93 lines
21 KiB
HTML
93 lines
21 KiB
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<!DOCTYPE html><html><head>
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<title>U232520</title>
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<style>
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code[class*=language-],pre[class*=language-]{color:#333;background:0 0;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}pre[class*=language-]{padding:.8em;overflow:auto;border-radius:3px;background:#f5f5f5}:not(pre)>code[class*=language-]{padding:.1em;border-radius:.3em;white-space:normal;background:#f5f5f5}.token.blockquote,.token.comment{color:#969896}.token.cdata{color:#183691}.token.doctype,.token.macro.property,.token.punctuation,.token.variable{color:#333}.token.builtin,.token.important,.token.keyword,.token.operator,.token.rule{color:#a71d5d}.token.attr-value,.token.regex,.token.string,.token.url{color:#183691}.token.atrule,.token.boolean,.token.code,.token.command,.token.constant,.token.entity,.token.number,.token.property,.token.symbol{color:#0086b3}.token.prolog,.token.selector,.token.tag{color:#63a35c}.token.attr-name,.token.class,.token.class-name,.token.function,.token.id,.token.namespace,.token.pseudo-class,.token.pseudo-element,.token.url-reference .token.variable{color:#795da3}.token.entity{cursor:help}.token.title,.token.title .token.punctuation{font-weight:700;color:#1d3e81}.token.list{color:#ed6a43}.token.inserted{background-color:#eaffea;color:#55a532}.token.deleted{background-color:#ffecec;color:#bd2c00}.token.bold{font-weight:700}.token.italic{font-style:italic}.language-json .token.property{color:#183691}.language-markup .token.tag .token.punctuation{color:#333}.language-css .token.function,code.language-css{color:#0086b3}.language-yaml .token.atrule{color:#63a35c}code.language-yaml{color:#183691}.language-ruby .token.function{color:#333}.language-markdown .token.url{color:#795da3}.language-makefile .token.symbol{color:#795da3}.language-makefile .token.variable{color:#183691}.language-makefile .token.builtin{color:#0086b3}.language-bash .token.keyword{color:#0086b3}pre[data-line]{position:relative;padding:1em 0 1em 3em}pre[data-line] .line-highlight-wrapper{position:absolute;top:0;left:0;background-color:transparent;display:block;width:100%}pre[data-line] .line-highlight{position:absolute;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}pre[data-line] .line-highlight:before,pre[data-line] .line-highlight[data-end]:after{content:attr(data-start);position:absolute;top:.4em;left:.6em;min-width:1em;padding:0 .5em;background-color:hsla(24,20%,50%,.4);color:#f4f1ef;font:bold 65%/1.5 sans-serif;text-align:center;vertical-align:.3em;border-radius:999px;text-shadow:none;box-shadow:0 1px #fff}pre[data-line] .line-highlight[data-end]:after{content:attr(data-end);top:auto;bottom:.4em}html body{font-family:'Helvetica Neue',Helvetica,'Segoe UI',Arial,freesans,sans-serif;font-size:16px;line-height:1.6;color:#333;background-color:#fff;overflow:initial;box-sizing:border-box;word-wrap:break-word}html body>:first-child{margin-top:0}html body h1,html body h2,html body h3,html body h4,html body h5,html body h6{line-height:1.2;margin-top:1em;margin-bottom:16px;color:#000}html body h1{font-size:2.25em;font-weight:300;padding-bottom:.3em}html body h2{font-size:1.75em;font-weight:400;padding-bottom:.3em}html body h3{font-size:1.5em;font-weight:500}html body h4{font-size:1.25em;font-weight:600}html body h5{font-size:1.1em;font-weight:600}html body h6{font-size:1em;font-weight:600}html body h1,html body h2,html body h3,html body h4,html body h5{font-weight:600}html body h5{font-size:1em}html body h6{color:#5c5c5c}html body strong{color:#000}html body del{color:#5c5c5c}html body a:not([href]){color:inherit;text-decoration:none}html body a{color:#08c;text-decoration:none}html body a:hover{color:#00a3f5;text-decoration:none}html body img{max-width:100%}html body>p{margin-top:0;margin-bottom:16px;word-wrap:break-word}html body>ol,html
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/* Please visit the URL below for more information: */
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/* https://shd101wyy.github.io/markdown-preview-enhanced/#/customize-css */
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</style>
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<!-- The content below will be included at the end of the <head> element. --><script type="text/javascript">
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document.addEventListener("DOMContentLoaded", function () {
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// your code here
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});
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</script></head><body for="html-export">
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<div class="crossnote markdown-preview ">
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<h1 id="黑色矩形">黑色矩形 </h1>
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<h2 id="题目描述">题目描述 </h2>
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<p>一个 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>n</mi><mo>×</mo><mi>n</mi></mrow><annotation encoding="application/x-tex">n\times n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord mathnormal">n</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal">n</span></span></span></span> 的黑白网格。定义黑色矩形为：</p>
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<ul>
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<li>矩形由至少2个格子构成，且构成矩形的格子都为黑色</li>
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</ul>
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<p>现在你要选择2个不重叠（没有公共格子）的黑色矩形，问有多少种方案，对 <code>1e4+7</code> 取模。2种方案不同，当且仅当选择的黑色矩形集合不同。</p>
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<p><img src="https://cdn.luogu.com.cn/upload/image_hosting/h7lgmovq.png" alt=""></p>
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<p>左图是2个不是黑色举行的例子；右图是3个是黑色矩形的例子。</p>
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<p>参见样例1解释。</p>
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<h2 id="输入格式">输入格式 </h2>
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<p>第一行1个整数 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>n</mi></mrow><annotation encoding="application/x-tex">n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal">n</span></span></span></span></p>
