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模板.html
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<!DOCTYPE html><html><head>
<title>模板</title>
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<link rel="stylesheet" href="file:///c:\Users\shixi\.vscode\extensions\shd101wyy.markdown-preview-enhanced-0.5.2\node_modules\@shd101wyy\mume\dependencies\katex\katex.min.css">
<style>
/**
* prism.js Github theme based on GitHub's theme.
* @author Sam Clarke
*/
code[class*="language-"],
pre[class*="language-"] {
color: #333;
background: none;
font-family: Consolas, "Liberation Mono", Menlo, Courier, monospace;
text-align: left;
white-space: pre;
word-spacing: normal;
word-break: normal;
word-wrap: normal;
line-height: 1.4;
-moz-tab-size: 8;
-o-tab-size: 8;
tab-size: 8;
-webkit-hyphens: none;
-moz-hyphens: none;
-ms-hyphens: none;
hyphens: none;
}
/* Code blocks */
pre[class*="language-"] {
padding: .8em;
overflow: auto;
/* border: 1px solid #ddd; */
border-radius: 3px;
/* background: #fff; */
background: #f5f5f5;
}
/* Inline code */
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padding: .1em;
border-radius: .3em;
white-space: normal;
background: #f5f5f5;
}
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color: #333;
}
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color: #a71d5d;
}
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color: #183691;
}
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color: #63a35c;
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color: #795da3;
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color: #55a532;
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/* JSON */
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color: #183691;
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color: #333;
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/* CSS */
code.language-css,
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color: #0086b3;
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/* YAML */
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code.language-yaml {
color: #183691;
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/* Ruby */
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color: #795da3;
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color: #0086b3;
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color: #0086b3;
}
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position: relative;
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pre[data-line] .line-highlight-wrapper {
position: absolute;
top: 0;
left: 0;
background-color: transparent;
display: block;
width: 100%;
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pre[data-line] .line-highlight {
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left: 0;
right: 0;
padding: inherit 0;
margin-top: 1em;
background: hsla(24, 20%, 50%,.08);
background: linear-gradient(to right, hsla(24, 20%, 50%,.1) 70%, hsla(24, 20%, 50%,0));
pointer-events: none;
line-height: inherit;
white-space: pre;
}
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pre[data-line] .line-highlight[data-end]:after {
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color: hsl(24, 20%, 95%);
font: bold 65%/1.5 sans-serif;
text-align: center;
vertical-align: .3em;
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box-shadow: 0 1px white;
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pre[data-line] .line-highlight[data-end]:after {
content: attr(data-end);
top: auto;
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/* Please visit the URL below for more information: */
/* https://shd101wyy.github.io/markdown-preview-enhanced/#/customize-css */
</style>
</head>
<body for="html-export">
<div class="mume markdown-preview ">
<h1 class="mume-header" id="hatching_chick-frog-chicken-%E5%8F%BD%E5%8F%BD%E5%96%B3%E5%96%B3%E5%8A%A8%E7%89%A9%E5%9B%AD%E6%A8%A1%E6%9D%BF">🐣 🐸 🐔 叽叽喳喳动物园模板</h1>
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<li><a href="#hatching_chick-frog-chicken-%E5%8F%BD%E5%8F%BD%E5%96%B3%E5%96%B3%E5%8A%A8%E7%89%A9%E5%9B%AD%E6%A8%A1%E6%9D%BF">🐣 🐸 🐔 叽叽喳喳动物园模板</a>
<ul>
<li><a href="#%E7%AE%97%E6%B3%95-%E6%95%B0%E6%8D%AE%E7%BB%93%E6%9E%84">算法 & 数据结构</a>
<ul>
<li><a href="#%E6%9C%80%E5%A4%A7%E4%B8%8A%E5%8D%87%E5%AD%90%E5%88%97">最大上升子列</a>
<ul>
<li><a href="#frog-%E6%9C%80%E5%A4%A7%E4%B8%8A%E5%8D%87%E5%AD%90%E5%88%97-%E6%A8%A1%E6%9D%BF">🐸 最大上升子列 模板</a></li>
<li><a href="#earth_asia-%E6%9C%80%E5%A4%A7%E4%B8%8A%E5%8D%87%E5%AD%90%E5%88%97-%E6%A8%A1%E6%9D%BF">🌏 最大上升子列 模板</a></li>
</ul>
</li>
<li><a href="#%E4%BA%8C%E5%88%86%E6%90%9C%E7%B4%A2">二分搜索</a>
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<li><a href="#frog-%E4%BA%8C%E5%88%86%E6%90%9C%E7%B4%A2-%E6%A8%A1%E6%9D%BF">🐸 二分搜索 模板</a></li>
</ul>
</li>
<li><a href="#%E6%9C%80%E5%A4%A7%E5%85%AC%E7%BA%A6%E6%95%B0">最大公约数</a>
<ul>
<li><a href="#frog-%E8%BE%97%E8%BD%AC%E7%9B%B8%E9%99%A4%E6%B3%95-%E6%A8%A1%E6%9D%BF">🐸 辗转相除法 模板</a></li>
</ul>
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<li><a href="#%E5%BF%AB%E9%80%9F%E5%B9%82">快速幂</a>
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<li><a href="#frog-%E5%BF%AB%E9%80%9F%E5%B9%82-%E6%A8%A1%E6%9D%BF">🐸 快速幂 模板</a></li>
</ul>
</li>
<li><a href="#%E9%80%86%E5%BA%8F%E5%AF%B9">逆序对</a>
<ul>
<li><a href="#frog-%E6%B1%82%E9%80%86%E5%BA%8F%E5%AF%B9%E6%95%B0-%E6%A8%A1%E6%9D%BF">🐸 求逆序对数 模板</a></li>
</ul>
</li>
<li><a href="#%E8%83%8C%E5%8C%85">背包</a>
<ul>
<li><a href="#hatching_chick-01%E8%83%8C%E5%8C%85%E4%BA%8C%E7%BB%B4%E6%95%B0%E7%BB%84-%E6%A8%A1%E6%9D%BF">🐣 01背包二维数组 模板</a></li>
<li><a href="#frog-01%E8%83%8C%E5%8C%85%E4%BA%8C%E7%BB%B4%E6%95%B0%E7%BB%84-%E6%A8%A1%E6%9D%BF">🐸 01背包二维数组 模板</a></li>
<li><a href="#hatching_chick-01%E8%83%8C%E5%8C%85%E6%BB%9A%E5%8A%A8%E6%95%B0%E7%BB%84-%E6%A8%A1%E6%9D%BF">🐣 01背包滚动数组 模板</a></li>
<li><a href="#frog-01%E8%83%8C%E5%8C%85%E6%BB%9A%E5%8A%A8%E6%95%B0%E7%BB%84-%E6%A8%A1%E6%9D%BF">🐸 01背包滚动数组 模板</a></li>
<li><a href="#frog-%E5%AE%8C%E5%85%A8%E8%83%8C%E5%8C%85%E6%BB%9A%E5%8A%A8%E6%95%B0%E7%BB%84-%E6%A8%A1%E6%9D%BF">🐸 完全背包滚动数组 模板</a></li>
</ul>
</li>
<li><a href="#%E4%BA%8C%E5%8F%89%E6%A0%91">二叉树</a>
<ul>
<li><a href="#frog-%E5%89%8D%E5%BA%8F%E4%B8%AD%E5%BA%8F%E6%B1%82%E5%90%8E%E5%BA%8F-%E6%A8%A1%E6%9D%BF">🐸 前序中序求后序 模板</a></li>
</ul>
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<li><a href="#%E5%A4%A7%E6%95%B0%E8%AE%A1%E7%AE%97">大数计算</a>
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<li><a href="#earth_asia-%E5%A4%A7%E6%95%B0%E5%8A%A0%E6%B3%95-%E6%A8%A1%E6%9D%BF">🌏 大数加法 模板</a></li>
<li><a href="#earth_asia-%E5%A4%A7%E6%95%B0%E5%87%8F%E6%B3%95-%E6%A8%A1%E6%9D%BF">🌏 大数减法 模板</a></li>
<li><a href="#earth_asia-%E5%A4%A7%E6%95%B0%E4%B9%98%E6%B3%95-%E6%A8%A1%E6%9D%BF">🌏 大数乘法 模板</a></li>
<li><a href="#earth_asia-%E5%A4%A7%E6%95%B0%E9%99%A4%E6%B3%95-%E6%A8%A1%E6%9D%BF">🌏 大数除法 模板</a></li>
</ul>
</li>
<li><a href="#%E5%88%A4%E6%96%AD%E7%B4%A0%E6%95%B0">判断素数</a>
<ul>
<li><a href="#earth_asia-%E5%88%A4%E6%96%AD%E7%B4%A0%E6%95%B0-%E6%A8%A1%E6%9D%BF">🌏 判断素数 模板</a></li>
</ul>
</li>
<li><a href="#kmp">KMP</a>
<ul>
<li><a href="#frog-kmp-%E6%A8%A1%E6%9D%BF">🐸 KMP 模板</a></li>
</ul>
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<li><a href="#%E5%B9%B6%E6%9F%A5%E9%9B%86">并查集</a>
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<li><a href="#frog-%E5%B9%B6%E6%9F%A5%E9%9B%86-%E6%A8%A1%E6%9D%BF">🐸 并查集 模板</a></li>
<li><a href="#chicken-%E5%B9%B6%E6%9F%A5%E9%9B%86-%E6%A8%A1%E6%9D%BF">🐔 并查集 模板</a></li>
<li><a href="#earth_asia-%E5%B9%B6%E6%9F%A5%E9%9B%86-%E6%A8%A1%E6%9D%BF">🌏 并查集 模板</a></li>
</ul>
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<li><a href="#dfs">DFS</a>
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<li><a href="#earth_asia-dfs-%E6%A8%A1%E6%9D%BF">🌏 DFS 模板</a></li>
</ul>
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<li><a href="#bfs">BFS</a>
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<li><a href="#frog-bfs-%E6%A8%A1%E6%9D%BF">🐸 BFS 模板</a></li>
</ul>
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</ul>
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<li><a href="#stl">STL</a>
<ul>
<li><a href="#algorithm">algorithm</a>
<ul>
<li><a href="#merge">merge()</a></li>
<li><a href="#next_permutation">next_permutation()</a></li>
<li><a href="#sort">sort()</a></li>
</ul>
</li>
<li><a href="#queue">queue</a>
<ul>
<li><a href="#priority_queue">priority_queue()</a></li>
</ul>
</li>
</ul>
</li>
</ul>
</li>
</ul>
<hr>
<h2 class="mume-header" id="%E7%AE%97%E6%B3%95-%E6%95%B0%E6%8D%AE%E7%BB%93%E6%9E%84">算法 & 数据结构</h2>
<h3 class="mume-header" id="%E6%9C%80%E5%A4%A7%E4%B8%8A%E5%8D%87%E5%AD%90%E5%88%97">最大上升子列</h3>
<h4 class="mume-header" id="frog-%E6%9C%80%E5%A4%A7%E4%B8%8A%E5%8D%87%E5%AD%90%E5%88%97-%E6%A8%A1%E6%9D%BF">🐸 最大上升子列 模板</h4>
<pre data-role="codeBlock" data-info="cpp" class="language-cpp"><span class="token macro property">#<span class="token directive keyword">include</span> <span class="token string"><iostream></span></span>
<span class="token macro property">#<span class="token directive keyword">include</span> <span class="token string"><algorithm></span></span>
<span class="token keyword">using</span> <span class="token keyword">namespace</span> std<span class="token punctuation">;</span>
<span class="token keyword">int</span> upp<span class="token punctuation">[</span><span class="token number">109</span><span class="token punctuation">]</span> <span class="token operator">=</span> <span class="token punctuation">{</span><span class="token number">0</span><span class="token punctuation">}</span><span class="token punctuation">;</span>
<span class="token keyword">int</span> num<span class="token punctuation">[</span><span class="token number">109</span><span class="token punctuation">]</span> <span class="token operator">=</span> <span class="token punctuation">{</span><span class="token number">0</span><span class="token punctuation">}</span><span class="token punctuation">;</span>
<span class="token comment">// 若求最大下降子序列 需将max()处判断条件反转（<>）并且将num[0]置为最大值</span>
<span class="token keyword">int</span> <span class="token function">main</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">{</span>
<span class="token keyword">int</span> n<span class="token punctuation">;</span>
cin<span class="token operator">>></span>n<span class="token punctuation">;</span>
<span class="token comment">// ------最大上升子列 O(n^2)------- //</span>
<span class="token keyword">for</span><span class="token punctuation">(</span><span class="token keyword">int</span> i <span class="token operator">=</span> <span class="token number">1</span><span class="token punctuation">;</span> i <span class="token operator"><=</span> n<span class="token punctuation">;</span> i<span class="token operator">++</span><span class="token punctuation">)</span> cin<span class="token operator">>></span>num<span class="token punctuation">[</span>i<span class="token punctuation">]</span><span class="token punctuation">;</span>
<span class="token keyword">for</span><span class="token punctuation">(</span><span class="token keyword">int</span> i <span class="token operator">=</span> <span class="token number">1</span><span class="token punctuation">;</span> i <span class="token operator"><=</span> n<span class="token punctuation">;</span> i<span class="token operator">++</span><span class="token punctuation">)</span><span class="token punctuation">{</span><span class="token comment">// 当前处理处于i处的最大值</span>
<span class="token keyword">for</span><span class="token punctuation">(</span><span class="token keyword">int</span> j <span class="token operator">=</span> <span class="token number">0</span><span class="token punctuation">;</span> j <span class="token operator"><</span> i<span class="token punctuation">;</span> j<span class="token operator">++</span><span class="token punctuation">)</span><span class="token punctuation">{</span><span class="token comment">// 注意这里用到index = 0, 当从后面往前求最大上升子列时要用到n+1 注意避免RE</span>
<span class="token keyword">if</span><span class="token punctuation">(</span>num<span class="token punctuation">[</span>j<span class="token punctuation">]</span> <span class="token operator"><</span> num<span class="token punctuation">[</span>i<span class="token punctuation">]</span><span class="token punctuation">)</span> upp<span class="token punctuation">[</span>i<span class="token punctuation">]</span> <span class="token operator">=</span> <span class="token function">max</span><span class="token punctuation">(</span>upp<span class="token punctuation">[</span>i<span class="token punctuation">]</span><span class="token punctuation">,</span> upp<span class="token punctuation">[</span>j<span class="token punctuation">]</span> <span class="token operator">+</span> <span class="token number">1</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
<span class="token punctuation">}</span>
<span class="token punctuation">}</span>
<span class="token keyword">int</span> res <span class="token operator">=</span> <span class="token operator">*</span><span class="token function">max_element</span><span class="token punctuation">(</span>upp <span class="token operator">+</span> <span class="token number">1</span><span class="token punctuation">,</span> upp <span class="token operator">+</span> n <span class="token operator">+</span> <span class="token number">1</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
cout<span class="token operator"><<</span>res<span class="token operator"><<</span>endl<span class="token punctuation">;</span>
<span class="token comment">// -------------------------------- //</span>
<span class="token keyword">return</span> <span class="token number">0</span><span class="token punctuation">;</span>
<span class="token punctuation">}</span>
</pre><h4 class="mume-header" id="earth_asia-%E6%9C%80%E5%A4%A7%E4%B8%8A%E5%8D%87%E5%AD%90%E5%88%97-%E6%A8%A1%E6%9D%BF">🌏 最大上升子列 模板</h4>
<pre data-role="codeBlock" data-info="cpp" class="language-cpp"><span class="token macro property">#<span class="token directive keyword">include</span><span class="token string"><iostream></span></span>
<span class="token macro property">#<span class="token directive keyword">include</span><span class="token string"><cstdio></span></span>
<span class="token macro property">#<span class="token directive keyword">include</span><span class="token string"><algorithm></span></span>
<span class="token keyword">using</span> <span class="token keyword">namespace</span> std<span class="token punctuation">;</span>
<span class="token keyword">int</span> n<span class="token punctuation">;</span>
<span class="token keyword">int</span> num<span class="token punctuation">[</span><span class="token number">200005</span><span class="token punctuation">]</span><span class="token punctuation">;</span>
<span class="token keyword">int</span> upp<span class="token punctuation">[</span><span class="token number">200005</span><span class="token punctuation">]</span><span class="token punctuation">;</span>
<span class="token keyword">int</span> <span class="token function">main</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">{</span>
<span class="token comment">//O(nlogn)</span>
cin<span class="token operator">>></span>n<span class="token punctuation">;</span>
<span class="token keyword">for</span><span class="token punctuation">(</span><span class="token keyword">int</span> i <span class="token operator">=</span> <span class="token number">1</span><span class="token punctuation">;</span> i <span class="token operator"><=</span> n<span class="token punctuation">;</span> <span class="token operator">++</span>i<span class="token punctuation">)</span> cin<span class="token operator">>></span>num<span class="token punctuation">[</span>i<span class="token punctuation">]</span><span class="token punctuation">;</span>
<span class="token keyword">int</span> ans <span class="token operator">=</span> <span class="token number">1</span><span class="token punctuation">;</span> upp<span class="token punctuation">[</span><span class="token number">1</span><span class="token punctuation">]</span> <span class="token operator">=</span> num<span class="token punctuation">[</span><span class="token number">1</span><span class="token punctuation">]</span><span class="token punctuation">;</span>
<span class="token keyword">for</span><span class="token punctuation">(</span><span class="token keyword">int</span> i <span class="token operator">=</span> <span class="token number">2</span><span class="token punctuation">;</span> i <span class="token operator"><=</span> n<span class="token punctuation">;</span> <span class="token operator">++</span>i<span class="token punctuation">)</span><span class="token punctuation">{</span>
