Problem p02648 (C++) — buggy submission, verdict: Time Limit Exceeded

#include <algorithm>
#include <cassert>
#include <chrono>
#include <cmath>
#include <cstdio>
#include <ctime>
#include <functional>
#include <iostream>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <string>
#include <tuple>
#include <utility>
#include <vector>
using namespace std;

namespace {
using Integer = long long; //__int128;
template <class T, class S> istream &operator>>(istream &is, pair<T, S> &p) {
  return is >> p.first >> p.second;
}
template <class T> istream &operator>>(istream &is, vector<T> &vec) {
  for (T &val : vec)
    is >> val;
  return is;
}
template <class T> istream &operator,(istream &is, T &val) { return is >> val; }
template <class T, class S>
ostream &operator<<(ostream &os, const pair<T, S> &p) {
  return os << p.first << " " << p.second;
}
template <class T> ostream &operator<<(ostream &os, const vector<T> &vec) {
  for (size_t i = 0; i < vec.size(); i++)
    os << vec[i] << (i == vec.size() - 1 ? "" : " ");
  return os;
}
template <class T> ostream &operator,(ostream &os, const T &val) {
  return os << " " << val;
}

template <class H> void print(const H &head) { cout << head; }
template <class H, class... T> void print(const H &head, const T &...tail) {
  cout << head << " ";
  print(tail...);
}
template <class... T> void println(const T &...values) {
  print(values...);
  cout << endl;
}

template <class H> void eprint(const H &head) { cerr << head; }
template <class H, class... T> void eprint(const H &head, const T &...tail) {
  cerr << head << " ";
  eprint(tail...);
}
template <class... T> void eprintln(const T &...values) {
  eprint(values...);
  cerr << endl;
}

class range {
  Integer start_, end_, step_;

public:
  struct range_iterator {
    Integer val, step_;
    range_iterator(Integer v, Integer step) : val(v), step_(step) {}
    Integer operator*() { return val; }
    void operator++() { val += step_; }
    bool operator!=(range_iterator &x) {
      return step_ > 0 ? val < x.val : val > x.val;
    }
  };
  range(Integer len) : start_(0), end_(len), step_(1) {}
  range(Integer start, Integer end) : start_(start), end_(end), step_(1) {}
  range(Integer start, Integer end, Integer step)
      : start_(start), end_(end), step_(step) {}
  range_iterator begin() { return range_iterator(start_, step_); }
  range_iterator end() { return range_iterator(end_, step_); }
};

inline string operator"" _s(const char *str, size_t size) {
  return move(string(str));
}
constexpr Integer my_pow(Integer x, Integer k, Integer z = 1) {
  return k == 0    ? z
         : k == 1  ? z * x
         : (k & 1) ? my_pow(x * x, k >> 1, z * x)
                   : my_pow(x * x, k >> 1, z);
}
constexpr Integer my_pow_mod(Integer x, Integer k, Integer M, Integer z = 1) {
  return k == 0    ? z % M
         : k == 1  ? z * x % M
         : (k & 1) ? my_pow_mod(x * x % M, k >> 1, M, z * x % M)
                   : my_pow_mod(x * x % M, k >> 1, M, z);
}
constexpr unsigned long long operator"" _ten(unsigned long long value) {
  return my_pow(10, value);
}

inline int k_bit(Integer x, int k) { return (x >> k) & 1; } // 0-indexed

mt19937 mt(chrono::duration_cast<chrono::nanoseconds>(
               chrono::steady_clock::now().time_since_epoch())
               .count());

template <class T> string join(const vector<T> &v, const string &sep) {
  stringstream ss;
  for (size_t i = 0; i < v.size(); i++) {
    if (i > 0)
      ss << sep;
    ss << v[i];
  }
  return ss.str();
}

inline string operator*(string s, int k) {
  string ret;
  while (k) {
    if (k & 1)
      ret += s;
    s += s;
    k >>= 1;
  }
  return ret;
}
} // namespace

struct Data {
  vector<pair<int, int>> vw;
  vector<pair<int, int>> query;
  vector<vector<int>> q_ids;
  vector<long long> ans;

  array<long long, 1 << 9> dp_v{};
  array<long long, 1 << 9> dp_w{};

  array<long long, 1 << 9> dp_v_{};
  array<long long, 1 << 9> dp_w_{};
  vector<pair<long long, long long>> max_v; // {w, v}
};

void dfs(Data &data, vector<pair<int, int>> &pack, int pos, int depth) {
  if (pos >= data.vw.size())
    return;

  pack.push_back(data.vw[pos]);

