n- \u5982\u679c\u4f60\u7684\u65e5\u5fd7\u5c06\u4f1a\u88ab\u6253\u5370\u5728\u5e38\u89c4\u7684 &lt;font color=\"orange\"&gt;Terminal&lt;/font&gt; \u4e0a\uff0c\u90a3\u4e48\u6211\u4eec\u63a8\u8350\u4f60\u8bbe\u7f6e &lt;font color=\"cyan\"&gt;CNH_MODE&lt;/font&gt; \u4e3a &lt;font color=\"cyan\"&gt;1&lt;/font&gt; \uff1b\n- \u5982\u679c\u4f60\u5e0c\u671b\u4f60\u7684\u65e5\u5fd7\u5185\u5bb9\u4e0d\u88ab\u6253\u5370\uff0c\u800c\u662f\u8f93\u51fa\u5230&lt;font color=\"orange\"&gt;\u6587\u4ef6&lt;/font&gt;\u4e2d\uff0c\u5219\u53ef\u4ee5\u8bbe\u7f6e &lt;font color=\"cyan\"&gt;CNH_MODE&lt;/font&gt; \u4e3a &lt;font color=\"cyan\"&gt;0&lt;/font&gt; \uff0c\u4f46\u662f\u8bf7\u6ce8\u610f\uff0cCNH \u65e0\u6cd5\u6e05\u7a7a\u8f93\u51fa\u6587\u4ef6\uff0c\u8bf7\u5728\u6bcf\u6b21\u8f93\u51fa\u7684\u65f6\u5019\u624b\u52a8\u6e05\u7406 &lt;font color=\"yellow\"&gt;CNH_log.txt&lt;/font&gt; \uff1b\n\n&lt;/font&gt;\n</code></pre> <p>\u6839\u636e\u6211\u7684\u89c2\u5bdf\uff0c\u5982\u679c\u9700\u8981\u5728<code>html</code>\u6807\u7b7e\u91cc\u4f7f\u7528<code>Markdown</code>\u8bed\u6cd5\uff0c\u6700\u597d\u5728\u6807\u7b7e\u548c\u8bed\u6cd5\u4e4b\u95f4\u52a0\u7a7a\u884c\u3002</p>"},{"location":"others/reveal-md2Slides/#\u5b9a\u5236\u4e0e\u7f8e\u5316","title":"\u5b9a\u5236\u4e0e\u7f8e\u5316","text":"<p>\u8fd9\u91cc\u6211\u63d0\u4f9b\u4e00\u4e2a\u6211\u81ea\u5df1\u7684\u6e90<code>md</code>\u6587\u4ef6\u5f00\u5934\u914d\u7f6e\u7684\u6a21\u677f\uff1a</p> <pre><code>---\ntitle: Title\nseparator: &lt;!--s--&gt;\nverticalSeparator: &lt;!--v--&gt;\ntheme: league\nhighlightTheme: tomorrow-night-bright\nrevealOptions:\n  width: 1520\nheight: 950\nmargin: 0.04\n  transition: 'convex'\nslideNumber: true\n---\n</code></pre> <ul> <li><code>title</code> \u5373\u663e\u793a\u5728\u7f51\u9875\u6807\u7b7e\u4e0a\u5185\u5bb9\uff1b</li> <li><code>(vertical)separator</code> \u5373\u4e4b\u524d\u63d0\u5230\u8fc7\u7684\u4e24\u4e2a <code>separator</code>\uff1b</li> <li><code>theme</code> \u4e3a Slides \u4e3b\u9898\uff0c\u53ef\u4f9b\u4f7f\u7528\u7684\u5b98\u65b9\u9ed8\u8ba4\u4e3b\u9898\u53ef\u4ee5\u770b\u8fd9\u91cc\uff1a\ud83d\udd17\uff1b</li> <li><code>highlightTheme</code> \u4e3a\u4ee3\u7801\u6846\u9ad8\u4eae\u4e3b\u9898\uff0c\u5b98\u65b9\u5bf9\u9ad8\u4eae\u4e3b\u9898\u7684\u8bf4\u660e\u5728\u8fd9\u91cc\uff1a\ud83d\udd17\uff1b</li> <li><code>revealOptions</code> \u5219\u5bf9\u5e94\u4e86 <code>reveal.js</code> \u4e2d config \u7684\u5185\u5bb9\uff1b</li> <li>\u8fd9\u4e00\u5757\u4e0d\u53ea\u8fd9\u4e9b\u5185\u5bb9\uff0c\u6d89\u53ca\u7684\u5185\u5bb9\u975e\u5e38\u591a\uff0c<code>reveal.js</code> \u5b98\u65b9\u7684\u6587\u6863\u4e2d\u90fd\u6709\u8be6\u7ec6\u7684\u5185\u5bb9\uff0c\u6211\u8fd9\u91cc\u5217\u51fa\u4e86 \u5bbd\u3001\u9ad8\u3001\u8fb9\u754c\u3001\u6362\u9875\u52a8\u753b\u3001\u6807\u53f7 \u7b49\u3002</li> </ul> <p>\u6211\u8fd9\u91cc\u586b\u5199\u7684\u662f\u6211\u81ea\u5df1\u8ba4\u4e3a\u6bd4\u8f83\u8212\u670d\u800c\u4e14\u597d\u770b\u7684\u3002\u5f53\u7136\uff0c\u5982\u679c\u672c\u5730\u5bf9\u5e94\u8d44\u6e90\u6587\u4ef6\u91cc\u6709\u60a8\u81ea\u5df1\u7f16\u5199\u7684\u8d44\u6e90\u4e5f\u662f\u53ef\u4ee5\u7528\u7684\u3002\u4f46\u662f\u8fd9\u4e00\u5757\u6211\u7684\u94bb\u7814\u4e5f\u4e0d\u662f\u7279\u522b\u6df1\uff0c\u6211\u672c\u8eab\u4e5f\u4e0d\u662f\u524d\u7aef\u4eba\uff0c\u6240\u4ee5\u53ea\u80fd\u4ecb\u7ecd\u5230\u8fd9\u91cc\u4e86\u3002</p>"},{"location":"others/reveal-md2Slides/#\u901a\u8fc7-github-pages-\u5b9e\u73b0\u9759\u6001\u90e8\u7f72","title":"\u901a\u8fc7 GitHub Pages \u5b9e\u73b0\u9759\u6001\u90e8\u7f72","text":"<p>\u5728\u8fd9\u4e2a\u7ae0\u8282\u4e2d\uff0c\u6211\u5c06\u4ecb\u7ecd\u5982\u4f55\u5229\u7528 GitHub Pages \u5b9e\u73b0 Slides \u7684\u90e8\u7f72\uff0c\u5728\u8bf8\u5982 Gitee Pages \u7684\u5e73\u53f0\u5b9e\u73b0\u8fd9\u4e9b\u529f\u80fd\u7684\u6d41\u7a0b\u4e5f\u662f\u7c7b\u4f3c\u7684\u3002 \u9996\u5148\u4f60\u9700\u8981\u521b\u5efa\u4e00\u4e2a Repo \u6765\u5b58\u653e\u4f60\u7684\u9759\u6001\u8d44\u6e90\uff0c\u4f8b\u5982\u3002\u6211\u4e2a\u4eba\u7684\u505a\u6cd5\u662f\u76f4\u63a5\u628a\u521d\u59cb\u7684 <code>md</code> \u6587\u672c\u548c\u9759\u6001\u8d44\u6e90\u6587\u672c\u90fd\u653e\u5728\u4e00\u4e2a\u5730\u65b9\u4e86\u3002 \u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u9700\u8981\u5bfc\u51fa\u9759\u6001\u8d44\u6e90\uff0c\u4f7f\u7528\u7684\u662f\u8fd9\u6761\u6307\u4ee4\uff1a</p> <pre><code>reveal-md your-md-file.md --static your-static-dir\n</code></pre> <p>\u63a5\u4e0b\u6765\uff0c\u4f60\u4f1a\u5f97\u5230\u4e00\u4e2a\u6587\u4ef6\u5939\uff0c\u5305\u542b\u8fd9\u4e2a Slides \u6240\u9700\u8981\u7684\u6240\u6709\u8d44\u6e90\u3002\u4f60\u53ea\u9700\u8981\u5c06\u5b83\u4f20\u5230\u4f60\u7684 Repo \u91cc\u5373\u53ef\u3002 \u4f8b\u5982\u6211\u7684\u4ed3\u5e93\u4e2d\uff1a</p> <p></p> <p>\u8fdb\u5165<code>repo/.../static-dir</code>\uff0c\u4e5f\u5c31\u662f\u4e0a\u56fe\u7684<code>slides</code>\uff0c\u6211\u4eec\u53ef\u4ee5\u770b\u5230\u7c7b\u4f3c\u8fd9\u6837\u7684\u4e00\u4e9b\u6587\u4ef6\uff1a</p> <p></p> <p>\u5176\u4e2d\u7684 <code>index.html</code> \u548c <code>slides.html</code> \u90fd\u662f Slides \u7684 <code>html</code> \u6587\u4ef6\u3002\u533a\u522b\u8c8c\u4f3c\u662f <code>index.html</code>\u4f1a \u6709\u4e00\u4e2a\u5f39\u7a97\u544a\u8bc9\u4f60\u4f7f\u7528\u7684\u662f <code>reveal.js</code>\u3002</p> <p>\u63a5\u4e0b\u6765\uff0c\u8bbe\u7f6e pages \u670d\u52a1\u4ee5\u540e\u901a\u8fc7 <code>https://&lt;github_id&gt;.github.io/&lt;repo_name&gt;/.../slides.html</code> \u5373\u53ef\u8bbf\u95ee\u5230\u9875\u9762\u5566\uff01 \u4f8b\u5982\u4e0a\u65b9\u8fd9\u4e2a\u4ed3\u5e93\u5bf9\u5e94\u7684 <code>URL</code> \u662f <code>https://isshikihugh.github.io/myReveal-md/projectsTutorial_CNewbieHelper/slides/slides.html</code>\u3002</p> <p>\u5229\u7528 Pages \u670d\u52a1\uff0c\u5c31\u53ef\u4ee5\u5feb\u901f\u4fbf\u6377\u5730\u5206\u4eab\u4f60\u7684 Slides\uff0c\u5bf9\u4e8e\u4e0d\u61c2\u6280\u672f\u7684\u4eba\u6765\u8bf4\u4e0d\u4ec5\u8868\u73b0\u6548\u679c\u4e0d\u5dee\uff0c\u800c\u4e14\u8fd8\u6709\u4e00\u4e1d\u903c\u683c\u3002\u4e0d\u8fc7\u5728\u56fd\u5185\u6216\u8bb8\u8bbf\u95ee\u4e0d\u592a\u7a33\u5b9a\uff0c\u6240\u4ee5\u53ef\u4ee5\u8003\u8651\u4f7f\u7528 Gitee Pages \u6765\u5b9e\u73b0\u3002\u4e0d\u8fc7 Gitee Pages \u670d\u52a1\u6bcf\u4e00\u6b21\u90fd\u9700\u8981\u4f60\u81ea\u5df1\u53bb\u66f4\u65b0\u4e00\u4e0b\uff0c\u8fd8\u6709\u4e00\u4e9b\u5ba1\u6838\u673a\u5236\u3002</p>"},{"location":"others/reveal-md2Slides/#\u4e00\u4e9b\u5751","title":"\u4e00\u4e9b\u5751","text":"<p><code>reveal-md</code> \u5df2\u7ecf\u6709\u5927\u6982\u4e00\u5e74\u7684\u65f6\u95f4\u6ca1\u6709\u7ef4\u62a4\u4e86\uff0c\u5176\u4e2d\u4e5f\u9047\u5230\u4e00\u4e9b\u95ee\u9898\uff0c\u6211\u9047\u5230\u4e86\u4e00\u4e9b\u5c31\u8bb0\u4e0b\u6765\u3002</p> <ul> <li>\u8fd9\u4e2a\u95ee\u9898\u6211\u8fd8\u63d0\u4e86\u4e2a issue\uff0c\u91cc\u9762\u4e5f\u9644\u4e86\u89e3\u51b3\u7684\u529e\u6cd5\uff1a--static with --theme generate the <code>index.html</code> with the wrong path of <code>theme.css</code></li> <li>\u5728\u4f7f\u7528 gh-page \u8fdb\u884c\u90e8\u7f72\uff0c\u5e76\u4e14\u6307\u5b9a\u4e86\u989d\u5916\u7684 <code>css</code> \u6587\u4ef6\u7684\u65f6\u5019\uff0c\u4e00\u5b9a\u8981\u6dfb\u52a0 <code>--assets-dir assets</code>\uff0c\u5426\u5219\u9ed8\u8ba4\u7684\u7d20\u6750\u6587\u4ef6\u5939\u7684\u540d\u5b57\u662f <code>_assets</code>\uff0c\u800c <code>_</code> \u5f00\u5934\u7684\u6587\u4ef6\u5939\u4f1a\u88ab gh-page \u5ffd\u7565\u3002</li> </ul>"},{"location":"pape_read/","title":"\u6249\u9875","text":"<p> \u7ea6 31 \u4e2a\u5b57 </p> <p> \u300e\u305d\u306e\u6642\u3092\u5f85\u3064\u3088\u300f      \u4f60\u4eec\u8981\u52aa\u529b\u8fdb\u7a84\u95e8\uff0c\u56e0\u4e3a\u5bbd\u95e8\u548c\u9614\u8def\u5f15\u5411\u6c89\u6ca6\u3002  \u2014\u2014\u5b89\u5fb7\u70c8\u00b7\u7eaa\u5fb7\u300a\u7a84\u95e8\u300b  </p>"},{"location":"pape_read/ACTOR/","title":"[ACTOR] Action-Conditioned 3D Human Motion Synthesis with Transformer VAE","text":"<p> \u7ea6 235 \u4e2a\u5b57  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 1 \u5206\u949f</p> <p><code>3DV</code> <code>Human-Motion</code> <code>Action-Control</code></p> <p>\u6587\u7ae0\u4fe1\u606f</p> <ul> <li>\u6587\u7ae0\u9898\u76ee\uff1aAction-Conditioned 3D Human Motion Synthesis with Transformer VAE</li> <li>\u5206\u7c7b\uff1a<code>Computer Science</code> &gt; <code>Computer Vision and Pattern Recognition</code></li> <li>\u4f5c\u8005\uff1aMathis Petrovich, Michael J. Black, G\u00fcl Varol</li> <li>\u9879\u76ee\u4e3b\u9875\uff1a\ud83d\udd17</li> <li>arXiv\uff1a\ud83d\udd17 2104.05670</li> <li>\u4ee3\u7801\uff1a\ud83d\udd17</li> </ul> <p>\u76f8\u5173\u5185\u5bb9</p> <ul> <li>Transformer</li> <li>VAE</li> <li>SMPL \u4e00\u4e2a\u6027\u8d28\u826f\u597d\u7684\u4eba\u4f53\u6a21\u578b\u89c4\u8303</li> <li>MoCap</li> </ul>"},{"location":"pape_read/ACTOR/#introduction","title":"Introduction","text":"<p>In this work, our goal is to take a semantic action label like \u201cThrow\u201d and generate an infinite number of realistic 3D human motion sequences, of varying length, that look like realistic throwing (Figure 1).</p> <p>\u5e76\u4e14\u53d7\u4f7f\u7528\u573a\u666f\u9650\u5236\uff0c\u5b83\u9700\u8981\u6709\u5f3a\u7ea6\u675f\u4ee5\u53ca\u76f8\u5bf9\u7684\u9ad8\u6548\u6027\u3002</p> <p>\u6d89\u53ca\u4eba\u4f53\u76ae\u80a4\u8868\u9762\u4e0e\u4e3b\u5ba2\u4f53\u7684\u4ea4\u4e92\uff0c\u6240\u4ee5\u4f7f\u7528 SMPL \u662f\u4e00\u4e2a\u975e\u5e38\u597d\u7684\u9009\u62e9\u3002</p> <p>noisy 3D body poses</p> <p>\u540c\u6837\u91c7\u7528 Positional Encoding\uff0c\u8fd9\u4e0e NeRF \u8054\u7cfb\u8d77\u6765\u3002</p>"},{"location":"pape_read/ACTOR/#related-work","title":"Related Work","text":"<ul> <li>Future human motion prediction</li> <li>Human motion synthesis</li> <li>Monocular human motion estimation</li> <li>Transformer VAEs</li> </ul> \u7591\u60d1 <p>his allows the generation of variable length sequences without the problem of the motions regressing to the mean pose. \u8fd9\u53e5\u8bdd\u662f\u4ec0\u4e48\u610f\u601d\uff1f</p> Translate <p>\u7ffb\u8bd1\u5185\u5bb9</p>"},{"location":"pape_read/ACTOR/trans/","title":"Translate","text":"<p> \u7ea6 4848 \u4e2a\u5b57  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 16 \u5206\u949f</p>"},{"location":"pape_read/ACTOR/trans/#abstract","title":"Abstract","text":"<p>\u6211\u4eec\u89e3\u51b3\u4e86\u4ee5\u52a8\u4f5c\u4e3a\u6761\u4ef6\u751f\u6210\u903c\u771f\u591a\u6837\u7684\u4eba\u4f53\u8fd0\u52a8\u5e8f\u5217\u7684\u95ee\u9898\u3002 \u4e0e\u5b8c\u6210\u6216\u6269\u5c55\u8fd0\u52a8\u5e8f\u5217\u7684\u65b9\u6cd5\u76f8\u6bd4\uff0c\u6b64\u4efb\u52a1\u4e0d\u9700\u8981\u521d\u59cb\u59ff\u52bf\u6216\u5e8f\u5217\u3002 \u5728\u8fd9\u91cc\uff0c\u6211\u4eec\u901a\u8fc7\u8bad\u7ec3\u751f\u6210\u53d8\u5206\u81ea\u52a8\u7f16\u7801\u5668 (VAE) \u6765\u5b66\u4e60\u4eba\u4f53\u52a8\u4f5c\u7684\u52a8\u4f5c\u611f\u77e5\u6f5c\u5728\u8868\u793a\u3002 \u901a\u8fc7\u4ece\u8fd9\u4e2a\u6f5c\u5728\u7a7a\u95f4\u4e2d\u91c7\u6837\u5e76\u901a\u8fc7\u4e00\u7cfb\u5217\u4f4d\u7f6e\u7f16\u7801\u67e5\u8be2\u67d0\u4e2a\u6301\u7eed\u65f6\u95f4\uff0c\u6211\u4eec\u5408\u6210\u4e86\u4ee5\u5206\u7c7b\u52a8\u4f5c\u4e3a\u6761\u4ef6\u7684\u53ef\u53d8\u957f\u5ea6\u8fd0\u52a8\u5e8f\u5217\u3002 \u5177\u4f53\u6765\u8bf4\uff0c\u6211\u4eec\u8bbe\u8ba1\u4e86\u4e00\u4e2a\u57fa\u4e8e Transformer \u7684\u67b6\u6784 ACTOR\uff0c\u7528\u4e8e\u7f16\u7801\u548c\u89e3\u7801\u4ece\u52a8\u4f5c\u8bc6\u522b\u6570\u636e\u96c6\u4f30\u8ba1\u7684\u4e00\u7cfb\u5217\u53c2\u6570\u5316 SMPL \u4eba\u4f53\u6a21\u578b\u3002 \u6211\u4eec\u5728 NTU RGB+D\u3001HumanAct12 \u548c UESTC \u6570\u636e\u96c6\u4e0a\u8bc4\u4f30\u4e86\u6211\u4eec\u7684\u65b9\u6cd5\uff0c\u5e76\u5c55\u793a\u4e86\u5bf9\u73b0\u6709\u6280\u672f\u7684\u6539\u8fdb\u3002 \u6b64\u5916\uff0c\u6211\u4eec\u8fd8\u5c55\u793a\u4e86\u4e24\u4e2a\u7528\u4f8b\uff1a\u901a\u8fc7\u5c06\u6211\u4eec\u7684\u5408\u6210\u6570\u636e\u6dfb\u52a0\u5230\u8bad\u7ec3\u4e2d\u6765\u6539\u8fdb\u52a8\u4f5c\u8bc6\u522b\uff0c\u4ee5\u53ca\u8fd0\u52a8\u53bb\u566a\u3002 \u4ee3\u7801\u548c\u6a21\u578b\u53ef\u5728\u6211\u4eec\u7684\u9879\u76ee\u9875\u9762 [57] \u4e0a\u627e\u5230\u3002</p>"},{"location":"pape_read/ACTOR/trans/#introduction","title":"Introduction","text":"<p>\u5c3d\u7ba1\u5bf9\u4eba\u4f53\u8fd0\u52a8\u5efa\u6a21\u8fdb\u884c\u4e86\u6570\u5341\u5e74\u7684\u7814\u7a76 [4\u30015]\uff0c\u4f46\u5408\u6210\u903c\u771f\u4e14\u53ef\u63a7\u7684\u5e8f\u5217\u4ecd\u7136\u6781\u5177\u6311\u6218\u6027\u3002 \u5728\u8fd9\u9879\u5de5\u4f5c\u4e2d\uff0c\u6211\u4eec\u7684\u76ee\u6807\u662f\u91c7\u7528\u50cf\u201c\u6295\u63b7\u201d\u8fd9\u6837\u7684\u8bed\u4e49\u52a8\u4f5c\u6807\u7b7e\uff0c\u5e76\u751f\u6210\u65e0\u9650\u6570\u91cf\u7684\u903c\u771f 3D \u4eba\u4f53\u8fd0\u52a8\u5e8f\u5217\uff0c\u957f\u5ea6\u5404\u4e0d\u76f8\u540c\uff0c\u770b\u8d77\u6765\u50cf\u771f\u5b9e\u7684\u6295\u63b7\uff08\u56fe 1\uff09\u3002\u5927\u91cf\u5148\u524d\u7684\u5de5\u4f5c\u90fd\u96c6\u4e2d\u5728\u91c7\u53d6\u4e00\u4e2a\u59ff\u52bf\u6216\u4e00\u7cfb\u5217\u59ff\u52bf\uff0c\u7136\u540e\u9884\u6d4b\u672a\u6765\u7684\u8fd0\u52a8 [3\u30016\u300122\u300171\u300174]\u3002 \u8fd9\u662f\u4e00\u4e2a\u8fc7\u4e8e\u53d7\u9650\u7684\u573a\u666f\uff0c\u56e0\u4e3a\u5b83\u5047\u8bbe\u5df2\u7ecf\u6709\u4e00\u4e2a\u8fd0\u52a8\u5e8f\u5217\u5e76\u4e14\u53ea\u9700\u8981\u66f4\u591a\u3002 \u53e6\u4e00\u65b9\u9762\uff0c\u8bb8\u591a\u5e94\u7528\u7a0b\u5e8f\uff0c\u5982\u865a\u62df\u73b0\u5b9e\u548c\u89d2\u8272\u63a7\u5236 [28\u300161] \u9700\u8981\u751f\u6210\u5177\u6709\u6307\u5b9a\u6301\u7eed\u65f6\u95f4\u7684\u7ed9\u5b9a\u7c7b\u578b\uff08\u8bed\u4e49\u52a8\u4f5c\u6807\u7b7e\uff09\u7684\u52a8\u4f5c\u3002</p> <p>\u56fe1\uff1a\u76ee\u6807\uff1a\u4ee5\u52a8\u4f5c\u4e3a\u6761\u4ef6\u7684 Transformer VAE\uff08ACTOR\uff09\u5b66\u4e60\u5408\u6210\u4ee5\u5206\u7c7b\u52a8\u4f5c\u548c\u6301\u7eed\u65f6\u95f4T\u4e3a\u6761\u4ef6\u7684\u4eba\u7c7b\u8fd0\u52a8\u5e8f\u5217\u3002\u5e8f\u5217\u662f\u901a\u8fc7\u4ece\u5355\u4e00\u7684\u8fd0\u52a8\u8868\u5f81\u6f5c\u4f0f\u5411\u91cfz\u4e2d\u53d6\u6837\u4ea7\u751f\u7684\uff0c\u800c\u4e0d\u662f\u5148\u524d\u5de5\u4f5c\u4e2d\u7684\u6846\u67b6\u7ea7\u5d4c\u5165\u7a7a\u95f4\u3002</p> <p>\u6211\u4eec\u901a\u8fc7\u4f7f\u7528\u5177\u6709\u76f8\u5e94\u52a8\u4f5c\u6807\u7b7e\u7684 3D \u4eba\u4f53\u8fd0\u52a8\u6570\u636e\u8bad\u7ec3\u52a8\u4f5c\u6761\u4ef6\u751f\u6210\u6a21\u578b\u6765\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\u3002\u7279\u522b\u662f\uff0c\u6211\u4eec\u6784\u5efa\u4e86\u4e00\u4e2a\u57fa\u4e8e Transformer \u7684\u7f16\u7801\u5668-\u89e3\u7801\u5668\u67b6\u6784\uff0c\u5e76\u4f7f\u7528 VAE \u76ee\u6807\u5bf9\u5176\u8fdb\u884c\u8bad\u7ec3\u3002 \u6211\u4eec\u4f7f\u7528 SMPL [46] \u5bf9\u4eba\u4f53\u8fdb\u884c\u53c2\u6570\u5316\uff0c\u56e0\u4e3a\u5b83\u53ef\u4ee5\u8f93\u51fa\u5173\u8282\u4f4d\u7f6e\u6216\u8eab\u4f53\u8868\u9762\u3002 \u8fd9\u4e3a\u66f4\u597d\u5730\u6a21\u62df\u4e0e\u73af\u5883\u7684\u76f8\u4e92\u4f5c\u7528\u94fa\u5e73\u4e86\u9053\u8def\uff0c\u56e0\u4e3a\u8868\u9762\u662f\u6a21\u62df\u63a5\u89e6\u6240\u5fc5\u9700\u7684\u3002 \u6b64\u5916\uff0c\u8fd9\u79cd\u8868\u793a\u5141\u8bb8\u4f7f\u7528\u591a\u79cd\u91cd\u5efa\u635f\u5931\uff1a\u7ea6\u675f\u8fd0\u52a8\u6811\u4e2d\u7684\u96f6\u4ef6\u65cb\u8f6c\u3001\u5173\u8282\u4f4d\u7f6e\u6216\u8868\u9762\u70b9\u3002\u6587\u732e [40] \u548c\u6211\u4eec\u7684\u7ed3\u679c\u8868\u660e\uff0c\u635f\u5931\u7684\u7ec4\u5408\u7ed9\u51fa\u4e86\u6700\u771f\u5b9e\u7684\u751f\u6210\u8fd0\u52a8\u3002</p> <p>\u8fd0\u52a8\u5408\u6210\u7684\u5173\u952e\u6311\u6218\u662f\u751f\u6210\u5728\u611f\u77e5\u4e0a\u903c\u771f\u7684\u540c\u65f6\u5177\u6709\u591a\u6837\u6027\u7684\u5e8f\u5217\u3002\u8bb8\u591a\u8fd0\u52a8\u751f\u6210\u65b9\u6cd5\u90fd\u91c7\u7528\u81ea\u56de\u5f52\u65b9\u6cd5\uff0c\u4f8b\u5982 LSTM [16] \u548c GRU [49]\u3002\u7136\u800c\uff0c\u8fd9\u4e9b\u65b9\u6cd5\u901a\u5e38\u4f1a\u5728\u4e00\u6bb5\u65f6\u95f4\u540e\u56de\u5f52\u5230\u5e73\u5747\u59ff\u52bf [49] \u5e76\u4e14\u5bb9\u6613\u6f02\u79fb\u3002 \u6211\u4eec\u7684 Transformer \u6a21\u578b\u7684\u5173\u952e\u521b\u65b0\u662f\u4e3a\u89e3\u7801\u5668\u63d0\u4f9b\u4f4d\u7f6e\u7f16\u7801\u5e76\u7acb\u5373\u8f93\u51fa\u5b8c\u6574\u5e8f\u5217\u3002 \u6700\u8fd1\u5173\u4e8e\u795e\u7ecf\u8f90\u5c04\u573a\u7684\u5de5\u4f5c\u5df2\u7ecf\u666e\u53ca\u4e86\u4f4d\u7f6e\u7f16\u7801 [50]\uff1b \u6211\u4eec\u8fd8\u6ca1\u6709\u770b\u5230\u5b83\u50cf\u6211\u4eec\u4e00\u6837\u7528\u4e8e\u8fd0\u52a8\u751f\u6210\u3002 \u8fd9\u5141\u8bb8\u751f\u6210\u53ef\u53d8\u957f\u5ea6\u5e8f\u5217\uff0c\u800c\u4e0d\u4f1a\u51fa\u73b0\u8fd0\u52a8\u56de\u5f52\u5230\u5e73\u5747\u59ff\u52bf\u7684\u95ee\u9898\u3002 \u6b64\u5916\uff0c\u636e\u6211\u4eec\u6240\u77e5\uff0c\u6211\u4eec\u7684\u65b9\u6cd5\u662f\u7b2c\u4e00\u4e2a\u521b\u5efa\u52a8\u4f5c\u6761\u4ef6\u5e8f\u5217\u7ea7\u5d4c\u5165\u7684\u65b9\u6cd5\u3002 \u6700\u63a5\u8fd1\u7684\u5de5\u4f5c\u662f Action2Motion [21]\uff0c\u76f8\u6bd4\u4e4b\u4e0b\uff0c\u5b83\u63d0\u51fa\u4e86\u4e00\u79cd\u81ea\u56de\u5f52\u65b9\u6cd5\uff0c\u5176\u4e2d\u6f5c\u5728\u8868\u793a\u5904\u4e8e\u5e27\u7ea7\u522b\u3002 \u83b7\u5f97\u5e8f\u5217\u7ea7\u5d4c\u5165\u9700\u8981\u6c47\u96c6\u65f6\u95f4\u7ef4\u5ea6\uff1a\u6211\u4eec\u4e3a\u6b64\u76ee\u7684\u5f15\u5165\u4e86\u4e00\u79cd\u7ed3\u5408 Transformers \u548c VAE \u7684\u65b0\u65b9\u6cd5\uff0c\u8fd9\u4e5f\u663e\u7740\u63d0\u9ad8\u4e86\u57fa\u7ebf\u7684\u6027\u80fd\u3002</p> <p>\u6211\u4eec\u7684\u52a8\u4f5c\u6761\u4ef6\u751f\u6210\u95ee\u9898\u7684\u4e00\u4e2a\u7279\u5b9a\u6311\u6218\u662f\u5b58\u5728\u4e0e\u4e0d\u540c\u52a8\u4f5c\u6807\u7b7e\u914d\u5bf9\u7684\u6709\u9650\u52a8\u4f5c\u6355\u6349 (MoCap) \u6570\u636e\uff0c\u901a\u5e38\u5728 10 \u4e2a\u7c7b\u522b\u4e2d [31\u300163]\u3002 \u76f8\u53cd\uff0c\u6211\u4eec\u4f9d\u9760\u5355\u76ee\u8fd0\u52a8\u4f30\u8ba1\u65b9\u6cd5 [38] \u6765\u83b7\u5f97 3D \u52a8\u4f5c\u5e8f\u5217\uff0c\u5e76\u5728 UESTC \u52a8\u4f5c\u8bc6\u522b\u6570\u636e\u96c6 [32] \u7684 40 \u4e2a\u7ec6\u7c92\u5ea6\u7c7b\u522b\u4e0a\u5448\u73b0\u6709\u5e0c\u671b\u7684\u7ed3\u679c\u3002 \u4e0e[21]\u76f8\u53cd\uff0c\u6211\u4eec\u4e0d\u9700\u8981\u591a\u89c6\u89d2\u76f8\u673a\u6765\u8fdb\u884c\u5355\u76ee\u8f68\u8ff9\u4f30\u8ba1\uff0c\u8fd9\u4f7f\u5f97\u6211\u4eec\u7684\u6a21\u578b\u53ef\u80fd\u9002\u7528\u4e8e\u66f4\u5927\u7684\u5c3a\u5ea6\u3002 \u5c3d\u7ba1\u6709\u566a\u97f3\uff0c\u5355\u773c\u4f30\u8ba1\u88ab\u8bc1\u660e\u8db3\u4ee5\u7528\u4e8e\u8bad\u7ec3\uff0c\u5e76\u4e14\u4f5c\u4e3a\u6211\u4eec\u6a21\u578b\u7684\u989d\u5916\u597d\u5904\uff0c\u6211\u4eec\u80fd\u591f\u901a\u8fc7\u6211\u4eec\u5b66\u4e60\u7684\u8fd0\u52a8\u8868\u793a\u6765\u7f16\u7801\u89e3\u7801\u53bb\u566a\u4f30\u8ba1\u5e8f\u5217\u3002 </p> <p>\u52a8\u4f5c\u6761\u4ef6\u751f\u6210\u6a21\u578b\u53ef\u4ee5\u589e\u5f3a\u73b0\u6709\u7684 MoCap \u6570\u636e\u96c6\uff0c\u8fd9\u4e9b\u6570\u636e\u96c6\u6602\u8d35\u4e14\u5927\u5c0f\u6709\u9650 [48,63]\u3002 \u6700\u8fd1\u7684\u7814\u7a76\u63d0\u4f9b\u4e86\u7528\u4e8e\u8bad\u7ec3\u52a8\u4f5c\u8bc6\u522b\u6a21\u578b\u7684\u5408\u6210\u4eba\u7c7b\u52a8\u4f5c\u89c6\u9891 [65]\uff0c\u663e\u793a\u4e86\u52a8\u4f5c\u591a\u6837\u6027\u548c\u6bcf\u4e2a\u52a8\u4f5c\u7684\u5927\u91cf\u6570\u636e\u7684\u91cd\u8981\u6027\u3002 \u8fd9\u79cd\u65b9\u6cd5\u53ef\u4ee5\u53d7\u76ca\u4e8e\u65e0\u9650\u6e90\u52a8\u4f5c\u6761\u4ef6\u8fd0\u52a8\u5408\u6210\u3002 \u6211\u4eec\u901a\u8fc7\u52a8\u4f5c\u8bc6\u522b\u5b9e\u9a8c\u6765\u63a2\u8ba8\u8fd9\u4e2a\u95ee\u9898\u3002 \u6211\u4eec\u89c2\u5bdf\u5230\uff0c\u5c3d\u7ba1\u5b58\u5728 domain gap\uff0c\u4f46\u751f\u6210\u7684\u8fd0\u52a8\u53ef\u4ee5\u4f5c\u4e3a\u989d\u5916\u7684\u8bad\u7ec3\u6570\u636e\uff0c\u5c24\u5176\u662f\u5728\u4f4e\u6570\u636e\u8bbe\u7f6e\u4e2d\u3002 \u6700\u540e\uff0c\u7d27\u51d1\u7684\u52a8\u4f5c\u611f\u77e5\u4eba\u4f53\u8fd0\u52a8\u6f5c\u5728\u7a7a\u95f4\u53ef\u4ee5\u7528\u4f5c\u5176\u4ed6\u4efb\u52a1\u7684\u5148\u51b3\u6761\u4ef6\uff0c\u4f8b\u5982\u89c6\u9891\u4e2d\u7684\u4eba\u4f53\u8fd0\u52a8\u4f30\u8ba1\u3002</p> <p>\u6211\u4eec\u7684\u8d21\u732e\u6709\u56db\u65b9\u9762\uff1a(i) \u6211\u4eec\u4ecb\u7ecd\u4e86 ACTOR\uff0c\u8fd9\u662f\u4e00\u79cd\u65b0\u578b\u7684\u57fa\u4e8e Transformer \u7684\u6761\u4ef6 VAE\uff0c\u5e76\u8bad\u7ec3\u5b83\u901a\u8fc7\u4ece\u5e8f\u5217\u7ea7\u6f5c\u5728\u5411\u91cf\u4e2d\u91c7\u6837\u6765\u751f\u6210\u52a8\u4f5c\u6761\u4ef6\u4eba\u4f53\u8fd0\u52a8\u3002 (ii) \u6211\u4eec\u8bc1\u660e\u53ef\u4ee5\u4f7f\u7528\u4ece\u5355\u773c\u89c6\u9891\u4f30\u8ba1\u7684\u5608\u6742 3D \u4eba\u4f53\u59ff\u52bf\u6765\u5b66\u4e60\u751f\u6210\u903c\u771f\u7684 3D \u4eba\u4f53\u8fd0\u52a8\uff1b (iii) \u6211\u4eec\u5bf9\u67b6\u6784\u548c\u635f\u5931\u7ec4\u4ef6\u8fdb\u884c\u5168\u9762\u7684\u6d88\u878d\u7814\u7a76\uff0c\u5728\u591a\u4e2a\u6570\u636e\u96c6\u4e0a\u83b7\u5f97\u6700\u5148\u8fdb\u7684\u6027\u80fd\uff1b (iv) \u6211\u4eec\u4e3a\u52a8\u4f5c\u8bc6\u522b\u548c MoCap \u53bb\u566a\u6a21\u578b\u8bf4\u660e\u4e86\u4e24\u4e2a\u7528\u4f8b\u3002 \u8be5\u4ee3\u7801\u53ef\u5728\u6211\u4eec\u7684\u9879\u76ee\u9875\u9762 [57] \u4e0a\u627e\u5230\u3002</p>"},{"location":"pape_read/ACTOR/trans/#related-work","title":"Related Work","text":"<p>\u6211\u4eec\u7b80\u8981\u56de\u987e\u4e86\u6709\u5173\u8fd0\u52a8\u9884\u6d4b\u3001\u8fd0\u52a8\u5408\u6210\u3001\u5355\u773c\u8fd0\u52a8\u4f30\u8ba1\u4ee5\u53ca VAE \u80cc\u666f\u4e0b\u7684 Transformers \u7684\u76f8\u5173\u6587\u732e\u3002</p> <p>\u672a\u6765\u4eba\u4f53\u8fd0\u52a8\u9884\u6d4b\u3002\u4eba\u4f53\u8fd0\u52a8\u5206\u6790\u7684\u7814\u7a76\u5386\u53f2\u60a0\u4e45\uff0c\u53ef\u4ee5\u8ffd\u6eaf\u5230 20 \u4e16\u7eaa 80 \u5e74\u4ee3 [5,17,19,52]\u3002 \u7ed9\u5b9a\u8fc7\u53bb\u7684\u8fd0\u52a8\u6216\u521d\u59cb\u59ff\u52bf\uff0c\u9884\u6d4b\u672a\u6765\u7684\u5e27\u88ab\u79f0\u4e3a\u8fd0\u52a8\u9884\u6d4b\u3002 \u65e9\u671f\u7814\u7a76\u4e2d\u5df2\u7ecf\u91c7\u7528\u4e86\u7edf\u8ba1\u6a21\u578b [7, 18]\u3002 \u6700\u8fd1\uff0c\u968f\u7740 GANs [20] \u6216 VAEs [37] \u7b49\u795e\u7ecf\u7f51\u7edc\u751f\u6210\u6a21\u578b\u7684\u8fdb\u5c55\uff0c\u4e00\u4e9b\u5de5\u4f5c\u663e\u793a\u51fa\u53ef\u559c\u7684\u7ed3\u679c\u3002 \u793a\u4f8b\u5305\u62ec\u7528\u4e8e\u672a\u6765\u8fd0\u52a8\u9884\u6d4b\u7684 HP-GAN [6] \u548c\u5faa\u73af VAE [22]\u3002 \u5927\u591a\u6570\u5de5\u4f5c\u5c06\u8eab\u4f53\u89c6\u4e3a\u9aa8\u67b6\uff0c\u5c3d\u7ba1\u6700\u8fd1\u7684\u5de5\u4f5c\u5229\u7528\u4e86\u5b8c\u6574\u7684 3D \u8eab\u4f53\u5f62\u72b6\u6a21\u578b [3, 74]\u3002 \u4e0e [74] \u7c7b\u4f3c\uff0c\u6211\u4eec\u4e5f\u8d85\u8d8a\u4e86\u7a00\u758f\u5173\u8282\u5e76\u5c06\u9876\u70b9\u5408\u5e76\u5230\u8eab\u4f53\u8868\u9762\u3002 DLow [71] \u4fa7\u91cd\u4e8e\u4ece\u9884\u8bad\u7ec3\u6a21\u578b\u4e2d\u591a\u6837\u5316\u672a\u6765\u8fd0\u52a8\u7684\u91c7\u6837\u3002 [11] \u4f7f\u7528\u5173\u4e8e\u5bf9\u8c61\u4ea4\u4e92\u7684\u4e0a\u4e0b\u6587\u7ebf\u7d22\u6267\u884c\u6709\u6761\u4ef6\u7684\u672a\u6765\u9884\u6d4b\u3002 \u6700\u8fd1\uff0c[42] \u63d0\u51fa\u4e86\u4e00\u79cd\u57fa\u4e8e Transformer \u7684\u821e\u8e48\u751f\u6210\u65b9\u6cd5\uff0c\u8be5\u65b9\u6cd5\u4ee5\u97f3\u4e50\u548c\u8fc7\u53bb\u7684\u52a8\u4f5c\u4e3a\u6761\u4ef6\u3002 \u6bb5\u7b49\u3002 [14] \u4f7f\u7528\u53d8\u5f62\u91d1\u521a\u5b8c\u6210\u8fd0\u52a8\u3002 \u6709\u4e00\u4e2a\u5173\u4e8e\u8fd0\u52a8\u201c\u4e2d\u95f4\u201d\u7684\u76f8\u5173\u5de5\u4f5c\uff0c\u5b83\u91c7\u7528\u8fc7\u53bb\u548c\u672a\u6765\u7684\u59ff\u52bf\uff0c\u5e76\u201c\u4fee\u590d\u201d\u5b83\u4eec\u4e4b\u95f4\u7684\u5408\u7406\u8fd0\u52a8\uff1b \u6709\u5173\u66f4\u591a\u4fe1\u606f\uff0c\u8bf7\u53c2\u89c1 [23]\u3002 \u4e0e\u4e4b\u524d\u7684\u5de5\u4f5c\u76f8\u6bd4\uff0c\u6211\u4eec\u7684\u76ee\u6807\u662f\u5728\u6ca1\u6709\u4efb\u4f55\u8fc7\u53bb\u89c2\u5bdf\u7684\u60c5\u51b5\u4e0b\u5408\u6210\u8fd0\u52a8\u3002 \u4eba\u4f53\u8fd0\u52a8\u5408\u6210\u3002 \u867d\u7136\u6709\u5927\u91cf\u5173\u4e8e\u672a\u6765\u9884\u6d4b\u7684\u6587\u732e\uff0c\u4f46\u4ece\u5934\u5f00\u59cb\u7efc\u5408\u53d7\u5230\u7684\u5173\u6ce8\u76f8\u5bf9\u8f83\u5c11\u3002 \u975e\u5e38\u65e9\u671f\u7684\u5de5\u4f5c\u4f7f\u7528 PCA [51] \u548c GPLVM [64] \u6765\u5b66\u4e60\u6b65\u884c\u548c\u8dd1\u6b65\u7b49\u5faa\u73af\u8fd0\u52a8\u7684\u7edf\u8ba1\u6a21\u578b\u3002 \u5bf9\u591a\u79cd\u591a\u6837\u7684\u52a8\u4f5c\u8fdb\u884c\u6761\u4ef6\u7efc\u5408\u8981\u56f0\u96be\u5f97\u591a\u3002 DVGAN [43] \u8bad\u7ec3\u4e00\u4e2a\u751f\u6210\u6a21\u578b\uff0c\u8be5\u6a21\u578b\u4ee5\u8868\u793a MoCap \u6570\u636e\u96c6\u4e2d\u52a8\u4f5c\u7684\u77ed\u6587\u672c\u4e3a\u6761\u4ef6\uff0c\u4f8b\u5982 Human3.6M [30\u300131] \u548c CMU [63]\u3002 Text2Action [1] \u548c Language2Pose [2] \u540c\u6837\u63a2\u7d22\u4e86\u6839\u636e\u6587\u672c\u63cf\u8ff0\u8c03\u8282\u52a8\u4f5c\u751f\u6210\u3002 Music-to-Dance [39] \u548c [41] \u7814\u7a76\u97f3\u4e50\u6761\u4ef6\u751f\u6210\u3002 QuaterNet [56] \u4fa7\u91cd\u4e8e\u5728\u7ed9\u5b9a\u5730\u9762\u8f68\u8ff9\u548c\u5e73\u5747\u901f\u5ea6\u7684\u60c5\u51b5\u4e0b\u751f\u6210\u884c\u8d70\u548c\u8dd1\u6b65\u7b49\u8fd0\u52a8\u52a8\u4f5c\u3002 [69] \u63d0\u51fa\u4e86\u4e00\u79cd\u57fa\u4e8e\u5377\u79ef\u7684\u751f\u6210\u6a21\u578b\uff0c\u7528\u4e8e\u5728\u4e0d\u6307\u5b9a\u52a8\u4f5c\u7684\u60c5\u51b5\u4e0b\u5b9e\u73b0\u903c\u771f\u7684\u4f46\u4e0d\u53d7\u7ea6\u675f\u7684\u8fd0\u52a8\u3002 \u7c7b\u4f3c\u5730\uff0c[73] \u5408\u6210\u4efb\u610f\u5e8f\u5217\uff0c\u5173\u6ce8\u65f6\u95f4\u4e0a\u7684\u65e0\u754c\u8fd0\u52a8\u3002</p> <p>\u65e0\u7ea6\u675f\u8fd0\u52a8\u5408\u6210\u7684\u8bb8\u591a\u65b9\u6cd5\u5f80\u5f80\u4ee5\u6b65\u884c\u548c\u8dd1\u6b65\u7b49\u52a8\u4f5c\u4e3a\u4e3b\u5bfc\u3002\u76f8\u6bd4\u4e4b\u4e0b\uff0c\u6211\u4eec\u7684\u6a21\u578b\u80fd\u591f\u4ece\u66f4\u4e00\u822c\u7684\uff0c\u65e0\u5468\u671f\u7684\uff0c\u9884\u5b9a\u4e49\u7684\u884c\u52a8\u7c7b\u522b\uff0c\u4e0e\u884c\u52a8\u8bc6\u522b\u6570\u636e\u96c6\u517c\u5bb9\u7684\u6837\u672c\u3002\u5728\u8fd9\u65b9\u9762\uff0c[75]\u5f15\u5165\u4e86\u8d1d\u53f6\u65af\u65b9\u6cd5\uff0c\u5176\u4e2d\u9690\u85cf\u534a\u9a6c\u5c14\u53ef\u592b\u6a21\u578b\u7528\u4e8e\u8054\u5408\u8bad\u7ec3\u751f\u6210\u6a21\u578b\u548c\u5224\u522b\u6a21\u578b\u3002\u4e0e\u6211\u4eec\u7c7b\u4f3c\uff0c[75]\u8868\u660e\uff0c\u4ed6\u4eec\u751f\u6210\u7684\u52a8\u4f5c\u53ef\u4ee5\u4f5c\u4e3a\u989d\u5916\u7684\u8bad\u7ec3\u6570\u636e\u7684\u884c\u52a8\u8bc6\u522b\u3002\u7136\u800c\uff0c\u6839\u636e\u5224\u522b\u5668\u5206\u7c7b\u7ed3\u679c\uff0c\u5b83\u4eec\u751f\u6210\u7684\u5e8f\u5217\u662f\u4f2a\u6807\u8bb0\u7684\u3002\u53e6\u4e00\u65b9\u9762\uff0c\u6211\u4eec\u7684\u6761\u4ef6\u6a21\u578b\u80fd\u591f\u4ee5\u4e00\u79cd\u53d7\u63a7\u7684\u65b9\u5f0f\u5408\u6210\u8fd0\u52a8\uff0c\u4f8b\u5982\u5e73\u8861\u8bad\u7ec3\u96c6\u3002\u4e0e\u6211\u4eec\u7684\u5de5\u4f5c\u6700\u76f8\u4f3c\u7684\u662f Action2Motion [21] \uff0c\u8fd9\u662f\u4e00\u4e2a\u57fa\u4e8e GRU \u67b6\u6784\u7684\u6bcf\u5e27\u64cd\u4f5c VAE\u3002\u6211\u4eec\u7684\u5e8f\u5217\u7ea7 VAE \u6f5c\u5728\u7a7a\u95f4\uff0c\u7ed3\u5408\u57fa\u4e8e\u53d8\u538b\u5668\u7684\u8bbe\u8ba1\u63d0\u4f9b\u4e86\u663e\u8457\u7684\u4f18\u52bf\uff0c\u5982\u6211\u4eec\u7684\u5b9e\u9a8c\u6240\u793a\u3002</p> <p>\u5176\u4ed6\u6700\u8fd1\u7684\u5de5\u4f5c[25,72]\u4f7f\u7528\u89c4\u8303\u5316\u6d41\u6765\u89e3\u51b3\u4eba\u4f53\u8fd0\u52a8\u4f30\u8ba1\u548c\u751f\u6210\u95ee\u9898\u3002\u51e0\u4e2a\u4f5c\u54c1[29,36,67]\u5b66\u4e60\u4e00\u4e2a\u8fd0\u52a8\u6d41\u5f62\uff0c\u5e76\u4f7f\u7528\u5b83\u7684\u8fd0\u52a8\u53bb\u566a\uff0c\u8fd9\u662f\u6211\u4eec\u7684\u7528\u4f8b\u4e4b\u4e00\u3002\u8fd8\u6709\u4e00\u4e2a\u91cd\u8981\u7684\u56fe\u5f62\u6587\u732e\u7684\u4e3b\u9898\uff0c\u8fd9\u5f80\u5f80\u96c6\u4e2d\u5728\u52a8\u753b\u5e08\u63a7\u5236\u3002\u770b\uff0c\u4f8b\u5982\uff0c[27]\u5b66\u4e60\u52a8\u4f5c\u5339\u914d\u548c[40]\u89d2\u8272\u52a8\u753b\u3002\u8fd9\u91cc\u6700\u76f8\u5173\u7684\u662f\u76f8\u51fd\u6570\u795e\u7ecf\u7f51\u7edc[28]\u548c\u795e\u7ecf\u72b6\u6001\u673a[61]\u3002\u4e24\u8005\u90fd\u5229\u7528\u4e86\u7531\u6b63\u5f26\u51fd\u6570\u76f8\u4f4d\u9a71\u52a8\u7684\u52a8\u4f5c\u7684\u6982\u5ff5\u3002\u8fd9\u4e0e\u4f4d\u7f6e\u7f16\u7801\u7684\u601d\u60f3\u6709\u5173\uff0c\u4f46\u4e0e\u6211\u4eec\u7684\u65b9\u6cd5\u4e0d\u540c\uff0c\u5b83\u4eec\u7684\u65b9\u6cd5\u9700\u8981\u4eba\u5de5\u5206\u5272\u64cd\u4f5c\u5e76\u6784\u5efa\u8fd9\u4e9b\u76f8\u51fd\u6570\u3002</p> <p>\u5355\u76ee\u4eba\u4f53\u8fd0\u52a8\u4f30\u8ba1\u3002\u6765\u81ea\u89c6\u9891\u7684\u8fd0\u52a8\u4f30\u8ba1[35,38,47]\u6700\u8fd1\u53d6\u5f97\u4e86\u91cd\u5927\u8fdb\u5c55\uff0c\u4f46\u8d85\u51fa\u4e86\u6211\u4eec\u7684\u8303\u56f4\u3002\u5728\u8fd9\u9879\u5de5\u4f5c\u4e2d\uff0c\u6211\u4eec\u91c7\u7528 VIBE [38]\u4ece\u52a8\u4f5c\u6807\u8bb0\u7684\u89c6\u9891\u6570\u636e\u96c6\u4e2d\u83b7\u5f97\u8bad\u7ec3\u8fd0\u52a8\u5e8f\u5217\u3002</p> <p>Transformer VAE\u3002Transformer \u6700\u8fd1\u5728\u8bed\u8a00\u4efb\u52a1\u65b9\u9762\u53d6\u5f97\u7684\u6210\u529f\u589e\u52a0\u4e86\u4eba\u4eec\u5bf9\u57fa\u4e8e\u6ce8\u610f\u529b\u7684\u795e\u7ecf\u7f51\u7edc\u6a21\u578b\u7684\u5174\u8da3\u3002\u4e00\u4e9b\u5de5\u7a0b\u4f7f\u7528\u53d8\u538b\u5668\u7ed3\u5408\u751f\u6210 VAE \u57f9\u8bad\u3002\u5177\u4f53\u7684\u4f8b\u5b50\u5305\u62ec\u6545\u4e8b\u751f\u6210[15] \uff0c\u60c5\u611f\u5206\u6790[10] \uff0c\u53cd\u5e94\u751f\u6210[44]\u548c\u97f3\u4e50\u751f\u6210[33]\u3002[33]\u7684\u5de5\u4f5c\u5b66\u4e60\u6bcf\u4e2a\u65f6\u95f4\u6846\u67b6\u7684\u6f5c\u5728\u5d4c\u5165\uff0c\u800c[10]\u5e73\u5747\u7684\u9690\u85cf\u72b6\u6001\uff0c\u4ee5\u83b7\u5f97\u4e00\u4e2a\u5355\u4e00\u7684\u6f5c\u5728\u4ee3\u7801\u3002\u53e6\u4e00\u65b9\u9762\uff0c[15]\u6267\u884c\u6ce8\u610f\u529b\u5e73\u5747\u6c60\u968f\u7740\u65f6\u95f4\u7684\u63a8\u79fb\u3002\u4e0e\u8fd9\u4e9b\u5de5\u4f5c\u76f8\u53cd\uff0c\u6211\u4eec\u91c7\u7528\u53ef\u5b66\u4e60\u7684\u6807\u8bb0\uff0c\u5982[12,13]\u4e2d\u6240\u793a\uff0c\u5c06\u8f93\u5165\u603b\u7ed3\u4e3a\u5e8f\u5217\u7ea7\u5d4c\u5165\u3002</p> <p>\u56fe2\uff1a\u65b9\u6cd5\u6982\u8ff0\u3002\u6211\u4eec\u8bf4\u660e\u4e86\u6211\u4eec\u57fa\u4e8eTransformer\u7684VAE\u6a21\u578b\u7684\u7f16\u7801\u5668\uff08\u5de6\uff09\u548c\u89e3\u7801\u5668\uff08\u53f3\uff09\uff0c\u8be5\u6a21\u578b\u751f\u6210\u4e86\u52a8\u4f5c\u6761\u4ef6\u7684\u8fd0\u52a8\u3002\u7ed9\u5b9a\u4e00\u4e32\u8eab\u4f53\u59ff\u52bfP1, ... , PT\u548c\u4e00\u4e2a\u52a8\u4f5c\u6807\u7b7ea\uff0c\u7f16\u7801\u5668\u8f93\u51fa\u5206\u5e03\u53c2\u6570\uff0c\u6211\u4eec\u5728\u6b64\u57fa\u7840\u4e0a\u5b9a\u4e49KL\u635f\u5931\uff08LKL\uff09\u3002\u6211\u4eec\u4f7f\u7528\u6bcf\u4e2a\u52a8\u4f5c\u7684\u989d\u5916\u53ef\u5b66\u4e60\u6807\u8bb0\uff08\u00b5 token a \u548c \u03a3 token a \uff09\u4f5c\u4e3a\u4eceTransformer\u7f16\u7801\u5668\u83b7\u5f97\u00b5\u548c\u03a3\u7684\u65b9\u6cd5\u3002\u4f7f\u7528\u00b5\u548c\u03a3\uff0c\u6211\u4eec\u5bf9\u8fd0\u52a8\u7684\u6f5c\u5728\u8868\u5f81z\u2208M\u8fdb\u884c\u91c7\u6837\u3002\u89e3\u7801\u5668\u5c06\u6f5c\u4f0f\u5411\u91cfz\u3001\u52a8\u4f5c\u6807\u7b7ea\u548c\u6301\u7eed\u65f6\u95f4T\u4f5c\u4e3a\u8f93\u5165\u3002\u884c\u52a8\u51b3\u5b9a\u4e86\u53ef\u5b66\u4e60\u7684b\u6807\u8bb0a\u52a0\u6cd5\u6807\u8bb0\uff0c\u6301\u7eed\u65f6\u95f4\u51b3\u5b9a\u4e86\u8f93\u5165\u5230\u89e3\u7801\u5668\u7684\u4f4d\u7f6e\u7f16\u7801\uff08PE\uff09\u7684\u6570\u91cf\u3002\u89e3\u7801\u5668\u8f93\u51fa\u6574\u4e2a\u5e8f\u5217Pb1, . . . , PbT\uff0c\u5728\u6b64\u57fa\u7840\u4e0a\u8ba1\u7b97\u91cd\u5efa\u635f\u5931LP\u3002\u6b64\u5916\uff0c\u6211\u4eec\u7528\u4e00\u4e2a\u53ef\u5fae\u5206\u7684SMPL\u5c42\u8ba1\u7b97\u9876\u70b9\uff0c\u4ee5\u5b9a\u4e49\u4e00\u4e2a\u9876\u70b9\u635f\u5931\uff08LV \uff09\u3002\u5bf9\u4e8e\u8bad\u7ec3\u6765\u8bf4\uff0cz\u662f\u4f5c\u4e3a\u7f16\u7801\u5668\u7684\u8f93\u51fa\u5f97\u5230\u7684\uff1b\u5bf9\u4e8e\u751f\u6210\u6765\u8bf4\uff0c\u5b83\u662f\u4ece\u9ad8\u65af\u5206\u5e03\u4e2d\u968f\u673a\u62bd\u53d6\u7684\u3002</p>"},{"location":"pape_read/ACTOR/trans/#action-conditioned-motion-generation","title":"Action-Conditioned Motion