{"id":203680,"date":"2023-08-13T01:56:41","date_gmt":"2023-08-12T17:56:41","guid":{"rendered":"https:\/\/www.idc.net\/help\/203680\/"},"modified":"2023-08-13T01:56:41","modified_gmt":"2023-08-12T17:56:41","slug":"%e5%8d%81%e5%a4%a7%e7%a8%8b%e5%ba%8f%e5%91%98%e5%bc%80%e5%8f%91%e7%94%a8%e5%88%b0%e7%9a%84%e5%9f%ba%e6%9c%ac%e7%ae%97%e6%b3%95","status":"publish","type":"post","link":"https:\/\/idc.net\/help\/203680\/","title":{"rendered":"\u5341\u5927\u7a0b\u5e8f\u5458\u5f00\u53d1\u7528\u5230\u7684\u57fa\u672c\u7b97\u6cd5"},"content":{"rendered":"

[[188736]]<\/span><\/p>\n

\u7b97\u6cd5\u4e00\uff1a\u5feb\u901f\u6392\u5e8f\u7b97\u6cd5<\/strong><\/p>\n

\u5feb\u901f\u6392\u5e8f\u662f\u7531\u4e1c\u5c3c\u00b7\u970d\u5c14\u6240\u53d1\u5c55\u7684\u4e00\u79cd\u6392\u5e8f\u7b97\u6cd5\u3002\u5728\u5e73\u5747\u72b6\u51b5\u4e0b\uff0c\u6392\u5e8f n \u4e2a\u9879\u76ee\u8981\u039f(n log n)\u6b21\u6bd4\u8f83\u3002\u5728\u6700\u574f\u72b6\u51b5\u4e0b\u5219\u9700\u8981\u039f(n2)\u6b21\u6bd4\u8f83\uff0c\u4f46\u8fd9\u79cd\u72b6\u51b5\u5e76\u4e0d\u5e38\u89c1\u3002\u4e8b\u5b9e\u4e0a\uff0c\u5feb\u901f\u6392\u5e8f\u901a\u5e38\u660e\u663e\u6bd4\u5176\u4ed6\u039f(n log n) \u7b97\u6cd5\u66f4\u5feb\uff0c\u56e0\u4e3a\u5b83\u7684\u5185\u90e8\u5faa\u73af(inner loop)\u53ef\u4ee5\u5728\u5927\u90e8\u5206\u7684\u67b6\u6784\u4e0a\u5f88\u6709\u6548\u7387\u5730\u88ab\u5b9e\u73b0\u51fa\u6765\u3002<\/p>\n

\u5feb\u901f\u6392\u5e8f\u4f7f\u7528\u5206\u6cbb\u6cd5(Divide and conquer)\u7b56\u7565\u6765\u628a\u4e00\u4e2a\u4e32\u884c(list)\u5206\u4e3a\u4e24\u4e2a\u5b50\u4e32\u884c(sub-lists)\u3002<\/p>\n

\u7b97\u6cd5\u6b65\u9aa4\uff1a<\/p>\n

1 \u4ece\u6570\u5217\u4e2d\u6311\u51fa\u4e00\u4e2a\u5143\u7d20\uff0c\u79f0\u4e3a \u201c\u57fa\u51c6\u201d(pivot)\uff0c<\/p>\n

2 \u91cd\u65b0\u6392\u5e8f\u6570\u5217\uff0c\u6240\u6709\u5143\u7d20\u6bd4\u57fa\u51c6\u503c\u5c0f\u7684\u6446\u653e\u5728\u57fa\u51c6\u524d\u9762\uff0c\u6240\u6709\u5143\u7d20\u6bd4\u57fa\u51c6\u503c\u5927\u7684\u6446\u5728\u57fa\u51c6\u7684\u540e\u9762(\u76f8\u540c\u7684\u6570\u53ef\u4ee5\u5230\u4efb\u4e00\u8fb9)\u3002\u5728\u8fd9\u4e2a\u5206\u533a\u9000\u51fa\u4e4b\u540e\uff0c\u8be5\u57fa\u51c6\u5c31\u5904\u4e8e\u6570\u5217\u7684\u4e2d\u95f4\u4f4d\u7f6e\u3002\u8fd9\u4e2a\u79f0\u4e3a\u5206\u533a(partition)\u64cd\u4f5c\u3002<\/p>\n

3 \u9012\u5f52\u5730(recursive)\u628a\u5c0f\u4e8e\u57fa\u51c6\u503c\u5143\u7d20\u7684\u5b50\u6570\u5217\u548c\u5927\u4e8e\u57fa\u51c6\u503c\u5143\u7d20\u7684\u5b50\u6570\u5217\u6392\u5e8f\u3002<\/p>\n

