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  140. 最小生成树
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  154. <span class="post-meta-item-text">Edited on</span>
  155. <time title="Modified: 2020-Mar-03 17:49:52" itemprop="dateModified" datetime="2020-03-03T17:49:52+08:00">2020-Mar-03</time>
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  162. <h3 id="&#x5F15;&#x5165;">&#x5F15;&#x5165;</h3>
  163. <p>&#x751F;&#x6210;&#x6811;&#xFF0C;&#x5C31;&#x662F;&#x4ECE;&#x4E00;&#x4E2A;&#x56FE;&#x4E2D;&#x9009;&#x4E2D;<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>n</mi><mo>&#x2212;</mo><mn>1</mn></mrow><annotation encoding="application/x-tex">n-1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.66666em;vertical-align:-0.08333em;"></span><span class="mord mathdefault">n</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">&#x2212;</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">1</span></span></span></span>&#x6761;&#x8FB9;&#xFF0C;&#x4F7F;&#x5F97;&#x8FD9;&#x4E9B;&#x8FB9;&#x6784;&#x6210;&#x4E00;&#x68F5;&#x6811;&#xFF0C;&#x5E76;&#x5305;&#x542B;&#x56FE;&#x4E2D;&#x7684;&#x6240;&#x6709;&#x8282;&#x70B9;&#x3002; &#x6700;&#x5C0F;&#x751F;&#x6210;&#x6811;&#xFF0C;&#x5C31;&#x662F;&#x627E;&#x5230;&#x4E00;&#x79CD;&#x751F;&#x6210;&#x6811;&#xFF0C;&#x4F7F;&#x5F97;&#x8FD9;&#x4E2A;&#x751F;&#x6210;&#x6811;&#x7684;&#x8FB9;&#x6743;&#x548C;&#x6700;&#x5C0F;&#x3002; <a id="more"></a> ### &#x751F;&#x6210;&#x65B9;&#x5F0F;&#x4E00;&#xFF1A;prim &#x8FD9;&#x79CD;&#x65B9;&#x6CD5;&#x6709;&#x70B9;&#x7C7B;&#x4F3C;<a href="http://baidu.physton.com/?q=dijkstra" target="_blank" rel="noopener" title="&#x8FD9;&#x90FD;&#x4E0D;&#x4F1A;&#xFF1F;">Dijstra</a>&#xFF0C;&#x5C31;&#x662F;&#x6BCF;&#x6B21;&#x4ECE;&#x6240;&#x6709;<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>v</mi><mi>i</mi><mi>s</mi></mrow><annotation encoding="application/x-tex">vis</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" style="margin-right:0.03588em;">v</span><span class="mord mathdefault">i</span><span class="mord mathdefault">s</span></span></span></span>&#x8FC7;&#x7684;&#x70B9;&#x904D;&#x5386;&#x80FD;&#x8FBE;&#x5230;&#x7684;&#x8FB9;&#xFF0C;&#x4ECE;&#x5176;&#x4E2D;&#x9009;&#x62E9;&#x4E00;&#x6761;&#x6700;&#x5C0F;&#x7684;&#xFF0C;&#x52A0;&#x5165;&#x751F;&#x6210;&#x6811;&#x3002;</p>
  164. <hr>
  165. <p>&#x5047;&#x8BBE;&#x6211;&#x4EEC;&#x6709;&#x8FD9;&#x4E48;&#x4E00;&#x5F20;&#x56FE;&#xFF1A; <a href="https://csacademy.com/app/graph_editor" target="_blank" rel="noopener" title="&#x70B9;&#x51FB;&#x67E5;&#x770B;&#x751F;&#x6210;&#x5DE5;&#x5177;"><img src="https://img-blog.csdnimg.cn/20200103203601629.png" alt="&#x5F1F;&#x5F1F;"></a></p>
  166. <p>&#x5C31;&#x4ECE;0&#x53F7;&#x70B9;&#x5F00;&#x59CB;&#x5427;&#xFF1A; <a href="https://csacademy.com/app/graph_editor" target="_blank" rel="noopener" title="&#x70B9;&#x51FB;&#x67E5;&#x770B;&#x751F;&#x6210;&#x5DE5;&#x5177;"><img src="https://img-blog.csdnimg.cn/20200103204749157.png" alt="&#x5728;&#x8FD9;&#x91CC;&#x63D2;&#x5165;&#x56FE;&#x7247;&#x63CF;&#x8FF0;"></a></p>
