test/semiring_matrix.test.cpp

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• Last update: 2022-01-28 13:07:07+09:00
• Problem: https://judge.yosupo.jp/problem/matrix_product

Depends on

• math/rem_euclid.cpp
• math/semiring_matrix.cpp
• math/static_modint.cpp
• math/totient.cpp
• traits/num_ring.cpp
• traits/product_monoid.cpp
• traits/sum_group.cpp
• utility/int_alias.cpp
• utility/rep.cpp

Code

#define PROBLEM "https://judge.yosupo.jp/problem/matrix_product"
#include <iostream>
#include <vector>
#include "../math/semiring_matrix.cpp"
#include "../math/static_modint.cpp"
#include "../traits/num_ring.cpp"
#include "../utility/int_alias.cpp"
#include "../utility/rep.cpp"

using Fp = Modint998244353;
using Matrix = SemiRingMatrix<NumRing<Fp>>;

int main() {
    int N, M, K;
    std::cin >> N >> M >> K;
    std::vector<std::vector<Fp>> A(N, std::vector<Fp>(M));
    std::vector<std::vector<Fp>> B(M, std::vector<Fp>(K));
    for (auto& v : A) {
        for (auto& x : v) {
            u32 t;
            std::cin >> t;
            x = Fp(t);
        }
    }
    for (auto& v : B) {
        for (auto& x : v) {
            u32 t;
            std::cin >> t;
            x = Fp(t);
        }
    }
    const auto C = Matrix(A) * Matrix(B);
    for (const auto i : rep(0, N)) {
        for (const auto j : rep(0, K)) {
            std::cout << C(i, j) << " \n"[j + 1 == K];
        }
    }
}

#line 1 "test/semiring_matrix.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/matrix_product"
#include <iostream>
#include <vector>
#line 2 "math/semiring_matrix.cpp"
#include <array>
#include <cassert>
#include <initializer_list>
#line 2 "utility/int_alias.cpp"
#include <cstdint>

using i32 = std::int32_t;
using u32 = std::uint32_t;
using i64 = std::int64_t;
using u64 = std::uint64_t;
using i128 = __int128_t;
using u128 = __uint128_t;
#line 2 "utility/rep.cpp"
#include <algorithm>

class Range {
    struct Iter {
        int itr;
        constexpr Iter(const int pos) noexcept : itr(pos) {}
        constexpr void operator++() noexcept { ++itr; }
        constexpr bool operator!=(const Iter& other) const noexcept { return itr != other.itr; }
        constexpr int operator*() const noexcept { return itr; }
    };
    const Iter first, last;

  public:
    explicit constexpr Range(const int first, const int last) noexcept : first(first), last(std::max(first, last)) {}
    constexpr Iter begin() const noexcept { return first; }
    constexpr Iter end() const noexcept { return last; }
};

constexpr Range rep(const int l, const int r) noexcept { return Range(l, r); }
constexpr Range rep(const int n) noexcept { return Range(0, n); }
#line 8 "math/semiring_matrix.cpp"

template <class S> class SemiRingMatrix {
    using T = typename S::Type;
    using A = typename S::Sum;
    using M = typename S::Product;
    using Self = SemiRingMatrix;
    std::vector<std::vector<T>> data;

  public:
    SemiRingMatrix() = default;
    explicit SemiRingMatrix(const int h, const int w, const T& val = A::zero()) : data(h, std::vector<T>(w, val)) {}

    SemiRingMatrix(const std::vector<std::vector<T>>& vec) : data(vec) {
        for (const auto& v : data) assert(v.size() == width());
    }
    SemiRingMatrix(const std::initializer_list<std::initializer_list<T>>& list) {
        data.reserve(list.size());
        for (const auto& v : list) data.emplace_back(v.begin(), v.end());
        for (const auto& v : data) assert(v.size() == width());
    }

    int height() const { return data.size(); }
    int width() const { return data.empty() ? 0 : data[0].size(); }

    T& operator()(const int i, const int j) {
        assert(0 <= i and i < height());
        assert(0 <= j and j < width());
        return data[i][j];
    }
    const T& operator()(const int i, const int j) const {
        assert(0 <= i and i < height());
        assert(0 <= j and j < width());
        return data[i][j];
    }

    Self operator+(const Self& other) const { return Self(*this) += other; }
    Self& operator+=(const Self& other) {
        assert(height() == other.height());
        assert(width() == other.width());
        for (const int i : rep(height()))
            for (const int j : rep(width())) data[i][j] = A::operation(data[i][j], other.data[i][j]);
        return *this;
    }

    Self operator*(const Self& other) const {
        assert(width() == other.height());
        Self ret(height(), other.width(), A::identity());
        for (const int i : rep(height()))
            for (const int k : rep(width()))
                for (const int j : rep(other.width()))
                    ret.data[i][j] = A::operation(ret.data[i][j], M::operation(data[i][k], other.data[k][j]));
        return ret;
    }

    Self operator*(const T& other) const { return Self(*this) *= other; }
    Self& operator*=(const T& other) {
        for (const int i : rep(height()))
            for (const int j : rep(width())) data[i][j] = M::operation(data[i][j], other);
    }

