【LeetCode】001 Nim Game 尼姆游戏

【题目】

You are playing the following Nim Game with your friend: There is a heap of stones on the table, each time one of you take turns to remove 1 to 3 stones. The one who removes the last stone will be the winner. You will take the first turn to remove the stones.

Both of you are very clever and have optimal strategies for the game. Write a function to determine whether you can win the game given the number of stones in the heap.

For example, if there are 4 stones in the heap, then you will never win the game: no matter 1, 2, or 3 stones you remove, the last stone will always be removed by your friend.

有一堆石头，甲乙两人分别从当中拿，每个人可以拿1-3个，拿到最后一块石头的人获胜。若甲先拿石头，那么当这堆石头数量为多少的​时候，甲按照最优策略一定可以获胜。

程序要求输入石头个数，输出1和0代表甲是否可以获胜。

【解析】

当这堆石头数量为4，甲​无论怎么拿都无法获胜，如果想要胜利就必须逼迫对方拿第4块，则甲要抢第5块，若要顺利抢到第5块，则必须逼迫对方拿第8块，以此策略类推。

​因此，若甲先拿，只要石头的总数不为4的倍数，甲就可以一直逼迫对方拿4的倍数，直至抢到最后一块石头。

【程序】​

​bool canWinNim(int n) {

   return n%4!=0;

}​

【小结】

感谢@summerxxxxdj 推荐网站。

英语水平不行，看歪果仁讨论一堆英文就头大，不如自己在博客里做做记录。​​​​​