\u9012\u5f52\u7684***\u90e8\u60c5\u5f62\uff0c\u662f\u6570\u5217\u7684\u5927\u5c0f\u662f\u96f6\u6216\u4e00\uff0c\u4e5f\u5c31\u662f\u6c38\u8fdc\u90fd\u5df2\u7ecf\u88ab\u6392\u5e8f\u597d\u4e86\u3002\u867d\u7136\u4e00\u76f4\u9012\u5f52\u4e0b\u53bb\uff0c\u4f46\u662f\u8fd9\u4e2a\u7b97\u6cd5\u603b\u4f1a\u9000\u51fa\uff0c\u56e0\u4e3a\u5728\u6bcf\u6b21\u7684\u8fed\u4ee3(iteration)\u4e2d\uff0c\u5b83\u81f3\u5c11\u4f1a\u628a\u4e00\u4e2a\u5143\u7d20\u6446\u5230\u5b83***\u7684\u4f4d\u7f6e\u53bb\u3002 <\/p>\n

 <\/p>\n

 <\/p>\n

 <\/p>\n

\u7b97\u6cd5\u4e8c\uff1a\u5806\u6392\u5e8f\u7b97\u6cd5<\/strong><\/p>\n

\u5806\u6392\u5e8f(Heapsort)\u662f\u6307\u5229\u7528\u5806\u8fd9\u79cd\u6570\u636e\u7ed3\u6784\u6240\u8bbe\u8ba1\u7684\u4e00\u79cd\u6392\u5e8f\u7b97\u6cd5\u3002\u5806\u79ef\u662f\u4e00\u4e2a\u8fd1\u4f3c\u5b8c\u5168\u4e8c\u53c9\u6811\u7684\u7ed3\u6784\uff0c\u5e76\u540c\u65f6\u6ee1\u8db3\u5806\u79ef\u7684\u6027\u8d28\uff1a\u5373\u5b50\u7ed3\u70b9\u7684\u952e\u503c\u6216\u7d22\u5f15\u603b\u662f\u5c0f\u4e8e(\u6216\u8005\u5927\u4e8e)\u5b83\u7684\u7236\u8282\u70b9\u3002\u5806\u6392\u5e8f\u7684\u5e73\u5747\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a\u039f(nlogn) \u3002<\/p>\n

\u7b97\u6cd5\u6b65\u9aa4\uff1a<\/p>\n

1.\u521b\u5efa\u4e00\u4e2a\u5806H[0..n-1]<\/p>\n

2.\u628a\u5806\u9996(***\u503c)\u548c\u5806\u5c3e\u4e92\u6362<\/p>\n

3.\u628a\u5806\u7684\u5c3a\u5bf8\u7f29\u5c0f1\uff0c\u5e76\u8c03\u7528shift_down(0),\u76ee\u7684\u662f\u628a\u65b0\u7684\u6570\u7ec4\u9876\u7aef\u6570\u636e\u8c03\u6574\u5230\u76f8\u5e94\u4f4d\u7f6e<\/p>\n

4.\u91cd\u590d\u6b65\u9aa42\uff0c\u76f4\u5230\u5806\u7684\u5c3a\u5bf8\u4e3a1 <\/p>\n

 <\/p>\n

 <\/p>\n

 <\/p>\n

\u7b97\u6cd5\u4e09\uff1a<\/strong><\/p>\n

\u5f52\u5e76\u6392\u5e8f(Merge sort\uff0c\u53f0\u6e7e\u8bd1\u4f5c\uff1a\u5408\u5e76\u6392\u5e8f)\u662f\u5efa\u7acb\u5728\u5f52\u5e76\u64cd\u4f5c\u4e0a\u7684\u4e00\u79cd\u6709\u6548\u7684\u6392\u5e8f\u7b97\u6cd5\u3002\u8be5\u7b97\u6cd5\u662f\u91c7\u7528\u5206\u6cbb\u6cd5(Divide and Conquer)\u7684\u4e00\u4e2a\u975e\u5e38\u5178\u578b\u7684\u5e94\u7528\u3002<\/p>\n

\u7b97\u6cd5\u6b65\u9aa4\uff1a<\/p>\n

\u7533\u8bf7\u7a7a\u95f4\uff0c\u4f7f\u5176\u5927\u5c0f\u4e3a\u4e24\u4e2a\u5df2\u7ecf\u6392\u5e8f\u5e8f\u5217\u4e4b\u548c\uff0c\u8be5\u7a7a\u95f4\u7528\u6765\u5b58\u653e\u5408\u5e76\u540e\u7684\u5e8f\u5217<\/p>\n

\u8bbe\u5b9a\u4e24\u4e2a\u6307\u9488\uff0c\u6700\u521d\u4f4d\u7f6e\u5206\u522b\u4e3a\u4e24\u4e2a\u5df2\u7ecf\u6392\u5e8f\u5e8f\u5217\u7684\u8d77\u59cb\u4f4d\u7f6e<\/p>\n

\u6bd4\u8f83\u4e24\u4e2a\u6307\u9488\u6240\u6307\u5411\u7684\u5143\u7d20\uff0c\u9009\u62e9\u76f8\u5bf9\u5c0f\u7684\u5143\u7d20\u653e\u5165\u5230\u5408\u5e76\u7a7a\u95f4\uff0c\u5e76\u79fb\u52a8\u6307\u9488\u5230\u4e0b\u4e00\u4f4d\u7f6e<\/p>\n

\u91cd\u590d\u6b65\u9aa43\u76f4\u5230\u67d0\u4e00\u6307\u9488\u8fbe\u5230\u5e8f\u5217\u5c3e<\/p>\n

