{"id":61606,"date":"2026-01-18T06:25:33","date_gmt":"2026-01-17T22:25:33","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/61606.html"},"modified":"2026-01-18T06:25:33","modified_gmt":"2026-01-17T22:25:33","slug":"2026-01-18%ef%bc%9a%e8%be%b9%e5%8f%8d%e8%bd%ac%e7%9a%84%e6%9c%80%e5%b0%8f%e8%b7%af%e5%be%84%e6%80%bb%e6%88%90%e6%9c%ac%e3%80%82%e7%94%a8go%e8%af%ad%e8%a8%80%ef%bc%8c%e7%bb%99%e5%ae%9a%e4%b8%80","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/61606.html","title":{"rendered":"2026-01-18\uff1a\u8fb9\u53cd\u8f6c\u7684\u6700\u5c0f\u8def\u5f84\u603b\u6210\u672c\u3002\u7528go\u8bed\u8a00\uff0c\u7ed9\u5b9a\u4e00\u4e2a\u5305\u542b n \u4e2a\u70b9\uff08\u7f16\u53f7 0 \u5230 n-1\uff09\u7684\u6709\u5411\u5e26\u6743\u56fe\u3002\u8fb9\u96c6\u5408 edges \u4e2d\u7684\u6bcf\u4e00\u9879 edges[i] = [ui, vi, wi] \u8868"},"content":{"rendered":"<p>2026-01-18&#xff1a;\u8fb9\u53cd\u8f6c\u7684\u6700\u5c0f\u8def\u5f84\u603b\u6210\u672c\u3002\u7528go\u8bed\u8a00&#xff0c;\u7ed9\u5b9a\u4e00\u4e2a\u5305\u542b n \u4e2a\u70b9&#xff08;\u7f16\u53f7 0 \u5230 n-1&#xff09;\u7684\u6709\u5411\u5e26\u6743\u56fe\u3002\u8fb9\u96c6\u5408 edges \u4e2d\u7684\u6bcf\u4e00\u9879 edges[i] &#061; [ui, vi, wi] \u8868\u793a\u4ece ui \u6307\u5411 vi \u7684\u6709\u5411\u8fb9&#xff0c;\u6743\u91cd\u4e3a wi\u3002 \u6bcf\u4e2a\u70b9\u90fd\u6709\u4e00\u6b21\u7279\u6b8a\u64cd\u4f5c\u7684\u673a\u4f1a&#xff1a;\u5f53\u4f60\u5230\u8fbe\u67d0\u4e2a\u70b9 u \u4e14\u8fd8\u6ca1\u4f7f\u7528\u8fc7\u8be5\u70b9\u7684\u8fd9\u6b21\u673a\u4f1a\u65f6&#xff0c;\u4f60\u53ef\u4ee5\u9009\u62e9\u4efb\u610f\u4e00\u6761\u539f\u672c\u6307\u5411 u \u7684\u5165\u8fb9 v \u2192 u&#xff0c;\u628a\u5b83\u4e34\u65f6\u6539\u4e3a u \u2192 v \u5e76\u7acb\u5373\u6cbf\u7740\u8fd9\u6761\u65b0\u65b9\u5411\u79fb\u52a8\u4e00\u6b21\u3002\u4f7f\u7528\u8fd9\u6b21\u4e34\u65f6\u6539\u5411\u5e76\u7a7f\u8d8a\u8be5\u8fb9\u7684\u4ee3\u4ef7\u4e3a\u539f\u8fb9\u6743\u7684\u4e24\u500d&#xff08;2*wi&#xff09;\u3002\u8fd9\u79cd\u6539\u5411\u4ec5\u5bf9\u8fd9\u6b21\u79fb\u52a8\u751f\u6548&#xff0c;\u4e4b\u540e\u8fb9\u7684\u65b9\u5411\u6062\u590d\u4e14\u8be5\u70b9\u7684\u673a\u4f1a\u5c31\u4e0d\u80fd\u518d\u7528\u4e86\u3002<\/p>\n<p>\u6c42\u4ece\u8d77\u70b9 0 \u5230\u7ec8\u70b9 n-1 \u7684\u6700\u5c0f\u53ef\u80fd\u603b\u82b1\u8d39&#xff0c;\u82e5\u65e0\u6cd5\u5230\u8fbe\u5219\u8fd4\u56de -1\u3002<\/p>\n<p>2 &lt;&#061; n &lt;&#061; 50000\u3002<\/p>\n<p>1 &lt;&#061; edges.length &lt;&#061; 100000\u3002<\/p>\n<p>edges[i] &#061; [ui, vi, wi]\u3002<\/p>\n<p>0 &lt;&#061; ui, vi &lt;&#061; n &#8211; 1\u3002<\/p>\n<p>1 &lt;&#061; wi &lt;&#061; 1000\u3002<\/p>\n<p>\u8f93\u5165: n &#061; 4, edges &#061; [[0,2,1],[2,1,1],[1,3,1],[2,3,3]]\u3002<\/p>\n<p>\u8f93\u51fa: 3\u3002<\/p>\n<p>\u89e3\u91ca:<\/p>\n<p>\u4e0d\u9700\u8981\u53cd\u8f6c\u3002\u8d70\u8def\u5f84 0 \u2192 2 (\u6210\u672c 1)&#xff0c;\u7136\u540e 2 \u2192 1 (\u6210\u672c 1)&#xff0c;\u518d\u7136\u540e 1 \u2192 3 (\u6210\u672c 1)\u3002<\/p>\n<p>\u603b\u6210\u672c\u4e3a 1 &#043; 1 &#043; 1 &#061; 3\u3002<\/p>\n<p>\u9898\u76ee\u6765\u81ea\u529b\u62633650\u3002<\/p>\n<h2>\u7b97\u6cd5\u8fc7\u7a0b\u8be6\u89e3<\/h2>\n<h3>1. \u56fe\u6784\u5efa&#xff08;\u90bb\u63a5\u8868&#xff09;<\/h3>\n<p>\u7b97\u6cd5\u9996\u5148\u5c06\u8f93\u5165\u7684\u6709\u5411\u56fe\u8f6c\u6362\u4e3a\u4e00\u4e2a\u65e0\u5411\u56fe\u7684\u90bb\u63a5\u8868&#xff0c;\u4f46\u5176\u4e2d\u8574\u542b\u4e86\u53cd\u8f6c\u8fb9\u7684\u89c4\u5219&#xff1a;<\/p>\n<ul>\n<li>\u5bf9\u4e8e\u539f\u59cb\u6709\u5411\u56fe\u4e2d\u7684\u6bcf\u6761\u8fb9 u -&gt; v&#xff08;\u6743\u91cd\u4e3a w&#xff09;&#xff0c;\u5728\u90bb\u63a5\u8868\u4e2d\u521b\u5efa\u4e24\u6761\u8fb9&#xff1a;\n<ul>\n<li>\u6b63\u5e38\u8fb9&#xff1a;\u4ece u \u5230 v&#xff0c;\u6743\u91cd\u4e3a w\u3002\u8fd9\u8868\u793a\u4e0d\u8fdb\u884c\u53cd\u8f6c&#xff0c;\u76f4\u63a5\u6cbf\u539f\u65b9\u5411\u79fb\u52a8\u3002<\/li>\n<li>\u53cd\u8f6c\u8fb9&#xff1a;\u4ece v \u5230 u&#xff0c;\u6743\u91cd\u4e3a 2 * w\u3002\u8fd9\u8868\u793a\u5f53\u4f4d\u4e8e\u8282\u70b9 v \u65f6&#xff0c;\u53ef\u4ee5\u4f7f\u7528\u5176\u7279\u6b8a\u64cd\u4f5c\u673a\u4f1a&#xff0c;\u5c06\u4e00\u6761\u6307\u5411 v \u7684\u5165\u8fb9&#xff08;\u5373 u -&gt; v&#xff09;\u53cd\u8f6c&#xff0c;\u5e76\u4ece v \u79fb\u52a8\u5230 u&#xff0c;\u4ee3\u4ef7\u662f\u539f\u6743\u91cd\u7684\u4e24\u500d \u3002<\/li>\n<\/ul>\n<\/li>\n<li>\u901a\u8fc7\u8fd9\u79cd\u65b9\u5f0f&#xff0c;\u8282\u70b9 v \u7684\u7279\u6b8a\u64cd\u4f5c\u673a\u4f1a\u88ab\u9690\u5f0f\u5730\u5efa\u6a21\u4e3a\u4e00\u6761\u4ece v \u51fa\u53d1\u3001\u6307\u5411\u5176\u67d0\u4e2a\u5165\u8fb9\u8d77\u70b9\u7684\u3001\u4ee3\u4ef7\u52a0\u500d\u7684\u8fb9 \u3002<\/li>\n<\/ul>\n<h3>2. \u521d\u59cb\u5316<\/h3>\n<ul>\n<li>\u521b\u5efa\u4e00\u4e2a\u8ddd\u79bb\u6570\u7ec4 dis&#xff0c;\u7528\u4e8e\u8bb0\u5f55\u4ece\u8d77\u70b9 0 \u5230\u6bcf\u4e2a\u8282\u70b9\u7684\u5f53\u524d\u5df2\u77e5\u6700\u77ed\u8ddd\u79bb\u3002\u521d\u59cb\u65f6&#xff0c;\u8d77\u70b9 0 \u7684\u8ddd\u79bb\u8bbe\u4e3a 0&#xff0c;\u5176\u4ed6\u6240\u6709\u8282\u70b9\u7684\u8ddd\u79bb\u8bbe\u4e3a\u6781\u5927\u503c&#xff08;math.MaxInt&#xff09;\u3002<\/li>\n<li>\u521b\u5efa\u4e00\u4e2a\u6700\u5c0f\u5806&#xff08;\u4f18\u5148\u961f\u5217&#xff09; h&#xff0c;\u7528\u4e8e\u9ad8\u6548\u5730\u83b7\u53d6\u5f53\u524d\u672a\u5904\u7406\u8282\u70b9\u4e2d\u8ddd\u79bb\u8d77\u70b9\u6700\u8fd1\u7684\u8282\u70b9\u3002\u5806\u4e2d\u5b58\u50a8\u7684\u662f (distance, node) \u5bf9\u3002\u521d\u59cb\u65f6&#xff0c;\u5c06\u8d77\u70b9 (0, 0) \u52a0\u5165\u5806\u4e2d \u3002<\/li>\n<\/ul>\n<h3>3. Dijkstra\u7b97\u6cd5\u4e3b\u5faa\u73af<\/h3>\n<p>\u7b97\u6cd5\u6838\u5fc3\u662f\u4e00\u4e2a\u5faa\u73af&#xff0c;\u76f4\u5230\u5806\u4e3a\u7a7a\u4e3a\u6b62&#xff1a;<\/p>\n<li>\u63d0\u53d6\u6700\u5c0f\u8282\u70b9&#xff1a;\u4ece\u6700\u5c0f\u5806\u4e2d\u5f39\u51fa\u5f53\u524d\u8ddd\u79bb\u8d77\u70b9\u6700\u8fd1\u7684\u8282\u70b9 