Problem p02539 (C++) — buggy submission, verdict: Time Limit Exceeded

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

// macros
#define pb emplace_back
#define mk make_pair
#define FOR(i, a, b) for (int i = (a); i < (b); ++i)
#define rep(i, n) FOR(i, 0, n)
#define rrep(i, n) for (int i = ((int)(n)-1); i >= 0; i--)
#define irep(itr, st) for (auto itr = (st).begin(); itr != (st).end(); ++itr)
#define irrep(itr, st) for (auto itr = (st).rbegin(); itr != (st).rend(); ++itr)
#define whole(x) (x).begin(), (x).end()
#define sz(x) ((int)(x).size())
#define bit(n) (1LL << (n))
#define F first
#define S second
// functions
template <typename T> void unique(T &c) {
  c.erase(std::unique(c.begin(), c.end()), c.end());
}
template <class T> bool chmax(T &a, const T &b) {
  if (a < b) {
    a = b;
    return 1;
  }
  return 0;
}
template <class T> bool chmin(T &a, const T &b) {
  if (a > b) {
    a = b;
    return 1;
  }
  return 0;
}
template <typename T> istream &operator>>(istream &is, vector<T> &vec) {
  for (auto &v : vec)
    is >> v;
  return is;
}
template <typename T> ostream &operator<<(ostream &os, const vector<T> &vec) {
  for (int i = 0; i < vec.size(); i++) {
    os << vec[i];
    if (i + 1 != vec.size())
      os << " ";
  }
  return os;
}
template <typename T> ostream &operator<<(ostream &os, const set<T> &st) {
  for (auto itr = st.begin(); itr != st.end(); ++itr) {
    os << *itr;
    auto titr = itr;
    if (++titr != st.end())
      os << " ";
  }
  return os;
}
template <typename T>
ostream &operator<<(ostream &os, const unordered_set<T> &st) {
  for (auto itr = st.begin(); itr != st.end(); ++itr) {
    os << *itr;
    auto titr = itr;
    if (++titr != st.end())
      os << " ";
  }
  return os;
}
template <typename T> ostream &operator<<(ostream &os, const multiset<T> &st) {
  for (auto itr = st.begin(); itr != st.end(); ++itr) {
    os << *itr;
    auto titr = itr;
    if (++titr != st.end())
      os << " ";
  }
  return os;
}
template <typename T>
ostream &operator<<(ostream &os, const unordered_multiset<T> &st) {
  for (auto itr = st.begin(); itr != st.end(); ++itr) {
    os << *itr;
    auto titr = itr;
    if (++titr != st.end())
      os << " ";
  }
  return os;
}
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>
ostream &operator<<(ostream &os, const map<T1, T2> &mp) {
  for (auto itr = mp.begin(); itr != mp.end(); ++itr) {
    os << "(" << itr->first << ", " << itr->second << ")";
    auto titr = itr;
    if (++titr != mp.end())
      os << " ";
  }
  return os;
}
template <typename T1, typename T2>
ostream &operator<<(ostream &os, const unordered_map<T1, T2> &mp) {
  for (auto itr = mp.begin(); itr != mp.end(); ++itr) {
    os << "(" << itr->first << ", " << itr->second << ")";
    auto titr = itr;
    if (++titr != mp.end())
      os << " ";
  }
  return os;
}
//  types
using ll = long long int;
using P = pair<int, int>;
// constants
const int inf = 1e9;
const ll linf = 1LL << 60;
const double EPS = 1e-10;
const int mod = 998244353;
const int dx[4] = {-1, 0, 1, 0};
const int dy[4] = {0, -1, 0, 1};
// io
struct fast_io {
  fast_io() {
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);
    cout << fixed << setprecision(20);
  }
} fast_io_;
template <typename T> T power(T a, T n, T mod) {
  T res = 1;
  T tmp = n;
  T curr = a;
  while (tmp) {
    if (tmp % 2 == 1) {
      res = (T)(res * curr % mod);
    }
    curr = (T)(curr * curr % mod);
    tmp >>= 1;
  }

