Problem p03174 (C++)

Buggy submission (status: Time Limit Exceeded):
#include <bits/stdc++.h>
using namespace std;
using uint = unsigned int;
using lint = long long int;
using ulint = unsigned long long int;
template <class T = int> using V = vector<T>;
template <class T = int> using VV = V<V<T>>;
template <class T, class U> void assign(V<T> &v, int n, const U &a) {
  v.assign(n, a);
}
template <class T, class... Args>
void assign(V<T> &v, int n, const Args &...args) {
  v.resize(n);
  for (auto &&e : v)
    assign(e, args...);
}

template <class Int> constexpr bool is_prime(Int n) {
  if (n < 2 or n > 2 and ~n & 1)
    return false;
  for (Int i = 3; i * i <= n; i += 2)
    if (n % i == 0)
      return false;
  return true;
}
template <uint P> struct ModInt {
  static_assert(is_prime(P), "template argument must be a prime number");
  using M = ModInt;
  uint v;
  ModInt() : v(0) {}
  template <class Int>
  ModInt(Int x) : v(x >= 0   ? x % P
                    : -x % P ? P - -x % P
                             : 0) {}
  constexpr ModInt(uint v, int _) : v(v) {} // 直接値を初期化
  static constexpr uint p() { return P; }
  M operator++(int) {
    M t = *this;
    if (++v == P)
      v = 0;
    return t;
  }
  M operator--(int) {
    M t = *this;
    v = (v ? v : P) - 1;
    return t;
  }
  M &operator++() {
    if (++v == P)
      v = 0;
    return *this;
  }
  M &operator--() {
    v = (v ? v : P) - 1;
    return *this;
  }
  M operator+() const { return *this; }
  M operator-() const { return {v ? P - v : 0, 0}; }
  explicit operator bool() const noexcept { return v; }
  bool operator!() const noexcept { return !static_cast<bool>(*this); }
  M operator*(M rhs) const { return M(*this) *= rhs; }
  M operator/(M rhs) const { return M(*this) /= rhs; }
  M operator+(M rhs) const { return M(*this) += rhs; }
  M operator-(M rhs) const { return M(*this) -= rhs; }
  bool operator==(M rhs) { return v == rhs.v; }
  bool operator!=(M rhs) { return !(*this == rhs); }
  M &operator*=(M rhs) {
    v = (ulint)v * rhs.v % P;
    return *this;
  }
  M &operator/=(M rhs) { return *this *= rhs.inv(); }
  M &operator+=(M rhs) {
    v = rhs.v < P - v ? v + rhs.v : v - (P - rhs.v);
    return *this;
  }
  M &operator-=(M rhs) {
    v = rhs.v <= v ? v - rhs.v : v + (P - rhs.v);
    return *this;
  }
  M inv() const {
    assert(v);
#ifdef __linux__ // ACとCFで動作を変えるための仮の対処
    return pow(P - 2);
#else
    int a = v, b = P, x = 1, u = 0;
    while (b) {
      int q = a / b;
      swap(a -= q * b, b);
      swap(x -= q * u, u);
    }
    return x;
#endif
  }
  template <class Int> M pow(Int n) const {
    n = n >= 0 ? n % (P - 1) : P - 1 - -n % (P - 1);
    M res = 1;
    for (M a = *this; n > 0; a *= a, n >>= 1)
      if (n & 1)
        res *= a;
    return res;
  }
  template <class Int> friend M operator*(Int lhs, M rhs) {
    return M(lhs) *= rhs;
  }
  template <class Int> friend M operator/(Int lhs, M rhs) {
    return M(lhs) /= rhs;
  }
  template <class Int> friend M operator+(Int lhs, M rhs) {
    return M(lhs) += rhs;
  }
  template <class Int> friend M operator-(Int lhs, M rhs) {
    return M(lhs) -= rhs;
  }
  friend ostream &operator<<(ostream &os, M rhs) { return os << rhs.v; }
  friend istream &operator>>(istream &is, M &rhs) {
    lint x;
    is >> x;
    rhs = x;
    return is;
  }
  template <class Int> friend bool operator==(Int lhs, M rhs) {
    return M(lhs) == rhs;
  }
  template <class Int> friend bool operator!=(Int lhs, M rhs) {
    return !(lhs == rhs);
  }
};

using Mint = ModInt<static_cast<uint>(1e9 + 7)>;

int main() {
  cin.tie(nullptr);
  ios_base::sync_with_stdio(false);
  int n;
  cin >> n;
  VV<> a;
  assign(a, n, n, 0);
  for (int i = 0; i < n; ++i)
    for (int j = 0; j < n; ++j)
      cin >> a[i][j];
  VV<Mint> dp;
  assign(dp, n + 1, 1 << n, 0);
  dp[0][0] = 1;
  for (int i = 0; i < n; ++i) {
    for (int bit = 0; bit < 1 << n; ++bit) {
      for (int j = 0; j < n; ++j)
        if (a[i][j] and !(bit & 1 << j)) {
          dp[i + 1][bit | 1 << j] += dp[i][bit];
        }
    }
  }
  cout << dp[n].back() << '\n';
}