  167. <p>&#x627E;&#x5230;&#x4ECE;<span class="katex"><span class="katex-mathml"><math><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:0.64444em;vertical-align:0em;"></span><span class="mord">0</span></span></span></span>&#x51FA;&#x53D1;&#x7684;&#x6700;&#x5C0F;&#x7684;&#x8FB9;&#xFF1A;<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo stretchy="false">[</mo><mn>0</mn><mo separator="true">,</mo><mn>2</mn><mo stretchy="false">]</mo></mrow><annotation encoding="application/x-tex">[0,2]</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">0</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>,&#x8FB9;&#x6743;&#x4E3A;<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>&#xFF0C;&#x90A3;&#x4E48;&#x5BF9;<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>&#x53F7;&#x70B9;&#x8FDB;&#x884C;&#x6807;&#x8BB0;&#x3002; <a href="https://csacademy.com/app/graph_editor" target="_blank" rel="noopener" title="&#x70B9;&#x51FB;&#x67E5;&#x770B;&#x751F;&#x6210;&#x5DE5;&#x5177;"><img src="https://img-blog.csdnimg.cn/20200103205741495.png"></a></p>
  168. <p>&#x7136;&#x540E;&#x4ECE;<span class="katex"><span class="katex-mathml"><math><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:0.64444em;vertical-align:0em;"></span><span class="mord">0</span></span></span></span>&#x53F7;&#x548C;<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>&#x53F7;&#x8282;&#x70B9;&#x7EE7;&#x7EED;&#x627E;&#xFF0C;&#x53D1;&#x73B0;&#x6700;&#x5C0F;&#x7684;&#x662F;<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>&#x8FB9;&#xFF0C;&#x90A3;&#x4E48;&#x5C31;&#x6807;&#x8BB0;<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>&#x53F7;&#x8282;&#x70B9;&#x3002; <a href="https://csacademy.com/app/graph_editor" target="_blank" rel="noopener" title="&#x70B9;&#x51FB;&#x67E5;&#x770B;&#x751F;&#x6210;&#x5DE5;&#x5177;"><img src="https://img-blog.csdnimg.cn/20200103210306831.png" alt="&#x5728;&#x8FD9;&#x91CC;&#x63D2;&#x5165;&#x56FE;&#x7247;&#x63CF;&#x8FF0;"></a></p>
  169. <p>&#x7136;&#x540E;&#x662F;<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo stretchy="false">[</mo><mn>4</mn><mo separator="true">,</mo><mn>1</mn><mo stretchy="false">]</mo></mrow><annotation encoding="application/x-tex">[4,1]</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="mclose">]</span></span></span></span>&#xFF0C;<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>&#x53F7;&#x3002; <a href="https://csacademy.com/app/graph_editor" target="_blank" rel="noopener" title="&#x70B9;&#x51FB;&#x67E5;&#x770B;&#x751F;&#x6210;&#x5DE5;&#x5177;"><img src="https://img-blog.csdnimg.cn/20200103210445854.png" alt="&#x5728;&#x8FD9;&#x91CC;&#x63D2;&#x5165;&#x56FE;&#x7247;&#x63CF;&#x8FF0;"></a></p>
  170. <p>&#x4EE5;&#x6B64;&#x7C7B;&#x63A8;&#xFF0C;&#x6700;&#x540E;&#x5C31;&#x751F;&#x6210;&#x51FA;&#x6765;&#x4E86;&#x8FD9;&#x6837;&#x4E00;&#x4E2A;&#x56FE;&#xFF1A;</p>
  171. <p><a href="https://csacademy.com/app/graph_editor" target="_blank" rel="noopener" title="&#x70B9;&#x51FB;&#x67E5;&#x770B;&#x751F;&#x6210;&#x5DE5;&#x5177;"><img src="https://img-blog.csdnimg.cn/20200103210621487.png" alt="&#x5728;&#x8FD9;&#x91CC;&#x63D2;&#x5165;&#x56FE;&#x7247;&#x63CF;&#x8FF0;"></a></p>