<span class="token keyword">int</span> l <span class="token operator">=</span> <span class="token number">1</span><span class="token punctuation">,</span> r <span class="token operator">=</span> ans<span class="token punctuation">,</span> mid<span class="token punctuation">;</span>
<span class="token keyword">while</span><span class="token punctuation">(</span>l <span class="token operator"><=</span> r<span class="token punctuation">)</span><span class="token punctuation">{</span>
mid <span class="token operator">=</span><span class="token punctuation">(</span>l <span class="token operator">+</span> r<span class="token punctuation">)</span><span class="token operator">>></span><span class="token number">1</span><span class="token punctuation">;</span>
<span class="token keyword">if</span><span class="token punctuation">(</span>num<span class="token punctuation">[</span>i<span class="token punctuation">]</span> <span class="token operator"><=</span> upp<span class="token punctuation">[</span>mid<span class="token punctuation">]</span><span class="token punctuation">)</span>r <span class="token operator">=</span> mid <span class="token operator">-</span> <span class="token number">1</span><span class="token punctuation">;</span>
<span class="token keyword">else</span> l <span class="token operator">=</span> mid <span class="token operator">+</span> <span class="token number">1</span><span class="token punctuation">;</span>
<span class="token punctuation">}</span>upp<span class="token punctuation">[</span>l<span class="token punctuation">]</span> <span class="token operator">=</span> num<span class="token punctuation">[</span>i<span class="token punctuation">]</span><span class="token punctuation">;</span>
<span class="token keyword">if</span><span class="token punctuation">(</span>l <span class="token operator">></span> ans<span class="token punctuation">)</span> <span class="token operator">++</span>ans<span class="token punctuation">;</span>
<span class="token punctuation">}</span>cout<span class="token operator"><<</span>ans<span class="token operator"><<</span>endl<span class="token punctuation">;</span>
<span class="token keyword">return</span> <span class="token number">0</span><span class="token punctuation">;</span>
<span class="token punctuation">}</span>
</pre><pre data-role="codeBlock" data-info="cpp" class="language-cpp"><span class="token macro property">#<span class="token directive keyword">include</span><span class="token string"><iostream></span></span>
<span class="token macro property">#<span class="token directive keyword">include</span><span class="token string"><cstdio></span></span>
<span class="token macro property">#<span class="token directive keyword">include</span><span class="token string"><algorithm></span></span>
<span class="token macro property">#<span class="token directive keyword">include</span><span class="token string"><vector></span></span>
<span class="token keyword">using</span> <span class="token keyword">namespace</span> std<span class="token punctuation">;</span>
<span class="token keyword">int</span> n<span class="token punctuation">;</span>
<span class="token keyword">int</span> num<span class="token punctuation">[</span><span class="token number">200005</span><span class="token punctuation">]</span><span class="token punctuation">;</span>
<span class="token comment">//O(nlogn)</span>
<span class="token keyword">int</span> <span class="token function">cal</span><span class="token punctuation">(</span><span class="token keyword">int</span> <span class="token operator">*</span>b<span class="token punctuation">)</span><span class="token punctuation">{</span>
vector<span class="token operator"><</span><span class="token keyword">int</span><span class="token operator">></span> s<span class="token punctuation">;</span>
<span class="token keyword">for</span><span class="token punctuation">(</span><span class="token keyword">int</span> i <span class="token operator">=</span> <span class="token number">0</span><span class="token punctuation">;</span> i <span class="token operator"><</span> n <span class="token punctuation">;</span>i<span class="token operator">++</span><span class="token punctuation">)</span><span class="token punctuation">{</span>
<span class="token keyword">if</span><span class="token punctuation">(</span>s<span class="token punctuation">.</span><span class="token function">empty</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">)</span> s<span class="token punctuation">.</span><span class="token function">push_back</span><span class="token punctuation">(</span>b<span class="token punctuation">[</span>i<span class="token punctuation">]</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
<span class="token keyword">else</span><span class="token punctuation">{</span>
vector<span class="token operator"><</span><span class="token keyword">int</span><span class="token operator">></span><span class="token operator">::</span>iterator it <span class="token operator">=</span> <span class="token function">upper_bound</span><span class="token punctuation">(</span>s<span class="token punctuation">.</span><span class="token function">begin</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">,</span> s<span class="token punctuation">.</span><span class="token function">end</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">,</span> b<span class="token punctuation">[</span>i<span class="token punctuation">]</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
<span class="token keyword">if</span><span class="token punctuation">(</span>it <span class="token operator">==</span> s<span class="token punctuation">.</span><span class="token function">end</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">)</span> s<span class="token punctuation">.</span><span class="token function">push_back</span><span class="token punctuation">(</span>b<span class="token punctuation">[</span>i<span class="token punctuation">]</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
<span class="token keyword">else</span> <span class="token operator">*</span>it <span class="token operator">=</span> b<span class="token punctuation">[</span>i<span class="token punctuation">]</span><span class="token punctuation">;</span>
<span class="token punctuation">}</span>
<span class="token punctuation">}</span>
<span class="token keyword">return</span> s<span class="token punctuation">.</span><span class="token function">size</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
<span class="token punctuation">}</span>
<span class="token keyword">int</span> <span class="token function">main</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">{</span>
cin<span class="token operator">>></span>n<span class="token punctuation">;</span>
<span class="token keyword">for</span><span class="token punctuation">(</span><span class="token keyword">int</span> i <span class="token operator">=</span> <span class="token number">1</span><span class="token punctuation">;</span> i <span class="token operator"><=</span> n<span class="token punctuation">;</span> <span class="token operator">++</span>i<span class="token punctuation">)</span> cin<span class="token operator">>></span>num<span class="token punctuation">[</span>i<span class="token punctuation">]</span><span class="token punctuation">;</span>
cout<span class="token operator"><<</span><span class="token function">cal</span><span class="token punctuation">(</span>num<span class="token punctuation">)</span><span class="token punctuation">;</span>
<span class="token keyword">return</span> <span class="token number">0</span><span class="token punctuation">;</span>
<span class="token punctuation">}</span>
</pre><h3 class="mume-header" id="%E4%BA%8C%E5%88%86%E6%90%9C%E7%B4%A2">二分搜索</h3>
<h4 class="mume-header" id="frog-%E4%BA%8C%E5%88%86%E6%90%9C%E7%B4%A2-%E6%A8%A1%E6%9D%BF">🐸 二分搜索 模板</h4>
<pre data-role="codeBlock" data-info="cpp" class="language-cpp"><span class="token function">sort</span><span class="token punctuation">(</span>arrA <span class="token operator">+</span> <span class="token number">1</span><span class="token punctuation">,</span> arrA <span class="token operator">+</span> <span class="token number">1</span> <span class="token operator">+</span> n<span class="token punctuation">)</span><span class="token punctuation">;</span><span class="token comment">// 首先保证有序</span>
<span class="token keyword">int</span> left <span class="token operator">=</span> <span class="token number">1</span><span class="token punctuation">,</span> right <span class="token operator">=</span> arrA<span class="token punctuation">[</span>n<span class="token punctuation">]</span><span class="token punctuation">;</span><span class="token comment">// 答案可能的范围</span>
<span class="token keyword">while</span><span class="token punctuation">(</span>left <span class="token operator"><=</span> right<span class="token punctuation">)</span><span class="token punctuation">{</span>
<span class="token keyword">int</span> mid <span class="token operator">=</span> <span class="token punctuation">(</span>left <span class="token operator">+</span> right<span class="token punctuation">)</span> <span class="token operator">/</span> <span class="token number">2</span><span class="token punctuation">;</span>
<span class="token keyword">if</span><span class="token punctuation">(</span><span class="token function">check</span><span class="token punctuation">(</span>mid<span class="token punctuation">)</span><span class="token comment">/*检查函数看当前mid是否符合条件*/</span><span class="token punctuation">)</span><span class="token punctuation">{</span><span class="token comment">// 符合的话区间还可以向右</span>
left <span class="token operator">=</span> mid <span class="token operator">+</span> <span class="token number">1</span><span class="token punctuation">;</span>
<span class="token punctuation">}</span><span class="token keyword">else</span><span class="token punctuation">{</span><span class="token comment">// 不符合向左</span>
right <span class="token operator">=</span> mid <span class="token operator">-</span> <span class="token number">1</span><span class="token punctuation">;</span>
<span class="token punctuation">}</span>
<span class="token punctuation">}</span>
</pre><h3 class="mume-header" id="%E6%9C%80%E5%A4%A7%E5%85%AC%E7%BA%A6%E6%95%B0">最大公约数</h3>
<h4 class="mume-header" id="frog-%E8%BE%97%E8%BD%AC%E7%9B%B8%E9%99%A4%E6%B3%95-%E6%A8%A1%E6%9D%BF">🐸 辗转相除法 模板</h4>
<pre data-role="codeBlock" data-info="cpp" class="language-cpp"><span class="token keyword">int</span> <span class="token function">gcd</span><span class="token punctuation">(</span><span class="token keyword">int</span> x<span class="token punctuation">,</span><span class="token keyword">int</span> y<span class="token punctuation">)</span><span class="token punctuation">{</span>
<span class="token keyword">if</span><span class="token punctuation">(</span><span class="token operator">!</span>y<span class="token punctuation">)</span> <span class="token keyword">return</span> x<span class="token punctuation">;</span>
<span class="token keyword">return</span> <span class="token function">gcd</span><span class="token punctuation">(</span>y<span class="token punctuation">,</span> x <span class="token operator">%</span> y<span class="token punctuation">)</span><span class="token punctuation">;</span>
<span class="token punctuation">}</span>
</pre><h3 class="mume-header" id="%E5%BF%AB%E9%80%9F%E5%B9%82">快速幂</h3>
<h4 class="mume-header" id="frog-%E5%BF%AB%E9%80%9F%E5%B9%82-%E6%A8%A1%E6%9D%BF">🐸 快速幂 模板</h4>
<pre data-role="codeBlock" data-info="cpp" class="language-cpp"><span class="token keyword">typedef</span> <span class="token keyword">long</span> <span class="token keyword">long</span> ll<span class="token punctuation">;</span>
ll <span class="token function">qPow</span><span class="token punctuation">(</span>ll x<span class="token punctuation">,</span> ll y<span class="token punctuation">)</span><span class="token punctuation">{</span>
ll res <span class="token operator">=</span> <span class="token number">1</span><span class="token punctuation">;</span>
<span class="token keyword">while</span><span class="token punctuation">(</span>y<span class="token punctuation">)</span><span class="token punctuation">{</span>
<span class="token keyword">if</span><span class="token punctuation">(</span>y <span class="token operator">&</span> <span class="token number">1</span><span class="token punctuation">)</span> res <span class="token operator">*=</span> x<span class="token punctuation">;</span>
x <span class="token operator">*=</span> x<span class="token punctuation">;</span>
y <span class="token operator">>>=</span> <span class="token number">1</span><span class="token punctuation">;</span>
<span class="token punctuation">}</span>
<span class="token keyword">return</span> res<span class="token punctuation">;</span>
<span class="token punctuation">}</span>
</pre><h3 class="mume-header" id="%E9%80%86%E5%BA%8F%E5%AF%B9">逆序对</h3>
<h4 class="mume-header" id="frog-%E6%B1%82%E9%80%86%E5%BA%8F%E5%AF%B9%E6%95%B0-%E6%A8%A1%E6%9D%BF">🐸 求逆序对数 模板</h4>
<pre data-role="codeBlock" data-info="cpp" class="language-cpp"><span class="token macro property">#<span class="token directive keyword">include</span><span class="token string"><iostream></span></span>
<span class="token macro property">#<span class="token directive keyword">include</span><span class="token string"><cstdio></span></span>
<span class="token keyword">using</span> <span class="token keyword">namespace</span> std<span class="token punctuation">;</span>
<span class="token keyword">int</span> n<span class="token punctuation">,</span> arrA<span class="token punctuation">[</span><span class="token number">500009</span><span class="token punctuation">]</span> <span class="token operator">=</span> <span class="token punctuation">{</span><span class="token number">0</span><span class="token punctuation">}</span><span class="token punctuation">,</span> arrB<span class="token punctuation">[</span><span class="token number">500009</span><span class="token punctuation">]</span> <span class="token operator">=</span> <span class="token punctuation">{</span><span class="token number">0</span><span class="token punctuation">}</span><span class="token punctuation">;</span>
<span class="token keyword">long</span> <span class="token keyword">long</span> sum <span class="token operator">=</span> <span class="token number">0</span><span class="token punctuation">;</span>
<span class="token keyword">void</span> <span class="token function">solve</span><span class="token punctuation">(</span><span class="token keyword">int</span> left<span class="token punctuation">,</span> <span class="token keyword">int</span> right<span class="token punctuation">)</span><span class="token punctuation">{</span>
<span class="token keyword">if</span><span class="token punctuation">(</span>left <span class="token operator">>=</span> right<span class="token punctuation">)</span> <span class="token keyword">return</span><span class="token punctuation">;</span>
<span class="token keyword">int</span> mid <span class="token operator">=</span> <span class="token punctuation">(</span>left <span class="token operator">+</span> right<span class="token punctuation">)</span> <span class="token operator">/</span> <span class="token number">2</span><span class="token punctuation">;</span>
<span class="token function">solve</span><span class="token punctuation">(</span>left<span class="token punctuation">,</span> mid<span class="token punctuation">)</span><span class="token punctuation">,</span> <span class="token function">solve</span><span class="token punctuation">(</span>mid <span class="token operator">+</span> <span class="token number">1</span><span class="token punctuation">,</span> right<span class="token punctuation">)</span><span class="token punctuation">;</span>
<span class="token keyword">int</span> i <span class="token operator">=</span> left<span class="token punctuation">,</span> j <span class="token operator">=</span> mid <span class="token operator">+</span> <span class="token number">1</span><span class="token punctuation">,</span> index <span class="token operator">=</span> left<span class="token punctuation">;</span>
<span class="token keyword">while</span><span class="token punctuation">(</span>i <span class="token operator"><=</span> mid <span class="token operator">&&</span> j <span class="token operator"><=</span> right<span class="token punctuation">)</span><span class="token punctuation">{</span>
