{"id":29771,"date":"2021-11-05T15:43:32","date_gmt":"2021-11-05T07:43:32","guid":{"rendered":"https:\/\/swarma.org\/?p=29771"},"modified":"2021-11-05T15:43:32","modified_gmt":"2021-11-05T07:43:32","slug":"%e4%bb%80%e4%b9%88%e6%98%af%e8%ae%a1%e7%ae%97%e5%a4%8d%e6%9d%82%e5%ba%a6-%e9%9b%86%e6%99%ba%e7%99%be%e7%a7%91","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=29771","title":{"rendered":"\u4ec0\u4e48\u662f\u8ba1\u7b97\u590d\u6742\u5ea6 | \u96c6\u667a\u767e\u79d1"},"content":{"rendered":"
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\u5728\u8ba1\u7b97\u673a\u79d1\u5b66 computer science\u4e2d\uff0c\u4e00\u4e2a\u7b97\u6cd5 algorithm\u7684\u8ba1\u7b97\u590d\u6742\u5ea6\u6216\u7b80\u5355\u7684\u590d\u6742\u5ea6\u5c31\u662f\u8fd0\u884c\u8fd9\u4e2a\u7b97\u6cd5\u6240\u9700\u8981\u7684\u8d44\u6e90\u91cf\uff0c\u7279\u522b\u662f\u65f6\u95f4\uff08CPU\u5360\u7528\u65f6\u95f4\uff09\u548c\u7a7a\u95f4\uff08\u5185\u5b58\u5360\u7528\u7a7a\u95f4\uff09\u9700\u6c42\u3002<\/span>
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\u7531\u4e8e\u8fd0\u884c\u4e00\u4e2a\u7b97\u6cd5\u6240\u9700\u7684\u8d44\u6e90\u91cf\u901a\u5e38\u968f\u8f93\u5165\u89c4\u6a21\u7684\u5927\u5c0f\u800c\u53d8\u5316\uff0c\u56e0\u6b64\u590d\u6742\u5ea6\u901a\u5e38\u7528\u51fd\u6570 f(n)\u8868\u793a\uff0c\u5176\u4e2dn\u662f\u8f93\u5165\u91cf\u7684\u5927\u5c0f\uff0cf(n)\u662f\u6700\u574f\u60c5\u51b5\u590d\u6742\u5ea6 worst-case complexity(\u8f93\u5165\u5927\u5c0f\u4e3a n\u65f6\u6240\u9700\u7684\u8d44\u6e90\u91cf\u7684\u6700\u5927\u503c) \uff0c\u6216\u662f\u5e73\u5747\u60c5\u51b5\u590d\u6742\u5ea6 average-case complexity(\u8d44\u6e90\u603b\u91cf\u76f8\u5bf9\u4e8en\u7684\u6240\u6709\u5360\u7528\u7684\u5e73\u5747\u503c)\u3002\u65f6\u95f4\u590d\u6742\u5ea6 Time complexity\u901a\u5e38\u8868\u793a\u4e3a\u5bf9\u4e00\u4e2a\u8f93\u5165\u503c\u957f\u5ea6\u6240\u9700\u57fa\u672c\u64cd\u4f5c\uff08\u901a\u5e38\u662f\u52a0\u6cd5\u64cd\u4f5c\u6216\u8005\u4e58\u6cd5\u64cd\u4f5c\uff09\u7684\u6570\u91cf\u3002\u6211\u4eec\u5047\u8bbe\u57fa\u672c\u64cd\u4f5c\u5728\u4e00\u53f0\u8ba1\u7b97\u673a\u4e0a\u53ea\u5360\u7528\u4e00\u4e2a\u4e0d\u53d8\u7684\u65f6\u95f4\u91cf\uff08\u6bd4\u59821\u7eb3\u79d2\uff09\uff0c\u800c\u5728\u53e6\u4e00\u53f0\u8ba1\u7b97\u673a\u4e0a\u8fd0\u884c\u65f6\uff0c\u53ea\u6839\u636e\u4e00\u4e2a\u5e38\u91cf\u56e0\u5b50\u8fdb\u884c\u6539\u53d8\uff08\u6bd4\u5982k*1\u7eb3\u79d2\uff09\u3002\u7a7a\u95f4\u590d\u6742\u5ea6 space complexity\u901a\u5e38\u8868\u793a\u4e3a\u7b97\u6cd5\u5bf9\u4e00\u4e2a\u8f93\u5165\u503c\u957f\u5ea6\u6240\u9700\u7684\u5185\u5b58\u91cf\u3002<\/span><\/p>\n


\u5bf9\u4e00\u4e2a\u6709\u660e\u786e\u5b9a\u4e49\u7684\u7b97\u6cd5\u7684\u590d\u6742\u5ea6\u8fdb\u884c\u7684\u7814\u7a76\u53eb\u505a<\/span>\u7b97\u6cd5\u5206\u6790<\/span> analysis of algorithm\uff0c\u800c\u5bf9\u95ee\u9898\u7684\u590d\u6742\u5ea6\u7814\u7a76\u53eb\u505a\u8ba1\u7b97\u590d\u6742\u5ea6\u7406\u8bba computation complexity theory\u5206\u6790\u3002\u4e3e\u4e2a\u4f8b\u5b50\uff0c\u600e\u6837\u628a\u4e00\u4e32\u6570\u5b57\u4ece\u5c0f\u5230\u5927\u8fdb\u884c\u6392\u5e8f\uff0c\u662f\u4e00\u4e2a\u95ee\u9898\uff1b\u800c\u9488\u5bf9\u8fd9\u4e00\u95ee\u9898\uff0c\u6211\u4eec\u6709\u591a\u79cd\u660e\u786e\u5b9a\u4e49\u7684\u7b97\u6cd5\uff0c\u5982\u9009\u62e9\u6392\u5e8f\uff0c\u5f52\u5e76\u6392\u5e8f\u7b49\u3002\u5047\u8bbe\u6211\u4eec\u6709n\u4e2a\u6570\u5b57\uff0c\u90a3\u4e48\u6392\u5e8f\u95ee\u9898\u7684\u590d\u6742\u5ea6\u5c31\u662fnlogn\uff0c\u800c\u9009\u62e9\u6392\u5e8f\u7684\u590d\u6742\u5ea6\u662fn^2\uff0c\u5f52\u5e76\u6392\u5e8f\u7684\u590d\u6742\u5ea6\u662f6nlogn\u3002<\/span><\/p>\n


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\u7b97\u672f\u8fd0\u7b97 arithmetic operations\u7684\u6570\u91cf\u662f\u53e6\u4e00\u79cd\u5e38\u7528\u7684\u8d44\u6e90\u3002\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u4eba\u4eec\u4f1a\u8c08\u5230\u7b97\u672f\u590d\u6742\u5ea6\u3002\u5982\u679c\u5df2\u77e5\u4e00\u4e2a\u8ba1\u7b97\u8fc7\u7a0b\u4e2d\u51fa\u73b0\u7684\u6570\u7684\u4e8c\u8fdb\u5236\u8868\u793a binary representation\u957f\u5ea6\u7684\u4e0a\u9650 upper bound\uff0c\u65f6\u95f4\u590d\u6742\u5ea6\u901a\u5e38\u662f\u8be5\u7b97\u672f\u590d\u6742\u5ea6\u4e58\u4ee5\u4e00\u4e2a\u5e38\u6570\u56e0\u5b50\u3002<\/span><\/p>\n


