{"id":201762,"date":"2024-05-10T02:50:53","date_gmt":"2024-05-09T18:50:53","guid":{"rendered":"https:\/\/docs.pingcode.com\/ask\/ask-ask\/201762.html"},"modified":"2024-05-10T02:50:58","modified_gmt":"2024-05-09T18:50:58","slug":"%e6%9c%89%e5%93%aa%e4%ba%9b%e5%9f%ba%e4%ba%8e%e5%9c%b0%e5%9b%be%e7%9a%84%e6%9c%80%e7%9f%ad%e8%b7%af%e5%be%84%e7%ae%97%e6%b3%95","status":"publish","type":"post","link":"https:\/\/docs.pingcode.com\/ask\/201762.html","title":{"rendered":"\u6709\u54ea\u4e9b\u57fa\u4e8e\u5730\u56fe\u7684\u6700\u77ed\u8def\u5f84\u7b97\u6cd5"},"content":{"rendered":"

\"\u6709\u54ea\u4e9b\u57fa\u4e8e\u5730\u56fe\u7684\u6700\u77ed\u8def\u5f84\u7b97\u6cd5\"<\/p>\n

\u57fa\u4e8e\u5730\u56fe\u7684\u6700\u77ed\u8def\u5f84\u7b97\u6cd5\u4e3b\u8981\u5305\u542b\u8fea\u6770\u65af\u7279\u62c9\u7b97\u6cd5 (Dijkstra's Algorithm)\u3001\u8d1d\u5c14\u66fc-\u798f\u7279\u7b97\u6cd5 (Bellman-Ford Algorithm)\u3001A\u7b97\u6cd5 (A<\/em> Algorithm)\u3001Floyd-Warshall\u7b97\u6cd5<\/strong>\uff0c\u4ee5\u53ca\u8fd1\u5e74\u6765\u53d1\u5c55\u8d77\u6765\u7684\u6539\u8fdb\u578b\u7b97\u6cd5<\/strong>\u3002\u8fd9\u4e9b\u7b97\u6cd5\u5404\u81ea\u9002\u7528\u4e8e\u4e0d\u540c\u7684\u573a\u666f\u548c\u9700\u6c42\u4e2d\uff0c\u5982\u8fea\u6770\u65af\u7279\u62c9\u7b97\u6cd5\u56e0\u5176\u9ad8\u6548\u6027\u800c\u5e7f\u6cdb\u5e94\u7528\u4e8e\u5e26\u6743\u56fe\u4e2d\u5bfb\u627e\u6700\u77ed\u8def\u5f84\u95ee\u9898\uff0c\u7279\u522b\u662f\u5728\u8def\u7f51\u4e0d\u542b\u6709\u8d1f\u6743\u8fb9\u7684\u573a\u666f\u4e2d<\/strong>\u3002<\/p>\n<\/p>\n

\u4e00\u3001\u8fea\u6770\u65af\u7279\u62c9\u7b97\u6cd5 (DIJKSTRA'S ALGORITHM)<\/h3>\n<\/p>\n

\u8fea\u6770\u65af\u7279\u62c9\u7b97\u6cd5\u662f\u57fa\u4e8e\u56fe\u4e2d\u7684\u8282\u70b9\u8fdb\u884c\u8fed\u4ee3\uff0c\u5bfb\u627e\u6700\u77ed\u8def\u5f84\u7684\u4e00\u79cd\u7b97\u6cd5\u3002\u5b83\u9002\u7528\u4e8e\u5e26\u6709\u6b63\u6743\u91cd\u7684\u56fe\uff0c\u53ef\u4ee5\u627e\u5230\u4e00\u4e2a\u9876\u70b9\u5230\u56fe\u4e2d\u5176\u4ed6\u6240\u6709\u9876\u70b9\u7684\u6700\u77ed\u8def\u5f84\u3002<\/p>\n<\/p>\n

