Extended Euclidean Algorithm (Solving Diophantine equations)

Extended Euclidean Algorithm (Solving Diophantine equations)

Algorithm

Code

ll gcd(ll a, ll b, ll & x, ll & y) {
    if (!a) {
        x = 0, y = 1;
        return b;
    }
    ll x1, y1;
    ll d = gcd(b % a, a, x1, y1);
    x = y1 - (b / a) * x1;
    y = x1;
    return d;
}

bool diophantine(ll a, ll b, ll c, ll & x0, ll & y0, ll & g) {
    g = gcd(abs(a), abs(b), x0, y0);
    if (c % g) return false;
    x0 *= c / g;
    y0 *= c / g;
    if (a < 0) x0 = -x0;
    if (b < 0) y0 = -y0;
    return true;
}