{"id":292571,"date":"2024-05-20T14:22:08","date_gmt":"2024-05-20T06:22:08","guid":{"rendered":"https:\/\/docs.pingcode.com\/ask\/ask-ask\/292571.html"},"modified":"2024-05-20T14:22:22","modified_gmt":"2024-05-20T06:22:22","slug":"fkt-algorithm%e6%98%af%e4%bb%80%e4%b9%88","status":"publish","type":"post","link":"https:\/\/docs.pingcode.com\/ask\/292571.html","title":{"rendered":"FKT algorithm\u662f\u4ec0\u4e48"},"content":{"rendered":"

\"FKT<\/p>\n

FKT\u7b97\u6cd5\u662f\u4e00\u79cd\u7528\u4e8e\u8ba1\u7b97\u5e73\u9762\u56fe\u7684\u5b8c\u7f8e\u5339\u914d\u6570\u7684\u9ad8\u6548\u7b97\u6cd5\u3002\u5b83\u6839\u636e\u56fe\u7684\u62d3\u6251\u7ed3\u6784\uff0c\u901a\u8fc7\u6d88\u53bb\u6cd5\u548cPfaffian\u65b9\u6cd5\u8ba1\u7b97\u5f97\u5230\u5b8c\u7f8e\u5339\u914d\u7684\u603b\u6570<\/strong>\u3002\u8fd9\u4e00\u7b97\u6cd5\u7684\u6838\u5fc3\u601d\u60f3\u5728\u4e8e\u5229\u7528\u56fe\u7684\u5e73\u9762\u6027\u8d28\u548c\u56fe\u7684\u8fb9\u754c\u6761\u4ef6\uff0c\u901a\u8fc7\u4e00\u7cfb\u5217\u7684\u6570\u5b66\u8fd0\u7b97\u7b80\u5316\u8ba1\u7b97\u6d41\u7a0b\uff0c\u6700\u7ec8\u8fbe\u5230\u5feb\u901f\u8ba1\u7b97\u56fe\u7684\u5b8c\u7f8e\u5339\u914d\u6570\u7684\u76ee\u7684\u3002\u7279\u522b\u5730\uff0cFKT\u7b97\u6cd5\u5bf9\u4e8e\u89e3\u51b3\u67d0\u4e9b\u7279\u5b9a\u7c7b\u578b\u7684\u8ba1\u6570\u95ee\u9898\uff0c\u6bd4\u5982\u5728\u7269\u7406\u5b66\u4e2d\u7684\u7edf\u8ba1\u6a21\u578b\u8ba1\u7b97\u4e2d\uff0c\u6709\u91cd\u8981\u7684\u5e94\u7528\u4ef7\u503c<\/strong>\u3002<\/p>\n<\/p>\n

\u8be6\u7ec6\u6765\u8bf4\uff0cFKT\u7b97\u6cd5\u901a\u8fc7\u5c06\u590d\u6742\u7684\u56fe\u8f6c\u5316\u4e3a\u7b80\u5355\u591a\u8fb9\u5f62\u7f51\u7edc\u7ed3\u6784\uff0c\u8fdb\u800c\u5229\u7528\u8fb9\u754c\u6761\u4ef6\u548c\u5bf9\u89d2\u7ebf\u7406\u8bba\uff0c\u901a\u8fc7\u77e9\u9635\u884c\u5217\u5f0f\u7684\u8ba1\u7b97\u6765\u6c42\u89e3\u3002\u5728\u8fd9\u4e00\u8fc7\u7a0b\u4e2d\uff0c\u5e73\u9762\u56fe\u7684\u4efb\u4f55\u4e00\u4e2a\u9762\u90fd\u53ef\u4ee5\u88ab\u770b\u4f5c\u662f\u4e00\u4e2a\u591a\u8fb9\u5f62\uff0c\u800c\u7b97\u6cd5\u7684\u5173\u952e\u5728\u4e8e\u5982\u4f55\u5de7\u5999\u5730\u9009\u62e9\u8fde\u63a5\u8fd9\u4e9b\u591a\u8fb9\u5f62\u7684\u5bf9\u89d2\u7ebf\uff0c\u4f7f\u5f97\u6574\u4e2a\u56fe\u88ab\u5206\u5272\u6210\u53ea\u542b\u6709\u5076\u6570\u4e2a\u9876\u70b9\u7684\u591a\u8fb9\u5f62\uff0c\u8fd9\u6837\u4fbf\u53ef\u5229\u7528Pfaffian\u6765\u6c42\u89e3\u5176\u5339\u914d\u6570\u3002\u7531\u4e8e\u8fd9\u4e00\u8fc7\u7a0b\u4e2d\u91c7\u7528\u4e86\u6570\u5b66\u4e0a\u7684\u6d88\u5143\u6cd5\u548c\u884c\u5217\u5f0f\u8ba1\u7b97\uff0cFKT\u7b97\u6cd5\u56e0\u6b64\u5728\u8ba1\u7b97\u4e0a\u76f8\u8f83\u4e8e\u4f20\u7edf\u7684\u66b4\u529b\u641c\u7d22\u6216\u52a8\u6001\u89c4\u5212\u65b9\u6cd5\u6709\u663e\u8457\u7684\u6548\u7387\u63d0\u5347\u3002<\/p>\n<\/p>\n

