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<!DOCTYPE html>
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<head>
<title>2020\day13.nim</title>
<link rel="icon" href="data:image/svg+xml,<svg xmlns=%22http://www.w3.org/2000/svg%22 viewBox=%220 0 100 100%22><text y=%22.9em%22 font-size=%2280%22>🐳</text></svg>">
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<div class="nb-box">
<span><a href="..">🏡</a></span>
<span><code>2020\day13.nim</code></span>
<span><a href="https://github.com/pietroppeter/adventofnim"><svg aria-hidden="true" width="1.2em" height="1.2em" style="vertical-align: middle; fill: #fff" preserveAspectRatio="xMidYMid meet" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8 0C3.58 0 0 3.58 0 8c0 3.54 2.29 6.53 5.47 7.59.4.07.55-.17.55-.38 0-.19-.01-.82-.01-1.49-2.01.37-2.53-.49-2.69-.94-.09-.23-.48-.94-.82-1.13-.28-.15-.68-.52-.01-.53.63-.01 1.08.58 1.23.82.72 1.21 1.87.87 2.33.66.07-.52.28-.87.51-1.07-1.78-.2-3.64-.89-3.64-3.95 0-.87.31-1.59.82-2.15-.08-.2-.36-1.02.08-2.12 0 0 .67-.21 2.2.82.64-.18 1.32-.27 2-.27.68 0 1.36.09 2 .27 1.53-1.04 2.2-.82 2.2-.82.44 1.1.16 1.92.08 2.12.51.56.82 1.27.82 2.15 0 3.07-1.87 3.75-3.65 3.95.29.25.54.73.54 1.48 0 1.07-.01 1.93-.01 2.2 0 .21.15.46.55.38A8.013 8.013 0 0016 8c0-4.42-3.58-8-8-8z"></path></svg></a></span>
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</header><main>
<h2>2020, day 13: Shuttle Search 🔍 🚀</h2>
<p>Today was another mathematical day and the main character was the
<a href="https://en.wikipedia.org/wiki/Chinese_remainder_theorem">Chinese Remainder Theorem</a> (CRT from now on).</p>
<p>Even though the day was rather straightforward for everyone which was able to recall that,
I find still very nice the fact that people could (and did) come up with very good solutions
without knowing about CRT. In particular most people who did solved the problem without knowing about CRT
did implement a very nice method to find solutions,
<a href="https://en.wikipedia.org/wiki/Chinese_remainder_theorem#Search_by_sieving">search by sieving</a>.</p>
<p>The CRT did click from me rightaway, so I did decide not to look for existing implementation
and decided to use the coefficient given by Bézout's identity, that can be computed with
<a href="https://en.wikipedia.org/wiki/Extended_Euclidean_algorithm">Extended Euclidean Algorithm</a>.</p>
<p>I also knew beforehand that I might run into overflow issues and I might need to use
<a href="https://github.com/def-/nim-bigints">bigints</a>. I decided to first implement with standard <code>int</code>s and only
later upgrade to bigints if needed.</p>
<p>In the end I found out that the solution was below <code>int.high</code> but my specific methods using Bézout's coefficients
did ran into an overflow, so I just applied a quick patch without changing proc's signature.</p>
<p>In the end I think that the solution with the sieve is the most elegant and practical, since it would not need this.</p>
<pre><code class="nim hljs"><span class="hljs-keyword">import</span>
strutils, sequtils
<span class="hljs-keyword">import</span>
sugar</code></pre>
<p>part 1 was rather straightforward. I solved first for the example then wrapped that in a template
and used it also to solve it for the real input. No reading from file this, just parsing directly in source and also very basic parsing.</p>
<pre><code class="nim hljs"><span class="hljs-keyword">template</span> solve1() =
