ku-library

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:heavy_check_mark: Matrix (行列) (math/matrix.hpp)

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#pragma once

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

/**
 * @brief Matrix (行列)
 */
template <typename T>
class Matrix {
  private:
    vector<vector<T>> data;

  public:
    Matrix() : Matrix(0) {}
    explicit Matrix(int _h) : Matrix(_h, _h) {}
    explicit Matrix(int _h, int _w) : data(_h, vector<T>(_w, T{})) {}

    //! 単位行列
    static Matrix identity(int s) {
        Matrix res(s);

        rep (i, 0, s) {
            res.set(i, i, T(1));
        }

        return res;
    }

    int row() const {
        return data.size();
    }

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

    T get(int i, int j) const {
        assert(0 <= i && i < row());
        assert(0 <= j && j < col());

        return data[i][j];
    }

    void set(int i, int j, const T v) {
        assert(0 <= i && i < row());
        assert(0 <= j && j < col());

        data[i][j] = v;

        return;
    }

    friend bool operator==(const Matrix& lhs, const Matrix& rhs) {
        return lhs.data == rhs.data;
    }

    friend bool operator!=(const Matrix& lhs, const Matrix& rhs) {
        return lhs.data != rhs.data;
    }

    friend Matrix operator*(const Matrix& lhs, const Matrix& rhs) {
        assert(lhs.col() == rhs.row());

        Matrix res(lhs.row(), rhs.col());
        rep (i, 0, lhs.row()) {
            rep (j, 0, rhs.col()) {
                rep (k, 0, lhs.col()) {
                    res.set(i, j, res.get(i, j) + lhs.get(i, k) * rhs.get(k, j));
                }
            }
        }

        return res;
    }

    Matrix& operator*=(const Matrix& rhs) {
        return *this = *this * rhs;
    }

    Matrix pow(ll y) const {
        assert(row() == col());
        assert(0 <= y);

        Matrix res = identity(row());
        Matrix x = *this;

        while (y > 0) {
            if ((y & 1) != 0) {
                res *= x;
            }

            x *= x;
            y >>= 1;
        }

        return res;
    }
};

#line 2 "math/matrix.hpp"

#line 2 "template/template.hpp"

/**
 * @author ku_senjan
 * @title 提出用テンプレート
 * @see https://github.com/kogetsu0728/ku-library
 */

#line 2 "template/constant.hpp"

#line 2 "template/include.hpp"

#ifdef LOCAL
#define _GLIBCXX_DEBUG
#endif

#include <bits/stdc++.h>
using namespace std;
#line 2 "template/type_alias.hpp"

#line 4 "template/type_alias.hpp"

using uint = unsigned int;
using ll = long long;
using ull = unsigned long long;

using ld = long double;

template <class T, bool REVERSE = false>
using heap = priority_queue<T, vector<T>, conditional_t<REVERSE, greater<T>, less<T>>>;
#line 5 "template/constant.hpp"

template <class T>
inline constexpr T INF = numeric_limits<T>::max() / 2;

inline constexpr array<int, 4> DY4 = {0, -1, 0, 1};
inline constexpr array<int, 4> DX4 = {1, 0, -1, 0};
inline constexpr array<int, 8> DY8 = {0, -1, -1, -1, 0, 1, 1, 1};
inline constexpr array<int, 8> DX8 = {1, 1, 0, -1, -1, -1, 0, 1};

inline constexpr char LF = '\n';
#line 2 "template/macro.hpp"

#line 5 "template/macro.hpp"

/**
 * @see https://trap.jp/post/1224/
 */

#ifdef LOCAL
inline constexpr bool IS_LOCAL = true;
#else
inline constexpr bool IS_LOCAL = false;
#endif

#define IF_LOCAL if constexpr (IS_LOCAL)

#define all(a) begin(a), end(a)
#define rall(a) rbegin(a), rend(a)

#define overload4(a, b, c, d, e, ...) e

#define rep1(i, a) for (ll i = 0; (i) < (ll)(a); ++(i))
#define rep2(i, a, b) for (ll i = (ll)(a); (i) < (ll)(b); ++(i))
#define rep3(i, a, b, c) for (ll i = (ll)(a); (i) < (ll)(b); (i) += (ll)(c))
#define rep(...) overload4(__VA_ARGS__, rep3, rep2, rep1)(__VA_ARGS__)

#define rrep1(i, a) for (ll i = (ll)(a); (i) >= 0; --(i))
#define rrep2(i, a, b) for (ll i = (ll)(a); (i) >= (ll)(b); --(i))
#define rrep3(i, a, b, c) for (ll i = (ll)(a); (i) >= (ll)(b); (i) -= (ll)(c))
#define rrep(...) overload4(__VA_ARGS__, rrep3, rrep2, rrep1)(__VA_ARGS__)
#line 13 "template/template.hpp"

#line 2 "utility/choose_min_max.hpp"

/**
 * @title Choose Minimum / Maximum
 */

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

    return false;
}

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

    return false;
}
#line 2 "utility/set_io.hpp"

#line 4 "utility/set_io.hpp"

void set_io(int d = 16) {
    cin.tie(nullptr);
    ios_base::sync_with_stdio(false);
    cout << fixed << setprecision(d);

    return;
}
#line 4 "math/matrix.hpp"

/**
 * @brief Matrix (行列)
 */
template <typename T>
class Matrix {
  private:
    vector<vector<T>> data;

  public:
    Matrix() : Matrix(0) {}
    explicit Matrix(int _h) : Matrix(_h, _h) {}
    explicit Matrix(int _h, int _w) : data(_h, vector<T>(_w, T{})) {}

    //! 単位行列
    static Matrix identity(int s) {
        Matrix res(s);

        rep (i, 0, s) {
            res.set(i, i, T(1));
        }

        return res;
    }

    int row() const {
        return data.size();
    }

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

    T get(int i, int j) const {
        assert(0 <= i && i < row());
        assert(0 <= j && j < col());

        return data[i][j];
    }

    void set(int i, int j, const T v) {
        assert(0 <= i && i < row());
        assert(0 <= j && j < col());

        data[i][j] = v;

        return;
    }

    friend bool operator==(const Matrix& lhs, const Matrix& rhs) {
        return lhs.data == rhs.data;
    }

    friend bool operator!=(const Matrix& lhs, const Matrix& rhs) {
        return lhs.data != rhs.data;
    }

    friend Matrix operator*(const Matrix& lhs, const Matrix& rhs) {
        assert(lhs.col() == rhs.row());

        Matrix res(lhs.row(), rhs.col());
        rep (i, 0, lhs.row()) {
            rep (j, 0, rhs.col()) {
                rep (k, 0, lhs.col()) {
                    res.set(i, j, res.get(i, j) + lhs.get(i, k) * rhs.get(k, j));
                }
            }
        }

        return res;
    }

    Matrix& operator*=(const Matrix& rhs) {
        return *this = *this * rhs;
    }

    Matrix pow(ll y) const {
        assert(row() == col());
        assert(0 <= y);

        Matrix res = identity(row());
        Matrix x = *this;

        while (y > 0) {
            if ((y & 1) != 0) {
                res *= x;
            }

            x *= x;
            y >>= 1;
        }

        return res;
    }
};
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