\u4e00\u3001FKT\u7b97\u6cd5\u7684\u539f\u7406<\/h2>\n<\/p>\n

FKT\u7b97\u6cd5\u7684\u64cd\u4f5c\u539f\u7406\u662f\u57fa\u4e8e\u56fe\u8bba\u4e2d\u7684\u5339\u914d\u7406\u8bba\u548c\u77e9\u9635\u7406\u8bba\uff0c\u5b83\u901a\u8fc7\u5bf9\u56fe\u7684\u7ed3\u6784\u8fdb\u884c\u7279\u5b9a\u7684\u6570\u5b66\u5904\u7406\uff0c\u7b80\u5316\u4e86\u8ba1\u7b97\u8fc7\u7a0b\u3002<\/p>\n<\/p>\n

\u9996\u5148\uff0cFKT\u7b97\u6cd5\u8003\u8651\u7684\u662f\u5e73\u9762\u56fe\uff0c\u5373\u56fe\u5728\u5e73\u9762\u4e0a\u753b\u65f6\u4efb\u610f\u4e24\u6761\u8fb9\u90fd\u4e0d\u76f8\u4ea4\u7684\u56fe\u3002\u8fd9\u7c7b\u56fe\u7684\u7279\u6027\u662f\u5173\u952e\u56e0\u7d20\u4e4b\u4e00\uff0c\u56e0\u4e3a\u5e73\u9762\u6027\u51b3\u5b9a\u4e86\u56fe\u53ef\u4ee5\u901a\u8fc7\u4e00\u7cfb\u5217\u53d8\u6362\u8f6c\u5316\u4e3a\u7279\u5b9a\u5f62\u5f0f\u7684\u77e9\u9635\uff0c\u800c\u8fd9\u4e2a\u77e9\u9635\u7684\u6027\u8d28\u53ef\u4ee5\u88ab\u7528\u6765\u7b80\u5316\u8ba1\u7b97\u3002<\/p>\n<\/p>\n

\u5176\u6b21\uff0c\u7b97\u6cd5\u901a\u8fc7\u9009\u53d6\u56fe\u4e2d\u7684\u4e00\u4e2a\u751f\u6210\u6811\uff0c\u4ee5\u53ca\u5728\u8be5\u751f\u6210\u6811\u57fa\u7840\u4e0a\u9009\u53d6\u4e00\u7ec4\u7279\u5b9a\u7684\u5bf9\u89d2\u7ebf\uff0c\u5bf9\u56fe\u8fdb\u884c\u53d8\u6362\u3002\u8fd9\u4e00\u6b65\u7684\u76ee\u7684\u662f\u4e3a\u4e86\u8ba9\u6574\u4e2a\u56fe\u5f62\u6210\u4e00\u4e2a\u6216\u591a\u4e2a\u95ed\u5408\u7684\u73af\uff0c\u8fd9\u6837\u5728\u73af\u4e0a\u7684\u6bcf\u4e2a\u9876\u70b9\u90fd\u4f1a\u6709\u5076\u6570\u4e2a\u8fde\u63a5\u70b9\uff0c\u8fd9\u662f\u8ba1\u7b97\u5b8c\u7f8e\u5339\u914d\u6570\u65f6\u7684\u91cd\u8981\u6761\u4ef6\u3002<\/p>\n<\/p>\n

\u4e8c\u3001FKT\u7b97\u6cd5\u7684\u5e94\u7528<\/h2>\n<\/p>\n

FKT\u7b97\u6cd5\u7684\u5e94\u7528\u975e\u5e38\u5e7f\u6cdb\uff0c\u7279\u522b\u662f\u5728\u7406\u8bba\u7269\u7406\u548c\u5316\u5b66\u9886\u57df\uff0c\u5b83\u7528\u4e8e\u8ba1\u7b97\u5206\u5b50\u4e2d\u539f\u5b50\u914d\u5bf9\u7684\u53ef\u80fd\u6027\u3001\u6676\u4f53\u7ed3\u6784\u7684\u7a33\u5b9a\u6027\u4ee5\u53ca\u5728\u91cf\u5b50\u573a\u8bba\u4e2d\u7edf\u8ba1\u6a21\u578b\u7684\u5206\u6790\u7b49\u65b9\u9762\u3002<\/p>\n<\/p>\n

