NumberTheory/Math/Extended_euclid.h

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• Last update: 2025-06-08 06:31:53+07:00

Depends on

• template.h

Verified with

• NumberTheory/Math/test/aizu_ntl_1_e_extended_euclid.test.cpp

Code

#include "../../template.h"


int extended1(int a, int b, int &x, int &y) {
    if (b == 0) {
        x = 1, y = 0;
        return a;
    }
    int x1, y1;
    int d = extended1(b, a%b, x1, y1);
    x = y1;
    y = x1-y1*(a/b);
    return d;
}

// Iterative version
int extended2(int a, int b, int &x, int &y) {
    x = 1, y = 0;
    int x1 = 0, y1 = 1;
    int a1 = a, b1 = b;
    while (b1) {
        int q = a1 / b1;
        tie(x, x1) = make_tuple(x1, x - q * x1);
        tie(y, y1) = make_tuple(y1, y - q * y1);
        tie(a1, b1) = make_tuple(b1, a1 - q * b1);
    }
    return a1;
}

#line 2 "template.h"

#include <bits/stdc++.h>
using namespace std;
 
#define ll long long
#define MOD (ll)(1e9+7)
#define all(x) (x).begin(),(x).end()
#define unique(x) x.erase(unique(all(x)), x.end())
#define INF32 ((1ull<<31)-1)
#define INF64 ((1ull<<63)-1)
#define inf (ll)1e18

#define vi vector<int>
#define pii pair<int, int>
#define pll pair<ll, ll>
#define fi first
#define se second

const int mod = 998244353;

void solve();

int main(){
    ios_base::sync_with_stdio(false);cin.tie(NULL);
    // cin.exceptions(cin.failbit);
    // int t; cin >> t;
    // while(t--)
        solve();
    cerr << "\nTime run: " << 1000 * clock() / CLOCKS_PER_SEC << "ms" << '\n';
    return 0;
}
#line 2 "NumberTheory/Math/Extended_euclid.h"


int extended1(int a, int b, int &x, int &y) {
    if (b == 0) {
        x = 1, y = 0;
        return a;
    }
    int x1, y1;
    int d = extended1(b, a%b, x1, y1);
    x = y1;
    y = x1-y1*(a/b);
    return d;
}

// Iterative version
int extended2(int a, int b, int &x, int &y) {
    x = 1, y = 0;
    int x1 = 0, y1 = 1;
    int a1 = a, b1 = b;
    while (b1) {
        int q = a1 / b1;
        tie(x, x1) = make_tuple(x1, x - q * x1);
        tie(y, y1) = make_tuple(y1, y - q * y1);
        tie(a1, b1) = make_tuple(b1, a1 - q * b1);
    }
    return a1;
}

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