{"id":69071,"date":"2026-01-31T03:57:23","date_gmt":"2026-01-30T19:57:23","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/69071.html"},"modified":"2026-01-31T03:57:23","modified_gmt":"2026-01-30T19:57:23","slug":"%e6%95%b0%e6%8d%ae%e7%bb%93%e6%9e%84-%e5%9b%be","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/69071.html","title":{"rendered":"\u6570\u636e\u7ed3\u6784-\u56fe"},"content":{"rendered":"<\/p>\n<h4>\u6570\u636e\u7ed3\u6784-\u56fe<\/h4>\n<ul>\n<li>1.\u56fe\u7684\u57fa\u672c\u6982\u5ff5<\/li>\n<li>2.\u56fe\u7684\u5b58\u50a8<\/li>\n<li>\n<ul>\n<li>2.1.\u90bb\u63a5\u77e9\u9635<\/li>\n<li>2.2.\u90bb\u63a5\u8868<\/li>\n<\/ul>\n<\/li>\n<li>3.\u56fe\u7684\u904d\u5386<\/li>\n<li>4.\u6700\u5c0f\u751f\u6210\u6811<\/li>\n<li>\n<ul>\n<li>4.1.Kruskal\u7b97\u6cd5<\/li>\n<li>4.2.Prim\u7b97\u6cd5<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>&#x1f31f;&#x1f31f;hello&#xff0c;\u5404\u4f4d\u8bfb\u8005\u5927\u5927\u4eec\u4f60\u4eec\u597d\u5440&#x1f31f;&#x1f31f; 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src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/01\/20260130195716-697d0d1cf20ef.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/> \u5b50\u56fe&#xff1a;\u8bbe\u56feG &#061; {V, E}\u548c\u56feG1 &#061; {V1&#xff0c;E1}&#xff0c;\u82e5V1\u5c5e\u4e8eV\u4e14E1\u5c5e\u4e8eE&#xff0c;\u5219\u79f0G1\u662fG\u7684\u5b50\u56fe\u3002 <img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/01\/20260130195717-697d0d1d1d204.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/> \u8fde\u901a\u56fe&#xff1a;\u5728\u65e0\u5411\u56fe\u4e2d&#xff0c;\u82e5\u4ece\u9876\u70b9v1\u5230\u9876\u70b9v2\u6709\u8def\u5f84&#xff0c;\u5219\u79f0\u9876\u70b9v1\u4e0e\u9876\u70b9v2\u662f\u8fde\u901a\u7684\u3002\u5982\u679c\u56fe\u4e2d\u4efb\u610f\u4e00\u5bf9\u9876\u70b9\u90fd\u662f\u8fde\u901a\u7684&#xff0c;\u5219\u79f0\u6b64\u56fe\u4e3a\u8fde\u901a\u56fe\u3002 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src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/01\/20260130195717-697d0d1d5d0c1.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/> \u65e0\u5411\u56fe\u7684\u90bb\u63a5\u77e9\u9635\u662f\u5bf9\u79f0\u7684&#xff0c;\u7b2ci\u884c(\u5217)\u5143\u7d20\u4e4b\u548c&#xff0c;\u5c31\u662f\u9876\u70b9i\u7684\u5ea6\u3002\u6709\u5411\u56fe\u7684\u90bb\u63a5\u77e9\u9635\u5219\u4e0d\u4e00\u5b9a\u662f\u5bf9\u79f0\u7684&#xff0c;\u7b2ci\u884c(\u5217)\u5143\u7d20\u4e4b\u540e\u5c31\u662f\u9876\u70b9i \u7684\u51fa(\u5165)\u5ea6\u3002 \u5982\u679c\u8fb9\u5e26\u6709\u6743\u503c&#xff0c;\u5e76\u4e14\u4e24\u4e2a\u8282\u70b9\u4e4b\u95f4\u662f\u8fde\u901a\u7684&#xff0c;\u4e0a\u56fe\u4e2d\u7684\u8fb9\u7684\u5173\u7cfb\u5c31\u7528\u6743\u503c\u4ee3\u66ff&#xff0c;\u5982\u679c\u4e24\u4e2a\u9876\u70b9\u4e0d\u901a&#xff0c;\u5219\u4f7f\u7528\u65e0\u7a77\u5927\u4ee3\u66ff <img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/01\/20260130195717-697d0d1d9826d.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/> \u7528\u90bb\u63a5\u77e9\u9635\u5b58\u50a8\u56fe\u7684\u4f18\u70b9\u662f\u80fd\u591f\u5feb\u901f\u77e5\u9053\u4e24\u4e2a\u9876\u70b9\u662f\u5426\u8fde\u901a&#xff0c;\u5e76\u4e14\u53d6\u5230\u6743\u503c&#xff0c;\u65f6\u95f4\u590d\u6742\u5ea6\u662fO(1)&#xff0c;\u5e76\u4e14\u8fd9\u79cd\u5b58\u50a8\u65b9\u5f0f\u975e\u5e38\u9002\u5408\u7a20\u5bc6\u56fe;\u4f46\u662f\u7f3a\u70b9\u662f\u4e0d\u65b9\u4fbf\u67e5\u627e\u4e00\u4e2a\u9876\u70b9\u94fe\u63a5\u7684\u6240\u6709\u8fb9&#xff0c;\u9700\u8981\u628a\u4e00\u6574\u884c\u90fd\u904d\u5386\u4e00\u904d&#xff0c;\u65f6\u95f4\u590d\u6742\u5ea6\u662fO(N)<\/p>\n<p><span class=\"token keyword\">namespace<\/span> Matrix<br \/>\n<span class=\"token punctuation\">{<\/span><br \/>\n<span class=\"token keyword\">template<\/span><span class=\"token operator\">&lt;<\/span><span class=\"token keyword\">class<\/span> <span class=\"token class-name\">V<\/span><span class=\"token punctuation\">,<\/span><span class=\"token keyword\">class<\/span> <span class=\"token class-name\">W<\/span><span class=\"token punctuation\">,<\/span> W MAX_W <span class=\"token operator\">&#061;<\/span> INT_MAX<span class=\"token punctuation\">,<\/span> <span class=\"token keyword\">bool<\/span> Direction <span class=\"token operator\">&#061;<\/span> <span class=\"token boolean\">false<\/span><span class=\"token operator\">&gt;<\/span><br \/>\n<span class=\"token keyword\">class<\/span> <span class=\"token class-name\">Graph<\/span><br \/>\n<span class=\"token punctuation\">{<\/span><br \/>\n<span class=\"token keyword\">public<\/span><span class=\"token operator\">:<\/span><br \/>\n<span class=\"token keyword\">typedef<\/span> Graph<span class=\"token operator\">&lt;<\/span>V<span class=\"token punctuation\">,<\/span> W<span class=\"token punctuation\">,<\/span> INT_MAX<span class=\"token punctuation\">,<\/span> <span class=\"token boolean\">false<\/span><span class=\"token operator\">&gt;<\/span> Self<span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token function\">Graph<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token punctuation\">{<\/span><span class=\"token punctuation\">}<\/span><\/p>\n<p><span class=\"token function\">Graph<\/span><span class=\"token punctuation\">(<\/span><span class=\"token keyword\">const<\/span> V<span class=\"token operator\">*<\/span> vertexs<span class=\"token punctuation\">,<\/span> <span class=\"token keyword\">int<\/span> n<span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token punctuation\">{<\/span><br \/>\n<span class=\"token comment\">\/\/\u5148\u521d\u59cb\u5316\u6240\u6709\u7684\u9876\u70b9<\/span><br \/>\n<span class=\"token comment\">\/\/\u5148\u63d0\u524d\u5f00\u8f9f\u5185\u5b58<\/span><br \/>\n_vertexs<span class=\"token punctuation\">.<\/span><span class=\"token function\">resize<\/span><span class=\"token punctuation\">(<\/span>n<span class=\"token punctuation\">,<\/span><span class=\"token function\">V<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> i <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span> i <span class=\"token operator\">&lt;<\/span> n<span class=\"token punctuation\">;<\/span> i<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token punctuation\">{<\/span><br \/>\n_vertexs<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> vertexs<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token comment\">\/\/\u5efa\u7acb\u6620\u5c04\u5173\u7cfb<\/span><br \/>\n_VIndexMap<span class=\"token punctuation\">[<\/span>vertexs<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> i<span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><\/p>\n<p><span class=\"token comment\">\/\/\u521d\u59cb\u5316\u90bb\u63a5\u77e9\u9635<\/span><br \/>\n_matrix<span class=\"token punctuation\">.<\/span><span class=\"token function\">resize<\/span><span class=\"token punctuation\">(<\/span>n<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">auto<\/span><span class=\"token operator\">&amp;<\/span> m<span class=\"token operator\">:<\/span> _matrix<span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token punctuation\">{<\/span><br \/>\nm<span class=\"token punctuation\">.<\/span><span class=\"token function\">resize<\/span><span class=\"token punctuation\">(<\/span>n<span class=\"token punctuation\">,<\/span> MAX_W<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><\/p>\n<p><span class=\"token punctuation\">}<\/span><\/p>\n<p><span class=\"token comment\">\/\/\u83b7\u53d6\u9876\u70b9\u7684\u4e0b\u6807<\/span><br \/>\n<span class=\"token keyword\">int<\/span> <span class=\"token function\">GetVertexIndex<\/span><span class=\"token punctuation\">(<\/span><span class=\"token keyword\">const<\/span> V<span class=\"token operator\">&amp;<\/span> v<span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token punctuation\">{<\/span><br \/>\n<span class=\"token keyword\">auto<\/span> iterator<span class=\"token operator\">&#061;<\/span>_VIndexMap<span class=\"token punctuation\">.<\/span><span class=\"token function\">find<\/span><span class=\"token punctuation\">(<\/span>v<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span>iterator<span class=\"token operator\">!