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

#pragma GCC optimize("O3", "unroll-loops")
#pragma GCC target("avx")
#include <bits/stdc++.h>
using namespace std;
struct fast_ios {
  fast_ios() {
    cin.tie(0);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(20);
  };
} fast_ios_;
#define FOR(i, begin, end) for (int i = (begin); i < (end); i++)
#define REP(i, n) FOR(i, 0, n)
#define IFOR(i, begin, end) for (int i = (end)-1; i >= (begin); i--)
#define IREP(i, n) IFOR(i, 0, n)
#define Sort(v) sort(v.begin(), v.end())
#define Reverse(v) reverse(v.begin(), v.end())
#define all(v) v.begin(), v.end()
#define SZ(v) ((int)v.size())
#define Lower_bound(v, x)                                                      \\
  distance(v.begin(), lower_bound(v.begin(), v.end(), x))
#define Upper_bound(v, x)                                                      \\
  distance(v.begin(), upper_bound(v.begin(), v.end(), x))
#define chmax(a, b) a = max(a, b)
#define chmin(a, b) a = min(a, b)
#define bit(n) (1LL << (n))
#define debug(x) cout << #x << "=" << x << endl;
#define vdebug(v)                                                              \\
  {                                                                            \\
    cout << #v << "=" << endl;                                                 \\
    REP(i_debug, v.size()) { cout << v[i_debug] << ","; }                      \\
    cout << endl;                                                              \\
  }
#define mdebug(m)                                                              \\
  {                                                                            \\
    cout << #m << "=" << endl;                                                 \\
    REP(i_debug, m.size()) {                                                   \\
      REP(j_debug, m[i_debug].size()) { cout << m[i_debug][j_debug] << ","; }  \\
      cout << endl;                                                            \\
    }                                                                          \\
  }
#define pb push_back
#define fi first
#define se second
#define int long long
#define INF 1000000000000000000
template <typename T> istream &operator>>(istream &is, vector<T> &v) {
  for (auto &x : v)
    is >> x;
  return is;
}
template <typename T> ostream &operator<<(ostream &os, vector<T> &v) {
  for (int i = 0; i < v.size(); i++) {
    cout << v[i];
    if (i != v.size() - 1)
      cout << endl;
  };
  return os;
}
template <typename T1, typename T2>
ostream &operator<<(ostream &os, pair<T1, T2> p) {
  cout << '(' << p.first << ',' << p.second << ')';
  return os;
}
template <typename T> void Out(T x) { cout << x << endl; }
template <typename T1, typename T2> void chOut(bool f, T1 y, T2 n) {
  if (f)
    Out(y);
  else
    Out(n);
}

using vec = vector<int>;
using mat = vector<vec>;
using Pii = pair<int, int>;
using v_bool = vector<bool>;
using v_Pii = vector<Pii>;

// int dx[4] = {1,0,-1,0};
// int dy[4] = {0,1,0,-1};
// char d[4] = {'D','R','U','L'};

const int mod = 1000000007;
// const int mod = 998244353;

template <long long MOD> struct ModInt {

  using ll = long long;
  ll val;

  void setval(ll v) { val = v % MOD; };
  ModInt() : val(0) {}
  ModInt(ll v) { setval(v); };

  ModInt operator+(const ModInt &x) const { return ModInt(val + x.val); }
  ModInt operator-(const ModInt &x) const { return ModInt(val - x.val + MOD); }
  ModInt operator*(const ModInt &x) const { return ModInt(val * x.val); }
  ModInt operator/(const ModInt &x) const { return *this * x.inv(); }
  ModInt operator-() const { return ModInt(MOD - val); }
  ModInt operator+=(const ModInt &x) { return *this = *this + x; }
  ModInt operator-=(const ModInt &x) { return *this = *this - x; }
  ModInt operator*=(const ModInt &x) { return *this = *this * x; }
  ModInt operator/=(const ModInt &x) { return *this = *this / x; }

  friend ostream &operator<<(ostream &os, const ModInt &x) {
    os << x.val;
    return os;
  }
  friend istream &operator>>(istream &is, ModInt &x) {
    is >> x.val;
    x.val = (x.val % MOD + MOD) % MOD;
    return is;
  }