x \u53ca\u5176\u8ddd\u79bb disX \u3002<\/li>\n<li>\u9a8c\u8bc1\u6700\u77ed\u8def\u5f84&#xff1a;\u68c0\u67e5\u5f39\u51fa\u7684 disX \u662f\u5426\u7b49\u4e8e dis[x] \u6570\u7ec4\u4e2d\u8bb0\u5f55\u7684\u503c\u3002\u5982\u679c disX &gt; dis[x]&#xff0c;\u8bf4\u660e\u8282\u70b9 x \u5df2\u7ecf\u88ab\u5904\u7406\u8fc7&#xff08;\u6709\u66f4\u77ed\u7684\u8def\u5f84\u5148\u5230\u8fbe\u4e86\u5b83&#xff09;&#xff0c;\u5f53\u524d\u8bb0\u5f55\u662f\u8fc7\u65f6\u7684&#xff0c;\u76f4\u63a5\u8df3\u8fc7 \u3002<\/li>\n<li>\u7ec8\u6b62\u6761\u4ef6&#xff1a;\u5982\u679c\u5f53\u524d\u5f39\u51fa\u7684\u8282\u70b9 x \u5c31\u662f\u7ec8\u70b9 n-1&#xff0c;\u5219\u7acb\u5373\u8fd4\u56de dis[x] \u4f5c\u4e3a\u7b54\u6848&#xff0c;\u56e0\u4e3aDijkstra\u7b97\u6cd5\u4fdd\u8bc1\u7b2c\u4e00\u6b21\u5904\u7406\u7ec8\u70b9\u65f6\u5f97\u5230\u7684\u5c31\u662f\u6700\u77ed\u8def\u5f84 \u3002<\/li>\n<li>\u677e\u5f1b\u64cd\u4f5c&#xff1a;\u904d\u5386\u8282\u70b9 x \u7684\u6240\u6709\u90bb\u5c45&#xff08;\u901a\u8fc7\u90bb\u63a5\u8868 g[x]&#xff09;\u3002\u5bf9\u4e8e\u6bcf\u6761\u4ece x \u5230 y\u3001\u6743\u91cd\u4e3a wt \u7684\u8fb9&#xff1a;\n<ul>\n<li>\u8ba1\u7b97\u7ecf\u7531 x \u5230\u8fbe y \u7684\u65b0\u8ddd\u79bb newDisY &#061; dis[x] &#043; wt\u3002<\/li>\n<li>\u5982\u679c newDisY \u5c0f\u4e8e dis[y] \u7684\u5f53\u524d\u503c&#xff0c;\u5219\u627e\u5230\u4e86\u4e00\u4e2a\u66f4\u77ed\u7684\u8def\u5f84\u3002\u6b64\u65f6\u66f4\u65b0 dis[y] &#061; newDisY&#xff0c;\u5e76\u5c06 (newDisY, y) \u8fd9\u4e2a\u65b0\u7684\u8ddd\u79bb\u4f30\u8ba1\u503c\u52a0\u5165\u6700\u5c0f\u5806\u4e2d \u3002<\/li>\n<\/ul>\n<\/li>\n<h3>4. \u8fd4\u56de\u7ed3\u679c<\/h3>\n<ul>\n<li>\u5982\u679c\u5faa\u73af\u7ed3\u675f&#xff08;\u5806\u4e3a\u7a7a&#xff09;\u4ecd\u672a\u5230\u8fbe\u7ec8\u70b9 n-1&#xff0c;\u8bf4\u660e\u7ec8\u70b9\u4e0d\u53ef\u8fbe&#xff0c;\u8fd4\u56de -1 \u3002<\/li>\n<\/ul>\n<h2>\u7b97\u6cd5\u903b\u8f91\u4e0e\u201c\u53cd\u8f6c\u201d\u673a\u4f1a\u7684\u4f53\u73b0<\/h2>\n<p>\u8be5\u7b97\u6cd5\u7684\u5de7\u5999\u4e4b\u5904\u5728\u4e8e&#xff0c;\u5b83\u901a\u8fc7\u56fe\u6784\u5efa\u9636\u6bb5\u7684\u201c\u52a0\u8fb9\u201d\u64cd\u4f5c&#xff0c;\u5c06\u8282\u70b9\u7684\u201c\u53cd\u8f6c\u201d\u673a\u4f1a\u76f4\u63a5\u878d\u5165\u4e86\u56fe\u7684\u7ed3\u6784\u4e2d\u3002<\/p>\n<ul>\n<li>\u5f53\u7b97\u6cd5\u5728\u8ba1\u7b97\u8def\u5f84\u65f6&#xff0c;\u5982\u679c\u5b83\u9009\u62e9\u4e86\u4e00\u6761\u6743\u91cd\u4e3a 2*w \u7684\u201c\u53cd\u8f6c\u8fb9\u201d&#xff08;\u4ece v \u5230 u&#xff09;&#xff0c;\u8fd9\u5728\u903b\u8f91\u4e0a\u5c31\u7b49\u4ef7\u4e8e&#xff1a;\u5728\u5230\u8fbe\u8282\u70b9 v \u540e&#xff0c;\u4f7f\u7528\u4e86\u5b83\u7684\u7279\u6b8a\u64cd\u4f5c&#xff0c;\u53cd\u8f6c\u4e86\u8fb9 u-&gt;v&#xff0c;\u5e76\u7acb\u5373\u79fb\u52a8\u5230\u4e86 u\u3002<\/li>\n<li>Dijkstra\u7b97\u6cd5\u4f1a\u81ea\u7136\u5730\u63a2\u7d22\u6240\u6709\u53ef\u80fd\u7684\u8def\u5f84&#xff08;\u5305\u542b\u6b63\u5e38\u8fb9\u548c\u53cd\u8f6c\u8fb9&#xff09;&#xff0c;\u5e76\u6700\u7ec8\u627e\u5230\u7efc\u5408\u6210\u672c\u6700\u4f4e\u7684\u8def\u5f84 \u3002<\/li>\n<\/ul>\n<h2>\u590d\u6742\u5ea6\u5206\u6790<\/h2>\n<h3>\u65f6\u95f4\u590d\u6742\u5ea6&#xff1a;O((V &#043; E) log V)<\/h3>\n<ul>\n<li>V \u662f\u8282\u70b9\u6570 n&#xff0c;E \u662f\u539f\u59cb\u6709\u5411\u56fe\u7684\u8fb9\u6570\u3002\u5728\u7b97\u6cd5\u6784\u5efa\u7684\u90bb\u63a5\u8868\u4e2d&#xff0c;\u8fb9\u7684\u6570\u91cf\u7ea6\u4e3a 2 * E\u3002<\/li>\n<li>\u6bcf\u4e2a\u8282\u70b9\u6700\u591a\u88ab\u4ece\u5806\u4e2d\u5f39\u51fa\u4e00\u6b21&#xff0c;\u6bcf\u6b21\u5f39\u51fa\u540e\u9700\u8981\u904d\u5386\u5176\u6240\u6709\u51fa\u8fb9\u8fdb\u884c\u677e\u5f1b\u64cd\u4f5c\u3002\u6bcf\u6761\u8fb9\u6700\u591a\u88ab\u5904\u7406\u4e00\u6b21\u3002<\/li>\n<li>\u6700\u5c0f\u5806\u7684\u63d2\u5165&#xff08;Push&#xff09;\u548c\u5220\u9664\u6700\u5c0f\u5143&#xff08;Pop&#xff09;\u64cd\u4f5c\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u5747\u4e3a O(log V)\u3002\u5728\u6700\u574f\u60c5\u51b5\u4e0b&#xff0c;\u6bcf\u6761\u8fb9\u90fd\u53ef\u80fd\u5f15\u53d1\u4e00\u6b21\u5806\u64cd\u4f5c&#xff08;\u63d2\u5165\u65b0\u8ddd\u79bb&#xff09;&#xff0c;\u56e0\u6b64\u603b\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a O((V &#043; E) log V) \u3002<\/li>\n<\/ul>\n<h3>\u7a7a\u95f4\u590d\u6742\u5ea6&#xff1a;O(V &#043; E)<\/h3>\n<ul>\n<li>O(V)&#xff1a;\u7528\u4e8e\u5b58\u50a8\u8ddd\u79bb\u6570\u7ec4 dis\u3002<\/li>\n<li>O(E)&#xff1a;\u7528\u4e8e\u5b58\u50a8\u90bb\u63a5\u8868 g\u3002\u56e0\u4e3a\u6bcf\u6761\u539f\u59cb\u8fb9\u88ab\u8868\u793a\u4e3a\u4e24\u6761\u8fb9&#xff0c;\u6240\u4ee5\u90bb\u63a5\u8868\u7684\u603b\u7a7a\u95f4\u662f O(E)\u3002<\/li>\n<li>O(V)&#xff1a;\u6700\u5c0f\u5806\u5728\u6700\u574f\u60c5\u51b5\u4e0b\u53ef\u80fd\u5305\u542b\u6240\u6709\u8282\u70b9\u3002<\/li>\n<li>\u56e0\u6b64&#xff0c;\u603b\u7684\u989d\u5916\u7a7a\u95f4\u590d\u6742\u5ea6\u4e3a O(V &#043; E) \u3002<\/li>\n<\/ul>\n<h2>\u603b\u7ed3<\/h2>\n<p>\u60a8\u63d0\u4f9b\u7684\u4ee3\u7801\u901a\u8fc7\u6269\u5c55\u56fe\u7ed3\u6784\u6765\u5efa\u6a21\u8282\u70b9\u7279\u6709\u7684\u201c\u8fb9\u53cd\u8f6c\u201d\u64cd\u4f5c&#xff0c;\u5e76\u6210\u529f\u8fd0\u7528\u4e86\u6807\u51c6\u7684Dijkstra\u7b97\u6cd5\u548c\u6700\u5c0f\u5806\u6765\u9ad8\u6548\u6c42\u89e3\u5355\u6e90\u6700\u77ed\u8def\u5f84\u95ee\u9898\u3002\u5176\u65f6\u95f4\u590d\u6742\u5ea6\u548c\u7a7a\u95f4\u590d\u6742\u5ea6\u5728\u56fe\u7b97\u6cd5\u4e2d\u5c5e\u4e8e\u9ad8\u6548\u8303\u7574&#xff0c;\u80fd\u591f\u5904\u7406\u9898\u76ee\u4e2d\u7ed9\u51fa\u7684\u6570\u636e\u89c4\u6a21&#xff08;n &lt;&#061; 50000, edges.length &lt;&#061; 