&#061;<\/span>_VIndexMap<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><br \/>\n<span class=\"token punctuation\">{<\/span><br \/>\n<span class=\"token keyword\">return<\/span> iterator<span class=\"token operator\">-&gt;<\/span>second<span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><br \/>\n<span class=\"token keyword\">else<\/span><br \/>\n<span class=\"token punctuation\">{<\/span><br \/>\n<span class=\"token function\">assert<\/span><span class=\"token punctuation\">(<\/span><span class=\"token boolean\">false<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token keyword\">throw<\/span> <span class=\"token function\">invalid_argument<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;v is not a normal vertex&#034;<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><\/p>\n<p><span class=\"token keyword\">void<\/span> <span class=\"token function\">AddEdge<\/span><span class=\"token punctuation\">(<\/span><span class=\"token keyword\">const<\/span> V<span class=\"token operator\">&amp;<\/span> src<span class=\"token punctuation\">,<\/span> <span class=\"token keyword\">const<\/span> V<span class=\"token operator\">&amp;<\/span> dest<span class=\"token punctuation\">,<\/span> <span class=\"token keyword\">const<\/span> W<span class=\"token operator\">&amp;<\/span> w<span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token punctuation\">{<\/span><br \/>\n<span class=\"token keyword\">int<\/span> srci <span class=\"token operator\">&#061;<\/span> <span class=\"token function\">GetVertexIndex<\/span><span class=\"token punctuation\">(<\/span>src<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token keyword\">int<\/span> desti <span class=\"token operator\">&#061;<\/span> <span class=\"token function\">GetVertexIndex<\/span><span class=\"token punctuation\">(<\/span>dest<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n_matrix<span class=\"token punctuation\">[<\/span>srci<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">[<\/span>desti<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> w<span class=\"token punctuation\">;<\/span><span class=\"token comment\">\/\/\u8fb9\u7684\u6743\u503c<\/span><br \/>\n<span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span>Direction <span class=\"token operator\">&#061;&#061;<\/span> <span class=\"token boolean\">false<\/span><span class=\"token punctuation\">)<\/span><span class=\"token comment\">\/\/\u5f53\u56fe\u4e3a\u65e0\u5411\u56fe\u65f6&#xff0c;\u8fb9\u7684\u5173\u7cfb\u662f\u76f8\u4e92\u7684<\/span><br \/>\n<span class=\"token punctuation\">{<\/span><br \/>\n_matrix<span class=\"token punctuation\">[<\/span>desti<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">[<\/span>srci<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> w<span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><\/p>\n<p><span class=\"token comment\">\/\/void Print()<\/span><br \/>\n<span class=\"token comment\">\/\/{<\/span><br \/>\n<span class=\"token comment\">\/\/\/\/\u6253\u5370\u9876\u70b9<\/span><br \/>\n<span class=\"token comment\">\/\/cout &lt;&lt; &#034;vertexs:&#034;&lt;&lt;endl;<\/span><br \/>\n<span class=\"token comment\">\/\/for (int i &#061; 0; i &lt; _vertexs.size(); i&#043;&#043;)<\/span><br \/>\n<span class=\"token comment\">\/\/{<\/span><br \/>\n<span class=\"token comment\">\/\/cout &lt;&lt; &#034;[&#034; &lt;&lt;i&lt;&lt; &#034;]&#061;&#034;&lt;&lt;_vertexs[i] &lt;&lt; endl;<\/span><br \/>\n<span class=\"token comment\">\/\/}<\/span><br \/>\n<span class=\"token comment\">\/\/cout &lt;&lt; endl;<\/span><\/p>\n<p><span class=\"token comment\">\/\/\/\/\u6253\u5370\u77e9\u9635<\/span><br \/>\n<span class=\"token comment\">\/\/\/\/\u5148\u6253\u5370\u77e9\u9635\u884c\u5217\u8868\u793a\u7684\u5185\u5bb9<\/span><br \/>\n<span class=\"token comment\">\/\/cout &lt;&lt; &#034;  &#034;;<\/span><br \/>\n<span class=\"token comment\">\/\/for (int i &#061; 0; i &lt; _vertexs.size(); i&#043;&#043;)<\/span><br \/>\n<span class=\"token comment\">\/\/{<\/span><br \/>\n<span class=\"token comment\">\/\/cout&lt;&lt; _vertexs[i] &lt;&lt; &#034; &#034;;<\/span><br \/>\n<span class=\"token comment\">\/\/}<\/span><br \/>\n<span class=\"token comment\">\/\/cout &lt;&lt; endl;<\/span><\/p>\n<p><span class=\"token comment\">\/\/for (int i &#061; 0; i &lt; _matrix.size(); i&#043;&#043;)<\/span><br \/>\n<span class=\"token comment\">\/\/{<\/span><br \/>\n<span class=\"token comment\">\/\/cout &lt;&lt; _vertexs[i] &lt;&lt; &#034; &#034;;<\/span><br \/>\n<span class=\"token comment\">\/\/for (int j &#061; 0; j &lt; _matrix[i].size(); j&#043;&#043;)<\/span><br \/>\n<span class=\"token comment\">\/\/{<\/span><br \/>\n<span class=\"token comment\">\/\/if (_matrix[i][j] &#061;&#061; MAX_W)<\/span><br \/>\n<span class=\"token comment\">\/\/{<\/span><br \/>\n<span class=\"token comment\">\/\/cout &lt;&lt; &#034;*&#034; &lt;&lt; &#034; &#034;;<\/span><br \/>\n<span class=\"token comment\">\/\/}<\/span><br \/>\n<span class=\"token comment\">\/\/else<\/span><br \/>\n<span class=\"token comment\">\/\/{<\/span><br \/>\n<span class=\"token comment\">\/\/cout &lt;&lt; _matrix[i][j] &lt;&lt; &#034; &#034;;<\/span><br \/>\n<span class=\"token comment\">\/\/}<\/span><br \/>\n<span class=\"token comment\">\/\/}<\/span><br \/>\n<span class=\"token comment\">\/\/cout &lt;&lt; endl;<\/span><br \/>\n<span class=\"token comment\">\/\/}<\/span><br \/>\n<span class=\"token comment\">\/\/}<\/span><\/p>\n<p><span class=\"token keyword\">void<\/span> <span class=\"token function\">Print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token punctuation\">{<\/span><br \/>\n<span class=\"token comment\">\/\/\u6253\u5370\u9876\u70b9<\/span><br \/>\ncout <span class=\"token operator\">&lt;&lt;<\/span> <span class=\"token string\">&#034;vertexs:&#034;<\/span> <span class=\"token operator\">&lt;&lt;<\/span> endl<span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> i <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span> i <span class=\"token operator\">&lt;<\/span> _vertexs<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> i<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token punctuation\">{<\/span><br \/>\ncout <span class=\"token operator\">&lt;&lt;<\/span> <span class=\"token string\">&#034;[&#034;<\/span> <span class=\"token operator\">&lt;&lt;<\/span> i <span class=\"token operator\">&lt;&lt;<\/span> <span class=\"token string\">&#034;]&#061;&#034;<\/span> <span class=\"token operator\">&lt;&lt;<\/span> _vertexs<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&lt;&lt;<\/span> endl<span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><br \/>\ncout <span class=\"token operator\">&lt;&lt;<\/span> endl<span class=\"token punctuation\">;<\/span><\/p>\n<p><span class=\"token comment\">\/\/\u6253\u5370\u77e9\u9635<\/span><br \/>\n<span class=\"token comment\">\/\/\u5148\u6253\u5370\u77e9\u9635\u884c\u5217\u8868\u793a\u7684\u5185\u5bb9<\/span><br \/>\ncout <span class=\"token operator\">&lt;&lt;<\/span> <span class=\"token string\">&#034;  &#034;<\/span><span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> i <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span> i <span class=\"token operator\">&lt;<\/span> _vertexs<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> i<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token punctuation\">{<\/span><br \/>\n<span class=\"token function\">printf<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;%4d&#034;<\/span><span class=\"token punctuation\">,<\/span> i<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><br \/>\ncout <span class=\"token operator\">&lt;&lt;<\/span> endl<span class=\"token punctuation\">;<\/span><\/p>\n<p><span class=\"token keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> i <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span> i <span class=\"token operator\">&lt;<\/span> _matrix<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> i<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token punctuation\">{<\/span><br \/>\ncout <span class=\"token operator\">&lt;&lt;<\/span> i <span class=\"token operator\">&lt;&lt;<\/span> <span class=\"token string\">&#034; &#034;<\/span><span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> j <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span> j <span class=\"token operator\">&lt;<\/span> _matrix<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><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> j<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token punctuation\">{<\/span><br \/>\n<span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span>_matrix<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\">&#061;&#061;<\/span> MAX_W<span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token punctuation\">{<\/span><br \/>\n<span class=\"token function\">printf<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;%4c&#034;<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token char\">&#039;*&#039;<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><br \/>\n<span class=\"token keyword\">else<\/span><br \/>\n<span class=\"token punctuation\">{<\/span><br \/>\n<span class=\"token function\">printf<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;%4d&#034;<\/span><span class=\"token punctuation\">,<\/span>_matrix<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 punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><br \/>\ncout <span class=\"token operator\">&lt;&lt;<\/span> endl<span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><\/p>\n<p><span class=\"token keyword\">private<\/span><span class=\"token operator\">:<\/span><br \/>\nvector<span class=\"token operator\">&lt;<\/span>V<span class=\"token operator\">&gt;<\/span> _vertexs<span class=\"token punctuation\">;<\/span><span class=\"token comment\">\/\/\u9876\u70b9\u96c6\u5408<\/span><br \/>\nmap<span class=\"token operator\">&lt;<\/span>V<span class=\"token punctuation\">,<\/span> <span class=\"token keyword\">int<\/span><span class=\"token operator\">&gt;<\/span> _VIndexMap<span class=\"token punctuation\">;<\/span><span class=\"token comment\">\/\/\u6620\u5c04\u5173\u7cfb&#xff0c;\u901a\u8fc7\u9876\u70b9\u627e\u4e0b\u6807<\/span><br \/>\nvector<span class=\"token operator\">&lt;<\/span>vector<span class=\"token operator\">&lt;<\/span>W<span class=\"token operator\">&gt;&gt;<\/span> _matrix<span class=\"token punctuation\">;<\/span><span class=\"token comment\">\/\/\u5b58\u50a8\u8fb9\u96c6\u5408\u7684\u77e9\u9635<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><span class=\"token punctuation\">;<\/span><\/p>\n<p>  <span class=\"token keyword\">void<\/span> <span class=\"token function\">TestMatrix<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token punctuation\">{<\/span><br \/>\n<span class=\"token comment\">\/*Matrix::Graph&lt;char, int, INT_MAX, true&gt; g(&#034;0123&#034;, 4);<br \/>\ng.AddEdge(&#039;0&#039;, &#039;1&#039;, 1);<br \/>\ng.AddEdge(&#039;0&#039;, &#039;3&#039;, 4);<br \/>\ng.AddEdge(&#039;1&#039;, &#039;3&#039;, 2);<br \/>\ng.AddEdge(&#039;1&#039;, &#039;2&#039;, 9);<br \/>\ng.AddEdge(&#039;2&#039;, &#039;3&#039;, 8);<br \/>\ng.AddEdge(&#039;2&#039;, &#039;1&#039;, 5);<br \/>\ng.AddEdge(&#039;2&#039;, &#039;0&#039;, 3);<br \/>\ng.AddEdge(&#039;3&#039;, &#039;2&#039;, 6);<br \/>\ng.Print();*\/<\/span><\/p>\n<p><span class=\"token punctuation\">}<\/span><\/p>\n<p><span class=\"token punctuation\">}<\/span><\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/01\/20260130195717-697d0d1db0c04.