hdu2669 6thweek trainning problem I、数论、线性方程

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

 

题意：

给你a和b，叫你求ax+by=1的x和y，要求是x为正整数，y为整数...   有就输出，没有就输出sorry。

 

分析：

扩展欧几里德算法。先用扩展欧几里德算法求出x，y然后再判断x是否大于0，如果小于0，则通过循环+b，直到x>0，在输出答案

 

 代码：

#include<iostream>
#include<cstdio>
using namespace std;

long long exgcd(long long a,long long b,long long& x,long long& y)
{
    if(b==0)
    {
        x=1,y=0;
        return a;
    }
    long long g = exgcd(b,a%b,y,x);
    y -= a/b*x;
    return g;
}

int main()
{
    long long m,n,x1,y1;
    while(cin >> m >> n)
    {
        if (exgcd(m,n,x1,y1) != 1)
            printf("sorry
");
        else
        {
            while(x1< 0)
            {
                 x1+= n;
                 y1-= m;
            }
            printf("%I64d %I64d
",x1,y1);
        }
    }
    return 0;
}