[leetcode] Nim Game

题目：

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?

分析：该题重在找规律，不在于编码，找不到真正的规律，代码会报Time Limit Exceeded. 下面AC代码：

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

附上Time Limit Exceeded代码，当n=1348820612时，代码不能AC：

    public boolean canWinNim(int n) {
        if (n <= 3) {
            return true;
        } else if (n == 4) {
            return false;
        } else {
            boolean a1 = false, a2 = false, a3 = true;
            for (int i = 5; i <= n; i++) {
                boolean bn = !(a1 && a2 && a3);
                a1 = a2;
                a2 = a3;
                a3 = bn;    
            }
            return a3;
        }
    }

Time Limit Exceeded