C++ Library for Competitive Programming
View the Project on GitHub emthrm/cp-library
#include "emthrm/math/matrix/linear_equation.hpp"
$O(M^2 N)$
template <typename T, typename U = double>
std::vector<U> linear_equation(const Matrix<T>& a, const std::vector<T>& b, const U eps = 1e-8);
https://onlinejudge.u-aizu.ac.jp/solutions/problem/2171/review/5899058/emthrm/C++17
#ifndef EMTHRM_MATH_MATRIX_LINEAR_EQUATION_HPP_ #define EMTHRM_MATH_MATRIX_LINEAR_EQUATION_HPP_ #include <algorithm> #include <cmath> #include <vector> #include "emthrm/math/matrix/gauss_jordan.hpp" #include "emthrm/math/matrix/matrix.hpp" namespace emthrm { template <typename T, typename U = double> std::vector<U> linear_equation(const Matrix<T>& a, const std::vector<T>& b, const U eps = 1e-8) { const int m = a.nrow(), n = a.ncol(); Matrix<U> c(m, n + 1); for (int i = 0; i < m; ++i) { std::copy(a[i].begin(), a[i].end(), c[i].begin()); c[i].back() = b[i]; } const int rank = gauss_jordan<true>(&c, eps); for (int row = rank; row < m; ++row) { if ((c[row].back() < 0 ? -c[row].back() : c[row].back()) > eps) { return std::vector<U>{}; } } std::vector<U> res(n, 0); for (int i = 0, j = 0; i < rank; ++i) { while ((c[i][j] < 0 ? -c[i][j] : c[i][j]) <= eps) ++j; res[j++] = c[i].back(); } return res; } } // namespace emthrm #endif // EMTHRM_MATH_MATRIX_LINEAR_EQUATION_HPP_
#line 1 "include/emthrm/math/matrix/linear_equation.hpp" #include <algorithm> #include <cmath> #include <vector> #line 1 "include/emthrm/math/matrix/gauss_jordan.hpp" #include <utility> #line 1 "include/emthrm/math/matrix/matrix.hpp" #line 5 "include/emthrm/math/matrix/matrix.hpp" namespace emthrm { template <typename T> struct Matrix { explicit Matrix(const int m, const int n, const T def = 0) : data(m, std::vector<T>(n, def)) {} int nrow() const { return data.size(); } int ncol() const { return data.empty() ? 0 : data.front().size(); } Matrix pow(long long exponent) const { const int n = nrow(); Matrix<T> res(n, n, 0), tmp = *this; for (int i = 0; i < n; ++i) { res[i][i] = 1; } for (; exponent > 0; exponent >>= 1) { if (exponent & 1) res *= tmp; tmp *= tmp; } return res; } inline const std::vector<T>& operator[](const int i) const { return data[i]; } inline std::vector<T>& operator[](const int i) { return data[i]; } Matrix& operator=(const Matrix& x) = default; Matrix& operator+=(const Matrix& x) { const int m = nrow(), n = ncol(); for (int i = 0; i < m; ++i) { for (int j = 0; j < n; ++j) { data[i][j] += x[i][j]; } } return *this; } Matrix& operator-=(const Matrix& x) { const int m = nrow(), n = ncol(); for (int i = 0; i < m; ++i) { for (int j = 0; j < n; ++j) { data[i][j] -= x[i][j]; } } return *this; } Matrix& operator*=(const Matrix& x) { const int m = nrow(), l = ncol(), n = x.ncol(); std::vector<std::vector<T>> res(m, std::vector<T>(n, 0)); for (int i = 0; i < m; ++i) { for (int k = 0; k < l; ++k) { for (int j = 0; j < n; ++j) { res[i][j] += data[i][k] * x[k][j]; } } } data.swap(res); return *this; } Matrix operator+(const Matrix& x) const { return Matrix(*this) += x; } Matrix operator-(const Matrix& x) const { return Matrix(*this) -= x; } Matrix operator*(const Matrix& x) const { return Matrix(*this) *= x; } private: std::vector<std::vector<T>> data; }; } // namespace emthrm #line 7 "include/emthrm/math/matrix/gauss_jordan.hpp" namespace emthrm { template <bool IS_EXTENDED = false, typename T> int gauss_jordan(Matrix<T>* a, const T eps = 1e-8) { const int m = a->nrow(), n = a->ncol(); int rank = 0; for (int col = 0; col < (IS_EXTENDED ? n - 1 : n); ++col) { int pivot = -1; T mx = eps; for (int row = rank; row < m; ++row) { const T abs = ((*a)[row][col] < 0 ? -(*a)[row][col] : (*a)[row][col]); if (abs > mx) { pivot = row; mx = abs; } } if (pivot == -1) continue; std::swap((*a)[rank], (*a)[pivot]); T tmp = (*a)[rank][col]; for (int col2 = 0; col2 < n; ++col2) { (*a)[rank][col2] /= tmp; } for (int row = 0; row < m; ++row) { if (row != rank && ((*a)[row][col] < 0 ? -(*a)[row][col] : (*a)[row][col]) > eps) { tmp = (*a)[row][col]; for (int col2 = 0; col2 < n; ++col2) { (*a)[row][col2] -= (*a)[rank][col2] * tmp; } } } ++rank; } return rank; } } // namespace emthrm #line 10 "include/emthrm/math/matrix/linear_equation.hpp" namespace emthrm { template <typename T, typename U = double> std::vector<U> linear_equation(const Matrix<T>& a, const std::vector<T>& b, const U eps = 1e-8) { const int m = a.nrow(), n = a.ncol(); Matrix<U> c(m, n + 1); for (int i = 0; i < m; ++i) { std::copy(a[i].begin(), a[i].end(), c[i].begin()); c[i].back() = b[i]; } const int rank = gauss_jordan<true>(&c, eps); for (int row = rank; row < m; ++row) { if ((c[row].back() < 0 ? -c[row].back() : c[row].back()) > eps) { return std::vector<U>{}; } } std::vector<U> res(n, 0); for (int i = 0, j = 0; i < rank; ++i) { while ((c[i][j] < 0 ? -c[i][j] : c[i][j]) <= eps) ++j; res[j++] = c[i].back(); } return res; } } // namespace emthrm