<span class="token keyword">if</span><span class="token punctuation">(</span>arrA<span class="token punctuation">[</span>i<span class="token punctuation">]</span> <span class="token operator">></span> arrA<span class="token punctuation">[</span>j<span class="token punctuation">]</span><span class="token punctuation">)</span><span class="token punctuation">{</span><span class="token comment">// 逆序</span>
arrB<span class="token punctuation">[</span>index<span class="token operator">++</span><span class="token punctuation">]</span> <span class="token operator">=</span> arrA<span class="token punctuation">[</span>j<span class="token operator">++</span><span class="token punctuation">]</span><span class="token punctuation">;</span>
sum <span class="token operator">+=</span> mid <span class="token operator">-</span> i <span class="token operator">+</span> <span class="token number">1</span><span class="token punctuation">;</span><span class="token comment">// i处元素大于j处元素 则i后面的元素也大于j处元素</span>
<span class="token punctuation">}</span><span class="token keyword">else</span> arrB<span class="token punctuation">[</span>index<span class="token operator">++</span><span class="token punctuation">]</span> <span class="token operator">=</span> arrA<span class="token punctuation">[</span>i<span class="token operator">++</span><span class="token punctuation">]</span><span class="token punctuation">;</span>
<span class="token punctuation">}</span>
<span class="token keyword">while</span><span class="token punctuation">(</span>i <span class="token operator"><=</span> mid<span class="token punctuation">)</span> arrB<span class="token punctuation">[</span>index<span class="token operator">++</span><span class="token punctuation">]</span> <span class="token operator">=</span> arrA<span class="token punctuation">[</span>i<span class="token operator">++</span><span class="token punctuation">]</span><span class="token punctuation">;</span>
<span class="token keyword">while</span><span class="token punctuation">(</span>j <span class="token operator"><=</span> right<span class="token punctuation">)</span> arrB<span class="token punctuation">[</span>index<span class="token operator">++</span><span class="token punctuation">]</span> <span class="token operator">=</span> arrA<span class="token punctuation">[</span>j<span class="token operator">++</span><span class="token punctuation">]</span><span class="token punctuation">;</span>
<span class="token keyword">for</span><span class="token punctuation">(</span><span class="token keyword">int</span> k <span class="token operator">=</span> left<span class="token punctuation">;</span> k <span class="token operator"><=</span> right<span class="token punctuation">;</span> k<span class="token operator">++</span><span class="token punctuation">)</span> arrA<span class="token punctuation">[</span>k<span class="token punctuation">]</span> <span class="token operator">=</span> arrB<span class="token punctuation">[</span>k<span class="token punctuation">]</span><span class="token punctuation">;</span>
<span class="token punctuation">}</span>
<span class="token keyword">int</span> <span class="token function">main</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">{</span>
<span class="token comment">// freopen("input.txt", "r", stdin);</span>
cin<span class="token operator">>></span>n<span class="token punctuation">;</span>
<span class="token keyword">for</span><span class="token punctuation">(</span><span class="token keyword">int</span> i <span class="token operator">=</span> <span class="token number">1</span><span class="token punctuation">;</span> i <span class="token operator"><=</span> n<span class="token punctuation">;</span> i<span class="token operator">++</span><span class="token punctuation">)</span><span class="token punctuation">{</span>
<span class="token function">scanf</span><span class="token punctuation">(</span><span class="token string">"%d"</span><span class="token punctuation">,</span> <span class="token operator">&</span>arrA<span class="token punctuation">[</span>i<span class="token punctuation">]</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
<span class="token punctuation">}</span>
<span class="token function">solve</span><span class="token punctuation">(</span><span class="token number">1</span><span class="token punctuation">,</span> n<span class="token punctuation">)</span><span class="token punctuation">;</span>
cout<span class="token operator"><<</span>sum<span class="token operator"><<</span>endl<span class="token punctuation">;</span>
<span class="token keyword">return</span> <span class="token number">0</span><span class="token punctuation">;</span>
<span class="token punctuation">}</span>
</pre><h3 class="mume-header" id="%E8%83%8C%E5%8C%85">背包</h3>
<h4 class="mume-header" id="hatching_chick-01%E8%83%8C%E5%8C%85%E4%BA%8C%E7%BB%B4%E6%95%B0%E7%BB%84-%E6%A8%A1%E6%9D%BF">🐣 01背包二维数组 模板</h4>
<pre data-role="codeBlock" data-info="cpp" class="language-cpp"><span class="token macro property">#<span class="token directive keyword">include</span><span class="token string"><iostream></span></span>
<span class="token macro property">#<span class="token directive keyword">include</span><span class="token string"><algorithm></span></span>
<span class="token macro property">#<span class="token directive keyword">include</span><span class="token string"><cstring></span></span>
<span class="token keyword">using</span> <span class="token keyword">namespace</span> std<span class="token punctuation">;</span>
<span class="token keyword">int</span> m<span class="token punctuation">,</span> n<span class="token punctuation">;</span> <span class="token comment">// m: 物品总数 n: 背包重量</span>
<span class="token keyword">int</span> dp<span class="token punctuation">[</span><span class="token number">1010</span><span class="token punctuation">]</span><span class="token punctuation">[</span><span class="token number">1010</span><span class="token punctuation">]</span><span class="token punctuation">;</span>
<span class="token keyword">struct</span> node<span class="token punctuation">{</span>
<span class="token keyword">int</span> w<span class="token punctuation">;</span>
<span class="token keyword">int</span> v<span class="token punctuation">;</span>
<span class="token punctuation">}</span>nn<span class="token punctuation">[</span><span class="token number">1010</span><span class="token punctuation">]</span><span class="token punctuation">;</span>
<span class="token comment">//结构用来存放物品重量和价值</span>
<span class="token keyword">void</span> <span class="token function">nodee</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">{</span>
<span class="token keyword">int</span> i <span class="token punctuation">,</span> j<span class="token punctuation">;</span>
<span class="token function">memset</span><span class="token punctuation">(</span>dp<span class="token punctuation">,</span><span class="token number">0</span><span class="token punctuation">,</span><span class="token keyword">sizeof</span><span class="token punctuation">(</span>dp<span class="token punctuation">)</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
<span class="token keyword">for</span><span class="token punctuation">(</span>i <span class="token operator">=</span> <span class="token number">1</span><span class="token punctuation">;</span> i <span class="token operator"><=</span> m<span class="token punctuation">;</span> i<span class="token operator">++</span><span class="token punctuation">)</span> <span class="token punctuation">{</span>
<span class="token keyword">for</span><span class="token punctuation">(</span>j <span class="token operator">=</span> <span class="token number">0</span><span class="token punctuation">;</span> j <span class="token operator"><=</span> n<span class="token punctuation">;</span> j<span class="token operator">++</span><span class="token punctuation">)</span> <span class="token punctuation">{</span>
<span class="token keyword">if</span><span class="token punctuation">(</span>nn<span class="token punctuation">[</span>i<span class="token punctuation">]</span><span class="token punctuation">.</span>w <span class="token operator">></span> j<span class="token punctuation">)</span> <span class="token punctuation">{</span>
dp<span class="token punctuation">[</span>i<span class="token punctuation">]</span><span class="token punctuation">[</span>j<span class="token punctuation">]</span> <span class="token operator">=</span> dp<span class="token punctuation">[</span>i <span class="token operator">-</span> <span class="token number">1</span><span class="token punctuation">]</span><span class="token punctuation">[</span>j<span class="token punctuation">]</span><span class="token punctuation">;</span> <span class="token comment">// 判断该物品与当前储存背包大小，如果大于，则不取。 </span>
<span class="token punctuation">}</span><span class="token keyword">else</span> <span class="token punctuation">{</span>
dp<span class="token punctuation">[</span>i<span class="token punctuation">]</span><span class="token punctuation">[</span>j<span class="token punctuation">]</span> <span class="token operator">=</span> <span class="token function">max</span><span class="token punctuation">(</span>dp<span class="token punctuation">[</span>i <span class="token operator">-</span> <span class="token number">1</span><span class="token punctuation">]</span><span class="token punctuation">[</span>j<span class="token punctuation">]</span><span class="token punctuation">,</span> dp<span class="token punctuation">[</span>i <span class="token operator">-</span> <span class="token number">1</span><span class="token punctuation">]</span><span class="token punctuation">[</span> j <span class="token operator">-</span> nn<span class="token punctuation">[</span>i<span class="token punctuation">]</span><span class="token punctuation">.</span>w<span class="token punctuation">]</span> <span class="token operator">+</span> nn<span class="token punctuation">[</span>i<span class="token punctuation">]</span><span class="token punctuation">.</span>v<span class="token punctuation">)</span><span class="token punctuation">;</span> <span class="token comment">// 反之判断价值大小，取大的。</span>
<span class="token punctuation">}</span>
<span class="token punctuation">}</span>
<span class="token punctuation">}</span>
<span class="token punctuation">}</span>
<span class="token keyword">int</span> <span class="token function">main</span><span class="token punctuation">(</span><span class="token punctuation">)</span>
<span class="token punctuation">{</span>
cin<span class="token operator">>></span>m<span class="token operator">>></span>n<span class="token punctuation">;</span>
<span class="token keyword">for</span><span class="token punctuation">(</span><span class="token keyword">int</span> i <span class="token operator">=</span> <span class="token number">1</span><span class="token punctuation">;</span> i <span class="token operator"><=</span> m<span class="token punctuation">;</span> i<span class="token operator">++</span><span class="token punctuation">)</span> <span class="token punctuation">{</span>
cin<span class="token operator">>></span>nn<span class="token punctuation">[</span>i<span class="token punctuation">]</span><span class="token punctuation">.</span>v<span class="token punctuation">;</span>
<span class="token punctuation">}</span>
<span class="token keyword">for</span><span class="token punctuation">(</span><span class="token keyword">int</span> i <span class="token operator">=</span> <span class="token number">1</span><span class="token punctuation">;</span> i<span class="token operator"><=</span> m<span class="token punctuation">;</span> i<span class="token operator">++</span><span class="token punctuation">)</span> <span class="token punctuation">{</span>
cin<span class="token operator">>></span>nn<span class="token punctuation">[</span>i<span class="token punctuation">]</span><span class="token punctuation">.</span>w<span class="token punctuation">;</span>
<span class="token punctuation">}</span>
<span class="token function">nodee</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
cout<span class="token operator"><<</span>dp<span class="token punctuation">[</span>m<span class="token punctuation">]</span><span class="token punctuation">[</span>n<span class="token punctuation">]</span><span class="token operator"><<</span>endl<span class="token punctuation">;</span>
<span class="token keyword">return</span> <span class="token number">0</span><span class="token punctuation">;</span>
<span class="token punctuation">}</span>
</pre><h4 class="mume-header" id="frog-01%E8%83%8C%E5%8C%85%E4%BA%8C%E7%BB%B4%E6%95%B0%E7%BB%84-%E6%A8%A1%E6%9D%BF">🐸 01背包二维数组 模板</h4>
<pre data-role="codeBlock" data-info="cpp" class="language-cpp"><span class="token macro property">#<span class="token directive keyword">include</span><span class="token string"><iostream></span></span>
<span class="token macro property">#<span class="token directive keyword">include</span><span class="token string"><cstring></span></span>
<span class="token keyword">using</span> <span class="token keyword">namespace</span> std<span class="token punctuation">;</span>
<span class="token keyword">int</span> _size<span class="token punctuation">[</span><span class="token number">3500</span><span class="token punctuation">]</span> <span class="token operator">=</span> <span class="token punctuation">{</span><span class="token number">0</span><span class="token punctuation">}</span><span class="token punctuation">;</span><span class="token comment">// 占用体积</span>
<span class="token keyword">int</span> _value<span class="token punctuation">[</span><span class="token number">3500</span><span class="token punctuation">]</span> <span class="token operator">=</span> <span class="token punctuation">{</span><span class="token number">0</span><span class="token punctuation">}</span><span class="token punctuation">;</span><span class="token comment">// 价值</span>
<span class="token keyword">int</span> dp<span class="token punctuation">[</span><span class="token number">1009</span><span class="token punctuation">]</span><span class="token punctuation">[</span><span class="token number">1009</span><span class="token punctuation">]</span> <span class="token operator">=</span> <span class="token punctuation">{</span><span class="token number">0</span><span class="token punctuation">}</span><span class="token punctuation">;</span><span class="token comment">// 结果集</span>
<span class="token comment">/*
01背包二维数组
*/</span>
<span class="token keyword">int</span> <span class="token function">main</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">{</span>
<span class="token keyword">int</span> n<span class="token punctuation">,</span> maxSize<span class="token punctuation">;</span><span class="token comment">// 物体数量和背包容量</span>
cin<span class="token operator">>></span>n<span class="token operator">>></span>maxSize<span class="token punctuation">;</span>
<span class="token keyword">for</span><span class="token punctuation">(</span><span class="token keyword">int</span> i <span class="token operator">=</span> <span class="token number">1</span><span class="token punctuation">;</span> i <span class="token operator"><=</span> n<span class="token punctuation">;</span> i<span class="token operator">++</span><span class="token punctuation">)</span><span class="token punctuation">{</span>
cin<span class="token operator">>></span>_size<span class="token punctuation">[</span>i<span class="token punctuation">]</span><span class="token operator">>></span>_value<span class="token punctuation">[</span>i<span class="token punctuation">]</span><span class="token punctuation">;</span>
<span class="token punctuation">}</span>
<span class="token keyword">for</span><span class="token punctuation">(</span><span class="token keyword">int</span> i <span class="token operator">=</span> <span class="token number">1</span><span class="token punctuation">;</span> i <span class="token operator"><=</span> n<span class="token punctuation">;</span> i<span class="token operator">++</span><span class="token punctuation">)</span><span class="token punctuation">{</span>
<span class="token keyword">for</span><span class="token punctuation">(</span><span class="token keyword">int</span> j <span class="token operator">=</span> <span class="token number">0</span><span class="token punctuation">;</span> j <span class="token operator"><=</span> maxSize<span class="token punctuation">;</span> j<span class="token operator">++</span><span class="token punctuation">)</span><span class="token punctuation">{</span>
<span class="token keyword">if</span><span class="token punctuation">(</span>_size<span class="token punctuation">[</span>i<span class="token punctuation">]</span> <span class="token operator"><=</span> j<span class="token punctuation">)</span><span class="token punctuation">{</span>
