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#include "matrix/base.hpp"
#pragma once #include <algorithm> #include <cassert> #include <iostream> #include <ranges> #include <vector> namespace ebi { template <class T> struct matrix; template <class T> matrix<T> identify_matrix(int n) { matrix<T> a(n, n); for (int i = 0; i < n; i++) { a[i][i] = 1; } return a; } template <class T> struct matrix { private: using Self = matrix<T>; public: matrix(int n_, int m_, T init_val = 0) : n(n_), m(m_), data(n * m, init_val) {} matrix(const std::vector<std::vector<T>> &a) : n((int)a.size()), m((int)a[0].size()) { data = std::vector(n * m); for (int i = 0; i < n; i++) { std::copy(a[i].begin(), a[i].end(), data.begin() + i * m); } } Self operator+(Self &rhs) const noexcept { return Self(*this) += rhs; } Self operator-(Self &rhs) const noexcept { return Self(*this) -= rhs; } Self operator*(Self &rhs) const noexcept { return Self(*this) *= rhs; } Self operator/(Self &rhs) const noexcept { return Self(*this) /= rhs; } friend Self operator*(const T &lhs, const Self &rhs) { return Self(rhs) *= lhs; } friend Self operator*(const Self &lhs, const T &rhs) { return Self(lhs) *= rhs; } Self &operator+=(Self &rhs) noexcept { assert(this->size() == rhs.size()); for (int i = 0; i < n; ++i) { for (int j = 0; j < m; ++j) { data[i][j] += rhs[i][j]; } } return *this; } Self &operator-=(Self &rhs) noexcept { assert(this->size() == rhs.size()); for (int i = 0; i < n; ++i) { for (int j = 0; j < m; ++j) { data[i][j] -= rhs[i][j]; } } return *this; } Self &operator*=(Self &rhs) noexcept { int h = n, w = rhs.column_size(); assert(m == rhs.row_size()); Self ret(h, w); for (int i = 0; i < h; ++i) { for (int k = 0; k < m; ++k) { for (int j = 0; j < w; ++j) { ret[i][j] += (*this)[i][k] * rhs[k][j]; } } } return *this = ret; } Self &operator/=(const Self &rhs) noexcept { auto ret = rhs.inv(); assert(ret); return *this *= ret.value(); } Self &operator*=(const T &rhs) noexcept { for (int i = 0; i < n; i++) { for (int j = 0; j < m; j++) { (*this)[i][j] *= rhs; } } return *this; } const auto operator[](int i) const { return std::ranges::subrange(data.begin() + i * m, data.begin() + (i + 1) * m); } auto operator[](int i) { return std::ranges::subrange(data.begin() + i * m, data.begin() + (i + 1) * m); } void swap(int i, int j) { std::swap_ranges(data.begin() + i * m, data.begin() + (i + 1) * m, data.begin() + j * m); } Self transposition() const { Self res(m, n); for (int i = 0; i < n; i++) { for (int j = 0; j < m; j++) { res[j][i] = data[i][j]; } } return res; } std::optional<Self> inv() const { assert(row_size() == column_size()); Self a = *this; Self b = identify_matrix<T>(n); for (int r = 0; r < n; r++) { for (int i = r; i < n; i++) { if (a[i][r] != 0) { a.swap(r, i); b.swap(r, i); break; } } if (a[r][r] == 0) return std::nullopt; T x = a[r][r].inv(); for (int j = 0; j < n; j++) { if (r < j) a[r][j] *= x; b[r][j] *= x; } for (int i = 0; i < n; i++) { if (i == r) continue; for (int j = 0; j < n; j++) { if (r < j) a[i][j] -= a[i][r] * a[r][j]; b[i][j] -= a[i][r] * b[r][j]; } } } return b; } Self pow(long long k) const { assert(row_size() == column_size() && k >= 0); Self res = identify_matrix<T>(row_size()); Self x = *this; while (k) { if (k & 1) res *= x; x *= x; k >>= 1; } return res; } int row_size() const { return n; } int column_size() const { return m; } std::pair<int, int> size() const { return {n, m}; } private: int n, m; std::vector<T> data; }; template <class T> T det(matrix<T> a) { assert(a.row_size() == a.column_size()); T d = 1; int n = a.row_size(); for (int r = 0; r < n; r++) { if (a[r][r] == 0) { for (int i = r + 1; i < n; i++) { if (a[i][r] != 0) { a.swap(r, i); d = -d; } } } if (a[r][r] == 0) return 0; d *= a[r][r]; T inv = a[r][r].inv(); for (int i = r + 1; i < n; i++) { T x = a[i][r] * inv; for (int j = r; j < n; j++) { a[i][j] -= x * a[r][j]; } } } return d; } template <class T> std::istream &operator>>(std::istream &os, matrix<T> &a) { for (int i = 0; i < a.row_size(); i++) { for (int j = 0; j < a.column_size(); j++) { os >> a[i][j]; } } return os; } template <class T> std::ostream &operator<<(std::ostream &os, const matrix<T> &a) { for (int i = 0; i < a.row_size(); i++) { for (int j = 0; j < a.column_size(); j++) { os << a[i][j]; if (j < a.column_size() - 1) os << ' '; } if (i < a.row_size() - 1) os << '\n'; } return os; } } // namespace ebi
