{"id":416,"date":"2010-10-28T17:50:00","date_gmt":"2010-10-28T09:50:00","guid":{"rendered":"http:\/\/localhost\/?p=416"},"modified":"2010-10-28T17:50:00","modified_gmt":"2010-10-28T09:50:00","slug":"a_problem_for_fun","status":"publish","type":"post","link":"https:\/\/www.shuizilong.com\/wjmzbmr\/?p=416","title":{"rendered":"A Problem For Fun"},"content":{"rendered":"\n

A Problem For Fun<\/p>\n

Time Limit:50000MS Memory Limit:265536K
Total Submit:7 Accepted:2
Case Time Limit:10000MS<\/p>\n

Description <\/strong><\/p>\n

\u7ed9\u51fa\u4e00\u4e2aN\u4e2a\u7ed3\u70b9\u7684\u6811\uff0c\u6bcf\u6761\u8fb9\u6709\u4e00\u4e2a\u6b63\u6574\u6570\u6743\u503c\uff0c\u5b9a\u4e49\u4e24\u4e2a\u7ed3\u70b9\u7684\u8ddd\u79bb\u4e3a\u8fde\u63a5\u8fd9\u4e24\u4e2a\u7ed3\u70b9\u8def\u5f84\u4e0a\u8fb9\u6743\u7684\u548c\u3002\u5bf9\u4e8e\u6bcf\u4e2a\u7ed3\u70b9i\uff0c\u5b83\u5230\u5176\u4ed6N-1\u4e2a\u7ed3\u70b9\u90fd\u6709\u4e00\u4e2a\u8ddd \u79bb\uff0c\u5c06\u8fd9\u4e9b\u8ddd\u79bb\u4ece\u5c0f\u5230\u5927\u6392\u5e8f\uff0c\u8f93\u51fa\u7b2cK\u4e2a\u8ddd\u79bb\u3002 <\/p>\n

Input <\/strong><\/p>\n

\u8f93\u5165\u6587\u4ef6\u603b\u5171N\u884c\u3002\u7b2c\u4e00\u884c\u6709\u4e24\u4e2a\u6b63\u6574\u6570N\u548cK\u3002\u4e0b\u9762N-1\u884c\u6bcf\u884c\u63cf\u8ff0\u6811\u7684\u4e00\u6761\u8fb9\uff08\u4fdd\u8bc1\u8fd9\u4e9b\u8fb9\u53ef\u4ee5\u6784\u6210\u4e00\u68f5\u6811\uff09\uff0c\u6bcf\u884c\u4e09\u4e2a\u6b63\u6574\u6570u\u3001v\u3001w\uff0c\u8868\u793a\u4ece\u7ed3\u70b9u\u5230 \u7ed3\u70b9v\u6709\u4e00\u6761\u6743\u503c\u4e3aw\u7684\u8fb9\u3002
\u8f93\u5165\u6587\u4ef6\u4fdd\u8bc1\uff1aN <= 50000, K < N, u <= N, v <= N, w <= 10000\u3002 <\/p>\n

Output <\/strong><\/p>\n

\u8f93\u51fa\u6587\u4ef6\u603b\u5171N\u884c\uff0c\u6bcf\u884c\u4e00\u4e2a\u6b63\u6574\u6570\uff0c\u7b2ci\u884c\u7684\u6570\u5bf9\u4e8e\u7ed3\u70b9i\u7684\u7b54\u6848\u3002 <\/p>\n

