verify/matrix/LC_matrix_det_mod_2.test.cpp

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• Last update: 2026-08-11 23:01:09+09:00
• Problem: https://judge.yosupo.jp/problem/matrix_det_mod_2

Depends on

• Dynamic Bitset (data-structure/dynamic-bitset.hpp)
• Matrix Mod 2 (matrix/matrix-mod2.hpp)
• template/debug.hpp
• template/inout.hpp
• template/macro.hpp
• template/template.hpp
• template/util.hpp

Code

#define PROBLEM "https://judge.yosupo.jp/problem/matrix_det_mod_2"

#include "template/template.hpp"
#include "matrix/matrix-mod2.hpp"

int main() {
  int n;
  in(n);
  MatrixMod2 a(n);
  string s;
  rep(i, 0, n) {
    in(s);
    a.set_row(i, s);
  }
  out(a.det());
}

#line 1 "verify/matrix/LC_matrix_det_mod_2.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/matrix_det_mod_2"

#line 2 "template/template.hpp"
#include <bits/stdc++.h>
using namespace std;

#line 2 "template/macro.hpp"
#define rep(i, a, b) for (int i = (a); i < (int)(b); i++)
#define rrep(i, a, b) for (int i = (int)(b) - 1; i >= (a); i--)
#define ALL(v) (v).begin(), (v).end()
#define UNIQUE(v) sort(ALL(v)), (v).erase(unique(ALL(v)), (v).end())
#define SZ(v) (int)v.size()
#define MIN(v) *min_element(ALL(v))
#define MAX(v) *max_element(ALL(v))
#define LB(v, x) int(lower_bound(ALL(v), (x)) - (v).begin())
#define UB(v, x) int(upper_bound(ALL(v), (x)) - (v).begin())
#define YN(b) cout << ((b) ? "YES" : "NO") << "\n";
#define Yn(b) cout << ((b) ? "Yes" : "No") << "\n";
#define yn(b) cout << ((b) ? "yes" : "no") << "\n";
#line 6 "template/template.hpp"

#line 2 "template/util.hpp"
using uint = unsigned int;
using ll = long long int;
using ull = unsigned long long;
using i128 = __int128_t;
using u128 = __uint128_t;
template <class T>
using priority_queue_asc = priority_queue<T, vector<T>, greater<T>>;

template <class T, class S = T>
S SUM(const vector<T>& a) {
  return accumulate(ALL(a), S(0));
}
template <class T1, class T2>
inline bool chmin(T1& a, T2 b) {
  if (a > b) {
    a = b;
    return true;
  }
  return false;
}
template <class T1, class T2>
inline bool chmax(T1& a, T2 b) {
  if (a < b) {
    a = b;
    return true;
  }
  return false;
}
template <class T1, class T2>
inline bool chmin_opt(optional<T1>& a, T2 b) {
  if (!a || a > b) {
    a = b;
    return true;
  }
  return false;
}
template <class T1, class T2>
inline bool chmax_opt(optional<T1>& a, T2 b) {
  if (!a || a < b) {
    a = b;
    return true;
  }
  return false;
}

template <class T>
int popcnt(T x) {
  return __builtin_popcountll(x);
}
template <class T>
int topbit(T x) {
  return (x == 0 ? -1 : 63 - __builtin_clzll(x));
}
template <class T>
int lowbit(T x) {
  return (x == 0 ? -1 : __builtin_ctzll(x));
}
#line 8 "template/template.hpp"

#line 2 "template/inout.hpp"
struct Fast {
  Fast() {
    cin.tie(nullptr);
    ios_base::sync_with_stdio(false);
    cout << fixed << setprecision(15);
  }
} fast;

