{"id":538,"date":"2019-09-15T06:36:06","date_gmt":"2019-09-14T22:36:06","guid":{"rendered":"http:\/\/120.55.184.7\/?p=538"},"modified":"2025-05-03T06:08:10","modified_gmt":"2025-05-02T22:08:10","slug":"538","status":"publish","type":"post","link":"https:\/\/beijian99.top\/?p=538","title":{"rendered":"\u6700\u77ed\u8def\u5f84\u7b97\u6cd5"},"content":{"rendered":"\n<p>\u6700\u77ed\u8def\u5f84\u7b97\u6cd5\u662f\u56fe\u8bba\u4e2d\u7684\u6838\u5fc3\u5185\u5bb9\uff0c\u7528\u4e8e\u5728\u52a0\u6743\u56fe\u4e2d\u5bfb\u627e\u4e24\u4e2a\u8282\u70b9\u4e4b\u95f4\u8def\u5f84\u6743\u503c\u4e4b\u548c\u6700\u5c0f\u7684\u8def\u5f84\u3002\u6839\u636e\u4e0d\u540c\u7684\u5e94\u7528\u573a\u666f\uff0c\u6700\u77ed\u8def\u5f84\u7b97\u6cd5\u53ef\u4ee5\u5206\u4e3a\u591a\u79cd\u7c7b\u578b\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"576\" src=\"https:\/\/beijian99.top\/wp-content\/uploads\/2019\/09\/image-1024x576.png\" alt=\"\" class=\"wp-image-998\" srcset=\"https:\/\/beijian99.top\/wp-content\/uploads\/2019\/09\/image-1024x576.png 1024w, https:\/\/beijian99.top\/wp-content\/uploads\/2019\/09\/image-300x169.png 300w, https:\/\/beijian99.top\/wp-content\/uploads\/2019\/09\/image-768x432.png 768w, https:\/\/beijian99.top\/wp-content\/uploads\/2019\/09\/image.png 1280w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\">\u4e00\u3001\u7b97\u6cd5\u5206\u7c7b\u4e0e\u7279\u70b9<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">1. \u5355\u6e90\u6700\u77ed\u8def\u5f84\u7b97\u6cd5\uff08\u4ece\u4e00\u4e2a\u56fa\u5b9a\u8d77\u70b9\u51fa\u53d1\uff09<\/h3>\n\n\n\n<p><strong>Dijkstra\u7b97\u6cd5<\/strong>\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u9002\u7528\u6761\u4ef6\uff1a\u8fb9\u6743\u975e\u8d1f\u7684\u6709\u5411\u56fe\u6216\u65e0\u5411\u56fe<\/li>\n\n\n\n<li>\u65f6\u95f4\u590d\u6742\u5ea6\uff1a<br>\u2022 \u57fa\u7840\u5b9e\u73b0\uff1aO(V<sup>2<\/sup>)<br>\u2022 \u4f18\u5148\u961f\u5217\u4f18\u5316\uff1aO((V+E) log<sup> V<\/sup>)<br>\u2022 \u6590\u6ce2\u90a3\u5951\u5806\u4f18\u5316\uff1aO(V log <sup>V<\/sup> + E)<\/li>\n\n\n\n<li>\u6838\u5fc3\u601d\u60f3\uff1a\u8d2a\u5fc3\u7b56\u7565\uff0c\u6bcf\u6b21\u9009\u62e9\u5f53\u524d\u672a\u8bbf\u95ee\u8282\u70b9\u4e2d\u8ddd\u79bb\u8d77\u70b9\u6700\u8fd1\u7684\u8282\u70b9<\/li>\n<\/ul>\n\n\n\n<p><strong>Bellman-Ford\u7b97\u6cd5<\/strong>\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u9002\u7528\u6761\u4ef6\uff1a\u5141\u8bb8\u8d1f\u6743\u8fb9\uff0c\u4f46\u4e0d\u80fd\u6709\u8d1f\u6743\u73af<\/li>\n\n\n\n<li>\u65f6\u95f4\u590d\u6742\u5ea6\uff1aO(VE)<