hdu 2669 Romantic

Problem 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

 此题是最基本的扩展欧几里得算法的应用，也是最好的理解和练手题。代码如下：

#include<stdio.h>
int exgcd(int a,int b,__int64&x,__int64 &y)
{
    if(b==0)
    { x=1;y=0;return a;}
    int r=exgcd(b,a%b,x,y);
    int t=x;x=y;y=t-a/b*y;
    return r;
}
int main()
{
    int a,b;__int64 x,y;//x,y在计算的过程中可能会溢出，故用__int64
    while(scanf("%d%d",&a,&b)!=EOF)
    {
        int m=exgcd(a,b,x,y);
        if(m!=1)
            printf("sorry
");
        else {
            x=(x%b+b)%b;
            y=(1-x*a)/b;
            printf("%I64d %I64d
",x,y);
        }
    }
    return 0;
}

如果不是很理解，可以先理解一下扩展欧几里得算法的原理。