Problem p02634 (C++) — buggy submission, verdict: Time Limit Exceeded

#include <bits/stdc++.h>

using namespace std;

#define DEBUG(x) cerr << #x << ": " << x << endl;
#define DEBUG_VEC(v)                                                           \\
  cerr << #v << ":";                                                           \\
  for (int i = 0; i < v.size(); i++)                                           \\
    cerr << " " << v[i];                                                       \\
  cerr << endl;
#define DEBUG_MAT(v)                                                           \\
  cerr << #v << endl;                                                          \\
  for (int i = 0; i < v.size(); i++) {                                         \\
    for (int j = 0; j < v[i].size(); j++) {                                    \\
      cerr << v[i][j] << " ";                                                  \\
    }                                                                          \\
    cerr << endl;                                                              \\
  }
typedef long long ll;
#define int ll

#define vi vector<int>
#define vl vector<ll>
#define vii vector<vector<int>>
#define vll vector<vector<ll>>
#define vs vector<string>
#define pii pair<int, int>
#define pis pair<int, string>
#define psi pair<string, int>
#define pll pair<ll, ll>
template <class S, class T>
pair<S, T> operator+(const pair<S, T> &s, const pair<S, T> &t) {
  return pair<S, T>(s.first + t.first, s.second + t.second);
}
template <class S, class T>
pair<S, T> operator-(const pair<S, T> &s, const pair<S, T> &t) {
  return pair<S, T>(s.first - t.first, s.second - t.second);
}
template <class S, class T> ostream &operator<<(ostream &os, pair<S, T> p) {
  os << "(" << p.first << ", " << p.second << ")";
  return os;
}
#define X first
#define Y second
#define rep(i, n) for (int i = 0; i < (int)(n); i++)
#define rep1(i, n) for (int i = 1; i <= (int)(n); i++)
#define rrep(i, n) for (int i = (int)(n)-1; i >= 0; i--)
#define rrep1(i, n) for (int i = (int)(n); i > 0; i--)
#define REP(i, a, b) for (int i = a; i < b; i++)
#define in(x, a, b) (a <= x && x < b)
#define all(c) c.begin(), 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;
}
#define UNIQUE(v) v.erase(std::unique(v.begin(), v.end()), v.end());
const ll inf = 1000000001;
const ll INF = (ll)1e18 + 1;
const long double pi = 3.1415926535897932384626433832795028841971L;
#define Sp(p) cout << setprecision(25) << fixed << p << endl;
// int dx[4] = {1, 0, -1, 0}, dy[4] = {0, 1, 0, -1};
// int dx2[8] = { 1,1,0,-1,-1,-1,0,1 }, dy2[8] = { 0,1,1,1,0,-1,-1,-1 };
vi dx = {1, 0, -1, 0}, dy = {0, 1, 0, -1};
vi dx2 = {1, 1, 0, -1, -1, -1, 0, 1}, dy2 = {0, 1, 1, 1, 0, -1, -1, -1};
#define fio()                                                                  \\
  cin.tie(0);                                                                  \\
  ios::sync_with_stdio(false);
// const ll MOD = 1000000007;
const ll MOD = 998244353;
// #define mp make_pair
// #define endl '\\n'

const int MAXN = 555555;

vl fact(MAXN);
vl rfact(MAXN);

ll mod_pow(ll x, ll p, ll M = MOD) {
  if (p < 0) {
    x = mod_pow(x, M - 2, M);
    p = -p;
  }
  ll a = 1;
  while (p) {
    if (p % 2)
      a = a * x % M;
    x = x * x % M;
    p /= 2;
  }
  return a;
}

ll mod_inverse(ll a, ll M = MOD) { return mod_pow(a, M - 2, M); }

void set_fact(ll n, ll M = MOD) {
  fact[0] = fact[1] = rfact[0] = rfact[1] = 1;
  for (ll i = 2; i <= n; i++) {
    fact[i] = i * fact[i - 1] % M;
    // rfact[i] = mod_inverse(fact[i], M);
  }
}

