cp-library

C++ Library for Competitive Programming

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:heavy_check_mark: 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)

Depends on

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 http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=2624
 */

#include <bitset>
#include <iostream>

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

int main() {
  constexpr int N = 600;
  using binary_matrix = emthrm::BinaryMatrix<N>;
  int n;
  std::cin >> n;
  binary_matrix a(n, n), v(n, 1);
  for (int i = 0; i < n; ++i) {
    for (int j = 0; j < n; ++j) {
      int a_ij;
      std::cin >> a_ij;
      a[i][j] = a_ij;
    }
  }
  for (int i = 0; i < n; ++i) {
    int v_i;
    std::cin >> v_i;
    v[i][0] = v_i;
  }
  int t;
  std::cin >> t;
  binary_matrix inv = emthrm::inverse_matrix(a);
  if (inv.nrow() == 0) {
    a = a.pow(t);
    binary_matrix av(n, n + 1);
    for (int i = 0; i < n; ++i) {
      for (int j = 0; j < n; ++j) {
        av[i][j] = a[i][j];
      }
      av[i][n] = v[i][0];
    }
    std::cout << (emthrm::gauss_jordan(&a) == emthrm::gauss_jordan(&av) ?
                  "ambiguous\n" : "none\n");
  } else {
    inv = inv.pow(t) * v;
    for (int i = 0; i < n; ++i) {
      std::cout << inv[i][0] << " \n"[i + 1 == 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 http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=2624
 */

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



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

#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 13 "test/math/matrix/binary_matrix/inverse_matrix.test.cpp"

int main() {
  constexpr int N = 600;
  using binary_matrix = emthrm::BinaryMatrix<N>;
  int n;
  std::cin >> n;
  binary_matrix a(n, n), v(n, 1);
  for (int i = 0; i < n; ++i) {
    for (int j = 0; j < n; ++j) {
      int a_ij;
      std::cin >> a_ij;
      a[i][j] = a_ij;
    }
  }
  for (int i = 0; i < n; ++i) {
    int v_i;
    std::cin >> v_i;
    v[i][0] = v_i;
  }
  int t;
  std::cin >> t;
  binary_matrix inv = emthrm::inverse_matrix(a);
  if (inv.nrow() == 0) {
    a = a.pow(t);
    binary_matrix av(n, n + 1);
    for (int i = 0; i < n; ++i) {
      for (int j = 0; j < n; ++j) {
        av[i][j] = a[i][j];
      }
      av[i][n] = v[i][0];
    }
    std::cout << (emthrm::gauss_jordan(&a) == emthrm::gauss_jordan(&av) ?
                  "ambiguous\n" : "none\n");
  } else {
    inv = inv.pow(t) * v;
    for (int i = 0; i < n; ++i) {
      std::cout << inv[i][0] << " \n"[i + 1 == n];
    }
  }
  return 0;
}
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