Sample Input <\/strong><\/p>\n<\/p>\n

Sample Output <\/strong><\/p>\n<\/p>\n

Source <\/strong><\/p>\n

\u9676\u6587\u535a<\/p>\n

\u8fd9\u4e2a\u9898\u76ee\u89e3\u6cd5\u6709\u597d\u591a\u3002\u3002\u771f\u662f\u9053\u597d\u9898\u3002\u3002\u6211\u6709\u65f6\u95f4\u5199\u4e2a\u5b8c\u6574\u4e00\u70b9\u7684\u89e3\u9898\u62a5\u544a\u7f57\u5217\u4e00\u4e0b\u89e3\u6cd5\u3002\u3002
\u6211\u5199\u7684\u662f\u8fb9\u5206\u6cbb\u3002\u3002\u56e0\u4e3a\u6bd4\u8f83\u597d\u5f04\u3002\u3002
\u9996\u5148\u901a\u8fc7\u6dfb\u52a0\u8f85\u52a9\u70b9\u7684\u529e\u6cd5\u8ba9\u70b9\u7684\u6700\u5927\u5ea6\u6570\u4e3a3\u3002\u3002
\u5177\u4f53\u7684\u8bf4\u5c31\u662f\u5bf9\u4e8e\u6bcf\u4e2a\u5ea6\u6570\u5927\u4e8e3\u7684\u70b9\u3002\u3002
\u6bd4\u5982\u8bf4\u5ea6\u6570\u4e3ad,\u6784\u9020d\u4e2a\u70b9\uff0c\u6bcf\u4e2a\u70b9\u5206\u5230\u4e00\u4e2a\u8fb9\u3002\u3002\u540c\u65f6\u8fd9d\u4e2a\u70b9\u7528\u957f\u4e3a0\u7684\u8fb9\u8fde\u8d77\u6765\u3002\u3002
\u7136\u540e\u8fb9\u5206\u6cbb\u3002\u3002\u627e\u5230\u5206\u6cbb\u7684\u8fb9\u3002\u3002
\u90a3\u4e48\u4e00\u4e2a\u70b9\u51fa\u53d1\u7684\u6240\u6709\u8def\u5f84\u6700\u591a\u51fa\u73b0\u5728LogN\u4e2a\u5206\u6cbb\u4e2d\u3002\u3002
\u8003\u8651“\u4e00\u4e2a\u70b9\u51fa\u53d1\u7684\u8def\u5f84\u957f\u5ea6<L\u7684\u6709\u591a\u5c11\u4e2a”\u8fd9\u6837\u7684\u8be2\u95ee\u3002\u3002
\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u6392\u5e8f\u7684\u529e\u6cd5\u5728LogN^2\u56de\u7b54\u8fd9\u4e2a\u95ee\u9898\u3002\u3002
\u7136\u540e\u901a\u8fc7\u4e8c\u5206\u6765\u56de\u7b54K\u8fd1\u9876\u70b9\u7684\u8bdd\u3002\u3002
\u5c31\u662fLogN^3\u4e86\u3002\u3002
N\u4e2a\u70b9\u5c31\u662fNLogN^3
\u597d\u8bf4\u4e0d\u597d\u5199\u3002\u3002\u5199\u4e869KB+\u3002\u3002
\u89e3\u6cd52\uff1a
\u8fd9\u4e2a\u60f3\u6cd5\u6765\u81eatwb\u3002\u3002\u5c31\u662fdfs\u4e00\u68f5\u6811\u7684\u8bdd\u3002\u3002
\u7528\u4e00\u4e2a\u6570\u636e\u7ed3\u6784\u7ef4\u62a4\u6811\u7684dfs\u5e8f\u5217\u3002\u3002
\u90a3\u4e48\u4e00\u4e2a\u5b57\u6811\u662f\u4e00\u4e2a\u533a\u95f4\u3002\u3002
\u6ce8\u610f\u5230\u6211\u6cbf\u7740\u4e00\u6761\u8fb9\u79fb\u52a8\u3002\u3002\u8bbe\u4ecei->j\u3002\u3002
