数学/行列/バイナリ行列/ガウス・ジョルダンの消去法 バイナリ行列版
(test/math/matrix/binary_matrix/gauss_jordan.test.cpp)

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• Last update: 2023-02-25 16:35:06+09:00
• Problem: https://yukicoder.me/problems/no/184

Depends on

• バイナリ行列 (include/emthrm/math/matrix/binary_matrix/binary_matrix.hpp)
• ガウス・ジョルダンの消去法 (Gauss–Jordan elimination) バイナリ行列版 (include/emthrm/math/matrix/binary_matrix/gauss_jordan.hpp)

Code

/*
 * @title 数学/行列/バイナリ行列/ガウス・ジョルダンの消去法 バイナリ行列版
 *
 * verification-helper: PROBLEM https://yukicoder.me/problems/no/184
 */

#include <bitset>
#include <iostream>

#include "emthrm/math/matrix/binary_matrix/binary_matrix.hpp"
#include "emthrm/math/matrix/binary_matrix/gauss_jordan.hpp"

int main() {
  constexpr int B = 61;
  int n;
  std::cin >> n;
  emthrm::BinaryMatrix<B> matrix(n);
  for (int i = 0; i < n; ++i) {
    long long a;
    std::cin >> a;
    matrix[i] = std::bitset<B>(a);
  }
  std::cout << (1LL << emthrm::gauss_jordan(&matrix)) << '\n';
  return 0;
}

#line 1 "test/math/matrix/binary_matrix/gauss_jordan.test.cpp"
/*
 * @title 数学/行列/バイナリ行列/ガウス・ジョルダンの消去法 バイナリ行列版
 *
 * verification-helper: PROBLEM https://yukicoder.me/problems/no/184
 */

#include <bitset>
#include <iostream>

#line 1 "include/emthrm/math/matrix/binary_matrix/binary_matrix.hpp"



#line 5 "include/emthrm/math/matrix/binary_matrix/binary_matrix.hpp"
#include <string>
#include <vector>

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 12 "test/math/matrix/binary_matrix/gauss_jordan.test.cpp"

int main() {
  constexpr int B = 61;
  int n;
  std::cin >> n;
  emthrm::BinaryMatrix<B> matrix(n);
  for (int i = 0; i < n; ++i) {
    long long a;
    std::cin >> a;
    matrix[i] = std::bitset<B>(a);
  }
  std::cout << (1LL << emthrm::gauss_jordan(&matrix)) << '\n';
  return 0;
}

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