ostream& operator<<(ostream& os, __uint128_t x) {
  char buf[40];
  size_t k = 0;
  while (x > 0) buf[k++] = (char)(x % 10 + '0'), x /= 10;
  if (k == 0) buf[k++] = '0';
  while (k) os << buf[--k];
  return os;
}
ostream& operator<<(ostream& os, __int128_t x) {
  return x < 0 ? (os << '-' << (__uint128_t)(-x)) : (os << (__uint128_t)x);
}
template <class T, size_t N>
ostream& operator<<(ostream& os, const array<T, N>& a);
template <class T1, class T2>
istream& operator>>(istream& is, pair<T1, T2>& p) {
  return is >> p.first >> p.second;
}
template <class T1, class T2>
ostream& operator<<(ostream& os, const pair<T1, T2>& p) {
  return os << p.first << " " << p.second;
}
template <class T>
istream& operator>>(istream& is, vector<T>& a) {
  for (auto& v : a) is >> v;
  return is;
}
template <class T>
ostream& operator<<(ostream& os, const vector<T>& a) {
  for (auto it = a.begin(); it != a.end();) {
    os << *it;
    if (++it != a.end()) os << " ";
  }
  return os;
}
template <class T, size_t N>
ostream& operator<<(ostream& os, const array<T, N>& a) {
  for (auto it = a.begin(); it != a.end();) {
    os << *it;
    if (++it != a.end()) os << " ";
  }
  return os;
}
template <class T>
ostream& operator<<(ostream& os, const set<T>& st) {
  os << "{";
  for (auto it = st.begin(); it != st.end();) {
    os << *it;
    if (++it != st.end()) os << ",";
  }
  os << "}";
  return os;
}
template <class T1, class T2>
ostream& operator<<(ostream& os, const map<T1, T2>& mp) {
  os << "{";
  for (auto it = mp.begin(); it != mp.end();) {
    os << it->first << ":" << it->second;
    if (++it != mp.end()) os << ",";
  }
  os << "}";
  return os;
}

void in() {}
template <typename T, class... U>
void in(T& t, U&... u) {
  cin >> t;
  in(u...);
}
template <class... T>
void in_zip(int n, T&... t) {
  assert(n >= 0 && ((size(t) >= static_cast<size_t>(n)) && ...));
  for (int i = 0; i < n; i++) in(t[i]...);
}
void out() { cout << "\n"; }
template <typename T, class... U, char sep = ' '>
void out(const T& t, const U&... u) {
  cout << t;
  if (sizeof...(u)) cout << sep;
  out(u...);
}
template <class T, class U>
void out_opt(const optional<T>& opt, const U& fallback, ostream& os = cout) {
  if (opt.has_value())
    os << opt.value();
  else
    os << fallback;
  os << "\n";
}
template <class T, class U>
void out_opt(const vector<optional<T>>& vec, const U& fallback, ostream& os = cout) {
  for (auto it = vec.begin(); it != vec.end();) {
    if ((*it).has_value())
      os << (*it).value();
    else
      os << fallback;
    if (++it != vec.end()) os << " ";
  }
  os << "\n";
}

namespace IO {
template <class T, class... U>
T read(U&&... u) {
  T t = T(forward<U>(u)...);
  in(t);
  return t;
}
namespace Graph {
vector<vector<int>> unweighted(int n, int m, bool directed = false, int offset = 1) {
  vector<vector<int>> g(n);
  for (int i = 0; i < m; i++) {
    int u, v;
    cin >> u >> v;
    u -= offset, v -= offset;
    g[u].push_back(v);
    if (!directed) g[v].push_back(u);
  }
  return g;
}
template <class T>
vector<vector<pair<int, T>>> weighted(int n, int m, bool directed = false, int offset = 1) {
  vector<vector<pair<int, T>>> g(n);
  for (int i = 0; i < m; i++) {
    int u, v;
    T w;
    cin >> u >> v >> w;
    u -= offset, v -= offset;
    g[u].push_back({v, w});
    if (!directed) g[v].push_back({u, w});
  }
  return g;
}
}  // namespace Graph
namespace Tree {
vector<vector<int>> unweighted(int n, bool directed = false, int offset = 1) {
  return Graph::unweighted(n, n - 1, directed, offset);
}
template <class T>
vector<vector<pair<int, T>>> weighted(int n, bool directed = false, int offset = 1) {
  return Graph::weighted<T>(n, n - 1, directed, offset);
}
vector<vector<int>> rooted(int n, bool to_root = true, bool to_leaf = true, int offset = 1) {
  vector<vector<int>> g(n);
  for (int i = 1; i < n; i++) {
    int p;
    cin >> p;
    p -= offset;
    if (to_root) g[i].push_back(p);
    if (to_leaf) g[p].push_back(i);
  }
  return g;
}
}  // namespace Tree
}  // namespace IO
#line 10 "template/template.hpp"

