cplib-cpp

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:heavy_check_mark: linear_algebra_matrix/test/linalg_semirings.yuki1340.test.cpp

Depends on

Code

#define PROBLEM "https://yukicoder.me/problems/no/1340"

#include "../../number/min_max_semiring.hpp"
#include "../../number/min_plus_semiring.hpp"
#include "../matrix.hpp"

#include <algorithm>
#include <cassert>
#include <iostream>
#include <utility>
using namespace std;

template <class Semiring> int solve(int N, const vector<pair<int, int>> &edges, long long T) {
    matrix<Semiring> mat(N, N);
    for (auto edge : edges) mat[edge.second][edge.first] = Semiring::id();
    vector<Semiring> initvec(N, Semiring());
    initvec[0] = Semiring::id();
    vector<Semiring> vec = mat.pow_vec(T, initvec);
    return count(vec.begin(), vec.end(), Semiring::id());
}

int main() {
    int N, M;
    long long T;
    cin >> N >> M >> T;
    vector<pair<int, int>> edges;
    while (M--) {
        int a, b;
        cin >> a >> b;
        edges.emplace_back(a, b);
    }

    auto sol1 = solve<min_max_semiring<int>>(N, edges, T);
    auto sol2 = solve<min_plus_semiring<int>>(N, edges, T);
    assert(sol1 == sol2);
    cout << sol1 << '\n';
}
#line 1 "linear_algebra_matrix/test/linalg_semirings.yuki1340.test.cpp"
#define PROBLEM "https://yukicoder.me/problems/no/1340"

#line 1 "number/min_max_semiring.hpp"
#include <limits>

// min-max 半環（加法が min, 乗法が max, 零元が INF, 単位元が -INF）
// Verified: abc236g
template <class T> struct min_max_semiring {
    T val;
    min_max_semiring() : val(std::numeric_limits<T>::max()) {
        static_assert(std::numeric_limits<T>::max() > 0,
                      "std::numeric_limits<>::max() must be properly defined");
    }
    min_max_semiring(T x) : val(x) {}
    static min_max_semiring id() { return T(std::numeric_limits<T>::min()); }
    static min_max_semiring max() { return T(); }
    min_max_semiring operator+(const min_max_semiring &r) const {
        return (this->val > r.val ? r.val : this->val);
    }
    min_max_semiring &operator+=(const min_max_semiring &r) { return *this = *this + r; }
    min_max_semiring operator*(const min_max_semiring &r) const {
        return (this->val < r.val ? r.val : this->val);
    }
    min_max_semiring &operator*=(const min_max_semiring &r) { return *this = *this * r; }
    bool operator==(const min_max_semiring &r) const { return this->val == r.val; }
    bool operator!=(const min_max_semiring &r) const { return !(*this == r); }
    template <class OStream> friend OStream &operator<<(OStream &os, const min_max_semiring &x) {
        return os << x.val;
    }
};
#line 2 "number/min_plus_semiring.hpp"

// min-plus 半環・トロピカル半環（加法が min, 乗法が plus, 零元が INF, 単位元が 0）
// INF = numeric_limits<T>::max() / 2 を超えたら INF に clamp する
// Verified: https://yukicoder.me/problems/no/1340
template <class T> struct min_plus_semiring {
    T val;
    static const T _T_inf() {
        static_assert(std::numeric_limits<T>::max() > 0,
                      "std::numeric_limits<>::max() must be properly defined");
        return std::numeric_limits<T>::max() / 2;
    }
    min_plus_semiring() : val(_T_inf()) {}
    min_plus_semiring(T x) : val(x) {}
    static min_plus_semiring id() { return min_plus_semiring(0); }
    min_plus_semiring operator+(const min_plus_semiring &r) const {
        return (this->val > r.val ? r.val : this->val);
    }
    min_plus_semiring &operator+=(const min_plus_semiring &r) { return *this = *this + r; }
    min_plus_semiring operator*(const min_plus_semiring &r) const {
        if (this->val == _T_inf() or r.val == _T_inf()) return min_plus_semiring();
        T tmp = this->val + r.val; // Watch out for overflow
        return _T_inf() < tmp ? min_plus_semiring() : min_plus_semiring(tmp);
    }
    min_plus_semiring &operator*=(const min_plus_semiring &r) { return *this = *this * r; }
    bool operator==(const min_plus_semiring &r) const { return this->val == r.val; }
    bool operator!=(const min_plus_semiring &r) const { return !(*this == r); }
    bool operator<(const min_plus_semiring &x) const { return this->val < x.val; }
    bool operator>(const min_plus_semiring &x) const { return this->val > x.val; }
    template <class OStream> friend OStream &operator<<(OStream &os, const min_plus_semiring &x) {
        return os << x.val;
    }
};
#line 2 "linear_algebra_matrix/matrix.hpp"
#include <algorithm>
#include <cassert>
#include <cmath>
#include <iterator>
#include <type_traits>
#include <utility>
#include <vector>

