Leetcode-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.

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

分析 ：
n在区间[1,3]时，先取的人必定赢
当n为4时，先取的必输
n为5时，先取的必然可以找到一个赢的方法，能够化为n为4的情况，相当于后取的必然输

总结为：
当n % 4不为0时，先取者必胜；否则先取者必负。