Problem p02875 (C++)

Buggy submission (status: Time Limit Exceeded):
#include <bits/stdc++.h>
#include <random>

using namespace std;

typedef unsigned long long ull;
typedef long long ll;
typedef double ld;
// #define ll __int128
// #define int ll
// #define int ll
// #define char ll
typedef vector<char> vc;
typedef vector<vc> vvc;
typedef vector<vvc> vvvc;
typedef pair<int, int> pii;
typedef pair<pii, pii> piii;
typedef pair<ll, ll> pll;
typedef vector<int> vi;
typedef vector<pii> vpi;
typedef vector<vi> vvi;
typedef vector<vvi> vvvi;
typedef vector<short> vs;
typedef vector<vs> vvs;
typedef vector<vvs> vvvs;
typedef vector<ll> vl;
typedef vector<vl> vvl;
typedef vector<vvl> vvvl;
typedef vector<ld> vld;
typedef vector<vld> vvld;
typedef vector<vvld> vvvld;
typedef vector<string> vst;
typedef vector<vst> vvst;
typedef pair<ld, ld> pld;

#define inmin(a, b) a = min(a, (b))
#define inmax(a, b) a = max(a, (b))
#define ALL(a) a.begin(), a.end()
#define RALL(a) a.rbegin(), a.rend()
#define sqr(x) ((x) * (x))
#define fori(i, n) for (int i = 0; i < int(n); ++i)
#define SZ(a) ((int)((a).size()))
#define triple(T) tuple<T, T, T>
#define quad(T) tuple<T, T, T, T>
#define watch(x) cerr << (#x) << " = " << (x) << endl;

#ifdef MAX_HOME
#define cerr cout
#else
#define cerr                                                                   \
  if (false)                                                                   \
  cerr
#endif

const double PI = 2 * acos(0.0);
#define rand shittttty_shit
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
mt19937_64 rng_64(chrono::steady_clock::now().time_since_epoch().count());

const string DIGITS = "0123456789";
const string ALPH = "abcdefghijklmnopqrstuvwxyz";

template <class T0, class T1>
inline ostream &operator<<(ostream &out, pair<T0, T1> &a) {
  return out << "{" << a.first << ", " << a.second << "}";
}

template <class T0, class T1>
inline istream &operator>>(istream &in, pair<T0, T1> &a) {
  return in >> a.first >> a.second;
}

template <class T0, class T1, class T2>
inline ostream &operator<<(ostream &out, tuple<T0, T1, T2> &a) {
  return out << "{" << get<0>(a) << ", " << get<1>(a) << ", " << get<2>(a)
             << "}";
}

template <class T0, class T1, class T2, class T3>
inline ostream &operator<<(ostream &out, tuple<T0, T1, T2, T3> &a) {
  return out << "{" << get<0>(a) << ", " << get<1>(a) << ", " << get<2>(a)
             << ", " << get<3>(a) << "}";
}

template <class T> inline ostream &operator<<(ostream &out, vector<T> &a) {
  out << "[";
  fori(i, a.size()) out << a[i]
                        << vector<string>{", ", "]  "}[i + 1 == a.size()];
  return out;
}

void smain();

signed main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
#ifdef MAX_HOME
  freopen("input.txt", "r", stdin);
  clock_t start = clock();
#endif
  cout << setprecision(4) << fixed;
  smain();
#ifdef MAX_HOME
  cout << "\n\n\n\nTOTAL EXECUTION TIME: "
       << float(clock() - start) / CLOCKS_PER_SEC << endl;
#endif
  return 0;
}

const int N = 1e7 + 10;
const int M = 998244353;

int pw(int a, int n = M - 2) {
  int ret = 1;
  while (n) {
    if (n & 1)
      ret = (ll)ret * a % M;
    a = (ll)a * a % M;
    n >>= 1;
  }
  return ret;
}

int fact[N], rfact[N];

int ncr(int n, int k) {
  if (k < 0 || k > n)
    return 0;
  return (ll)fact[n] * rfact[k] % M * rfact[n - k] % M;
}
void init() {
  fact[0] = 1;
  for (int i = 1; i < N; ++i) {
    fact[i] = (ll)i * fact[i - 1] % M;
  }
  rfact[N - 1] = pw(fact[N - 1]);
  for (int i = N - 2; i >= 0; --i) {
    rfact[i] = (ll)(i + 1) * rfact[i + 1] % M;
  }
}

int naive(int n) {
  n >>= 1;

  int ans = 0;
  fori(a0, n + 1) {
    fori(b0, n - a0 + 1) {
      int c0 = n - a0 - b0;
      fori(a1, n + 1) {
        fori(b1, n + 1 - a1) {
          int c1 = n - a1 - b1;
          bool ok = 1;
          ok &= max(0, a0 - a1) + max(0, b0 - b1) <= c1;
          ok &= max(0, a1 - a0) + max(0, b1 - b0) <= c0;
          if (ok) {
            int cur =
                (ll)fact[n] * rfact[a0] % M * rfact[b0] % M * rfact[c0] % M;
            cur = (ll)cur * fact[n] % M * rfact[a1] % M * rfact[b1] % M *
                  rfact[c1] % M;
            ans = (ans + cur) % M;
          }
        }
      }
    }
  }
  return ans;
}

void insum(int &a, int b) { a = (a + b) % M; }

int solve(int n) {
  n >>= 1;

  int ans = 0;
  fori(x, n + 1) {
    fori(y, n + 1) { insum(ans, (ll)ncr(2 * n, x) * ncr(2 * n - x, y) % M); }
  }
  return ans;
}

void smain() {
  init();
  int n;
  cin >> n;