\u5c06\u53e6\u4e00\u5e8f\u5217\u5269\u4e0b\u7684\u6240\u6709\u5143\u7d20\u76f4\u63a5\u590d\u5236\u5230\u5408\u5e76\u5e8f\u5217\u5c3e <\/p>\n

  <\/p>\n

\u7b97\u6cd5\u56db\uff1a\u4e8c\u5206\u67e5\u627e\u7b97\u6cd5<\/strong><\/p>\n

\u4e8c\u5206\u67e5\u627e\u7b97\u6cd5\u662f\u4e00\u79cd\u5728\u6709\u5e8f\u6570\u7ec4\u4e2d\u67e5\u627e\u67d0\u4e00\u7279\u5b9a\u5143\u7d20\u7684\u641c\u7d22\u7b97\u6cd5\u3002\u641c\u7d20\u8fc7\u7a0b\u4ece\u6570\u7ec4\u7684\u4e2d\u95f4\u5143\u7d20\u5f00\u59cb\uff0c\u5982\u679c\u4e2d\u95f4\u5143\u7d20\u6b63\u597d\u662f\u8981\u67e5\u627e\u7684\u5143\u7d20\uff0c\u5219\u641c \u7d20\u8fc7\u7a0b\u7ed3\u675f;\u5982\u679c\u67d0\u4e00\u7279\u5b9a\u5143\u7d20\u5927\u4e8e\u6216\u8005\u5c0f\u4e8e\u4e2d\u95f4\u5143\u7d20\uff0c\u5219\u5728\u6570\u7ec4\u5927\u4e8e\u6216\u5c0f\u4e8e\u4e2d\u95f4\u5143\u7d20\u7684\u90a3\u4e00\u534a\u4e2d\u67e5\u627e\uff0c\u800c\u4e14\u8ddf\u5f00\u59cb\u4e00\u6837\u4ece\u4e2d\u95f4\u5143\u7d20\u5f00\u59cb\u6bd4\u8f83\u3002\u5982\u679c\u5728\u67d0\u4e00\u6b65\u9aa4\u6570\u7ec4 \u4e3a\u7a7a\uff0c\u5219\u4ee3\u8868\u627e\u4e0d\u5230\u3002\u8fd9\u79cd\u641c\u7d22\u7b97\u6cd5\u6bcf\u4e00\u6b21\u6bd4\u8f83\u90fd\u4f7f\u641c\u7d22\u8303\u56f4\u7f29\u5c0f\u4e00\u534a\u3002\u6298\u534a\u641c\u7d22\u6bcf\u6b21\u628a\u641c\u7d22\u533a\u57df\u51cf\u5c11\u4e00\u534a\uff0c\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a\u039f(logn) \u3002<\/p>\n

\u7b97\u6cd5\u4e94\uff1aBFPRT(\u7ebf\u6027\u67e5\u627e\u7b97\u6cd5)<\/strong><\/p>\n

BFPRT\u7b97\u6cd5\u89e3\u51b3\u7684\u95ee\u9898\u5341\u5206\u7ecf\u5178\uff0c\u5373\u4ece\u67d0n\u4e2a\u5143\u7d20\u7684\u5e8f\u5217\u4e2d\u9009\u51fa\u7b2ck\u5927(\u7b2ck\u5c0f)\u7684\u5143\u7d20\uff0c\u901a\u8fc7\u5de7\u5999\u7684\u5206 \u6790\uff0cBFPRT\u53ef\u4ee5\u4fdd\u8bc1\u5728\u6700\u574f\u60c5\u51b5\u4e0b\u4ecd\u4e3a\u7ebf\u6027\u65f6\u95f4\u590d\u6742\u5ea6\u3002\u8be5\u7b97\u6cd5\u7684\u601d\u60f3\u4e0e\u5feb\u901f\u6392\u5e8f\u601d\u60f3\u76f8\u4f3c\uff0c\u5f53\u7136\uff0c\u4e3a\u4f7f\u5f97\u7b97\u6cd5\u5728\u6700\u574f\u60c5\u51b5\u4e0b\uff0c\u4f9d\u7136\u80fd\u8fbe\u5230o(n)\u7684\u65f6\u95f4\u590d\u6742 \u5ea6\uff0c\u4e94\u4f4d\u7b97\u6cd5\u4f5c\u8005\u505a\u4e86\u7cbe\u5999\u7684\u5904\u7406\u3002<\/p>\n

\u7b97\u6cd5\u6b65\u9aa4\uff1a<\/p>\n

\u5c06n\u4e2a\u5143\u7d20\u6bcf5\u4e2a\u4e00\u7ec4\uff0c\u5206\u6210n\/5(\u4e0a\u754c)\u7ec4\u3002<\/p>\n

\u53d6\u51fa\u6bcf\u4e00\u7ec4\u7684\u4e2d\u4f4d\u6570\uff0c\u4efb\u610f\u6392\u5e8f\u65b9\u6cd5\uff0c\u6bd4\u5982\u63d2\u5165\u6392\u5e8f\u3002<\/p>\n