100000&#xff09;\u3002<\/p>\n<h2>Go\u5b8c\u6574\u4ee3\u7801\u5982\u4e0b&#xff1a;<\/h2>\n<p><span class=\"token keyword\">package<\/span> main<\/p>\n<p><span class=\"token keyword\">import<\/span> <span class=\"token punctuation\">(<\/span><br \/>\n<span class=\"token string\">&#034;container\/heap&#034;<\/span><br \/>\n<span class=\"token string\">&#034;fmt&#034;<\/span><br \/>\n<span class=\"token string\">&#034;math&#034;<\/span><br \/>\n<span class=\"token punctuation\">)<\/span><\/p>\n<p><span class=\"token keyword\">func<\/span> <span class=\"token function\">minCost<\/span><span class=\"token punctuation\">(<\/span>n <span class=\"token builtin\">int<\/span><span class=\"token punctuation\">,<\/span> edges <span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span><span class=\"token builtin\">int<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token builtin\">int<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n<span class=\"token keyword\">type<\/span> edge <span class=\"token keyword\">struct<\/span><span class=\"token punctuation\">{<\/span> to<span class=\"token punctuation\">,<\/span> wt <span class=\"token builtin\">int<\/span> <span class=\"token punctuation\">}<\/span><br \/>\ng <span class=\"token operator\">:&#061;<\/span> <span class=\"token function\">make<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span>edge<span class=\"token punctuation\">,<\/span> n<span class=\"token punctuation\">)<\/span> <span class=\"token comment\">\/\/ \u90bb\u63a5\u8868<\/span><br \/>\n<span class=\"token keyword\">for<\/span> <span class=\"token boolean\">_<\/span><span class=\"token punctuation\">,<\/span> e <span class=\"token operator\">:&#061;<\/span> <span class=\"token keyword\">range<\/span> edges <span class=\"token punctuation\">{<\/span><br \/>\nx<span class=\"token punctuation\">,<\/span> y<span class=\"token punctuation\">,<\/span> wt <span class=\"token operator\">:&#061;<\/span> e<span class=\"token punctuation\">[<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span> e<span class=\"token punctuation\">[<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span> e<span class=\"token punctuation\">[<\/span><span class=\"token number\">2<\/span><span class=\"token punctuation\">]<\/span><br \/>\ng<span class=\"token punctuation\">[<\/span>x<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> <span class=\"token function\">append<\/span><span class=\"token punctuation\">(<\/span>g<span class=\"token punctuation\">[<\/span>x<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span> edge<span class=\"token punctuation\">{<\/span>y<span class=\"token punctuation\">,<\/span> wt<span class=\"token punctuation\">}<\/span><span class=\"token punctuation\">)<\/span><br \/>\ng<span class=\"token punctuation\">[<\/span>y<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> <span class=\"token function\">append<\/span><span class=\"token punctuation\">(<\/span>g<span class=\"token punctuation\">[<\/span>y<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span> edge<span class=\"token punctuation\">{<\/span>x<span class=\"token punctuation\">,<\/span> wt <span class=\"token operator\">*<\/span> <span class=\"token number\">2<\/span><span class=\"token punctuation\">}<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token comment\">\/\/ \u53cd\u8f6c\u8fb9<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><\/p>\n<p>dis <span class=\"token operator\">:&#061;<\/span> <span class=\"token function\">make<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span><span class=\"token builtin\">int<\/span><span class=\"token punctuation\">,<\/span> n<span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token keyword\">for<\/span> i <span class=\"token operator\">:&#061;<\/span> <span class=\"token keyword\">range<\/span> dis <span class=\"token punctuation\">{<\/span><br \/>\ndis<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> math<span class=\"token punctuation\">.<\/span>MaxInt<br \/>\n<span class=\"token punctuation\">}<\/span><br \/>\ndis<span class=\"token punctuation\">[<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span> <span class=\"token comment\">\/\/ \u8d77\u70b9\u5230\u81ea\u5df1\u7684\u8ddd\u79bb\u662f 0<\/span><br \/>\n<span class=\"token comment\">\/\/ \u5806\u4e2d\u4fdd\u5b58 (\u8d77\u70b9\u5230\u8282\u70b9 x \u7684\u6700\u77ed\u8def\u957f\u5ea6&#xff0c;\u8282\u70b9 x)<\/span><br \/>\nh <span class=\"token operator\">:&#061;<\/span> <span class=\"token operator\">&amp;<\/span>hp<span class=\"token punctuation\">{<\/span><span class=\"token punctuation\">{<\/span><span class=\"token punctuation\">}<\/span><span class=\"token punctuation\">}<\/span><\/p>\n<p><span class=\"token keyword\">for<\/span> h<span class=\"token punctuation\">.<\/span><span class=\"token function\">Len<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token operator\">&gt;<\/span> <span class=\"token number\">0<\/span> <span class=\"token punctuation\">{<\/span><br \/>\np <span class=\"token operator\">:&#061;<\/span> heap<span class=\"token punctuation\">.<\/span><span class=\"token function\">Pop<\/span><span class=\"token punctuation\">(<\/span>h<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span><span class=\"token punctuation\">(<\/span>pair<span class=\"token punctuation\">)<\/span><br \/>\ndisX<span class=\"token punctuation\">,<\/span> x <span class=\"token operator\">:&#061;<\/span> p<span class=\"token punctuation\">.<\/span>dis<span class=\"token punctuation\">,<\/span> p<span class=\"token punctuation\">.