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 哈哈，简单到爆，没有。 ### 引入 并查集是一种快到爆炸的集合算法，可以进行两项基本操作：合并两个集合（并）、查询两个参数是否在一个集合内（查）。这也是它名字的由来。">
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 哈哈，简单到爆，没有。 ### 引入 并查集是一种快到爆炸的集合算法，可以进行两项基本操作：合并两个集合（并）、查询两个参数是否在一个集合内（查）。这也是它名字的由来。">
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          并查集
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<p>&#x54C8;&#x54C8;&#xFF0C;&#x7B80;&#x5355;&#x5230;&#x7206;&#xFF0C;&#x6CA1;&#x6709;&#x3002; ### &#x5F15;&#x5165; &#x5E76;&#x67E5;&#x96C6;&#x662F;&#x4E00;&#x79CD;&#x5FEB;&#x5230;&#x7206;&#x70B8;&#x7684;&#x96C6;&#x5408;&#x7B97;&#x6CD5;&#xFF0C;&#x53EF;&#x4EE5;&#x8FDB;&#x884C;&#x4E24;&#x9879;&#x57FA;&#x672C;&#x64CD;&#x4F5C;&#xFF1A;&#x5408;&#x5E76;&#x4E24;&#x4E2A;&#x96C6;&#x5408;&#xFF08;&#x5E76;&#xFF09;&#x3001;&#x67E5;&#x8BE2;&#x4E24;&#x4E2A;&#x53C2;&#x6570;&#x662F;&#x5426;&#x5728;&#x4E00;&#x4E2A;&#x96C6;&#x5408;&#x5185;&#xFF08;&#x67E5;&#xFF09;&#x3002;&#x8FD9;&#x4E5F;&#x662F;&#x5B83;&#x540D;&#x5B57;&#x7684;&#x7531;&#x6765;&#x3002; <a id="more"></a> ### &#x901F;&#x5EA6; &#x4ED6;&#x6709;&#x591A;&#x5FEB;&#x5462;&#xFF1F; <span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>O</mi><mo stretchy="false">(</mo><mo>&#x2217;</mo><mi>l</mi><mi>o</mi><mi>g</mi><mi>n</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">O(*log 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class="mord">&#x2217;</span><span class="mord mathdefault" style="margin-right:0.01968em;">l</span><span class="mord mathdefault">o</span><span class="mord mathdefault" style="margin-right:0.03588em;">g</span><span class="mord mathdefault">n</span></span></span></span>| |-|-| |<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo stretchy="false">(</mo><mn>1</mn><mo separator="true">,</mo><mn>2</mn><mo stretchy="false">]</mo></mrow><annotation encoding="application/x-tex">(1,2]</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">1</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord">2</span><span class="mclose">]</span></span></span></span>|<span class="katex"><span class="katex-mathml"><math><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:0.64444em;vertical-align:0em;"></span><span class="mord">1</span></span></span></span>| |<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo stretchy="false">(</mo><mn>2</mn><mo separator="true">,</mo><mn>4</mn><mo stretchy="false">]</mo></mrow><annotation encoding="application/x-tex">(2,4]</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">2</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord">4</span><span class="mclose">]</span></span></span></span>|<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mn>2</mn></mrow><annotation encoding="application/x-tex">2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">2</span></span></span></span>| |<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo stretchy="false">(</mo><mn>4</mn><mo separator="true">,</mo><mn>16</mn><mo stretchy="false">]</mo></mrow><annotation encoding="application/x-tex">(4,16]</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">4</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord">1</span><span class="mord">6</span><span class="mclose">]</span></span></span></span>|<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mn>3</mn></mrow><annotation encoding="application/x-tex">3</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">3</span></span></span></span>| |<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo stretchy="false">(</mo><mn>16</mn><mo separator="true">,</mo><mn>65536</mn><mo