\u90a3\u4e48j\u5bf9\u5e94\u7684\u533a\u95f4\u5230\u5f53\u524d\u70b9\u7684\u8ddd\u79bb\u5168\u90e8\u964d\u4f4ecost(i->j)
\u5176\u5b83\u7684\u70b9\u5168\u90e8\u589e\u52a0cost(i->j)
\u90a3\u4e48\u6211\u4eec\u8981\u56de\u9e58\u4e00\u4e2a\u6570\u636e\u7ed3\u6784\u3002\u3002
\u652f\u6301:
\u7ed9\u4e00\u6bb5\u6570\u90fd\u589e\u52a0\u4e00\u4e2a\u503c\u3002\u3002
\u627e\u6240\u6709\u6570\u4e2d\u7684K\u5927\u3002\u3002
\u8fd9\u4e2a\u60c5\u51b5\u6ca1\u6709\u529e\u6cd5\u7528\u795e\u9a6c\u6709\u6548\u7684\u529e\u6cd5\u89e3\u51b3\u3002\u3002\u53ea\u80fd\u5757\u72b6\u4e86\u3002\u3002
\u5757\u72b6\u7684\u8bdd\u627eK\u5927\u8fd8\u662f\u5f97\u5148\u4e8c\u5206\u3002\u3002\u5c31\u6709\u4e2aLogN\u4e86\u3002\u3002
\u5c31\u662f\u8f6c\u53d8\u6210\u89e3\u51b3\u8be2\u95ee\u6bd4\u4e00\u4e2a\u6570\u5c0f\u7684\u6570\u6709\u51e0\u4e2a\u8fd9\u4e2a\u95ee\u9898\u3002\u3002
\u8003\u8651\u6211\u4eec\u628a\u5e8f\u5217\u5206\u6210L\u5757\u3002\u3002
\u8003\u8651\u5404\u79cd\u590d\u6742\u5ea6\uff1a
\u4e3a\u4e86\u652f\u6301\u8be2\u95ee\u6211\u4eec\u5f97\u7ed9\u6bcf\u4e2a\u5757\u7ef4\u62a4\u4e00\u4e2a\u6392\u8fc7\u5e8f\u7684\u6570\u5217\u3002\u3002
\u7ed9\u4e00\u4e2a\u5757\u90e8\u5206\u589e\u52a0\u503c\uff1a
\u627e\u51fa\u90a3\u90e8\u5206\uff0c\u589e\u52a0\uff0c\u5f52\u5e76\uff0cO(L)
\u7ed9\u4e00\u4e2a\u5757\u6574\u4f53\u589e\u52a0\u503c\uff1a
\u76f4\u63a5\u7ef4\u62a4\u4e00\u4e2a\u6807\u8bb0 O(1)
\u4e00\u4e2a\u5757\u7684\u8be2\u95ee O(LogL)<O(LogN)(\u4e3a\u4e86\u65b9\u4fbf\u770b\u6210LogN)
\u6240\u6709\u5757\u7684\u4e00\u6b21\u8be2\u95ee (N\/L)*LogL< (NLogN)\/L
\u6240\u6709\u5757\u7684\u67e5\u8be2K\u5927 LogN*(NLogN)\/L=(NLogN^2)\/L
\u4fee\u6539\u4e00\u4e2a\u533a\u95f4 O(L+N\/L) \u5047\u8bbeL>N\/L\u3002\u3002\u5219\u4e3aO(L)
\u6211\u4eec\u5728dfs\u7684\u8fc7\u7a0b\u4e2d\u3002\u3002
\u8981\u8fdb\u884cO\uff08N\uff09\u6b21\u8be2\u95ee\uff0cO(N)\u6b21\u4fee\u6539\u64cd\u4f5c\u3002\u3002
\u6240\u4ee5\u8ba9\u8fd9\u4e24\u4e2a\u64cd\u4f5c\u5e73\u8861\u8d77\u6765\u3002\u3002
\u65e2L=(NLogN^2)\/L
\u89e3\u5f97L=Sqrt(N)LogN
\u603b\u5171\u5c31\u662fN*Sqrt(N)LogN\u4e86\u3002\u3002
\u6bd4\u7b2c\u4e00\u4e2a\u8981\u597d\u5199\u4e00\u70b9\u3002\u3002\u901f\u5ea6\u4e5f\u5dee\u4e0d\u591a\u3002\u3002<\/p>\n