\u5bf9\u4e8e\u8bb8\u591a\u7b97\u6cd5\uff0c\u5728\u8ba1\u7b97\u8fc7\u7a0b\u4e2d\u4f7f\u7528\u7684\u6574\u6570\u5927\u5c0f\u662f\u6ca1\u6709\u754c\u9650\u7684\uff0c\u5e76\u4e14\u8003\u8651\u7b97\u672f\u8fd0\u7b97\u5360\u7528\u4e00\u4e2a\u5e38\u91cf\u65f6\u95f4\u662f\u4e0d\u73b0\u5b9e\u7684\u3002\u56e0\u6b64\uff0c\u65f6\u95f4\u590d\u6742\u5ea6\uff0c\u5728\u6b64\u4e0a\u4e0b\u6587\u4e2d\u901a\u5e38\u79f0\u4e3a \u4f4d\u590d\u6742\u5ea6 bit complexity\uff0c\u53ef\u80fd\u8fdc\u8fdc\u5927\u4e8e\u7b97\u672f\u590d\u6742\u5ea6\u3002\u4f8b\u5982\uff0c\u6839\u636e\u901a\u5e38\u7684\u7b97\u6cd5 \u9ad8\u65af\u6d88\u53bb\u6cd5 Gaussian elimination \u8ba1\u7b97\u4e00\u4e2an\u00d7n \u6574\u6570\u77e9\u9635\u884c\u5217\u5f0f \u7684\u7b97\u672f\u590d\u6742\u5ea6\u662fO(n^3)\u3002\u56e0\u4e3a\u7cfb\u6570\u7684\u5927\u5c0f\u53ef\u80fd\u5728\u8ba1\u7b97\u8fc7\u7a0b\u4e2d\u5448\u6307\u6570\u589e\u957f\uff0c\u76f8\u540c\u7b97\u6cd5\u7684\u4f4d\u590d\u6742\u5ea6\u662f\u6307\u6570\u7ea7\u7684\u3002\u53e6\u4e00\u65b9\u9762\uff0c\u5982\u679c\u8fd9\u4e9b\u7b97\u6cd5\u4e0e\u591a\u6a21\u8fd0\u7b97\u76f8\u7ed3\u5408\uff0c\u4f4d\u590d\u6742\u5ea6\u53ef\u4ee5\u964d\u4f4e\u5230O~(n4)\u3002<\/span><\/p>\n


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\u8ba1\u7b97\u4e00\u4e2a\u7b97\u6cd5\u5bf9\u4e8e\u6240\u6709\u53ef\u80fd\u8f93\u5165\u7684\u6240\u9700\u8981\u7684\u6b65\u9aa4\u6570\u662f\u4e0d\u53ef\u80fd\u7684\u3002\u7531\u4e8e\u590d\u6742\u5ea6\u901a\u5e38\u968f\u7740\u8f93\u5165\u7684\u89c4\u6a21\u800c\u589e\u52a0\uff0c\u590d\u6742\u5ea6\u901a\u5e38\u8868\u793a\u4e3a\u8f93\u5165\u503c n \u957f\u5ea6\uff08\u4ee5\u6bd4\u7279 bit\u4e3a\u5355\u4f4d\uff09\u7684\u51fd\u6570\u3002\u56e0\u6b64\uff0c\u590d\u6742\u5ea6\u662f\u4e00\u4e2a\u5173\u4e8e n \u7684\u51fd\u6570\u3002\u7136\u800c\uff0c\u5bf9\u4e8e\u540c\u6837\u957f\u5ea6\u7684\u4e0d\u540c\u8f93\u5165\uff0c\u7b97\u6cd5\u7684\u590d\u6742\u5ea6\u53ef\u80fd\u4f1a\u5927\u4e0d\u76f8\u540c\u3002\u56e0\u6b64\uff0c\u6709\u591a\u79cd\u4e0d\u540c\u7684\u590d\u6742\u5ea6\u51fd\u6570\u88ab\u5e7f\u6cdb\u4f7f\u7528\u3002<\/span><\/section>\n

\u6700\u574f\u60c5\u51b5\u590d\u6742\u5ea6 worst-case complexity\u662f\u5bf9\u6240\u6709\u8f93\u5165n\u957f\u5ea6\u4e2d\u7684\u6700\u5927\u590d\u6742\u5ea6\uff0c\u5e73\u5747\u60c5\u51b5\u590d\u6742\u5ea6 average-case complexity\u662f\u5bf9\u6240\u6709\u8f93\u5165n\u957f\u5ea6\u4e2d\u7684\u5e73\u5747\u590d\u6742\u5ea6\u3002\u4e00\u822c\u6765\u8bf4\uff0c\u5982\u679c\u4f7f\u7528\u201c\u590d\u6742\u5ea6\u201d\u4e00\u8bcd\u4e14\u4e0d\u8fdb\u884c\u8fdb\u4e00\u6b65\u8bf4\u660e \uff0c\u5373\u8003\u8651\u6700\u574f\u60c5\u51b5\u65f6\u95f4\u590d\u6742\u5ea6\u3002<\/span><\/section>\n

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\u901a\u5e38\u5f88\u96be\u7cbe\u786e\u8ba1\u7b97\u6700\u574f\u60c5\u51b5\u548c\u5e73\u5747\u60c5\u51b5\u590d\u6742\u5ea6\u3002\u6b64\u5916\uff0c\u7531\u4e8e\u8ba1\u7b97\u673a\u6216\u8ba1\u7b97\u6a21\u578b\u7684\u4efb\u4f55\u53d8\u5316\u90fd\u4f1a\u6539\u53d8\u590d\u6742\u5ea6\uff0c\u7cbe\u786e\u7684\u590d\u6742\u5ea6\u503c\u6ca1\u591a\u5c11\u5b9e\u9645\u610f\u4e49\u3002\u66f4\u591a\u5730\uff0c\u5bf9\u4e8e\u8f83\u5c0f\u7684n\u503c\uff0c\u8d44\u6e90\u7684\u4f7f\u7528\u5e76\u4e0d\u662f\u5173\u952e\u3002\u56e0\u6b64\u5bf9\u4e8e\u5c0f n\uff0c\u4eba\u4eec\u901a\u5e38\u66f4\u5728\u4e4e\u4e00\u4e2a\u7b97\u6cd5\u7684\u7b80\u5355\u6027\u548c\u6613\u5b9e\u73b0\u6027\uff0c\u800c\u975e\u590d\u6742\u5ea6\u3002<\/span>
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\u7531\u4e8e\u8fd9\u4e9b\u539f\u56e0\uff0c\u4eba\u4eec\u901a\u5e38\u628a\u6ce8\u610f\u529b\u96c6\u4e2d\u5728\u5927n\u7684\u590d\u6742\u5ea6\u4e0a\uff0c\u5373\u8f93\u5165\u89c4\u6a21\u8d8b\u4e8e\u65e0\u7a77\u5927\u7684\u6e10\u8fd1\u884c\u4e3a asymptotic behavior\u4e0a\u3002\u56e0\u6b64\uff0c\u590d\u6742\u5ea6\u901a\u5e38\u7528\u5927O\u7b26\u53f7 big O notation\u6765\u8868\u793a\u3002<\/span><\/section>\n