Generation","text":"<p>\u95ee\u9898\u5b9a\u4e49\u3002\u8eab\u4f53\u8fd0\u52a8\u6240\u5b9a\u4e49\u7684\u52a8\u4f5c\u53ef\u4ee5\u662f\u8eab\u4f53\u90e8\u4f4d\u7684\u65cb\u8f6c\u62e5\u6709\u5c5e\u6027\uff0c\u4e0e\u8eab\u4efd\u7279\u5b9a\u7684\u8eab\u4f53\u5f62\u72b6\u65e0\u5173\u3002\u4e3a\u4e86\u80fd\u591f\u4ea7\u751f\u4e0e\u4e0d\u540c\u5f62\u6001\u7684\u884c\u4e3a\u8005\u7684\u8fd0\u52a8\uff0c\u8fd9\u662f\u7406\u60f3\u7684\u5206\u79bb\u59ff\u52bf\u548c\u5f62\u72b6\u3002\u56e0\u6b64\uff0c\u4e0d\u5931\u4e00\u822c\u6027\uff0c\u6211\u4eec\u91c7\u7528\u4e86 SMPL \u8eab\u4f53\u6a21\u578b[46] \uff0c\u8fd9\u662f\u4e00\u4e2a\u5206\u79bb\u7684\u8eab\u4f53\u8868\u793a(\u7c7b\u4f3c\u4e8e\u6700\u8fd1\u7684\u6a21\u578b[53,55,58,68])\u3002\u5ffd\u7565\u5f62\u72b6\uff0c\u6211\u4eec\u7684\u76ee\u6807\u662f\u751f\u6210\u4e00\u7cfb\u5217\u7684\u59ff\u6001\u53c2\u6570\u3002\u66f4\u6b63\u5f0f\u5730\u8bf4\uff0c\u7ed9\u5b9a\u4e00\u4e2a\u52a8\u4f5c\u6807\u7b7e a (\u6765\u81ea\u4e00\u7ec4\u9884\u5b9a\u4e49\u7684\u52a8\u4f5c\u8303\u7574 a \u2208 A)\u548c\u4e00\u4e2a\u6301\u7eed\u65f6\u95f4 T\uff0c\u6211\u4eec\u751f\u6210\u4e00\u4e2a\u4f53\u6784\u6210\u7684\u5e8f\u5217 R1\uff0c... \uff0cRT \u548c\u4e00\u4e2a\u6839\u5173\u8282\u7684\u5e73\u79fb\u5e8f\u5217\u8868\u793a\u4e3a\u4f4d\u79fb\uff0cD1\uff0c... \uff0cDT (\u4e0e DT \u2208 R3\uff0csomething t \u2208{1\uff0c... \uff0cT })</p> <p>\u52a8\u4f5c\u8868\u73b0\u6cd5\u3002\u6bcf\u5e27 SMPL \u59ff\u6001\u53c2\u6570\u8868\u793a\u8fd0\u52a8\u5b66\u6811\u4e2d\u768423\u4e2a\u5173\u8282\u65cb\u8f6c\u548c\u4e00\u4e2a\u5168\u5c40\u65cb\u8f6c\u3002\u91c7\u7528\u8fde\u7eed6D \u65cb\u8f6c\u8868\u793a\u6cd5\u8fdb\u884c\u8bad\u7ec3[76] \uff0c\u4f7f Rt \u2208 R24 \u00d7 6\u3002\u8bbe Pt \u662f Rt \u548c Dt \u7684\u7ec4\u5408\uff0c\u8868\u793a\u5355\u5e27\u4e2d\u8eab\u4f53\u7684\u59ff\u52bf\u548c\u4f4d\u7f6e t\u3002\u5b8c\u6574\u7684\u52a8\u4f5c\u662f P1\uff0c. . \uff0cPT\u3002\u7ed9\u5b9a\u4e00\u4e2a\u751f\u6210\u5668\u8f93\u51fa\u4f4d\u59ff Pt \u548c\u4efb\u610f\u5f62\u72b6\u53c2\u6570\uff0c\u6211\u4eec\u53ef\u4ee5\u7528[46]\u53ef\u5fae\u5730\u5f97\u5230\u4f53\u7f51\u683c\u9876\u70b9(Vt)\u548c\u4f53\u5173\u8282\u5750\u6807(Jt)\u3002</p>"},{"location":"pape_read/ACTOR/trans/#conditional-transformer-vae-for-motions","title":"Conditional Transformer VAE for Motions","text":"<p>\u6211\u4eec\u91c7\u7528\u6761\u4ef6\u53d8\u5206\u81ea\u52a8\u7f16\u7801\u5668(CVAE)\u6a21\u578b[60] \uff0c\u5e76\u5c06\u52a8\u4f5c\u7c7b\u522b\u4fe1\u606f\u8f93\u5165\u5230\u7f16\u7801\u5668\u548c\u89e3\u7801\u5668\u3002\u66f4\u5177\u4f53\u5730\u8bf4\uff0c\u6211\u4eec\u7684\u6a21\u578b\u662f\u4e00\u4e2a\u52a8\u4f5c\u6761\u4ef6\u53d8\u538b\u5668 VAE (ACTOR) \uff0c\u5176\u7f16\u7801\u5668\u548c\u89e3\u7801\u5668\u7531\u53d8\u538b\u5668\u5c42\u7ec4\u6210(\u53c2\u89c1\u56fe2\u4ee5\u83b7\u5f97\u6982\u8ff0)\u3002</p> <p>\u7f16\u7801\u5668\u3002\u8be5\u7f16\u7801\u5668\u91c7\u7528\u4efb\u610f\u957f\u5ea6\u7684\u59ff\u6001\u5e8f\u5217\uff0c\u4ee5\u52a8\u4f5c\u6807\u7b7e a \u4e3a\u8f93\u5165\uff0c\u8f93\u51fa\u8fd0\u52a8\u6f5c\u4f0f\u7a7a\u95f4\u7684\u5206\u5e03\u53c2\u6570 \u03bc \u548c \u03a3\u3002\u5229\u7528\u91cd\u53c2\u6570\u5316\u6280\u5de7[37] \uff0c\u6211\u4eec\u4ece\u8fd9\u4e2a\u5206\u5e03\u4e2d\u62bd\u6837\u51fa\u4e00\u4e2a\u6f5c\u5411\u91cf z \u2208 M\uff0c\u5176\u4e2d MdRd\u3002\u9996\u5148\u5c06\u6240\u6709\u8f93\u5165\u59ff\u6001\u53c2\u6570(R)\u548c\u5e73\u79fb(D)\u7ebf\u6027\u5d4c\u5165\u5230 Rd \u7a7a\u95f4\u4e2d\u3002\u5f53\u6211\u4eec\u5c06\u4efb\u610f\u957f\u5ea6\u7684\u5e8f\u5217\u5d4c\u5165\u5230\u4e00\u4e2a\u6f5c\u5728\u7a7a\u95f4(\u5e8f\u5217\u7ea7\u5d4c\u5165)\u65f6\uff0c\u6211\u4eec\u9700\u8981\u5408\u5e76\u65f6\u95f4\u7ef4\u6570\u3002\u5728\u5176\u4ed6\u9886\u57df\u4e2d\uff0c\u5df2\u7ecf\u5f15\u5165\u4e86[\u7c7b]\u4ee4\u724c\u7528\u4e8e\u6c60\u7684\u76ee\u7684\uff0c\u4f8b\u5982\uff0c\u5728\u5e26\u6709 BERT [12]\u7684 NLP \u4e2d\uff0c\u4ee5\u53ca\u6700\u8fd1\u5728\u5e26\u6709 ViT [13]\u7684\u8ba1\u7b97\u673a\u89c6\u89c9\u4e2d\u3002\u53d7\u6b64\u65b9\u6cd5\u7684\u542f\u53d1\uff0c\u6211\u4eec\u7c7b\u4f3c\u5730\u5728\u8f93\u5165\u524d\u9762\u52a0\u4e0a\u53ef\u5b66\u4e60\u7684\u4ee4\u724c\uff0c\u5e76\u4e14\u53ea\u4f7f\u7528\u76f8\u5e94\u7684\u7f16\u7801\u5668\u8f93\u51fa\u4f5c\u4e3a\u6c47\u96c6\u65f6\u95f4\u7ef4\u5ea6\u7684\u65b9\u6cd5\u3002\u4e3a\u6b64\uff0c\u6211\u4eec\u5728\u6bcf\u4e2a\u64cd\u4f5c\u4e2d\u5305\u62ec\u4e24\u4e2a\u989d\u5916\u7684\u53ef\u5b66\u4e60\u53c2\u6570: \u03bc \u6807\u8bb0 a \u548c \u03a3 \u6807\u8bb0 a\uff0c\u6211\u4eec\u79f0\u4e4b\u4e3a\u201c\u5206\u5e03\u53c2\u6570\u6807\u8bb0\u201d\u3002\u6211\u4eec\u5c06\u5d4c\u5165\u7684\u59ff\u52bf\u5e8f\u5217\u9644\u52a0\u5230\u8fd9\u4e9b\u6807\u8bb0\u3002\u4ea7\u751f\u7684\u53d8\u538b\u5668\u7f16\u7801\u5668\u8f93\u5165\u662f\u4f4d\u7f6e\u7f16\u7801\u7684\u6b63\u5f26\u51fd\u6570\u5f62\u5f0f\u7684\u603b\u548c\u3002\u6211\u4eec\u901a\u8fc7\u53d6\u7f16\u7801\u5668\u7684\u524d\u4e24\u4e2a\u8f93\u51fa\u5bf9\u5e94\u4e8e\u5206\u5e03\u53c2\u6570\u6807\u8bb0\u6765\u83b7\u5f97\u5206\u5e03\u53c2\u6570 \u03bc \u548c \u03a3 (\u5373\u53bb\u6389\u5176\u4f59\u7684\u6807\u8bb0)\u3002\u89e3\u7801\u5668\u3002\u7ed9\u5b9a\u4e00\u4e2a\u6f5c\u5728\u5411\u91cf z \u548c\u4e00\u4e2a\u52a8\u4f5c\u6807\u7b7e a\uff0c\u89e3\u7801\u5668\u5728\u4e00\u6b21\u62cd\u6444\u4e2d\u5728\u7ed9\u5b9a\u7684\u6301\u7eed\u65f6\u95f4\u5185\u751f\u6210\u4e00\u4e2a\u771f\u5b9e\u7684\u4eba\u4f53\u8fd0\u52a8(\u5373\uff0c\u4e0d\u662f\u81ea\u56de\u5f52)\u3002\u6211\u4eec\u4f7f\u7528\u53d8\u538b\u5668\u89e3\u7801\u5668\u6a21\u578b\uff0c\u5176\u4e2d\u6211\u4eec\u63d0\u4f9b\u7684\u65f6\u95f4\u4fe1\u606f\u4f5c\u4e3a\u4e00\u4e2a\u67e5\u8be2(\u5728 T \u6b63\u5f26\u4f4d\u7f6e\u7f16\u7801\u7684\u5f62\u5f0f) \uff0c\u548c\u6f5c\u5728\u7684\u5411\u91cf\u7ed3\u5408\u7684\u884c\u52a8\u4fe1\u606f\uff0c\u4f5c\u4e3a\u5173\u952e\u548c\u503c\u3002\u4e3a\u4e86\u5408\u5e76\u52a8\u4f5c\u4fe1\u606f\uff0c\u6211\u4eec\u7b80\u5355\u5730\u6dfb\u52a0\u4e00\u4e2a\u53ef\u5b66\u4e60\u7684\u504f\u89c1 b \u6807\u8bb0 a \u6765\u5c06\u6f5c\u5728\u8868\u5f81\u8f6c\u79fb\u5230\u4e00\u4e2a\u52a8\u4f5c\u4f9d\u8d56\u7684\u7a7a\u95f4\u3002\u53d8\u538b\u5668\u89e3\u7801\u5668\u8f93\u51fa\u4e00\u7cfb\u5217\u7684 T \u77e2\u91cf\uff0c\u4ece\u4e2d\u6211\u4eec\u53ef\u4ee5\u5f97\u5230\u6700\u7ec8\u7684 Pb1\uff0c. . \uff0cPbT \u7684\u7ebf\u6027\u6295\u5f71\u3002\u5229\u7528\u53ef\u5fae SMPL \u5c42\u83b7\u5f97\u7ed9\u5b9a\u7684\u4f4d\u59ff\u53c2\u6570\u4f5c\u4e3a\u89e3\u7801\u5668\u8f93\u51fa\u7684\u9876\u70b9\u548c\u5173\u8282\u3002</p>"},{"location":"pape_read/ACTOR/trans/#training","title":"Training","text":"<p>\u6211\u4eec\u5b9a\u4e49\u4e86\u51e0\u4e2a\u635f\u5931\u9879\u6765\u8bad\u7ec3\u6211\u4eec\u7684\u6a21\u578b\uff0c\u5e76\u5728\u7b2c 4.2 \u8282\u4e2d\u8fdb\u884c\u4e86\u6d88\u878d\u7814\u7a76\u3002 \u59ff\u52bf\u53c2\u6570 (LP) \u7684\u91cd\u5efa\u635f\u5931\u3002 \u6211\u4eec\u5728\u5730\u9762\u5b9e\u51b5\u59ff\u52bf P1,... \u4e4b\u95f4\u4f7f\u7528 L2 \u635f\u5931\u3002 . . , PT \u548c\u6211\u4eec\u7684\u9884\u6d4b Pb1, . . . , PbT \u4f5c\u4e3a LP = PT t=1\u2225Pt \u2212 Pbt\u2225 2 2 \u3002 \u8bf7\u6ce8\u610f\uff0c\u6b64\u635f\u5931\u5305\u542b SMPL \u65cb\u8f6c\u548c\u6839\u5e73\u79fb\u3002 \u5f53\u6211\u4eec\u901a\u8fc7\u4e22\u5f03\u5e73\u79fb\u8fdb\u884c\u5b9e\u9a8c\u65f6\uff0c\u6211\u4eec\u5c06\u8fd9\u4e2a\u672f\u8bed\u5206\u6210\u4e24\u90e8\u5206\uff1aLR \u548c LD\uff0c\u5206\u522b\u7528\u4e8e\u65cb\u8f6c\u548c\u5e73\u79fb\u3002</p> <p>\u9876\u70b9\u5750\u6807 (LV) \u4e0a\u7684\u91cd\u5efa\u635f\u5931\u3002 \u6211\u4eec\u5c06 SMPL \u59ff\u52bf Pt \u548c Pbt \u9988\u9001\u5230\u5177\u6709\u5e73\u5747\u5f62\u72b6\uff08\u5373 \u03b2 = \u20d70\uff09\u7684\u53ef\u5fae\u5206 SMPL \u5c42\uff08\u6ca1\u6709\u53ef\u5b66\u4e60\u53c2\u6570\uff09\u4ee5\u83b7\u5f97\u7f51\u683c Vt \u548c Vbt \u7684\u6839\u4e2d\u5fc3\u9876\u70b9\u3002 \u6211\u4eec\u901a\u8fc7\u4e0e\u5730\u9762\u5b9e\u51b5\u9876\u70b9 Vt \u6bd4\u8f83\u6765\u5b9a\u4e49 L2 \u635f\u5931\uff0c\u5373 LV = PT t=1\u2225Vt \u2212 Vbt\u2225 2 2 \u3002 \u6211\u4eec\u8fdb\u4e00\u6b65\u5728\u4e00\u7ec4\u66f4\u7a00\u758f\u7684\u70b9\u4e0a\u4f7f\u7528\u635f\u5931 LJ \u8fdb\u884c\u5b9e\u9a8c\uff0c\u4f8b\u5982\u901a\u8fc7 SMPL \u8054\u5408\u56de\u5f52\u5668\u83b7\u5f97\u7684\u8054\u5408\u4f4d\u7f6e Jbt\u3002 \u7136\u800c\uff0c\u6b63\u5982\u7b2c 4.2 \u8282\u6240\u793a\uff0c\u6211\u4eec\u6ca1\u6709\u5728\u6700\u7ec8\u6a21\u578b\u4e2d\u5305\u542b\u8be5\u672f\u8bed\u3002 KL\u635f\u5931\uff08LKL\uff09\u3002 \u4e0e\u6807\u51c6 VAE \u4e00\u6837\uff0c\u6211\u4eec\u901a\u8fc7\u9f13\u52b1\u6f5c\u5728\u7a7a\u95f4\u7c7b\u4f3c\u4e8e\u9ad8\u65af\u5206\u5e03\u6765\u89c4\u8303\u5316\u6f5c\u5728\u7a7a\u95f4\uff0c\u5176\u4e2d \u00b5 \u662f\u7a7a\u5411\u91cf\uff0c\u03a3 \u662f\u8eab\u4efd\u77e9\u9635\u3002 \u6211\u4eec\u6700\u5c0f\u5316\u7f16\u7801\u5668\u5206\u5e03\u548c\u8be5\u76ee\u6807\u5206\u5e03\u4e4b\u95f4\u7684 Kullback\u2013Leibler (KL) \u6563\u5ea6\u3002 \u7531\u6b64\u4ea7\u751f\u7684\u603b\u635f\u5931\u88ab\u5b9a\u4e49\u4e3a\u4e0d\u540c\u9879\u7684\u603b\u548c\uff1aL = LP + LV + \u03bbKLLKL\u3002 \u6211\u4eec\u51ed\u7ecf\u9a8c\u8bc1\u660e\u4e86\u5728\u6211\u4eec\u7684\u5b9e\u9a8c\u4e2d\u4f7f\u7528 \u03bbKL\uff08\u76f8\u5f53\u4e8e \u03b2-VAE [26] \u4e2d\u7684 \u03b2 \u9879\uff09\u8fdb\u884c\u52a0\u6743\u4ee5\u83b7\u5f97\u591a\u6837\u6027\u548c\u73b0\u5b9e\u4e3b\u4e49\u4e4b\u95f4\u7684\u826f\u597d\u6743\u8861\u7684\u91cd\u8981\u6027\uff08\u53c2\u89c1\u9644\u5f55 A.1 \u8282\uff09 ). \u5269\u4f59\u7684\u635f\u5931\u9879\u53ea\u662f\u7b80\u5355\u5730\u540c\u7b49\u52a0\u6743\uff0c\u901a\u8fc7\u8c03\u6574\u53ef\u80fd\u4f1a\u8fdb\u4e00\u6b65\u6539\u8fdb\u3002 \u6211\u4eec\u4f7f\u7528\u56fa\u5b9a\u5b66\u4e60\u7387\u4e3a 0.0001 \u7684 AdamW \u4f18\u5316\u5668\u3002 \u5c0f\u6279\u91cf\u5927\u5c0f\u8bbe\u7f6e\u4e3a 20\uff0c\u6211\u4eec\u53d1\u73b0\u6027\u80fd\u5bf9\u8fd9\u4e2a\u8d85\u53c2\u6570\u5f88\u654f\u611f\uff08\u53c2\u89c1\u9644\u5f55 A.2 \u8282\uff09\u3002 \u6211\u4eec\u5206\u522b\u5728 NTU-13\u3001HumanAct12 \u548c UESTC \u6570\u636e\u96c6\u4e0a\u8bad\u7ec3\u6211\u4eec\u7684\u6a21\u578b 2000\u30015000 \u548c 1000 \u4e2a\u65f6\u671f\u3002 \u603b\u7684\u6765\u8bf4\uff0c\u66f4\u591a\u7684\u65f6\u671f\u4f1a\u4ea7\u751f\u66f4\u597d\u7684\u6027\u80fd\uff0c\u4f46\u6211\u4eec\u505c\u6b62\u8bad\u7ec3\u4ee5\u4fdd\u6301\u8f83\u4f4e\u7684\u8ba1\u7b97\u6210\u672c\u3002 \u8bf7\u6ce8\u610f\uff0c\u4e3a\u4e86\u5141\u8bb8\u66f4\u5feb\u7684\u8fed\u4ee3\u3001\u635f\u5931\u548c\u67b6\u6784\u7684\u6d88\u878d\uff0c\u6211\u4eec\u5728 NTU-13 \u4e0a\u8bad\u7ec3\u4e86 1000 \u4e2a epoch\uff0c\u5728 UESTC \u4e0a\u8bad\u7ec3\u4e86 500 \u4e2a epoch\u3002 \u5176\u4f59\u7684\u5b9e\u65bd\u7ec6\u8282\u53ef\u4ee5\u5728\u9644\u5f55\u7684 C \u8282\u4e2d\u627e\u5230\u3002</p>"},{"location":"pape_read/ACTOR/trans/#experiments","title":"Experiments","text":"<p>\u6682\u7565</p>"},{"location":"pape_read/ACTOR/trans/#conclusions","title":"Conclusions","text":"<p>\u6211\u4eec\u63d0\u51fa\u4e86\u4e00\u79cd\u65b0\u7684\u57fa\u4e8e Transformer \u7684 VAE \u6a21\u578b\u6765\u5408\u6210\u4ee5\u52a8\u4f5c\u4e3a\u6761\u4ef6\u7684\u4eba\u4f53\u8fd0\u52a8\u3002\u6211\u4eec\u63d0\u4f9b\u4e86\u8be6\u7ec6\u7684\u5206\u6790\u6765\u8bc4\u4f30\u6211\u4eec\u63d0\u8bae\u7684\u65b9\u6cd5\u7684\u4e0d\u540c\u7ec4\u6210\u90e8\u5206\u3002 \u6211\u4eec\u5728\u52a8\u4f5c\u6761\u4ef6\u8fd0\u52a8\u751f\u6210\u65b9\u9762\u83b7\u5f97\u4e86\u6700\u5148\u8fdb\u7684\u6027\u80fd\uff0c\u4e0e\u4e4b\u524d\u7684\u5de5\u4f5c\u76f8\u6bd4\u6709\u4e86\u663e\u7740\u6539\u8fdb\u3002 \u6b64\u5916\uff0c\u6211\u4eec\u63a2\u7d22\u4e86\u8fd0\u52a8\u53bb\u566a\u548c\u52a8\u4f5c\u8bc6\u522b\u4e2d\u7684\u5404\u79cd\u7528\u4f8b\u3002 \u6211\u4eec\u65b9\u6cd5\u7684\u4e00\u4e2a\u7279\u522b\u5438\u5f15\u4eba\u7684\u7279\u6027\u662f\u5b83\u5728\u5e8f\u5217\u7ea7\u6f5c\u5728\u7a7a\u95f4\u4e0a\u8fd0\u884c\u3002\u56e0\u6b64\uff0c\u672a\u6765\u7684\u5de5\u4f5c\u53ef\u4ee5\u5229\u7528\u6211\u4eec\u7684\u6a21\u578b\u5bf9\u8fd0\u52a8\u4f30\u8ba1\u6216\u52a8\u4f5c\u8bc6\u522b\u95ee\u9898\u65bd\u52a0\u5148\u9a8c\u3002</p>"},{"location":"pape_read/EG3D/","title":"[EG3D] Efficient Geometry-aware 3D Generative Adversarial Networks","text":"<p> \u7ea6 479 \u4e2a\u5b57  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 2 \u5206\u949f</p> <p><code>3DV</code> <code>Generation</code></p> <p>\u6587\u7ae0\u4fe1\u606f</p> <ul> <li>\u6587\u7ae0\u9898\u76ee\uff1aEG3D: Efficient Geometry-aware 3D Generative Adversarial Networks</li> <li>\u4f5c\u8005\uff1a     Eric Ryan Chan  * 1, 2 ,      Connor Zhizhen Lin  * 1 ,      Matthew Aaron Chan  * 1 ,      Koki Nagano  * 2 ,      Boxiao Pan  1 ,      Shalini De Mello 2 ,      Orazio Gallo  2 ,      Leonidas Guibas  1 ,      Jonathan Tremblay  2 ,      Sameh Khamis  2 ,      Tero Karras  2 ,      Gordon Wetzstein  1 </li> <li>\u9879\u76ee\u4e3b\u9875\uff1a\ud83d\udd17</li> <li>arXiv\uff1a\ud83d\udd17 2112.07945</li> <li>\u4ee3\u7801\uff1a\ud83d\udd17</li> </ul>"},{"location":"pape_read/EG3D/#\u8bba\u6587\u7b14\u8bb0","title":"\u8bba\u6587\u7b14\u8bb0","text":""},{"location":"pape_read/EG3D/#tri-plane-hybrid-3d-representation","title":"Tri-plane hybrid 3D representation","text":"<p>\u8ba8\u8bba\u4e00\u4e0b NeRF \u548c Tri-plane hybrid 3D representation \u7684\u5173\u7cfb\u3002</p> <p>NeRF \u6309 ray \u4f53\u79ef\u6e32\u67d3\u8fc7\u7a0b\u4e2d\u91c7\u6837\u7684\u70b9\u4ece\u8bad\u7ec3\u597d\u7684 MLP \u91cc\u62ff\uff1b\u800c EG3D \u5219\u662f\u5f97\u5230\u4e09\u4e2a\u6295\u5f71\u65b9\u5411\u4e0a\u7684\u7279\u5f81\u5411\u91cf\uff0c\u6bcf\u4e00\u4e2a\u6295\u5f71\u65b9\u5411\u4e0a\u7684\u7279\u5f81\u5411\u91cf\u90fd\u662f\u6cbf\u7740\u6d88\u5931\u7684\u90a3\u4e2a\u7ef4\u5ea6\u805a\u5408\u5f97\u5230\u7684\uff0c\u53ef\u4ee5\u770b\u4f5c\u662f\u62ff\u5230\u4e86\u7a7a\u95f4\u4e2d\u4e09\u6761\u6b63\u4ea4\u7684\u7ebf\u7684\u7279\u5f81\uff0c\u800c\u4e4b\u540e\u7528\u4e00\u4e2a\u8f7b\u91cf MLP \u53bb\u4ece\u8fd9\u4e09\u4e2a\u7279\u5f81\u5411\u91cf\u91cc\u628a\u8fd9\u4e2a\u70b9\u7684\u989c\u8272\u5bc6\u5ea6\u62ff\u51fa\u6765\uff0c\u7c7b\u4f3c\u4e8e\u6c42\u4e09\u6761\u7ebf\u7684\u4ea4\u70b9\u3002</p> <p>\u76f8\u6bd4\u4e8e NeRF \u5c06\u6570\u636e\u53c2\u6570\u5316\uff0c\u6bcf\u6b21\u67e5\u8be2\u90fd\u9700\u8981\u8d70\u4e00\u8fb9 MLP\uff0cEG3D Sec3 \u5219\u663e\u793a\u7684\u5c06\u7279\u5f81\u5b58\u5728\u4e09\u4e2a\u4e8c\u7ef4\u8868\u91cc\uff0c\u6bcf\u6b21\u67e5\u8be2\u53ea\u9700\u8981 O(1) \u7684\u5f00\u9500\uff0c\u56e0\u6b64\u6548\u7387\u4e3b\u8981\u53d6\u51b3\u4e8e\u540e\u9762\u90a3\u4e2a\u8f7b\u91cf MLP\uff0c\u4ee5\u6b64\u6765\u5b9e\u73b0\u6548\u7387\u4e0a\u7684\u63d0\u9ad8\u3002</p> <p>\u800c\u5b9e\u73b0\u6548\u679c\u4e0a\uff0c\u6211\u80e1\u731c EG3D \u7684\u65b9\u6cd5\u597d\u7684\u539f\u56e0\uff1a</p> <ol> <li>\u7531\u4e8e\u4f7f\u7528\u4e86\u5ea7\u6807\u6295\u5f71\uff0c\u6240\u4ee5\u76f8\u5bf9\u4e8e NeRF \u7684\u53c2\u6570\u8868\u8fbe\uff0cEG3D \u5bf9\u4e8e\u67d0\u4e2a\u70b9\u7684\u7a7a\u95f4\u4f4d\u7f6e\u5177\u6709\u66f4\u5f3a\u7684\u7ea6\u675f\uff0c\u56e0\u800c\u53ef\u80fd\u5bf9\u7ec6\u8282\u7684\u628a\u63a7\u7ea6\u675f\u66f4\u76f4\u63a5\uff0c\u6216\u8005\u8bf4\u76f4\u89c9\u4e0a\u6211\u611f\u89c9 EG3D \u8fd9\u79cd\u8868\u8fbe\u5bf9\u201c\u7279\u5f81-\u5ea7\u6807\u201d\u7684\u5173\u7cfb\u66f4\u5177\u4f53\uff1b</li> <li>\u4e09\u4e2a\u6b63\u4ea4\u65b9\u5411\u585e\u8fdb\u5c0f MLP \u91cc\u5b66\uff0c\u53ef\u80fd\u4f1a\u66f4\u5bb9\u6613\u8ba9 MLP \u77e5\u9053\u53bb\u627e\u4ea4\u70b9\u9644\u8fd1\u7684\u90a3\u4e9b\u70b9\u53bb\u5b66\u4e60\uff0c\u611f\u89c9\u6709\u70b9\u7c7b\u4f3c\u4e8e\u5728\u4e00\u4e2a\u957f\u5f97\u50cf\u66fc\u54c8\u987f\u8ddd\u79bb\u90a3\u79cd\u7acb\u65b9\u4f53\u4e00\u6837\u7684\u7a7a\u95f4\u91cc\u53bb\u5b66\u4e60\u5468\u56f4\u7684\u4fe1\u606f\uff1b</li> </ol> <p>\u53c2\u8003\u8d44\u6599</p> <ul> <li>https://www.cnblogs.com/ghostcai/p/16615616.html \uff08\u7b14\u8bb0\uff09</li> </ul>"},{"location":"pape_read/MAS/","title":"[MAS] Multi-view Ancestral Sampling for 3D Motion Generation Using 2D Diffusion","text":"<p> \u7ea6 211 \u4e2a\u5b57  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 1 \u5206\u949f</p> <p><code>3DV</code> <code>Motion</code> <code>Diffusion</code></p> <p>\u6587\u7ae0\u4fe1\u606f</p> <ul> <li>\u6587\u7ae0\u9898\u76ee\uff1aMAS: Multi-view Ancestral Sampling for 3D Motion Generation Using 2D Diffusion </li> <li>\u4f5c\u8005\uff1aRoy Kapon, Guy Tevet, Daniel Cohen-Or, Amit H. Bermano</li> <li>\u9879\u76ee\u4e3b\u9875\uff1a\ud83d\udd17</li> <li>arXiv\uff1a\ud83d\udd17 2310.14729</li> </ul>"},{"location":"pape_read/MAS/#\u8bba\u6587\u7b14\u8bb0","title":"\u8bba\u6587\u7b14\u8bb0","text":"<p>\u5229\u7528\u4e00\u4e2a\u5728 2D \u5355\u76ee\u6570\u636e\u96c6\u4e0a train \u51fa\u6765\u7684 diffusion model \u505a 3D Motion \u7684\u751f\u6210\u3002</p> <ul> <li> <p>\u7531\u4e8e\u4f7f\u7528 ancestral sampling\uff0cMAS \u751f\u6210 3D motion \u7684\u6548\u7387\u5f88\u9ad8\uff1b</p> </li> <li> <p>\u6570\u636e\u8868\u793a\uff1a</p> <ul> <li>\u8868\u793a J \u4e2a joint \u5728 L \u5e27\u91cc\u7684 xyz\uff0c\u800c\u4e14\u4e0d\u5bf9\u9aa8\u68d2\u957f\u5ea6\u505a\u7ea6\u675f\uff08\u5728\u505a\u6cd5\u4e2d\u4e5f\u4e0d\u7ea6\u675f\uff09\uff1b<ul> <li>\u8fd9\u5e26\u6765\u7684\u597d\u5904\u662f\u53ef\u4ee5\u589e\u52a0\u573a\u666f\u4e2d\u66f4\u591a\u7684\u8fd0\u52a8\u7269\u4f53\uff1b</li> </ul> </li> </ul> </li> <li> <p>\u65b9\u6cd5</p> <ul> <li>\u591a\u89c6\u89d2\u7684\u4e00\u81f4\u6027\uff1a<ul> <li>\u5728\u6bcf\u4e2a diffusion denoising step \u90fd\u5229\u7528 \"triangulate\" \u8fdb\u884c\u4e00\u6b21 \\(n*2D \\rightarrow 1*3D \\rightarrow n*2D\\) \u7684\u8fc7\u7a0b\uff1b</li> <li> TODO: \u8fd9\u4e2a \"triangulate\" \u662f\u4ec0\u4e48\uff1f \u4e09\u89d2\u6d4b\u91cf\u3002</li> </ul> </li> <li>\u5b9e\u9a8c\u8ba4\u4e3a V = 3 \u5c31\u591f\u4e86\uff0c\u518d\u591a\u5f71\u54cd\u4e5f\u4e0d\u5927\uff1b</li> <li></li> </ul> </li> </ul>"},{"location":"pape_read/NSM/","title":"[NSM] Neural State Machine for Character-Scene Interactions","text":"<p> \u7ea6 1434 \u4e2a\u5b57  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 5 \u5206\u949f</p> <p><code>3DV</code> <code>Human-Motion</code> <code>Scene-Aware</code></p> <p>\u6587\u7ae0\u4fe1\u606f</p> <ul> <li>\u6587\u7ae0\u9898\u76ee\uff1aNeural State Machine for Character-Scene Interactions</li> <li>\u4f5c\u8005\uff1aSebastian Starke, He Zhang, Taku Komura, Jun Saito</li> <li>\u8bba\u6587\uff1a\ud83d\udd17</li> </ul>"},{"location":"pape_read/NSM/#\u8bba\u6587\u7b14\u8bb0","title":"\u8bba\u6587\u7b14\u8bb0","text":""},{"location":"pape_read/NSM/#\u6982\u8ff0","title":"\u6982\u8ff0","text":"<p>NSM \u63d0\u51fa\u4e00\u79cd\u65b0\u7684\u76ee\u6807\u5bfc\u5411\u81ea\u56de\u5f52\u6a21\u578b\u6765\u89e3\u51b3\u4eba\u4f53\u52a8\u4f5c\u751f\u6210\u95ee\u9898\uff0c\u80fd\u5b9e\u73b0\u8868\u73b0\u826f\u597d\u7684\u5750\u3001\u6301\u7269\u3001\u907f\u969c\u7684\u884c\u4e3a\u3002\u8be5\u95ee\u9898\u4e3b\u8981\u96be\u70b9\u5728\u4e8e\uff0c\u5b8c\u6210\u4e00\u9879\u4efb\u52a1\u6240\u9700\u8981\u751f\u6210\u7684\u52a8\u4f5c\u5e8f\u5217\u4e2d\u5305\u542b\u5468\u671f\u6027\u548c\u975e\u5468\u671f\u6027\u7684\u90e8\u5206\uff0c\u5e76\u4e14\u9700\u8981\u5bf9\u5468\u56f4\u73af\u5883\u8fdb\u884c\u611f\u77e5\u3002\u901a\u8fc7\u4f7f\u7528\u4e8c\u7ef4\u76f8\u4f4d\u8868\u793a\u7684 Kronecker \u4e58\u79ef\u3001\u4e00\u79cd\u53cc\u5411\u63a7\u5236\uff08\u76ee\u6807\u4e2d\u5fc3\u548c\u81ea\u6211\u4e2d\u5fc3\uff09\u89c4\u5219\u3001\u4ea4\u4e92\u4f53\u7d20\u4f20\u611f\u5668\u548c\u73af\u5883\u4f53\u7d20\u4f20\u611f\u5668\u7b49\u6280\u672f\u6765\u589e\u5f3a\u6548\u679c\uff0c\u66f4\u5b8f\u89c2\u7684\u8bf4\uff0cNSM \u4f7f\u7528\u4e86\u4e00\u79cd\u76ee\u6807\u9a71\u52a8\u7684\u6a21\u578b\u6765\u5b9e\u73b0\u6548\u679c\u826f\u597d\u7684\u52a8\u4f5c\u751f\u6210\u3002</p>"},{"location":"pape_read/NSM/#\u65b9\u6cd5","title":"\u65b9\u6cd5","text":"<p>\u6574\u4e2a\u4efb\u52a1\u53ef\u4ee5\u5212\u5206\u4e3a\u4e24\u4e2a\u90e8\u5206\uff0c\u7b2c\u4e00\u90e8\u5206\u662f\u5bfb\u8def\u81f3\u76ee\u6807\uff0c\u8981\u6c42\u4ee3\u7406\u4eba\u80fd\u591f\u81ea\u7136\u89c4\u907f\u969c\u788d\u5e76\u627e\u5230\u76ee\u6807\u5e76\u4e14\u6700\u7ec8\u9762\u671d\u76ee\u6807\uff0c\u8fd9\u4e00\u90e8\u5206\u4e3b\u8981\u7684\u96be\u70b9\u5c31\u662f\u9700\u8981\u80fd\u591f\u5bf9\u73af\u5883\u8fdb\u884c\u611f\u77e5\uff0c\u4e3a\u6b64 NSM \u56e2\u961f\u9009\u62e9\u4e86\u4f53\u7d20\u8868\u8fbe\uff0c\u5e76\u8bbe\u8ba1\u4e86\u73af\u5883\u4f53\u7d20\u4f20\u611f\u5668\u2014\u2014\u5176\u8303\u56f4\u8986\u76d6\u4ee5\u4ee3\u7406\u4eba\u4e3a\u4e2d\u5fc3\u7684\u4e00\u4e2a\u5706\u67f1\u5f62\u533a\u57df\uff0c\u533a\u57df\u5185\u7684\u6240\u6709\u5177\u6709\u4f53\u7d20\u7684\u7269\u4f53\u90fd\u4f1a\u88ab\u7403\u5f62\u91c7\u6837\u4e3a\u4e00\u4e2a 0~1 \u548c\u4e4b\u95f4\u7684\u503c\uff0c\u5982\u8bba\u6587\u4e2d Fig5\u3002\u800c\u8fd9\u4e9b\u503c\u88ab\u79f0\u4e3a\u73af\u5883\u8f93\u5165\uff0c\u5728\u6a21\u578b\u7684 pipeline \u4e2d\u4f5c\u4e3a\u8f93\u5165\u3002\u73af\u5883\u8f93\u5165\u6709\u6548\u589e\u52a0\u4ee3\u7406\u4eba\u5bf9\u73af\u5883\u7684\u7406\u89e3\u80fd\u529b\uff0c\u6539\u5584\u4e86\u8bf8\u5982\u4e0e\u76ee\u6807\u4ea4\u4e92\u65f6\u4ece\u80cc\u540e\u7a7f\u900f\u6905\u5b50\u5750\u4e0b\u7684\u8fd9\u79cd\u95ee\u9898\uff0c\u5982 Fig14\u3002\u6b64\u5916\uff0cNSM \u56e2\u961f\u5b66\u4e60\u4e86 PFNN\uff0c\u4f7f\u7528 phase \u6765\u5b9e\u73b0\u72b6\u6001\u673a\uff0c\u4f46\u521b\u65b0\u6027\u7684\u4f7f\u7528\u4e86\u6807\u6ce8\u79bb\u6563\u7279\u5b9a\u76f8\u4f4d\uff08\u5982\u884c\u8d70\u65f6\u5de6\u811a\u843d\u5730\u88ab\u6807\u6ce8\u4e3a \\(2k\\pi\\)\uff0c\u53f3\u811a\u843d\u5730\u88ab\u6807\u6ce8\u4e3a \\((2k+1)\\pi\\)\uff0c\u800c\u4e2d\u95f4\u8fc7\u7a0b\u901a\u8fc7\u63d2\u503c\u8ba1\u7b97\uff09\uff0c\u901a\u8fc7\u7f51\u7edc\u5b66\u4e60\u63d2\u503c\u76f8\u4f4d\u7684\u5f62\u5f0f\uff0c\u89e3\u51b3\u4e86 PFNN \u4e2d\u5148\u9a8c\u76f8\u4f4d\u5e26\u6765\u7684\uff0c\u4ee3\u7406\u4eba\u8d8b\u5411\u4e8e\u4e0d\u884c\u52a8\u7684\u7f3a\u70b9\u3002\u800c\u5728\u5bfb\u627e\u76ee\u6807\u65f6\uff0c\u4f20\u7edf\u7684\u5355\u5411\u8868\u8fbe\u5bb9\u6613\u4ea7\u751f\u8bef\u5dee\u7d2f\u8ba1\uff0c\u5bfc\u81f4\u6700\u7ec8\u76ee\u6807\u5b9a\u4f4d\u504f\u79fb\uff0cNSM \u56e2\u961f\u4f7f\u7528\u76ee\u6807\u4e2d\u5fc3\u3001\u81ea\u6211\u4e2d\u5fc3\u53cc\u5411\u8868\u8fbe\uff0c\u663e\u8457\u6539\u5584\u4e86\u8be5\u95ee\u9898\uff0c\u5b9e\u9a8c\u6548\u679c\u5982 Fig11 \u4e0a\u56fe\u3002</p> <p>\u7b2c\u4e8c\u90e8\u5206\u9700\u8981\u4ee3\u7406\u4eba\u80fd\u591f\u81ea\u7136\u7684\u548c\u76ee\u6807\u8fdb\u884c\u4ea4\u4e92\uff0c\u5982\u5728\u6905\u5b50\u4e0a\u5750\u4e0b\u3001\u6253\u5f00\u95e8\u3001\u7a7f\u8fc7\u5899\u4e0a\u7684\u6d1e\u3002\u8fd9\u9700\u8981\u4ee3\u7406\u4eba\u5bf9\u4ea4\u4e92\u76ee\u6807\u5177\u6709\u7cbe\u786e\u7684\u611f\u77e5\uff0c\u4e0e\u73af\u5883\u4f53\u7d20\u4f20\u611f\u5668\u7c7b\u4f3c\uff0cNSM \u4e5f\u63d0\u51fa\u4e86\u4ea4\u4e92\u4f53\u7d20\u4f20\u611f\u5668\uff0c\u4e3a\u4e86\u63d0\u9ad8\u7cbe\u5ea6\uff0c\u4f53\u7d20\u4f20\u611f\u5668\u4ee5 8x8x8 \u7684\u4f53\u7d20\u4e3a\u5355\u4f4d\uff0c\u540c\u6837\u91c7\u6837\u4e3a 0~1 \u4e4b\u95f4\u7684\u503c\uff0c\u88ab\u4f5c\u4e3a\u6a21\u578b\u7684\u4e00\u90e8\u5206\u8f93\u5165\u3002</p> <p>\u6574\u4f53\u6a21\u578b\u4f7f\u7528\u4e86 MoE \u6280\u672f\uff0c\u5373\u591a\u4e13\u5bb6\u6a21\u578b\uff0c\u901a\u8fc7 Gating Networks \u6765\u8ba1\u7b97\u5176\u6df7\u5408\u6743\u91cd\uff0c\u5176\u8f93\u5165\u4e3b\u8981\u4e3a\u5f53\u524d\u7684\u52a8\u4f5c\u6807\u7b7e\u548c\u4e8c\u7ef4\u76f8\u4f4d\uff08\u4ee5\u89e3\u51b3\u4e00\u7ef4\u76f8\u4f4d\u5e26\u6765\u7684\u4e0d\u53ef\u5fae\u7684\u95ee\u9898\uff09\u3002\u6a21\u578b\u9884\u6d4b\u7f51\u7edc\u5206\u4e3a\u7f16\u7801\u6a21\u5757\u548c\u9884\u6d4b\u6a21\u5757\u4e24\u90e8\u5206\uff0c\u6a21\u578b\u8f93\u5165\u5305\u542b\u56db\u4e2a\u90e8\u5206\uff1a\u5173\u4e8e\u4ee3\u7406\u4eba\u7684\u5f53\u524d\u5e27\uff08\u548c\u7a97\u53e3\u5185\u9644\u8fd1\u5e27\uff09\u7684\u4fe1\u606f\u3001\u76ee\u6807\u4fe1\u606f\uff08\u4f4d\u7f6e\u3001\u671d\u5411\u3001\u4ea4\u4e92\u52a8\u4f5c\u6807\u7b7e\uff09\u4ee5\u53ca\u5148\u524d\u63d0\u5230\u7684\u73af\u5883\u8f93\u5165\u548c\u4ea4\u4e92\u8f93\u5165\u3002\u5c06\u8f93\u51fa\u9884\u6d4b\u540e\u7684\u4ee3\u7406\u4eba\u52a8\u4f5c\u4fe1\u606f\u3001\u884c\u52a8\u8f68\u8ff9\u4fe1\u606f\u3001\u76f8\u4f4d\u4fe1\u606f\u3001\u4ea4\u4e92\u63a5\u89e6\u70b9\u4fe1\u606f\u7b49\u3002\u800c\u8fd9\u6837\u7684\u8bbe\u8ba1\u7ed9\u4e86\u6a21\u578b\u826f\u597d\u7684\u5728\u4e24\u79cd\u7528\u6237\u64cd\u4f5c\u6a21\u5f0f\uff08\u624b\u52a8\u63a7\u5236\u79fb\u52a8\u65b9\u5411\u548c\u53ea\u6307\u5b9a\u4ea4\u4e92\u76ee\u6807\uff09\u4e4b\u95f4\u5207\u6362\u7684\u80fd\u529b\uff0c\u53ea\u9700\u8981\u6539\u53d8\u76ee\u6807\u8f93\u5165\u7684\u5b9a\u4e49\u5373\u53ef\u65e0\u7f1d\u8854\u63a5\u3002</p>"},{"location":"pape_read/NSM/#\u5b9e\u9a8c\u6548\u679c\u4e0e\u548c\u76f8\u5173\u5de5\u4f5c\u7684\u5bf9\u6bd4","title":"\u5b9e\u9a8c\u6548\u679c\u4e0e\u548c\u76f8\u5173\u5de5\u4f5c\u7684\u5bf9\u6bd4","text":"<p>\u8fd9\u79cd\u8bbe\u8ba1\u901a\u8fc7\u4e86\u5b9e\u9a8c\u9a8c\u8bc1\uff0c\u5728 NSM \u56e2\u961f\u8bbe\u8ba1\u7684\u4e00\u79cd\u7279\u6b8a\u60c5\u51b5\u4e0b\u8868\u73b0\u826f\u597d\u2014\u2014\u5750\u4e0a\u4e00\u5f20\u534a\u63d2\u8fdb\u684c\u5b50\u7684\u6905\u5b50\u3002\u5e76\u4e14\u5728\u4e0e\u5176\u4ed6\u6a21\u578b\u7684\u5bf9\u6bd4\u4e2d\uff0c\u5728\u54cd\u5e94\u65f6\u95f4\u3001\u6ed1\u6b65\uff08\u4e0d\u81ea\u7136\u7684\u8d70\u52a8\uff09\u8868\u73b0\u3001\u4f4d\u7f6e\u7cbe\u5ea6\u3001\u65cb\u8f6c\u7cbe\u5ea6\u7b49\u65b9\u9762\u603b\u4f53\u8868\u73b0\u826f\u597d\uff0c\u51e0\u4e4e\u5b8c\u5168\u8d85\u8fc7\u4e86\u4ee5\u5f80\u7684\u540c\u7c7b\u5de5\u4f5c\uff0c\u6587\u7ae0\u4e5f\u5bf9\u8868\u73b0\u826f\u597d\u7684\u539f\u56e0\u8fdb\u884c\u4e86\u4e00\u4e9b\u5206\u6790\u3002</p> <p>LSTM \u6a21\u578b\u901a\u8fc7\u751f\u6210\u5927\u91cf\u77ed\u7247\u6bb5\u7684\u52a8\u4f5c\u6765\u589e\u5f3a\u6570\u636e\uff0c\u800c\u5b9e\u9645\u4e5f\u662f\u901a\u8fc7\u5c06\u8fc7\u7a0b\u4ece\u8fd9\u4e9b\u7247\u6bb5\u4e2d\u5b66\u4e60\u7684\u5185\u5bb9\u8fdb\u884c\u7ec4\u5408\u5b9e\u73b0\uff0c\u56e0\u6b64\u6269\u5c55\u6027\u8f83\u5dee\uff0c\u4e0d\u9002\u5408\u8fd0\u52a8\u6570\u636e\u4e0d\u591f\u5145\u5206\u7684\u60c5\u51b5\u3002</p> <p>\u800c\u4e0e PFNN \u76f8\u6bd4\uff0cNSM \u9650\u5236\u66f4\u5c11\uff0c\u56e0\u4e3a PFNN \u7684\u5148\u9a8c\u7684\u5916\u90e8 phase \u63a7\u5236\u673a\u5236\u8ba9\u5b83\u65e0\u6cd5\u5f88\u597d\u7684\u89e3\u51b3\u5bf9\u975e\u5468\u671f\u6027\u52a8\u4f5c\u751f\u6210\u3002</p> <p>\u800c MANN \u867d\u7136\u76f8\u5e94\u901f\u5ea6\u5feb\uff0c\u4f46\u5b58\u5728\u66f4\u660e\u663e\u7684\u6ed1\u6b65\u73b0\u8c61\uff0c\u5e76\u4e14\u5728\u63a7\u5236\u6a21\u5f0f\u53d8\u5316\u7684\u65f6\u5019\u52a8\u4f5c\u5341\u5206\u50f5\u786c\uff0c\u800c\u6b63\u662f\u56e0\u4e3a\u52a8\u4f5c\u50f5\u786c\u800c\u4ee3\u7406\u4eba\u7684\u6839\u90e8\u79fb\u52a8\u4ecd\u7136\u5b58\u5728\uff0c\u624d\u51fa\u73b0\u4e86\u66f4\u660e\u663e\u7684\u6ed1\u6b65\u73b0\u8c61\u3002</p>"},{"location":"pape_read/NSM/#\u6570\u636e\u589e\u5f3a","title":"\u6570\u636e\u589e\u5f3a","text":"<p>\u6b64\u5916\uff0c\u4e3a\u4e86\u589e\u5f3a\u6a21\u578b\u7684\u53ef\u6269\u5c55\u6027\u548c\u9002\u5e94\u6027\uff0cNSM \u56e2\u961f\u4e5f\u63d0\u51fa\u4e86\u4e00\u79cd\u65b0\u7684\u6570\u636e\u589e\u5f3a\u65b9\u6848\u3002\u6784\u5efa\u573a\u666f\u540e\u91c7\u96c6\u4e00\u7cfb\u5217\u573a\u666f\u4ea4\u4e92\u52a8\u4f5c\uff0c\u5e76\u901a\u8fc7\u955c\u50cf\u6765\u589e\u52a0\u6570\u636e\u4f53\u91cf\uff0c\u4eba\u5de5\u6807\u8bb0\u52a8\u4f5c\u6807\u7b7e\u548c\u76f8\u4f4d\u6807\u7b7e\u3002\u63a5\u4e0b\u6765\u901a\u8fc7\u6570\u636e\u589e\u5f3a\u7cfb\u7edf\u6765\u589e\u5f3a\u6570\u636e\u3002</p> <p>\u5177\u4f53\u6765\u8bf4\uff0c\u5c31\u662f\u4f7f\u7528 ShapeNet \u6570\u636e\u96c6\u4e2d\u7b26\u5408\u6a21\u578b\u7684\u7269\u4f53\u4e0d\u65ad\u66ff\u6362\u8bad\u7ec3\u7269\u4f53\uff0c\u5e76\u8fdb\u884c\u53d8\u6362\uff0c\u540c\u65f6\u8981\u6ce8\u610f\u66f4\u65b0\u63a5\u89e6\u70b9\u548c\u4ea4\u4e92\u65b9\u5411\u7b49\u3002\u4ee5\u6b64\u5728\u8bad\u7ec3\u8fc7\u7a0b\u4e2d\u63d0\u9ad8\u6a21\u578b\u8303\u7528\u6027\u3002</p>"},{"location":"pape_read/NeRF/","title":"[NeRF] Representing Scenes as Neural Radiance Fields for View Synthesis","text":"<p> \u7ea6 1701 \u4e2a\u5b57  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 6 \u5206\u949f</p> <p><code>3DV</code> <code>Reconstruction</code></p> <p>\u6587\u7ae0\u4fe1\u606f</p> <ul> <li>\u6587\u7ae0\u9898\u76ee\uff1aNeRF: Representing Scenes as Neural Radiance Fields for View Synthesis \uff08\u795e\u7ecf\u8f90\u5c04\u573a\uff09</li> <li>\u5206\u7c7b\uff1a<code>Computer Science</code> &gt; <code>Computer Vision and Pattern Recognition</code></li> <li>\u4f5c\u8005\uff1aBen Mildenhall, Pratul P. Srinivasan, Matthew Tancik, Jonathan T. Barron, Ravi Ramamoorthi, Ren Ng</li> <li>\u9879\u76ee\u4e3b\u9875\uff1a\ud83d\udd17</li> <li>arXiv\uff1a\ud83d\udd17 2003.08934</li> <li>\u4ee3\u7801\uff1a\ud83d\udd17</li> </ul>"},{"location":"pape_read/NeRF/#\u8bba\u6587\u7b14\u8bb0","title":"\u8bba\u6587\u7b14\u8bb0","text":""},{"location":"pape_read/NeRF/#\u8d21\u732e","title":"\u8d21\u732e","text":"<ol> <li>\u5c06\u590d\u6742\u96c6\u5408\u5f62\u72b6\u548c\u6750\u8d28\u7684\u8fde\u7eed\u573a\u666f\u8868\u8fbe\u4e3a 5D \u795e\u7ecf\u8f90\u5c04\u573a\u7684\u65b9\u6cd5\uff0c\u5c06\u5176\u53c2\u6570\u5316\u4e3a\u57fa\u672c\u7684 MLP \u7f51\u7edc\uff1b</li> <li>\u57fa\u4e8e\u7ecf\u5178\u4f53\u79ef\u6e32\u67d3\u6280\u672f\u7684\u53ef\u5fae\u5206\u6e32\u67d3\u7a0b\u5e8f\uff0c\u6211\u4eec\u7528\u5b83\u4ece\u6807\u51c6 RGB \u56fe\u50cf\u4e2d\u4f18\u5316\u8fd9\u4e9b\u8868\u793a\u3002\u8fd9\u5305\u62ec\u4e00\u79cd\u5206\u5c42\u91c7\u6837\u7b56\u7565\uff0c\u5c06 MLP \u7684\u5bb9\u91cf\u5206\u914d\u7ed9\u5177\u6709\u53ef\u89c1\u573a\u666f\u5185\u5bb9\u7684\u7a7a\u95f4\uff1b</li> <li>\u4f7f\u7528\u4f4d\u7f6e\u7f16\u7801(positional encoding)\uff0c\u5c06 5D \u5ea7\u6807\u6620\u5c04\u5230\u66f4\u9ad8\u7ef4\u7684\u7a7a\u95f4\uff0c\u4ee5\u5b9e\u73b0\u66f4\u9ad8\u9891\u7387\u7684\u573a\u666f\u5185\u5bb9\u7684\u8868\u793a\uff1b</li> </ol> <p>\u63d0\u51fa\u7684\u8868\u793a\u65b9\u6cd5\u6709\u5982\u4e0b\u597d\u5904\uff1a</p> <ul> <li>\u53ef\u4ee5\u8868\u8fbe\u590d\u6742\u771f\u5b9e\u7684\u51e0\u4f55\u5f62\u72b6</li> <li>\u9002\u5408\u4f7f\u7528\u6295\u5f71\u56fe\u50cf\u505a\u68af\u5ea6\u4f18\u5316<ul> <li> \u95ee\u9898\uff1a\u4ec0\u4e48\u610f\u601d\uff1f</li> </ul> </li> <li>\u964d\u4f4e\u4e86\u9ad8\u5206\u8fa8\u7387\u7a7a\u95f4\u56fe\u50cf\u7684\u5b58\u50a8\u6210\u672c</li> </ul>"},{"location":"pape_read/NeRF/#\u65b9\u6cd5","title":"\u65b9\u6cd5","text":"<p>\u4f7f\u7528\u5982\u4e0b\u4e00\u4e2a\u201c\u51fd\u6570\u201d\u6765\u8868\u793a\u4e00\u4e2a\u9759\u6001\u573a\u666f\uff1a</p> \\[ \\begin{aligned}     &amp; F_{\\Theta}:(\\mathrm{x}, \\mathrm{d}) \\rightarrow (\\mathrm{c}, \\sigma)     \\\\     &amp; \\text{where } \\mathrm{x} = (x,y,z), \\; \\mathrm{d} \\text{ is a 3D Cartesian unit vector}, \\; \\mathrm{c} = (r,g,b), \\; \\sigma \\text{ is the density}. \\end{aligned}  \\] <ul> <li>\u5168\u662f FC\uff1b</li> <li>\u8f93\u5165\u662f 5D \u5ea7\u6807\u2014\u2014\u70b9\u7684\u7a7a\u95f4\u5ea7\u6807 \\((x,y,z)\\) \u548c\u89c6\u89d2\u65b9\u5411 \\((\\theta, \\phi)\\)\uff1b</li> <li>\u8f93\u51fa\u662f\u4f53\u79ef\u5bc6\u5ea6\u4ee5\u53ca\u5bf9\u5e94\u7a7a\u95f4\u4f4d\u7f6e\u7684\u4e0e\u89c6\u89d2\u6709\u5173\u7684\u8f90\u5c04\uff08\u6216\u8005\u8bf4\u89c6\u89d2\u6709\u5173\u7684 RGB \u989c\u8272\uff09\uff1b</li> </ul> <p>\u4e3a\u4e86\u4fdd\u8bc1\u591a\u89c6\u89d2\u4e0b\u89c2\u5bdf\u5230\u7684\u5185\u5bb9\u5177\u6709\u4e00\u81f4\u6027\uff0c\u505a\u5982\u4e0b\u7ea6\u675f\uff1a</p> <ul> <li>\u5173\u4e8e\u5bc6\u5ea6 \\(\\sigma\\) \u7684\u51fd\u6570\uff0c\u4ec5\u4e0e\u70b9\u7684\u7a7a\u95f4\u4f4d\u7f6e \\(\\mathrm{x} = (x,y,z)\\) \u6709\u5173\uff0c\u800c\u4e0e\u89c6\u89d2\u65e0\u5173\uff1b</li> <li>\u5173\u4e8e\u989c\u8272 \\(\\mathrm{c}\\) \u7684\u51fd\u6570\uff0c\u4e0e\u70b9\u7684\u7a7a\u95f4\u4f4d\u7f6e \\(\\mathrm{x} = (x,y,z)\\) \u548c\u89c2\u5bdf\u65b9\u5411 \\(\\mathrm{d}\\) \u540c\u65f6\u6709\u5173\uff1b<ul> <li>\u8fd9\u5927\u6982\u4e0e NeRF \u5728\u4e0d\u540c\u89c6\u89d2\u4e0a\u5149\u5f71\u8868\u73b0\u7684\u826f\u597d\u4e5f\u6709\u8f83\u5927\u5173\u7cfb\uff1b</li> </ul> </li> <li>\u5b9e\u73b0\u4e0a\u662f\u5148\u901a\u8fc7 MLP \u7528 \\(\\mathrm{x}\\) \u8bad\u7ec3\u51fa \\(\\sigma\\) \u548c\u4e00\u4e2a\u4e2d\u95f4\u7279\u5f81\u5411\u91cf\uff0c\u518d\u5c06\u8fd9\u4e2a\u4e2d\u95f4\u5411\u91cf\u4e0e \\(\\mathrm{d}\\) \u62fc\u63a5\uff0c\u7ee7\u7eed\u653e\u5230 MLP \u4e2d\uff1b</li> </ul> <p>\u5229\u7528\u5982\u4e0a\u201c\u51fd\u6570\u201d\uff0c\u5177\u4f53\u6765\u8bf4\u64cd\u4f5c\u5982\u4e0b\uff1a</p> <ul> <li>\u5728\u573a\u666f\u4e2d\u5339\u914d\u7a7f\u8fc7\u7684\u76f8\u673a\u5149\u7ebf\u4ee5\u751f\u6210\u91c7\u6837\u7684 3D \u70b9\u96c6\u5408\uff1b</li> <li>\u4f7f\u7528\u8fd9\u4e9b\u70b9\u4ee5\u53ca\u5bf9\u5e94\u7684 2D \u89c6\u89d2\u65b9\u5411\u8f93\u5165\u5230\u7f51\u7edc\u4e2d\uff0c\u4ee5\u5f97\u5230\u989c\u8272\u548c\u5bc6\u5ea6\u96c6\u5408\uff1b</li> <li>\u4f7f\u7528\u4f20\u7edf\u7684\u4f53\u79ef\u6e32\u67d3\u6280\u672f\u7d2f\u79ef\u8fd9\u4e9b\u989c\u8272\u548c\u5bc6\u5ea6\u4ee5\u5f97\u5230 2D \u56fe\u50cf\uff1b</li> </ul> <p>\u4e3a\u4e86\u80fd\u591f\u8ba9 MLP \u8868\u793a\u66f4\u9ad8\u9891\u7387\u7684\u51fd\u6570\uff0c\u5f15\u5165\u4e86\u4f4d\u7f6e\u7f16\u7801(positional encoding)\u3002</p> <p>\u6b64\u5916\uff0c\u5173\u4e8e\u6e32\u67d3\uff0c\u4f7f\u7528\u7684\u662f\u4f20\u7edf\u7684\u4f53\u79ef\u6e32\u67d3\u65b9\u6cd5\uff0c\u7d2f\u79ef\u4e00\u6761\u5149\u7ebf\u4e0a\u7684\u989c\u8272\u548c\u5bc6\u5ea6\uff0c\u5f97\u5230\u6700\u7ec8\u7684\u989c\u8272\uff0c\u6240\u4f7f\u7528\u7684\u516c\u5f0f\u5982\u4e0b\uff1a</p> \\[ \\begin{aligned}     &amp; \\mathrm{C}(\\mathrm{r})=     \\int_{t_n}^{t_f}      T(t) \\cdot \\sigma\\left(         \\mathrm{r}(t)      \\right)  \\cdot \\mathrm{c} \\left(         \\mathrm{r}(t), \\mathrm{d}     \\right) \\cdot \\mathrm{d}t \\end{aligned},\\;\\; \\text{where } T(t) = \\exp\\left(     -\\int_{t_n}^t \\sigma\\left(\\mathrm{r}(s)\\right) \\; \\mathrm{d}s \\right) \\] <p>\u5bf9\u8fd9\u4e2a\u5f0f\u5b50\u7a0d\u4f5c\u89e3\u91ca\uff0c\\(t_n\\) \u548c \\(t_f\\) \u5206\u522b\u8868\u793a near \u548c far \u7684\u5149\u7ebf\u8fb9\u754c(bound)\uff0c\u5149\u7ebf\u7ed3\u679c \\(C(\\mathrm{r})\\) \u901a\u8fc7\u7d2f\u79ef\u8fd9\u4e24\u4e2a\u7aef\u70b9\u4e4b\u95f4\u7684\u6309\u6743\u7d2f\u79ef\u5f97\u5230\uff0c\u5176\u6743\u91cd\u4e3a \\(T(t)\\)\uff0c\u89c2\u5bdf\u5176\u5b9a\u4e49\u5f0f\u53ef\u53d1\u73b0\uff0c\u968f\u7740 \\(t\\) \u7684\u589e\u5927\uff0c\\(T(t) \\rightarrow 0\\)\uff0c\u5373\u7ea6\u5f80\u540e\u7684\u70b9\u7ea6\u4e0d\u5bb9\u6613\u88ab\u770b\u5230\uff0c\u8fd9\u4e5f\u662f\u7b26\u5408\u5e38\u8bc6\u7684\u3002\u800c\u7d2f\u79ef\u7684\u5bf9\u8c61\u4e3a \\(\\sigma(\\mathrm{r}(t)) \\cdot \\mathrm{c}(\\mathrm{r}(t), \\mathrm{d})\\)\uff0c\u5373\u5bc6\u5ea6\u548c\u989c\u8272\u7684\u4e58\u79ef\uff0c\u6ce8\u610f\u4e24\u4e2a\u53c2\u6570\u2014\u2014\u5bc6\u5ea6\u8868\u5f81\u5f62\u72b6\u7279\u5f81\uff0c\u4ec5\u4e0e\u7a7a\u95f4\u4f4d\u7f6e\u6709\u5173\uff1b\u800c\u989c\u8272\u540c\u65f6\u4e0e\u89c2\u5bdf\u89d2\u5ea6\u6709\u5173\uff0c\u8fd9\u6697\u542b\u7740\u5149\u5f71\u4fe1\u606f\u3002</p> <p>\u7136\u800c\uff0c\u7531\u4e8e\u79ef\u5206\u7684\u64cd\u4f5c\u6027\u5dee\uff0c\u6240\u4ee5\u4f7f\u7528\u4e00\u79cd\u79bb\u6563\u7684\u62bd\u6837\u7d2f\u79ef\u6765\u5b9e\u73b0\u8fd9\u4ef6\u4e8b\uff0c\u5c06\u5149\u7ebf\u5747\u5300\u5212\u5206\u4e3a \\(N\\) \u4e2a\u533a\u95f4\uff0c\u6309\u5747\u5300\u5206\u5e03\u5728\u6bcf\u4e2a\u70b9\u91c7\u6837\u4e00\u4e2a\u70b9\uff0c\u8fdb\u884c\u7d2f\u79ef\uff0c\u5373\u5bf9\u4e8e\u533a\u95f4 \\(t_i\\)\uff1a</p> \\[ t_i \\sim U \\left[      t_n + \\frac{i-1}{N} \\left( t_f - t_n \\right),      t_n + \\frac{i}{N} \\left( t_f - t_n \\right) \\right] \\] <p>\u5bf9\u5e94\u7684\u989c\u8272\u8ba1\u7b97\u516c\u5f0f\u6539\u5199\u4e3a\uff1a</p> \\[ \\begin{aligned} \\hat{C}(\\mathrm{r}) = \\sum_{i=1}^{N} T_i \\cdot (1 - \\exp(-\\sigma_i \\delta_i)) \\cdot \\mathrm{c}_i, \\;\\; \\text{where } T_i = \\exp\\left(     -\\sum_{j=1}^{i-1} \\sigma_j \\delta_j \\right) \\text{ and } \\delta_i = t_{i+1} - t_i \\end{aligned} \\] <p>\u5176\u4e2d\uff0c\\(\\sigma(\\mathrm{r}(t))\\) \u522b\u66ff\u6362\u4e3a \\((1-\\exp(-\\sigma_i\\delta_i))\\)\uff0c\u5728\u7ed3\u5408\u4e86\u533a\u95f4\u957f\u5ea6\u7684\u60c5\u51b5\u4e0b\u53c8\u91cd\u65b0\u5c06\u5bc6\u5ea6\u6620\u5c04\u56de\u4e86 \\([0,1]\\)\u3002</p> <p>\u5728\u4e4b\u540e\u7684\u7b56\u7565\u4e2d\uff0c\u8fd8\u4f1a\u5bf9\u91c7\u6837\u89c4\u5219\u505a\u8fdb\u4e00\u6b65\u4f18\u5316\u3002</p> <p>\u81f3\u6b64\u4e3a\u6b62\u662f NeRF \u4e3b\u8981\u7684\u65b9\u6cd5\uff0c\u4f46\u662f\u8fd9\u4e9b\u65b9\u6cd5\u4ecd\u7136\u4e0d\u8db3\u4ee5\u8ba9\u5b83\u8fbe\u5230\u6700\u5148\u8fdb\u7684\u6548\u679c\uff0c\u56e0\u6b64\u8fd9\u91cc\u5f15\u5165\u4e24\u4e2a\u6539\u8fdb\u63aa\u65bd\u3002</p> <ol> <li>\u4f7f\u7528\u4f4d\u7f6e\u7f16\u7801(positional encoding)\u6765\u4f7f MLP \u80fd\u591f\u652f\u6301\u66f4\u9ad8\u9891\u7684\u56fe\u50cf\u4fe1\u606f\uff1b</li> <li>\u4f7f\u7528\u7ed3\u6784\u5316\u7684\u91c7\u6837(hierarchical sampling)\u4f7f\u80fd\u591f\u66f4\u6709\u6548\u5730\u5bf9\u8fd9\u79cd\u9ad8\u9891\u8868\u793a\u8fdb\u884c\u91c7\u6837\uff1b</li> </ol> <p>\u4f4d\u7f6e\u7f16\u7801\u4e3a\u4e00\u4e2a \\(\\gamma : \\R \\rightarrow \\R^{2L}\\)\uff1a</p> \\[ \\gamma(p) = \\left( \\sin(2^0 \\pi p), \\cos(2^0 \\pi p), \\cdots, \\sin(2^{L-1} \\pi p), \\cos(2^{L-1} \\pi p) \\right) \\] <p>\u5c06 \\(\\gamma(\\cdot)\\) \u5e94\u7528\u4e8e \\(\\mathrm{x}\\) \u7684\u4e09\u4e2a\u5206\u91cf\uff08\u88ab\u6807\u51c6\u5316\u5230 \\([-1,1]\\) \u4e0a\uff09\u548c \\(\\mathrm{d}\\) \u7684\u4e24\u4e2a\u5206\u91cf\u4e0a\uff0c\u5b9e\u73b0\u7ef4\u5ea6\u63d0\u5347\uff0c\u4ee5\u6b64\u4f18\u5316\u5728\u9ad8\u9891\u5185\u5bb9\u4e0a\u7684\u8868\u73b0\u3002\u5728\u6587\u7ae0\u4e2d\u63d0\u5230\uff0c\\(L_\\mathrm{x} = 10, L_\\mathrm{d} = 4\\)\u3002</p> <p>\u800c\u5206\u5c42\u91c7\u6837\uff0c\u9488\u5bf9\u7684\u662f\u4e4b\u524d\u7684\u5747\u5300\u5212\u5206\u4e3a \\(N\\) \u4e2a\u533a\u95f4\u8fdb\u884c\u5747\u5300\u91c7\u6837\u3002\u663e\u7136\uff0c\u67d0\u4e9b\u201c\u7a7a\u6c14\u201d\u533a\u57df\u548c\u88ab\u906e\u6321\u7684\u533a\u57df\u5bf9\u6e32\u67d3\u7ed3\u679c\u5e76\u4e0d\u4f1a\u6709\u5f88\u5927\u5f71\u54cd\uff0c\u800c\u5728\u7a7a\u95f4\u4e0a\u8fd9\u4e9b\u5185\u5bb9\u53ef\u80fd\u5360\u4e86\u7edd\u5927\u90e8\u5206\uff08\u5c24\u5176\u662f\u6ca1\u6709\u534a\u900f\u660e\u7269\u4f53\u7684\u60c5\u51b5\u4e0b\uff09\uff0c\u5747\u5300\u91c7\u6837\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\u5c31\u663e\u5f97\u975e\u5e38\u4f4e\u6548\u3002</p> <p>\u5206\u5c42\u91c7\u6837\u7684\u5927\u81f4\u601d\u8def\u662f\uff0c\u9996\u5148\u4f7f\u7528\u4e00\u4e2a\u7c97\u7565(coarse)\u7684\u7f51\u7edc\uff0c\u5229\u7528 \\(N_c\\) \u4e2a\u7c97\u7565(coarse)\u7684\u5747\u5300\u91c7\u6837\u70b9\uff0c\u901a\u8fc7\u8ba1\u7b97 \\(\\hat{w}_i = normalize\\left( T_i \\cdot (1 - \\exp(-\\sigma_i \\delta_i)) \\right)\\) \u5f97\u5230\u6bcf\u4e2a\u70b9\u7684\u6743\u91cd\uff0c\u800c\u8fd9\u4e2a\u6743\u91cd\u5219\u53cd\u5e94\u4e86\u6bcf\u4e00\u4e2a\u91c7\u6837\u70b9\u9644\u8fd1\u6709\u6548\u70b9\u7684\u5206\u5e03\u60c5\u51b5\uff0c\u53ef\u4ee5\u770b\u4f5c\u4e00\u4e2a\u6982\u7387\u5bc6\u5ea6\u51fd\u6570(PDF)\u3002\u63a5\u4e0b\u6765\u6211\u4eec\u5728\u8fd9\u4e2a\u5206\u5e03\u7684\u57fa\u7840\u4e0a\u518d\u91c7\u6837\u5f97\u5230 \\(N_f\\) \u4e2a\u7cbe\u7ec6(fine)\u91c7\u6837\u70b9\uff0c\u4e0e \\(N_c\\) \u4e2a\u7c97\u7565(coarse)\u70b9\u4e00\u8d77\u653e\u5230\u7cbe\u7ec6(fine)\u7f51\u7edc\u4e2d\u8fdb\u884c\u8bad\u7ec3\u3002</p> <p>\u4f7f\u7528\u7684 loss \u5982\u4e0b\uff1a</p> \\[ \\mathcal{L} = \\sum_\\mathrm{r\\in \\text{Rays}} \\left[ \\left\\| \\hat{C}_c(\\mathrm{r}) - C_{g.t.}(\\mathrm{r}) \\right\\|_2^2 + \\left\\| \\hat{C}_f(\\mathrm{r}) - C_{g.t.}(\\mathrm{r}) \\right\\|_2^2 \\right] \\] \u53c2\u8003\u8d44\u6599 <ul> <li>https://zhuanlan.zhihu.com/p/360365941 \uff08\u7b14\u8bb0 \u5173\u4e8e\u4f53\u79ef\u6e32\u67d3\u8bb2\u5f97\u5f88\u6e05\u6670\uff09</li> <li>https://zhuanlan.zhihu.com/p/380015071 \uff08\u7b14\u8bb0\uff09</li> <li>https://wandb.ai/wandb_fc/chinese/reports/NeRF-Neural-Radiance-Fields-View-Synthesis---VmlldzozNDQxNzk \uff08\u4fa7\u91cd\u5982\u4f55\u4f7f\u7528\uff09</li> <li>https://www.youtube.com/watch?v=nCpGStnayHk\uff08\u4e0a\u9762\u90a3\u7bc7\u6587\u7ae0\u7684\u4ecb\u7ecd\u89c6\u9891\uff09</li> <li>https://blog.csdn.net/qq_43620967/article/details/124467551 \uff08\u7ffb\u8bd1\uff09</li> <li>https://blog.csdn.net/weixin_44292547/article/details/126042398 \uff08\u7ffb\u8bd1\uff09</li> <li>https://blog.csdn.net/weixin_44580210/article/details/122284120 \uff08\u7b14\u8bb0\uff09</li> </ul> <p>\u793e\u533a Pytorch \u590d\u73b0\u4ee3\u7801\u7684\u6ce8\u91ca\uff1ahttps://github.com/IsshikiHugh/nerf-pytorch</p>"},{"location":"pape_read/SA-MHR/","title":"[SA-HMR] Learning Human Mesh Recovery in 3D Scenes","text":"<p> \u7ea6 1927 \u4e2a\u5b57  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 6 \u5206\u949f</p> <p><code>3DV</code> <code>HMR</code> <code>Scene-Aware</code></p> <p>\u6587\u7ae0\u4fe1\u606f</p> <ul> <li>\u6587\u7ae0\u9898\u76ee\uff1aLearning Human Mesh Recovery in 3D Scenes</li> <li>\u4f5c\u8005\uff1a     Zehong Shen,      Zhi Cen,      Sida Peng,      Qing Shuai,      Hujun Bao,      Xiaowei Zhou</li> <li>\u9879\u76ee\u4e3b\u9875\uff1a\ud83d\udd17</li> <li>\u8bba\u6587\uff1a\ud83d\udd17</li> <li>\u4ee3\u7801\uff1a\ud83d\udd17</li> </ul>"},{"location":"pape_read/SA-MHR/#\u7b14\u8bb0","title":"\u7b14\u8bb0","text":""},{"location":"pape_read/SA-MHR/#\u4efb\u52a1\u5b9a\u4e49","title":"\u4efb\u52a1\u5b9a\u4e49","text":"<ul> <li>SA-HMR = scene-aware human mesh recovery</li> <li>\u9884\u5148\u7ed9\u5b9a\u626b\u63cf\u597d\u7684\u573a\u666f\uff0c\u518d\u6839\u636e\u5355\u5f20\u7167\u7247\u4f30\u8ba1\u4eba\u7684\u7edd\u5bf9\u4f4d\u7f6e\u548c\u59ff\u52bf</li> </ul>"},{"location":"pape_read/SA-MHR/#\u4f18\u52bf\u4e0e\u8d21\u732e","title":"\u4f18\u52bf\u4e0e\u8d21\u732e","text":"<ul> <li>\u76f8\u6bd4\u4f20\u7edf\u7684\u901a\u8fc7\u4f18\u5316\u8fed\u4ee3\u7684\u751f\u6210\u529e\u6cd5\uff0c\u672c\u65b9\u6cd5\u5728\u63a8\u65ad\u8fc7\u7a0b\u4e2d\u66f4\u52a0\u8fc5\u901f\uff1b</li> <li> \u95ee\u9898\uff1a\u6700\u4f18\u5316\u4e2d\u7684 contact regions \u7684 chamfer distance \u7ea6\u675f\u662f\u4e3a\u4e86\u4ec0\u4e48\uff1f \u5c3d\u53ef\u80fd\u589e\u52a0\u4e00\u56e2\u7684\u805a\u5408\u6027\uff1f \u662f\u3002</li> </ul> <p>\u6982\u62ec\u8d21\u732e\uff1a</p> <ol> <li>\u975e\u4f18\u5316\u505a\u6cd5\u7684\uff0c\u573a\u666f\u611f\u77e5\u7684\u3001\u5355\u7167\u7247\u3001\u9884\u7ed9\u573a\u666f\u7684\u4eba\u4f53\u7f51\u683c\u6062\u590d\u6846\u67b6\uff1b</li> <li>\u9884\u8bad\u7ec3\u7684 HMR \u7f51\u7edc\u4e0e\u5e73\u884c\u7f51\u7edc\u7684\u673a\u9047 cross-attention \u7684\u5904\u7406\u8bbe\u8ba1\uff0c\u662f\u897f\u5b89\u4e86\u5bf9\u4eba\u4f53\u59ff\u52bf\u548c\u573a\u666f\u51e0\u4f55\u7279\u5f81\u7684\u8054\u5408\u5b66\u4e60\uff1b</li> <li>\u5728\u51c6\u786e\u5ea6\u548c\u901f\u5ea6\u4e0a\u90fd\u8584\u7eb1\u4f18\u5316\u505a\u6cd5\u7684\u57fa\u7ebf\uff1b</li> </ol>"},{"location":"pape_read/SA-MHR/#\u65b9\u6cd5","title":"\u65b9\u6cd5","text":"<ul> <li>\u4f30\u8ba1\u4eba\u4f53\u7684\u5168\u5c40\u4f4d\u7f6e(absolute human position)\u3001\u573a\u666f\u63a5\u89e6\u70b9(dense scene contacts)\u3001\u4ee5\u53ca\u4e00\u4e2a\u573a\u666f\u611f\u77e5\u7684\u4eba\u4f53\u7f51\u683c(scene aware human mesh)\uff1b</li> <li>\u51c6\u5907\u5de5\u4f5c\uff1a<ul> <li>\u4eba\u4f53<ul> <li>\u4f7f\u7528 SMPL \u6765\u8868\u793a\u4eba\u4f53\uff0c\u8ba1\u7b97\u7f51\u683c\u9876\u70b9 \\(V\\in\\mathrm{R}^{6890\\times 3}\\)\uff1b</li> <li>\u4f7f\u7528 H36M \u5173\u952e\u70b9\u56de\u5f52\u77e9\u9635(joint regression matrix) \\(M \\in \\mathrm{R}^{14\\times 6890}\\)\uff1b<ul> <li> \u95ee\u9898\uff1a\u8fd9\u662f\u4ec0\u4e48\uff1f \u4e00\u4e2a from smpl to h36m \u7684\u77e9\u9635\u3002</li> </ul> </li> <li>\u8ba1\u7b97 3D \u5173\u952e\u70b9 \\(J\\in \\mathrm{R}^{14\\times 3} = MV\\)\uff1b</li> </ul> </li> <li>\u573a\u666f<ul> <li>\u7528\u4e00\u4e2a bbox \u53bb\u6846\u9009\u76ee\u6807\u4eba\u4f53\uff1b</li> <li>\u8f6c\u5316\u4e3a\u7279\u5b9a\u5927\u5c0f\u7684\u56fe\u50cf \\(I \\in \\mathrm{R}^{224\\times 224\\times 3}\\)\uff1b</li> <li>\u6839\u636e\u7ed9\u5b9a\u7684\u56fe\u50cf\u533a\u57df\u548c\u76f8\u673a\u53c2\u6570\uff0c\u5f97\u5230\u5bf9\u5e94\u4e8e\u7a7a\u95f4\u4e2d\u7684\u4e00\u4e2a\u89c6\u9525\u4f53\u7a7a\u95f4\uff0c\u9009\u53d6\u8fd9\u90e8\u5206\u70b9\u4e91\u4f5c\u4e3a\u8f93\u5165\u7684\u70b9\u4e91 \\(S \\in \\mathrm{R}^{N_S \\times 3}\\)\uff1b</li> </ul> </li> <li>\u4eba\u4e0e\u573a\u666f\u7684\u63a5\u89e6<ul> <li>\u4f7f\u7528 7 \u4e2a\u6700\u5bb9\u6613\u6210\u4e3a\u63a5\u89e6\u70b9\u7684\u533a\u57df\u548c 1 \u4e2a\u8868\u793a\u4e0d\u63a5\u89e6\u7684\u533a\u57df\uff0c\u8fd9 8 \u4e2a\u6807\u7b7e\u5728\u70b9\u4e91\u4e2d\u505a\u5206\u5272\u4efb\u52a1\uff1b</li> </ul> </li> </ul> </li> <li>\u4eba\u4f53\u6839\u4f4d\u7f6e\u548c\u573a\u666f\u63a5\u89e6\u70b9\u7684\u4f30\u8ba1\uff1a<ul> <li>\u6982\u8ff0<ul> <li>\u9996\u5148\u4f7f\u7528\u4e00\u4e2a\u7a00\u758f 3D CNN \u6765\u4f30\u8ba1\u5bc6\u5ea6\u573a\u666f\u7684\u63a5\u89e6\u70b9\u2014\u2014\u70b9\u4e91\u6807\u7b7e\u4efb\u52a1(point cloud labeling task)\u548c\u7edd\u5bf9\u7684\u4eba\u4f53\u4f4d\u7f6e\u2014\u2014\u6295\u7968\u5411\u91cf\u573a\u4fee\u6b63\u4efb\u52a1(voting vector field refinement task)\uff0c\u6839\u636e\u5f97\u5230\u7684\u7ed3\u679c\uff0c\u4ee5\u7edd\u5bf9\u4f4d\u7f6e\u4e3a\u4e2d\u5fc3\u8868\u793a\u63a5\u89e6\u70b9\uff1b<ul> <li> \u95ee\u9898\uff1a\u4ec0\u4e48\u662f voting vector field refinement task\uff1f\u540e\u9762\u6709\u5199\u3002</li> </ul> </li> </ul> </li> <li>\u7c97\u4f30\u6839<ul> <li>\u4f7f\u7528\u4e00\u4e2a CNN \u5f97\u5230\u4e00\u4e2a\u70ed\u56fe\u548c\u5f52\u4e00\u5316\u7684\u6df1\u5ea6\u56fe\uff1b</li> <li>\u4ece\u70ed\u56fe\u4e2d\u80fd\u4f7f\u7528 <code>argmax</code> \u5f97\u5230\u521d\u59cb\u7684\u4eba\u4f53\u6839\u90e8\u5ea7\u6807 \\((x,y)\\)\uff0c\u4ece\u6df1\u5ea6\u56fe\u4e2d\u4f30\u8ba1\u51fa \\(\\tilde Z\\)\uff1b</li> <li>\u5229\u7528\u76f8\u673a\u5185\u53c2\u53ef\u4ee5\u8ba1\u7b97\u51fa 3D \u7a7a\u95f4\u4e2d\u7684\u5ea7\u6807 \\((X,Y,Z)\\)\uff1a<ul> <li>\\(Z = \\tilde{Z} \\frac{f}{w},\\quad X = \\frac{x - c_x}{f} \\cdot Z,\\quad Y = \\frac{y-c_y}{f}\\cdot Z\\)</li> </ul> </li> <li>\u4ece\u7ed3\u679c\u6765\u770b\uff0c\\((x, y)\\) \u7684\u4f30\u8ba1\u662f\u6bd4\u8f83\u51c6\u786e\u7684\uff0c\u4f46 \\(\\tilde{Z}\\) \u7684\u6548\u679c\u6bd4\u8f83\u5dee\uff1b</li> </ul> </li> <li>3D \u7279\u5f81\u6784\u9020<ul> <li>\u5728\u70b9\u4e91\u4e2d\u5bfb\u627e ROI\u2014\u2014\u4ee5 \\(r=(X,Y,Z)\\) \u4e3a\u4e2d\u5fc3\uff0c\\(\\gamma_1\\) \u4e3a\u534a\u5f84\u7684\u7403\u5f62\u533a\u57df\uff0c\u7531 \\(\\tilde{Z}\\) \u7684\u4f30\u8ba1\u5e76\u4e0d\u51c6\u786e\uff0c\u6240\u4ee5\u5728\u8ddd\u79bb \\(\\gamma_2\\) \u7684\u3001\u6cbf\u7740 \\(z\\) \u8f74\u7684\u5730\u65b9\u518d\u91c7\u4e24\u4e2a\u7403\u5f62 ROI\uff1b<ul> <li> \u95ee\u9898\uff1a\u4e0d\u51c6\u786e\u7684\u662f \\(\\tilde{Z}\\)\uff0c\u53ef\u662f \\(X, Y\\) \u7684\u5f97\u5230\u4e5f\u4e0e \\(\\tilde{Z}\\) \u6709\u5173\u5440\uff1f \u900f\u89c6\u6295\u5f71\uff0c\u800c\u975e\u6b63\u4ea4\u6295\u5f71\u3002</li> </ul> </li> <li>\u63a5\u4e0b\u6765\u5c06 ROI \u4e2d\u7684\u70b9\u4e91\u4f53\u7d20\u5316\uff0c\u5e76\u4e14\u8ba1\u7b97\u5f97\u5230\u6bcf\u4e00\u4e2a\u4f53\u7d20\u7684\u7279\u5f81\uff0c\u7279\u5f81\u5305\u62ec\u4e24\u4e2a\u90e8\u5206\uff1a<ul> <li>\u7531\u4f53\u7d20\u4e2d\u5fc3 \\(\\overline{s}_i\\) \u6307\u5411\u6839 \\(r\\) \u7684\u504f\u79fb\u5411\u91cf(offset vector) \\(o_i = r - \\overline{s}_i\\)\uff1b</li> <li>\u5229\u7528\u76f8\u673a\u53c2\u6570\uff0c\u5c06 \\(\\overline{s}_i\\) \u6295\u5f71\u56de\u56fe\u7247\u540e\uff0c\u5728\u7279\u5f81 map \u4e0a\u8fdb\u884c\u53cc\u7ebf\u6027\u91c7\u6837\u5f97\u5230\u7684\u4e0d\u6295\u5f71\u56fe\u50cf\u7279\u5f81(unprojecting image feature) \\(\\hat{f}\\)\uff1b</li> </ul> </li> </ul> </li> <li>\u4f30\u8ba1\u4fee\u6b63\u6839\u548c\u573a\u666f\u63a5\u89e6\u70b9<ul> <li>\u4f7f\u7528\u4e00\u4e2a\u7a00\u758f 3D CNN \u6765\u5904\u7406 3D \u7279\u5f81\uff0c\u4ee5\u6c42\u4f18\u5316\u6839\u7684\u4f30\u8ba1\u5e76\u4f30\u8ba1\u573a\u666f\u63a5\u89e6\u4f4d\u7f6e\uff0c\u7f51\u7edc\u7684\u8f93\u51fa\u5305\u62ec\u4e09\u4e2a\u90e8\u5206\uff1a\u66f4\u65b0\u540e\u7684\u504f\u79fb\u5411\u91cf(updated offset vector) \\(o_i^*\\)\u3001\u5176\u7f6e\u4fe1\u5ea6(confidence) \\(c_i\\)\u3001\u4ee5\u53ca\u5173\u4e8e\u516b\u4e2a\u63a5\u89e6\u4f4d\u7f6e\u6216\u4e0d\u63a5\u89e6\u4f4d\u7f6e\u7684\u5206\u5272\u7ed3\u679c\uff1b</li> <li>\u4f7f\u7528 \\(r^* = \\sum \\limits_i c_i \\cdot (o^*_i + \\overline{s}_i)\\) \u6765\u8ba1\u7b97\u4f18\u5316\u540e\u7684\u6839\uff0c\u5176\u4e2d \\(i\\) \u4e3a ROI \u4e2d\u7684\u4f53\u7d20\u7684 index\uff08\u4e4b\u524d\u63d0\u5230\u7684 voting vector field refinement task\uff09\uff1b</li> <li>\u63a5\u89e6\u70b9\u5206\u7c7b\u5305\u62ec 7 \u4e2a\u6700\u5bb9\u6613\u6210\u4e3a\u63a5\u89e6\u70b9\u7684\u5206\u7c7b\uff0c\u548c 1 \u4e2a\u7528\u6765\u8868\u793a\u4e0d\u63a5\u89e6\u7684\u7c7b\u522b\uff0c\u901a\u8fc7\u53d6\u5f97\u5206\u6700\u9ad8\u7684\u5f97\u5230\u70b9\u4e91\u7684\u6807\u7b7e\uff0c\u6700\u7ec8\u5f97\u5230\u4e00\u4e2a\u6709\u6807\u7b7e\u7684\u70b9\u4e91\u6570\u636e\u4f5c\u4e3a\u4e4b\u540e\u7684\u8f93\u5165\uff08\u4e4b\u524d\u63d0\u5230\u7684 point cloud labeling task\uff09\uff1b</li> </ul> </li> </ul> </li> <li>SA-HMR\uff1a<ul> <li></li> <li>\u53d7\u6570\u636e\u96c6\u9650\u5236\uff0c\u672c\u90e8\u5206\u7684\u5de5\u4f5c\u4ee5\u9884\u8bad\u7ec3\u597d\u7684 METRO \u4e3a\u57fa\u7840 SA-HMR \u6dfb\u52a0\u4e00\u4e2a\u5e73\u884c\u7684\u573a\u666f\u76f8\u5173\u7f51\u7edc\uff0c\u4f7f\u7528\u4ea4\u53c9\u6ce8\u610f\u529b\u673a\u5236\u6765\u63d0\u9ad8 METRO \u7684\u573a\u666f\u611f\u77e5\uff1b</li> <li>METRO<ul> <li>\u4f7f\u7528\u81ea\u6ce8\u610f\u529b\u673a\u5236\u5b9e\u73b0\u5355\u76ee\u7684\u4eba\u4f53\u7f51\u683c\u6062\u590d\uff1b</li> <li>\u63d0\u53d6\u5168\u5c40\u7684 CNN \u7279\u5f81 \u27a1\ufe0f \u5c06\u7279\u5f81\u5408\u5e76\u5230\u65e0\u59ff\u52bf\u7684 SMPL \u7f51\u683c\u9876\u70b9\u4e0a \u27a1\ufe0f \u9884\u6d4b\u5305\u542b\u5f62\u4f53\u7684\u59ff\u52bf\uff1b</li> </ul> </li> <li>\u4ea4\u53c9\u6ce8\u610f\u529b\u4e0b\u7684 METRO<ul> <li>\u9996\u5148\u4f7f\u7528 METRO \u9aa8\u5e72\u90e8\u5206\u4e2d\u7684 CNN \u4ece\u56fe\u7247\u4e2d\u63d0\u53d6\u51fa\u56fe\u50cf\u7279\u5f81\uff0c\u5e76\u6620\u5c04\u3001\u6c60\u5316\u5f97\u5230\u4e0e\u4eba\u4f53 mesh \u9876\u70b9\u4e2a\u6570\u4e00\u81f4\u7684 tokens\uff1b</li> <li>\u5c06\u521d\u59cb\u9876\u70b9\u4e0e\u8fd9\u4e9b\u751f\u6210\u7684 token \u76f4\u63a5\u62fc\u63a5\uff0c\u585e\u8fdb transformer \u91cc\uff0c\u4ee5\u6b64\u6765\u8ba9 transformer \u80fd\u66f4\u597d\u7684\u6ce8\u610f\u5230\u8bed\u4e49\u4e0a\u66f4\u76f8\u5173\u7684\u90e8\u5206\uff1b</li> <li>\u4e3a\u4e86\u5c06\u7528\u6765\u4f30\u8ba1\u4eba\u4f53\u59ff\u6001\u7684 METRO \u4e0e\u9879\u76ee\u63d0\u51fa\u7684\u573a\u666f\u7f51\u7edc\u76f8\u7ed3\u5408\uff0c\u4f7f\u7528\u4e86\u4ea4\u53c9\u6ce8\u610f\u529b(cross attention)\uff1b<ul> <li>\u5373 Q \u548c K \u4e0d\u540c\u5c5e\u4e00\u4e2a\u6a21\u5757\uff0c\u5728\u672c\u9879\u76ee\u7684\u8bed\u5883\u4e0b\uff0c\u6307\u4e24\u4e2a\u6a21\u5757\u7684 Q \u548c K \u90fd\u6765\u81ea\u5bf9\u65b9\uff1b</li> </ul> </li> <li>\u8fd9\u91cc\u5bf9 METRO \u4f7f\u7528\u5171\u4eab\u6743\u91cd\u7684\u56de\u5f52\u5c42\uff0c\u5177\u4f53\u5e94\u7528\u5728\u4ece\u9010\u70b9\u7279\u5f81\u5230\u70b9\u4f4d\u7f6e\u7684\u56de\u5f52\uff1b<ul> <li>\u56e0\u6b64\uff0c\u5f53\u7279\u5f81\u76f8\u4f3c\u7684\u70b9\u88ab\u8f93\u5165\u4ee5\u540e\uff0c\u8f93\u51fa\u7684\u5ea7\u6807\u4e5f\u503e\u5411\u4e8e\u76f8\u4f3c\uff0c\u76f8\u5f53\u4e8e\u8bf4\u5728\u505a scene image \u548c real image \u7684\u7279\u5f81\u5339\u914d\uff1b</li> <li>\u8fd9\u9690\u5f0f\u5730\u5c06\u76f8\u4f3c\u7684\u4eba\u4f53\u9876\u70b9\u548c\u573a\u666f\u70b9\u5bf9\u9f50\uff0c\u4ee5\u4fbf\u4e8e transformer \u5bfb\u627e\u5bf9\u5e94\u5173\u7cfb\uff1b</li> </ul> </li> </ul> </li> </ul> </li> <li>Loss<ul> <li>\u7b2c\u4e00\u90e8\u5206 \u00b7 \u6839\u548c\u63a5\u89e6\u70b9<ul> <li>\\(L_ {RC} = L_ {R2D} + w_ {RZ} \\cdot L_ {RZ} + L_ {ROV} + L_ {R3D} + L_ {C}\\)</li> <li>\\(L_ {R2D}\\) \u662f\u6839\u7684\u70ed\u529b\u56fe\u7684 MSE loss\uff1b</li> <li>\\(L_{RZ},L_{ROV},L_{R3D}\\) \u662f\u76f8\u5bf9\u6df1\u5ea6\u3001\u504f\u79fb\u5411\u91cf\u3001\u6839\u7684 3D \u5ea7\u6807\u7684 L1 loss\uff1b</li> <li>\\(L_C\\) \u662f\u63a5\u89e6\u70b9\u7684\u6807\u7b7e\u7684\u4ea4\u53c9\u71b5 loss\uff1b</li> </ul> </li> <li>\u7b2c\u4e8c\u90e8\u5206 \u00b7 HMR<ul> <li>\\(L_{\\mathrm{HMR}}=L_\\mathrm{V}+L_\\mathrm{J}+L_{\\mathrm{CP}}+L_\\mathrm{GV}\\)</li> <li>\u56db\u4e2a term \u5206\u522b\u662f\u5e73\u79fb\u5bf9\u9f50\u7684\u4eba\u4f53\u9876\u70b9\u7684\u3001\u4eba\u4f53\u5173\u952e\u70b9\u7684\u3001\u91cd\u5efa\u7684\u63a5\u89e6\u70b9\u7684\u3001\u5168\u5c40\u4eba\u4f53\u9876\u70b9\u7684 L1 loss\uff1b</li> </ul> </li> </ul> </li> </ul>"},{"location":"pape_read/SA-MHR/#\u6570\u636e\u96c6","title":"\u6570\u636e\u96c6","text":"<ul> <li>RICH<ul> <li>\u573a\u666f\uff1a6 \u5ba4\u5916 &amp; 2 \u5ba4\u5185</li> <li>\u4e0d\u5904\u7406\u591a\u4eba\u3001\u4e0d\u5904\u7406 bbox \u51fa\u753b\u9762\u7684\u60c5\u51b5</li> </ul> </li> <li>PROX <ul> <li>\u573a\u666f\uff1a12 \u5ba4\u5185</li> </ul> </li> </ul>"},{"location":"pape_read/SA-MHR/#\u6548\u679c\u5ea6\u91cfmetrics","title":"\u6548\u679c\u5ea6\u91cf(metrics)","text":"<ul> <li>HMR<ul> <li>G-MPJPE: Global Mean-Per-Joint-Position-Error</li> <li>G-MPVE: Global Mean-Per-Vertex-Error</li> <li>\u5373\u5168\u5c40\u7684 JP \u548c V \u7684 L2 \u8bef\u5dee\uff0c\u76f8\u5bf9\u7684\uff0c\u540e\u9762\u8fd8\u6709\u4e00\u4e2a\u975e\u5168\u5c40\u7684\u8bef\u5dee\uff0c\u8868\u793a\u7684\u662f\u8282\u70b9/\u9876\u70b9\u76f8\u5bf9\u4e8e pelvis \u7684\u5ea7\u6807\u7684\u8bef\u5dee\uff0c\u5168\u5c40\u7684\u8bef\u5dee\u66f4\u80fd\u4f53\u73b0\u5728\u5168\u5c40\u8303\u56f4\u5185\u7684\u6548\u679c\uff1b</li> </ul> </li> <li>contact<ul> <li>PenE: Penetration Error <ul> <li>\u5373\u7a7f\u6a21\u8bef\u5dee\uff0c\u5bf9\u4e8e\u6240\u6709\u7a7f\u5165\u6a21\u8868\u9762\u7684\u70b9\uff0c\u7d2f\u52a0\u5176\u5230\u8868\u9762\u7684\u8ddd\u79bb\uff0c\u8d8a\u7a7f\u8d8a\u574f\uff1b</li> <li> \u95ee\u9898\uff1a\u5177\u4f53\u6765\u8bf4\u5982\u4f55\u8861\u91cf v to scene \u7684\u8ddd\u79bb\uff1f\u5982\u679c\u7a7f\u4e86\u4e00\u4e2a\u6241\u5e73\u6a21\u662f\u5426\u8868\u8fbe\u4e0d\u660e\u663e\uff1f \u662f\uff0c\u6240\u4ee5\u8fd9\u4e2a\u6807\u51c6\u53ea\u662f\u793a\u610f\uff0c\u5b9e\u9645\u5f88\u96be\u505a\u3002</li> </ul> </li> <li>ConFE: Contact Failure Error<ul> <li>\u524d\u4e00\u4e2a term \u8868\u793a\u5f53\u8fd9\u91cc\u662f\u63a5\u89e6\u65f6\uff0c\u8981\u5c3d\u53ef\u80fd\u63a5\u8fd1\uff1b\u540e\u4e00\u4e2a term \u8868\u793a\u5f53\u8fd9\u91cc\u4e0d\u63a5\u89e6\u65f6\uff0c\u8981\u5c3d\u53ef\u80fd\u4e0d\u7a7f\u6a21\uff1b</li> <li> \u95ee\u9898\uff1a\u7b2c\u4e8c\u4e2a term \u662f\u4e0d\u662f\u4e0e PenE \u7684\u529f\u80fd\u91cd\u5408\u4e86\uff1f \u6709\u4e00\u90e8\u5206\u91cd\u5408\uff0c\u4f46\u662f\u662f\u5fc5\u8981\u7684\uff0c\u5b83\u8861\u91cf\u7684\u6709\u4e24\u4e2a\u5185\u5bb9\uff1a1. \u5c5e\u4e8e\u63a5\u89e6\u70b9\u7684\uff0c\u8981\u5c3d\u53ef\u80fd\u201c\u63a5\u89e6\u201d\uff1b2. \u4e0d\u5c5e\u4e8e\u63a5\u89e6\u70b9\u7684\uff0c\u8981\u5c3d\u53ef\u80fd\u201c\u4e0d\u63a5\u89e6\u201d\uff1b</li> </ul> </li> </ul> </li> </ul>"},{"location":"pape_read/SAMP/","title":"[SAMP] Stochastic Scene-Aware Motion Prediction","text":"<p> \u7ea6 1427 \u4e2a\u5b57  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 5 \u5206\u949f</p> <p><code>3DV</code> <code>Human-Motion</code> <code>Scene-Aware</code></p> <p>\u6587\u7ae0\u4fe1\u606f</p> <ul> <li>\u6587\u7ae0\u9898\u76ee\uff1aStochastic Scene-Aware Motion Prediction</li> <li>\u4f5c\u8005\uff1aMohamed Hassan, Duygu Ceylan, Ruben Villegas, Jun Saito, Jimei Yang, Yi Zhou, and Michael Black</li> <li>\u9879\u76ee\u4e3b\u9875\uff1a\ud83d\udd17</li> <li>\u8bba\u6587\uff1a\ud83d\udd17</li> <li>Demo\uff1a\ud83d\udd17</li> <li>\u4ee3\u7801\uff1a\ud83d\udd17</li> </ul>"},{"location":"pape_read/SAMP/#\u8bba\u6587\u7b14\u8bb0","title":"\u8bba\u6587\u7b14\u8bb0","text":""},{"location":"pape_read/SAMP/#\u95ee\u9898\u4e0e\u73b0\u72b6\u4e0e\u8109\u7edc","title":"\u95ee\u9898\u4e0e\u73b0\u72b6\u4e0e\u8109\u7edc","text":"<p>\u52a8\u4f5c\u751f\u6210\u7684\u5b9e\u73b0\u5212\u5206\u4e3a\u4e09\u4e2a\u90e8\u5206\uff1a</p> <ol> <li>\u5bfc\u822a\u81f3\u4ea4\u4e92\u76ee\u6807\uff1b</li> <li>\u5bfb\u627e\u4ea4\u4e92\u63a5\u89e6\u70b9(contact point)\uff1b</li> <li>\u751f\u6210\u4ea4\u4e92\u52a8\u4f5c\uff0c\u5e76\u4e14\u9700\u8981\u4fdd\u8bc1\u751f\u6210\u7ed3\u679c\u4f1a\u81ea\u7136\u53d8\u5316\uff08\u4ee5\u7b26\u5408\u73b0\u5b9e\u611f\u89c9\uff09\uff1b</li> </ol> <p>\u7531\u4e8e\u8fd9\u4e9b\u52a8\u4f5c\u4e2d\u6709\u4e00\u90e8\u5206\u662f\u201c\u5faa\u73af\u7684(cyclic)\u201d\uff0c\u4e00\u90e8\u5206\u662f\u201c\u4e0d\u5faa\u73af\u7684(acyclic)\u201d\uff0c\u6240\u4ee5\u9700\u8981\u4e00\u4e2a\u63a8\u7406\u7cfb\u7edf\u6765\u534f\u8c03\u4e24\u8005 -&gt; \u63d0\u51fa SAMP\uff0c\u573a\u666f\u53ef\u611f\u77e5\u7684\u52a8\u4f5c\u9884\u6d4b\u7cfb\u7edf(Scene-Aware Motion Prediction)\uff1a</p> <ul> <li>\u968f\u673a\u6a21\u578b</li> <li>\u8f93\u5165 3D \u573a\u666f</li> <li>\u91c7\u6837\u6709\u6548\u4ea4\u4e92\u76ee\u6807</li> <li>\u751f\u6210\u76ee\u6807\u9650\u5236\u7684\u3001\u573a\u666f\u611f\u77e5\u7684\u3001\u903c\u771f\u7684\u4eba\u4f53\u52a8\u4f5c\u5e8f\u5217</li> </ul>"},{"location":"pape_read/SAMP/#\u8d21\u732e","title":"\u8d21\u732e","text":"<ol> <li>\u65b0\u9896\u7684\u968f\u673a\u6a21\u578b\u4ee5\u751f\u6210\u5b9e\u65f6\u7684\u3001\u591a\u6837\u7684\u3001goal driven \u7684\u4eba\u7269\u5bf9\u573a\u666f\u7684\u4ea4\u4e92\uff1b</li> <li>\uff08\u5bf9 1. \u7684\u7ec6\u5316\uff09\u7ed9\u5b9a\u76ee\u6807\u51e0\u4f55\u4f53\u540e\u751f\u6210\u53ef\u4fe1\u7684\u3001\u52a8\u4f5c\u76f8\u5173\u7684\u4ea4\u4e92\u4f4d\u7f6e\u548c\u65b9\u5411\u7684\u65b0\u5efa\u6a21\u65b9\u6cd5\uff1b</li> <li>\uff08\u5bf9 1. \u7684\u7ec6\u5316\uff09\u5c06\u5177\u4f53\u8def\u5f84\u89c4\u5212\u7eb3\u5165\u53d8\u5206\u8fd0\u52a8\u5408\u6210\u7f51\u7edc\uff0c\u5b9e\u73b0\u5728\u590d\u6742\u573a\u666f\u4e2d\u7684\u5bfc\u822a\uff1b</li> <li>\u5305\u542b\u591a\u6837\u4eba\u4f53\u573a\u666f\u4ea4\u4e92\u6570\u636e\u7684\u65b0\u7684 MoCap \u6570\u636e\u96c6\uff1b</li> </ol>"},{"location":"pape_read/SAMP/#\u65b9\u6cd5","title":"\u65b9\u6cd5","text":"<ul> <li><code>MotionNet</code>(core)\uff1a\u4e00\u4e2a cVAE\uff0c\u8f93\u5165\u76ee\u6807\u5bf9\u8c61\u548c\u52a8\u4f5c\uff0c<code>MotionNet</code> \u6bcf\u4e00\u5e27\u5c06\u91c7\u6837\u4e00\u4e2a\u6f5c\u5411\u91cf\uff0c\u8054\u5408\u524d\u4e00\u5e27\u7684\u52a8\u4f5c\u6765\u63a7\u5236\uff08\u5373\u9884\u6d4b\uff09\u4e0b\u4e00\u4e2a\u52a8\u4f5c\uff1b<ul> <li>\u5305\u542b\u4e00\u4e2a encoder \u548c\u4e00\u4e2a decoder\uff1b  </li> <li>\\(X_i\\) \u8868\u793a\u7b2c \\(i\\) \u65f6\u523b\u7684\u72b6\u6001\uff0c\\(Z\\) \u4e3a\u751f\u6210\u7684\u6f5c\u5411\u91cf\uff0c\\(I\\) \u4e3a\u4ea4\u4e92\u5bf9\u8c61(interaction objects)\uff08\u4ee5\u4eba\u7269\u4e3a\u539f\u70b9\u7684\u4f53\u7d20\u7a7a\u95f4\u8868\u8fbe\uff09\uff1b<ul> <li>encoder \u5305\u542b Interaction Encoder \u548c State Encoder\uff0c\u5206\u522b\u5c06 \\(I\\) \u548c \\(X\\) \u7f16\u7801\uff08\u4f7f\u7528 3 \u4e2a FC\uff09\u4e3a\u4f4e\u7ef4\u5ea6\u5411\u91cf\uff0c\u518d\u62fc\u63a5\u8d77\u6765\u8f93\u5165\u5230\u4e24\u4e2a\u5b8c\u5168\u76f8\u540c\u7684 FC \u4e2d\u4ee5\u9884\u6d4b \\(\\mu\\) \u548c \\(\\sigma\\) \u5373\u4e00\u4e2a\u6f5c\u5d4c\u5165\u7a7a\u95f4(latent embedding space)\uff1b</li> <li>\u4e8e\u662f\u6211\u4eec\u53ef\u4ee5\u4ece\u4ee5\u4e0a\u8ff0\u7ed3\u679c\u4e3a\u53c2\u6570\u7684\u9ad8\u65af\u5206\u5e03\u4e2d\u91c7\u6837\u51fa\u6f5c\u5411\u91cf \\(Z\\) \u4f5c\u4e3a decoder \u7684\u8f93\u5165\uff1b </li> <li> \u95ee\u9898\uff1a\u4e3a\u4ec0\u4e48\u8fd9\u91cc\u7684 \\(j^r_i\\) \u662f 6d \u7684\uff1f\uff08\u5b9e\u9645\u4e0a\u662f 9d \u65cb\u8f6c\u77e9\u9635\u4e2d\u4f1a\u53d8\u5143\u6709 6 \u4e2a\uff0c\u901a\u8fc7\u8fd9\u4e2a 6d \u7684\u5411\u91cf\u80fd\u591f\u8fd8\u539f\u51fa\u8fd9\u4e2a\u77e9\u9635\uff0c\u800c\u81f3\u4e8e\u4e3a\u4ec0\u4e48\u7528\u8fd9\u4e2a 6d \u5185\u5bb9\u800c\u975e\u89d2\u5ea6\uff0c\u53ef\u4ee5\u53c2\u8003\u8fd9\u7bc7\u6587\u7ae0\uff0c\u89d2\u5ea6\u5177\u6709\u7a81\u53d8\u4e0d\u8fde\u7eed\uff1a\\(2pi = 0\\)\uff0c\u6240\u4ee5\u90fd\u4e0d\u600e\u4e48\u7528\u4e86\uff09</li> <li>decoder \u662f\u4e00\u4e2a MoE\uff0c\u6709 Prediction Network \u548c Gating Network \u4e24\u4e2a\u90e8\u5206\uff0c\u524d\u8005\u8d1f\u8d23\u751f\u6210\u9884\u6d4b\u7ed3\u679c\uff0c\u540e\u8005\u8d1f\u8d23\u751f\u6210\u5404\u4e2a\u4e13\u5bb6\u7f51\u7edc\u7684\u7ed3\u679c\u5408\u6210\u8fc7\u7a0b\u4e2d\u7684\u6743\u91cd\uff1b</li> </ul> </li> <li>\u4f7f\u7528\u7684 loss \u4e3a \\(||\\hat{X_i} - X_i||^2_2 + \\beta_1\\mathop{KL}(Q(Z|X_i, X_{i-1}, I) || p(Z))\\)\uff1b</li> <li>\u7279\u522b\u6ce8\u610f\uff0c\u5728\u6d4b\u8bd5\u8fc7\u7a0b\u4e2d\uff0c\u6211\u4eec\u4ec5\u4ec5\u4ece\u6807\u51c6\u6b63\u6001\u5206\u5e03\u4e2d\u91c7\u6837\u6f5c\u5411\u91cf\uff1b<ul> <li> \u95ee\u9898\uff1a\u4e3a\u4ec0\u4e48\uff1f</li> </ul> </li> </ul> </li> <li><code>GoalNet</code>\uff1a\u7528\u6765\u751f\u6210\u4ea4\u4e92\u70b9\u548c\u4ea4\u4e92\u65b9\u5411(contact points and orientations)\uff0c\u5373\u76ee\u6807(goals)\uff1b<ul> <li>\u8be5\u6a21\u5757\u8ba9 SAMP \u80fd\u591f\u9002\u5e94\u4e0d\u540c\u7684\u76ee\u6807\u51e0\u4f55\u4f53\uff1b</li> <li>\u540c\u6837\u5305\u542b\u4e00\u4e2a encoder \u548c\u4e00\u4e2a decoder\uff1b  </li> <li>\\(I\\) \u4e3a\u4ea4\u4e92\u5bf9\u8c61(interaction objects)\uff08\u4ee5\u7269\u4f53\u81ea\u8eab\u4e3a\u539f\u70b9\u7684\u4f53\u7d20\u7a7a\u95f4\u8868\u8fbe\uff09\uff0c\\(\\{g^p, g^d\\}\\) \u5206\u522b\u4e3a\u76ee\u6807(goal)\u7684\u4f4d\u7f6e\u548c\u65b9\u5411\uff0c\\(Z_{goal}\\) \u4e3a\u6f5c\u5411\u91cf\uff1b</li> <li>\u4f7f\u7528\u7684 loss \u4e3a \\(||\\hat{g}^p - g^p||^2_2 + ||\\hat{g}^d - g^d||^2_2 + \\beta_2 \\mathop{KL}(Q(Z_{goal}|g^p, g^d, I) || p(Z_{goal}))\\)\uff1b</li> </ul> </li> <li><code>Path Planning Module</code>\uff1a\u4f7f\u7528 A* \u5bfb\u8def\u4ee5\u907f\u969c(obstacles)\uff1b<ul> <li>\u751f\u6210\u7684\u8def\u7ebf\u4e2d\u5c06\u4f1a\u6709\u8bb8\u591a\u8def\u70b9(way-points)\u4f5c\u4e3a\u8fc7\u7a0b\u4e2d\u7684\u76ee\u6807\u70b9(goals)\uff1b</li> <li>explicit A*\uff1b</li> <li>\u6240\u8c13\u7684\u201c\u8def\u5f84\u201d\uff0c\u5177\u4f53\u6307\u7684\u662f\u4e00\u7cfb\u5217\u8def\u70b9(way point)\uff0c\u901a\u8fc7\u8fd9\u4e9b\u201c\u5c0f\u76ee\u6807\u201d\uff0c\u6765\u4e00\u6b65\u6b65\u5f15\u5bfc\u865a\u62df\u4eba\u5230\u8fbe\u76ee\u6807\u524d\uff0c\u5728\u6700\u540e\u4e00\u4e2a\u8def\u70b9\u8fdb\u884c\u76ee\u6807\u52a8\u4f5c\u7684\u751f\u6210\uff1b</li> <li>\u8fd9\u4e00\u65b9\u9762\u4e0e NSM \u4f7f\u7528 sensor \u68c0\u6d4b\u4e0d\u540c\uff0c\u66f4\u52a0\u9ad8\u6548\uff1b</li> </ul> </li> </ul> <p>\u8fd9\u4e9b\u72ec\u7acb\u7ec4\u4ef6\u4f7f SAMP \u79f0\u4e3a\u7b2c\u4e00\u4e2a\u89e3\u51b3\u751f\u6210\u591a\u6837\u52a8\u6001\u52a8\u4f5c\u5e8f\u5217\uff0c\u5e76\u4e14\u80fd\u771f\u5b9e\u5e94\u7528\u4e8e\u590d\u6742\u573a\u666f\u4e2d\u7684\u3002 - [x] \u95ee\u9898\uff1a\u8fd9\u91cc\u6700\u5173\u952e\u7684\u662f\u54ea\u4e00\u4e2a\u90e8\u5206\uff1f\u4e0e NSM \u76f8\u6bd4\u72ec\u521b\u6027\u7684\u5730\u65b9\u5177\u4f53\u5728\u54ea\u91cc\uff1f\u5230\u5e95\u5982\u4f55\u5b9a\u4e49\u201cdiverse human-scene interactions\u201d\uff0c\u548c Motion VAE \u90a3\u79cd\u751f\u6210\u5206\u5e03\u6a21\u578b\u7684\u6709\u4ec0\u4e48\u533a\u522b\uff1f\uff08Motion VAE \u662f\u5229\u7528\u5206\u5e03\u7684\u6781\u5927\u4f3c\u7136\u4f30\u8ba1\u5f97\u5230\u7ed3\u679c\u7684\uff0cMoGlow \u8c8c\u4f3c\u548c\u573a\u666f\u6ca1\u5173\u7cfb\uff09</p> <p>\u56e0\u6b64\uff0c\u8bad\u7ec3 SAMP \u6240\u9700\u7684\u6570\u636e\u96c6\u9700\u8981\u4e30\u5bcc\u4e14\u4e0d\u540c\u7684\u573a\u666f\u4ea4\u4e92\uff0c\u73b0\u6709\u6570\u636e\u96c6\u7f3a\u5c11\u4ea4\u4e92\u884c\u4e3a -&gt; \u81ea\u5df1\u505a\u4e86\u4e00\u4e2a\u3002</p> <ul> <li> \u95ee\u9898\uff1atrajectory \u548c path \u548c pose \u7684\u533a\u522b\uff1f\u662f\u6307\u5305\u62ec\u4e86\u52a8\u4f5c\u548c\u884c\u52a8\u8def\u7ebf\u7684\u8f68\u8ff9\u5417\uff1f</li> </ul> <p>\u5982\u4f55\u8861\u91cf\u4eba\u4f53\u52a8\u4f5c\u7684\u968f\u673a\u6027(stochasticity)\u662f\u4e00\u4e2a\u6709\u5f85\u63a2\u7d22\u7684\u9886\u57df\u3002</p>"},{"location":"pape_read/SAMP/#\u8bad\u7ec3\u7b56\u7565","title":"\u8bad\u7ec3\u7b56\u7565","text":"<p>\u4f7f\u7528\u6b63\u5e38\u7684\u76d1\u7763\u8bad\u7ec3\u4f1a\u5bfc\u81f4\u9519\u8bef\u7d2f\u79ef(accumulation of error)\uff0c\u56e0\u4e3a\u4e00\u6b21\u7684\u8f93\u51fa\u4f1a\u4f5c\u4e3a\u8f93\u5165\u8fdb\u5165\u5230\u4e0b\u4e00\u4e2a\u7f51\u7edc\u3002\u6240\u4ee5 SAMP \u91c7\u7528\u9884\u8ba2\u91c7\u6837(scheduled sampling)\uff0c\u5b83\u80fd\u591f\u7a33\u5b9a\u751f\u6210\u957f\u65f6\u95f4\u7684\u52a8\u4f5c\u9884\u4f30\u3002</p> <p>\u5177\u4f53\u6765\u8bf4\uff0c\u4e0a\u4e00\u6b21\u7684\u9884\u6d4b\u7ed3\u679c\u4ee5 \\(1-P\\) \u7684\u6982\u7387\u4f5c\u4e3a\u4e0b\u4e00\u6b21\u9884\u6d4b\u7684\u8f93\u5165\uff0c\u5176\u4e2d \\(P\\) \u7684\u5b9a\u4e49\u5982\u4e0b\uff1a </p>"},{"location":"pape_read/SAMP/#\u5b9e\u9a8c\u548c\u8bc4\u4f30","title":"\u5b9e\u9a8c\u548c\u8bc4\u4f30","text":"<p>\u5728\u540c\u521d\u59cb\u6761\u4ef6\u4e0b\u591a\u6b21\u6267\u884c\u540c\u4e00\u4efb\u52a1\uff0c\u4f7f\u7528 APD(Average Pairwise Distance) \u6765\u8861\u91cf\u5176\u8fd0\u52a8\u5e45\u5ea6\uff1a </p>"},{"location":"pape_read/SAMP/#\u4ee3\u7801\u9605\u8bfb","title":"\u4ee3\u7801\u9605\u8bfb","text":""},{"location":"pape_read/SAMP/#motionnet","title":"MotionNet","text":"<p>\u516c\u5f0f\u63a8\u5bfc\uff1a</p> <p>\u6b63\u6001\u5206\u5e03\u7684\u71b5\u516c\u5f0f</p> <p>\u5047\u8bbe \\(x\\sim N(\\mu, \\sigma^2)\\)\uff0c\u4e8e\u662f\u6709\uff1a</p> <p>  \u5e76\u4e14\u6709\u7ed3\u8bba\uff1a</p> \\[ \\int_{-\\infty}^{\\infty} e^{-x^2} \\mathrm{d}x = \\sqrt{\\pi} \\] <p>\u90a3\u4e48\u6709\u5176\u71b5\u516c\u5f0f\uff1a</p> \\[ \\begin{aligned}     -\\int_{-\\infty}^{\\infty} p(x)\\ln p(x) \\mathrm{d}x     &amp;=     -\\int_{-\\infty}^{\\infty}\\frac{1}{\\sqrt{2\\pi\\sigma^2}}\\exp\\left(         -\\frac{(x-\\mu)^2}{\\sqrt{2\\sigma^2}}      \\right)     \\ln\\left[     \\frac{1}{\\sqrt{2\\pi\\sigma^2}} \\exp\\left(         -\\frac{(x-\\mu)^2}{2\\sigma^2}     \\right)     \\right]     \\mathrm{d}x \\\\     &amp;=      \\frac{1}{2}\\left(         \\ln\\left(             2\\pi\\sigma^2         \\right) + 1     \\right) \\end{aligned} \\]"},{"location":"pape_read/TRACE/","title":"[TRACE] 5D Temporal Regression of Avatars with Dynamic Cameras in 3D Environments","text":"<p> \u7ea6 1352 \u4e2a\u5b57  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 5 \u5206\u949f</p> <p><code>3DV</code> <code>HMR</code> <code>Global-Coordinates</code> <code>Track</code></p> <p>\u6587\u7ae0\u4fe1\u606f</p> <ul> <li>\u6587\u7ae0\u9898\u76ee\uff1aTRACE: 5D Temporal Regression of Avatars with Dynamic Cameras in 3D Environments</li> <li>\u4f5c\u8005\uff1aAuthors:Yu Sun, Qian Bao, Wu Liu, Tao Mei, Michael J. Black</li> <li>\u9879\u76ee\u4e3b\u9875\uff1a\ud83d\udd17</li> <li>\u8bba\u6587\uff1a\ud83d\udd17</li> <li>\u4ee3\u7801\uff1a\ud83d\udd17</li> </ul>"},{"location":"pape_read/TRACE/#\u4efb\u52a1--\u6311\u6218","title":"\u4efb\u52a1 &amp; \u6311\u6218","text":""},{"location":"pape_read/TRACE/#\u80cc\u666f","title":"\u80cc\u666f","text":"<p>\u867d\u7136\u76ee\u524d\u5bf9\u4e8e HPS(Human Pose &amp; Shape) \u7684\u4f30\u8ba1\u5df2\u7ecf\u6709\u5f88\u591a\u5f88\u597d\u7684\u5de5\u4f5c\uff0c\u4f46\u662f\u90fd\u662f\u5f97\u5230\u76f8\u673a\u5ea7\u6807\u4e0b\u7684\u7ed3\u679c\uff0c\u65e0\u6cd5\u5f88\u597d\u7684\u5f97\u5230\u5168\u5c40\u5ea7\u6807\u7cfb\u4e0b\u7684\u7ed3\u679c\u3002\u5c24\u5176\u662f\u5728\u76f8\u673a\u79fb\u52a8\u7684\u60c5\u51b5\u4e0b\uff0c\u8fd9\u4e2a\u4efb\u52a1\u5c24\u5176\u56f0\u96be\u3002\u800c\u5f97\u5230\u6062\u590d\u51fa\u6765\u7684 Human \u7684\u5168\u5c40\u5ea7\u6807\u5177\u6709\u91cd\u5927\u610f\u4e49\u3002</p>"},{"location":"pape_read/TRACE/#\u6311\u6218","title":"\u6311\u6218","text":"<ol> <li>\u9700\u8981\u89e3\u5076 human \u7684\u8fd0\u52a8\u548c camera \u7684\u8fd0\u52a8\uff0c\u8fd9\u6837\u624d\u80fd\u5728\u5168\u5c40\u5ea7\u6807\u7cfb\u4e0b\u6062\u590d human \u7684\u8f68\u8ff9\uff1b<ol> <li>\u4e00\u79cd\u65b9\u6cd5\uff1a\u4f7f\u7528 SfM \u6062\u590d\u51fa\u76f8\u673a\u5173\u4e8e rigid scene \u7684\u76f8\u5bf9\u8fd0\u52a8\uff0c\u4f46\u662f\u5728\u7279\u6b8a\u73af\u5883\uff08\u753b\u9762\u7684\u5927\u90e8\u5206\u90fd\u4e0d\u600e\u4e48 rigid\uff0c\u6bd4\u5982\u5927\u91cf\u4eba\u6d41\uff09\u4e0b\u975e\u5e38\u4e0d\u53ef\u9760\uff1b</li> <li>\u53e6\u5916\u4e00\u79cd\u6765\u81ea GLAMR \u7684\u65b9\u6cd5\uff1a\u901a\u8fc7\u5df2\u6709\u7684\u5c40\u90e8\u59ff\u6001\u6765\u63a8\u65ad\u5168\u5c40\u4f4d\u7f6e\uff0c\u5c31\u7c7b\u4f3c\u4e8e\u770b\u4f60\u8d70\u4e86\u51e0\u6b65\u7136\u540e\u4f30\u8ba1\u4f60\u52a8\u4e86\u51e0\u7c73\uff1b</li> <li>TRACE \u9009\u62e9\u4e86\u7b2c\u4e8c\u79cd\u65b9\u6cd5\u7684\u53d8\u79cd\uff0c\u901a\u8fc7\u4f7f\u7528\u6574\u4e2a\u753b\u9762\u6765\u9884\u6d4b\u79fb\u52a8\u8ddd\u79bb\uff0c\u6539\u5584\u4e86 GLAMR \u539f\u672c\u4e0d\u600e\u4e48\u597d\u7684\u6548\u679c\u3002\u4e0d\u4ec5\u5982\u6b64\uff0cGLAMR \u662f\u591a\u9636\u6bb5\u7684\uff0c\u9c81\u68d2\u6027\u4e0d\u654c TRACE\uff1b</li> </ol> </li> <li>\u5c24\u5176\u9488\u5bf9\u4e8e\u8ffd\u8e2a\u529f\u80fd\uff0c\u5728\u5bc6\u96c6\u4eba\u7fa4\u573a\u666f\uff0c\u5b58\u5728\u5f88\u4e25\u91cd\u7684\u906e\u6321\u95ee\u9898\uff1b<ol> <li>\u6700\u5e38\u89c1\u7684\u89e3\u51b3\u529e\u6cd5\u662f\u4f7f\u7528\u65f6\u5e8f\u5148\u9a8c\u5047\u8bbe\uff0c\u5982 Kalman filter\uff0c\u4f46\u662f\u5728\u590d\u6742\u573a\u666f\u4e0b\u4e5f\u5f88\u5bb9\u6613\u5931\u6548\uff1b</li> <li> \u95ee\u9898\uff1aKalman filter \u597d\u50cf\u548c\u6ee4\u6ce2\u6709\u5173\uff1f\u4e3a\u4ec0\u4e48\u8bf4\u662f temporal priors\uff1f \u4f7f\u5e73\u6ed1\u3002</li> <li>PHALP \u662f\u4e3a\u6570\u4e0d\u591a\u7684\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\u7684\u65b9\u6cd5\u4e4b\u4e00\uff0c\u4f46\u662f\u5b83\u5e76\u975e one-stage\uff0c\u800c\u4e14\u5e76\u4e0d\u5bf9\u5e8f\u5217\u8fdb\u884c\u5168\u9762\u7684\u63a8\u7406\uff1b</li> <li> \u95ee\u9898\uff1a\u9700\u8981\u4e86\u89e3\u8fd9\u4e2a\u5417\uff1f \u8df3\u8fc7\u3002</li> </ol> </li> </ol>"},{"location":"pape_read/TRACE/#\u4efb\u52a1\u4e0e\u6210\u679c","title":"\u4efb\u52a1\u4e0e\u6210\u679c","text":"<p>\u672c\u5de5\u4f5c\u5b9e\u73b0\u4e86\u52a8\u6001\u76f8\u673a\u89c6\u9891\uff08DC-videos\uff09\u4e0b\u5728\uff08\u865a\u62df\u7684\uff09\u7a7a\u95f4\u4e2d\u7684\u65f6\u5e8f\u7684\u5bf9\u4e8e K \u76ee\u6807\u7684\u5b9a\u4f4d\u68c0\u6d4b\u3001\u59ff\u6001\u4f30\u8ba1\u3001\u8ffd\u8e2a\u548c\u51b2\u7a81\u9002\u914d\uff0c\u5e76\u4e14\u80fd\u591f\u5f97\u5230\u5168\u5c40\u7684\u5ea7\u6807\u3002 - \u65f6\u5e8f &amp; \u5168\u5c40\u5ea7\u6807 &amp; \u8ffd\u8e2a\uff1b</p> <p>\u5bf9 K \u4e2a\u6709\u9650\u76ee\u6807\u8fdb\u884c\u8ffd\u8e2a\uff0c\u5373\u4f7f\u4e2d\u9014\u77ed\u6682\u7684\u5931\u914d\uff0c\u4e5f\u80fd\u5728\u4e4b\u540e\u88ab\u91cd\u65b0\u8bc6\u522b\uff08\u4e00\u5f00\u59cb\u51b3\u5b9a\u4e86\u54ea K \u4e2a\u5c31\u4e00\u76f4\u662f\u54ea K \u4e2a\u4eba\uff09\u3002</p>"},{"location":"pape_read/TRACE/#\u521b\u65b0\u70b9--\u8d21\u732e","title":"\u521b\u65b0\u70b9 &amp; \u8d21\u732e","text":"<ul> <li>\u63d0\u4f9b\u4e86 5D \u7684\u8868\u8fbe\u65b9\u5f0f\uff0c\u62bd\u8c61\u6765\u8bf4\u9700\u8981\u5305\u62ec\uff1a\u65f6(1)\u7a7a(3)\u5ea7\u6807 + \u4e3b\u4f53\u7279\u5f81(1\uff0c\u62bd\u8c61\u4e00\u70b9\u6765\u770b)\uff1b</li> <li>end2end \u5e76\u4e14 one stage \u7684\u65b9\u6cd5\uff1b</li> <li>\u53d7\u5230 BEV \u542f\u53d1\uff0c\u5f15\u5165\u4e86\u4e86\u4e00\u79cd\u9e1f\u77b0\u89c6\u89d2\u7684 2D map \u6765\u63a8\u7406 3D \u4e2d\u7684 Human\u3002\u8fd9\u4e2a map \u548c\u4e00\u4e2a\u4ee5\u56fe\u7247\u4e3a\u4e2d\u5fc3\u7684 map \u4e00\u8d77\u7528\u6765\u63a8\u7406 Human \u7684 3D \u5ea7\u6807\u3002\u7c7b\u4f3c\u7684\u8fd8\u6709\u4e00\u5806\u5176\u4ed6\u7684 map\uff1b</li> <li>\u4e00\u4e2a memory unit\uff0c\u6765\u505a\u4e00\u4e9b long-term \u7684\u4e8b\u60c5\uff0c\u6bd4\u5982\u5bf9\u906e\u6321\u751a\u81f3\u6682\u65f6\u5931\u914d\u7684\u9c81\u68d2\u7684\u8ffd\u8e2a\uff1b</li> <li>\u4e00\u4e2a\u4e3b\u8981\u7528\u5168\u666f\u89c6\u9891\u6a21\u62df  DC-video \u7684\u6570\u636e\u96c6\uff1b</li> </ul>"},{"location":"pape_read/TRACE/#\u65b9\u6cd5","title":"\u65b9\u6cd5","text":"<p>\u53c2\u8003\u6d41\u7a0b\u56fe\u505a\u89e3\u91ca\u3002</p> <ul> <li>\u8f93\u5165\u7684 Video \u6309\u5e27\u8f93\u5165\uff0c\u5373\u8f93\u5165 N \u5f20\u56fe\u7247\uff1b\u540c\u65f6 user \u6307\u5b9a\u9700\u8981\u8ffd\u8e2a\u7684\u4eba\u6570 K\uff1b</li> <li>\u968f\u540e\uff0c\u56fe\u7247\u5e8f\u5217\u5206\u522b\u901a\u8fc7 Image backbone \u548c Motion backbone \u5f97\u5230\u5355\u5e27\u7684\u7279\u5f81 map \\(F_i\\) \u548c\u5149\u6d41 map \\(O_i\\)\uff1b<ul> <li>Image backbone(HRNet-32) \u7ebf\u91cc\uff0c\u5229\u7528 \\(F_{i-1}\\) \u548c \\(F_{i}\\)\uff0c\u4ee5\u53ca\u4e0a\u4e00\u4e2a\u65f6\u5e8f\u7279\u5f81\u4f20\u64ad\u6a21(temporal feature propagation module, ConvGRU)\u5757\u5f97\u5230\u7684 \\(H_{i-1}\\)\uff0c\u9884\u6d4b\u8fd9\u4e00\u5e27\u7684\u65f6\u5e8f\u7279\u5f81\uff0c\u5e76\u5f97\u5230\u7ecf\u8fc7\u6a21\u7cca\u7684\u2014\u2014\u5305\u542b\u65f6\u5e8f\u4fe1\u606f\u7684\u7279\u5f81 map \\(F_i'\\)\uff1b<ul> <li> \u95ee\u9898\uff1a\u8fd9\u91cc\u7684 ConvGRU \u76f8\u5173\u7684\u4e0d\u662f\u5f88\u6e05\u695a\uff0c\u6bd4\u5982 \\(H_i\\) \u662f\u4ec0\u4e48\uff1f \u6682\u65f6\u8df3\u8fc7\u3002</li> </ul> </li> <li>Motion backbone(RAFT) \u8ba1\u7b97\u5149\u6d41\uff1b</li> </ul> </li> <li>\u5728\u5b8c\u6210\u65f6\u5e8f\u7279\u5f81\u63d0\u53d6(temporal feature extraction)\u4ee5\u540e\uff0c\u662f\u4e00\u7cfb\u5217\u7684 head network\uff0c\u5b83\u4eec\u5e76\u4e0d\u5b8c\u5168\u5e73\u884c\uff0c\u90e8\u5206 branch \u548c\u5176\u5b83 branch \u6709\u5148\u540e\u8981\u6c42\uff0c\u4f46\u662f\u65e2\u7136\u56fe\u90fd\u8fd9\u4e48\u753b\u4e86\uff0c\u8fd9\u91cc\u5c31\u5f53\u5e73\u884c\u7684\u6a21\u5757\u6765\u8bb2\uff1b<ul> <li>Detection \u6a21\u5757\uff0c\u4ee5\u65f6\u5e8f\u56fe\u50cf\u7279\u5f81 \\(F_i'\\) \u4e3a\u8f93\u5165\uff1b<ul> <li>\u76f8\u673a\u5ea7\u6807\u7cfb\uff1b</li> <li>\u4f7f\u7528\u6b63\u89c6\u548c\u4fef\u89c6\u4e24\u4e2a\u65b9\u5411\u7684 view maps \u5408\u6210\u9884\u6d4b\uff08\u6765\u5219 BEV\uff09\uff0c\u5f97\u5230\u4e00\u4e2a 3D \u4e2d\u5fc3 map(3D Center map) \\(M_C^{3D}\\in \\mathrm{R}^{1\\times D\\times H\\times W}\\) \u548c\u4e00\u4e2a 3D \u5b9a\u4f4d map(3D Localization map) \\(M_{L}^{3D} \\in \\mathrm{R}^{1\\times D\\times H\\times W}\\)\uff1b</li> <li>\u4ece \\(M_C^{3D}\\) \u4e2d\u5f97\u5230 K \u4e2a\u5bf9\u8c61\u7684 3D \u4e2d\u5fc3 \\(\\tilde t_{i}\\) \u53ca\u5176\u7f6e\u4fe1\u5ea6 \\(c_i\\)\uff0c\u7136\u540e\u4ece \\(M_{L}^{3D}\\) \u4e2d\u5728 \\(\\tilde t_{i}\\) \u5904\u91c7\u6837\u4ece \\(\\tilde t_{i}\\) \u6307\u5411\u7cbe\u786e\u4f4d\u7f6e\u7684\u504f\u79fb\u5411\u91cf \\(\\Delta t_i\\)\uff0c\u4e8e\u662f\u5f97\u5230\u7cbe\u786e\u7684\u4f4d\u7f6e\u4e3a \\(t_i = \\tilde{t}_i + \\Delta t\\)\uff1b<ul> <li> \u95ee\u9898\uff1a\u4e3a\u5565\u8981\u4e24\u6b65\uff0c\u4e0d\u80fd\u76f4\u63a5\u5f97\u5230\u7cbe\u786e\u4f4d\u7f6e\u5417\uff1f \u9700\u8981\u5b9e\u9a8c\u8bc1\u660e\u3002</li> </ul> </li> </ul> </li> <li>Tracking \u6a21\u5757\uff0c\u4ee5\u65f6\u5e8f\u56fe\u50cf\u7279\u5f81 \\(F_i'\\) \u548c\u5149\u6d41 \\(O_i\\) \u4e3a\u8f93\u5165\uff1b<ul> <li>\u76f8\u673a\u5ea7\u6807\u7cfb\uff1b</li> <li>\u4f7f\u7528 \\(F_i'\\) \u548c \\(O_i\\) \u9884\u6d4b 3D \u8fd0\u52a8\u504f\u79fb map(3D Motion Offset map) \\(M^{3D}_{M} \\in \\mathrm{R}^{3\\times D\\times H\\times W}\\)\uff0c\u6765\u63a8\u7406\u4eba\u5728 3D \u7a7a\u95f4\u4e2d\u7684\u4f4d\u7f6e\u504f\u79fb \\(\\Delta m_i\\)\uff0c\u8fd9\u4e2a\u504f\u79fb\u53ea\u662f\u7528\u6765\u505a tracking \u7684\uff1b</li> <li>\u5229\u7528 \\(\\Delta m_i\\)\uff0c\\(t_i\\) \u548c \\(c_i\\)\uff0c\u5728 Memory unit \u7684\u4f5c\u7528\u4e0b\u5b9e\u73b0\u8ffd\u8e2a\uff1b</li> <li>Memory unit \u7684\u5de5\u4f5c\u6d41\u7a0b\u5206\u4e09\u4e2a\u6b65\u9aa4\uff1a<ul> <li>\u521d\u59cb\u5316\uff1b</li> <li>\u5339\u914d\uff1b</li> <li>\u66f4\u65b0\uff1b</li> </ul> </li> </ul> </li> <li>Mesh \u6a21\u5757\uff0c\u4ee5\u65f6\u5e8f\u56fe\u50cf\u7279\u5f81 \\(F_i'\\) \u548c\u5149\u6d41 \\(O_i\\) \u4e3a\u8f93\u5165\uff1b<ul> <li>\u5f97\u5230 SMPL \u7ed3\u679c\uff1b</li> </ul> </li> <li>World \u6a21\u5757\uff0c\u4ee5\u65f6\u5e8f\u56fe\u50cf\u7279\u5f81 \\(F_i'\\) \u548c\u5149\u6d41 \\(O_i\\) \u4e3a\u8f93\u5165\uff1b<ul> <li>\u5373\u4e4b\u524d\u63d0\u5230\u7684\u4f7f\u7528 pose \u6765\u4f30\u8ba1\u5168\u5c40\u7684\u52a8\u4f5c\uff1b</li> </ul> </li> </ul> </li> </ul>"},{"location":"pape_read/TRACE/#\u6570\u636e\u96c6","title":"\u6570\u636e\u96c6","text":"<p>\u7565\u3002</p>"},{"location":"pape_read/TRACE/#loss","title":"Loss","text":"<p>\u7565\u3002</p>"},{"location":"tech_accu/","title":"\u6249\u9875","text":"<p> \u7ea6 15 \u4e2a\u5b57 </p> <p> \u300e\u305d\u306e\u6642\u3092\u5f85\u3064\u3088\u300f      \u9761\u4e0d\u6709\u521d\uff0c\u9c9c\u514b\u6709\u7ec8\u3002  \u2014\u2014\u300a\u8bd7\u7ecf\u300b  </p>"},{"location":"tech_accu/ai/","title":"\u6249\u9875","text":"<p> \u7ea6 15 \u4e2a\u5b57 </p> <p> \u300e\u305d\u306e\u6642\u3092\u5f85\u3064\u3088\u300f      \u9761\u4e0d\u6709\u521d\uff0c\u9c9c\u514b\u6709\u7ec8\u3002  \u2014\u2014\u300a\u8bd7\u7ecf\u300b  </p>"},{"location":"tech_accu/ai/hydra/","title":"Hydra","text":"<p> \u7ea6 1136 \u4e2a\u5b57  42 \u884c\u4ee3\u7801  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 4 \u5206\u949f</p> <p>\u76f8\u5173\u94fe\u63a5</p> <ul> <li>\u5b98\u65b9\u6587\u6863 \ud83d\udd17</li> <li>\u7b14\u8bb0 \ud83d\udd17</li> </ul> <p>\u7b80\u4ecb</p> <p>Hydra \u4ea6\u53ef\u7528\u4e8e\u5176\u5b83 Python APP\uff0c\u4f46\u672c\u6587\u53ea\u4ee5 Research \u7684\u89c6\u89d2\u6765\u8c08\u8fd9\u4e2a\u5de5\u5177\u3002</p> <p>\u5728\u8fdb\u884c\u5b9e\u9a8c\u65f6\uff0c\u6211\u4eec\u53ef\u80fd\u4f1a\u5e0c\u671b\u4e00\u4e2a\u9879\u76ee\u80fd\u652f\u6301\u5207\u6362\u5176\u4e2d\u7684\u82e5\u5e72\u90e8\u4ef6\uff0c\u5c31\u597d\u50cf\u7ed9\u673a\u5668\u4eba\u66f4\u6362\u4e0d\u540c\u7684\u90e8\u4ef6\uff0c\u6765\u6d4b\u8bd5\u5176\u6027\u80fd\u3002\u800c\u6bcf\u4e00\u4e2a\u90e8\u4ef6\u90fd\u6709\u53ef\u80fd\u6709\u81ea\u5df1\u7684\u8d85\u53c2\u6570\u9700\u8981\u8bbe\u7f6e\u3002</p> <p>\u786c\u7f16\u7801\u8bbe\u7f6e\u5f53\u7136\u4e0d\u53ef\u53d6\uff0c\u8fd9\u592a\u4e0d\u4f18\u96c5\u4e86\u3002\u6240\u4ee5\u6211\u4eec\u901a\u5e38\u4f7f\u7528\u547d\u4ee4\u884c\u53c2\u6570\uff0c\u5373 args \u6765\u5b9e\u73b0\u8d85\u53c2\u6570\u7684\u4f20\u5165\u3002\u4f46\u968f\u7740\u6a21\u578b\u8d8a\u6765\u8d8a\u590d\u6742\uff0c\u9700\u8981\u7684\u8d85\u53c2\u6570\u8d8a\u6765\u8d8a\u591a\uff0c\u547d\u4ee4\u884c\u5c31\u4f1a\u8d8a\u6765\u8d8a\u957f\uff1b\u800c\u4e14\u4e0d\u540c\u7684\u201c\u90e8\u4ef6\u201d\u53ef\u80fd\u9700\u8981\u4e0d\u540c\u7684\u8d85\u53c2\u6570\uff0c\u56e0\u6b64\uff0c\u4f7f\u7528\u547d\u4ee4\u884c\u53c2\u6570\u7075\u6d3b\u6027\u5c31\u5927\u5927\u4e0b\u964d\u4e86\u3002</p> <p>\u56e0\u6b64\uff0c\u6211\u4eec\u8003\u8651\u628a\u8fd9\u4e9b\u4e1c\u897f\u653e\u5728\u6587\u4ef6\u91cc\uff0c\u9700\u8981\u4fee\u6539\u65f6\u5c31\u76f4\u63a5\u4fee\u6539\u6587\u4ef6\uff0c\u8fd9\u6837\u4fee\u6539\u53c2\u6570\u76f8\u5bf9\u5c31\u7075\u6d3b\u4e00\u4e9b\u3002\u66f4\u8fdb\u4e00\u6b65\u7684\uff0c\u6211\u4eec\u8fd8\u53ef\u4ee5\u901a\u8fc7\u5c06\u4e0d\u540c\u7684\u7ec4\u5408\u5206\u522b\u4fdd\u5b58\u4e3a\u4e00\u4e2a\u6587\u4ef6\uff0c\u7528\u6307\u5b9a\u7279\u5b9a\u6587\u4ef6\u7684\u65b9\u5f0f\u6765\u9009\u62e9\u4e00\u4e2a\u5df2\u7ecf\u8bbe\u7f6e\u597d\u7684 pipeline\u3002</p> <p>\u4f46\u662f\u8fd9\u6837\u8fd8\u6709\u4e24\u4e2a\u95ee\u9898\uff0c\u9996\u5148\uff0c\u8fd9\u6837\u5199\u7684\u8bdd\uff0c\u914d\u7f6e\u6587\u4ef6\u7684\u590d\u7528\u7387\u662f\u6bd4\u8f83\u4f4e\u7684\uff0c\u56e0\u4e3a\u5404\u4e2a\u914d\u7f6e\u4e4b\u95f4\u5dee\u522b\u53ef\u80fd\u4e0d\u5927\uff0c\u53ef\u80fd\u4e92\u76f8\u53ea\u6709\u4e00\u5c0f\u90e8\u5206\u7684\u4e0d\u540c\uff0c\u800c\u590d\u7528\u7387\u4f4e\u7684\u574f\u5904\u5c31\u4e0d\u5fc5\u591a\u8bf4\u4e86\uff1b\u5176\u6b21\uff0c\u5c31\u7b97\u6211\u4eec\u7528\u5c42\u6b21\u5316\u7684\u914d\u7f6e\u6587\u4ef6\u6765\u89e3\u51b3\u590d\u7528\u7684\u95ee\u9898\uff0c\u6211\u4eec\u5728\u5b9e\u9645\u4ee3\u7801\u91cc\u4e5f\u9700\u8981\u4f7f\u7528\u7e41\u590d\u7684\u5206\u652f\u8bed\u53e5\u624d\u80fd\u5f88\u597d\u5730\u63a7\u5236\u914d\u7f6e\u7684\u9009\u62e9\u3002</p> <p>\u4e8e\u662f\uff0cHydra \u5e94\u8fd0\u800c\u751f\u3002Hydra \u4f1a\u4ee5\u7279\u5b9a\u7684\u65b9\u5f0f\u5904\u7406\u5c42\u6b21\u5316\u7684\u914d\u7f6e\u6587\u4ef6\uff0c\u5b83\u7684\u884c\u4e3a\u5f88\u50cf Cpp \u7684 <code>#include</code>\uff0c\u4f1a\u628a\u9009\u4e2d\u7684\u540e\u4ee3 Group \u91cc\u7684\u914d\u7f6e\u6587\u4ef6\u5d4c\u5165\u5230\u5f53\u524d\u914d\u7f6e\u6587\u4ef6\u91cc\u3002</p> <p>\u66f4\u5177\u4f53\u7684\u5173\u4e8e Hydra \u7684\u89c4\u8303\uff0c\u8bf7\u53c2\u8003\u5b98\u65b9\u6587\u6863\uff0c\u672c\u6587\u4e3b\u8981\u5bf9\u5b98\u65b9\u6587\u6863\u505a\u4e00\u4e9b\u8865\u5145\uff0c\u901a\u8fc7\u5b9e\u9a8c\u63a2\u7d22\u4e00\u4e9b Hydra \u6587\u6863\u4e2d\u6ca1\u6709\u63d0\u5230\u7684\u6027\u8d28\u3002</p>"},{"location":"tech_accu/ai/hydra/#\u5173\u4e8e-ab-\u8bed\u6cd5","title":"\u5173\u4e8e +A=B \u8bed\u6cd5","text":"<p>\u5728\u6587\u6863\u4e2d\uff0c\u6709\u4e24\u4e2a\u5730\u65b9\u63d0\u5230\u4e86 +A=B \u7684\u8bed\u6cd5\u3002\u7b2c\u4e00\u6b21\u662f\u5728\u8fd9\u91cc\uff1a</p> <p>You can add config values via the command line. The <code>+</code> indicates that the field is new.</p> <pre><code>$ python my_app.py +db.driver=mysql +db.user=omry +db.password=secret\ndb:\n  driver: mysql\n  user: omry\n  password: secret\n</code></pre> files my_app.py<pre><code>from omegaconf import DictConfig, OmegaConf\nimport hydra\n\n@hydra.main(version_base=None)\ndef my_app(cfg: DictConfig) -&gt; None:\n    print(OmegaConf.to_yaml(cfg))\n\nif __name__ == \"__main__\":\n    my_app()\n</code></pre> <p>\u7b2c\u4e8c\u6b21\u662f\u5728\u8fd9\u91cc\uff1a</p> <p>Select an item from a config group with <code>+GROUP=OPTION</code>, e.g:</p> <pre><code>$ python my_app.py +db=postgresql\ndb:\n  driver: postgresql\n  pass: drowssap\n  timeout: 10\n  user: postgres_user\n</code></pre> files Directory layout<pre><code>    \u251c\u2500 conf\n    \u2502  \u2514\u2500 db\n    \u2502      \u251c\u2500 mysql.yaml\n    \u2502      \u2514\u2500 postgresql.yaml\n    \u2514\u2500\u2500 my_app.py\n</code></pre> db/mysql.yaml<pre><code>driver: mysql\nuser: omry\npassword: secret\n</code></pre> db/postgresql.yaml<pre><code>driver: postgresql\nuser: postgres_user\npassword: drowssap\ntimeout: 10\n</code></pre> my_app.py<pre><code>from omegaconf import DictConfig, OmegaConf\nimport hydra\n\n@hydra.main(version_base=None)\ndef my_app(cfg: DictConfig) -&gt; None:\n    print(OmegaConf.to_yaml(cfg))\n\nif __name__ == \"__main__\":\n    my_app()\n</code></pre> <p>\u524d\u8005\u8868\u793a\u589e\u52a0\u4e00\u4e2a field\uff0c\u540e\u8005\u8868\u793a\u6307\u5b9a\u4e00\u4e2a group\uff0c\u5176\u542b\u4e49\u662f\u4e0d\u540c\u7684\uff0c\u800c\u770b\u8d77\u6765\u662f\u6709\u6b67\u4e49\u7684\u3002</p> <p>\u6839\u636e\u6211\u7684\u6d4b\u8bd5\uff0c<code>+A=B</code> \u5177\u4f53\u662f\u54ea\u4e00\u79cd\uff0c\u53d6\u51b3\u4e8e\u662f\u5426\u5b58\u5728\u540d\u4e3a A \u7684 folder\u3002\u5373\uff1a</p> <ul> <li>\u5982\u679c\u5b58\u5728\u540d\u4e3a A \u7684 folder\uff0c\u5219 <code>+A=B</code> \u8868\u793a\u6307\u5b9a A group \u91cc\u7684 <code>b.yaml</code> \u9879\uff1b</li> <li>\u5982\u679c\u4e0d\u5b58\u5728\u540d\u4e3a A \u7684 folder\uff0c\u5219 <code>+A=B</code> \u8868\u793a\u589e\u52a0\u4e00\u4e2a field\uff0c\u5176 key \u4e3a A\uff0cvalue \u4e3a B\uff1b</li> </ul> <p>\u66f4\u8fdb\u4e00\u6b65\u7684\uff0c\u53ea\u8981\u5f53\u524d\u76ee\u5f55\u5b58\u5728\u540d\u4e3a <code>A</code> \u7684 folder\uff0c\u90a3\u4e48\u5728\u5f53\u524d <code>yaml</code> \u6587\u4ef6\u4e2d\u5c31\u65e0\u6cd5\u5c06 <code>A</code> \u4f5c\u4e3a\u4e00\u4e2a field \u7684 key\u3002</p> <p>\u4e4b\u6240\u4ee5\u5f3a\u8c03\u5f53\u524d\uff0c\u662f\u56e0\u4e3a\u5b83\u53ef\u4ee5\u88ab\u7236\u6bcd\u7684 <code>yaml</code> \u6587\u4ef6\u4e2d\u7684\uff0c\u4ee5 <code>A</code> \u4e3a key \u7684 k-v \u5bf9\u8986\u76d6\u3002</p> <p>\u4f8b\u5982\uff0c\u867d\u7136\u6dfb\u52a0 <code>A=1</code> \u66ff\u6362\u4f5c\u4e3a group \u7684 <code>A</code> \u4f1a\u62a5\u9519\uff0c\u4f46\u662f\u6dfb\u52a0 <code>A.B=1</code> \u5374\u53ef\u4ee5\u8986\u76d6 <code>A</code> \u4e0b\u7684\u4f5c\u4e3a group \u7684 <code>B</code>\uff1b\u4ea6\u6216\u5728\u6700\u7684 <code>config.yaml</code> \u91cc\u6dfb\u52a0\u8fd9\u6837\u4e00\u6bb5\u4e5f\u53ef\u4ee5\u8d77\u5230\u540c\u6837\u7684\u6548\u679c\uff1a</p> <pre><code>A:\nB: 1\n</code></pre> <p>\u5373\uff0c\u5bf9\u4e8e\u201c\u65e0\u6cd5\u5c06 group \u8986\u76d6\u4e3a field\u201d\u8fd9\u4ef6\u4e8b\u7684\u4fdd\u62a4\uff0c\u53ea\u6709\u76ee\u5f55\u4e00\u5c42\u5185\u6709\u6548\u3002</p>"},{"location":"tech_accu/ai/hydra/#\u8986\u76d6\u5173\u7cfb","title":"\u8986\u76d6\u5173\u7cfb","text":"<p>\u9996\u5148\uff0c\u9664\u4e86\u5728\u4e0a\u4e00\u8282\u63d0\u5230\u7684\u5173\u4e8e field \u548c group \u7684\u8986\u76d6\u5173\u7cfb\uff0c\u66f4\u91cd\u8981\u7684\u662f\u5728\u4e0d\u540c\u5c42\u7684 yaml \u4e4b\u95f4\uff0c\u76f8\u540c\u952e\u7684\u503c\u7684\u8986\u76d6\u5173\u7cfb\u3002</p> <p>\u9996\u5148\uff0c\u5355\u770b defaults\uff0c\u5b98\u65b9\u5728\u6587\u6863\u4e2d\u6709\u63d0\u5230\u89c4\u5219\uff1a</p> <p>The defaults are ordered:</p> <ul> <li>If multiple configs define the same value, the last one wins.</li> <li>If multiple configs contribute to the same dictionary, the result is the combined dictionary.</li> </ul> <p>\u6b64\u5916\uff0c\u5982\u679c\u5df2\u7ecf\u5728\u5185\u5c42 defaults \u8bbe\u7f6e\u4e86\u952e\u7684\u9ed8\u8ba4\u503c\uff0c\u5c31\u4e0d\u80fd\u5728\u5916\u5c42\u4e3a\u8fd9\u4e2a\u952e\u8bbe\u7f6e\u9ed8\u8ba4\u503c\uff0c\u53cd\u4e4b\u4ea6\u7136\u3002</p> <p>\ud83c\udf30</p> <p>\u4f8b\u5982\u4e0b\u9762\u8fd9\u4e24\u4e2a\u6587\u4ef6\u4e2d\uff0c<code>- group1/group2: option1_1</code> \u548c <code>- group2: option1_1</code> \u8fd9\u4e24\u884c\u662f\u51b2\u7a81\u7684\uff0c\u53ea\u80fd\u9009\u5176\u4e00\u7684\u3002</p> config.yaml<pre><code>defaults:\n- group1: option1\n- group1/group2: option1_1\n</code></pre> group1/option1.yaml<pre><code>defaults:\n- group2: option1_1\n</code></pre> <p>\u56e0\u6b64\uff0c\u4e00\u822c\u6765\u8bf4\u5c3d\u91cf\u907f\u514d\u8ba9\u914d\u7f6e\u5c42\u6570\u8d85\u8fc7\u4e24\u5c42\u3002</p> <p>\u800c\u5173\u4e8e defaults \u4ee5\u5916\u7684\u90e8\u5206\uff0c\u89c4\u5219\u5982\u4e0b\uff1a</p> <ol> <li>\u5f53\u6700\u5916\u5c42\u7684 <code>config.yaml</code> \u548c\u5728 <code>defaults:</code> \u91cc\u6307\u5b9a\u7684 <code>yaml</code> \u914d\u7f6e\u6587\u4ef6\u5b58\u5728\u51b2\u7a81\u7684\u952e\u65f6\uff0c\u4ee5 <code>config.yaml</code> \u91cc\u7684\u4e3a\u51c6\uff0c\uff08\u65e0\u8bba\u662f\u5426\u6709 <code>GROUP=OPTION</code> \u9009\u9879\uff09\uff1b</li> <li>\u5f53\u952e\u4e0d\u5b58\u5728\u4e8e <code>defaults:</code> \u4e2d\uff0c\u800c\u53ea\u5728\u547d\u4ee4\u884c\u4e2d\u901a\u8fc7 <code>+GROUP=OPTION</code> \u9009\u4e2d\u65f6\uff0c\u4ee5 <code>OPTION.yaml</code> \u91cc\u7684\u4e3a\u51c6\uff1b</li> </ol>"},{"location":"tech_accu/ai/pytorch/","title":"PyTorch","text":"<p> \u7ea6 565 \u4e2a\u5b57  48 \u884c\u4ee3\u7801  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 2 \u5206\u949f</p> <p>\u5f03\u5751\u4e86\uff0c\u611f\u89c9\u6ca1\u5565\u5199\u7684\u5fc5\u8981</p> <ul> <li>PyTorch \u4e3b\u8981\u6709\u4e24\u4e2a\u7528\u9014\uff1a<ul> <li>\u80fd\u591f\u4f7f\u7528 GPU \u52a0\u901f\u7684 NumPy \u66ff\u4ee3\u54c1\uff1b</li> <li>\u5185\u7f6e\u7684\u81ea\u52a8\u5fae\u5206\u5e93\u7b49\u5bf9\u795e\u7ecf\u7f51\u7edc\u7684\u5b9e\u73b0\u4ea7\u751f\u8f83\u5927\u7684\u5e2e\u52a9\uff1b</li> </ul> </li> </ul> \u53c2\u8003\u8d44\u6599 <ul> <li>PyTorch \u5b98\u7f51\uff1a\ud83d\udd17</li> <li>A 60 MINUTE BLITZ\uff1a\ud83d\udd17<ul> <li>*\u672c\u6587\u4e3b\u8981\u6309\u7167\u8fd9\u7bc7\u6587\u7ae0\u7684\u601d\u8def\u6765\uff1b</li> </ul> </li> <li>PyTorch \u5b98\u65b9\u6559\u7a0b\u4e2d\u6587\u7248\uff1a\ud83d\udd17</li> <li>PyTorch\u7b80\u660e\u6559\u7a0b\uff1a\ud83d\udd17</li> </ul>"},{"location":"tech_accu/ai/pytorch/#\u5b89\u88c5","title":"\u5b89\u88c5","text":"<p>\u6839\u636e \u8fd9\u91cc \u63d0\u4f9b\u7684\u65b9\u6cd5\u83b7\u53d6\u5b89\u88c5\u9014\u5f84\uff0c\u6ce8\u610f\u9009\u62e9\u4e0e\u60a8\u7684\u73af\u5883\u76f8\u7b26\u7684\u6761\u4ef6\u3002</p> <p>\u4f9d\u8d56\u4e4b\u7c7b\u7684\u90fd\u5df2\u7ecf\u5728\u8be5\u9875\u9762\u5199\u7684\u5f88\u6e05\u695a\u4e86\u3002</p> <p>\u5b8c\u6210\u5b89\u88c5\u540e\uff0c\u6211\u4eec\u901a\u8fc7\u5982\u4e0b\u65b9\u6cd5\u6765\u68c0\u6d4b\u662f\u5426\u5b89\u88c5\u6210\u529f\uff1a</p> <pre><code>$ python\n&gt;&gt;&gt; import torch\n&gt;&gt;&gt; x = torch.rand(5, 3)\n&gt;&gt;&gt; print(x)\ntensor([[0.8577, 0.6416, 0.2632],\n        [0.3853, 0.8534, 0.4877],\n        [0.0628, 0.2360, 0.8810],\n        [0.1766, 0.8024, 0.5447],\n        [0.3938, 0.9232, 0.4407]])\n</code></pre>"},{"location":"tech_accu/ai/pytorch/#\u5f20\u91cf--tensors","title":"\u5f20\u91cf | Tensors","text":"<p>Tensors \u662f NumPy \u4e2d ndarrys \u7684\u4e00\u79cd\u65e0\u75db\u66ff\u4ee3\uff0c\u53ea\u4e0d\u8fc7 tensors \u80fd\u591f\u6709\u6548\u5229\u7528 GPU \u8fdb\u884c\u52a0\u901f\u3002</p>"},{"location":"tech_accu/ai/pytorch/#\u521d\u59cb\u5316","title":"\u521d\u59cb\u5316","text":"<p>\u663e\u7136\uff0c\u521d\u59cb\u5316\u6709\u5f88\u591a\u65b9\u6cd5\uff0c\u8fd9\u91cc\u63d0\u4f9b\u51e0\u79cd\u3002</p> \u901a\u8fc7\u6570\u636e\u751f\u6210\u901a\u8fc7 NumPy array \u751f\u6210\u901a\u8fc7\u53e6\u5916\u4e00\u4e2a tensor \u751f\u6210\u4f7f\u7528\u5e38\u6570\u6216\u968f\u673a\u521d\u59cb\u5316 <p><pre><code>data = [[1, 2], [3, 4]]\nx_data = torch.tensor(data)\nprint(x_data)\n</code></pre> \u9884\u671f\u8f93\u51fa\u5982\u4e0b\uff1a</p> <p>Output</p> <pre><code>tensor([[1, 2],\n        [3, 4]])\n</code></pre> <p><pre><code>np_array = np.array(data)\nx_np = torch.from_numpy(np_array)\nprint(x_np)\n</code></pre> \u9884\u671f\u8f93\u51fa\u5982\u4e0b\uff1a</p> <p>Output</p> <pre><code>tensor([[1, 2],\n        [3, 4]])\n</code></pre> <p><pre><code>x_ones = torch.ones_like(x_data) # retains the properties of x_data\nprint(f\"Ones Tensor: \\n {x_ones} \\n\")\n\nx_rand = torch.rand_like(x_data, dtype=torch.float) # overrides the datatype of x_data\nprint(f\"Random Tensor: \\n {x_rand} \\n\")\n</code></pre> \u9884\u671f\u8f93\u51fa\u5982\u4e0b\uff1a</p> <p>Output</p> <pre><code>Ones Tensor:\ntensor([[1, 1],\n        [1, 1]])\n\nRandom Tensor:\ntensor([[0.4557, 0.7406],\n        [0.5935, 0.1859]])\n</code></pre> <p><pre><code>    shape = (2, 3)\n    rand_tensor = torch.rand(shape)\n    ones_tensor = torch.ones(shape)\n    zeros_tensor = torch.zeros(shape)\n\n    print(f\"Random Tensor: \\n {rand_tensor} \\n\")\n    print(f\"Ones Tensor: \\n {ones_tensor} \\n\")\n    print(f\"Zeros Tensor: \\n {zeros_tensor}\")\n</code></pre> \u9884\u671f\u8f93\u51fa\u5982\u4e0b\uff1a</p> <p>Output</p> <pre><code>Random Tensor:\n tensor([[0.4434, 0.1717, 0.7331],\n        [0.4211, 0.8945, 0.2239]])\n\nOnes Tensor:\n tensor([[1., 1., 1.],\n        [1., 1., 1.]])\n\nZeros Tensor:\n tensor([[0., 0., 0.],\n        [0., 0., 0.]])\n</code></pre>"},{"location":"tech_accu/ai/pytorch/#\u5c5e\u6027","title":"\u5c5e\u6027","text":"<p>\u8fd9\u91cc\u4e3b\u8981\u6d89\u53ca\u7684\u5f20\u91cf\u7684\u5c5e\u6027\u4e3a \u5f62\u72b6(<code>shape</code>)\u3001\u6570\u636e\u7c7b\u578b(<code>dtype</code>) \u548c \u6570\u636e\u6240\u5b58\u50a8\u5728\u7684\u786c\u4ef6\u8bbe\u5907(<code>device</code>)\u3002</p> <pre><code>tensor = torch.rand(3, 4)\n\nprint(f\"Shape of tensor: {tensor.shape}\")\nprint(f\"Datatype of tensor: {tensor.dtype}\")\nprint(f\"Device tensor is stored on: {tensor.device}\")\n</code></pre> <p>\u9884\u671f\u8f93\u51fa\u5982\u4e0b\uff1a</p> <p>Output</p> <pre><code>Shape of tensor: torch.Size([3, 4])\nDatatype of tensor: torch.float32\nDevice tensor is stored on: cpu\n</code></pre>"},{"location":"tech_accu/ai/pytorch/#\u65b9\u6cd5\u4e0e\u64cd\u4f5c","title":"\u65b9\u6cd5\u4e0e\u64cd\u4f5c","text":"<p>\u5bf9\u5f20\u91cf\u7684\u64cd\u4f5c\u65b9\u6cd5\u975e\u5e38\u4e4b\u591a\uff0c\u5f88\u96be\u5728\u672c\u6587\u4e2d\u5168\u90e8\u6d89\u53ca\uff0c\u56e0\u800c\u4e5f\u53ea\u662f\u653e\u4e2a \u6587\u6863 \u5728\u8fd9\u8fb9\uff0c\u5728\u6b64\u53ea\u4ecb\u7ecd\u6bd4\u8f83\u57fa\u7840\u7684\u51e0\u4e2a\u3002</p>"},{"location":"tech_accu/ai/pytorch/#\u4f7f\u7528-gpu-\u52a0\u901f","title":"\u4f7f\u7528 GPU \u52a0\u901f","text":"<p>\u4ee4\u4eba\u5e78\u559c\u7684\u662f\uff0c\u5bf9\u5f20\u91cf\u7684\u8fd9\u4e9b\u64cd\u4f5c\u90fd\u53ef\u4ee5\u4f7f\u7528 GPU \u6765\u8fdb\u884c\u52a0\u901f\uff0c\u5f53\u7136\u5728\u6b64\u4e4b\u524d\u6211\u4eec\u9700\u8981\u5c06\u5b83\u8f6c\u79fb\u5230 GPU \u4e0a\u2014\u2014\u5982\u679c\u53ef\u4ee5\u7684\u8bdd\u3002</p> <pre><code># We move our tensor to the GPU if available\nif torch.cuda.is_available():\n    tensor = tensor.to('cuda')\n    print(f\"Device tensor is stored on: {tensor.device}\")\n</code></pre> <p>Output</p> <pre><code>Device tensor is stored on: cuda:0\n</code></pre>"},{"location":"tech_accu/ai/pytorch/#\u8fd0\u7b97","title":"\u8fd0\u7b97","text":"<p>\u6ce8\u610f</p> <p>\u5982\u679c\u4e00\u4e2a tensor \u7684\u65b9\u6cd5\u4ee5 <code>_</code> \u7ed3\u5c3e\uff0c\u90a3\u4e48\u8bf4\u660e\u8fd9\u4e2a\u8fd0\u7b97\u4f1a\u4fee\u6539\u8fd9\u4e2a tensor \u81ea\u8eab\u3002</p> <p>\u5373\uff0c<code>x.method_(...)</code> \u5c06\u4f1a\u4fee\u6539 <code>x</code> \u672c\u8eab\u3002</p> <p>PyTorch \u5bf9\u56db\u5219\u8fd0\u7b97\u7b26\u8fdb\u884c\u4e86\u4e00\u4e9b\u91cd\u8f7d\uff0c\u5176\u4e0e\u6b63\u5e38\u65b9\u6cd5\u7684\u6620\u5c04\u5173\u7cfb\u5982\u4e0b\uff1a</p> \u8fd0\u7b97\u7b26 \u7b49\u4ef7\u65b9\u6cd5 <code>+</code> <code>torch.add()</code> <code>-</code> <code>torch.sub()</code> <code>*</code> <code>torch.mul()</code> <code>/</code> <code>torch.div()</code>"},{"location":"tech_accu/ai/pytorch/#\u7d22\u5f15\u4e0e\u5207\u7247","title":"\u7d22\u5f15\u4e0e\u5207\u7247","text":"<p><pre><code>tensor = torch.ones(4, 4)\ntensor[:,1] = 0\nprint(tensor)\n</code></pre> \u9884\u671f\u8f93\u51fa\u5982\u4e0b\uff1a</p> <p>Output</p> <pre><code>tensor([[1., 0., 1., 1.],\n        [1., 0., 1., 1.],\n        [1., 0., 1., 1.],\n        [1., 0., 1., 1.]])\n</code></pre>"},{"location":"tech_accu/language/cpp/","title":"Cpp about OOP","text":"<p> \u7ea6 53 \u4e2a\u5b57 </p> <p>\u76f8\u5173\u4fe1\u606f</p> <p>\u8fd9\u4e2a\u6761\u76ee\u653e\u7684\u4e3b\u8981\u662f Cpp \u5173\u4e8e OOP \u7684\u4e00\u4e9b\u8bed\u6cd5\u3002</p> <p>\u4e3b\u8981\u8fc1\u79fb\u81ea\u5927\u4e00\u7684 yuque \u6587\u6863\uff0c\u518d\u4e4b\u540e\u4e5f\u4f1a\u6709\u4e00\u4e9b\u4fee\u6539\u3002</p> <p>\u8fc1\u79fb\u524d\u7684\u6587\u4ef6</p>"},{"location":"tech_accu/language/cpp/Part0/","title":"[pre] \u524d\u7f6e\u4e0e\u6742\u9879","text":"<p> \u7ea6 1746 \u4e2a\u5b57  74 \u884c\u4ee3\u7801  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 7 \u5206\u949f</p>"},{"location":"tech_accu/language/cpp/Part0/#1x-\u5f15\u7528reference","title":"[1.x] \u5f15\u7528reference","text":"<p>1.