stretchy="false">]</mo></mrow><annotation encoding="application/x-tex">(16,65536]</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">1</span><span class="mord">6</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord">6</span><span class="mord">5</span><span class="mord">5</span><span class="mord">3</span><span class="mord">6</span><span class="mclose">]</span></span></span></span>|<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mn>4</mn></mrow><annotation encoding="application/x-tex">4</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">4</span></span></span></span>| |<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo stretchy="false">(</mo><mn>65536</mn><mo separator="true">,</mo><msup><mn>2</mn><mn>65536</mn></msup><mo stretchy="false">]</mo></mrow><annotation encoding="application/x-tex">(65536,2^{65536}]</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.064108em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">6</span><span class="mord">5</span><span class="mord">5</span><span class="mord">3</span><span class="mord">6</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mord">2</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141079999999999em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">6</span><span class="mord mtight">5</span><span class="mord mtight">5</span><span class="mord mtight">3</span><span class="mord mtight">6</span></span></span></span></span></span></span></span></span><span class="mclose">]</span></span></span></span>|<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mn>5</mn></mrow><annotation encoding="application/x-tex">5</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">5</span></span></span></span>| &#x6240;&#x4EE5;n&#x662F;<span class="katex"><span class="katex-mathml"><math><semantics><mrow><msup><mn>2</mn><mn>65536</mn></msup></mrow><annotation encoding="application/x-tex">2^{65536}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8141079999999999em;vertical-align:0em;"></span><span class="mord"><span class="mord">2</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141079999999999em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">6</span><span class="mord mtight">5</span><span class="mord mtight">5</span><span class="mord mtight">3</span><span class="mord mtight">6</span></span></span></span></span></span></span></span></span></span></span></span>&#x7684;&#x65F6;&#x5019;&#x590D;&#x6742;&#x5EA6;&#x8FD8;&#x53EA;&#x6709;5&#x3002; <a href="https://sites.google.com/site/largenumbers/home/appendix/a/numbers/265536" target="_blank" rel="noopener" title="&#x54C8;&#x54C8;&#xFF01;&#x4E0D;&#x8DE8;&#x8D8A;GREATWALL&#x6253;&#x4E0D;&#x5F00;"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><msup><mn>2</mn><mn>65536</mn></msup></mrow><annotation encoding="application/x-tex">2^{65536}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8141079999999999em;vertical-align:0em;"></span><span class="mord"><span class="mord">2</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141079999999999em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">6</span><span class="mord mtight">5</span><span class="mord mtight">5</span><span class="mord mtight">3</span><span class="mord mtight">6</span></span></span></span></span></span></span></span></span></span></span></span></a>&#x6709;&#x591A;&#x5927;&#xFF0C;&#x6211;&#x628A;&#x4ED6;&#x62F7;&#x8FDB;&#x6765;&#x7684;&#x65F6;&#x5019;&#x6574;&#x4E2A;&#x7535;&#x8111;&#x5361;&#x6B7B;&#x4E86;&#x3002;&#x6211;&#x4E0D;&#x5F97;&#x4E0D;&#x5F3A;&#x5236;&#x91CD;&#x542F;&#xFF0C;&#x7136;&#x540E;&#x91CD;&#x65B0;&#x5199;&#x4E00;&#x904D;&#x8FD9;&#x6BB5;&#x3002;&#x4ED6;&#x6709;19729&#x4F4D;&#x3002;&#x60F3;&#x901A;&#x4E86;&#x5427;&#xFF1F; ### &#x5982;&#x4F55;&#x5B9E;&#x73B0; &#x8FD9;&#x4E48;&#x9AD8;&#x7AEF;&#x7684;&#x7B97;&#x6CD5;&#xFF0C;&#x662F;&#x600E;&#x4E48;&#x5B9E;&#x73B0;&#x7684;&#x5462;&#xFF1F; &#x5176;&#x5B9E;</p>
