{"id":27,"date":"2009-11-14T22:17:00","date_gmt":"2009-11-14T14:17:00","guid":{"rendered":"http:\/\/localhost\/?p=27"},"modified":"2009-11-14T22:17:00","modified_gmt":"2009-11-14T14:17:00","slug":"usaco_fall_2003_solution_to_a_problem","status":"publish","type":"post","link":"https:\/\/www.shuizilong.com\/wjmzbmr\/?p=27","title":{"rendered":"USACO FALL 200\uff13\u9898\u89e3"},"content":{"rendered":"

\u4e3a\u4e86\u70ed\u8eabNOIP\u505a\u4e86\u8fd9\u4e2a\u6bd4\u8d5b\u3002\u3002
Fall 2003
\u6c34\u5e73\u6709\u9650\u3002\u3002\u6211\u662f\u6c99\u8336\u3002\u3002
Problem 1:
\u6709\u9650\u5236\u7684\u80cc\u5305\u95ee\u9898\u3002\u3002
\u9996\u5148\u628aS\u3001B\u90fd\u5927\u4e8e0\u7684\u9009\u4e86\u3002\u3002
\u9996\u5148\u628aS\u3001B\u90fd\u5c0f\u4e8e\u6216\u7b49\u4e8e0\u7684\u6254\u6389\u3002\u3002
\u90a3\u4e48\u6240\u5269\u7684\u5c31\u662f\u4e00\u9879\u6b63\u4e00\u9879\u8d1f\u4e86\u3002\u3002
\u6309\u7167\u5176\u4e2d\u7684\u4e00\u9879\u4ece\u5927\u5230\u5c0f\u6392\u5e8f\u3002\u3002\u5fc5\u7136\u662f\u5982\u4e0b\u5f62\u5f0f\u3002\u3002
S B
\uff0b \uff0d
\uff0b \uff0d
\u3002\u3002\u3002\u4ee5\uff08S\u7684\u6b63\u8d1f\u6027\u4e3a\u5212\u5206\u7ebf\uff09
\uff0d  +
\uff0d  \uff0b
\u3002\u3002\u3002
\u8bbeS\u5df2\u7ecf\u6709\u4e86HaveS\uff08\u6765\u6e90\u4e8e\u5148\u524d\u5df2\u7ecf\u9009\u7684\u4e1c\u897f\u3002\u3002\u80af\u5b9a\u4e3a\u6b63\u3002\u3002\uff09
\u5bf9\u4e0a\u4e0b\u4e24\u4e2a\u5206\u522b\u8fd0\u884c\u80cc\u5305\u3002\u3002\u6c42\u51fa\u4e0a\u4e0b\u4e24\u4e2a\u5bb9\u91cf\u5404\u4e2a\u9009\u62e9\u5bb9\u91cf\u65f6B\u548c\u7684\u6700\u5927\u503c\u3002\u3002
\u4e3a\u4e86\u65b9\u4fbf\u628a\u4e0b\u9762\u7684\u90a3\u4e2a\u80cc\u5305\u4ef7\u683cS\u503c\u5168\u90e8\u53d6\u53cd\u3002\u3002\u8fd9\u6837\u5f53\u4e0a\u9762\u80cc\u5305S\u4e3a\u548cX\u65f6\u3002\u3002\u4e0b\u9762\u7684\u6700\u591a\u4e3aX\uff0bHaveS\u4e2a\u3002\u3002
\u90a3\u4e48\u53ef\u4ee5\u679a\u4e3e\u4e0a\u9762\u7684\u80cc\u5305\u7684S\u503c\u3002\u5e76\u7528\u4e2a\u53d8\u91cf\u8bb0\u5f55\u4e0b\u9762\u7684\u6700\u5c0f\u503c\u3002\u3002\u82e5B\u548c\u7684\u6700\u5927\u503c\u52a0\u4e0a\u539f\u6765\u5148\u524d\u9009\u7684B\u7684\u548c\u5927\u4e8e0\u7684\u8bdd\u3002\u3002
\u7528\u4e8e\u66f4\u65b0\u6700\u4f18\u89e3\u3002\u3002