\u521b\u5efabinding\u5173\u7cfb</p> <p>\u9700\u8981\u7406\u89e3\u7684\u662f\uff0c\u5f15\u7528\u672c\u8d28\u5c31\u662f\u6307\u9488\u3002\u5b83\u662f\u6307\u9488\u7684\u7cd6\u3002</p> <p><code>typename &amp; refname = name;</code> \u521b\u5efa\u4e86 <code>(typename)name</code> \u7684\u5f15\u7528 <code>(reference)refname</code></p> <p>\u5728bingding\u5173\u7cfb\u5efa\u7acb\u540e\uff0c\u5728 <code>name</code> \u548c <code>refname</code> \u7684\u4f5c\u7528\u57df\u5185 <code>refname</code> \u548c <code>name</code> \u57fa\u672c\u7b49\u6548\uff08\u662f\u53d8\u91cf\u7684\u7ed1\u5b9a\u5173\u7cfb\uff0c\u800c\u975e\u50cf <code>#define</code> \u90a3\u6837\u7684\u5b57\u7b26\u66ff\u6362\u5173\u7cfb</p> <ul> <li>\u4e00\u822c\u6765\u8bf4(\u4e0d\u8003\u8651const+reference)\u80fd\u521b\u5efa\u7684\u5f15\u7528\u7684\u5fc5\u987b\u662f\u4e2a\u53d8\u91cf\uff0c\u800c\u4e0d\u80fd\u662f\u4e2a\u8868\u8fbe\u5f0f\u3001\u5e38\u91cf\u3002<ul> <li>\u6362\u53e5\u8bdd\u8bf4\uff0c\u53ea\u80fd\u7ed9\u5de6\u503c(left value)\u521b\u5efa\u5f15\u7528 \u7279\u522b\u7684\uff1a</li> </ul> </li> </ul> <pre><code>int x = 1, y = 10, *p = &amp;x, &amp;ref = *p;\n// \u6b64\u65f6 x = 1, y = 10, *p = 1, ref = 1\n\n*p = 2;\n// \u6b64\u65f6 x = 2, y = 10, *p = 2, ref = 2\n\np = &amp;y;\n// \u6b64\u65f6 x = 2, y = 10, *p = 10, ref = 2\n</code></pre> <ul> <li>\u5f15\u7528\u5728\u521b\u5efa\u7684\u65f6\u5019\u5fc5\u987b\u521d\u59cb\u5316\uff0c\u5373<code>int &amp;x;</code>\u9519\u8bef\uff1b<code>int &amp;x = y;</code>\u6b63\u786e\u3002</li> <li>Bindings\u4e00\u65e6\u5efa\u7acb\uff0c\u65e0\u6cd5\u53d6\u6d88</li> <li>reference\u672c\u8d28\u4e0a\u5c31\u662f\u53d7\u9650\u7684pointer</li> <li>reference\u4e0d\u5b58\u5728reference</li> <li>reference\u4e0d\u5b58\u5728pointer<ul> <li>\u5b9a\u4e49<code>int *p = &amp;x;</code></li> <li><code>int&amp;* ref = ...;</code>\u975e\u6cd5\uff0c<code>ref</code>\u4e0d\u80fd\u662f\u4e00\u4e2a\u5f15\u7528\u7684\u6307\u9488</li> <li><code>int*&amp; ref = p;</code>\u5408\u6cd5\uff0c<code>ref</code>\u662f\u4e00\u4e2a\u6307\u9488\u7684\u5f15\u7528</li> </ul> </li> <li>\u4e0d\u5b58\u5728reference\u6570\u7ec4</li> </ul> <p>2.\u5229\u7528reference\u4f20\u53c2</p> <p>\u5229\u7528reference\u53ef\u4ee5\u7c7b\u4f3c\u4f20\u6307\u9488\u4e00\u6837\uff0c\u5728\u53d8\u91cf\u539f\u672c\u7684\u4f5c\u7528\u57df\u5916\u5bf9\u53d8\u91cf\u8fdb\u884c\u4fee\u6539</p> <pre><code>void f(int &amp;x){\nx = 1;\n}\n\nint main(){\nint p = 0;\n// \u6b64\u65f6 p = 0\nf(p);\n// \u6b64\u65f6 p = 1\n}\n</code></pre> <p>\u4f46\u6b64\u65f6\uff0c\u4f20\u5165 <code>f(p)</code> \u7684\u5b9e\u53c2 <code>p</code> \u5fc5\u987b\u4e3a\u4e00\u4e2a\u53d8\u91cf\uff0c\u4e0d\u53ef\u4ee5\u662f\u5e38\u91cf\u3001\u8868\u8fbe\u5f0f\u7b49\u3002</p> <p>3.<code>reference</code> \u4e0e <code>const</code></p> <p>\u8fdb\u884c <code>const int &amp;refA = A;</code> \u64cd\u4f5c\u540e\uff0c\u6211\u4eec\u53d1\u73b0 <code>refA</code> \u4e0d\u53ef\u4fee\u6539\uff0c\u4f46 <code>A</code> \u53ef\u4ee5\u4fee\u6539</p> <p>\u5982\u679c <code>A</code> \u5982\u6b64\u5b9a\u4e49\uff1a<code>const int A = 1;</code>\uff0c\u90a3\u4e48\uff1a</p> <ul> <li><code>int &amp;refA = A;</code>\u975e\u6cd5</li> <li><code>const int &amp;refA = A;</code>\u5408\u6cd5</li> <li><code>const int &amp;refA = 1;</code>\u5408\u6cd5</li> <li>\u51fd\u6570\u4f20\u53c2\u540c\u7406</li> </ul>"},{"location":"tech_accu/language/cpp/Part0/#2x-\u8303\u56f4\u89e3\u6790\u8fd0\u7b97\u7b26resolver","title":"[2.x] \u8303\u56f4\u89e3\u6790\u8fd0\u7b97\u7b26resolver","text":"<ul> <li><code>&lt;Class Name&gt;::&lt;Function Name&gt;</code> \u8868\u793a\u8fd9\u4e2a <code>&lt;Function Name&gt;</code> \u662f\u4e0d\u81ea\u7531\u7684\uff0c\u5c5e\u4e8e <code>&lt;Class Name&gt;</code>\u7684\uff1b</li> <li><code>::&lt;Function Name&gt;</code> \u8868\u793a\u8fd9\u4e2a <code>&lt;Function Name&gt;</code>\u662f\u5168\u5c40\u53d8\u91cf\u4e2d\u7684\u81ea\u7531\u51fd\u6570\uff08\u53d8\u91cf\u540c\u7406\uff09\uff1b</li> </ul> <pre><code>#include&lt;iostream&gt;\nusing namespace std;\n\nclass S{\npublic:\nvoid f();\nprivate:\nint a;\n};\n\nint a;\n\nvoid f(){\ncout &lt;&lt; \"qwq\\n\";\n}\n\nvoid S::f(){ // \u8fd9\u91cc\u6b63\u5728\u5b9a\u4e49\u4e00\u4e2a\u5c5e\u4e8e\u7c7bS\u7684\u7684\u51fd\u6570\n++a;     // \u8fd9\u91cc\u5bf9\u4e00\u4e2a\u7c7bS\u7684\u6210\u5458\u53d8\u91cfa\u8fdb\u884c\u4e86\u81ea\u589e\u64cd\u4f5c\n::f();   // \u8fd9\u91cc\u8c03\u7528\u4e86\u4e00\u4e2a\u5168\u5c40\u4e0b\u7684\u81ea\u7531\u51fd\u6570\n++::a;   // \u8fd9\u91cc\u5bf9\u4e00\u4e2a\u5168\u5c40\u53d8\u91cfa\u8fdb\u884c\u4e86\u81ea\u589e\u64cd\u4f5c\ncout &lt;&lt; a &lt;&lt; \" \" &lt;&lt; ::a &lt;&lt; \"\\n\";\n}\n\nint main(){\nS k;\nk.f(); }\n</code></pre> <ul> <li>\u7c7b\u7684\u9759\u6001\u53d8\u91cf\u5c5e\u4e8e\u7c7b\u4e0d\u5c5e\u4e8e\u5b9e\u4f8b\uff0c\u4e0d\u80fd\u901a\u8fc7\u6b63\u5e38\u7684\u65b9\u5f0f\u521d\u59cb\u5316\uff0c\u53ef\u4ee5\u7528\u8fc7\u8303\u56f4\u89e3\u6790\u8fd0\u7b97\u7b26\u5728\u5168\u5c40\u521d\u59cb\u5316</li> <li>\u5b9e\u9645\u4e0a\uff0c\u7f16\u8bd1\u5668\u5c06\u5bf9\u8c61\u5bf9\u9759\u6001\u53d8\u91cf\u7684\u8bbf\u95ee\u81ea\u52a8\u8f6c\u6362\u6210\u4e86\u7c7b\u5bf9\u9759\u6001\u53d8\u91cf\u7684\u8bbf\u95ee\u3002\u56e0\u6b64\uff0c\u5efa\u8bae\u59cb\u7ec8\u4f7f\u7528<code>className::staticVar</code>\u8bbf\u95ee\u9759\u6001\u53d8\u91cf_(xxjj\u5728\u8fd9\u91cc\u8bf4\u7684)_</li> </ul>"},{"location":"tech_accu/language/cpp/Part0/#3x-\u51fd\u6570\u7684\u91cd\u8f7doverload","title":"[3.x] \u51fd\u6570\u7684\u91cd\u8f7dOverload","text":"<p>\u53ef\u4ee5\u5b58\u5728\u51fd\u6570\u540d\u76f8\u540c\u4f46\u662f\u53c2\u6570\u8868\u4e0d\u540c\u7684\u591a\u4e2a\u51fd\u6570\uff0c\u5373\u51fd\u6570\u7684\u91cd\u8f7d\u3002</p> <p>\u7c7b\u4f3cGolang\u7684interface\uff0c\u53c2\u6570\u8868\u5b8c\u5168\u7b26\u5408\u54ea\u4e2a\u5c31\u6267\u884c\u54ea\u4e2a(\u51fa\u73b0\u6b67\u4e49\u65f6\u4f1a\u629b\u51fa\u9519\u8bef)</p> <pre><code>int k(int x){ return x; }\n\nchar k(long x){ return 'a'; }\n\nint main(){\ncout &lt;&lt; k(1L);   // \u8f93\u51fa\uff1aa\ncout &lt;&lt; k(1);    // \u8f93\u51fa\uff1a1\n}\n</code></pre> <ul> <li>overload\u4e0d\u652f\u6301\u81ea\u52a8\u7c7b\u578b\u8f6c\u6362</li> </ul>"},{"location":"tech_accu/language/cpp/Part0/#4x-\u51fd\u6570\u7684\u9ed8\u8ba4\u53c2\u6570default-argument","title":"[4.x] \u51fd\u6570\u7684\u9ed8\u8ba4\u53c2\u6570Default Argument","text":"<p>\u5f62\u5f0f\uff1a<code>void fun(int a = 0);</code></p> <ul> <li>\u6b64\u65f6\u8c03\u7528<code>fun()</code>\u53ef\u4ee5\u7701\u7565\u5b58\u5728\u9ed8\u8ba4\u53c2\u6570\u7684\u53c2\u6570</li> <li>\u4f46\u662f\u4e0d\u5b58\u5728\u9ed8\u8ba4\u503c\u7684\u53c2\u6570\u5fc5\u987b\u5728\u5b58\u5728\u9ed8\u8ba4\u503c\u7684\u53c2\u6570\u524d\u9762</li> <li><code>void fun(int x, int a = 0);</code>\u5408\u6cd5</li> <li><code>void fun(int x = 0, int a);</code>\u975e\u6cd5</li> <li>\u5982\u679c\u540c\u65f6\u5b58\u5728\u51fd\u6570\u58f0\u660e\u548c\u51fd\u6570body\uff0c\u5219\u5728\u8fd9\u4e24\u90e8\u5206\u4e2dDefault Argument\u53ea\u80fd\u5728\u5176\u4e2d\u4e00\u4e2a</li> </ul> <pre><code>// \u5408\u6cd5\nvoid fun(int x,int y);\n\nvoid fun(int x = 1,int y = 2){\n// ...\n}\n</code></pre> <pre><code>// \u975e\u6cd5\uff0c\u56e0\u4e3ax\u4e0d\u80fd\u5728y\u524d\nvoid fun(int x = 1,int y); void fun(int x,int y = 2){\n// ...\n}\n</code></pre> <pre><code>// \u5408\u6cd5\nvoid fun(int x = 1,int y = 2);\n\nvoid fun(int x,int y){\n// ...\n}\n</code></pre>"},{"location":"tech_accu/language/cpp/Part0/#5x-\u5185\u8054\u51fd\u6570inline","title":"[5.x] \u5185\u8054\u51fd\u6570<code>inline</code>","text":"<p>\u4e3b\u8981\u4f5c\u7528\u662f\u5728\u51fd\u6570\u4f18\u5316\u4e0a\uff0c\u6548\u679c\u662f\u727a\u7272\u7a7a\u95f4\u6362\u6548\u7387\uff0c\u9002\u7528\u4e8e\u77ed\u5c0f\u4e14\u9891\u7e41\u4f7f\u7528\u7684\u51fd\u6570\u4ee3\u7801</p> <p>\u5b9e\u73b0\u5c31\u662f\u7f16\u8bd1\u5668\u628a\u51fd\u6570\u5185\u5bb9\u8d34\u5230\u8c03\u7528\u51fd\u6570\u7684\u5730\u65b9\u6765\u51cf\u5c11\u6808\u6d88\u8017</p> <ul> <li><code>inline</code>\u4ec5\u4ec5\u662f\u5bf9\u7f16\u8bd1\u5668\u7684\u4e00\u4e2a\u5efa\u8bae</li> <li>\ud83d\udd17\u5f15\u7528\u4e00\u4e0bxxjj\u7684\u6587\u7ae0</li> <li>\u9700\u8981\u6ce8\u610f\u7684\u662f\uff0c<code>inline</code>\u662f\u5728\u6bcf\u4e00\u4e2a\u7f16\u8bd1\u5355\u5143\u4e2d\u8fdb\u884c\u7684\uff0c\u6240\u4ee5\u8fd9\u5c31\u5bfc\u81f4\u4e86\u5185\u8054\u51fd\u6570\u7684\u539f\u578b\u5e94\u5f53\u80fd\u76f4\u63a5\u88ab\u8c03\u7528\u8be5\u51fd\u6570\u7684\u6587\u4ef6\u8bbf\u95ee\u5230\u3002</li> <li>eg.<ul> <li>\u5728<code>a.cpp</code>\u4e2d\u8c03\u7528<code>f();</code>\u5e76<code>#include \"b.h\"</code></li> <li>\u5728<code>b.h</code>\u4e2d\u58f0\u660e<code>inline void f();</code></li> <li>\u5728<code>b.cpp</code>\u4e2d\u5199\u660e<code>f()</code>\u7684body</li> </ul> </li> <li>\u7ed3\u679c\u5c31\u662f\u4f1a\u7f16\u8bd1\u9519\u8bef\u2014\u2014\u9700\u8981\u5c06<code>f()</code>\u7684body\u653e\u5230<code>a.cpp</code>\u6216\u8005<code>b.h</code>\u4e2d\u624d\u53ef\u4ee5\u2014\u2014\u56e0\u4e3a\u5728\u7f16\u8bd1\u7684\u65f6\u5019<code>a.cpp</code>\u4ec5\u548c<code>b.h</code>\u4e00\u8d77\u7f16\u8bd1\uff0c\u5e76\u4e0d\u77e5\u9053<code>f()</code>\u7684body\u5728\u54ea\u91cc\uff0c\u65e0\u6cd5\u8fdb\u884c\u201c\u5185\u8054\u201d</li> <li><code>inline</code>\u4e0e \u5b8f \u5f88\u76f8\u4f3c\uff0c\u4f46\u662f\u6709\u4e00\u4e9b\u533a\u522b\uff1a</li> </ul> <p></p> <ul> <li>\u505a\u7684\u4e8b\u60c5\u662f\u7c7b\u4f3c\u7684\uff0c\u4f46\u7528\u5b8f\u65e0\u6cd5\u5b9e\u73b0\u9690\u5f0f\u7c7b\u578b\u8f6c\u5316</li> <li>\u5bf9\u7f16\u8bd1\u5668\u6765\u8bf4<code>inline</code>\u53ea\u662f\u4e2a\u5efa\u8bae\uff0c\u7f16\u8bd1\u5668\u672a\u5fc5\u4f1a\u5b9e\u73b0</li> <li>\u5728\u4e00\u4e2a\u7c7b\u91cc\u5b9a\u4e49body\u7684\u51fd\u6570\uff0c\u5b83\u9ed8\u8ba4\u662f<code>inline</code>\u51fd\u6570</li> <li>\u5982\u679c\u5728\u7c7b\u91cc\u6ca1\u6709\u5b9a\u4e49body\uff0c\u90a3\u4e48\u8be5\u51fd\u6570\u662f\u5185\u8054\u51fd\u6570\u5f53\u4e14\u4ec5\u5f53\u524d\u9762\u6709<code>inline</code>\u5173\u952e\u8bcd</li> </ul>"},{"location":"tech_accu/language/cpp/Part0/#6x-const","title":"[6.x] const","text":"<p><code>const</code>\u5bf9\u6570\u636e\u7684\u4fdd\u62a4\u51fa\u73b0\u5728\u7f16\u8bd1\u65f6\u523b\uff0c\u5982\u679c\u5f3a\u884c\u901a\u8fc7\u67d0\u79cd\u624b\u6bb5\u83b7\u53d6\u5176\u5730\u5740\uff0c\u4ecd\u7136\u53ef\u4ee5\u4fee\u6539\uff0c\u7f16\u8bd1\u5668\u4ec5\u4ec5\u4fdd\u8bc1<code>const</code>\u4fee\u9970\u8fc7\u7684\u53d8\u91cf\u9664\u4e86\u5b9a\u4e49\u65f6\uff0c\u4e0d\u80fd\u4f5c\u4e3a\u5de6\u503c</p> <ul> <li><code>char * const p;</code>\u4fee\u9970\u7684\u662f<code>p</code></li> <li><code>const char *p;</code>\u4fee\u9970\u7684\u662f<code>*p</code></li> <li><code>char const *p;</code>\u4fee\u9970\u7684\u662f<code>*p</code></li> <li><code>const char * const p;``*p</code>\u548c<code>p</code>\u90fd\u88ab\u4fee\u9970</li> <li><code>const</code>\u51fa\u73b0\u5728<code>*</code>\u5de6\u4fa7\uff0c\u4fee\u9970\u7684\u662f<code>*p</code></li> <li><code>const</code>\u51fa\u73b0\u5728<code>*</code>\u53f3\u4fa7\uff0c\u4fee\u9970\u7684\u662f<code>p</code></li> <li>\uff08\u82e5<code>const char *p = &amp;ch;</code>\uff0c\u867d\u7136\u901a\u8fc7<code>*p</code>\u65e0\u6cd5\u66f4\u6539\u6307\uff0c\u4f46<code>ch</code>\u4ecd\u7136\u53ef\u4ee5\u4fee\u6539\uff0c\u8fdb\u4e00\u6b65\u4f53\u73b0\u8fd9\u662f\u4e2a\u7f16\u8bd1\u65f6\u523b\u884c\u4e3a\uff09</li> <li></li> <li>\u5728\u8fd9\u4e9b\u6027\u8d28\u4e0b\uff0c\u6211\u4eec\u53ef\u4ee5\u628a\u4e00\u4e2a\u975e<code>const</code>\u7684\u53d8\u91cf\u8d4b\u503c\u7ed9<code>const</code>\u53d8\u91cf\uff08\u7279\u522b\u662f\u51fd\u6570\u4f20\u53c2\uff09\uff0c\u6765\u63a7\u5236\u6307\u9488\u7684\u8bfb\u5199\u6743\u9650\uff08\u53ef\u4ee5\u7528\u6765\u51cf\u5c11\u4ee3\u7801\u5199\u9519\u7684\u60c5\u51b5\uff09</li> <li></li> <li>\u4e00\u4e2a\u88ab<code>const</code>\u4fee\u9970\u8fc7\u7684\u5bf9\u8c61\u7684\u6210\u5458\u51fd\u6570\u53ea\u6709\u5728\u8be5\u51fd\u6570\u4e5f\u88ab<code>const</code>\u4fee\u9970\u8fc7\u4e14\u7ecf\u8fc7\u7f16\u8bd1\u5668\u68c0\u6d4b\u786e\u5b9e\u4e0d\u4fee\u6539\u6210\u5458\u53d8\u91cf\u7684\u60c5\u51b5\u4e0b\u624d\u80fd\u6267\u884c</li> <li></li> <li><code>int A::fun() const;</code>\u548c<code>int A::fun();</code>\u53ef\u4ee5\u6784\u6210overload\u5173\u7cfb\uff0c\u56e0\u4e3a\u8fd9\u91cc\u7684<code>const</code>\u5b9e\u9645\u4e0a\u6307\u7684\u662f\u9690\u85cf\u7684<code>A *this</code>\u88ab<code>const</code>\u4fee\u9970\uff0c\u53c2\u6570\u8868\u4e0d\u540c\uff0c\u7b26\u5408overload\u6761\u4ef6</li> <li>\u5f53\u4e0a\u8ff0\u4e24\u4e2a\u51fd\u6570\u90fd\u5b58\u5728\u65f6\uff0c\u5f53\u4e14\u4ec5\u5f53\u5bf9\u8c61\u88ab<code>const</code>\u4fee\u9970\u624d\u4f1a\u8c03\u7528\u524d\u8005</li> <li>\u5982\u679c\u6210\u5458\u53d8\u91cf\u662f<code>const</code>\uff0c\u90a3\u5fc5\u987b\u5b58\u5728\u521d\u59cb\u5316\u65b9\u6848</li> </ul>"},{"location":"tech_accu/language/cpp/Part0/#7x-static","title":"[7.x] static","text":"<p>\u867d\u7136\u5728\u5355\u4e2a\u6587\u4ef6\u5185\uff0c\u9759\u6001\u5168\u5c40\u53d8\u91cf\u7684\u58f0\u660e\u987a\u5e8f\u53ef\u4ee5\u786e\u8ba4\uff0c\u4f46\u6587\u4ef6\u95f4\u7684\u987a\u5e8f\u65e0\u6cd5\u786e\u8ba4\uff0c\u8fd9\u53ef\u80fd\u9020\u6210\u4f9d\u8d56\u95ee\u9898\uff0c\u6240\u4ee5\u5c3d\u53ef\u80fd\u907f\u514d\u591a\u6587\u4ef6\u9759\u6001\u5168\u5c40\u53d8\u91cf\u7684\u4f9d\u8d56\u5173\u7cfb</p> <ul> <li>\u7c7b\u7684\u9759\u6001\u53d8\u91cf\u5c5e\u4e8e\u7c7b\u4e0d\u5c5e\u4e8e\u5b9e\u4f8b\uff0c\u4e0d\u80fd\u901a\u8fc7\u6b63\u5e38\u7684\u65b9\u5f0f\u521d\u59cb\u5316\uff0c\u53ef\u4ee5\u7528\u8fc7\u8303\u56f4\u89e3\u6790\u8fd0\u7b97\u7b26\u5728\u5168\u5c40\u521d\u59cb\u5316</li> <li>\u5b9e\u9645\u4e0a\uff0c\u7f16\u8bd1\u5668\u5c06\u5bf9\u8c61\u5bf9\u9759\u6001\u53d8\u91cf\u7684\u8bbf\u95ee\u81ea\u52a8\u8f6c\u6362\u6210\u4e86\u7c7b\u5bf9\u9759\u6001\u53d8\u91cf\u7684\u8bbf\u95ee\u3002\u56e0\u6b64\uff0c\u5efa\u8bae\u59cb\u7ec8\u4f7f\u7528<code>className::staticVar</code>\u8bbf\u95ee\u9759\u6001\u53d8\u91cf_(xxjj\u5728\u8fd9\u91cc\u8bf4\u7684)_</li> <li>\u7c7b\u7684\u9759\u6001\u51fd\u6570\u4e0d\u518d\u5177\u6709<code>this</code>\u6307\u9488\uff0c\u4e5f\u4e0d\u80fd\u76f4\u63a5\u8bbf\u95ee\u975e\u9759\u6001\u6210\u5458\u53d8\u91cf\u6216\u8005\u975e\u9759\u6001\u6210\u5458\u51fd\u6570</li> <li>\u4e00\u822c\u60c5\u51b5\u4e0b\uff0c\u5982\u679c\u8981\u5728<code>class</code>\u91cc\u58f0\u660e<code>static</code>\u53d8\u91cf/\u51fd\u6570\uff0c\u5219\u53ea\u5728<code>.h</code>\u6587\u4ef6\u4e2d\u51fa\u73b0\u5173\u952e\u5b57\uff0c\u4e0d\u8981\u5728<code>.cpp</code>\u4e2d\u51fa\u73b0</li> </ul>"},{"location":"tech_accu/language/cpp/Part0/#8x-\u547d\u540d\u7a7a\u95f4namespace--using\u5173\u952e\u5b57","title":"[8.x] \u547d\u540d\u7a7a\u95f4namespace &amp; using\u5173\u952e\u5b57","text":"<p>\u53ef\u4ee5\u7528<code>namespace</code>\u6765\u5c01\u88c5\u4ee3\u7801</p> <pre><code>namespace &lt;Space Name&gt;{\n// \u5185\u5bb9\n} </code></pre> <p>\u5728\u4e4b\u540e\u4f7f\u7528\u91cc\u9762\u7684\u53d8\u91cf/\u51fd\u6570\u9700\u8981\u4f7f\u7528\u8303\u56f4\u89e3\u6790\u8fd0\u7b97\u7b26<code>::</code>\uff0c\u5373<code>&lt;Space Name&gt;::&lt;Function Name&gt;();</code></p> <ul> <li><code>using namespace xxx;</code>\u540e\u53ef\u4ee5\u7701\u7565<code>&lt;Space Name&gt;::</code>\uff0c\u4f46\u662f\u8981\u6ce8\u610f\u6b67\u4e49\u95ee\u9898</li> <li><code>using xxx::yyy;</code>\u540e\u4ec5\u4ec5\u5bf9<code>yyy</code>\u6765\u8bf4\u53ef\u4ee5\u7701\u7565<code>&lt;Space Name&gt;::</code>\uff0c\u540c\u6837\u8981\u6ce8\u610f\u6b67\u4e49\u95ee\u9898</li> <li>\u4e24\u4e2a\u547d\u540d\u7a7a\u95f4\u6709\u76f8\u540c\u51fd\u6570/\u53d8\u91cf\u7684\u65f6\u5019\uff0c\u9700\u8981\u5199\u660e\u547d\u540d\u7a7a\u95f4</li> <li><code>namespace x = y;</code>\u8868\u793a\u53ef\u4ee5\u7528<code>x</code>\u6765\u8868\u793a\u547d\u540d\u7a7a\u95f4<code>y</code>\uff0c\u4f46\u662f\u5728\u6b64\u524d<code>y</code>\u5fc5\u987b\u5df2\u7ecf\u5b9a\u4e49</li> <li><code>namespace</code>\u91cc\u4e5f\u53ef\u4ee5\u6709<code>namespace</code>\uff0c\u6211\u4eec\u79f0\u4e4b\u4e3a \u7ec4\u5408</li> </ul>"},{"location":"tech_accu/language/cpp/Part0/#9x-\u5de6\u503c\u4e0e\u53f3\u503c\u53f3\u503c\u5f15\u7528","title":"[9.x] \u5de6\u503c\u4e0e\u53f3\u503c&amp;\u53f3\u503c\u5f15\u7528","text":""},{"location":"tech_accu/standard/","title":"\u6249\u9875","text":"<p> \u7ea6 15 \u4e2a\u5b57 </p> <p> \u300e\u305d\u306e\u6642\u3092\u5f85\u3064\u3088\u300f      \u9761\u4e0d\u6709\u521d\uff0c\u9c9c\u514b\u6709\u7ec8\u3002  \u2014\u2014\u300a\u8bd7\u7ecf\u300b  </p>"},{"location":"tech_accu/standard/BVH_format/","title":"BVH \u683c\u5f0f\u8be6\u89e3","text":"<p> \u7ea6 1312 \u4e2a\u5b57  116 \u884c\u4ee3\u7801  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 6 \u5206\u949f</p>"},{"location":"tech_accu/standard/BVH_format/#\u7b80\u4ecb","title":"\u7b80\u4ecb","text":"<p>BVH \u8868\u793a Biovision Hierarchy Data\uff0c\u662f Biovision \u52a8\u6355\u8bbe\u5907\u7684\u6570\u636e\u8f93\u51fa\u683c\u5f0f\uff0c\u662f BVA \u683c\u5f0f\u7684\u6539\u8fdb\uff0c\u5e7f\u6cdb\u5e94\u7528\u4e8e\u52a8\u753b\u5236\u4f5c\u8f6f\u4ef6\u3002\u800c\u8be5\u683c\u5f0f\u4ee5\u6587\u672c\u5f62\u5f0f\u50a8\u5b58\uff0c\u6240\u4ee5\u4fbf\u4e8e\u5f00\u53d1\u3002 \u4ece\u9700\u6c42\u7684\u89d2\u5ea6\u6765\u8bb2\uff0c\u4e3a\u4e86\u4f18\u96c5\u5730\u89e3\u51b3\u52a8\u753b\u5236\u4f5c\u95ee\u9898\uff0c\u5b83\u88ab\u5206\u4e3a\u4e86\u201c\u8499\u76ae\u201d\u548c\u201c\u9aa8\u9abc\u201d\u4e24\u4e2a\u90e8\u5206\u3002\u800c BVH \u5c31\u8d1f\u8d23\u5b58\u50a8 \u9aa8\u9abc\u67b6\u7ed3\u6784 \u548c \u52a8\u4f5c\u4fe1\u606f\u3002 BVH \u683c\u5f0f\u603b\u4f53\u6765\u8bf4\u6bd4\u8f83\u4f18\u79c0\uff0c\u4f46\u662f\u7f3a\u4e4f\u5bf9\u8fd0\u52a8\u65f6\u7684\u9aa8\u67b6\u59ff\u52bf\u7684\u5b8c\u6574\u89e3\u91ca\u3002\u56e0\u4e3a BVH \u662f\u901a\u8fc7 \u504f\u79fb(Offset) \u6765\u63cf\u8ff0\u8fd0\u52a8\u7684\uff0c\u5373\u4fdd\u5b58\u7684\u662f\u6bcf\u4e00\u5e27\u5173\u952e\u8282\u70b9\u5bf9\u4e8e\u7236\u8282\u70b9\u7684\u76f8\u5bf9\u4f4d\u79fb\u3002</p>"},{"location":"tech_accu/standard/BVH_format/#\u6587\u4ef6\u89e3\u6790","title":"\u6587\u4ef6\u89e3\u6790","text":"<p>A BVH file has two parts, a header section which describes the hierarchy and initial pose of the skeleton; and a data section which contains the motion data. </p> <p>BVH \u6587\u4ef6\u6570\u636e\u5206\u4e3a\u4e24\u4e2a\u90e8\u5206\uff1a</p> <ul> <li>\u9aa8\u67b6\u4fe1\u606f(header section)\uff1a\u5b9a\u4e49\u4e86\u9aa8\u67b6\u7684\u7ec4\u7ec7\u7ed3\u6784\uff0c\u6307\u5bfc\u5982\u4f55\u89e3\u6790\u6570\u636e\u5757\u3002</li> <li>\u6570\u636e\u5757(data section)\uff1a\u5305\u542b\u4e86\u6bcf\u4e00\u5e27\u5404\u90e8\u5206\u7684\u6570\u636e\u4fe1\u606f\u3002</li> </ul> <p>\u5e76\u4e14\u4ee5\u9012\u5f52\u7684\u5f62\u5f0f\u7ed9\u51fa\u5b9a\u4e49\u3002 \u4e0b\u9762\u7ed9\u51fa\u4e00\u4e2a\u793a\u4f8b\u6587\u4ef6\uff0c\u7136\u540e\u505a\u8fdb\u4e00\u6b65\u5206\u6790\u3002</p> Summary <pre><code>HIERARCHY\nROOT Hips\n{\nOFFSET  0.00    0.00    0.00\nCHANNELS 6 Xposition Yposition Zposition Zrotation Xrotation Yrotation\nJOINT Chest\n{\nOFFSET   0.00    5.21    0.00\nCHANNELS 3 Zrotation Xrotation Yrotation\nJOINT Neck\n{\nOFFSET   0.00    18.65   0.00\nCHANNELS 3 Zrotation Xrotation Yrotation\nJOINT Head\n{\nOFFSET   0.00    5.45    0.00\nCHANNELS 3 Zrotation Xrotation Yrotation\nEnd Site {\nOFFSET   0.00    3.87    0.00\n}\n}\n}\nJOINT LeftCollar\n{\nOFFSET   1.12    16.23   1.87\nCHANNELS 3 Zrotation Xrotation Yrotation\nJOINT LeftUpArm\n{\nOFFSET   5.54    0.00    0.00\nCHANNELS 3 Zrotation Xrotation Yrotation\nJOINT LeftLowArm\n{\nOFFSET   0.00   -11.96   0.00\nCHANNELS 3 Zrotation Xrotation Yrotation\nJOINT LeftHand\n{\nOFFSET   0.00   -9.93    0.00\nCHANNELS 3 Zrotation Xrotation Yrotation\nEnd Site {\nOFFSET   0.00   -7.00    0.00\n}\n}\n}\n}\n}\nJOINT RightCollar\n{\nOFFSET  -1.12    16.23   1.87\nCHANNELS 3 Zrotation Xrotation Yrotation\nJOINT RightUpArm\n{\nOFFSET  -6.07    0.00    0.00\nCHANNELS 3 Zrotation Xrotation Yrotation\nJOINT RightLowArm\n{\nOFFSET   0.00   -11.82   0.00\nCHANNELS 3 Zrotation Xrotation Yrotation\nJOINT RightHand\n{\nOFFSET   0.00   -10.65   0.00\nCHANNELS 3 Zrotation Xrotation Yrotation\nEnd Site {\nOFFSET   0.00   -7.00    0.00\n}\n}\n}\n}\n}\n}\nJOINT LeftUpLeg\n{\nOFFSET   3.91    0.00    0.00\nCHANNELS 3 Zrotation Xrotation Yrotation\nJOINT LeftLowLeg\n{\nOFFSET   0.00   -18.34   0.00\nCHANNELS 3 Zrotation Xrotation Yrotation\nJOINT LeftFoot\n{\nOFFSET   0.00   -17.37   0.00\nCHANNELS 3 Zrotation Xrotation Yrotation\nEnd Site {\nOFFSET   0.00   -3.46    0.00\n}\n}\n}\n}\nJOINT RightUpLeg\n{\nOFFSET  -3.91    0.00    0.00\nCHANNELS 3 Zrotation Xrotation Yrotation\nJOINT RightLowLeg\n{\nOFFSET   0.00   -17.63   0.00\nCHANNELS 3 Zrotation Xrotation Yrotation\nJOINT RightFoot\n{\nOFFSET   0.00   -17.14   0.00\nCHANNELS 3 Zrotation Xrotation Yrotation\nEnd Site {\nOFFSET   0.00   -3.75    0.00\n}\n}\n}\n}\n}\nMOTION\nFrames:    2\nFrame Time: 0.033333\n8.03     35.01   88.36  -3.41    14.78  -164.35  13.09   40.30  -24.60   7.88    43.80   0.00   -3.61   -41.45   5.82    10.08   0.00    10.21   97.95  -23.53  -2.14   -101.86 -80.77  -98.91   0.69    0.03    0.00   -14.04   0.00   -10.50  -85.52  -13.72  -102.93  61.91  -61.18   65.18  -1.57    0.69    0.02    15.00   22.78  -5.92    14.93   49.99   6.60    0.00   -1.14    0.00   -16.58  -10.51  -3.11    15.38   52.66  -21.80   0.00   -23.95   0.00   7.81     35.10   86.47  -3.78    12.94  -166.97  12.64   42.57  -22.34   7.67    43.61   0.00   -4.23   -41.41   4.89    19.10   0.00    4.16    93.12  -9.69   -9.43    132.67 -81.86   136.80  0.70    0.37    0.00   -8.62    0.00   -21.82  -87.31  -27.57  -100.09  56.17  -61.56   58.72  -1.63    0.95    0.03    13.16   15.44  -3.56    7.97    59.29   4.97    0.00    1.64    0.00   -17.18  -10.02  -3.08    13.56   53.38  -18.07   0.00   -25.93   0.00   </code></pre> <p>\u8be5\u6837\u4f8b\u7ed9\u51fa\u4e86\u8fd9\u6837\u4e00\u4e2a\u9aa8\u67b6\uff1a</p> <p></p> \\[ vR = vYXZ\\\\ vM= vM_{child}M_{parent}M_{grandparent}... \\]"},{"location":"tech_accu/standard/BVH_format/#header-section","title":"header section","text":"<p><code>HIERARCHY</code>\u5173\u952e\u5b57\u6807\u8bc6<code>header section</code>\u7684\u5f00\u59cb\uff0c\u968f\u540e\u5728\u4e0b\u4e00\u884c\u5b9a\u4e49\u4e86\u6839\u8282\u70b9<code>ROOT</code>\uff0c\u800c<code>Hips</code>\u5219\u662f\u8be5\u8282\u70b9\u7684\u540d\u79f0\u3002\u89c2\u5bdf\u4e0a\u65b9\u7ed9\u51fa\u7684\u9aa8\u67b6\u793a\u610f\u56fe\uff0c<code>Hips</code>\u8282\u70b9\u4f5c\u4e3a\u6574\u4e2a\u9aa8\u67b6\u7684\u6839\u8282\u70b9\uff0c\u4fdd\u8bc1\u4e86\u6574\u4e2a\u6811\u5f62\u56fe\u7684\u6700\u5927\u6df1\u5ea6\u76f8\u5bf9\u8f83\u5c0f\uff0c\u51cf\u5c0f\u8bef\u5dee\u3002</p> <p>\u5176\u540e\u7ed9\u51fa\u4e86<code>OFFSET</code>\u548c<code>CHANNELS</code>\u4e24\u4e2a\u5c5e\u6027\u3002</p> <ul> <li><code>OFFSET</code>\u8868\u793a\u76f8\u5bf9\u4e0e\u7236\u8282\u70b9\uff0c\u8be5\u8282\u70b9\u7684\u504f\u79fb\uff1b</li> <li>\u5bf9\u4e8e \u6839\u8282\u70b9 \u6765\u8bf4\uff0c\u5b83\u4e00\u822c\u662f<code>0 0 0</code>\uff1b</li> <li>\u00b7<code>CHANNELS</code>\u540e\u6709\u4e24\u4e2a\u90e8\u5206\uff0c\u9996\u5148\u662f\u4e00\u4e2a\u6570\u5b57\u8868\u793a\u540e\u9762\u6709\u51e0\u4e2a\u901a\u9053\u3002</li> <li>\u4e00\u822c\u6765\u8bf4\uff0c\u6839\u8282\u70b9 \u4f1a\u6709 6 \u4e2a\u901a\u9053\uff0c\u5982\u4e0a\u793a\u4f8b\u6709<code>Xposition Yposition Zposition Zrotation Yrotation Xrotation</code>\uff0c\u5206\u522b\u4ee3\u8868\u5728<code>data section</code>\u4e2d\uff0c\u5e27\u5e8f\u5217\u7684\u6570\u636e\u6309\u8fd9\u6837\u7684\u65b9\u5f0f\u5b58\u50a8\uff0c\u524d\u4e09\u4e2a\u4ee3\u8868\u7684\u662f \u4f4d\u79fb \u4e0b\u6bcf\u4e2a\u5206\u91cf\u7684\u987a\u5e8f\uff08\u6b64\u5904\u8868\u793a\uff1a\u4f9d\u6b21\u4e3a x \u5750\u6807\uff0c y \u5750\u6807\uff0c z \u5750\u6807\uff0c\u4e00\u822c\u53ea\u6709\u6839\u8282\u70b9\u6709\u8fd9\u4e09\u4e2a\u901a\u9053\uff0c\u7528\u6765\u8868\u793a\u9aa8\u67b6\u7684\u4f4d\u79fb\uff09\uff0c\u540e\u4e09\u4e2a\u4ee3\u8868\u7684\u662f \u65cb\u8f6c\u89d2\u5ea6 \u987a\u5e8f\uff1b</li> <li>\u800c\u5bf9\u4e8e \u975e\u6839\u8282\u70b9\uff0c\u4e00\u822c\u6709 3 \u4e2a\u901a\u9053\uff0c\u4ee3\u8868\u7684 \u65cb\u8f6c\u89d2\u5ea6 \u987a\u5e8f\uff1b</li> <li>\u6ce8\u610f\uff0c\u8fd9\u91cc\u4f7f\u7528\u7684 \u89d2\u5ea6\u5236 \u800c\u975e\u5f27\u5ea6\u5236\uff1b</li> </ul> <p>\u800c\u5728\u5176\u540e\uff0c\u4ee5<code>JOINT</code>\u4e3a\u5173\u952e\u5b57\u53c8\u8868\u793a\u4e86\u5176\u5b50\u8282\u70b9\u7684\u5b9a\u4e49\uff0c\u5373\u4ee5 \u9012\u5f52 \u7684\u5f62\u5f0f\u7ed9\u51fa\u5b9a\u4e49\u3002</p> <p></p> <ul> <li>\u5728\u8fd9\u5f20\u56fe\u4e2d\uff0c<code>Neck``LeftCollar``RightCollar</code>\u662f<code>Chest</code>\u7684\u5b50\u8282\u70b9\uff0c\u5219<code>Neck``LeftCollar``RightCollar</code>\u7684\u76f8\u5bf9\u4f4d\u7f6e\u5e94\u5f53\u4e0d\u53d8\uff0c\u4e4b\u540e\u7684\u53d8\u6362\u4ec5\u4ec5\u901a\u8fc7\u5b83\u4eec\u6574\u4f53\u76f8\u5bf9\u4e8e<code>Chest</code>\u7684\u65cb\u8f6c\u5b9e\u73b0\u3002</li> </ul> <p>\u53ef\u4ee5\u8fd9\u4e48\u7406\u89e3\uff1a</p> <ul> <li><code>ROOT</code>\u548c<code>JOINT</code>\u5728\u8bed\u6cd5\u4e0a\u57fa\u672c\u4e00\u81f4\uff0c</li> <li>\u53ea\u4e0d\u8fc7\u7b2c\u4e00\u4e2a\u51fa\u73b0\u7684\u8282\u70b9\u9700\u8981\u7528<code>ROOT</code>\u7d22\u5f15\uff0c\u4e14\u5b83\u67096\u4e2a\u901a\u9053\uff1b</li> <li>\u800c\u4e4b\u540e\u7684\u5b50\u8282\u70b9\u901a\u8fc7<code>JOINT</code>\u7d22\u5f15\uff0c\u4e14\u67093\u4e2a\u901a\u9053\u3002</li> </ul> <p>\u800c\u5728\u9012\u5f52\u5b9a\u4e49\u7684\u672b\u7aef\uff0c\u4f60\u4f1a\u53d1\u73b0\u4e00\u4e2a<code>End Site</code>\uff0c\u5b83\u53ea\u6709<code>OFFSET</code>\u5c5e\u6027\u800c\u6ca1\u6709<code>CHANNELS</code>\u5c5e\u6027\uff0c\u8fd9\u662f\u56e0\u4e3a\uff1a</p> <ul> <li>\u9aa8\u67b6\u662f\u6709\u82e5\u5e72\u201c\u9aa8\u68d2\u201d\u7ec4\u6210\u7684\uff0c\u8fd9\u4e2a\u201c\u9aa8\u68d2\u201d\u79f0\u4e3a<code>segment</code>\uff0c\u800c\u5b9a\u4e49\u4e00\u4e2a<code>segment</code>\u9700\u8981\u4e24\u4e2a\u7aef\u70b9\uff0c\u800c<code>End Site</code>\u5c31\u662f\u8fd9\u4e2a<code>segment</code>\u94fe\u7684\u672b\u7aef\uff0c\u5b83\u4e0d\u5177\u5907\u65cb\u8f6c\u4fe1\u606f\uff0c\u56e0\u4e3a\u5b83\u6ca1\u6709\u5b50\u8282\u70b9\uff0c\u4ec5\u4ec5\u7528\u6765\u901a\u8fc7\u5750\u6807\u8868\u8fbe\u6700\u540e\u4e00\u4e2a<code>segment</code>\u7684\u957f\u5ea6\u3002</li> </ul> <p>One last note about the BVH hierarchy, the world space is defined as a right handed coordinate system with the Y axis as the world up vector. Thus you will typically find that BVH skeletal segments are aligned along the Y or negative Y axis (since the characters are often have a zero pose where the character stands straight up with the arms straight down to the side).</p> <p>\u5373\u4e16\u754c\u5750\u6807\u7cfb\u4e00\u822c\u662f\u4e00\u4e2a\\(y\\)\u8f74\u671d\u4e0a\u7684\u53f3\u624b\u7cfb\uff0c\u5e76\u4e14\u9aa8\u67b6\u7684\u521d\u59cb\u59ff\u52bf\u603b\u662f T-Pose \uff0c\u5373\u4eba\u6253\u5f00\u53cc\u624b\uff0c\u50cf\u5b57\u6bcd<code>T</code>\u4e00\u6837\u7ad9\u5728\u5730\u4e0a\u3002</p>"},{"location":"tech_accu/standard/BVH_format/#data-section","title":"data section","text":"<p><code>MOTION</code>\u5173\u952e\u5b57\u6807\u8bc6<code>data section</code>\u7684\u5f00\u59cb\uff0c\u4e4b\u540e\u4e24\u884c\u5206\u522b\u662f<code>Frames</code>\u548c<code>Frame Time</code>\uff0c\u8868\u793a \u5e27\u6570 \u548c \u5e27\u6570\u957f\u5ea6\uff08\u5373\u5e27\u7387\u5012\u6570\uff0c0.033333\u5c31\u662f30\u5e27\uff09\u3002 \u800c\u518d\u4e4b\u540e\uff0c\u5219\u662f\u771f\u6b63\u7684\u52a8\u753b\u6570\u636e\uff0c\u6839\u636e<code>header section</code>\u7ed9\u51fa\u7684\u901a\u9053\u5b9a\u4e49\u4f9d\u6b21\u6765\u7ed9\u51fa\u6bcf\u4e00\u5e27\u7684\u76f8\u5bf9\u53d8\u5316\u6570\u636e\u3002 </p>"},{"location":"tech_accu/standard/BVH_format/#\u7406\u89e3","title":"\u7406\u89e3","text":"<p>\u6839\u636e\u6211\u7684\u4e2a\u4eba\u7406\u89e3\uff0c<code>header section</code>\u7c7b\u4f3c\u4e8e\u5c06\u4e00\u6839\u6839\u68d2\u710a\u63a5\u5728\u80fd\u591f\u81ea\u7531\u65cb\u8f6c\u7684\u8282\u70b9\u4e0a\uff0c\u5e76\u89c4\u5b9a\u6570\u636e\u7684\u7ec4\u7ec7\u987a\u5e8f\uff0c\u5373\u89e3\u51b3\u4e86\u9aa8\u67b6\u201c\u957f\u4ec0\u4e48\u6837\u201d\u7684\u95ee\u9898\uff0c\u5e76\u6307\u5bfc\u5982\u4f55\u63cf\u8ff0\u9aa8\u67b6\u201c\u600e\u4e48\u52a8\u201d\uff1b \u800c<code>data section</code>\u5219\u7c7b\u4f3c\u4e8e\u6309\u7167<code>header section</code>\u7ed9\u51fa\u7684\u5b9a\u4e49\uff0c\u5177\u4f53\u8be5\u5982\u4f55\u6539\u53d8\u5404\u4e2a\u8282\u70b9\u7684\u72b6\u6001\u3002 \u9664\u4e86\u53d1\u9001\u7ed9<code>ROOT</code>\u7684\u4f4d\u7f6e\u5750\u6807\u6765\u8868\u793a\u9aa8\u67b6\u7684\u4f4d\u79fb\uff08\u5e73\u79fb\u77e9\u9635\uff09\uff0c\u4e4b\u540e\u7684\u4e00\u7cfb\u5217\u6570\u636e\u90fd\u8868\u793a\u8be5\u8282\u70b9\u8be5\u5982\u4f55\u65cb\u8f6c\uff08\u65cb\u8f6c\u77e9\u9635\uff09\uff0c\u90a3\u4e48\u7406\u6240\u5f53\u7136\u7684\uff0c\u8fd9\u4e2a\u8282\u70b9\u7684\u6240\u6709\u5b50\u8282\u70b9\u90fd\u4f1a\u4ee5\u8fd9\u4e2a\u8282\u70b9\u4e3a\u4e2d\u5fc3\u8fdb\u884c\u76f8\u5e94\u7684\u65cb\u8f6c\uff1b\u6bcf\u6b21\u9012\u5f52\u90fd\u91cd\u590d\u8fd9\u6837\u7684\u64cd\u4f5c\uff0c\u6700\u7ec8\u6307\u6325\u6574\u4e2a\u9aa8\u67b6\u7684\u53d8\u6362\u3002 \u90a3\u4e48\uff0c\u5b9e\u9645\u4e0a\uff0c\u6bcf\u4e00\u4e2a\u8282\u70b9\u76f8\u5bf9\u4e8e\u6839\u8282\u70b9\u7684\u53d8\u5316\u5c31\u53ef\u4ee5\u901a\u8fc7\u8fd9\u4e9b\u53d8\u6362\u77e9\u9635\u6309\u7167\u987a\u5e8f\u7d2f\u4e58\u5f97\u5230\u3002</p>"},{"location":"tech_accu/standard/BVH_format/#\u53c2\u8003\u8d44\u6599","title":"\u53c2\u8003\u8d44\u6599","text":"<ul> <li>https://en.wikipedia.org/wiki/Biovision_Hierarchy</li> <li>https://research.cs.wisc.edu/graphics/Courses/cs-838-1999/Jeff/BVH.html</li> <li>https://blog.csdn.net/u012336923/article/details/50972968</li> <li>https://blog.csdn.net/u012336923/article/details/50979894</li> <li>https://zhuanlan.zhihu.com/p/71818887</li> <li>https://www.4k8k.xyz/article/one_2_one/97963901</li> <li>https://www.youizone.com/2015/06/04/bvh-files.html</li> </ul>"},{"location":"tech_accu/tool/","title":"\u6249\u9875","text":"<p> \u7ea6 15 \u4e2a\u5b57 </p> <p> \u300e\u305d\u306e\u6642\u3092\u5f85\u3064\u3088\u300f      \u9761\u4e0d\u6709\u521d\uff0c\u9c9c\u514b\u6709\u7ec8\u3002  \u2014\u2014\u300a\u8bd7\u7ecf\u300b  </p>"},{"location":"tech_accu/tool/Colab/","title":"Google Colaboratory","text":"<p> \u7ea6 477 \u4e2a\u5b57  6 \u884c\u4ee3\u7801  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 2 \u5206\u949f</p> <p>\u7b80\u4ecb</p> <p>Google Colab \u662f\u4e00\u4e2a\u5141\u8bb8\u7f16\u5199\u548c\u6267\u884c\u4ee3\u7801\u7684\u4ea4\u4e92\u5f0f\u73af\u5883\uff0c\u4ee5\u4e0b\u662f\u5206\u522b\u4e3a Colab \u7684\u7f51\u5740\u4ee5\u53ca\u5b98\u65b9 Q&amp;A\u3002</p> <ul> <li>Colab URL: \ud83d\udd17 </li> <li>A&amp;Q: \ud83d\udd17</li> </ul> <p>\u5bf9\u6211\u6765\u8bf4\uff0cGolab \u4e3a\u6211\u63d0\u4f9b\u4e86\u4e00\u4e2a\u6bd4\u8f83\u65b9\u4fbf\u4e14\u6709\u4e00\u5b9a\u7b97\u529b\u7684\u5728\u7ebf\u5e73\u53f0\uff0c\u800c\u4e14\u6211\u89c9\u5f97\u4f5c\u4e3a\u7b14\u8bb0\u672c\u8c8c\u4f3c\u4e5f\u633a\u597d\u7528\u7684\u3002</p> <p>\u7b80\u5355\u6765\u8bf4\uff0cColab \u4e2d\u5b58\u5728 \u6587\u672c\u5355\u5143 \u548c \u4ee3\u7801\u5355\u5143 \u8fd9\u4e24\u79cd\u6a21\u5757\u3002</p> <ul> <li>\u5728\u6587\u672c\u5355\u5143\u4e2d\uff0c\u4f60\u53ef\u7528\u96c6\u6210\\(\\LaTeX\\)\u3001<code>HTML</code>\u3001\u5bcc\u6587\u672c\u3001Markdown \u7b49\uff1b</li> <li>\u800c\u5bf9\u4e8e\u4ee3\u7801\u5355\u5143\uff0c\u4f60\u5219\u53ef\u4ee5\u76f4\u63a5\u628a\u5b83\u5f53\u4f5c\u4e00\u4e2a<code>Python</code>\u89e3\u91ca\u5668\uff1a</li> </ul> <p></p> <ul> <li>\u540c\u65f6\uff0c\u5728\u4e00\u884c\u7684\u6700\u524d\u9762\u52a0\u4e0a<code>!