leetcode:292 Nim Game－每日编程第一题

[title3]Nim Game[/title3]

Total Accepted: 24894 Total Submissions: 49816 Difficulty: Easy



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.

思路：

1).当石子数量为4*n时，无论Ａ取1〜3个石头，Ｂ都可取3〜1个石头，使得每一轮石子总数－4，因此Ｂ可以确保取胜，Ａ输。

2).当石子总数为其他情况时，Ａ可取1~3个石头，使得石子总数变成4*n，跟据1).的分析，Ｂ此时必输，Ａ胜。

因此，当石子数量为 4*n时，Ａ输，其他情况Ａ胜。

<span style="font-weight: normal;">class Solution {
public:
    bool canWinNim(int n) {
        if(0==n%4) 
            return false;
        else
            return true;
    }
};</span>