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<h3>2.2.\u90bb\u63a5\u8868<\/h3>\n<p>\u90bb\u63a5\u8868\u662f\u4f7f\u7528vector\u8868\u793a\u9876\u70b9\u7684\u96c6\u5408&#xff0c;\u4f7f\u7528\u94fe\u8868\u6765\u8868\u793a\u9876\u70b9\u548c\u8fb9\u7684\u5173\u7cfb <img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/01\/20260130195717-697d0d1de905b.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/> \u65e0\u5411\u56fe\u4e2d\u540c\u4e00\u6761\u8fb9\u5728\u90bb\u63a5\u8868\u4e2d\u51fa\u73b0\u4e86\u4e24\u6b21\u3002\u5982\u679c\u60f3\u77e5\u9053\u9876\u70b9vi\u7684\u5ea6&#xff0c;\u53ea\u9700\u8981\u77e5\u9053\u9876\u70b9vi\u8fb9\u94fe\u8868\u96c6\u5408\u4e2d\u7ed3\u70b9\u7684\u6570\u76ee\u5373\u53ef\u3002 <img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/01\/20260130195718-697d0d1e30cbb.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/> \u6709\u5411\u56fe\u4e2d\u6bcf\u6761\u8fb9\u5728\u90bb\u63a5\u8868\u4e2d\u53ea\u51fa\u73b0\u4e00\u6b21&#xff0c;\u4e0e\u9876\u70b9vi\u5bf9\u5e94\u7684\u90bb\u63a5\u8868\u6240\u542b\u7ed3\u70b9\u7684\u4e2a\u6570&#xff0c;\u5c31\u662f\u8be5\u9876\u70b9\u7684\u51fa\u5ea6&#xff0c;\u4e5f\u79f0\u51fa\u5ea6\u8868&#xff0c;\u8981\u5f97\u5230vi\u9876\u70b9\u7684\u5165\u5ea6&#xff0c;\u5fc5\u987b\u68c0\u6d4b\u5176\u4ed6\u6240\u6709\u9876\u70b9\u5bf9\u5e94\u7684\u8fb9\u94fe\u8868&#xff0c;\u770b\u6709\u591a\u5c11\u8fb9\u9876\u70b9\u7684dst\u53d6\u503c\u662fi\u3002 \u90bb\u63a5\u8868\u7684\u4f18\u70b9\u662f\u9002\u5408\u5b58\u50a8\u7a00\u758f\u56fe&#xff0c;\u9002\u5408\u67e5\u627e\u4e00\u4e2a\u9876\u70b9\u8fde\u63a5\u51fa\u53bb\u7684\u8fb9&#xff0c;\u4e0d\u9002\u5408\u786e\u5b9a\u4e24\u4e2a\u9876\u70b9\u662f\u5426\u76f8\u8fde\u4ee5\u53ca\u5b83\u4eec\u7684\u6743\u503c \u4e0b\u9762\u4ee3\u7801\u4e2d\u53ea\u5b9e\u73b0\u4e86\u6709\u5411\u56fe\u7684\u51fa\u5ea6\u60c5\u51b5<\/p>\n<p><span class=\"token comment\">\/\/\u90bb\u63a5\u8868<\/span><br \/>\n<span class=\"token keyword\">namespace<\/span> AdjList<br \/>\n<span class=\"token punctuation\">{<\/span><br \/>\n<span class=\"token comment\">\/\/\u8fb9\u7684\u60c5\u51b5<\/span><br \/>\n<span class=\"token keyword\">template<\/span><span class=\"token operator\">&lt;<\/span><span class=\"token keyword\">class<\/span> <span class=\"token class-name\">W<\/span><span class=\"token operator\">&gt;<\/span><br \/>\n<span class=\"token keyword\">struct<\/span> <span class=\"token class-name\">Edge<\/span><br \/>\n<span class=\"token punctuation\">{<\/span><br \/>\nW _w<span class=\"token punctuation\">;<\/span><span class=\"token comment\">\/\/\u6743\u503c<\/span><br \/>\n<span class=\"token keyword\">int<\/span> _desti<span class=\"token punctuation\">;<\/span><span class=\"token comment\">\/\/\u76ee\u6807\u4f4d\u7f6e\u7684\u4e0b\u6807<\/span><br \/>\nEdge<span class=\"token operator\">&lt;<\/span>W<span class=\"token operator\">&gt;<\/span><span class=\"token operator\">*<\/span> _next<span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token function\">Edge<\/span><span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> desti<span class=\"token punctuation\">,<\/span>W w<span class=\"token punctuation\">,<\/span>Edge<span class=\"token operator\">&lt;<\/span>W<span class=\"token operator\">&gt;<\/span><span class=\"token operator\">*<\/span> next<span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token operator\">:<\/span><span class=\"token function\">_desti<\/span><span class=\"token punctuation\">(<\/span>desti<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span><br \/>\n<span class=\"token function\">_w<\/span><span class=\"token punctuation\">(<\/span>w<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span><br \/>\n<span class=\"token function\">_next<\/span><span class=\"token punctuation\">(<\/span>next<span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token punctuation\">{<\/span><span class=\"token punctuation\">}<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><span class=\"token punctuation\">;<\/span><\/p>\n<p><span class=\"token keyword\">template<\/span><span class=\"token operator\">&lt;<\/span><span class=\"token keyword\">class<\/span> <span class=\"token class-name\">V<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token keyword\">class<\/span> <span class=\"token class-name\">W<\/span><span class=\"token punctuation\">,<\/span><span class=\"token keyword\">bool<\/span> Direction <span class=\"token operator\">&#061;<\/span> <span class=\"token boolean\">false<\/span><span class=\"token operator\">&gt;<\/span><br \/>\n<span class=\"token keyword\">class<\/span> <span class=\"token class-name\">Graph<\/span><br \/>\n<span class=\"token punctuation\">{<\/span><br \/>\n<span class=\"token keyword\">public<\/span><span class=\"token operator\">:<\/span><br \/>\n<span class=\"token function\">Graph<\/span><span class=\"token punctuation\">(<\/span><span class=\"token keyword\">const<\/span> V<span class=\"token operator\">*<\/span> vertexs<span class=\"token punctuation\">,<\/span> <span class=\"token keyword\">int<\/span> n<span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token punctuation\">{<\/span><br \/>\n<span class=\"token comment\">\/\/\u5148\u521d\u59cb\u5316\u6240\u6709\u7684\u9876\u70b9<\/span><br \/>\n<span class=\"token comment\">\/\/\u5148\u63d0\u524d\u5f00\u8f9f\u5185\u5b58<\/span><br \/>\n_vertexs<span class=\"token punctuation\">.<\/span><span class=\"token function\">resize<\/span><span class=\"token punctuation\">(<\/span>n<span class=\"token punctuation\">,<\/span> <span class=\"token function\">V<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> i <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span> i <span class=\"token operator\">&lt;<\/span> n<span class=\"token punctuation\">;<\/span> i<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token punctuation\">{<\/span><br \/>\n_vertexs<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> vertexs<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token comment\">\/\/\u5efa\u7acb\u6620\u5c04\u5173\u7cfb<\/span><br \/>\n_VIndexMap<span class=\"token punctuation\">[<\/span>vertexs<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> i<span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><\/p>\n<p><span class=\"token comment\">\/\/\u521d\u59cb\u5316\u90bb\u63a5\u8868<\/span><br \/>\n_AdjTable<span class=\"token punctuation\">.<\/span><span class=\"token function\">resize<\/span><span class=\"token punctuation\">(<\/span>n<span class=\"token punctuation\">,<\/span> <span class=\"token keyword\">nullptr<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><\/p>\n<p><span class=\"token punctuation\">}<\/span><\/p>\n<p><span class=\"token comment\">\/\/\u83b7\u53d6\u9876\u70b9\u7684\u4e0b\u6807<\/span><br \/>\n<span class=\"token keyword\">int<\/span> <span class=\"token function\">GetVertexIndex<\/span><span class=\"token punctuation\">(<\/span><span class=\"token keyword\">const<\/span> V<span class=\"token operator\">&amp;<\/span> v<span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token punctuation\">{<\/span><br \/>\n<span class=\"token keyword\">auto<\/span> iterator <span class=\"token operator\">&#061;<\/span> _VIndexMap<span class=\"token punctuation\">.<\/span><span class=\"token function\">find<\/span><span class=\"token punctuation\">(<\/span>v<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span>iterator <span class=\"token operator\">!