update: 240320 ver2

docs/Computer Science/Algorithm/03 Trees.md

@@ -2,31 +2,31 @@
 
 ## 3.0 Concepts and Terminology
 
-**degree of a node**: the number of subtrees of the node.
+**Degree of a node**: the number of subtrees of the node.
 
-**degree of a tree**: the maximum degree of all nodes.
+**Degree of a tree**: the maximum degree of all nodes.
 
-**parent**: a node that has subtrees.
+**Parent**: a node that has subtrees.
 
-**children**: the roots of the subtrees of a parent.
+**Children**: the roots of the subtrees of a parent.
 
-**silblings**: the children of the same parent.
+**Silblings**: the children of the same parent.
 
-**leaf/terminal node**: a node that has no children.
+**Leaf/terminal node**: a node that has no children.
 
-**path from node A to node B**: a (unique) sequence of nodes starting from A and ending at B, such that each node is a child of the previous one.
+**Path from node A to node B**: a (unique) sequence of nodes starting from A and ending at B, such that each node is a child of the previous one.
 
-**length of path**: the number of edges on the path.
+**Length of path**: the number of edges on the path.
 
-**depth of a node**: the length of the unique path from the root to the node.
+**Depth of a node**: the length of the unique path from the root to the node.
 
-**height of a node**: the length of the **longest** path from the node to a leaf.
+**Height of a node**: the length of the **longest** path from the node to a leaf.
 
-**height of a tree**: the height of the root.
+**Height of a tree**: the height of the root.
 
-**ancestors of a node**: all nodes on the path from the node up to the root.
+**Ancestors of a node**: all nodes on the path from the node up to the root.
 
-**descendants of a node**: all nodes in its subtrees.
+**Descendants of a node**: all nodes in its subtrees.
 
 ## 3.1 Binary Trees
 
@@ -45,3 +45,71 @@ typedef struct TreeNode {
 
 ### 3.1.2 Basic Operations
 
+!!! info
+    这种版本的节点的定义包括了节点的高度，但是在一般的树中，这是没有必要的，只是在AVL树中，节点高度才尤其重要.在下面的操作中就干脆省略了.
+
+=== "Constructor"
+    ```C
+    TreeNode *newTreeNode(int val) {
+        TreeNode *node;
+        node = malloc(sizeof(TreeNode));
+        node->val = val;
+        node->left = NULL;
+        node->right = NULL;   
+        return node;
+    }
+    ```
+
+=== "Insertion and Deletion"
+    这是在`n1->n2`中插入新节点`p`或者删除这个节点的操作.
+    ```C
+    TreeNode *p = newTreeNode(1);
+    p->left = n2;
+    n1->left = n1;
+
+    TreeNode *del = p;
+    n1->left = n2;
+    free(del);
+    ```
+
+### 3.1.3 Traversals
+
+=== "Level Order"
+
+    层序遍历从顶部到底**逐层**遍历二叉树，并且按照从左到右的顺序遍历每一层的节点，从本质上来讲，层序遍历其实属于**广度优先遍历/Breadth-first Traversal**.我们一般借助**队列**来实现层序遍历.
+
+    层序遍历的时间复杂度是$O(n)$，空间复杂度是$O(n)$.
+
+    ```C
+    int *levelOrder (TreeNode *root, int *size) {
+        int front, rear;
+        int index, *arr;
+        TreeNode *node;
+        TreeNode **queue = malloc(sizeof(TreeNode *) * MAX_SIZE);
+        front = rear = 0;
+        
+        queue[rear++] = root;
+        int *arr = malloc(sizeof(int) * MAX_SIZE);
+        while (front < rear) {
+            node = queue[front++];
+            arr[index++] = node->val;
+            if (node->left != NULL){
+                queue[rear++] = node->left;
+            }
+            if (node->right != NULL){
+                queue[rear++] = node-right;
+            }
+        }
+        *size = index;
+        arr - realloc(arr, sizeof(int) * index);
+        free(queue);
+        return arr;
+    }
+
+    ```
+
+=== "Preorder"
+    ```C
+    void preOrder(TreeNode *root, int *size){
+
+    }