{"id":302606,"date":"2024-05-20T18:39:41","date_gmt":"2024-05-20T10:39:41","guid":{"rendered":"https:\/\/docs.pingcode.com\/ask\/ask-ask\/302606.html"},"modified":"2024-05-20T18:39:51","modified_gmt":"2024-05-20T10:39:51","slug":"%e7%ae%97%e6%b3%95%e6%97%b6%e9%97%b4%e5%a4%8d%e6%9d%82%e5%ba%a6%e4%b8%bao%ef%bc%88n%ef%bc%89%e7%9a%84%e6%98%af%e4%bb%80%e4%b9%88%e7%ae%97%e6%b3%95-3","status":"publish","type":"post","link":"https:\/\/docs.pingcode.com\/ask\/302606.html","title":{"rendered":"\u7b97\u6cd5\u65f6\u95f4\u590d\u6742\u5ea6\u4e3aO\uff08n!\uff09\u7684\u662f\u4ec0\u4e48\u7b97\u6cd5"},"content":{"rendered":"<p style=\"text-align:center\"><img decoding=\"async\" src=\"https:\/\/cdn-kb.worktile.com\/kb\/wp-content\/uploads\/2024\/04\/26214853\/d139c463-fe97-40f6-87e8-c43d1720e02d.webp\" alt=\"\u7b97\u6cd5\u65f6\u95f4\u590d\u6742\u5ea6\u4e3aO\uff08n!\uff09\u7684\u662f\u4ec0\u4e48\u7b97\u6cd5\" 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TSP\uff09\u7684\u7a77\u4e3e\u641c\u7d22\u7b97\u6cd5<\/strong>\u3002\u5728\u8be6\u7ec6\u63cf\u8ff0\u4e2d\uff0c\u5bf9\u65c5\u884c\u5546\u95ee\u9898\u4e2d\u7684\u7a77\u4e3e\u641c\u7d22\u7b97\u6cd5\u8fdb\u884c\u5c55\u5f00\uff1a\u7a77\u4e3e\u641c\u7d22\u7b97\u6cd5\u5373\u5c1d\u8bd5\u8f93\u5165\u6570\u636e\u6240\u6709\u53ef\u80fd\u7684\u6392\u5217\u987a\u5e8f\uff0c\u6765\u5bfb\u627e\u6700\u4f18\u89e3\u3002\u4ee5TSP\u4e3a\u4f8b\uff0c\u5982\u679c\u6709n\u4e2a\u57ce\u5e02\uff0c\u90a3\u4e48\u7a77\u4e3e\u641c\u7d22\u5c06\u4f1a\u68c0\u67e5\u6240\u6709\u53ef\u80fd\u7684\u57ce\u5e02\u6392\u5217\u4ee5\u627e\u5230\u4e00\u6761\u6700\u77ed\u7684\u65c5\u884c\u8def\u5f84\uff0c\u8fd9\u6d89\u53ca\u5230n!\u4e2a\u4e0d\u540c\u7684\u6392\u5217\uff0c\u56e0\u6b64\u7b97\u6cd5\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4e3aO(n!)\u3002<\/p>\n<\/p>\n<p><h3>\u4e00\u3001\u65f6\u95f4\u590d\u6742\u5ea6O(n!)\u7b97\u6cd5\u7b80\u4ecb<\/h3>\n<\/p>\n<p><p>\u7b97\u6cd5\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u662f\u8bc4\u4ef7\u7b97\u6cd5\u6548\u7387\u7684\u4e00\u79cd\u6807\u51c6\uff0cO(n!)