&#061;<\/span> _VIndexMap<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><br \/>\n<span class=\"token punctuation\">{<\/span><br \/>\n<span class=\"token keyword\">return<\/span> iterator<span class=\"token operator\">-&gt;<\/span>second<span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><br \/>\n<span class=\"token keyword\">else<\/span><br \/>\n<span class=\"token punctuation\">{<\/span><br \/>\n<span class=\"token function\">assert<\/span><span class=\"token punctuation\">(<\/span><span class=\"token boolean\">false<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token keyword\">throw<\/span> <span class=\"token function\">invalid_argument<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;v is not a normal vertex&#034;<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><\/p>\n<p><span class=\"token keyword\">void<\/span> <span class=\"token function\">AddEdge<\/span><span class=\"token punctuation\">(<\/span><span class=\"token keyword\">const<\/span> V<span class=\"token operator\">&amp;<\/span> src<span class=\"token punctuation\">,<\/span> <span class=\"token keyword\">const<\/span> V<span class=\"token operator\">&amp;<\/span> dest<span class=\"token punctuation\">,<\/span> <span class=\"token keyword\">const<\/span> W<span class=\"token operator\">&amp;<\/span> w<span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token punctuation\">{<\/span><br \/>\n<span class=\"token keyword\">int<\/span> srci <span class=\"token operator\">&#061;<\/span> <span class=\"token function\">GetVertexIndex<\/span><span class=\"token punctuation\">(<\/span>src<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token keyword\">int<\/span> desti <span class=\"token operator\">&#061;<\/span> <span class=\"token function\">GetVertexIndex<\/span><span class=\"token punctuation\">(<\/span>dest<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token comment\">\/\/\u521b\u5efa\u65b0\u8fb9<\/span><br \/>\nEdge<span class=\"token operator\">&lt;<\/span>W<span class=\"token operator\">&gt;<\/span><span class=\"token operator\">*<\/span> newEdge <span class=\"token operator\">&#061;<\/span> <span class=\"token keyword\">new<\/span> <span class=\"token generic-function\"><span class=\"token function\">Edge<\/span><span class=\"token generic class-name\"><span class=\"token operator\">&lt;<\/span>W<span class=\"token operator\">&gt;<\/span><\/span><\/span><span class=\"token punctuation\">(<\/span>desti<span class=\"token punctuation\">,<\/span>w<span class=\"token punctuation\">,<\/span>_AdjTable<span class=\"token punctuation\">[<\/span>srci<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token comment\">\/\/\u8fdb\u884c\u94fe\u63a5<\/span><br \/>\n_AdjTable<span class=\"token punctuation\">[<\/span>srci<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> newEdge<span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span>Direction <span class=\"token operator\">&#061;&#061;<\/span> <span class=\"token boolean\">false<\/span><span class=\"token punctuation\">)<\/span><span class=\"token comment\">\/\/\u5f53\u56fe\u4e3a\u65e0\u5411\u56fe\u65f6&#xff0c;\u8fb9\u7684\u5173\u7cfb\u662f\u76f8\u4e92\u7684<\/span><br \/>\n<span class=\"token punctuation\">{<\/span><br \/>\nEdge<span class=\"token operator\">&lt;<\/span>W<span class=\"token operator\">&gt;<\/span><span class=\"token operator\">*<\/span> newEdge <span class=\"token operator\">&#061;<\/span> <span class=\"token keyword\">new<\/span> <span class=\"token generic-function\"><span class=\"token function\">Edge<\/span><span class=\"token generic class-name\"><span class=\"token operator\">&lt;<\/span>W<span class=\"token operator\">&gt;<\/span><\/span><\/span><span class=\"token punctuation\">(<\/span>srci<span class=\"token punctuation\">,<\/span> w<span class=\"token punctuation\">,<\/span> _AdjTable<span class=\"token punctuation\">[<\/span>desti<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n_AdjTable<span class=\"token punctuation\">[<\/span>desti<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> newEdge<span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><\/p>\n<p><span class=\"token keyword\">void<\/span> <span class=\"token function\">Print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token punctuation\">{<\/span><br \/>\n<span class=\"token comment\">\/\/\u6253\u5370\u9876\u70b9<\/span><br \/>\ncout <span class=\"token operator\">&lt;&lt;<\/span> <span class=\"token string\">&#034;vertexs:&#034;<\/span> <span class=\"token operator\">&lt;&lt;<\/span> endl<span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> i <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span> i <span class=\"token operator\">&lt;<\/span> _vertexs<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> i<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token punctuation\">{<\/span><br \/>\ncout <span class=\"token operator\">&lt;&lt;<\/span> <span class=\"token string\">&#034;[&#034;<\/span> <span class=\"token operator\">&lt;&lt;<\/span> i <span class=\"token operator\">&lt;&lt;<\/span> <span class=\"token string\">&#034;]&#061;&#034;<\/span> <span class=\"token operator\">&lt;&lt;<\/span> _vertexs<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&lt;&lt;<\/span> endl<span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><br \/>\ncout <span class=\"token operator\">&lt;&lt;<\/span> endl<span class=\"token punctuation\">;<\/span><\/p>\n<p><span class=\"token comment\">\/\/\u6253\u5370\u90bb\u63a5\u8868<\/span><br \/>\n<span class=\"token keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> i <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span> i <span class=\"token operator\">&lt;<\/span> _vertexs<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> i<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token punctuation\">{<\/span><br \/>\ncout <span class=\"token operator\">&lt;&lt;<\/span> _vertexs<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&lt;&lt;<\/span> <span class=\"token string\">&#034;:&#034;<\/span><span class=\"token punctuation\">;<\/span><br \/>\nEdge<span class=\"token operator\">&lt;<\/span>W<span class=\"token operator\">&gt;<\/span><span class=\"token operator\">*<\/span> cur <span class=\"token operator\">&#061;<\/span> _AdjTable<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token keyword\">while<\/span> <span class=\"token punctuation\">(<\/span>cur<span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token punctuation\">{<\/span><br \/>\ncout <span class=\"token operator\">&lt;&lt;<\/span> <span class=\"token string\">&#034;[&#034;<\/span> <span class=\"token operator\">&lt;&lt;<\/span> _vertexs<span class=\"token punctuation\">[<\/span>cur<span class=\"token operator\">-&gt;<\/span>_desti<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&lt;&lt;<\/span> <span class=\"token string\">&#034;:&#034;<\/span> <span class=\"token operator\">&lt;&lt;<\/span> cur<span class=\"token operator\">-&gt;<\/span>_w <span class=\"token operator\">&lt;&lt;<\/span> <span class=\"token string\">&#034;]-&gt;&#034;<\/span><span class=\"token punctuation\">;<\/span><br \/>\ncur <span class=\"token operator\">&#061;<\/span> cur<span class=\"token operator\">-&gt;<\/span>_next<span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><br \/>\ncout <span class=\"token operator\">&lt;&lt;<\/span> <span class=\"token string\">&#034;nullptr&#034;<\/span> <span class=\"token operator\">&lt;&lt;<\/span> endl<span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><\/p>\n<p><span class=\"token punctuation\">}<\/span><\/p>\n<p><span class=\"token keyword\">private<\/span><span class=\"token operator\">:<\/span><br \/>\nvector<span class=\"token operator\">&lt;<\/span>V<span class=\"token operator\">&gt;<\/span> _vertexs<span class=\"token punctuation\">;<\/span><span class=\"token comment\">\/\/\u9876\u70b9\u96c6\u5408<\/span><br \/>\nmap<span class=\"token operator\">&lt;<\/span>V<span class=\"token punctuation\">,<\/span> <span class=\"token keyword\">int<\/span><span class=\"token operator\">&gt;<\/span> _VIndexMap<span class=\"token punctuation\">;<\/span><span class=\"token comment\">\/\/\u6620\u5c04\u5173\u7cfb&#xff0c;\u901a\u8fc7\u9876\u70b9\u627e\u4e0b\u6807<\/span><br \/>\nvector<span class=\"token operator\">&lt;<\/span>Edge<span class=\"token operator\">&lt;<\/span>W<span class=\"token operator\">&gt;<\/span><span class=\"token operator\">*<\/span><span class=\"token operator\">&gt;<\/span> _AdjTable<span class=\"token punctuation\">;<\/span><span class=\"token comment\">\/\/\u90bb\u63a5\u8868<\/span><\/p>\n<p><span class=\"token punctuation\">}<\/span><span class=\"token punctuation\">;<\/span><\/p>\n<p><span class=\"token keyword\">void<\/span> <span class=\"token function\">TestGraph<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token punctuation\">{<\/span><br \/>\nstring a<span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> <span class=\"token punctuation\">{<\/span> <span class=\"token string\">&#034;\u5f20\u4e09&#034;<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token string\">&#034;\u674e\u56db&#034;<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token string\">&#034;\u738b\u4e94&#034;<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token string\">&#034;\u8d75\u516d&#034;<\/span> <span class=\"token punctuation\">}<\/span><span class=\"token punctuation\">;<\/span><br \/>\nGraph<span class=\"token operator\">&lt;<\/span>string<span class=\"token punctuation\">,<\/span> <span class=\"token keyword\">int<\/span><span class=\"token operator\">&gt;<\/span> <span class=\"token function\">g1<\/span><span class=\"token punctuation\">(<\/span>a<span class=\"token punctuation\">,<\/span> <span class=\"token number\">4<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\ng1<span class=\"token punctuation\">.<\/span><span class=\"token function\">AddEdge<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;\u5f20\u4e09&#034;<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token string\">&#034;\u674e\u56db&#034;<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">100<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\ng1<span class=\"token punctuation\">.<\/span><span class=\"token function\">AddEdge<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;\u5f20\u4e09&#034;<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token string\">&#034;\u738b\u4e94&#034;<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">200<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\ng1<span class=\"token punctuation\">.