\u9012\u5f52\u7684\u8c03\u7528selection\u7b97\u6cd5\u67e5\u627e\u4e0a\u4e00\u6b65\u4e2d\u6240\u6709\u4e2d\u4f4d\u6570\u7684\u4e2d\u4f4d\u6570\uff0c\u8bbe\u4e3ax\uff0c\u5076\u6570\u4e2a\u4e2d\u4f4d\u6570\u7684\u60c5\u51b5\u4e0b\u8bbe\u5b9a\u4e3a\u9009\u53d6\u4e2d\u95f4\u5c0f\u7684\u4e00\u4e2a\u3002<\/p>\n

\u7528x\u6765\u5206\u5272\u6570\u7ec4\uff0c\u8bbe\u5c0f\u4e8e\u7b49\u4e8ex\u7684\u4e2a\u6570\u4e3ak\uff0c\u5927\u4e8ex\u7684\u4e2a\u6570\u5373\u4e3an-k\u3002<\/p>\n

\u82e5i==k\uff0c\u8fd4\u56dex;\u82e5i<k\uff0c\u5728\u5c0f\u4e8ex\u7684\u5143\u7d20\u4e2d\u9012\u5f52\u67e5\u627e\u7b2ci\u5c0f\u7684\u5143\u7d20;\u82e5i>k\uff0c\u5728\u5927\u4e8ex\u7684\u5143\u7d20\u4e2d\u9012\u5f52\u67e5\u627e\u7b2ci-k\u5c0f\u7684\u5143\u7d20\u3002<\/p>\n

\u7ec8\u6b62\u6761\u4ef6\uff1an=1\u65f6\uff0c\u8fd4\u56de\u7684\u5373\u662fi\u5c0f\u5143\u7d20\u3002<\/p>\n

\u7b97\u6cd5\u516d\uff1aDFS(\u6df1\u5ea6\u4f18\u5148\u641c\u7d22)<\/strong><\/p>\n

\u6df1\u5ea6\u4f18\u5148\u641c\u7d22\u7b97\u6cd5(Depth-First-Search)\uff0c\u662f\u641c\u7d22\u7b97\u6cd5\u7684\u4e00\u79cd\u3002\u5b83\u6cbf\u7740\u6811\u7684\u6df1\u5ea6\u904d\u5386\u6811\u7684\u8282\u70b9\uff0c\u5c3d\u53ef\u80fd\u6df1\u7684\u641c\u7d22\u6811\u7684\u5206 \u652f\u3002\u5f53\u8282\u70b9v\u7684\u6240\u6709\u8fb9\u90fd\u5df1\u88ab\u63a2\u5bfb\u8fc7\uff0c\u641c\u7d22\u5c06\u56de\u6eaf\u5230\u53d1\u73b0\u8282\u70b9v\u7684\u90a3\u6761\u8fb9\u7684\u8d77\u59cb\u8282\u70b9\u3002\u8fd9\u4e00\u8fc7\u7a0b\u4e00\u76f4\u8fdb\u884c\u5230\u5df2\u53d1\u73b0\u4ece\u6e90\u8282\u70b9\u53ef\u8fbe\u7684\u6240\u6709\u8282\u70b9\u4e3a\u6b62\u3002\u5982\u679c\u8fd8\u5b58\u5728\u672a\u88ab\u53d1 \u73b0\u7684\u8282\u70b9\uff0c\u5219\u9009\u62e9\u5176\u4e2d\u4e00\u4e2a\u4f5c\u4e3a\u6e90\u8282\u70b9\u5e76\u91cd\u590d\u4ee5\u4e0a\u8fc7\u7a0b\uff0c\u6574\u4e2a\u8fdb\u7a0b\u53cd\u590d\u8fdb\u884c\u76f4\u5230\u6240\u6709\u8282\u70b9\u90fd\u88ab\u8bbf\u95ee\u4e3a\u6b62\u3002DFS\u5c5e\u4e8e\u76f2\u76ee\u641c\u7d22\u3002<\/p>\n

\u6df1\u5ea6\u4f18\u5148\u641c\u7d22\u662f\u56fe\u8bba\u4e2d\u7684\u7ecf\u5178\u7b97\u6cd5\uff0c\u5229\u7528\u6df1\u5ea6\u4f18\u5148\u641c\u7d22\u7b97\u6cd5\u53ef\u4ee5\u4ea7\u751f\u76ee\u6807\u56fe\u7684\u76f8\u5e94\u62d3\u6251\u6392\u5e8f\u8868\uff0c\u5229\u7528\u62d3\u6251\u6392\u5e8f\u8868\u53ef\u4ee5\u65b9\u4fbf\u7684\u89e3\u51b3\u5f88\u591a\u76f8\u5173\u7684\u56fe\u8bba\u95ee\u9898\uff0c\u5982***\u8def\u5f84\u95ee\u9898\u7b49\u7b49\u3002\u4e00\u822c\u7528\u5806\u6570\u636e\u7ed3\u6784\u6765\u8f85\u52a9\u5b9e\u73b0DFS\u7b97\u6cd5\u3002<\/p>\n