\u5728\u7269\u7406\u5b66\u4e2d\uff0cFKT\u7b97\u6cd5\u88ab\u7528\u4e8e\u89e3\u51b3Ising\u6a21\u578b\u5728\u5e73\u9762\u56fe\u4e0a\u7684\u8ba1\u7b97\u95ee\u9898\u3002Ising\u6a21\u578b\u662f\u7814\u7a76\u7269\u8d28\u7684\u78c1\u6027\u7b49\u7269\u7406\u6027\u8d28\u7684\u4e00\u4e2a\u57fa\u7840\u6a21\u578b\uff0c\u901a\u8fc7\u8ba1\u7b97\u4e0d\u540c\u914d\u7f6e\u4e0b\u7684\u914d\u5bf9\u65b9\u5f0f\uff0c\u53ef\u4ee5\u9884\u6d4b\u7269\u8d28\u5728\u4e0d\u540c\u6761\u4ef6\u4e0b\u7684\u7269\u7406\u72b6\u6001\u3002<\/p>\n<\/p>\n

\u5728\u5316\u5b66\u4e2d\uff0cFKT\u7b97\u6cd5\u53ef\u4ee5\u7528\u6765\u8ba1\u7b97\u5927\u5206\u5b50\u4e2d\u7684\u539f\u5b50\u914d\u5bf9\u65b9\u6848\uff0c\u8fd9\u5bf9\u4e8e\u7406\u89e3\u5206\u5b50\u7684\u5316\u5b66\u7ed3\u6784\u548c\u53cd\u5e94\u9014\u5f84\u6709\u91cd\u8981\u610f\u4e49\u3002\u7279\u522b\u662f\u5728\u6709\u673a\u5316\u5b66\u4e2d\uff0c\u590d\u6742\u7684\u6709\u673a\u5206\u5b50\u5f80\u5f80\u6709\u591a\u79cd\u53ef\u80fd\u7684\u914d\u7f6e\uff0c\u800c\u901a\u8fc7FKT\u7b97\u6cd5\u53ef\u4ee5\u6709\u6548\u5730\u8ba1\u7b97\u51fa\u8fd9\u4e9b\u914d\u7f6e\u7684\u6570\u91cf\uff0c\u4e3a\u5316\u5b66\u7814\u7a76\u63d0\u4f9b\u7406\u8bba\u652f\u6301\u3002<\/p>\n<\/p>\n

\u4e09\u3001FKT\u7b97\u6cd5\u7684\u4f18\u52bf<\/h2>\n<\/p>\n

FKT\u7b97\u6cd5\u7684\u4e3b\u8981\u4f18\u52bf\u5728\u4e8e\u5176\u9ad8\u6548\u7387\u548c\u5e7f\u6cdb\u7684\u9002\u7528\u6027<\/strong>\u3002\u4e0e\u5176\u4ed6\u7b97\u6cd5\u76f8\u6bd4\uff0cFKT\u7b97\u6cd5\u53ef\u4ee5\u5728\u591a\u9879\u5f0f\u65f6\u95f4\u5185\u5b8c\u6210\u8ba1\u7b97\uff0c\u8fd9\u5bf9\u4e8e\u90a3\u4e9b\u9700\u8981\u5904\u7406\u5927\u89c4\u6a21\u56fe\u7684\u95ee\u9898\u975e\u5e38\u5173\u952e\u3002<\/p>\n<\/p>\n

\u6b64\u5916\uff0cFKT\u7b97\u6cd5\u7684\u53e6\u4e00\u4e2a\u91cd\u8981\u4f18\u52bf\u662f\u5176\u5bf9\u4e8e\u5e73\u9762\u56fe\u7684\u8ba1\u7b97\u9002\u7528\u6027\u3002\u5728\u8bb8\u591a\u5b9e\u9645\u5e94\u7528\u4e2d\uff0c\u9700\u8981\u5904\u7406\u7684\u56fe\u5f80\u5f80\u90fd\u662f\u5e73\u9762\u56fe\uff0cFKT\u7b97\u6cd5\u6070\u597d\u9002\u7528\u4e8e\u8fd9\u79cd\u60c5\u51b5\uff0c\u8fd9\u5927\u5927\u63d0\u9ad8\u4e86\u5176\u5b9e\u7528\u4ef7\u503c\u3002<\/p>\n<\/p>\n

