{"id":2649,"date":"2020-01-04T14:34:54","date_gmt":"2020-01-04T06:34:54","guid":{"rendered":"http:\/\/www.sniper97.cn\/?p=2649"},"modified":"2020-01-04T14:34:54","modified_gmt":"2020-01-04T06:34:54","slug":"%e3%80%90%e7%ae%97%e6%b3%95%e5%88%86%e6%9e%90%e4%b8%8e%e8%ae%be%e8%ae%a1%e3%80%91%e5%8d%95%e6%ba%90%e6%9c%80%e7%9f%ad%e8%b7%af%e5%be%84","status":"publish","type":"post","link":"http:\/\/www.sniper97.cn\/index.php\/note\/introduction_to_algorithms\/2649\/","title":{"rendered":"\u3010\u7b97\u6cd5\u5bfc\u8bba\u3011\u5355\u6e90\u6700\u77ed\u8def\u5f84"},"content":{"rendered":"\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img loading=\"lazy\" decoding=\"async\" width=\"345\" height=\"214\" src=\"\/wp-content\/uploads\/2020\/01\/\u56fe\u7247-15.png\" alt=\"\" class=\"wp-image-2657\" srcset=\"http:\/\/www.sniper97.cn\/wp-content\/uploads\/2020\/01\/\u56fe\u7247-15.png 345w, http:\/\/www.sniper97.cn\/wp-content\/uploads\/2020\/01\/\u56fe\u7247-15-300x186.png 300w\" sizes=\"(max-width: 345px) 100vw, 345px\" \/><\/figure><\/div>\n\n\n<p><strong>\u5355\u6e90\u6700\u77ed\u8def\u5f84<\/strong>\uff1a\u7ed9\u5b9a\u4e00\u4e2a\u56fe\uff0c\u6211\u4eec\u5e0c\u671b\u627e\u5230\u4ece\u5b9a\u6e90\u8282\u70b9s\u5230\u6bcf\u4e2a\u7ed3\u70b9v\u7684\u6700\u77ed\u8def\u5f84\u3002<\/p>\n\n\n<p><strong>\u677e\u5f1b\u64cd\u4f5c<\/strong>\uff1a\u672c\u7ae0\u7684\u7b97\u6cd5\u9700\u8981\u4f7f\u7528\u677e\u5f1b\u6280\u672f\uff0c\u5bf9\u4e8e\u6bcf\u4e00\u4e2a\u70b9\uff0c\u6211\u4eec\u591a\u7ef4\u62a4\u4e00\u4e2a\u53d8\u91cfd\uff0c\u7528\u6765\u8bb0\u5f55\u4ece\u6e90\u8282\u70b9\u5230\u7ed3\u70b9v\u7684\u6700\u77ed\u8def\u7684\u6743\u91cd\u4e0a\u754c\uff08\u4e5f\u5c31\u662f\u7c7b\u4f3c\u4e8e\u591a\u4e00\u4e2a\u53d8\u91cf\u7528\u6765\u4fdd\u5b58\u904d\u5386\u5230\u5f53\u524d\u60c5\u51b5\u4e0b\u5230\u8be5\u7ed3\u70b9\u7684\u6700\u77ed\u8ddd\u79bb\uff09\uff0c\u6211\u4eec\u79f0d\u4e3as\u5230v\u7684<strong>\u6700\u77ed\u8def\u5f84\u4f30\u8ba1<\/strong>\u3002<\/p>\n\n\n<h2 class=\"wp-block-heading\">1.Bellman-Ford\u7b97\u6cd5<\/h2>\n\n\n<p>Bellman-Ford\u7b97\u6cd5\u89e3\u51b3\u7684\u662f\u4e00\u822c\u60c5\u51b5\u4e0b\u7684\u5355\u6e90\u6700\u77ed\u8def\u5f84\u95ee\u9898\uff0c\u5728\u8fd9\u91cc\uff0c\u8fb9\u7684\u6743\u91cd\u53ef\u4ee5\u4e3a\u8d1f\u503c\u3002<\/p>\n\n\n<p>Bellman-Ford\u7b97\u6cd5\u8fd4\u56de\u4e00\u4e2a\u5e03\u5c14\u503c\uff0c\u4ee5\u8868\u660e\u662f\u5426\u5b58\u5728\u4e00\u4e2a\u4ece\u6e90\u8282\u70b9\u53ef\u4ee5\u5230\u8fbe\u7684\u6743\u91cd\u4e3a\u8d1f\u503c\u7684\u73af\u8def\uff08\u5c31\u662f\u4e00\u4e2a\u73af\u8def\u7684\u603b\u4ee3\u4ef7\u4e3a\u8d1f\u6570\uff09\u3002\u5982\u679c\u5b58\u5728\u8fd9\u6837\u4e00\u4e2a\u73af\u8def\uff0c\u7b97\u6cd5\u5c06\u544a\u8bc9\u6211\u4eec\u4e0d\u5b58\u5728\u89e3\u51b3\u65b9\u6848\u3002\u5982\u679c\u6ca1\u6709\u8fd9\u79cd\u73af\u8def\u5b58\u5728\uff0c\u7b97\u6cd5\u5c06\u7ed9\u51fa\u6700\u77ed\u8def\u5f84\u548c\u4ed6\u4eec\u7684\u6743\u91cd\u3002<\/p>\n\n\n<p> Bellman-Ford \u7b97\u6cd5\u5f15\u5165\u4e86\u4e00\u4e2a\u677e\u5f1b\u64cd\u4f5c\u7528\u6765\u68c0\u67e5\u662f\u5426\u5b58\u5728\u8d1f\u503c\u73af\u8def\u3002<\/p>\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img loading=\"lazy\" decoding=\"async\" width=\"602\" height=\"276\" src=\"\/wp-content\/uploads\/2020\/01\/\u56fe\u7247-10.png\" alt=\"\" class=\"wp-image-2651\" srcset=\"http:\/\/www.sniper97.cn\/wp-content\/uploads\/2020\/01\/\u56fe\u7247-10.png 602w, http:\/\/www.sniper97.cn\/wp-content\/uploads\/2020\/01\/\u56fe\u7247-10-300x138.png 300w\" sizes=\"(max-width: 602px) 100vw, 602px\" \/><\/figure><\/div>\n\n\n<pre class=\"wp-block-preformatted\">def bellman_ford(self, graph):\n    <em>\"\"\"\n    bellman_ford\u7b97\u6cd5(\u9ed8\u8ba4\u4ece0\u5f00\u59cb\n    <\/em><strong><em>:param<\/em><\/strong><em> graph:\n    <\/em><strong><em>:return<\/em><\/strong><em>:\n    \"\"\"\n    <\/em>weight = [float('inf') for _ in range(len(graph))]\n    weight[0] = 0\n    # \u5411\u524d\u5bfb\u627e\u5e76\u4fee\u6539\u677e\u5f1b\u53d8\u91cf\n    for k in range(len(graph) - 1):\n        for i in range(len(graph)):\n            for j in range(len(graph[0])):\n                if graph[i][j] != 0:\n                    if weight[j] &gt; weight[i] + graph[i][j]:\n                        weight[j] = weight[i] + graph[i][j]\n    # \u518d\u904d\u5386\u4e00\u904d\u5224\u65ad\u662f\u5426\u6709\u8d1f\u73af\u8def\uff08\u6709\u7684\u8bdd\u518d\u6765\u4e00\u904d\u4ee3\u4ef7\u5fc5\u7136\u4f1a\u66f4\u4f4e\uff09\n    for i in range(len(graph)):\n        for j in range(len(graph[0])):\n            if graph[i][j] != 0:\n                if weight[j] &gt; weight[i] + graph[i][j]:\n                    return False\n    return weight\n<\/pre>\n\n\n<h2 class=\"wp-block-heading\">2.Dijsktra\u7b97\u6cd5<\/h2>\n\n\n<p>Dijkstra\u7b97\u6cd5\u89e3\u51b3\u7684\u662f\u5e26\u6743\u91cd\u7684\u6709\u5411\u56fe\u4e0a\u5355\u6e90\u6700\u77ed\u8def\u5f84\u7684\u95ee\u9898\uff0c\u8be5\u7b97\u6cd5\u8981\u6c42\u6240\u6709\u8fb9\u7684\u6743\u91cd\u90fd\u4e3a\u975e\u8d1f\u503c\u3002\u65f6\u95f4\u590d\u6742\u5ea6O(V^2+E)=O(V^2)\u3002<\/p>\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img loading=\"lazy\" decoding=\"async\" width=\"841\" height=\"421\" src=\"\/wp-content\/uploads\/2020\/01\/\u56fe\u7247-18.png\" alt=\"\" class=\"wp-image-2664\" srcset=\"http:\/\/www.sniper97.cn\/wp-content\/uploads\/2020\/01\/\u56fe\u7247-18.png 841w, http:\/\/www.sniper97.cn\/wp-content\/uploads\/2020\/01\/\u56fe\u7247-18-300x150.png 300w, http:\/\/www.sniper97.cn\/wp-content\/uploads\/2020\/01\/\u56fe\u7247-18-768x384.png 768w\" sizes=\"(max-width: 841px) 100vw, 841px\" \/><\/figure><\/div>\n\n\n<p>Dijsktra\u6bcf\u6b21\u90fd\u8d2a\u5fc3\u7684\u83b7\u53d6\u5f53\u524d\u72b6\u6001\u4e0b\u7684\u6700\u5c0f\u8ddd\u79bb\u4f5c\u4e3a\u4e0b\u4e00\u6b21\u8ba1\u7b97\u7684\u57fa\u51c6\u3002<\/p>\n\n\n<pre