93 lines
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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> |