\u7b97\u6cd5\u6b65\u9aa4\uff1a<\/p>\n

\u8bbf\u95ee\u9876\u70b9v;<\/p>\n

\u4f9d\u6b21\u4ecev\u7684\u672a\u88ab\u8bbf\u95ee\u7684\u90bb\u63a5\u70b9\u51fa\u53d1\uff0c\u5bf9\u56fe\u8fdb\u884c\u6df1\u5ea6\u4f18\u5148\u904d\u5386;\u76f4\u81f3\u56fe\u4e2d\u548cv\u6709\u8def\u5f84\u76f8\u901a\u7684\u9876\u70b9\u90fd\u88ab\u8bbf\u95ee;<\/p>\n

\u82e5\u6b64\u65f6\u56fe\u4e2d\u5c1a\u6709\u9876\u70b9\u672a\u88ab\u8bbf\u95ee\uff0c\u5219\u4ece\u4e00\u4e2a\u672a\u88ab\u8bbf\u95ee\u7684\u9876\u70b9\u51fa\u53d1\uff0c\u91cd\u65b0\u8fdb\u884c\u6df1\u5ea6\u4f18\u5148\u904d\u5386\uff0c\u76f4\u5230\u56fe\u4e2d\u6240\u6709\u9876\u70b9\u5747\u88ab\u8bbf\u95ee\u8fc7\u4e3a\u6b62\u3002<\/p>\n

\u4e0a\u8ff0\u63cf\u8ff0\u53ef\u80fd\u6bd4\u8f83\u62bd\u8c61\uff0c\u4e3e\u4e2a\u5b9e\u4f8b\uff1a<\/p>\n

DFS \u5728\u8bbf\u95ee\u56fe\u4e2d\u67d0\u4e00\u8d77\u59cb\u9876\u70b9 v \u540e\uff0c\u7531 v \u51fa\u53d1\uff0c\u8bbf\u95ee\u5b83\u7684\u4efb\u4e00\u90bb\u63a5\u9876\u70b9 w1;\u518d\u4ece w1 \u51fa\u53d1\uff0c\u8bbf\u95ee\u4e0e w1\u90bb \u63a5\u4f46\u8fd8\u6ca1\u6709\u8bbf\u95ee\u8fc7\u7684\u9876\u70b9 w2;\u7136\u540e\u518d\u4ece w2 \u51fa\u53d1\uff0c\u8fdb\u884c\u7c7b\u4f3c\u7684\u8bbf\u95ee\uff0c\u2026 \u5982\u6b64\u8fdb\u884c\u4e0b\u53bb\uff0c\u76f4\u81f3\u5230\u8fbe\u6240\u6709\u7684\u90bb\u63a5\u9876\u70b9\u90fd\u88ab\u8bbf\u95ee\u8fc7\u7684\u9876\u70b9 u \u4e3a\u6b62\u3002<\/p>\n

\u63a5\u7740\uff0c\u9000\u56de\u4e00\u6b65\uff0c\u9000\u5230\u524d\u4e00\u6b21\u521a\u8bbf\u95ee\u8fc7\u7684\u9876\u70b9\uff0c\u770b\u662f\u5426\u8fd8\u6709\u5176\u5b83\u6ca1\u6709\u88ab\u8bbf\u95ee\u7684\u90bb\u63a5\u9876\u70b9\u3002\u5982\u679c\u6709\uff0c\u5219\u8bbf\u95ee\u6b64\u9876\u70b9\uff0c\u4e4b\u540e\u518d\u4ece\u6b64\u9876\u70b9\u51fa\u53d1\uff0c\u8fdb\u884c\u4e0e\u524d\u8ff0\u7c7b\u4f3c\u7684\u8bbf\u95ee;\u5982\u679c\u6ca1\u6709\uff0c\u5c31\u518d\u9000\u56de\u4e00\u6b65\u8fdb\u884c\u641c\u7d22\u3002\u91cd\u590d\u4e0a\u8ff0\u8fc7\u7a0b\uff0c\u76f4\u5230\u8fde\u901a\u56fe\u4e2d\u6240\u6709\u9876\u70b9\u90fd\u88ab\u8bbf\u95ee\u8fc7\u4e3a\u6b62\u3002<\/p>\n

\u7b97\u6cd5\u4e03\uff1aBFS(\u5e7f\u5ea6\u4f18\u5148\u641c\u7d22)<\/strong><\/p>\n

\u5e7f\u5ea6\u4f18\u5148\u641c\u7d22\u7b97\u6cd5(Breadth-First-Search)\uff0c\u662f\u4e00\u79cd\u56fe\u5f62\u641c\u7d22\u7b97\u6cd5\u3002\u7b80\u5355\u7684\u8bf4\uff0cBFS\u662f\u4ece\u6839\u8282\u70b9\u5f00\u59cb\uff0c\u6cbf\u7740\u6811(\u56fe)\u7684\u5bbd\u5ea6\u904d\u5386\u6811(\u56fe)\u7684\u8282\u70b9\u3002\u5982\u679c\u6240\u6709\u8282\u70b9\u5747\u88ab\u8bbf\u95ee\uff0c\u5219\u7b97\u6cd5\u4e2d\u6b62\u3002BFS\u540c\u6837\u5c5e\u4e8e\u76f2\u76ee\u641c\u7d22\u3002\u4e00\u822c\u7528\u961f\u5217\u6570\u636e\u7ed3\u6784\u6765\u8f85\u52a9\u5b9e\u73b0BFS\u7b97\u6cd5\u3002<\/p>\n

