数学概念——I - 数论，线性方程

I - 数论，线性方程

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

Submit Status

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

解题思路：

这里用到了扩展欧里几德算法模板

但是主要的内容是最大公约数的问题

程序代码：

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