数论-线性方程——Program H

线性方程

Time Limit:1000MS     Memory Limit:32768KB     64bit IO Format:%I64d & %I64u

Description

The Sky is Sprite. 
The Birds is Fly in the Sky. 
The Wind is Wonderful. 
Blew Throw the Trees 
Trees are Shaking, Leaves are Falling. 
Lovers Walk passing, and so are You. 
................................Write in English class by yifenfei

Girls are clever and bright. In HDU every girl like math. Every girl like to solve math problem! 
Now tell you two nonnegative integer a and b. Find the nonnegative integer X and integer Y to satisfy X*a + Y*b = 1. If no such answer print "sorry" instead.

Input

The input contains multiple test cases. 
Each case two nonnegative integer a,b (0<a, b<=2^31)

Output

output nonnegative integer X and integer Y, if there are more answers than the X smaller one will be choosed. If no answer put "sorry" instead.

Sample Input

　　77 　　51

　　10 　　44

　　34 　　79

Sample Output

　　2　　　-3

　　sorry

　　7　　　-3

题目大意：已知线性方程ax+by=1；输入a，b的值，要求输出x，y的值，若没有，输出“sorry”。

分析：求线性方程的解用扩展欧几里得算法，再判断gcd(a,b)=d是否等于1.

代码如下：

#include <iostream>
#include <cstdio>

using namespace std;
void gcd(long long a,long long b,long long &d,long long &x,long long &y)
{
	if(!b)
	{
		d=a;
		x=1;
		y=0;
	}
	else
	{
		gcd(b,a%b,d,y,x);
		y-=x*(a/b);
	}
}
int main()
{
	long long  a,b;
	while(scanf("%lld%lld",&a,&b)==2)
	{
		long long d,x,y;
		gcd(a,b,d,x,y);
		if(d==1)
		{
			while(x<0)
			{
				x=x+b;
				y=y-a;
			}
			printf("%lld %lld\n",x,y);
		}
		else
			printf("sorry\n");
	}
	return 0;
}