<span class="hljs-keyword">echo</span> $buses <span class="hljs-comment">## why nimsuggest complains when no $?</span>
<span class="hljs-keyword">var</span> id, wait, minWait: <span class="hljs-built_in">int</span>
minWait = <span class="hljs-built_in">int</span>.<span class="hljs-keyword">high</span>
<span class="hljs-keyword">for</span> bus <span class="hljs-keyword">in</span> buses:
wait = bus - (timestamp <span class="hljs-keyword">mod</span> bus)
<span class="hljs-keyword">echo</span> bus, <span class="hljs-string">": "</span>, wait
<span class="hljs-keyword">if</span> wait < minWait:
minWait = wait
id = bus
<span class="hljs-keyword">echo</span> (id, minWait, id * minWait)
<span class="hljs-keyword">block</span> example:
<span class="hljs-keyword">let</span>
timestamp = <span class="hljs-number">939</span>
buses = <span class="hljs-string">"7,13,x,x,59,x,31,19"</span>.replace(<span class="hljs-string">",x"</span>, <span class="hljs-string">""</span>).split(<span class="hljs-string">","</span>).map(parseInt)
solve1
<span class="hljs-keyword">block</span> part1:
<span class="hljs-keyword">let</span>
timestamp = <span class="hljs-number">1003055</span>
buses = <span class="hljs-string">"37,x,x,x,x,x,x,x,x,x,x,x,x,x,x,x,x,x,x,x,x,x,x,x,x,x,x,41,x,x,x,x,x,x,x,x,x,433,x,x,x,x,x,x,x,23,x,x,x,x,x,x,x,x,17,x,19,x,x,x,x,x,x,x,x,x,29,x,593,x,x,x,x,x,x,x,x,x,x,x,x,13"</span>.replace(
<span class="hljs-string">",x"</span>, <span class="hljs-string">""</span>).split(<span class="hljs-string">","</span>).map(parseInt)
solve1</code></pre>
<pre><samp>@[7, 13, 59, 31, 19]
7: 6
13: 10
59: 5
31: 22
19: 11
(59, 5, 295)
@[37, 41, 433, 23, 17, 19, 29, 593, 13]
37: 15
41: 10
433: 206
23: 21
17: 13
19: 12
29: 26
593: 301
13: 12
(41, 10, 410)</samp></pre>
<p>That's the right answer! You are <em class="star">one gold star</em> closer to saving your vacation.</p>
<h3>Part 2</h3>
<p>As mentioned I need Extended Euclidean Algorithm. I went with a rather straightforward implementation.
I do not think my <code>if</code> and <code>return</code> here do conform to
<a href="https://gist.github.com/disruptek/6d0cd6774d05adaa894db4deb646fc1d#miscellaneous">disruptek's tips and tricks</a>.</p>
<p>I did have some debugging to do, and Wikipedia's worked example was very useful</p>
<pre><code class="nim hljs"><span class="hljs-keyword">type</span>
<span class="hljs-type">Eq</span> = <span class="hljs-keyword">tuple</span>[modulus, remainder: <span class="hljs-built_in">int</span>]
<span class="hljs-keyword">func</span> extEuclid(n1, n2: <span class="hljs-built_in">int</span>): (<span class="hljs-built_in">int</span>, <span class="hljs-built_in">int</span>, <span class="hljs-built_in">int</span>) =
<span class="hljs-keyword">let</span> (a, b) = <span class="hljs-keyword">if</span> n1 > n2:
(n1, n2) <span class="hljs-keyword">else</span>:
(n2, n1)
<span class="hljs-keyword">var</span>
r0 = a
r1 = b
s0 = <span class="hljs-number">1</span>
s1 = <span class="hljs-number">0</span>
t0 = <span class="hljs-number">0</span>
t1 = <span class="hljs-number">1</span>
q1 = r0 <span class="hljs-keyword">div</span> r1
r2 = r0 - q1 * r1
s2 = s0 - q1 * s1
t2 = t0 - q1 * t1
<span class="hljs-keyword">when</span> <span class="hljs-literal">false</span>:
dump (r0, r1, r2)
dump q1
dump (s0, s1, s2)
dump (t0, t1, t2)
<span class="hljs-keyword">while</span> r2 != <span class="hljs-number">0</span>:
<span class="hljs-keyword">when</span> <span class="hljs-literal">false</span>:
debugecho <span class="hljs-string">"iterate:"</span>