  172. <p>&#x628A;&#x6CA1;&#x6709;&#x6807;&#x8BB0;&#x7684;&#x8FB9;&#x5220;&#x6389;&#xFF0C;&#x5C31;&#x662F;&#x6700;&#x5C0F;&#x751F;&#x6210;&#x6811;&#x3002; <a href="https://csacademy.com/app/graph_editor" target="_blank" rel="noopener" title="&#x70B9;&#x51FB;&#x67E5;&#x770B;&#x751F;&#x6210;&#x5DE5;&#x5177;"><img src="https://img-blog.csdnimg.cn/20200103210727778.png"></a></p>
  173. <p>&#x8FD9;&#x5C31;&#x662F;prim&#x7B97;&#x6CD5; <del>&#xFF0C;&#x4EE3;&#x7801;&#x6211;&#x4E0D;&#x4F1A;&#x5199;</del>&#x5728;&#x540E;&#x9762;&#x3002;</p>
  174. <h3 id="&#x751F;&#x6210;&#x65B9;&#x5F0F;&#x4E8C;kruskal">&#x751F;&#x6210;&#x65B9;&#x5F0F;&#x4E8C;&#xFF1A;kruskal</h3>
  175. <p>&#x8FD9;&#x4E2A;&#x7B97;&#x6CD5;&#x672C;&#x8D28;&#x4E0A;&#x5C31;&#x662F;&#x628A;&#x6240;&#x6709;&#x8FB9;&#x6309;&#x7167;&#x8FB9;&#x6743;&#x6392;&#x5E8F;&#xFF0C;&#x7136;&#x540E;&#x76F4;&#x63A5;<del>&#x7206;&#x70B8;</del>&#x6309;&#x987A;&#x5E8F;&#x5224;&#x65AD;&#x8981;&#x4E0D;&#x8981;&#x52A0;&#x8FDB;&#x751F;&#x6210;&#x6811;&#x91CC;&#x3002; kruskal&#x7B97;&#x6CD5;&#x4F7F;&#x7528;&#x4E86;&#x4E00;&#x79CD;&#x6781;&#x901F;&#x95EA;&#x7535;&#x81F4;&#x547D;&#x53C8;&#x81EA;&#x6740;&#x7684;&#x4E1C;&#x897F;&#xFF1A;&#x5E76;&#x67E5;&#x96C6;&#x3002; <a href="https://schtonn.github.io/post/union-find-set" target="_blank" rel="noopener">&#x4ED6;&#x6709;&#x591A;&#x5FEB;&#x5462;&#xFF1F;</a></p>
  176. <hr>
  177. <p>&#x597D;&#x4E86;&#x6211;&#x4EEC;&#x5728;&#x5EFA;&#x4E00;&#x4E2A;&#x56FE;&#x6A21;&#x62DF;&#x4E00;&#x4E0B;&#x5427; <img src="https://img-blog.csdnimg.cn/20200103215213917.png" alt="&#x5728;&#x8FD9;&#x91CC;&#x63D2;&#x5165;&#x56FE;&#x7247;&#x63CF;&#x8FF0;"></p>
  178. <p>&#x5148;&#x7ED9;&#x8FB9;&#x6392;&#x5E8F;&#x3002;&#x6700;&#x5C0F;&#x7684;&#x662F;<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo stretchy="false">[</mo><mn>2</mn><mo separator="true">,</mo><mn>3</mn><mo stretchy="false">]</mo></mrow><annotation encoding="application/x-tex">[2,3]</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">3</span><span class="mclose">]</span></span></span></span>&#xFF0C;&#x628A;&#x4ED6;&#x62FF;&#x51FA;&#x6765;&#xFF0C;&#x5224;&#x65AD;&#x4E00;&#x4E0B;&#x3002;&#x600E;&#x4E48;&#x5224;&#x65AD;&#x5462;&#xFF1F;&#x9996;&#x5148;&#x8BBF;&#x95EE;&#x4E00;&#x4E0B;&#x5E76;&#x67E5;&#x96C6;&#x770B;&#x4E00;&#x770B;&#xFF0C;&#x8FD9;&#x4E2A;&#x8FB9;&#x8FDE;&#x63A5;&#x7684;&#x4E24;&#x4E2A;&#x70B9;&#x5728;&#x4E0D;&#x5728;&#x540C;&#x4E00;&#x4E2A;&#x96C6;&#x5408;&#x5185;&#xFF0C;&#x4E0D;&#x5728;&#x7684;&#x8BDD;&#x5C31;&#x628A;&#x8FD9;&#x6761;&#x8FB9;&#x52A0;&#x5165;&#x751F;&#x6210;&#x6811;&#xFF0C;&#x7136;&#x540E;&#x628A;&#x4E24;&#x4E2A;&#x70B9;&#x5408;&#x5E76;&#x3002;&#x5426;&#x5219;&#x5FFD;&#x7565;&#x8FD9;&#x4E00;&#x6761;&#x53D8;&#xFF0C;&#x7EE7;&#x7EED;&#x3002;&#x8FD9;&#x4E00;&#x6761;&#x8FB9;&#x7B26;&#x5408;&#x8981;&#x6C42;&#xFF0C;&#x52A0;&#x8FDB;&#x5E76;&#x67E5;&#x96C6;&#x91CC;&#xFF0C;&#x73B0;&#x5728;<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mn>2</mn><mo separator="true">,</mo><mn>3</mn></mrow><annotation encoding="application/x-tex">{2,3}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8388800000000001em;vertical-align:-0.19444em;"></span><span class="mord"><span class="mord">2</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord">3</span></span></span></span></span>&#x662F;&#x4E00;&#x4E2A;&#x96C6;&#x5408;&#xFF0C;&#x5269;&#x4E0B;&#x90FD;&#x662F;&#x72EC;&#x7ACB;&#x7684;&#x3002;</p>
