{"id":3857,"date":"2012-03-20T18:08:46","date_gmt":"2012-03-20T10:08:46","guid":{"rendered":"http:\/\/edsionte.com\/techblog\/?p=3857"},"modified":"2012-04-28T09:21:21","modified_gmt":"2012-04-28T01:21:21","slug":"%e5%86%85%e9%83%a8%e6%8e%92%e5%ba%8f%e7%ae%97%e6%b3%95%e5%b0%8f%e7%bb%93","status":"publish","type":"post","link":"http:\/\/edsionte.com\/techblog\/archives\/3857","title":{"rendered":"\u5185\u90e8\u6392\u5e8f\u7b97\u6cd5\u5c0f\u7ed3"},"content":{"rendered":"

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1.\u63d2\u5165\u7c7b\u6392\u5e8f<\/h3>\n

\u76f4\u63a5\u63d2\u5165\u6392\u5e8f<\/strong><\/p>\n

<\/strong>\u5982\u679c\u5f85\u6392\u5e8f\u8bb0\u5f55\u4e4b\u95f4\u662f\u987a\u5e8f\u6392\u5217\uff0c\u6b64\u65f6\u6574\u4e2a\u6392\u5e8f\u8fc7\u7a0b\u4e2d\u5143\u7d20\u6bd4\u8f83\u7684\u6b21\u6570\u4e3an-1\u6b21\uff0c\u79fb\u52a8\u6b21\u6570\u4e3a0\u6b21\u3002\u5982\u679c\u5f85\u6392\u5e8f\u8bb0\u5f55\u4e4b\u95f4\u662f\u9006\u5e8f\u6392\u5217\uff0c\u7b2ci\u8d9f\u6392\u5e8f\u6bd4\u8f83\u6b21\u6570\u4e3ai\uff0c\u79fb\u52a8\u7684\u6b21\u6570\u4e3ai+1\uff0c\u5176\u4e2di\u7684\u8303\u56f4\u662f2\u5230n\u3002\u56e0\u6b64\uff0c\u6574\u4e2a\u6392\u5e8f\u8fc7\u7a0b\u4e2d\u5143\u7d20\u7684\u6bd4\u8f83\u6b21\u6570\u4e3a(n+2)(n-1)\/2\uff0c\u79fb\u52a8\u6b21\u6570\u4e3a(n+4)(n-1)\/2\u3002<\/p>\n

\u76f4\u63a5\u63d2\u5165\u6392\u5e8f\u7b97\u6cd5\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4e3aO(n^2)\uff0c\u7a7a\u95f4\u590d\u6742\u5ea6\u4e3aO(1)\u3002\u4ece\u76f4\u63a5\u63d2\u5165\u6392\u5e8f\u7b97\u6cd5\u7684\u5b9e\u73b0\u53ef\u4ee5\u53d1\u73b0\uff0c\u4f4d\u7f6e\u9760\u540e\u7684\u8bb0\u5f55\u662f\u4e0d\u53ef\u80fd\u63d2\u5165\u5230\u76f8\u540c\u5927\u5c0f\u7684\u8bb0\u5f55\u4e4b\u524d\u7684\uff0c\u56e0\u6b64\u76f4\u63a5\u63d2\u5165\u6392\u5e8f\u7b97\u6cd5\u662f\u7a33\u5b9a\u7684\u3002<\/p>\n

\u6298\u534a\u63d2\u5165\u6392\u5e8f<\/strong><\/p>\n

\u6298\u534a\u63d2\u5165\u6392\u5e8f\u7b97\u6cd5\u4e0e\u76f4\u63a5\u63d2\u5165\u6392\u5e8f\u7b97\u6cd5\u76f8\u6bd4\uff0c\u6bcf\u8d9f\u7684\u6bd4\u8f83\u6b21\u6570\u4e3alog2^i\uff0c\u56e0\u6b64\u6574\u4f53\u7684\u6bd4\u8f83\u6b21\u6570\u4e3aO(nlog2^n)\u3002\u4f46\u662f\u6298\u534a\u7b97\u6cd5\u7684\u79fb\u52a8\u6b21\u6570\u8f83\u76f4\u63a5\u63d2\u5165\u7b97\u6cd5\u5e76\u672a\u6539\u53d8\u3002<\/p>\n

\u6298\u534a\u7b97\u6cd5\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4ecd\u7136\u662fO(n^2)\uff0c\u7a7a\u95f4\u590d\u6742\u5ea6\u4e3aO(1)\u3002\u4ece\u7b97\u6cd5\u5b9e\u73b0\u53ef\u4ee5\u770b\u51fa\u6298\u534a\u63d2\u5165\u6392\u5e8f\u7b97\u6cd5\u662f\u7a33\u5b9a\u7684\u3002<\/p>\n