4
6
4
7
5
6<\/p>\n

6 3
1 2 2
1 3 4
1 4 3
3 5 1
3 6 2 <\/p>\n","protected":false},"excerpt":{"rendered":"

A Problem For Fun Time Limit:50000MS Memory Limit:265536KTotal Submit:7 Accepted:2 Case Time Limit:10000MS Description \u7ed9\u51fa\u4e00\u4e2aN\u4e2a\u7ed3\u70b9\u7684\u6811\uff0c\u6bcf\u6761\u8fb9\u6709\u4e00\u4e2a\u6b63\u6574\u6570\u6743\u503c\uff0c\u5b9a\u4e49\u4e24\u4e2a\u7ed3\u70b9\u7684\u8ddd\u79bb\u4e3a\u8fde\u63a5\u8fd9\u4e24\u4e2a\u7ed3\u70b9\u8def\u5f84\u4e0a\u8fb9\u6743\u7684\u548c\u3002\u5bf9\u4e8e\u6bcf\u4e2a\u7ed3\u70b9i\uff0c\u5b83\u5230\u5176\u4ed6N-1\u4e2a\u7ed3\u70b9\u90fd\u6709\u4e00\u4e2a\u8ddd \u79bb\uff0c\u5c06\u8fd9\u4e9b\u8ddd\u79bb\u4ece\u5c0f\u5230\u5927\u6392\u5e8f\uff0c\u8f93\u51fa\u7b2cK\u4e2a\u8ddd\u79bb\u3002 Input \u8f93\u5165\u6587\u4ef6\u603b\u5171N\u884c\u3002\u7b2c\u4e00\u884c\u6709\u4e24\u4e2a\u6b63\u6574\u6570N\u548cK\u3002\u4e0b\u9762N-1\u884c\u6bcf\u884c\u63cf\u8ff0\u6811\u7684\u4e00\u6761\u8fb9\uff08\u4fdd\u8bc1\u8fd9\u4e9b\u8fb9\u53ef\u4ee5\u6784\u6210\u4e00\u68f5\u6811\uff09\uff0c\u6bcf\u884c\u4e09\u4e2a\u6b63\u6574\u6570u\u3001v\u3001w\uff0c\u8868\u793a\u4ece\u7ed3\u70b9u\u5230 \u7ed3\u70b9v\u6709\u4e00\u6761\u6743\u503c\u4e3aw\u7684\u8fb9\u3002 \u8f93\u5165\u6587\u4ef6\u4fdd\u8bc1\uff1aN <= 50000, K < N, u <= N, v <= N, w <= 10000\u3002 Output \u8f93\u51fa\u6587\u4ef6\u603b\u5171N\u884c\uff0c\u6bcf\u884c\u4e00\u4e2a\u6b63\u6574\u6570\uff0c\u7b2ci\u884c\u7684\u6570\u5bf9\u4e8e\u7ed3\u70b9i\u7684\u7b54\u6848\u3002 Sample Input Sample Output Source \u9676\u6587\u535a \u8fd9\u4e2a\u9898\u76ee\u89e3\u6cd5\u6709\u597d\u591a\u3002\u3002\u771f\u662f\u9053\u597d\u9898\u3002\u3002\u6211\u6709\u65f6\u95f4\u5199\u4e2a\u5b8c\u6574\u4e00\u70b9\u7684\u89e3\u9898\u62a5\u544a\u7f57\u5217\u4e00\u4e0b\u89e3\u6cd5\u3002\u3002\u6211\u5199\u7684\u662f\u8fb9\u5206\u6cbb\u3002\u3002\u56e0\u4e3a\u6bd4\u8f83\u597d\u5f04\u3002\u3002\u9996\u5148\u901a\u8fc7\u6dfb\u52a0\u8f85\u52a9\u70b9\u7684\u529e\u6cd5\u8ba9\u70b9\u7684\u6700\u5927\u5ea6\u6570\u4e3a3\u3002\u3002\u5177\u4f53\u7684\u8bf4\u5c31\u662f\u5bf9\u4e8e\u6bcf\u4e2a\u5ea6\u6570\u5927\u4e8e3\u7684\u70b9\u3002\u3002\u6bd4\u5982\u8bf4\u5ea6\u6570\u4e3ad,\u6784\u9020d\u4e2a\u70b9\uff0c\u6bcf\u4e2a\u70b9\u5206\u5230\u4e00\u4e2a\u8fb9\u3002\u3002\u540c\u65f6\