{"id":913,"date":"2016-12-02T11:20:17","date_gmt":"2016-12-02T03:20:17","guid":{"rendered":"http:\/\/yaochenkun.site\/?p=913"},"modified":"2024-11-23T15:54:17","modified_gmt":"2024-11-23T07:54:17","slug":"travelproblem_article","status":"publish","type":"post","link":"http:\/\/yaochenkun.site\/index.php\/2016\/12\/02\/travelproblem_article\/","title":{"rendered":"\u65c5\u884c\u5546\u95ee\u9898 (TSP) \u6982\u8ff0"},"content":{"rendered":"

\u5f15\u8a00<\/h3>\n

TSP(Traveling Salesman Problem)\u5373\u65c5\u884c\u5546\u95ee\u9898\uff0c\u662f\u6570\u5b66\u9886\u57df\u4e2d\u8457\u540d\u95ee\u9898\u4e4b\u4e00\u3002\u8fd9\u4e2a\u95ee\u9898\u662f\u8fd9\u6837\u7684\uff1a\u5047\u8bbe\u6709\u4e00\u4e2a\u65c5\u884c\u5546\u4eba\u8981\u62dc\u8bbfn\u4e2a\u57ce\u5e02\uff0c\u4ed6\u5fc5\u987b\u9009\u62e9\u6240\u8981\u8d70\u7684\u8def\u5f84\uff0c\u8def\u5f84\u7684\u9650\u5236\u662f\u6bcf\u4e2a\u57ce\u5e02\u53ea\u80fd\u62dc\u8bbf\u4e00\u6b21\uff0c\u800c\u4e14\u6700\u540e\u8981\u56de\u5230\u539f\u6765\u51fa\u53d1\u7684\u57ce\u5e02\u3002\u8def\u5f84\u7684\u9009\u62e9\u76ee\u6807\u662f\u8981\u6c42\u5f97\u7684\u8def\u5f84\u957f\u5ea6\u4e3a\u6240\u6709\u8def\u5f84\u4e4b\u4e2d\u7684\u6700\u5c0f\u503c\u3002TSP\u662f\u4e00\u4e2a\u5178\u578b\u7684\u7ec4\u5408\u4f18\u5316\u95ee\u9898\uff0c\u4e14\u662f\u4e00\u4e2aNP\u5b8c\u5168\u96be\u9898\uff0c\u5173\u4e8eNP\u7684\u8fd9\u4e2a\u6982\u5ff5\u672c\u6587\u5c31\u4e0d\u505a\u8be6\u7ec6\u4ecb\u7ecd\u4e86\uff0c\u4f46\u7b80\u5355\u7684\u8bf4\u5c31\u662f\uff1aTSP\u95ee\u9898\u76ee\u524d\u5c1a\u4e0d\u80fd\u627e\u5230\u4e00\u4e2a\u591a\u9879\u5f0f\u65f6\u95f4\u590d\u6742\u5ea6\u7684\u7b97\u6cd5\u6765\u6c42\u89e3\u3002<\/p>\n

\u95ee\u9898\u5206\u6790<\/h3>\n

1<\/strong> \u8bc6\u522b\u672c\u8d28<\/h4>\n

\u8fd9\u4e2a\u95ee\u9898\u4e4d\u4e00\u770b\uff0c\u6709\u90a3\u4e48\u4e00\u70b9\u50cf\u201c\u6700\u77ed\u8def\u5f84\u95ee\u9898\u201d\uff0c\u7136\u540e\u6211\u4eec\u5c31\u4f1a\u81ea\u7136\u5730\u60f3\u5230\u7528Dijkstra\u7b97\u6cd5\u53bb\u6c42\u5f97\u201c\u4ece\u67d0\u4e00\u4e2a\u57ce\u5e02\u51fa\u53d1\uff0c\u5230\u5176\u4ed6\u6240\u6709\u5269\u4f59\u57ce\u5e02\u7684\u6700\u77ed\u8def\u5f84\u201d\uff0c\u518d\u6216\u8005\u5982\u679c\u662f\u4e2a\u771f\u5b9e\u5730\u56fe\uff0c\u6211\u4eec\u53ef\u4ee5\u7528\u542f\u53d1\u5f0f\u7684\u201cA\u661f\u7b97\u6cd5\u201d\u5feb\u901f\u641c\u7d22\u51fa\u201c\u4ece\u67d0\u4e00\u4e2a\u57ce\u5e02\u5230\u53e6\u4e00\u4e2a\u6307\u5b9a\u57ce\u5e02\u95f4\u7684\u6700\u77ed\u8def\u5f84\u201d\u3002\u7684\u786e\uff0c\u5982\u679c\u662f\u8fd9\u6837\u771f\u7684\u633a\u597d\uff0c\u4f46\u4ed4\u7ec6\u60f3\uff0c\u8fd9\u4e2a\u95ee\u9898\u5e76\u975e\u5355\u7eaf\u8fd9\u4e48\u7b80\u5355\uff0c\u5b83\u8fd8\u8981\u6c42\u53bb\u5bfb\u627e\u201c\u4ece\u67d0\u4e2a\u57ce\u5e02\u5f00\u59cb\uff0c\u5206\u522b\u7ecf\u8fc7\u5176\u5b83\u57ce\u5e02\u4e00\u6b21\u4e14\u4ec5\u4e00\u6b21\uff0c\u6700\u540e\u518d\u56de\u5230\u8fd9\u4e2a\u51fa\u53d1\u57ce\u5e02\u7684\u6700\u77ed\u5de1\u56de\u8def\u5f84\u201d\u3002<\/p>\n