  return res;
}

struct Factorial {
  int n = 0;
  static const long long mod_default = mod;
  long long MOD = mod_default;
  vector<long long> fac;
  vector<long long> inv_;
  explicit Factorial() {}
  explicit Factorial(int n, long long mod_ = mod_default) : n(n), MOD(mod_) {
    assert(MOD > 0 && n < MOD);
    fac.resize(n + 1);
    inv_.resize(n + 1);
    calc_factorial();
    calc_inv();
  }
  void calc_factorial() {
    fac[0] = 1;
    for (int i = 1; i <= n; i++) {
      fac[i] = i * fac[i - 1] % MOD;
    }
  }
  void calc_inv() {
    inv_[n] = power<long long>(fac[n], MOD - 2, MOD);
    for (int i = n - 1; i >= 0; i--) {
      inv_[i] = (i + 1) * inv_[i + 1] % MOD;
    }
  }
  long long &operator[](size_t i) {
    if ((int)i > n) {
      cerr << "list index out of range" << endl;
      abort();
    }
    return fac[i];
  }
  long long inv(size_t i) {
    if ((int)i > n) {
      cerr << "list index out of range" << endl;
      abort();
    }
    return inv_[i];
  }
  long long comb(int n, int k) {
    if (n < 0 || k < 0 || n < k)
      return 0;
    long long res = fac[n];
    res = res * inv_[n - k] % MOD;
    res = res * inv_[k] % MOD;
    return res;
  }
  long long perm(int n, int k) {
    if (n < 0 || k < 0 || n < k)
      return 0;
    long long res = fac[n];
    res = res * inv_[n - k] % MOD;
    return res;
  }
  long long h(int n, int k) {
    if (n == 0 && k == 0)
      return 1;
    return comb(n + k - 1, k);
  }
};

template <typename T> T extgcd(T a, T b, T &x, T &y) {
  T d = a;
  if (b != 0) {
    d = extgcd(b, a % b, y, x);
    y -= (a / b) * x;
  } else {
    x = 1, y = 0;
  }
  return d;
}

template <typename T> T modinv(T a, T m) {
  long long x = 0, y = 0;
  extgcd<long long>(a, m, x, y);
  x %= m;
  if (x < 0)
    x += m;
  return x;
}

template <typename T> long long garner(vector<T> b, vector<T> m, T MOD) {
  m.emplace_back(MOD);
  vector<long long> coef(m.size(), 1);
  vector<long long> consts(m.size(), 0);
  for (int i = 0; i < b.size(); i++) {
    long long t =
        ((b[i] - consts[i]) % m[i]) * modinv<long long>(coef[i], m[i]) % m[i];
    if (t < 0)
      t += m[i];
    for (int j = i + 1; j < m.size(); j++) {
      consts[j] = (consts[j] + t * coef[j] % m[j]) % m[j];
      coef[j] = coef[j] * m[i] % m[j];
    }
  }
  return consts.back();
}

template <int MOD, int g> struct NTT {
  int get_mod() { return MOD; }
  void _ntt(vector<long long> &f, bool inv = false) {
    int n = f.size(), mask = n - 1;
    int h = power<long long>(g, (MOD - 1) / n, MOD);
    if (inv)
      h = modinv(h, MOD);
    vector<long long> tmp(n);
    for (int i = n >> 1; i >= 1; i >>= 1) {
      long long zeta = power<long long>(h, i, MOD);
      long long w = 1;
      for (int j = 0; j < n; j += i) {
        for (int k = 0; k < i; k++) {
          tmp[j + k] = (f[((j << 1) & mask) + k] +
                        w * f[(((j << 1) + i) & mask) + k] % MOD) %
                       MOD;
        }
        w = w * zeta % MOD;
      }
      swap(f, tmp);
    }
  }
  void ntt(vector<long long> &f) { _ntt(f, false); }
  void intt(vector<long long> &f) {
    _ntt(f, true);
    int n = f.size();
    int ni = modinv(n, MOD);
    for (int i = 0; i < n; i++)
      f[i] = f[i] * ni % MOD;
  }
  vector<long long> convolution(vector<long long> f, vector<long long> h) {
    int n = 1;
    while (n < int(f.size() + h.size()))
      n *= 2;
    f.resize(n, 0);
    h.resize(n, 0);
    ntt(f);
    ntt(h);
    for (int i = 0; i < n; i++)
      f[i] = f[i] * h[i] % MOD;
    intt(f);
    return f;
  }
};

