quotient ring / 剰余環 $\mathbb{Z}/n\mathbb{Z}$
(modulus/mint.hpp)

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• Last update: 2021-08-30 04:35:37+09:00
• Include: #include "modulus/mint.hpp"

Depends on

• modulus/modinv.hpp
• modulus/modpow.hpp

Required by

• the Bell number (前処理 $O(NK)$ + $O(1)$) (modulus/bell_number.hpp)
• combination / 組合せ ${} _ n C _ r$ (前処理 $O(n)$ + $O(1)$) (modulus/choose.hpp)
• combination / 組合せ ${} _ n C _ r$ (愚直 $O(r)$) (modulus/choose_simple.hpp)
• modulus/factorial.hpp
• formal power series / 形式的羃級数環 $\mathbb{Z}/n\mathbb{Z}\lbrack\lbrack x\rbrack\rbrack$ (modulus/formal_power_series.hpp)
• Garner's algorithm (modulus/garner.hpp)
• $\mathbb{Z}$ の乗除算を $\mathbb{Z}/n\mathbb{Z}$ の上でやるデータ構造 (modulus/mint_with_zero.hpp)
• 重複組合せ ${} _ n H _ r = {} _ {n + r - 1} C _ r$ (前処理 $O(n)$ + $O(1)$) (modulus/multichoose.hpp)
• 重複組合せ ${} _ n H _ r = {} _ {n + r - 1} C _ r$ (愚直 $O(r)$) (modulus/multichoose_simple.hpp)
• Number Theoretic Transformation (NTT) for Proth primes (modulus/number_theoretic_transformation.hpp)
• multiprecation on $\mathbb{Z}/n\mathbb{Z}[x]$ (modulus/number_theoretic_transformation_with_garner.hpp)
• the partition number (前処理 $O(NK)$ + $O(1)$) (modulus/partition_number.hpp)
• permutation / 順列 ${} _ n P _ r$ (前処理 $O(n)$ + $O(1)$) (modulus/permute.hpp)
• the Stirling number of the second kind (for given $N$, compute $S(N, \ast)$ in $O(N \log N)$) (modulus/stirling_number_of_the_second_kind_convolution.hpp)
• the Stirling number of the second kind ($O(K \log N)$) (modulus/stirling_number_of_the_second_kind_direct.hpp)
• the Stirling number of the second kind (前処理 $O(NK)$ + $O(1)$) (modulus/stirling_number_of_the_second_kind_table.hpp)
• twelvefold way / 写像12相 (modulus/twelvefold_way.hpp)

Verified with

• data_structure/lazy_propagation_red_black_tree.range_affine_range_sum.test.cpp
• data_structure/lazy_propagation_segment_tree.range_affine_range_sum.test.cpp
• data_structure/link_cut_tree.dynamic_tree_vertex_set_path_composite.test.cpp
• data_structure/link_cut_tree.vertex_set_path_composite.test.cpp
• data_structure/segment_tree.point_set_range_composite.test.cpp
• data_structure/sliding_window_aggregation.yosupo.test.cpp
• graph/tree_decomposition.aoj_2405.test.cpp
• modulus/choose.yukicoder-1035.test.cpp
• modulus/formal_power_series.exp.test.cpp
• modulus/formal_power_series.inv.test.cpp
• modulus/formal_power_series.log.test.cpp
• modulus/formal_power_series.yukicoder-1145.test.cpp
• modulus/mint_with_zero.test.cpp
• modulus/number_theoretic_transformation.yosupo.test.cpp
• modulus/number_theoretic_transformation_with_garner.yosupo.test.cpp
• modulus/stirling_number_of_the_second_kind_convolution.yosupo.test.cpp
• modulus/twelvefold_way.balls_and_boxes_1.test.cpp
• modulus/twelvefold_way.balls_and_boxes_10.test.cpp
• modulus/twelvefold_way.balls_and_boxes_11.test.cpp
• modulus/twelvefold_way.balls_and_boxes_2.test.cpp
• modulus/twelvefold_way.balls_and_boxes_3.test.cpp
• modulus/twelvefold_way.balls_and_boxes_4.test.cpp
• modulus/twelvefold_way.balls_and_boxes_5.test.cpp
• modulus/twelvefold_way.balls_and_boxes_6.test.cpp
• modulus/twelvefold_way.balls_and_boxes_7.test.cpp
• modulus/twelvefold_way.balls_and_boxes_8.test.cpp
• modulus/twelvefold_way.balls_and_boxes_9.test.cpp
• number/fast_fourier_transformation.yukicoder-856.test.cpp
• number/matrix.yukicoder-1073.test.cpp
• number/matrix_template.yukicoder-1073.test.cpp
• number/primes_extra.yukicoder-1659.test.cpp

