Problem p02604 (C++) — buggy submission, verdict: Time Limit Exceeded

// >>> TEMPLATES
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ld = long double;
using i32 = int32_t;
using i64 = int64_t;
using u32 = uint32_t;
using u64 = uint64_t;
#define int ll
#define double ld
#define rep(i, n) for (int i = 0; i < (int)(n); i++)
#define rep1(i, n) for (int i = 1; i <= (int)(n); i++)
#define repR(i, n) for (int i = (int)(n)-1; i >= 0; i--)
#define rep1R(i, n) for (int i = (int)(n); i >= 1; i--)
#define loop(i, a, B) for (int i = a; i B; i++)
#define loopR(i, a, B) for (int i = a; i B; i--)
#define all(x) (x).begin(), (x).end()
#define allR(x) (x).rbegin(), (x).rend()
#define pb push_back
#define eb emplace_back
#define mp make_pair
#define fst first
#define snd second
template <class Int> auto constexpr inf = numeric_limits<Int>::max() / 2 - 1;
auto constexpr INF32 = inf<int32_t>;
auto constexpr INF64 = inf<int64_t>;
auto constexpr INF = inf<int>;
#ifdef LOCAL
#include "debug.hpp"
#else
#define dump(...) (void)(0)
#define say(x) (void)(0)
#define debug if (0)
#endif
template <class T> using pque_max = priority_queue<T>;
template <class T> using pque_min = priority_queue<T, vector<T>, greater<T>>;
template <class T, class = typename T::iterator,
          class = typename enable_if<!is_same<T, string>::value>::type>
ostream &operator<<(ostream &os, T const &v) {
  bool f = true;
  for (auto const &x : v)
    os << (f ? "" : " ") << x, f = false;
  return os;
}
template <class T, class = typename T::iterator,
          class = typename enable_if<!is_same<T, string>::value>::type>
istream &operator>>(istream &is, T &v) {
  for (auto &x : v)
    is >> x;
  return is;
}
template <class T, class S>
ostream &operator<<(ostream &os, pair<T, S> const &p) {
  return os << "(" << p.first << ", " << p.second << ")";
}
template <class T, class S> istream &operator>>(istream &is, pair<T, S> &p) {
  return is >> p.first >> p.second;
}
struct IOSetup {
  IOSetup() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(15);
  }
} iosetup;
template <class F> struct FixPoint : private F {
  constexpr FixPoint(F &&f) : F(forward<F>(f)) {}
  template <class... T> constexpr auto operator()(T &&...x) const {
    return F::operator()(*this, forward<T>(x)...);
  }
};
struct MakeFixPoint {
  template <class F> constexpr auto operator|(F &&f) const {
    return FixPoint<F>(forward<F>(f));
  }
};
#define MFP MakeFixPoint() |
#define def(name, ...) auto name = MFP[&](auto &&name, __VA_ARGS__)
template <class T, size_t d> struct vec_impl {
  using type = vector<typename vec_impl<T, d - 1>::type>;
  template <class... U> static type make_v(size_t n, U &&...x) {
    return type(n, vec_impl<T, d - 1>::make_v(forward<U>(x)...));
  }
};
template <class T> struct vec_impl<T, 0> {
  using type = T;
  static type make_v(T const &x = {}) { return x; }
};
template <class T, size_t d = 1> using vec = typename vec_impl<T, d>::type;
template <class T, size_t d = 1, class... Args> auto make_v(Args &&...args) {
  return vec_impl<T, d>::make_v(forward<Args>(args)...);
}
template <class T> void quit(T const &x) {
  cout << x << endl;
  exit(0);
}
template <class T, class U> constexpr bool chmin(T &x, U const &y) {
  if (x > y) {
    x = y;
    return true;
  }
  return false;
}
template <class T, class U> constexpr bool chmax(T &x, U const &y) {
  if (x < y) {
    x = y;
    return true;
  }
  return false;
}
template <class It> constexpr auto sumof(It b, It e) {
  return accumulate(b, e, typename iterator_traits<It>::value_type{});
}
template <class T> int sz(T const &x) { return x.size(); }
template <class C, class T> int lbd(C const &v, T const &x) {
  return lower_bound(v.begin(), v.end(), x) - v.begin();
}
template <class C, class T> int ubd(C const &v, T const &x) {
  return upper_bound(v.begin(), v.end(), x) - v.begin();
}
const int dx[] = {1, 0, -1, 0};
const int dy[] = {0, 1, 0, -1};
constexpr int popcnt(ll x) { return __builtin_popcountll(x); }
template <class Int> struct Random {
  mt19937_64 mt{random_device{}()};
  // mt19937_64 mt{(unsigned)time(0)};
  Int a, b; // [a,b]
  Random(Int a, Int b) : a(a), b(b) {}
  Int operator()() { return uniform_int_distribution<Int>(a, b)(mt); }
};
template <class Int> Int rand(Int a, Int b) { // [a,b]
  static mt19937_64 mt{random_device{}()};
  return uniform_int_distribution<Int>(a, b)(mt);
}
// <<<
bool next_product(int m, vector<int> &v) {
  rep(i, v.size()) {
    if (++v[i] < m)
      return true;
    v[i] = 0;
  }
  return false;
}

