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.

这也可以看成一个博弈论问题。需要知道的问题是哪个点是决胜点，经过观察思考以后可以发现，距离N为四的整数倍的点是决胜点，能取到这个点的人肯定不会输。

例如N=7，决胜点是3，明显的第一个人可以取到它，所以他肯定能赢。对于N=8，决胜点是4，明显的第一个人不能取到他，所以怎么样都赢不了，一旦被对手取了4这个点，我怎么取都达到不了8。

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