verify/LibraryChecker/linear-algebra/InverseMatrixMod2.test.cpp

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• Last update: 2026-03-24 21:06:50+09:00
• Problem: https://judge.yosupo.jp/problem/inverse_matrix_mod_2

Depends on

• Matrix (Mod 2) (linear-algebra/BitMatrix.hpp)
• Template (template/template.hpp)

Code

#include "../../../template/template.hpp"

#include "../../../linear-algebra/BitMatrix.hpp"

#define PROBLEM "https://judge.yosupo.jp/problem/inverse_matrix_mod_2"

int main() {
  cin.tie(0)->sync_with_stdio(0);
  int n;
  in(n);
  BitMatrix a(n);
  rep(i, n) {
    string s;
    in(s);
    rep(j, n) {
      if (s[j] == '1') a[i][j] = 1;
    }
  }

  auto [res, inva] = a.inverse();
  if (!res) {
    out(-1);
    return 0;
  }
  rep(i, n) {
    string s = inva[i].to_string();
    reverse(all(s));
    out(s);
  }
}

#line 2 "template/template.hpp"
#pragma region Macros
#include <bits/stdc++.h>
#include <tr2/dynamic_bitset>

using namespace std;
using namespace tr2;
using lint = long long;
using ull = unsigned long long;
using ld = long double;
using int128 = __int128_t;
#define all(x) (x).begin(), (x).end()
#define uniqv(v) v.erase(unique(all(v)), v.end())
#define OVERLOAD_REP(_1, _2, _3, name, ...) name
#define REP1(i, n) for (auto i = std::decay_t<decltype(n)>{}; (i) != (n); ++(i))
#define REP2(i, l, r) for (auto i = (l); (i) != (r); ++(i))
#define rep(...) OVERLOAD_REP(__VA_ARGS__, REP2, REP1)(__VA_ARGS__)
#define logfixed(x) cout << fixed << setprecision(10) << x << endl;

ostream &operator<<(ostream &dest, __int128_t value) {
  ostream::sentry s(dest);
  if (s) {
    __uint128_t tmp = value < 0 ? -value : value;
    char buffer[128];
    char *d = end(buffer);
    do {
      --d;
      *d = "0123456789"[tmp % 10];
      tmp /= 10;
    } while (tmp != 0);
    if (value < 0) {
      --d;
      *d = '-';
    }
    int len = end(buffer) - d;
    if (dest.rdbuf()->sputn(d, len) != len) {
      dest.setstate(ios_base::badbit);
    }
  }
  return dest;
}

template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v) {
  for (int i = 0; i < (int)v.size(); i++) {
    os << v[i] << (i + 1 != (int)v.size() ? " " : "");
  }
  return os;
}

template <typename T>
ostream &operator<<(ostream &os, const set<T> &set_var) {
  for (auto itr = set_var.begin(); itr != set_var.end(); itr++) {
    os << *itr;
    ++itr;
    if (itr != set_var.end()) os << " ";
    itr--;
  }
  return os;
}

template <typename T>
ostream &operator<<(ostream &os, const unordered_set<T> &set_var) {
  for (auto itr = set_var.begin(); itr != set_var.end(); itr++) {
    os << *itr;
    ++itr;
    if (itr != set_var.end()) os << " ";
    itr--;
  }
  return os;
}

template <typename T, typename U>
ostream &operator<<(ostream &os, const map<T, U> &map_var) {
  for (auto itr = map_var.begin(); itr != map_var.end(); itr++) {
    os << itr->first << " -> " << itr->second << "\n";
  }
  return os;
}

template <typename T, typename U>
ostream &operator<<(ostream &os, const unordered_map<T, U> &map_var) {
  for (auto itr = map_var.begin(); itr != map_var.end(); itr++) {
    os << itr->first << " -> " << itr->second << "\n";
  }
  return os;
}

template <typename T, typename U>
ostream &operator<<(ostream &os, const pair<T, U> &pair_var) {
  os << pair_var.first << " " << pair_var.second;
  return os;
}

void out() { cout << '\n'; }
template <class T, class... Ts>
void out(const T &a, const Ts &...b) {
  cout << a;
  (cout << ... << (cout << ' ', b));
  cout << '\n';
}