u8fd9d\u4e2a\u70b9\u7528\u957f\u4e3a0\u7684\u8fb9\u8fde\u8d77\u6765\u3002\u3002\u7136\u540e\u8fb9\u5206\u6cbb\u3002\u3002\u627e\u5230\u5206\u6cbb\u7684\u8fb9\u3002\u3002\u90a3\u4e48\u4e00\u4e2a\u70b9\u51fa\u53d1\u7684\u6240\u6709\u8def\u5f84\u6700\u591a\u51fa\u73b0\u5728LogN\u4e2a\u5206\u6cbb\u4e2d\u3002\u3002\u8003\u8651“\u4e00\u4e2a\u70b9\u51fa\u53d1\u7684\u8def\u5f84\u957f\u5ea6<L\u7684\u6709\u591a\u5c11\u4e2a”\u8fd9\u6837\u7684\u8be2\u95ee\u3002\u3002\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u6392\u5e8f\u7684\u529e\u6cd5\u5728LogN^2\u56de\u7b54\u8fd9\u4e2a\u95ee\u9898\u3002\u3002\u7136\u540e\u901a\u8fc7\u4e8c\u5206\u6765\u56de\u7b54K\u8fd1\u9876\u70b9\u7684\u8bdd\u3002\u3002\u5c31\u662fLogN^3\u4e86\u3002\u3002N\u4e2a\u70b9\u5c31\u662fNLogN^3\u597d\u8bf4\u4e0d\u597d\u5199\u3002\u3002\u5199\u4e869KB+\u3002\u3002\u89e3\u6cd52\uff1a\u8fd9\u4e2a\u60f3\u6cd5\u6765\u81eatwb\u3002\u3002\u5c31\u662fdfs\u4e00\u68f5\u6811\u7684\u8bdd\u3002\u3002\u7528\u4e00\u4e2a\u6570\u636e\u7ed3\u6784\u7ef4\u62a4\u6811\u7684dfs\u5e8f\u5217\u3002\u3002\u90a3\u4e48\u4e00\u4e2a\u5b57\u6811\u662f\u4e00\u4e2a\u533a\u95f4\u3002\u3002\u6ce8\u610f\u5230\u6211\u6cbf\u7740\u4e00\u6761\u8fb9\u79fb\u52a8\u3002\u3002\u8bbe\u4ecei->j\u3002\u3002\u90a3\u4e48j\u5bf9\u5e94\u7684\u533a\u95f4\u5230\u5f53\u524d\u70b9\u7684\u8ddd\u79bb\u5168\u90e8\u964d\u4f4ecost(i->j)\u5176\u5b83\u7684\u70b9\u5168\u90e8\u589e\u52a0cost(i->j)\u90a3\u4e48\u6211\u4eec\u8981\u56de\u9e58\u4e00\u4e2a\u6570\u636e\u7ed3\u6784\u3002\u3002\u652f\u6301:\u7ed9\u4e00\u6bb5\u6570\u90fd\u589e\u52a0\u4e00\u4e2a\u503c\u3002\u3002\u627e\u6240\u6709\u6570\u4e2d\u7684K\u5927\u3002\u3002\u8fd9\u4e2a\u60c5\u51b5\u6ca1\u6709\u529e\u6cd5\u7528\u795e\u9a6c\u6709\u6548\u7684\u529e\u6cd5\u89e3\u51b3\u3002\u3002\u53ea\u80fd\u5757\u72b6\u4e86\u3002\u3002\u5757\u72b6\u7684\u8bdd\u627eK\u5927\u8fd8\u662f\u5f97\u5148\u4e8c\u5206\u3002\u3002\u5c31\u6709\u4e2aLogN\u4e86\u3002\u3002\u5c31\u662f\u8f6c\u53d8\u6210\u89e3\u51b3\u8be2\u95ee\u6bd4\u4e00\u4e2a\u6570\u5c0f\u7684\u6570\u6709\u51e0\u4e2a\u8fd9\u4e2a\u95ee\u9898\u3002\u3002\u8003\u8651\u6211\u4eec\u628a\u5e8f\u5217\u5206\u6210L\u5757\u3002\u3002\u8003\u8651\u5404\u79cd\u590d\u6742\u5ea6\uff1a\u4e3a\u4e86\u652f\u6301\u8be2\u95ee\u6211\u4eec\u5f97\u7ed9\u6bcf\u4e2a\u5757\u7ef4\u62a4\u4e00\u4e2a\u6392\u8fc7\u5e8f\u7684\u6570\u5217\u3002\u3002\u7ed9\u4e00\u4e2a\u5757\u90e8\u5206\u589e\u52a0\u503c\uff1a\u627e\u51fa\u90a3\u90e8\u5206\uff0c\u589e\u52a0\uff0c\u5f52\u5e76\uff0cO(L)\u7ed9\u4e00\u4e2a\u5757\u6574\u4f53\u589e\u52a0\u503c\uff1a\u76f4\u63a5\u7ef4\u62a4\u4e00\u4e2a\u6807\u8bb0 