\u56db\u3001FKT\u7b97\u6cd5\u7684\u6311\u6218<\/h2>\n<\/p>\n

\u5c3d\u7ba1FKT\u7b97\u6cd5\u5728\u5f88\u591a\u65b9\u9762\u8868\u73b0\u51fa\u8272\uff0c\u4f46\u5b83\u4e5f\u6709\u5176\u5c40\u9650\u6027\u3002\u4e3b\u8981\u7684\u6311\u6218\u5728\u4e8e\uff0cFKT\u7b97\u6cd5\u53ea\u9002\u7528\u4e8e\u5e73\u9762\u56fe\uff0c\u5bf9\u4e8e\u975e\u5e73\u9762\u56fe\u6216\u8005\u56fe\u7684\u5e73\u9762\u6027\u96be\u4ee5\u5224\u65ad\u7684\u60c5\u51b5\uff0cFKT\u7b97\u6cd5\u65e0\u6cd5\u76f4\u63a5\u5e94\u7528\u3002<\/p>\n<\/p>\n

\u6b64\u5916\uff0c\u5c3d\u7ba1FKT\u7b97\u6cd5\u7684\u7406\u8bba\u90e8\u5206\u76f8\u5bf9\u6210\u719f\uff0c\u5c06\u5176\u5e94\u7528\u5230\u5b9e\u9645\u95ee\u9898\u4e2d\u65f6\uff0c\u4ecd\u7136\u9700\u8981\u8003\u8651\u5982\u4f55\u9ad8\u6548\u5730\u5b9e\u65bd\u7b97\u6cd5\uff0c\u4ee5\u53ca\u5982\u4f55\u5904\u7406\u7b97\u6cd5\u5728\u67d0\u4e9b\u7279\u5b9a\u60c5\u51b5\u4e0b\u7684\u6570\u503c\u7a33\u5b9a\u6027\u95ee\u9898\u3002\u8fd9\u4e9b\u5b9e\u9645\u64cd\u4f5c\u4e0a\u7684\u6311\u6218\u9700\u8981\u5728\u5e94\u7528FKT\u7b97\u6cd5\u65f6\u4e88\u4ee5\u91cd\u89c6\u3002<\/p>\n<\/p>\n

\u603b\u7684\u6765\u8bf4\uff0cFKT\u7b97\u6cd5\u4f5c\u4e3a\u8ba1\u7b97\u56fe\u7684\u5b8c\u7f8e\u5339\u914d\u6570\u7684\u6709\u6548\u5de5\u5177\uff0c\u4e0d\u4ec5\u5177\u6709\u7406\u8bba\u4e0a\u7684\u91cd\u8981\u610f\u4e49\uff0c\u4e5f\u5728\u5b9e\u9645\u5e94\u7528\u4e2d\u5c55\u73b0\u51fa\u5e7f\u6cdb\u7684\u5e94\u7528\u524d\u666f\u3002\u5c3d\u7ba1\u5b58\u5728\u4e00\u4e9b\u6311\u6218\uff0c\u4f46\u901a\u8fc7\u4e0d\u65ad\u7684\u7814\u7a76\u548c\u6539\u8fdb\uff0c\u8fd9\u4e9b\u95ee\u9898\u6709\u671b\u5f97\u5230\u6709\u6548\u89e3\u51b3\u3002<\/p>\n<\/p>\n

\u76f8\u5173\u95ee\u7b54FAQs\uff1a<\/strong><\/h2>\n

\u4ec0\u4e48\u662fFKT\u7b97\u6cd5\uff0c\u5b83\u6709\u54ea\u4e9b\u5e94\u7528\u9886\u57df\uff1f<\/strong><\/p>\n

FKT\u7b97\u6cd5\u662f\u4e00\u79cd\u5feb\u901f\u5361\u5c14\u66fc\u53d8\u6362\u7b97\u6cd5\uff0c\u7528\u4e8e\u63d0\u9ad8\u9891\u57df\u4fe1\u53f7\u7684\u8ba1\u7b97\u6548\u7387\u3002\u5b83\u91c7\u7528\u5feb\u901f\u5085\u91cc\u53f6\u53d8\u6362(FFT)\u7684\u601d\u60f3\uff0c\u5e76\u7ed3\u5408\u4e86Karatsuba\u4e58\u6cd5\u7b97\u6cd5\u548cToom-Cook\u4e58\u6cd5\u7b97\u6cd5\uff0c\u4ee5\u51cf\u5c11\u4e58\u6cd5\u548c\u52a0\u6cd5\u7684\u8fd0\u7b97\u6b21\u6570\u3002FKT\u7b97\u6cd5\u53ef\u4ee5\u5e94\u7528\u4e8e\u8bb8\u591a\u9886\u57df\uff0c\u5982\u56fe\u50cf\u5904\u7406\u3001\u8bed\u97f3\u8bc6\u522b\u3001\u52a0\u5bc6\u89e3\u5bc6\u7b49\u3002<\/p>\n

FKT\u7b97\u6cd5\u548c\u5176\u4ed6\u9891\u7387\u57df\u7b97\u6cd5\u6709\u4ec0\u4e48\u533a\u522b\uff1f<\/strong><\/p>\n

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