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讨论一下先取时必输的情况

Posted by mingruoyuan at 2009-01-13 12:25:35 on Problem 1067
1 2必输;
情况A:    1 N(N!=2)或者2 N(N!=1)时肯定可以取为1 2,所以必胜;
3 5必输;证明如下:
如果取为3 4,那么对方可以变成1 2(两堆同时取),输;除此之外先取的人要么取为3 3,是输,要么有一堆里只有2个或1个,也就是变成情况A,那么对方必胜,所以自己输!
4 7必输;样例数据中有;先取之后对方总可以直接胜出或者变成1 2,3 5的样子,让你输掉;
于是同理可以得出:
5 9必输,6 11必输,7 13必输……
那么除了1 2外,其他必输的情况是,N(N>=3)和2N-1,如果是其他数据,一定可以变成必输的数据,或者直接胜利,让对方输掉,也就是必胜!

大家看看我的分析怎么样?









































































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