<\/span>x<br \/>\n<span class=\"token keyword\">if<\/span> disX <span class=\"token operator\">&gt;<\/span> dis<span class=\"token punctuation\">[<\/span>x<span class=\"token punctuation\">]<\/span> <span class=\"token punctuation\">{<\/span> <span class=\"token comment\">\/\/ x \u4e4b\u524d\u51fa\u5806\u8fc7<\/span><br \/>\n<span class=\"token keyword\">continue<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><br \/>\n<span class=\"token keyword\">if<\/span> x <span class=\"token operator\">&#061;&#061;<\/span> n<span class=\"token operator\">&#8211;<\/span><span class=\"token number\">1<\/span> <span class=\"token punctuation\">{<\/span> <span class=\"token comment\">\/\/ \u5230\u8fbe\u7ec8\u70b9<\/span><br \/>\n<span class=\"token keyword\">return<\/span> disX<br \/>\n<span class=\"token punctuation\">}<\/span><br \/>\n<span class=\"token keyword\">for<\/span> <span class=\"token boolean\">_<\/span><span class=\"token punctuation\">,<\/span> e <span class=\"token operator\">:&#061;<\/span> <span class=\"token keyword\">range<\/span> g<span class=\"token punctuation\">[<\/span>x<span class=\"token punctuation\">]<\/span> <span class=\"token punctuation\">{<\/span><br \/>\ny <span class=\"token operator\">:&#061;<\/span> e<span class=\"token punctuation\">.<\/span>to<br \/>\nnewDisY <span class=\"token operator\">:&#061;<\/span> disX <span class=\"token operator\">&#043;<\/span> e<span class=\"token punctuation\">.<\/span>wt<br \/>\n<span class=\"token keyword\">if<\/span> newDisY <span class=\"token operator\">&lt;<\/span> dis<span class=\"token punctuation\">[<\/span>y<span class=\"token punctuation\">]<\/span> <span class=\"token punctuation\">{<\/span><br \/>\ndis<span class=\"token punctuation\">[<\/span>y<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> newDisY <span class=\"token comment\">\/\/ \u66f4\u65b0 x \u7684\u90bb\u5c45\u7684\u6700\u77ed\u8def<\/span><br \/>\n<span class=\"token comment\">\/\/ \u61d2\u66f4\u65b0\u5806&#xff1a;\u53ea\u63d2\u5165\u6570\u636e&#xff0c;\u4e0d\u66f4\u65b0\u5806\u4e2d\u6570\u636e<\/span><br \/>\n<span class=\"token comment\">\/\/ \u76f8\u540c\u8282\u70b9\u53ef\u80fd\u6709\u591a\u4e2a\u4e0d\u540c\u7684 newDisY&#xff0c;\u9664\u4e86\u6700\u5c0f\u7684 newDisY&#xff0c;\u5176\u4f59\u503c\u90fd\u4f1a\u89e6\u53d1\u4e0a\u9762\u7684 continue<\/span><br \/>\nheap<span class=\"token punctuation\">.<\/span><span class=\"token function\">Push<\/span><span class=\"token punctuation\">(<\/span>h<span class=\"token punctuation\">,<\/span> pair<span class=\"token punctuation\">{<\/span>newDisY<span class=\"token punctuation\">,<\/span> y<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\">return<\/span> <span class=\"token operator\">&#8211;<\/span><span class=\"token number\">1<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><\/p>\n<p><span class=\"token keyword\">type<\/span> pair <span class=\"token keyword\">struct<\/span><span class=\"token punctuation\">{<\/span> dis<span class=\"token punctuation\">,<\/span> x <span class=\"token builtin\">int<\/span> <span class=\"token punctuation\">}<\/span><br \/>\n<span class=\"token keyword\">type<\/span> hp <span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span>pair<\/p>\n<p><span class=\"token keyword\">func<\/span> <span class=\"token punctuation\">(<\/span>h hp<span class=\"token punctuation\">)<\/span> <span class=\"token function\">Len<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token builtin\">int<\/span>           <span class=\"token punctuation\">{<\/span> <span class=\"token keyword\">return<\/span> <span class=\"token function\">len<\/span><span class=\"token punctuation\">(<\/span>h<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">}<\/span><br \/>\n<span class=\"token keyword\">func<\/span> <span class=\"token punctuation\">(<\/span>h hp<span class=\"token punctuation\">)<\/span> <span class=\"token function\">Less<\/span><span class=\"token punctuation\">(<\/span>i<span class=\"token punctuation\">,<\/span> j <span class=\"token builtin\">int<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token builtin\">bool<\/span> <span class=\"token punctuation\">{<\/span> <span class=\"token keyword\">return<\/span> h<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">.<\/span>dis <span class=\"token operator\">&lt;<\/span> h<span class=\"token punctuation\">[<\/span>j<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">.<\/span>dis <span class=\"token punctuation\">}<\/span><br \/>\n<span class=\"token keyword\">func<\/span> <span class=\"token punctuation\">(<\/span>h hp<span class=\"token punctuation\">)<\/span> <span class=\"token function\">Swap<\/span><span class=\"token punctuation\">(<\/span>i<span class=\"token punctuation\">,<\/span> j <span class=\"token builtin\">int<\/span><span class=\"token punctuation\">)<\/span>      <span class=\"token punctuation\">{<\/span> h<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span> h<span class=\"token punctuation\">[<\/span>j<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> h<span class=\"token punctuation\">[<\/span>j<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span> h<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span> <span class=\"token punctuation\">}<\/span><br \/>\n<span class=\"token keyword\">func<\/span> <span class=\"token punctuation\">(<\/span>h <span class=\"token operator\">*<\/span>hp<span class=\"token punctuation\">)<\/span> <span class=\"token function\">Push<\/span><span class=\"token punctuation\">(<\/span>v any<span class=\"token punctuation\">)<\/span>        <span class=\"token punctuation\">{<\/span> <span class=\"token operator\">*<\/span>h <span class=\"token operator\">&#061;<\/span> <span class=\"token function\">append<\/span><span class=\"token punctuation\">(<\/span><span class=\"token operator\">*<\/span>h<span class=\"token punctuation\">,<\/span> v<span class=\"token punctuation\">.