using NTT1 = NTT<998244353, 3>;
using NTT2 = NTT<469762049, 3>;
using NTT3 = NTT<1224736769, 3>;

vector<long long> arbitrary_mod_convolution(vector<long long> f,
                                            vector<long long> g,
                                            long long MOD) {
  for (size_t i = 0; i < f.size(); i++)
    f[i] %= MOD;
  for (size_t i = 0; i < g.size(); i++)
    g[i] %= MOD;
  NTT1 ntt1;
  NTT2 ntt2;
  NTT3 ntt3;
  auto x1 = ntt1.convolution(f, g);
  auto x2 = ntt2.convolution(f, g);
  auto x3 = ntt3.convolution(f, g);

  vector<long long> res(x1.size());
  vector<long long> b(3), m(3);
  m[0] = ntt1.get_mod();
  m[1] = ntt2.get_mod();
  m[2] = ntt3.get_mod();
  for (size_t i = 0; i < x1.size(); i++) {
    b[0] = x1[i];
    b[1] = x2[i];
    b[2] = x3[i];
    res[i] = garner<long long>(b, m, MOD);
  }
  return res;
}

ll ti[100010];

const int B = 100010;

int main(int argc, char const *argv[]) {
  ti[B - 1] = modinv<ll>(power<ll>(2, B - 1, mod), mod);
  for (int i = B - 2; i >= 0; i--)
    ti[i] = ti[i + 1] * 2 % mod;
  int n;
  cin >> n;
  vector<int> h(2 * n);
  cin >> h;
  vector<int> cnt(B, 0);
  rep(i, 2 * n) cnt[h[i]]++;
  int maxi = 0;
  rep(i, B) chmax(maxi, cnt[i]);
  vector<ll> ccnt(maxi + 1, 0);
  rep(i, B) ccnt[cnt[i]]++;
  vector<ll> v(1, 1);
  Factorial fac(4 * n);
  auto fg = [&](int k) {
    return (fac[2 * k] * ti[k] % mod) * fac.inv(k) % mod;
  };
  NTT1 ntt;
  queue<vector<ll>> q;
  q.push(v);
  auto calci = [&](int i) {
    if (ccnt[i] == 0)
      return vector<ll>(1, 1);
    int k = i / 2;
    vector<ll> g(k + 1, 0);
    vector<ll> xh(1, 1);
    rep(j, k + 1) g[j] = fac.comb(i, 2 * j) * fg(j) % mod;
    int tmp = ccnt[i];
    while (tmp) {
      if (tmp & 1)
        xh = ntt.convolution(xh, g);
      g = ntt.convolution(g, g);
      tmp /= 2;
    }
    return xh;
  };
  FOR(i, 2, sz(ccnt)) {
    if (ccnt[i] == 0)
      continue;
    q.push(calci(i));
  }
  while (q.size() > 1) {
    auto p1 = q.front();
    q.pop();
    auto p2 = q.front();
    q.pop();
    q.push(ntt.convolution(p1, p2));
  }

  v = q.front();
  ll res = fg(n);
  FOR(i, 1, n + 1) {
    if (i >= sz(v))
      break;
    ll tmp = v[i] * fg(n - i) % mod;
    if (i & 1)
      res = (res - tmp) % mod;
    else
      res = (res + tmp) % mod;
  }
  if (res < 0)
    res += mod;
  cout << res << endl;
  return 0;
}