\u662f\u5176\u4e2d\u4e00\u79cd\u65f6\u95f4\u590d\u6742\u5ea6\u8868\u793a\uff0c\u5b83\u4ee3\u8868\u7740\u7b97\u6cd5\u6267\u884c\u65f6\u95f4\u968f\u8f93\u5165\u6570\u636e\u89c4\u6a21\u7684\u589e\u957f\u800c\u5448\u73b0\u9636\u4e58\u7684\u589e\u957f\u901f\u7387\u3002\u8fd9\u79cd\u65f6\u95f4\u590d\u6742\u5ea6\u5c5e\u4e8e\u975e\u5e38\u9ad8\u7684\u65f6\u95f4\u590d\u6742\u5ea6\uff0c\u901a\u5e38\u53ea\u9002\u7528\u4e8e\u5c0f\u89c4\u6a21\u6570\u636e\u7684\u5904\u7406\u3002<\/p>\n<\/p>\n<p><h4>\u65c5\u884c\u5546\u95ee\u9898<\/h4>\n<\/p>\n<p><p>\u4e00\u4e2a\u5178\u578b\u7684O(n!)\u65f6\u95f4\u590d\u6742\u5ea6\u7b97\u6cd5\u5e94\u7528\u662f\u89e3\u51b3\u65c5\u884c\u5546\u95ee\u9898\u3002\u8fd9\u4e2a\u95ee\u9898\u95ee\u7684\u662f\uff1a\u4e00\u4e2a\u65c5\u884c\u5546\u8981\u62dc\u8bbf\u4e00\u7cfb\u5217\u57ce\u5e02\uff0c\u5e76\u4e14\u8981\u786e\u4fdd\u6bcf\u4e2a\u57ce\u5e02\u53ea\u8bbf\u95ee\u4e00\u6b21\uff0c\u6700\u540e\u8981\u56de\u5230\u51fa\u53d1\u70b9\uff0c\u600e\u6837\u89c4\u5212\u8def\u7ebf\u624d\u80fd\u4f7f\u603b\u65c5\u884c\u8ddd\u79bb\u6700\u77ed\uff1f<\/p>\n<\/p>\n<p><p>\u7a77\u4e3e\u641c\u7d22\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\u65f6\uff0c\u4f1a\u5c1d\u8bd5\u6bcf\u4e00\u79cd\u53ef\u80fd\u7684\u57ce\u5e02\u6392\u5217\u7ec4\u5408\uff0c\u8fd9\u4f1a\u5bfc\u81f4\u8ba1\u7b97\u91cf\u968f\u7740\u57ce\u5e02\u6570\u91cf\u7684\u589e\u52a0\u800c\u6025\u5267\u589e\u52a0\u3002<\/p>\n<\/p>\n<p><h3>\u4e8c\u3001\u4e3a\u4ec0\u4e48\u662fO(n!)\u590d\u6742\u5ea6<\/h3>\n<\/p>\n<p><p>O(n!)\u590d\u6742\u5ea6\u7684\u7b97\u6cd5\u5e38\u89c1\u4e8e\u6392\u5217\u76f8\u5173\u95ee\u9898\uff0c\u56e0\u4e3a\u6392\u5217\u95ee\u9898\u7684\u672c\u8d28\u662f\u4ecen\u4e2a\u4e0d\u540c\u7684\u5143\u7d20\u4e2d\u6309\u7167\u4e00\u5b9a\u7684\u987a\u5e8f\u8fdb\u884c\u6392\u5217\u3002<\/p>\n<\/p>\n<p><h4>\u6392\u5217\u751f\u6210<\/h4>\n<\/p>\n<p><p>\u5f53\u6211\u4eec\u751f\u6210\u4e00\u4e2an\u5143\u7d20\u96c6\u5408\u7684\u6240\u6709\u6392\u5217\u65f6\uff0c\u7b2c\u4e00\u4e2a\u4f4d\u7f6e\u6709n\u79cd\u53ef\u80fd\uff0c\u7b2c\u4e8c\u4e2a\u4f4d\u7f6e\u6709n-1\u79cd\uff0c\u4ee5\u6b64\u7c7b\u63a8\uff0c\u76f4\u5230\u6700\u540e\u4e00\u4e2a\u4f4d\u7f6e\u53ea\u67091\u79cd\u53ef\u80fd\u6027\u3002\u6240\u4ee5\u603b\u7684\u6392\u5217\u6570\u91cf\u4e3an * (n-1) * &#8230; * 2 * 1\uff0c\u4e5f\u5c31\u662fn!