\u9996\u5148\uff0c\u8be5\u7b97\u6cd5\u9009\u53d6\u56fe\u4e2d\u7684\u8d77\u70b9\u4f5c\u4e3a\u5f53\u524d\u8282\u70b9\uff0c\u7136\u540e\u5c06\u6240\u6709\u8282\u70b9\u7684\u6700\u77ed\u8def\u5f84\u503c\u521d\u59cb\u5316\u3002\u5bf9\u4e8e\u8d77\u70b9\uff0c\u8fd9\u4e2a\u503c\u4e3a0\uff1b\u5bf9\u4e8e\u6240\u6709\u5176\u4ed6\u8282\u70b9\uff0c\u8fd9\u4e2a\u503c\u901a\u5e38\u521d\u59cb\u5316\u4e3a\u65e0\u7a77\u5927\u3002\u7b97\u6cd5\u9010\u4e2a\u8bbf\u95ee\u672a\u88ab\u9009\u4e2d\u7684\u90bb\u5c45\u8282\u70b9\uff0c\u66f4\u65b0\u5b83\u4eec\u5230\u8d77\u70b9\u7684\u8ddd\u79bb\u3002\u8fd9\u4e2a\u8fc7\u7a0b\u91cd\u590d\u8fdb\u884c\uff0c\u76f4\u5230\u6240\u6709\u7684\u8282\u70b9\u90fd\u88ab\u8bbf\u95ee\u8fc7\u3002\u8be5\u7b97\u6cd5\u5229\u7528\u8d2a\u5fc3\u7b56\u7565\u786e\u4fdd\u6bcf\u4e00\u6b65\u90fd\u671d\u7740\u6700\u7ec8\u89e3\u7684\u65b9\u5411\u524d\u8fdb\u3002<\/p>\n<\/p>\n

\u4e8c\u3001\u8d1d\u5c14\u66fc-\u798f\u7279\u7b97\u6cd5 (BELLMAN-FORD ALGORITHM)<\/h3>\n<\/p>\n

\u8d1d\u5c14\u66fc-\u798f\u7279\u7b97\u6cd5\u4e0e\u8fea\u6770\u65af\u7279\u62c9\u7b97\u6cd5\u4e0d\u540c\u4e4b\u5904\u5728\u4e8e\u5b83\u53ef\u4ee5\u5904\u7406\u56fe\u4e2d\u5b58\u5728\u8d1f\u6743\u8fb9\u7684\u60c5\u51b5\u3002\u5b83\u901a\u8fc7\u5bf9\u56fe\u4e2d\u6240\u6709\u8fb9\u7684\u53cd\u590d\u8fed\u4ee3\u6765\u5bfb\u627e\u6700\u77ed\u8def\u5f84\u3002<\/p>\n<\/p>\n

\u8be5\u7b97\u6cd5\u9996\u5148\u521d\u59cb\u5316\u6240\u6709\u8282\u70b9\u5230\u8d77\u70b9\u7684\u8ddd\u79bb\uff0c\u7136\u540e\u5bf9\u6bcf\u6761\u8fb9\u91cd\u590d\u6267\u884c\u677e\u5f1b\u64cd\u4f5c\uff0c\u901a\u8fc7\u6bd4\u8f83\u5f53\u524d\u7684\u6700\u77ed\u8def\u5f84\u4f30\u8ba1\u548c\u901a\u8fc7\u7ed9\u5b9a\u8fb9\u53ef\u4ee5\u5f97\u5230\u7684\u8def\u5f84\u957f\u5ea6\u6765\u66f4\u65b0\u3002\u8fd9\u4e00\u8fc7\u7a0b\u91cd\u590d\u8fdb\u884c\u76f4\u5230\u6ca1\u6709\u8def\u5f84\u53ef\u4ee5\u8fdb\u4e00\u6b65\u88ab\u7f29\u77ed\u4e3a\u6b62\u3002\u867d\u7136\u8be5\u7b97\u6cd5\u8f83\u4e3a\u9ad8\u6548\uff0c\u4f46\u5728\u542b\u6709\u8d1f\u6743\u56de\u8def\u7684\u56fe\u4e2d\u65e0\u6cd5\u627e\u5230\u6700\u77ed\u8def\u5f84\u3002<\/p>\n<\/p>\n

\u4e09\u3001A\u7b97\u6cd5 (A<\/em> ALGORITHM)<\/h3>\n<\/p>\n

A*\u7b97\u6cd5\u662f\u4e00\u79cd\u5728\u56fe\u5f62\u5e73\u9762\u4e0a\uff0c\u5bf9\u4e8e\u6709\u591a\u4e2a\u8282\u70b9\u7684\u8def\u5f84\uff0c\u5c1d\u8bd5\u5bfb\u627e\u8def\u5f84\u4e2d\u603b\u6210\u672c\u6700\u4f4e\u7684\u90a3\u4e00\u6761\u8def\u5f84\u7684\u7b97\u6cd5\u3002\u7279\u522b\u9002\u7528\u4e8e\u5e26\u6709\u542f\u53d1\u5f0f\u4fe1\u606f\u7684\u56fe\u641c\u7d22\u95ee\u9898\uff0c\u4f8b\u5982\u5728\u5730\u56fe\u5e94\u7528\u4e2d\u5bfb\u627e\u4e24\u70b9\u95f4\u7684\u6700\u77ed\u884c\u9a76\u8def\u5f84\u3002<\/p>\n<\/p>\n