<\/span><span class=\"token punctuation\">(<\/span>pair<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">}<\/span><br \/>\n<span class=\"token keyword\">func<\/span> <span class=\"token punctuation\">(<\/span>h <span class=\"token operator\">*<\/span>hp<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>v any<span class=\"token punctuation\">)<\/span>      <span class=\"token punctuation\">{<\/span> a <span class=\"token operator\">:&#061;<\/span> <span class=\"token operator\">*<\/span>h<span class=\"token punctuation\">;<\/span> <span class=\"token operator\">*<\/span>h<span class=\"token punctuation\">,<\/span> v <span class=\"token operator\">&#061;<\/span> a<span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">:<\/span><span class=\"token function\">len<\/span><span class=\"token punctuation\">(<\/span>a<span class=\"token punctuation\">)<\/span><span class=\"token operator\">&#8211;<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span> a<span class=\"token punctuation\">[<\/span><span class=\"token function\">len<\/span><span class=\"token punctuation\">(<\/span>a<span class=\"token punctuation\">)<\/span><span class=\"token operator\">&#8211;<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span> <span class=\"token keyword\">return<\/span> <span class=\"token punctuation\">}<\/span><\/p>\n<p><span class=\"token keyword\">func<\/span> <span class=\"token function\">main<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\nn <span class=\"token operator\">:&#061;<\/span> <span class=\"token number\">4<\/span><br \/>\nedges <span class=\"token operator\">:&#061;<\/span> <span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span><span class=\"token builtin\">int<\/span><span class=\"token punctuation\">{<\/span><span class=\"token punctuation\">{<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">2<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">}<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token punctuation\">{<\/span><span class=\"token number\">2<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">}<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token punctuation\">{<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">3<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">}<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token punctuation\">{<\/span><span class=\"token number\">2<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">3<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">3<\/span><span class=\"token punctuation\">}<\/span><span class=\"token punctuation\">}<\/span><br \/>\nresult <span class=\"token operator\">:&#061;<\/span> <span class=\"token function\">minCost<\/span><span class=\"token punctuation\">(<\/span>n<span class=\"token punctuation\">,<\/span> edges<span class=\"token punctuation\">)<\/span><br \/>\nfmt<span class=\"token punctuation\">.<\/span><span class=\"token function\">Println<\/span><span class=\"token punctuation\">(<\/span>result<span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/01\/20260117222532-696c0c5c0b0a6.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<h2>Python\u5b8c\u6574\u4ee3\u7801\u5982\u4e0b&#xff1a;<\/h2>\n<p><span class=\"token comment\"># -*-coding:utf-8-*-<\/span><\/p>\n<p><span class=\"token keyword\">import<\/span> heapq<br \/>\n<span class=\"token keyword\">from<\/span> typing <span class=\"token keyword\">import<\/span> List<\/p>\n<p><span class=\"token keyword\">def<\/span> <span class=\"token function\">minCost<\/span><span class=\"token punctuation\">(<\/span>n<span class=\"token punctuation\">:<\/span> <span class=\"token builtin\">int<\/span><span class=\"token punctuation\">,<\/span> edges<span class=\"token punctuation\">:<\/span> List<span class=\"token punctuation\">[<\/span>List<span class=\"token punctuation\">[<\/span><span class=\"token builtin\">int<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token operator\">&#8211;<\/span><span class=\"token operator\">&gt;<\/span> <span class=\"token builtin\">int<\/span><span class=\"token punctuation\">:<\/span><br \/>\n    <span class=\"token comment\"># \u90bb\u63a5\u8868<\/span><br \/>\n    g <span class=\"token operator\">&#061;<\/span> <span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span> <span class=\"token keyword\">for<\/span> _ <span class=\"token keyword\">in<\/span> <span class=\"token builtin\">range<\/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> x<span class=\"token punctuation\">,<\/span> y<span class=\"token punctuation\">,<\/span> wt <span class=\"token keyword\">in<\/span> edges<span class=\"token punctuation\">:<\/span><br \/>\n        g<span class=\"token punctuation\">[<\/span>x<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">.<\/span>append<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">(<\/span>y<span class=\"token punctuation\">,<\/span> wt<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span>          <span class=\"token comment\"># \u539f\u8fb9<\/span><br \/>\n        g<span class=\"token punctuation\">[<\/span>y<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">.