Problem p02591 (C++) — buggy submission, verdict: Time Limit Exceeded

#include <bits/stdc++.h>

using namespace std;

using int64 = long long;
const int mod = (1e9 + 7);

const int64 infll = (1LL << 62) - 1;
const int inf = (1 << 30) - 1;

struct IoSetup {
  IoSetup() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(10);
    cerr << fixed << setprecision(10);
  }
} iosetup;

template <typename T1, typename T2>
ostream &operator<<(ostream &os, const pair<T1, T2> &p) {
  os << p.first << " " << p.second;
  return os;
}

template <typename T1, typename T2>
istream &operator>>(istream &is, pair<T1, T2> &p) {
  is >> p.first >> p.second;
  return is;
}

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 != v.size() ? " " : "");
  }
  return os;
}

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

template <typename T1, typename T2> inline bool chmax(T1 &a, T2 b) {
  return a < b && (a = b, true);
}

template <typename T1, typename T2> inline bool chmin(T1 &a, T2 b) {
  return a > b && (a = b, true);
}

template <typename T = int64> vector<T> make_v(size_t a) {
  return vector<T>(a);
}

template <typename T, typename... Ts> auto make_v(size_t a, Ts... ts) {
  return vector<decltype(make_v<T>(ts...))>(a, make_v<T>(ts...));
}

template <typename T, typename V>
typename enable_if<is_class<T>::value == 0>::type fill_v(T &t, const V &v) {
  t = v;
}

template <typename T, typename V>
typename enable_if<is_class<T>::value != 0>::type fill_v(T &t, const V &v) {
  for (auto &e : t)
    fill_v(e, v);
}

template <typename F> struct FixPoint : F {
  FixPoint(F &&f) : F(forward<F>(f)) {}

  template <typename... Args> decltype(auto) operator()(Args &&...args) const {
    return F::operator()(*this, forward<Args>(args)...);
  }
};

template <typename F> inline decltype(auto) MFP(F &&f) {
  return FixPoint<F>{forward<F>(f)};
}

static constexpr uint32_t mul_inv(uint32_t n, int e = 5, uint32_t x = 1) {
  return e == 0 ? x : mul_inv(n, e - 1, x * (2 - x * n));
}

template <uint32_t mod, bool fast = true> struct ModInt2 {
  using u32 = uint32_t;
  using u64 = uint64_t;

  static constexpr u32 inv = mul_inv(mod);
  static constexpr u32 r2 = -uint64_t(mod) % mod;

  uint32_t x;

  ModInt2() : x(0) {}

  ModInt2(const int64_t &y)
      : x(reduce(u64(fast ? y : (y >= 0 ? y % mod : (mod - (-y) % mod) % mod)) *
                 r2)) {}

  u32 reduce(const u64 &w) const {
    return u32(w >> 32) + mod - u32((u64(u32(w) * inv) * mod) >> 32);
  }

  ModInt2 &operator+=(const ModInt2 &p) {
    if (int(x += p.x - 2 * mod) < 0)
      x += 2 * mod;
    return *this;
  }

  ModInt2 &operator-=(const ModInt2 &p) {
    if (int(x -= p.x) < 0)
      x += 2 * mod;
    return *this;
  }

  ModInt2 &operator*=(const ModInt2 &p) {
    x = reduce(uint64_t(x) * p.x);
    return *this;
  }

  ModInt2 &operator/=(const ModInt2 &p) {
    *this *= p.inverse();
    return *this;
  }

  ModInt2 operator-() const { return ModInt2() - *this; }

  ModInt2 operator+(const ModInt2 &p) const { return ModInt2(*this) += p; }

  ModInt2 operator-(const ModInt2 &p) const { return ModInt2(*this) -= p; }

  ModInt2 operator*(const ModInt2 &p) const { return ModInt2(*this) *= p; }

  ModInt2 operator/(const ModInt2 &p) const { return ModInt2(*this) /= p; }

  bool operator==(const ModInt2 &p) const { return get() == p.get(); }

  bool operator!=(const ModInt2 &p) const { return get() != p.get(); }

  int get() const { return reduce(x) % mod; }

  ModInt2 pow(int64_t n) const {
    ModInt2 ret(1), mul(*this);
    while (n > 0) {
      if (n & 1)
        ret *= mul;
      mul *= mul;
      n >>= 1;
    }
    return ret;
  }