2 \u6df1\u5165\u5206\u6790<\/strong><\/h4>\n

\u6240\u4ee5\u8be5\u600e\u4e48\u6c42\u89e3\u5462\uff0c\u6211\u4eec\u5f88\u5bb9\u6613\u60f3\u5230\u4e00\u79cd\u7c7b\u4f3c\u4e8e\u7a77\u4e3e\u7684\u601d\u8def\uff1a\u73b0\u5728\u5047\u8bbe\u6211\u4eec\u8981\u62dc\u8bbf11\u4e2a\u57ce\u5e02\uff0c\u4ece\u57ce\u5e021\u51fa\u53d1\uff0c\u6700\u540e\u56de\u5230\u57ce\u5e021\u3002\u663e\u7136\uff0c\u4ece\u57ce\u5e021\u51fa\u6765\u540e\uff0c\u6211\u4eec\u968f\u5373\u53ef\u4ee5\u9009\u62e9\u5269\u4f59\u768410\u4e2a\u57ce\u5e02\u4e4b\u4e00\u8fdb\u884c\u62dc\u8bbf\uff08\u8fd9\u91cc\u6240\u6709\u57ce\u5e02\u90fd\u662f\u8fde\u901a\u7684\uff0c\u603b\u662f\u53ef\u8fbe\u7684\uff0c\u800c\u4e0d\u8fde\u901a\u7684\u60c5\u51b5\u5c5e\u4e8e\u4e2a\u4eba\u7279\u6b8a\u4e1a\u52a1\u7684\u88c5\u9970\u5904\u7406\uff0c\u4e0d\u662f\u672c\u6587\u8003\u8651\u8303\u7574\uff09\uff0c\u90a3\u4e48\u5f88\u663e\u7136\u8fd9\u91cc\u5c31\u670910\u79cd\u9009\u62e9\uff0c\u4ee5\u6b64\u7c7b\u63a8\uff0c\u4e0b\u4e00\u6b21\u5c31\u67099\u79cd\u9009\u62e9…\u603b\u7684\u53ef\u9009\u8def\u7ebf\u6570\u5c31\u662f\uff1a\\(10!\\)\u3002\u4e5f\u5c31\u662f\u8bf4\u9700\u8981\u7528for\u5faa\u73af\u8fed\u4ee3\\(10!\\)\u6b21\uff0c\u624d\u80fd\u627e\u51fa\u6240\u6709\u7684\u8def\u7ebf\uff0c\u8fdb\u800c\u7b5b\u9009\u51fa\u6700\u77ed\u7684\u90a3\u6761\u6765\u3002\u5982\u679c\u53ea\u62dc\u8bbf\u4e2a10\u4e2a\u57ce\u5e02\u6216\u8bb8\u8fd8\u597d\u7684\u8bdd\uff08\u9700\u8981\u8fed\u4ee33 628 800\u6b21\uff09\uff0c\u90a3\u8981\u62dc\u8bbf100\u4e2a\u57ce\u5e02\uff08\u9700\u8981\u8fed\u4ee3\\(9.3326215443944 \\times 10{\\;^{157}}\\)\uff09\u7b80\u76f4\u5c31\u662f\u8ba1\u7b97\u673a\u7684\u5669\u68a6\uff01\u66f4\u591a\u4e2a\u57ce\u5e02\u7684\u8bdd\uff0c\u8ba1\u7b97\u7684\u65f6\u95f4\u5f00\u9500\u53ef\u60f3\u800c\u77e5\uff01<\/p>\n

