Cod sursa(job #1818914)

Utilizator zeboftwAlex Mocanu zeboftw Data 29 noiembrie 2016 22:35:48
Problema Algoritmul lui Euclid extins Scor 100
Compilator cpp Status done
Runda Arhiva educationala Marime 0.93 kb
#include <fstream>

using namespace std;

ifstream fin("euclid3.in");
ofstream fout("euclid3.out");

// a * x + b * y = d
// b * x0 + a % b * y0 = d
// b * x0 + (a - b * c) * y0 = a * x + b * y
// b * x0 - b * y - b * c * y0 = a * x - a * y0
// b * (x0 - y - c * y0) = a * (x-y0)
// x0 - y - c * y0 = 0
// y = x0 - c * y0

void euclidE (int a, int b, int *d, int *x, int *y)
{
    if (b == 0)
    {
        *d = a;
        *x = 1;
        *y = 0;
    }
    else
    {
        int x0, y0;
        euclidE(b, a%b, d, &x0, &y0);
        *x = y0;
        *y = x0 - (a / b) * y0;
    }
}

int main()
{
    int n;
    fin >> n;
    for (int i = 1; i <= n; i++)
    {
        int a, b, gcd, x, x0, y0;
        fin >> a >> b >> x;
        euclidE(a, b, &gcd, &x0, &y0);
        if (x % gcd == 0) fout << x0 * (x / gcd) << ' ' << y0 * (x / gcd);
        else fout << "0 0";
        fout << '\n';
    }
    return 0;
}