<\/span><span class=\"token function\">AddEdge<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#034;\u738b\u4e94&#034;<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token string\">&#034;\u8d75\u516d&#034;<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">30<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\ng1<span class=\"token punctuation\">.<\/span><span class=\"token function\">Print<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><\/p>\n<p><span class=\"token punctuation\">}<\/span><\/p>\n<p><span class=\"token punctuation\">}<\/span><\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/01\/20260130195718-697d0d1e79a3f.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<h2>3.\u56fe\u7684\u904d\u5386<\/h2>\n<p>\u56fe\u7684\u904d\u5386\u65b9\u5f0f\u4e00\u5171\u6709\u4e24\u79cd&#xff0c;\u5206\u522b\u662f\u5e7f\u5ea6\u4f18\u5148\u904d\u5386\u548c\u6df1\u5ea6\u4f18\u5148\u904d\u5386 \u5148\u8bf4\u5e7f\u5ea6\u4f18\u5148\u904d\u5386&#xff1a;\u4ece\u8d77\u59cb\u8282\u70b9\u5f00\u59cb&#xff0c;\u9010\u5c42\u8bbf\u95ee\u6240\u6709\u76f8\u90bb\u8282\u70b9&#xff0c;\u518d\u4f9d\u6b21\u8bbf\u95ee\u4e0b\u4e00\u5c42\u8282\u70b9\u3002\u8be5\u7b97\u6cd5\u901a\u5e38\u501f\u52a9\u961f\u5217\u5b9e\u73b0&#xff0c;\u4fdd\u8bc1\u6309\u5c42\u7ea7\u987a\u5e8f\u8bbf\u95ee\u8282\u70b9\u3002\u5728\u4e8c\u53c9\u6811\u4e2d&#xff0c;\u5c42\u5e8f\u904d\u5386\u5c31\u662f\u5e7f\u5ea6\u4f18\u5148\u904d\u5386 <img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/01\/20260130195718-697d0d1ebfb05.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/> \u5728\u56fe\u4e2d\u8fdb\u884c\u5e7f\u5ea6\u4f18\u5148\u904d\u5386\u9700\u8981\u5148\u786e\u5b9a\u4ece\u54ea\u4e00\u4e2a\u9876\u70b9\u5f00\u59cb\u904d\u5386&#xff0c;\u5e76\u4e14\u6211\u4eec\u9700\u8981\u4e00\u4e2a\u961f\u5217\u548c\u4e00\u4e2a\u6807\u8bb0\u5bb9\u5668 \u4e4b\u6240\u4ee5\u9700\u8981\u6807\u8bb0\u5bb9\u5668\u662f\u56e0\u4e3a\u9632\u6b62\u91cd\u590d\u9876\u70b9\u8fdb\u5165\u5230\u961f\u5217\u4e2d\u3002\u5f53\u6211\u4eec\u5c06\u9876\u70b9\u5165\u961f\u5217\u540e\u5c31\u8fdb\u884c\u6807\u8bb0\u4e00\u4e0b&#xff0c;\u8fd9\u6837\u5c31\u53ef\u4ee5\u4fdd\u8bc1\u5f53A\u51fa\u7684\u65f6\u5019\u5c06BCD\u5165\u961f\u5217&#xff0c;\u4f46\u5f53B\u51fa\u7684\u65f6\u5019\u53ea\u4f1a\u5c06E\u5165\u961f\u5217&#xff0c;\u800c\u4e0d\u4f1a\u5c06AC\u653e\u5165\u961f\u5217<\/p>\n<p><span class=\"token comment\">\/\/\u5e7f\u5ea6\u4f18\u5148\u904d\u5386<\/span><br \/>\n<span class=\"token keyword\">void<\/span> <span class=\"token function\">_BFS<\/span><span class=\"token punctuation\">(<\/span><span class=\"token keyword\">const<\/span> V<span class=\"token operator\">&amp;<\/span> src<span class=\"token punctuation\">,<\/span> queue<span class=\"token operator\">&lt;<\/span><span class=\"token keyword\">int<\/span><span class=\"token operator\">&gt;<\/span><span class=\"token operator\">&amp;<\/span> q<span class=\"token punctuation\">,<\/span> vector<span class=\"token operator\">&lt;<\/span><span class=\"token keyword\">bool<\/span><span class=\"token operator\">&gt;<\/span><span class=\"token operator\">&amp;<\/span> visited<span class=\"token punctuation\">)<\/span><span class=\"token comment\">\/\/\u4ece\u4e00\u4e2a\u9876\u70b9\u5f00\u59cb\u904d\u5386<\/span><br \/>\n<span class=\"token punctuation\">{<\/span><br \/>\nvisited<span class=\"token punctuation\">.<\/span><span class=\"token function\">resize<\/span><span class=\"token punctuation\">(<\/span>_vertexs<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 boolean\">false<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><span class=\"token comment\">\/\/\u9ed8\u8ba4\u662f\u6ca1\u6709\u6807\u8bb0\u8fc7\u7684<\/span><br \/>\n<span class=\"token keyword\">int<\/span> index <span class=\"token operator\">&#061;<\/span> <span class=\"token function\">GetVertexIndex<\/span><span class=\"token punctuation\">(<\/span>src<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><span class=\"token comment\">\/\/\u83b7\u53d6\u9876\u70b9\u4e0b\u6807<\/span><br \/>\nq<span class=\"token punctuation\">.<\/span><span class=\"token function\">push<\/span><span class=\"token punctuation\">(<\/span>index<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\nvisited<span class=\"token punctuation\">[<\/span>index<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> <span class=\"token boolean\">true<\/span><span class=\"token punctuation\">;<\/span><span class=\"token comment\">\/\/\u8bbf\u95ee\u8fc7\u4e86\u5c31\u8bbe\u4e3atrue<\/span><br \/>\n<span class=\"token keyword\">while<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token operator\">!<\/span>q<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><span class=\"token comment\">\/\/\u4e0d\u4e3a\u7a7a\u5c31\u4e00\u76f4\u904d\u5386\u4e0b\u53bb<\/span><br \/>\n<span class=\"token punctuation\">{<\/span><br \/>\nindex <span class=\"token operator\">&#061;<\/span> q<span class=\"token punctuation\">.<\/span><span class=\"token function\">front<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><span class=\"token comment\">\/\/\u53d6\u961f\u5934<\/span><br \/>\nq<span class=\"token punctuation\">.<\/span><span class=\"token function\">pop<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\ncout <span class=\"token operator\">&lt;&lt;<\/span> _vertexs<span class=\"token punctuation\">[<\/span>index<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&lt;&lt;<\/span> <span class=\"token string\">&#034; &#034;<\/span><span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> j <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span> j <span class=\"token operator\">&lt;<\/span> _vertexs<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> j<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">)<\/span><span class=\"token comment\">\/\/\u7ee7\u7eed\u5c06\u540e\u7eed\u7684\u9876\u70b9\u5165\u961f\u5217<\/span><br \/>\n<span class=\"token punctuation\">{<\/span><br \/>\n<span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span>_matrix<span class=\"token punctuation\">[<\/span>index<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">[<\/span>j<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">!&#061;<\/span> MAX_W<span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token punctuation\">{<\/span><br \/>\n<span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span>visited<span class=\"token punctuation\">[<\/span>j<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;&#061;<\/span> <span class=\"token boolean\">false<\/span><span class=\"token punctuation\">)<\/span><span class=\"token comment\">\/\/\u5224\u65ad\u662f\u5426\u5df2\u7ecf\u6807\u8bb0\u8fc7<\/span><br \/>\n<span class=\"token punctuation\">{<\/span><br \/>\nq<span class=\"token punctuation\">.<\/span><span class=\"token function\">push<\/span><span class=\"token punctuation\">(<\/span>j<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\nvisited<span class=\"token punctuation\">[<\/span>j<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> <span class=\"token boolean\">true<\/span><span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><\/p>\n<p><span class=\"token keyword\">void<\/span> <span class=\"token function\">BFS<\/span><span class=\"token punctuation\">(<\/span><span class=\"token keyword\">const<\/span> V<span class=\"token operator\">&amp;<\/span> src<span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token punctuation\">{<\/span><br \/>\nqueue<span class=\"token operator\">&lt;<\/span><span class=\"token keyword\">int<\/span><span class=\"token operator\">&gt;<\/span> q<span class=\"token punctuation\">;<\/span><span class=\"token comment\">\/\/\u7528\u6765\u5b58\u653e\u9876\u70b9\u4e0b\u6807<\/span><br \/>\nvector<span class=\"token operator\">&lt;<\/span><span class=\"token keyword\">bool<\/span><span class=\"token operator\">&gt;<\/span> visited<span class=\"token punctuation\">;<\/span><span class=\"token comment\">\/\/\u6807\u8bb0\u5bb9\u5668&#xff0c;\u5df2\u7ecf\u5165\u8fc7\u961f\u5217\u7684\u5c31\u8fdb\u884c\u8bbe\u7f6e&#xff0c;\u4fdd\u8bc1\u4e0d\u4f1a\u7528\u91cd\u590d\u7684\u5143\u7d20\u8fdb\u5165\u961f\u5217<\/span><br \/>\n<span class=\"token function\">_BFS<\/span><span class=\"token punctuation\">(<\/span>src<span class=\"token punctuation\">,<\/span>q<span class=\"token punctuation\">,<\/span>visited<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> i <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span> i <span class=\"token operator\">&lt;<\/span> visited<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> i<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token punctuation\">{<\/span><br \/>\n<span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span>visited<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;&#061;<\/span><span class=\"token boolean\">false<\/span><span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token punctuation\">{<\/span><br \/>\n<span class=\"token function\">_BFS<\/span><span class=\"token punctuation\">(<\/span>_vertexs<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span> q<span class=\"token punctuation\">,<\/span> visited<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><\/p>\n<p><span class=\"token punctuation\">}<\/span><\/p>\n<p>\u5e76\u4e14\u8fd8\u8981\u6ce8\u610f\u4e00\u4e2a\u70b9\u5c31\u662f\u904d\u5386\u7684\u8fd9\u4e2a\u56fe\u53ef\u80fd\u4e0d\u662f\u4e00\u4e2a\u8fde\u901a\u7684&#xff0c;\u56e0\u6b64\u6700\u540e\u9700\u8981\u4e00\u4e2a\u5faa\u73af\u6765\u904d\u5386\u6240\u6709\u7684\u9876\u70b9&#xff0c;\u5c06\u6ca1\u6709\u904d\u5386\u7684\u9876\u70b9\u8fdb\u884c\u904d\u5386<\/p>\n<p>\u63a5\u4e0b\u6765\u5c31\u662f\u6df1\u5ea6\u4f18\u5148\u904d\u5386&#xff1a;\u5c3d\u53ef\u80fd\u6df1\u5730\u63a2\u7d22\u5206\u652f&#xff0c;\u76f4\u5230\u65e0\u6cd5\u7ee7\u7eed\u4e3a\u6b62&#xff0c;\u518d\u56de\u6eaf\u5230\u4e0a\u4e00\u4e2a\u8282\u70b9\u7ee7\u7eed\u63a2\u7d22\u5176\u4ed6\u5206\u652f\u3002DFS\u901a\u5e38\u901a\u8fc7\u9012\u5f52\u6216\u663e\u5f0f\u6808\u5b9e\u73b0\u3002\u5728\u4e8c\u53c9\u6811\u4e2d&#xff0c;\u524d\u5e8f\u4e2d\u5e8f\u540e\u5e8f\u5c31\u662f\u6df1\u5ea6\u4f18\u5148\u904d\u5386 <img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/01\/20260130195718-697d0d1ee8754.