poj 2234 Matches Game 尼姆博弈

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本文介绍了一个简单的游戏——匹配游戏，并提出了一种算法来预测游戏中先手玩家是否能赢得比赛。游戏中两名玩家轮流从几堆火柴中取走任意数量的火柴，直到某一方无法继续取火柴时游戏结束。通过计算每堆火柴数的异或值来快速判断先手玩家是否有必胜策略。

Matches Game

Time Limit: 1000MS		Memory Limit: 65536K
Total Submissions: 11065		Accepted: 6466

Description

Here is a simple game. In this game, there are several piles of matches and two players. The two player play in turn. In each turn, one can choose a pile and take away arbitrary number of matches from the pile (Of course the number of matches, which is taken away, cannot be zero and cannot be larger than the number of matches in the chosen pile). If after a player’s turn, there is no match left, the player is the winner. Suppose that the two players are all very clear. Your job is to tell whether the player who plays first can win the game or not.

Input

The input consists of several lines, and in each line there is a test case. At the beginning of a line, there is an integer M (1 <= M <=20), which is the number of piles. Then comes M positive integers, which are not larger than 10000000. These M integers represent the number of matches in each pile.

Output

For each test case, output "Yes" in a single line, if the player who play first will win, otherwise output "No".

Sample Input

2 45 45
3 3 6 9

Sample Output

No
Yes

#include<iostream>
#include<algorithm>
#include<cstdio>
#include<cmath>
using namespace std;
int main() 
{
	int m,num;
	int ans;
	while(scanf("%d",&m)!=EOF)
	{
		cin>>ans;
		for(int i=1;i<m;i++)
		{
			cin>>num;
			ans=ans^num;
		}
		if(ans!=0)
		   cout<<"Yes"<<endl;
		else
		  cout<<"No"<<endl;
	}
	return 0;
}