  if (depth <= 8) {
    for (int i = 0; i < (1 << depth); i++) {
      data.dp_v[i | (1 << depth)] = data.dp_v[i] + data.vw[pos].first;
      data.dp_w[i | (1 << depth)] = data.dp_w[i] + data.vw[pos].second;
    }
  } else {
    int d = depth - 9;
    for (int i = 0; i < (1 << d); i++) {
      data.dp_v_[i | (1 << d)] = data.dp_v_[i] + data.vw[pos].first;
      data.dp_w_[i | (1 << d)] = data.dp_w_[i] + data.vw[pos].second;
    }
  }
  if (depth == 8) {
    data.max_v.resize(0);
    data.max_v.emplace_back(0, 0);
    data.max_v.emplace_back(1ll << 60, 0);
    for (int i = 1; i < data.dp_v.size(); i++) {
      data.max_v.emplace_back(data.dp_w[i], data.dp_v[i]);
    }
    sort(begin(data.max_v), end(data.max_v));
    for (int i = 1; i < data.max_v.size(); i++) {
      data.max_v[i].second =
          max(data.max_v[i].second, data.max_v[i - 1].second);
    }
  }

  int l = pos * 2;
  int r = l + 1;

  dfs(data, pack, l, depth + 1);
  dfs(data, pack, r, depth + 1);

  for (int id : data.q_ids[pos]) {
    int v, l;
    tie(v, l) = data.query[id];
    long long tmp = 0;
    if (depth <= 8) {
      for (int i = 0; i < (1 << (depth + 1)); i++) {
        if (data.dp_w[i] <= l) {
          tmp = max(tmp, data.dp_v[i]);
        }
      }
    } else {
      int d = depth - 9;
      for (int i = 0; i < (1 << (d + 1)); i++) {
        if (data.dp_w_[i] > l)
          continue;
        long long r = l - data.dp_w_[i];
        auto itr = prev(lower_bound(begin(data.max_v), end(data.max_v),
                                    pair<long long, long long>{r + 1, 0}));
        tmp = max(tmp, data.dp_v_[i] + itr->second);
      }
    }
    data.ans[id] = tmp;
  }

  pack.pop_back();
}

int main() {
  int n;
  cin >> n;

  vector<pair<int, int>> vw(n + 1);
  for (int i = 1; i <= n; i++) {
    cin >> vw[i];
  }

  int q;
  cin >> q;

  vector<pair<int, int>> query(q);
  cin >> query;

  vector<vector<int>> q_ids(n + 1);
  for (int i = 0; i < q; i++) {
    int v, l;
    tie(v, l) = query[i];
    q_ids[v].push_back(i);
  }

  vector<long long> ans(q);
  Data data{
      vw,
      query,
      q_ids,
      ans,
  };

  vector<pair<int, int>> pack;
  dfs(data, pack, 1, 0);

  println(join(data.ans, "\\n"));

  return 0;
}


Error: TLE

Fixed submission:

#include <algorithm>
#include <cassert>
#include <chrono>
#include <cmath>
#include <cstdio>
#include <ctime>
#include <functional>
#include <iostream>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <string>
#include <tuple>
#include <utility>
#include <vector>
using namespace std;

namespace {
using Integer = long long; //__int128;
template <class T, class S> istream &operator>>(istream &is, pair<T, S> &p) {
  return is >> p.first >> p.second;
}
template <class T> istream &operator>>(istream &is, vector<T> &vec) {
  for (T &val : vec)
    is >> val;
  return is;
}
template <class T> istream &operator,(istream &is, T &val) { return is >> val; }
template <class T, class S>
ostream &operator<<(ostream &os, const pair<T, S> &p) {
  return os << p.first << " " << p.second;
}
template <class T> ostream &operator<<(ostream &os, const vector<T> &vec) {
  for (size_t i = 0; i < vec.size(); i++)
    os << vec[i] << (i == vec.size() - 1 ? "" : " ");
  return os;
}
template <class T> ostream &operator,(ostream &os, const T &val) {
  return os << " " << val;
}

template <class H> void print(const H &head) { cout << head; }
template <class H, class... T> void print(const H &head, const T &...tail) {
  cout << head << " ";
  print(tail...);
}
template <class... T> void println(const T &...values) {
  print(values...);
  cout << endl;
}

template <class H> void eprint(const H &head) { cerr << head; }
template <class H, class... T> void eprint(const H &head, const T &...tail) {
  cerr << head << " ";
  eprint(tail...);
}
template <class... T> void eprintln(const T &...values) {
  eprint(values...);
  cerr << endl;
}

class range {
  Integer start_, end_, step_;

public:
  struct range_iterator {
    Integer val, step_;
    range_iterator(Integer v, Integer step) : val(v), step_(step) {}
    Integer operator*() { return val; }
    void operator++() { val += step_; }
    bool operator!=(range_iterator &x) {
      return step_ > 0 ? val < x.val : val > x.val;
    }
  };
  range(Integer len) : start_(0), end_(len), step_(1) {}
  range(Integer start, Integer end) : start_(start), end_(end), step_(1) {}
  range(Integer start, Integer end, Integer step)
      : start_(start), end_(end), step_(step) {}
  range_iterator begin() { return range_iterator(start_, step_); }
  range_iterator end() { return range_iterator(end_, step_); }
};

