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

// #define _GLIBCXX_DEBUG

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

#define endl '\\n'
#define lfs cout << fixed << setprecision(10)
#define ALL(a) (a).begin(), (a).end()
#define ALLR(a) (a).rbegin(), (a).rend()
#define spa << " " <<
#define fi first
#define se second
#define MP make_pair
#define MT make_tuple
#define PB push_back
#define EB emplace_back
#define rep(i, n, m) for (ll i = (n); i < (ll)(m); i++)
#define rrep(i, n, m) for (ll i = (ll)(m)-1; i >= (ll)(n); i--)
using ll = long long;
using ld = long double;
const ll MOD1 = 1e9 + 7;
const ll MOD9 = 998244353;
const ll INF = 1e18;
using P = pair<ll, ll>;
template <typename T1, typename T2> bool chmin(T1 &a, T2 b) {
  if (a > b) {
    a = b;
    return true;
  } else
    return false;
}
template <typename T1, typename T2> bool chmax(T1 &a, T2 b) {
  if (a < b) {
    a = b;
    return true;
  } else
    return false;
}
ll median(ll a, ll b, ll c) {
  return a + b + c - max({a, b, c}) - min({a, b, c});
}
void ans1(bool x) {
  if (x)
    cout << "Yes" << endl;
  else
    cout << "No" << endl;
}
void ans2(bool x) {
  if (x)
    cout << "YES" << endl;
  else
    cout << "NO" << endl;
}
void ans3(bool x) {
  if (x)
    cout << "Yay!" << endl;
  else
    cout << ":(" << endl;
}
template <typename T1, typename T2> void ans(bool x, T1 y, T2 z) {
  if (x)
    cout << y << endl;
  else
    cout << z << endl;
}
template <typename T> void debug(vector<vector<T>> &v, ll h, ll w) {
  for (ll i = 0; i < h; i++) {
    cout << v[i][0];
    for (ll j = 1; j < w; j++)
      cout spa v[i][j];
    cout << endl;
  }
};
void debug(vector<string> &v, ll h, ll w) {
  for (ll i = 0; i < h; i++) {
    for (ll j = 0; j < w; j++)
      cout << v[i][j];
    cout << endl;
  }
};
template <typename T> void debug(vector<T> &v, ll n) {
  if (n != 0)
    cout << v[0];
  for (ll i = 1; i < n; i++)
    cout spa v[i];
  cout << endl;
};
template <typename T> vector<vector<T>> vec(ll x, ll y, T w) {
  vector<vector<T>> v(x, vector<T>(y, w));
  return v;
}
ll gcd(ll x, ll y) {
  ll r;
  while (y != 0 && (r = x % y) != 0) {
    x = y;
    y = r;
  }
  return y == 0 ? x : y;
}
vector<ll> dx = {1, -1, 0, 0, 1, 1, -1, -1};
vector<ll> dy = {0, 0, 1, -1, 1, -1, 1, -1};
template <typename T> vector<T> make_v(size_t a, T b) {
  return vector<T>(a, b);
}
template <typename... Ts> auto make_v(size_t a, Ts... ts) {
  return vector<decltype(make_v(ts...))>(a, make_v(ts...));
}
template <typename T1, typename T2>
ostream &operator<<(ostream &os, const pair<T1, T2> &p) {
  return os << p.first << " " << p.second;
}
template <typename T> ostream &operator<<(ostream &os, const vector<T> &v) {
  for (auto &z : v)
    os << z << " ";
  cout << "|";
  return os;
}
// mt19937 mt(chrono::steady_clock::now().time_since_epoch().count());
template <int mod> struct NumberTheoreticTransform {

  vector<int> rev, rts;
  int base, max_base, root;

  NumberTheoreticTransform() : base(1), rev{0, 1}, rts{0, 1} {
    assert(mod >= 3 && mod % 2 == 1);
    auto tmp = mod - 1;
    max_base = 0;
    while (tmp % 2 == 0)
      tmp >>= 1, max_base++;
    root = 2;
    while (mod_pow(root, (mod - 1) >> 1) == 1)
      ++root;
    assert(mod_pow(root, mod - 1) == 1);
    root = mod_pow(root, (mod - 1) >> max_base);
  }

  inline int mod_pow(int x, int n) {
    int ret = 1;
    while (n > 0) {
      if (n & 1)
        ret = mul(ret, x);
      x = mul(x, x);
      n >>= 1;
    }
    return ret;
  }