  179. <p><img src="https://img-blog.csdnimg.cn/20200103215304212.png" alt="&#x5728;&#x8FD9;&#x91CC;&#x63D2;&#x5165;&#x56FE;&#x7247;&#x63CF;&#x8FF0;"> &#x73B0;&#x5728;&#x6700;&#x5C0F;&#x7684;&#x6709;<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo stretchy="false">[</mo><mn>1</mn><mo separator="true">,</mo><mn>4</mn><mo stretchy="false">]</mo></mrow><annotation encoding="application/x-tex">[1,4]</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">1</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>&#x548C;<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo stretchy="false">[</mo><mn>4</mn><mo separator="true">,</mo><mn>5</mn><mo stretchy="false">]</mo></mrow><annotation encoding="application/x-tex">[4,5]</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">5</span><span class="mclose">]</span></span></span></span>&#xFF0C;&#x6211;&#x4EEC;&#x90FD;&#x5224;&#x65AD;&#x4E00;&#x4E0B;&#xFF0C;&#x90FD;&#x53EF;&#x4EE5;&#x3002; <img src="https://img-blog.csdnimg.cn/20200103215356204.png" alt="&#x5728;&#x8FD9;&#x91CC;&#x63D2;&#x5165;&#x56FE;&#x7247;&#x63CF;&#x8FF0;"></p>
  180. <p>&#x7136;&#x540E;&#x5C31;&#x662F;<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo stretchy="false">[</mo><mn>0</mn><mo separator="true">,</mo><mn>4</mn><mo stretchy="false">]</mo></mrow><annotation encoding="application/x-tex">[0,4]</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">0</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>&#x548C;<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>&#xFF0C;&#x4F9D;&#x7136;&#x90FD;&#x662F;&#x53EF;&#x4EE5;&#x7684;&#x3002; <img src="https://img-blog.csdnimg.cn/20200103215507942.png" alt="&#x5728;&#x8FD9;&#x91CC;&#x63D2;&#x5165;&#x56FE;&#x7247;&#x63CF;&#x8FF0;"> &#x8FD9;&#x6837;&#xFF0C;&#x4E00;&#x9897;&#x6D3B;&#x7075;&#x6D3B;&#x73B0;&#x7684;&#x751F;&#x6210;&#x6811;&#x5C31;&#x51FA;&#x73B0;&#x4E86;&#x3002; <img src="https://img-blog.csdnimg.cn/20200103215600881.png"></p>
  181. <p>&#x597D;&#x4E86;&#xFF01; ### &#x4EE3;&#x7801;&#xFF08;<a href="https://www.luogu.com.cn/problem/P3366" target="_blank" rel="noopener">luoguP3366</a>&#xFF09; kruskal&#x7684;&#x4EE3;&#x7801;&#x53C8;&#x77ED;&#x53C8;&#x6613;&#x4E8E;&#x7406;&#x89E3;&#xFF0C;&#x751A;&#x81F3;&#x53EF;&#x4EE5;&#x76F4;&#x63A5;&#x7528;&#x6570;&#x7EC4;&#x5B58;&#x8FB9;&#xFF0C;&#x6240;&#x4EE5;&#x4ED6;&#x975E;&#x5E38;&#x597D;&#x5199;&#xFF0C;&#x63A8;&#x8350;&#x3002;</p>
  182. <h4 id="prim">prim</h4>
  183. <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><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><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br><span class="line">36</span><br><span class="line">37</span><br><span class="line">38</span><br><span class="line">39</span><br><span class="line">40</span><br><span class="line">41</span><br><span class="line">42</span><br><span class="line">43</span><br><span class="line">44</span><br><span class="line">45</span><br><span class="line">46</span><br><span class="line">47</span><br><span class="line">48</span><br><span class="line">49</span><br><span class="line">50</span><br><span