// http://drken1215.hatenablog.com/entry/2018/06/08/210000
// n���傫��fact���v�Z�ł��Ȃ��Ƃ��̂ق��̌v�Z���@�ɂ��ď����Ă���
ll nCr(ll n, ll r, ll M = MOD) {
  if (r > n)
    return 0;
  assert(fact[2] == 2);
  ll ret = fact[n];
  if (rfact[r] == 0) {
    rfact[r] = mod_inverse(fact[r], M);
  }
  ret = (ret * rfact[r]) % M;
  if (rfact[n - r] == 0) {
    rfact[n - r] = mod_inverse(fact[n - r], M);
  }
  ret = (ret * rfact[n - r]) % M;
  return ret;
}

ll nHr(ll n, ll r) { return nCr(n + r - 1, r); }

ll dp[3001][3001];

signed main() {
  fio();
  int a, b, c, d;
  cin >> a >> b >> c >> d;
  // vll dp(c + 1, vl(d + 1));
  dp[c][d] = 1;
  for (int i = c; i >= a + 1; i--) {
    ll add = 0;
    ll inv_i = mod_inverse(i);
    ll pp = mod_pow(i, d);
    ll pp2 = mod_pow(i, -d - 1);
    for (int j = d; j >= b; j--) {
      dp[i - 1][j] += dp[i][j] * j % MOD;
      ll mul = j * pp2 % MOD;
      pp2 = pp2 * i % MOD;
      if (j + 1 <= d) {
        (add += dp[i][j + 1] * pp % MOD) %= MOD;
        pp = pp * inv_i % MOD;
      }
      dp[i - 1][j] += add * mul % MOD;
      dp[i - 1][j] %= MOD;
    }
    // DEBUG_MAT(dp);
  }
  for (int j = d; j > b; j--) {
    dp[a][b] += dp[a][j] * mod_pow(a, j - b) % MOD;
  }
  dp[a][b] %= MOD;
  cout << dp[a][b] << endl;
}

Error: TLE

Fixed submission:

#include <bits/stdc++.h>

using namespace std;

#define DEBUG(x) cerr << #x << ": " << x << endl;
#define DEBUG_VEC(v)                                                           \\
  cerr << #v << ":";                                                           \\
  for (int i = 0; i < v.size(); i++)                                           \\
    cerr << " " << v[i];                                                       \\
  cerr << endl;
#define DEBUG_MAT(v)                                                           \\
  cerr << #v << endl;                                                          \\
  for (int i = 0; i < v.size(); i++) {                                         \\
    for (int j = 0; j < v[i].size(); j++) {                                    \\
      cerr << v[i][j] << " ";                                                  \\
    }                                                                          \\
    cerr << endl;                                                              \\
  }
typedef long long ll;
#define int ll

