[博弈游戏]Euclid's Game(0099)-SWUST_OJ

Description

Starts with two unequal positive numbers (M,N and M>N) on the board. Two players move in turn. On each move, a player has to write on the board a positive number equal to the difference of two numbers already on the board; this number must be new, i.e., different from all the numbers already on the board. The player who cannot move loses the game. Should you choose to move first or second in this game? 

According to the above rules, there are two players play tihs game. Assumptions A write a number on the board at first, then B write it. 

Your task is write a program to judge the winner is A or B.

 

Two unequal positive numbers M and N , M>N (M<1000000)

A or B

3 1

A

#include<iostream>
using namespace std;
int main()
{
	int m, n, c,x,y;
	cin >> m >> n;
	x = m;
	y = n;
	while (y)
	{
		c = x%y;
		x=y;
		y = c;
	}
	m /= x;
	if (m % 2)
		cout << "A" << endl;
	else
		cout << "B" << endl;
	return 0;
}

利用欧几里得算法将求出最大公约数，而又有规律可知结果与m的奇偶性有关系，使m,n互质，再根据规律得出A还是Ｂ会赢得这次比赛