Description

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.

Example:

Input:

4

Output:

 false

Explanation:

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

题目的意思是：有一堆石头，然后两个人个人轮流搬石头，每次可以搬1～3个，最后搬完的人获胜，每个人的策略都是最优的。

1    Win

2    Win

3    Win

4    Lost

5    Win

6    Win

7    Win

8    Lost

9    Win

10   Win

由此我们可以发现规律，只要是4的倍数个，我们一定会输，所以对4取余即可。

代码

class Solution {
public:
    bool canWinNim(int n) {
        return n%4;
    }
};

参考文献

​​[LeetCode] Nim Game 尼姆游戏​​