#define vi vector<int>
#define vl vector<ll>
#define vii vector<vector<int>>
#define vll vector<vector<ll>>
#define vs vector<string>
#define pii pair<int, int>
#define pis pair<int, string>
#define psi pair<string, int>
#define pll pair<ll, ll>
template <class S, class T>
pair<S, T> operator+(const pair<S, T> &s, const pair<S, T> &t) {
  return pair<S, T>(s.first + t.first, s.second + t.second);
}
template <class S, class T>
pair<S, T> operator-(const pair<S, T> &s, const pair<S, T> &t) {
  return pair<S, T>(s.first - t.first, s.second - t.second);
}
template <class S, class T> ostream &operator<<(ostream &os, pair<S, T> p) {
  os << "(" << p.first << ", " << p.second << ")";
  return os;
}
#define X first
#define Y second
#define rep(i, n) for (int i = 0; i < (int)(n); i++)
#define rep1(i, n) for (int i = 1; i <= (int)(n); i++)
#define rrep(i, n) for (int i = (int)(n)-1; i >= 0; i--)
#define rrep1(i, n) for (int i = (int)(n); i > 0; i--)
#define REP(i, a, b) for (int i = a; i < b; i++)
#define in(x, a, b) (a <= x && x < b)
#define all(c) c.begin(), 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;
}
#define UNIQUE(v) v.erase(std::unique(v.begin(), v.end()), v.end());
const ll inf = 1000000001;
const ll INF = (ll)1e18 + 1;
const long double pi = 3.1415926535897932384626433832795028841971L;
#define Sp(p) cout << setprecision(25) << fixed << p << endl;
// int dx[4] = {1, 0, -1, 0}, dy[4] = {0, 1, 0, -1};
// int dx2[8] = { 1,1,0,-1,-1,-1,0,1 }, dy2[8] = { 0,1,1,1,0,-1,-1,-1 };
vi dx = {1, 0, -1, 0}, dy = {0, 1, 0, -1};
vi dx2 = {1, 1, 0, -1, -1, -1, 0, 1}, dy2 = {0, 1, 1, 1, 0, -1, -1, -1};
#define fio()                                                                  \\
  cin.tie(0);                                                                  \\
  ios::sync_with_stdio(false);
// const ll MOD = 1000000007;
const ll MOD = 998244353;
// #define mp make_pair
// #define endl '\\n'

const int MAXN = 555555;

vl fact(MAXN);
vl rfact(MAXN);

ll mod_pow(ll x, ll p, ll M = MOD) {
  if (p < 0) {
    x = mod_pow(x, M - 2, M);
    p = -p;
  }
  ll a = 1;
  while (p) {
    if (p % 2)
      a = a * x % M;
    x = x * x % M;
    p /= 2;
  }
  return a;
}

ll mod_inverse(ll a, ll M = MOD) { return mod_pow(a, M - 2, M); }

void set_fact(ll n, ll M = MOD) {
  fact[0] = fact[1] = rfact[0] = rfact[1] = 1;
  for (ll i = 2; i <= n; i++) {
    fact[i] = i * fact[i - 1] % M;
    // rfact[i] = mod_inverse(fact[i], M);
  }
}

// http://drken1215.hatenablog.com/entry/2018/06/08/210000
// n���傫��fact���v�Z�ł��Ȃ��Ƃ��̂ق��̌v�Z���@�ɂ��ď����Ă���
ll nCr(ll n, ll r, ll M = MOD) {
  if (r > n)
    return 0;
  assert(fact[2] == 2);
  ll ret = fact[n];
  if (rfact[r] == 0) {
    rfact[r] = mod_inverse(fact[r], M);
  }
  ret = (ret * rfact[r]) % M;
  if (rfact[n - r] == 0) {
    rfact[n - r] = mod_inverse(fact[n - r], M);
  }
  ret = (ret * rfact[n - r]) % M;
  return ret;
}

ll nHr(ll n, ll r) { return nCr(n + r - 1, r); }

signed main() {
  fio();
  int a, b, c, d;
  cin >> a >> b >> c >> d;
  vll dp(c + 1, vl(d + 1));
  dp[c][d] = 1;
  for (int i = c; i >= a + 1; i--) {
    ll add = 0;
    for (int j = d; j >= b; j--) {
      dp[i - 1][j] += dp[i][j] * j % MOD;
      ll mul = j * mod_pow(i, -j - 1) % MOD;
      if (j + 1 <= d) {
        (add += dp[i][j + 1] * mod_pow(i, j + 1) % MOD) %= MOD;
      }
      dp[i - 1][j] += add * mul % MOD;
      // for (int j2 = j + 1; j2 <= d; j2++) {
      // 	dp[i - 1][j] += dp[i][j2] * mod_pow(i, j2) % MOD * mul % MOD;
      // }
      dp[i - 1][j] %= MOD;
    }
    // DEBUG_MAT(dp);
  }
  for (int j = d; j > b; j--) {
    dp[a][b] += dp[a][j] * mod_pow(a, j - b) % MOD;
  }
  dp[a][b] %= MOD;
  cout << dp[a][b] << endl;
}