#line 2 "template/debug.hpp"
#ifdef LOCAL
#define debug 1
#define show(...) _show(0, #__VA_ARGS__, __VA_ARGS__)
#else
#define debug 0
#define show(...) true
#endif
template <class T>
void _show(int, T) {
  cerr << '\n';
}
template <class T1, class T2, class... T3>
void _show(int i, const T1& a, const T2& b, const T3&... c) {
  for (; a[i] != ',' && a[i] != '\0'; i++) cerr << a[i];
  cerr << ":" << b << " ";
  _show(i + 1, a, c...);
}
#line 2 "matrix/matrix-mod2.hpp"

#line 2 "data-structure/dynamic-bitset.hpp"

struct DynamicBitset {
  using u64 = uint64_t;
  struct reference {
    DynamicBitset* b;
    int pos;
    reference& operator=(bool v) {
      b->set(pos, v);
      return *this;
    }
    reference& operator=(const reference& r) { return *this = bool(r); }
    reference& flip() {
      b->flip(pos);
      return *this;
    }
    operator bool() const { return b->test(pos); }
  };

  DynamicBitset() : _n(0) {}
  explicit DynamicBitset(int n, bool value = false) : _n(n), a(blocks(n), value ? ~0ull : 0ull) {
    trim();
  }

  int size() const { return _n; }
  bool empty() const { return _n == 0; }
  bool test(int pos) const {
    assert(0 <= pos && pos < _n);
    return (a[pos / W] >> (pos % W)) & 1ull;
  }
  bool operator[](int pos) const { return test(pos); }
  reference operator[](int pos) {
    assert(0 <= pos && pos < _n);
    return reference{this, pos};
  }
  DynamicBitset& set() {
    fill(a.begin(), a.end(), ~0ull);
    trim();
    return *this;
  }
  DynamicBitset& set(int pos, bool value = true) {
    assert(0 <= pos && pos < _n);
    if (value)
      a[pos / W] |= 1ull << (pos % W);
    else
      a[pos / W] &= ~(1ull << (pos % W));
    return *this;
  }
  DynamicBitset& reset() {
    fill(a.begin(), a.end(), 0);
    return *this;
  }
  DynamicBitset& reset(int pos) { return set(pos, false); }
  DynamicBitset& flip() {
    for (auto& x : a) x = ~x;
    trim();
    return *this;
  }
  DynamicBitset& flip(int pos) {
    assert(0 <= pos && pos < _n);
    a[pos / W] ^= 1ull << (pos % W);
    return *this;
  }
  int count() const {
    int ret = 0;
    for (u64 x : a) ret += __builtin_popcountll(x);
    return ret;
  }
  bool any() const {
    for (u64 x : a)
      if (x) return true;
    return false;
  }
  bool none() const { return !any(); }
  bool all() const { return count() == _n; }