A\u7b97\u6cd5\u901a\u8fc7\u7ed3\u5408\u8282\u70b9\u5230\u8d77\u70b9\u7684\u8ddd\u79bb\uff08g(n)\uff09\u548c\u8282\u70b9\u5230\u7ec8\u70b9\u7684\u4f30\u8ba1\u8ddd\u79bb\uff08h(n)\uff09\uff0c\u6765\u8ba1\u7b97f(n)=g(n)+h(n)\uff0c\u5e76\u4f18\u5148\u641c\u7d22\u5177\u6709\u6700\u5c0ff(n)\u503c\u7684\u8def\u5f84\u3002\u8fd9\u79cd\u542f\u53d1\u5f0f\u641c\u7d22\u51cf\u5c11\u4e86\u641c\u7d22\u7a7a\u95f4\uff0c\u63d0\u9ad8\u4e86\u641c\u7d22\u6548\u7387\u3002\u9009\u62e9\u5408\u9002\u7684\u542f\u53d1\u5f0f\u51fd\u6570\u662f\u4f7f\u7528A<\/em>\u7b97\u6cd5\u6210\u529f\u7684\u5173\u952e\u3002<\/p>\n<\/p>\n

\u56db\u3001\u5f17\u6d1b\u4f0a\u5fb7-\u6c83\u820d\u5c14\u7b97\u6cd5 (FLOYD-WARSHALL ALGORITHM)<\/h3>\n<\/p>\n

\u5f17\u6d1b\u4f0a\u5fb7-\u6c83\u820d\u5c14\u7b97\u6cd5\u662f\u4e00\u79cd\u8ba1\u7b97\u56fe\u4e2d\u6240\u6709\u8282\u70b9\u5bf9\u4e4b\u95f4\u6700\u77ed\u8def\u5f84\u7684\u7b97\u6cd5\u3002\u5b83\u901a\u8fc7\u8fed\u4ee3\u8fc7\u7a0b\u4e2d\u4e0d\u65ad\u5c1d\u8bd5\u65b0\u7684\u4e2d\u95f4\u8282\u70b9\u6765\u66f4\u65b0\u8def\u5f84\u957f\u5ea6\uff0c\u4ee5\u8fbe\u5230\u6700\u7ec8\u76ee\u6807\u3002<\/p>\n<\/p>\n

\u8be5\u7b97\u6cd5\u7684\u6838\u5fc3\u662f\u52a8\u6001\u89c4\u5212\u3002\u5bf9\u4e8e\u56fe\u4e2d\u7684\u6bcf\u4e00\u5bf9\u9876\u70b9\uff0c\u7b97\u6cd5\u5c1d\u8bd5\u901a\u8fc7\u5176\u4ed6\u9876\u70b9\u4f5c\u4e3a\u201c\u4e2d\u95f4\u4eba\u201d\u5bfb\u627e\u4e00\u6761\u6bd4\u76f4\u63a5\u8def\u5f84\u66f4\u77ed\u7684\u8def\u5f84\u3002\u5b83\u7684\u4e3b\u8981\u4f18\u52bf\u662f\u80fd\u591f\u540c\u65f6\u8ba1\u7b97\u56fe\u4e2d\u6240\u6709\u8282\u70b9\u5bf9\u4e4b\u95f4\u7684\u6700\u77ed\u8def\u5f84\uff0c\u4f46\u52a3\u52bf\u662f\u5176\u65f6\u95f4\u548c\u7a7a\u95f4\u590d\u6742\u5ea6\u8f83\u9ad8\uff0c\u7279\u522b\u662f\u5728\u5904\u7406\u5927\u89c4\u6a21\u56fe\u65f6\u3002<\/p>\n<\/p>\n

