LeetCode_292. Nim Game

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.

Hint :
If there are 5 stones in the heap, could you figure out a way to remove the stones such that you will always be the winner?

题意理解：
两人轮流从一堆石头中取1~3块，拿到最后那块石头的人获胜。假设你第一个取，当石头的总数为多少时，你可以获胜？

思路关键：找规律

TotalNum 我 对方 Result 4 lose 5 1 (1,2,3) win 6 2 (1,2,3) win 7 3 (1,2,3) win 8 lose

那么，从中看到规律：只要总数是4的倍数，不管我取几块，都会输。其他情况可以赢。

c++:

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