<p>&#x5B83;&#x7684;&#x672C;&#x8D28;&#x5C31;&#x662F;&#x4E00;&#x4E2A;&#x6570;&#x7EC4;<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>f</mi><mo stretchy="false">[</mo><mo stretchy="false">]</mo></mrow><annotation encoding="application/x-tex">f[]</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathdefault" style="margin-right:0.10764em;">f</span><span class="mopen">[</span><span class="mclose">]</span></span></span></span>&#xFF0C;&#x548C;&#x4E00;&#x4E2A;&#x51FD;&#x6570;<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>g</mi><mi>e</mi><mi>t</mi><mi>f</mi><mo stretchy="false">(</mo><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">getf()</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathdefault" style="margin-right:0.03588em;">g</span><span class="mord mathdefault">e</span><span class="mord mathdefault">t</span><span class="mord mathdefault" style="margin-right:0.10764em;">f</span><span class="mopen">(</span><span class="mclose">)</span></span></span></span> <span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>f</mi><mo stretchy="false">[</mo><mo stretchy="false">]</mo></mrow><annotation encoding="application/x-tex">f[]</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathdefault" style="margin-right:0.10764em;">f</span><span class="mopen">[</span><span class="mclose">]</span></span></span></span>&#x5B58;&#x7684;&#x5B9E;&#x9645;&#x4E0A;&#x5C31;&#x662F;&#x51E0;&#x68F5;&#x6811;&#x3002; <span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>f</mi><mo stretchy="false">[</mo><mi>i</mi><mo stretchy="false">]</mo></mrow><annotation encoding="application/x-tex">f[i]</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathdefault" style="margin-right:0.10764em;">f</span><span class="mopen">[</span><span class="mord mathdefault">i</span><span class="mclose">]</span></span></span></span>&#x5C31;&#x662F;<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>i</mi></mrow><annotation encoding="application/x-tex">i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.65952em;vertical-align:0em;"></span><span class="mord mathdefault">i</span></span></span></span>&#x7684;&#x7236;&#x4EB2;&#x3002; <span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>g</mi><mi>e</mi><mi>t</mi><mi>f</mi><mo stretchy="false">(</mo><mi>i</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">getf(i)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathdefault" style="margin-right:0.03588em;">g</span><span class="mord mathdefault">e</span><span class="mord mathdefault">t</span><span class="mord mathdefault" style="margin-right:0.10764em;">f</span><span class="mopen">(</span><span class="mord mathdefault">i</span><span class="mclose">)</span></span></span></span>&#x505A;&#x7684;&#x64CD;&#x4F5C;&#x5C31;&#x662F;&#x9012;&#x5F52;&#x987A;&#x7740;<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>f</mi><mo stretchy="false">[</mo><mi>i</mi><mo stretchy="false">]</mo></mrow><annotation encoding="application/x-tex">f[i]</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathdefault" style="margin-right:0.10764em;">f</span><span class="mopen">[</span><span class="mord mathdefault">i</span><span