\u4f8b\u5982\uff0c\u901a\u5e38\u6574\u6570\u4e58\u6cd5 multiplication\u7684\u590d\u6742\u5ea6\u662fO(n^2)\uff0c\u8fd9\u610f\u5473\u7740\u5b58\u5728\u4e00\u4e2a\u5e38\u6570Cu\uff0c\u4f7f\u5f97\u4e24\u4e2a\u6700\u591an\u4f4d\u7684\u6574\u6570\u4e58\u6cd5\u53ef\u4ee5\u5728\u5c0f\u4e8eCun^2\u7684\u65f6\u95f4\u5185\u5b8c\u6210\u3002\u8fd9\u4e2a\u754c\u9650\u662f\u5c16\u9510\u7684\uff0c\u56e0\u4e3a\u6700\u574f\u60c5\u51b5\u590d\u6742\u5ea6\u548c\u5e73\u5747\u60c5\u51b5\u590d\u6742\u5ea6\u662f\u03a9(n^2)\u3002\u610f\u5473\u7740\u5b58\u5728\u4e00\u4e2a\u5e38\u6570Cl\uff0c\u4f7f\u5f97\u8fd9\u4e9b\u590d\u6742\u5ea6\u6bd4Cln^2\u5927\u3002<\/span><\/section>\n


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\u590d\u6742\u5ea6\u7684\u8bc4\u4f30\u4f9d\u8d56\u4e8e<\/span>\u8ba1\u7b97\u6a21\u578b<\/span> model of computation\u7684\u9009\u62e9\uff0c\u5305\u62ec\u5b9a\u4e49\u5728\u4e00\u4e2a\u65f6\u95f4\u5355\u4f4d\u5185\u5b8c\u6210\u7684\u57fa\u672c\u64cd\u4f5c\u3002\u5f53\u6ca1\u6709\u660e\u786e\u6307\u5b9a\u65f6\uff0c\u9ed8\u8ba4\u4f7f\u7528\u7684\u8ba1\u7b97\u6a21\u578b\u662f\u591a\u5e26<\/span>\u56fe\u7075\u673a<\/span> multitape Turing machine\u3002<\/span>
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\u786e\u5b9a\u6027\u6a21\u578b<\/span><\/strong><\/span><\/h3>\n
\u4e00\u4e2a\u786e\u5b9a\u6027\u6a21\u578b deterministic model \u7684\u8ba1\u7b97\u662f\u4e00\u79cd\u673a\u5668\u7684\u540e\u7eed\u72b6\u6001\u548c\u8981\u6267\u884c\u7684\u64cd\u4f5c\u5b8c\u5168\u7531\u524d\u9762\u7684\u72b6\u6001\u51b3\u5b9a\u7684\u8ba1\u7b97\u6a21\u578b\u3002\u5386\u53f2\u4e0a\uff0c\u6700\u65e9\u7684\u786e\u5b9a\u6027\u6a21\u578b\u662f<\/span>\u9012\u5f52<\/span>\u51fd\u6570 recursive functions\u3001 lambda\u6f14\u7b97 lambda calculus\u548c<\/span>\u56fe\u7075\u673a<\/span> Turing machines\u3002\u968f\u673a\u5b58\u53d6\u673a\u5668 Random access machine (\u4e5f\u79f0 RAM-machines)\u7684\u6a21\u578b\u4e5f\u88ab\u5e7f\u6cdb\u4f7f\u7528\uff0c\u66f4\u63a5\u8fd1\u771f\u5b9e\u7684\u8ba1\u7b97\u673a computer\u3002<\/span><\/section>\n

\u5f53\u8ba1\u7b97\u6a21\u578b\u6ca1\u6709\u88ab\u6307\u5b9a\u65f6\uff0c\u901a\u5e38\u5047\u8bbe\u5b83\u662f\u4e00\u4e2a\u591a\u5e26\u56fe\u7075\u673a multitape Turing machine\u3002\u5bf9\u4e8e\u5927\u591a\u6570\u7b97\u6cd5\uff0c\u5728\u591a\u5e26\u56fe\u7075\u673a\u4e0a\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4e0e\u5728RAM-machines\u4e0a\u7684\u76f8\u540c\uff0c\u5c3d\u7ba1\u53ef\u80fd\u9700\u8981\u6ce8\u610f\u5982\u4f55\u5c06\u6570\u636e\u5b58\u50a8\u5728\u5185\u5b58\u4e2d\uff0c\u4ee5\u786e\u4fdd\u8fd9\u79cd\u7b49\u4ef7\u6027\u3002<\/span><\/section>\n

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\u975e\u786e\u5b9a\u6027\u8ba1\u7b97<\/span><\/strong><\/span><\/h3>\n
\u5728\u975e\u786e\u5b9a\u6027\u8ba1\u7b97\u6a21\u578b non-deterministic model of computation\u4e2d\uff0c\u4f8b\u5982\u4e0d\u786e\u5b9a\u7684\u56fe\u7075\u673a non-deterministic Turing machine\uff0c\u5728\u8ba1\u7b97\u7684\u67d0\u4e9b\u6b65\u9aa4\u4e2d\u53ef\u80fd\u4f1a\u8fdb\u884c\u4e00\u4e9b\u9009\u62e9\u3002\u5728\u590d\u6742\u5ea6\u7406\u8bba\u4e2d\uff0c\u975e\u786e\u5b9a\u6027\u65f6\u95f4\u590d\u6742\u5ea6\u5373\u4e3a\uff0c\u540c\u65f6\u8003\u8651\u6240\u6709\u53ef\u80fd\u7684\u9009\u62e9\u4e14\u505a\u51fa\u6700\u4f73\u9009\u62e9\u65f6\u6240\u9700\u7684\u65f6\u95f4\u3002\u6362\u53e5\u8bdd\u8bf4\uff0c\u6211\u4eec\u8ba4\u4e3a\u8ba1\u7b97\u662f\u591a\u4e2a\uff08\u76f8\u540c\u7684\uff09\u5904\u7406\u5668\u4e0a\u540c\u65f6\u8fdb\u884c\u7684\uff0c\u800c\u4e0d\u786e\u5b9a\u8ba1\u7b97\u65f6\u95f4\u662f\u7b2c\u4e00\u4e2a\u5b8c\u6210\u8ba1\u7b97\u7684\u5904\u7406\u5668\u6240\u82b1\u8d39\u7684\u65f6\u95f4\u3002\u8fd9\u79cd\u5e76\u884c\u6027\u5728\u4e00\u5b9a\u7a0b\u5ea6\u4e0a\u53ef\u4ee5\u901a\u8fc7\u8fd0\u884c\u7279\u5b9a<\/span>\u91cf\u5b50\u7b97\u6cd5<\/span> quantum algorithm\u7684\u53e0\u52a0\u7ea0\u7f20\u6001 entangled state\u6765\u5b9e\u73b0<\/span>\u91cf\u5b50\u8ba1\u7b97<\/span> quantum computing\u3002\u4f8b\u5982\u5c0f\u6574\u6570\u4e0a\u7684\u8096\u5c14\u56e0\u5f0f\u5206\u89e3 Shor’s factorization\u3002<\/span><\/section>\n