  ModInt2 inverse() const { return pow(mod - 2); }

  friend ostream &operator<<(ostream &os, const ModInt2 &p) {
    return os << p.get();
  }

  friend istream &operator>>(istream &is, ModInt2 &a) {
    int64_t t;
    is >> t;
    a = ModInt2<mod, fast>(t);
    return (is);
  }

  static int get_mod() { return mod; }
};

using modint = ModInt2<mod>;

int main() {
  int H;
  cin >> H;
  vector<int> P(1 << (H - 1));
  cin >> P;
  for (auto &p : P)
    --p;

  // 多分LCAを固定するべきじゃないでしょうか

  int64 s = 1 << (H - 1);

  vector<int> left((1 << H) + 1), right((1 << H) + 1);
  for (int i = 0; i < 1 << (H - 1); i++) {
    left[i + s] = i + s;
    right[i + s] = i + s + 1;
  }
  for (int i = s - 1; i >= 1; i--) {
    left[i] = left[i * 2 + 0];
    right[i] = right[i * 2 + 1];
  }

  modint ret = 0;

  vector<modint> bits((1 << H) + 1);
  auto dfs = MFP([&](auto dfs, int idx) -> pair<int, int> {
    if (idx >= s) {
      return {idx, idx + 1};
    }
    int l = idx * 2 + 0;
    int r = idx * 2 + 1;
    auto x = dfs(l);
    auto y = dfs(r);

    for (int i = x.first; i < x.second; i++) {
      int to = i;
      modint mul = to;
      while (to > idx) {
        to /= 2;
        mul *= to;
      }
      to = P[i - s] + s;
      mul *= to;
      while (to >= 1) {
        bits[to] += mul;
        to /= 2;
        mul *= to;
      }
    }

    modint rev = modint(1) / idx;

    for (int i = y.first; i < y.second; i++) {
      int to = i;
      modint mul = to;
      while (to > idx) {
        to /= 2;
        mul *= to;
      }
      mul *= rev;

      to = P[i - s] + s;
      while (to > 1) {
        mul *= to;
        if (to & 1) {
          ret += bits[(to / 2) * 2 + 0] * mul * (to / 2);
        } else {
          ret += bits[(to / 2) * 2 + 1] * mul * (to / 2);
        }
        to /= 2;
      }
    }

    for (int i = x.first; i < x.second; i++) {
      int to = i;
      modint mul = to;
      while (to > idx) {
        to /= 2;
        mul *= to;
      }
      to = P[i - s] + s;
      mul *= to;
      while (to >= 1) {
        bits[to] -= mul;
        to /= 2;
        mul *= to;
      }
    }

    return {x.first, y.second};
  });
  dfs(1);
  cout << ret << "\\n";
}


Error: TLE

Fixed submission:

#include <bits/stdc++.h>

using namespace std;

using int64 = long long;
const int mod = (1e9 + 7);

const int64 infll = (1LL << 62) - 1;
const int inf = (1 << 30) - 1;

struct IoSetup {
  IoSetup() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(10);
    cerr << fixed << setprecision(10);
  }
} iosetup;

template <typename T1, typename T2>
ostream &operator<<(ostream &os, const pair<T1, T2> &p) {
  os << p.first << " " << p.second;
  return os;
}

template <typename T1, typename T2>
istream &operator>>(istream &is, pair<T1, T2> &p) {
  is >> p.first >> p.second;
  return is;
}

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 != v.size() ? " " : "");
  }
  return os;
}

