LeetCode292. Nim Game

船桥

于 2018-12-09 20:40:27 发布

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本文探讨了Nim游戏的胜负策略，通过分析游戏规则，得出了一种简单有效的获胜方法：只要确保每次两人共拿4个石头，用总数对4取余，根据余数决定首次拿取数量，即可在Nim游戏中稳操胜券。

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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.

Example:

Input: 
4
Output: false 
Explanation: 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:小时候玩过的游戏,只要确保每次两个人共拿(1+3)=4个,用总数对4取余.看余出几个,第一次就取几个,然后一直取和为4,就可以赢了.

class Solution:
    def canWinNim(self, n):
        """
        :type n: int
        :rtype: bool
        """
        return n%4 != 0