\u5373\u4f7f\u8fd9\u6837\u7684\u8ba1\u7b97\u6a21\u578b\u8fd8\u4e0d\u73b0\u5b9e\uff0c\u5b83\u4ecd\u7136\u5177\u6709\u91cd\u8981\u7684\u7406\u8bba\u610f\u4e49\uff0c\u4e3b\u8981\u6d89\u53caP = NP? \u95ee\u9898\u3002\u5982\u679c\u4e00\u4e2a\u95ee\u9898\u53ef\u4ee5\u5728\u786e\u5b9a\u6027\u56fe\u7075\u673a\u4e0a\u4ee5\u591a\u9879\u5f0f\u65f6\u95f4 polynomial time\u6c42\u89e3\uff0c\u5219\u8be5\u95ee\u9898\u5c5e\u4e8e P \u7c7b\u95ee\u9898\u3002\u5982\u679c\u4e00\u4e2a\u95ee\u9898\u53ef\u4ee5\u5728\u975e\u786e\u5b9a\u6027\u673a\u5668\u4e0a\u4ee5\u591a\u9879\u5f0f\u65f6\u95f4 polynomial time\u6c42\u89e3\uff0c\u5219\u8be5\u95ee\u9898\u5c5e\u4e8e NP \u7c7b\u95ee\u9898\u3002\u6211\u4eec\u77e5\u9053\u6240\u6709P\u7c7b\u95ee\u9898\u90fd\u5c5e\u4e8eNP\u7c7b\u95ee\u9898\uff0c\u4f46\u662f\u5426\u6240\u6709NP\u7c7b\u95ee\u9898\u4e5f\u5c5e\u4e8eP\u7c7b\u95ee\u9898\uff1f\u4ea6\u5373\uff0c\u662f\u5426P\u7c7b\u95ee\u9898\u548cNP\u7c7b\u95ee\u9898\u662f\u7b49\u4ef7\u7684\uff1f\u8fd9\u5c31\u662f\u6240\u8c13\u7684 P=NP? \u95ee\u9898<\/span><\/section>\n

\u5982\u679c\u4e00\u4e2a\u95ee\u9898\u5c5e\u4e8e NP \u95ee\u9898\uff0c\u4e14\u4e0d\u6bd4\u5176\u4ed6\u4efb\u4f55 NP \u95ee\u9898\u7b80\u5355\uff0c\u5219\u79f0\u8be5\u95ee\u9898\u4e3a NP\u5b8c\u5168\u95ee\u9898 NP-complete\u3002\u8bb8\u591a\u7ec4\u5408 combinatorial\u95ee\u9898\uff0c\u4f8b\u5982\u80cc\u5305\u95ee\u9898 Knapsack problem\u3001\u65c5\u884c\u63a8\u9500\u5458\u95ee\u9898 travelling salesman problem\u548c\u5e03\u5c14\u53ef\u6ee1\u8db3\u6027\u95ee\u9898 Boolean satisfiability problem\u90fd\u662fNP\u5b8c\u5168\u95ee\u9898\u3002\u5bf9\u4e8e\u6240\u6709\u8fd9\u4e9b\u95ee\u9898\uff0c\u6700\u8457\u540d\u7684\u7b97\u6cd5\u5177\u6709\u6307\u6570\u590d\u6742\u5ea6\u3002\u5982\u679c\u8fd9\u4e9b\u95ee\u9898\u4e2d\u7684\u4efb\u4f55\u4e00\u4e2a\u90fd\u53ef\u4ee5\u5728\u786e\u5b9a\u6027\u673a\u5668\u4e0a\u5728\u591a\u9879\u5f0f\u65f6\u95f4\u5185\u6c42\u89e3\uff0c\u90a3\u5c31\u610f\u5473\u7740\u6240\u6709 NP \u95ee\u9898\u90fd\u53ef\u4ee5\u5728\u591a\u9879\u5f0f\u65f6\u95f4\u5185\u6c42\u89e3\uff0c\u6211\u4eec\u7acb\u5373\u53ef\u4ee5\u5f97\u51fa\u7ed3\u8bba\uff1aP = NP\u3002\u4e00\u822c\u8ba4\u4e3aP\u7c7b\u95ee\u9898\u548cNP\u7c7b\u95ee\u9898\u662f\u7b49\u4ef7\u7684\uff0c\u5373\u6240\u6709NP\u7c7b\u95ee\u9898\u90fd\u6709\u5728\u786e\u5b9a\u6027\u56fe\u7075\u673a\u4e0a\u4ee5\u591a\u9879\u5f0f\u65f6\u95f4\u89e3\u51b3\u7684\u65b9\u6cd5\u3002\u73b0\u5728\u6211\u4eec\u4e3b\u8981\u7684\u731c\u60f3\u662f\uff0cNP \u95ee\u9898\u7684\u6700\u574f\u60c5\u51b5\u672c\u8d28\u4e0a\u662f\u96be\u4ee5\u89e3\u51b3\u7684\uff0c\u5373P\u2260NP\u3002<\/span><\/section>\n

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\u5e76\u884c\u5904\u7406\u5668\u548c\u5206\u5e03\u5f0f\u8ba1\u7b97\u5904\u7406\u5668\u7531\u540c\u65f6\u5de5\u4f5c\u7684\u591a\u4e2a\u5904\u7406\u5668\u7ec4\u6210\u3002\u4e0d\u540c\u6a21\u578b\u4e4b\u95f4\u7684\u5dee\u5f02\u4e3b\u8981\u4f53\u73b0\u5728\u5904\u7406\u5668\u4e4b\u95f4\u7684\u4fe1\u606f\u4f20\u8f93\u65b9\u5f0f\u4e0a\u3002\u901a\u5e38\u60c5\u51b5\u4e0b\uff0c\u5728\u5e76\u884c\u8ba1\u7b97\u4e2d\u5904\u7406\u5668\u4e4b\u95f4\u7684\u6570\u636e\u4f20\u8f93\u975e\u5e38\u5feb\uff0c\u800c\u5728\u5206\u5e03\u5f0f\u8ba1\u7b97\u4e2d\uff0c\u6570\u636e\u4f20\u8f93\u901a\u8fc7\u7f51\u7edc\u5b8c\u6210\uff0c\u56e0\u6b64\u901f\u5ea6\u8981\u6162\u5f97\u591a\u3002<\/span><\/section>\n

\u5728N\u4e2a\u5904\u7406\u5668\u4e0a\u8fdb\u884c\u8ba1\u7b97\u6240\u9700\u7684\u65f6\u95f4\u81f3\u5c11\u662f\u5355\u4e2a\u5904\u7406\u5668\u6240\u9700\u65f6\u95f4\u7684N\u7684\u5546\u3002\u4f46\u5b9e\u9645\u4e0a\uff0c\u8fd9\u4e2a\u7406\u8bba\u4e0a\u7684\u6700\u4f18\u754c\u9650\u6c38\u8fdc\u4e0d\u53ef\u80fd\u8fbe\u5230\uff0c\u7531\u4e8e\u6709\u4e9b\u5b50\u4efb\u52a1\u4e0d\u80fd\u5e76\u884c\u5316\uff0c\u90e8\u5206\u5904\u7406\u5668\u4e0d\u5f97\u4e0d\u5148\u7b49\u5f85\u53e6\u4e00\u4e2a\u5904\u7406\u5668\u7684\u7ed3\u679c\u3002<\/span><\/section>\n

