数学/行列/バイナリ行列/逆行列 バイナリ行列版
(test/math/matrix/binary_matrix/inverse_matrix.test.cpp)

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• Last update: 2024-06-22 01:08:25+09:00
• Problem: https://judge.yosupo.jp/problem/inverse_matrix_mod_2

Depends on

• バイナリ行列 (include/emthrm/math/matrix/binary_matrix/binary_matrix.hpp)
• 逆行列 (inverse matrix) バイナリ行列版 (include/emthrm/math/matrix/binary_matrix/inverse_matrix.hpp)

Code

/*
 * @title 数学/行列/バイナリ行列/逆行列 バイナリ行列版
 *
 * verification-helper: PROBLEM https://judge.yosupo.jp/problem/inverse_matrix_mod_2
 */

#include <iostream>
#include <string>

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

int main() {
  constexpr int kMaxN = (1 << 12) * 2;
  int n;
  std::cin >> n;
  emthrm::BinaryMatrix<kMaxN> a(n, n);
  for (int i = 0; i < n; ++i) {
    std::string a_i;
    std::cin >> a_i;
    for (int j = 0; j < n; ++j) {
      if (a_i[j] == '1') a[i].set(j);
    }
  }
  a = inverse_matrix(a);
  if (a.nrow() == 0) {
    std::cout << "-1\n";
  } else {
    for (int i = 0; i < n; ++i) {
      for (int j = 0; j < n; ++j) {
        std::cout << a[i][j];
      }
      std::cout << '\n';
    }
  }
  return 0;
}

#line 1 "test/math/matrix/binary_matrix/inverse_matrix.test.cpp"
/*
 * @title 数学/行列/バイナリ行列/逆行列 バイナリ行列版
 *
 * verification-helper: PROBLEM https://judge.yosupo.jp/problem/inverse_matrix_mod_2
 */

#include <iostream>
#include <string>

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



#include <bitset>
#line 6 "include/emthrm/math/matrix/binary_matrix/binary_matrix.hpp"
#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/inverse_matrix.hpp"



#include <cassert>
#include <utility>

#line 8 "include/emthrm/math/matrix/binary_matrix/inverse_matrix.hpp"

namespace emthrm {

template <int N>
BinaryMatrix<N> inverse_matrix(const BinaryMatrix<N>& a) {
  const int n = a.nrow();
  BinaryMatrix<N> b(n, n << 1, 0);
  for (int i = 0; i < n; ++i) {
    for (int j = 0; j < n; ++j) {
      b[i][j] = a[i][j];
    }
    b[i][n + i] = 1;
  }
  for (int col = 0; col < n; ++col) {
    int pivot = -1;
    for (int row = col; row < n; ++row) {
      if (b[row][col]) {
        pivot = row;
        break;
      }
    }
    if (pivot == -1) return BinaryMatrix<N>(0, 0);
    std::swap(b[col], b[pivot]);
    for (int row = 0; row < n; ++row) {
      if (row != col && b[row][col]) b[row] ^= b[col];
    }
  }
  BinaryMatrix<N> inv(n, n);
  for (int i = 0; i < n; ++i) {
    for (int j = 0; j < n; ++j) {
      inv[i][j] = b[i][n + j];
    }
  }
  return inv;
}

}  // namespace emthrm


#line 12 "test/math/matrix/binary_matrix/inverse_matrix.test.cpp"

int main() {
  constexpr int kMaxN = (1 << 12) * 2;
  int n;
  std::cin >> n;
  emthrm::BinaryMatrix<kMaxN> a(n, n);
  for (int i = 0; i < n; ++i) {
    std::string a_i;
    std::cin >> a_i;
    for (int j = 0; j < n; ++j) {
      if (a_i[j] == '1') a[i].set(j);
    }
  }
  a = inverse_matrix(a);
  if (a.nrow() == 0) {
    std::cout << "-1\n";
  } else {
    for (int i = 0; i < n; ++i) {
      for (int j = 0; j < n; ++j) {
        std::cout << a[i][j];
      }
      std::cout << '\n';
    }
  }
  return 0;
}

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