\u7b97\u6cd5\u6b65\u9aa4\uff1a<\/p>\n

\u9996\u5148\u5c06\u6839\u8282\u70b9\u653e\u5165\u961f\u5217\u4e2d\u3002<\/p>\n

\u4ece\u961f\u5217\u4e2d\u53d6\u51fa***\u4e2a\u8282\u70b9\uff0c\u5e76\u68c0\u9a8c\u5b83\u662f\u5426\u4e3a\u76ee\u6807\u3002<\/p>\n

\u5982\u679c\u627e\u5230\u76ee\u6807\uff0c\u5219\u7ed3\u675f\u641c\u5bfb\u5e76\u56de\u4f20\u7ed3\u679c\u3002<\/p>\n

\u5426\u5219\u5c06\u5b83\u6240\u6709\u5c1a\u672a\u68c0\u9a8c\u8fc7\u7684\u76f4\u63a5\u5b50\u8282\u70b9\u52a0\u5165\u961f\u5217\u4e2d\u3002<\/p>\n

\u82e5\u961f\u5217\u4e3a\u7a7a\uff0c\u8868\u793a\u6574\u5f20\u56fe\u90fd\u68c0\u67e5\u8fc7\u4e86\u2014\u2014\u4ea6\u5373\u56fe\u4e2d\u6ca1\u6709\u6b32\u641c\u5bfb\u7684\u76ee\u6807\u3002\u7ed3\u675f\u641c\u5bfb\u5e76\u56de\u4f20\u201c\u627e\u4e0d\u5230\u76ee\u6807\u201d\u3002<\/p>\n

\u91cd\u590d\u6b65\u9aa42\u3002 <\/p>\n

 <\/p>\n

 <\/p>\n

 <\/p>\n

\u7b97\u6cd5\u516b\uff1aDijkstra\u7b97\u6cd5<\/strong><\/p>\n

\u6234\u514b\u65af\u7279\u62c9\u7b97\u6cd5(Dijkstra\u2019s algorithm)\u662f\u7531\u8377\u5170\u8ba1\u7b97\u673a\u79d1\u5b66\u5bb6\u827e\u5179\u8d6b\u5c14\u00b7\u6234\u514b\u65af\u7279\u62c9\u63d0\u51fa\u3002\u8fea\u79d1\u65af\u5f7b\u7b97\u6cd5\u4f7f\u7528\u4e86\u5e7f\u5ea6\u4f18\u5148\u641c\u7d22\u89e3\u51b3\u975e\u8d1f\u6743\u6709\u5411\u56fe\u7684\u5355\u6e90\u6700\u77ed\u8def\u5f84\u95ee\u9898\uff0c\u7b97\u6cd5\u6700\u7ec8\u5f97\u5230\u4e00\u4e2a\u6700\u77ed\u8def\u5f84\u6811\u3002\u8be5\u7b97\u6cd5\u5e38\u7528\u4e8e\u8def\u7531\u7b97\u6cd5\u6216\u8005\u4f5c\u4e3a\u5176\u4ed6\u56fe\u7b97\u6cd5\u7684\u4e00\u4e2a\u5b50\u6a21\u5757\u3002<\/p>\n

\u8be5\u7b97\u6cd5\u7684\u8f93\u5165\u5305\u542b\u4e86\u4e00\u4e2a\u6709\u6743\u91cd\u7684\u6709\u5411\u56fe G\uff0c\u4ee5\u53caG\u4e2d\u7684\u4e00\u4e2a\u6765\u6e90\u9876\u70b9 S\u3002\u6211\u4eec\u4ee5 V \u8868\u793a G \u4e2d\u6240\u6709\u9876\u70b9\u7684\u96c6\u5408\u3002\u6bcf\u4e00\u4e2a\u56fe\u4e2d\u7684\u8fb9\uff0c\u90fd\u662f\u4e24\u4e2a\u9876\u70b9\u6240\u5f62\u6210\u7684\u6709\u5e8f\u5143\u7d20\u5bf9\u3002(u, v) \u8868\u793a\u4ece\u9876\u70b9 u \u5230 v \u6709\u8def\u5f84\u76f8\u8fde\u3002\u6211\u4eec\u4ee5 E \u8868\u793aG\u4e2d\u6240\u6709\u8fb9\u7684\u96c6\u5408\uff0c\u800c\u8fb9\u7684\u6743\u91cd\u5219\u7531\u6743\u91cd\u51fd\u6570 w: E \u2192 [0, \u221e] \u5b9a\u4e49\u3002\u56e0\u6b64\uff0cw(u, v) \u5c31\u662f\u4ece\u9876\u70b9 u \u5230\u9876\u70b9 v \u7684\u975e\u8d1f\u6743\u91cd(weight)\u3002\u8fb9\u7684\u6743\u91cd\u53ef\u4ee5\u60f3\u50cf\u6210\u4e24\u4e2a\u9876\u70b9\u4e4b\u95f4\u7684\u8ddd\u79bb\u3002\u4efb\u4e24\u70b9\u95f4\u8def\u5f84\u7684\u6743\u91cd\uff0c\u5c31\u662f\u8be5\u8def\u5f84\u4e0a\u6240\u6709\u8fb9\u7684\u6743\u91cd\u603b\u548c\u3002\u5df2\u77e5\u6709 V \u4e2d\u6709\u9876\u70b9 s \u53ca t\uff0cDijkstra \u7b97\u6cd5\u53ef\u4ee5\u627e\u5230 s \u5230 t\u7684***\u6743\u91cd\u8def\u5f84(\u4f8b\u5982\uff0c\u6700\u77ed\u8def\u5f84)\u3002\u8fd9\u4e2a\u7b97\u6cd5\u4e5f\u53ef\u4ee5\u5728\u4e00\u4e2a\u56fe\u4e2d\uff0c\u627e\u5230\u4ece\u4e00\u4e2a\u9876\u70b9 s \u5230\u4efb\u4f55\u5176\u4ed6\u9876\u70b9\u7684\u6700\u77ed\u8def\u5f84\u3002\u5bf9\u4e8e\u4e0d\u542b\u8d1f\u6743\u7684\u6709\u5411\u56fe\uff0cDijkstra\u7b97\u6cd5\u662f\u76ee\u524d\u5df2\u77e5\u7684\u6700\u5feb\u7684\u5355\u6e90\u6700\u77ed\u8def\u5f84\u7b97\u6cd5\u3002<\/p>\n