P.S\u5b9e\u9645\u4e0a\u76f4\u63a5\u66b4\u529b\u80cc\u5305\u4e5f\u53ef\u4ee5\u3002\u3002\u4f46\u6211\u4f30\u8ba1\u8981TLE\u3002\u3002\u8fdb\u884c\u4e00\u4e9b\u4f18\u5316\u4e4b\u540e\u53ef\u4ee5\u5febN\u591a\u3002\u3002
\u51e0\u4e2a\u5c0f\u4f18\u5316\u3002\u3002
\u9996\u5148\u82e5\u4e0a\u9762S\u7684\u548c\u4e3aSumS\uff0c\u5219\u4e0d\u9700\u8981\u8003\u8651\u4e0b\u9762SumS\uff0bHaveS\u4ee5\u540e\u7684\u72b6\u6001\u3002\u3002\u56e0\u4e3a\u6839\u672c\u4e0d\u4f1a\u7528\u5230\u3002\u3002
\u90a3\u4e48\u4e0a\u9762\u7684\u7684\u548c\u81ea\u7136\u8981\u5c0f\u3002\u3002
\u6545\u5728\u4e0b\u9762\u6bd4\u4e0a\u9762\u77ed\u7684\u65f6\u5019\u53ef\u4ee5\u4ea4\u6362\u4e0a\u4e0b\u4e24\u4e2a\u3002\u3002\uff08\u4e5f\u5c31\u662f\u4ea4\u6362S\u548cB\u7684\u4f4d\u7f6e\uff09
\u4f17\u6240\u5468\u77e5DP\u9700\u8981\u4e00\u4e2a\u5e8f
\u76f4\u63a5\u7684\u66b4\u529bDP\u6ca1\u6709\u8003\u8651\u5230\u9898\u76ee\u7684\u7279\u6027\u800c\u8fd0\u7528\u4e86\u76f2\u76ee\u7684\u5e8f\u3002\u3002
\u800c\u7ed3\u5408\u9898\u76ee\u7684\u7279\u6027\u53ef\u4ee5\u5f97\u51fa\u66f4\u597d\u7684\u5e8f\u4ece\u800c\u66f4\u9ad8\u6548\u7684\u7b97\u6cd5\u4fc4\u3002\u3002
Problem 2:
\u597d\u96be\u963f\u3002\u3002\u5e94\u8be5\u8981\u7528\u5230\u5206\u6cbb\u5427\u3002\u3002\u6211\u4e0d\u4f1a\u963f\u3002\u3002\u6559\u6559\u6211\u963f\u3002\u3002
Promblem 3\uff1a
\u6bd4\u8f83\u6c34\u7684\u95ee\u9898\u3002\u3002\u9996\u5148\u5f88\u660e\u663e\u8981\u6c42\u51fa\u5f3a\u8fde\u540c\u5206\u91cf\u3002\u3002\u7136\u540e\u8f6c\u5316\u6210DAG\u3002\u3002
\u9898\u76ee\u5c31\u662f\u6c42\u4e00\u4e2a\u8282\u70b9\u5230\u5176\u4ed6\u6240\u6709\u8282\u70b9\u90fd\u6709\u8def\u5f84\u3002\u3002
\u56e0\u4e3a\u6ca1\u6709\u73af\u3002\u3002\u6545\u4e00\u4e2a\u8282\u70b9\u5982\u679c\u6709\u5165\u5ea6\u90a3\u4e48\u4e00\u5b9a\u4e0d\u80fd\u5230\u8fbe\u5c04\u5411\u4ed6\u7684\u90a3\u4e2a\u9876\u70b9\u3002\u3002\u4e0d\u7136\u5c31\u6709\u73af\u4e86\u3002\u3002
\u6545\u53ea\u6709\u6ca1\u6709\u5165\u5ea6\u7684\u8282\u70b9\u53ef\u80fd\u6ee1\u8db3\u6761\u4ef6\u3002\u3002
\u5982\u679c\u6709\u4e24\u4e2a\u6216\u4ee5\u4e0a\u7684\u8bdd\u3002\u3002\u90a3\u4e48\u8fd9\u4e24\u4e2a\u8282\u70b9\u5fc5\u4e0d\u80fd\u4e92\u8fbe\u3002\u3002\u6545\u65e0\u89e3
\u5982\u679c\u6709\u4e00\u4e2a\u7684\u8bdd\u3002\u3002\u90a3\u4e2a\u8282\u70b9\u5c31\u662f\u7b54\u6848\u4e86\u3002\u3002