namespace matrix_ {
struct has_id_method_impl {
    template <class T_> static auto check(T_ *) -> decltype(T_::id(), std::true_type());
    template <class T_> static auto check(...) -> std::false_type;
};
template <class T_> struct has_id : decltype(has_id_method_impl::check<T_>(nullptr)) {};
} // namespace matrix_

template <typename T> struct matrix {
    int H, W;
    std::vector<T> elem;
    typename std::vector<T>::iterator operator[](int i) { return elem.begin() + i * W; }
    inline T &at(int i, int j) { return elem[i * W + j]; }
    inline T get(int i, int j) const { return elem[i * W + j]; }
    int height() const { return H; }
    int width() const { return W; }
    std::vector<std::vector<T>> vecvec() const {
        std::vector<std::vector<T>> ret(H);
        for (int i = 0; i < H; i++) {
            std::copy(elem.begin() + i * W, elem.begin() + (i + 1) * W, std::back_inserter(ret[i]));
        }
        return ret;
    }
    operator std::vector<std::vector<T>>() const { return vecvec(); }
    matrix() = default;
    matrix(int H, int W) : H(H), W(W), elem(H * W) {}
    matrix(const std::vector<std::vector<T>> &d) : H(d.size()), W(d.size() ? d[0].size() : 0) {
        for (auto &raw : d) std::copy(raw.begin(), raw.end(), std::back_inserter(elem));
    }

    template <typename T2, typename std::enable_if<matrix_::has_id<T2>::value>::type * = nullptr>
    static T2 _T_id() {
        return T2::id();
    }
    template <typename T2, typename std::enable_if<!matrix_::has_id<T2>::value>::type * = nullptr>
    static T2 _T_id() {
        return T2(1);
    }

    static matrix Identity(int N) {
        matrix ret(N, N);
        for (int i = 0; i < N; i++) ret.at(i, i) = _T_id<T>();
        return ret;
    }