\u56e0\u6b64\uff0c\u4e3b\u8981\u7684\u590d\u6742\u5ea6\u95ee\u9898\u662f\u5982\u4f55\u8bbe\u8ba1\u7b97\u6cd5\uff0c\u4f7f\u5f97\u8ba1\u7b97\u65f6\u95f4\u4e0e\u5904\u7406\u5668\u6570\u91cf\u7684\u4e58\u79ef\u5c3d\u53ef\u80fd\u63a5\u8fd1\u5728\u5355\u4e2a\u5904\u7406\u5668\u4e0a\u8fdb\u884c\u540c\u4e00\u8ba1\u7b97\u6240\u9700\u7684\u65f6\u95f4\u3002<\/span><\/section>\n

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\u91cf\u5b50\u8ba1\u7b97<\/span><\/strong><\/span><\/h3>\n
\u91cf\u5b50\u8ba1\u7b97\u673a quantum computer\u662f\u4e00\u79cd\u57fa\u4e8e\u91cf\u5b50\u529b\u5b66 quantum mechanics\u7684\u8ba1\u7b97\u673a\u3002\u4e18\u5947-\u56fe\u7075\u7406\u8bba Church\u2013Turing thesis\u9002\u7528\u4e8e\u91cf\u5b50\u8ba1\u7b97\u673a\uff0c\u4e5f\u5c31\u662f\u8bf4\uff0c\u4efb\u4f55\u53ef\u4ee5\u7531\u91cf\u5b50\u8ba1\u7b97\u673a\u89e3\u51b3\u7684\u95ee\u9898\u4e5f\u53ef\u4ee5\u7531\u56fe\u7075\u673a\u89e3\u51b3\u3002\u7136\u800c\uff0c\u6709\u4e9b\u95ee\u9898\u7406\u8bba\u4e0a\u53ef\u4ee5\u7528\u91cf\u5b50\u8ba1\u7b97\u673a\u4ee5\u6781\u4f4e\u7684\u65f6\u95f4\u590d\u6742\u5ea6 time complexity\u89e3\u51b3\uff0c\u800c\u7528\u4f20\u7edf\u56fe\u7075\u673a\u5219\u65e0\u6cd5\u89e3\u51b3\u3002\u7531\u4e8e\u6ca1\u6709\u4eba\u77e5\u9053\u5982\u4f55\u5efa\u9020\u4e00\u53f0\u9ad8\u6548\u7684\u91cf\u5b50\u8ba1\u7b97\u673a\uff0c\u76ee\u524d\u8fd9\u7eaf\u7cb9\u53ea\u662f\u7406\u8bba\u4e0a\u53ef\u884c\u7684\u3002<\/span><\/section>\n

\u91cf\u5b50\u590d\u6742\u5ea6\u7406\u8bba Quantum complexity theory\u7814\u7a76\u7528\u91cf\u5b50\u8ba1\u7b97\u673a\u89e3\u51b3\u7684\u95ee\u9898\u7684\u590d\u6742\u5ea6\u7c7b\u3002\u5b83\u4e3b\u8981\u7528\u4e8e\u540e\u91cf\u5b50\u5bc6\u7801\u5b66 post-quantum cryptography\uff0c\u5305\u62ec\u8bbe\u8ba1\u80fd\u62b5\u5fa1\u91cf\u5b50\u8ba1\u7b97\u673a\u653b\u51fb\u7684\u5b89\u5168\u534f\u8bae cryptographic protocol\u3002<\/span><\/section>\n

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\u95ee\u9898\u7684\u590d\u6742\u5ea6\u662f\u89e3\u51b3\u95ee\u9898\u7b97\u6cd5(\u5305\u62ec\u672a\u77e5\u7b97\u6cd5)\u590d\u6742\u5ea6\u7684\u4e0b\u786e\u754c infimum\uff0c\u5373\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\u6240\u9700\u7684\u6700\u5c11\u65f6\u95f4\u3002\u56e0\u6b64\uff0c\u95ee\u9898\u7684\u590d\u6742\u5ea6\u6bd4\u4efb\u4f55\u89e3\u51b3\u8be5\u95ee\u9898\u7684\u7b97\u6cd5\u7684\u590d\u6742\u5ea6\u90fd\u8981\u5c0f\u3002<\/span><\/h2>\n

\u7528\u5927O\u7b26\u53f7 big O notation\u8868\u793a\u7684\u6bcf\u4e00\u4e2a\u590d\u6742\u5ea6\u90fd\u662f\u7b97\u6cd5\u7684\u590d\u6742\u5ea6\uff0c\u4e5f\u662f\u76f8\u5e94\u95ee\u9898\u7684\u590d\u6742\u5ea6\u3002<\/span><\/section>\n

\u53e6\u4e00\u65b9\u9762\uff0c\u95ee\u9898\u590d\u6742\u5ea6\u7684\u975e\u5e73\u51e1\uff08nontrivial\uff09\u4e0b\u754c\u4e00\u822c\u96be\u4ee5\u83b7\u5f97\uff0c\u5e76\u4e14\u83b7\u5f97\u8fd9\u79cd\u4e0b\u754c\u7684\u65b9\u6cd5\u5f88\u5c11\u3002<\/span><\/section>\n

\u4e3a\u4e86\u89e3\u51b3\u5927\u591a\u6570\u95ee\u9898\uff0c\u5f80\u5f80\u9700\u8981\u4e0e\u6570\u636e\u5927\u5c0f\u6210\u6bd4\u4f8b\u7684\u65f6\u95f4\u6765\u8bfb\u53d6\u6240\u6709\u8f93\u5165\u6570\u636e\u3002\u56e0\u6b64\uff0c\u8fd9\u4e9b\u95ee\u9898\u7684\u590d\u6742\u5ea6\u81f3\u5c11\u662f\u7ebf\u6027\u7684 linear\uff0c\u4f7f\u7528\u5927\u6b27\u7c73\u8304\u7b26\u53f7 big omega notation\uff0c\u8bb0\u4e3a\u590d\u6742\u5ea6\u03a9(n)\u3002<\/span><\/section>\n

\u4e00\u4e9b\u95ee\u9898\u7684\u89e3\u53ef\u80fd\u662f\u975e\u5e38\u5927\u7684\uff0c\u7279\u522b\u662f\u8ba1\u7b97\u673a\u4ee3\u6570 computer algebra\u548c\u8ba1\u7b97\u4ee3\u6570\u51e0\u4f55 computational algebraic geometry\u3002\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u590d\u6742\u5ea6\u4ee5\u8f93\u51fa\u7684\u6700\u5927\u957f\u5ea6\u4e3a\u4e0b\u754c\uff0c\u56e0\u6b64\u8f93\u51fa\u5fc5\u987b\u88ab\u5199\u5165\u3002\u4f8b\u5982\uff0c\u5982\u679c\u89e3\u7684\u4e2a\u6570\u662f\u6709\u9650\u7684\uff0cn\u4e2ad\u6b21\u4e0d\u786e\u5b9a\u591a\u9879\u5f0f\u65b9\u7a0b\u7ec4 system of n polynomial equations of degree d in indeterminates \u53ef\u80fd\u6709\u591a\u8fbed^n\u4e2a\u590d\u89e3(\u8fd9\u662f\u8d1d\u4f50\u5b9a\u7406 B\u00e9zout’s theorem)\u3002\u7531\u4e8e\u8fd9\u4e9b\u89e3\u5fc5\u987b\u88ab\u5199\u5165\uff0c\u6240\u4ee5\u8fd9\u4e2a\u95ee\u9898\u7684\u590d\u6742\u5ea6\u662f\u03a9(d^n)\u3002\u5bf9\u4e8e\u8fd9\u4e2a\u95ee\u9898\uff0c\u5df2\u77e5\u4e00\u4e2a\u590d\u6742\u5ea6\u4e3ad^(O(n))\u7684\u7b97\u6cd5\uff0c\u56e0\u6b64\u53ef\u4ee5\u8ba4\u4e3a\u662f\u6e10\u8fd1\u62df\u6700\u4f18\u7684\u3002<\/span><\/section>\n