\u66f4\u4e00\u822c\u5730\uff0c\u5982\u679c\u8981\u62dc\u8bbfn+1\u4e2a\u57ce\u5e02\uff0c\u603b\u7684\u53ef\u9009\u8def\u7ebf\u6570\u5c31\u662f\\(n!\\)\uff0c\u8fdb\u800c\u65f6\u95f4\u590d\u6742\u5ea6\u5c31\u662f\\(O\\left( {n!} \\right)\\)\uff0c\u4ece\u8fd9\u91cc\u6211\u4eec\u540c\u7406\u4e5f\u53ef\u4ee5\u770b\u51fa\uff0c\u8fd9\u4e2a\u7b97\u6cd5\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u662f\u975e\u591a\u9879\u5f0f\u7684\uff0c\u5b83\u7684\u5f00\u9500\u5927\u662f\u663e\u800c\u6613\u89c1\u7684\u3002\u6240\u4ee5\u95ee\u9898\u7684\u5173\u952e\u4e0d\u5728\u4e8e\u5bfb\u627e\u4e24\u4e24\u57ce\u5e02\u95f4\u7684\u6700\u77ed\u8def\u5f84\uff0c\u800c\u5728\u4e8e\u53bb\u5bfb\u627e\u4e00\u90a3\u6761\u6700\u77ed\u7684\u5de1\u56de\u8def\u5f84\uff0c\u6362\u53e5\u8bdd\u8bf4\uff0c\u5c31\u662f\u5bfb\u627e\u4e00\u7ec4\u62dc\u8bbf\u57ce\u5e02\u7684\u5148\u540e\u6b21\u5e8f\u5e8f\u5217 \\({n_1}{n_2}{n_3} \\ldots {n_i}{n_{i + 1}} \\ldots {n_n}{n_1}\\)\u3002<\/p>\n

\u89e3\u51b3\u65b9\u6848<\/h3>\n

\u8fd9\u662f\u4e2aNP\u5b8c\u5168\u95ee\u9898\uff0c\u7a77\u4e3e\u7b97\u6cd5\u7684\u6548\u7387\u53c8\u4e0d\u9ad8\uff0c\u90a3\u6211\u4eec\u8be5\u5982\u4f55\u901a\u8fc7\u4e00\u4e2a\u591a\u9879\u5f0f\u65f6\u95f4\u590d\u6742\u5ea6\u7684\u7b97\u6cd5\u5feb\u901f\u6c42\u51fa\u8fd9\u4e2a\u5148\u540e\u6b21\u5e8f\u5462\uff1f\u76ee\u524d\u6bd4\u8f83\u4e3b\u6d41\u7684\u65b9\u6cd5\u662f\u91c7\u7528\u4e00\u4e9b\u968f\u673a\u7684\u3001\u542f\u53d1\u5f0f\u7684\u641c\u7d22\u7b97\u6cd5\uff0c\u6bd4\u5982\u9057\u4f20\u7b97\u6cd5\u3001\u8681\u7fa4\u7b97\u6cd5\u3001\u6a21\u62df\u9000\u8d27\u7b97\u6cd5\u3001\u7c92\u5b50\u7fa4\u7b97\u6cd5\u7b49\u3002\u4f46\u8fd9\u4e9b\u7b97\u6cd5\u90fd\u6709\u4e00\u4e2a\u7f3a\u70b9\uff0c\u5c31\u662f\u4e0d\u4e00\u5b9a\u80fd\u6c42\u51fa\u6700\u4f18\u89e3\uff0c\u53ea\u80fd\u6536\u655b\u4e8e\uff08\u8fd1\u4f3c\u903c\u8fd1\uff09\u6700\u4f18\u89e3\uff0c\u5f97\u5230\u4e00\u4e2a\u6b21\u4f18\u89e3\uff0c\u56e0\u4e3a\u4ed6\u4eec\u672c\u8d28\u90fd\u662f\u968f\u673a\u7b97\u6cd5\uff0c\u5927\u591a\u90fd\u4f1a\u4ee5\u7c7b\u4f3c\u201c\u4e00\u5b9a\u6982\u7387\u63a5\u53d7\u6216\u820d\u53bb\u201d\u7684\u601d\u8def\u53bb\u7b5b\u9009\u89e3\u3002\u5404\u7b97\u6cd5\u7684\u5b9e\u73b0\u601d\u8def\u90fd\u6709\u4e0d\u540c\uff0c\u4f46\u4e5f\u6216\u591a\u6216\u5c11\u6709\u4e92\u76f8\u501f\u9274\u7684\u5730\u65b9\uff0c\u6709\u7684\u4e0e\u968f\u673a\u56e0\u5b50\u6709\u5173\u3001\u6709\u7684\u4e0e\u521d\u59cb\u72b6\u6001\u6709\u5173\u3001\u6709\u7684\u4e0e\u968f\u673a\u51fd\u6570\u6709\u5173\u3001\u6709\u7684\u4e0e\u9009\u62e9\u7b56\u7565\u6709\u5173\u2026\u2026\u672c\u6587\u4e3b\u8981\u8bb2\u8ff0\u9057\u4f20\u7b97\u6cd5\u548c\u8681\u7fa4\u7b97\u6cd5\u7684\u6c42\u89e3\u601d\u8def\uff0c\u5173\u4e8e\u5176\u4ed6\u66f4\u591a\u7c7b\u578b\u7684\u641c\u7d22\u7b97\u6cd5\u53ef\u4ee5\u5728\u7f51\u4e0a\u67e5\u9605\uff0c\u90fd\u6709\u5f88\u591a\u8d44\u6599\u54d2\u3002<\/p>\n