\u7b97\u6cd5\u6b65\u9aa4\uff1a<\/p>\n

\u521d\u59cb\u65f6\u4ee4 S={V0},T={\u5176\u4f59\u9876\u70b9}\uff0cT\u4e2d\u9876\u70b9\u5bf9\u5e94\u7684\u8ddd\u79bb\u503c<\/p>\n

\u82e5\u5b58\u5728<V0,Vi>\uff0cd(V0,Vi)\u4e3a<V0,Vi>\u5f27\u4e0a\u7684\u6743\u503c<\/p>\n

\u82e5\u4e0d\u5b58\u5728<V0,Vi>\uff0cd(V0,Vi)\u4e3a\u221e<\/p>\n

\u4eceT\u4e2d\u9009\u53d6\u4e00\u4e2a\u5176\u8ddd\u79bb\u503c\u4e3a\u6700\u5c0f\u7684\u9876\u70b9W\u4e14\u4e0d\u5728S\u4e2d\uff0c\u52a0\u5165S<\/p>\n

\u5bf9\u5176\u4f59T\u4e2d\u9876\u70b9\u7684\u8ddd\u79bb\u503c\u8fdb\u884c\u4fee\u6539\uff1a\u82e5\u52a0\u8fdbW\u4f5c\u4e2d\u95f4\u9876\u70b9\uff0c\u4eceV0\u5230Vi\u7684\u8ddd\u79bb\u503c\u7f29\u77ed\uff0c\u5219\u4fee\u6539\u6b64\u8ddd\u79bb\u503c<\/p>\n

\u91cd\u590d\u4e0a\u8ff0\u6b65\u9aa42\u30013\uff0c\u76f4\u5230S\u4e2d\u5305\u542b\u6240\u6709\u9876\u70b9\uff0c\u5373W=Vi\u4e3a\u6b62 <\/p>\n

 <\/p>\n

 <\/p>\n

 <\/p>\n

\u7b97\u6cd5\u4e5d\uff1a\u52a8\u6001\u89c4\u5212\u7b97\u6cd5<\/strong><\/p>\n

\u52a8\u6001\u89c4\u5212(Dynamic programming)\u662f\u4e00\u79cd\u5728\u6570\u5b66\u3001\u8ba1\u7b97\u673a\u79d1\u5b66\u548c\u7ecf\u6d4e\u5b66\u4e2d\u4f7f\u7528\u7684\uff0c\u901a\u8fc7\u628a\u539f\u95ee\u9898\u5206\u89e3\u4e3a\u76f8\u5bf9\u7b80\u5355\u7684\u5b50\u95ee\u9898\u7684\u65b9\u5f0f\u6c42\u89e3\u590d\u6742\u95ee\u9898\u7684\u65b9\u6cd5\u3002 \u52a8\u6001\u89c4\u5212\u5e38\u5e38\u9002\u7528\u4e8e\u6709\u91cd\u53e0\u5b50\u95ee\u9898\u548c***\u5b50\u7ed3\u6784\u6027\u8d28\u7684\u95ee\u9898\uff0c\u52a8\u6001\u89c4\u5212\u65b9\u6cd5\u6240\u8017\u65f6\u95f4\u5f80\u5f80\u8fdc\u5c11\u4e8e\u6734\u7d20\u89e3\u6cd5\u3002<\/p>\n