#line 2 "matrix/base.hpp" #include <algorithm> #include <cassert> #include <iostream> #include <ranges> #include <vector> namespace ebi { template <class T> struct matrix; template <class T> matrix<T> identify_matrix(int n) { matrix<T> a(n, n); for (int i = 0; i < n; i++) { a[i][i] = 1; } return a; } template <class T> struct matrix { private: using Self = matrix<T>; public: matrix(int n_, int m_, T init_val = 0) : n(n_), m(m_), data(n * m, init_val) {} matrix(const std::vector<std::vector<T>> &a) : n((int)a.size()), m((int)a[0].size()) { data = std::vector(n * m); for (int i = 0; i < n; i++) { std::copy(a[i].begin(), a[i].end(), data.begin() + i * m); } } Self operator+(Self &rhs) const noexcept { return Self(*this) += rhs; } Self operator-(Self &rhs) const noexcept { return Self(*this) -= rhs; } Self operator*(Self &rhs) const noexcept { return Self(*this) *= rhs; } Self operator/(Self &rhs) const noexcept { return Self(*this) /= rhs; } friend Self operator*(const T &lhs, const Self &rhs) { return Self(rhs) *= lhs; } friend Self operator*(const Self &lhs, const T &rhs) { return Self(lhs) *= rhs; } Self &operator+=(Self &rhs) noexcept { assert(this->size() == rhs.size()); for (int i = 0; i < n; ++i) { for (int j = 0; j < m; ++j) { data[i][j] += rhs[i][j]; } } return *this; } Self &operator-=(Self &rhs) noexcept { assert(this->size() == rhs.size()); for (int i = 0; i < n; ++i) { for (int j = 0; j < m; ++j) { data[i][j] -= rhs[i][j]; } } return *this; } Self &operator*=(Self &rhs) noexcept { int h = n, w = rhs.column_size(); assert(m == rhs.row_size()); Self ret(h, w); for (int i = 0; i < h; ++i) { for (int k = 0; k < m; ++k) { for (int j = 0; j < w; ++j) { ret[i][j] += (*this)[i][k] * rhs[k][j]; } } } return *this = ret; } Self &operator/=(const Self &rhs) noexcept { auto ret = rhs.inv(); assert(ret); return *this *= ret.value(); } Self &operator*=(const T &rhs) noexcept { for (int i = 0; i < n; i++) { for (int j = 0; j < m; j++) { (*this)[i][j] *= rhs; } } return *this; } const auto operator[](int i) const { return std::ranges::subrange(data.begin() + i * m, data.begin() + (i + 1) * m); } auto operator[](int i) { return std::ranges::subrange(data.begin() + i * m, data.begin() + (i + 1) * m); } void swap(int i, int j) { std::swap_ranges(data.begin() + i * m, data.begin() + (i + 1) * m, data.begin() + j * m); } Self transposition() const { Self res(m, n); for (int i = 0; i < n; i++) { for (int j = 0; j < m; j++) { res[j][i] = data[i][j]; } } return res; } std::optional<Self> inv() const { assert(row_size() == column_size()); Self a = *this; Self b = identify_matrix<T>(n); for (int r = 0; r < n; r++) { for (int i = r; i < n; i++) { if (a[i][r] != 0) { a.swap(r, i); b.swap(r, i); break; } } if (a[r][r] == 0) return std::nullopt; T x = a[r][r].inv(); for (int j = 0; j < n; j++) { if (r < j) a[r][j] *= x; b[r][j] *= x; } for (int i = 0; i < n; i++) { if (i == r) continue; for (int j = 0; j < n; j++) { if (r < j) a[i][j] -= a[i][r] * a[r][j]; b[i][j] -= a[i][r] * b[r][j]; } } } return b; } Self pow(long long k) const { assert(row_size() == column_size() && k >= 0); Self res = identify_matrix<T>(row_size()); Self x = *this; while (k) { if (k & 1) res *= x; x *= x; k >>= 1; } return res; } int row_size() const { return n; } int column_size() const { return m; } std::pair<int, int> size() const { return {n, m}; } private: int n, m; std::vector<T> data; }; template <class T> T det(matrix<T> a) { assert(a.row_size() == a.column_size()); T d = 1; int n = a.row_size(); for (int r = 0; r < n; r++) { if (a[r][r] == 0) { for (int i = r + 1; i < n; i++) { if (a[i][r] != 0) { a.swap(r, i); d = -d; } } } if (a[r][r] == 0) return 0; d *= a[r][r]; T inv = a[r][r].inv(); for (int i = r + 1; i < n; i++) { T x = a[i][r] * inv; for (int j = r; j < n; j++) { a[i][j] -= x * a[r][j]; } } } return d; } template <class T> std::istream &operator>>(std::istream &os, matrix<T> &a) { for (int i = 0; i < a.row_size(); i++) { for (int j = 0; j < a.column_size(); j++) { os >> a[i][j]; } } return os; } template <class T> std::ostream &operator<<(std::ostream &os, const matrix<T> &a) { for (int i = 0; i < a.row_size(); i++) { for (int j = 0; j < a.column_size(); j++) { os << a[i][j]; if (j < a.column_size() - 1) os << ' '; } if (i < a.row_size() - 1) os << '\n'; } return os; } } // namespace ebi