    Self pow(u64 exp) const {
        assert(height() == width());
        Self ret(height(), width(), A::identity()), mult(*this);
        for (const int i : rep(height())) ret.data[i][i] = M::identity();
        for (; exp > 0; exp >>= 1) {
            if (exp & 1) ret = ret * mult;
            mult = mult * mult;
        }
        return ret;
    }
};
#line 2 "math/static_modint.cpp"
#include <ostream>
#include <type_traits>
#line 3 "math/rem_euclid.cpp"

template <class T> constexpr T rem_euclid(T value, const T& mod) {
    assert(mod > 0);
    return (value %= mod) >= 0 ? value : value + mod;
}
#line 2 "math/totient.cpp"

template <class T> constexpr T totient(T x) {
    T ret = x;
    for (T i = 2; i * i <= x; ++i) {
        if (x % i == 0) {
            ret /= i;
            ret *= i - 1;
            while (x % i == 0) x /= i;
        }
    }
    if (x > 1) {
        ret /= x;
        ret *= x - 1;
    }
    return ret;
}
#line 7 "math/static_modint.cpp"

template <u32 MOD, std::enable_if_t<((u32)1 <= MOD and MOD <= ((u32)1 << 31))>* = nullptr> class StaticModint {
    using Self = StaticModint;

    static inline constexpr u32 PHI = totient(MOD);
    u32 v;

  public:
    static constexpr u32 mod() noexcept { return MOD; }

    template <class T, std::enable_if_t<std::is_integral_v<T>>* = nullptr>
    static constexpr T normalize(const T& x) noexcept {
        return rem_euclid<std::common_type_t<T, i64>>(x, MOD);
    }

    constexpr StaticModint() noexcept : v(0) {}
    template <class T> constexpr StaticModint(const T& x) noexcept : v(normalize(x)) {}
    template <class T> static constexpr Self raw(const T& x) noexcept {
        Self ret;
        ret.v = x;
        return ret;
    }

    constexpr u32 val() const noexcept { return v; }
    constexpr Self neg() const noexcept { return raw(v == 0 ? 0 : MOD - v); }
    constexpr Self inv() const noexcept { return pow(PHI - 1); }
    constexpr Self pow(u64 exp) const noexcept {
        Self ret(1), mult(*this);
        for (; exp > 0; exp >>= 1) {
            if (exp & 1) ret *= mult;
            mult *= mult;
        }
        return ret;
    }

    constexpr Self operator-() const noexcept { return neg(); }
    constexpr Self operator~() const noexcept { return inv(); }

    constexpr Self operator+(const Self& rhs) const noexcept { return Self(*this) += rhs; }
    constexpr Self& operator+=(const Self& rhs) noexcept {
        if ((v += rhs.v) >= MOD) v -= MOD;
        return *this;
    }

    constexpr Self operator-(const Self& rhs) const noexcept { return Self(*this) -= rhs; }
    constexpr Self& operator-=(const Self& rhs) noexcept {
        if (v < rhs.v) v += MOD;
        v -= rhs.v;
        return *this;
    }

    constexpr Self operator*(const Self& rhs) const noexcept { return Self(*this) *= rhs; }
    constexpr Self& operator*=(const Self& rhs) noexcept {
        v = (u64)v * rhs.v % MOD;
        return *this;
    }

    constexpr Self operator/(const Self& rhs) const noexcept { return Self(*this) /= rhs; }
    constexpr Self& operator/=(const Self& rhs) noexcept { return *this *= rhs.inv(); }

    constexpr bool operator==(const Self& rhs) const noexcept { return v == rhs.v; }
    constexpr bool operator!=(const Self& rhs) const noexcept { return v != rhs.v; }
    friend std::ostream& operator<<(std::ostream& stream, const Self& rhs) { return stream << rhs.v; }
};

using Modint1000000007 = StaticModint<1000000007>;
using Modint998244353 = StaticModint<998244353>;
#line 2 "traits/sum_group.cpp"

template <class T> struct SumGroup {
    using Type = T;
    static constexpr T identity() { return T(0); }
    static constexpr T operation(const T& l, const T& r) { return l + r; }
    static constexpr T inverse(const T& x) { return -x; }
};
#line 2 "traits/product_monoid.cpp"

template <class T> struct ProductMonoid {
    using Type = T;
    static constexpr T identity() { return T(1); }
    static constexpr T operation(const T& l, const T& r) { return l * r; }
};
#line 4 "traits/num_ring.cpp"

template <class T> struct NumRing {
    using Type = T;
    using Sum = SumGroup<T>;
    using Product = ProductMonoid<T>;
};
#line 9 "test/semiring_matrix.test.cpp"

using Fp = Modint998244353;
using Matrix = SemiRingMatrix<NumRing<Fp>>;

int main() {
    int N, M, K;
    std::cin >> N >> M >> K;
    std::vector<std::vector<Fp>> A(N, std::vector<Fp>(M));
    std::vector<std::vector<Fp>> B(M, std::vector<Fp>(K));
    for (auto& v : A) {
        for (auto& x : v) {
            u32 t;
            std::cin >> t;
            x = Fp(t);
        }
    }
    for (auto& v : B) {
        for (auto& x : v) {
            u32 t;
            std::cin >> t;
            x = Fp(t);
        }
    }
    const auto C = Matrix(A) * Matrix(B);
    for (const auto i : rep(0, N)) {
        for (const auto j : rep(0, K)) {
            std::cout << C(i, j) << " \n"[j + 1 == K];
        }
    }
}

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