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

template <typename T1, typename T2> inline bool chmax(T1 &a, T2 b) {
  return a < b && (a = b, true);
}

template <typename T1, typename T2> inline bool chmin(T1 &a, T2 b) {
  return a > b && (a = b, true);
}

template <typename T = int64> vector<T> make_v(size_t a) {
  return vector<T>(a);
}

template <typename T, typename... Ts> auto make_v(size_t a, Ts... ts) {
  return vector<decltype(make_v<T>(ts...))>(a, make_v<T>(ts...));
}

template <typename T, typename V>
typename enable_if<is_class<T>::value == 0>::type fill_v(T &t, const V &v) {
  t = v;
}

template <typename T, typename V>
typename enable_if<is_class<T>::value != 0>::type fill_v(T &t, const V &v) {
  for (auto &e : t)
    fill_v(e, v);
}

template <typename F> struct FixPoint : F {
  FixPoint(F &&f) : F(forward<F>(f)) {}

  template <typename... Args> decltype(auto) operator()(Args &&...args) const {
    return F::operator()(*this, forward<Args>(args)...);
  }
};

template <typename F> inline decltype(auto) MFP(F &&f) {
  return FixPoint<F>{forward<F>(f)};
}

static constexpr uint32_t mul_inv(uint32_t n, int e = 5, uint32_t x = 1) {
  return e == 0 ? x : mul_inv(n, e - 1, x * (2 - x * n));
}

template <uint32_t mod, bool fast = true> struct ModInt2 {
  using u32 = uint32_t;
  using u64 = uint64_t;

  static constexpr u32 inv = mul_inv(mod);
  static constexpr u32 r2 = -uint64_t(mod) % mod;

  uint32_t x;

  ModInt2() : x(0) {}

  ModInt2(const int64_t &y)
      : x(reduce(u64(fast ? y : (y >= 0 ? y % mod : (mod - (-y) % mod) % mod)) *
                 r2)) {}

  u32 reduce(const u64 &w) const {
    return u32(w >> 32) + mod - u32((u64(u32(w) * inv) * mod) >> 32);
  }

  ModInt2 &operator+=(const ModInt2 &p) {
    if (int(x += p.x - 2 * mod) < 0)
      x += 2 * mod;
    return *this;
  }

  ModInt2 &operator-=(const ModInt2 &p) {
    if (int(x -= p.x) < 0)
      x += 2 * mod;
    return *this;
  }

  ModInt2 &operator*=(const ModInt2 &p) {
    x = reduce(uint64_t(x) * p.x);
    return *this;
  }

  ModInt2 &operator/=(const ModInt2 &p) {
    *this *= p.inverse();
    return *this;
  }

  ModInt2 operator-() const { return ModInt2() - *this; }

  ModInt2 operator+(const ModInt2 &p) const { return ModInt2(*this) += p; }

  ModInt2 operator-(const ModInt2 &p) const { return ModInt2(*this) -= p; }

  ModInt2 operator*(const ModInt2 &p) const { return ModInt2(*this) *= p; }

  ModInt2 operator/(const ModInt2 &p) const { return ModInt2(*this) /= p; }

  bool operator==(const ModInt2 &p) const { return get() == p.get(); }

  bool operator!=(const ModInt2 &p) const { return get() != p.get(); }

  int get() const { return reduce(x) % mod; }

  ModInt2 pow(int64_t n) const {
    ModInt2 ret(1), mul(*this);
    while (n > 0) {
      if (n & 1)
        ret *= mul;
      mul *= mul;
      n >>= 1;
    }
    return ret;
  }

  ModInt2 inverse() const { return pow(mod - 2); }

  friend ostream &operator<<(ostream &os, const ModInt2 &p) {
    return os << p.get();
  }

  friend istream &operator>>(istream &is, ModInt2 &a) {
    int64_t t;
    is >> t;
    a = ModInt2<mod, fast>(t);
    return (is);
  }

  static int get_mod() { return mod; }
};

using modint = ModInt2<mod>;