</code>\u8868\u793a\u8fd9\u662f\u4e00\u4e2a\u7ec8\u7aef\u547d\u4ee4</li> <li>\u4f8b\u5982\u5728 \u4ee3\u7801\u5355\u5143 \u4e2d\u8f93\u5165<code>!pwd</code>\u5c31\u7b49\u4ef7\u4e8e\u5728\u7ec8\u7aef\u4e2d\u8f93\u5165<code>pwd</code></li> <li>\u4f46\u5728 \u4ee3\u7801\u5355\u5143 \u4e2d\u8f93\u5165<code>pwd</code>\u5219\u4f1a\u62a5\u9519\uff0c\u56e0\u4e3a\u8fd9\u4e0d\u662f\u4e00\u4e2a<code>Python</code>\u547d\u4ee4</li> </ul> <p>\u4ece\u7528\u9014\u4e0a\u6765\u8bb2\uff0cColab \u5728\u6570\u636e\u79d1\u5b66\u548c\u673a\u5668\u5b66\u4e60\u8fd9\u4e24\u65b9\u9762\u6709\u8f83\u5927\u7528\u5904\u3002</p> <ul> <li>\u6570\u636e\u79d1\u5b66: \ud83d\udd17</li> <li>\u673a\u5668\u5b66\u4e60: \ud83d\udd17</li> </ul>"},{"location":"tech_accu/tool/Colab/#\u6587\u4ef6\u4e92\u52a8","title":"\u6587\u4ef6\u4e92\u52a8","text":"<p>Colab \u81ea\u5e26\u6587\u4ef6\u6d4f\u89c8\u754c\u9762</p> <p>\u901a\u8fc7\u8fd9\u4e09\u4e2a\u6309\u94ae\u53ef\u4ee5\u5b9e\u73b0 \u4e0a\u4f20\u6587\u4ef6\u3001\u5237\u65b0\u3001\u88c5\u8f7d Google \u4e91\u76d8\uff1a</p> <p></p>"},{"location":"tech_accu/tool/Colab/#\u786c\u4ef6\u52a0\u901f","title":"\u786c\u4ef6\u52a0\u901f","text":"<p>\u5173\u4e8eGPU\u52a0\u901f\u7684\u5177\u4f53\u4fe1\u606f\uff0c\u8bf7\u67e5\u770b\u8fd9\u91cc \ud83d\udd17\u3002</p>"},{"location":"tech_accu/tool/Colab/#\u8d44\u6e90\u9650\u5236","title":"\u8d44\u6e90\u9650\u5236","text":"<ul> <li> <p>\u5173\u4e8e\u8d44\u6e90\u9650\u5236\u7684\u5b98\u65b9\u8bf4\u660e: \ud83d\udd17 </p> </li> <li> <p>\u6761\u76ee\uff1a</p> <ul> <li>\u4e3a\u4ec0\u4e48 Colab \u4e0d\u80fd\u4fdd\u8bc1\u8d44\u6e90\u4f9b\u5e94\uff1f</li> <li>Colab \u7684\u7528\u91cf\u9650\u989d\u662f\u591a\u5c11\uff1f</li> <li>Colab \u63d0\u4f9b\u54ea\u4e9b\u7c7b\u578b\u7684 GPU\uff1f</li> <li>\u5728 Colab \u4e2d\uff0c\u7b14\u8bb0\u672c\u53ef\u4ee5\u8fd0\u884c\u591a\u957f\u65f6\u95f4\uff1f</li> <li>Colab \u63d0\u4f9b\u591a\u5927\u5185\u5b58\uff1f</li> <li>\u5982\u4f55\u624d\u80fd\u5145\u5206\u5229\u7528 Colab\uff1f</li> <li>\u7cfb\u7edf\u663e\u793a\u4e00\u6761\u6d88\u606f\uff0c\u63d0\u793a\u6211\u6ca1\u6709\u4f7f\u7528 GPU\u3002\u6211\u8be5\u600e\u4e48\u529e\uff1f</li> </ul> </li> </ul>"},{"location":"tech_accu/tool/Colab/#\u5947\u6280\u6deb\u5de7","title":"\u5947\u6280\u6deb\u5de7","text":""},{"location":"tech_accu/tool/Colab/#\u5360\u7528\u663e\u5b58","title":"\u5360\u7528\u663e\u5b58","text":"<p>\u5f53\u4f60\u7684\u6574\u4e2a\u9879\u76ee\u9700\u8981<code>GPU</code>\u4f46\u662f\u73b0\u5728\u4e0d\u592a\u9700\u8981\u7684\u65f6\u5019\uff0c\u53ef\u4ee5\u901a\u8fc7\u4e0b\u9762\u8fd9\u6837\u4e00\u6bb5\u4ee3\u7801\u6765\u5148\u5360\u7528\u4e00\u90e8\u5206\u663e\u5b58\u3002</p> <pre><code>import torch\n## about 1.1 GB\na = torch.Tensor([1000, 1000, 1000]).cuda()\n</code></pre>"},{"location":"tech_accu/tool/Colab/#\u67e5\u770b\u663e\u5361\u4fe1\u606f","title":"\u67e5\u770b\u663e\u5361\u4fe1\u606f","text":"<pre><code>!nvidia-smi\n</code></pre>"},{"location":"tech_accu/tool/Colab/#\u6302\u8f7d-google-drive","title":"\u6302\u8f7d Google Drive","text":"<pre><code>from google.colab import drive\ndrive.mount('/content/drive/')\n</code></pre>"},{"location":"tech_accu/tool/Colab/#\u53ef\u53c2\u8003\u8d44\u6599","title":"\u53ef\u53c2\u8003\u8d44\u6599","text":"<ul> <li>https://zhuanlan.zhihu.com/p/387509768</li> <li>https://itiandong.com/2021/colab-tips/</li> </ul>"},{"location":"tech_accu/tool/Colab/#\u5176\u4ed6\u8d44\u6599","title":"\u5176\u4ed6\u8d44\u6599","text":"<ul> <li>https://jishuin.proginn.com/p/763bfbd316dc</li> </ul>"},{"location":"tech_accu/tool/Git/","title":"Git","text":"<p> \u7ea6 67 \u4e2a\u5b57 </p> <p>Git \u662f\u4ee3\u7801\u534f\u4f5c\u7684\u91cd\u8981\u5de5\u5177\uff0c\u540c\u65f6\u4e5f\u5bf9\u4e2a\u4eba\u4ee3\u7801\u7684\u7248\u672c\u7ba1\u7406\u6709\u91cd\u8981\u4f5c\u7528\uff0c\u56e0\u6b64\u53ef\u4ee5\u8bf4 Git \u662f\u7834\u5199\u4ee3\u7801\u7684\u4eba\u7684\u5fc5\u5907\u6280\u80fd\u4e4b\u4e00\u3002</p> <p>List</p> <ul> <li> Workflow </li> <li> Commands </li> <li> Commits Convention\uff08\u8ba1\u5212\u4e2d\uff09</li> <li> Lazy Git\uff08\u8ba1\u5212\u4e2d\uff09</li> </ul>"},{"location":"tech_accu/tool/Git/Commands/","title":"Git Commands","text":"<p> \u7ea6 1464 \u4e2a\u5b57  110 \u884c\u4ee3\u7801  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 6 \u5206\u949f</p> <p>\u7b80\u4ecb</p> <p>\u672c\u6587\u5185\u5bb9\u57fa\u4e8e\u6211\u81ea\u5df1\u7684\u7406\u89e3\u548c\u4e00\u4e9b\u6587\u7ae0\uff0c\u662f\u5b66\u4e60\u7b14\u8bb0\uff0c\u4f46\u540c\u65f6\u6211\u4e5f\u5e0c\u671b\u5b83\u80fd\u88ab\u4f5c\u4e3a\u4e00\u4e2a\u5b66\u4e60\u53c2\u8003\u8d44\u6599\u3002</p> <p>\u6240\u4ee5\u5982\u679c\u6709\u9519\u8bef\u8bf7\u53ca\u65f6\u8bc4\u8bba\u6216\u8005\u8054\u7cfb\u6211\uff0c\u5e0c\u671b\u80fd\u4e3a\u5927\u5bb6\u63d0\u4f9b\u4e00\u4e2a\u6bd4\u8f83\u597d\u7684\u5b66\u4e60\u53c2\u8003\uff01</p> <p>\u56e0\u4e3a\u6211\u81ea\u5df1\u7684\u5f00\u53d1\u7ecf\u5386\u6709\u9650\uff0c\u6240\u4ee5\u5e76\u4e0d\u80fd\u4fdd\u8bc1\u81ea\u5df1\u7684\u7406\u89e3\u662f\u5408\u9002\u4e14\u6b63\u786e\u7684\uff0c\u6240\u4ee5\u5e0c\u671b\u5927\u5bb6\u72e0\u72e0\u5730 educate \u6211\uff01</p> <p>\u672c\u6761\u76ee\u5c06\u628a\u76ee\u5149\u653e\u5728\u5177\u4f53\u7684<code>git</code> \u547d\u4ee4 \u7684\u4ecb\u7ecd\u4e0e\u4f7f\u7528\uff0c\u65e8\u5728\u6307\u5bfc\u8fdb\u884c\u5177\u4f53\u7684\u5de5\u4f5c\u3002</p> <p>Git \u6709\u8bb8\u591a\u547d\u4ee4\uff0c\u4f46\u662f\u5176\u5b9e\u5e38\u7528\u7684\u5c31\u56fe\u4e2d\u7684\u8fd9\u4e48\u51e0\u4e2a\uff0c\u751a\u81f3\u5728 \u521a\u5f00\u59cb \u5b66\u4e60\u4f7f\u7528\u7684\u65f6\u5019\u53ea\u9700\u8981\u8bb0\u4f4f\u5176\u4e2d\u7684\u4e00\u4e24\u4e2a\uff0c\u4f46\u662f</p> <p>\u8fd9\u5e76\u4e0d\u662f\u8bf4\u5176\u4ed6\u547d\u4ee4\u5c31\u662f\u6ca1\u7528\u7684\uff0c\u6211\u4f1a\u5728\u8fd9\u91cc\u6309\u7167\u4f7f\u7528\u573a\u666f\u5206\u7c7b\uff0c\u5c3d\u53ef\u80fd\u5730\u4ecb\u7ecd Git \u547d\u4ee4\u3002</p> <p>  \u5e38\u7528\u547d\u4ee4 </p> <p>\u7531\u4e8e\u4e00\u822c\u6765\u8bf4\u8fd0\u884c\u547d\u4ee4\u90fd\u662f\u4ee5\u672c\u5730\u89c6\u89d2\uff0c\u6240\u4ee5\u8fd9\u91cc\u7684\u300c\u4f7f\u7528\u573a\u666f\u300d\u7684\u5212\u5206\u4e5f\u662f\u4ee5\u672c\u5730\u89c6\u89d2\u5c55\u5f00\u7684\u3002 \u5e76\u4e14\u5728\u67d0\u4e9b\u9700\u8981\u6d89\u53ca\u8fdc\u7a0b\u4ed3\u5e93\u7684\u5730\u65b9\u4e3b\u8981\u4ee5 Github \u7684\u4f7f\u7528\u4e3a\u53c2\u8003\u3002</p>"},{"location":"tech_accu/tool/Git/Commands/#\u7b80\u6d01\u7248\u672c","title":"\u7b80\u6d01\u7248\u672c","text":"<p>\u8be5\u6761\u76ee\u4e3b\u8981\u9002\u7528\u4e8e\u521d\u5b66\u4e0e\u7b80\u5355\u4f7f\u7528 Git \uff0c\u5e76\u4e0d\u9002\u5408\u957f\u671f\u7ef4\u62a4\u7684\u5927\u578b\u9879\u76ee\u3002</p> \u5feb\u9910 <pre><code># \u5728 Github \u521b\u5efa\u4ed3\u5e93\n# \u83b7\u53d6\u4ed3\u5e93\u7684 http / SSH clone \u547d\u4ee4\n\n# \u4ece\u8fdc\u7a0b\u5c06\u4ed3\u5e93\u514b\u9686\u5230\u672c\u5730\ngit clone &lt;repo-url&gt;\n\n# \u5b8c\u6210\u4ee3\u7801\u4fee\u6539\u540e\u5c06\u4fee\u6539\u6dfb\u52a0\u5230\u6682\u5b58\u533a\ngit add -A # \u6dfb\u52a0\u6240\u6709\u4fee\u6539\ngit add .  # \u6dfb\u52a0\u5f53\u524d\u76ee\u5f55\u4e0b\u7684\u4fee\u6539\n\n# \u63d0\u4ea4\u4fee\u6539\ngit commit -m \"Write commit message here.\"\n\n# push \u5230\u8fdc\u7a0b\u4ed3\u5e93\ngit push origin\n</code></pre>"},{"location":"tech_accu/tool/Git/Commands/#\u914d\u7f6e","title":"\u914d\u7f6e","text":"<p>Git \u7684\u914d\u7f6e\u6587\u4ef6\u540d\u53eb <code>.gitconfig</code>\uff0c\u7528\u6765\u5b58\u653e\u4e00\u4e9b\u914d\u7f6e\u4fe1\u606f\uff0c\u5728\u7528\u6237\u76ee\u5f55\u4e0b\u7684\u4e3a\u5168\u5c40\u914d\u7f6e\u4fe1\u606f\uff0c\u800c\u5728\u9879\u76ee\u76ee\u5f55\u4e0b\u7684\u5219\u4e3a\u9879\u76ee\u914d\u7f6e\u4fe1\u606f\u3002</p> <pre><code># \u663e\u793a\u914d\u7f6e\ngit config --list\n</code></pre>"},{"location":"tech_accu/tool/Git/Commands/#\u751f\u6210\u672c\u5730\u4ed3\u5e93","title":"\u751f\u6210\u672c\u5730\u4ed3\u5e93","text":"<p>\u672c\u5730\u751f\u6210\u4ed3\u5e93\u4e3b\u8981\u6709\u4e24\u79cd\u9014\u5f84\uff0c\u4e00\u662f\u5728\u672c\u5730\u76f4\u63a5\u65b0\u5efa\u4e00\u4e2a\u4ed3\u5e93\uff0c\u800c\u662f\u514b\u9686\u4e00\u4e2a\u8fdc\u7a0b\u4ed3\u5e93\u3002</p> <pre><code># \u5728\u5f53\u524d\u76ee\u5f55 . \u65b0\u5efa\u4e00\u4e2a\u4ed3\u5e93\ngit init\n\n# \u521b\u5efa\u4e00\u4e2a\u540d\u4e3a &lt;dir-name&gt; \u7684\u76ee\u5f55\uff0c\u5c06\u5176\u521d\u59cb\u5316\u4e3a\u4e00\u4e2a Git \u4ed3\u5e93\ngit init &lt;dir-name&gt;\n\n# \u4ece &lt;repo-url&gt; \u514b\u9686\u4e00\u4e2a\u8fdc\u7a0b\u4ed3\u5e93\uff08\u5305\u62ec\u6240\u6709\u7684 git \u4fe1\u606f\uff09\ngit clone &lt;repo-url&gt;\n</code></pre> <p>\u4ece\u6587\u4ef6\u89d2\u5ea6\u6765\u8bb2\uff0c\u5b9e\u9645\u4e0a\u5b83\u662f\u751f\u6210\u4e86\u4e00\u4e2a\u6709<code>.git</code>\u6587\u4ef6\u5939\u7684\u6587\u4ef6\u5939\uff0c\u800c<code>.git</code>\u6587\u4ef6\u5939\u5b58\u50a8\u4e86 Git \u6240\u9700\u8981\u7684\u5927\u90e8\u5206\u4fe1\u606f\u3002 \u4f7f\u7528\u5e38\u89c1\u7684 shell \u8fdb\u5165\u4ed3\u5e93\u6587\u4ef6\u5939\u540e\uff0c\u4e00\u822c\u4f1a\u6709\u4e00\u4e2a label \u8868\u793a\u4f60\u5df2\u7ecf\u8fdb\u5165\u4e86\u4e00\u4e2a\u4ed3\u5e93\u7684\u67d0\u4e2a\u5206\u652f\u4e86\u3002\u6bd4\u5982\u8fdb\u5165\u4e00\u4e2a\u65b0\u7684\u4ed3\u5e93\u65f6\uff0c\u4f1a\u6709\u4e00\u4e2amaster\u7684 label \uff0c\u5177\u4f53\u8868\u73b0\u5f62\u5f0f\u4e3b\u8981\u770b\u4f60\u7684 shell \u548c\u4e3b\u9898\u4e86\u3002</p> <p>\u9700\u8981\u6ce8\u610f\u7684\u662f\uff0c\u5728\u672c\u5730\u76f4\u63a5\u521b\u5efa\u7684\u4ed3\u5e93\u4ec5\u4ec5\u53ea\u662f\u4e00\u4e2a\u672c\u5730\u4ed3\u5e93\uff0c\u4e0d\u5177\u5907\u8fdc\u7a0b\u534f\u4f5c\u529f\u80fd\uff0c\u9700\u8981\u8fdb\u884c\u5bf9\u5e94\u7684\u914d\u7f6e\uff0c\u53c2\u8003 \"Git Workflow\" \u6761\u76ee\uff1b\u800c\u4e00\u822c\u4ece\u8fdc\u7a0b\u4ed3\u5e93\u514b\u9686\u4e0b\u6765\u7684\u4ed3\u5e93\u90fd\u5df2\u7ecf\u7ecf\u8fc7\u8bbe\u7f6e\uff0c\u53ef\u4ee5\u76f4\u63a5\u8fdb\u884c\u8fdc\u7a0b\u534f\u4f5c\u3002</p>"},{"location":"tech_accu/tool/Git/Commands/#\u7248\u672c\u7ba1\u7406","title":"\u7248\u672c\u7ba1\u7406","text":"<p>Git \u57fa\u4e8e\u7248\u672c\u4e4b\u95f4\u7684\u5dee\u5f02\u8fdb\u884c\u4ee3\u7801\u7ba1\u7406\uff0c\u4f7f\u7528 Git \u8fdb\u884c\u4ee3\u7801\u7ba1\u7406\u4e3b\u8981\u6307\u5728\u505a\u5b8c\u7279\u5b9a\u4fee\u6539\u4ee5\u540e\u5c06\u5176\u6dfb\u52a0\u5230\u5bf9\u5e94\u5206\u652f\u4e2d\u3002 \u5728\u8003\u8651 Git \u64cd\u4f5c\u4e4b\u524d\uff0c\u4f60\u53ef\u4ee5\u653e\u5fc3\u5730\u8fdb\u884c\u4f60\u7684\u4ee3\u7801\u7f16\u8f91\u5de5\u4f5c\uff0c\u4e0d\u8fc7\u8bb0\u5f97\u5728\u5408\u9002\u7684\u65f6\u673a\u8fdb\u884c\u7248\u672c\u7ba1\u7406\u3002</p>"},{"location":"tech_accu/tool/Git/Commands/#\u67e5\u770b\u5dee\u5f02\u6587\u4ef6","title":"\u67e5\u770b\u5dee\u5f02\u6587\u4ef6","text":"<p>\u901a\u8fc7\u5982\u4e0b\u6307\u4ee4\u53ef\u4ee5 \u67e5\u770b\u5dee\u5f02\u6587\u4ef6\uff1a</p> <pre><code># \u663e\u793a\u68c0\u6d4b\u5230\u5dee\u5f02\u7684\u6587\u4ef6\uff0c\u5b83\u4eec\u6b63\u5728\u7b49\u5f85\u88ab\u63d0\u4ea4\ngit status\n</code></pre>"},{"location":"tech_accu/tool/Git/Commands/#\u6dfb\u52a0\u5230\u6682\u5b58\u533a","title":"\u6dfb\u52a0\u5230\u6682\u5b58\u533a","text":"<p>\u5728\u5b8c\u6210\u4ee3\u7801\u4fee\u6539\u5de5\u4f5c\u540e\u9700\u8981\u5c06\u4ee3\u7801 \u6dfb\u52a0 \u5230\u6682\u5b58\u533a\uff1a</p> <pre><code># \u5c06 &lt;target&gt; \u4e2d\u7684\u4fee\u6539\u6dfb\u52a0\u7684\u6682\u5b58\u533a\uff0c\u6587\u4ef6\u5939\u548c\u6587\u4ef6\u540c\u7406\uff0c'.' \u540c\u7406 \ngit add &lt;target&gt;\n\n# \u5bf9\u4e8e\u6240\u6709\u7684\u4fee\u6539\u4f9d\u6b21\u8fdb\u884c\u6dfb\u52a0\u786e\u8ba4\uff08\u5305\u62ec\u5355\u4e00\u6587\u4ef6\u7684\u591a\u5904\u4fee\u6539\uff09\ngit add -p\n\n# \u7528\u4ea4\u4e92\u5f0f\u7684\u65b9\u6cd5\u8fdb\u884c\u6dfb\u52a0\ngit add -i\n</code></pre>"},{"location":"tech_accu/tool/Git/Commands/#\u63d0\u4ea4\u5230\u4ed3\u5e93","title":"\u63d0\u4ea4\u5230\u4ed3\u5e93","text":"<p>\u6dfb\u52a0\u5b8c\u540e\u9700\u8981\u8fdb\u884c \u63d0\u4ea4\uff0c\u5728\u4ed3\u5e93\u4e2d\u5f62\u6210\u4e00\u4e2a\u8282\u70b9\uff1a</p> <pre><code># \u63d0\u4ea4\u5230\u4ed3\u5e93\ngit commit -m \"Write commit message here.\"\n\n# \u4fee\u6b63\u4e0a\u4e00\u6b21\u63d0\u4ea4\uff0c\u610f\u601d\u662f\u8bf4\u4f1a\u6269\u5145\u5e76\u66ff\u4ee3\u4e0a\u4e00\u6b21\u63d0\u4ea4\n# \u5e94\u7528\u573a\u666f\u5982\uff1a\u4e0a\u4e00\u6b21\u63d0\u4ea4\u6709\u9057\u6f0f\u3001\u4e0a\u4e00\u6b21\u63d0\u4ea4\u7684\u63d0\u4ea4\u4fe1\u606f\u6709\u95ee\u9898\u7b49\ngit commit --amend -m \"Write commit message here.\"\n</code></pre>"},{"location":"tech_accu/tool/Git/Commands/#\u67e5\u770b\u63d0\u4ea4\u8bb0\u5f55","title":"\u67e5\u770b\u63d0\u4ea4\u8bb0\u5f55","text":"<p>\u5b8c\u6210\u63d0\u4ea4\u540e\u8fd9\u4e00\u6b21\u4fee\u6539\u5c31\u4f1a\u88ab\u5199\u5165\u5386\u53f2\u8bb0\u5f55\u4e2d\uff0c\u4f60\u53ef\u4ee5\u901a\u8fc7<code>log</code>\u6765 \u67e5\u770b\uff1a</p> <pre><code>git log\n</code></pre>"},{"location":"tech_accu/tool/Git/Commands/#\u56de\u6eaf--\u62b5\u6d88\u8bb0\u5f55","title":"\u56de\u6eaf / \u62b5\u6d88\u8bb0\u5f55","text":"<p>\u5728<code>log</code>\u4e2d\u53ef\u4ee5\u67e5\u8be2\u5f97\u5230\u6bcf\u4e00\u6b21<code>commit</code>\u7684\u54c8\u5e0c\uff0c\u5f97\u5230\u8fd9\u4e9b\u54c8\u5e0c(\u4e5f\u53ef\u4ee5\u4f7f\u7528\u6807\u7b7e)\u4ee5\u540e\u6211\u4eec\u53ef\u4ee5\u7528\u5b83\u6765\u8fdb\u884c \u56de\u6eaf \u548c \u62b5\u6d88 \u64cd\u4f5c\uff1a</p> <pre><code># \u56de\u6eaf\u5230\u7279\u5b9a commit \uff0c\u6bd4\u8f83\u5371\u9669\ngit reset HEAD                  # \u56de\u6eaf\u5230\u4e0a\u4e00\u4e2a commit \uff0c\u6548\u679c\u4e0a\u6e05\u7a7a\u4e86\u6682\u5b58\u533a\uff0c\u4e0d\u5f71\u54cd\u5de5\u4f5c\u533a\ngit reset --hard &lt;commit-id&gt;    # \u629b\u5f03\u5f53\u524d\u7684\u5de5\u4f5c\u533a\u5e76\u56de\u6eaf\u5230\u67d0\u4e2a\u7248\u672c\n\n# \u62b5\u6d88\u4e00\u6b21 commit \uff0c\u4ea7\u751f\u4e00\u4e2a\u4e0e\u76ee\u6807 commit \u4e92\u9006\u7684 commit\ngit revert HEAD                     # \u62b5\u6d88\u4e0a\u4e00\u6b21 commit\ngit revert &lt;commit-id&gt;              # \u62b5\u6d88\u7279\u5b9a commit\n</code></pre>"},{"location":"tech_accu/tool/Git/Commands/#\u5220\u9664--\u79fb\u52a8\u91cd\u547d\u540d","title":"\u5220\u9664 / \u79fb\u52a8(\u91cd\u547d\u540d)","text":"<p>\u5220\u9664 \u6587\u4ef6\u548c \u79fb\u52a8(\u91cd\u547d\u540d) \u6587\u4ef6\u53ef\u4ee5\u4f7f\u7528<code>rm</code>\u548c<code>mv</code>\uff0c\u5173\u4e8e<code>rm</code>(<code>mv</code>)\u548c<code>git rm</code>(<code>git mv</code>)\u7684\u533a\u522b\u53ef\u4ee5\u770b\u8fd9\u91cc\u3002 \u7b80\u5355\u6765\u8bf4\u5c31\u662f\uff0c<code>git rm &lt;file&gt;</code>\u7b49\u4ef7\u4e8e<code>rm &lt;file&gt; ; git add &lt;file&gt;</code>\uff1b<code>mv</code>\u540c\u7406\uff0c\u4f46\u662f\u4f60\u65e0\u6cd5\u628a\u4e00\u4e2a\u6587\u4ef6\u901a\u8fc7<code>git mv</code>\u79fb\u52a8\u5230 repo dir \u4e4b\u5916\u3002</p> <pre><code># \u5220\u9664\u67d0\u4e2a\u6587\u4ef6\ngit rm &lt;file&gt;\n# \u79fb\u52a8(\u91cd\u547d\u540d)\u67d0\u4e2a\u6587\u4ef6\ngit mv &lt;from&gt; &lt;to&gt;\n\n# \u4f7f\u7528\u5982\u4e0b\u547d\u4ee4\u8fd8\u53ef\u4ee5\u505c\u6b62\u5bf9\u67d0\u4e2a\u6587\u4ef6\u7684\u8ffd\u8e2a\uff0c\u6700\u5e38\u7528\u7684\u60c5\u51b5\u4e00\u822c\u548c`.gitignore`\u6709\u5173\ngit rm --cache &lt;file&gt;\n</code></pre>"},{"location":"tech_accu/tool/Git/Commands/#\u6807\u7b7e\u64cd\u4f5c","title":"\u6807\u7b7e\u64cd\u4f5c","text":"<p>\u4e0a\u9762\u8bb8\u591a\u6d89\u53ca\u5b9a\u4f4d\u7279\u5b9a commit \u7684\u64cd\u4f5c\u90fd\u9700\u8981\u83b7\u53d6 commit \u7684\u54c8\u5e0c\u3002\u4e0d\u8fc7\u5982\u679c\u5bf9\u67d0\u4e9b\u7279\u5b9a\u7248\u672c\u8fdb\u884c\u4e00\u4e9b\u6807\u7b7e\u7ba1\u7406\uff0c\u90a3\u6211\u4eec\u5c31\u53ef\u4ee5\u901a\u8fc7\u8bbf\u95ee\u6807\u7b7e\u6765\u7d22\u5f15\u7279\u5b9a commit \uff0c\u56e0\u800c\uff0ctag \u5b9e\u9645\u4e0a\u662f\u4e0d\u53ef\u91cd\u590d\u7684\u3002</p> <pre><code># \u4e3a\u7279\u5b9a commit \u6dfb\u52a0 tag\ngit tag &lt;tag name&gt; &lt;commit id&gt;\n\n# \u5220\u9664\u7279\u5b9a tag\ngit tag -d &lt;tag name&gt;\n</code></pre> <p>\u53e6\u5916\uff0c\u9700\u8981\u63d0\u9192\u7684\u662f\uff0c\u9ed8\u8ba4\u60c5\u51b5\u4e0b<code>git push</code>\u4e0d\u4f1a\u5c06 tag \u4e0a\u4f20\u5230\u8fdc\u7a0b\u4ed3\u5e93\uff0c\u9700\u8981\u5728\u547d\u4ee4\u540e\u52a0\u5165<code>--tags</code>\u6765\u4e00\u6b21\u6027 push \u6240\u6709\u7684 tag \u6216\u8005\u6dfb\u52a0<code>&lt;tag name&gt;</code>\u6765\u4e0a\u4f20 tag \u3002</p>"},{"location":"tech_accu/tool/Git/Commands/#\u8fdc\u7a0b\u534f\u4f5c","title":"\u8fdc\u7a0b\u534f\u4f5c","text":"<p>\u8fdc\u7a0b\u7ba1\u7406\u4e3b\u8981\u6307\u591a\u4eba\u9879\u76ee\u65f6\u9700\u8981\u901a\u8fc7\u8fdc\u7a0b\u4ed3\u5e93\u6765\u5b8c\u6210\u534f\u4f5c\u3002\u8fd9\u91cc\u4ee5 GitHub \u4e3a\u4f8b\u3002 \u5f53\u4f60\u5728 Github \u521b\u5efa\u4e00\u4e2a\u7a7a repo \u4ee5\u540e\uff0c\u4f1a\u6709\u8fd9\u6837\u4e00\u4e2a\u9ed8\u8ba4\u9875\u9762\uff1a</p> <p> IsshikiHugh \u662f\u6211\u7684 User ID\uff0cnothing \u662f\u6211\u7684 Repo Name</p> <p>\u6211\u4eec\u91cd\u70b9\u5173\u6ce8\u4e2d\u95f4\u4e24\u4e2a\u4ee3\u7801\u6846\uff0c\u5199\u7684\u5df2\u7ecf\u975e\u5e38\u6e05\u695a\u4e86\u3002</p> <p><code>create a new repository on the command line</code>\u6307\u5bfc\u4f60\u5728\u672c\u5730\u521b\u5efa\u4e00\u4e2a\u65b0\u7684\u7a7a\u4ed3\u5e93\uff0c\u5e76\u4e0e\u8fdc\u7a0b\u4ed3\u5e93\u94fe\u63a5\uff1b</p> <p><code>push an existing repository from the command line</code>\u6307\u5bfc\u4f60\u5982\u4f55\u5c06\u8fdc\u7a0b\u4ed3\u5e93\u548c\u672c\u5730\u4ed3\u5e93\u94fe\u63a5\u8d77\u6765\uff0c\u5e76 push \u3002</p>"},{"location":"tech_accu/tool/Git/Commands/#\u8fdc\u7a0b\u4ed3\u5e93\u7ba1\u7406","title":"\u8fdc\u7a0b\u4ed3\u5e93\u7ba1\u7406","text":"<p>\u6765\u81ea GitHub \u7684\u6307\u5bfc\u6587\u4ef6\u4e2d\u6700\u6838\u5fc3\u7684\u4e00\u6761\u6307\u4ee4\u662f\u5982\u4f55\u94fe\u63a5\u672c\u5730\u4ed3\u5e93\u4e0e\u8fdc\u7a0b\u4ed3\u5e93\uff1a</p> <p><pre><code># \u5728\u672c\u5730\u6dfb\u52a0\u8fdc\u7a0b\u4ed3\u5e93\uff0c\u547d\u540d\u4e3a &lt;remote name&gt; \uff0c\u6ce8\u610f\u8fd9\u91cc\u7684 &lt;url&gt; \u5e76\u4e0d\u662f\u6d4f\u89c8\u5668\u4e0a\u9762\n# \u90a3\u4e2a\uff0c\u800c\u662f\u4ece github \u590d\u5236\u8fc7\u6765\u7684 http \u6216\u8005 ssh \u63a8\u9001\ngit remote add &lt;remote name&gt; &lt;url&gt;\n# \u5e38\u7528\u7684 &lt;remote name&gt; \u662f origin\n</code></pre> \u9664\u6b64\u4e4b\u5916\uff0c\u5173\u4e8e\u8fdc\u7a0b\u4ed3\u5e93\u7684\u76f8\u5173\u547d\u4ee4\u8fd8\u6709\u5982\u4e0b\uff1a <pre><code>git remote -v                  # \u663e\u793a\u8fdc\u7a0b\u4ed3\u5e93(\u8be6\u7ec6\u4fe1\u606f)\ngit remote rm &lt;remote name&gt;    # \u89e3\u9664\u4e0e\u5bf9\u5e94\u8fdc\u7a0b\u4ed3\u5e93\u7684\u7ed1\u5b9a\u5173\u7cfb\ngit remote rename &lt;from&gt; &lt;to&gt;  # \u91cd\u547d\u540d\u7279\u5b9a\u8fdc\u7a0b\u4ed3\u5e93\n</code></pre></p>"},{"location":"tech_accu/tool/Git/Commands/#\u672c\u5730\u4ece\u8fdc\u7a0b\u4ed3\u5e93\u62c9\u53d6\u5185\u5bb9","title":"\u672c\u5730\u4ece\u8fdc\u7a0b\u4ed3\u5e93\u62c9\u53d6\u5185\u5bb9","text":"<p>\u4e3b\u8981\u6709\u4e24\u79cd\u65b9\u5f0f\uff0c\u5373<code>pull</code>\u548c<code>fetch</code>\uff0c\u533a\u522b\u5728\u4e8e<code>fetch</code>\u5e76\u4e0d\u4f1a\u5408\u5e76\u5185\u5bb9\uff0c\u800c\u4ec5\u4ec5\u662f\u4e0b\u8f7d\u8fdc\u7a0b\u4ed3\u5e93\u4e2d\u7684\u53d8\u52a8\u4fe1\u606f\u3002\u7b80\u5355\u6765\u8bf4\u5c31\u662f<code>pull</code>\u7b49\u6548\u4e8e<code>fetch</code>\u5e76<code>merge</code>\u3002</p> <pre><code># \u4ece\u8fdc\u7a0b\u4ed3\u5e93\u4e0b\u8f7d\u53d8\u52a8\u5185\u5bb9\ngit fetch &lt;remote name&gt;\n\n# \u4ece\u8fdc\u7a0b\u4ed3\u5e93\u62c9\u53d6\u53d8\u52a8\u5185\u5bb9\u5e76\u4e14\u5408\u5e76\u5230\u6307\u5b9a\u5206\u652f\ngit pull &lt;remote name&gt; &lt;branch&gt;\n</code></pre>"},{"location":"tech_accu/tool/Git/Commands/#\u672c\u5730\u5411\u8fdc\u7a0b\u4ed3\u5e93\u63a8\u9001\u5185\u5bb9","title":"\u672c\u5730\u5411\u8fdc\u7a0b\u4ed3\u5e93\u63a8\u9001\u5185\u5bb9","text":"<p>\u5728\u672c\u5730\u5b8c\u6210 commit \u64cd\u4f5c\u540e\uff0c\u5c31\u53ef\u4ee5 push \u5230\u8fdc\u7a0b\u4ed3\u5e93\uff1a</p> <pre><code># \u63a8\u9001 &lt;branch&gt; \u7684\u5185\u5bb9\u5230 &lt;remote&gt; \uff0c\u5e76\u81ea\u52a8\u8bbe\u7f6e\u4e0a\u6e38\uff0c\u8fd9\u610f\u5473\u7740\u5728\u8fd9\u4e2a\u5206\u652f\u91cc\uff0c\n# \u4e0b\u4e00\u6b21 push \u53ea\u9700\u8981\u8f93\u5165 git push \u5373\u53ef\ngit push -u &lt;remote&gt; &lt;branch&gt;\n# eg: \u63a8\u9001 master \u5206\u652f\u7684\u5185\u5bb9\u5230 origin \uff0c\u5e76\u81ea\u52a8\u8bbe\u7f6e\u4e0a\u6e38\ngit push -u origin master\n\ngit push --force    # \u5f3a\u5236\u63a8\u9001\u5f53\u524d\u5206\u652f\uff0c\u5373\u4f7f\u6709\u51b2\u7a81\u5b58\u5728\n--all      # \u63a8\u9001\u6240\u6709\u5206\u652f\u7684\u5185\u5bb9\n</code></pre>"},{"location":"tech_accu/tool/Git/Commands/#\u5206\u652f\u7ba1\u7406","title":"\u5206\u652f\u7ba1\u7406","text":""},{"location":"tech_accu/tool/Git/Commands/#\u67e5\u770b\u5206\u652f","title":"\u67e5\u770b\u5206\u652f","text":"<pre><code>git branch        # \u663e\u793a\u672c\u5730\u6240\u6709\u5206\u652f\n-r     # \u663e\u793a\u8fdc\u7a0b\u6240\u6709\u5206\u652f\n-a     # \u663e\u793a\u6240\u6709\u5206\u652f\n</code></pre>"},{"location":"tech_accu/tool/Git/Commands/#\u65b0\u5efa\u5206\u652f--\u5207\u6362\u5206\u652f--\u8bbe\u7f6e\u4e0a\u6e38","title":"\u65b0\u5efa\u5206\u652f / \u5207\u6362\u5206\u652f / \u8bbe\u7f6e\u4e0a\u6e38","text":"<pre><code># \u65b0\u5efa\u4e00\u4e2a\u540d\u4e3a &lt;branch name&gt; \u7684\u65b0\u5206\u652f\uff0c\u4f46\u4e0d\u5207\u6362\ngit branch &lt;branch name&gt;\n# \u901a\u8fc7 checkout \u6765\u5207\u6362\u5206\u652f\uff0c\u6bd4\u5982\u8fdb\u5165\u5230\u521a\u521a\u521b\u5efa\u7684\u5206\u652f\u6c47\u603b\ngit checkout &lt;branch&gt;         # \u8be5\u547d\u4ee4\u4f1a\u66f4\u65b0\u5de5\u4f5c\u533a\n# \u521b\u5efa\u5b8c\u5206\u652f\u540e\u901a\u8fc7\u5982\u4e0b\u547d\u4ee4\u8bbe\u7f6e\u4e0a\u6e38\ngit branch --set-upstream &lt;local branch&gt; &lt;remote branch&gt;\n\n# \u5c06\u4e0a\u9762\u7684\u547d\u4ee4\u8fdb\u884c\u96c6\u6210\uff0c\u6709\uff1a\n\n# \u76f4\u63a5\u65b0\u5efa\u4e00\u4e2a\u540d\u4e3a &lt;branch name&gt; \u7684\u65b0\u5206\u652f\u5e76\u5207\u6362\ngit checkout -b &lt;branch name&gt;\n# \u65b0\u5efa\u4e00\u4e2a\u540d\u4e3a &lt;local branch&gt; \u7684\u65b0\u5206\u652f\uff0c\u5e76\u8bbe &lt;remote branch&gt; \u4e3a\u4e0a\u6e38\ngit branch --track &lt;local branch&gt; &lt;remote branch&gt;\n</code></pre>"},{"location":"tech_accu/tool/Git/Commands/#\u5206\u652f\u5408\u5e76","title":"\u5206\u652f\u5408\u5e76","text":"<pre><code># \u5c06\u6307\u5b9a\u5206\u652f\u5408\u5e76\u5230\u5f53\u524d\u5206\u652f\uff0c\u9700\u8981\u5904\u7406\u51b2\u7a81\u90e8\u5206\uff08\u6c9f\u901a\u534f\u5546\u3001\u624b\u52a8\u89e3\u51b3\uff09\ngit merge &lt;branch&gt;\n\n# \u5c06\u7279\u5b9a commit \u5408\u5e76\u8fdb\u5f53\u524d\u5206\u652f\ngit cherry-pick &lt;commit id&gt;\n</code></pre>"},{"location":"tech_accu/tool/Git/Commands/#\u5206\u652f\u5220\u9664","title":"\u5206\u652f\u5220\u9664","text":"<pre><code># \u5220\u9664\u672c\u5730\u5206\u652f\ngit branch -d &lt;branch&gt;\n\n# \u5220\u9664\u8fdc\u7a0b\u5206\u652f\ngit push &lt;remote&gt; --delete &lt;branch&gt;\ngit branch -dr &lt;remote&gt;/&lt;branch&gt;\n# eg:\ngit branch -dr origin/testbrach\n</code></pre>"},{"location":"tech_accu/tool/Git/Commands/#\u4f60\u53ef\u80fd\u8fd8\u8981\u4e86\u89e3\u7684--\u672c\u6587\u8fd8\u6ca1\u8bb2\u7684\u4e1c\u897f","title":"\u4f60\u53ef\u80fd\u8fd8\u8981\u4e86\u89e3\u7684 / \u672c\u6587\u8fd8\u6ca1\u8bb2\u7684\u4e1c\u897f","text":"<ul> <li><code>.gitignore</code>\u6587\u4ef6</li> <li>\u8054\u7cfb<code>git rm --cached &lt;file&gt;</code></li> <li>\u201c\u8ffd\u8e2a\u201d\u7684\u6982\u5ff5</li> <li><code>HEAD</code></li> <li>git stash</li> </ul>"},{"location":"tech_accu/tool/Git/Commands/#\u53c2\u8003\u8d44\u6599--ref","title":"\u53c2\u8003\u8d44\u6599 | Ref","text":"<ul> <li>https://www.ruanyifeng.com/blog/2015/12/git-cheat-sheet.html</li> <li>https://www.cnblogs.com/lance-ehf/p/3871643.html</li> <li>https://blog.csdn.net/Lakers2015/article/details/111318801</li> </ul>"},{"location":"tech_accu/tool/Git/Workflow/","title":"Git Workflow","text":"<p> \u7ea6 1267 \u4e2a\u5b57  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 4 \u5206\u949f</p> <p>\u7b80\u4ecb</p> <p>\u672c\u6587\u5185\u5bb9\u57fa\u4e8e\u6211\u81ea\u5df1\u7684\u7406\u89e3\u548c\u4e00\u4e9b\u6587\u7ae0\uff0c\u662f\u5b66\u4e60\u7b14\u8bb0\uff0c\u4f46\u540c\u65f6\u6211\u4e5f\u5e0c\u671b\u5b83\u80fd\u88ab\u4f5c\u4e3a\u4e00\u4e2a\u5b66\u4e60\u53c2\u8003\u8d44\u6599\u3002</p> <p>\u6240\u4ee5\u5982\u679c\u6709\u9519\u8bef\u8bf7\u53ca\u65f6\u8bc4\u8bba\u6216\u8005\u8054\u7cfb\u6211\uff0c\u5e0c\u671b\u80fd\u4e3a\u5927\u5bb6\u63d0\u4f9b\u4e00\u4e2a\u6bd4\u8f83\u597d\u7684\u5b66\u4e60\u53c2\u8003\uff01</p> <p>\u56e0\u4e3a\u6211\u81ea\u5df1\u7684\u5f00\u53d1\u7ecf\u5386\u6709\u9650\uff0c\u6240\u4ee5\u5e76\u4e0d\u80fd\u4fdd\u8bc1\u81ea\u5df1\u7684\u7406\u89e3\u662f\u5408\u9002\u4e14\u6b63\u786e\u7684\uff0c\u6240\u4ee5\u5e0c\u671b\u5927\u5bb6\u72e0\u72e0\u5730 educate \u6211\uff01</p> <p>\u672c\u6761\u76ee\u4e3b\u8981\u4ecb\u7ecd\u6709\u5173 Git Workflow \u7684\u6982\u5ff5\u6027\u8d28\u548c\u6307\u5bfc\u6027\u8d28\u7684\u4e00\u4e9b\u5185\u5bb9\uff0c\u5b83\u4eec\u5e76\u4e0d\u5177\u4f53\uff0c\u4f46\u662f\u4f1a\u6307\u5bfc\u60a8\u7684\u4f7f\u7528\u3002</p> <p>\u7531\u4e8e mkdocs \u5e76\u6ca1\u6709\u6807\u7b7e\u529f\u80fd\uff0c\u6240\u4ee5\u5176\u5b9e\u8fd8\u662f\u8bed\u96c0\u4e0a\u7684\u6587\u7ae0\u66f4\u597d\u770b\uff0c\u4f46\u662f\u6211\u5e76\u4e0d\u6253\u7b97\u66f4\u65b0\u8bed\u96c0\u4e86\uff0c\u6545\u8fd9\u91cc\u53ea\u653e\u4e00\u4e2a\u4ee5\u524d\u7684\u6307\u8def\u94fe\u63a5\uff1a\ud83d\udd17\u3002</p> <p>Git branch \u53ef\u89c6\u5316\u7ec3\u4e60\u7f51\u7ad9\uff1ahttps://note.isshikih.top/tech_accu/tool/Git/Workflow/</p>"},{"location":"tech_accu/tool/Git/Workflow/#\u4f55\u4e3a-git-workflow","title":"\u4f55\u4e3a 'Git Workflow'","text":"<p>Git Workflow \u662f\u4e00\u79cd\u89c4\u8303\u7684\u5de5\u4f5c\u6d41\u7a0b\uff0c\u800c\u5e76\u4e0d\u662f\u4e00\u4e2a\u5177\u4f53\u7684\u5de5\u5177\u6216\u8005\u6280\u672f\uff0c\u5f53\u7136\u8c8c\u4f3c\u6709\u4e00\u4e2a\u53eb\u505a Gitflow \u7684\u5de5\u5177\uff0c\u4f46\u5728\u672c\u6587\u4e2d\u6682\u65f6\u4e0d\u4ecb\u7ecd\u3002 \u73b0\u5728\u88ab\u5e7f\u6cdb\u4f7f\u7528\u7684 Workflow \u4e3b\u8981\u6709\u4e09\u79cd\uff1a</p> <ul> <li>Git Workflow</li> <li>Github Workflow</li> <li>Gitlab Workflow</li> </ul> <p>\u4ed6\u4eec\u7684\u5173\u7cfb\u662f\uff0c\u4f9d\u6b21\u5438\u6536\u4e0e\u6539\u8fdb\uff0c\u5404\u6709\u7279\u70b9\uff0c\u4e14\u4e0e\u5bf9\u5e94\u7684\u4f7f\u7528\u5e73\u53f0\u76f8\u9002\u5e94\uff0c\u4e0b\u9762\u5c06\u5206\u6761\u6982\u8ff0\u3002 \u5728\u4e0d\u540c\u7684 Workflow \u4e2d\uff0c\u6700\u4e3b\u8981\u7684\u533a\u522b\u5c31\u662f\u4e0d\u540c\u5206\u652f\u95f4\u7684\u5408\u4f5c\u5f62\u5f0f\u548c\u7ec4\u7ec7\u5f62\u5f0f\uff0c\u5982\u679c\u4f60\u5bf9 Git \u7684\u5206\u652f\u8fd8\u4e0d\u662f\u5f88\u719f\u6089\uff0c\u8bf7\u5148\u53c2\u8003 Git Commands \u7684\u90e8\u5206\u5185\u5bb9\uff0c\u7b80\u5355\u4e86\u89e3\u4e00\u4e0b\u57fa\u7840\u6307\u4ee4\u3002</p>"},{"location":"tech_accu/tool/Git/Workflow/#git-workflow_1","title":"Git Workflow","text":"<p> [Source] https://gitbook.tw/chapters/gitflow/why-need-git-flow</p> <p>Tips: \u5728\u9605\u8bfb\u63a5\u4e0b\u6765\u7684\u4e00\u4e9b\u8bf4\u660e\u65f6\uff0c\u53ef\u4ee5\u8054\u7cfb\u4e0a\u65b9\u8fd9\u5f20\u56fe\u8fdb\u884c\u7406\u89e3\u3002</p> <p>\u5728 Git Workflow \u4e2d\uff0c\u4e3b\u8981\u6709 5 \u7c7b\u5206\u652f\uff0c\u4ed6\u4eec\u5206\u522b\u662f master hotfix release develop feature\uff0c\u5b83\u4eec\u6709\u7740\u4e0d\u540c\u7684\u4f5c\u7528\u548c\u4f7f\u7528\u89c4\u8303\u3002\u5176\u4e2dmasterdevelop\u662f\u957f\u671f\u5206\u652f\uff0c\u4ed6\u4eec\u4f1a\u968f\u7740\u9879\u76ee\u7684\u7ef4\u62a4\u4e00\u76f4\u5b58\u5728\uff0c\u800chotfixreleasefeature\u8fd9\u4e9b\u77ed\u671f\u5206\u652f\u5219\u4f1a\u5728\u5b8c\u6210\u5bf9\u5e94\u5f00\u53d1\u540e\u88ab\u5408\u5e76\u6216\u8005\u5220\u9664\u3002</p>"},{"location":"tech_accu/tool/Git/Workflow/#master-\u5206\u652f\u4e3b\u5206\u652f","title":"Master \u5206\u652f\uff08\u4e3b\u5206\u652f\uff09","text":"<p>\u76f4\u63a5\u9762\u5411\u4f7f\u7528\u65b9\u7684\u5206\u652f\uff0c\u5728master\u4e2d\u5b58\u653e\u7684\u5e94\u5f53\u662f\u53ef\u4ee5\u4f7f\u7528\u7684\u7a33\u5b9a\u7248\u672c\uff0c\u56e0\u800c\u901a\u5e38\u4e5f\u4f1a\u5728\u5176\u4e2d\u6dfb\u52a0\u7248\u672c\u7f16\u53f7\u3002 \u6211\u4eec\u5e0c\u671b master \u4e2d\u7684\u4ee3\u7801\u603b\u662f\u4ece\u522b\u7684\u5206\u652f\u4e2d\u5408\u5e76\u8fc7\u6765\u7684\uff0c\u800c\u5e76\u4e0d\u5e0c\u671b\u4efb\u4f55\u4eba\u76f4\u63a5 commit \u5230 master \u4e2d\u3002</p>"},{"location":"tech_accu/tool/Git/Workflow/#develop-\u5206\u652f\u5f00\u53d1\u5206\u652f","title":"Develop \u5206\u652f\uff08\u5f00\u53d1\u5206\u652f\uff09","text":"<p>\u6240\u6709\u5f00\u53d1\u5de5\u4f5c\u90fd\u57fa\u4e8e\u8be5\u5206\u652f\u8fdb\u884c\uff0c\u53ef\u4ee5\u7406\u89e3\u4e3a\u9879\u76ee\u4ee3\u7801\u7684\u6c47\u6d41\u5904\uff0c\u800c master \u5219\u662f develop \u4e2d\u7279\u5b9a\u8282\u70b9\u53ef\u7528\u53d1\u884c\u3002 \u5f53\u9700\u8981\u6dfb\u52a0\u65b0\u7684\u529f\u80fd\u65f6\uff0c\u6211\u4eec\u9700\u8981\u65b0\u5efa\u4e00\u4e2a feature (\u5982\u56fe)\uff0c\u7136\u540e\u5728\u5b8c\u6210\u5bf9\u5e94\u5f00\u53d1\u540e\u5408\u5e76\u56de develop\u3002</p>"},{"location":"tech_accu/tool/Git/Workflow/#hotfix-\u5206\u652f\u8865\u4e01\u5206\u652f","title":"Hotfix \u5206\u652f\uff08\u8865\u4e01\u5206\u652f\uff09","text":"<p>\u5f53 master \u4e2d\u51fa\u73b0\u95ee\u9898\uff0c\u6211\u4eec\u9700\u8981\u4ee5\u51fa\u95ee\u9898\u7684\u8282\u70b9\u4e3a\u57fa\u7840\u521b\u5efa\u4e00\u4e2a hotfix\uff0c\u7136\u540e\u5728\u8fd9\u4e2a hotfix \u4e2d\u8fdb\u884c bug \u7684\u4fee\u590d\u5de5\u4f5c\u3002 \u5728\u5b8c\u6210\u4fee\u590d\u540e\uff0c\u6211\u4eec\u9700\u8981\u628a\u8fd9\u4e2a hotfix \u540c\u65f6\u5408\u5e76\u5230 master \u548c develop(\u5982\u56fe)\uff0c\u4e00\u65b9\u9762\u786e\u4fdd\u4e0b\u4e00\u4e2a\u7a33\u5b9a\u7248\u672c\u53ef\u7528\uff0c\u4e00\u65b9\u9762\u786e\u4fdd\u672a\u6765\u7684\u7248\u672c\u4e5f\u4fee\u590d\u4e86\u8be5 bug\u3002</p>"},{"location":"tech_accu/tool/Git/Workflow/#release-\u5206\u652f\u9884\u53d1\u5206\u652f","title":"Release \u5206\u652f\uff08\u9884\u53d1\u5206\u652f\uff09","text":"<p>\u5f53 develop \u8db3\u591f\u6210\u719f\u65f6\uff0c\u6211\u4eec\u4f1a\u5e0c\u671b\u5b83\u88ab\u5408\u5e76\u5230 master \u4e2d\u4f5c\u4e3a\u4e00\u4e2a\u7a33\u5b9a\u7248\u672c\u53d1\u5e03\uff0c\u4f46\u5728\u8fd9\u4e4b\u524d\uff0c\u6211\u4eec\u9700\u8981\u5728 release \u4e2d\u8fdb\u884c\u6700\u540e\u7684\u6d4b\u8bd5\u548c\u4fee\u6b63\u3002 \u5728\u5b8c\u6210\u8fd9\u4e9b\u5de5\u4f5c\u540e\uff0c\u6211\u4eec\u9700\u8981\u628a release \u540c\u65f6\u5408\u5e76\u5230 master \u548c develop (\u5982\u56fe)\uff0c\u4e00\u65b9\u9762\u786e\u4fdd\u4e0b\u4e00\u4e2a\u7a33\u5b9a\u7248\u672c\u53ef\u7528\uff0c\u4e00\u65b9\u9762\u786e\u4fdd\u672a\u6765\u7684\u7248\u672c\u4e5f\u4fee\u590d\u4e86\u8fd9\u4e9b\u95ee\u9898\u3002</p> <p>hotfix\u548crelease\u662f\u7c7b\u4f3c\u7684\uff0c\u4ed6\u4eec\u4e00\u4e2a\u662f\u57fa\u4e8emaster\u5bf9\u4e24\u4e2a\u957f\u671f\u5206\u652f\u8fdb\u884c\u7ef4\u62a4\uff0c\u4e00\u4e2a\u662f\u57fa\u4e8edevelop\u3002</p>"},{"location":"tech_accu/tool/Git/Workflow/#feature-\u5206\u652f\u529f\u80fd\u5206\u652f","title":"Feature \u5206\u652f\uff08\u529f\u80fd\u5206\u652f\uff09","text":"<p>\u5f53\u6211\u4eec\u9700\u8981\u5f00\u53d1\u65b0\u7684\u529f\u80fd\uff0c\u6216\u8005\u8bf4\u5bf9\u4e8e\u5927\u90e8\u5206\u5f00\u53d1\u5de5\u4f5c\uff0c\u5728\u5408\u7406\u7684\u6a21\u5757\u5212\u5206\u540e\uff0c\u5c31\u9700\u8981\u521b\u5efa\u5408\u9002\u7684 feature \u5206\u652f\u6765\u8fdb\u884c\u5bf9\u5e94\u7684\u5f00\u53d1\u5de5\u4f5c\u3002\u56e0\u4e3a feature \u5f80\u5f80\u6bd4\u8f83\u591a\uff0c\u6240\u4ee5\u8981\u6c42\u5404\u4e2afeature\u4e4b\u95f4\u8026\u5408\u7a0b\u5ea6\u4e0d\u5b9c\u8fc7\u9ad8\uff0c\u4ee5\u51cf\u5c11\u51b2\u7a81\uff0c\u8fd9\u5c31\u9700\u8981\u8fdb\u884c\u5408\u7406\u7684\u5212\u5206\u3002</p>"},{"location":"tech_accu/tool/Git/Workflow/#github-workflow","title":"Github Workflow","text":"<ul> <li>\u8fd9\u91cc\u7684 Workflow \u4e0e Github Action \u4e2d\u7684 Workflow \u6709\u533a\u522b\uff01</li> </ul> <p>Github Workflow \u5bf9 Git Workflow \u8fdb\u884c\u4e86\u7b80\u5316\uff0c\u5728 Github Workflow \u4e0b\u4ec5\u4ec5\u533a\u5206 master \u548c branch\uff0c\u800c\u5177\u4f53\u529f\u80fd\u7531\u5404\u4e2a branch \u7684\u547d\u540d\u6765\u4f53\u73b0\uff0c\u5373\u8981\u6c42 branch \u7684\u547d\u540d\u5177\u6709\u53d9\u4e8b\u6027\u3002</p> <p>\u6700\u91cd\u8981\u7684\u662f\uff0c\u6ca1\u6709\u4e86 develop \u5206\u652f\u4ee5\u540e\uff0c\u957f\u671f\u7ef4\u62a4\u7684\u5c31\u53ea\u6709 master \u4e86\uff0c\u8fd9\u5c31\u610f\u5473\u7740\u53d1\u5e03\u7684\u4ee3\u7801\u4e00\u822c\u90fd\u662f\u8fdb\u5ea6\u6700\u65b0\u7684\u4ee3\u7801\u3002\u800c\u8fd9\u4ef6\u4e8b\u662f\u6709\u597d\u6709\u574f\u7684\u3002 \u57fa\u4e8e Github Workflow \u7684\u5de5\u4f5c\u6d41\u7a0b\u4e3b\u8981\u5982\u4e0b\uff1a</p> <ol> <li>\u521b\u5efa\u5206\u652f (create a branch or fork)\uff1b</li> <li>\u5728\u5206\u652f\u4e2d\u8fdb\u884c\u5f00\u53d1\u5e76\u5b8c\u6210\u63d0\u4ea4 (add commits)\uff1b</li> <li>\u53d1\u9001 Pull Request (open a pull request)\uff1b</li> <li>\u4eba\u5de5\u5ba1\u6838\u4ee3\u7801\u3001\u6c9f\u901a\u4ea4\u6d41\uff0c\u4ee5\u53ca\u5fc5\u8981\u7684\u6d4b\u8bd5 (discuss and review)\uff1b</li> <li>\u5408\u5e76\u8fdb master (merge)</li> </ol> <p>\u56e0\u800c\uff0c\u5728\u8fd9\u6837\u4e00\u4e2a\u5de5\u4f5c\u6d41\u7a0b\u4e0b\uff0c\u5408\u4f5c\u8005\u4e4b\u95f4\u7684\u4ea4\u6d41\u5c31\u66f4\u52a0\u91cd\u8981\u4e86\u3002</p>"},{"location":"tech_accu/tool/Git/Workflow/#gitlab-workflow","title":"Gitlab Workflow","text":"<ul> <li> \u5495\u5495\u5495</li> </ul>"},{"location":"tech_accu/tool/Git/Workflow/#\u53c2\u8003\u8d44\u6599--ref","title":"\u53c2\u8003\u8d44\u6599 | Ref","text":"<ul> <li>https://nvie.com/posts/a-successful-git-branching-model/</li> <li>https://www.ruanyifeng.com/blog/2015/12/git-workflow.html</li> <li>https://gitbook.tw/chapters/gitflow/why-need-git-flow</li> <li>https://medium.com/i-think-so-i-live/git\u4e0a\u7684\u4e09\u7a2e\u5de5\u4f5c\u6d41\u7a0b-10f4f915167e</li> <li>https://github.com/xirong/my-git/blob/master/git-workflow-tutorial.md</li> <li>https://about.gitlab.com/topics/version-control/what-is-git-workflow/</li> </ul>"},{"location":"tech_accu/tool/Shell/","title":"Shell","text":"<p> \u7ea6 4930 \u4e2a\u5b57  462 \u884c\u4ee3\u7801  \u9884\u8ba1\u9605\u8bfb\u65f6\u95f4 22 \u5206\u949f</p> <p>\u6587\u7ae0\u76ee\u6807</p> <p>\u5728\u5b8c\u6210\u672c\u6587\u5b66\u4e60\u540e\uff0c\u6211\u4eec\u671f\u5f85\u60a8\u5bf9 Shell \u80fd\u6709\u66f4\u5177\u4f53\u7684\u8ba4\u8bc6\uff0c\u5e76\u80fd\u505a\u5230\u901a\u8fc7 Command Line \u5b9e\u73b0\u57fa\u7840\u4ea4\u4e92\u5e76\u4e86\u89e3\u5982\u4f55\u5b66\u4e60 Shell\u3002\u9664\u6b64\u4e4b\u5916\uff0c\u4e5f\u53ef\u4ee5\u901a\u8fc7\u64b0\u5199 Shell \u811a\u672c\u6765\u5b9e\u73b0\u4e00\u4e9b\u81ea\u52a8\u5316\u3002</p> <p>\u6b64\u5916\uff0c\u4ece Shell \u5165\u95e8\u5230\u547d\u4ee4\u884c\u5927\u5e08\uff0c\u5176\u4e2d\u80af\u5b9a\u6709\u5f88\u957f\u7684\u8def\u8981\u8d70\uff0c\u6211\u4eec\u6ca1\u6cd5\u6d89\u53ca Shell \u7684\u5168\u90e8\u77e5\u8bc6\u70b9\uff0c\u5149\u547d\u4ee4\u5c31\u80fd\u8bb2\u4e0a\u5f88\u4e45\uff0c\u6240\u4ee5\u4e00\u5b9a\u8981\u5b66\u4f1a\u5982\u4f55\u5229\u7528\u624b\u518c\u548c\u6587\u6863\u7b49\u67e5\u8be2\u547d\u4ee4\u7684\u4f7f\u7528\u65b9\u6cd5\uff0c\u672c\u6587\u5e0c\u671b\u505a\u5230\u7684\u662f\u6388\u4eba\u4ee5\u6e14\u800c\u975e\u6388\u4eba\u4ee5\u9c7c\u3002</p> <p>\u6b64\u5916\uff0c\u6211\u4f1a\u5728\u6587\u4e2d\u591a\u6b21\u5c06 Shell \u4e0e C \u8bed\u8a00\u7684\u4e00\u4e9b\u5185\u5bb9\u76f8\u8054\u7cfb\uff0c\u5982\u679c\u60a8\u6709 C \u7684\u57fa\u7840\uff0c\u90a3\u5c06\u518d\u597d\u4e0d\u8fc7\u3002</p>"},{"location":"tech_accu/tool/Shell/#\u6982\u8ff0","title":"\u6982\u8ff0","text":""},{"location":"tech_accu/tool/Shell/#\u7b80\u4ecb","title":"\u7b80\u4ecb","text":"<p>Shell \u7684\u4e2d\u6587\u540d\u79f0\u4e3a\u201c\u58f3\u5c42\u201d\uff0c\u987e\u540d\u601d\u4e49\u5c31\u662f\u201c\u6700\u5916\u5c42\u201d\u3002Wiki \u5bf9\u5176\u63cf\u8ff0\u4e3a\uff1a</p> <p>It is named a shell because it is the outermost layer around the operating system.