292. 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.

思路：莱维汀《算法设计与分析基础》书中有讲解。对于单堆的拈游戏，只要你让对方的每次取棋的时候，n=k(m+1)，对方就必输了，n为取子的时候，棋子总数，m为每次能取的最大个数，k为倍数。

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