\u6240\u4ee5\uff0c\u7efc\u5408\u4e0a\u8ff0\u5206\u6790\uff0c\u6211\u4eec\u4e0d\u96be\u770b\u51faTSP\u95ee\u9898\u7684\u6c42\u89e3\u5927\u6982\u662f\u7531\u4e24\u6b65\u6784\u6210\u7684\uff1a<\/p>\n

    \n
  1. \u8ba1\u7b97\u4e24\u4e24\u57ce\u5e02\u95f4\u7684\u6700\u77ed\u8def\u5f84\uff1a\u5229\u7528\u7c7b\u4f3cDijkstra\u3001Flord\u3001A\u661f\u7684\u7b97\u6cd5\u6c42\u51fa\u6700\u77ed\u8def\u7ebf<\/li>\n
  2. \u8ba1\u7b97\u6700\u77ed\u5de1\u56de\u8def\u5f84\uff1a\u5229\u7528\u7c7b\u4f3c\u9057\u4f20\u7b97\u6cd5\u3001\u8681\u7fa4\u7b97\u6cd5\u7684\u641c\u7d22\u7b97\u6cd5\u6c42\u51fa\u5de1\u56de\u62dc\u8bbf\u7684\u6b21\u5e8f\u5e8f\u5217<\/span><\/li>\n<\/ol>\n

    \u5173\u4e8e1\u9700\u8981\u8bf4\u660e\u4e00\u70b9\uff0c\u5c31\u662f\u73b0\u5b9e\u751f\u6d3b\u4e2d\u6211\u4eec\u7684\u5730\u56fe\u5f80\u5f80\u4e0d\u662f\u4e00\u4e2a\u5b8c\u5168\u56fe\uff0c\u800c\u662f\u4e00\u4e2a\u975e\u5b8c\u5168\u56fe\uff0c\u751a\u81f3\u6709\u4e9b\u8282\u70b9\u4ec5\u4ec5\u662f\u9053\u8def\u7684\u5206\u5c94\u53e3\uff0c\u800c\u4e0d\u662f\u57ce\u5e02\u8282\u70b9\u3002<\/p>\n

      \n
    • \u5b8c\u5168\u56fe\uff1a\u4e24\u4e24\u57ce\u5e02\u95f4\u90fd\u6709\u76f4\u8fbe\u7684\u8def\u7ebf\uff0c\u8fd9\u6761\u8def\u7ebf\u4e0d\u9700\u8981\u7ecf\u8fc7\u4e2d\u95f4\u5176\u4ed6\u8282\u70b9\uff1b<\/li>\n<\/ul>\n

      \"wanquantu\"<\/p>\n

        \n
      • \u975e\u5b8c\u5168\u56fe\uff1a\u5076\u5c14\u6709\u4e24\u4e2a\u57ce\u5e02\u95f4\u7684\u8def\u7ebf\u9700\u8981\u7ecf\u8fc7\u5176\u4ed6\u4e2d\u95f4\u8282\u70b9\u3002<\/li>\n<\/ul>\n

