Problem p02662 (C++) — buggy submission, verdict: Time Limit Exceeded

#include <bits/stdc++.h>
using namespace std;
using LL = long long;
using LD = long double;
using PII = pair<int, int>;
using PLI = pair<long long, int>;
using PLL = pair<long long, long long>;
template <class A, class B>
ostream &operator<<(ostream &out, const pair<A, B> &p) {
  return out << "(" << p.first << ", " << p.second << ")";
}
template <typename T, size_t N>
ostream &operator<<(ostream &out, const array<T, N> &a) {
  out << "[";
  bool first = true;
  for (auto &v : a) {
    out << (first ? "" : ", ");
    out << v;
    first = 0;
  }
  out << "]";
  return out;
}
template <typename T> ostream &operator<<(ostream &out, const vector<T> &a) {
  out << "[";
  bool first = true;
  for (auto &v : a) {
    out << (first ? "" : ", ");
    out << v;
    first = 0;
  }
  out << "]";
  return out;
}
template <typename T> ostream &operator<<(ostream &out, const deque<T> &a) {
  out << "[";
  bool first = true;
  for (auto &v : a) {
    out << (first ? "" : ", ");
    out << v;
    first = 0;
  }
  out << "]";
  return out;
}
template <typename T, class Cmp>
ostream &operator<<(ostream &out, const set<T, Cmp> &a) {
  out << "{";
  bool first = true;
  for (auto &v : a) {
    out << (first ? "" : ", ");
    out << v;
    first = 0;
  }
  out << "}";
  return out;
}
template <typename U, typename T, class Cmp>
ostream &operator<<(ostream &out, const map<U, T, Cmp> &a) {
  out << "{";
  bool first = true;
  for (auto &p : a) {
    out << (first ? "" : ", ");
    out << p.first << ":" << p.second;
    first = 0;
  }
  out << "}";
  return out;
}
template <class T> inline void YES(T condition) {
  if (condition)
    cout << "YES" << endl;
  else
    cout << "NO" << endl;
}
template <class T> inline void Yes(T condition) {
  if (condition)
    cout << "Yes" << endl;
  else
    cout << "No" << endl;
}
template <class T> T gcd(T a, T b) {
  while (b) {
    T tmp = b;
    b = a % b;
    a = tmp;
  }
  return a;
}
template <class T> T lcm(T a, T b) { return a / gcd(a, b) * b; }

#define trace(...) __f(#__VA_ARGS__, __VA_ARGS__)
template <typename Arg1> void __f(const char *name, Arg1 &&arg1) {
  cerr << name << ": " << arg1 << endl;
}
template <typename Arg1, typename... Args>
void __f(const char *names, Arg1 &&arg1, Args &&...args) {
  const char *comma = strchr(names + 1, ',');
  cerr.write(names, comma - names) << ": " << arg1 << " |";
  __f(comma + 1, args...);
}

long long qpow(long long a, long long b, int MOD) {
  if (b == 0)
    return 1;
  long long res = 1;
  while (b) {
    if (b & 1)
      res = (res * a) % MOD;
    a = (a * a) % MOD;
    b >>= 1;
  }
  return res;
}

const int MOD = 998244353;
const int maxn = 2e6;
int fac[maxn + 5];
int invfac[maxn + 5];
void init() {
  fac[0] = 1;
  for (int i = 1; i <= maxn; i++)
    fac[i] = 1LL * fac[i - 1] * i % MOD;
  invfac[maxn] = (int)(qpow(fac[maxn], MOD - 2, MOD));
  for (int i = maxn - 1; i >= 0; i--)
    invfac[i] = 1LL * invfac[i + 1] * (i + 1) % MOD;
}
int C(int n, int k) {
  assert(0 <= k && n >= k);
  int tmp = (int)(1LL * invfac[k] * invfac[n - k] % MOD);
  return (int)(1LL * fac[n] * tmp % MOD);
}

int main() {
  cin.tie(nullptr);
  ios::sync_with_stdio(false);

  int n, s;
  cin >> n >> s;
  vector<int> a(n);
  for (int i = 0; i < n; i++)
    cin >> a[i];
  sort(a.begin(), a.end());
  // vector<int> dp(s + 1);
  // dp[0] = 1;
  // for (auto& x: a) {
  //     for (int y = s - x; y >= 0 ; y--) {
  //         dp[y + x] += dp[y];
  //     }
  // }

  // vector<vector<int>> dp(s + 1);
  // vector<PLL> dp(s + 1, {0LL, 0LL});
  // dp[0]= make_pair(0LL, 1LL);
  // for (auto& x: a) {
  //     for (int y = s - x; y >= 0; y--) {
  // if ((int)dp[y].size() == 0) continue;
  // for(auto&pre: dp[y]) {
  //     dp[y + x].push_back(pre + 1);
  // }
  //         dp[y + x].first += dp[y].second * x;
  //         dp[y + x].second += dp[y].second;
  //     }
  // }
  // LL ans = 0;
  // for(auto& x: dp[s]) {
  //     ans += qpow(2, n - x, MOD);
  //     ans %= MOD;
  // }
  // cout << ans << '\\n';
  LL rev2 = qpow(2, MOD - 2, MOD);
  vector<LL> dp(s + 1, 0);
  dp[0] = qpow(2, n, MOD);
  for (auto &x : a) {
    for (int y = s - x; y >= 0; y--) {
      dp[y + x] += dp[y] * rev2;
      dp[y + x] %= MOD;
    }
  }
  cout << dp[s] << endl;

  return 0;
}


Error: TLE

Fixed submission:

#include <bits/stdc++.h>
using namespace std;
using LL = long long;
using LD = long double;
using PII = pair<int, int>;
using PLI = pair<long long, int>;
using PLL = pair<long long, long long>;
template <class A, class B>
ostream &operator<<(ostream &out, const pair<A, B> &p) {
  return out << "(" << p.first << ", " << p.second << ")";
}
template <typename T, size_t N>
ostream &operator<<(ostream &out, const array<T, N> &a) {
  out << "[";
  bool first = true;
  for (auto &v : a) {
    out << (first ? "" : ", ");
    out << v;
    first = 0;
  }
  out << "]";
  return out;
}
template <typename T> ostream &operator<<(ostream &out, const vector<T> &a) {
  out << "[";
  bool first = true;
  for (auto &v : a) {
    out << (first ? "" : ", ");
    out << v;
    first = 0;
  }
  out << "]";
  return out;
}
template <typename T> ostream &operator<<(ostream &out, const deque<T> &a) {
  out << "[";
  bool first = true;
  for (auto &v : a) {
    out << (first ? "" : ", ");
    out << v;
    first = 0;
  }
  out << "]";
  return out;
}
template <typename T, class Cmp>
ostream &operator<<(ostream &out, const set<T, Cmp> &a) {
  out << "{";
  bool first = true;
  for (auto &v : a) {
    out << (first ? "" : ", ");
    out << v;
    first = 0;
  }
  out << "}";
  return out;
}
template <typename U, typename T, class Cmp>
ostream &operator<<(ostream &out, const map<U, T, Cmp> &a) {
  out << "{";
  bool first = true;
  for (auto &p : a) {
    out << (first ? "" : ", ");
    out << p.first << ":" << p.second;
    first = 0;
  }
  out << "}";
  return out;
}
template <class T> inline void YES(T condition) {
  if (condition)
    cout << "YES" << endl;
  else
    cout << "NO" << endl;
}
template <class T> inline void Yes(T condition) {
  if (condition)
    cout << "Yes" << endl;
  else
    cout << "No" << endl;
}
template <class T> T gcd(T a, T b) {
  while (b) {
    T tmp = b;
    b = a % b;
    a = tmp;
  }
  return a;
}
template <class T> T lcm(T a, T b) { return a / gcd(a, b) * b; }

#define trace(...) __f(#__VA_ARGS__, __VA_ARGS__)
template <typename Arg1> void __f(const char *name, Arg1 &&arg1) {
  cerr << name << ": " << arg1 << endl;
}
template <typename Arg1, typename... Args>
void __f(const char *names, Arg1 &&arg1, Args &&...args) {
  const char *comma = strchr(names + 1, ',');
  cerr.write(names, comma - names) << ": " << arg1 << " |";
  __f(comma + 1, args...);
}

long long qpow(long long a, long long b, int MOD) {
  if (b == 0)
    return 1;
  long long res = 1;
  while (b) {
    if (b & 1)
      res = (res * a) % MOD;
    a = (a * a) % MOD;
    b >>= 1;
  }
  return res;
}

const int MOD = 998244353;
const int maxn = 2e6;
int fac[maxn + 5];
int invfac[maxn + 5];
void init() {
  fac[0] = 1;
  for (int i = 1; i <= maxn; i++)
    fac[i] = 1LL * fac[i - 1] * i % MOD;
  invfac[maxn] = (int)(qpow(fac[maxn], MOD - 2, MOD));
  for (int i = maxn - 1; i >= 0; i--)
    invfac[i] = 1LL * invfac[i + 1] * (i + 1) % MOD;
}
int C(int n, int k) {
  assert(0 <= k && n >= k);
  int tmp = (int)(1LL * invfac[k] * invfac[n - k] % MOD);
  return (int)(1LL * fac[n] * tmp % MOD);
}

int main() {
  cin.tie(nullptr);
  ios::sync_with_stdio(false);

  int n, s;
  cin >> n >> s;
  vector<int> a(n);
  for (int i = 0; i < n; i++)
    cin >> a[i];
  sort(a.begin(), a.end());
  // vector<int> dp(s + 1);
  // dp[0] = 1;
  // for (auto& x: a) {
  //     for (int y = s - x; y >= 0 ; y--) {
  //         dp[y + x] += dp[y];
  //     }
  // }

  // vector<vector<int>> dp(s + 1);
  // vector<PLL> dp(s + 1, {0LL, 0LL});
  // dp[0]= make_pair(0LL, 1LL);
  // for (auto& x: a) {
  //     for (int y = s - x; y >= 0; y--) {
  // if ((int)dp[y].size() == 0) continue;
  // for(auto&pre: dp[y]) {
  //     dp[y + x].push_back(pre + 1);
  // }
  //         dp[y + x].first += dp[y].second * x;
  //         dp[y + x].second += dp[y].second;
  //     }
  // }
  // LL ans = 0;
  // for(auto& x: dp[s]) {
  //     ans += qpow(2, n - x, MOD);
  //     ans %= MOD;
  // }
  // cout << ans << '\\n';
  vector<LL> dp(s + 1, 0);
  dp[0] = qpow(2, n, MOD);
  for (auto &x : a) {
    for (int y = s - x; y >= 0; y--) {
      dp[y + x] += dp[y] * qpow(2, MOD - 2, MOD);
      dp[y + x] %= MOD;
    }
  }
  cout << dp[s] << endl;

  return 0;
}