LeetCode 292. Nim Game

Posted 2020-08-17

Problem:
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.

 此题为技巧题,需知道Nim Game的Wining Strange，即在自己的局中，如果剩余数目为4的倍数，则不可能取胜。因此检测N是否为4的倍数即可。Background参见http://www.cdf.toronto.edu/~ajr/270/probsess/03/strategy.html

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