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\u83b7\u5f97\u590d\u6742\u5ea6\u4e0b\u9650\u7684\u6807\u51c6\u65b9\u6cd5\u5305\u62ec\u5c06\u4e00\u4e2a\u95ee\u9898\u8f6c\u5316\u4e3a\u53e6\u4e00\u4e2a\u95ee\u9898\u3002\u66f4\u51c6\u786e\u5730\u8bf4\uff0c\u5047\u8bbe\u4e00\u4e2a\u5927\u5c0f\u4e3an\u7684\u95ee\u9898A\u53ef\u4ee5\u7f16\u7801\u6210\u5927\u5c0f\u4e3af(n)\u7684\u95ee\u9898B\uff0c\u5219\u95ee\u9898A\u7684\u590d\u6742\u5ea6\u4e3a\u03a9(g(n))\u3002\u4e0d\u5931\u4e00\u822c\u6027\u5730\uff0c\u6211\u4eec\u53ef\u4ee5\u5047\u8bbe\u51fd\u6570f\u968f\u7740n\u7684\u589e\u52a0\u800c\u589e\u52a0\uff0c\u5e76\u4e14\u6709\u4e00\u4e2a\u53cd\u51fd\u6570 inverse function\uff0c\u90a3\u4e48\u95ee\u9898B\u7684\u590d\u6742\u5ea6\u5c31\u662f\u03a9(g(h(n)))\u3002\u8fd9\u4e2a\u65b9\u6cd5\u53ef\u4ee5\u7528\u6765\u8bc1\u660e\uff0c\u82e5P \u2260 NP(\u4e00\u4e2a\u672a\u89e3\u51b3\u7684\u731c\u60f3) \uff0c\u5bf9\u4e8e\u6bcf\u4e2a\u6b63\u6574\u6570k\uff0c\u6bcf\u4e2aNP\u5b8c\u5168\u95ee\u9898 NP-complete problem\u7684\u590d\u6742\u5ea6\u90fd\u662f\u03a9(n^k)\u3002<\/span><\/section>\n

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\u8bc4\u4f30\u7b97\u6cd5\u7684\u590d\u6742\u5ea6\u662f\u7b97\u6cd5\u8bbe\u8ba1 algorithm design\u7684\u4e00\u4e2a\u91cd\u8981\u7ec4\u6210\u90e8\u5206\uff0c\u56e0\u4e3a\u8fd9\u7ed9\u51fa\u4e86\u4e00\u4e2a\u7b97\u6cd5\u5173\u4e8e\u9884\u671f\u6027\u80fd\u7684\u6709\u7528\u4fe1\u606f\u3002<\/span>
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\u6709\u4e00\u4e2a\u5e38\u89c1\u7684\u8bef\u89e3\uff0c\u7531\u4e8e\u6469\u5c14\u5b9a\u5f8b Moore’s law\u5047\u5b9a\u4e86\u73b0\u4ee3\u8ba1\u7b97\u673a\u529f\u7387\u7684\u6307\u6570\u589e\u957f exponential growth\uff0c\u5bf9\u7b97\u6cd5\u590d\u6742\u5ea6\u7684\u8bc4\u4f30\u5c06\u53d8\u5f97\u4e0d\u90a3\u4e48\u91cd\u8981\u3002\u8fd9\u662f\u9519\u8bef\u7684\uff0c\u56e0\u4e3a\u8fd9\u79cd\u529f\u7387\u589e\u52a0\u540c\u6837\u4e5f\u4f1a\u5bb9\u4f7f\u5f97\u5904\u7406\u8f83\u5927\u7684\u8f93\u5165\u6570\u636e\uff08\u5927\u6570\u636e\uff09\u6210\u4e3a\u53ef\u80fd\u3002\u4f8b\u5982\uff0c\u5f53\u4e00\u4e2a\u4eba\u60f3\u8981\u6309\u5b57\u6bcd\u987a\u5e8f\u5bf9\u6570\u767e\u4e2a\u6761\u76ee\u7684\u5217\u8868\u8fdb\u884c\u6392\u5e8f\u65f6\uff0c\u6bd4\u5982\u4e00\u672c\u4e66\u7684\u53c2\u8003\u4e66\u76ee\uff0c\u4efb\u4f55\u7b97\u6cd5\u90fd\u5e94\u8be5\u5728\u4e0d\u5230\u4e00\u79d2\u7684\u65f6\u95f4\u5185\u5c31\u80fd\u6b63\u5e38\u5de5\u4f5c\u3002\u53e6\u4e00\u65b9\u9762\uff0c\u5bf9\u4e8e\u4e00\u4e2a\u5305\u542b100\u4e07\u4e2a\u6761\u76ee\u7684\u5217\u8868(\u4f8b\u5982\u4e00\u4e2a\u5927\u57ce\u9547\u7684\u7535\u8bdd\u53f7\u7801) \uff0c\u9700\u8981O(n^2)\u6b21\u6bd4\u8f83\u7684\u57fa\u672c\u7b97\u6cd5\uff0c\u987b\u8fdb\u884c1\u4e07\u4ebf\u6b21\u6bd4\u8f83\u8fd0\u7b97\uff0c\u5373\u4ee5\u6bcf\u79d21000\u4e07\u6b21\u7684\u901f\u5ea6\u8fdb\u884c\u6bd4\u8f83\u9700\u8981\u5927\u7ea63\u4e2a\u5c0f\u65f6\u3002\u53e6\u4e00\u65b9\u9762\uff0c\u5feb\u901f\u6392\u5e8f\u548c\u5408\u5e76\u6392\u5e8f \u53ea\u9700\u8981nlog2n\u6b21\u6bd4\u8f83(\u524d\u8005\u4e3a\u5e73\u5747\u60c5\u51b5\u590d\u6742\u5ea6\uff0c\u540e\u8005\u4e3a\u6700\u574f\u60c5\u51b5\u590d\u6742\u5ea6)\u3002\u8fd9\u5927\u7ea6\u662f3000\u4e07\u6b21\u6bd4\u8f83\uff0c\u4ee5\u6bcf\u79d21000\u4e07\u6b21\u6bd4\u8f83\u8ba1\u7b97\uff0c\u53ea\u9700\u89813\u79d2\u949f\u3002<\/span><\/section>\n