Fixed submission:
#include <bits/stdc++.h>
using namespace std;
using uint = unsigned int;
using lint = long long int;
using ulint = unsigned long long int;
template <class T = int> using V = vector<T>;
template <class T = int> using VV = V<V<T>>;
template <class T, class U> void assign(V<T> &v, int n, const U &a) {
  v.assign(n, a);
}
template <class T, class... Args>
void assign(V<T> &v, int n, const Args &...args) {
  v.resize(n);
  for (auto &&e : v)
    assign(e, args...);
}

template <class Int> constexpr bool is_prime(Int n) {
  if (n < 2 or n > 2 and ~n & 1)
    return false;
  for (Int i = 3; i * i <= n; i += 2)
    if (n % i == 0)
      return false;
  return true;
}
template <uint P> struct ModInt {
  static_assert(is_prime(P), "template argument must be a prime number");
  using M = ModInt;
  uint v;
  ModInt() : v(0) {}
  template <class Int>
  ModInt(Int x) : v(x >= 0   ? x % P
                    : -x % P ? P - -x % P
                             : 0) {}
  constexpr ModInt(uint v, int _) : v(v) {} // 直接値を初期化
  static constexpr uint p() { return P; }
  M operator++(int) {
    M t = *this;
    if (++v == P)
      v = 0;
    return t;
  }
  M operator--(int) {
    M t = *this;
    v = (v ? v : P) - 1;
    return t;
  }
  M &operator++() {
    if (++v == P)
      v = 0;
    return *this;
  }
  M &operator--() {
    v = (v ? v : P) - 1;
    return *this;
  }
  M operator+() const { return *this; }
  M operator-() const { return {v ? P - v : 0, 0}; }
  explicit operator bool() const noexcept { return v; }
  bool operator!() const noexcept { return !static_cast<bool>(*this); }
  M operator*(M rhs) const { return M(*this) *= rhs; }
  M operator/(M rhs) const { return M(*this) /= rhs; }
  M operator+(M rhs) const { return M(*this) += rhs; }
  M operator-(M rhs) const { return M(*this) -= rhs; }
  bool operator==(M rhs) { return v == rhs.v; }
  bool operator!=(M rhs) { return !(*this == rhs); }
  M &operator*=(M rhs) {
    v = (ulint)v * rhs.v % P;
    return *this;
  }
  M &operator/=(M rhs) { return *this *= rhs.inv(); }
  M &operator+=(M rhs) {
    v = rhs.v < P - v ? v + rhs.v : v - (P - rhs.v);
    return *this;
  }
  M &operator-=(M rhs) {
    v = rhs.v <= v ? v - rhs.v : v + (P - rhs.v);
    return *this;
  }
  M inv() const {
    assert(v);
#ifdef __linux__ // ACとCFで動作を変えるための仮の対処
    return pow(P - 2);
#else
    int a = v, b = P, x = 1, u = 0;
    while (b) {
      int q = a / b;
      swap(a -= q * b, b);
      swap(x -= q * u, u);
    }
    return x;
#endif
  }
  template <class Int> M pow(Int n) const {
    n = n >= 0 ? n % (P - 1) : P - 1 - -n % (P - 1);
    M res = 1;
    for (M a = *this; n > 0; a *= a, n >>= 1)
      if (n & 1)
        res *= a;
    return res;
  }
  template <class Int> friend M operator*(Int lhs, M rhs) {
    return M(lhs) *= rhs;
  }
  template <class Int> friend M operator/(Int lhs, M rhs) {
    return M(lhs) /= rhs;
  }
  template <class Int> friend M operator+(Int lhs, M rhs) {
    return M(lhs) += rhs;
  }
  template <class Int> friend M operator-(Int lhs, M rhs) {
    return M(lhs) -= rhs;
  }
  friend ostream &operator<<(ostream &os, M rhs) { return os << rhs.v; }
  friend istream &operator>>(istream &is, M &rhs) {
    lint x;
    is >> x;
    rhs = x;
    return is;
  }
  template <class Int> friend bool operator==(Int lhs, M rhs) {
    return M(lhs) == rhs;
  }
  template <class Int> friend bool operator!=(Int lhs, M rhs) {
    return !(lhs == rhs);
  }
};

using Mint = ModInt<static_cast<uint>(1e9 + 7)>;

int main() {
  cin.tie(nullptr);
  ios_base::sync_with_stdio(false);
  int n;
  cin >> n;
  VV<> a;
  assign(a, n, n, 0);
  for (int i = 0; i < n; ++i)
    for (int j = 0; j < n; ++j)
      cin >> a[i][j];
  VV<Mint> dp;
  assign(dp, n + 1, 1 << n, 0);
  dp[0][0] = 1;
  for (int i = 0; i < n; ++i) {
    for (int bit = 0; bit < 1 << n; ++bit)
      if (__builtin_popcount(bit) == i) {
        for (int j = 0; j < n; ++j)
          if (a[i][j] and !(bit & 1 << j)) {
            dp[i + 1][bit | 1 << j] += dp[i][bit];
          }
      }
  }
  cout << dp[n].back() << '\n';
}