Code

#pragma once
#include <cstdint>
#include <iostream>
#include "../modulus/modpow.hpp"
#include "../modulus/modinv.hpp"

/**
 * @brief quotient ring / 剰余環 $\mathbb{Z}/n\mathbb{Z}$
 */
template <int32_t MOD>
struct mint {
    int32_t value;
    mint() : value() {}
    mint(int64_t value_) : value(value_ < 0 ? value_ % MOD + MOD : value_ >= MOD ? value_ % MOD : value_) {}
    mint(int32_t value_, std::nullptr_t) : value(value_) {}
    explicit operator bool() const { return value; }
    inline mint<MOD> operator + (mint<MOD> other) const { return mint<MOD>(*this) += other; }
    inline mint<MOD> operator - (mint<MOD> other) const { return mint<MOD>(*this) -= other; }
    inline mint<MOD> operator * (mint<MOD> other) const { return mint<MOD>(*this) *= other; }
    inline mint<MOD> & operator += (mint<MOD> other) { this->value += other.value; if (this->value >= MOD) this->value -= MOD; return *this; }
    inline mint<MOD> & operator -= (mint<MOD> other) { this->value -= other.value; if (this->value <    0) this->value += MOD; return *this; }
    inline mint<MOD> & operator *= (mint<MOD> other) { this->value = (uint_fast64_t)this->value * other.value % MOD; return *this; }
    inline mint<MOD> operator - () const { return mint<MOD>(this->value ? MOD - this->value : 0, nullptr); }
    inline bool operator == (mint<MOD> other) const { return value == other.value; }
    inline bool operator != (mint<MOD> other) const { return value != other.value; }
    inline mint<MOD> pow(uint64_t k) const { return mint<MOD>(modpow(value, k, MOD), nullptr); }
    inline mint<MOD> inv() const { return mint<MOD>(modinv(value, MOD), nullptr); }
    inline mint<MOD> operator / (mint<MOD> other) const { return *this * other.inv(); }
    inline mint<MOD> & operator /= (mint<MOD> other) { return *this *= other.inv(); }
};
template <int32_t MOD> mint<MOD> operator + (int64_t value, mint<MOD> n) { return mint<MOD>(value) + n; }
template <int32_t MOD> mint<MOD> operator - (int64_t value, mint<MOD> n) { return mint<MOD>(value) - n; }
template <int32_t MOD> mint<MOD> operator * (int64_t value, mint<MOD> n) { return mint<MOD>(value) * n; }
template <int32_t MOD> mint<MOD> operator / (int64_t value, mint<MOD> n) { return mint<MOD>(value) / n; }
template <int32_t MOD> std::istream & operator >> (std::istream & in, mint<MOD> & n) { int64_t value; in >> value; n = value; return in; }
template <int32_t MOD> std::ostream & operator << (std::ostream & out, mint<MOD> n) { return out << n.value; }