dp<span class="token punctuation">[</span>i<span class="token punctuation">]</span><span class="token punctuation">[</span>j<span class="token punctuation">]</span> <span class="token operator">=</span> <span class="token function">max</span><span class="token punctuation">(</span>dp<span class="token punctuation">[</span>i <span class="token operator">-</span> <span class="token number">1</span><span class="token punctuation">]</span><span class="token punctuation">[</span>j<span class="token punctuation">]</span><span class="token punctuation">,</span> dp<span class="token punctuation">[</span>i <span class="token operator">-</span> <span class="token number">1</span><span class="token punctuation">]</span><span class="token punctuation">[</span>j <span class="token operator">-</span> _size<span class="token punctuation">[</span>i<span class="token punctuation">]</span><span class="token punctuation">]</span> <span class="token operator">+</span> _value<span class="token punctuation">[</span>i<span class="token punctuation">]</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
<span class="token punctuation">}</span><span class="token keyword">else</span><span class="token punctuation">{</span>
dp<span class="token punctuation">[</span>i<span class="token punctuation">]</span><span class="token punctuation">[</span>j<span class="token punctuation">]</span> <span class="token operator">=</span> dp<span class="token punctuation">[</span>i <span class="token operator">-</span> <span class="token number">1</span><span class="token punctuation">]</span><span class="token punctuation">[</span>j<span class="token punctuation">]</span><span class="token punctuation">;</span>
<span class="token punctuation">}</span>
<span class="token punctuation">}</span>
<span class="token punctuation">}</span>
cout<span class="token operator"><<</span>dp<span class="token punctuation">[</span>n<span class="token punctuation">]</span><span class="token punctuation">[</span>maxSize<span class="token punctuation">]</span><span class="token punctuation">;</span>
<span class="token keyword">return</span> <span class="token number">0</span><span class="token punctuation">;</span>
<span class="token punctuation">}</span>
</pre><h4 class="mume-header" id="hatching_chick-01%E8%83%8C%E5%8C%85%E6%BB%9A%E5%8A%A8%E6%95%B0%E7%BB%84-%E6%A8%A1%E6%9D%BF">🐣 01背包滚动数组 模板</h4>
<pre data-role="codeBlock" data-info="cpp" class="language-cpp"><span class="token macro property">#<span class="token directive keyword">include</span><span class="token string"><iostream></span></span>
<span class="token macro property">#<span class="token directive keyword">include</span><span class="token string"><algorithm></span></span>
<span class="token macro property">#<span class="token directive keyword">include</span><span class="token string"><cstring></span></span>
<span class="token keyword">using</span> <span class="token keyword">namespace</span> std<span class="token punctuation">;</span>
<span class="token keyword">int</span> m<span class="token punctuation">,</span> n<span class="token punctuation">;</span> <span class="token comment">// m: 物品总数 n: 背包重量</span>
<span class="token keyword">int</span> dp<span class="token punctuation">[</span><span class="token number">1010</span><span class="token punctuation">]</span><span class="token punctuation">;</span>
<span class="token keyword">struct</span> node<span class="token punctuation">{</span>
<span class="token keyword">int</span> w<span class="token punctuation">;</span>
<span class="token keyword">int</span> v<span class="token punctuation">;</span>
<span class="token punctuation">}</span>nn<span class="token punctuation">[</span><span class="token number">1010</span><span class="token punctuation">]</span><span class="token punctuation">;</span>
<span class="token comment">//结构用来存放物品重量和价值</span>
<span class="token keyword">void</span> <span class="token function">nodee</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">{</span> <span class="token comment">// 滚动数组</span>
<span class="token keyword">int</span> i<span class="token punctuation">,</span> j<span class="token punctuation">;</span>
<span class="token function">memset</span><span class="token punctuation">(</span>dp<span class="token punctuation">,</span><span class="token number">0</span><span class="token punctuation">,</span><span class="token keyword">sizeof</span><span class="token punctuation">(</span>dp<span class="token punctuation">)</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
<span class="token keyword">for</span><span class="token punctuation">(</span>i <span class="token operator">=</span> <span class="token number">1</span><span class="token punctuation">;</span> i <span class="token operator"><=</span> m<span class="token punctuation">;</span> i<span class="token operator">++</span><span class="token punctuation">)</span> <span class="token punctuation">{</span>
<span class="token keyword">for</span><span class="token punctuation">(</span>j <span class="token operator">=</span> n<span class="token punctuation">;</span> j <span class="token operator">>=</span> nn<span class="token punctuation">[</span>i<span class="token punctuation">]</span><span class="token punctuation">.</span>w<span class="token punctuation">;</span> j<span class="token operator">--</span><span class="token punctuation">)</span> <span class="token punctuation">{</span>
dp<span class="token punctuation">[</span>j<span class="token punctuation">]</span> <span class="token operator">=</span> <span class="token function">max</span><span class="token punctuation">(</span>dp<span class="token punctuation">[</span>j<span class="token punctuation">]</span><span class="token punctuation">,</span> dp<span class="token punctuation">[</span>j <span class="token operator">-</span> nn<span class="token punctuation">[</span>j<span class="token punctuation">]</span><span class="token punctuation">.</span>w<span class="token punctuation">]</span> <span class="token operator">+</span> nn<span class="token punctuation">[</span>j<span class="token punctuation">]</span><span class="token punctuation">.</span>v<span class="token punctuation">)</span><span class="token punctuation">;</span>
<span class="token punctuation">}</span>
<span class="token punctuation">}</span>
<span class="token punctuation">}</span>
<span class="token keyword">int</span> <span class="token function">main</span><span class="token punctuation">(</span><span class="token punctuation">)</span>
<span class="token punctuation">{</span>
cin<span class="token operator">>></span>m<span class="token operator">>></span>n<span class="token punctuation">;</span>
<span class="token keyword">for</span><span class="token punctuation">(</span><span class="token keyword">int</span> i <span class="token operator">=</span> <span class="token number">1</span><span class="token punctuation">;</span> i <span class="token operator"><=</span> m<span class="token punctuation">;</span> i<span class="token operator">++</span><span class="token punctuation">)</span> <span class="token punctuation">{</span>
cin<span class="token operator">>></span>nn<span class="token punctuation">[</span>i<span class="token punctuation">]</span><span class="token punctuation">.</span>v<span class="token punctuation">;</span>
<span class="token punctuation">}</span>
<span class="token keyword">for</span><span class="token punctuation">(</span><span class="token keyword">int</span> i <span class="token operator">=</span> <span class="token number">1</span><span class="token punctuation">;</span> i<span class="token operator"><=</span> m<span class="token punctuation">;</span> i<span class="token operator">++</span><span class="token punctuation">)</span> <span class="token punctuation">{</span>
cin<span class="token operator">>></span>nn<span class="token punctuation">[</span>i<span class="token punctuation">]</span><span class="token punctuation">.</span>w<span class="token punctuation">;</span>
<span class="token punctuation">}</span>
<span class="token function">nodee</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
cout<span class="token operator"><<</span>dp<span class="token punctuation">[</span>n<span class="token punctuation">]</span><span class="token operator"><<</span>endl<span class="token punctuation">;</span>
<span class="token keyword">return</span> <span class="token number">0</span><span class="token punctuation">;</span>
<span class="token punctuation">}</span>
</pre><h4 class="mume-header" id="frog-01%E8%83%8C%E5%8C%85%E6%BB%9A%E5%8A%A8%E6%95%B0%E7%BB%84-%E6%A8%A1%E6%9D%BF">🐸 01背包滚动数组 模板</h4>
<pre data-role="codeBlock" data-info="cpp" class="language-cpp"><span class="token macro property">#<span class="token directive keyword">include</span><span class="token string"><iostream></span></span>
<span class="token macro property">#<span class="token directive keyword">include</span><span class="token string"><cstring></span></span>
<span class="token keyword">using</span> <span class="token keyword">namespace</span> std<span class="token punctuation">;</span>
<span class="token keyword">int</span> _size<span class="token punctuation">[</span><span class="token number">3500</span><span class="token punctuation">]</span> <span class="token operator">=</span> <span class="token punctuation">{</span><span class="token number">0</span><span class="token punctuation">}</span><span class="token punctuation">;</span><span class="token comment">// 占用体积</span>
<span class="token keyword">int</span> _value<span class="token punctuation">[</span><span class="token number">3500</span><span class="token punctuation">]</span> <span class="token operator">=</span> <span class="token punctuation">{</span><span class="token number">0</span><span class="token punctuation">}</span><span class="token punctuation">;</span><span class="token comment">// 价值</span>
<span class="token keyword">int</span> dp<span class="token punctuation">[</span><span class="token number">13000</span><span class="token punctuation">]</span> <span class="token operator">=</span> <span class="token punctuation">{</span><span class="token number">0</span><span class="token punctuation">}</span><span class="token punctuation">;</span><span class="token comment">// 结果集</span>
<span class="token comment">/*
01背包滚动数组
*/</span>
<span class="token keyword">int</span> <span class="token function">main</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">{</span>
<span class="token keyword">int</span> n<span class="token punctuation">,</span> maxSize<span class="token punctuation">;</span><span class="token comment">// 物体数量和背包容量</span>
cin<span class="token operator">>></span>n<span class="token operator">>></span>maxSize<span class="token punctuation">;</span>
<span class="token keyword">for</span><span class="token punctuation">(</span><span class="token keyword">int</span> i <span class="token operator">=</span> <span class="token number">1</span><span class="token punctuation">;</span> i <span class="token operator"><=</span> n<span class="token punctuation">;</span> i<span class="token operator">++</span><span class="token punctuation">)</span><span class="token punctuation">{</span>
cin<span class="token operator">>></span>_size<span class="token punctuation">[</span>i<span class="token punctuation">]</span><span class="token operator">>></span>_value<span class="token punctuation">[</span>i<span class="token punctuation">]</span><span class="token punctuation">;</span>
<span class="token punctuation">}</span>
<span class="token keyword">for</span><span class="token punctuation">(</span><span class="token keyword">int</span> i <span class="token operator">=</span> <span class="token number">1</span><span class="token punctuation">;</span> i <span class="token operator"><=</span> n<span class="token punctuation">;</span> i<span class="token operator">++</span><span class="token punctuation">)</span><span class="token punctuation">{</span>
<span class="token keyword">for</span><span class="token punctuation">(</span><span class="token keyword">int</span> j <span class="token operator">=</span> maxSize<span class="token punctuation">;</span> j <span class="token operator">>=</span> _size<span class="token punctuation">[</span>i<span class="token punctuation">]</span><span class="token punctuation">;</span> j<span class="token operator">--</span><span class="token punctuation">)</span><span class="token punctuation">{</span>
dp<span class="token punctuation">[</span>j<span class="token punctuation">]</span> <span class="token operator">=</span> <span class="token function">max</span><span class="token punctuation">(</span>dp<span class="token punctuation">[</span>j<span class="token punctuation">]</span><span class="token punctuation">,</span> dp<span class="token punctuation">[</span>j <span class="token operator">-</span> _size<span class="token punctuation">[</span>i<span class="token punctuation">]</span><span class="token punctuation">]</span> <span class="token operator">+</span> _value<span class="token punctuation">[</span>i<span class="token punctuation">]</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
<span class="token punctuation">}</span>
<span class="token punctuation">}</span>
cout<span class="token operator"><<</span>dp<span class="token punctuation">[</span>maxSize<span class="token punctuation">]</span><span class="token punctuation">;</span>
<span class="token keyword">return</span> <span class="token number">0</span><span class="token punctuation">;</span>
<span class="token punctuation">}</span>
</pre><h4 class="mume-header" id="frog-%E5%AE%8C%E5%85%A8%E8%83%8C%E5%8C%85%E6%BB%9A%E5%8A%A8%E6%95%B0%E7%BB%84-%E6%A8%A1%E6%9D%BF">🐸 完全背包滚动数组 模板</h4>
<pre data-role="codeBlock" data-info="cpp" class="language-cpp"><span class="token macro property">#<span class="token directive keyword">include</span><span class="token string"><iostream></span></span>
<span class="token macro property">#<span class="token directive keyword">include</span><span class="token string"><cstring></span></span>
<span class="token keyword">using</span> <span class="token keyword">namespace</span> std<span class="token punctuation">;</span>
<span class="token keyword">int</span> _size<span class="token punctuation">[</span><span class="token number">13000</span><span class="token punctuation">]</span> <span class="token operator">=</span> <span class="token punctuation">{</span><span class="token number">0</span><span class="token punctuation">}</span><span class="token punctuation">;</span><span class="token comment">// 占用体积</span>
<span class="token keyword">int</span> _value<span class="token punctuation">[</span><span class="token number">13000</span><span class="token punctuation">]</span> <span class="token operator">=</span> <span class="token punctuation">{</span><span class="token number">0</span><span class="token punctuation">}</span><span class="token punctuation">;</span><span class="token comment">// 价值</span>
<span class="token keyword">int</span> dp<span class="token punctuation">[</span><span class="token number">13000</span><span class="token punctuation">]</span> <span class="token operator">=</span> <span class="token punctuation">{</span><span class="token number">0</span><span class="token punctuation">}</span><span class="token punctuation">;</span><span class="token comment">// 结果集</span>
<span class="token comment">/*
完全背包滚动数组
*/</span>
<span class="token keyword">int</span> <span class="token function">main</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">{</span>
<span class="token keyword">int</span> n<span class="token punctuation">,</span> maxSize<span class="token punctuation">;</span><span class="token comment">// 物体数量和背包容量</span>
cin<span class="token operator">>></span>n<span class="token operator">>></span>maxSize<span class="token punctuation">;</span>
<span class="token keyword">for</span><span class="token punctuation">(</span><span class="token keyword">int</span> i <span class="token operator">=</span> <span class="token number">1</span><span class="token punctuation">;</span> i <span class="token operator"><=</span> n<span class="token punctuation">;</span> i<span class="token operator">++</span><span class="token punctuation">)</span><span class="token punctuation">{</span>
cin<span class="token operator">>></span>_size<span class="token punctuation">[</span>i<span class="token punctuation">]</span><span class="token operator">>></span>_value<span class="token punctuation">[</span>i<span class="token punctuation">]</span><span class="token punctuation">;</span>
<span class="token punctuation">}</span>