</p> <p>\u7b80\u5355\u6765\u8bf4\uff0cShell \u5c06\u8bfb\u5165\u6765\u81ea Keyboard \u7684\u5185\u5bb9\uff0c\u5e76\u5c06\u6307\u4ee4\u53d1\u9001\u7ed9 OS \u4ee5\u8c03\u7528\u7cfb\u7edf\u670d\u52a1\u3002</p> <p>\u5728\u5e38\u89c1\u7684\u65e5\u7528\u64cd\u4f5c\u7cfb\u7edf\uff0c\u5982 Windows \u4e0e MacOS\uff0c\u4f60\u53ef\u80fd\u5c1d\u8bd5\u8fc7\u4f7f\u7528 GUI(Graphical User Interface)\uff0c\u5373\u56fe\u5f62\u7528\u6237\u754c\u9762\u6765\u4e0e\u4f60\u7684\u7cfb\u7edf\u6109\u5feb\u73a9\u800d\uff1b\u4e0e\u4e4b\u5bf9\u5e94\u7684\uff0cShell \u5219\u662f\u4e00\u79cd CLI(Command Line Interface)\uff0c\u4e0d\u540c\u4e8e GUIs \u901a\u8fc7\u70b9\u51fb\u6309\u94ae\u7b49\u64cd\u4f5c\u4e0e\u7cfb\u7edf\u4ea4\u4e92\u7b49\u65b9\u5f0f\uff0cCLI \u8981\u6c42\u7528\u6237\u901a\u8fc7\u547d\u4ee4\u884c\u6765\u4e0e\u7cfb\u7edf\u4ea4\u4e92\u3002\u800c\u4f5c\u4e3a\u4e00\u4e2a\u5408\u683c\u7684\u7a0b\u5e8f\u5458\uff0c\u6211\u4eec\u63a5\u89e6\u5230\u7684\u5927\u591a\u6570\u751f\u4ea7\u573a\u666f\u4e2d\uff0c\u4f7f\u7528 CLI \u662f\u4e00\u79cd\u66f4\u52a0\u9ad8\u6548\u7684\u9009\u62e9\uff0c\u4e8b\u5b9e\u4e0a\u4f60\u4e5f\u5f88\u96be\u907f\u514d\u5b83\u2014\u2014\u56e0\u800c\uff0c\u6211\u4eec\u9700\u8981\u638c\u63e1 Shell \u7684\u57fa\u672c\u4f7f\u7528\u3002</p> <p>\u5982\u4eca\uff0c\u5df2\u7ecf\u6709\u975e\u5e38\u591a\u7684 Shell \u53ef\u4ee5\u4f7f\u7528\uff0c\u800c\u4ed6\u4eec\u57fa\u672c\u4e0a\u90fd\u4ee5 <code>sh</code> \u7ed3\u5c3e\uff0c\u4f8b\u5982\u5e38\u89c1\u7684 <code>bash</code> \u548c <code>zsh</code> ,\u518d\u6bd4\u5982\u8bb8\u591a\u57fa\u4e8e Alpine \u7684 Docker Image\uff0c\u5185\u7f6e\u7684 Shell \u90fd\u662f <code>sh</code>\u3002\u5176\u4ed6\u7684\u8fd8\u6709 <code>dash</code> <code>csh</code> <code>ksh</code> \u7b49\u7b49\u3002</p>"},{"location":"tech_accu/tool/Shell/#shell-vs-terminal","title":"Shell vs Terminal","text":"<p>\u5728\u6b63\u5f0f\u5f00\u59cb\u4ecb\u7ecd Shell \u4e4b\u524d\uff0c\u6211\u8ba4\u4e3a\u6709\u5fc5\u8981\u505a\u4e00\u4e9b\u8fa8\u6790\u3002</p> <p>\u5728\u73b0\u4ee3\u7684\u8ba1\u7b97\u673a\u7cfb\u7edf\u4e2d\uff0c\u60f3\u8981\u4f7f\u7528 Shell\uff0c\u4f60\u9700\u8981\u501f\u52a9 Terminal\uff0c\u5373\u7ec8\u7aef\uff08\u66f4\u51c6\u786e\u7684\u8bf4\uff0c\u662f terminal emulator\uff0c\u4e0d\u8fc7\u5728\u672c\u6587\u4e2d\u6211\u4eec\u5e76\u4e0d\u4f1a\u5c31\u6b64\u5c55\u5f00\uff09\u3002Terminal \u4e4b\u4e8e Shell\uff0c\u5c31\u597d\u50cf\u7535\u8bdd\u4e4b\u4e8e\u901a\u8baf\u670d\u52a1\u3002</p> <p></p> <p>\u4f8b\u5982\uff0c\u56fe\u4e2d\u6253\u5f00\u7684\u8fd9\u4e2a\u201c\u7a97\u53e3\u201d\u5c31\u662f\u4e00\u4e2a\u53eb\u505a iTerm2 \u7684 terminal emulator\uff0c\u800c\u6211\u4f7f\u7528\u7684 <code>fish</code> \u5219\u662f\u4e00\u79cd Shell\u3002</p> <p>\u80fd\u4e0e\u8fd9\u4e24\u4e2a\u4e1c\u897f\u8fdb\u884c\u6bd4\u8f83\u548c\u8fa8\u6790\u7684\u4e1c\u897f\u5176\u5b9e\u8fd8\u6709\u5f88\u591a\uff0c\u4f46\u5e76\u975e\u672c\u6587\u4e3b\u9898\uff0c\u6240\u4ee5\u4e0d\u518d\u5c55\u5f00\u3002</p>"},{"location":"tech_accu/tool/Shell/#\u4ee5-bash-\u4e3a\u4f8b","title":"\u4ee5 Bash \u4e3a\u4f8b","text":"<p><code>bash</code> \u5168\u79f0 Bourne Again Shell\uff0c\u662f\u5982\u4eca\u6700\u5e38\u7528\u7684 Shell \u4e4b\u4e00\uff0c\u4e14\u5927\u90e8\u5206 Linux \u90fd\u4f1a\u5185\u7f6e bash\uff0c\u8fd9\u4e5f\u907f\u514d\u4e86\u66f4\u591a\u7684\u73af\u5883\u914d\u7f6e\u8d1f\u62c5\uff0c\u6240\u4ee5\u5728\u672c\u7ae0\u79cd\uff0c\u6211\u4eec\u5c06\u4ee5 <code>bash</code> \u4e3a\u4f8b\uff0c\u4ecb\u7ecd\u4e00\u4e9b Shell \u5e38\u7528\u6307\u4ee4\u548c\u6280\u5de7\u3002</p> <p>\u6b64\u5916\uff0c\u6211\u4eec\u63a5\u4e0b\u6765\u63d0\u4f9b\u7684\u5927\u591a\u6570\u8bba\u65ad\u4e3b\u8981\u57fa\u4e8e Linux \u7cfb\u7edf\u3002\u90e8\u5206\u7ed3\u8bba\u5728 Windows \u7b49\u7cfb\u7edf\u4e2d\u53ef\u80fd\u5e76\u4e0d\u6210\u7acb\u3002\u5982\u679c\u60a8\u6709\u5174\u8da3\uff0c\u53ef\u4ee5\u81ea\u884c\u67e5\u8be2\u8d44\u6599\u3002</p>"},{"location":"tech_accu/tool/Shell/#\u51c6\u5907\u5de5\u4f5c","title":"\u51c6\u5907\u5de5\u4f5c","text":"<p>\u5728\u5f00\u59cb\u4e4b\u524d\uff0c\u6211\u5e0c\u671b\u60a8\u786e\u4fdd\u60a8\u672c\u5730\u5df2\u6709\u53ef\u7528\u7684 <code>bash</code> \u73af\u5883\uff0c\u4ee5\u4fbf\u4e8e\u60a8\u80fd\u8ddf\u7740\u6559\u7a0b\u8fb9\u5b9e\u8df5\u8fb9\u5b66\u4e60\u3002</p> <p>\u5728\u8fd9\u91cc\uff0c\u6211\u5c06\u63d0\u4f9b\u4e00\u79cd\u7b80\u5355\u7684\u914d\u7f6e <code>bash</code> \u73af\u5883\u7684\u65b9\u6848\uff1a</p> <ul> <li>\u5982\u679c\u60a8\u662f Linux/MacOS \u7528\u6237\uff0c\u90a3\u4e48\u60a8\u7684\u7cfb\u7edf\u4e00\u822c\u90fd\u4f1a\u81ea\u5e26 Terminal \u7a0b\u5e8f\uff0c\u76f4\u63a5\u6253\u5f00\u5e76\u8f93\u5165 bash \u4ee5\u542f\u7528 bash\uff1b</li> <li>\u5982\u679c\u60a8\u662f Windows \u7528\u6237\uff0c\u90a3\u4e48\u60a8\u53ef\u4ee5\u9009\u62e9\u76f4\u63a5\u4e0b\u8f7d Git Bash\uff1b</li> </ul> <p>\u5f53\u7136\uff0c\u6211\u4eec\u6700\u63a8\u8350\u7684\u8fd8\u662f\u60a8\u53ef\u4ee5\u914d\u7f6e\u4e00\u4e2a Linux \u73af\u5883\u4ee5\u8fdb\u884c\u5b9e\u8df5\u548c\u5b66\u4e60\u3002</p> <p>\u5f53\u60a8\u5b8c\u6210\u8fd9\u4e9b\u5de5\u4f5c\u540e\uff0c\u60a8\u53ef\u80fd\u770b\u5230\u7c7b\u4f3c\u4e8e\u5982\u4e0b\u5217\u4e3e\u7684\u5185\u5bb9\u7684\u60c5\u51b5\uff1a</p> <pre><code># \u4e5f\u8bb8\u662f\u8fd9\u6837\nxxx:~$ {\u4f60\u7684\u5149\u6807\u5728\u8fd9\u91cc}\n# \u6216\u8005\u8fd9\u6837\n[xxx@yyy]~$ {\u4f60\u7684\u5149\u6807\u5728\u8fd9\u91cc}\n# \u53c8\u6216\u8005\u8fd9\u6837\nxxxx yyyy ~\n$ {\u4f60\u7684\u5149\u6807\u5728\u8fd9\u91cc}\n# ...\n</code></pre> <p>\u5b9e\u9645\u60c5\u51b5\u8fd8\u6709\u5f88\u591a\u79cd\uff0c\u56e0\u4e3a\u8fd9\u4e9b\u201c\u5f62\u5f0f\u201d\u90fd\u662f\u53ef\u4ee5\u88ab\u8bbe\u7f6e\u7684\u3002\u6bd4\u5982\u8fd9\u91cc\u7684 <code>$</code> \u88ab\u79f0\u4e3a prompt\uff0c\u5728\u672c\u6587\u7b2c\u4e00\u5f20\u56fe\u7247\u4e2d\u6211\u5c31\u5c06\u5b83\u8bbe\u7f6e\u4e3a\u4e86\u4e00\u4e2a Emoji \u56fe\u6807\u3002\u800c\u6211\u4eec\u53d1\u73b0\u8fd9\u91cc\u8fd8\u6709\u4e00\u4e2a <code>~</code> \uff0c\u5b83\u8868\u793a\u7684\u662f\u60a8\u7684\u201c\u5bb6\u76ee\u5f55\u201d\u3002\u66f4\u51c6\u786e\u7684\u8bf4\uff0c\u5b83\u7684\u542b\u4e49\u662f\u60a8\u5f53\u524d\u6240\u5728\u7684\u4f4d\u7f6e\u662f\u60a8\u7684\u5bb6\u76ee\u5f55\u3002\u5173\u4e8e\u8fd9\u4e00\u70b9\u6211\u4eec\u5c06\u5728\u63a5\u4e0b\u6765\u5c55\u5f00\u3002</p> <p>\u6b64\u5916\uff0c\u5982\u679c\u60a8\u5bf9 Linux \u7cfb\u7edf\u6709\u4e00\u5b9a\u8ba4\u8bc6\uff0c\u90a3\u65e0\u7591\u4f1a\u5e2e\u52a9\u60a8\u7406\u89e3\u672c\u6587\u3002</p> <p>\u90a3\u4e48\u63a5\u4e0b\u6765\uff0c\u8ba9\u6211\u4eec\u5f00\u59cb\u5427\uff01</p>"},{"location":"tech_accu/tool/Shell/#\u5e2e\u52a9\u624b\u518c","title":"\u5e2e\u52a9\u624b\u518c","text":"<p>\u5de6\u601d\u53f3\u60f3\uff0c\u6700\u540e\u6211\u8fd8\u662f\u628a\u8fd9\u6761\u6307\u4ee4\u653e\u5230\u4e86\u6700\u524d\u6765\u8bb2\u3002\u6211\u4eec\u4e0d\u53ef\u80fd\u4ec5\u4ec5\u901a\u8fc7\u4e00\u7bc7\u6587\u7ae0\u5c31\u4e86\u89e3\u547d\u4ee4\u884c\u7684\u5168\u90e8\u77e5\u8bc6\uff0c\u6240\u4ee5\u6211\u89c9\u5f97\u628a <code>man</code> \u653e\u5230\u6700\u524d\u9762\u6765\u8bb2\u662f\u5f88\u6709\u610f\u4e49\u7684\u3002</p> <p><code>man</code> \u7684\u4f5c\u7528\u662f\u6253\u5f00\u4e00\u4e2a user manual\u3002\u4f8b\u5982\uff0c\u5982\u679c\u6211\u4eec\u5728\u7ec8\u7aef\u4e2d\u8f93\u5165 <code>man man</code>\uff0c\u5c31\u4f1a\u5f97\u5230\u5982\u4e0b\u7ed3\u679c\uff0c\u5373\u4f7f\u7528 <code>man</code> \u6253\u5f00\u4e86 <code>man</code> \u7684\u624b\u518c\uff1a</p> <pre><code>man(1)                                     General Commands Manual                                    man(1)\n\nNAME\n       man - format and display the on-line manual pages\n\nSYNOPSIS\n       man [-acdfFhkKtwW] [--path] [-m system] [-p string] [-C config_file] [-M pathlist] [-P pager] [-B\n       browser] [-H htmlpager] [-S section_list] [section] name ...\n\nDESCRIPTION\n       man formats and displays the on-line manual pages.  If you specify section, man only looks in that\n       section of the manual.  name is normally the name of the manual page, which is typically the name of\n       a command, function, or file.  However, if name contains a slash (/) then man interprets it as a file\n       specification, so that you can do man ./foo.5 or even man /cd/foo/bar.1.gz.\n\n       See below for a description of where man looks for the manual page files.\n\n......\n</code></pre> <ul> <li>\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528\u9f20\u6807\u6eda\u8f6e/\u624b\u52bf\u7ffb\u9875/\u56de\u8f66\u7b49\u9014\u5f84\u53ef\u4ee5\u67e5\u770b\u63a5\u4e0b\u6765\u7684\u5185\u5bb9\uff0c\u6309\u4e0b <code>q</code> \u79bb\u5f00\u624b\u518c\u9875\u9762\u3002</li> <li>\u6b64\u5916\uff0cuser manual \u7684\u5185\u5bb9\u53ef\u80fd\u4f1a\u6839\u636e\u4f7f\u7528\u7684 Shell \u4e0d\u540c\u800c\u4e0d\u540c\uff0c\u751a\u81f3\u5728\u4e00\u4e9b Shell \u90fd\u4e0d\u4e00\u5b9a\u6709 user manual\u3002</li> </ul> <p>\u4e3a\u4e86\u5b9e\u73b0\u629b\u7816\u5f15\u7389\u7684\u76ee\u7684\uff0c\u73b0\u5728\u6211\u4eec\u4ec5\u4ec5\u4ecb\u7ecd <code>man</code> \u7684\u8fd9\u4e9b\u90e8\u5206\uff0c\u5b9e\u9645\u4e0a\u5149\u770b manual \u7684\u6587\u672c\u91cf\u5c31\u80fd\u611f\u53d7\u5230\uff0c <code>man</code> \u8fdc\u4e0d\u6b62\u5982\u6b64\uff0c\u4f46\u672c\u6587\u5e76\u4e0d\u6253\u7b97\u5c31\u6b64\u6df1\u5165\u3002\u800c\u5728\u8fd9\u91cc\u4ecb\u7ecd <code>man</code> \u7684\u76ee\u7684\uff0c\u4e00\u65b9\u9762\u662f\u5e0c\u671b\u5927\u5bb6\u5728\u5b66\u4e60\u4e4b\u540e\u7684\u547d\u4ee4\u65f6\uff0c\u53ef\u4ee5\u53c2\u8003 user manual\uff0c\u4e8b\u5b9e\u4e0a\u672c\u6587\u6d89\u53ca\u7684\u547d\u4ee4\u4e5f\u5e76\u4e0d\u4f1a\u4ecb\u7ecd\u5176\u5168\u90e8\u7528\u6cd5\uff1b\u53e6\u4e00\u65b9\u9762\u662f\u9f13\u52b1\u5927\u5bb6\u5728\u9047\u5230\u4e3a\u6b62\u7684\u6307\u4ee4\u65f6\uff0c\u901a\u8fc7\u624b\u518c\u7b49\u9014\u5f84\u5148\u67e5\u8be2\u5176\u884c\u4e3a\u3001\u7528\u6cd5\uff0c\u518d\u4f7f\u7528\u5b83\u3002</p>"},{"location":"tech_accu/tool/Shell/#\u6253\u5370\u5b57\u7b26\u4e32--echo","title":"\u6253\u5370\u5b57\u7b26\u4e32 | echo","text":"<p><code>echo</code> \u5373\u56de\u54cd\uff0c\u8fd9\u4e2a\u5355\u8bcd\u975e\u5e38\u5f62\u8c61\u5730\u63cf\u8ff0\u4e86\u8fd9\u4e2a\u547d\u4ee4\u7684\u4f5c\u7528\uff0c\u5c06\u5176\u63a5\u53d7\u5230\u7684\u5185\u5bb9\u201c\u56de\u54cd\u201d\u51fa\u6765\u3002</p> <pre><code># echo \u4f1a\u5c06\u5b83\u62ff\u5230\u7684\u53c2\u6570\u5168\u90fd\u5f53\u4f5c\u5b57\u7b26\u4e32\u6253\u5370\u51fa\u6765\uff0c\u4f46\u6210\u5bf9\u5f15\u53f7\u5e76\u4e0d\u4f1a\n$ echo &lt;something&gt;\n$ echo \"something 1 2 3\"\nsomething 1 2 3\n$ echo something 1 2 3\nsomething 1 2 3\n\n# \u5982\u679c\u4f60\u53ea\u8f93\u5165\u4e86\u4e00\u4e2a\u5f15\u53f7\uff0c\u5b83\u4f1a\u7b49\u4f60\u628a\u4ed6\u8865\u5b8c\u518d\u8f93\u51fa\n# \u5982\u679c\u60f3\u8f93\u51fa\u5f15\u53f7\uff0c\u9700\u8981\u4f7f\u7528 \\\" \u8f6c\u4e49\n$ echo \"\nFine, \\\"I\\\" will finish the string.\n\"\nFine, \"I\" will finish the string.\n\n# echo \u652f\u6301\u8f93\u51fa\u53c2\u6570\uff0c\u4ee5 $ \u5f00\u5934\uff0c\u5728\u547d\u4ee4\u884c\u73af\u5883\u4e0b\u4ed6\u4eec\u6307\u73af\u5883\u53d8\u91cf\uff0c\u5728\u811a\u672c\u73af\u5883\u4e0b\u8fd8\u53ef\u4ee5\u8fdb\u884c\u4e00\u4e9b\u53c2\u6570\u4f20\u9012\n# \u4e0b\u9762\u7684\u547d\u4ee4\u8f93\u51fa\u4e86\u5f53\u524d\u7528\u6237\uff0cUSER \u662f\u4e00\u4e2a\u503c\u4e3a\u5f53\u524d\u7528\u6237\u7684\u7528\u6237\u540d\u7684\u73af\u5883\u53d8\u91cf\u3002\necho $USER\nisshikih\n</code></pre>"},{"location":"tech_accu/tool/Shell/#\u67e5\u770b\u5f53\u524d\u8def\u5f84--pwd","title":"\u67e5\u770b\u5f53\u524d\u8def\u5f84 | pwd","text":"<p>\u5728\u8fd9\u91cc\u6211\u4eec\u60f3\u4ecb\u7ecd\u7684\u7b2c\u4e8c\u4e2a\u6307\u4ee4\u662f <code>pwd</code>\uff0c\u5b83\u7684\u6548\u679c\u662f\u8f93\u51fa\u60a8\u5f53\u524d\u7684\u4f4d\u7f6e\u3002</p> <pre><code>$ pwd\n# \u6bd4\u5982\u6211\u7684\u73af\u5883\u4e0b\uff0c\u5728 ~ \u4e0b\u8f93\u51fa\u5982\u4e0b\n/Users/isshikih\n# \u8868\u793a\u6211\u5f53\u524d\u7684\u4f4d\u7f6e\u662f /Users/isshikih\n</code></pre> <p>\u4e00\u5207\u7686\u6587\u4ef6 \u662f Linux \u7684\u8bbe\u8ba1\u7406\u5ff5\uff0c\u800c Shell \u7684\u4f7f\u7528\u6709\u76f8\u5f53\u4e00\u90e8\u5206\u662f\u57fa\u4e8e\u6587\u4ef6\u4f53\u7cfb\u7684\u3002\u800c\u5982\u4f55 \u7d22\u5f15 \u4e00\u4e2a\u6587\u4ef6\u5462\uff1f\u6211\u4eec\u9700\u8981\u63d0\u4f9b\u8fd9\u4e2a\u6587\u4ef6\u7684\u8def\u5f84\u548c\u6587\u4ef6\u540d\uff01\u4f8b\u5982\uff0c\u60a8\u9700\u8981\u53bb\u4e00\u53f0 Windows \u7535\u8111\u4e2d\u627e\u5230\u60a8\u4e0a\u5b66\u671f\u7684\u8bfe\u7a0b\u4f5c\u4e1a\uff0c\u5b83\u7684\u6587\u4ef6\u540d\u4e3a <code>myHomework.pdf</code> \uff0c\u4e5f\u8bb8\u4f60\u9700\u8981\u6253\u5f00D\u76d8\u4e2d\u7684 Homework \u6587\u4ef6\u5939\u3002\u90a3\u4e48\u62bd\u8c61\u5730\u6765\u8bf4\uff0c\u8fd9\u4e2a\u6587\u4ef6\u7684\u8def\u5f84\u4e3a <code>D:\\Homework\\myHomework.pdf</code> \uff08\u8fd9\u662f\u5728 Windows \u4e0a\u7684\u5199\u6cd5\uff09\u3002\u8fd9\u79cd\u5f62\u5f0f\u7684\u201c\u4f4d\u7f6e\u201d\u88ab\u79f0\u4e3a \u7edd\u5bf9\u8def\u5f84\uff0c\u5373\u6211\u4eec\u9700\u8981\u586b\u5199\u6587\u4ef6\u7684\u5b8c\u6574\u8def\u5f84\u624d\u80fd\u627e\u5230\u8fd9\u4e2a\u6587\u4ef6\u3002\u5728\u4e4b\u540e\u7684\u90e8\u5206\u4e2d\uff0c\u6211\u4eec\u63d0\u5230\u7684<code>&lt;filename&gt;&lt;dirname&gt;</code>\u7b49\u90fd\u5305\u62ec\u4e86\u6587\u4ef6\u7684\u8def\u5f84\u3002</p> <p>\ud83d\udc49\u00a0\u4e8b\u5b9e\u4e0a\uff0c\u6709\u76f8\u5f53\u4e00\u90e8\u5206 Shell \u8bed\u6cd5\u662f\u56f4\u7ed5\u7740\u6587\u4ef6\u5c55\u5f00\u7684\u3002</p>"},{"location":"tech_accu/tool/Shell/#\u5207\u6362\u76ee\u5f55--cd","title":"\u5207\u6362\u76ee\u5f55 | cd","text":"<p><code>cd</code> \u662f change directory \u7684\u7f29\u5199\uff0c\u5b83\u7684\u6548\u679c\u662f\u5c06\u60a8\u5f53\u524d\u7684\u4f4d\u7f6e\u8f6c\u79fb\u5230\u76ee\u6807\u76ee\u5f55\u4e2d\u3002\u5b83\u7684\u5199\u6cd5\u5982\u4e0b\uff1a</p> <pre><code>cd {target directory}\n\n# eg 1: =========================================\n$ pwd\n/home/username\n\n$ cd /home/username/aaa\n$ pwd\n/home/username/aaa\n\n# eg 2: =========================================\n$ pwd\n/home/username\n\n$ cd ./aaa/bbb\n$ pwd\n/home/username/aaa/bbb\n\n# eg 3: =========================================\n$ pwd\n/home/username\n\n$ cd ./../aaa\n$ pwd\n/home/aaa\n</code></pre> <p>\u63a5\u4e0b\u6765\u5bf9\u4e0a\u9762 eg \u7684\u90e8\u5206\u7b26\u53f7\u505a\u4e00\u4e0b\u89e3\u91ca\uff1a</p> <ul> <li><code>.</code> \u8868\u793a\u5f53\u524d\u8def\u5f84\uff1b</li> <li><code>..</code> \u8868\u793a\u4e0a\u7ea7\u8def\u5f84\uff08\u6307\u4e0a\u4e00\u4e2a\uff09 \uff1b</li> </ul> <p>\u6b64\u5916\uff0c\u8fd9\u91cc\u8fd8\u6709\u4e00\u4e9b\u5feb\u6377\u65b9\u5f0f\uff1a</p> <ul> <li>\u5982\u679c\u53ea\u6709 <code>cd</code> \uff0c\u5219\u8fd4\u56de\u5bb6\u76ee\u5f55 <code>~</code> \uff08\u53ef\u4ee5\u53d1\u73b0 eg 4 \u548c eg 5 \u7b49\u4ef7\uff09\uff1b</li> <li><code>cd -</code> \u8fd4\u56de\u4e0a\u4e00\u6b21 <code>cd</code> \u4e4b\u524d\u6240\u5728\u7684\u4f4d\u7f6e\uff1b</li> <li><code>cd ~username</code> \u5207\u6362\u5230\u76ee\u6807\u7528\u6237\u7684\u5bb6\u76ee\u5f55\uff1b</li> </ul>"},{"location":"tech_accu/tool/Shell/#\u7f57\u5217\u76ee\u5f55\u4e0b\u5185\u5bb9--ls","title":"\u7f57\u5217\u76ee\u5f55\u4e0b\u5185\u5bb9 | ls","text":"<p><code>ls</code> \u6307\u4ee4\u7528\u6765\u67e5\u770b\u76ee\u6807\u76ee\u5f55\u4e0b\u7684\u6587\u4ef6\u3002\u5e38\u7528\u7684\u53c2\u6570\u4e3b\u8981\u6709 <code>-l</code> \uff08\u957f\u683c\u5f0f\uff09\u548c <code>-a</code> \uff08\u663e\u793a\u5168\u90e8\uff09\u3002</p> <p>\u5177\u4f53\u5199\u6cd5\u5982\u4e0b\uff1a</p> <pre><code># \u5047\u8bbe\u6211\u4eec\u5f53\u524d\u5728\u6587\u4ef6\u5939 my_ \u4e0b\uff0c\u6587\u4ef6\u5939\u5185\u6709\u4e24\u4e2a\u6587\u4ef6\u548c\u4e00\u4e2a\u6587\u4ef6\u5939\n# \u6587\u4ef6 .hidden \u548c\u6587\u4ef6 file1.md\n# \u6587\u4ef6\u5939 dir1\uff0c\u91cc\u9762\u6709\u4e2a\u6587\u4ef6 file2.md\n\n$ ls\ndir1        file1.md\n\n$ ls -a\n.               ..      .hiden1     dir1        file1.md\n\n$ ls -l\ndrwxr-xr-x  2 isshikih  staff  64 10 12 12:15 dir1\n-rw-r--r--  1 isshikih  staff   7 10 12 12:16 file1.md\n\n$ ls -la\ndrwxr-xr-x  5 isshikih  staff  160 10 12 12:15 .\ndrwxr-xr-x  6 isshikih  staff  192 10 12 12:14 ..\n-rw-r--r--  1 isshikih  staff    0 10 12 12:15 .hiden1\ndrwxr-xr-x  2 isshikih  staff   96 10 12 12:15 dir1\n-rw-r--r--  1 isshikih  staff    7 10 12 12:16 file1.md\n\n# \u5982\u679c\u540e\u9762\u8ddf\u7740\u4e00\u4e2a\u6587\u4ef6\u5939\uff0c\u5219\u663e\u793a\u76ee\u6807\u8def\u5f84\u4e0b\u7684\u5185\u5bb9\uff0c\u5426\u5219\u663e\u793a\u5f53\u524d\u8def\u5f84\u4e0b\u7684\u5185\u5bb9\u3002\n$ ls dir1\nfile2.md\n</code></pre> <ul> <li>\u6709\u65f6\uff0c\u6211\u4eec\u4f1a\u4e3a <code>ls -l</code> \u8bbe\u7f6e\u4e00\u4e2a alias\uff0c\u5373 <code>alias ll=\"ls -l\"</code> \uff0c\u8fd9\u6837\uff0c\u6211\u4eec\u5c31\u53ef\u4ee5\u66f4\u65b9\u4fbf\u7684 <code>ll</code> \u4e86\u3002</li> <li>\u5176\u4e2d\uff0c <code>l</code> \u4e2d\u7684\u5177\u4f53\u683c\u5f0f\u5982\u4e0b\uff1a</li> </ul> <pre><code>-rw-------   1 me       me            576 Apr 17  2019 weather.txt\ndrwxr-xr-x   6 me       me           1024 Oct  9  2019 web_page\n-rw-rw-r--   1 me       me         276480 Feb 11 20:41 web_site.tar\n-rw-------   1 me       me           5743 Dec 16  2018 xmas_file.txt\n\n----------  -------  -------     -------- ------------ -------------\n|          |        |            |         |             |\n|          |        |            |         |\n|          |        |            |         |           \u6587\u4ef6\u540d\n|          |        |            |         |\n|          |        |            |         +---       \u4fee\u6539\u65f6\u95f4\n|          |        |            |\n|          |        |            +-------------   \u6587\u4ef6\u5927\u5c0f(in bytes)\n|          |        |\n|          |        +--------------------------       \u6240\u5c5e\u7528\u6237\u7ec4\n|          |\n|          +-----------------------------------       \u6240\u5c5e\u7528\u6237\n|\n+----------------------------------------------       \u6587\u4ef6\u6743\u9650\n# Edited from https://linuxcommand.org/lc3_lts0030.php\n</code></pre> <ul> <li>\u5173\u4e8e\u8fd9\u90e8\u5206\u5177\u4f53\u90e8\u5206\u5b57\u6bb5\u7684\u5177\u4f53\u89e3\u91ca\uff0c\u8bf7\u53c2\u8003\u76f8\u5173\u8d44\u6599\uff0c\u4e0d\u5c5e\u4e8e\u672c\u6587\u7684\u8303\u7574\u3002</li> </ul>"},{"location":"tech_accu/tool/Shell/#\u6253\u5370\u6587\u4ef6\u5185\u5bb9--cat","title":"\u6253\u5370\u6587\u4ef6\u5185\u5bb9 | cat","text":"<p><code>cat</code> \u6307\u4ee4\u4f1a\u8fde\u63a5\u6587\u4ef6\u5e76\u5c06\u5185\u5bb9\u6253\u5370\u5230\u6807\u51c6\u8f93\u51fa\u6d41\u3002</p> <pre><code># &lt;filename&gt; \u662f\u76ee\u6807\u6587\u4ef6\u7684\u540d\u5b57\u3002\n$ cat &lt;filename&gt;\n</code></pre> <ul> <li>\u800c\u5b9e\u9645\u4e0a <code>cat</code> \u547d\u4ee4\u6700\u91cd\u8981\u7684\u4f5c\u7528\u5e76\u4e0d\u662f \u663e\u793a \u6587\u4ef6\u5185\u5bb9\uff0c\u4ed4\u7ec6\u89c2\u5bdf\u63cf\u8ff0\uff0c\u5b83\u7684\u4f5c\u7528\u662f \u6253\u5370\u5230\u6807\u51c6\u8f93\u51fa\u6d41\uff0c\u5176\u4f5c\u7528\u5728\u4e4b\u540e\u4ecb\u7ecd\u4e86\u91cd\u5b9a\u5411\u4e4b\u540e\u4f1a\u51f8\u663e\u51fa\u6765\u3002</li> </ul>"},{"location":"tech_accu/tool/Shell/#\u6253\u5370\u6587\u4ef6\u9996\u5c3e\u5185\u5bb9--head--tail","title":"\u6253\u5370\u6587\u4ef6\u9996\u5c3e\u5185\u5bb9 | head &amp; tail","text":"<p><code>head</code> \u548c <code>tail</code> \u8bed\u6cd5\u7c7b\u4f3c\uff0c\u529f\u80fd\u7c7b\u4f3c\uff0c\u5206\u522b\u4e3a\u67e5\u770b\u76ee\u6807\u6587\u4ef6\u7684\u5f00\u5934\u90e8\u5206\u7684\u5185\u5bb9\u548c\u7ed3\u5c3e\u90e8\u5206\u7684\u5185\u5bb9\u3002\u4e0d\u8fc7\u7531\u4e8e\u6211\u4eec\u5bf9\u6587\u672c\u6587\u4ef6\u9664\u4e86\u8bfb\u5199\uff0c\u8fd8\u6709\u4e00\u4e2a\u53eb\u505a\u201c\u8ffd\u52a0\u201d\u7684\u64cd\u4f5c\uff08\u7c7b\u6bd4 C \u8bed\u8a00\u4e2d <code>fopen()</code> \u7684 <code>\u2018a\u2019</code> \u6a21\u5f0f\uff09 <code>tail</code> \u4f1a\u6301\u7eed\u6253\u5370\u65b0\u8ffd\u52a0\u8fdb\u6587\u4ef6\u7684\u5185\u5bb9\uff0c\u6240\u4ee5\u82b1\u6837\u7a0d\u5fae\u6bd4 <code>head</code> \u591a\u4e00\u70b9\u3002</p> <pre><code># `head` \u548c `tail` \u90fd\u6709\u9ed8\u8ba4\u53c2\u6570 `-n 10`\n# \u4e5f\u5c31\u662f\uff0c\u4e0b\u9762\u4e24\u4e2a\u6307\u4ee4\u662f\u7b49\u4ef7\u7684\uff0c\u5b83\u4eec\u90fd\u4f1a\u6253\u5370\u76ee\u6807\u6587\u4ef6\u7684\u524d 10 \u884c\n$ head &lt;filename&gt;\n$ head -n 10 &lt;filename&gt;\n# \u4e0b\u9762\u8fd9\u4e24\u6761\u6307\u4ee4\u4e5f\u662f\u7b49\u4ef7\u7684\uff0c\u5b83\u4eec\u90fd\u4f1a\u6253\u5370\u76ee\u6807\u6587\u4ef6\u7684\u672b 10 \u884c\n$ tail &lt;filename&gt;\n$ tail -n 10 &lt;filename&gt;\n\n# \u5c06 10 \u6539\u6210\u5176\u4ed6\u6570\u5b57\u5c31\u53ef\u4ee5\u4fee\u6539\u663e\u793a\u7684\u884c\u6570\uff0c\u4f8b\u5982\u4e0b\u9762\u7684\u6307\u4ee4\u4f1a\u6253\u5370\u76ee\u6807\u6587\u4ef6\u7684\u9996/\u672b 4 \u884c\n$ head -n 4 &lt;filename&gt;\n$ tail -n 4 &lt;filename&gt;\n\n# \u9664\u4e86\u884c\u6570\uff0c\u4f60\u4e5f\u53ef\u4ee5\u6307\u5b9a\u6253\u5370\u7684\u5b57\u8282\u6570\uff0c\u5982\u4e0b\u9762\u6307\u4ee4\u4f1a\u6253\u5370\u76ee\u6807\u6587\u4ef6\u7684\u9996/\u672b 20 \u4e2a\u5b57\u8282\n$ head -c 20 &lt;filename&gt;\n$ tail -c 20 &lt;filename&gt;\n</code></pre> <p><pre><code># `tail` \u6bd4 `head` \u8fd8\u8981\u591a\u4e00\u4e9b\u53c2\u6570\uff0c\u6bd4\u5982 `-f`\n# `-f` \u5728\u6253\u5370\u5b8c\u5df2\u6709\u7684\u6587\u4ef6\u5185\u5bb9\u540e\u4f1a\u963b\u585e\uff0c\u7b49\u5f85\u76ee\u6807\u6587\u4ef6\u7684\u66f4\u65b0\n# \u4e00\u65e6\u6709\u5185\u5bb9\u8ffd\u52a0\u8fdb\u76ee\u6807\u6587\u4ef6\uff0c`tail` \u5c31\u4f1a\u5c06\u5b83\u6253\u5370\u51fa\u6765\n$ tail -f &lt;filename&gt;\n</code></pre> </p> <p>\u6ce8\u610f\uff0c\u8fd9\u91cc\u7684 echo \u5f00\u5934\u7684\u8bed\u53e5\u662f\u5728\u505a\u8ffd\u52a0\u64cd\u4f5c\uff0c\u4e4b\u540e\u4f1a\u8bb2\u5230\u3002</p> <p>\u800c\u81f3\u4e8e\u5177\u4f53\u7684\u5f15\u7528\u573a\u666f\uff0c\u6bd4\u5982\u6709\u4e9b\u5de5\u5177\u7684\u65e5\u5fd7\u4f1a\u4e0d\u65ad\u8ffd\u52a0\u5230\u67d0\u4e2a\u65e5\u5fd7\u6587\u4ef6\u4e2d\uff0c\u8fd9\u65f6\u5019\u5c31\u53ef\u4ee5\u7528 <code>tail -f</code> \u6765\u5b9e\u65f6\u8ddf\u8e2a\u65e5\u5fd7\u4fe1\u606f\u3002</p>"},{"location":"tech_accu/tool/Shell/#\u67e5\u770b\u6587\u672c\u6587\u4ef6\u5185\u5bb9--less","title":"\u67e5\u770b\u6587\u672c\u6587\u4ef6\u5185\u5bb9 | less","text":"<p><code>less</code> \u5219\u662f\u771f\u6b63\u7528\u6765\u663e\u793a\u6587\u4ef6\u5185\u5bb9\u7684\u6307\u4ee4\uff0c\u5b83\u4f1a\u4ee5\u6587\u672c\u6587\u4ef6\u7684\u5f62\u5f0f\u5c55\u793a\u6587\u4ef6\u5185\u5bb9\u2014\u2014\u8fd9\u610f\u5473\u7740\u4f60\u5982\u679c\u5f3a\u884c\u4f7f\u7528 <code>less</code> \u6765\u67e5\u770b\u4e00\u4e2a\u4e8c\u8fdb\u5236\u6587\u4ef6\uff0c\u5219\u4f1a\u5f97\u5230\u4e00\u5806\u4e71\u7801\u3002</p> <pre><code># &lt;textFilename&gt; \u4e3a\u76ee\u6807\u6587\u4ef6\u7684\u540d\u5b57\n$ less &lt;textFilename&gt;\n</code></pre> <p>\u4f7f\u7528 <code>less</code> \u67e5\u770b\u6587\u4ef6\u65f6\uff0c\u4f60\u4f1a\u53d1\u73b0\u4f60\u6253\u5f00\u4e86\u4e00\u4e2a\u5f88\u50cf <code>man</code> \u7684\u754c\u9762\uff08\u76f8\u4fe1\u4f60\u5df2\u7ecf\u6ce8\u610f\u5230\u4e86\u8fd9\u4e2a\u8bf4\u6cd5\u6709\u70b9\u672c\u672b\u98a0\u5012\uff09\uff0c\u90a3\u5b9e\u9645\u4e0a\u6d4f\u89c8\u7684\u65b9\u5f0f\u4e5f\u662f\u7c7b\u4f3c\u7684\uff0c\u8fd9\u91cc\u518d\u591a\u4ecb\u7ecd\u4e00\u4e9b\u5728\u6d4f\u89c8\u6587\u4ef6\u7684\u65f6\u5019\u53ef\u80fd\u7528\u5230\u7684\u6280\u5de7\uff1a</p> <ul> <li>\u9f20\u6807\u6eda\u8f6e / \u89e6\u63a7\u677f\u624b\u52bf\uff1a\u7ffb\u9875\u6d4f\u89c8\uff1b</li> <li><code>[space]</code> / <code>PageDown</code> \uff1a\u5f80\u540e\u7ffb\u4e00\u9875\uff1b</li> <li><code>b</code> / <code>PageUp</code> \uff1a\u5f80\u524d\u7ffb\u4e00\u9875\uff1b</li> <li><code>shift</code> + <code>g</code> \uff08\u8f93\u5165 <code>G</code>\uff09\uff1a\u8df3\u8f6c\u7684\u6587\u672b\uff1b</li> <li>1,\u00a0<code>shift</code> + <code>g</code> \uff08\u8f93\u5165 <code>1G</code>\uff09\uff1a\u8df3\u8f6c\u5230\u6587\u9996\uff1b</li> <li><code>/{something}</code> , <code>Enter</code> \uff1a\u641c\u7d22 <code>{something}</code> \uff0c\u7c7b\u4f3c\u4e8e\u5e38\u89c1\u8f6f\u4ef6\u7684 <code>Ctrl</code> + <code>f</code> \uff1b</li> <li><code>n</code> \uff1a\u91cd\u590d\u4e0a\u4e00\u6b21\u641c\u7d22\u64cd\u4f5c\uff0c\u9002\u5408\u5728\u641c\u7d22\u5185\u5bb9\u6709\u591a\u4e2a\u7684\u65f6\u5019\uff0c\u8df3\u8f6c\u5230\u4e0b\u4e00\u4e2a\u641c\u7d22\u7ed3\u679c\uff1b</li> <li><code>h</code> \uff1a\u5e2e\u52a9\u624b\u518c\uff1b</li> <li><code>q</code> \uff1a\u9000\u51fa\uff1b</li> </ul>"},{"location":"tech_accu/tool/Shell/#\u4fee\u6539\u6587\u4ef6\u65f6\u95f4\u5c5e\u6027\u521b\u5efa\u6587\u4ef6--touch","title":"\u4fee\u6539\u6587\u4ef6\u65f6\u95f4\u5c5e\u6027(\u521b\u5efa\u6587\u4ef6) | touch","text":"<p><code>touch</code>\u5b9e\u9645\u4e0a\u662f\u7528\u6765\u4fee\u6539\u6587\u4ef6\u548c\u76ee\u5f55\u7684\u65f6\u95f4\u5c5e\u6027\u7684\uff0c\u4f46\u662f\u7531\u4e8e\u5b83\u5177\u6709\u201c\u5982\u679c\u6587\u4ef6\u4e0d\u5b58\u5728\u5219\u521b\u5efa\u4e00\u4e2a\u201d\u7684\u7279\u6027\uff0c\u6240\u4ee5\u4e5f\u5e38\u5e38\u7528\u6765\u521b\u5efa\u4e00\u4e2a\u65b0\u6863\u6848\u3002</p> <pre><code>$ ls -l\ntotal 0\n\n# \u5982\u679c\u5f53\u524d\u76ee\u5f55\u4e0b\u6ca1\u6709\u53eb\u505a &lt;filename&gt; \u7684\u6587\u4ef6\uff0c\u5219\u521b\u5efa\u4e00\u4e2a &lt;filename&gt;\n$ touch file\n$ ls -l\ntotal 0\n-rw-r--r--  1 isshikih  staff  0 10 25 10:07 file\n# \u5176\u4e2d\u6587\u4ef6\u7684\u65f6\u95f4\u4e3a\u7cfb\u7edf\u7684\u5f53\u524d\u65f6\u95f4\n\n# \u5982\u679c\u6b64\u65f6\u518d\u6b21 touch &lt;filename&gt;\uff0c\u5219\u4f1a\u66f4\u65b0\u5176\u65f6\u95f4\u4e3a\u5f53\u524d\u7cfb\u7edf\u65f6\u95f4\n$ touch file\n$ ls -l\ntotal 0\n-rw-r--r--  1 isshikih  staff  0 10 25 10:10 file\n</code></pre>"},{"location":"tech_accu/tool/Shell/#\u521b\u5efa\u6587\u4ef6\u5939--mkdir","title":"\u521b\u5efa\u6587\u4ef6\u5939 | mkdir","text":"<p><code>mkdir</code>\u662f make directory \u7684\u7f29\u5199\uff0c\u4e5f\u5c31\u662f\u521b\u5efa\u4e00\u4e2a\u201c\u6587\u4ef6\u5939\u201d\u3002</p> <pre><code># &lt;dirname&gt; \u53ef\u4ee5\u662f\u4e00\u4e2a\u590d\u6742\u8def\u5f84\u4e0b\u7684\u76ee\u5f55\uff0c\u4f46\u662f\u4e00\u5b9a\u8981\u6c42\u5176\u524d\u7f6e\u76ee\u5f55\u90fd\u5b58\u5728\n$ mkdir &lt;dirname&gt;\n$ ls -l\ntotal 0\n$ mkdir dir1/dir2\nmkdir: dir1: No such file or directory\n# \u8bf4\u660e\u76ee\u6807\u76ee\u5f55 dir2 \u7684\u524d\u7f6e\u8def\u5f84 ./dir1 \u7f3a\u5931\n\n# \u6211\u4eec\u53ef\u4ee5\u4f9d\u6b21\u521b\u5efa\u8fd9\u4e9b\u76ee\u5f55\n$ mkdir dir1 dir1/dir2\n$ tree      # \u8be5\u6307\u4ee4\u4f1a\u663e\u793a\u5f53\u524d\u7684\u6587\u4ef6\u7ed3\u6784\n.\n\u251c\u2500\u2500 dir1\n\u2502\u00a0\u00a0 \u251c\u2500\u2500 dir2\n\u2502\u00a0\u00a0 \u2502\u00a0\u00a0 \u2514\u2500\u2500 file2\n\u2502\u00a0\u00a0 \u2514\u2500\u2500 file1\n\u2514\u2500\u2500 newDir\n    \u251c\u2500\u2500 dir2\n    \u2502\u00a0\u00a0 \u2514\u2500\u2500 file2\n    \u2514\u2500\u2500 file1\n\n4 directories, 4 files\n\n# \u6216\u8005\u4f7f\u7528 -p \u53c2\u6570\uff0c\u5b83\u5141\u8bb8\u521b\u5efa\u5d4c\u5957\u76ee\u5f55\uff0c\u5373\u5982\u679c\u524d\u7f6e\u76ee\u5f55\u4e0d\u5b58\u5728\u5b83\u4f1a\u521b\u5efa\u4e00\u4e2a\n$ mkdir -p dir1/dir2\n$ tree      # \u8be5\u6307\u4ee4\u4f1a\u663e\u793a\u5f53\u524d\u7684\u6587\u4ef6\u7ed3\u6784\n.\n\u251c\u2500\u2500 dir1\n\u2502\u00a0\u00a0 \u251c\u2500\u2500 dir2\n\u2502\u00a0\u00a0 \u2502\u00a0\u00a0 \u2514\u2500\u2500 file2\n\u2502\u00a0\u00a0 \u2514\u2500\u2500 file1\n\u2514\u2500\u2500 newDir\n    \u251c\u2500\u2500 dir2\n    \u2502\u00a0\u00a0 \u2514\u2500\u2500 file2\n    \u2514\u2500\u2500 file1\n\n4 directories, 4 files\n</code></pre>"},{"location":"tech_accu/tool/Shell/#\u79fb\u52a8\u91cd\u547d\u540d--mv","title":"\u79fb\u52a8(\u91cd\u547d\u540d) | mv","text":"<p><code>mv</code>\u5373 move\uff0c\u542b\u4e49\u5f88\u660e\u663e\uff0c\u5373\u6539\u53d8\u6587\u4ef6\u6216\u76ee\u5f55\u7684\u4f4d\u7f6e\u3002\u4e0d\u8fc7\u7531\u4e8e\u201c\u4f4d\u7f6e\u201d\u8fd9\u4ef6\u4e8b\uff0c\u5b9e\u9645\u4e0a\u4e5f\u53ef\u4ee5\u5305\u542b\u6587\u4ef6\u672c\u8eab\u7684\u540d\u5b57\uff0c\u6240\u4ee5\u4e5f\u53ef\u4ee5\u7528\u6765\u505a\u91cd\u547d\u540d\uff0c\u5b9e\u9645\u4e0a\u5c31\u662f\u4fee\u6539\u76ee\u6807\u4f4d\u7f6e\u5230\u540c\u4e00\u4e2a\u8def\u5f84\u4e0b\u7684\u53e6\u5916\u4e00\u4e2a\u540d\u5b57\u3002</p> <pre><code># \u6ce8\u610f\uff0c\u6211\u4eec\u5728\u8fd9\u4e00\u8282\u4e34\u65f6\u628a &lt;path&gt; \u4ece &lt;filename&gt; \u548c &lt;dirname&gt; \u4e2d\u62c6\u51fa\u6765\n# \u8be5\u6307\u4ee4\u4f1a\u5c06 &lt;target1&gt; \u79fb\u52a8\u5230 &lt;path2&gt; \u5e76\u6539\u540d\u4e3a &lt;target2&gt;\uff0c\u5f53\u7136\u5141\u8bb8\u540c\u540d\n$ mv &lt;path1&gt;/&lt;target1&gt; &lt;path2&gt;/&lt;target2&gt;\n\n# \u7701\u7565 &lt;target2&gt;\uff0c\u5219\u4f1a\u79fb\u52a8\u6587\u4ef6\u4f4d\u7f6e\u4f46\u4e0d\u4fee\u6539\u6587\u4ef6\u540d\uff0c\u5373\u4e0b\u9762\u4e24\u4e2a\u6307\u4ee4\u7b49\u4ef7\n$ mv &lt;path1&gt;/&lt;target1&gt; &lt;path2&gt;\n$ mv &lt;path1&gt;/&lt;target1&gt; &lt;path2&gt;/&lt;target1&gt;\n\n# \u79fb\u52a8\u5230\u540c\u4e00\u76ee\u5f55\uff0c\u5373\u5b9e\u73b0\u91cd\u547d\u540d\uff0c\u5f53\u7136 &lt;path1&gt;/ \u53ef\u4ee5\u7701\u7565\uff0c\u5373\u6b64\u65f6 &lt;path1&gt; \u4e3a .