        \"feiwanquantu\"<\/p>\n

        \u7531\u4e8e\u672c\u6587\u7740\u91cd\u53d9\u8ff0\u6b65\u9aa42)\uff0c\u66f4\u4fa7\u91cd\u4e8e\u641c\u7d22\u7b97\u6cd5\u672c\u8eab\uff0c\u6240\u4ee5\u540e\u7eed\u6587\u7ae0\u4e00\u5f8b\u5c06\u5730\u56fe\u7b80\u5316\u4e3a\u4e00\u4e2a\u5b8c\u5168\u56fe<\/strong>\u3002\u56e0\u4e3a\u5c31\u7b97\u662f\u975e\u5b8c\u5168\u56fe\uff0c\u6211\u4eec\u4e5f\u5b8c\u5168\u53ef\u4ee5\u4e8b\u5148\u5730\u3001\u79bb\u7ebf\u5730\u91c7\u7528\u6b65\u9aa41)\u4e2d\u7684\u7b97\u6cd5\u6c42\u89e3\uff0c\u5f97\u5230\u4e24\u4e24\u57ce\u5e02\u95f4\u7684\u6700\u77ed\u8def\u7ebf\uff0c\u5b58\u5165\u6570\u636e\u5e93\uff0c\u4f5c\u4e3a\u6301\u4e45\u6570\u636e\u63d0\u4f9b\u7ed9\u540e\u7eed\u5728\u7ebf\u7684\u3001\u9700\u7531\u7528\u6237\u6307\u5b9a\u62dc\u8bbf\u7684\u57ce\u5e02\u7684\u6b65\u9aa42)\u4f7f\u7528\uff0c\u6240\u4ee5\u7b80\u5316\u6210\u5b8c\u5168\u56fe\u662f\u5408\u4e4e\u60c5\u7406\u7684\u3002<\/p>\n

        \u7ed3\u8bed<\/h3>\n

        \u672c\u7ae0\u5c31\u5148\u8bb2\u5230\u8fd9\u5566\uff0c\u4e0b\u4e00\u7bc7\u4f1a\u7740\u91cd\u8bb2\u8ff0\u201c\u9057\u4f20\u7b97\u6cd5\u201d\uff0c\u56e0\u4e3a\u5b83\u5728\u7b97\u6cd5\u601d\u60f3\u3001\u6700\u4f18\u89e3\u51c6\u786e\u7387\u3001\u9002\u7528\u9762\u7b49\u5404\u65b9\u9762\u8868\u73b0\u90fd\u6bd4\u8f83\u597d\uff08\u4e00\u65b9\u9762\u662f\u6211\u81ea\u5df1\u7684\u611f\u53d7\uff0c\u4e00\u65b9\u9762\u5f88\u591a\u8bba\u6587\u4e5f\u8fd9\u6837\u5199\u5230\uff09\uff0c\u6240\u4ee5\u6211\u9009\u62e9\u628a\u5b83\u7684\u8bbe\u8ba1\u4e0e\u5b9e\u73b0\u8fc7\u7a0b\u5206\u4eab\u7ed9\u5927\u5bb6\u4f5c\u4e3a\u53c2\u8003\uff08\u5982\u679c\u4e0d\u5acc\u5f03\u7684\u8bdd\uff09\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"

        \u5f15\u8a00 TSP(Traveling Salesman Problem)\u5373\u65c5\u884c\u5546\u95ee\u9898\uff0c\u662f\u6570\u5b66\u9886\u57df\u4e2d\u8457\u540d\u95ee\u9898\u4e4b\u4e00\u3002\u8fd9 […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[56,46],"tags":[],"_links":{"self":[{"href":"http:\/\/yaochenkun.site\/index.php\/wp-json\/wp\/v2\/posts\/913"}],"collection":[{"href":"http:\/\/yaochenkun.site\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/yaochenkun.site\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/yaochenkun.site\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/yaochenkun.site\/index.php\/wp-json\/wp\/v2\/comments?post=913"}],"version-history":[{"count":19,"href":"http:\/\/yaochenkun.site\/index.php\/wp-json\/wp\/v2\/posts\/913\/revisions"}],"predecessor-version":[{"id":3177,"href":"http:\/\/yaochenkun.site\/index.php\/wp-json\/wp\/v2\/posts\/913\/revisions\/3177"}],"wp:attachment":[{"href":"http:\/\/yaochenkun.site\/index.php\/wp-json\/wp\/v2\/media?parent=913"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/yaochenkun.site\/index.php\/wp-json\/wp\/v2\/categories?post=913"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/yaochenkun.site\/index.php\/wp-json\/wp\/v2\/tags?post=913"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}