\/li>\n\n\n\n<li>\u7279\u70b9\uff1a\u53ef\u4ee5\u68c0\u6d4b\u8d1f\u6743\u73af<\/li>\n<\/ul>\n\n\n\n<p><strong>SPFA\u7b97\u6cd5<\/strong>\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u9002\u7528\u6761\u4ef6\uff1a\u5141\u8bb8\u8d1f\u6743\u8fb9\uff0c\u4f46\u4e0d\u80fd\u6709\u8d1f\u6743\u73af<\/li>\n\n\n\n<li>\u65f6\u95f4\u590d\u6742\u5ea6\uff1a\u5e73\u5747O(E)\uff0c\u6700\u574fO(V E)<\/li>\n\n\n\n<li>\u7279\u70b9\uff1aBellman-Ford\u7684\u961f\u5217\u4f18\u5316\u7248\u672c<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">2. \u591a\u6e90\u6700\u77ed\u8def\u5f84\u7b97\u6cd5\uff08\u4efb\u610f\u4e24\u70b9\u95f4\uff09<\/h3>\n\n\n\n<p><strong>Floyd-Warshall\u7b97\u6cd5<\/strong>\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u9002\u7528\u6761\u4ef6\uff1a\u4efb\u610f\u6743\u503c\u56fe\uff08\u53ef\u5904\u7406\u8d1f\u6743\u8fb9\uff09<\/li>\n\n\n\n<li>\u65f6\u95f4\u590d\u6742\u5ea6\uff1aO(V<sup>3<\/sup>)<\/li>\n\n\n\n<li>\u7a7a\u95f4\u590d\u6742\u5ea6\uff1aO(V<sup>2<\/sup>)<\/li>\n\n\n\n<li>\u7279\u70b9\uff1a\u52a8\u6001\u89c4\u5212\u601d\u60f3\uff0c\u4ee3\u7801\u7b80\u6d01<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">\u4e8c\u3001\u7b97\u6cd5\u8be6\u7ec6\u89e3\u6790<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Dijkstra\u7b97\u6cd5\u5b9e\u73b0\uff08C++\u4f18\u5148\u961f\u5217\u7248\uff09<\/h3>\n\n\n<div class=\"wp-block-syntaxhighlighter-code \"><pre class=\"brush: cpp; title: ; notranslate\" title=\"\">\ntypedef pair&lt;int, int&gt; pii;\n\nvector&lt;int&gt; dijkstra(vector&lt;vector&lt;pii&gt;&gt;&amp; graph, int start) {\n    int n = graph.size();\n    vector&lt;int&gt; dist(n, INT_MAX);\n    priority_queue&lt;pii, vector&lt;pii&gt;, greater&lt;pii&gt;&gt; pq;\n\n    dist&#x5B;start] = 0;\n    pq.push({0, start});\n\n    while (!pq.empty()) {\n        auto &#x5B;d, u] = pq.top(); pq.pop();\n        if (d &gt; dist&#x5B;u]) continue;\n\n        for (auto &#x5B;v, w] : graph&#x5B;u]) {\n            if (dist&#x5B;v] &gt; dist&#x5B;u] + w) {\n                dist&#x5B;v] = dist&#x5B;u] + w;\n                pq.push({dist&#x5B;v], v});\n            }\n        }\n    }\n    return dist;\n}\n<\/pre><\/div>\n\n\n<h3 class=\"wp-block-heading\">Floyd\u7b97\u6cd5\u5b9e\u73b0\uff08C++\u7248\uff09<\/h3>\n\n\n<div class=\"wp-block-syntaxhighlighter-code \"><pre class=\"brush: cpp; title: ; notranslate\" title=\"\">\nvoid floyd(vector&lt;vector&lt;int&gt;&gt;&amp; dist) {\n    int n = dist.size();\n    for (int k = 0; k &lt; n; ++k)\n        for (int i = 0; i &lt; n; ++i)\n            