class="mclose">]</span></span></span></span>&#x627E;<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>i</mi></mrow><annotation encoding="application/x-tex">i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.65952em;vertical-align:0em;"></span><span class="mord mathdefault">i</span></span></span></span>&#x6240;&#x5728;&#x7684;&#x6811;&#x7684;&#x6839;&#x3002; <span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>g</mi><mi>e</mi><mi>t</mi><mi>f</mi><mo stretchy="false">(</mo><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">getf()</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathdefault" style="margin-right:0.03588em;">g</span><span class="mord mathdefault">e</span><span class="mord mathdefault">t</span><span class="mord mathdefault" style="margin-right:0.10764em;">f</span><span class="mopen">(</span><span class="mclose">)</span></span></span></span>&#x4EE3;&#x7801;&#xFF1A; <figure class="highlight cpp"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br></pre></td><td class="code"><pre><span class="line"><span class="function"><span class="keyword">int</span> <span class="title">getf</span><span class="params">(<span class="keyword">int</span> x)</span></span>{</span><br><span class="line">	<span class="keyword">if</span>(f[x]==x)<span class="keyword">return</span> x;</span><br><span class="line">	<span class="keyword">else</span> <span class="keyword">return</span> getf(f[x]);</span><br><span class="line">}</span><br></pre></td></tr></table></figure> <span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi mathvariant="normal">.</mi><mi mathvariant="normal">.</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">...</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.10556em;vertical-align:0em;"></span><span class="mord">.</span><span class="mord">.</span><span class="mord">.</span></span></span></span></p>
<p>&#x90A3;&#x8FD9;&#x4E2A;&#x7B97;&#x6CD5;&#x5C31;&#x5F88;&#x4F4E;&#x7AEF;&#x4E86;<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi mathvariant="normal">.</mi><mi mathvariant="normal">.</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">...</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.10556em;vertical-align:0em;"></span><span class="mord">.</span><span class="mord">.</span><span class="mord">.</span></span></span></span></p>
<p>&#x90A3;&#x8FD8;&#x8BB2;&#x4E2A;&#x9B3C;&#x554A;<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi mathvariant="normal">.</mi><mi mathvariant="normal">.</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">...</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.10556em;vertical-align:0em;"></span><span class="mord">.</span><span class="mord">.</span><span class="mord">.</span></span></span></span></p>
<p>&#x6240;&#x4EE5; ### &#x8D85;&#x7EA7;&#x4F18;&#x5316; &#x6211;&#x4EEC;&#x9996;&#x5148;&#x968F;&#x673A;&#x9020;&#x51FA;&#x4E00;&#x4E9B;&#x64CD;&#x4F5C;&#xFF1A; <figure class="highlight plain"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br></pre></td><td class="code"><pre><span class="line">10</span><br><span class="line">merge 1 5</span><br><span class="line">merge 5 2</span><br><span class="line">merge 1 3</span><br><span class="line">check 2 3</span><br><span class="line">merge 3 4</span><br><span class="line">merge 6 7</span><br><span class="line">check 1 7</span><br><span class="line">merge 7 8</span><br><span class="line">merge 8 9</span><br><span class="line">merge 1 9</span><br><span class="line">check 7 