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<p>    <span class=\"token keyword\">void<\/span> <span class=\"token function\">_DFS<\/span><span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> index<span class=\"token punctuation\">,<\/span> vector<span class=\"token operator\">&lt;<\/span><span class=\"token keyword\">bool<\/span><span class=\"token operator\">&gt;<\/span><span class=\"token operator\">&amp;<\/span> visited<span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token punctuation\">{<\/span><br \/>\ncout <span class=\"token operator\">&lt;&lt;<\/span> _vertexs<span class=\"token punctuation\">[<\/span>index<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&lt;&lt;<\/span> <span class=\"token string\">&#034; &#034;<\/span><span class=\"token punctuation\">;<\/span><br \/>\nvisited<span class=\"token punctuation\">[<\/span>index<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> <span class=\"token boolean\">true<\/span><span class=\"token punctuation\">;<\/span><span class=\"token comment\">\/\/\u8fdb\u884c\u6807\u8bb0<\/span><\/p>\n<p><span class=\"token keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> i <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span> i <span class=\"token operator\">&lt;<\/span> _vertexs<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> i<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token punctuation\">{<\/span><br \/>\n<span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span>_matrix<span class=\"token punctuation\">[<\/span>index<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">!&#061;<\/span> MAX_W<span class=\"token operator\">&amp;&amp;<\/span> visited<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;&#061;<\/span> <span class=\"token boolean\">false<\/span><span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token punctuation\">{<\/span><br \/>\n<span class=\"token function\">_DFS<\/span><span class=\"token punctuation\">(<\/span>i<span class=\"token punctuation\">,<\/span> visited<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><\/p>\n<p><span class=\"token comment\">\/\/\u6df1\u5ea6\u4f18\u5148\u904d\u5386<\/span><br \/>\n<span class=\"token keyword\">void<\/span> <span class=\"token function\">DFS<\/span><span class=\"token punctuation\">(<\/span><span class=\"token keyword\">const<\/span> V<span class=\"token operator\">&amp;<\/span> src<span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token punctuation\">{<\/span><br \/>\n<span class=\"token keyword\">int<\/span> index<span class=\"token operator\">&#061;<\/span><span class=\"token function\">GetVertexIndex<\/span><span class=\"token punctuation\">(<\/span>src<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\nvector<span class=\"token operator\">&lt;<\/span><span class=\"token keyword\">bool<\/span><span class=\"token operator\">&gt;<\/span> visited<span class=\"token punctuation\">;<\/span><span class=\"token comment\">\/\/\u7528\u6765\u9632\u6b62\u91cd\u590d\u8bbf\u95ee<\/span><br \/>\nvisited<span class=\"token punctuation\">.<\/span><span class=\"token function\">resize<\/span><span class=\"token punctuation\">(<\/span>_vertexs<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 boolean\">false<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token function\">_DFS<\/span><span class=\"token punctuation\">(<\/span>index<span class=\"token punctuation\">,<\/span> visited<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><\/p>\n<p><span class=\"token keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> i<span class=\"token operator\">&#061;<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span>i<span class=\"token operator\">&lt;<\/span>visited<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>i<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token punctuation\">{<\/span><br \/>\n<span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span>visited<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token operator\">&#061;&#061;<\/span><span class=\"token boolean\">false<\/span><span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token punctuation\">{<\/span><br \/>\n<span class=\"token function\">_DFS<\/span><span class=\"token punctuation\">(<\/span>i<span class=\"token punctuation\">,<\/span> visited<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><\/p>\n<p>\u5728\u6df1\u5ea6\u4f18\u5148\u904d\u5386\u4e2d\u4e5f\u662f\u9700\u8981\u6709\u4e00\u4e2a\u6807\u8bb0\u5bb9\u5668\u6765\u4fdd\u8bc1\u4e0d\u4f1a\u8fdb\u884c\u91cd\u590d\u8bbf\u95ee&#xff0c;\u5e76\u4e14\u4e5f\u8981\u5173\u6ce8\u4e00\u4e0b\u4e0d\u8fde\u901a\u56fe\u65f6&#xff0c;\u4e5f\u8981\u8bbf\u95ee\u5230\u6240\u6709\u7684\u7ed3\u70b9\u3002\u5b83\u7684\u6df1\u5ea6\u4f18\u5148\u904d\u5386\u5176\u5b9e\u548c\u4e8c\u53c9\u6811\u4e00\u6837&#xff0c;\u9700\u8981\u4f7f\u7528\u9012\u5f52\u6765\u5b9e\u73b0\u7684 <img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/01\/20260130195719-697d0d1f28306.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<h2>4.\u6700\u5c0f\u751f\u6210\u6811<\/h2>\n<p>\u8fde\u901a\u56fe\u4e2d\u7684\u6bcf\u4e00\u68f5\u751f\u6210\u6811&#xff0c;\u90fd\u662f\u539f\u56fe\u7684\u4e00\u4e2a\u6781\u5927\u65e0\u73af\u5b50\u56fe&#xff0c;\u5373&#xff1a;\u4ece\u5176\u4e2d\u5220\u53bb\u4efb\u4f55\u4e00\u6761\u8fb9&#xff0c;\u751f\u6210\u6811\u5c31\u4e0d\u5728\u8fde\u901a&#xff1b;\u53cd\u4e4b&#xff0c;\u5728\u5176\u4e2d\u5f15\u5165\u4efb\u4f55\u4e00\u6761\u65b0\u8fb9&#xff0c;\u90fd\u4f1a\u5f62\u6210\u4e00\u6761\u56de\u8def\u3002 \u82e5\u8fde\u901a\u56fe\u7531n\u4e2a\u9876\u70b9\u7ec4\u6210&#xff0c;\u5219\u5176\u751f\u6210\u6811\u5fc5\u542bn\u4e2a\u9876\u70b9\u548cn-1\u6761\u8fb9\u3002\u56e0\u6b64\u6784\u9020\u6700\u5c0f\u751f\u6210\u6811\u7684\u51c6\u5219\u6709\u4e09\u6761&#xff1a; \u2460\u53ea\u80fd\u4f7f\u7528\u56fe\u4e2d\u6743\u503c\u6700\u5c0f\u7684\u8fb9\u6765\u6784\u9020\u6700\u5c0f\u751f\u6210\u6811 \u2461 \u53ea\u80fd\u4f7f\u7528\u6070\u597dn-1\u6761\u8fb9\u6765\u8fde\u63a5\u56fe\u4e2d\u7684n\u4e2a\u9876\u70b9 \u2462 \u9009\u7528\u7684n-1\u6761\u8fb9\u4e0d\u80fd\u6784\u6210\u56de\u8def \u6784\u9020\u6700\u5c0f\u751f\u6210\u6811\u7684\u65b9\u6cd5&#xff1a;Kruskal\u7b97\u6cd5\u548cPrim\u7b97\u6cd5\u3002\u8fd9\u4e24\u4e2a\u7b97\u6cd5\u90fd\u91c7\u7528\u4e86\u9010\u6b65\u6c42\u89e3\u7684\u8d2a\u5fc3\u7b56\u7565\u3002 \u8d2a\u5fc3\u7b97\u6cd5&#xff1a;\u662f\u6307\u5728\u95ee\u9898\u6c42\u89e3\u65f6&#xff0c;\u603b\u662f\u505a\u51fa\u5f53\u524d\u770b\u8d77\u6765\u6700\u597d\u7684\u9009\u62e9\u3002\u4e5f\u5c31\u662f\u8bf4\u8d2a\u5fc3\u7b97\u6cd5\u505a\u51fa\u7684\u4e0d\u662f\u6574\u4f53\u6700\u4f18\u7684\u7684\u9009\u62e9&#xff0c;\u800c\u662f\u67d0\u79cd\u610f\u4e49\u4e0a\u7684\u5c40\u90e8\u6700\u4f18\u89e3\u3002\u8d2a\u5fc3\u7b97\u6cd5\u4e0d\u662f\u5bf9\u6240\u6709\u7684\u95ee\u9898\u90fd\u80fd\u5f97\u5230\u6574\u4f53\u6700\u4f18\u89e3\u3002<\/p>\n<h3>4.1.Kruskal\u7b97\u6cd5<\/h3>\n<p>\u9996\u5148\u6784\u9020\u4e00\u4e2a\u7531\u8fd9n\u4e2a\u9876\u70b9\u7ec4\u6210\u3001\u4e0d\u542b\u4efb\u4f55\u8fb9\u7684\u56feG&#061;{V,NULL}&#xff0c;\u5176\u4e2d\u6bcf\u4e2a\u9876\u70b9\u81ea\u6210\u4e00\u4e2a\u8fde\u901a\u5206\u91cf&#xff0c;\u5176\u6b21\u4e0d\u65ad\u4eceE\u4e2d\u53d6\u51fa\u6743\u503c\u6700\u5c0f\u7684\u4e00\u6761\u8fb9(\u82e5\u6709\u591a\u6761\u4efb\u53d6\u5176\u4e00)&#xff0c;\u82e5\u8be5\u8fb9\u7684\u4e24\u4e2a\u9876\u70b9\u6765\u81ea\u4e0d\u540c\u7684\u8fde\u901a\u5206\u91cf&#xff0c;\u5219\u5c06\u6b64\u8fb9\u52a0\u5165\u5230G\u4e2d\u3002\u5982\u6b64\u91cd\u590d&#xff0c;\u76f4\u5230\u6240\u6709\u9876\u70b9\u5728\u540c\u4e00\u4e2a\u8fde\u901a\u5206\u91cf\u4e0a\u4e3a\u6b62\u3002 \u6838\u5fc3&#xff1a;\u6bcf\u6b21\u8fed\u4ee3\u65f6&#xff0c;\u9009\u51fa\u4e00\u6761\u5177\u6709\u6700\u5c0f\u6743\u503c&#xff0c;\u4e14\u4e24\u7aef\u70b9\u4e0d\u5728\u540c\u4e00\u8fde\u901a\u5206\u91cf\u4e0a\u7684\u8fb9&#xff08;\u4e0d\u80fd\u6784\u6210\u73af&#xff09;&#xff0c;\u52a0\u5165\u751f\u6210\u6811\u3002 <img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/01\/20260130195719-697d0d1f89d38.