    matrix operator-() const {
        matrix ret(H, W);
        for (int i = 0; i < H * W; i++) ret.elem[i] = -elem[i];
        return ret;
    }
    matrix operator*(const T &v) const {
        matrix ret = *this;
        for (auto &x : ret.elem) x *= v;
        return ret;
    }
    matrix operator/(const T &v) const {
        matrix ret = *this;
        const T vinv = _T_id<T>() / v;
        for (auto &x : ret.elem) x *= vinv;
        return ret;
    }
    matrix operator+(const matrix &r) const {
        matrix ret = *this;
        for (int i = 0; i < H * W; i++) ret.elem[i] += r.elem[i];
        return ret;
    }
    matrix operator-(const matrix &r) const {
        matrix ret = *this;
        for (int i = 0; i < H * W; i++) ret.elem[i] -= r.elem[i];
        return ret;
    }
    matrix operator*(const matrix &r) const {
        matrix ret(H, r.W);
        for (int i = 0; i < H; i++) {
            for (int k = 0; k < W; k++) {
                for (int j = 0; j < r.W; j++) ret.at(i, j) += this->get(i, k) * r.get(k, j);
            }
        }
        return ret;
    }
    matrix &operator*=(const T &v) { return *this = *this * v; }
    matrix &operator/=(const T &v) { return *this = *this / v; }
    matrix &operator+=(const matrix &r) { return *this = *this + r; }
    matrix &operator-=(const matrix &r) { return *this = *this - r; }
    matrix &operator*=(const matrix &r) { return *this = *this * r; }
    bool operator==(const matrix &r) const { return H == r.H and W == r.W and elem == r.elem; }
    bool operator!=(const matrix &r) const { return H != r.H or W != r.W or elem != r.elem; }
    bool operator<(const matrix &r) const { return elem < r.elem; }
    matrix pow(int64_t n) const {
        matrix ret = Identity(H);
        bool ret_is_id = true;
        if (n == 0) return ret;
        for (int i = 63 - __builtin_clzll(n); i >= 0; i--) {
            if (!ret_is_id) ret *= ret;
            if ((n >> i) & 1) ret *= (*this), ret_is_id = false;
        }
        return ret;
    }
    std::vector<T> pow_vec(int64_t n, std::vector<T> vec) const {
        matrix x = *this;
        while (n) {
            if (n & 1) vec = x * vec;
            x *= x;
            n >>= 1;
        }
        return vec;
    };
    matrix transpose() const {
        matrix ret(W, H);
        for (int i = 0; i < H; i++) {
            for (int j = 0; j < W; j++) ret.at(j, i) = this->get(i, j);
        }
        return ret;
    }
    // Gauss-Jordan elimination
    // - Require inverse for every non-zero element
    // - Complexity: O(H^2 W)
    template <typename T2, typename std::enable_if<std::is_floating_point<T2>::value>::type * = nullptr>
    static int choose_pivot(const matrix<T2> &mtr, int h, int c) noexcept {
        int piv = -1;
        for (int j = h; j < mtr.H; j++) {
            if (mtr.get(j, c) and (piv < 0 or std::abs(mtr.get(j, c)) > std::abs(mtr.get(piv, c))))
                piv = j;
        }
        return piv;
    }
    template <typename T2, typename std::enable_if<!std::is_floating_point<T2>::value>::type * = nullptr>
    static int choose_pivot(const matrix<T2> &mtr, int h, int c) noexcept {
        for (int j = h; j < mtr.H; j++) {
            if (mtr.get(j, c) != T2()) return j;
        }
        return -1;
    }
    matrix gauss_jordan() const {
        int c = 0;
        matrix mtr(*this);
        std::vector<int> ws;
        ws.reserve(W);
        for (int h = 0; h < H; h++) {
            if (c == W) break;
            int piv = choose_pivot(mtr, h, c);
            if (piv == -1) {
                c++;
                h--;
                continue;
            }
            if (h != piv) {
                for (int w = 0; w < W; w++) {
                    std::swap(mtr[piv][w], mtr[h][w]);
                    mtr.at(piv, w) *= -_T_id<T>(); // To preserve sign of determinant
                }
            }
            ws.clear();
            for (int w = c; w < W; w++) {
                if (mtr.at(h, w) != T()) ws.emplace_back(w);
            }
            const T hcinv = _T_id<T>() / mtr.at(h, c);
            for (int hh = 0; hh < H; hh++)
                if (hh != h) {
                    const T coeff = mtr.at(hh, c) * hcinv;
                    for (auto w : ws) mtr.at(hh, w) -= mtr.at(h, w) * coeff;
                    mtr.at(hh, c) = T();
                }
            c++;
        }
        return mtr;
    }
    int rank_of_gauss_jordan() const {
        for (int i = H * W - 1; i >= 0; i--) {
            if (elem[i] != 0) return i / W + 1;
        }
        return 0;
    }
    int rank() const { return gauss_jordan().rank_of_gauss_jordan(); }

