Nim Game

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.

 

分析：寻找先手必胜的情况。由于双方都足够聪明，结果是可预知的：

1，2，3     先手必胜;

4　　　　  后手必胜;

5，6，7     先手必胜（通过让对手得到只有四个石头剩余的情况取胜）;

4　　　　  后手必胜;（无论怎样都不可避免拿到只有四个石头剩余的情况）;

思路：判断是否为4的整数倍即可。

JAVACODE

class Solution {
    public boolean canWinNim(int n) {
        return !(n % 4 == 0);
    }
}