for (int j = 0; j &lt; n; ++j)\n                if (dist&#x5B;i]&#x5B;k] != INT_MAX &amp;&amp; dist&#x5B;k]&#x5B;j] != INT_MAX)\n                    dist&#x5B;i]&#x5B;j] = min(dist&#x5B;i]&#x5B;j], dist&#x5B;i]&#x5B;k] + dist&#x5B;k]&#x5B;j]);\n}\n<\/pre><\/div>\n\n\n<h2 class=\"wp-block-heading\">\u4e09\u3001\u7b97\u6cd5\u9009\u62e9\u6307\u5357<\/h2>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>\u573a\u666f<\/th><th>\u63a8\u8350\u7b97\u6cd5<\/th><th>\u539f\u56e0<\/th><\/tr><\/thead><tbody><tr><td>\u975e\u8d1f\u6743\u56fe\uff0c\u5355\u6e90<\/td><td>Dijkstra<\/td><td>\u6548\u7387\u9ad8<\/td><\/tr><tr><td>\u542b\u8d1f\u6743\u8fb9\uff0c\u5355\u6e90<\/td><td>Bellman-Ford\/SPFA<\/td><td>\u80fd\u5904\u7406\u8d1f\u6743<\/td><\/tr><tr><td>\u591a\u6e90\u6700\u77ed\u8def\u5f84<\/td><td>Floyd-Warshall<\/td><td>\u76f4\u63a5\u8ba1\u7b97\u6240\u6709\u70b9\u5bf9<\/td><\/tr><tr><td>\u7a00\u758f\u56fe<\/td><td>SPFA<\/td><td>\u5e73\u5747\u6548\u7387\u9ad8<\/td><\/tr><tr><td>\u7a20\u5bc6\u56fe<\/td><td>Dijkstra<\/td><td>\u66f4\u7a33\u5b9a<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\">\u56db\u3001\u5178\u578b\u5e94\u7528\u573a\u666f<\/h2>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u5730\u56fe\u5bfc\u822a<\/strong>\uff1a\u8ba1\u7b97\u4e24\u70b9\u95f4\u6700\u77ed\u884c\u8f66\u8def\u7ebf\uff08Dijkstra\uff09<\/li>\n\n\n\n<li><strong>\u7f51\u7edc\u8def\u7531<\/strong>\uff1a\u5bfb\u627e\u6700\u4f18\u6570\u636e\u4f20\u8f93\u8def\u5f84\uff08Bellman-Ford\uff09<\/li>\n\n\n\n<li><strong>\u4ea4\u901a\u89c4\u5212<\/strong>\uff1a\u8ba1\u7b97\u6240\u6709\u5730\u70b9\u95f4\u7684\u6700\u77ed\u8ddd\u79bb\uff08Floyd\uff09<\/li>\n\n\n\n<li><strong>\u6e38\u620fAI<\/strong>\uff1a\u5bfb\u8def\u7b97\u6cd5\uff08A*\u7b97\u6cd5\uff0cDijkstra\u53d8\u79cd\uff09<\/li>\n\n\n\n<li><strong>\u793e\u4ea4\u7f51\u7edc<\/strong>\uff1a\u8ba1\u7b97\u4eba\u4e0e\u4eba\u4e4b\u95f4\u7684&#8221;\u8ddd\u79bb&#8221;\uff08\u5e7f\u5ea6\u4f18\u5148\u641c\u7d22\uff09<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"<p>\u6700\u77ed\u8def\u5f84\u7b97\u6cd5\u662f\u56fe\u8bba\u4e2d\u7684\u6838\u5fc3\u5185\u5bb9\uff0c\u7528\u4e8e\u5728\u52a0\u6743\u56fe\u4e2d\u5bfb\u627e\u4e24\u4e2a\u8282\u70b9\u4e4b\u95f4\u8def\u5f84\u6743\u503c\u4e4b\u548c\u6700\u5c0f\u7684\u8def\u5f84\u3002\u6839\u636e\u4e0d\u540c\u7684\u5e94\u7528\u573a\u666f\uff0c\u6700\u77ed [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":998,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center 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