#line 2 "modulus/mint.hpp"
#include <cstdint>
#include <iostream>
#line 2 "modulus/modpow.hpp"
#include <cassert>
#line 4 "modulus/modpow.hpp"

inline int32_t modpow(uint_fast64_t x, uint64_t k, int32_t MOD) {
    assert (/* 0 <= x and */ x < (uint_fast64_t)MOD);
    uint_fast64_t y = 1;
    for (; k; k >>= 1) {
        if (k & 1) (y *= x) %= MOD;
        (x *= x) %= MOD;
    }
    assert (/* 0 <= y and */ y < (uint_fast64_t)MOD);
    return y;
}
#line 2 "modulus/modinv.hpp"
#include <algorithm>
#line 5 "modulus/modinv.hpp"

inline int32_t modinv_nocheck(int32_t value, int32_t MOD) {
    assert (0 <= value and value < MOD);
    if (value == 0) return -1;
    int64_t a = value, b = MOD;
    int64_t x = 0, y = 1;
    for (int64_t u = 1, v = 0; a; ) {
        int64_t q = b / a;
        x -= q * u; std::swap(x, u);
        y -= q * v; std::swap(y, v);
        b -= q * a; std::swap(b, a);
    }
    if (not (value * x + MOD * y == b and b == 1)) return -1;
    if (x < 0) x += MOD;
    assert (0 <= x and x < MOD);
    return x;
}

inline int32_t modinv(int32_t x, int32_t MOD) {
    int32_t y = modinv_nocheck(x, MOD);
    assert (y != -1);
    return y;
}
#line 6 "modulus/mint.hpp"

/**
 * @brief quotient ring / 剰余環 $\mathbb{Z}/n\mathbb{Z}$
 */
template <int32_t MOD>
struct mint {
    int32_t value;
    mint() : value() {}
    mint(int64_t value_) : value(value_ < 0 ? value_ % MOD + MOD : value_ >= MOD ? value_ % MOD : value_) {}
    mint(int32_t value_, std::nullptr_t) : value(value_) {}
    explicit operator bool() const { return value; }
    inline mint<MOD> operator + (mint<MOD> other) const { return mint<MOD>(*this) += other; }
    inline mint<MOD> operator - (mint<MOD> other) const { return mint<MOD>(*this) -= other; }
    inline mint<MOD> operator * (mint<MOD> other) const { return mint<MOD>(*this) *= other; }
    inline mint<MOD> & operator += (mint<MOD> other) { this->value += other.value; if (this->value >= MOD) this->value -= MOD; return *this; }
    inline mint<MOD> & operator -= (mint<MOD> other) { this->value -= other.value; if (this->value <    0) this->value += MOD; return *this; }
    inline mint<MOD> & operator *= (mint<MOD> other) { this->value = (uint_fast64_t)this->value * other.value % MOD; return *this; }
    inline mint<MOD> operator - () const { return mint<MOD>(this->value ? MOD - this->value : 0, nullptr); }
    inline bool operator == (mint<MOD> other) const { return value == other.value; }
    inline bool operator != (mint<MOD> other) const { return value != other.value; }
    inline mint<MOD> pow(uint64_t k) const { return mint<MOD>(modpow(value, k, MOD), nullptr); }
    inline mint<MOD> inv() const { return mint<MOD>(modinv(value, MOD), nullptr); }
    inline mint<MOD> operator / (mint<MOD> other) const { return *this * other.inv(); }
    inline mint<MOD> & operator /= (mint<MOD> other) { return *this *= other.inv(); }
};
template <int32_t MOD> mint<MOD> operator + (int64_t value, mint<MOD> n) { return mint<MOD>(value) + n; }
template <int32_t MOD> mint<MOD> operator - (int64_t value, mint<MOD> n) { return mint<MOD>(value) - n; }
template <int32_t MOD> mint<MOD> operator * (int64_t value, mint<MOD> n) { return mint<MOD>(value) * n; }
template <int32_t MOD> mint<MOD> operator / (int64_t value, mint<MOD> n) { return mint<MOD>(value) / n; }
template <int32_t MOD> std::istream & operator >> (std::istream & in, mint<MOD> & n) { int64_t value; in >> value; n = value; return in; }
template <int32_t MOD> std::ostream & operator << (std::ostream & out, mint<MOD> n) { return out << n.value; }

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