class=\"wp-block-preformatted\">def Dijsktra(self, graph):\n    <em>\"\"\"\n    Dijsktra\u7b97\u6cd5(\u9ed8\u8ba4\u4ece0\u5f00\u59cb\n    <\/em><strong><em>:param<\/em><\/strong><em> graph:\n    <\/em><strong><em>:return<\/em><\/strong><em>:\n    \"\"\"\n    <\/em>weight = []\n    # \u521d\u59cb\u5316\u8ddd\u79bb\u5411\u91cf\uff08\u56e0\u4e3a\u8c03\u7528\u7684\u65f6\u5019\u54270\u4f5c\u4e3ainf\u4e86\uff0c\u8fd9\u91cc\u9700\u8981\u5904\u7406\u4e00\u4e0bx\uff09\n    for i in range(len(graph[0])):\n        if graph[0][i] != 0:\n            weight.append(graph[0][i])\n        else:\n            weight.append(float('inf'))\n    # \u8bbf\u95ee\u5217\u8868\n    vis = [0 for _ in range(len(graph))]\n    vis[0] = 1\n    weight[0] = 0\n    # \u67e5\u627e\u6700\u77ed\u8def\n    while sum(vis) != len(graph[0]):\n        min_value = float('inf')\n        min_index = 0\n        # \u5bfb\u627e\u672a\u88ab\u8bbf\u95ee\u8fc7\u7684\u6700\u5c0f\u70b9\n        for j in range(len(graph[0])):\n            if weight[j] &lt; min_value and vis[j] == 0:\n                min_value = weight[j]\n                min_index = j\n        vis[min_index] = 1\n        # \u66f4\u65b0\u8ddd\u79bb\n        for j in range(len(graph[0])):\n            if weight[j] &gt; weight[min_index] + graph[min_index][j]:\n                weight[j] = weight[min_index] + graph[min_index][j]\n    return weight<\/pre>\n\n\n<p>\u4e8b\u5b9e\u4e0a\uff0c\u6211\u4eec\u53ef\u4ee5\u4f18\u5316Dijsktra\u5230\u7684\u590d\u6742\u5ea6\u5230 O(V*lgV+E)\uff0c\u65b9\u6cd5\u662f\u4f7f\u7528\u6590\u6ce2\u90a3\u5951\u5806\uff0c\u6539\u5584\u7684\u662f\u6bcf\u6b21\u5bfb\u627e\u6700\u5c0f\u503c\u7684\u8fc7\u7a0b\uff0c\u5c06\u590d\u6742\u5ea6\u4eceV\u964d\u4e3algV\u3002 <\/p>\n\n\n<h2 class=\"wp-block-heading\">3.\u5dee\u5206\u7ea6\u675f\u548c\u6700\u77ed\u8def\u5f84<\/h2>\n\n\n<h3 class=\"wp-block-heading\">\u5dee\u5206\u7ea6\u675f\u7cfb\u7edf<\/h3>\n\n\n<p>\u5047\u5982\u4ee5\u4e0b\u65b9\u7a0b\u7ec4\uff1a<\/p>\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img loading=\"lazy\" decoding=\"async\" width=\"315\" height=\"186\" src=\"\/wp-content\/uploads\/2020\/01\/\u56fe\u7247-12.png\" alt=\"\" class=\"wp-image-2654\" srcset=\"http:\/\/www.sniper97.cn\/wp-content\/uploads\/2020\/01\/\u56fe\u7247-12.png 315w, http:\/\/www.sniper97.cn\/wp-content\/uploads\/2020\/01\/\u56fe\u7247-12-300x177.png 300w\" sizes=\"(max-width: 315px) 100vw, 315px\" \/><\/figure><\/div>\n\n\n<p>\u6211\u4eec\u53ef\u4ee5\u6574\u7406\u51fa\u5982\u4e0b\u4e0d\u7b49\u5f0f\u7ec4\uff1a<\/p>\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img