Error: TLE

Fixed submission:

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

// macros
#define pb emplace_back
#define mk make_pair
#define FOR(i, a, b) for (int i = (a); i < (b); ++i)
#define rep(i, n) FOR(i, 0, n)
#define rrep(i, n) for (int i = ((int)(n)-1); i >= 0; i--)
#define irep(itr, st) for (auto itr = (st).begin(); itr != (st).end(); ++itr)
#define irrep(itr, st) for (auto itr = (st).rbegin(); itr != (st).rend(); ++itr)
#define whole(x) (x).begin(), (x).end()
#define sz(x) ((int)(x).size())
#define bit(n) (1LL << (n))
#define F first
#define S second
// functions
template <typename T> void unique(T &c) {
  c.erase(std::unique(c.begin(), c.end()), c.end());
}
template <class T> bool chmax(T &a, const T &b) {
  if (a < b) {
    a = b;
    return 1;
  }
  return 0;
}
template <class T> bool chmin(T &a, const T &b) {
  if (a > b) {
    a = b;
    return 1;
  }
  return 0;
}
template <typename T> istream &operator>>(istream &is, vector<T> &vec) {
  for (auto &v : vec)
    is >> v;
  return is;
}
template <typename T> ostream &operator<<(ostream &os, const vector<T> &vec) {
  for (int i = 0; i < vec.size(); i++) {
    os << vec[i];
    if (i + 1 != vec.size())
      os << " ";
  }
  return os;
}
template <typename T> ostream &operator<<(ostream &os, const set<T> &st) {
  for (auto itr = st.begin(); itr != st.end(); ++itr) {
    os << *itr;
    auto titr = itr;
    if (++titr != st.end())
      os << " ";
  }
  return os;
}
template <typename T>
ostream &operator<<(ostream &os, const unordered_set<T> &st) {
  for (auto itr = st.begin(); itr != st.end(); ++itr) {
    os << *itr;
    auto titr = itr;
    if (++titr != st.end())
      os << " ";
  }
  return os;
}
template <typename T> ostream &operator<<(ostream &os, const multiset<T> &st) {
  for (auto itr = st.begin(); itr != st.end(); ++itr) {
    os << *itr;
    auto titr = itr;
    if (++titr != st.end())
      os << " ";
  }
  return os;
}
template <typename T>
ostream &operator<<(ostream &os, const unordered_multiset<T> &st) {
  for (auto itr = st.begin(); itr != st.end(); ++itr) {
    os << *itr;
    auto titr = itr;
    if (++titr != st.end())
      os << " ";
  }
  return os;
}
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>
ostream &operator<<(ostream &os, const map<T1, T2> &mp) {
  for (auto itr = mp.begin(); itr != mp.end(); ++itr) {
    os << "(" << itr->first << ", " << itr->second << ")";
    auto titr = itr;
    if (++titr != mp.end())
      os << " ";
  }
  return os;
}
template <typename T1, typename T2>
ostream &operator<<(ostream &os, const unordered_map<T1, T2> &mp) {
  for (auto itr = mp.begin(); itr != mp.end(); ++itr) {
    os << "(" << itr->first << ", " << itr->second << ")";
    auto titr = itr;
    if (++titr != mp.end())
      os << " ";
  }
  return os;
}
//  types
using ll = long long int;
using P = pair<int, int>;
// constants
const int inf = 1e9;
const ll linf = 1LL << 60;
const double EPS = 1e-10;
const int mod = 998244353;
const int dx[4] = {-1, 0, 1, 0};
const int dy[4] = {0, -1, 0, 1};
// io
struct fast_io {
  fast_io() {
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);
    cout << fixed << setprecision(20);
  }
} fast_io_;
template <typename T> T power(T a, T n, T mod) {
  T res = 1;
  T tmp = n;
  T curr = a;
  while (tmp) {
    if (tmp % 2 == 1) {
      res = (T)(res * curr % mod);
    }
    curr = (T)(curr * curr % mod);
    tmp >>= 1;
  }