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\u56e0\u6b64\uff0c\u5bf9\u590d\u6742\u5ea6\u7684\u8bc4\u4f30\u5141\u8bb8\u5728\u7f16\u7a0b\u5b9e\u73b0\u4e4b\u524d\u5c31\u6d88\u9664\u8bb8\u591a\u4f4e\u6548\u7387\u7684\u7b97\u6cd5\u3002\u8fd9\u4e5f\u53ef\u7528\u4e8e\u5728\u4e0d\u7528\u6d4b\u8bd5\u6240\u6709\u53d8\u91cf\u7684\u60c5\u51b5\u4e0b\u8c03\u4f18\u590d\u6742\u7684\u7b97\u6cd5\u3002\u901a\u8fc7\u786e\u5b9a\u590d\u6742\u7b97\u6cd5\u4e2d\u6700\u590d\u6742\u7684\u6b65\u9aa4\uff0c\u5bf9\u590d\u6742\u5ea6\u7684\u7814\u7a76\u8fd8\u53ef\u4ee5\u5c06\u91cd\u70b9\u653e\u5728\u8fd9\u4e9b\u6b65\u9aa4\u4e0a\uff0c\u4ece\u800c\u63d0\u9ad8\u5b9e\u73b0\u7684\u6548\u7387\u3002<\/span><\/section>\n

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\u627e\u5230\u4f60\u6df7\u4e71\u751f\u6d3b\u4e2d\u7684\u79e9\u5e8f\u2014\u2014Kolmogorov\u590d\u6742\u5ea6<\/strong><\/span><\/a>
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\u5982\u4f55\u5224\u65ad\u4e00\u6bb5\u8bdd\u4fe1\u606f\u91cf\u662f\u5927\u662f\u5c0f\uff1f\u5728\u9999\u519c\u90a3\u91cc\uff0c\u53ef\u4ee5\u7528\u201c\u514b\u670d\u4e86\u591a\u5c11\u4e0d\u786e\u5b9a\u6027\u201d\u6765\u63cf\u8ff0\u3002\u800c\u5728\u67ef\u5c14\u83ab\u54e5\u6d1b\u592b\u90a3\u91cc\uff0c\u8981\u770b\u201c\u7528\u591a\u957f\u7684\u4ee3\u7801\u80fd\u751f\u6210\u8fd9\u53e5\u8bdd\u201d\u3002<\/span><\/section>\n

\u91cf\u5b50\u8ba1\u7b97\u65f6\u4ee3\u7684\u673a\u5668\u5b66\u4e60<\/span><\/strong><\/section>\n
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\u73b0\u5728\u673a\u5668\u5b66\u4e60\u8fd9\u4e48\u706b\uff0c\u5927\u5bb6\u81ea\u7136\u60f3\u77e5\u9053\u4ee5\u540e20\u300130\u5e74\u4eba\u5de5\u667a\u80fd\u4f1a\u5f80\u54ea\u4e2a\u65b9\u5411\u53d1\u5c55\u3002\u800c\u6b63\u5982\u6211\u4eec\u4e4b\u524d\u8bf4\u5230\u7684\uff0c\u4eba\u5de5\u667a\u80fd\u7684\u53d1\u5c55\u79bb\u4e0d\u5f00\u8ba1\u7b97\u529b\u6309\u6469\u5c14\u5b9a\u5f8b\u5730\u63d0\u5347\uff0c\u5f53\u6211\u4eec\u628a\u82af\u7247\u505a\u5f97\u8d8a\u6765\u8d8a\u5c0f\uff0c\u6676\u4f53\u7ba1\u7684\u5c3a\u5bf8\u8d8a\u6765\u8d8a\u63a5\u8fd1\u5355\u4e2a\u539f\u5b50\u7684\u5927\u5c0f\uff0c\u8fd9\u4e2a\u65f6\u5019\u91cf\u5b50\u6548\u5e94\u5c31\u4f1a\u51fa\u73b0\uff0c\u5e72\u6270\u5668\u4ef6\u7684\u6b63\u5e38\u5de5\u4f5c\uff0c\u6bd4\u5982\u4ee5\u524d\u6676\u4f53\u7ba1\u53ef\u4ee5\u901a\u8fc7\u7535\u6d41\u662f\u5426\u901a\u8fc7\u6765\u8868\u793a\u5f00\u548c\u5173\uff0c\u5f53\u6709\u91cf\u5b50\u6548\u5e94\u540e\uff0c\u539f\u672c\u4e0d\u80fd\u6d41\u8fc7\u7684\u7535\u5b50\u73b0\u5728\u6709\u4e00\u5b9a\u7684\u6982\u7387\u201d\u96a7\u7a7f\u201c\uff08tunnel\uff09\u8fc7\u53bb\uff0c\u5bfc\u81f4\u6676\u4f53\u7ba1\u6ca1\u6cd5\u7ee7\u7eed\u5de5\u4f5c\u4e86\u3002\u6240\u4ee5\u6469\u5c14\u5b9a\u5f8b\u4f1a\u4e0d\u518d\u6210\u7acb\u4e86\uff0c\u90a3\u6211\u4eec\u600e\u4e48\u529e\uff1f<\/span><\/section>\n
\u4e00\u4e2a\u65b9\u6848\u5c31\u662f\u91cf\u5b50\u8ba1\u7b97\u82af\u7247\uff0c\u50a8\u5b58\u7684\u5bf9\u8c61\u4e0d\u518d\u662fbit\uff0c\u800c\u662fqubit\uff0c\u5916\u90e8\u8bbe\u5907\u628a\u547d\u4ee4\u53d1\u9001\u7ed9\u82af\u7247\uff0c\u82af\u7247\u4ee5\u91cf\u5b50\u7684\u65b9\u5f0f\u5904\u7406\u5b8c\u4fe1\u606f\u540e\u518d\u628a\u7ed3\u679c\u4f20\u51fa\u53bb\u3002\u7531\u4e8e\u91cf\u5b50\u6548\u5e94\u9700\u8981\u6781\u4f4e\u7684\u6e29\u5ea6\uff08\u6bebK\u91cf\u7ea7\uff09\uff0c\u6211\u4eec\u73b0\u5728\u770b\u5230\u7684\u623f\u95f4\u90a3\u4e48\u5927\u7684\u91cf\u5b50\u8ba1\u7b97\u673a\u5176\u5b9e\u7edd\u5927\u90e8\u5206\u662f\u51b7\u5374\u88c5\u7f6e\uff0c\u771f\u6b63\u7684\u91cf\u5b50\u7684\u90e8\u5206\u53ea\u6709\u6700\u4e2d\u5fc3\u7684\u90a3\u5757\u82af\u7247\u3002<\/span><\/section>\n

\u5982\u4f55\u628a\u91cf\u5b50\u8ba1\u7b97\u673a\u8c03\u6559\u6210\u7ec8\u6781\u968f\u673a\u6570\u751f\u6210\u5668\uff1f<\/span>\u5982\u4f55\u628a\u91cf\u5b50\u8ba1\u7b97\u673a\u8c03\u6559\u6210\u7ec8\u6781\u968f\u673a\u6570\u751f\u6210\u5668\uff1f<\/span>\u5982\u4f55\u628a\u91cf\u5b50\u8ba1\u7b97\u673a\u8c03\u6559\u6210\u7ec8\u6781\u968f\u673a\u6570\u751f\u6210\u5668\uff1f<\/span><\/span><\/section>\n