loading=\"lazy\" decoding=\"async\" width=\"122\" height=\"191\" src=\"\/wp-content\/uploads\/2020\/01\/\u56fe\u7247-13.png\" alt=\"\" class=\"wp-image-2655\"\/><\/figure><\/div>\n\n\n<p>\u5bf9\u4e8e\u8be5\u7ec4\u4e0d\u7b49\u5f0f\uff0c\u6211\u4eec\u53ef\u4ee5\u63a5\u89e6\u591a\u4e2a\u89e3\u3002<\/p>\n\n\n<p>\u8fd9\u79cd\u5c31\u53eb\u505a\u5dee\u5206\u7ea6\u675f\u7cfb\u7edf\uff0c\u6bd4\u5982\u5728x1\u65f6\u523b\u8fdb\u884c\u4e00\u4e2a\u5de5\u4f5c\uff0c\u5fc5\u987b\u5728n\u4e2a\u5c0f\u65f6\u540e\u8fdb\u884c\u4e0b\u4e00\u4e2a\u540e\u7f6e\u5de5\u4f5cx2\uff0c\u56e0\u6b64\u5c31\u6709\u7ea6\u675fx2-x1&gt;=n\u3002<\/p>\n\n\n<h3 class=\"wp-block-heading\">\u7ea6\u675f\u56fe<\/h3>\n\n\n<p>\u5bf9\u4e8e\u4e0a\u8ff0\u4e0d\u7b49\u5f0f\u7ec4\uff0c\u6211\u4eec\u53ef\u4ee5\u753b\u51fa\u5982\u4e0b\u7684\u56fe\uff1a<\/p>\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img loading=\"lazy\" decoding=\"async\" width=\"341\" height=\"244\" src=\"\/wp-content\/uploads\/2020\/01\/\u56fe\u7247-14.png\" alt=\"\" class=\"wp-image-2656\" srcset=\"http:\/\/www.sniper97.cn\/wp-content\/uploads\/2020\/01\/\u56fe\u7247-14.png 341w, http:\/\/www.sniper97.cn\/wp-content\/uploads\/2020\/01\/\u56fe\u7247-14-300x215.png 300w\" sizes=\"(max-width: 341px) 100vw, 341px\" \/><\/figure><\/div>\n\n\n<p>\u5176\u4e2d\u8fb9\u5373\u4e3a\u4e0d\u7b49\u5f0f\u7684\u53f3\u8fb9\u3002<\/p>\n\n\n<h3 class=\"wp-block-heading\">\u6c42\u89e3\u5dee\u5206\u7ea6\u675f\u7cfb\u7edf<\/h3>\n\n\n<p>\u5bf9\u4e8e\u4e0a\u56fe\uff0c\u5f88\u660e\u663e\u6211\u4eec\u9700\u8981\u4f7f\u7528bellman-ford\u7b97\u6cd5\u6765\u89e3\u51b3\uff08\u56e0\u4e3a\u51fa\u73b0\u4e86\u8d1f\u8fb9\uff09\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u5355\u6e90\u6700\u77ed\u8def\u5f84\uff1a\u7ed9\u5b9a\u4e00\u4e2a\u56fe\uff0c\u6211\u4eec\u5e0c\u671b\u627e\u5230\u4ece\u5b9a\u6e90\u8282\u70b9s\u5230\u6bcf\u4e2a\u7ed3\u70b9v\u7684\u6700\u77ed\u8def\u5f84\u3002 \u677e\u5f1b\u64cd\u4f5c\uff1a\u672c\u7ae0\u7684\u7b97\u6cd5\u9700\u8981 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"om_disable_all_campaigns":false,"_mi_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"categories":[11],"tags":[],"views":5759,"_links":{"self":[{"href":"http:\/\/www.sniper97.cn\/index.php\/wp-json\/wp\/v2\/posts\/2649"}],"collection":[{"href":"http:\/\/www.sniper97.cn\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/www.sniper97.cn\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/www.sniper97.cn\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/www.sniper97.cn\/index.php\/wp-json\/wp\/v2\/comments?post=2649"}],"version-history":[{"count":0,"href":"http:\/\/www.sniper97.cn\/index.php\/wp-json\/wp\/v2\/posts\/2649\/revisions"}],"wp:attachment":[{"href":"http:\/\/www.sniper97.cn\/index.php\/wp-json\/wp\/v2\/media?parent=2649"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/www.sniper97.cn\/index.php\/wp-json\/wp\/v2\/categories?post=2649"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/www.sniper97.cn\/index.php\/wp-json\/wp\/v2\/tags?post=2649"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}