modulus/modinv.hpp

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• Last update: 2020-06-16 07:51:56+09:00
• Include: #include "modulus/modinv.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)
• quotient ring / 剰余環 $\mathbb{Z}/n\mathbb{Z}$ (modulus/mint.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)
• discrete log / 離散対数 (the baby-step giant-step, $O(\sqrt{m})$) (modulus/modlog.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/modlog.yosupo.test.cpp
• modulus/modlog.yuki1255.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 <algorithm>
#include <cassert>
#include <cstdint>

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 2 "modulus/modinv.hpp"
#include <algorithm>
#include <cassert>
#include <cstdint>

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;
}

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