  DynamicBitset& operator&=(const DynamicBitset& r) {
    assert(_n == r._n);
    for (int i = 0; i < (int)a.size(); i++) a[i] &= r.a[i];
    return *this;
  }
  DynamicBitset& operator|=(const DynamicBitset& r) {
    assert(_n == r._n);
    for (int i = 0; i < (int)a.size(); i++) a[i] |= r.a[i];
    return *this;
  }
  DynamicBitset& operator^=(const DynamicBitset& r) {
    assert(_n == r._n);
    for (int i = 0; i < (int)a.size(); i++) a[i] ^= r.a[i];
    return *this;
  }
  DynamicBitset operator~() const {
    DynamicBitset ret(*this);
    ret.flip();
    return ret;
  }
  DynamicBitset operator&(const DynamicBitset& r) const { return DynamicBitset(*this) &= r; }
  DynamicBitset operator|(const DynamicBitset& r) const { return DynamicBitset(*this) |= r; }
  DynamicBitset operator^(const DynamicBitset& r) const { return DynamicBitset(*this) ^= r; }
  DynamicBitset& operator<<=(int k) {
    assert(k >= 0);
    if (k >= _n) return reset();
    int q = k / W, r = k % W;
    if (q) {
      for (int i = (int)a.size() - 1; i >= 0; i--) a[i] = i >= q ? a[i - q] : 0;
    }
    if (r) {
      for (int i = (int)a.size() - 1; i > 0; i--) a[i] = (a[i] << r) | (a[i - 1] >> (W - r));
      a[0] <<= r;
    }
    trim();
    return *this;
  }
  DynamicBitset& operator>>=(int k) {
    assert(k >= 0);
    if (k >= _n) return reset();
    int q = k / W, r = k % W;
    if (q) {
      for (int i = 0; i < (int)a.size(); i++) a[i] = i + q < (int)a.size() ? a[i + q] : 0;
    }
    if (r) {
      for (int i = 0; i + 1 < (int)a.size(); i++) a[i] = (a[i] >> r) | (a[i + 1] << (W - r));
      a.back() >>= r;
    }
    return *this;
  }
  DynamicBitset operator<<(int k) const { return DynamicBitset(*this) <<= k; }
  DynamicBitset operator>>(int k) const { return DynamicBitset(*this) >>= k; }
  bool operator==(const DynamicBitset& r) const { return _n == r._n && a == r.a; }
  bool operator!=(const DynamicBitset& r) const { return !(*this == r); }
  int find_first() const { return find_next(-1); }
  int find_next(int pos) const {
    assert(-1 <= pos && pos < _n);
    int i = pos + 1;
    if (i >= _n) return _n;
    int b = i / W;
    u64 x = a[b] & (~0ull << (i % W));
    while (true) {
      if (x) {
        int ret = b * W + __builtin_ctzll(x);
        return ret < _n ? ret : _n;
      }
      if (++b == (int)a.size()) return _n;
      x = a[b];
    }
  }
  string to_string() const {
    string s(_n, '0');
    for (int i = 0; i < _n; i++)
      if (test(i)) s[_n - 1 - i] = '1';
    return s;
  }

 private:
  static constexpr int W = 64;
  int _n;
  vector<u64> a;
  static int blocks(int n) { return (n + W - 1) / W; }
  void trim() {
    if (_n == 0) return;
    int r = _n % W;
    if (r) a.back() &= (1ull << r) - 1;
  }
};

/**
 * @brief Dynamic Bitset
 * @docs docs/data-structure/dynamic-bitset.md
 */
#line 4 "matrix/matrix-mod2.hpp"

struct MatrixMod2 {
  using BS = DynamicBitset;
  int h, w;
  vector<BS> a;
  MatrixMod2() : h(0), w(0) {}
  MatrixMod2(int n) : h(n), w(n), a(n, BS(n)) {}
  MatrixMod2(int h_, int w_) : h(h_), w(w_), a(h, BS(w)) {}

  bool get(int i, int j) const { return a[i][j]; }
  void set(int i, int j, bool v = true) { a[i].set(j, v); }
  void add(int i, int j, bool v = true) {
    if (v) a[i].flip(j);
  }
  void sub(int i, int j, bool v = true) { add(i, j, v); }
  static MatrixMod2 id(int n) {
    MatrixMod2 mat(n);
    for (int i = 0; i < n; i++) mat.set(i, i);
    return mat;
  }
  MatrixMod2& operator+=(const MatrixMod2& r) {
    assert(h == r.h && w == r.w);
    for (int i = 0; i < h; i++) a[i] ^= r.a[i];
    return *this;
  }
  MatrixMod2& operator-=(const MatrixMod2& r) { return *this += r; }
  MatrixMod2 operator+(const MatrixMod2& r) const { return MatrixMod2(*this) += r; }
  MatrixMod2 operator-(const MatrixMod2& r) const { return MatrixMod2(*this) -= r; }
  MatrixMod2 operator*(const MatrixMod2& r) const {
    if (w <= 256) return multiply_sparse(r);
    return multiply_four_russians(r);
  }
  MatrixMod2 multiply_sparse(const MatrixMod2& r) const {
    assert(w == r.h);
    MatrixMod2 ret(h, r.w);
    for (int i = 0; i < h; i++)
      for (int k = a[i].find_first(); k < w; k = a[i].find_next(k))
        ret.a[i] ^= r.a[k];
    return ret;
  }
  MatrixMod2 multiply_four_russians(const MatrixMod2& r, int block = 0) const {
    assert(w == r.h);
    if (block == 0) block = four_russians_block_size(w);
    assert(block > 0);
    MatrixMod2 ret(h, r.w);
    for (int l = 0; l < w; l += block) {
      int len = min(block, w - l);
      vector<BS> table(1 << len, BS(r.w));
      for (int mask = 1; mask < (1 << len); mask++) {
        int b = __builtin_ctz(mask);
        table[mask] = table[mask ^ (1 << b)];
        table[mask] ^= r.a[l + b];
      }
      for (int i = 0; i < h; i++) {
        int mask = 0;
        for (int j = 0; j < len; j++)
          if (get(i, l + j)) mask |= 1 << j;
        ret.a[i] ^= table[mask];
      }
    }
    return ret;
  }
  static int four_russians_block_size(int n) {
    if (n <= 512) return 4;
    if (n <= 1024) return 5;
    if (n <= 2048) return 6;
    return 7;
  }
  MatrixMod2& operator*=(const MatrixMod2& r) { return *this = *this * r; }