r0 = r1
r1 = r2
s0 = s1
s1 = s2
t0 = t1
t1 = t2
q1 = r0 <span class="hljs-keyword">div</span> r1
r2 = r0 - q1 * r1
s2 = s0 - q1 * s1
t2 = t0 - q1 * t1
<span class="hljs-keyword">when</span> <span class="hljs-literal">false</span>:
dump (r0, r1, r2)
dump q1
dump (s0, s1, s2)
dump (t0, t1, t2)
<span class="hljs-keyword">return</span> <span class="hljs-keyword">if</span> n1 > n2:
(r1, s1, t1) <span class="hljs-keyword">else</span>:
(r1, t1, s1)
<span class="hljs-keyword">echo</span> extEuclid(<span class="hljs-number">240</span>, <span class="hljs-number">46</span>) <span class="hljs-comment">## (2, -9, 47)</span></code></pre>
<pre><samp>(2, -9, 47)</samp></pre>
<p>my CRT solution algorithm did ran into overflows and I applied a patch inside using bigints</p>
<pre><code class="nim hljs"><span class="hljs-keyword">import</span>
bigints
<span class="hljs-comment">## why can it have side effects?</span>
<span class="hljs-keyword">proc</span> crt(eqs: <span class="hljs-built_in">seq</span>[<span class="hljs-type">Eq</span>]): <span class="hljs-built_in">int</span> =
<span class="hljs-keyword">if</span> eqs.len == <span class="hljs-number">1</span>:
<span class="hljs-keyword">return</span> eqs[<span class="hljs-number">0</span>].remainder
<span class="hljs-keyword">if</span> eqs.len == <span class="hljs-number">2</span>:
<span class="hljs-keyword">let</span>
(n1, a1) = eqs[<span class="hljs-number">0</span>]
(n2, a2) = eqs[<span class="hljs-number">1</span>]
(gcd, m1, m2) = extEuclid(n1, n2)
<span class="hljs-keyword">if</span> gcd != <span class="hljs-number">1</span>:
<span class="hljs-keyword">echo</span> <span class="hljs-string">"ERROR n1, n2 not coprime: "</span>, (n1, n2, gcd)
<span class="hljs-comment">## gives me overflow here but result is good for int64. let's just patch this part with bigints:</span>
<span class="hljs-keyword">let</span>
ba1 = a1.initBigInt
bm2 = m2.initBigInt
bn2 = n2.initBigInt
ba2 = a2.initBigInt
bm1 = m1.initBigInt
bn1 = n1.initBigInt
bres = (ba1 * bm2 * bn2 + ba2 * bm1 * bn1) <span class="hljs-keyword">mod</span> (bn1 * bn2)
<span class="hljs-literal">result</span> = parseInt($bres)
<span class="hljs-keyword">return</span> <span class="hljs-literal">result</span>
<span class="hljs-keyword">let</span>
a12 = crt(eqs[<span class="hljs-number">0</span> .. <span class="hljs-number">1</span>])
n12 = eqs[<span class="hljs-number">0</span>].modulus * eqs[<span class="hljs-number">1</span>].modulus
<span class="hljs-keyword">var</span> eqs = @[(n12, a12)] & eqs[<span class="hljs-number">2</span> .. eqs.<span class="hljs-keyword">high</span>]
<span class="hljs-keyword">return</span> crt(eqs)
dump crt(@[(<span class="hljs-number">3</span>, <span class="hljs-number">2</span>), (<span class="hljs-number">5</span>, <span class="hljs-number">3</span>), (<span class="hljs-number">7</span>, <span class="hljs-number">2</span>)]) <span class="hljs-comment">## from sun-tzu: 23</span>
dump crt(@[(<span class="hljs-number">3</span>, <span class="hljs-number">0</span>), (<span class="hljs-number">4</span>, <span class="hljs-number">3</span>), (<span class="hljs-number">5</span>, <span class="hljs-number">4</span>)]) <span class="hljs-comment">## wiki: 39</span></code></pre>
<pre><samp>crt(@[(3, 2), (5, 3), (7, 2)]) = 23
crt(@[(3, 0), (4, 3), (5, 4)]) = 39</samp></pre>
<p>Once I got both implementations right I applied to the example
(first manually parsed than I wrote the parse which also preprocesses stuff).
