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

#include <bits/stdc++.h>
using namespace std;
using ll = long long;
#ifdef tabr
#include "library/debug.cpp"
#else
#define debug(...)
#endif

template <long long mod> struct modular {
  long long value;
  modular(long long x = 0) {
    value = x % mod;
    if (value < 0)
      value += mod;
  }
  modular &operator+=(modular other) {
    if ((value += other.value) >= mod)
      value -= mod;
    return *this;
  }
  modular &operator-=(modular other) {
    if ((value -= other.value) < 0)
      value += mod;
    return *this;
  }
  modular &operator*=(modular other) {
    value = value * other.value % mod;
    return *this;
  }
  modular &operator/=(modular other) {
    long long a = 0, b = 1, c = other.value, m = mod;
    while (c != 0) {
      long long t = m / c;
      m -= t * c;
      swap(c, m);
      a -= t * b;
      swap(a, b);
    }
    a %= mod;
    if (a < 0)
      a += mod;
    value = value * a % mod;
    return *this;
  }
  modular operator-() { return modular(-value); }
  modular operator+(modular rhs) { return modular(*this) += rhs; }
  modular operator-(modular rhs) { return modular(*this) -= rhs; }
  modular operator*(modular rhs) { return modular(*this) *= rhs; }
  modular operator/(modular rhs) { return modular(*this) /= rhs; }
  bool operator==(modular rhs) { return value == rhs.value; }
  bool operator!=(modular rhs) { return value != rhs.value; }
  bool operator<(modular rhs) { return value < rhs.value; }
};
template <long long mod> string to_string(modular<mod> x) {
  return to_string(x.value);
}
template <long long mod> ostream &operator<<(ostream &stream, modular<mod> x) {
  x.value %= mod;
  if (x.value < 0)
    x.value += mod;
  return stream << x.value;
}
template <long long mod> istream &operator>>(istream &stream, modular<mod> &x) {
  stream >> x.value;
  x.value %= mod;
  if (x.value < 0)
    x.value += mod;
  return stream;
};
const long long mod = 998244353LL;
using mint = modular<mod>;

inline mint pw(mint a, long long n) {
  mint res = 1;
  while (n > 0) {
    if (n & 1) {
      res *= a;
    }
    a *= a;
    n >>= 1;
  }
  return res;
}
vector<mint> fact, finv;
inline void cinit(int n) {
  fact.resize(n, 1);
  finv.resize(n, 1);
  for (int i = 2; i < n; i++) {
    fact[i] = fact[i - 1] * i;
  }
  finv[n - 1] /= fact[n - 1];
  for (int i = n - 2; i >= 2; i--) {
    finv[i] = finv[i + 1] * (i + 1);
  }
}
inline mint C(int n, int k) {
  if (n < k || k < 0 || n < 0)
    return 0;
  return fact[n] * finv[k] * finv[n - k];
}

int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  int n, s;
  cin >> n >> s;
  vector<int> a(n);
  for (int i = 0; i < n; i++) {
    cin >> a[i];
  }
  vector<vector<mint>> dp(n + 1, vector<mint>(s + 1));
  dp[0][0] = pw(2, n);
  for (int i = 0; i < n; i++) {
    dp[i + 1] = dp[i];
    for (int j = 0; j + a[i] <= s; j++) {
      dp[i + 1][j + a[i]] += dp[i][j] / 2;
    }
  }
  cout << dp[n][s] << '\\n';
  return 0;
}


Error: TLE

Fixed submission:

#include <bits/stdc++.h>
using namespace std;
using ll = long long;
#ifdef tabr
#include "library/debug.cpp"
#else
#define debug(...)
#endif

template <long long mod> struct modular {
  long long value;
  modular(long long x = 0) {
    value = x % mod;
    if (value < 0)
      value += mod;
  }
  modular &operator+=(modular other) {
    if ((value += other.value) >= mod)
      value -= mod;
    return *this;
  }
  modular &operator-=(modular other) {
    if ((value -= other.value) < 0)
      value += mod;
    return *this;
  }
  modular &operator*=(modular other) {
    value = value * other.value % mod;
    return *this;
  }
  modular &operator/=(modular other) {
    long long a = 0, b = 1, c = other.value, m = mod;
    while (c != 0) {
      long long t = m / c;
      m -= t * c;
      swap(c, m);
      a -= t * b;
      swap(a, b);
    }
    a %= mod;
    if (a < 0)
      a += mod;
    value = value * a % mod;
    return *this;
  }
  modular operator-() { return modular(-value); }
  modular operator+(modular rhs) { return modular(*this) += rhs; }
  modular operator-(modular rhs) { return modular(*this) -= rhs; }
  modular operator*(modular rhs) { return modular(*this) *= rhs; }
  modular operator/(modular rhs) { return modular(*this) /= rhs; }
  bool operator==(modular rhs) { return value == rhs.value; }
  bool operator!=(modular rhs) { return value != rhs.value; }
  bool operator<(modular rhs) { return value < rhs.value; }
};
template <long long mod> string to_string(modular<mod> x) {
  return to_string(x.value);
}
template <long long mod> ostream &operator<<(ostream &stream, modular<mod> x) {
  x.value %= mod;
  if (x.value < 0)
    x.value += mod;
  return stream << x.value;
}
template <long long mod> istream &operator>>(istream &stream, modular<mod> &x) {
  stream >> x.value;
  x.value %= mod;
  if (x.value < 0)
    x.value += mod;
  return stream;
};
const long long mod = 998244353LL;
using mint = modular<mod>;

inline mint pw(mint a, long long n) {
  mint res = 1;
  while (n > 0) {
    if (n & 1) {
      res *= a;
    }
    a *= a;
    n >>= 1;
  }
  return res;
}
vector<mint> fact, finv;
inline void cinit(int n) {
  fact.resize(n, 1);
  finv.resize(n, 1);
  for (int i = 2; i < n; i++) {
    fact[i] = fact[i - 1] * i;
  }
  finv[n - 1] /= fact[n - 1];
  for (int i = n - 2; i >= 2; i--) {
    finv[i] = finv[i + 1] * (i + 1);
  }
}
inline mint C(int n, int k) {
  if (n < k || k < 0 || n < 0)
    return 0;
  return fact[n] * finv[k] * finv[n - k];
}

int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  int n, s;
  cin >> n >> s;
  vector<int> a(n);
  for (int i = 0; i < n; i++) {
    cin >> a[i];
  }
  vector<map<int, mint>> dp(n + 1);
  dp[0][0] = 1;
  for (int i = 0; i < n; i++) {
    for (int j = i; j >= 0; j--) {
      for (auto e : dp[j]) {
        if (e.first + a[i] <= s) {
          dp[j + 1][e.first + a[i]] += e.second;
        } else {
          break;
        }
      }
    }
  }
  mint ans = 0;
  for (int i = 1; i <= n; i++) {
    ans += dp[i][s] * pw(2, n - i);
  }
  cout << ans << '\\n';
  return 0;
}