codeforce 7C 扩展欧几里得算法

http://codeforces.com/problemset/problem/7/C

A line on the plane is described by an equation Ax + By + C =0. You are to find any point on this line, whose coordinates are integer numbers from  - 5·1018 to 5·1018 inclusive, or to find out that such points do not exist.

Input

The first line contains three integers A, B and C ( - 2·109 ≤ A, B, C ≤ 2·109) — corresponding coefficients of the line equation. It is guaranteed that A2 + B2 > 0.

Output

If the required point exists, output its coordinates, otherwise output -1.

Sample test(s)

input

2 5 3

output

6 -3

扩展欧几里得  http://blog.csdn.net/lvshubao1314/article/details/249327330

思路：先将A,B,C除以gcd(a,b)，此时保证A,B已经互素，调用模板求出的特解x，y 只需乘上c即为答案。

#include <iostream>
#include <string.h>
#include <algorithm>
#include <stdio.h>

using namespace std;
typedef long long LL;
LL gcd(LL a,LL b)
{
    return b ? gcd(b,a%b):a;
}
void extend_Euclid(LL a,LL b,LL &x,LL & y)
{
    if(b == 0)
    {
        x = 1;
        y = 0;
        return;
    }
    extend_Euclid(b,a%b,x,y);
    LL tmp = x;
    x = y;
    y = tmp - (a / b) * y;
}
int main()
{
    LL a,b,c,x,y;;
    while(cin>>a>>b>>c)
    {
        c=-c;
        LL g=gcd(a,b);
        if(c%g)
        {
            printf("-1\n");
            continue;
        }
        a/=g;
        b/=g;
        c/=g;
        extend_Euclid(a,b,x,y);
        printf("%lld %lld\n",x*c,y*c);
    }
    return 0;
}