  inline int inverse(int x) { return mod_pow(x, mod - 2); }

  inline unsigned add(unsigned x, unsigned y) {
    x += y;
    if (x >= mod)
      x -= mod;
    return x;
  }

  inline unsigned mul(unsigned a, unsigned b) {
    return 1ull * a * b % (unsigned long long)mod;
  }

  void ensure_base(int nbase) {
    if (nbase <= base)
      return;
    rev.resize(1 << nbase);
    rts.resize(1 << nbase);
    for (int i = 0; i < (1 << nbase); i++) {
      rev[i] = (rev[i >> 1] >> 1) + ((i & 1) << (nbase - 1));
    }
    assert(nbase <= max_base);
    while (base < nbase) {
      int z = mod_pow(root, 1 << (max_base - 1 - base));
      for (int i = 1 << (base - 1); i < (1 << base); i++) {
        rts[i << 1] = rts[i];
        rts[(i << 1) + 1] = mul(rts[i], z);
      }
      ++base;
    }
  }

  void ntt(vector<int> &a) {
    const int n = (int)a.size();
    assert((n & (n - 1)) == 0);
    int zeros = __builtin_ctz(n);
    ensure_base(zeros);
    int shift = base - zeros;
    for (int i = 0; i < n; i++) {
      if (i < (rev[i] >> shift)) {
        swap(a[i], a[rev[i] >> shift]);
      }
    }
    for (int k = 1; k < n; k <<= 1) {
      for (int i = 0; i < n; i += 2 * k) {
        for (int j = 0; j < k; j++) {
          int z = mul(a[i + j + k], rts[j + k]);
          a[i + j + k] = add(a[i + j], mod - z);
          a[i + j] = add(a[i + j], z);
        }
      }
    }
  }

  vector<int> multiply(vector<int> a, vector<int> b) {
    int need = a.size() + b.size() - 1;
    int nbase = 1;
    while ((1 << nbase) < need)
      nbase++;
    ensure_base(nbase);
    int sz = 1 << nbase;
    a.resize(sz, 0);
    b.resize(sz, 0);
    ntt(a);
    ntt(b);
    int inv_sz = inverse(sz);
    for (int i = 0; i < sz; i++) {
      a[i] = mul(a[i], mul(b[i], inv_sz));
    }
    reverse(a.begin() + 1, a.end());
    ntt(a);
    a.resize(need);
    return a;
  }
};
template <int mod> struct ModInt {
  int x;

  ModInt() : x(0) {}

  ModInt(int64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}

  ModInt &operator+=(const ModInt &p) {
    if ((x += p.x) >= mod)
      x -= mod;
    return *this;
  }

  ModInt &operator-=(const ModInt &p) {
    if ((x += mod - p.x) >= mod)
      x -= mod;
    return *this;
  }

  ModInt &operator*=(const ModInt &p) {
    x = (int)(1LL * x * p.x % mod);
    return *this;
  }

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

  ModInt operator-() const { return ModInt(-x); }

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

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

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

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

  bool operator==(const ModInt &p) const { return x == p.x; }

  bool operator!=(const ModInt &p) const { return x != p.x; }

  ModInt inverse() const {
    int a = x, b = mod, u = 1, v = 0, t;
    while (b > 0) {
      t = a / b;
      swap(a -= t * b, b);
      swap(u -= t * v, v);
    }
    return ModInt(u);
  }

  ModInt pow(int64_t n) const {
    ModInt ret(1), mul(x);
    while (n > 0) {
      if (n & 1)
        ret *= mul;
      mul *= mul;
      n >>= 1;
    }
    return ret;
  }
  friend ostream &operator<<(ostream &os, const ModInt &p) { return os << p.x; }

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

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

template <typename T> struct Combination {
  vector<T> _fact, _rfact, _inv;

  Combination(ll sz) : _fact(sz + 1), _rfact(sz + 1), _inv(sz + 1) {
    _fact[0] = _rfact[sz] = _inv[0] = 1;
    for (ll i = 1; i <= sz; i++)
      _fact[i] = _fact[i - 1] * i;
    _rfact[sz] /= _fact[sz];
    for (ll i = sz - 1; i >= 0; i--)
      _rfact[i] = _rfact[i + 1] * (i + 1);
    for (ll i = 1; i <= sz; i++)
      _inv[i] = _rfact[i] * _fact[i - 1];
  }

  inline T fact(ll k) const { return _fact[k]; }

  inline T rfact(ll k) const { return _rfact[k]; }

  inline T inv(ll k) const { return _inv[k]; }

  T P(ll n, ll r) const {
    if (r < 0 || n < r)
      return 0;
    return fact(n) * rfact(n - r);
  }

