結果

問題 No.803 Very Limited Xor Subset
コンテスト
ユーザー hashiryo
提出日時 2020-04-22 22:40:43
言語 C++14
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 4 ms / 2,000 ms
コード長 6,702 bytes
コンパイル時間 2,339 ms
コンパイル使用メモリ 194,900 KB
実行使用メモリ 6,824 KB
最終ジャッジ日時 2024-10-12 07:20:21
合計ジャッジ時間 3,915 ms
ジャッジサーバーID
（参考情報） 		judge3 / judge2
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 4
other AC * 43
権限があれば一括ダウンロードができます

ソースコード

diff # 

#include <bits/stdc++.h>
using namespace std;

template <int mod>
struct ModInt {
  int x;
  ModInt() : x(0) {}
  ModInt(int64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod)) {}
  ModInt &operator+=(const ModInt &p) {
    if ((x += p.x) >= mod) x -= mod;
    return *this;
  }
  ModInt &operator-=(const ModInt &p) {
    if ((x += mod - p.x) >= mod) x -= mod;
    return *this;
  }
  ModInt &operator*=(const ModInt &p) {
    x = (int)(1LL * x * p.x % mod);
    return *this;
  }
  ModInt &operator/=(const ModInt &p) { return *this *= p.inverse(); }
  ModInt operator-() const { return ModInt() - *this; }
  ModInt operator+(const ModInt &p) const { return ModInt(*this) += p; }
  ModInt operator-(const ModInt &p) const { return ModInt(*this) -= p; }
  ModInt operator*(const ModInt &p) const { return ModInt(*this) *= p; }
  ModInt operator/(const ModInt &p) const { return ModInt(*this) /= p; }
  bool operator==(const ModInt &p) const { return x == p.x; }
  bool operator!=(const ModInt &p) const { return x != p.x; }
  ModInt inverse() const {
    int a = x, b = mod, u = 1, v = 0, t;
    while (b) t = a / b, swap(a -= t * b, b), swap(u -= t * v, v);
    return ModInt(u);
  }
  ModInt pow(int64_t e) const {
    ModInt ret(1);
    for (ModInt b = *this; e; e >>= 1, b *= b)
      if (e & 1) ret *= b;
    return ret;
  }
  friend ostream &operator<<(ostream &os, const ModInt &p) { return os << p.x; }
  friend istream &operator>>(istream &is, ModInt &a) {
    int64_t t;
    is >> t;
    a = ModInt<mod>(t);
    return (is);
  }
  static int modulo() { return mod; }
};

struct BitMatrix {
 private:
  vector<vector<short>> a;

 public:
  BitMatrix() {}
  BitMatrix(size_t n, size_t m) : a(n, vector<short>(m, 0)) {}
  BitMatrix(size_t n) : BitMatrix(n, n) {}
  inline const vector<short> &operator[](size_t k) const { return a[k]; }
  inline vector<short> &operator[](size_t k) { return a[k]; }
  size_t height() const { return a.size(); }
  size_t width() const { return a[0].size(); }

  static BitMatrix I(size_t n) {
    BitMatrix mat(n);
    for (int i = 0; i < n; i++) mat[i][i] = 1;
    return mat;
  }
  BitMatrix operator+(const BitMatrix &b) const {
    size_t n = height(), m = width();
    BitMatrix c(n, m);
    for (int i = 0; i < n; i++)
      for (int j = 0; j < m; j++) c[i][j] = (*this)[i][j] ^ b[i][j];
    return c;
  }
  BitMatrix operator*(const BitMatrix &b) const {
    if (width() <= 64) return mul<64>(b);
    if (width() <= 2600) return mul<2600>(b);
    return mul<100010>(b);
  }
  BitMatrix &operator+=(const BitMatrix &b) { return *this = (*this) + b; }
  BitMatrix &operator*=(const BitMatrix &b) { return *this = (*this) * b; }
  bool operator==(const BitMatrix &b) const { return a == b.a; }
  BitMatrix pow(uint64_t e) const {
    BitMatrix ret = I(height());
    for (BitMatrix base = *this; e; e >>= 1, base *= base)
      if (e & 1) ret *= base;
    return ret;
  }

