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 pint = pair<int, int>;
using pll = pair<ll, ll>;
using Edge = pair<int, ll>;
using Graph = vector<vector<int>>;
using WeightedGraph = vector<vector<Edge>>;
const ll INF64 = 1LL << 60;
const int INF32 = 1 << 29;
const ll MOD = 998244353;

const int CASES = 3;

template <int MOD> struct Fp {
  long long val;
  constexpr Fp(long long v = 0) noexcept : val(v % MOD) {
    if (val < 0)
      v += MOD;
  }
  constexpr int getmod() { return MOD; }
  constexpr Fp operator-() const noexcept { return val ? MOD - val : 0; }
  constexpr Fp operator+(const Fp &r) const noexcept { return Fp(*this) += r; }
  constexpr Fp operator-(const Fp &r) const noexcept { return Fp(*this) -= r; }
  constexpr Fp operator*(const Fp &r) const noexcept { return Fp(*this) *= r; }
  constexpr Fp operator/(const Fp &r) const noexcept { return Fp(*this) /= r; }
  constexpr Fp &operator+=(const Fp &r) noexcept {
    val += r.val;
    if (val >= MOD)
      val -= MOD;
    return *this;
  }
  constexpr Fp &operator-=(const Fp &r) noexcept {
    val -= r.val;
    if (val < 0)
      val += MOD;
    return *this;
  }
  constexpr Fp &operator*=(const Fp &r) noexcept {
    val = val * r.val % MOD;
    return *this;
  }
  constexpr Fp &operator/=(const Fp &r) noexcept {
    long long a = r.val, b = MOD, u = 1, v = 0;
    while (b) {
      long long t = a / b;
      a -= t * b;
      swap(a, b);
      u -= t * v;
      swap(u, v);
    }
    val = val * u % MOD;
    if (val < 0)
      val += MOD;
    return *this;
  }
  constexpr bool operator==(const Fp &r) const noexcept {
    return this->val == r.val;
  }
  constexpr bool operator!=(const Fp &r) const noexcept {
    return this->val != r.val;
  }
  friend constexpr ostream &operator<<(ostream &os, const Fp<MOD> &x) noexcept {
    return os << x.val;
  }
  friend constexpr istream &operator>>(istream &is, Fp<MOD> &x) noexcept {
    return is >> x.val;
  }
  friend constexpr Fp<MOD> modpow(const Fp<MOD> &a, long long n) noexcept {
    if (n == 0)
      return 1;
    auto t = modpow(a, n / 2);
    t = t * t;
    if (n & 1)
      t = t * a;
    return t;
  }
};

template <class T> struct BiCoef {
  vector<T> fact_, inv_, finv_;
  constexpr BiCoef() {}
  constexpr BiCoef(int n) noexcept : fact_(n, 1), inv_(n, 1), finv_(n, 1) {
    init(n);
  }
  constexpr void init(int n) noexcept {
    fact_.assign(n, 1), inv_.assign(n, 1), finv_.assign(n, 1);
    int MOD = fact_[0].getmod();
    for (int i = 2; i < n; i++) {
      fact_[i] = fact_[i - 1] * i;
      inv_[i] = -inv_[MOD % i] * (MOD / i);
      finv_[i] = finv_[i - 1] * inv_[i];
    }
  }
  constexpr T com(int n, int k) const noexcept {
    if (n < k || n < 0 || k < 0)
      return 0;
    return fact_[n] * finv_[k] * finv_[n - k];
  }
  constexpr T fact(int n) const noexcept {
    if (n < 0)
      return 0;
    return fact_[n];
  }
  constexpr T inv(int n) const noexcept {
    if (n < 0)
      return 0;
    return inv_[n];
  }
  constexpr T finv(int n) const noexcept {
    if (n < 0)
      return 0;
    return finv_[n];
  }
};

using mint = Fp<MOD>;

// DPテーブル
const int MAX = 3010;

mint two = 2;

void solve() {
  int N, X;
  cin >> N >> X;
  vector<int> a(N);
  for (int i = 0; i < N; ++i)
    cin >> a[i];

  // DP
  vector<vector<mint>> dp(N + 1, vector<mint>(MAX));
  dp[0][0] = 1;
  for (int i = 0; i < N; ++i) {
    for (int j = 0; j < MAX; ++j) {
      dp[i + 1][j] += two * dp[i][j];
      if (j + a[i] < MAX)
        dp[i + 1][j + a[i]] += dp[i][j];
    }
  }

  cout << dp[N][X] << endl;
}

int main() {
#ifdef MYLOCAL
  vector<string> filenames{"input1.txt", "input2.txt", "input3.txt",
                           "input4.txt", "input5.txt"};
  cout << "------------\\n";
  for (int i = 0; i < CASES; ++i) {
    ifstream in(filenames[i]);
    cin.rdbuf(in.rdbuf());
    solve();
    cout << "------------\\n";
  }
#else

  solve();

#endif
  return 0;
}


Error: TLE

Fixed submission:

