Problem p03513 (C++) — buggy submission, verdict: Time Limit Exceeded

#include <bits/stdc++.h>
using namespace std;
using lint = long long;
template <class T = int> using V = vector<T>;
template <class T = int> using VV = V<V<T>>;

template <unsigned P> struct ModInt {
  using M = ModInt;
  unsigned v;
  constexpr ModInt() : v(0) {}
  constexpr ModInt(unsigned _v, int) : v(_v) {}
  template <class Z> ModInt(const Z &a) : v((a < 0 ? P - -a % P : a) % P) {}
  static constexpr unsigned p() { return P; }
  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 !(bool)*this; }
  M &operator*=(M r) {
    v = (uint64_t)v * r.v % P;
    return *this;
  }
  M &operator/=(M r) { return *this *= r.inv(); }
  M &operator+=(M r) {
    if ((v += r.v) >= P)
      v -= P;
    return *this;
  }
  M &operator-=(M r) {
    if ((v += P - r.v) >= P)
      v -= P;
    return *this;
  }
  M inv() const {
    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);
    }
    assert(a == 1);
    return x;
  }
  template <class Z> M pow(Z n) const {
    if (n < 0)
      return pow(-n).inv();
    M res = 1;
    for (M a = *this; n; a *= a, n >>= 1)
      if (n & 1)
        res *= a;
    return res;
  }
  friend M operator*(M l, M r) { return M(l) *= r; }
  friend M operator/(M l, M r) { return M(l) /= r; }
  friend M operator+(M l, M r) { return M(l) += r; }
  friend M operator-(M l, M r) { return M(l) -= r; }
  friend ostream &operator<<(ostream &os, M r) { return os << r.v; }
  friend bool operator==(M l, M r) { return l.v == r.v; }
  friend bool operator!=(M l, M r) { return !(l == r); }
};
using Mint = ModInt<(unsigned)1e9 + 7>;

int main() {
  cin.tie(nullptr);
  ios::sync_with_stdio(false);
  int n, m;
  cin >> n >> m;
  V<bitset<15>> g(n);
  for (int _ = 0; _ < m; ++_) {
    int u, v;
    cin >> u >> v, --u, --v;
    g[u][v] = g[v][u] = 1;
  }
  V<Mint> ipw(m + 1, 1);
  for (int i = 1; i <= m; ++i) {
    ipw[i] = ipw[i - 1] / 2;
  }

  auto fn = [&](int r) -> V<Mint> {
    V<Mint> dp(1 << n);
    for (int S = 0; S < 1 << n; ++S)
      if (S >> r & 1) {
        int c = 0;
        for (int u = 0; u < n; ++u)
          if (S >> u & 1) {
            for (int v = 0; v < n; ++v)
              if (~S >> v & 1) {
                c += g[u][v];
              }
          }
        dp[S] = ipw[c];
        V<> a(n);
        for (int u = 0; u < n; ++u)
          if (~S >> u & 1) {
            for (int v = 0; v < n; ++v)
              if (S >> v & 1) {
                a[v] += g[u][v];
              }
          }
        for (int T = (S - 1) & S;; T = (T - 1) & S) {
          c = 0;
          for (int v = 0; v < n; ++v)
            if ((S ^ T) >> v & 1) {
              c += a[v];
            }
          dp[S] -= dp[T] * ipw[c];
          if (!T)
            break;
        }
      }
    return dp;
  };

  auto dp0 = fn(0);
  auto dp1 = fn(1);
  Mint res = 1;
  for (int S = 0; S < 1 << n; ++S) {
    int nS = S;
    for (int u = 0; u < n; ++u)
      if (S >> u & 1) {
        for (int v = 0; v < n; ++v)
          if (g[u][v]) {
            nS |= 1 << v;
          }
      }
    for (int T = nS ^ ~(~0U << n);; T = (T - 1) & (nS ^ ~(~0U << n))) {
      res -= dp0[S] * dp1[T];
      if (!T)
        break;
    }
  }
  res *= Mint(2).pow(m);
  cout << res << '\\n';
}