Of course here the good strategy is, while parsing, to keep track of position and add remainder to my data.</p>
<pre><code class="nim hljs"><span class="hljs-keyword">let</span>
<span class="hljs-comment">## buses = "7,13,x,x,59,x,31,19"</span>
example2 = @[(<span class="hljs-number">7</span>, <span class="hljs-number">0</span>), (<span class="hljs-number">13</span>, <span class="hljs-number">13</span> - <span class="hljs-number">1</span>), (<span class="hljs-number">59</span>, <span class="hljs-number">59</span> - <span class="hljs-number">4</span>), (<span class="hljs-number">31</span>, <span class="hljs-number">31</span> - <span class="hljs-number">6</span>), (<span class="hljs-number">19</span>, <span class="hljs-number">19</span> - <span class="hljs-number">7</span>)]
<span class="hljs-keyword">echo</span> crt(example2)
<span class="hljs-keyword">proc</span> parse(text: <span class="hljs-built_in">string</span>): <span class="hljs-built_in">seq</span>[<span class="hljs-type">Eq</span>] =
<span class="hljs-keyword">var</span> i = <span class="hljs-number">0</span>
<span class="hljs-keyword">for</span> n <span class="hljs-keyword">in</span> text.split(<span class="hljs-string">","</span>):
<span class="hljs-keyword">if</span> n != <span class="hljs-string">"x"</span>:
<span class="hljs-literal">result</span>.add (parseInt(n), i)
inc i
<span class="hljs-keyword">for</span> i <span class="hljs-keyword">in</span> <span class="hljs-number">1</span> .. <span class="hljs-literal">result</span>.<span class="hljs-keyword">high</span>:
<span class="hljs-literal">result</span>[i][<span class="hljs-number">1</span>] = <span class="hljs-literal">result</span>[i][<span class="hljs-number">0</span>] - <span class="hljs-literal">result</span>[i][<span class="hljs-number">1</span>]
<span class="hljs-keyword">echo</span> parse <span class="hljs-string">"7,13,x,x,59,x,31,19"</span></code></pre>
<pre><samp>1068781
@[(modulus: 7, remainder: 0), (modulus: 13, remainder: 12), (modulus: 59, remainder: 55), (modulus: 31, remainder: 25), (modulus: 19, remainder: 12)]</samp></pre>
<p>to make sure at least the solution was below int.high I did print my expected upper bound. Ah, I did assume all modulus were coprime and I actually suspect they are all prime but did not check</p>
<pre><code class="nim hljs"><span class="hljs-keyword">let</span> part2input = parse <span class="hljs-string">"37,x,x,x,x,x,x,x,x,x,x,x,x,x,x,x,x,x,x,x,x,x,x,x,x,x,x,41,x,x,x,x,x,x,x,x,x,433,x,x,x,x,x,x,x,23,x,x,x,x,x,x,x,x,17,x,19,x,x,x,x,x,x,x,x,x,29,x,593,x,x,x,x,x,x,x,x,x,x,x,x,13"</span>
<span class="hljs-keyword">echo</span> part2input
<span class="hljs-keyword">var</span> n = <span class="hljs-number">1</span>
<span class="hljs-keyword">for</span> eq <span class="hljs-keyword">in</span> part2input:
n *= eq.modulus
<span class="hljs-keyword">echo</span> n
<span class="hljs-keyword">echo</span> <span class="hljs-built_in">int</span>.<span class="hljs-keyword">high</span>
<span class="hljs-keyword">echo</span> <span class="hljs-string">"part2: "</span>, crt(part2input)</code></pre>
<pre><samp>@[(modulus: 37, remainder: 0), (modulus: 41, remainder: 14), (modulus: 433, remainder: 396), (modulus: 23, remainder: -22), (modulus: 17, remainder: -37), (modulus: 19, remainder: -37), (modulus: 29, remainder: -37), (modulus: 593, remainder: 525), (modulus: 13, remainder: -68)]
37
1517
656861
15107803
256832651
4879820369
141514790701
83918270885693
1090937521514009
9223372036854775807
part2: 600691418730595</samp></pre>
<p>That's the right answer! You are <em class="star">one gold star</em> closer to saving your vacation.</p>
</main>
<footer>
<hr>
<div class="nb-box">
<span><span class="nb-small">made with <a href="https://pietroppeter.github.io/nimib/">nimib 🐳</a></span></span>
<span></span>
<span><button class="nb-small" id="show" onclick="toggleSourceDisplay()">Show Source</button></span>
</div>
</footer>
<section id="source">
<pre><code class="nim hljs"><span class="hljs-keyword">import</span> nimib, animu, nimoji
nbInit
nbText: <span class="hljs-string">"""## 2020, day 13: Shuttle Search :mag: :rocket:
Today was another mathematical day and the main character was the
[Chinese Remainder Theorem](https://en.wikipedia.org/wiki/Chinese_remainder_theorem) (CRT from now on).