void outf() { cout << '\n'; }
template <class T, class... Ts>
void outf(const T &a, const Ts &...b) {
  cout << fixed << setprecision(14) << a;
  (cout << ... << (cout << ' ', b));
  cout << '\n';
}

template <typename T>
istream &operator>>(istream &is, vector<T> &v) {
  for (T &in : v) is >> in;
  return is;
}

inline void in(void) { return; }
template <typename First, typename... Rest>
void in(First &first, Rest &...rest) {
  cin >> first;
  in(rest...);
  return;
}

template <typename T>
bool chmax(T &a, const T &b) {
  if (a < b) {
    a = b;
    return true;
  }
  return false;
}
template <typename T>
bool chmin(T &a, const T &b) {
  if (a > b) {
    a = b;
    return true;
  }
  return false;
}

vector<lint> dx8 = {1, 1, 0, -1, -1, -1, 0, 1};
vector<lint> dy8 = {0, 1, 1, 1, 0, -1, -1, -1};
vector<lint> dx4 = {1, 0, -1, 0};
vector<lint> dy4 = {0, 1, 0, -1};

#pragma endregion
#line 2 "verify/LibraryChecker/linear-algebra/InverseMatrixMod2.test.cpp"

#line 1 "linear-algebra/BitMatrix.hpp"


struct BitMatrix {
 private:
 public:
  vector<dynamic_bitset<>> A;
  BitMatrix() {}
  BitMatrix(int n, int m) : A(n, dynamic_bitset<>(m)) {}
  BitMatrix(int n) : A(n, dynamic_bitset<>(n)) {}

  inline int size() const { return A.size(); }
  inline int height() const { return A.size(); }
  inline int width() const { return A[0].size(); }
  inline const dynamic_bitset<>& operator[](int h) const { return (A[h]); }
  inline dynamic_bitset<>& operator[](int h) { return (A[h]); }

  BitMatrix& operator+=(const BitMatrix& B) {
    int h = height();
    for (int i = 0; i < h; i++) (*this)[i] ^= B[i];
    return (*this);
  }
  BitMatrix& operator-=(const BitMatrix& B) {
    int h = height();
    for (int i = 0; i < h; i++) (*this)[i] ^= B[i];
    return (*this);
  }

  BitMatrix& operator*=(const BitMatrix& B) {
    int h = height();
    int w = B.width();
    int c = width();
    vector<dynamic_bitset<>> C(h, dynamic_bitset<>(w));
    for (int i = 0; i < h; i++) {
      for (int j = 0; j < c; j++) {
        if ((*this)[i][j]) C[i] ^= B[j];
      }
    }
    A = move(C);
    return (*this);
  }

  BitMatrix operator+(const BitMatrix& B) const { return (BitMatrix(*this) += B); }
  BitMatrix operator-(const BitMatrix& B) const { return (BitMatrix(*this) -= B); }
  BitMatrix operator*(const BitMatrix& B) const { return (BitMatrix(*this) *= B); }

  int rank() {
    BitMatrix B(*this);
    if (B.height() == 0 or B.width() == 0) return 0;
    int res = 0;
    int h = height();
    int w = width();
    int ch = 0;
    int cw = 0;
    while (ch < h and cw < w) {
      bool ok = false;
      for (int j = cw; j < w; j++) {
        for (int i = ch; i < h; i++) {
          if (B[i][j]) {
            ok = true;
            swap(B[ch], B[i]);
            for (int i2 = 0; i2 < h; i2++) {
              if (B[i2][j] != 0 and i2 != ch) B[i2] ^= B[ch];
            }
            res++;
            ch++;
            cw = j + 1;
            break;
          }
        }
        if (ok) break;
      }
      if (!ok) break;
    }
    return res;
  }

