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 vi = vector<int>;
using vvi = vector<vi>;
using vll = vector<ll>;
using vvll = vector<vll>;
using vb = vector<bool>;
using vs = vector<string>;
using vld = vector<ld>;
using vvld = vector<vld>;

typedef pair<ll, ll> P;

#define bit(n) (1LL << (n))

// #define int long long

#define all(v) v.begin(), v.end()

#define rep(i, n) for (ll i = 0; i < n; i++)
#define REP(i, n) for (ll i = 1; i < n; i++)

#define FOR(i, a, b) for (ll i = (a); i < (b); i++)
#define FORm(i, m) for (auto i = m.begin(); i != m.end(); i++)

template <class T> inline void chmax(T &a, T b) { a = std::max(a, b); }
template <class T> inline void chmin(T &a, T b) { a = std::min(a, b); }

#define mod (ll)(998244353ll)
const long long INF = 1LL << 60;

// #define mod (ll)(1e9 + 7)

template <ll ModVal> struct ModInt {
  ll x;

  ModInt(ll _x = 0) : x((_x % ModVal + ModVal) % ModVal) {}

  ModInt operator-() const { return ModInt(-x); }
  ModInt &operator+=(const ModInt a) {
    x += a.x;
    if (x >= ModVal)
      x -= ModVal;
    return *this;
  }
  ModInt &operator-=(const ModInt a) {
    x = x + ModVal - a.x;
    if (x >= ModVal)
      x -= ModVal;
    return *this;
  }
  ModInt &operator*=(const ModInt a) {
    x *= a.x;
    x %= ModVal;
    return *this;
  }

  ll ext_gcd(ll a, ll b, ll &x, ll &y) {
    if (b == 0) {
      x = 1;
      y = 0;
      return a;
    }
    ll tmp = a / b;
    ll d = ext_gcd(b, a - b * tmp, y, x);
    y -= tmp * x;
    return d;
  }

  // 逆元
  ModInt inv() {
    ll u, v;
    ext_gcd(x, ModVal, u, v);
    return ModInt(u);
  }

  ModInt inv(const ModInt a) {
    ll u, v;
    ext_gcd(a.x, ModVal, u, v);
    return ModInt(u);
  }

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

  ModInt operator+(const ModInt a) const {
    ModInt retval(*this);
    return retval += a;
  }
  ModInt operator-(const ModInt a) const {
    ModInt retval(*this);
    return retval -= a;
  }
  ModInt operator*(const ModInt a) const {
    ModInt retval(*this);
    return retval *= a;
  }
  ModInt operator/(const ModInt a) const {
    ModInt retval(*this);
    return retval /= a;
  }

  ModInt pow(ll n) {
    ModInt ans(1);
    while (n) {
      if (n & 1)
        ans = ans * x;
      *this = (*this) * (*this);
      n = n >> 1;
    }
    return ans;
  }

  constexpr const ll &value() { return this->x; }
};

template <ll ModVal> ostream &operator<<(ostream &os, const ModInt<ModVal> &a) {
  os << a.x;
  return os;
}

using mint = ModInt<mod>;

signed main() {
  cin.tie(0);
  ios::sync_with_stdio(false);
  cout << fixed << setprecision(20);

  ll n, s;
  cin >> n >> s;

  vll a(n + 1);
  REP(i, n + 1) { cin >> a[i]; }

  vector<vector<mint>> dp(n + 1, vector<mint>(s + 1));
  dp[0][0] = 1;
  REP(i, n + 1) {
    rep(j, s + 1) {
      dp[i][j] += dp[i - 1][j] * 2;
      if (j + a[i] <= s) {
        dp[i][j + a[i]] += dp[i - 1][j];
      }
    }
  }

  cout << dp[n][s] << endl;

  return 0;
}


Error: TLE

Fixed submission:

#include <bits/stdc++.h>

using namespace std;

using ll = long long;
using ld = long double;

using vi = vector<int>;
using vvi = vector<vi>;
using vll = vector<ll>;
using vvll = vector<vll>;
using vb = vector<bool>;
using vs = vector<string>;
using vld = vector<ld>;
using vvld = vector<vld>;

typedef pair<ll, ll> P;

#define bit(n) (1LL << (n))

// #define int long long

#define all(v) v.begin(), v.end()

#define rep(i, n) for (ll i = 0; i < n; i++)
#define REP(i, n) for (ll i = 1; i < n; i++)

