hide handkerchief

本文通过一个有趣的寻宝游戏场景,介绍了如何使用最大公约数算法判断玩家是否能遍历所有位置找到宝藏。文章通过具体实例解释了算法原理,并提供了一段简洁的C语言代码实现。

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Problem Description
The Children’s Day has passed for some days .Has you remembered something happened at your childhood? I remembered I often played a game called hide handkerchief with my friends.
Now I introduce the game to you. Suppose there are N people played the game ,who sit on the ground forming a circle ,everyone owns a box behind them .Also there is a beautiful handkerchief hid in a box which is one of the boxes .
Then Haha(a friend of mine) is called to find the handkerchief. But he has a strange habit. Each time he will search the next box which is separated by M-1 boxes from the current box. For example, there are three boxes named A,B,C, and now Haha is at place of A. now he decide the M if equal to 2, so he will search A first, then he will search the C box, for C is separated by 2-1 = 1 box B from the current box A . Then he will search the box B ,then he will search the box A.
So after three times he establishes that he can find the beautiful handkerchief. Now I will give you N and M, can you tell me that Haha is able to find the handkerchief or not. If he can, you should tell me "YES", else tell me "POOR Haha".
 

Input
There will be several test cases; each case input contains two integers N and M, which satisfy the relationship: 1<=M<=100000000 and 3<=N<=100000000. When N=-1 and M=-1 means the end of input case, and you should not process the data.
 

Output
For each input case, you should only the result that Haha can find the handkerchief or not.
 

Sample Input
3 2 -1 -1

行吧,想必各位读者看到这题肯定与我当年一样,十分头大,这是啥啊,啥玩意儿啊,咋回事啊 。现在我们来抓一下题目的关键点,主要在于这位haha同学(个人感觉有强迫症)玩丢手绢游戏,非要跟别人不一样,偏不一个一个丢,一定要隔m-1个丢。但是,他又是围成圈丢的,所以haha一定能不断丢下去,并且每个人都能被丢到一次。等一下,想必所有读者听我说到这里,都发现了一个问题,那如果m与n不互质,haha怎么丢都会有人丢不到啊。所以,拨丝抽茧这道题的本质就是一个判断质数!当然,还要注意输入输出(永恒的命题)!

#include<stdio.h>
int gcd(int m,int n);
int main()
{
	int m,n;
	while(scanf("%d%d",&m,&n)&&m!=-1||n!=-1)
	{
		if(gcd(m,n)==1)
		{
			printf("YES\n");
		}
		else
		printf("POOR Haha\n");
	}
	return 0;
}
int gcd(int m,int n)
{
	int r;
	do
	{
		r=m%n;
		m=n;
		n=r;
	}while(r);
	return m;
}
所以很多时候做题看到复杂的题目,
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