\u3002<\/p>\n<\/p>\n<p><h4>\u5b9e\u4f8b\u5206\u6790<\/h4>\n<\/p>\n<p><p>\u5728\u5177\u4f53\u7684\u7b97\u6cd5\u5b9e\u73b0\u4e2d\uff0c\u6bd4\u5982\u901a\u8fc7\u9012\u5f52\u51fd\u6570\u6765\u751f\u6210\u6240\u6709\u6392\u5217\uff0c\u6bcf\u9012\u5f52\u4e00\u6b21\u51fd\u6570\u5c06\u5904\u7406\u4e00\u4e2a\u5143\u7d20\uff0c\u5171\u6709n\u5c42\u9012\u5f52\uff0c\u6bcf\u5c42\u9012\u5f52\u4e2d\u53ef\u80fd\u4f1a\u8fdb\u884cn\u6b21\u8fed\u4ee3\uff0c\u56e0\u6b64\u590d\u6742\u5ea6\u4e3aO(n*n!)\u3002<\/p>\n<\/p>\n<p><h3>\u4e09\u3001O(n!)\u590d\u6742\u5ea6\u7b97\u6cd5\u7684\u5e94\u7528\u573a\u666f<\/h3>\n<\/p>\n<p><p>\u5c3d\u7ba1O(n!)\u590d\u6742\u5ea6\u7684\u7b97\u6cd5\u975e\u5e38\u8017\u65f6\uff0c\u4f46\u5b83\u4eec\u5728\u4e00\u4e9b\u7279\u5b9a\u7684\u9886\u57df\u8fd8\u662f\u5f88\u6709\u4ef7\u503c\u7684\uff0c\u7279\u522b\u662f\u5728\u8f93\u5165\u89c4\u6a21\u8f83\u5c0f\u7684\u60c5\u5f62\u4e0b\u3002<\/p>\n<\/p>\n<p><h4>\u7b97\u6cd5\u7684\u5e94\u7528<\/h4>\n<\/p>\n<p><p>\u6b64\u7c7b\u7b97\u6cd5\u901a\u5e38\u7528\u4e8e\u9700\u8981\u5b8c\u6574\u89e3\u7a7a\u95f4\u63a2\u7d22\u7684\u573a\u5408\u3002\u4f8b\u5982\uff0c\u9664\u4e86\u65c5\u884c\u5546\u95ee\u9898\uff0c\u5176\u5b83\u50cf\u5bc6\u7801\u7834\u89e3\u3001\u89e3\u51b3\u67d0\u4e9b\u903b\u8f91\u8c1c\u9898\u7b49\u60c5\u51b5\uff0c\u53ef\u80fd\u6d89\u53ca\u5230\u5168\u6392\u5217\u7684\u751f\u6210\u548c\u68c0\u9a8c\u3002<\/p>\n<\/p>\n<p><h4>\u9650\u5b9a\u6761\u4ef6\u4e0b\u7684\u5e94\u7528<\/h4>\n<\/p>\n<p><p>\u5c3d\u7ba1\u65f6\u95f4\u590d\u6742\u5ea6\u975e\u5e38\u9ad8\uff0c\u4f46\u5728\u4e00\u4e9b\u6709\u7279\u5b9a\u7ea6\u675f\u7684\u95ee\u9898\u4e2d\uff0c\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u4f18\u5316\u51cf\u5c11\u5b9e\u9645\u7684\u8ba1\u7b97\u91cf\u3002\u4f8b\u5982\uff0c\u5982\u679c\u5728\u95ee\u9898\u6c42\u89e3\u8fc7\u7a0b\u4e2d\u52a0\u5165\u526a\u679d\uff08pruning\uff09\u6b65\u9aa4\uff0c\u53ef\u4ee5\u6709\u6548\u5730\u51cf\u5c11\u4e0d\u5fc5\u8981\u7684\u6392\u5217\u751f\u6210\uff0c\u4ece\u800c\u5728\u5b9e\u8df5\u4e2d\u4f18\u5316\u7b97\u6cd5\u7684\u6027\u80fd\u3002<\/p>\n<\/p>\n<p><h3>\u56db\u3001\u4f18\u5316O(n!)\u590d\u6742\u5ea6\u7b97\u6cd5<\/h3>\n<\/p>\n<p><p>\u5728\u5b9e\u9645\u5e94\u7528\u4e2d\uff0c\u76f4\u63a5\u4f7f\u7528O(n!)