Even though the day was rather straightforward for everyone which was able to recall that,
I find still very nice the fact that people could (and did) come up with very good solutions
without knowing about CRT. In particular most people who did solved the problem without knowing about CRT
did implement a very nice method to find solutions,
[search by sieving](https://en.wikipedia.org/wiki/Chinese_remainder_theorem#Search_by_sieving).
The CRT did click from me rightaway, so I did decide not to look for existing implementation
and decided to use the coefficient given by Bézout's identity, that can be computed with
[Extended Euclidean Algorithm](https://en.wikipedia.org/wiki/Extended_Euclidean_algorithm).
I also knew beforehand that I might run into overflow issues and I might need to use
[bigints](https://github.com/def-/nim-bigints). I decided to first implement with standard `int`s and only
later upgrade to bigints if needed.
In the end I found out that the solution was below `int.high` but my specific methods using Bézout's coefficients
did ran into an overflow, so I just applied a quick patch without changing proc's signature.
In the end I think that the solution with the sieve is the most elegant and practical, since it would not need this.
"""</span>.emojize
nbCode:
<span class="hljs-keyword">import</span> strutils, sequtils
<span class="hljs-keyword">import</span> sugar
nbText: <span class="hljs-string">"""part 1 was rather straightforward. I solved first for the example then wrapped that in a template
and used it also to solve it for the real input. No reading from file this, just parsing directly in source and also very basic parsing."""</span>
nbCode:
<span class="hljs-keyword">template</span> solve1 =
<span class="hljs-keyword">echo</span> $buses <span class="hljs-comment">## why nimsuggest complains when no $?</span>
<span class="hljs-keyword">var</span>
id, wait, minWait: <span class="hljs-built_in">int</span>
minWait = <span class="hljs-built_in">int</span>.<span class="hljs-keyword">high</span>
<span class="hljs-keyword">for</span> bus <span class="hljs-keyword">in</span> buses:
wait = bus - (timestamp <span class="hljs-keyword">mod</span> bus)
<span class="hljs-keyword">echo</span> bus, <span class="hljs-string">": "</span>, wait
<span class="hljs-keyword">if</span> wait < minWait:
minWait = wait
id = bus
<span class="hljs-keyword">echo</span> (id, minWait, id*minWait)
<span class="hljs-keyword">block</span> example:
<span class="hljs-keyword">let</span>
timestamp = <span class="hljs-number">939</span>
buses = <span class="hljs-string">"7,13,x,x,59,x,31,19"</span>.replace(<span class="hljs-string">",x"</span>, <span class="hljs-string">""</span>).split(<span class="hljs-string">","</span>).map(parseInt)
solve1
<span class="hljs-keyword">block</span> part1:
<span class="hljs-keyword">let</span>
timestamp = <span class="hljs-number">1003055</span>
buses = <span class="hljs-string">"37,x,x,x,x,x,x,x,x,x,x,x,x,x,x,x,x,x,x,x,x,x,x,x,x,x,x,41,x,x,x,x,x,x,x,x,x,433,x,x,x,x,x,x,x,23,x,x,x,x,x,x,x,x,17,x,19,x,x,x,x,x,x,x,x,x,29,x,593,x,x,x,x,x,x,x,x,x,x,x,x,13"</span>.replace(<span class="hljs-string">",x"</span>, <span class="hljs-string">""</span>).split(<span class="hljs-string">","</span>).map(parseInt)
solve1
gotTheStar
nbText: <span class="hljs-string">"""### Part 2
As mentioned I need Extended Euclidean Algorithm. I went with a rather straightforward implementation.
I do not think my `if` and `return` here do conform to
[disruptek's tips and tricks](https://gist.github.com/disruptek/6d0cd6774d05adaa894db4deb646fc1d#miscellaneous).