Problem 4:
OI\u4e2d\u6570\u636e\u8303\u56f4\u4e0d\u4e00\u6837\u7684\u9898\u76ee\u771f\u4e0d\u662f\u4e00\u9053\u9898\u76ee\u963f\u3002\u3002
\u9898\u76ee\u5c31\u662f\u6c42N\u4e2a\u70b9\u4e2d\u6700\u957f\u7684\u4e24\u70b9\u95f4\u8ddd\u79bb\u3002\u3002\u5047\u5982N<1000\u7684\u8bdd\u76f4\u63a5\u66b4\u529b\u5c31OK\u4e86\u3002\u3002\u53ef\u60dcN<50000
\u5148\u6c42\u51fa\u51f8\u5305\u3002\u3002\u90a3\u4e48\u6700\u957f\u8ddd\u79bb\u4e00\u5b9a\u5728\u51f8\u5305\u4e0a\u3002\u3002
\u5c3d\u7ba1\u5e73\u5747\u610f\u4e49\u4e0a\u51f8\u5305\u4e0a\u7684\u70b9\u4e3aN\u7684\u4e09\u6b21\u65b9\u6839\u7684\u6570\u91cf\u7ea7\u3002\u3002\u90a3\u4e48\u76f4\u63a5\u679a\u4e3e\u51f8\u5305\u4e0a\u7684\u70b9\u5bf9\u5c31\u662fN\u7684\u4e09\u5206\u4e4b\u4e8c\u6b21\u65b9\u3002\u3002
\u53ef\u60dc\u90a3\u662f\u5e73\u5747\u610f\u4e49\u4e0a\u7684\u3002\u3002\u5f88\u5bb9\u6613\u5c31\u53ef\u4ee5\u6784\u9020\u51fa\u6240\u6709\u70b9\u90fd\u5728\u51f8\u5305\u4e0a\u7684BT\u6570\u636e\u3002\u3002\u663e\u7136\u4e0d\u884c\u3002\u3002
\u5b9e\u9645\u4e0a\u6c42\u51f8\u5305\u4e0a\u7684\u6700\u8fdc\u70b9\u5229\u7528\u5bf9\u91cd\u70b9\u53ef\u4ee5\u505a\u5230O\uff08N\uff09\u4f46\u6211\u4e0d\u4f1a\u3002\u3002
\u6211\u53d1\u73b0\u51f8\u5305\u4e0a\u7684\u70b9\u7684\u8ddd\u79bb\u662f\u6709\u5355\u5cf0\u6027\u7684\u3002\u3002\u6545\u53ef\u4ee5\u7528ternary\u67e5\u627e\u5176\u6700\u503c\u3002\u3002\u662flogn\u7684\u3002\u3002
\u52a0\u4e0a\u6392\u5e8f\u3002\u3002\u8fd8\u662fNlogN\u3002\u3002\u52c9\u5f3a\u8fc7\u5427\u3002\u3002 <\/p>\n","protected":false},"excerpt":{"rendered":"

\u4e3a\u4e86\u70ed\u8eabNOIP\u505a\u4e86\u8fd9\u4e2a\u6bd4\u8d5b\u3002\u3002Fall 2003\u6c34\u5e73\u6709\u9650\u3002\u3002\u6211\u662f\u6c99\u8336\u3002\u3002Problem 1:\u6709\u9650\u5236\u7684\u80cc\u5305\u95ee\u9898\u3002\u3002\u9996\u5148\u628aS\u3001B\u90fd\u5927\u4e8e0\u7684\u9009\u4e86\u3002\u3002\u9996\u5148\u628aS\u3001B\u90fd\u5c0f\u4e8e\u6216\u7b49\u4e8e0\u7684\u6254\u6389\u3002\u3002\u90a3\u4e48\u6240\u5269\u7684\u5c31\u662f\u4e00\u9879\u6b63\u4e00\u9879\u8d1f\u4e86\u3002\u3002\u6309\u7167\u5176\u4e2d\u7684\u4e00\u9879\u4ece\u5927\u5230\u5c0f\u6392\u5e8f\u3002\u3002\u5fc5\u7136\u662f\u5982\u4e0b\u5f62\u5f0f\u3002\u3002S B\uff0b \uff0d\uff0b \uff0d\u3002\u3002\u3002\u4ee5\uff08S\u7684\u6b63\u8d1f\u6027\u4e3a\u5212\u5206\u7ebf\uff09\uff0d  +\uff0d  \uff0b\u3002\u3002\u3002\u8bbeS\u5df2\u7ecf\u6709\u4e86HaveS\uff08\u6765\u6e90\u4e8e\u5148\u524d\u5df2\u7ecf\u9009\u7684\u4e1c\u897f\u3002\u3002\u80af\u5b9a\u4e3a\u6b63\u3002\u3002\uff09\u5bf9\u4e0a\u4e0b\u4e24\u4e2a\u5206\u522b\u8fd0\u884c\u80cc\u5305\u3002\u3002\u6c42\u51fa\u4e0a\u4e0b\u4e24\u4e2a\u5bb9\u91cf\u5404\u4e2a\u9009\u62e9\u5bb9\u91cf\u65f6B\u548c\u7684\u6700\u5927\u503c\u3002\u3002\u4e3a\u4e86\u65b9\u4fbf\u628a\u4e0b\u9762\u7684\u90a3\u4e2a\u80cc\u5305\u4ef7\u683cS\u503c\u5168\u90e8\u53d6\u53cd\u3002\u3002\u8fd9\u6837\u5f53\u4e0a\u9762\u80cc\u5305S\u4e3a\u548cX\u65f6\u3002\u3002\u4e0b\u9762\u7684\u6700\u591a\u4e3aX\uff0bHaveS\u4e2a\u3002\u3002\u90a3\u4e48\u53ef\u4ee5\u679a\u4e3e\u4e0a\u9762\u7684\u80cc\u5305\u7684S\u503c\u3002\u5e76\u7528\u4e2a\u53d8\u91cf\u8bb0\u5f55\u4e0b\u9762\u7684\u6700\u5c0f\u503c\u3002\u3002\u82e5B\u548c\u7684\u6700\u5927\u503c\u52a0\u4e0a\u539f\u6765\u5148\u524d\u9009\u7684B\u7684\u548c\u5927\u4e8e0\u7684\u8bdd\u3002\u3002\u7528\u4e8e\u66f4\u65b0\u6700\u4f18\u89e3\u3002\u3002P.S\u5b9e\u9645\u4e0a\u76f4\u63a5\u66b4\u529b\u80cc\u5305\u4e5f\u53ef\u4ee5\u3002\u3002\u4f46\u6211\u4f30\u8ba1\u8981TLE\u3002\u3002\u8fdb\u884c\u4e00\u4e9b\u4f18\u5316\u4e4b\u540e\u53ef\u4ee5\u5febN\u591a\u3002\u3002\u51e0\u4e2a\u5c0f\u4f18\u5316\u3002\u3002\u9996\u5148\u82e5\u4e0a\u9762S\u7684\u548c\u4e3aSumS\uff0c\u5219\u4e0d\u9700\u8981\u8003\u8651\u4e0b\u9762SumS\uff0bHaveS\u4ee5\u540e\u7684\u72b6\u6001\u3002\u3002\u56e0\u4e3a\u6839\u672c\u4e0d\u4f1a\u7528\u5230\u3002\u3002\u90a3\u4e48\u4e0a\u9762\u7684\u7684\u548c\u81ea\u7136\u8981\u5c0f\u3002\u3002\u6545\u5728\u4e0b\u9762\u6bd4\u4e0a\u9762\u77ed\u7684\u65f6\u5019\u53ef\u4ee5\u4ea4\u6362\u4e0a\u4e0b\u4e24\u4e2a\u3002\u3002\uff08\u4e5f\u5c31\u662f\u4ea4\u6362S\u548cB\u7684\u4f4d\u7f6e\uff09\u4f17\u6240\u5468\u77e5DP\u9700\u8981\u4e00\u4e2a\u5e8f\u76f4\u63a5\u7684\u66b4\u529bDP\u6ca1\u6709\u8003\u8651\u5230\u9898\u76ee\u7684\u7279\u6027\u800c\u8fd0\u7528\u4e86\u76f2\u76ee\u7684\u5e8f\u3002\u3002\u800c\u7ed3\u5408\u9898\u76ee\u7684\u7279\u6027\u53ef\u4ee5\u5f97\u51fa\u66f4\u597d\u7684\u5e8f\u4ece\u800c\u66f4\u9ad8\u6548\u7684\u7b97\u6cd5\u4fc4\u3002\u3002Problem 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