\u52a8\u6001\u89c4\u5212\u80cc\u540e\u7684\u57fa\u672c\u601d\u60f3\u975e\u5e38\u7b80\u5355\u3002\u5927\u81f4\u4e0a\uff0c\u82e5\u8981\u89e3\u4e00\u4e2a\u7ed9\u5b9a\u95ee\u9898\uff0c\u6211\u4eec\u9700\u8981\u89e3\u5176\u4e0d\u540c\u90e8\u5206(\u5373\u5b50\u95ee\u9898)\uff0c\u518d\u5408\u5e76\u5b50\u95ee\u9898\u7684\u89e3\u4ee5\u5f97\u51fa\u539f\u95ee\u9898\u7684\u89e3\u3002 \u901a\u5e38\u8bb8\u591a \u5b50\u95ee\u9898\u975e\u5e38\u76f8\u4f3c\uff0c\u4e3a\u6b64\u52a8\u6001\u89c4\u5212\u6cd5\u8bd5\u56fe\u4ec5\u4ec5\u89e3\u51b3\u6bcf\u4e2a\u5b50\u95ee\u9898\u4e00\u6b21\uff0c\u4ece\u800c\u51cf\u5c11\u8ba1\u7b97\u91cf\uff1a \u4e00\u65e6\u67d0\u4e2a\u7ed9\u5b9a\u5b50\u95ee\u9898\u7684\u89e3\u5df2\u7ecf\u7b97\u51fa\uff0c\u5219\u5c06\u5176\u8bb0\u5fc6\u5316\u5b58\u50a8\uff0c\u4ee5\u4fbf\u4e0b\u6b21\u9700\u8981\u540c\u4e00\u4e2a \u5b50\u95ee\u9898\u89e3\u4e4b\u65f6\u76f4\u63a5\u67e5\u8868\u3002 \u8fd9\u79cd\u505a\u6cd5\u5728\u91cd\u590d\u5b50\u95ee\u9898\u7684\u6570\u76ee\u5173\u4e8e\u8f93\u5165\u7684\u89c4\u6a21\u5448\u6307\u6570\u589e\u957f\u65f6\u7279\u522b\u6709\u7528\u3002<\/p>\n

\u5173\u4e8e\u52a8\u6001\u89c4\u5212\u6700\u7ecf\u5178\u7684\u95ee\u9898\u5f53\u5c5e\u80cc\u5305\u95ee\u9898\u3002<\/p>\n

\u7b97\u6cd5\u6b65\u9aa4\uff1a<\/p>\n

***\u5b50\u7ed3\u6784\u6027\u8d28\u3002\u5982\u679c\u95ee\u9898\u7684***\u89e3\u6240\u5305\u542b\u7684\u5b50\u95ee\u9898\u7684\u89e3\u4e5f\u662f***\u7684\uff0c\u6211\u4eec\u5c31\u79f0\u8be5\u95ee\u9898\u5177\u6709***\u5b50\u7ed3\u6784\u6027\u8d28(\u5373\u6ee1\u8db3***\u5316\u539f\u7406)\u3002***\u5b50\u7ed3\u6784\u6027\u8d28\u4e3a\u52a8\u6001\u89c4\u5212\u7b97\u6cd5\u89e3\u51b3\u95ee\u9898\u63d0\u4f9b\u4e86\u91cd\u8981\u7ebf\u7d22\u3002<\/p>\n

\u5b50\u95ee\u9898\u91cd\u53e0\u6027\u8d28\u3002\u5b50\u95ee\u9898\u91cd\u53e0\u6027\u8d28\u662f\u6307\u5728\u7528\u9012\u5f52\u7b97\u6cd5\u81ea\u9876\u5411\u4e0b\u5bf9\u95ee\u9898\u8fdb\u884c\u6c42\u89e3\u65f6\uff0c\u6bcf\u6b21\u4ea7\u751f\u7684\u5b50\u95ee\u9898\u5e76\u4e0d\u603b\u662f\u65b0\u95ee\u9898\uff0c\u6709\u4e9b\u5b50\u95ee\u9898\u4f1a\u88ab\u91cd\u590d\u8ba1\u7b97\u591a\u6b21\u3002 \u52a8\u6001\u89c4\u5212\u7b97\u6cd5\u6b63\u662f\u5229\u7528\u4e86\u8fd9\u79cd\u5b50\u95ee\u9898\u7684\u91cd\u53e0\u6027\u8d28\uff0c\u5bf9\u6bcf\u4e00\u4e2a\u5b50\u95ee\u9898\u53ea\u8ba1\u7b97\u4e00\u6b21\uff0c\u7136\u540e\u5c06\u5176\u8ba1\u7b97\u7ed3\u679c\u4fdd\u5b58\u5728\u4e00\u4e2a\u8868\u683c\u4e2d\uff0c\u5f53\u518d\u6b21\u9700\u8981\u8ba1\u7b97\u5df2\u7ecf\u8ba1\u7b97\u8fc7\u7684\u5b50\u95ee\u9898\u65f6\uff0c\u53ea\u662f \u5728\u8868\u683c\u4e2d\u7b80\u5355\u5730\u67e5\u770b\u4e00\u4e0b\u7ed3\u679c\uff0c\u4ece\u800c\u83b7\u5f97\u8f83\u9ad8\u7684\u6548\u7387\u3002<\/p>\n

\u7b97\u6cd5\u5341\uff1a\u6734\u7d20\u8d1d\u53f6\u65af\u5206\u7c7b\u7b97\u6cd5<\/strong><\/p>\n

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