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<p>接下来 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>n</mi></mrow><annotation encoding="application/x-tex">n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal">n</span></span></span></span> 行，每行1个长度为 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>n</mi></mrow><annotation encoding="application/x-tex">n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal">n</span></span></span></span> 的01串，<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1</mn></mrow><annotation encoding="application/x-tex">1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">1</span></span></span></span> 代表黑色，<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>0</mn></mrow><annotation encoding="application/x-tex">0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">0</span></span></span></span> 代表白色。</p>
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<h2 id="输出格式">输出格式 </h2>
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<p>输出1个整数代表答案，对 <code>1e4+7</code> 取模。</p>
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<h2 id="样例-1">样例 #1 </h2>
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<h3 id="样例输入-1">样例输入 #1 </h3>
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<pre data-role="codeBlock" data-info="" class="language-text"><code>2
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11
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11
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</code></pre><h3 id="样例输出-1">样例输出 #1 </h3>
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<pre data-role="codeBlock" data-info="" class="language-text"><code>2
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</code></pre><h2 id="样例-2">样例 #2 </h2>
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<h3 id="样例输入-2">样例输入 #2 </h3>
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<pre data-role="codeBlock" data-info="" class="language-text"><code>3
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110
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110
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100
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</code></pre><h3 id="样例输出-2">样例输出 #2 </h3>
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<pre data-role="codeBlock" data-info="" class="language-text"><code>5
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</code></pre><h2 id="样例-3">样例 #3 </h2>
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<h3 id="样例输入-3">样例输入 #3 </h3>
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<pre data-role="codeBlock" data-info="" class="language-text"><code>5
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01100
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00100
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01100
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00000
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11000
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</code></pre><h3 id="样例输出-3">样例输出 #3 </h3>
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<pre data-role="codeBlock" data-info="" class="language-text"><code>8
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</code></pre><h2 id="样例-4">样例 #4 </h2>
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<h3 id="样例输入-4">样例输入 #4 </h3>
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<pre data-role="codeBlock" data-info="" class="language-text"><code>见下发文件
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</code></pre><h3 id="样例输出-4">样例输出 #4 </h3>
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<pre data-role="codeBlock" data-info="" class="language-text"><code>见下发文件
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</code></pre><h2 id="提示">提示 </h2>
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<h4 id="样例1解释">样例1解释 </h4>
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<p>共两种方案：选择第1行和第2行，或者选择第1列和第2列</p>
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<h4 id="数据范围">数据范围 </h4>
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<p>对于所有数据，<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1</mn><mo>≤</mo><mi>n</mi><mo>≤</mo><mn>1500</mn></mrow><annotation encoding="application/x-tex">1\le n \le 1500</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7804em;vertical-align:-0.136em;"></span><span class="mord">1</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≤</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7719em;vertical-align:-0.136em;"></span><span class="mord mathnormal">n</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≤</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">1500</span></span></span></span></p>
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<p>subtask1(20pts)：<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>n</mi><mo>≤</mo><mn>10</mn></mrow><annotation encoding="application/x-tex">n\le 10</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7719em;vertical-align:-0.136em;"></span><span class="mord mathnormal">n</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≤</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">10</span></span></span></span></p>
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<p>subtask2(20pts)：<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>n</mi><mo>≤</mo><mn>50</mn></mrow><annotation encoding="application/x-tex">n\le 50</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7719em;vertical-align:-0.136em;"></span><span class="mord mathnormal">n</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≤</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">50</span></span></span></span></p>
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<p>subtask3(20pts)：<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>n</mi><mo>≤</mo><mn>500</mn></mrow><annotation encoding="application/x-tex">n\le 500</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7719em;vertical-align:-0.136em;"></span><span class="mord mathnormal">n</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≤</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">500</span></span></span></span></p>
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<p>subtask4(10pts)：网格中全部为黑色</p>
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<p>subtask5(30pts)：无特殊限制</p>
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</div>
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</body></html>
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