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\u5982\u4f55\u628a\u91cf\u5b50\u8ba1\u7b97\u673a\u8c03\u6559\u6210\u7ec8\u6781\u968f\u673a\u6570\u751f\u6210\u5668\uff1f<\/a><\/span><\/strong><\/section>\n
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\u6211\u4eec\u7684\u76ee\u6807\u662f\u83b7\u5f97\u4e00\u4e2a\u5b8c\u5168\u968f\u673a\u4e14\u6ed4\u6ed4\u4e0d\u7edd\u7684 01 \u6570\u636e\u6d41<\/span><\/span><\/section>\n
\u968f\u673a\u6570\u5728\u8ba1\u7b97\u673a\u548c\u5bc6\u7801\u5b66\u7b49\u9886\u57df\u6709\u5e7f\u6cdb\u7684\u5e94\u7528\uff0c\u76ee\u524d\u5df2\u7ecf\u6709\u4e86\u8bb8\u591a\u751f\u6210\u968f\u673a\u6570\u7684\u65b9\u6cd5\u3002\u4f46\u4e8b\u5b9e\u4e0a\uff0c\u4efb\u4f55\u57fa\u4e8e\u7ecf\u5178\u529b\u5b66\u7684\u8fc7\u7a0b\u6240\u4ea7\u751f\u7684\u968f\u673a\u6570\uff0c\u672c\u8d28\u4e0a\u90fd\u4e0d\u662f\u771f\u968f\u673a\u7684\u3002\u800c\u91cf\u5b50\u4e16\u754c\u7279\u6709\u6027\u8d28\u4f7f\u5f97\u53ef\u4ee5\u4ece\u4e2d\u4ea7\u751f\u53ef\u4ee5\u9a8c\u8bc1\u7684\u7eaf\u968f\u673a (pure random) \u6570\u3002\u672c\u6587\u5c06\u4ecb\u7ecd\u4e24\u4e2a\u628a\u91cf\u5b50\u8ba1\u7b97\u673a\u53d8\u6210\u968f\u673a\u6570\u5236\u9020\u5de5\u5382\u7684\u6280\u672f\u3002<\/span><\/section>\n

\u5f20\u91cf\u7f51\u7edc\u89e3\u7801\u5668\u52a9\u529b\u91cf\u5b50\u7ea0\u9519 | \u590d\u6742\u6027\u79d1\u5b66\u9876\u520a\u7cbe\u90096\u7bc7<\/a><\/span><\/strong><\/section>\n
2021\u5e747\u670819\u65e5-7\u670825\u65e5\u6765\u81eaComplexity Express\u7684\u590d\u6742\u6027\u79d1\u5b66\u8bba\u6587\u7cbe\u9009\u3002<\/span><\/section>\n

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\u767e\u79d1\u9879\u76ee\u5fd7\u613f\u8005\u62db\u52df<\/span><\/strong><\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

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\u4f5c\u4e3a\u96c6\u667a\u767e\u79d1\u9879\u76ee\u56e2\u961f\u7684\u6210\u5458\uff0c\u672c\u6587\u5185\u5bb9\u7531<\/span>\u5c0f\u7af9\u51c9<\/span><\/strong>\u7ffb\u8bd1\uff0c<\/span>Ricky<\/span><\/strong>\u5ba1\u6821\uff0c<\/span>\u7cd6\u7cd6<\/span><\/strong>\u7f16\u8f91\u3002<\/span>\u6211\u4eec\u4e5f\u4e3a\u6bcf\u4f4d\u4f5c\u8005\u548c\u5fd7\u613f\u8005\u51c6\u5907\u4e86\u4e13\u5c5e\u7b80\u4ecb\u548c\u4e2a\u4eba\u96c6\u667a\u767e\u79d1\u4e3b\u9875\uff0c\u66f4\u591a\u4fe1\u606f\u53ef\u4ee5\u8bbf\u95ee\u5176\u96c6\u667a\u767e\u79d1\u4e2a\u4eba\u4e3b\u9875\u3002<\/span><\/section>\n
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\u4ee5\u4e0a\u5185\u5bb9\u90fd\u662f\u6211\u4eec\u505a\u8fd9\u9879\u76ee\u7684\u8d77\u70b9\uff0c\u4f5c\u4e3a\u6765\u81ea\u4e0d\u540c\u5b66\u79d1\u548c\u9886\u57df\u7684\u5fd7\u613f\u8005\uff0c\u6211\u4eec\u5efa\u7acb\u8d77\u4e00\u4e2a\u6709\u6548\u7684\u767e\u79d1\u56e2\u961f\uff0c\u5206\u914d\u6709\u5ba1\u6821\u3001\u7ffb\u8bd1\u3001\u7f16\u8f91\u3001\u5ba3\u4f20\u7b49\u5de5\u4f5c\u3002\u6211\u4eec\u79c9\u6301\uff1a\u77e5\u8bc6\u4ece\u6211\u800c\u6765\uff0c\u95ee\u9898\u5230\u6211\u4e3a\u6b62\u7684\u4fe1\u5ff5\uff0c\u8ba4\u771f\u8d1f\u8d23\u7f16\u64b0\u6bcf\u4e00\u4e2a\u8bcd\u6761\u3002<\/span>
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\u5728\u8fd9\u91cc\u4ece\u590d\u6742\u6027\u77e5\u8bc6\u51fa\u53d1\u4e0e\u4f19\u4f34\u540c\u884c\uff0c\u540c\u65f6\u6211\u4eec\u5e0c\u671b\u6709\u66f4\u591a\u5fd7\u613f\u8005\u52a0\u5165\u8fd9\u4e2a\u56e2\u961f\uff0c\u4f7f\u767e\u79d1\u8bcd\u6761\u5185\u5bb9\u5f97\u5230\u6269\u5145\uff0c\u5e76\u4e3a\u6bcf\u4f4d\u5fd7\u613f\u8005\u63d0\u4f9b\u76f8\u5e94\u5956\u52b1\u4e0e\u8d44\u6e90\uff0c\u5efa\u7acb\u4e2a\u4eba\u4e3b\u9875\u4e0e\u8d21\u732e\u8bb0\u5f55\uff0c\u4f7f\u5176\u80fd\u591f\u7ee7\u7eed\u63a2\u7d22\u590d\u6742\u4e16\u754c\u3002<\/span><\/p>\n


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\u5982\u679c\u4f60\u6709\u610f\u53c2\u4e0e\u66f4\u52a0\u7cfb\u7edf\u7cbe\u7ec6\u7684\u5206\u5de5\uff0c\u626b\u63cf\u4e8c\u7ef4\u7801\u586b\u5199\u62a5\u540d\u8868\uff0c\u6211\u4eec\u671f\u5f85\u4f60\u7684\u52a0\u5165\uff01<\/span><\/p>\n


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\u96c6\u667a\u767e\u79d1\u62a5\u540d\u8868<\/span><\/section>\n


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\u6765\u6e90\uff1a\u96c6\u667a\u767e\u79d1<\/p>\n

\u7f16\u8f91\uff1a\u738b\u5efa\u840d<\/p>\n<\/section>\n<\/blockquote>\n<\/section>\n


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\u63a8\u8350\u9605\u8bfb<\/span><\/strong><\/span><\/section>\n