{"id":2659,"date":"2020-01-04T16:12:49","date_gmt":"2020-01-04T08:12:49","guid":{"rendered":"http:\/\/www.sniper97.cn\/?p=2659"},"modified":"2020-01-04T16:12:49","modified_gmt":"2020-01-04T08:12:49","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%e6%89%80%e6%9c%89%e7%bb%93%e7%82%b9%e5%af%b9%e7%9a%84%e6%9c%80%e7%9f%ad%e8%b7%af%e5%be%84%e9%97%ae%e9%a2%98","status":"publish","type":"post","link":"http:\/\/www.sniper97.cn\/index.php\/note\/introduction_to_algorithms\/2659\/","title":{"rendered":"\u3010\u7b97\u6cd5\u5bfc\u8bba\u3011\u6240\u6709\u7ed3\u70b9\u5bf9\u7684\u6700\u77ed\u8def\u5f84\u95ee\u9898"},"content":{"rendered":"\n

\uff08\u591a\u6e90\u6700\u77ed\u8def\u5f84\u95ee\u9898\uff09<\/p>\n\n\n

\"\"<\/figure><\/div>\n\n\n

\u5728\u672c\u7ae0\u4e2d\uff0c\u6211\u4eec\u8003\u8651\u5982\u4f55\u627e\u5230\u4e00\u4e2a\u56fe\u4e2d\u6240\u6709\u7ed3\u70b9\u4e4b\u95f4\u7684\u6700\u77ed\u8def\u5f84\uff0c\u8be5\u95ee\u9898\u5728\u8ba1\u7b97\u6240\u6709\u57ce\u5e02\u4e4b\u95f4\u7684\u4ea4\u901a\u9053\u8def\u8ddd\u79bb\u65f6\u5e38\u51fa\u73b0\u3002<\/p>\n\n\n

\u6211\u4eec\u5f53\u7136\u53ef\u4ee5\u8fd0\u884cn\u6b21\u57fa\u4e8e\u8d2a\u5fc3\u7684\u5355\u6e90\u6700\u77ed\u8def\u5f84\u6765\u8ba1\u7b97\u51fa\u7ed3\u679c\uff0c\u672c\u7ae0\u4e5f\u4ecb\u7ecd\u4e86\u4e00\u4e2a\u57fa\u4e8e\u52a8\u6001\u89c4\u5212\u7b97\u6cd5\u6765\u89e3\u51b3\u6700\u77ed\u8def\u5f84\u95ee\u9898\u3002<\/p>\n\n\n

1.Floyd-Warshall\u7b97\u6cd5<\/h2>\n\n\n

\u65f6\u95f4\u590d\u6742\u5ea6O(n^3)\u3002<\/p>\n\n\n

\u6700\u77ed\u8def\u5f84\u7684\u7ed3\u6784<\/h3>\n\n\n

\u5982\u679c\u4e00\u6761\u8def\u5f84\u662f\u6700\u77ed\u8def\uff0c\u90a3\u4e48\u8fd9\u6761\u8def\u5f84\u7684\u4efb\u4f55\u5b50\u8def\u5f84\u4f9d\u7136\u662f\u6700\u77ed\u8def\u3002\u6240\u4ee5\u5229\u7528\u8fd9\u6761\u6211\u4eec\u53ef\u4ee5\u627e\u5230\u52a8\u6001\u89c4\u5212\u7684\u6700\u4f18\u5b50\u7ed3\u6784\u3002<\/p>\n\n\n

\u6240\u6709\u7ed3\u70b9\u5bf9\u6700\u77ed\u8def\u5f84\u95ee\u9898\u7684\u9012\u5f52\u89e3<\/h3>\n\n\n

\u56e0\u6b64\u6211\u4eec\u53ef\u4ee5\u8bbe\u8ba1\u51fa\u5982\u4e0b\u9012\u5f52\u5b9a\u4e49\uff1a<\/p>\n\n\n

\"\"<\/figure><\/div>\n\n\n

\u521d\u59cb\u5316\u4e3aw_ij\uff0c\u4e4b\u540e\u90fd\u8fdb\u884c\u677e\u5f1b\u64cd\u4f5c\u3002<\/p>\n\n\n

\u81ea\u5e95\u5411\u4e0a\u8ba1\u7b97\u6700\u77ed\u8def\u5f84\u6743\u91cd<\/h3>\n\n\n

