#ifndef EMTHRM_MATH_MATRIX_BINARY_MATRIX_LINEAR_EQUATION_HPP_
#define EMTHRM_MATH_MATRIX_BINARY_MATRIX_LINEAR_EQUATION_HPP_
#include <vector>
#include "emthrm/math/matrix/binary_matrix/binary_matrix.hpp"
#include "emthrm/math/matrix/binary_matrix/gauss_jordan.hpp"
namespace emthrm {
template <int N>
std::vector<bool> linear_equation(const BinaryMatrix<N>& a,
const std::vector<bool>& b) {
const int m = a.nrow(), n = a.ncol();
BinaryMatrix<N> c(m, n + 1);
for (int i = 0; i < m; ++i) {
for (int j = 0; j < n; ++j) {
c[i][j] = a[i][j];
}
c[i][n] = b[i];
}
const int rank = gauss_jordan<true>(&c);
for (int row = rank; row < m; ++row) {
if (c[row][n]) return std::vector<bool>{};
}
std::vector<bool> res(n, false);
for (int i = 0, j = -1; i < rank; ++i) {
j = (i == 0 ? c[i]._Find_first() : c[i]._Find_next(j));
res[j] = c[i][n];
}
return res;
}
} // namespace emthrm
#endif // EMTHRM_MATH_MATRIX_BINARY_MATRIX_LINEAR_EQUATION_HPP_
#line 1 "include/emthrm/math/matrix/binary_matrix/linear_equation.hpp"
#include <vector>
#line 1 "include/emthrm/math/matrix/binary_matrix/binary_matrix.hpp"
#include <bitset>
#include <string>
#line 7 "include/emthrm/math/matrix/binary_matrix/binary_matrix.hpp"
namespace emthrm {
template <int N>
struct BinaryMatrix {
explicit BinaryMatrix(const int m, const int n = N, const bool def = false)
: n(n), data(m, std::bitset<N>(std::string(n, def ? '1' : '0'))) {}
int nrow() const { return data.size(); }
int ncol() const { return n; }
BinaryMatrix pow(long long exponent) const {
BinaryMatrix res(n, n), tmp = *this;
for (int i = 0; i < n; ++i) {
res[i].set(i);
}
for (; exponent > 0; exponent >>= 1) {
if (exponent & 1) res *= tmp;
tmp *= tmp;
}
return res;
}
inline const std::bitset<N>& operator[](const int i) const { return data[i]; }
inline std::bitset<N>& operator[](const int i) { return data[i]; }
BinaryMatrix& operator=(const BinaryMatrix& x) = default;
BinaryMatrix& operator+=(const BinaryMatrix& x) {
const int m = nrow();
for (int i = 0; i < m; ++i) {
data[i] ^= x[i];
}
return *this;
}
BinaryMatrix& operator*=(const BinaryMatrix& x) {
const int m = nrow(), l = x.ncol();
BinaryMatrix t_x(l, n), res(m, l);
for (int i = 0; i < l; ++i) {
for (int j = 0; j < n; ++j) {
t_x[i][j] = x[j][i];
}
}
for (int i = 0; i < m; ++i) {
for (int j = 0; j < l; ++j) {
if ((data[i] & t_x[j]).count() & 1) res[i].set(j);
}
}
return *this = res;
}
BinaryMatrix operator+(const BinaryMatrix& x) const {
return BinaryMatrix(*this) += x;
}
BinaryMatrix operator*(const BinaryMatrix& x) const {
return BinaryMatrix(*this) *= x;
}
private:
int n;
std::vector<std::bitset<N>> data;
};
} // namespace emthrm
#line 1 "include/emthrm/math/matrix/binary_matrix/gauss_jordan.hpp"
#include <utility>
#line 7 "include/emthrm/math/matrix/binary_matrix/gauss_jordan.hpp"
namespace emthrm {
template <bool IS_EXTENDED = false, int N>
int gauss_jordan(BinaryMatrix<N>* a) {
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;
for (int row = rank; row < m; ++row) {
if ((*a)[row][col]) {
pivot = row;
break;
}
}
if (pivot == -1) continue;
std::swap((*a)[rank], (*a)[pivot]);
for (int row = 0; row < m; ++row) {
if (row != rank && (*a)[row][col]) (*a)[row] ^= (*a)[rank];
}
++rank;
}
return rank;
}
} // namespace emthrm
#line 8 "include/emthrm/math/matrix/binary_matrix/linear_equation.hpp"
namespace emthrm {
template <int N>
std::vector<bool> linear_equation(const BinaryMatrix<N>& a,
const std::vector<bool>& b) {
const int m = a.nrow(), n = a.ncol();
BinaryMatrix<N> c(m, n + 1);
for (int i = 0; i < m; ++i) {
for (int j = 0; j < n; ++j) {
c[i][j] = a[i][j];
}
c[i][n] = b[i];
}
const int rank = gauss_jordan<true>(&c);
for (int row = rank; row < m; ++row) {
if (c[row][n]) return std::vector<bool>{};
}
std::vector<bool> res(n, false);
for (int i = 0, j = -1; i < rank; ++i) {
j = (i == 0 ? c[i]._Find_first() : c[i]._Find_next(j));
res[j] = c[i][n];
}
return res;
}
} // namespace emthrm
連立一次方程式 (linear equation) バイナリ行列版