  static pair<BitMatrix, BitMatrix> Gauss_Jordan(const BitMatrix &a,
                                                 const BitMatrix &b) {
    if (a.width() + b.width() <= 64) return gauss_jordan_content<64>(a, b);
    if (a.width() + b.width() <= 2600) return gauss_jordan_content<2600>(a, b);
    return gauss_jordan_content<100010>(a, b);
  }
  static pair<vector<int>, vector<vector<int>>> linear_equations(
      const BitMatrix &a, const vector<int> &b) {
    int n = a.height(), m = a.width();
    BitMatrix B(n, 1);
    for (int i = 0; i < n; i++) B[i][0] = b[i];
    auto p = Gauss_Jordan(a, B);
    vector<int> jdx(n, -1), idx(m, -1);
    for (int i = 0, j; i < n; i++) {
      for (j = 0; j < m; j++) {
        if (p.first[i][j]) {
          jdx[i] = j, idx[j] = i;
          break;
        }
      }
      if (j == m && p.second[i][0])
        return make_pair(vector<int>(), vector<vector<int>>());  // no solutions
    }
    vector<int> c(m);
    vector<vector<int>> d;
    for (int j = 0; j < m; j++) {
      if (idx[j] != -1)
        c[j] = p.second[idx[j]][0];
      else {
        vector<int> v(m);
        v[j] = 1;
        for (int i = 0; i < n; i++)
          if (jdx[i] != -1) v[jdx[i]] = p.first[i][j];
        d.push_back(v);
      }
    }
    return make_pair(c, d);
  }
  int rank() const {
    int n = height(), m = width();
    BitMatrix b(n, 0);
    BitMatrix p = Gauss_Jordan(*this, b).first;
    for (int i = 0, j; i < n; i++) {
      for (j = 0; j < m; j++)
        if (p[i][j] != 0) break;
      if (j == m) return i;
    }
    return n;
  }

 private:
  template <size_t SIZE>
  BitMatrix mul(const BitMatrix &b) const {
    size_t n = height(), m = width(), l = b.width();
    assert(m == b.height());
    vector<bitset<SIZE>> tb(l);
    for (int i = 0; i < l; ++i)
      for (int j = 0; j < m; ++j) tb[i][j] = b[j][i];
    BitMatrix c(n, l);
    for (int i = 0; i < n; i++) {
      bitset<SIZE> abit;
      for (int k = 0; k < m; k++) abit[k] = (*this)[i][k];
      for (int j = 0; j < l; j++) c[i][j] = ((abit & tb[j]).count() & 1);
    }
    return c;
  }

  template <size_t SIZE>
  static pair<BitMatrix, BitMatrix> gauss_jordan_content(const BitMatrix &a,
                                                         const BitMatrix &b) {
    size_t n = a.height(), m = a.width(), l = b.width();
    vector<bitset<SIZE>> c(n);
    for (int i = 0; i < n; i++)
      for (int j = 0; j < m; j++) c[i][j] = a[i][j];
    for (int i = 0; i < n; i++)
      for (int j = 0; j < l; j++) c[i][j + m] = b[i][j];
    int d = 0;
    for (int j = 0; j < m; j++) {
      int p = d;
      for (int i = d + 1; i < n; i++)
        if (c[i][j]) p = i;
      if (!c[p][j]) continue;
      swap(c[p], c[d]);
      for (int i = 0; i < n; i++)
        if (i != d && c[i][j]) c[i] ^= c[d];
      d++;
    }
    BitMatrix reta(n, m), retb(n, l);
    for (int i = 0; i < n; i++)
      for (int j = 0; j < m; j++) reta[i][j] = c[i][j];
    for (int i = 0; i < n; i++)
      for (int j = 0; j < l; j++) retb[i][j] = c[i][j + m];
    return make_pair(reta, retb);
  }
};

signed main() {
  cin.tie(0);
  ios::sync_with_stdio(0);
  int N, M, X;
  cin >> N >> M >> X;
  BitMatrix A(30 + M, N);
  vector<int> b(30 + M);
  for (int i = 0; i < 30; i++) {
    b[i] = (X >> i) & 1;
  }
  for (int j = 0; j < N; j++) {
    int a;
    cin >> a;
    for (int i = 0; i < 30; i++) {
      A[i][j] = (a >> i) & 1;
    }
  }
  for (int i = 0; i < M; i++) {
    int type, l, r;
    cin >> type >> l >> r;
    l--, r--;
    for (int j = l; j <= r; j++) {
      A[30 + i][j] = 1;
    }
    b[30 + i] = type;
  }
  auto ans = BitMatrix::linear_equations(A, b);
  if (ans.first.size())
    cout << ModInt<int(1e9 + 7)>(2).pow(ans.second.size()) << endl;
  else
    cout << 0 << endl;
  return 0;
}
0