4</span><br></pre></td></tr></table></figure> &#x5176;&#x4E2D;&#xFF0C;merge&#x4EE3;&#x8868;&#x5408;&#x5E76;&#xFF0C;check&#x4EE3;&#x8868;&#x67E5;&#x8BE2;&#x3002; &#x5982;&#x679C;&#x6309;&#x7167;&#x521A;&#x624D;&#x6240;&#x7684;&#x7B97;&#x6CD5;&#xFF0C;&#x90A3;&#x4E48;&#x5728;&#x7B2C;&#x4E00;&#x6B21;&#x67E5;&#x8BE2;&#x4E4B;&#x524D;&#xFF0C;&#x5C31;&#x4F1A;&#x51FA;&#x6765;&#x8FD9;&#x6837;&#x7684;&#x68EE;&#x6797;&#xFF1A;<img src="https://img-blog.csdnimg.cn/20200105142700396.png" alt="Insert mother fucker"> &#x5230;&#x6700;&#x540E;&#xFF0C;&#x5C31;&#x5F62;&#x6210;&#x4E86;&#x8FD9;&#x6837;&#x4E00;&#x4E2A;&#x7E41;&#x6742;&#x7684;&#x68EE;&#x6797;&#xFF0C;&#x8981;&#x627E;&#x5230;&#x4E00;&#x4E2A;&#x70B9;&#x7684;&#x6839;&#xFF0C;&#x5C31;&#x9700;&#x8981;&#x8D70;&#x5F88;&#x957F;&#x4E00;&#x6BB5;&#x8DEF;&#x3002;&#x8FD9;&#x5C31;&#x62C9;&#x957F;&#x4E86;&#x65F6;&#x95F4;&#x3002; <img src="https://img-blog.csdnimg.cn/20200105142531778.png" alt="Insert mother fucker"> &#x4E3A;&#x4E86;&#x7F29;&#x51CF;&#x65F6;&#x95F4;&#xFF0C;&#x8D85;&#x7EA7;&#x4F18;&#x5316;&#x5C31;&#x51FA;&#x73B0;&#x4E86;&#xFF1A;&#x8DEF;&#x5F84;&#x538B;&#x7F29;&#x3002; &#x8DEF;&#x5F84;&#x538B;&#x7F29;&#x5176;&#x5B9E;&#x4E5F;&#x5F88;&#x7B80;&#x5355;&#xFF1A;&#x5728;<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>g</mi><mi>e</mi><mi>t</mi><mi>f</mi><mo stretchy="false">(</mo><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">getf()</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathdefault" style="margin-right:0.03588em;">g</span><span class="mord mathdefault">e</span><span class="mord mathdefault">t</span><span class="mord mathdefault" style="margin-right:0.10764em;">f</span><span class="mopen">(</span><span class="mclose">)</span></span></span></span>&#x67E5;&#x627E;&#x6839;&#x8282;&#x70B9;&#x7684;&#x540C;&#x65F6;&#xFF0C;&#x628A;&#x81EA;&#x5DF1;&#x4E5F;&#x94FE;&#x63A5;&#x5230;&#x6839;&#x8282;&#x70B9;&#x4E0A;&#xFF0C;&#x4F7F;&#x5F97;&#x6811;&#x7684;&#x6DF1;&#x5EA6;&#x4E0D;&#x8D85;&#x8FC7;2&#x3002; &#x4EE3;&#x7801;&#xFF1A; <figure class="highlight cpp"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br></pre></td><td class="code"><pre><span class="line"><span class="function"><span class="keyword">int</span> <span class="title">getf</span><span class="params">(<span class="keyword">int</span> x)</span></span>{</span><br><span class="line">	<span class="keyword">if</span>(f[x]==x)<span class="keyword">return</span> x;</span><br><span class="line">	<span class="keyword">else</span> <span class="keyword">return</span> f[x]=getf(f[x]);</span><br><span class="line">}</span><br></pre></td></tr></table></figure> &#x53D1;&#x73B0;&#x6CA1;&#x6709;&#xFF0C;&#x548C;&#x4E4B;&#x524D;&#x7684;&#x4EE3;&#x7801;&#x76F8;&#x6BD4;&#xFF0C;&#x53EA;&#x6539;&#x4E86;&#x4E00;&#x4E2A;&#x5730;&#x65B9;&#xFF0C;&#x5C31;&#x8BA9;&#x65F6;&#x95F4;&#x5927;&#x5927;&#x538B;&#x7F29;&#x3002; &#x8FD9;&#x65F6;&#x6211;&#x4EEC;&#x5728;&#x6A21;&#x62DF;&#x4E00;&#x4E0B;&#x3002; &#x7B2C;&#x4E00;&#x6B21;&#x5408;&#x5E76;&#xFF1A;<img src="https://img-blog.csdnimg.cn/20200105143342729.png" alt="Insert mother fucker"> &#x7B2C;&#x4E8C;&#x6B21;&#x5408;&#x5E76;&#x65F6;&#xFF0C;&#x9996;&#x5148;&#x5BFB;&#x627E;2,5&#x4E24;&#x4E2A;&#x8282;&#x70B9;&#x7684;&#x6839;&#x8282;&#x70B9;&#xFF0C;2&#x7684;&#x6839;&#x5C31;&#x662F;2&#xFF0C;5&#x7684;&#x6839;&#x662F;1&#xFF0C;&#x4E8E;&#x662F;&#x76F4;&#x63A5;&#x628A;2&#x94FE;&#x63A5;&#x5230;1&#x4E0A;&#x3002; <img src="https://img-blog.csdnimg.cn/20200105144059847.png" alt="Insert mother fucker"> &#x7B2C;&#x4E09;&#x6B21;&#xFF0C;&#x7B2C;&#x56DB;&#x6B21;&#x5408;&#x5E76;&#x628A;3&#x94FE;&#x63A5;&#x5230;&#x4E86;1&#x4E0A;&#xFF0C;&#x7136;&#x540E;&#x628A;4&#x987A;&#x7740;3&#x4E5F;&#x94FE;&#x63A5;&#x5230;&#x4E86;1&#x4E0A;&#xFF0C;&#x7B2C;&#x4E94;&#x6B21;&#x8FDE;&#x63A5;&#x4E86;6&#x548C;7&#x3002; <img