leetcode 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.

NIM博弈游戏

这道题可以倒推，当轮到自己的时候，剩的石头和结果如下：

1块石头      赢

2块石头      赢

3块石头      赢

4块石头      输   无论怎么取，都会落到对方面对1，2，3的情况，于是对方赢

5块石头      赢   取1块石头，变成对方面对4块石头

6块石头      赢   取2块石头，变成对方面对4块石头

……

以此类推，为了使自己赢，当不是4的倍数的时候就可以将对方的情况变成4的倍数，对方只能取1，2，3，于是自己再次可以将对方变成4的倍数，如此到对方面对4块石头必输；当自己是4的倍数的时候，与上述情况相反，于是必输。

这道题就可以通过判断n是否是4的倍数从而得到答案。

bool canWinNim(int n) {    if(n%4) return true;    return false;}