modint
(utility/modint.hpp)

• View this file on GitHub
• Last update: 2023-11-14 18:27:43+09:00
• Include: #include "utility/modint.hpp"

説明

modを自動で取ってくれる構造体。割り算は素数の場合のみ正常に動作。

Depends on

• テンプレート (template/template.hpp)

Required by

• NTT convolution (convolution/ntt.hpp)
• convolution/ntt4.hpp
• $f(g(x))$ (fps/composition_of_fps.hpp)
• $f(x)$ の逆関数 (fps/compositional_inverse_of_fps.hpp)
• Formal Power Series (fps/fps.hpp)
• Multipoint Evaluation (fps/multipoint_evaluation.hpp)
• Polynomial Interpolation (fps/polynomial_interpolation.hpp)
• $f(x + c)$ (fps/taylor_shift.hpp)

Verified with

• test/convolution/Convolution_mod.test.cpp
• test/convolution/Convolution_mod_ntt4.test.cpp
• test/convolution/Subset_Convolution.test.cpp
• test/data_structure/Point_Set_Range_Composite.test.cpp
• test/data_structure/Range_Affine_Range_Sum.test.cpp
• test/math/Sum_of_Totient_Function.test.cpp
• test/polynomial/Composition_of_Formal_Power_Series.test.cpp
• test/polynomial/Compositional_Inverse_of_Formal_Power_Series.test.cpp
• test/polynomial/Exp_of_FPS_Sparse.test.cpp
• test/polynomial/Exp_of_Formal_Power_Series.test.cpp
• test/polynomial/Inv_of_FPS_Sparse.test.cpp
• test/polynomial/Inv_of_Formal_Power_Series.test.cpp
• test/polynomial/Kth_term_of_Linearly_Recurrent_Sequence.test.cpp
• test/polynomial/Log_of_FPS_Sparse.test.cpp
• test/polynomial/Log_of_Formal_Power_Series.test.cpp
• test/polynomial/Multipoint_Evaluation.test.cpp
• test/polynomial/Polynomial_Interpolation.test.cpp
• test/polynomial/Polynomial_Taylor_Shift.test.cpp
• test/polynomial/Pow_of_FPS_Sparse.test.cpp
• test/polynomial/Pow_of_Formal_Power_Series.test.cpp
• test/tree/Tree_Path_Composite_Sum.test.cpp

Code

#pragma once

#include "../template/template.hpp"

namespace lib {

template <ll m> struct modint {
    using mint = modint;
    ll a;

    modint(ll x = 0) : a((x % m + m) % m) {}
    static constexpr ll mod() {
        return m;
    }
    ll val() const {
        return a;
    }
    ll& val() {
        return a;
    }
    mint pow(ll n) const {
        mint res = 1;
        mint x = a;
        while (n) {
            if (n & 1) res *= x;
            x *= x;
            n >>= 1;
        }
        return res;
    }
    mint inv() const {
        return pow(m - 2);
    }
    mint& operator+=(const mint rhs) {
        a += rhs.a;
        if (a >= m) a -= m;
        return *this;
    }
    mint& operator-=(const mint rhs) {
        if (a < rhs.a) a += m;
        a -= rhs.a;
        return *this;
    }
    mint& operator*=(const mint rhs) {
        a = a * rhs.a % m;
        return *this;
    }
    mint& operator/=(mint rhs) {
        *this *= rhs.inv();
        return *this;
    }
    friend mint operator+(const mint& lhs, const mint& rhs) {
        return mint(lhs) += rhs;
    }
    friend mint operator-(const mint& lhs, const mint& rhs) {
        return mint(lhs) -= rhs;
    }
    friend mint operator*(const mint& lhs, const mint& rhs) {
        return mint(lhs) *= rhs;
    }
    friend mint operator/(const mint& lhs, const mint& rhs) {
        return mint(lhs) /= rhs;
    }
    friend bool operator==(const modint &lhs, const modint &rhs) {
        return lhs.a == rhs.a;
    }
    friend bool operator!=(const modint &lhs, const modint &rhs) {
        return !(lhs == rhs);
    }
    mint operator+() const {
        return *this;
    }
    mint operator-() const {
        return mint() - *this;
    }
};

using modint998244353 = modint<998244353>;
using modint1000000007 = modint<1'000'000'007>;

}  // namespace lib

#line 2 "utility/modint.hpp"

#line 2 "template/template.hpp"

#include <bits/stdc++.h>

#define rep(i, s, n) for (int i = (int)(s); i < (int)(n); i++)
#define rrep(i, s, n) for (int i = (int)(n)-1; i >= (int)(s); i--)
#define all(v) v.begin(), v.end()

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

template <typename T> bool chmin(T &a, const T &b) {
    if (a <= b) return false;
    a = b;
    return true;
}
template <typename T> bool chmax(T &a, const T &b) {
    if (a >= b) return false;
    a = b;
    return true;
}

namespace lib {

using namespace std;

}  // namespace lib

// using namespace lib;
#line 4 "utility/modint.hpp"

namespace lib {

template <ll m> struct modint {
    using mint = modint;
    ll a;

    modint(ll x = 0) : a((x % m + m) % m) {}
    static constexpr ll mod() {
        return m;
    }
    ll val() const {
        return a;
    }
    ll& val() {
        return a;
    }
    mint pow(ll n) const {
        mint res = 1;
        mint x = a;
        while (n) {
            if (n & 1) res *= x;
            x *= x;
            n >>= 1;
        }
        return res;
    }
    mint inv() const {
        return pow(m - 2);
    }
    mint& operator+=(const mint rhs) {
        a += rhs.a;
        if (a >= m) a -= m;
        return *this;
    }
    mint& operator-=(const mint rhs) {
        if (a < rhs.a) a += m;
        a -= rhs.a;
        return *this;
    }
    mint& operator*=(const mint rhs) {
        a = a * rhs.a % m;
        return *this;
    }
    mint& operator/=(mint rhs) {
        *this *= rhs.inv();
        return *this;
    }
    friend mint operator+(const mint& lhs, const mint& rhs) {
        return mint(lhs) += rhs;
    }
    friend mint operator-(const mint& lhs, const mint& rhs) {
        return mint(lhs) -= rhs;
    }
    friend mint operator*(const mint& lhs, const mint& rhs) {
        return mint(lhs) *= rhs;
    }
    friend mint operator/(const mint& lhs, const mint& rhs) {
        return mint(lhs) /= rhs;
    }
    friend bool operator==(const modint &lhs, const modint &rhs) {
        return lhs.a == rhs.a;
    }
    friend bool operator!=(const modint &lhs, const modint &rhs) {
        return !(lhs == rhs);
    }
    mint operator+() const {
        return *this;
    }
    mint operator-() const {
        return mint() - *this;
    }
};

using modint998244353 = modint<998244353>;
using modint1000000007 = modint<1'000'000'007>;

}  // namespace lib

Back to top page