class="line">51</span><br><span class="line">52</span><br><span class="line">53</span><br><span class="line">54</span><br><span class="line">55</span><br><span class="line">56</span><br><span class="line">57</span><br><span class="line">58</span><br><span class="line">59</span><br><span class="line">60</span><br><span class="line">61</span><br><span class="line">62</span><br><span class="line">63</span><br><span class="line">64</span><br><span class="line">65</span><br><span class="line">66</span><br><span class="line">67</span><br></pre></td><td class="code"><pre><span class="line"><span class="meta">#<span class="meta-keyword">include</span> <span class="meta-string">&quot;iostream&quot;</span></span></span><br><span class="line"><span class="meta">#<span class="meta-keyword">include</span> <span class="meta-string">&quot;queue&quot;</span></span></span><br><span class="line"><span class="meta">#<span class="meta-keyword">include</span> <span class="meta-string">&quot;cstring&quot;</span></span></span><br><span class="line"><span class="keyword">using</span> <span class="keyword">namespace</span> <span class="built_in">std</span>;</span><br><span class="line"><span class="meta">#<span class="meta-keyword">define</span> maxm 5000010</span></span><br><span class="line"><span class="meta">#<span class="meta-keyword">define</span> maxn 1000010</span></span><br><span class="line"><span class="meta">#<span class="meta-keyword">define</span> inf 0x3f3f3f3f</span></span><br><span class="line"><span class="keyword">int</span> ans=<span class="number">0</span>;</span><br><span class="line"><span class="class"><span class="keyword">struct</span> <span class="title">node</span>{</span></span><br><span class="line"> <span class="keyword">int</span> v,next,c;</span><br><span class="line">}e[maxm&lt;&lt;<span class="number">1</span>];</span><br><span class="line"><span class="keyword">int</span> h[maxn],tot,n,m;</span><br><span class="line"><span class="function"><span class="keyword">void</span> <span class="title">adde</span><span class="params">(<span class="keyword">int</span> u,<span class="keyword">int</span> v,<span class="keyword">int</span> c)</span></span>{</span><br><span class="line"> tot++;</span><br><span class="line"> e[tot].v=v;</span><br><span class="line"> e[tot].c=c;</span><br><span class="line"> e[tot].next=h[u];</span><br><span class="line"> h[u]=tot;</span><br><span class="line">}</span><br><span class="line"><span class="keyword">int</span> dis[maxn];</span><br><span class="line"><span class="keyword">bool</span> vis[maxn];</span><br><span class="line"><span class="class"><span class="keyword">struct</span> <span class="title">qu</span>{</span></span><br><span class="line"> <span class="keyword">int</span> id,dis;</span><br><span class="line"> <span class="keyword">bool</span> <span class="keyword">operator</span> &lt; (<span class="keyword">const</span> qu t)<span class="keyword">const</span>{</span><br><span class="line"> <span class="keyword">return</span> dis&gt;t.dis;</span><br><span class="line"> }</span><br><span class="line">};</span><br><span class="line">priority_queue&lt;qu&gt; q;</span><br><span