  return res;
}

struct Factorial {
  int n = 0;
  static const long long mod_default = mod;
  long long MOD = mod_default;
  vector<long long> fac;
  vector<long long> inv_;
  explicit Factorial() {}
  explicit Factorial(int n, long long mod_ = mod_default) : n(n), MOD(mod_) {
    assert(MOD > 0 && n < MOD);
    fac.resize(n + 1);
    inv_.resize(n + 1);
    calc_factorial();
    calc_inv();
  }
  void calc_factorial() {
    fac[0] = 1;
    for (int i = 1; i <= n; i++) {
      fac[i] = i * fac[i - 1] % MOD;
    }
  }
  void calc_inv() {
    inv_[n] = power<long long>(fac[n], MOD - 2, MOD);
    for (int i = n - 1; i >= 0; i--) {
      inv_[i] = (i + 1) * inv_[i + 1] % MOD;
    }
  }
  long long &operator[](size_t i) {
    if ((int)i > n) {
      cerr << "list index out of range" << endl;
      abort();
    }
    return fac[i];
  }
  long long inv(size_t i) {
    if ((int)i > n) {
      cerr << "list index out of range" << endl;
      abort();
    }
    return inv_[i];
  }
  long long comb(int n, int k) {
    if (n < 0 || k < 0 || n < k)
      return 0;
    long long res = fac[n];
    res = res * inv_[n - k] % MOD;
    res = res * inv_[k] % MOD;
    return res;
  }
  long long perm(int n, int k) {
    if (n < 0 || k < 0 || n < k)
      return 0;
    long long res = fac[n];
    res = res * inv_[n - k] % MOD;
    return res;
  }
  long long h(int n, int k) {
    if (n == 0 && k == 0)
      return 1;
    return comb(n + k - 1, k);
  }
};

template <typename T> T extgcd(T a, T b, T &x, T &y) {
  T d = a;
  if (b != 0) {
    d = extgcd(b, a % b, y, x);
    y -= (a / b) * x;
  } else {
    x = 1, y = 0;
  }
  return d;
}

template <typename T> T modinv(T a, T m) {
  long long x = 0, y = 0;
  extgcd<long long>(a, m, x, y);
  x %= m;
  if (x < 0)
    x += m;
  return x;
}

template <typename T> long long garner(vector<T> b, vector<T> m, T MOD) {
  m.emplace_back(MOD);
  vector<long long> coef(m.size(), 1);
  vector<long long> consts(m.size(), 0);
  for (int i = 0; i < b.size(); i++) {
    long long t =
        ((b[i] - consts[i]) % m[i]) * modinv<long long>(coef[i], m[i]) % m[i];
    if (t < 0)
      t += m[i];
    for (int j = i + 1; j < m.size(); j++) {
      consts[j] = (consts[j] + t * coef[j] % m[j]) % m[j];
      coef[j] = coef[j] * m[i] % m[j];
    }
  }
  return consts.back();
}

