{"id":474,"date":"2023-04-06T10:55:01","date_gmt":"2023-04-06T02:55:01","guid":{"rendered":"https:\/\/blog.cirno.fun\/?p=474"},"modified":"2025-03-19T00:34:57","modified_gmt":"2025-03-18T16:34:57","slug":"%e6%9c%b4%e7%b4%a0dijkstra%e7%ae%97%e6%b3%95","status":"publish","type":"post","link":"https:\/\/blog.sssn.tech\/?p=474","title":{"rendered":"\u6734\u7d20dijkstra\u7b97\u6cd5"},"content":{"rendered":"<p>dijkstra\u7b97\u6cd5\u662f\u89e3\u51b3<strong>\u5355\u6e90\u6700\u77ed\u8def\u95ee\u9898<\/strong>\u7684\u91cd\u8981\u7b97\u6cd5<\/p>\n<p>\u5176\u4e3b\u8981\u601d\u60f3\u5982\u4e0b:<\/p>\n<ul>\n<li>\u7ef4\u62a4\u4e00\u4e2a\u96c6\u5408s\uff0c\u5176\u5143\u7d20\u662f<strong>\u5df2\u7ecf\u786e\u5b9a\u6700\u77ed\u8def\u8ddd\u79bb\u7684\u70b9<\/strong><\/li>\n<li>\u7ef4\u62a4\u4e00\u4e2a\u6570\u7ec4d[i]\uff0c\u4ee3\u8868\u8d77\u70b9\u5230i\u7684\u6700\u77ed\u8ddd\u79bb\uff0c\u521d\u59cb\u5316\u5168\u90e8\u4e3a\u65e0\u7a77\u5927\uff0c\u8d77\u70b9\u7684d\u4e3a0<\/li>\n<li>\u6bcf\u6b21\u9009\u62e9\u4e00\u4e2a\u4e0d\u5728\u96c6\u5408s\u4e2d\uff0c\u79bb\u8d77\u70b9\u6700\u8fd1\u7684\u70b9:\n<ul>\n<li>\u5c06\u5176\u52a0\u5165\u5230\u96c6\u5408s\u4e2d<\/li>\n<li>\u7528\u4ed6\u6765\u677e\u5f1b\u5176\u4ed6\u7684\u90bb\u63a5\u70b9<\/li>\n<li>\u677e\u5f1b\u5c31\u662f\u5c1d\u8bd5\u5237\u65b0\u5176\u90bb\u63a5\u70b9\u7684\u6700\u77ed\u8def<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>\u56e0\u4e3a\u6bcf\u6b21\u786e\u5b9a\u7684\u5c06\u4e00\u4e2a\u70b9\u52a0\u5165\u96c6\u5408n\uff0c\u6bcf\u6b21\u52a0\u5165\u540e\u90fd\u5c1d\u8bd5\u677e\u5f1b\uff0c\u6240\u4ee5\u6734\u7d20dijk\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u662f<\/p>\n<pre><code class=\"language-katex\">O(N^2)<\/code><\/pre>\n<p><img decoding=\"async\" src=\"https:\/\/blog.sssn.tech\/wp-content\/uploads\/2023\/04\/image-1680749632697.png\" alt=\"file\" \/><\/p>\n<p>\u89c2\u5bdf\u6570\u636e\u8303\u56f4\u7528\u4e8c\u7ef4\u6570\u7ec4\u5b58\u8fb9<\/p>\n<pre><code class=\"language-cpp\">#include &lt;bits\/stdc++.h&gt;\n\nusing namespace std;\n\nconst int N = 510, M = 1e5 + 10;\n\nint g[N][N], n, m;\n\nint d[N];\nbool v[N];\nvoid dijk(int s)\n{\n    memset(d, 0x3f, sizeof d);\n    d[s] = 0;\n\n    for (int i = 1; i &lt;= n; i++)\n    {\n        \/\/ \u8fd9\u4e2a-1\u662f\u4e2a\u5c0f\u6280\u5de7\uff0c\u65b9\u4fbf\u9009\u62e9\u51fa\u96c6\u5408\u5916\u7684\u70b9\n        int t = -1;\n        for (int j = 1; j &lt;= n; j++)\n            if (!v[j] &amp;&amp; (t == -1 || d[j] &lt; d[t]))\n                t = j;\n        v[t] = true;\n        for (int j = 1; j &lt;= n; j++)\n            if (d[j] &gt; d[t] + g[t][j])\n                d[j] = d[t] + g[t][j];\n    }\n}\n\nint main()\n{\n    memset(g, 0x3f, sizeof g);\n    cin &gt;&gt; n &gt;&gt; m;\n    while (m--)\n    {\n        int x, y, w;\n        cin &gt;&gt; x &gt;&gt; y &gt;&gt; w;\n        if (x == y)\n            continue;\n        g[x][y] = min(g[x][y], w);\n    }\n\n    dijk(1);\n\n    cout &lt;&lt; (d[n] == d[0] ? -1 : d[n]) &lt;&lt; endl;\n\n    return 0;\n}\n<\/code><\/pre>\n","protected":false},"excerpt":{"rendered":"<p>dijkstra\u7b97\u6cd5\u662f\u89e3\u51b3\u5355\u6e90\u6700\u77ed\u8def\u95ee\u9898\u7684\u91cd\u8981\u7b97\u6cd5 \u5176\u4e3b\u8981\u601d\u60f3\u5982\u4e0b: \u7ef4\u62a4\u4e00\u4e2a\u96c6 [&#8230;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[12,13],"tags":[],"class_list":["post-474","post","type-post","status-publish","format-standard","hentry","category-12","category-13"],"_links":{"self":[{"href":"https:\/\/blog.sssn.tech\/index.php?rest_route=\/wp\/v2\/posts\/474","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blog.sssn.tech\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blog.sssn.tech\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blog.sssn.tech\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.sssn.tech\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=474"}],"version-history":[{"count":2,"href":"https:\/\/blog.sssn.tech\/index.php?rest_route=\/wp\/v2\/posts\/474\/revisions"}],"predecessor-version":[{"id":842,"href":"https:\/\/blog.sssn.tech\/index.php?rest_route=\/wp\/v2\/posts\/474\/revisions\/842"}],"wp:attachment":[{"href":"https:\/\/blog.sssn.tech\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=474"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.sssn.tech\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=474"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.sssn.tech\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=474"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}