\n$ mv &lt;path1&gt;/&lt;target1&gt; &lt;path1&gt;/&lt;target2&gt;\n</code></pre>"},{"location":"tech_accu/tool/Shell/#\u590d\u5236--cp","title":"\u590d\u5236 | cp","text":"<p><code>cp</code>\u5373 copy\uff0c\u7528\u6765\u590d\u5236\u6587\u4ef6\u6216\u76ee\u5f55\uff0c\u57fa\u672c\u8bed\u6cd5\u548c<code>mv</code>\u7c7b\u4f3c\uff0c\u6211\u4eec\u518d\u591a\u4ecb\u7ecd\u4e00\u4e2a<code>-r</code>\u53c2\u6570\u3002</p> <pre><code># \u8be5\u6307\u4ee4\u4f1a\u590d\u5236\u4e00\u4e2a\u6587\u4ef6 &lt;filename&gt; \u5230 &lt;path&gt; \u4e0b\n$ cp &lt;filename&gt; &lt;path&gt;\n\n# cp \u65e0\u6cd5\u590d\u5236\u6587\u4ef6\u5939\n$ cp &lt;dir&gt; &lt;path&gt;\ncp: &lt;dir&gt; is a directory (not copied).\n# \u4f46\u662f\u4f7f\u7528 -r \u53c2\u6570\u53ef\u4ee5\u590d\u5236 &lt;path1&gt; \u4e0b\u6240\u6709\u5185\u5bb9\u5230 &lt;path2&gt; \u4e0b\n$ cp -r &lt;path1&gt; &lt;path2&gt;\n$ cp -r dir1 newDir\n$ tree      # \u8be5\u6307\u4ee4\u4f1a\u663e\u793a\u5f53\u524d\u7684\u6587\u4ef6\u7ed3\u6784\n.\n\u251c\u2500\u2500 dir1\n\u2502\u00a0\u00a0 \u251c\u2500\u2500 dir2\n\u2502\u00a0\u00a0 \u2502\u00a0\u00a0 \u2514\u2500\u2500 file2\n\u2502\u00a0\u00a0 \u2514\u2500\u2500 file1\n\u2514\u2500\u2500 newDir\n    \u251c\u2500\u2500 dir2\n    \u2502\u00a0\u00a0 \u2514\u2500\u2500 file2\n    \u2514\u2500\u2500 file1\n\n4 directories, 4 files\n</code></pre>"},{"location":"tech_accu/tool/Shell/#\u5220\u9664--rm","title":"\u5220\u9664 | rm","text":"<p>\u628a<code>rm</code>\u653e\u5728\u6700\u540e\u8bb2\u662f\u6709\u539f\u56e0\u7684\uff0c\u6216\u8bb8\u4f60\u542c\u8bf4\u8fc7 <code>rm / -rf</code> \u8fd9\u6761\u6307\u4ee4\uff0c\u5374\u4e0d\u77e5\u9053\u5b83\u7684\u542b\u4e49\uff0c\u90a3\u4e48\u770b\u5b8c\u8fd9\u4e00\u5c0f\u8282\u4f60\u5c31\u77e5\u9053\u8fd9\u4e2a\u6307\u4ee4\u6709\u591a\u6050\u6016\u4e86\uff08\u5343\u4e07\u4e0d\u8981\u8dd1\u8fd9\u6761\u6307\u4ee4\uff09\u3002</p> <p>\u9996\u5148\u6211\u4eec\u9700\u8981\u77e5\u9053\uff0cLinux \u4e0b<code>rm</code>\u6307\u4ee4\u5e76\u4e0d\u5b58\u5728\u201c\u5783\u573e\u7bb1\u201d\u8fd9\u4e2a\u673a\u5236\uff0c\u5373\u7528<code>rm</code>\u5220\u6389\u7684\u4e1c\u897f\u662f\u6ca1\u6cd5\u901a\u8fc7\u6b63\u5e38\u624b\u6bb5\u590d\u539f\u7684\uff0c\u800c\u4e0a\u9762\u90a3\u6761\u6307\u4ee4\u7684\u610f\u601d\u5c31\u662f\u5f3a\u5236\u9012\u5f52\u5220\u9664\u7cfb\u7edf\u6839\u76ee\u5f55\u4e0b\u6240\u6709\u5185\u5bb9\uff0c\u4e5f\u5c31\u662f \u5565\u90fd\u5220\u5149\u4e86\u3002</p> <p>\u6240\u4ee5\uff0c\u4e00\u822c\u6211\u4eec\u90fd\u4f1a\u5efa\u8bae\u4f7f\u7528<code>alias</code>\u4fdd\u62a4<code>rm</code>\u6307\u4ee4\uff08\u6211\u5199\u8fc7<code>fish</code>\u7684<code>rmalias</code>\u4fdd\u62a4\u6d41\u7a0b\uff0c\u53ef\u4ee5\u53c2\u8003\u8fd9\u7bc7\u6587\u7ae0\uff09\u3002</p> <p><code>rm</code>\u5373 remove\uff0c\u987e\u540d\u601d\u4e49\u5c31\u662f\u7528\u6765\u5220\u9664\u4e1c\u897f\u7684\uff0c\u8fd9\u662f\u4e2a\u975e\u5e38\u5371\u9669\u7684\u6307\u4ee4\u3002\u5e38\u7528\u7684\u53c2\u6570\u6709<code>-r</code>\u548c<code>-f</code>\uff0c\u5206\u522b\u8868\u793a\u9012\u5f52\u5220\u9664\u548c\u5f3a\u5236\u5220\u9664\uff1b\u6b64\u5916\uff0c\u6211\u4eec\u8fd8\u5c06\u4ecb\u7ecd\u4e00\u4e2a<code>-i</code>\u53c2\u6570\u3002</p> <pre><code># \u5220\u9664\u4e00\u4e2a\u6587\u4ef6\n$ rm &lt;filename&gt;\n\n# \u5220\u9664 &lt;dirname&gt; \u4e0b\u6240\u6709\u7684\u4e00\u7ea7\u6587\u4ef6\n$ rm &lt;dirname&gt;/*\n\n$ tree\n.\n\u251c\u2500\u2500 dir2\n\u2502\u00a0\u00a0 \u2514\u2500\u2500 file3\n\u251c\u2500\u2500 file1\n\u2514\u2500\u2500 file2\n\n1 directory, 3 files\n$ rm ./*\nrm: ./dir2: is a directory\n$ tree\n.\n\u2514\u2500\u2500 dir2\n    \u2514\u2500\u2500 file3\n\n1 directory, 1 file\n# \u53ef\u4ee5\u53d1\u73b0\uff0c\u4e2d\u9014\u62a5\u9519\u8bf4 dir2 \u662f\u4e2a\u76ee\u5f55\u5e76\u4e14\u6ca1\u6709\u5220\u6389\uff0c\u5b9e\u9645\u4e0a\uff0c\u5982\u679c dir2 \u662f\u4e2a\u7a7a\u76ee\u5f55\uff0c\u90a3\u5b83\u662f\u4f1a\u88ab\u5220\u6389\u7684\n# \u800c\u5982\u679c\u8981\u771f\u6b63\u5220\u9664\u8fd9\u4e2a\u76ee\u5f55\u4e0b\u6240\u6709\u7684\u5185\u5bb9\uff0c\u5c31\u9700\u8981\u6211\u4eec\u201c\u9012\u5f52\u201d\u5220\u9664\uff0c\u5373\u4f7f\u7528 -r\n\n# \u9012\u5f52\u5220\u9664 &lt;dirname&gt; \u4e0b\u6240\u6709\u5185\u5bb9\n$ rm -r &lt;dirname&gt;/*\n\n# \u9012\u5f52\u5220\u9664 &lt;dirname&gt;\n$ rm -r &lt;dirname&gt;\n\n# \u5371\u9669\uff1a\u5f3a\u5236\u9012\u5f52\u5220\u9664 &lt;dirname&gt;\n$ rm -rf &lt;dirname&gt;\n\n# \u63a8\u8350\uff1a\u9012\u5f52\u5220\u9664\u65f6\u9010\u4e00\u786e\u8ba4\n$ rm -ri dir2\nexamine files in directory dir2/? y     # \u8fd9\u91cc\u8f93\u5165\u7684 y \u8868\u793a\u786e\u8ba4\uff0c\u5426\u5219\u90fd\u4e0d\u4f1a\u6267\u884c\u5220\u9664\nremove dir2//file3? y                                   # \u8fd9\u91cc\u8f93\u5165\u7684 y \u8868\u793a\u786e\u8ba4\uff0c\u5426\u5219\u90fd\u4e0d\u4f1a\u6267\u884c\u5220\u9664\nremove dir2/? y                                             # \u8fd9\u91cc\u8f93\u5165\u7684 y \u8868\u793a\u786e\u8ba4\uff0c\u5426\u5219\u90fd\u4e0d\u4f1a\u6267\u884c\u5220\u9664\n</code></pre>"},{"location":"tech_accu/tool/Shell/#\u91cd\u5b9a\u5411\u76f8\u5173-","title":"\u91cd\u5b9a\u5411\u76f8\u5173 \ud83d\udca1","text":"<p>\u53ef\u4ee5\u8bf4\u8fd9\u662f Shell \u4e2d\u6700\u6709\u610f\u601d\u7684\u77e5\u8bc6\u70b9\u4e4b\u4e00\u4e86\u3002\u91cd\u5b9a\u5411\uff0c\u987e\u540d\u601d\u4e49\u5c31\u662f\u91cd\u65b0\u5b9a\u5411\uff0c\u66f4\u51c6\u786e\u7684\u6765\u8bf4\u662f\u7ed9\u6570\u636e\u6d41\u91cd\u65b0\u5b9a\u5411\u3002\u9996\u5148\uff0c\u6211\u4eec\u6765\u770b\u770b\u8fd9\u5f20\u56fe\uff0c\u5b83\u63cf\u8ff0\u4e86\u547d\u4ee4\u8fd0\u884c\u65f6\u7684\u6570\u636e\u4ea4\u4e92\u3002</p> <pre><code>flowchart TD;\ninput[\"file, keyboard, etc\"] \ncommand\noutput[\"file, screen, etc\"]\nerror[\"file, screen, etc\"]\n\ninput --&gt;|\"Standard Input (stdin)\"| command\ncommand --&gt;|\"Standard Output (stdout)\"| output\ncommand --&gt;|\"Standard Error (stderr)\"| error</code></pre> <p>\u7b80\u5355\u7684\u63cf\u8ff0\u4e00\u4e0b\uff0c\u547d\u4ee4\u4ece\u6807\u51c6\u8f93\u5165\u6d41 <code>stdin</code> \u4e2d\u8bfb\u53d6\u8f93\u5165\u6570\u636e\uff0c\u5904\u7406\u8fc7\u7a0b\u4e2d\u6216\u8005\u662f\u5904\u7406\u7ed3\u675f\u540e\uff0c\u4f1a\u5411\u6807\u51c6\u8f93\u51fa\u6d41 <code>stdout</code> \u548c\u6807\u51c6\u9519\u8bef\u6d41 <code>stderr</code> \u4e2d\u5199\u5165\u6570\u636e\uff0c\u4e00\u822c\u6765\u8bf4 <code>stdout</code> \u627f\u8f7d\u7684\u662f\u6b63\u5e38\u7684\u8f93\u51fa\u6570\u636e\uff0c\u800c <code>stderr</code> \u627f\u8f7d\u7684\u662f\u62a5\u9519\u7b49\u4fe1\u606f\u3002</p> <p>\u800c\u6240\u8c13\u7684\u91cd\u5b9a\u5411\uff0c\u6b63\u662f\u6307\u91cd\u5b9a\u5411\u8fd9\u4e09\u4e2a\u6d41\uff0c\u800c\u4e14\u66f4\u591a\u7684\u6307\u7684\u662f\u91cd\u5b9a\u5411 <code>stdin</code> \u548c <code>stdout</code>\u3002</p> <p>\u800c\u5728 Shell \u4e2d\uff0c\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u4ed6\u4eec\u7684\u4ee3\u7801\u6765\u6307\u4ee3\u4ed6\u4eec\uff0c\u5177\u4f53\u5185\u5bb9\u672c\u6587\u4e0d\u4f1a\u8fc7\u591a\u6d89\u53ca\uff0c\u5982\u679c\u60f3\u8981\u6df1\u5165\u4e86\u89e3\u53ef\u4ee5\u4ed4\u7ec6\u770b\u770b\u201c\u5408\u5e76\u201d\u8fd9\u4e00\u8282\u7684\u5185\u5bb9\u3002</p> Stream: stdin stdout stderr Code: 0 1 2"},{"location":"tech_accu/tool/Shell/#\u6807\u51c6\u8f93\u51fa\u6d41\u91cd\u5b9a\u5411---","title":"\u6807\u51c6\u8f93\u51fa\u6d41\u91cd\u5b9a\u5411 | &gt; &gt;&gt;","text":"<p>\u57fa\u672c\u4e0a\u6240\u6709\u8bed\u8a00\u7684\u6559\u7a0b\u4e2d\u90fd\u4f1a\u5148\u4ecb\u7ecd\u5982\u4f55\u8f93\u51fa \u201dHello World!\u201c\uff08\u5f53\u7136\u4ed6\u4eec\u4e5f\u53ef\u80fd\u66f4\u60f3\u548c\u522b\u4eba\u6253\u62db\u547c\uff09\u3002\u603b\u800c\u8a00\u4e4b\uff0c\u8f93\u51fa\u5bf9\u4e00\u4e2a\u547d\u4ee4\u3001\u4e00\u4e2a\u7a0b\u5e8f\u662f\u81f3\u5173\u91cd\u8981\u7684\u3002\u4f46\u662f\u4f60\u4f1a\u53d1\u73b0\uff0c\u8fd9\u4e9b\u6307\u4ee4\u90fd\u53ea\u662f\u5c06\u5185\u5bb9\u6253\u5370\u5230\u4f60\u7684\u7ec8\u7aef\u91cc\uff0c\u5373 <code>stdout</code> \u91cc\uff0c\u53ea\u4e0d\u8fc7\u4e00\u822c\u88ab\u9001\u8fdb <code>stdout</code> \u7684\u4e1c\u897f\u4f1a\u88ab\u6253\u5370\u5728 screen \u4e0a\u3002</p> <p>\u4f46\u662f\u73b0\u5728\u6211\u4eec\u60f3\u8981\u5b83\u88ab\u5199\u5165\u5230\u4e00\u4e2a\u53eb <code>chat.txt</code> \u7684\u6587\u4ef6\u91cc\uff0c\u4f60\u5f53\u7136\u53ef\u4ee5\u4f7f\u7528 <code>fopen()</code> \u4e4b\u7c7b\u7684\u4e1c\u897f\u6765\u5b9e\u73b0\uff0c\u4f46\u662f\u73b0\u5728\u6211\u4eec\u60f3\u7528 Shell \u6765\u5b9e\u73b0\u8fd9\u4e2a\u6548\u679c\u3002</p> <p>\u6211\u4eec\u518d\u6b21\u56de\u5fc6\u6574\u4e2a\u8fc7\u7a0b\u4e2d\u6570\u636e\u7684\u6d41\u52a8\uff1a\u7a0b\u5e8f\u4e2d\u7684\u6570\u636e \u2192 <code>stdout</code> \u2192 screen\uff0c\u800c\u91cd\u5b9a\u5411\u505a\u7684\u4e8b\u60c5\u5c31\u662f\u6539\u53d8 <code>stdout</code> \u2192 screen \u8fd9\u4e2a\u6b65\u9aa4\u3002</p> <pre><code># \"command\" \u7684\u8f93\u51fa\u4f1a\u88ab\u8986\u5199\u8fdb \"file\"\n$ command &gt; file\n\n# \u4e0b\u9762\u8fd9\u6761\u6307\u4ee4\u5c31\u5b9e\u73b0\u4e86\u5c06 \"Hello World!\" \u5199\u5165\u4e86 chat.txt\n$ echo \"Hello World!\" &gt; chat.txt\n$ cat chat.txt\nHello World!\n\n# \"command\" \u7684\u8f93\u51fa\u4f1a\u88ab\u8ffd\u52a0\u8fdb \"file\"\n$ command &gt;&gt; file\n\n# \u4e0b\u9762\u8fd9\u6761\u6307\u4ee4\u5c31\u5b9e\u73b0\u4e86\u5c06 \"Hello World!\" \u8ffd\u52a0\u8fdb chat.txt\n$ echo \"Hello Human!\" &gt;&gt; chat.txt\n$ cat chat.txt\nHello World!\nHello Human!\n\n# \u4e0b\u9762\u8fd9\u6761\u6307\u4ee4\u5b9e\u73b0\u4e86\u5c06\u5f53\u524d\u76ee\u5f55\u4e0b\u7684\u6587\u4ef6/\u6587\u4ef6\u5939\u5217\u8868\u5199\u5165 \"index.txt\"\n$ ls -al &gt; index.txt\n</code></pre> <p>\u8bf6\u7b49\u7b49\uff0c\u4e0a\u9762\u600e\u4e48\u7a81\u7136\u51fa\u73b0\u4e86\u201c\u8ffd\u52a0\u201d\u8fd9\u4e2a\u8bcd\uff1f\u522b\u6025\u3002\u8ba9\u6211\u4eec\u56de\u987e\u4e00\u4e0b <code>fopen()</code> \u3002\u5982\u679c\u9700\u8981\u521b\u5efa\u4e00\u4e2a\u53ef\u5199\u6587\u4ef6\uff0c<code>fopen()</code> \u7684\u6a21\u5f0f\u53c2\u6570\u4e00\u822c\u662f <code>w</code> \uff0c\u6216\u8005\u662f <code>a</code>\u3002\u4ed6\u4eec\u5206\u522b\u4ee3\u8868 write \u548c append\uff0c\u5373\u8986\u5199\u548c\u8ffd\u52a0\u3002\u524d\u8005\u5c06\u76ee\u6807\u6587\u4ef6\u7684\u5185\u5bb9\u5168\u90e8\u8986\u76d6\uff0c\u5199\u5165\u65b0\u7684\u5185\u5bb9\uff0c\u5373\u76f8\u5f53\u4e8e\u6e05\u7a7a\u76ee\u6807\u6587\u4ef6\u7136\u540e\u5199\u5165\u5185\u5bb9\uff1b\u540e\u8005\u662f\u5728\u76ee\u6807\u6587\u4ef6\u7684\u5c3e\u90e8\u5f00\u59cb\u5199\u5165\u65b0\u5185\u5bb9\uff0c\u65e7\u7684\u5185\u5bb9\u4ecd\u7136\u4fdd\u7559\u3002\u6240\u4ee5\u4e0a\u9762\u7684\u4ee3\u7801\u4f1a\u51fa\u73b0 \u201cHello Human!\u201d \u88ab\u8ffd\u52a0\u5728 \u201cHello World!\u201d \u540e\u9762\u7684\u60c5\u51b5\u3002</p> <p>\u73b0\u5728\uff0c\u5982\u679c\u4f60\u60f3\u8ba9\u4f60\u7684 <code>a.exe</code> \u8f93\u51fa\u7684\u4e1c\u897f\u88ab\u5199\u5165 <code>out.txt</code> \u4e2d\uff0c\u4e5f\u53ef\u4ee5\u5c1d\u8bd5\u8fd9\u6837\u8fd0\u884c\u5b83\uff1a</p> <pre><code>$ a.exe &gt; out.txt\n</code></pre>"},{"location":"tech_accu/tool/Shell/#\u6807\u51c6\u8f93\u5165\u6d41\u91cd\u5b9a\u5411--","title":"\u6807\u51c6\u8f93\u5165\u6d41\u91cd\u5b9a\u5411 | &lt;","text":"<p>\u4e0e\u8f93\u51fa\u76f8\u5bf9\u5e94\uff0c\u5982\u679c\u6211\u4eec\u60f3\u4ece\u6587\u4ef6\u4e2d\u8bfb\u53d6\u6570\u636e\u800c\u975e\u4ece Keyboard \u5199\u5165\u7684\u7f13\u51b2\u533a\u8bfb\u53d6\u5185\u5bb9\uff0c\u800c\u662f\u4ece\u67d0\u4e2a\u6587\u4ef6\uff0c\u6211\u4eec\u4e5f\u53ef\u4ee5\u4f7f\u7528 <code>&lt;</code> \u6765\u91cd\u5b9a\u5411\u8f93\u5165\u3002</p> <pre><code>// \u5047\u8bbe a.exe \u7684\u6e90\u7801\u662f\u8fd9\u6837\u7684\n#include &lt;stdio.h&gt;\nint main(){\nchar str[1024];\nscanf(\"%s\", str);\nprintf(\"Hello %s!\", str);\n}\n</code></pre> <pre><code>// \u5047\u8bbe in.txt \u4e2d\u7684\u5185\u5bb9\u4e3a\u5982\u4e0b\nisshikih\n</code></pre> <pre><code># \"file\" \u4f1a\u88ab\u5f53\u4f5c \"command\" \u7684\u8f93\u5165\u53c2\u6570\n$ command &lt; file\n\n# \"a.exe\" \u4f1a\u8bfb\u5165 \"chat.txt\" \u7684\u5185\u5bb9\u4f5c\u4e3a\u8f93\u5165\n$ a.exe &lt; in.txt\nHello isshikh!\n\n# \u7efc\u5408\u8d77\u6765\uff0c\u6211\u4eec\u8fd8\u53ef\u4ee5\u8fd9\u6837\n$ a.exe &lt; in.txt &gt; out.txt\n$ cat out.txt\nHello isshikih! </code></pre>"},{"location":"tech_accu/tool/Shell/#\u6807\u51c6\u9519\u8bef\u6d41\u91cd\u5b9a\u5411--2-2","title":"\u6807\u51c6\u9519\u8bef\u6d41\u91cd\u5b9a\u5411 | 2&gt; 2&gt;&gt;","text":"<p><code>stderr</code> \u7684\u91cd\u5b9a\u5411\u57fa\u672c\u4e0a\u548c <code>stdout</code> \u662f\u4e00\u6837\u7684\u3002</p> <pre><code># \"command\" \u7684\u9519\u8bef\u6d41\u4f1a\u88ab\u8986\u5199\u8fdb \"file\"\n$ command 2&gt; file\n\n# \"command\" \u7684\u9519\u8bef\u6d41\u4f1a\u88ab\u8ffd\u52a0\u8fdb \"file\"\n$ command &gt;&gt; file\n</code></pre> <p>\u4f46\u5bf9\u4e8e <code>stderr</code> \uff0c\u6211\u4eec\u4f7f\u7528\u91cd\u5b9a\u5411\u7684\u76ee\u7684\u4e5f\u53ef\u80fd\u662f\u4e3a\u4e86\u8ba9\u4ed6\u4e0d\u8981\u5728\u5c4f\u5e55\u4e0a\u663e\u793a\u51fa\u6765\uff0c\u5373\u5c06\u5b83\u91cd\u5b9a\u5411\u5230\u522b\u7684\u5730\u65b9\u53bb\u3002</p> <p>\u8fd9\u91cc\u9700\u8981\u4ecb\u7ecd\u4e00\u4e2a\u7279\u6b8a\u7684\u201c\u6587\u4ef6\u201d\uff0c <code>/dev/null</code> \u2014\u2014\u4efb\u4f55\u5199\u5165\u5230\u5b83\u7684\u5185\u5bb9\u90fd\u4f1a\u88ab\u4e22\u5f03\u3002\u4e5f\u5c31\u662f\u8bf4\uff0c\u53ea\u8981\u6211\u4eec\u5c06 <code>stderr</code> \u91cd\u5b9a\u5411\u5230 <code>/dev/null</code> \uff0c\u5c31\u80fd\u5b9e\u73b0\u7c7b\u4f3c\u4e8e\u201c\u5ffd\u7565\u9519\u8bef\u6d41\u201d\u7684\u6548\u679c\u3002 </p> <pre><code># \"command\" \u7684\u9519\u8bef\u4fe1\u606f\u90fd\u4f1a\u88ab\u4e22\u5f03\n$ command 2&gt; /dev/null\n</code></pre>"},{"location":"tech_accu/tool/Shell/#\u5408\u5e76--","title":"\u5408\u5e76 | &lt;&amp; &gt;&amp;","text":"<p>\u6b64\u5916\uff0c\u8fd8\u6709 <code>&lt;&amp;</code> \u548c <code>&gt;&amp;</code> \u8fd9\u4e24\u4e2a\u7b26\u53f7\uff0c\u7531\u4e8e\u7bc7\u5e45\u6709\u9650\uff0c\u6211\u4e0d\u6253\u7b97\u5c55\u5f00\u8bb2\u8fd9\u4ef6\u4e8b\u3002\u8fd9\u91cc\u5f15\u7528\u8fd9\u4e00\u6279\u56de\u7b54\uff1a</p> <ul> <li>shell - What does \u201csh a.sh &lt;&amp;0 &gt;&amp;0\u201d mean? - Unix &amp; Linux Stack Exchange</li> </ul> <p><code>n&gt;&amp;p</code>\u00a0and\u00a0<code>n&lt;&amp;p</code>\u00a0are the same operator and are for duplicating the file descriptor (fd)\u00a0<code>p</code>\u00a0onto the file descriptor\u00a0<code>n</code>. Or said otherwise, they redirect the file descriptor\u00a0<code>n</code>\u00a0to whatever resource fd\u00a0<code>p</code>\u00a0is redirected to.</p> <p>The\u00a0<code>&lt;</code>\u00a0and\u00a0<code>&gt;</code>\u00a0are not used to determine what direction (reading or writing) the redirected file descriptor will be used.\u00a0<code>n</code>\u00a0will get the same direction as\u00a0<code>p</code>. That is, if\u00a0<code>p</code>\u00a0was open for writing, so will be\u00a0<code>n</code>\u00a0even if the\u00a0<code>n&lt;&amp;p</code>\u00a0operator is used.</p> <p>The only difference between the two operators is when\u00a0<code>n</code>\u00a0is not specified.\u00a0<code>&gt;&amp;p</code>\u00a0redirects stdout (is like\u00a0<code>1&gt;&amp;p</code>\u00a0or\u00a0<code>1&lt;&amp;p</code>) and\u00a0<code>&lt;&amp;p</code>\u00a0redirects stdin (is like\u00a0<code>0&lt;&amp;p</code>\u00a0or\u00a0<code>0&gt;&amp;p</code>).</p> <p>So\u00a0<code>&lt;&amp;0</code>\u00a0is like\u00a0<code>0&lt;&amp;0</code>, so redirects stdin to whatever resource stdin was redirected to, so does nothing useful, it's usually a no-op and doesn't make much sense.</p> <p>But not always a no-op, not in every shell. When job control is disabled, POSIX requires stdin of command in the background to be redirected to\u00a0<code>/dev/null</code>\u00a0or an equivalent file. In Bash (tested in 4.4.12)\u00a0<code>&lt;&amp;0</code>\u00a0overrides this. Compare\u00a0<code>(ls -l /proc/self/fd/0 &amp;)</code>\u00a0and\u00a0<code>(&lt;&amp;0 ls -l /proc/self/fd/0 &amp;)</code>. In some cases this is useful.</p> <p><code>&gt;&amp;0</code>\u00a0duplicates the fd 0 onto the fd 1. Because the fd 1 (stdout), is by convention only used for writing, that\u00a0<code>&gt;&amp;0</code>\u00a0only makes sense if fd 0 was open in read+write mode.</p> <p>That would be the case in cases where fd 0 points to the terminal device, because terminal emulators or\u00a0<code>getty</code>\u00a0would generally open the terminal device in read+write mode and assign fds 0, 1 and 2 to it.</p> <p>So maybe whoever wrote that wanted to redirect stdout to the terminal assuming that stdin was pointing to it.</p> <p>One place where\u00a0<code>n&gt;&amp;n</code>\u00a0makes sense is with zsh and its\u00a0<code>mult_IOs</code>\u00a0feature. In\u00a0<code>zsh</code>:</p> <pre><code>some-cmd &gt;&amp;1 &gt; some-file\n# that is: some-cmd 1&gt;&amp;1 1&gt; some-file\n</code></pre> <p>Redirects the standard output of\u00a0<code>some-cmd</code>\u00a0to both whatever stdout was before (&amp;1) and\u00a0<code>some-file</code>, as if you had written:</p> <pre><code>some-cmd | tee some-file\n</code></pre> <p>While</p> <pre><code>some-cmd &lt;&amp;0 &lt; some-file\n# that is: some-cmd 0&lt;&amp;0 0&lt; some-file\n</code></pre> <p>would feed first the original stdin and then\u00a0<code>some-file</code>\u00a0as input to\u00a0<code>some-cmd</code>\u00a0as if you had written:</p> <pre><code>cat - some-file | some-cmd\n</code></pre> <p>But in\u00a0<code>cmd &lt;&amp;0 &gt;&amp;0</code>, fd 0 is redirected only once, so that does not apply.</p> <p><code>n&gt;&amp;n</code>\u00a0can also have an interesting side effect in some shells (<code>ksh</code>,\u00a0<code>zsh</code>, not\u00a0<code>dash</code>,\u00a0<code>bash</code>\u00a0nor\u00a0<code>yash</code>) in that it triggers an error and gives up running the command if the file descriptor\u00a0<code>n</code>\u00a0is not open. So, in those shells,</p> <pre><code>cmd 0&lt;&amp;0\n</code></pre> <p>would avoid running\u00a0<code>cmd</code>\u00a0in the pathological condition where\u00a0<code>stdin</code>\u00a0is closed:</p> <pre><code>$ ksh -c 'cat file - &lt;&amp;0' &lt;&amp;-\nksh: 0: cannot open [Bad file descriptor]\n$ mksh -c 'cat file - &lt;&amp;0' &lt;&amp;-\nmksh: &lt;&amp;0 : bad file descriptor\n$ zsh -c 'cat file - &lt;&amp;0' &lt;&amp;-\nzsh:1: 0: bad file descriptor\n\n$ bash -c 'cat file - &lt;&amp;0' &lt;&amp;-\ncontents of file\ncat: -: Bad file descriptor\ncat: closing standard input: Bad file descriptor\n</code></pre> <ul> <li>Copy from the top answer from: https://unix.stackexchange.com/questions/84620/what-does-sh-a-sh-0-0-mean</li> </ul>"},{"location":"tech_accu/tool/Shell/#\u7ba1\u9053\u7b26--","title":"\u7ba1\u9053\u7b26 | |","text":"<p>\u524d\u9762\u8bb2\u4e86\u5982\u4f55\u5c06\u8f93\u5165\u8f93\u51fa\u91cd\u5b9a\u5411\u81f3 \u6587\u4ef6\uff0c\u5373\u6570\u636e\u7684\u6d41\u52a8\u662f \u4ece\u547d\u4ee4\u5230\u6587\u4ef6 \u6216\u662f \u4ece\u6587\u4ef6\u5230\u547d\u4ee4\u3002\u800c\u7ba1\u9053\u7b26 <code>|</code> \u5219\u5b9e\u73b0\u4e86\u5c06\u6570\u636e\u7684\u6d41\u52a8\u5b9a\u5411\u4e3a \u4ece\u547d\u4ee4\u5230\u547d\u4ee4\u3002</p> <pre><code># \"command_1\" \u7684\u8f93\u51fa\u4f1a\u4f5c\u4e3a \"command_2\" \u7684\u8f93\u5165\n$ command_1 | command_2\n\n# \u4f7f\u7528 less \u6765\u67e5\u770b\u5f53\u524d\u76ee\u5f55\u4e0b\u7684\u6587\u4ef6/\u6587\u4ef6\u5939\u5217\u8868\n$ ls -al | less\n\n# \u4e00\u4e2a\u5e38\u7528\u7684\u7528\u6cd5\u662f\u642d grep \u5728\u65e5\u5fd7\u4e2d\u627e\u5230\u4f60\u60f3\u8981\u7684\u4e00\u884c\n# \u6bd4\u5982\u4e0b\u9762\u7684\u547d\u4ee4\u4f1a\u5728 xxx.log \u6587\u4ef6\u4e2d\u627e\u5230\u5e26\u6709\u5173\u952e\u8bcd \"lean_shell\" \u7684\u82e5\u5e72\u884c\n$ cat xxx.log | grep \"lean_shell\"\nLet us learn_shell together!\nLearn_shell means learn_shell and learn_shell!\n$ cat xxx.log\nCommand line is powerful!\nLet us learn_shell together!\nHave you ever see this?\nLearn_shell means learn_shell and learn_shell!\n\n# \u53c8\u6216\u8005\u8ba1\u7b97\u5f53\u524d\u76ee\u5f55\u4e0b\u6709\u591a\u5c11\u6587\u4ef6\u5939\u548c\u6587\u4ef6\n$ ls -a | wc -w\n5\n$ ls -a\n.   ..  x   xx  xxx.log\n\n# \u518d\u6bd4\u5982\uff0c\u7edf\u8ba1\u5f53\u524d\u76ee\u5f55\u4e0b\u5404\u4e2a\u6587\u4ef6\u5939\u7684\u5927\u5c0f\uff0c\u5e76\u8f93\u51fa\u4ece\u5927\u5230\u5c0f\u7684 10 \u9879\n$ du | sort -nr | head\n# \u627e\u51fa\u5f53\u524d\u76ee\u5f55\u4e0b\uff08\u9012\u5f52\uff09\u6240\u6709\u53eb\u505a \"xxx\" \u7684\u6587\u4ef6\u5e76\u5220\u9664\n$ find . -name \"xxx\"  | xargs rm -f\n</code></pre>"},{"location":"tech_accu/tool/Shell/#\u7b5b\u9009\u5668","title":"\u7b5b\u9009\u5668","text":"<p>\u53ef\u4ee5\u53d1\u73b0\uff0c\u91cd\u5b9a\u5411\u7684\u529f\u80fd\u975e\u5e38\u5f3a\u5927\u3002\u540c\u65f6\uff0c\u8fd9\u91cc\u4e5f\u6709\u5f88\u591a\u7b5b\u9009\u5668\u4f9b\u4f60\u9009\u62e9\uff0c\u4ed6\u4eec\u7ecf\u5e38\u642d\u914d\u7ba1\u9053\u7b26\u4f7f\u7528\uff0c\u4ee5\u8f85\u52a9\u7ba1\u9053\u7b26\u8fdb\u884c\u4e00\u4e9b\u66f4\u590d\u6742\u7684\u5de5\u4f5c\u3002</p> <p></p> <p>Source: https://linuxcommand.org/lc3_lts0070.php</p>"},{"location":"tech_accu/tool/Shell/#\u811a\u672c-shell","title":"\u811a\u672c Shell","text":"<p>\u7b80\u5355\u6765\u8bf4\uff0cShell \u811a\u672c\u53ef\u4ee5\u770b\u4f5c\u4e00\u6761\u6761 Shell \u6307\u4ee4\u7684\u96c6\u5408\uff0c\u6211\u4eec\u5728\u8fd0\u884c Shell \u811a\u672c\u65f6\uff0cShell \u811a\u672c\u4e2d\u7684\u6307\u4ee4\u6309\u7167\u7279\u5b9a\u987a\u5e8f\u4e00\u884c\u4e00\u884c\u7684\u88ab\u6267\u884c\u4e0b\u6765\u3002</p> <p>Shell \u811a\u672c\u4e00\u822c\u662f\u4ee5 <code>.sh</code> \u4e3a\u540e\u7f00\u7684\u7eaf\u6587\u672c\u6587\u4ef6\uff0c\u800c\u6267\u884c Shell \u811a\u672c\u7684\u65b9\u6cd5\u5927\u81f4\u6709\u4e09\u79cd\uff1a</p> <ul> <li><code>./script.sh</code> \uff08\u9700\u8981\u811a\u672c\u5177\u6709\u53ef\u6267\u884c\u6743\u9650\uff09</li> <li><code>source script.sh</code></li> <li><code>bash script.sh</code> / <code>sh script.sh</code> / ...</li> </ul> <p>\u4ed6\u4eec\u7684\u533a\u522b\u4e3b\u8981\u5982\u4e0b\uff1a</p> <ul> <li>\u4f7f\u7528 <code>bash script.sh</code> / <code>sh script.sh</code> / ... \u7684\u65b9\u5f0f\u6267\u884c\u811a\u672c\uff0c\u4e3b\u8fdb\u7a0b\u4f1a\u4f11\u7720\uff0c\u5e76\u5f00\u59cb\u4e00\u4e2a\u65b0\u8fdb\u7a0b\u6765\u6267\u884c\u811a\u672c\u5185\u5bb9\uff1b</li> <li>\u4f7f\u7528 <code>source script.sh</code> \u7684\u65b9\u5f0f\u6267\u884c\u811a\u672c\uff0c\u811a\u672c\u5185\u5bb9\u4f1a\u5728\u4e3b\u8fdb\u7a0b\u8fdb\u884c\uff0c\u8fd9\u4e5f\u662f\u4e3a\u4ec0\u4e48\u6211\u4eec\u5728\u66f4\u65b0\u5b8c <code>.bashrc</code> \u8fd9\u79cd\u6587\u4ef6\u4ee5\u540e\u4f1a\u4f7f\u7528 <code>source</code> \u6765\u6267\u884c\u5b83\u4ee5\u6c42\u6548\u679c\u9a6c\u4e0a\u88ab\u52a0\u8f7d\u51fa\u6765\uff1b</li> </ul>"},{"location":"tech_accu/tool/Shell/#\u6d41\u7a0b\u63a7\u5236---\u6761\u4ef6\u8bed\u53e5","title":"\u6d41\u7a0b\u63a7\u5236 - \u6761\u4ef6\u8bed\u53e5","text":"<pre><code># \u6761\u4ef6\u5206\u652f\u8bed\u53e5\nif condition1\nthen\ncommands\nelif condition2\nthen\ncommands else\ncommands\nfi\n</code></pre> <pre><code># \u5f53 $var \u4e3a \"A\" \u65f6\u6267\u884c\u7b2c\u4e00\u5757\uff0c\u5f53 $var \u4e3a \"B\" \u65f6\u6267\u884c\u7b2c\u4e8c\u5757\uff0c*) \u5373\u5176\u4ed6\u60c5\u51b5\ncase $var in \"A\")\ncommands\n    ;;\n\"B\")\ncommands\n    ;; *)\ncommands\n    ;;\nesac\n</code></pre>"},{"location":"tech_accu/tool/Shell/#\u6d41\u7a0b\u63a7\u5236---\u5faa\u73af\u8bed\u53e5","title":"\u6d41\u7a0b\u63a7\u5236 - \u5faa\u73af\u8bed\u53e5","text":"<pre><code># \u4f9d\u6b21\u679a\u4e3e\u82e5\u5e72 item\uff0cvar \u8868\u793a\u6b63\u5728\u679a\u4e3e\u7684\u5185\u5bb9\nfor var in item1 item2 ... itemN\ndo\ncommands\ndone\n</code></pre> <pre><code># \u8fd0\u884c\u5230 condition \u4e3a\u5047\u65f6\u7ed3\u675f\nwhile condition\ndo\ncommands\ndone\n</code></pre> <pre><code># \u8fd0\u884c\u5230 condition \u4e3a\u771f\u65f6\u7ed3\u675f\nuntil condition\ndo\ncommands\ndone\n</code></pre>"},{"location":"tech_accu/tool/Shell/#\u6d41\u7a0b\u63a7\u5236---\u51fd\u6570","title":"\u6d41\u7a0b\u63a7\u5236 - \u51fd\u6570","text":"<pre><code># \u5b9a\u4e49\u4e86\u4e00\u4e2a\u53eb\u505a foo \u7684\u51fd\u6570\uff0cfunction \u53ef\u4ee5\u4e0d\u5199\nfunction foo(){\ncommands\n}\n</code></pre>"},{"location":"tech_accu/tool/Shell/#\u53c2\u6570\u4f20\u9012","title":"\u53c2\u6570\u4f20\u9012","text":"<p>\u5bf9\u4e8e\u51fd\u6570\u6216\u547d\u4ee4\u53ef\u4ee5\u7528 <code>$n</code> \u6765\u83b7\u53d6\u7b2c n \u4e2a\u53c2\u6570\u3002\u4f46\u5f53 n \u4e0d\u6b62\u4e00\u4f4d\u6570\u65f6\uff0c\u53ef\u4ee5\u4f7f\u7528 <code>${n}</code> \u7684\u65b9\u5f0f\u6765\u83b7\u53d6\u7b2c n \u4e2a\u53c2\u6570\u3002</p> <ul> <li>\u5047\u8bbe <code>script.sh</code> \u7684\u5185\u5bb9\u5982\u4e0b</li> </ul> <pre><code>#! /bin/bash\necho $1\necho $2\necho $3\necho $4\necho $5\necho $6\necho $7\necho $8\necho $9\necho $10\necho ${10}\n</code></pre> <ul> <li>\u5219\u5982\u4e0b\u8fd0\u884c\u7ed3\u679c\u5982\u4e0b\uff1a</li> </ul> <pre><code>$ ./foo.sh a b c d e f g h i j\na\nb\nc\nd\ne\nf\ng\nh\ni\na0\nj\n</code></pre> <ul> <li>\u5047\u8bbe <code>script.sh</code> \u7684\u5185\u5bb9\u5982\u4e0b</li> </ul> <pre><code>#! /bin/bash\nfunction foo(){\necho $1\necho $2\necho $3\necho $4\necho $5\necho $6\necho $7\necho $8\necho $9\necho $10\necho ${10}\n}\n\nfoo a b c d e f g h i j\n</code></pre> <ul> <li>\u5219\u5982\u4e0b\u8fd0\u884c\u7ed3\u679c\u5982\u4e0b\uff1a</li> </ul> <pre><code>$ ./script.sh\na\nb\nc\nd\ne\nf\ng\nh\ni\na0\nj\n</code></pre>"},{"location":"tech_accu/tool/Shell/#\u5c06\u547d\u4ee4\u7ed3\u679c\u4f5c\u4e3a\u53c2\u6570\u5217\u8868","title":"\u5c06\u547d\u4ee4\u7ed3\u679c\u4f5c\u4e3a\u53c2\u6570\u5217\u8868","text":"<p>\u56de\u5fc6\u5faa\u73af\u8bed\u53e5\u7684\u7ed3\u6784\uff0c\u6211\u4eec\u9700\u8981\u5199\u51fa\u679a\u4e3e\u7684\u6bcf\u4e00\u4e2a\u9879\u76ee\u3002\u663e\u7136\uff0c\u5728\u5927\u91cf\u679a\u4e3e\u76ee\u6807\u7684\u60c5\u51b5\u4e0b\uff0c\u624b\u5199\u51fa\u5168\u90e8\u7684\u679a\u4e3e\u53ef\u80fd\u4e0d\u592a\u73b0\u5b9e\uff0c\u6240\u4ee5\u6211\u4eec\u53ef\u80fd\u4f1a\u60f3\u8981\u4f7f\u7528\u6587\u4ef6\u503c\u6216\u662f\u547d\u4ee4\u7684\u8f93\u51fa\u6765\u5b9e\u73b0\u3002\u8fd9\u4e2a\u65f6\u5019\uff0c\u6211\u4eec\u53ef\u4ee5\u7528 ``` \u628a\u628a\u547d\u4ee4\u7ed9\u62ec\u8d77\u6765\u3002</p> <ul> <li>\u5047\u8bbe <code>file</code> \u7684\u5185\u5bb9\u5982\u4e0b</li> </ul> <pre><code>A\nB\nC\n</code></pre> <ul> <li>\u6267\u884c\u4e0b\u5217\u8bed\u53e5</li> </ul> <pre><code>for var in `cat file`\ndo\necho - var done\n</code></pre> <ul> <li>\u7ed3\u679c\u4e3a</li> </ul> <pre><code>- A\n- B\n- C\n</code></pre>"},{"location":"tech_accu/tool/Shell/#\u6307\u5b9a\u6267\u884c\u811a\u672c\u6240\u4f7f\u7528\u7684-shell","title":"\u6307\u5b9a\u6267\u884c\u811a\u672c\u6240\u4f7f\u7528\u7684 Shell","text":"<p>\u53ef\u4ee5\u53d1\u73b0\uff0c\u5728\u524d\u9762\u7ed9\u51fa\u7684\u82e5\u5e72\u811a\u672c\u6837\u4f8b\u4e2d\uff0c\u6211\u4eec\u7684\u7b2c\u4e00\u884c\u90fd\u6709\u4e00\u884c\u5947\u602a\u7684\u6ce8\u91ca\uff1a</p> <pre><code>#! /bin/bash\n</code></pre> <p>\u8fd9\u53e5\u8bdd\u7684\u610f\u601d\u662f\uff0c\u6307\u5b9a\u8be5\u811a\u672c\u9ed8\u8ba4\u4f7f\u7528 <code>/bin/bash</code> \u6765\u6267\u884c\u3002\u8fd9\u91cc\u9700\u8981\u4f7f\u7528\u7edd\u5bf9\u8def\u5f84\u6765\u7d22\u5f15 Shell \u7684\u53ef\u6267\u884c\u6587\u4ef6\u3002</p>"},{"location":"tech_accu/tool/Shell/#\u4e00\u4e2a\u6a21\u677f","title":"\u4e00\u4e2a\u6a21\u677f","text":"<p>\u8fd9\u91cc\u518d\u8d34\u4e00\u4e2a\u6211\u81ea\u5df1\u5199 Shell \u811a\u672c\u7684\u65f6\u5019\u4f1a\u91c7\u7528\u7684\u6a21\u677f\u3002</p> <pre><code>#! /bin/bash\n\n# get current direction\ncurDir=`pwd`\n# get shell direction\nworkDir=$(cd \"$(dirname \"$0\")\";pwd)\n\ncd $workDir\n\n# Write your script here.\n\ncd $curDir\n</code></pre>"},{"location":"tech_accu/tool/Shell/#\u5176\u4ed6","title":"\u5176\u4ed6","text":"<p>\u547d\u4ee4\u884c\u5e38\u89c1\u5feb\u6377\u952e\uff0cSource: https://lym.readthedocs.io/en/latest/startingcommands.html?highlight=mkdir#moving-around-in-the-command-line</p> <ul> <li>Linux \u547d\u4ee4\u5927\u5168</li> </ul>"},{"location":"tech_accu/tool/Shell/#\u76f8\u5173\u8d44\u6599","title":"\u76f8\u5173\u8d44\u6599","text":"<ul> <li>Shell (computing) - Wikipedia</li> <li>Terminal emulator - Wikipedia</li> <li>Introducing the Shell \u2013 Introduction to the Command Line for Genomics (datacarpentry.org)</li> <li>LinuxCommand.org: Learning the shell.</li> <li>\u8bfe\u7a0b\u6982\u89c8\u4e0e shell \u00b7 the missing semester of your cs education (missing-semester-cn.github.io)</li> <li>man command in Linux with Examples - GeeksforGeeks</li> <li>Shell commands \u2014 Linux command line for you and me 0.1 documentation (lym.readthedocs.io)</li> </ul>"},{"location":"tech_accu/tool/Shell/#\u76f8\u5173\u77e5\u8bc6\u70b9","title":"\u76f8\u5173\u77e5\u8bc6\u70b9","text":"<ul> <li>Linux</li> <li>vi / vim</li> </ul>"}]}
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diff --git a/sitemap.xml.gz b/sitemap.xml.gz
index edc75a12..83e17150 100644
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diff --git a/tech_accu/ai/hydra/index.html b/tech_accu/ai/hydra/index.html
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--- a/tech_accu/ai/hydra/index.html
+++ b/tech_accu/ai/hydra/index.html
@@ -496,13 +496,13 @@
 <ul class="md-nav__list" data-md-scrollfix="">
 <li class="md-nav__item">
 <a class="md-nav__link" href="../../../cour_note/D1QD_CXiaoCheng/">
-        [大一秋冬] C小程 琐碎知识点整理
+        🔮 C小程 琐碎知识点整理
       </a>
 </li>
 <li class="md-nav__item md-nav__item--nested">
 <input class="md-nav__toggle md-toggle" id="__nav_3_3" type="checkbox"/>
 <div class="md-nav__link md-nav__link--index">
-<a href="../../../cour_note/D1CX_ProbabilityAndStatistics/">[大一春夏] 概率论与数理统计</a>
+<a href="../../../cour_note/D1CX_ProbabilityAndStatistics/">🔮 概率论与数理统计</a>
 <label for="__nav_3_3">
 <span class="md-nav__icon md-icon"></span>
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@@ -510,7 +510,7 @@
 <nav aria-expanded="false" aria-labelledby="__nav_3_3_label" class="md-nav" data-md-level="2">
 <label class="md-nav__title" for="__nav_3_3">
 <span class="md-nav__icon md-icon"></span>
-          [大一春夏] 概率论与数理统计
+          🔮 概率论与数理统计
         </label>
 <ul class="md-nav__list" data-md-scrollfix="">
 <li class="md-nav__item">
@@ -558,18 +558,18 @@
 </li>
 <li class="md-nav__item">
 <a class="md-nav__link" href="../../../cour_note/D1SJ_StanfordCS231n/">
-        [大一暑假] Deep Learning for Computer Vision | CS231N
+        🔮 Deep Learning for Computer Vision | CS231N
       </a>
 </li>
 <li class="md-nav__item">
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-<a href="../../cour_note/D3QD_OperatingSystem/">[大三秋冬] 操作系统 | Operating System</a>
+<a href="../../cour_note/D3QD_OperatingSystem/">💎 操作系统 | Operating System</a>
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-          [大三秋冬] 操作系统 | Operating System
+          💎 操作系统 | Operating System
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@@ -911,13 +911,13 @@
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-          [大三秋冬] 计算理论 | Theorem of Computing
+          🔮 计算理论 | Theorem of Computing
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-          [大三秋冬] 计算理论 | Theorem of Computing
+          🔮 计算理论 | Theorem of Computing
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