<\/span>append<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">(<\/span>x<span class=\"token punctuation\">,<\/span> wt <span class=\"token operator\">*<\/span> <span class=\"token number\">2<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span>      <span class=\"token comment\"># \u53cd\u5411\u8fb9&#xff0c;\u6743\u91cd\u7ffb\u500d<\/span><\/p>\n<p>    <span class=\"token comment\"># \u521d\u59cb\u5316\u8ddd\u79bb\u6570\u7ec4<\/span><br \/>\n    dist <span class=\"token operator\">&#061;<\/span> <span class=\"token punctuation\">[<\/span><span class=\"token builtin\">float<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">&#039;inf&#039;<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">]<\/span> <span class=\"token operator\">*<\/span> n<br \/>\n    dist<span class=\"token punctuation\">[<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><\/p>\n<p>    <span class=\"token comment\"># \u6700\u5c0f\u5806&#xff0c;\u5143\u7d20\u4e3a (\u8d77\u70b9\u5230\u8282\u70b9x\u7684\u6700\u77ed\u8ddd\u79bb, \u8282\u70b9x)<\/span><br \/>\n    heap <span class=\"token operator\">&#061;<\/span> <span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">(<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">]<\/span>  <span class=\"token comment\"># (\u8ddd\u79bb, \u8282\u70b9)<\/span><\/p>\n<p>    <span class=\"token keyword\">while<\/span> heap<span class=\"token punctuation\">:<\/span><br \/>\n        dis_x<span class=\"token punctuation\">,<\/span> x <span class=\"token operator\">&#061;<\/span> heapq<span class=\"token punctuation\">.<\/span>heappop<span class=\"token punctuation\">(<\/span>heap<span class=\"token punctuation\">)<\/span><\/p>\n<p>        <span class=\"token comment\"># \u5982\u679c\u5f53\u524d\u8ddd\u79bb\u5927\u4e8e\u5df2\u8bb0\u5f55\u7684\u6700\u77ed\u8ddd\u79bb&#xff0c;\u8df3\u8fc7<\/span><br \/>\n        <span class=\"token keyword\">if<\/span> dis_x <span class=\"token operator\">&gt;<\/span> dist<span class=\"token punctuation\">[<\/span>x<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">:<\/span><br \/>\n            <span class=\"token keyword\">continue<\/span><\/p>\n<p>        <span class=\"token comment\"># \u5230\u8fbe\u7ec8\u70b9<\/span><br \/>\n        <span class=\"token keyword\">if<\/span> x <span class=\"token operator\">&#061;&#061;<\/span> n <span class=\"token operator\">&#8211;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">:<\/span><br \/>\n            <span class=\"token keyword\">return<\/span> dis_x<\/p>\n<p>        <span class=\"token comment\"># \u904d\u5386\u90bb\u63a5\u8282\u70b9<\/span><br \/>\n        <span class=\"token keyword\">for<\/span> y<span class=\"token punctuation\">,<\/span> wt <span class=\"token keyword\">in<\/span> g<span class=\"token punctuation\">[<\/span>x<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">:<\/span><br \/>\n            new_dis_y <span class=\"token operator\">&#061;<\/span> dis_x <span class=\"token operator\">&#043;<\/span> wt<br \/>\n            <span class=\"token keyword\">if<\/span> new_dis_y <span class=\"token operator\">&lt;<\/span> dist<span class=\"token punctuation\">[<\/span>y<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">:<\/span><br \/>\n                dist<span class=\"token punctuation\">[<\/span>y<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> new_dis_y<br \/>\n                heapq<span class=\"token punctuation\">.<\/span>heappush<span class=\"token punctuation\">(<\/span>heap<span class=\"token punctuation\">,<\/span> <span class=\"token punctuation\">(<\/span>new_dis_y<span class=\"token punctuation\">,<\/span> y<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><\/p>\n<p>    <span class=\"token keyword\">return<\/span> <span class=\"token operator\">&#8211;<\/span><span class=\"token number\">1<\/span><\/p>\n<p><span class=\"token keyword\">if<\/span> __name__ <span class=\"token operator\">&#061;&#061;<\/span> <span class=\"token string\">&#034;__main__&#034;<\/span><span class=\"token punctuation\">:<\/span><br \/>\n    n <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">4<\/span><br \/>\n    edges <span class=\"token operator\">&#061;<\/span> <span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">[<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">2<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token punctuation\">[<\/span><span class=\"token number\">2<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token punctuation\">[<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">3<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token punctuation\">[<\/span><span class=\"token number\">2<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">3<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">3<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">]<\/span><br \/>\n    result <span class=\"token operator\">&#061;<\/span> minCost<span class=\"token punctuation\">(<\/span>n<span class=\"token punctuation\">,<\/span> edges<span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token keyword\">print<\/span><span class=\"token punctuation\">(<\/span>result<span class=\"token punctuation\">)<\/span><\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/01\/20260117222532-696c0c5c6ef28.