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/> \u5728\u67e5\u627e\u6700\u5c0f\u6743\u503c\u8def\u5f84\u7684\u8fc7\u7a0b\u4e2d&#xff0c;\u4e0d\u80fd\u51fa\u73b0\u73af&#xff0c;\u56e0\u6b64\u6211\u4eec\u5728\u7f16\u5199\u4ee3\u7801\u7684\u8fc7\u7a0b\u4e2d&#xff0c;\u9700\u8981\u60f3\u529e\u6cd5\u5224\u522b\u6709\u6ca1\u6709\u6784\u6210\u73af\u3002\u8fd9\u4e2a\u65f6\u5019\u5c31\u7528\u5230\u4e86\u6211\u4eec\u4e4b\u524d\u8bb2\u7684\u5e76\u67e5\u96c6&#xff0c;\u5c06\u9009\u51fa\u7684\u6700\u5c0f\u6743\u503c\u7684\u8fb9\u7684\u4e24\u4e2a\u9876\u70b9\u653e\u5165\u5230\u5e76\u67e5\u96c6\u4e2d&#xff0c;\u5728\u540e\u7eed\u7684\u9009\u62e9\u8fc7\u7a0b\u4e2d&#xff0c;\u4e00\u65e6\u51fa\u73b0\u6709\u9876\u70b9\u662f\u5728\u540c\u4e00\u4e2a\u96c6\u5408\u91cc\u9762&#xff0c;\u8bf4\u660e\u6709\u73af&#xff0c;\u5c31\u4e0d\u80fd\u9009\u62e9\u3002\u5e76\u4e14\u6211\u4eec\u9700\u8981\u9009\u51fa\u6700\u6743\u503c\u6700\u5c0f\u7684\u8fb9\u5c31\u9700\u8981\u4f7f\u7528\u5230\u4f18\u5148\u7ea7\u961f\u5217\u3002<\/p>\n<p>    <span class=\"token comment\">\/\/\u6700\u5c0f\u751f\u6210\u6811\u7b97\u6cd5<\/span><br \/>\nW <span class=\"token function\">Kruskal<\/span><span class=\"token punctuation\">(<\/span>Self<span class=\"token operator\">&amp;<\/span> minTree<span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token punctuation\">{<\/span><br \/>\n<span class=\"token keyword\">int<\/span> size <span class=\"token operator\">&#061;<\/span> _vertexs<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><\/p>\n<p>minTree<span class=\"token punctuation\">.<\/span>_vertexs <span class=\"token operator\">&#061;<\/span> _vertexs<span class=\"token punctuation\">;<\/span><br \/>\nminTree<span class=\"token punctuation\">.<\/span>_VIndexMap <span class=\"token operator\">&#061;<\/span> _VIndexMap<span class=\"token punctuation\">;<\/span><br \/>\nminTree<span class=\"token punctuation\">.<\/span>_matrix<span class=\"token punctuation\">.<\/span><span class=\"token function\">resize<\/span><span class=\"token punctuation\">(<\/span>size<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> i <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span> i <span class=\"token operator\">&lt;<\/span> size<span class=\"token punctuation\">;<\/span> i<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token punctuation\">{<\/span><br \/>\nminTree<span class=\"token punctuation\">.<\/span>_matrix<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">.<\/span><span class=\"token function\">resize<\/span><span class=\"token punctuation\">(<\/span>size<span class=\"token punctuation\">,<\/span>MAX_W<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><\/p>\n<p><span class=\"token comment\">\/\/\u4f7f\u7528\u4f18\u5148\u7ea7\u961f\u5217\u6765\u4f9d\u6b21\u9009\u62e9\u6700\u5c0f\u7684\u8fb9<\/span><br \/>\npriority_queue<span class=\"token operator\">&lt;<\/span>Edge<span class=\"token operator\">&lt;<\/span>W<span class=\"token operator\">&gt;<\/span><span class=\"token punctuation\">,<\/span> deque<span class=\"token operator\">&lt;<\/span>Edge<span class=\"token operator\">&lt;<\/span>W<span class=\"token operator\">&gt;&gt;<\/span><span class=\"token punctuation\">,<\/span> greater<span class=\"token operator\">&lt;<\/span>Edge<span class=\"token operator\">&lt;<\/span>W<span class=\"token operator\">&gt;&gt;<\/span><span class=\"token operator\">&gt;<\/span> pquemin<span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> i <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span> i <span class=\"token operator\">&lt;<\/span> size<span class=\"token punctuation\">;<\/span> i<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token punctuation\">{<\/span><br \/>\n<span class=\"token keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> j <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span> j <span class=\"token operator\">&lt;<\/span> i<span class=\"token punctuation\">;<\/span> j<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">)<\/span><span class=\"token comment\">\/\/\u65e0\u5411\u56fe\u7684\u90bb\u63a5\u77e9\u9635\u662f\u5bf9\u79f0\u7684&#xff0c;\u53ea\u53d6\u4e00\u534a\u5c31\u53ef\u4ee5\u4e86<\/span><br \/>\n<span class=\"token punctuation\">{<\/span><br \/>\n<span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span>_matrix<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\">!&#061;<\/span> MAX_W<span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token punctuation\">{<\/span><br \/>\npquemin<span class=\"token punctuation\">.<\/span><span class=\"token function\">push<\/span><span class=\"token punctuation\">(<\/span><span class=\"token generic-function\"><span class=\"token function\">Edge<\/span><span class=\"token generic class-name\"><span class=\"token operator\">&lt;<\/span>W<span class=\"token operator\">&gt;<\/span><\/span><\/span><span class=\"token punctuation\">(<\/span>i<span class=\"token punctuation\">,<\/span> j<span class=\"token punctuation\">,<\/span> _matrix<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 punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><\/p>\n<p><span class=\"token keyword\">int<\/span> edge_count <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span><span class=\"token comment\">\/\/\u8bb0\u5f55\u8fb9\u6570<\/span><br \/>\nUnionFindSet<span class=\"token operator\">&lt;<\/span><span class=\"token keyword\">int<\/span><span class=\"token operator\">&gt;<\/span> <span class=\"token function\">ufs<\/span><span class=\"token punctuation\">(<\/span>_vertexs<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><br \/>\nW totalW <span class=\"token operator\">&#061;<\/span> <span class=\"token function\">W<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><\/p>\n<p><span class=\"token keyword\">while<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token operator\">!<\/span>pquemin<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><br \/>\n<span class=\"token punctuation\">{<\/span><br \/>\nEdge<span class=\"token operator\">&lt;<\/span>W<span class=\"token operator\">&gt;<\/span> e<span class=\"token operator\">&#061;<\/span>pquemin<span class=\"token punctuation\">.<\/span><span class=\"token function\">top<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><span class=\"token comment\">\/\/\u9009\u51fa\u6743\u503c\u6700\u5c0f\u7684\u8fb9<\/span><br \/>\npquemin<span class=\"token punctuation\">.<\/span><span class=\"token function\">pop<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><\/p>\n<p><span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token operator\">!<\/span>ufs<span class=\"token punctuation\">.<\/span><span class=\"token function\">InSet<\/span><span class=\"token punctuation\">(<\/span>e<span class=\"token punctuation\">.<\/span>_srci<span class=\"token punctuation\">,<\/span> e<span class=\"token punctuation\">.<\/span>_desti<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><span class=\"token comment\">\/\/\u5224\u65ad\u662f\u5426\u51fa\u73b0\u73af<\/span><br \/>\n<span class=\"token punctuation\">{<\/span><br \/>\ncout <span class=\"token operator\">&lt;&lt;<\/span> _vertexs<span class=\"token punctuation\">[<\/span>e<span class=\"token punctuation\">.<\/span>_srci<span class=\"token punctuation\">]<\/span><span class=\"token operator\">&lt;&lt;<\/span> <span class=\"token string\">&#034;-&gt;&#034;<\/span> <span class=\"token operator\">&lt;&lt;<\/span> _vertexs<span class=\"token punctuation\">[<\/span>e<span class=\"token punctuation\">.<\/span>_desti<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&lt;&lt;<\/span> <span class=\"token string\">&#034;:&#034;<\/span> <span class=\"token operator\">&lt;&lt;<\/span> e<span class=\"token punctuation\">.<\/span>_w <span class=\"token operator\">&lt;&lt;<\/span> endl<span class=\"token punctuation\">;<\/span><br \/>\nufs<span class=\"token punctuation\">.<\/span><span class=\"token function\">Union<\/span><span class=\"token punctuation\">(<\/span>e<span class=\"token punctuation\">.<\/span>_srci<span class=\"token punctuation\">,<\/span> e<span class=\"token punctuation\">.<\/span>_desti<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\nminTree<span class=\"token punctuation\">.<\/span><span class=\"token function\">AddEdge<\/span><span class=\"token punctuation\">(<\/span>_vertexs<span class=\"token punctuation\">[<\/span>e<span class=\"token punctuation\">.<\/span>_srci<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span> _vertexs<span class=\"token punctuation\">[<\/span>e<span class=\"token punctuation\">.<\/span>_desti<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span>e<span class=\"token punctuation\">.<\/span>_w<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\ntotalW <span class=\"token operator\">&#043;&#061;<\/span> e<span class=\"token punctuation\">.<\/span>_w<span class=\"token punctuation\">;<\/span><br \/>\nedge_count<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">;<\/span><span class=\"token comment\">\/\/\u8fb9\u6570&#043;1<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><br \/>\n<span class=\"token keyword\">else<\/span><br \/>\n<span class=\"token punctuation\">{<\/span><br \/>\ncout <span class=\"token operator\">&lt;&lt;<\/span><span class=\"token string\">&#034;\u6784\u6210\u73af&#xff1a;&#034;<\/span> <span class=\"token operator\">&lt;&lt;<\/span> _vertexs<span class=\"token punctuation\">[<\/span>e<span class=\"token punctuation\">.<\/span>_srci<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&lt;&lt;<\/span> <span class=\"token string\">&#034;-&gt;&#034;<\/span> <span class=\"token operator\">&lt;&lt;<\/span> _vertexs<span class=\"token punctuation\">[<\/span>e<span class=\"token punctuation\">.<\/span>_desti<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&lt;&lt;<\/span> <span class=\"token string\">&#034;:&#034;<\/span> <span class=\"token operator\">&lt;&lt;<\/span> e<span class=\"token punctuation\">.