  MatrixMod2 pow(long long n) const {
    assert(h == w);
    MatrixMod2 ret = id(h);
    MatrixMod2 mat(*this);
    while (n > 0) {
      if (n & 1) ret *= mat;
      mat *= mat;
      n >>= 1;
    }
    return ret;
  }
  int rank() const {
    MatrixMod2 mat(*this);
    int r = 0;
    for (int c = 0; c < w && r < h; c++) {
      int p = r;
      while (p < h && !mat.get(p, c)) p++;
      if (p == h) continue;
      mat.swap_row(r, p);
      for (int i = 0; i < h; i++)
        if (i != r && mat.get(i, c)) mat.add_row(i, r);
      r++;
    }
    return r;
  }
  int det() const {
    assert(h == w);
    MatrixMod2 mat(*this);
    for (int c = 0; c < w; c++) {
      int p = c;
      while (p < h && !mat.get(p, c)) p++;
      if (p == h) return 0;
      mat.swap_row(c, p);
      for (int i = c + 1; i < h; i++) {
        if (mat.get(i, c)) mat.add_row(i, c);
      }
    }
    return 1;
  }
  optional<MatrixMod2> inv() const {
    assert(h == w);
    MatrixMod2 mat(*this);
    MatrixMod2 imat = id(h);
    for (int c = 0; c < w; c++) {
      int p = c;
      while (p < h && !mat.get(p, c)) p++;
      if (p == h) return nullopt;
      mat.swap_row(c, p);
      imat.swap_row(c, p);
      for (int i = 0; i < h; i++) {
        if (i == c || !mat.get(i, c)) continue;
        mat.add_row(i, c);
        imat.add_row(i, c);
      }
    }
    return imat;
  }

  void swap_row(int i, int j) {
    if (i == j) return;
    swap(a[i], a[j]);
  }
  void add_row(int i, int j) { a[i] ^= a[j]; }
  void set_row(int i, const string& s) {
    assert((int)s.size() == w);
    a[i].reset();
    for (int j = 0; j < w; j++) {
      assert(s[j] == '0' || s[j] == '1');
      if (s[j] == '1') a[i].set(j);
    }
  }
  string row_string(int i) const {
    string s(w, '0');
    for (int j = 0; j < w; j++)
      if (get(i, j)) s[j] = '1';
    return s;
  }
  friend ostream& operator<<(ostream& os, const MatrixMod2& mat) {
    for (int i = 0; i < mat.h; i++) {
      os << mat.row_string(i);
      if (i + 1 < mat.h) os << "\n";
    }
    return os;
  }
};

/**
 * @brief Matrix Mod 2
 * @docs docs/matrix/matrix-mod2.md
 */
#line 5 "verify/matrix/LC_matrix_det_mod_2.test.cpp"

int main() {
  int n;
  in(n);
  MatrixMod2 a(n);
  string s;
  rep(i, 0, n) {
    in(s);
    a.set_row(i, s);
  }
  out(a.det());
}

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