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<h2>C&#043;&#043;\u5b8c\u6574\u4ee3\u7801\u5982\u4e0b&#xff1a;<\/h2>\n<p><span class=\"token macro property\"><span class=\"token directive-hash\">#<\/span><span class=\"token directive keyword\">include<\/span> <span class=\"token string\">&lt;iostream&gt;<\/span><\/span><br \/>\n<span class=\"token macro property\"><span class=\"token directive-hash\">#<\/span><span class=\"token directive keyword\">include<\/span> <span class=\"token string\">&lt;vector&gt;<\/span><\/span><br \/>\n<span class=\"token macro property\"><span class=\"token directive-hash\">#<\/span><span class=\"token directive keyword\">include<\/span> <span class=\"token string\">&lt;queue&gt;<\/span><\/span><br \/>\n<span class=\"token macro property\"><span class=\"token directive-hash\">#<\/span><span class=\"token directive keyword\">include<\/span> <span class=\"token string\">&lt;climits&gt;<\/span><\/span><br \/>\n<span class=\"token macro property\"><span class=\"token directive-hash\">#<\/span><span class=\"token directive keyword\">include<\/span> <span class=\"token string\">&lt;functional&gt;<\/span><\/span><\/p>\n<p><span class=\"token keyword\">using<\/span> <span class=\"token keyword\">namespace<\/span> std<span class=\"token punctuation\">;<\/span><\/p>\n<p><span class=\"token keyword\">int<\/span> <span class=\"token function\">minCost<\/span><span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> n<span class=\"token punctuation\">,<\/span> vector<span class=\"token operator\">&lt;<\/span>vector<span class=\"token operator\">&lt;<\/span><span class=\"token keyword\">int<\/span><span class=\"token operator\">&gt;&gt;<\/span><span class=\"token operator\">&amp;<\/span> edges<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n    <span class=\"token comment\">\/\/ \u90bb\u63a5\u8868&#xff1a;\u5b58\u50a8 (\u90bb\u5c45\u8282\u70b9, \u6743\u91cd)<\/span><br \/>\n    vector<span class=\"token operator\">&lt;<\/span>vector<span class=\"token operator\">&lt;<\/span>pair<span class=\"token operator\">&lt;<\/span><span class=\"token keyword\">int<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token keyword\">int<\/span><span class=\"token operator\">&gt;&gt;<\/span><span class=\"token operator\">&gt;<\/span> <span class=\"token function\">g<\/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\">const<\/span> <span class=\"token keyword\">auto<\/span><span class=\"token operator\">&amp;<\/span> e <span class=\"token operator\">:<\/span> edges<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n        <span class=\"token keyword\">int<\/span> x <span class=\"token operator\">&#061;<\/span> e<span class=\"token punctuation\">[<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span> y <span class=\"token operator\">&#061;<\/span> e<span class=\"token punctuation\">[<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span> wt <span class=\"token operator\">&#061;<\/span> e<span class=\"token punctuation\">[<\/span><span class=\"token number\">2<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        g<span class=\"token punctuation\">[<\/span>x<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">.<\/span><span class=\"token function\">emplace_back<\/span><span class=\"token punctuation\">(<\/span>y<span class=\"token punctuation\">,<\/span> wt<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span>          <span class=\"token comment\">\/\/ \u539f\u8fb9<\/span><br \/>\n        g<span class=\"token punctuation\">[<\/span>y<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">.<\/span><span class=\"token function\">emplace_back<\/span><span class=\"token punctuation\">(<\/span>x<span class=\"token punctuation\">,<\/span> wt <span class=\"token operator\">*<\/span> <span class=\"token number\">2<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span>      <span class=\"token comment\">\/\/ \u53cd\u5411\u8fb9&#xff0c;\u6743\u91cd\u7ffb\u500d<\/span><br \/>\n    <span class=\"token punctuation\">}<\/span><\/p>\n<p>    <span class=\"token comment\">\/\/ \u521d\u59cb\u5316\u8ddd\u79bb\u6570\u7ec4<\/span><br \/>\n    vector<span class=\"token operator\">&lt;<\/span><span class=\"token keyword\">int<\/span><span class=\"token operator\">&gt;<\/span> <span class=\"token function\">dist<\/span><span class=\"token punctuation\">(<\/span>n<span class=\"token punctuation\">,<\/span> INT_MAX<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n    dist<span class=\"token punctuation\">[<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span><\/p>\n<p>    <span class=\"token comment\">\/\/ \u6700\u5c0f\u5806&#xff1a;\u5143\u7d20\u4e3a (\u8d77\u70b9\u5230\u8282\u70b9x\u7684\u6700\u77ed\u8ddd\u79bb, \u8282\u70b9x)<\/span><br \/>\n    <span class=\"token comment\">\/\/ \u4f7f\u7528 greater \u4f7f priority_queue \u6210\u4e3a\u6700\u5c0f\u5806<\/span><br \/>\n    priority_queue<span class=\"token operator\">&lt;<\/span>pair<span class=\"token operator\">&lt;<\/span><span class=\"token keyword\">int<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token keyword\">int<\/span><span class=\"token operator\">&gt;<\/span><span class=\"token punctuation\">,<\/span> vector<span class=\"token operator\">&lt;<\/span>pair<span class=\"token operator\">&lt;<\/span><span class=\"token keyword\">int<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token keyword\">int<\/span><span class=\"token operator\">&gt;&gt;<\/span><span class=\"token punctuation\">,<\/span> greater<span class=\"token operator\">&lt;<\/span>pair<span class=\"token operator\">&lt;<\/span><span class=\"token keyword\">int<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token keyword\">int<\/span><span class=\"token operator\">&gt;&gt;<\/span><span class=\"token operator\">&gt;<\/span> pq<span class=\"token punctuation\">;<\/span><br \/>\n    pq<span class=\"token punctuation\">.