292. Nim Game

Total Accepted: 55175  Total Submissions: 105975  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.

Hint:

1. If there are 5 stones in the heap, could you figure out a way to remove the stones such that you will always be the winner?

分析：

将问题规模缩小，找规律：
桌子上只有1个我必赢，2个我必赢，3个我必赢，4个我必输，5个我必赢，6个必赢，7个必赢，

8个，也就是两个4，我无论怎么摸石头都能让对手以4为一个坎最后摸完石头，所以必输
也就是说n%4==0必输了哦？最后试了一下，的确是这样的。

class Solution {
public:
    bool canWinNim(int n) {
        return n%4!=0;//卧槽，此题代码可以如此简单，意义何在？
    }
};

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原文地址：http://blog.csdn.net/ebowtang/article/details/50435187

原作者博客：http://blog.csdn.net/ebowtang