I did have some debugging to do, and Wikipedia's worked example was very useful
"""</span>
nbCode:
<span class="hljs-keyword">type</span> <span class="hljs-type">Eq</span> = <span class="hljs-keyword">tuple</span>[modulus, remainder: <span class="hljs-built_in">int</span>]
<span class="hljs-keyword">func</span> extEuclid(n1, n2: <span class="hljs-built_in">int</span>): (<span class="hljs-built_in">int</span>, <span class="hljs-built_in">int</span>, <span class="hljs-built_in">int</span>) =
<span class="hljs-keyword">let</span> (a,b) = <span class="hljs-keyword">if</span> n1 > n2:
(n1, n2)
<span class="hljs-keyword">else</span>:
(n2, n1)
<span class="hljs-keyword">var</span>
<span class="hljs-comment"># intialize</span>
r0 = a
r1 = b
s0 = <span class="hljs-number">1</span>
s1 = <span class="hljs-number">0</span>
t0 = <span class="hljs-number">0</span>
t1 = <span class="hljs-number">1</span>
<span class="hljs-comment"># iterate</span>
q1 = r0 <span class="hljs-keyword">div</span> r1
r2 = r0 - q1*r1 <span class="hljs-comment"># = r0 mod r1</span>
s2 = s0 - q1*s1
t2 = t0 - q1*t1
<span class="hljs-keyword">when</span> <span class="hljs-literal">false</span>:
dump (r0, r1, r2)
dump q1
dump (s0, s1, s2)
dump (t0, t1, t2)
<span class="hljs-keyword">while</span> r2 != <span class="hljs-number">0</span>:
<span class="hljs-keyword">when</span> <span class="hljs-literal">false</span>: debugecho <span class="hljs-string">"iterate:"</span>
<span class="hljs-comment"># shift</span>
r0 = r1
r1 = r2
s0 = s1
s1 = s2
t0 = t1
t1 = t2
<span class="hljs-comment"># iterate</span>
q1 = r0 <span class="hljs-keyword">div</span> r1
r2 = r0 - q1*r1 <span class="hljs-comment"># = r0 mod r1</span>
s2 = s0 - q1*s1
t2 = t0 - q1*t1
<span class="hljs-keyword">when</span> <span class="hljs-literal">false</span>:
dump (r0, r1, r2)
dump q1
dump (s0, s1, s2)
dump (t0, t1, t2)
<span class="hljs-keyword">return</span> <span class="hljs-keyword">if</span> n1 > n2:
(r1, s1, t1)
<span class="hljs-keyword">else</span>:
(r1, t1, s1)
<span class="hljs-keyword">echo</span> extEuclid(<span class="hljs-number">240</span>, <span class="hljs-number">46</span>) <span class="hljs-comment">## (2, -9, 47)</span>
nbText: <span class="hljs-string">"my CRT solution algorithm did ran into overflows and I applied a patch inside using bigints"</span>
nbCode:
<span class="hljs-keyword">import</span> bigints
<span class="hljs-comment">## why can it have side effects?</span>
<span class="hljs-keyword">proc</span> crt(eqs: <span class="hljs-built_in">seq</span>[<span class="hljs-type">Eq</span>]): <span class="hljs-built_in">int</span> =
<span class="hljs-keyword">if</span> eqs.len == <span class="hljs-number">1</span>:
<span class="hljs-keyword">return</span> eqs[<span class="hljs-number">0</span>].remainder
<span class="hljs-keyword">if</span> eqs.len == <span class="hljs-number">2</span>:
<span class="hljs-comment">#dump eqs</span>
<span class="hljs-keyword">let</span>
(n1, a1) = eqs[<span class="hljs-number">0</span>]
(n2, a2) = eqs[<span class="hljs-number">1</span>]
(gcd, m1, m2) = extEuclid(n1, n2)
<span class="hljs-keyword">if</span> gcd != <span class="hljs-number">1</span>:
<span class="hljs-keyword">echo</span> <span class="hljs-string">"ERROR n1, n2 not coprime: "</span>, (n1, n2, gcd)
<span class="hljs-comment">## gives me overflow here but result is good for int64. let's just patch this part with bigints:</span>
<span class="hljs-keyword">let</span>
ba1 = a1.initBigInt
bm2 = m2.initBigInt
bn2 = n2.initBigInt
ba2 = a2.initBigInt
bm1 = m1.initBigInt
bn1 = n1.initBigInt
bres = (ba1*bm2*bn2 + ba2*bm1*bn1) <span class="hljs-keyword">mod</span> (bn1*bn2)
<span class="hljs-literal">result</span> = parseInt($bres)
<span class="hljs-keyword">return</span> <span class="hljs-literal">result</span>
<span class="hljs-keyword">let</span>
a12 = crt(eqs[<span class="hljs-number">0.</span>.<span class="hljs-number">1</span>])
n12 = eqs[<span class="hljs-number">0</span>].modulus*eqs[<span class="hljs-number">1</span>].modulus
<span class="hljs-comment">#dump (n12, a12)</span>
<span class="hljs-keyword">var</span> eqs = @[(n12, a12)] & eqs[<span class="hljs-number">2</span> .. eqs.<span class="hljs-keyword">high</span>]
<span class="hljs-keyword">return</span> crt(eqs)
dump crt(@[(<span class="hljs-number">3</span>, <span class="hljs-number">2</span>), (<span class="hljs-number">5</span>, <span class="hljs-number">3</span>), (<span class="hljs-number">7</span>, <span class="hljs-number">2</span>)]) <span class="hljs-comment">## from sun-tzu: 23</span>
dump crt(@[(<span class="hljs-number">3</span>, <span class="hljs-number">0</span>), (<span class="hljs-number">4</span>, <span class="hljs-number">3</span>), (<span class="hljs-number">5</span>, <span class="hljs-number">4</span>)]) <span class="hljs-comment">## wiki: 39</span>
nbText: <span class="hljs-string">"""Once I got both implementations right I applied to the example
(first manually parsed than I wrote the parse which also preprocesses stuff).
