math/inv_mod.hpp

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Last update: 2024-02-23 10:38:03+09:00
Include: #include "math/inv_mod.hpp"

Depends on

math/extended_gcd.hpp

Required by

math/baby_step_giant_step.hpp

Code

#pragma once

#include <cassert>
#include "math/extended_gcd.hpp"

// mod >= 2
long long inv_mod(long long a, long long mod) {
    a %= mod;
    if (a < 0) a += mod;
    assert(a != 0);
    auto [x, y, g] = extended_gcd(a, mod);
    x %= mod;
    if (x < 0) x += mod;
    return x;
}

#line 2 "math/inv_mod.hpp"

#include <cassert>
#line 2 "math/extended_gcd.hpp"

#include <tuple>
// find (x, y) s.t. ax + by = gcd(a, b)
// a, b >= 0
// return {x, y, gcd(a, b)}
template <class T> std::tuple<T, T, T> extended_gcd(T a, T b) {
    if (b == 0) return {1, 0, a};
    auto [y, x, g] = extended_gcd(b, a % b);
    return {x, y - (a / b) * x, g};
}
#line 5 "math/inv_mod.hpp"

// mod >= 2
long long inv_mod(long long a, long long mod) {
    a %= mod;
    if (a < 0) a += mod;
    assert(a != 0);
    auto [x, y, g] = extended_gcd(a, mod);
    x %= mod;
    if (x < 0) x += mod;
    return x;
}