Error: TLE

Fixed submission:

#include <bits/stdc++.h>
using namespace std;
using lint = long long;
template <class T = int> using V = vector<T>;
template <class T = int> using VV = V<V<T>>;

template <unsigned P> struct ModInt {
  using M = ModInt;
  unsigned v;
  constexpr ModInt() : v(0) {}
  constexpr ModInt(unsigned _v, int) : v(_v) {}
  template <class Z> ModInt(const Z &a) : v((a < 0 ? P - -a % P : a) % P) {}
  static constexpr unsigned p() { return P; }
  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 !(bool)*this; }
  M &operator*=(M r) {
    v = (uint64_t)v * r.v % P;
    return *this;
  }
  M &operator/=(M r) { return *this *= r.inv(); }
  M &operator+=(M r) {
    if ((v += r.v) >= P)
      v -= P;
    return *this;
  }
  M &operator-=(M r) {
    if ((v += P - r.v) >= P)
      v -= P;
    return *this;
  }
  M inv() const {
    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);
    }
    assert(a == 1);
    return x;
  }
  template <class Z> M pow(Z n) const {
    if (n < 0)
      return pow(-n).inv();
    M res = 1;
    for (M a = *this; n; a *= a, n >>= 1)
      if (n & 1)
        res *= a;
    return res;
  }
  friend M operator*(M l, M r) { return M(l) *= r; }
  friend M operator/(M l, M r) { return M(l) /= r; }
  friend M operator+(M l, M r) { return M(l) += r; }
  friend M operator-(M l, M r) { return M(l) -= r; }
  friend ostream &operator<<(ostream &os, M r) { return os << r.v; }
  friend bool operator==(M l, M r) { return l.v == r.v; }
  friend bool operator!=(M l, M r) { return !(l == r); }
};
using Mint = ModInt<(unsigned)1e9 + 7>;

int main() {
  cin.tie(nullptr);
  ios::sync_with_stdio(false);
  int n, m;
  cin >> n >> m;
  V<bitset<15>> g(n);
  for (int _ = 0; _ < m; ++_) {
    int u, v;
    cin >> u >> v, --u, --v;
    g[u][v] = g[v][u] = 1;
  }

  auto fn = [&](int r) -> V<Mint> {
    V<Mint> dp(1 << n);
    for (int S = 0; S < 1 << n; ++S)
      if (S >> r & 1) {
        int c = 0;
        for (int u = 0; u < n; ++u)
          if (S >> u & 1) {
            for (int v = 0; v < n; ++v)
              if (~S >> v & 1) {
                c += g[u][v];
              }
          }
        dp[S] = Mint(2).pow(-c);
        for (int T = (S - 1) & S;; T = (T - 1) & S) {
          c = 0;
          for (int u = 0; u < n; ++u)
            if (S >> u & 1 and ~T >> u & 1) {
              for (int v = 0; v < n; ++v)
                if (~S >> v & 1) {
                  c += g[u][v];
                }
            }
          dp[S] -= dp[T] * Mint(2).pow(-c);
          if (!T)
            break;
        }
      }
    return dp;
  };

  auto dp0 = fn(0);
  auto dp1 = fn(1);
  Mint res = 1;
  for (int S = 0; S < 1 << n; ++S) {
    int Sc = S ^ ~(~0U << n);
    for (int T = Sc;; T = (T - 1) & Sc) {
      int c = 0;
      for (int u = 0; u < n; ++u)
        if (S >> u & 1) {
          for (int v = 0; v < n; ++v)
            if (T >> v & 1) {
              c += g[u][v];
            }
        }
      if (!c) {
        res -= dp0[S] * dp1[T];
      }
      if (!T)
        break;
    }
  }
  res *= Mint(2).pow(m);
  cout << res << '\\n';
}