Problem p03313 (C++)

Buggy submission (status: Time Limit Exceeded):
#define LOCAL
#ifdef LOCAL
#define _GLIBCXX_DEBUG
#endif
#include <bits/stdc++.h>
using namespace std;
#define rep(i, x) for (ll i = 0; i < (ll)(x); i++)
#define rrep(i, x) for (ll i = (ll)(x)-1; 0 <= i; i--)
#define reps(i, x) for (ll i = 1; i < (ll)(x) + 1; i++)
#define rreps(i, x) for (ll i = (ll)(x); 1 <= i; i--)
#define all(x) (x).begin(), (x).end()
typedef long long ll;
typedef long double ld;
typedef pair<ll, ll> Pll;
typedef vector<ll> vl;
typedef vector<vl> vvl;
typedef vector<vvl> vvvl;
constexpr ll INF = numeric_limits<ll>::max() / 4;
constexpr ll n_max = 2e5 + 10;
#define int ll

template <typename A, typename B> string to_string(pair<A, B> p);
string to_string(const string &s) { return '"' + s + '"'; }
string to_string(const char c) { return to_string((string)&c); }
string to_string(bool b) { return (b ? "true" : "false"); }
template <size_t N> string to_string(bitset<N> v) {
  string res = "";
  for (size_t i = 0; i < N; i++)
    res += static_cast<char>('0' + v[i]);
  return res;
}
template <typename A> string to_string(A v) {
  bool first = true;
  string res = "{";
  for (const auto &x : v) {
    if (!first)
      res += ", ";
    first = false;
    res += to_string(x);
  }
  res += "}";
  return res;
}
template <typename A, typename B> string to_string(pair<A, B> p) {
  return "(" + to_string(p.first) + ", " + to_string(p.second) + ")";
}

void debug_out() { cerr << endl; }
template <typename Head, typename... Tail> void debug_out(Head H, Tail... T) {
  cerr << " " << to_string(H);
  debug_out(T...);
}

#ifdef LOCAL
#define debug(...) cerr << "[" << #__VA_ARGS__ << "]:", debug_out(__VA_ARGS__)
#else
#define debug(...) 42
#endif

template <class T> bool chmax(T &a, T b) {
  if (a < b) {
    a = b;
    return true;
  }
  return false;
}
template <class T> bool chmin(T &a, T b) {
  if (a > b) {
    a = b;
    return true;
  }
  return false;
}

signed main() {
  cin.tie(nullptr);
  ios::sync_with_stdio(false);
  ll N;
  cin >> N;
  ll n = 1LL << N;
  vector<ll> a(n);
  rep(i, n) cin >> a[i];
  vector<vector<Pll>> dp(n, vector<Pll>(N + 1, {0, 0}));
  rep(i, n) { dp[i][0] = {a[i], 0}; }
  auto merge = [&](Pll &a, Pll &b) -> Pll {
    vector<ll> vec = {a.first, a.second, b.first, b.second};
    sort(all(vec), greater<ll>());
    return {vec[0], vec[1]};
  };
  rep(i, n) {
    rep(j, N) {
      if ((i >> j) & 1) {
        dp[i][j + 1] = merge(dp[i][j], dp[i & ~(1LL << j)][j]);
      } else {
        dp[i][j + 1] = dp[i][j];
      }
    }
  }

  vector<ll> ans(n);
  reps(i, n - 1) {
    chmax(ans[i], ans[i - 1]);
    chmax(ans[i], dp[i][N].first + dp[i][N].second);
  }

  reps(i, n - 1) { cout << ans[i] << endl; }
}

Fixed submission:
#define LOCAL
#ifdef LOCAL
#define _GLIBCXX_DEBUG
#endif
#include <bits/stdc++.h>
using namespace std;
#define rep(i, x) for (ll i = 0; i < (ll)(x); i++)
#define rrep(i, x) for (ll i = (ll)(x)-1; 0 <= i; i--)
#define reps(i, x) for (ll i = 1; i < (ll)(x) + 1; i++)
#define rreps(i, x) for (ll i = (ll)(x); 1 <= i; i--)
#define all(x) (x).begin(), (x).end()
typedef long long ll;
typedef long double ld;
typedef pair<ll, ll> Pll;
typedef vector<ll> vl;
typedef vector<vl> vvl;
typedef vector<vvl> vvvl;
constexpr ll INF = numeric_limits<ll>::max() / 4;
constexpr ll n_max = 2e5 + 10;
#define int ll

template <typename A, typename B> string to_string(pair<A, B> p);
string to_string(const string &s) { return '"' + s + '"'; }
string to_string(const char c) { return to_string((string)&c); }
string to_string(bool b) { return (b ? "true" : "false"); }
template <size_t N> string to_string(bitset<N> v) {
  string res = "";
  for (size_t i = 0; i < N; i++)
    res += static_cast<char>('0' + v[i]);
  return res;
}
template <typename A> string to_string(A v) {
  bool first = true;
  string res = "{";
  for (const auto &x : v) {
    if (!first)
      res += ", ";
    first = false;
    res += to_string(x);
  }
  res += "}";
  return res;
}
template <typename A, typename B> string to_string(pair<A, B> p) {
  return "(" + to_string(p.first) + ", " + to_string(p.second) + ")";
}

void debug_out() { cerr << endl; }
template <typename Head, typename... Tail> void debug_out(Head H, Tail... T) {
  cerr << " " << to_string(H);
  debug_out(T...);
}

#ifdef LOCAL
#define debug(...) cerr << "[" << #__VA_ARGS__ << "]:", debug_out(__VA_ARGS__)
#else
#define debug(...) 42
#endif

template <class T> bool chmax(T &a, T b) {
  if (a < b) {
    a = b;
    return true;
  }
  return false;
}
template <class T> bool chmin(T &a, T b) {
  if (a > b) {
    a = b;
    return true;
  }
  return false;
}

signed main() {
  cin.tie(nullptr);
  ios::sync_with_stdio(false);
  ll N;
  cin >> N;
  ll n = 1LL << N;
  vector<ll> a(n);
  rep(i, n) cin >> a[i];
  vector<vector<Pll>> dp(n, vector<Pll>(N + 1, {0, 0}));
  rep(i, n) { dp[i][0] = {a[i], 0}; }
  auto merge = [&](Pll &a, Pll &b) -> Pll {
    Pll ret;
    if (a.first > b.first) {
      ret.first = a.first;
      if (a.second > b.first)
        ret.second = a.second;
      else
        ret.second = b.first;
    } else {
      ret.first = b.first;
      if (a.first > b.second)
        ret.second = a.first;
      else
        ret.second = b.second;
    }
    return ret;
  };
  rep(i, n) {
    rep(j, N) {
      if ((i >> j) & 1) {
        dp[i][j + 1] = merge(dp[i][j], dp[i & ~(1LL << j)][j]);
      } else {
        dp[i][j + 1] = dp[i][j];
      }
    }
  }

  vector<ll> ans(n);
  reps(i, n - 1) {
    chmax(ans[i], ans[i - 1]);
    chmax(ans[i], dp[i][N].first + dp[i][N].second);
  }

  reps(i, n - 1) { cout << ans[i] << endl; }
}