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.

這道題的感想就是要多找找規律。

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

其實用遞歸和動態規劃也可以模擬的，只是到後面就超時了。

public class Solution {
    public boolean canWinNim(int n) {
        if (n == 1 || n == 2 || n == 3) {
            return true;
        }
        if (n == 4) {
            return false;
        }
        boolean first = canWinNim(n - 1);
        boolean second = canWinNim(n - 2);
        boolean third = canWinNim(n - 3);
        if (!first || !second || !third) {
            return true;
        }
        return false;
    }
}

Nim Game Leetcode