inline string operator"" _s(const char *str, size_t size) {
  return move(string(str));
}
constexpr Integer my_pow(Integer x, Integer k, Integer z = 1) {
  return k == 0    ? z
         : k == 1  ? z * x
         : (k & 1) ? my_pow(x * x, k >> 1, z * x)
                   : my_pow(x * x, k >> 1, z);
}
constexpr Integer my_pow_mod(Integer x, Integer k, Integer M, Integer z = 1) {
  return k == 0    ? z % M
         : k == 1  ? z * x % M
         : (k & 1) ? my_pow_mod(x * x % M, k >> 1, M, z * x % M)
                   : my_pow_mod(x * x % M, k >> 1, M, z);
}
constexpr unsigned long long operator"" _ten(unsigned long long value) {
  return my_pow(10, value);
}

inline int k_bit(Integer x, int k) { return (x >> k) & 1; } // 0-indexed

mt19937 mt(chrono::duration_cast<chrono::nanoseconds>(
               chrono::steady_clock::now().time_since_epoch())
               .count());

template <class T> string join(const vector<T> &v, const string &sep) {
  stringstream ss;
  for (size_t i = 0; i < v.size(); i++) {
    if (i > 0)
      ss << sep;
    ss << v[i];
  }
  return ss.str();
}

inline string operator*(string s, int k) {
  string ret;
  while (k) {
    if (k & 1)
      ret += s;
    s += s;
    k >>= 1;
  }
  return ret;
}
} // namespace

struct Data {
  vector<pair<int, int>> vw;
  vector<pair<int, int>> query;
  vector<vector<int>> q_ids;
  vector<long long> ans;
};

struct Knapsack {
  vector<pair<int, int>> vw;
  long long max_w;
  long long lb = 0;
  const int use = 1;
  const int unuse = 2;
  const int unknown = 0;

  pair<pair<double, double>, bool> get_ub(vector<int> &state) {
    double v = 0;
    double w = 0;

    bool feasible = true;
    for (int i = 0; i < state.size(); i++) {
      double r = max_w - w;
      if (state[i] == use) {
        v += vw[i].first;
        w += vw[i].second;
      } else if (state[i] == unuse) {
        continue;
      } else {
        if (r > vw[i].second) {
          double k = r;
          double p = k / vw[i].second;
          feasible = false;
          v += vw[i].first * p;
          w += k;
        } else {
          v += vw[i].first;
          w += vw[i].second;
        }
      }
      if (feasible && w <= max_w) {
        lb = max<long long>(lb, v);
      }
      if (r <= 0.0)
        break;
    }
    if (w > max_w)
      feasible = false;
    return {{v, w}, feasible};
  }

  Knapsack(vector<pair<int, int>> pack, long long max_w_)
      : vw(pack), max_w(max_w_) {
    sort(begin(vw), end(vw), [&](pair<int, int> a, pair<int, int> b) {
      return a.first * (long long)b.second > b.first * (long long)a.second;
    });
    int n = vw.size();

    vector<int> state(n, unknown);
    solve(state, 0, max_w);
  }

  long long solve(vector<int> &state, int pos, long long rem_w) {
    auto relax = get_ub(state);
    if (relax.second == true) {
      lb = max<long long>(relax.first.first, lb);
      return lb;
    }
    if (relax.first.first <= lb)
      return 0;

    bool can_put = false;
    for (int i = pos; i < vw.size(); i++) {
      if (rem_w >= vw[i].second) {
        can_put = true;
        break;
      }
    }

    if (pos == vw.size() || !can_put) {
      return 0;
    }

    long long res = 0;
    if (rem_w >= vw[pos].second) {
      state[pos] = use;
      long long res_use = solve(state, pos + 1, rem_w - vw[pos].second);
      lb = max<long long>(res_use, lb);
    }

    state[pos] = unuse;
    long long res_unuse = solve(state, pos + 1, rem_w);
    lb = max<long long>(res_unuse, lb);

    state[pos] = unknown;
    return lb;
  }
};

void dfs(Data &data, vector<pair<int, int>> &pack, int pos) {
  if (pos >= data.vw.size())
    return;

  pack.push_back(data.vw[pos]);

  int l = pos * 2;
  int r = l + 1;

  dfs(data, pack, l);
  dfs(data, pack, r);

  for (int id : data.q_ids[pos]) {
    int v, l;
    tie(v, l) = data.query[id];

    Knapsack k(pack, l);

    long long tmp = k.lb;
    data.ans[id] = tmp;
  }

  pack.pop_back();
}

int main() {
  int n;
  cin >> n;

  vector<pair<int, int>> vw(n + 1);
  for (int i = 1; i <= n; i++) {
    cin >> vw[i];
  }

  int q;
  cin >> q;

  vector<pair<int, int>> query(q);
  cin >> query;

  vector<vector<int>> q_ids(n + 1);
  for (int i = 0; i < q; i++) {
    int v, l;
    tie(v, l) = query[i];
    q_ids[v].push_back(i);
  }

  vector<long long> ans(q);
  Data data{
      vw,
      query,
      q_ids,
      ans,
  };

  vector<pair<int, int>> pack;
  dfs(data, pack, 1);

  println(join(data.ans, "\\n"));

  return 0;
}