<\/span><span class=\"token function\">emplace<\/span><span class=\"token punctuation\">(<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span>  <span class=\"token comment\">\/\/ (\u8ddd\u79bb, \u8282\u70b9)<\/span><\/p>\n<p>    <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> <span class=\"token punctuation\">{<\/span><br \/>\n        <span class=\"token keyword\">auto<\/span> <span class=\"token punctuation\">[<\/span>dis_x<span class=\"token punctuation\">,<\/span> x<span class=\"token punctuation\">]<\/span> <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 \/>\n        pq<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 comment\">\/\/ \u5982\u679c\u5f53\u524d\u8ddd\u79bb\u5927\u4e8e\u5df2\u8bb0\u5f55\u7684\u6700\u77ed\u8ddd\u79bb&#xff0c;\u8df3\u8fc7<\/span><br \/>\n        <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span>dis_x <span class=\"token operator\">&gt;<\/span> dist<span class=\"token punctuation\">[<\/span>x<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n            <span class=\"token keyword\">continue<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token punctuation\">}<\/span><\/p>\n<p>        <span class=\"token comment\">\/\/ \u5230\u8fbe\u7ec8\u70b9<\/span><br \/>\n        <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span>x <span class=\"token operator\">&#061;&#061;<\/span> n <span class=\"token operator\">&#8211;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n            <span class=\"token keyword\">return<\/span> dis_x<span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token punctuation\">}<\/span><\/p>\n<p>        <span class=\"token comment\">\/\/ \u904d\u5386\u90bb\u63a5\u8282\u70b9<\/span><br \/>\n        <span class=\"token keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">const<\/span> <span class=\"token keyword\">auto<\/span><span class=\"token operator\">&amp;<\/span> <span class=\"token punctuation\">[<\/span>y<span class=\"token punctuation\">,<\/span> wt<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">:<\/span> g<span class=\"token punctuation\">[<\/span>x<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n            <span class=\"token keyword\">int<\/span> new_dis_y <span class=\"token operator\">&#061;<\/span> dis_x <span class=\"token operator\">&#043;<\/span> wt<span class=\"token punctuation\">;<\/span><br \/>\n            <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span>new_dis_y <span class=\"token operator\">&lt;<\/span> dist<span class=\"token punctuation\">[<\/span>y<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n                dist<span class=\"token punctuation\">[<\/span>y<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> new_dis_y<span class=\"token punctuation\">;<\/span><br \/>\n                pq<span class=\"token punctuation\">.<\/span><span class=\"token function\">emplace<\/span><span class=\"token punctuation\">(<\/span>new_dis_y<span class=\"token punctuation\">,<\/span> y<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\">return<\/span> <span class=\"token operator\">&#8211;<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><\/p>\n<p><span class=\"token keyword\">int<\/span> <span class=\"token function\">main<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n    <span class=\"token keyword\">int<\/span> n <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">4<\/span><span class=\"token punctuation\">;<\/span><br \/>\n    vector<span class=\"token operator\">&lt;<\/span>vector<span class=\"token operator\">&lt;<\/span><span class=\"token keyword\">int<\/span><span class=\"token operator\">&gt;&gt;<\/span> edges <span class=\"token operator\">&#061;<\/span> <span class=\"token punctuation\">{<\/span><span class=\"token punctuation\">{<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">2<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">}<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token punctuation\">{<\/span><span class=\"token number\">2<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">}<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token punctuation\">{<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">3<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">}<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token punctuation\">{<\/span><span class=\"token number\">2<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">3<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">3<\/span><span class=\"token punctuation\">}<\/span><span class=\"token punctuation\">}<\/span><span class=\"token punctuation\">;<\/span><br \/>\n    <span class=\"token keyword\">int<\/span> result <span class=\"token operator\">&#061;<\/span> <span class=\"token function\">minCost<\/span><span class=\"token punctuation\">(<\/span>n<span class=\"token punctuation\">,<\/span> edges<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n    cout <span class=\"token operator\">&lt;&lt;<\/span> result <span class=\"token operator\">&lt;&lt;<\/span> endl<span class=\"token punctuation\">;<\/span><br \/>\n    <span class=\"token keyword\">return<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/01\/20260117222532-696c0c5ca6b74.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n","protected":false},"excerpt":{"rendered":"<p>2026-01-18&#xff1a;\u8fb9\u53cd\u8f6c\u7684\u6700\u5c0f\u8def\u5f84\u603b\u6210\u672c\u3002\u7528go\u8bed\u8a00&#xff0c;\u7ed9\u5b9a\u4e00\u4e2a\u5305\u542b n \u4e2a\u70b9&#xff08;\u7f16\u53f7 0 \u5230 n-1&#xff09;\u7684\u6709\u5411\u5e26\u6743\u56fe\u3002\u8fb9\u96c6\u5408 edges \u4e2d\u7684\u6bcf\u4e00\u9879 edges[i]  [ui, vi, wi] \u8868\u793a\u4ece ui \u6307\u5411 vi \u7684\u6709\u5411\u8fb9&#xff0c;\u6743\u91cd\u4e3a wi\u3002 \u6bcf\u4e2a\u70b9\u90fd\u6709\u4e00\u6b21\u7279\u6b8a\u64cd\u4f5c\u7684\u673a\u4f1a&#xff1a;\u5f53\u4f60\u5230\u8fbe\u67d0\u4e2a\u70b9 u 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