  T C(ll p, ll q) const {
    if (q < 0 || p < q)
      return 0;
    return fact(p) * rfact(q) * rfact(p - q);
  }

  T RC(ll p, ll q) const {
    if (q < 0 || p < q)
      return 0;
    return rfact(p) * fact(q) * fact(p - q);
  }

  T H(ll n, ll r) const {
    if (n < 0 || r < 0)
      return (0);
    return r == 0 ? 1 : C(n + r - 1, r);
  }
};
using modint = ModInt<MOD9>;
modint pow(ll n, ll x) { return modint(n).pow(x); }
modint pow(modint n, ll x) { return n.pow(x); }
// using modint=ld;
using Comb = Combination<modint>;
int main() {
  cin.tie(nullptr);
  ios_base::sync_with_stdio(false);
  ll res = 0, buf = 0;
  bool judge = true;
  NumberTheoreticTransform<MOD9> ntt;
  Comb comb(200005);
  ll n;
  cin >> n;
  map<ll, ll> mp;
  rep(i, 0, 2 * n) {
    ll h;
    cin >> h;
    mp[h]++;
  }
  ll lim = 100005;
  vector<modint> calc(lim);
  rep(i, 0, lim) { calc[i] = comb.C(i * 2, i) * comb.fact(i) / pow(2LL, i); }
  vector<vector<int>> ret;
  for (auto z : mp) {
    vector<int> mul(z.se / 2 + 1, 0);
    rep(i, 0, z.se / 2 + 1) mul[i] = (comb.C(z.se, i * 2) * calc[i]).x;
    ret.PB(mul);
  }
  priority_queue<P, vector<P>, greater<P>> que;
  rep(i, 0, ret.size()) que.emplace(ret[i].size(), i);
  while (que.size() > 1) {
    auto p = que.top().se;
    que.pop();
    auto pp = que.top().se;
    que.pop();
    ret[p] = ntt.multiply(ret[p], ret[pp]);
    que.emplace(ret[p].size(), p);
  }
  modint x = 0;
  ll idx = que.top().se;
  rep(i, 0, ret[idx].size()) {
    if (i > n)
      continue;
    if (~i & 1)
      x += calc[n - i] * ret[idx][i];
    else
      x -= calc[n - i] * ret[idx][i];
  }
  cout << x << endl;
  return 0;
}

Error: TLE

Fixed submission:

// #define _GLIBCXX_DEBUG

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

#define endl '\\n'
#define lfs cout << fixed << setprecision(10)
#define ALL(a) (a).begin(), (a).end()
#define ALLR(a) (a).rbegin(), (a).rend()
#define spa << " " <<
#define fi first
#define se second
#define MP make_pair
#define MT make_tuple
#define PB push_back
#define EB emplace_back
#define rep(i, n, m) for (ll i = (n); i < (ll)(m); i++)
#define rrep(i, n, m) for (ll i = (ll)(m)-1; i >= (ll)(n); i--)
using ll = long long;
using ld = long double;
const ll MOD1 = 1e9 + 7;
const ll MOD9 = 998244353;
const ll INF = 1e18;
using P = pair<ll, ll>;
template <typename T1, typename T2> bool chmin(T1 &a, T2 b) {
  if (a > b) {
    a = b;
    return true;
  } else
    return false;
}
template <typename T1, typename T2> bool chmax(T1 &a, T2 b) {
  if (a < b) {
    a = b;
    return true;
  } else
    return false;
}
ll median(ll a, ll b, ll c) {
  return a + b + c - max({a, b, c}) - min({a, b, c});
}
void ans1(bool x) {
  if (x)
    cout << "Yes" << endl;
  else
    cout << "No" << endl;
}
void ans2(bool x) {
  if (x)
    cout << "YES" << endl;
  else
    cout << "NO" << endl;
}
void ans3(bool x) {
  if (x)
    cout << "Yay!" << endl;
  else
    cout << ":(" << endl;
}
template <typename T1, typename T2> void ans(bool x, T1 y, T2 z) {
  if (x)
    cout << y << endl;
  else
    cout << z << endl;
}
template <typename T> void debug(vector<vector<T>> &v, ll h, ll w) {
  for (ll i = 0; i < h; i++) {
    cout << v[i][0];
    for (ll j = 1; j < w; j++)
      cout spa v[i][j];
    cout << endl;
  }
};
void debug(vector<string> &v, ll h, ll w) {
  for (ll i = 0; i < h; i++) {
    for (ll j = 0; j < w; j++)
      cout << v[i][j];
    cout << endl;
  }
};
template <typename T> void debug(vector<T> &v, ll n) {
  if (n != 0)
    cout << v[0];
  for (ll i = 1; i < n; i++)
    cout spa v[i];
  cout << endl;
};
template <typename T> vector<vector<T>> vec(ll x, ll y, T w) {
  vector<vector<T>> v(x, vector<T>(y, w));
  return v;
}
ll gcd(ll x, ll y) {
  ll r;
  while (y != 0 && (r = x % y) != 0) {
    x = y;
    y = r;
  }
  return y == 0 ? x : y;
}
vector<ll> dx = {1, -1, 0, 0, 1, 1, -1, -1};
vector<ll> dy = {0, 0, 1, -1, 1, -1, 1, -1};
template <typename T> vector<T> make_v(size_t a, T b) {
  return vector<T>(a, b);
}
template <typename... Ts> auto make_v(size_t a, Ts... ts) {
  return vector<decltype(make_v(ts...))>(a, make_v(ts...));
}
template <typename T1, typename T2>
ostream &operator<<(ostream &os, const pair<T1, T2> &p) {
  return os << p.first << " " << p.second;
}
template <typename T> ostream &operator<<(ostream &os, const vector<T> &v) {
  for (auto &z : v)
    os << z << " ";
  cout << "|";
  return os;
}
// mt19937 mt(chrono::steady_clock::now().time_since_epoch().count());
template <int mod> struct NumberTheoreticTransform {