<\/span>_w <span class=\"token operator\">&lt;&lt;<\/span> endl<span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><\/p>\n<p><span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span>edge_count <span class=\"token operator\">&#061;&#061;<\/span> size <span class=\"token operator\">&#8211;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token punctuation\">{<\/span><br \/>\n<span class=\"token keyword\">return<\/span> totalW<span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><br \/>\n<span class=\"token keyword\">else<\/span><br \/>\n<span class=\"token punctuation\">{<\/span><br \/>\n<span class=\"token keyword\">return<\/span> <span class=\"token function\">W<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><\/p>\n<h3>4.2.Prim\u7b97\u6cd5<\/h3>\n<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/01\/20260130195720-697d0d20ea240.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<p>Prim\u7b97\u6cd5\u7b80\u5355\u6765\u8bf4\u4ece\u4e00\u4e2a\u8d77\u59cb\u9876\u70b9\u51fa\u53d1&#xff0c;\u6bcf\u6b21\u53ea\u9009\u300c\u5df2\u8fde\u901a\u9876\u70b9\u548c\u672a\u8fde\u901a\u9876\u70b9\u4e4b\u95f4\u6743\u91cd\u6700\u5c0f\u7684\u8fb9\u300d&#xff0c;\u628a\u672a\u8fde\u901a\u9876\u70b9\u7eb3\u5165\u8fde\u901a\u96c6\u5408&#xff0c;\u91cd\u590d\u76f4\u5230\u6240\u6709\u9876\u70b9\u90fd\u8fde\u901a \u2014\u2014 \u6700\u7ec8\u5f62\u6210\u65e0\u73af\u3001\u603b\u6743\u91cd\u6700\u5c0f\u7684\u751f\u6210\u6811\u3002 \u5728\u5b9e\u73b0\u7684Prim\u7b97\u6cd5\u4e2d&#xff0c;\u4f7f\u7528\u4e86vector X \u548c vector Y&#xff0c;\u5b83\u4eec\u662f\u4e00\u5bf9\u4e92\u8865\u7684\u9876\u70b9\u72b6\u6001\u6807\u8bb0\u5bb9\u5668&#xff0c;\u6838\u5fc3\u4f5c\u7528\u662f\u300c\u8ddf\u8e2a\u6bcf\u4e2a\u9876\u70b9\u662f\u5426\u5df2\u52a0\u5165\u6700\u5c0f\u751f\u6210\u6811&#xff08;MST&#xff09;\u300d\u2014\u2014 \u672c\u8d28\u662f\u7528\u4e24\u4e2a\u6570\u7ec4\u76f4\u89c2\u533a\u5206\u300c\u5df2\u9009\u9876\u70b9\u96c6\u5408\u300d\u548c\u300c\u672a\u9009\u9876\u70b9\u96c6\u5408\u300d&#xff0c;\u914d\u5408\u7b97\u6cd5\u6d41\u7a0b\u5b9e\u73b0\u300c\u65e0\u73af\u8fde\u901a\u300d\u7684\u6838\u5fc3\u76ee\u6807\u3002<\/p>\n<p><span class=\"token comment\">\/\/\u6700\u5c0f\u751f\u6210\u6811\u7b97\u6cd5<\/span><br \/>\nW <span class=\"token function\">Prim<\/span><span class=\"token punctuation\">(<\/span>Self<span class=\"token operator\">&amp;<\/span> minTree<span class=\"token punctuation\">,<\/span> <span class=\"token keyword\">const<\/span> V<span class=\"token operator\">&amp;<\/span> src<span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token punctuation\">{<\/span><br \/>\n<span class=\"token keyword\">int<\/span> srci <span class=\"token operator\">&#061;<\/span><span class=\"token function\">GetVertexIndex<\/span><span class=\"token punctuation\">(<\/span>src<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><span class=\"token comment\">\/\/\u627e\u5230\u5f00\u59cb\u7ed3\u70b9\u7684\u4e0b\u6807<\/span><br \/>\n<span class=\"token comment\">\/\/\u5148\u5bf9\u6700\u5c0f\u751f\u6210\u6811\u8fdb\u884c\u57fa\u672c\u521d\u59cb\u5316<\/span><br \/>\nminTree<span class=\"token punctuation\">.<\/span>_vertexs <span class=\"token operator\">&#061;<\/span> _vertexs<span class=\"token punctuation\">;<\/span><br \/>\nminTree<span class=\"token punctuation\">.<\/span>_VIndexMap <span class=\"token operator\">&#061;<\/span> _VIndexMap<span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token keyword\">int<\/span> n <span class=\"token operator\">&#061;<\/span> _matrix<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><br \/>\nminTree<span class=\"token punctuation\">.<\/span>_matrix<span class=\"token punctuation\">.<\/span><span class=\"token function\">resize<\/span><span class=\"token punctuation\">(<\/span>n<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> i <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span> i <span class=\"token operator\">&lt;<\/span> n<span class=\"token punctuation\">;<\/span> i<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token punctuation\">{<\/span><br \/>\nminTree<span class=\"token punctuation\">.<\/span>_matrix<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">.<\/span><span class=\"token function\">resize<\/span><span class=\"token punctuation\">(<\/span>n<span class=\"token punctuation\">,<\/span> MAX_W<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><\/p>\n<p><span class=\"token comment\">\/\/\u521b\u5efa\u4e24\u4e2a\u6807\u8bb0\u5bb9\u5668&#xff0c;X\u4ee3\u8868\u5df2\u7ecf\u88ab\u9009\u62e9&#xff0c;Y\u4ee3\u8868\u6ca1\u6709\u88ab\u9009\u62e9<\/span><br \/>\nvector<span class=\"token operator\">&lt;<\/span><span class=\"token keyword\">bool<\/span><span class=\"token operator\">&gt;<\/span> <span class=\"token function\">X<\/span><span class=\"token punctuation\">(<\/span>n<span class=\"token punctuation\">,<\/span> <span class=\"token boolean\">false<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><span class=\"token comment\">\/\/\u51fa\u961f\u65f6\u5224\u73af&#xff0c;\u907f\u514d\u52a0\u5165\u73af\u8fb9<\/span><br \/>\nvector<span class=\"token operator\">&lt;<\/span><span class=\"token keyword\">bool<\/span><span class=\"token operator\">&gt;<\/span> <span class=\"token function\">Y<\/span><span class=\"token punctuation\">(<\/span>n<span class=\"token punctuation\">,<\/span> <span class=\"token boolean\">true<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><span class=\"token comment\">\/\/\u5165\u961f\u65f6\u8fc7\u6ee4\u65e0\u6548\u8fb9&#xff0c;\u51cf\u5c11\u961f\u5217\u5197\u4f59 <\/span><\/p>\n<p><span class=\"token comment\">\/\/\u9700\u8981\u4f18\u5148\u7ea7\u961f\u5217\u6765\u9009\u62e9\u6743\u503c<\/span><br \/>\npriority_queue<span class=\"token operator\">&lt;<\/span>Edge<span class=\"token operator\">&lt;<\/span>W<span class=\"token operator\">&gt;<\/span><span class=\"token punctuation\">,<\/span> vector<span class=\"token operator\">&lt;<\/span>Edge<span class=\"token operator\">&lt;<\/span>W<span class=\"token operator\">&gt;&gt;<\/span><span class=\"token punctuation\">,<\/span> greater<span class=\"token operator\">&lt;<\/span>Edge<span class=\"token operator\">&lt;<\/span>W<span class=\"token operator\">&gt;&gt;<\/span><span class=\"token operator\">&gt;<\/span> pq<span class=\"token punctuation\">;<\/span><\/p>\n<p><span class=\"token comment\">\/\/\u5148\u5904\u7406\u7ed9\u7684\u521d\u59cb\u9876\u70b9<\/span><br \/>\nX<span class=\"token punctuation\">[<\/span>srci<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> <span class=\"token boolean\">true<\/span><span class=\"token punctuation\">;<\/span><br \/>\nY<span class=\"token punctuation\">[<\/span>srci<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> <span class=\"token boolean\">false<\/span><span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token comment\">\/\/\u901a\u8fc7\u4f18\u5148\u7ea7\u961f\u5217\u627e\u5c40\u90e8\u6700\u5c0f\u6743\u503c&#xff0c;\u5148\u8fdb\u884c\u5b58\u50a8<\/span><br \/>\n<span class=\"token keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> i <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span> i <span class=\"token operator\">&lt;<\/span> n<span class=\"token punctuation\">;<\/span> i<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token punctuation\">{<\/span><br \/>\n<span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span>_matrix<span class=\"token punctuation\">[<\/span>srci<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">!&#061;<\/span> MAX_W<span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token punctuation\">{<\/span><br \/>\npq<span class=\"token punctuation\">.<\/span><span class=\"token function\">push<\/span><span class=\"token punctuation\">(<\/span><span class=\"token generic-function\"><span class=\"token function\">Edge<\/span><span class=\"token generic class-name\"><span class=\"token operator\">&lt;<\/span>W<span class=\"token operator\">&gt;<\/span><\/span><\/span><span class=\"token punctuation\">(<\/span>srci<span class=\"token punctuation\">,<\/span> i<span class=\"token punctuation\">,<\/span> _matrix<span class=\"token punctuation\">[<\/span>srci<span class=\"token punctuation\">]<\/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 punctuation\">;<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><\/p>\n<p>W totalW <span class=\"token operator\">&#061;<\/span> <span class=\"token function\">W<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token keyword\">int<\/span> size <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span><\/p>\n<p><span class=\"token comment\">\/\/\u6b63\u5f0f\u5f00\u59cb\u627e\u6700\u5c0f\u751f\u6210\u6811<\/span><br \/>\n<span class=\"token keyword\">while<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token operator\">!<\/span>pq<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><br \/>\n<span class=\"token punctuation\">{<\/span><br \/>\nEdge<span class=\"token operator\">&lt;<\/span>W<span class=\"token operator\">&gt;<\/span> min <span class=\"token operator\">&#061;<\/span> pq<span class=\"token punctuation\">.<\/span><span class=\"token function\">top<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\npq<span class=\"token punctuation\">.<\/span><span class=\"token function\">pop<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token comment\">\/\/\u5165\u961f\u548c\u51fa\u961f\u6709\u65f6\u95f4\u5dee\u2014\u2014 \u53ef\u80fd\u67d0\u6761\u8fb9\u5165\u961f\u65f6&#xff0c;\u76ee\u6807\u9876\u70b9\u8fd8\u5728 Y&#xff08;\u672a\u52a0\u5165 MST&#xff09;&#xff0c;<\/span><br \/>\n<span class=\"token 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