\u4e94\u3001 \u6539\u8fdb\u578b\u7b97\u6cd5<\/h3>\n<\/p>\n

\u968f\u7740\u8ba1\u7b97\u673a\u79d1\u5b66\u7684\u53d1\u5c55\uff0c\u57fa\u4e8e\u5730\u56fe\u7684\u6700\u77ed\u8def\u5f84\u7b97\u6cd5\u4e5f\u4e0d\u65ad\u88ab\u6539\u8fdb\u548c\u4f18\u5316\u3002\u4f8b\u5982\uff0c\u5bf9\u8fea\u6770\u65af\u7279\u62c9\u7b97\u6cd5\u7684\u6539\u8fdb\u4f7f\u5176\u80fd\u591f\u66f4\u597d\u5730\u5904\u7406\u52a8\u6001\u53d8\u5316\u7684\u56fe\uff0c\u6bd4\u5982\u5b9e\u65f6\u4ea4\u901a\u4fe1\u606f\u66f4\u65b0\u7684\u8def\u7f51\u3002\u53e6\u5916\uff0c\u6709\u7684\u7b97\u6cd5\u901a\u8fc7\u5c06\u56fe\u5212\u5206\u6210\u591a\u4e2a\u5b50\u56fe\uff0c\u72ec\u7acb\u8ba1\u7b97\u6bcf\u4e2a\u5b50\u56fe\u7684\u6700\u77ed\u8def\u5f84\uff0c\u7136\u540e\u5c06\u7ed3\u679c\u7efc\u5408\u8d77\u6765\uff0c\u4ee5\u6b64\u6765\u4f18\u5316\u8ba1\u7b97\u6548\u7387\u548c\u5904\u7406\u5927\u89c4\u6a21\u56fe\u7684\u80fd\u529b\u3002<\/p>\n<\/p>\n

\u6539\u8fdb\u578b\u7b97\u6cd5\u901a\u5e38\u7ed3\u5408\u4e86\u591a\u79cd\u7b56\u7565\uff0c\u5982\u5229\u7528\u5e76\u884c\u8ba1\u7b97\u8d44\u6e90\u3001\u5f15\u5165\u66f4\u9ad8\u6548\u7684\u6570\u636e\u7ed3\u6784\u3001\u91c7\u7528\u542f\u53d1\u5f0f\u641c\u7d22\u65b9\u6cd5\u7b49\uff0c\u4ee5\u9002\u5e94\u66f4\u52a0\u590d\u6742\u548c\u591a\u53d8\u7684\u5e94\u7528\u573a\u666f\u9700\u6c42\u3002\u8fd9\u4e9b\u7b97\u6cd5\u4e3a\u89e3\u51b3\u5b9e\u9645\u95ee\u9898\u63d0\u4f9b\u4e86\u66f4\u591a\u7684\u53ef\u80fd\u6027\u548c\u7075\u6d3b\u6027\uff0c\u5c55\u793a\u4e86\u8be5\u9886\u57df\u6280\u672f\u8fdb\u6b65\u7684\u8d8b\u52bf\u3002<\/p>\n<\/p>\n

\u76f8\u5173\u95ee\u7b54FAQs\uff1a<\/strong><\/h2>\n

1. \u4ec0\u4e48\u662f\u57fa\u4e8e\u5730\u56fe\u7684\u6700\u77ed\u8def\u5f84\u7b97\u6cd5\uff1f<\/strong><\/p>\n

\u57fa\u4e8e\u5730\u56fe\u7684\u6700\u77ed\u8def\u5f84\u7b97\u6cd5\u662f\u4e00\u79cd\u8ba1\u7b97\u4ece\u4e00\u4e2a\u8d77\u70b9\u5230\u4e00\u4e2a\u7ec8\u70b9\u7684\u6700\u77ed\u8def\u5f84\u7684\u65b9\u6cd5\uff0c\u5176\u7279\u70b9\u662f\u4f7f\u7528\u5730\u56fe\u6570\u636e\u8fdb\u884c\u8ba1\u7b97\u3002\u8fd9\u79cd\u7b97\u6cd5\u7684\u8f93\u5165\u901a\u5e38\u662f\u4e00\u5f20\u5730\u56fe\uff0c\u5730\u56fe\u4e0a\u6807\u6ce8\u4e86\u9053\u8def\u548c\u8282\u70b9\u7684\u4fe1\u606f\uff0c\u800c\u8f93\u51fa\u5219\u662f\u4ece\u8d77\u70b9\u5230\u7ec8\u70b9\u7684\u6700\u77ed\u8def\u5f84\u3002<\/p>\n

2. \u57fa\u4e8e\u5730\u56fe\u7684\u6700\u77ed\u8def\u5f84\u7b97\u6cd5\u6709\u54ea\u4e9b\u5e38\u89c1\u7684\u5e94\u7528\u573a\u666f\uff1f<\/strong><\/p>\n