src="https://img-blog.csdnimg.cn/20200105143532966.png" alt="Insert mother fucker"> &#x7B2C;&#x4E03;&#x6B21;&#x7B2C;&#x516B;&#x6B21;&#x94FE;&#x63A5;&#x6210;&#x4E86;<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mn>9</mn><mo>&#x2192;</mo><mn>8</mn><mo>&#x2192;</mo><mn>7</mn><mo>&#x2192;</mo><mn>6</mn></mrow><annotation encoding="application/x-tex">9\rightarrow8\rightarrow7\rightarrow6</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">9</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">&#x2192;</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">8</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">&#x2192;</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">7</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">&#x2192;</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">6</span></span></span></span>&#x4E00;&#x957F;&#x4E32;&#xFF0C;&#x7136;&#x540E;&#x7ECF;&#x8FC7;&#x8DEF;&#x5F84;&#x538B;&#x7F29;&#x90FD;&#x94FE;&#x63A5;&#x5230;6&#x4E0A;&#x4E86;&#x3002; <img src="https://img-blog.csdnimg.cn/20200105143644622.png" alt="Insert mother fucker"> &#x6700;&#x540E;&#x4E00;&#x6B21;&#xFF0C;&#x628A;9&#x548C;1&#x94FE;&#x63A5;&#x8D77;&#x6765;&#x4E86;&#xFF0C;&#x8FD9;&#x65F6;&#x6DF1;&#x5EA6;&#x53C8;&#x8D85;&#x8FC7;&#x4E86;2&#xFF0C;&#x4E00;&#x4E0B;&#x8FD8;&#x538B;&#x7F29;&#x4E0D;&#x4E0B;&#x53BB;&#xFF0C;&#x4E0D;&#x8FC7;&#x6CA1;&#x5173;&#x7CFB;&#xFF0C;&#x67E5;&#x8BE2;&#x7684;&#x65F6;&#x5019;&#x5C31;&#x4F1A;&#x628A;&#x5B83;&#x538B;&#x7F29;&#x7684;&#x3002;<img src="https://img-blog.csdnimg.cn/20200105143847598.png" alt="Insert mother fucker"> &#x6BD4;&#x5982;&#x67E5;&#x8BE2;7&#x548C;4&#x7684;&#x65F6;&#x5019;&#x5C31;&#x4F1A;&#x5206;&#x522B;&#x5BFB;&#x627E;7&#x548C;4&#x7684;&#x6839;&#x8282;&#x70B9;&#xFF0C;&#x4E00;&#x8DEF;&#x9012;&#x5F52;&#x627E;&#x4E0A;&#x53BB;&#x7684;&#x65F6;&#x5019;&#x5C31;&#x76F4;&#x63A5;&#x628A;&#x8DEF;&#x5F84;&#x538B;&#x7F29;&#x597D;&#x4E86;&#xFF0C;&#x9664;&#x4E86;8&#x8FD8;&#x94FE;&#x63A5;&#x5728;6&#x4E0A;&#xFF0C;&#x5176;&#x4ED6;&#x5168;&#x90E8;&#x94FE;&#x63A5;&#x5230;1&#x4E0A;&#x4E86;&#x3002; <img src="https://img-blog.csdnimg.cn/20200105144933595.png" alt="Insert mother fucker"> &#x591A;&#x4E48;&#x6709;&#x8DA3;&#x554A;&#xFF01; ### &#x4EE3;&#x7801; &#x81EA;&#x5DF1;&#x60F3;&#x53BB;&#x5427;&#xFF0C;&#x6838;&#x5FC3;&#x4EE3;&#x7801;&#x548C;&#x601D;&#x8DEF;&#x90FD;&#x7ED9;&#x51FA;&#x6765;&#x4E86;&#x3002; &#x6709;&#x4E00;&#x4E2A;&#x5DE8;&#x5927;&#x7684;&#x5751;&#xFF0C;&#x5C31;&#x662F;<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>f</mi><mo stretchy="false">[</mo><mi>i</mi><mo stretchy="false">]</mo></mrow><annotation encoding="application/x-tex">f[i]</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathdefault" style="margin-right:0.10764em;">f</span><span class="mopen">[</span><span class="mord mathdefault">i</span><span class="mclose">]</span></span></span></span>&#x8981;&#x9884;&#x8BBE;&#x6210;<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>i</mi></mrow><annotation encoding="application/x-tex">i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.65952em;vertical-align:0em;"></span><span class="mord mathdefault">i</span></span></span></span>&#xFF0C;&#x4E0D;&#x7136;&#x4F1A;&#x7206;&#x70B8;&#x3002; &#x52A0;&#x6CB9;&#xFF01;<del>&#x514B;&#x670D;&#x6050;&#x60E7;&#x7684;&#x6700;&#x597D;&#x529E;&#x6CD5;&#x5C31;&#x662F;&#x9762;&#x5BF9;&#x6050;&#x5FC4;</del>&#x5FEB;&#x53BB;&#x5199;&#x5427;&#xFF01;</p>

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