Cod sursa(job #3348697)

Utilizator Carnu_EmilianCarnu Emilian Carnu_Emilian Data 23 martie 2026 16:50:04
Problema Algoritmul lui Euclid extins Scor 100
Compilator cpp-64 Status done
Runda Arhiva educationala Marime 0.81 kb
#include <bits/stdc++.h>
using namespace std;
ifstream fin("euclid3.in");
ofstream fout("euclid3.out");
typedef long long ll;

int t, a, b, c;

/*
ax + by = c
ax0 + by0 = cmmdc(a, b)
b * x0 + (a % b) * y0 = d
a / b = c
a % b = r
b * c + r = a
r = a - b * c
b * x0 + (a - b * c) * y0 = d
a * y0 + b * (x0 - c * y0) = d
 */

int euclid(int a, int b, int &x, int &y)
{
    if (b == 0)
    {
        // ax = a
        x = 1;
        y = 0;
        return a;
    }
    int x0, y0, d;
    d = euclid(b, a % b, x0, y0);
    x = y0;
    y = x0 - (a / b) * y0;
    return d;
}

int main()
{
    fin >> t;
    while(t--)
    {
        fin >> a >> b >> c;
        int x, y, d;
        d = euclid(a,b,x, y);
        if (c % d != 0)
            x = y = 0;
        x *= c / d;
        y *= c / d;
        fout << x << " " << y << '\n';
    }
}