<span class="token keyword">for</span><span class="token punctuation">(</span><span class="token keyword">int</span> i <span class="token operator">=</span> <span class="token number">1</span><span class="token punctuation">;</span> i <span class="token operator"><=</span> n<span class="token punctuation">;</span> i<span class="token operator">++</span><span class="token punctuation">)</span><span class="token punctuation">{</span>
<span class="token keyword">for</span><span class="token punctuation">(</span><span class="token keyword">int</span> j <span class="token operator">=</span> _size<span class="token punctuation">[</span>i<span class="token punctuation">]</span><span class="token punctuation">;</span> j <span class="token operator"><=</span> maxSize<span class="token punctuation">;</span> j<span class="token operator">++</span><span class="token punctuation">)</span><span class="token punctuation">{</span>
dp<span class="token punctuation">[</span>j<span class="token punctuation">]</span> <span class="token operator">=</span> <span class="token function">max</span><span class="token punctuation">(</span>dp<span class="token punctuation">[</span>j<span class="token punctuation">]</span><span class="token punctuation">,</span> dp<span class="token punctuation">[</span>j <span class="token operator">-</span> _size<span class="token punctuation">[</span>i<span class="token punctuation">]</span><span class="token punctuation">]</span> <span class="token operator">+</span> _value<span class="token punctuation">[</span>i<span class="token punctuation">]</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
<span class="token punctuation">}</span>
<span class="token punctuation">}</span>
cout<span class="token operator"><<</span><span class="token punctuation">[</span>maxSize<span class="token punctuation">]</span><span class="token punctuation">;</span>
<span class="token keyword">return</span> <span class="token number">0</span><span class="token punctuation">;</span>
<span class="token punctuation">}</span>
</pre><h3 class="mume-header" id="%E4%BA%8C%E5%8F%89%E6%A0%91">二叉树</h3>
<h4 class="mume-header" id="frog-%E5%89%8D%E5%BA%8F%E4%B8%AD%E5%BA%8F%E6%B1%82%E5%90%8E%E5%BA%8F-%E6%A8%A1%E6%9D%BF">🐸 前序中序求后序 模板</h4>
<pre data-role="codeBlock" data-info="cpp" class="language-cpp"><span class="token macro property">#<span class="token directive keyword">include</span><span class="token string"><iostream></span></span>
<span class="token macro property">#<span class="token directive keyword">include</span><span class="token string"><string></span></span>
<span class="token keyword">using</span> <span class="token keyword">namespace</span> std<span class="token punctuation">;</span>
string pre<span class="token punctuation">,</span> mid<span class="token punctuation">;</span>
<span class="token keyword">int</span> n <span class="token operator">=</span> <span class="token operator">-</span><span class="token number">1</span><span class="token punctuation">;</span>
<span class="token comment">/*
beginIndex从0 , endIndex从长度减一
注意n需要初始化-1
*/</span>
<span class="token keyword">void</span> <span class="token function">solve</span><span class="token punctuation">(</span><span class="token keyword">int</span> beginIndex<span class="token punctuation">,</span> <span class="token keyword">int</span> endIndex<span class="token punctuation">)</span><span class="token punctuation">{</span>
<span class="token keyword">if</span><span class="token punctuation">(</span>beginIndex <span class="token operator">></span> endIndex<span class="token punctuation">)</span> <span class="token keyword">return</span><span class="token punctuation">;</span>
n<span class="token operator">++</span><span class="token punctuation">;</span>
<span class="token keyword">int</span> i<span class="token punctuation">;</span>
<span class="token keyword">for</span><span class="token punctuation">(</span>i <span class="token operator">=</span> beginIndex<span class="token punctuation">;</span> i <span class="token operator"><=</span> endIndex<span class="token punctuation">;</span> i<span class="token operator">++</span><span class="token punctuation">)</span><span class="token punctuation">{</span>
<span class="token keyword">if</span><span class="token punctuation">(</span>pre<span class="token punctuation">[</span>n<span class="token punctuation">]</span> <span class="token operator">==</span> mid<span class="token punctuation">[</span>i<span class="token punctuation">]</span><span class="token punctuation">)</span> <span class="token keyword">break</span><span class="token punctuation">;</span>
<span class="token punctuation">}</span>
<span class="token function">solve</span><span class="token punctuation">(</span>beginIndex<span class="token punctuation">,</span> i <span class="token operator">-</span> <span class="token number">1</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
<span class="token function">solve</span><span class="token punctuation">(</span>i <span class="token operator">+</span> <span class="token number">1</span><span class="token punctuation">,</span> endIndex<span class="token punctuation">)</span><span class="token punctuation">;</span>
cout<span class="token operator"><<</span>mid<span class="token punctuation">[</span>i<span class="token punctuation">]</span><span class="token punctuation">;</span>
<span class="token punctuation">}</span>
<span class="token keyword">int</span> <span class="token function">main</span><span class="token punctuation">(</span><span class="token punctuation">)</span> <span class="token punctuation">{</span>
<span class="token keyword">while</span><span class="token punctuation">(</span>cin<span class="token operator">>></span>pre<span class="token operator">>></span>mid<span class="token punctuation">)</span> <span class="token punctuation">{</span>
<span class="token function">solve</span><span class="token punctuation">(</span><span class="token number">0</span><span class="token punctuation">,</span> pre<span class="token punctuation">.</span><span class="token function">length</span><span class="token punctuation">(</span><span class="token punctuation">)</span> <span class="token operator">-</span> <span class="token number">1</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
n <span class="token operator">=</span> <span class="token operator">-</span><span class="token number">1</span><span class="token punctuation">;</span>
cout<span class="token operator"><<</span>endl<span class="token punctuation">;</span>
<span class="token punctuation">}</span>
<span class="token keyword">return</span> <span class="token number">0</span><span class="token punctuation">;</span>
<span class="token punctuation">}</span>
</pre><h3 class="mume-header" id="%E5%A4%A7%E6%95%B0%E8%AE%A1%E7%AE%97">大数计算</h3>
<h4 class="mume-header" id="earth_asia-%E5%A4%A7%E6%95%B0%E5%8A%A0%E6%B3%95-%E6%A8%A1%E6%9D%BF">🌏 大数加法 模板</h4>
<pre data-role="codeBlock" data-info="cpp" class="language-cpp"><span class="token macro property">#<span class="token directive keyword">include</span><span class="token string"><iostream></span></span>
<span class="token macro property">#<span class="token directive keyword">include</span><span class="token string"><string></span></span>
<span class="token macro property">#<span class="token directive keyword">include</span><span class="token string"><algorithm></span></span>
<span class="token keyword">using</span> <span class="token keyword">namespace</span> std<span class="token punctuation">;</span>
<span class="token macro property">#<span class="token directive keyword">define</span> n 10</span>
<span class="token comment">/*
大数加法
如果遇到加负数的情况需要使用减法模版
*/</span>
string <span class="token function">dezero</span><span class="token punctuation">(</span>string a<span class="token punctuation">)</span><span class="token comment">//用来去掉正数前面的0，也就是说可以输入000001类似这样的数字</span>
<span class="token punctuation">{</span>
<span class="token keyword">long</span> <span class="token keyword">int</span> i<span class="token punctuation">;</span>
<span class="token keyword">for</span><span class="token punctuation">(</span>i<span class="token operator">=</span><span class="token number">0</span><span class="token punctuation">;</span>i<span class="token operator"><</span>a<span class="token punctuation">.</span><span class="token function">length</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">;</span>i<span class="token operator">++</span><span class="token punctuation">)</span>
<span class="token punctuation">{</span>
<span class="token keyword">if</span><span class="token punctuation">(</span>a<span class="token punctuation">.</span><span class="token function">at</span><span class="token punctuation">(</span>i<span class="token punctuation">)</span><span class="token operator">></span><span class="token number">48</span><span class="token punctuation">)</span> <span class="token keyword">break</span><span class="token punctuation">;</span>
<span class="token punctuation">}</span>
<span class="token keyword">if</span><span class="token punctuation">(</span>i<span class="token operator">==</span>a<span class="token punctuation">.</span><span class="token function">length</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">)</span> <span class="token keyword">return</span> <span class="token string">"0"</span><span class="token punctuation">;</span>
a<span class="token punctuation">.</span><span class="token function">erase</span><span class="token punctuation">(</span><span class="token number">0</span><span class="token punctuation">,</span>i<span class="token punctuation">)</span><span class="token punctuation">;</span>
<span class="token keyword">return</span> a<span class="token punctuation">;</span>
<span class="token punctuation">}</span>
string <span class="token function">add</span><span class="token punctuation">(</span>string a<span class="token punctuation">,</span>string b<span class="token punctuation">)</span><span class="token comment">//自然数加法</span>
<span class="token punctuation">{</span>
a<span class="token operator">=</span><span class="token function">dezero</span><span class="token punctuation">(</span>a<span class="token punctuation">)</span><span class="token punctuation">;</span>
b<span class="token operator">=</span><span class="token function">dezero</span><span class="token punctuation">(</span>b<span class="token punctuation">)</span><span class="token punctuation">;</span>
string c<span class="token punctuation">;</span>
string d<span class="token operator">=</span><span class="token string">"0"</span><span class="token punctuation">;</span>
<span class="token keyword">long</span> <span class="token keyword">int</span> kmin<span class="token punctuation">,</span>kmax<span class="token punctuation">,</span>i<span class="token punctuation">;</span>
<span class="token function">reverse</span><span class="token punctuation">(</span>a<span class="token punctuation">.</span><span class="token function">begin</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">,</span>a<span class="token punctuation">.</span><span class="token function">end</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
<span class="token function">reverse</span><span class="token punctuation">(</span>b<span class="token punctuation">.</span><span class="token function">begin</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">,</span>b<span class="token punctuation">.</span><span class="token function">end</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
<span class="token keyword">if</span><span class="token punctuation">(</span>a<span class="token punctuation">.</span><span class="token function">length</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token operator">></span>b<span class="token punctuation">.</span><span class="token function">length</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">)</span> <span class="token punctuation">{</span>kmin<span class="token operator">=</span>b<span class="token punctuation">.</span><span class="token function">length</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">;</span>kmax<span class="token operator">=</span>a<span class="token punctuation">.</span><span class="token function">length</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">;</span>c<span class="token operator">=</span>a<span class="token punctuation">;</span><span class="token punctuation">}</span>
<span class="token keyword">else</span> <span class="token punctuation">{</span>kmin<span class="token operator">=</span>a<span class="token punctuation">.</span><span class="token function">length</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">;</span>kmax<span class="token operator">=</span>b<span class="token punctuation">.</span><span class="token function">length</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">;</span>c<span class="token operator">=</span>b<span class="token punctuation">;</span><span class="token punctuation">}</span>
c<span class="token punctuation">.</span><span class="token function">insert</span><span class="token punctuation">(</span>c<span class="token punctuation">.</span><span class="token function">length</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">,</span>d<span class="token punctuation">)</span><span class="token punctuation">;</span>
<span class="token keyword">for</span><span class="token punctuation">(</span>i<span class="token operator">=</span><span class="token number">0</span><span class="token punctuation">;</span>i<span class="token operator"><</span>kmin<span class="token punctuation">;</span>i<span class="token operator">++</span><span class="token punctuation">)</span>
<span class="token punctuation">{</span>
<span class="token keyword">if</span><span class="token punctuation">(</span>a<span class="token punctuation">.</span><span class="token function">at</span><span class="token punctuation">(</span>i<span class="token punctuation">)</span><span class="token operator">>=</span><span class="token number">48</span><span class="token operator">&&</span>a<span class="token punctuation">.</span><span class="token function">at</span><span class="token punctuation">(</span>i<span class="token punctuation">)</span><span class="token operator"><=</span><span class="token number">57</span><span class="token punctuation">)</span> a<span class="token punctuation">.</span><span class="token function">at</span><span class="token punctuation">(</span>i<span class="token punctuation">)</span><span class="token operator">-=</span><span class="token number">48</span><span class="token punctuation">;</span>
<span class="token keyword">if</span><span class="token punctuation">(</span>a<span class="token punctuation">.</span><span class="token function">at</span><span class="token punctuation">(</span>i<span class="token punctuation">)</span><span class="token operator">>=</span><span class="token number">97</span><span class="token operator">&&</span>a<span class="token punctuation">.</span><span class="token function">at</span><span class="token punctuation">(</span>i<span class="token punctuation">)</span><span class="token operator"><=</span><span class="token number">122</span><span class="token punctuation">)</span> a<span class="token punctuation">.</span><span class="token function">at</span><span class="token punctuation">(</span>i<span class="token punctuation">)</span><span class="token operator">-=</span><span class="token number">87</span><span class="token punctuation">;</span>
<span class="token keyword">if</span><span class="token punctuation">(</span>b<span class="token punctuation">.</span><span class="token function">at</span><span class="token punctuation">(</span>i<span class="token punctuation">)</span><span class="token operator">>=</span><span class="token number">48</span><span class="token operator">&&</span>b<span class="token punctuation">.</span><span class="token function">at</span><span class="token punctuation">(</span>i<span class="token punctuation">)</span><span class="token operator"><=</span><span class="token number">57</span><span class="token punctuation">)</span> b<span class="token punctuation">.</span><span class="token function">at</span><span class="token punctuation">(</span>i<span class="token punctuation">)</span><span class="token operator">-=</span><span class="token number">48</span><span class="token punctuation">;</span>