class="line"><span class="function"><span class="keyword">void</span> <span class="title">dijk</span><span class="params">(<span class="keyword">int</span> s)</span></span>{</span><br><span class="line"> <span class="built_in">memset</span>(dis,<span class="number">0x3f</span>,<span class="keyword">sizeof</span>(dis));</span><br><span class="line"> <span class="built_in">memset</span>(vis,<span class="number">0</span>,<span class="keyword">sizeof</span>(vis));</span><br><span class="line"> <span class="keyword">while</span>(!q.empty())q.pop();</span><br><span class="line"> qu t;</span><br><span class="line"> t.dis=<span class="number">0</span>;</span><br><span class="line"> t.id=s;</span><br><span class="line"> dis[s]=<span class="number">0</span>;</span><br><span class="line"> q.push(t);</span><br><span class="line"> <span class="keyword">while</span>(!q.empty()){</span><br><span class="line"> t=q.top();q.pop();</span><br><span class="line"> <span class="keyword">if</span>(vis[t.id])<span class="keyword">continue</span>;</span><br><span class="line"> vis[t.id]=<span class="literal">true</span>;</span><br><span class="line"> ans+=t.dis;</span><br><span class="line"> <span class="keyword">for</span>(<span class="keyword">int</span> j=h[t.id];j;j=e[j].next){</span><br><span class="line"> <span class="keyword">int</span> v=e[j].v;</span><br><span class="line"> <span class="keyword">if</span>(!vis[v]&amp;&amp;dis[v]&gt;e[j].c){</span><br><span class="line"> dis[v]=e[j].c;</span><br><span class="line"> qu now;</span><br><span class="line"> now.id=v;</span><br><span class="line"> now.dis=dis[v];</span><br><span class="line"> q.push(now);</span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="keyword">int</span> <span class="title">main</span><span class="params">()</span></span>{</span><br><span class="line"> <span class="keyword">int</span> s=<span class="number">1</span>;</span><br><span class="line"> <span class="built_in">cin</span>&gt;&gt;n&gt;&gt;m;</span><br><span class="line"> <span class="keyword">int</span> u,v,c;</span><br><span class="line"> <span class="keyword">for</span>(<span class="keyword">int</span> i=<span class="number">1</span>;i&lt;=m;i++){</span><br><span class="line"> <span class="built_in">cin</span>&gt;&gt;u&gt;&gt;v&gt;&gt;c;</span><br><span class="line"> adde(u,v,c);</span><br><span class="line">adde(v,u,c);</span><br><span class="line"> }</span><br><span class="line"> dijk(s);</span><br><span class="line"><span class="built_in">cout</span>&lt;&lt;ans&lt;&lt;<span class="built_in">endl</span>;</span><br><span class="line"> <span class="keyword">return</span> <span class="number">0</span>;</span><br><span class="line">}</span><br></pre></td></tr></table></figure>
  184. <h4 id="kruskal">kruskal</h4>
