Cod sursa(job #2971681)

Utilizator HandoMihnea-Vicentiu Hando Data 27 ianuarie 2023 20:02:13
Problema Algoritmul lui Euclid extins Scor 100
Compilator cpp-64 Status done
Runda Arhiva educationala Marime 2.93 kb
#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>

#define ar array
#define vt vector
#define pq priority_queue
#define pu push
#define pub push_back
#define em emplace
#define emb emplace_back

#define all(x) x.begin(), x.end()
#define allr(x) x.rbegin(), x.rend()
#define allp(x, l, r) x.begin() + l, x.begin() + r
#define len(x) (int)x.size()

using namespace std;
using namespace __gnu_pbds;

using ll = long long;
using ld = long double;
using ull = unsigned long long;

template <class T, size_t N>
void re(array <T, N>& x);
template <class T> 
void re(vt <T>& x);

template <class T> 
void re(T& x) {
    cin >> x;
}

template <class T, class... M> 
void re(T& x, M&... args) {
    re(x); re(args...);
}

template <class T> 
void re(vt <T>& x) {
    for(auto& it : x)
        re(it);
}

template <class T, size_t N>
void re(array <T, N>& x) {
    for(auto& it : x)
        re(it);
}

template <class T, size_t N>
void wr(array <T, N> x);
template <class T> 
void wr(vt <T> x);

template <class T> 
void wr(T x) {
    cout << x;
}

template <class T, class ...M>  void wr(T x, M... args) {
    wr(x), wr(args...);
}

template <class T> 
void wr(vt <T> x) {
    for(auto it : x)
        wr(it, ' ');
}

template <class T, size_t N>
void wr(array <T, N> x) {
    for(auto it : x)
        wr(it, ' ');
}


inline void Open(const string Name) {
    #ifndef ONLINE_JUDGE
        (void)!freopen((Name + ".in").c_str(), "r", stdin);
        (void)!freopen((Name + ".out").c_str(), "w", stdout);
    #endif
}

void solve() {
    /* Not: gcd(a, b) = g */
    /* There is always: a * x + b * y = g */
    /* gcd(m * a, m * b) = m * g */

    function <ll(ll, ll, ll&, ll&)> gcd;
    ll a, b, c; re(a, b, c);

    gcd = [&](ll a, ll b, ll& x, ll& y) {
        if (b == 0) {
            /* g * 1 + 0 * 0 = g */
            x = 1;
            y = 0;
            return a;
        }

        /* Let's assume we found the coefficients (x1, y1) for (b, a mod b);
           and we want to find the pair (x, y) for (a, b): */

        ll x1, y1;
        ll d = gcd(b, a % b, x1, y1);

        /*  a mod b = a - floor(a / b) * b => 
            g = b * x1 + (a mod b) * y1 = b * x1 + (a - floor(a / b) * b) * y1 => after rearranging the terms 
            g = a * y1 + b * (x1 - y1 * floor(a / b))
            -------------------------------------------
            x = y1 and y = x1 - y1 * floor(a / b)
        */

        x = y1;
        y = x1 - y1 * floor(a / b);
        return d;
    };

    ll x, y;
    ll d = gcd(a, b, x, y);

    if(c % d == 0) {
        wr(x * c / d, ' ', y * c / d, '\n');
        return;
    }

    wr("0 0\n");
}

int main() {
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);

    Open("euclid3");

    int t; re(t);
    for(;t;t--) {
        solve();
    }
    
    return 0;
}