    T determinant_of_upper_triangle() const {
        T ret = _T_id<T>();
        for (int i = 0; i < H; i++) ret *= get(i, i);
        return ret;
    }
    int inverse() {
        assert(H == W);
        std::vector<std::vector<T>> ret = Identity(H), tmp = *this;
        int rank = 0;
        for (int i = 0; i < H; i++) {
            int ti = i;
            while (ti < H and tmp[ti][i] == T()) ti++;
            if (ti == H) {
                continue;
            } else {
                rank++;
            }
            ret[i].swap(ret[ti]), tmp[i].swap(tmp[ti]);
            T inv = _T_id<T>() / tmp[i][i];
            for (int j = 0; j < W; j++) ret[i][j] *= inv;
            for (int j = i + 1; j < W; j++) tmp[i][j] *= inv;
            for (int h = 0; h < H; h++) {
                if (i == h) continue;
                const T c = -tmp[h][i];
                for (int j = 0; j < W; j++) ret[h][j] += ret[i][j] * c;
                for (int j = i + 1; j < W; j++) tmp[h][j] += tmp[i][j] * c;
            }
        }
        *this = ret;
        return rank;
    }
    friend std::vector<T> operator*(const matrix &m, const std::vector<T> &v) {
        assert(m.W == int(v.size()));
        std::vector<T> ret(m.H);
        for (int i = 0; i < m.H; i++) {
            for (int j = 0; j < m.W; j++) ret[i] += m.get(i, j) * v[j];
        }
        return ret;
    }
    friend std::vector<T> operator*(const std::vector<T> &v, const matrix &m) {
        assert(int(v.size()) == m.H);
        std::vector<T> ret(m.W);
        for (int i = 0; i < m.H; i++) {
            for (int j = 0; j < m.W; j++) ret[j] += v[i] * m.get(i, j);
        }
        return ret;
    }
    std::vector<T> prod(const std::vector<T> &v) const { return (*this) * v; }
    std::vector<T> prod_left(const std::vector<T> &v) const { return v * (*this); }
    template <class OStream> friend OStream &operator<<(OStream &os, const matrix &x) {
        os << "[(" << x.H << " * " << x.W << " matrix)";
        os << "\n[column sums: ";
        for (int j = 0; j < x.W; j++) {
            T s = T();
            for (int i = 0; i < x.H; i++) s += x.get(i, j);
            os << s << ",";
        }
        os << "]";
        for (int i = 0; i < x.H; i++) {
            os << "\n[";
            for (int j = 0; j < x.W; j++) os << x.get(i, j) << ",";
            os << "]";
        }
        os << "]\n";
        return os;
    }
    template <class IStream> friend IStream &operator>>(IStream &is, matrix &x) {
        for (auto &v : x.elem) is >> v;
        return is;
    }
};
#line 6 "linear_algebra_matrix/test/linalg_semirings.yuki1340.test.cpp"

#line 9 "linear_algebra_matrix/test/linalg_semirings.yuki1340.test.cpp"
#include <iostream>
#line 11 "linear_algebra_matrix/test/linalg_semirings.yuki1340.test.cpp"
using namespace std;

template <class Semiring> int solve(int N, const vector<pair<int, int>> &edges, long long T) {
    matrix<Semiring> mat(N, N);
    for (auto edge : edges) mat[edge.second][edge.first] = Semiring::id();
    vector<Semiring> initvec(N, Semiring());
    initvec[0] = Semiring::id();
    vector<Semiring> vec = mat.pow_vec(T, initvec);
    return count(vec.begin(), vec.end(), Semiring::id());
}

int main() {
    int N, M;
    long long T;
    cin >> N >> M >> T;
    vector<pair<int, int>> edges;
    while (M--) {
        int a, b;
        cin >> a >> b;
        edges.emplace_back(a, b);
    }

    auto sol1 = solve<min_max_semiring<int>>(N, edges, T);
    auto sol2 = solve<min_plus_semiring<int>>(N, edges, T);
    assert(sol1 == sol2);
    cout << sol1 << '\n';
}
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