\u5e0c\u5c14\u6392\u5e8f<\/strong><\/p>\n

\u5e0c\u5c14\u6392\u5e8f\u5229\u7528\u4e86\u5f53\u201c\u5f85\u6392\u5e8f\u8bb0\u5f55n\u8f83\u5c0f\uff0c\u5e8f\u5217\u57fa\u672c\u6709\u5e8f\u201d\u65f6\u4f7f\u7528\u76f4\u63a5\u63d2\u5165\u7b97\u6cd5\u6027\u80fd\u8f83\u597d\u8fd9\u4e00\u7279\u70b9\u800c\u6539\u8fdb\u3002\u5e0c\u5c14\u6392\u5e8f\u7b97\u6cd5\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4e3aO(n^1.5)\uff0c\u7a7a\u95f4\u590d\u6742\u5ea6\u4e3aO(1)\uff0c\u5b83\u662f\u4e0d\u7a33\u5b9a\u7684\u6392\u5e8f\u7b97\u6cd5\u3002\u4e3e\u53cd\u4f8b\u5982\u4e0b\uff1a\u5f85\u6392\u5e8f\u5e8f\u5217\u4e3a{2\uff0c4\uff0c1\uff0c(2)}\uff0c\u8bbedelta[1]=2\uff0c\u5219\u4e00\u8d9f\u6392\u5e8f\u540e\u5e8f\u5217\u4e3a{1,(2),2,4}\u3002<\/p>\n

2.\u4ea4\u6362\u7c7b\u6392\u5e8f<\/h3>\n

\u5192\u6ce1\u6392\u5e8f<\/strong><\/p>\n

\u5f53\u5f85\u6392\u5e8f\u8bb0\u5f55\u9006\u5e8f\u6392\u5217\u65f6\uff0c\u6bcf\u8d9f\u5192\u6ce1\u7b97\u6cd5\u8fdb\u884ci\u6b21\u6bd4\u8f83\u548c3i\u6b21\u4ea4\u6362\uff08\u4e24\u4e2a\u5143\u7d20\u4ea4\u6362\uff09\uff0ci\u7684\u8303\u56f4\u662f1\u5230n-1\u3002\u56e0\u6b64\u603b\u7684\u6bd4\u8f83\u6b21\u6570\u4e3an(n-1)\/2\uff0c\u603b\u7684\u79fb\u52a8\u6b21\u6570\u4e3a3n(n-1)\/2\u3002\u5192\u6ce1\u6392\u5e8f\u7b97\u6cd5\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4e3aO(n^2)\uff0c\u7a7a\u95f4\u590d\u6742\u5ea6O\u4e3a(1)\uff0c\u662f\u4e00\u79cd\u7a33\u5b9a\u7684\u6392\u5e8f\u7b97\u6cd5\u3002<\/p>\n

\u5feb\u901f\u6392\u5e8f<\/strong><\/p>\n

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\u5feb\u901f\u6392\u5e8f\u7684\u5e73\u5747\u590d\u6742\u5ea6\u4e3aO(nlog2^n)\uff0c\u7a7a\u95f4\u590d\u6742\u5ea6\u4e3aO(log2^n)\uff0c\u5b83\u662f\u4e00\u79cd\u4e0d\u7a33\u5b9a\u7684\u6392\u5e8f\u7b97\u6cd5\u3002\u4e3e\u53cd\u4f8b\u5982\u4e0b\uff1a\u5f85\u6392\u5e8f\u5e8f\u5217\u4e3a{3,2,(2)},\u5219\u4e00\u8d9f\u6392\u5e8f\u540e\u8bb0\u5f55\u4e3a{(2),2,3}\u3002<\/p>\n

3.\u9009\u62e9\u7c7b\u6392\u5e8f<\/h3>\n

\u7b80\u5355\u9009\u62e9\u6392\u5e8f<\/strong><\/p>\n

\u65e0\u8bba\u5f85\u6392\u5e8f\u8bb0\u5f55\u7684\u521d\u59cb\u6392\u5217\u5982\u4f55\uff0c\u7b80\u5355\u9009\u62e9\u6392\u5e8f\u603b\u7684\u6bd4\u8f83\u6b21\u6570\u603b\u4e3an(n-1)\/2\uff0c\u56e0\u4e3a\u5b83\u6bcf\u8d9f\u6bd4\u8f83\u7684\u6b21\u6570\u4e3an-i\uff0ci\u7684\u8303\u56f4\u4ece1\u5230n-1\u3002\u6700\u597d\u7684\u60c5\u51b5\u4e0b\uff0c\u7b80\u5355\u9009\u62e9\u6392\u5e8f\u7b97\u6cd5\u7684\u79fb\u52a8\u6b21\u6570\u4e3a0\uff0c\u6700\u574f\u60c5\u51b5\u4e0b\u79fb\u52a8\u76843(n-1)\u3002<\/p>\n