#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ld = long double;
using pint = pair<int, int>;
using pll = pair<ll, ll>;
using Edge = pair<int, ll>;
using Graph = vector<vector<int>>;
using WeightedGraph = vector<vector<Edge>>;
const ll INF64 = 1LL << 60;
const int INF32 = 1 << 29;
const ll MOD = 998244353;

const int CASES = 3;

template <int MOD> struct Fp {
  long long val;
  constexpr Fp(long long v = 0) noexcept : val(v % MOD) {
    if (val < 0)
      v += MOD;
  }
  constexpr int getmod() { return MOD; }
  constexpr Fp operator-() const noexcept { return val ? MOD - val : 0; }
  constexpr Fp operator+(const Fp &r) const noexcept { return Fp(*this) += r; }
  constexpr Fp operator-(const Fp &r) const noexcept { return Fp(*this) -= r; }
  constexpr Fp operator*(const Fp &r) const noexcept { return Fp(*this) *= r; }
  constexpr Fp operator/(const Fp &r) const noexcept { return Fp(*this) /= r; }
  constexpr Fp &operator+=(const Fp &r) noexcept {
    val += r.val;
    if (val >= MOD)
      val -= MOD;
    return *this;
  }
  constexpr Fp &operator-=(const Fp &r) noexcept {
    val -= r.val;
    if (val < 0)
      val += MOD;
    return *this;
  }
  constexpr Fp &operator*=(const Fp &r) noexcept {
    val = val * r.val % MOD;
    return *this;
  }
  constexpr Fp &operator/=(const Fp &r) noexcept {
    long long a = r.val, b = MOD, u = 1, v = 0;
    while (b) {
      long long t = a / b;
      a -= t * b;
      swap(a, b);
      u -= t * v;
      swap(u, v);
    }
    val = val * u % MOD;
    if (val < 0)
      val += MOD;
    return *this;
  }
  constexpr bool operator==(const Fp &r) const noexcept {
    return this->val == r.val;
  }
  constexpr bool operator!=(const Fp &r) const noexcept {
    return this->val != r.val;
  }
  friend constexpr ostream &operator<<(ostream &os, const Fp<MOD> &x) noexcept {
    return os << x.val;
  }
  friend constexpr istream &operator>>(istream &is, Fp<MOD> &x) noexcept {
    return is >> x.val;
  }
  friend constexpr Fp<MOD> modpow(const Fp<MOD> &a, long long n) noexcept {
    if (n == 0)
      return 1;
    auto t = modpow(a, n / 2);
    t = t * t;
    if (n & 1)
      t = t * a;
    return t;
  }
};

template <class T> struct BiCoef {
  vector<T> fact_, inv_, finv_;
  constexpr BiCoef() {}
  constexpr BiCoef(int n) noexcept : fact_(n, 1), inv_(n, 1), finv_(n, 1) {
    init(n);
  }
  constexpr void init(int n) noexcept {
    fact_.assign(n, 1), inv_.assign(n, 1), finv_.assign(n, 1);
    int MOD = fact_[0].getmod();
    for (int i = 2; i < n; i++) {
      fact_[i] = fact_[i - 1] * i;
      inv_[i] = -inv_[MOD % i] * (MOD / i);
      finv_[i] = finv_[i - 1] * inv_[i];
    }
  }
  constexpr T com(int n, int k) const noexcept {
    if (n < k || n < 0 || k < 0)
      return 0;
    return fact_[n] * finv_[k] * finv_[n - k];
  }
  constexpr T fact(int n) const noexcept {
    if (n < 0)
      return 0;
    return fact_[n];
  }
  constexpr T inv(int n) const noexcept {
    if (n < 0)
      return 0;
    return inv_[n];
  }
  constexpr T finv(int n) const noexcept {
    if (n < 0)
      return 0;
    return finv_[n];
  }
};

using mint = Fp<MOD>;

// DPテーブル
const int MAX = 3010;

void rec(const vector<vector<long long>> &dp, const vector<int> &a, int i,
         int j, int keiro, vector<int> &ans) {
  if (i == 0) {
    if (j == 0) {
      ans.push_back(keiro);
    }
    return;
  }

  // 上へ遡る (dp[i-1][j] == 0) だったら無視)
  if (dp[i - 1][j]) {
    rec(dp, a, i - 1, j, keiro, ans);
  }

  // 左上へ遡る (dp[i-1][j-a[i-1]] == 0 だったら無視)
  if (j - a[i - 1] >= 0 && dp[i - 1][j - a[i - 1]]) {
    ++keiro;
    rec(dp, a, i - 1, j - a[i - 1], keiro, ans);
    --keiro;
  }
}

void solve() {
  int N, X;
  cin >> N >> X;
  vector<int> a(N);
  for (int i = 0; i < N; ++i)
    cin >> a[i];

  // DP
  vector<vector<long long>> dp(N + 1, vector<long long>(MAX, 0));
  dp[0][0] = 1;
  for (int i = 0; i < N; ++i) {
    for (int j = 0; j < MAX; ++j) {
      dp[i + 1][j] += dp[i][j];
      if (j + a[i] < MAX)
        dp[i + 1][j + a[i]] += dp[i][j];
    }
  }

  // 復元
  int keiro = 0;
  vector<int> ans;
  rec(dp, a, N, X, keiro, ans);
  mint sum = 0;
  mint two = 2;
  for (int i = 0; i < ans.size(); ++i) {
    ll m = ans[i];
    ll rem = N - m;
    sum += modpow(two, rem);
  }
  cout << sum << endl;
}

int main() {
#ifdef MYLOCAL
  vector<string> filenames{"input1.txt", "input2.txt", "input3.txt",
                           "input4.txt", "input5.txt"};
  cout << "------------\\n";
  for (int i = 0; i < CASES; ++i) {
    ifstream in(filenames[i]);
    cin.rdbuf(in.rdbuf());
    solve();
    cout << "------------\\n";
  }
#else

  solve();

#endif
  return 0;
}