<span class="token keyword">if</span><span class="token punctuation">(</span>b<span class="token punctuation">.</span><span class="token function">at</span><span class="token punctuation">(</span>i<span class="token punctuation">)</span><span class="token operator">>=</span><span class="token number">97</span><span class="token operator">&&</span>b<span class="token punctuation">.</span><span class="token function">at</span><span class="token punctuation">(</span>i<span class="token punctuation">)</span><span class="token operator"><=</span><span class="token number">122</span><span class="token punctuation">)</span> b<span class="token punctuation">.</span><span class="token function">at</span><span class="token punctuation">(</span>i<span class="token punctuation">)</span><span class="token operator">-=</span><span class="token number">87</span><span class="token punctuation">;</span>
c<span class="token punctuation">.</span><span class="token function">at</span><span class="token punctuation">(</span>i<span class="token punctuation">)</span><span class="token operator">=</span>a<span class="token punctuation">.</span><span class="token function">at</span><span class="token punctuation">(</span>i<span class="token punctuation">)</span><span class="token operator">+</span>b<span class="token punctuation">.</span><span class="token function">at</span><span class="token punctuation">(</span>i<span class="token punctuation">)</span><span class="token punctuation">;</span>
<span class="token punctuation">}</span>
<span class="token keyword">for</span><span class="token punctuation">(</span>i<span class="token operator">=</span>kmin<span class="token punctuation">;</span>i<span class="token operator"><</span>kmax<span class="token operator">+</span><span class="token number">1</span><span class="token punctuation">;</span>i<span class="token operator">++</span><span class="token punctuation">)</span>
<span class="token punctuation">{</span>
<span class="token keyword">if</span><span class="token punctuation">(</span>c<span class="token punctuation">.</span><span class="token function">at</span><span class="token punctuation">(</span>i<span class="token punctuation">)</span><span class="token operator">>=</span><span class="token number">48</span><span class="token operator">&&</span>c<span class="token punctuation">.</span><span class="token function">at</span><span class="token punctuation">(</span>i<span class="token punctuation">)</span><span class="token operator"><=</span><span class="token number">57</span><span class="token punctuation">)</span> c<span class="token punctuation">.</span><span class="token function">at</span><span class="token punctuation">(</span>i<span class="token punctuation">)</span><span class="token operator">-=</span><span class="token number">48</span><span class="token punctuation">;</span>
<span class="token keyword">if</span><span class="token punctuation">(</span>c<span class="token punctuation">.</span><span class="token function">at</span><span class="token punctuation">(</span>i<span class="token punctuation">)</span><span class="token operator">>=</span><span class="token number">97</span><span class="token operator">&&</span>c<span class="token punctuation">.</span><span class="token function">at</span><span class="token punctuation">(</span>i<span class="token punctuation">)</span><span class="token operator"><=</span><span class="token number">122</span><span class="token punctuation">)</span> c<span class="token punctuation">.</span><span class="token function">at</span><span class="token punctuation">(</span>i<span class="token punctuation">)</span><span class="token operator">-=</span><span class="token number">87</span><span class="token punctuation">;</span>
<span class="token punctuation">}</span>
<span class="token keyword">for</span><span class="token punctuation">(</span>i<span class="token operator">=</span><span class="token number">0</span><span class="token punctuation">;</span>i<span class="token operator"><</span>kmax<span class="token punctuation">;</span>i<span class="token operator">++</span><span class="token punctuation">)</span>
<span class="token punctuation">{</span>
<span class="token keyword">if</span><span class="token punctuation">(</span>c<span class="token punctuation">.</span><span class="token function">at</span><span class="token punctuation">(</span>i<span class="token punctuation">)</span><span class="token operator">>=</span>n<span class="token punctuation">)</span>
<span class="token punctuation">{</span>
c<span class="token punctuation">.</span><span class="token function">at</span><span class="token punctuation">(</span>i<span class="token operator">+</span><span class="token number">1</span><span class="token punctuation">)</span><span class="token operator">+=</span>c<span class="token punctuation">.</span><span class="token function">at</span><span class="token punctuation">(</span>i<span class="token punctuation">)</span><span class="token operator">/</span>n<span class="token punctuation">;</span>
c<span class="token punctuation">.</span><span class="token function">at</span><span class="token punctuation">(</span>i<span class="token punctuation">)</span><span class="token operator">=</span>c<span class="token punctuation">.</span><span class="token function">at</span><span class="token punctuation">(</span>i<span class="token punctuation">)</span><span class="token operator">%</span>n<span class="token punctuation">;</span>
<span class="token punctuation">}</span>
<span class="token punctuation">}</span>
<span class="token keyword">if</span><span class="token punctuation">(</span>c<span class="token punctuation">.</span><span class="token function">at</span><span class="token punctuation">(</span>kmax<span class="token punctuation">)</span><span class="token operator">==</span><span class="token number">0</span><span class="token punctuation">)</span>
<span class="token punctuation">{</span>
c<span class="token punctuation">.</span><span class="token function">erase</span><span class="token punctuation">(</span>kmax<span class="token punctuation">,</span>kmax<span class="token operator">+</span><span class="token number">1</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
<span class="token punctuation">}</span>
<span class="token keyword">for</span><span class="token punctuation">(</span>i<span class="token operator">=</span><span class="token number">0</span><span class="token punctuation">;</span>i<span class="token operator"><</span>c<span class="token punctuation">.</span><span class="token function">length</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">;</span>i<span class="token operator">++</span><span class="token punctuation">)</span>
<span class="token punctuation">{</span>
<span class="token keyword">if</span><span class="token punctuation">(</span>c<span class="token punctuation">.</span><span class="token function">at</span><span class="token punctuation">(</span>i<span class="token punctuation">)</span><span class="token operator">>=</span><span class="token number">10</span><span class="token punctuation">)</span> c<span class="token punctuation">.</span><span class="token function">at</span><span class="token punctuation">(</span>i<span class="token punctuation">)</span><span class="token operator">+=</span><span class="token number">87</span><span class="token punctuation">;</span>
<span class="token keyword">if</span><span class="token punctuation">(</span>c<span class="token punctuation">.</span><span class="token function">at</span><span class="token punctuation">(</span>i<span class="token punctuation">)</span><span class="token operator"><</span><span class="token number">10</span><span class="token punctuation">)</span> c<span class="token punctuation">.</span><span class="token function">at</span><span class="token punctuation">(</span>i<span class="token punctuation">)</span><span class="token operator">+=</span><span class="token number">48</span><span class="token punctuation">;</span>
<span class="token punctuation">}</span>
<span class="token function">reverse</span><span class="token punctuation">(</span>c<span class="token punctuation">.</span><span class="token function">begin</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">,</span>c<span class="token punctuation">.</span><span class="token function">end</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
<span class="token keyword">return</span> c<span class="token punctuation">;</span>
<span class="token punctuation">}</span>
<span class="token keyword">int</span> <span class="token function">main</span><span class="token punctuation">(</span><span class="token punctuation">)</span>
<span class="token punctuation">{</span>
string a<span class="token punctuation">,</span>b<span class="token punctuation">;</span>
<span class="token keyword">while</span><span class="token punctuation">(</span>cin<span class="token operator">>></span>a<span class="token operator">>></span>b<span class="token punctuation">)</span>
<span class="token punctuation">{</span>
cout<span class="token operator"><<</span><span class="token function">add</span><span class="token punctuation">(</span>a<span class="token punctuation">,</span>b<span class="token punctuation">)</span><span class="token punctuation">;</span>
<span class="token punctuation">}</span>
<span class="token keyword">return</span> <span class="token number">0</span><span class="token punctuation">;</span>
<span class="token punctuation">}</span>
</pre><h4 class="mume-header" id="earth_asia-%E5%A4%A7%E6%95%B0%E5%87%8F%E6%B3%95-%E6%A8%A1%E6%9D%BF">🌏 大数减法 模板</h4>
<pre data-role="codeBlock" data-info="cpp" class="language-cpp"><span class="token macro property">#<span class="token directive keyword">include</span><span class="token string"><iostream></span></span>
<span class="token macro property">#<span class="token directive keyword">include</span><span class="token string"><string></span></span>
<span class="token macro property">#<span class="token directive keyword">include</span><span class="token string"><algorithm></span></span>
<span class="token keyword">using</span> <span class="token keyword">namespace</span> std<span class="token punctuation">;</span>
<span class="token macro property">#<span class="token directive keyword">define</span> n 10</span>
<span class="token comment">/*
大数减法
同样不支持负数加减
*/</span>
string <span class="token function">dezero</span><span class="token punctuation">(</span>string a<span class="token punctuation">)</span><span class="token comment">//用来去掉正数前面的0，也就是说可以输入000001类似这样的数字</span>
<span class="token punctuation">{</span>
<span class="token keyword">long</span> <span class="token keyword">int</span> i<span class="token punctuation">;</span>
<span class="token keyword">for</span><span class="token punctuation">(</span>i<span class="token operator">=</span><span class="token number">0</span><span class="token punctuation">;</span>i<span class="token operator"><</span>a<span class="token punctuation">.</span><span class="token function">length</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">;</span>i<span class="token operator">++</span><span class="token punctuation">)</span>
<span class="token punctuation">{</span>
<span class="token keyword">if</span><span class="token punctuation">(</span>a<span class="token punctuation">.</span><span class="token function">at</span><span class="token punctuation">(</span>i<span class="token punctuation">)</span><span class="token operator">></span><span class="token number">48</span><span class="token punctuation">)</span> <span class="token keyword">break</span><span class="token punctuation">;</span>
<span class="token punctuation">}</span>
<span class="token keyword">if</span><span class="token punctuation">(</span>i<span class="token operator">==</span>a<span class="token punctuation">.</span><span class="token function">length</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">)</span> <span class="token keyword">return</span> <span class="token string">"0"</span><span class="token punctuation">;</span>
a<span class="token punctuation">.</span><span class="token function">erase</span><span class="token punctuation">(</span><span class="token number">0</span><span class="token punctuation">,</span>i<span class="token punctuation">)</span><span class="token punctuation">;</span>
<span class="token keyword">return</span> a<span class="token punctuation">;</span>
<span class="token punctuation">}</span>
<span class="token keyword">int</span> <span class="token function">judge</span><span class="token punctuation">(</span>string a<span class="token punctuation">,</span>string b<span class="token punctuation">)</span><span class="token comment">//判断两个正数的大小</span>
<span class="token punctuation">{</span>
<span class="token keyword">if</span><span class="token punctuation">(</span>a<span class="token punctuation">.</span><span class="token function">length</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token operator">></span>b<span class="token punctuation">.</span><span class="token function">length</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">)</span> <span class="token keyword">return</span> <span class="token number">1</span><span class="token punctuation">;</span>
<span class="token keyword">if</span><span class="token punctuation">(</span>a<span class="token punctuation">.</span><span class="token function">length</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token operator"><</span>b<span class="token punctuation">.</span><span class="token function">length</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">)</span> <span class="token keyword">return</span> <span class="token operator">-</span><span class="token number">1</span><span class="token punctuation">;</span>
<span class="token keyword">long</span> <span class="token keyword">int</span> i<span class="token punctuation">;</span>
<span class="token keyword">for</span><span class="token punctuation">(</span>i<span class="token operator">=</span><span class="token number">0</span><span class="token punctuation">;</span>i<span class="token operator"><</span>a<span class="token punctuation">.</span><span class="token function">length</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">;</span>i<span class="token operator">++</span><span class="token punctuation">)</span>
<span class="token punctuation">{</span>
<span class="token keyword">if</span><span class="token punctuation">(</span>a<span class="token punctuation">.</span><span class="token function">at</span><span class="token punctuation">(</span>i<span class="token punctuation">)</span><span class="token operator">></span>b<span class="token punctuation">.</span><span class="token function">at</span><span class="token punctuation">(</span>i<span class="token punctuation">)</span><span class="token punctuation">)</span> <span class="token keyword">return</span> <span class="token number">1</span><span class="token punctuation">;</span>
<span class="token keyword">if</span><span class="token punctuation">(</span>a<span class="token punctuation">.</span><span class="token function">at</span><span class="token punctuation">(</span>i<span class="token punctuation">)</span><span class="token operator"><</span>b<span class="token punctuation">.</span><span class="token function">at</span><span class="token punctuation">(</span>i<span class="token punctuation">)</span><span class="token punctuation">)</span> <span class="token keyword">return</span> <span class="token operator">-</span><span class="token number">1</span><span class="token punctuation">;</span>
<span class="token punctuation">}</span>
<span class="token keyword">return</span> <span class="token number">0</span><span class="token punctuation">;</span>
<span class="token punctuation">}</span>
string <span class="token function">sub</span><span class="token punctuation">(</span>string a<span class="token punctuation">,</span>string b<span class="token punctuation">)</span><span class="token comment">//自然数减法</span>
<span class="token punctuation">{</span>
a<span class="token operator">=</span><span class="token function">dezero</span><span class="token punctuation">(</span>a<span class="token punctuation">)</span><span class="token punctuation">;</span>
b<span class="token operator">=</span><span class="token function">dezero</span><span class="token punctuation">(</span>b<span class="token punctuation">)</span><span class="token punctuation">;</span>
<span class="token keyword">long</span> <span class="token keyword">int</span> i<span class="token punctuation">,</span>j<span class="token operator">=</span><span class="token number">0</span><span class="token punctuation">;</span>
string c<span class="token operator">=</span><span class="token string">"0"</span><span class="token punctuation">;</span>
string c1<span class="token punctuation">,</span>c2<span class="token punctuation">;</span>