Of course here the good strategy is, while parsing, to keep track of position and add remainder to my data.
"""</span>
nbCode:
<span class="hljs-keyword">let</span>
<span class="hljs-comment">## buses = "7,13,x,x,59,x,31,19"</span>
example2 = @[(<span class="hljs-number">7</span>, <span class="hljs-number">0</span>),(<span class="hljs-number">13</span>, <span class="hljs-number">13</span> - <span class="hljs-number">1</span>),(<span class="hljs-number">59</span>, <span class="hljs-number">59</span> - <span class="hljs-number">4</span>),(<span class="hljs-number">31</span>, <span class="hljs-number">31</span> - <span class="hljs-number">6</span>),(<span class="hljs-number">19</span>, <span class="hljs-number">19</span> - <span class="hljs-number">7</span>)]
<span class="hljs-keyword">echo</span> crt(example2) <span class="hljs-comment"># 1068781</span>
<span class="hljs-keyword">proc</span> parse(text: <span class="hljs-built_in">string</span>): <span class="hljs-built_in">seq</span>[<span class="hljs-type">Eq</span>] =
<span class="hljs-keyword">var</span> i = <span class="hljs-number">0</span>
<span class="hljs-keyword">for</span> n <span class="hljs-keyword">in</span> text.split(<span class="hljs-string">","</span>):
<span class="hljs-keyword">if</span> n != <span class="hljs-string">"x"</span>:
<span class="hljs-literal">result</span>.add (parseInt(n), i)
inc i
<span class="hljs-keyword">for</span> i <span class="hljs-keyword">in</span> <span class="hljs-number">1.</span>.<span class="hljs-literal">result</span>.<span class="hljs-keyword">high</span>:
<span class="hljs-literal">result</span>[i][<span class="hljs-number">1</span>] = <span class="hljs-literal">result</span>[i][<span class="hljs-number">0</span>] - <span class="hljs-literal">result</span>[i][<span class="hljs-number">1</span>]
<span class="hljs-keyword">echo</span> parse <span class="hljs-string">"7,13,x,x,59,x,31,19"</span>
nbText: <span class="hljs-string">"to make sure at least the solution was below int.high I did print my expected upper bound. Ah, I did assume all modulus were coprime and I actually suspect they are all prime but did not check"</span>
nbCode:
<span class="hljs-keyword">let</span> part2input = parse <span class="hljs-string">"37,x,x,x,x,x,x,x,x,x,x,x,x,x,x,x,x,x,x,x,x,x,x,x,x,x,x,41,x,x,x,x,x,x,x,x,x,433,x,x,x,x,x,x,x,23,x,x,x,x,x,x,x,x,17,x,19,x,x,x,x,x,x,x,x,x,29,x,593,x,x,x,x,x,x,x,x,x,x,x,x,13"</span>
<span class="hljs-keyword">echo</span> part2input
<span class="hljs-keyword">var</span> n = <span class="hljs-number">1</span>
<span class="hljs-keyword">for</span> eq <span class="hljs-keyword">in</span> part2input:
n *= eq.modulus
<span class="hljs-keyword">echo</span> n
<span class="hljs-keyword">echo</span> <span class="hljs-built_in">int</span>.<span class="hljs-keyword">high</span>
<span class="hljs-keyword">echo</span> <span class="hljs-string">"part2: "</span>, crt(part2input)
gotTheStar
nbSave</code></pre>
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