\u7b80\u5355\u9009\u62e9\u6392\u5e8f\u7b97\u6cd5\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4e3aO(n^2)\uff0c\u7a7a\u95f4\u590d\u6742\u5ea6\u4e3aO(1)\uff0c\u5b83\u662f\u4e0d\u7a33\u5b9a\u7684\u6392\u5e8f\u7b97\u6cd5\u3002\u4e3e\u53cd\u4f8b\u5982\u4e0b\uff1a\u5f85\u6392\u5e8f\u8bb0\u5f55\u4e3a{6,8,(6),2,7}\uff0c\u4e00\u8d9f\u6392\u5e8f\u540e\u8bb0\u5f55\u4e3a{2,8,(6),6,7}\uff0c\u4e8c\u8d9f\u6392\u5e8f\u540e\u8bb0\u5f55\u4e3a{2,(6),8,6,7}\u3002<\/p>\n

\u5806\u6392\u5e8f<\/strong><\/p>\n

\u5806\u6392\u5e8f\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4e3aO(nlog2^n)\uff0c\u7a7a\u95f4\u590d\u6742\u5ea6\u4e3aO(1)\uff0c\u5b83\u662f\u4e0d\u7a33\u5b9a\u7684\u6392\u5e8f\u7b97\u6cd5\u3002<\/p>\n

4.\u5f52\u5e76\u6392\u5e8f<\/h3>\n

\u5f52\u5e76\u6392\u5e8f\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4e3aO(nlog2^n)\uff0c\u7a7a\u95f4\u590d\u6742\u5ea6\u4e3aO(n)\uff0c\u5b83\u662f\u7a33\u5b9a\u7684\u6392\u5e8f\u7b97\u6cd5\u3002<\/p>\n

5.\u603b\u7ed3<\/h3>\n

\u7efc\u4e0a\u6240\u8ff0\uff0c\u5185\u90e8\u6392\u5e8f\u7b97\u6cd5\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u3001\u7a7a\u95f4\u590d\u6742\u5ea6\u548c\u7a33\u5b9a\u6027\u603b\u7ed3\u5982\u4e0b\u8868\uff1a<\/p>\n

\"\"<\/a><\/p>\n

1.\u76f4\u63a5\u63d2\u5165\u6392\u5e8f\u3001\u6298\u534a\u63d2\u5165\u6392\u5e8f\u3001\u5192\u6ce1\u6392\u5e8f\u548c\u7b80\u5355\u9009\u62e9\u6392\u5e8f\u5408\u79f0\u4e3a\u7b80\u5355\u6392\u5e8f\uff0c\u5b83\u4eec\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u5747\u4e3aO(n^2)\uff0c\u7a7a\u95f4\u590d\u6742\u5ea6\u4e3aO(1)\u3002\u7a33\u5b9a\u6027\u65b9\u9762\u53ea\u6709\u7b80\u5355\u9009\u62e9\u6392\u5e8f\u662f\u4e0d\u7a33\u5b9a\u7684\u6392\u5e8f\u7b97\u6cd5\u3002\u7b80\u5355\u6392\u5e8f\u53ea\u9002\u5408n\u8f83\u5c0f\u7684\u60c5\u51b5\u3002<\/p>\n

2.\u5f53\u5f85\u6392\u5e8f\u8bb0\u5f55\u57fa\u672c\u6709\u5e8f\u65f6\uff0c\u76f4\u63a5\u63d2\u5165\u6392\u5e8f\u662f\u6700\u4f73\u7684\u6392\u5e8f\u7b97\u6cd5\u3002\u5b83\u5e38\u4e0e\u5feb\u901f\u6392\u5e8f\u548c\u5f52\u5e76\u6392\u5e8f\u7b49\u7ed3\u5408\u4f7f\u7528\uff0c\u56e0\u4e3a\u8fd9\u4e9b\u7b97\u6cd5\u4f1a\u5c06\u6574\u4e2a\u6253\u6392\u5e8f\u8bb0\u5f55\u5212\u5206\u4e3a\u82e5\u5e72\u4e2a\u5b50\u8bb0\u5f55\uff0c\u8fd9\u4e9b\u5b50\u8bb0\u5f55\u6570\u91cf\u8f83\u5c0f\u800c\u4e14\u57fa\u672c\u6709\u5e8f\u3002<\/p>\n

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