\u57fa\u4e8e\u5730\u56fe\u7684\u6700\u77ed\u8def\u5f84\u7b97\u6cd5\u5728\u8bb8\u591a\u5b9e\u9645\u5e94\u7528\u4e2d\u90fd\u88ab\u5e7f\u6cdb\u4f7f\u7528\u3002\u4f8b\u5982\uff0c\u4ea4\u901a\u5bfc\u822a\u7cfb\u7edf\u5229\u7528\u6700\u77ed\u8def\u5f84\u7b97\u6cd5\u8ba1\u7b97\u51fa\u4ece\u5f53\u524d\u4f4d\u7f6e\u5230\u76ee\u7684\u5730\u7684\u6700\u77ed\u8def\u5f84\uff1b\u7269\u6d41\u516c\u53f8\u53ef\u4ee5\u4f7f\u7528\u6700\u77ed\u8def\u5f84\u7b97\u6cd5\u89c4\u5212\u8d27\u7269\u7684\u8fd0\u8f93\u8def\u7ebf\uff1b\u57ce\u5e02\u89c4\u5212\u5e08\u53ef\u4ee5\u4f7f\u7528\u6700\u77ed\u8def\u5f84\u7b97\u6cd5\u8bc4\u4f30\u4e0d\u540c\u9053\u8def\u65b9\u6848\u7684\u4ea4\u901a\u6d41\u91cf\u7b49\u3002<\/p>\n

3. \u5e38\u89c1\u7684\u57fa\u4e8e\u5730\u56fe\u7684\u6700\u77ed\u8def\u5f84\u7b97\u6cd5\u6709\u54ea\u4e9b\uff1f\u5b83\u4eec\u6709\u4ec0\u4e48\u7279\u70b9\uff1f<\/strong><\/p>\n

\u5e38\u89c1\u7684\u57fa\u4e8e\u5730\u56fe\u7684\u6700\u77ed\u8def\u5f84\u7b97\u6cd5\u6709Dijkstra\u7b97\u6cd5\u3001Bellman-Ford\u7b97\u6cd5\u548cA*\u7b97\u6cd5\u7b49\u3002<\/p>\n

    \n
  • Dijkstra\u7b97\u6cd5\u662f\u4e00\u79cd\u8d2a\u5fc3\u7b97\u6cd5\uff0c\u5b83\u4ee5\u8d77\u70b9\u4e3a\u4e2d\u5fc3\uff0c\u9010\u6b65\u66f4\u65b0\u5230\u8fbe\u6bcf\u4e2a\u8282\u70b9\u7684\u6700\u77ed\u8def\u5f84\u3002Dijkstra\u7b97\u6cd5\u9002\u7528\u4e8e\u65e0\u6743\u56fe\u6216\u6b63\u6743\u56fe\uff0c\u4f46\u4e0d\u9002\u7528\u4e8e\u8d1f\u6743\u56fe\u3002<\/li>\n
  • Bellman-Ford\u7b97\u6cd5\u662f\u4e00\u79cd\u52a8\u6001\u89c4\u5212\u7b97\u6cd5\uff0c\u5b83\u901a\u8fc7\u4e0d\u65ad\u8fed\u4ee3\u8ba1\u7b97\u6bcf\u4e2a\u8282\u70b9\u7684\u6700\u77ed\u8def\u5f84\uff0c\u76f4\u5230\u6536\u655b\u4e3a\u6b62\u3002Bellman-Ford\u7b97\u6cd5\u9002\u7528\u4e8e\u6709\u8d1f\u6743\u8fb9\u7684\u56fe\u3002<\/li>\n
  • A\u7b97\u6cd5\u662f\u4e00\u79cd\u542f\u53d1\u5f0f\u641c\u7d22\u7b97\u6cd5\uff0c\u5b83\u901a\u8fc7\u8ba1\u7b97\u5f53\u524d\u70b9\u5230\u76ee\u6807\u70b9\u7684\u4f30\u8ba1\u8ddd\u79bb\u6765\u9009\u62e9\u4e0b\u4e00\u4e2a\u8981\u63a2\u7d22\u7684\u8282\u70b9\u3002A<\/em>\u7b97\u6cd5\u9002\u7528\u4e8e\u6709\u542f\u53d1\u4fe1\u606f\u7684\u56fe\uff0c\u53ef\u4ee5\u5feb\u901f\u627e\u5230\u6700\u77ed\u8def\u5f84\u3002<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"\u57fa\u4e8e\u5730\u56fe\u7684\u6700\u77ed\u8def\u5f84\u7b97\u6cd5\u4e3b\u8981\u5305\u542b\u8fea\u6770\u65af\u7279\u62c9\u7b97\u6cd5 (Dijkstra's Algorithm)\u3001\u8d1d\u5c14\u66fc- […]","protected":false},"author":3,"featured_media":201768,"comment_status":"closed","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[37],"tags":[],"acf":[],"_links":{"self":[{"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/posts\/201762"}],"collection":[{"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/comments?post=201762"}],"version-history":[{"count":0,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/posts\/201762\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/media\/201768"}],"wp:attachment":[{"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/media?parent=201762"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/categories?post=201762"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/tags?post=201762"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}