/**
 * @brief Binary-Indexed-Tree(BIT)
 * @docs docs/binary-indexed-tree.md
 */
template <typename T> struct BinaryIndexedTree {
  vector<T> data;

  BinaryIndexedTree() = default;

  explicit BinaryIndexedTree(size_t sz) : data(sz + 1, 0) {}

  void add(int k, const T &x) {
    for (++k; k < (int)data.size(); k += k & -k)
      data[k] += x;
  }

  T query(int k) const {
    T ret = T();
    for (++k; k > 0; k -= k & -k)
      ret += data[k];
    return ret;
  }

  int lower_bound(T x) const {
    int i = 0;
    for (int k = 1 << (__lg(data.size() - 1) + 1); k > 0; k >>= 1) {
      if (i + k < data.size() && data[i + k] < x) {
        x -= data[i + k];
        i += k;
      }
    }
    return i;
  }

  int upper_bound(T x) const {
    int i = 0;
    for (int k = 1 << (__lg(data.size() - 1) + 1); k > 0; k >>= 1) {
      if (i + k < data.size() && data[i + k] <= x) {
        x -= data[i + k];
        i += k;
      }
    }
    return i;
  }
};

int main() {
  int H;
  cin >> H;
  vector<int> P(1 << (H - 1));
  cin >> P;
  for (auto &p : P)
    --p;

  // 多分LCAを固定するべきじゃないでしょうか

  int64 s = 1 << (H - 1);

  vector<int> left((1 << H) + 1), right((1 << H) + 1);
  for (int i = 0; i < 1 << (H - 1); i++) {
    left[i + s] = i + s;
    right[i + s] = i + s + 1;
  }
  for (int i = s - 1; i >= 1; i--) {
    left[i] = left[i * 2 + 0];
    right[i] = right[i * 2 + 1];
  }

  vector<BinaryIndexedTree<modint>> bits;
  for (int i = 0; i + 1 < H; i++)
    bits.emplace_back((1 << (H - 1)) + 1);

  modint ret = 0;

  auto dfs = MFP([&](auto dfs, int idx) -> pair<int, int> {
    if (idx >= s) {
      return {idx, idx + 1};
    }
    int l = idx * 2 + 0;
    int r = idx * 2 + 1;
    auto x = dfs(l);
    auto y = dfs(r);

    for (int i = x.first; i < x.second; i++) {
      int to = i;
      modint mul = to;
      while (to > idx) {
        to /= 2;
        mul *= to;
      }
      to = P[i - s] + s;
      mul *= to;
      int dep = H - 2;
      while (dep >= 0) {
        to /= 2;
        mul *= to;
        bits[dep].add(P[i - s], mul);
        --dep;
      }
    }
    modint rev = modint(1) / idx;

    for (int i = y.first; i < y.second; i++) {
      int to = i;
      modint mul = to;
      while (to > idx) {
        to /= 2;
        mul *= to;
      }
      mul *= rev;

      to = P[i - s] + s;
      mul *= to;

      int dep = H - 2;

      while (dep >= 0) {
        int latte = -1, malta = -1;
        if (to % 2 == 0) {
          latte = left[(to / 2) * 2 + 1];
          malta = right[(to / 2) * 2 + 1];
        } else {
          latte = left[(to / 2) * 2 + 0];
          malta = right[(to / 2) * 2 + 0];
        }
        to /= 2;
        ret +=
            (bits[dep].query(malta - 1 - s) - bits[dep].query(latte - 1 - s)) *
            mul;
        mul *= to;
        --dep;
      }
    }

    for (int i = x.first; i < x.second; i++) {
      int to = i;
      modint mul = to;
      while (to > idx) {
        to /= 2;
        mul *= to;
      }
      to = P[i - s] + s;
      mul *= to;
      int dep = H - 2;
      while (dep >= 0) {
        to /= 2;
        mul *= to;
        bits[dep].add(P[i - s], -mul);
        --dep;
      }
    }

    return {x.first, y.second};
  });
  dfs(1);
  cout << ret << "\\n";
}