\u590d\u6742\u5ea6\u7684\u7b97\u6cd5\u5f80\u5f80\u662f\u4e0d\u73b0\u5b9e\u7684\uff0c\u4f46\u53ef\u4ee5\u901a\u8fc7\u5404\u79cd\u7b56\u7565\u6765\u4f18\u5316\u8fd9\u7c7b\u7b97\u6cd5\u3002<\/p>\n<\/p>\n<p><h4>\u526a\u679d\u6280\u5de7<\/h4>\n<\/p>\n<p><p>\u526a\u679d\u662f\u51cf\u5c11\u641c\u7d22\u7a7a\u95f4\u7684\u6709\u6548\u65b9\u6cd5\uff0c\u5b83\u901a\u8fc7\u907f\u514d\u90a3\u4e9b\u663e\u7136\u4e0d\u4f1a\u4ea7\u751f\u6700\u4f18\u89e3\u7684\u8def\u5f84\u6765\u51cf\u5c11\u8ba1\u7b97\u91cf\u3002\u4f8b\u5982\uff0c\u5982\u679c\u5728TSP\u95ee\u9898\u4e2d\u5f53\u524d\u7684\u8def\u5f84\u5df2\u7ecf\u8d85\u8fc7\u4e86\u5f53\u524d\u6700\u77ed\u8def\u5f84\u7684\u957f\u5ea6\uff0c\u90a3\u4e48\u5c31\u6ca1\u6709\u7ee7\u7eed\u63a2\u7d22\u8fd9\u6761\u8def\u5f84\u7684\u5fc5\u8981\u4e86\u3002<\/p>\n<\/p>\n<p><h4>\u542f\u53d1\u5f0f\u65b9\u6cd5<\/h4>\n<\/p>\n<p><p>\u542f\u53d1\u5f0f\u7b97\u6cd5\u662f\u53e6\u4e00\u79cd\u51cf\u5c11\u6307\u6570\u65f6\u95f4\u590d\u6742\u5ea6\u7684\u6709\u6548\u65b9\u6cd5\u3002\u4f8b\u5982\uff0c\u57fa\u4e8e\u8d2a\u5a6a\u7b56\u7565\u7684\u8d2a\u5a6a\u542f\u53d1\u5f0f\u7b97\u6cd5\u6216\u57fa\u4e8e\u5c40\u90e8\u641c\u7d22\u7684\u6a21\u62df\u9000\u706b\u7b97\u6cd5\uff0c\u867d\u7136\u5b83\u4eec\u4e0d\u4fdd\u8bc1\u627e\u5230\u6700\u4f18\u89e3\uff0c\u4f46\u5728\u5408\u7406\u65f6\u95f4\u5185\u53ef\u4ee5\u63d0\u4f9b\u597d\u7684\u8fd1\u4f3c\u89e3\u3002<\/p>\n<\/p>\n<p><p>\u901a\u8fc7\u8fd9\u4e9b\u65b9\u5f0f\uff0c\u6211\u4eec\u53ef\u4ee5\u4f7fO(n!)\u590d\u6742\u5ea6\u7684\u7b97\u6cd5\u5728\u5b9e\u8df5\u4e2d\u66f4\u52a0\u53ef\u884c\uff0c\u5c3d\u7ba1\u5b83\u4eec\u5728\u7406\u8bba\u4e0a\u590d\u6742\u5ea6\u975e\u5e38\u9ad8\u3002\u901a\u5e38\uff0c\u5728\u89e3\u51b3\u5b9e\u9645\u590d\u6742\u95ee\u9898\u65f6\uff0c\u5b8c\u5168\u4f9d\u8d56\u4e8e\u65f6\u95f4\u590d\u6742\u5ea6\u975e\u5e38\u9ad8\u7684\u7b97\u6cd5\u5e76\u4e0d\u73b0\u5b9e\uff0c\u4f46\u662f\u4e86\u89e3\u5e76\u638c\u63e1\u8fd9\u4e9b\u7b97\u6cd5\u7684\u539f\u7406\u5bf9\u4e8e\u7406\u89e3\u7b97\u6cd5\u8bbe\u8ba1\u548c\u4f18\u5316\u4ecd\u7136\u5177\u6709\u91cd\u8981\u610f\u4e49\u3002<\/p>\n<\/p>\n<h2><strong>\u76f8\u5173\u95ee\u7b54FAQs\uff1a<\/strong><\/h2>\n<p><strong>Q1\uff1a\u6709\u54ea\u4e9b\u7b97\u6cd5\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4e3aO\uff08n!\uff09\uff1f<\/strong><br 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