template <int MOD, int g> struct NTT {
  int get_mod() { return MOD; }
  void _ntt(vector<long long> &f, bool inv = false) {
    int n = f.size(), mask = n - 1;
    int h = power<long long>(g, (MOD - 1) / n, MOD);
    if (inv)
      h = modinv(h, MOD);
    vector<long long> tmp(n);
    for (int i = n >> 1; i >= 1; i >>= 1) {
      long long zeta = power<long long>(h, i, MOD);
      long long w = 1;
      for (int j = 0; j < n; j += i) {
        for (int k = 0; k < i; k++) {
          tmp[j + k] = (f[((j << 1) & mask) + k] +
                        w * f[(((j << 1) + i) & mask) + k] % MOD) %
                       MOD;
        }
        w = w * zeta % MOD;
      }
      swap(f, tmp);
    }
  }
  void ntt(vector<long long> &f) { _ntt(f, false); }
  void intt(vector<long long> &f) {
    _ntt(f, true);
    int n = f.size();
    int ni = modinv(n, MOD);
    for (int i = 0; i < n; i++)
      f[i] = f[i] * ni % MOD;
  }
  vector<long long> convolution(vector<long long> f, vector<long long> h) {
    int n = 1;
    while (n < int(f.size() + h.size()))
      n *= 2;
    f.resize(n, 0);
    h.resize(n, 0);
    ntt(f);
    ntt(h);
    for (int i = 0; i < n; i++)
      f[i] = f[i] * h[i] % MOD;
    intt(f);
    return f;
  }
};

using NTT1 = NTT<998244353, 3>;
using NTT2 = NTT<469762049, 3>;
using NTT3 = NTT<1224736769, 3>;

vector<long long> arbitrary_mod_convolution(vector<long long> f,
                                            vector<long long> g,
                                            long long MOD) {
  for (size_t i = 0; i < f.size(); i++)
    f[i] %= MOD;
  for (size_t i = 0; i < g.size(); i++)
    g[i] %= MOD;
  NTT1 ntt1;
  NTT2 ntt2;
  NTT3 ntt3;
  auto x1 = ntt1.convolution(f, g);
  auto x2 = ntt2.convolution(f, g);
  auto x3 = ntt3.convolution(f, g);

  vector<long long> res(x1.size());
  vector<long long> b(3), m(3);
  m[0] = ntt1.get_mod();
  m[1] = ntt2.get_mod();
  m[2] = ntt3.get_mod();
  for (size_t i = 0; i < x1.size(); i++) {
    b[0] = x1[i];
    b[1] = x2[i];
    b[2] = x3[i];
    res[i] = garner<long long>(b, m, MOD);
  }
  return res;
}

ll ti[100010];

const int B = 100010;

int main(int argc, char const *argv[]) {
  ti[B - 1] = modinv<ll>(power<ll>(2, B - 1, mod), mod);
  for (int i = B - 2; i >= 0; i--)
    ti[i] = ti[i + 1] * 2 % mod;
  int n;
  cin >> n;
  vector<int> h(2 * n);
  cin >> h;
  vector<int> cnt(B, 0);
  rep(i, 2 * n) cnt[h[i]]++;
  int maxi = 0;
  rep(i, B) chmax(maxi, cnt[i]);
  vector<ll> ccnt(maxi + 1, 0);
  rep(i, B) ccnt[cnt[i]]++;
  vector<ll> v(1, 1);
  Factorial fac(4 * n);
  auto fg = [&](int k) {
    return (fac[2 * k] * ti[k] % mod) * fac.inv(k) % mod;
  };
  NTT1 ntt;
  FOR(i, 2, sz(ccnt)) {
    if (ccnt[i] == 0)
      continue;
    int k = i / 2;
    vector<ll> g(k + 1, 0);
    vector<ll> xh(1, 1);
    rep(j, k + 1) g[j] = fac.comb(i, 2 * j) * fg(j) % mod;
    rep(j, ccnt[i]) v = ntt.convolution(v, g);
    /*
    int tmp = ccnt[i];
    while(tmp){
      if(tmp & 1)xh = ntt.convolution(xh, g);
      g = ntt.convolution(g, g);
      tmp /= 2;
    }
    v = ntt.convolution(v, xh);
    */
  }
  ll res = fg(n);
  FOR(i, 1, n + 1) {
    if (i >= sz(v))
      break;
    ll tmp = v[i] * fg(n - i) % mod;
    if (i & 1)
      res = (res - tmp) % mod;
    else
      res = (res + tmp) % mod;
  }
  if (res < 0)
    res += mod;
  cout << res << endl;
  return 0;
}