O(1)\u4e00\u4e2a\u5757\u7684\u8be2\u95ee O(LogL)<O(LogN)(\u4e3a\u4e86\u65b9\u4fbf\u770b\u6210LogN)\u6240\u6709\u5757\u7684\u4e00\u6b21\u8be2\u95ee (N\/L)*LogL< (NLogN)\/L\u6240\u6709\u5757\u7684\u67e5\u8be2K\u5927 LogN*(NLogN)\/L=(NLogN^2)\/L\u4fee\u6539\u4e00\u4e2a\u533a\u95f4 O(L+N\/L) \u5047\u8bbeL>N\/L\u3002\u3002\u5219\u4e3aO(L)\u6211\u4eec\u5728dfs\u7684\u8fc7\u7a0b\u4e2d\u3002\u3002\u8981\u8fdb\u884cO\uff08N\uff09\u6b21\u8be2\u95ee\uff0cO(N)\u6b21\u4fee\u6539\u64cd\u4f5c\u3002\u3002\u6240\u4ee5\u8ba9\u8fd9\u4e24\u4e2a\u64cd\u4f5c\u5e73\u8861\u8d77\u6765\u3002\u3002\u65e2L=(NLogN^2)\/L\u89e3\u5f97L=Sqrt(N)LogN\u603b\u5171\u5c31\u662fN*Sqrt(N)LogN\u4e86\u3002\u3002\u6bd4\u7b2c\u4e00\u4e2a\u8981\u597d\u5199\u4e00\u70b9\u3002\u3002\u901f\u5ea6\u4e5f\u5dee\u4e0d\u591a\u3002\u3002 464756 6 31 2 21 […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[10],"tags":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/www.shuizilong.com\/wjmzbmr\/index.php?rest_route=\/wp\/v2\/posts\/416"}],"collection":[{"href":"https:\/\/www.shuizilong.com\/wjmzbmr\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.shuizilong.com\/wjmzbmr\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.shuizilong.com\/wjmzbmr\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.shuizilong.com\/wjmzbmr\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=416"}],"version-history":[{"count":0,"href":"https:\/\/www.shuizilong.com\/wjmzbmr\/index.php?rest_route=\/wp\/v2\/posts\/416\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.shuizilong.com\/wjmzbmr\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=416"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.shuizilong.com\/wjmzbmr\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=416"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.shuizilong.com\/wjmzbmr\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=416"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}