string d<span class="token operator">=</span><span class="token string">"-"</span><span class="token punctuation">;</span>
<span class="token keyword">if</span><span class="token punctuation">(</span><span class="token function">judge</span><span class="token punctuation">(</span>a<span class="token punctuation">,</span>b<span class="token punctuation">)</span><span class="token operator">==</span><span class="token number">0</span><span class="token punctuation">)</span> <span class="token keyword">return</span> c<span class="token punctuation">;</span>
<span class="token keyword">if</span><span class="token punctuation">(</span><span class="token function">judge</span><span class="token punctuation">(</span>a<span class="token punctuation">,</span>b<span class="token punctuation">)</span><span class="token operator">==</span><span class="token number">1</span><span class="token punctuation">)</span>
<span class="token punctuation">{</span>
c1<span class="token operator">=</span>a<span class="token punctuation">;</span>
c2<span class="token operator">=</span>b<span class="token punctuation">;</span>
<span class="token punctuation">}</span>
<span class="token keyword">if</span><span class="token punctuation">(</span><span class="token function">judge</span><span class="token punctuation">(</span>a<span class="token punctuation">,</span>b<span class="token punctuation">)</span><span class="token operator">==</span><span class="token operator">-</span><span class="token number">1</span><span class="token punctuation">)</span>
<span class="token punctuation">{</span>
c1<span class="token operator">=</span>b<span class="token punctuation">;</span>
c2<span class="token operator">=</span>a<span class="token punctuation">;</span>
j<span class="token operator">=</span><span class="token operator">-</span><span class="token number">1</span><span class="token punctuation">;</span>
<span class="token punctuation">}</span>
<span class="token function">reverse</span><span class="token punctuation">(</span>c1<span class="token punctuation">.</span><span class="token function">begin</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">,</span>c1<span class="token punctuation">.</span><span class="token function">end</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
<span class="token function">reverse</span><span class="token punctuation">(</span>c2<span class="token punctuation">.</span><span class="token function">begin</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">,</span>c2<span class="token punctuation">.</span><span class="token function">end</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
<span class="token keyword">for</span><span class="token punctuation">(</span>i<span class="token operator">=</span><span class="token number">0</span><span class="token punctuation">;</span>i<span class="token operator"><</span>c2<span class="token punctuation">.</span><span class="token function">length</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">;</span>i<span class="token operator">++</span><span class="token punctuation">)</span>
<span class="token punctuation">{</span>
<span class="token keyword">if</span><span class="token punctuation">(</span>c2<span class="token punctuation">.</span><span class="token function">at</span><span class="token punctuation">(</span>i<span class="token punctuation">)</span><span class="token operator">>=</span><span class="token number">48</span><span class="token operator">&&</span>c2<span class="token punctuation">.</span><span class="token function">at</span><span class="token punctuation">(</span>i<span class="token punctuation">)</span><span class="token operator"><=</span><span class="token number">57</span><span class="token punctuation">)</span> c2<span class="token punctuation">.</span><span class="token function">at</span><span class="token punctuation">(</span>i<span class="token punctuation">)</span><span class="token operator">-=</span><span class="token number">48</span><span class="token punctuation">;</span>
<span class="token keyword">if</span><span class="token punctuation">(</span>c2<span class="token punctuation">.</span><span class="token function">at</span><span class="token punctuation">(</span>i<span class="token punctuation">)</span><span class="token operator">>=</span><span class="token number">97</span><span class="token operator">&&</span>c2<span class="token punctuation">.</span><span class="token function">at</span><span class="token punctuation">(</span>i<span class="token punctuation">)</span><span class="token operator"><=</span><span class="token number">122</span><span class="token punctuation">)</span> c2<span class="token punctuation">.</span><span class="token function">at</span><span class="token punctuation">(</span>i<span class="token punctuation">)</span><span class="token operator">-=</span><span class="token number">87</span><span class="token punctuation">;</span>
<span class="token punctuation">}</span>
<span class="token keyword">for</span><span class="token punctuation">(</span>i<span class="token operator">=</span><span class="token number">0</span><span class="token punctuation">;</span>i<span class="token operator"><</span>c1<span class="token punctuation">.</span><span class="token function">length</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">;</span>i<span class="token operator">++</span><span class="token punctuation">)</span>
<span class="token punctuation">{</span>
<span class="token keyword">if</span><span class="token punctuation">(</span>c1<span class="token punctuation">.</span><span class="token function">at</span><span class="token punctuation">(</span>i<span class="token punctuation">)</span><span class="token operator">>=</span><span class="token number">48</span><span class="token operator">&&</span>c1<span class="token punctuation">.</span><span class="token function">at</span><span class="token punctuation">(</span>i<span class="token punctuation">)</span><span class="token operator"><=</span><span class="token number">57</span><span class="token punctuation">)</span> c1<span class="token punctuation">.</span><span class="token function">at</span><span class="token punctuation">(</span>i<span class="token punctuation">)</span><span class="token operator">-=</span><span class="token number">48</span><span class="token punctuation">;</span>
<span class="token keyword">if</span><span class="token punctuation">(</span>c1<span class="token punctuation">.</span><span class="token function">at</span><span class="token punctuation">(</span>i<span class="token punctuation">)</span><span class="token operator">>=</span><span class="token number">97</span><span class="token operator">&&</span>c1<span class="token punctuation">.</span><span class="token function">at</span><span class="token punctuation">(</span>i<span class="token punctuation">)</span><span class="token operator"><=</span><span class="token number">122</span><span class="token punctuation">)</span> c1<span class="token punctuation">.</span><span class="token function">at</span><span class="token punctuation">(</span>i<span class="token punctuation">)</span><span class="token operator">-=</span><span class="token number">87</span><span class="token punctuation">;</span>
<span class="token punctuation">}</span>
<span class="token keyword">for</span><span class="token punctuation">(</span>i<span class="token operator">=</span><span class="token number">0</span><span class="token punctuation">;</span>i<span class="token operator"><</span>c2<span class="token punctuation">.</span><span class="token function">length</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">;</span>i<span class="token operator">++</span><span class="token punctuation">)</span>
<span class="token punctuation">{</span>
c1<span class="token punctuation">.</span><span class="token function">at</span><span class="token punctuation">(</span>i<span class="token punctuation">)</span><span class="token operator">=</span>c1<span class="token punctuation">.</span><span class="token function">at</span><span class="token punctuation">(</span>i<span class="token punctuation">)</span><span class="token operator">-</span>c2<span class="token punctuation">.</span><span class="token function">at</span><span class="token punctuation">(</span>i<span class="token punctuation">)</span><span class="token punctuation">;</span>
<span class="token punctuation">}</span>
<span class="token keyword">for</span><span class="token punctuation">(</span>i<span class="token operator">=</span><span class="token number">0</span><span class="token punctuation">;</span>i<span class="token operator"><</span>c1<span class="token punctuation">.</span><span class="token function">length</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token operator">-</span><span class="token number">1</span><span class="token punctuation">;</span>i<span class="token operator">++</span><span class="token punctuation">)</span>
<span class="token punctuation">{</span>
<span class="token keyword">if</span><span class="token punctuation">(</span>c1<span class="token punctuation">.</span><span class="token function">at</span><span class="token punctuation">(</span>i<span class="token punctuation">)</span><span class="token operator"><</span><span class="token number">0</span><span class="token punctuation">)</span>
<span class="token punctuation">{</span>
c1<span class="token punctuation">.</span><span class="token function">at</span><span class="token punctuation">(</span>i<span class="token punctuation">)</span><span class="token operator">+=</span>n<span class="token punctuation">;</span>
c1<span class="token punctuation">.</span><span class="token function">at</span><span class="token punctuation">(</span>i<span class="token operator">+</span><span class="token number">1</span><span class="token punctuation">)</span><span class="token operator">--</span><span class="token punctuation">;</span>
<span class="token punctuation">}</span>
<span class="token punctuation">}</span>
<span class="token keyword">for</span><span class="token punctuation">(</span>i<span class="token operator">=</span>c1<span class="token punctuation">.</span><span class="token function">length</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token operator">-</span><span class="token number">1</span><span class="token punctuation">;</span>i<span class="token operator">>=</span><span class="token number">0</span><span class="token punctuation">;</span>i<span class="token operator">--</span><span class="token punctuation">)</span>
<span class="token punctuation">{</span>
<span class="token keyword">if</span><span class="token punctuation">(</span>c1<span class="token punctuation">.</span><span class="token function">at</span><span class="token punctuation">(</span>i<span class="token punctuation">)</span><span class="token operator">></span><span class="token number">0</span><span class="token punctuation">)</span> <span class="token keyword">break</span><span class="token punctuation">;</span>
<span class="token punctuation">}</span>
c1<span class="token punctuation">.</span><span class="token function">erase</span><span class="token punctuation">(</span>i<span class="token operator">+</span><span class="token number">1</span><span class="token punctuation">,</span>c1<span class="token punctuation">.</span><span class="token function">length</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
<span class="token keyword">for</span><span class="token punctuation">(</span>i<span class="token operator">=</span><span class="token number">0</span><span class="token punctuation">;</span>i<span class="token operator"><</span>c1<span class="token punctuation">.</span><span class="token function">length</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">;</span>i<span class="token operator">++</span><span class="token punctuation">)</span>
<span class="token punctuation">{</span>
<span class="token keyword">if</span><span class="token punctuation">(</span>c1<span class="token punctuation">.</span><span class="token function">at</span><span class="token punctuation">(</span>i<span class="token punctuation">)</span><span class="token operator">>=</span><span class="token number">10</span><span class="token punctuation">)</span> c1<span class="token punctuation">.</span><span class="token function">at</span><span class="token punctuation">(</span>i<span class="token punctuation">)</span><span class="token operator">+=</span><span class="token number">87</span><span class="token punctuation">;</span>
<span class="token keyword">if</span><span class="token punctuation">(</span>c1<span class="token punctuation">.</span><span class="token function">at</span><span class="token punctuation">(</span>i<span class="token punctuation">)</span><span class="token operator"><</span><span class="token number">10</span><span class="token punctuation">)</span> c1<span class="token punctuation">.</span><span class="token function">at</span><span class="token punctuation">(</span>i<span class="token punctuation">)</span><span class="token operator">+=</span><span class="token number">48</span><span class="token punctuation">;</span>
<span class="token punctuation">}</span>
<span class="token function">reverse</span><span class="token punctuation">(</span>c1<span class="token punctuation">.</span><span class="token function">begin</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">,</span>c1<span class="token punctuation">.</span><span class="token function">end</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
<span class="token keyword">if</span><span class="token punctuation">(</span>j<span class="token operator">==</span><span class="token operator">-</span><span class="token number">1</span><span class="token punctuation">)</span> c1<span class="token punctuation">.</span><span class="token function">insert</span><span class="token punctuation">(</span><span class="token number">0</span><span class="token punctuation">,</span>d<span class="token punctuation">)</span><span class="token punctuation">;</span>
<span class="token keyword">return</span> c1<span class="token punctuation">;</span>
<span class="token punctuation">}</span>
<span class="token keyword">int</span> <span class="token function">main</span><span class="token punctuation">(</span><span class="token punctuation">)</span>
<span class="token punctuation">{</span>
string a<span class="token punctuation">,</span>b<span class="token punctuation">;</span>
<span class="token keyword">while</span><span class="token punctuation">(</span>cout<span class="token operator"><<</span><span class="token string">"input:"</span><span class="token operator">&&</span>cin<span class="token operator">>></span>a<span class="token operator">>></span>b<span class="token punctuation">)</span>
<span class="token punctuation">{</span>
cout<span class="token operator"><<</span><span class="token string">"output:"</span><span class="token operator"><<</span><span class="token function">sub</span><span class="token punctuation">(</span>a<span class="token punctuation">,</span>b<span class="token punctuation">)</span><span class="token operator"><<</span>endl<span class="token punctuation">;</span>
<span class="token punctuation">}</span>
<span class="token keyword">return</span> <span class="token number">0</span><span class="token punctuation">;</span>
<span class="token punctuation">}</span>
</pre><h4 class="mume-header" id="earth_asia-%E5%A4%A7%E6%95%B0%E4%B9%98%E6%B3%95-%E6%A8%A1%E6%9D%BF">🌏 大数乘法 模板</h4>
<pre data-role="codeBlock" data-info="cpp" class="language-cpp"><span class="token macro property">#<span class="token directive keyword">include</span><span class="token string"><iostream></span></span>
<span class="token macro property">#<span class="token directive keyword">include</span><span class="token string"><string></span></span>
<span class="token macro property">#<span class="token directive keyword">include</span><span class="token string"><algorithm></span></span>
<span class="token keyword">using</span> <span class="token keyword">namespace</span> std<span class="token punctuation">;</span>
<span class="token macro property">#<span class="token directive keyword">define</span> n 10</span>
<span class="token comment">/*
大数乘法
整数乘法，正整数，负整数，0均可，主要思想就是乘法的笔算方法
*/</span>
string <span class="token function">dezero</span><span class="token punctuation">(</span>string a<span class="token punctuation">)</span><span class="token comment">//用来去掉正数前面的0，也就是说可以输入000001类似这样的数字</span>
<span class="token punctuation">{</span>
<span class="token keyword">long</span> <span class="token keyword">int</span> i<span class="token punctuation">;</span>