  vector<int> rev, rts;
  int base, max_base, root;

  NumberTheoreticTransform() : base(1), rev{0, 1}, rts{0, 1} {
    assert(mod >= 3 && mod % 2 == 1);
    auto tmp = mod - 1;
    max_base = 0;
    while (tmp % 2 == 0)
      tmp >>= 1, max_base++;
    root = 2;
    while (mod_pow(root, (mod - 1) >> 1) == 1)
      ++root;
    assert(mod_pow(root, mod - 1) == 1);
    root = mod_pow(root, (mod - 1) >> max_base);
  }

  inline int mod_pow(int x, int n) {
    int ret = 1;
    while (n > 0) {
      if (n & 1)
        ret = mul(ret, x);
      x = mul(x, x);
      n >>= 1;
    }
    return ret;
  }

  inline int inverse(int x) { return mod_pow(x, mod - 2); }

  inline unsigned add(unsigned x, unsigned y) {
    x += y;
    if (x >= mod)
      x -= mod;
    return x;
  }

  inline unsigned mul(unsigned a, unsigned b) {
    return 1ull * a * b % (unsigned long long)mod;
  }

  void ensure_base(int nbase) {
    if (nbase <= base)
      return;
    rev.resize(1 << nbase);
    rts.resize(1 << nbase);
    for (int i = 0; i < (1 << nbase); i++) {
      rev[i] = (rev[i >> 1] >> 1) + ((i & 1) << (nbase - 1));
    }
    assert(nbase <= max_base);
    while (base < nbase) {
      int z = mod_pow(root, 1 << (max_base - 1 - base));
      for (int i = 1 << (base - 1); i < (1 << base); i++) {
        rts[i << 1] = rts[i];
        rts[(i << 1) + 1] = mul(rts[i], z);
      }
      ++base;
    }
  }

  void ntt(vector<int> &a) {
    const int n = (int)a.size();
    assert((n & (n - 1)) == 0);
    int zeros = __builtin_ctz(n);
    ensure_base(zeros);
    int shift = base - zeros;
    for (int i = 0; i < n; i++) {
      if (i < (rev[i] >> shift)) {
        swap(a[i], a[rev[i] >> shift]);
      }
    }
    for (int k = 1; k < n; k <<= 1) {
      for (int i = 0; i < n; i += 2 * k) {
        for (int j = 0; j < k; j++) {
          int z = mul(a[i + j + k], rts[j + k]);
          a[i + j + k] = add(a[i + j], mod - z);
          a[i + j] = add(a[i + j], z);
        }
      }
    }
  }

  vector<int> multiply(vector<int> a, vector<int> b) {
    int need = a.size() + b.size() - 1;
    int nbase = 1;
    while ((1 << nbase) < need)
      nbase++;
    ensure_base(nbase);
    int sz = 1 << nbase;
    a.resize(sz, 0);
    b.resize(sz, 0);
    ntt(a);
    ntt(b);
    int inv_sz = inverse(sz);
    for (int i = 0; i < sz; i++) {
      a[i] = mul(a[i], mul(b[i], inv_sz));
    }
    reverse(a.begin() + 1, a.end());
    ntt(a);
    a.resize(need);
    return a;
  }
};
template <int mod> struct ModInt {
  int x;

