mod int
(math/modint.cpp)

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• Last update: 2021-09-12 23:44:25+09:00

概要

演算で全て mod を取る整数型。mod の除算などで何も考えないで済む。

• 四則演算 , 代入 ( +, -, *, /, +=, -=, *=, /=)
• pow(x) : x 乗
• inverse() : mod上の逆元

計算量

• 除算 : $O(log\ mod)$
• pow(x) : $O(log\ n)$
• inverse() : $O(log\ mod)$
• その他 : $O(1)$

Depends on

• math/extgcd.cpp
• template/template.cpp

Required by

• Combination (nCk) (math/Combination.cpp)
• math/combination_big.cpp
• math/matrix.cpp

Verified with

• test/Combination.test.cpp
• test/SegmentTree.test.cpp

Code

#pragma once
#include "../template/template.cpp"
#include "math/extgcd.cpp"

template <int MOD>
struct mint {
    int32_t n;
    mint() : n(0) {}
    mint(ll x) : n(x >= 0 ? x % MOD : (MOD - (-x) % MOD) % MOD) {}

    mint &operator+=(const mint &p) {
        if ((n += p.n) >= MOD) n -= MOD;
        return *this;
    }
    mint &operator-=(const mint &p) {
        if ((n += MOD - p.n) >= MOD) n -= MOD;
        return *this;
    }
    mint &operator*=(const mint &p) {
        n = 1ll * n * p.n % MOD;
        return *this;
    }
    mint &operator/=(const mint &p) {
        *this *= p.inverse();
        return *this;
    }
    mint operator-() const { return mint(-n); }
    mint operator+(const mint &p) const { return mint(*this) += p; }
    mint operator-(const mint &p) const { return mint(*this) -= p; }
    mint operator*(const mint &p) const { return mint(*this) *= p; }
    mint operator/(const mint &p) const { return mint(*this) /= p; }
    bool operator==(const mint &p) const { return n == p.n; }
    bool operator!=(const mint &p) const { return n != p.n; }

    friend ostream &operator<<(ostream &os, const mint &p) {
        return os << p.n;
    }
    friend istream &operator>>(istream &is, mint &p) {
        int x;
        is >> x;
        p = mint(x);
        return is;
    }
    mint pow(int64_t x) const {
        mint res(1), mul(n);
        while (x > 0) {
            if (x & 1) res *= mul;
            mul *= mul;
            x >>= 1;
        }
        return res;
    }
    mint inverse() const {
        return mint(modinv(n,MOD));
    }
};
/*
@brief mod int
@docs docs/modint.md
*/

#line 2 "template/template.cpp"
#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define rep(i, n) for (int i = 0; i < n; i++)
#define REP(i, n) for (int i = 1; i < n; i++)
#define rev(i, n) for (int i = n - 1; i >= 0; i--)
#define REV(i, n) for (int i = n - 1; i > 0; i--)
#define all(v) v.begin(), v.end()
#define PL pair<ll, ll>
#define PI pair<int, int>
#define pi acos(-1)
#define len(s) (int)s.size()
#define compress(v) \
    sort(all(v));   \
    v.erase(unique(all(v)), v.end());
#define comid(v, x) lower_bound(all(v), x) - v.begin()

template<class T>
using prique=priority_queue<T,vector<T>,greater<>>;

template <class T, class U>
inline bool chmin(T &a, U b) {
    if (a > b) {
        a = b;
        return true;
    }
    return false;
}
template <class T, class U>
inline bool chmax(T &a, U b) {
    if (a < b) {
        a = b;
        return true;
    }
    return false;
}
constexpr ll inf = 3e18;
#line 3 "math/extgcd.cpp"

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

ll modinv(ll a, ll m) {
    ll x, y;
    extGCD(a, m, x, y);
    return (x % m + m) % m;
}
#line 4 "math/modint.cpp"

template <int MOD>
struct mint {
    int32_t n;
    mint() : n(0) {}
    mint(ll x) : n(x >= 0 ? x % MOD : (MOD - (-x) % MOD) % MOD) {}

    mint &operator+=(const mint &p) {
        if ((n += p.n) >= MOD) n -= MOD;
        return *this;
    }
    mint &operator-=(const mint &p) {
        if ((n += MOD - p.n) >= MOD) n -= MOD;
        return *this;
    }
    mint &operator*=(const mint &p) {
        n = 1ll * n * p.n % MOD;
        return *this;
    }
    mint &operator/=(const mint &p) {
        *this *= p.inverse();
        return *this;
    }
    mint operator-() const { return mint(-n); }
    mint operator+(const mint &p) const { return mint(*this) += p; }
    mint operator-(const mint &p) const { return mint(*this) -= p; }
    mint operator*(const mint &p) const { return mint(*this) *= p; }
    mint operator/(const mint &p) const { return mint(*this) /= p; }
    bool operator==(const mint &p) const { return n == p.n; }
    bool operator!=(const mint &p) const { return n != p.n; }

    friend ostream &operator<<(ostream &os, const mint &p) {
        return os << p.n;
    }
    friend istream &operator>>(istream &is, mint &p) {
        int x;
        is >> x;
        p = mint(x);
        return is;
    }
    mint pow(int64_t x) const {
        mint res(1), mul(n);
        while (x > 0) {
            if (x & 1) res *= mul;
            mul *= mul;
            x >>= 1;
        }
        return res;
    }
    mint inverse() const {
        return mint(modinv(n,MOD));
    }
};
/*
@brief mod int
@docs docs/modint.md
*/

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