  //    cout << naive(n) << endl;
  cout << solve(n);
}

Fixed submission:
#include <bits/stdc++.h>
#include <random>

using namespace std;

typedef unsigned long long ull;
typedef long long ll;
typedef double ld;
// #define ll __int128
// #define int ll
// #define int ll
// #define char ll
typedef vector<char> vc;
typedef vector<vc> vvc;
typedef vector<vvc> vvvc;
typedef pair<int, int> pii;
typedef pair<pii, pii> piii;
typedef pair<ll, ll> pll;
typedef vector<int> vi;
typedef vector<pii> vpi;
typedef vector<vi> vvi;
typedef vector<vvi> vvvi;
typedef vector<short> vs;
typedef vector<vs> vvs;
typedef vector<vvs> vvvs;
typedef vector<ll> vl;
typedef vector<vl> vvl;
typedef vector<vvl> vvvl;
typedef vector<ld> vld;
typedef vector<vld> vvld;
typedef vector<vvld> vvvld;
typedef vector<string> vst;
typedef vector<vst> vvst;
typedef pair<ld, ld> pld;

#define inmin(a, b) a = min(a, (b))
#define inmax(a, b) a = max(a, (b))
#define ALL(a) a.begin(), a.end()
#define RALL(a) a.rbegin(), a.rend()
#define sqr(x) ((x) * (x))
#define fori(i, n) for (int i = 0; i < int(n); ++i)
#define SZ(a) ((int)((a).size()))
#define triple(T) tuple<T, T, T>
#define quad(T) tuple<T, T, T, T>
#define watch(x) cerr << (#x) << " = " << (x) << endl;

#ifdef MAX_HOME
#define cerr cout
#else
#define cerr                                                                   \
  if (false)                                                                   \
  cerr
#endif

const double PI = 2 * acos(0.0);
#define rand shittttty_shit
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
mt19937_64 rng_64(chrono::steady_clock::now().time_since_epoch().count());

const string DIGITS = "0123456789";
const string ALPH = "abcdefghijklmnopqrstuvwxyz";

template <class T0, class T1>
inline ostream &operator<<(ostream &out, pair<T0, T1> &a) {
  return out << "{" << a.first << ", " << a.second << "}";
}

template <class T0, class T1>
inline istream &operator>>(istream &in, pair<T0, T1> &a) {
  return in >> a.first >> a.second;
}

template <class T0, class T1, class T2>
inline ostream &operator<<(ostream &out, tuple<T0, T1, T2> &a) {
  return out << "{" << get<0>(a) << ", " << get<1>(a) << ", " << get<2>(a)
             << "}";
}

template <class T0, class T1, class T2, class T3>
inline ostream &operator<<(ostream &out, tuple<T0, T1, T2, T3> &a) {
  return out << "{" << get<0>(a) << ", " << get<1>(a) << ", " << get<2>(a)
             << ", " << get<3>(a) << "}";
}

template <class T> inline ostream &operator<<(ostream &out, vector<T> &a) {
  out << "[";
  fori(i, a.size()) out << a[i]
                        << vector<string>{", ", "]  "}[i + 1 == a.size()];
  return out;
}

void smain();

signed main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
#ifdef MAX_HOME
  freopen("input.txt", "r", stdin);
  clock_t start = clock();
#endif
  cout << setprecision(4) << fixed;
  smain();
#ifdef MAX_HOME
  cout << "\n\n\n\nTOTAL EXECUTION TIME: "
       << float(clock() - start) / CLOCKS_PER_SEC << endl;
#endif
  return 0;
}

const int N = 1e7 + 10;
const int M = 998244353;

int pw(int a, int n = M - 2) {
  int ret = 1;
  while (n) {
    if (n & 1)
      ret = (ll)ret * a % M;
    a = (ll)a * a % M;
    n >>= 1;
  }
  return ret;
}

int fact[N], rfact[N];

int ncr(int n, int k) {
  if (k < 0 || k > n)
    return 0;
  return (ll)fact[n] * rfact[k] % M * rfact[n - k] % M;
}
void init() {
  fact[0] = 1;
  for (int i = 1; i < N; ++i) {
    fact[i] = (ll)i * fact[i - 1] % M;
  }
  rfact[N - 1] = pw(fact[N - 1]);
  for (int i = N - 2; i >= 0; --i) {
    rfact[i] = (ll)(i + 1) * rfact[i + 1] % M;
  }
}

int naive(int n) {
  n >>= 1;

  int ans = 0;
  fori(a0, n + 1) {
    fori(b0, n - a0 + 1) {
      int c0 = n - a0 - b0;
      fori(a1, n + 1) {
        fori(b1, n + 1 - a1) {
          int c1 = n - a1 - b1;
          bool ok = 1;
          ok &= max(0, a0 - a1) + max(0, b0 - b1) <= c1;
          ok &= max(0, a1 - a0) + max(0, b1 - b0) <= c0;
          if (ok) {
            int cur =
                (ll)fact[n] * rfact[a0] % M * rfact[b0] % M * rfact[c0] % M;
            cur = (ll)cur * fact[n] % M * rfact[a1] % M * rfact[b1] % M *
                  rfact[c1] % M;
            ans = (ans + cur) % M;
          }
        }
      }
    }
  }
  return ans;
}

void insum(int &a, int b) { a = (a + b) % M; }

int solve(int n) {
  n >>= 1;

  int ans = pw(3, n * 2);
  for (int x = n + 1; x <= n * 2; ++x) {
    int cur = 2LL * ncr(n * 2, x) * pw(2, n * 2 - x) % M;
    ans = (ans + M - cur) % M;
  }
  return ans;
}

void smain() {
  init();
  int n;
  cin >> n;

  //    cout << naive(n) << endl;
  cout << solve(n);
}