\u4e2d\u95f4\u77e9\u9635\uff1a<\/p>\n\n\n

\"\"<\/figure><\/div>\n\n\n

\u4ee3\u7801\uff1a<\/p>\n\n\n

def floyd_warshall(self, graph):
    \"\"\"
<\/em>    floyd_warshall<\/em>\u7b97\u6cd5\u5b9e\u73b0\uff0c\u5176\u4e2d<\/em>graph<\/em>\u5c31\u662f<\/em>weight
<\/em>    <\/em>:param<\/em><\/strong> graph: 
<\/em>    <\/em>:return<\/em><\/strong>: 
<\/em>    \"\"\"
<\/em>    <\/em>inf = float('inf')
    # \u521d\u59cb\u5316path
    path = [[inf for _ in range(len(graph[0]))] for _ in range(len(graph))]
    for i in range(len(path)):
        for j in range(len(path[0])):
            if graph[i][j] != inf and i != j:
                path[i][j] = i
    for k in range(len(graph)):
        for i in range(len(graph)):
            for j in range(len(graph[0])):
                if graph[i][j] > graph[i][k] + graph[k][j]:
                    graph[i][j] = graph[i][k] + graph[k][j]
                    path[i][j] = k
    return graph, path<\/pre>\n\n\n
\u6784\u5efa\u4e00\u6761\u6700\u77ed\u8def\u5f84<\/h3>\n\n\n
\u9700\u8981\u6ce8\u610f\uff0c\u4e0a\u8ff0\u4ee3\u7801\u6700\u7ec8\u7ed3\u679c\u4e0e\u4e0a\u56fe\u5e76\u4e0d\u5b8c\u5168\u4e00\u81f4<\/p>\n\n\n
\"\"<\/figure><\/div>\n\n\n
\u89c2\u5bdf\u5728\uff080\uff0c2\uff09\u3001\uff081\uff0c5\uff09\u3001\uff084\uff0c2\uff09\u4f4d\u7f6e\u5747\u4e0d\u4e00\u6837\uff0c\u4e0a\u56fe\u4e3a\u8d77\u59cb\u70b9\u7b2c\u4e8c\u4e2a\u70b9\u7684\u7d22\u5f15\uff0c\u800c\u6211\u7684\u4ee3\u7801\u662f\u7ec8\u70b9\u524d\u7b2c\u4e00\u4e2a\u70b9\u7684\u6240\u6709\uff08\u5373\u771f\u5b9e\u8def\u5f84\u4e00\u4e2a\u6b63\u5e8f\u8f93\u51fa\u4e00\u4e2a\u5012\u5e8f\u8f93\u51fa\uff0c\u8fd9\u4e48\u505a\u7684\u76ee\u7684\u662f\u4ee3\u7801\u7b80\u5355\uff09\u3002<\/p>\n\n\n
2.\u7528\u4e8e\u7a00\u758f\u56fe\u7684Johnson\u7b97\u6cd5<\/h2>\n\n\n
\u4e0a\u8ff0Floyd\u7b97\u6cd5\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4e3aO(n^3)\uff0c\u5f53\u7528\u4e8e\u7a00\u758f\u56fe\u7684\u65f6\u5019\u4ee3\u4ef7\u672a\u514d\u8fc7\u5927\uff0c\u672c\u8282\u4ecb\u7ecd\u7684Johnson\u7b97\u6cd5\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4e3aO(V^2lgV+VE)\u7684\u7b97\u6cd5\u3002<\/p>\n\n\n
 Johnson \u7b97\u6cd5\u4f7f\u7528\u7684\u6280\u672f\u79f0\u4e3a\u91cd\u65b0\u8d4b\u4e88\u6743\u91cd<\/strong>\u3002\u4ec0\u4e48\u662f\u91cd\u65b0\u8d4b\u4e88\u6743\u91cd\u5462\uff0c\u5b57\u9762\u610f\u601d\u5c31\u662f\u91cd\u65b0\u8d4b\u4e88\u8fb9\u7684\u6743\u91cd\u3002<\/p>\n\n\n
\u90a3\u4e48\u8fd9\u4e2a\u7b97\u6cd5\u662f\u4ec0\u4e48\u6837\u5b50\u5462\uff1f\u8bf4\u51fa\u6765\u4f60\u53ef\u80fd\u4e0d\u4fe1\uff0c\u5c31\u662f\u8fdb\u884cn\u6b21Dijsktra\u7b97\u6cd5\uff08\u90a3\u4e48\u4e3a\u4ec0\u4e48\u662flgV\u5462\uff0c\u5f53\u7136\u662f\u4f7f\u7528\u6539\u8fdb\u7684Dijsktra\uff0c\u9009\u62e9\u7684\u65f6\u95f4\u7531V\u964d\u4e3algV\uff09\uff0c\u56e0\u4e3a\u6bcf\u6b21Dijsktra\u7ed3\u679c\u90fd\u4f1a\u4fee\u6539\u5f53\u524d\u7ed3\u70b9\u5230\u5176\u4ed6\u7ed3\u70b9\u7684\u8ddd\u79bb\uff0c\u4e0b\u6b21\u8ba1\u7b97\u65f6\uff0c\u6211\u4eec\u5c31\u4f7f\u7528\u4e0a\u4e00\u6b21\u7684\u7ed3\u679c\u4f5c\u4e3a\u8f93\u5165\uff0c\u56e0\u6b64\u53eb\u91cd\u65b0\u8d4b\u4e88\u6743\u91cd\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"
\uff08\u591a\u6e90\u6700\u77ed\u8def\u5f84\u95ee\u9898\uff09 \u5728\u672c\u7ae0\u4e2d\uff0c\u6211\u4eec\u8003\u8651\u5982\u4f55\u627e\u5230\u4e00\u4e2a\u56fe\u4e2d\u6240\u6709\u7ed3\u70b9\u4e4b\u95f4\u7684\u6700\u77ed\u8def\u5f84\uff0c\u8be5\u95ee\u9898\u5728\u8ba1\u7b97\u6240\u6709\u57ce\u5e02 […]<\/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":5378,"_links":{"self":[{"href":"http:\/\/www.sniper97.cn\/index.php\/wp-json\/wp\/v2\/posts\/2659"}],"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=2659"}],"version-history":[{"count":0,"href":"http:\/\/www.sniper97.cn\/index.php\/wp-json\/wp\/v2\/posts\/2659\/revisions"}],"wp:attachment":[{"href":"http:\/\/www.sniper97.cn\/index.php\/wp-json\/wp\/v2\/media?parent=2659"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/www.sniper97.cn\/index.php\/wp-json\/wp\/v2\/categories?post=2659"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/www.sniper97.cn\/index.php\/wp-json\/wp\/v2\/tags?post=2659"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}