  185. <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><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><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br></pre></td><td class="code"><pre><span class="line"><span class="meta">#<span class="meta-keyword">include</span> <span class="meta-string">&quot;iostream&quot;</span></span></span><br><span class="line"><span class="meta">#<span class="meta-keyword">include</span> <span class="meta-string">&quot;algorithm&quot;</span></span></span><br><span class="line"><span class="keyword">using</span> <span class="keyword">namespace</span> <span class="built_in">std</span>;</span><br><span class="line"><span class="keyword">int</span> n,m,tot,sum,f[<span class="number">5001</span>];</span><br><span class="line"><span class="class"><span class="keyword">struct</span> <span class="title">node</span>{</span></span><br><span class="line"> <span class="keyword">int</span> u,v,c;</span><br><span class="line">}a[<span class="number">200010</span>];</span><br><span class="line"><span class="function"><span class="keyword">int</span> <span class="title">cmp</span><span class="params">(<span class="keyword">const</span> node &amp;u,<span class="keyword">const</span> node &amp;v)</span></span>{</span><br><span class="line"> <span class="keyword">return</span> u.c&lt;v.c;</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="keyword">int</span> <span class="title">getf</span><span class="params">(<span class="keyword">int</span> u)</span></span>{</span><br><span class="line"> <span class="keyword">if</span>(f[u]==u)<span class="keyword">return</span> u;</span><br><span class="line"> <span class="keyword">return</span> f[u]=getf(f[u]);</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="keyword">int</span> <span class="title">main</span><span class="params">()</span></span>{</span><br><span class="line"> <span class="built_in">cin</span>&gt;&gt;n&gt;&gt;m;</span><br><span class="line"> <span class="keyword">if</span>(m&lt;n<span class="number">-1</span>){<span class="built_in">cout</span>&lt;&lt;<span class="string">&quot;orz&quot;</span>&lt;&lt;<span class="built_in">endl</span>;<span class="keyword">return</span> <span class="number">0</span>;}</span><br><span class="line"> <span class="keyword">for</span>(<span class="keyword">int</span> i=<span class="number">1</span>;i&lt;=m;i++)<span class="built_in">cin</span>&gt;&gt;a[i].u&gt;&gt;a[i].v&gt;&gt;a[i].c;</span><br><span class="line"> <span class="keyword">for</span>(<span class="keyword">int</span> i=<span class="number">1</span>;i&lt;=n;i++)f[i]=i;</span><br><span class="line"> sort(a+<span class="number">1</span>,a+m+<span class="number">1</span>,cmp);</span><br><span class="line"> <span class="keyword">for</span>(<span class="keyword">int</span> i=<span class="number">1</span>;i&lt;=m;i++){</span><br><span class="line"> <span class="keyword">int</span> fu=getf(a[i].u),fv=getf(a[i].v);</span><br><span class="line"> <span class="keyword">if</span>(fu!=fv){</span><br><span class="line"> f[fu]=fv;</span><br><span class="line"> sum++;</span><br><span class="line"> tot+=a[i].c;</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">if</span>(sum==n<span class="number">-1</span>)<span class="keyword">break</span>;</span><br><span class="line"> }</span><br><span class="line"> <span class="built_in">cout</span>&lt;&lt;tot&lt;&lt;<span class="built_in">endl</span>;</span><br><span class="line">}</span><br></pre></td></tr></table></figure>
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