  int determinant() {
    BitMatrix B(*this);
    if (B.height() == 0 or B.width() == 0) return 0;
    assert(B.height() == B.width());
    int h = height();
    int w = width();
    int ch = 0;
    int cw = 0;
    while (ch < h and cw < w) {
      bool ok = false;
      for (int j = cw; j < w; j++) {
        for (int i = ch; i < h; i++) {
          if (B[i][j]) {
            ok = true;
            swap(B[ch], B[i]);
            for (int i2 = 0; i2 < h; i2++) {
              if (B[i2][j] != 0 and i2 != ch) B[i2] ^= B[ch];
            }
            ch++;
            cw = j + 1;
            break;
          }
        }
        if (ok) {
          break;
        } else {
          return 0;
        }
      }
      if (!ok) break;
    }
    return 1;
  }

  pair<bool, BitMatrix> inverse() {
    int h = height();
    int w = width();
    assert(h == w);
    BitMatrix B(h, w * 2);
    for (int i = 0; i < h; i++) {
      dynamic_bitset<> tmp = (*this)[i];
      tmp.resize(w * 2);
      tmp[i + w] = 1;
      B[i] ^= tmp;
    }

    w *= 2;
    int rnk = 0;

    int ch = 0;
    int cw = 0;
    while (ch < h and cw < h) {
      bool ok = false;
      for (int j = cw; j < h; j++) {
        for (int i = ch; i < h; i++) {
          if (B[i][j] != 0) {
            ok = true;
            swap(B[ch], B[i]);
            for (int i2 = 0; i2 < h; i2++) {
              if (B[i2][j] != 0 and i2 != ch) B[i2] ^= B[ch];
            }
            rnk++;
            ch++;
            cw = j + 1;
            break;
          }
        }
        if (ok) break;
      }
      if (!ok) break;
    }
    BitMatrix res(h);
    if (rnk == h) {
      for (int i = 0; i < h; i++) {
        B[i] >>= h;
        B[i].resize(h);
        res[i] ^= B[i];
      }
      return {true, res};
    } else {
      return {false, res};
    }
  }

  BitMatrix linear_equation(dynamic_bitset<> b) {
    BitMatrix A(*this);
    int rnk = 0;
    assert(A.height() == b.size());
    int h = height();
    int w = width();
    int ch = 0;
    int cw = 0;
    vector<int> pivot_row(w, -1);
    while (ch < h and cw < w) {
      bool ok = false;
      for (int j = cw; j < w; j++) {
        for (int i = ch; i < h; i++) {
          if (A[i][j] != 0) {
            ok = true;
            swap(A[ch], A[i]);
            bool tmp = b[ch];
            b[ch] = b[i];
            b[i] = tmp;
            for (int i2 = 0; i2 < h; i2++) {
              if (A[i2][j] != 0 and i2 != ch) {
                A[i2] ^= A[ch];
                b[i2] = b[i2] ^ b[ch];
              }
            }
            pivot_row[j] = ch;
            rnk++;
            ch++;
            cw = j + 1;
            break;
          }
        }
        if (ok) break;
      }
      if (!ok) break;
    }

    for (int i = rnk; i < h; i++) {
      if (b[i] != 0) return BitMatrix(0);
    }
    BitMatrix sol(w - rnk + 1, w);
    int idx = 1;
    for (int j = 0; j < w; j++) {
      if (pivot_row[j] != -1) {
        sol[0][j] = b[pivot_row[j]];
      } else {
        sol[idx][j] = 1;
        for (int i = 0; i < w; i++) {
          if (pivot_row[i] != -1) {
            sol[idx][i] = A[pivot_row[i]][j];
          }
        }
        idx++;
      }
    }
    return sol;
  }
};
#line 4 "verify/LibraryChecker/linear-algebra/InverseMatrixMod2.test.cpp"

#define PROBLEM "https://judge.yosupo.jp/problem/inverse_matrix_mod_2"

int main() {
  cin.tie(0)->sync_with_stdio(0);
  int n;
  in(n);
  BitMatrix a(n);
  rep(i, n) {
    string s;
    in(s);
    rep(j, n) {
      if (s[j] == '1') a[i][j] = 1;
    }
  }

  auto [res, inva] = a.inverse();
  if (!res) {
    out(-1);
    return 0;
  }
  rep(i, n) {
    string s = inva[i].to_string();
    reverse(all(s));
    out(s);
  }
}

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