int32_t main() {
  int n;
  cin >> n;
  vector<int> x(n), y(n), p(n);
  rep(i, n) cin >> x[i] >> y[i] >> p[i];

  vector<int> ord_x(n), ord_y(n);
  iota(all(ord_x), 0);
  sort(all(ord_x), [&](int i, int j) { return x[i] < x[j]; });
  iota(all(ord_y), 0);
  sort(all(ord_y), [&](int i, int j) { return y[i] < y[j]; });

  vector<int> ans(n + 1, INF), a(n), b(n), v(n);
  do {
    int k = 0;
    rep(i, n) if (v[i] != 0) k++;
    if (k > n)
      continue;

    rep(i, n) a[i] = abs(x[i]);
    rep(_, 2) {
      int pre = -1;
      for (int i : ord_x) {
        if (v[i] == 1)
          pre = i;
        if (pre >= 0)
          chmin(a[i], abs(x[i] - x[pre]));
      }
      reverse(all(ord_x));
    }

    rep(i, n) b[i] = abs(y[i]);
    rep(_, 2) {
      int pre = -1;
      for (int i : ord_y) {
        if (v[i] == 2)
          pre = i;
        if (pre >= 0)
          chmin(b[i], abs(y[i] - y[pre]));
      }
      reverse(all(ord_y));
    }

    int s = 0;
    rep(i, n) s += p[i] * min(a[i], b[i]);
    chmin(ans[k], s);

  } while (next_product(3, v));

  rep(k, n + 1) cout << ans[k] << "\\n";
}


Error: TLE

Fixed submission:

// >>> TEMPLATES
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ld = long double;
using i32 = int32_t;
using i64 = int64_t;
using u32 = uint32_t;
using u64 = uint64_t;
#define int ll
#define double ld
#define rep(i, n) for (int i = 0; i < (int)(n); i++)
#define rep1(i, n) for (int i = 1; i <= (int)(n); i++)
#define repR(i, n) for (int i = (int)(n)-1; i >= 0; i--)
#define rep1R(i, n) for (int i = (int)(n); i >= 1; i--)
#define loop(i, a, B) for (int i = a; i B; i++)
#define loopR(i, a, B) for (int i = a; i B; i--)
#define all(x) (x).begin(), (x).end()
#define allR(x) (x).rbegin(), (x).rend()
#define pb push_back
#define eb emplace_back
#define mp make_pair
#define fst first
#define snd second
template <class Int> auto constexpr inf = numeric_limits<Int>::max() / 2 - 1;
auto constexpr INF32 = inf<int32_t>;
auto constexpr INF64 = inf<int64_t>;
auto constexpr INF = inf<int>;
#ifdef LOCAL
#include "debug.hpp"
#else
#define dump(...) (void)(0)
#define say(x) (void)(0)
#define debug if (0)
#endif
template <class T> using pque_max = priority_queue<T>;
template <class T> using pque_min = priority_queue<T, vector<T>, greater<T>>;
template <class T, class = typename T::iterator,
          class = typename enable_if<!is_same<T, string>::value>::type>
ostream &operator<<(ostream &os, T const &v) {
  bool f = true;
  for (auto const &x : v)
    os << (f ? "" : " ") << x, f = false;
  return os;
}
template <class T, class = typename T::iterator,
          class = typename enable_if<!is_same<T, string>::value>::type>
istream &operator>>(istream &is, T &v) {
  for (auto &x : v)
    is >> x;
  return is;
}
template <class T, class S>
ostream &operator<<(ostream &os, pair<T, S> const &p) {
  return os << "(" << p.first << ", " << p.second << ")";
}
template <class T, class S> istream &operator>>(istream &is, pair<T, S> &p) {
  return is >> p.first >> p.second;
}
struct IOSetup {
  IOSetup() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(15);
  }
} iosetup;
template <class F> struct FixPoint : private F {
  constexpr FixPoint(F &&f) : F(forward<F>(f)) {}
  template <class... T> constexpr auto operator()(T &&...x) const {
    return F::operator()(*this, forward<T>(x)...);
  }
};
struct MakeFixPoint {
  template <class F> constexpr auto operator|(F &&f) const {
    return FixPoint<F>(forward<F>(f));
  }
};
#define MFP MakeFixPoint() |
#define def(name, ...) auto name = MFP[&](auto &&name, __VA_ARGS__)
template <class T, size_t d> struct vec_impl {
  using type = vector<typename vec_impl<T, d - 1>::type>;
  template <class... U> static type make_v(size_t n, U &&...x) {
    return type(n, vec_impl<T, d - 1>::make_v(forward<U>(x)...));
  }
};
template <class T> struct vec_impl<T, 0> {
  using type = T;
  static type make_v(T const &x = {}) { return x; }
};
template <class T, size_t d = 1> using vec = typename vec_impl<T, d>::type;
template <class T, size_t d = 1, class... Args> auto make_v(Args &&...args) {
  return vec_impl<T, d>::make_v(forward<Args>(args)...);
}
template <class T> void quit(T const &x) {
  cout << x << endl;
  exit(0);
}
template <class T, class U> constexpr bool chmin(T &x, U const &y) {
  if (x > y) {
    x = y;
    return true;
  }
  return false;
}
template <class T, class U> constexpr bool chmax(T &x, U const &y) {
  if (x < y) {
    x = y;
    return true;
  }
  return false;
}
template <class It> constexpr auto sumof(It b, It e) {
  return accumulate(b, e, typename iterator_traits<It>::value_type{});
}
template <class T> int sz(T const &x) { return x.size(); }
template <class C, class T> int lbd(C const &v, T const &x) {
  return lower_bound(v.begin(), v.end(), x) - v.begin();
}
template <class C, class T> int ubd(C const &v, T const &x) {
  return upper_bound(v.begin(), v.end(), x) - v.begin();
}
const int dx[] = {1, 0, -1, 0};
const int dy[] = {0, 1, 0, -1};
constexpr int popcnt(ll x) { return __builtin_popcountll(x); }
template <class Int> struct Random {
  mt19937_64 mt{random_device{}()};
  // mt19937_64 mt{(unsigned)time(0)};
  Int a, b; // [a,b]
  Random(Int a, Int b) : a(a), b(b) {}
  Int operator()() { return uniform_int_distribution<Int>(a, b)(mt); }
};
template <class Int> Int rand(Int a, Int b) { // [a,b]
  static mt19937_64 mt{random_device{}()};
  return uniform_int_distribution<Int>(a, b)(mt);
}
// <<<
bool next_product(int m, vector<int> &v) {
  rep(i, v.size()) {
    if (++v[i] < m)
      return true;
    v[i] = 0;
  }
  return false;
}

int32_t main() {
  int n;
  cin >> n;
  vector<int> x(n), y(n), p(n);
  rep(i, n) cin >> x[i] >> y[i] >> p[i];

  vector<int> ans(n + 1, INF), v(n);
  set<int> a, b;
  do {
    a.clear();
    b.clear();
    rep(i, n) {
      if (v[i] == 1)
        a.insert(x[i]);
      if (v[i] == 2)
        b.insert(y[i]);
    }
    int k = a.size() + b.size();
    if (k > n)
      continue;

    a.insert(0);
    a.insert(-INF);
    a.insert(+INF);
    b.insert(0);
    b.insert(-INF);
    b.insert(+INF);
    int s = 0;
    rep(i, n) {
      int xx = [&]() {
        auto it = a.lower_bound(x[i]);
        auto jt = prev(it);
        return min(abs(x[i] - *it), abs(x[i] - *jt));
      }();
      int yy = [&]() {
        auto it = b.lower_bound(y[i]);
        auto jt = prev(it);
        return min(abs(y[i] - *it), abs(y[i] - *jt));
      }();
      s += p[i] * min(xx, yy);
    }

    chmin(ans[k], s);

  } while (next_product(3, v));

  rep(k, n + 1) cout << ans[k] << "\\n";
}