  ModInt() : x(0) {}

  ModInt(int64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}

  ModInt &operator+=(const ModInt &p) {
    if ((x += p.x) >= mod)
      x -= mod;
    return *this;
  }

  ModInt &operator-=(const ModInt &p) {
    if ((x += mod - p.x) >= mod)
      x -= mod;
    return *this;
  }

  ModInt &operator*=(const ModInt &p) {
    x = (int)(1LL * x * p.x % mod);
    return *this;
  }

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

  ModInt operator-() const { return ModInt(-x); }

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

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

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

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

  bool operator==(const ModInt &p) const { return x == p.x; }

  bool operator!=(const ModInt &p) const { return x != p.x; }

  ModInt inverse() const {
    int a = x, b = mod, u = 1, v = 0, t;
    while (b > 0) {
      t = a / b;
      swap(a -= t * b, b);
      swap(u -= t * v, v);
    }
    return ModInt(u);
  }

  ModInt pow(int64_t n) const {
    ModInt ret(1), mul(x);
    while (n > 0) {
      if (n & 1)
        ret *= mul;
      mul *= mul;
      n >>= 1;
    }
    return ret;
  }
  friend ostream &operator<<(ostream &os, const ModInt &p) { return os << p.x; }

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

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

template <typename T> struct Combination {
  vector<T> _fact, _rfact, _inv;

  Combination(ll sz) : _fact(sz + 1), _rfact(sz + 1), _inv(sz + 1) {
    _fact[0] = _rfact[sz] = _inv[0] = 1;
    for (ll i = 1; i <= sz; i++)
      _fact[i] = _fact[i - 1] * i;
    _rfact[sz] /= _fact[sz];
    for (ll i = sz - 1; i >= 0; i--)
      _rfact[i] = _rfact[i + 1] * (i + 1);
    for (ll i = 1; i <= sz; i++)
      _inv[i] = _rfact[i] * _fact[i - 1];
  }

  inline T fact(ll k) const { return _fact[k]; }

  inline T rfact(ll k) const { return _rfact[k]; }

  inline T inv(ll k) const { return _inv[k]; }

  T P(ll n, ll r) const {
    if (r < 0 || n < r)
      return 0;
    return fact(n) * rfact(n - r);
  }

  T C(ll p, ll q) const {
    if (q < 0 || p < q)
      return 0;
    return fact(p) * rfact(q) * rfact(p - q);
  }

  T RC(ll p, ll q) const {
    if (q < 0 || p < q)
      return 0;
    return rfact(p) * fact(q) * fact(p - q);
  }

  T H(ll n, ll r) const {
    if (n < 0 || r < 0)
      return (0);
    return r == 0 ? 1 : C(n + r - 1, r);
  }
};
using modint = ModInt<MOD9>;
modint pow(ll n, ll x) { return modint(n).pow(x); }
modint pow(modint n, ll x) { return n.pow(x); }
// using modint=ld;
using Comb = Combination<modint>;
int main() {
  cin.tie(nullptr);
  ios_base::sync_with_stdio(false);
  ll res = 0, buf = 0;
  bool judge = true;
  NumberTheoreticTransform<MOD9> ntt;
  Comb comb(200005);
  ll n;
  cin >> n;
  map<ll, ll> mp;
  rep(i, 0, 2 * n) {
    ll h;
    cin >> h;
    mp[h]++;
  }
  ll lim = 100005;
  vector<modint> calc(lim);
  rep(i, 0, lim) { calc[i] = comb.C(i * 2, i) * comb.fact(i) / pow(2LL, i); }
  vector<int> ret(1, 1);
  for (auto z : mp) {
    vector<int> mul(z.se / 2 + 1, 0);
    rep(i, 0, z.se / 2 + 1) mul[i] = (comb.C(z.se, i * 2) * calc[i]).x;
    ret = ntt.multiply(ret, mul);
  }
  modint x = 0;
  rep(i, 0, ret.size()) {
    if (i > n)
      continue;
    if (~i & 1)
      x += calc[n - i] * ret[i];
    else
      x -= calc[n - i] * ret[i];
  }
  cout << x << endl;
  return 0;
}