Leetcode #292 Nim Game

Description

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.

Explain

显然1,2,3为必胜态，4时无论取1,2,3都会进入必胜态，故4为必败态，以此类推可以在O（n）复杂度推出n为必胜或必败，也可看规律，4的倍数为必败态，O（1）复杂度判即可

Code

class Solution(object):    def canWinNim(self, n):        """        :type n: int        :rtype: bool        """        if n % 4 == 0:            return False        else:            return True