  ModInt pow(ll n) const {
    ModInt a = 1;
    if (n == 0)
      return a;
    int i0 = 64 - __builtin_clzll(n);
    for (int i = i0 - 1; i >= 0; i--) {
      a = a * a;
      if ((n >> i) & 1)
        a *= (*this);
    }
    return a;
  }
  ModInt inv() const { return this->pow(MOD - 2); }
};

using mint = ModInt<mod>;
mint pow(mint x, long long n) { return x.pow(n); }
// using mint = double; //for debug
using mvec = vector<mint>;
using mmat = vector<mvec>;

struct Combination {

  vector<mint> fact, invfact;

  Combination(int N) {
    fact = vector<mint>({mint(1)});
    invfact = vector<mint>({mint(1)});
    fact_initialize(N);
  }

  void fact_initialize(int N) {
    int i0 = fact.size();
    if (i0 >= N + 1)
      return;
    fact.resize(N + 1);
    invfact.resize(N + 1);
    for (int i = i0; i <= N; i++)
      fact[i] = fact[i - 1] * i;
    invfact[N] = (mint)1 / fact[N];
    for (int i = N - 1; i >= i0; i--)
      invfact[i] = invfact[i + 1] * (i + 1);
  }

  mint nCr(int n, int r) {
    if (n < 0 || r < 0 || r > n)
      return mint(0);
    if (fact.size() < n + 1)
      fact_initialize(n);
    return fact[n] * invfact[r] * invfact[n - r];
  }

  mint nPr(int n, int r) {
    if (n < 0 || r < 0 || r > n)
      return mint(0);
    if (fact.size() < n + 1)
      fact_initialize(n);
    return fact[n] * invfact[n - r];
  }

  mint Catalan(int n) {
    if (n < 0)
      return 0;
    else if (n == 0)
      return 1;
    if (fact.size() < 2 * n + 1)
      fact_initialize(2 * n);
    return fact[2 * n] * invfact[n + 1] * invfact[n];
  }
};

void dfs1(int v, mint t, mvec &dp) {
  if (v == 1)
    return;
  t *= (v / 2);
  dp[v] += t;
  dfs1(v / 2, t, dp);
}

void dfs2(int v, mint t, mvec &dp, mint &ans) {
  if (v == 1)
    return;
  ans += t * dp[v ^ 1];
  t *= (v / 2);
  dfs2(v / 2, t, dp, ans);
}

void clear(int v, mvec &dp) {
  dp[v] = 0;
  if (v > 1)
    clear(v / 2, dp);
}

signed main() {

  int H;
  cin >> H;
  int L = bit(H - 1);
  vec P(L);
  cin >> P;

  mvec dp(bit(H));
  mint ans = 0;

  FOR(i, 1, L) {
    int h = 64 - __builtin_clzll(i);
    REP(j, bit(H - h - 1)) {
      int l = (i << (H - h)) + j;

      int now = l;
      mint t = 1;
      while (now >= i) {
        t *= now;
        now /= 2;
      }
      int l2 = P[l - L] + L - 1;
      dfs1(l2, t * l2, dp);
    }

    REP(j, bit(H - h - 1)) {
      int l = (i << (H - h)) + j + bit(H - h - 1);
      int now = l;
      mint t = 1;
      while (now != i) {
        t *= now;
        now /= 2;
      }
      int l2 = P[l - L] + L - 1;
      dfs2(l2, t * l2, dp, ans);
    }

    REP(j, bit(H - h)) {
      int l = (i << (H - h)) + j;
      int l2 = P[l - L] + L - 1;
      clear(l2, dp);
    }
  }
  Out(ans);

  return 0;
}


Error: TLE

Fixed submission:

#pragma GCC optimize("O3", "unroll-loops")
#pragma GCC target("avx")
#include <bits/stdc++.h>
using namespace std;
struct fast_ios {
  fast_ios() {
    cin.tie(0);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(20);
  };
} fast_ios_;
#define FOR(i, begin, end) for (int i = (begin); i < (end); i++)
#define REP(i, n) FOR(i, 0, n)
#define IFOR(i, begin, end) for (int i = (end)-1; i >= (begin); i--)
#define IREP(i, n) IFOR(i, 0, n)
#define Sort(v) sort(v.begin(), v.end())
#define Reverse(v) reverse(v.begin(), v.end())
#define all(v) v.begin(), v.end()
#define SZ(v) ((int)v.size())
#define Lower_bound(v, x)                                                      \\
  distance(v.begin(), lower_bound(v.begin(), v.end(), x))
#define Upper_bound(v, x)                                                      \\
  distance(v.begin(), upper_bound(v.begin(), v.end(), x))
#define chmax(a, b) a = max(a, b)
#define chmin(a, b) a = min(a, b)
#define bit(n) (1LL << (n))
#define debug(x) cout << #x << "=" << x << endl;
#define vdebug(v)                                                              \\
  {                                                                            \\
    cout << #v << "=" << endl;                                                 \\
    REP(i_debug, v.size()) { cout << v[i_debug] << ","; }                      \\
    cout << endl;                                                              \\
  }
#define mdebug(m)                                                              \\
  {                                                                            \\
    cout << #m << "=" << endl;                                                 \\
    REP(i_debug, m.size()) {                                                   \\
      REP(j_debug, m[i_debug].size()) { cout << m[i_debug][j_debug] << ","; }  \\
      cout << endl;                                                            \\
    }                                                                          \\
  }
#define pb push_back
#define fi first
#define se second
#define int long long
#define INF 1000000000000000000
template <typename T> istream &operator>>(istream &is, vector<T> &v) {
  for (auto &x : v)
    is >> x;
  return is;
}
template <typename T> ostream &operator<<(ostream &os, vector<T> &v) {
  for (int i = 0; i < v.size(); i++) {
    cout << v[i];
    if (i != v.size() - 1)
      cout << endl;
  };
  return os;
}
template <typename T1, typename T2>
ostream &operator<<(ostream &os, pair<T1, T2> p) {
  cout << '(' << p.first << ',' << p.second << ')';
  return os;
}
template <typename T> void Out(T x) { cout << x << endl; }
template <typename T1, typename T2> void chOut(bool f, T1 y, T2 n) {
  if (f)
    Out(y);
  else
    Out(n);
}

using vec = vector<int>;
using mat = vector<vec>;
using Pii = pair<int, int>;
using v_bool = vector<bool>;
using v_Pii = vector<Pii>;

// int dx[4] = {1,0,-1,0};
// int dy[4] = {0,1,0,-1};
// char d[4] = {'D','R','U','L'};

const int mod = 1000000007;
// const int mod = 998244353;

int modpow(int x, int n) {
  int a = 1;
  if (n == 0)
    return a;
  int i0 = 64 - __builtin_clzll(n);
  for (int i = i0 - 1; i >= 0; i--) {
    a = (a * a) % mod;
    if ((n >> i) & 1)
      (a *= x) %= mod;
  }
  return a;
}

signed main() {

  int H;
  cin >> H;
  int L = bit(H - 1);
  vec P(L);
  cin >> P;

  vec val(bit(H));
  IFOR(i, 1, bit(H)) {
    int now = 1;
    val[i] = modpow(i, mod - 2);
    int i0 = i / 2;
    if (i0 > 0) {
      (now *= i0 * i0) %= mod;
      now = (mod - now) % mod;
      (val[i] += now * modpow(i0, mod - 2)) %= mod;
      i0 /= 2;
    }
  }
  // vdebug(val);

  vector<unordered_map<int, int>> dp(bit(H));
  int ans = 0;
  REP(i, L) {
    int a = L + i, b = L + P[i] - 1;

    int a0 = a;
    int Pa = a0;
    REP(x, H) {
      int b0 = b;
      int P = (b0 * Pa) % mod;
      REP(y, H) {
        int c = (val[a0] * val[b0]) % mod;
        (ans += ((dp[a0][b0] * P) % mod) * c) %= mod;
        (dp[a0][b0] += P) %= mod;
        b0 /= 2;
        (P *= b0) %= mod;
      }
      a0 /= 2;
      (Pa *= a0) %= mod;
    }
  }
  Out(ans);

  return 0;
}