<span class="token keyword">for</span><span class="token punctuation">(</span>i<span class="token operator">=</span><span class="token number">0</span><span class="token punctuation">;</span>i<span class="token operator"><</span>a<span class="token punctuation">.</span><span class="token function">length</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">;</span>i<span class="token operator">++</span><span class="token punctuation">)</span>
<span class="token punctuation">{</span>
<span class="token keyword">if</span><span class="token punctuation">(</span>a<span class="token punctuation">.</span><span class="token function">at</span><span class="token punctuation">(</span>i<span class="token punctuation">)</span><span class="token operator">></span><span class="token number">48</span><span class="token punctuation">)</span> <span class="token keyword">break</span><span class="token punctuation">;</span>
<span class="token punctuation">}</span>
<span class="token keyword">if</span><span class="token punctuation">(</span>i<span class="token operator">==</span>a<span class="token punctuation">.</span><span class="token function">length</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">)</span> <span class="token keyword">return</span> <span class="token string">"0"</span><span class="token punctuation">;</span>
a<span class="token punctuation">.</span><span class="token function">erase</span><span class="token punctuation">(</span><span class="token number">0</span><span class="token punctuation">,</span>i<span class="token punctuation">)</span><span class="token punctuation">;</span>
<span class="token keyword">return</span> a<span class="token punctuation">;</span>
<span class="token punctuation">}</span>
string <span class="token function">multiply</span><span class="token punctuation">(</span>string a<span class="token punctuation">,</span>string b<span class="token punctuation">)</span><span class="token comment">//整数</span>
<span class="token punctuation">{</span>
<span class="token keyword">long</span> <span class="token keyword">int</span> i<span class="token punctuation">,</span>j<span class="token punctuation">,</span>k<span class="token punctuation">,</span>yao<span class="token operator">=</span><span class="token number">0</span><span class="token punctuation">,</span>kai<span class="token punctuation">;</span>
string c1<span class="token punctuation">,</span>c2<span class="token punctuation">;</span>
string c3<span class="token operator">=</span>a<span class="token operator">+</span>b<span class="token punctuation">;</span>
<span class="token keyword">if</span><span class="token punctuation">(</span>a<span class="token punctuation">.</span><span class="token function">at</span><span class="token punctuation">(</span><span class="token number">0</span><span class="token punctuation">)</span><span class="token operator">==</span><span class="token string">'-'</span><span class="token punctuation">)</span>
<span class="token punctuation">{</span>
a<span class="token punctuation">.</span><span class="token function">erase</span><span class="token punctuation">(</span><span class="token number">0</span><span class="token punctuation">,</span><span class="token number">1</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
yao<span class="token operator">++</span><span class="token punctuation">;</span>
<span class="token punctuation">}</span>
<span class="token keyword">if</span><span class="token punctuation">(</span>b<span class="token punctuation">.</span><span class="token function">at</span><span class="token punctuation">(</span><span class="token number">0</span><span class="token punctuation">)</span><span class="token operator">==</span><span class="token string">'-'</span><span class="token punctuation">)</span>
<span class="token punctuation">{</span>
b<span class="token punctuation">.</span><span class="token function">erase</span><span class="token punctuation">(</span><span class="token number">0</span><span class="token punctuation">,</span><span class="token number">1</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
yao<span class="token operator">++</span><span class="token punctuation">;</span>
<span class="token punctuation">}</span>
a<span class="token operator">=</span><span class="token function">dezero</span><span class="token punctuation">(</span>a<span class="token punctuation">)</span><span class="token punctuation">;</span>
b<span class="token operator">=</span><span class="token function">dezero</span><span class="token punctuation">(</span>b<span class="token punctuation">)</span><span class="token punctuation">;</span>
<span class="token keyword">if</span><span class="token punctuation">(</span>a<span class="token punctuation">.</span><span class="token function">at</span><span class="token punctuation">(</span><span class="token number">0</span><span class="token punctuation">)</span><span class="token operator">==</span><span class="token number">48</span><span class="token operator">||</span>b<span class="token punctuation">.</span><span class="token function">at</span><span class="token punctuation">(</span><span class="token number">0</span><span class="token punctuation">)</span><span class="token operator">==</span><span class="token number">48</span><span class="token punctuation">)</span> <span class="token keyword">return</span> <span class="token string">"0"</span><span class="token punctuation">;</span>
<span class="token keyword">if</span><span class="token punctuation">(</span>a<span class="token punctuation">.</span><span class="token function">length</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token operator">></span>b<span class="token punctuation">.</span><span class="token function">length</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">)</span>
<span class="token punctuation">{</span>
c1<span class="token operator">=</span>a<span class="token punctuation">;</span>
c2<span class="token operator">=</span>b<span class="token punctuation">;</span>
<span class="token punctuation">}</span>
<span class="token keyword">else</span>
<span class="token punctuation">{</span>
c1<span class="token operator">=</span>b<span class="token punctuation">;</span>
c2<span class="token operator">=</span>a<span class="token punctuation">;</span>
<span class="token punctuation">}</span>
<span class="token function">reverse</span><span class="token punctuation">(</span>c1<span class="token punctuation">.</span><span class="token function">begin</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">,</span>c1<span class="token punctuation">.</span><span class="token function">end</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
<span class="token function">reverse</span><span class="token punctuation">(</span>c2<span class="token punctuation">.</span><span class="token function">begin</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">,</span>c2<span class="token punctuation">.</span><span class="token function">end</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
<span class="token keyword">for</span><span class="token punctuation">(</span>i<span class="token operator">=</span><span class="token number">0</span><span class="token punctuation">;</span>i<span class="token operator"><</span>c2<span class="token punctuation">.</span><span class="token function">length</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">;</span>i<span class="token operator">++</span><span class="token punctuation">)</span>
<span class="token punctuation">{</span>
<span class="token keyword">if</span><span class="token punctuation">(</span>c2<span class="token punctuation">.</span><span class="token function">at</span><span class="token punctuation">(</span>i<span class="token punctuation">)</span><span class="token operator">>=</span><span class="token number">48</span><span class="token operator">&&</span>c2<span class="token punctuation">.</span><span class="token function">at</span><span class="token punctuation">(</span>i<span class="token punctuation">)</span><span class="token operator"><=</span><span class="token number">57</span><span class="token punctuation">)</span> c2<span class="token punctuation">.</span><span class="token function">at</span><span class="token punctuation">(</span>i<span class="token punctuation">)</span><span class="token operator">-=</span><span class="token number">48</span><span class="token punctuation">;</span>
<span class="token keyword">if</span><span class="token punctuation">(</span>c2<span class="token punctuation">.</span><span class="token function">at</span><span class="token punctuation">(</span>i<span class="token punctuation">)</span><span class="token operator">>=</span><span class="token number">97</span><span class="token operator">&&</span>c2<span class="token punctuation">.</span><span class="token function">at</span><span class="token punctuation">(</span>i<span class="token punctuation">)</span><span class="token operator"><=</span><span class="token number">122</span><span class="token punctuation">)</span> c2<span class="token punctuation">.</span><span class="token function">at</span><span class="token punctuation">(</span>i<span class="token punctuation">)</span><span class="token operator">-=</span><span class="token number">87</span><span class="token punctuation">;</span>
<span class="token punctuation">}</span>
<span class="token keyword">for</span><span class="token punctuation">(</span>i<span class="token operator">=</span><span class="token number">0</span><span class="token punctuation">;</span>i<span class="token operator"><</span>c1<span class="token punctuation">.</span><span class="token function">length</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">;</span>i<span class="token operator">++</span><span class="token punctuation">)</span>
<span class="token punctuation">{</span>
<span class="token keyword">if</span><span class="token punctuation">(</span>c1<span class="token punctuation">.</span><span class="token function">at</span><span class="token punctuation">(</span>i<span class="token punctuation">)</span><span class="token operator">>=</span><span class="token number">48</span><span class="token operator">&&</span>c1<span class="token punctuation">.</span><span class="token function">at</span><span class="token punctuation">(</span>i<span class="token punctuation">)</span><span class="token operator"><=</span><span class="token number">57</span><span class="token punctuation">)</span> c1<span class="token punctuation">.</span><span class="token function">at</span><span class="token punctuation">(</span>i<span class="token punctuation">)</span><span class="token operator">-=</span><span class="token number">48</span><span class="token punctuation">;</span>
<span class="token keyword">if</span><span class="token punctuation">(</span>c1<span class="token punctuation">.</span><span class="token function">at</span><span class="token punctuation">(</span>i<span class="token punctuation">)</span><span class="token operator">>=</span><span class="token number">97</span><span class="token operator">&&</span>c1<span class="token punctuation">.</span><span class="token function">at</span><span class="token punctuation">(</span>i<span class="token punctuation">)</span><span class="token operator"><=</span><span class="token number">122</span><span class="token punctuation">)</span> c1<span class="token punctuation">.</span><span class="token function">at</span><span class="token punctuation">(</span>i<span class="token punctuation">)</span><span class="token operator">-=</span><span class="token number">87</span><span class="token punctuation">;</span>
<span class="token punctuation">}</span>
<span class="token keyword">for</span><span class="token punctuation">(</span>i<span class="token operator">=</span><span class="token number">0</span><span class="token punctuation">;</span>i<span class="token operator"><</span>c3<span class="token punctuation">.</span><span class="token function">length</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">;</span>i<span class="token operator">++</span><span class="token punctuation">)</span> c3<span class="token punctuation">.</span><span class="token function">at</span><span class="token punctuation">(</span>i<span class="token punctuation">)</span><span class="token operator">=</span><span class="token number">0</span><span class="token punctuation">;</span>
<span class="token keyword">for</span><span class="token punctuation">(</span>i<span class="token operator">=</span><span class="token number">0</span><span class="token punctuation">;</span>i<span class="token operator"><</span>c2<span class="token punctuation">.</span><span class="token function">length</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">;</span>i<span class="token operator">++</span><span class="token punctuation">)</span>
<span class="token punctuation">{</span>
<span class="token keyword">for</span><span class="token punctuation">(</span>j<span class="token operator">=</span><span class="token number">0</span><span class="token punctuation">;</span>j<span class="token operator"><</span>c1<span class="token punctuation">.</span><span class="token function">length</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">;</span>j<span class="token operator">++</span><span class="token punctuation">)</span>
<span class="token punctuation">{</span>
kai<span class="token operator">=</span>c2<span class="token punctuation">.</span><span class="token function">at</span><span class="token punctuation">(</span>i<span class="token punctuation">)</span><span class="token operator">*</span>c1<span class="token punctuation">.</span><span class="token function">at</span><span class="token punctuation">(</span>j<span class="token punctuation">)</span><span class="token punctuation">;</span>
c3<span class="token punctuation">.</span><span class="token function">at</span><span class="token punctuation">(</span>i<span class="token operator">+</span>j<span class="token operator">+</span><span class="token number">1</span><span class="token punctuation">)</span><span class="token operator">+=</span>kai<span class="token operator">/</span>n<span class="token punctuation">;</span>
c3<span class="token punctuation">.</span><span class="token function">at</span><span class="token punctuation">(</span>i<span class="token operator">+</span>j<span class="token punctuation">)</span><span class="token operator">+=</span>kai<span class="token operator">%</span>n<span class="token punctuation">;</span>
<span class="token keyword">for</span><span class="token punctuation">(</span>k<span class="token operator">=</span>i<span class="token operator">+</span>j<span class="token punctuation">;</span>k<span class="token operator"><</span>c3<span class="token punctuation">.</span><span class="token function">length</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token operator">-</span><span class="token number">1</span><span class="token punctuation">;</span>k<span class="token operator">++</span><span class="token punctuation">)</span>
<span class="token punctuation">{</span>
<span class="token keyword">if</span><span class="token punctuation">(</span>c3<span class="token punctuation">.</span><span class="token function">at</span><span class="token punctuation">(</span>k<span class="token punctuation">)</span><span class="token operator">>=</span>n<span class="token punctuation">)</span>
<span class="token punctuation">{</span>
c3<span class="token punctuation">.</span><span class="token function">at</span><span class="token punctuation">(</span>k<span class="token operator">+</span><span class="token number">1</span><span class="token punctuation">)</span><span class="token operator">+=</span>c3<span class="token punctuation">.</span><span class="token function">at</span><span class="token punctuation">(</span>k<span class="token punctuation">)</span><span class="token operator">/</span>n<span class="token punctuation">;</span>
c3<span class="token punctuation">.</span><span class="token function">at</span><span class="token punctuation">(</span>k<span class="token punctuation">)</span><span class="token operator">=</span>c3<span class="token punctuation">.</span><span class="token function">at</span><span class="token punctuation">(</span>k<span class="token punctuation">)</span><span class="token operator">%</span>n<span class="token punctuation">;</span>
<span class="token punctuation">}</span>
<span class="token keyword">else</span>
<span class="token punctuation">{</span>
<span class="token keyword">break</span><span class="token punctuation">;</span>
<span class="token punctuation">}</span>