#define FOR(i, a, b) for (ll i = (a); i < (b); i++)
#define FORm(i, m) for (auto i = m.begin(); i != m.end(); i++)

template <class T> inline void chmax(T &a, T b) { a = std::max(a, b); }
template <class T> inline void chmin(T &a, T b) { a = std::min(a, b); }

#define mod (ll)(998244353ll)
const long long INF = 1LL << 60;

// #define mod (ll)(1e9 + 7)

template <ll ModVal> struct ModInt {
  ll x;

  ModInt(ll _x = 0) : x((_x % ModVal + ModVal) % ModVal) {}

  ModInt operator-() const { return ModInt(-x); }
  ModInt &operator+=(const ModInt a) {
    x += a.x;
    if (x >= ModVal)
      x -= ModVal;
    return *this;
  }
  ModInt &operator-=(const ModInt a) {
    x = x + ModVal - a.x;
    if (x >= ModVal)
      x -= ModVal;
    return *this;
  }
  ModInt &operator*=(const ModInt a) {
    x *= a.x;
    x %= ModVal;
    return *this;
  }

  ll ext_gcd(ll a, ll b, ll &x, ll &y) {
    if (b == 0) {
      x = 1;
      y = 0;
      return a;
    }
    ll tmp = a / b;
    ll d = ext_gcd(b, a - b * tmp, y, x);
    y -= tmp * x;
    return d;
  }

  // 逆元
  ModInt inv() {
    ll u, v;
    ext_gcd(x, ModVal, u, v);
    return ModInt(u);
  }

  ModInt inv(const ModInt a) {
    ll u, v;
    ext_gcd(a.x, ModVal, u, v);
    return ModInt(u);
  }

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

  ModInt operator+(const ModInt a) const {
    ModInt retval(*this);
    return retval += a;
  }
  ModInt operator-(const ModInt a) const {
    ModInt retval(*this);
    return retval -= a;
  }
  ModInt operator*(const ModInt a) const {
    ModInt retval(*this);
    return retval *= a;
  }
  ModInt operator/(const ModInt a) const {
    ModInt retval(*this);
    return retval /= a;
  }

  ModInt pow(ll n) {
    ModInt ans(1);
    while (n) {
      if (n & 1)
        ans = ans * x;
      *this = (*this) * (*this);
      n = n >> 1;
    }
    return ans;
  }

  constexpr const ll &value() { return this->x; }
};

template <ll ModVal> ostream &operator<<(ostream &os, const ModInt<ModVal> &a) {
  os << a.x;
  return os;
}

using mint = ModInt<mod>;

template <typename T> class Combination {
public:
  Combination(ll _max_n) : max_n(_max_n), factional(max_n + 1), inv(max_n + 1) {
    factional[0] = 1;
    inv[0] = 1;
    for (ll i = 0; i < max_n; i++) {
      factional[i + 1] = factional[i] * (i + 1); // n!(mod M)
      inv[i + 1] = inv[i] / (i + 1);             // k!^(M-2) (mod M)
    }
  }

  // nCk
  T choose(ll n, ll k) {
    if (n == 0 && k == 0)
      return 1;
    if (n < k || n < 0)
      return 0;
    T tmp = inv[n - k] * inv[k];
    return tmp * factional[n];
  }

  T permutation(ll n, ll k) {
    if (n - k < 0) {
      return 0;
    }
    return factional[n] / factional[n - k];
  }

private:
  const ll max_n;
  std::vector<T> factional;
  std::vector<T> inv;
};

using Comb = Combination<mint>;

signed main() {
  cin.tie(0);
  ios::sync_with_stdio(false);
  cout << fixed << setprecision(20);

  ll n, s;
  cin >> n >> s;

  vll a(n + 1);
  REP(i, n + 1) { cin >> a[i]; }
  sort(all(a));
  // vector<vector<mint>> dp(n + 2, vector<mint>(n + 1));
  vvll dp(s + 1, vll(n + 2));

  ll sum = 0;

  dp[0][0] = 1;
  REP(i, n + 1) {
    vvll prev = dp;
    ll v = a[i];
    sum += a[i];
    chmin(sum, s);

    rep(j, sum + 1 - v) {
      rep(k, i) { dp[j + v][k + 1] += prev[j][k]; }
    }
  }

  mint ans = 0;
  REP(i, n + 1) { ans += mint(2).pow(n - i) * dp[s][i]; }

  cout << ans << endl;

  return 0;
}