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
纯数学题，这种题目一般找规律用数学归纳法
- stones = 1: 拿一个，必赢
- stones = 2: 拿两个，必赢
- stones = 3: 拿三个，必赢
stones = 4: 不管拿几个，必输- stones = 5: 拿一个，必赢
- stones = 6: 拿两个，必赢
- stones = 7: 拿三个，必赢
stones = 8: 不管拿几个，必输- ...........
由此可见 当 stones 是 4 的倍数是必输
bool canWinNim(int n) {
return n % 4; // 无需考虑负数的情况，这个应该是调用者自己负责
}
