292. Nim Game

题目描述：

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.

思路一：

如果n是4的整数倍，无论第一个人怎么挑选，第二个人都可以挑选到最后一个石头

如果n不是4的整数倍，第一个人可以挑选石头，使得剩下的石头的个数是4的整数倍，这样，第一个人可以挑选到最后一个石头。

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

思路二： Memory Limit Exceeded

class Solution {
    public boolean canWinNim(int n) {
        if (n <= 0)
            return false;
        if (n < 4)
            return true;
        boolean[] res = new boolean[n + 1];
        res[1] = true;
        res[2] = true;
        res[3] = true;
        for (int i = 4; i <= n; i++)
            res[i] = !(res[i - 1] && res[i - 2] && res[i - 3]);
        return res[n];
    }
}