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

#ifdef LOCAL
#define _GLIBCXX_DEBUG
#define __clock__
#else
#pragma GCC optimize("Ofast")
#endif
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ld = long double;
using VI = vector<ll>;
using VV = vector<VI>;
using VS = vector<string>;
using PII = pair<ll, ll>;

// tourist set
template <typename A, typename B> string to_string(pair<A, B> p);

template <typename A, typename B, typename C>
string to_string(tuple<A, B, C> p);

template <typename A, typename B, typename C, typename D>
string to_string(tuple<A, B, C, D> p);

string to_string(const string &s) { return '"' + s + '"'; }

string to_string(const char *s) { return to_string((string)s); }

string to_string(bool b) { return (b ? "true" : "false"); }

string to_string(vector<bool> v) {
  bool first = true;
  string res = "{";
  for (int i = 0; i < static_cast<int>(v.size()); i++) {
    if (!first) {
      res += ", ";
    }
    first = false;
    res += to_string(v[i]);
  }
  res += "}";
  return res;
}

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) + ")";
}

template <typename A, typename B, typename C>
string to_string(tuple<A, B, C> p) {
  return "(" + to_string(get<0>(p)) + ", " + to_string(get<1>(p)) + ", " +
         to_string(get<2>(p)) + ")";
}

template <typename A, typename B, typename C, typename D>
string to_string(tuple<A, B, C, D> p) {
  return "(" + to_string(get<0>(p)) + ", " + to_string(get<1>(p)) + ", " +
         to_string(get<2>(p)) + ", " + to_string(get<3>(p)) + ")";
}

void debug_out() { cerr << '\\n'; }

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
// tourist set end

template <class T> bool chmax(T &a, const T &b) {
  if (a < b) {
    a = b;
    return 1;
  }
  return 0;
}
template <class T> bool chmin(T &a, const T &b) {
  if (b < a) {
    a = b;
    return 1;
  }
  return 0;
}

#define FOR(i, a, b) for (ll i = (a); i < (b); ++i)
#define rep(i, b) FOR(i, 0, b)
#define ALL(v) (v).begin(), (v).end()
#define p(s) cout << (s) << '\\n'
#define p2(s, t) cout << (s) << " " << (t) << '\\n'
#define br() p("")
#define pn(s) cout << (#s) << " " << (s) << '\\n'
#define SZ(x) ((int)(x).size())
#define SORT(A) sort(ALL(A))
#define RSORT(A) sort(ALL(A), greater<ll>())
#define MP make_pair
#define p_yes() p("YES")
#define p_no() p("NO")

ll SUM(VI &V) { return accumulate(ALL(V), 0LL); }

ll MIN(VI &V) { return *min_element(ALL(V)); }
ll MAX(VI &V) { return *max_element(ALL(V)); }

void print_vector(VI &V) {
  ll n = V.size();
  rep(i, n) {
    if (i)
      cout << ' ';
    cout << V[i];
  }
  cout << endl;
}

ll gcd(ll a, ll b) {
  if (b == 0)
    return a;
  return gcd(b, a % b);
}

ll lcm(ll a, ll b) {
  ll g = gcd(a, b);
  return a / g * b;
}

// long double
using ld = long double;
#define EPS (1e-14)
#define equals(a, b) (fabs((a) - (b)) < EPS)

void no() {
  p_no();
  exit(0);
}
void yes() {
  p_yes();
  exit(0);
}

const ll mod = 1e9 + 7;
const ll inf = 1e18;
const double PI = acos(-1);

// snuke's mint
// auto mod int
// https://youtu.be/L8grWxBlIZ4?t=9858
// https://youtu.be/ERZuLAxZffQ?t=4807 : optimize
// https://youtu.be/8uowVvQ_-Mo?t=1329 : division
// const int mod = 1000000007;
struct mint {
  ll x; // typedef long long ll;
  mint(ll x = 0) : x((x % mod + mod) % mod) {}
  mint operator-() const { return mint(-x); }
  mint &operator+=(const mint a) {
    if ((x += a.x) >= mod)
      x -= mod;
    return *this;
  }
  mint &operator-=(const mint a) {
    if ((x += mod - a.x) >= mod)
      x -= mod;
    return *this;
  }
  mint &operator*=(const mint a) {
    (x *= a.x) %= mod;
    return *this;
  }
  mint operator+(const mint a) const {
    mint res(*this);
    return res += a;
  }
  mint operator-(const mint a) const {
    mint res(*this);
    return res -= a;
  }
  mint operator*(const mint a) const {
    mint res(*this);
    return res *= a;
  }
  mint pow(ll t) const {
    if (!t)
      return 1;
    mint a = pow(t >> 1);
    a *= a;
    if (t & 1)
      a *= *this;
    return a;
  }

  // for prime mod
  mint inv() const { return pow(mod - 2); }
  mint &operator/=(const mint a) { return (*this) *= a.inv(); }
  mint operator/(const mint a) const {
    mint res(*this);
    return res /= a;
  }
};

// for codeforces
void solve() {
  ll N;
  cin >> N;
  VI A(N);
  rep(i, N) { cin >> A[i]; }
}

ll memo_x[15][1LL << 15];
ll memo_y[15][1LL << 15];
void initialize() {
  rep(i, 15) {
    rep(j, 1LL << 15) {
      memo_x[i][j] = inf;
      memo_y[i][j] = inf;
    }
  }
}

int main() {
  cin.tie(0);
  ios::sync_with_stdio(false);

  // input
  ll N;
  cin >> N;

  VI X(N);
  VI Y(N);
  VI P(N);
  rep(i, N) { cin >> X[i] >> Y[i] >> P[i]; }

  VI Ans(N + 1, inf);

  // 0:none
  // 1:x line
  // 2:y line

  auto dist = [&](ll idx, ll f, char type) {
    if (type == 'x' && memo_x[idx][f] != inf)
      return memo_x[idx][f];
    if (type == 'y' && memo_y[idx][f] != inf)
      return memo_y[idx][f];

    ll pos;
    if (type == 'x') {
      pos = X[idx];
    } else {
      pos = Y[idx];
    }

    VI Xs = {0};
    rep(i, N) {
      if (f >> i & 1) {
        if (type == 'x') {
          Xs.push_back(X[i]);
        } else {
          Xs.push_back(Y[i]);
        }
      }
    }
    ll min_dist = inf;
    for (ll x : Xs) {
      chmin(min_dist, abs(pos - x));
    }

    if (type == 'x') {
      return memo_x[idx][f] = min_dist;
    } else {
      return memo_y[idx][f] = min_dist;
    }
  };

  // 高速化のための前処理（メモ）
  initialize();
  rep(i, N) {
    rep(j, 1LL << N) {
      dist(i, j, 'x');
      dist(i, j, 'y');
    }
  }

  // スコアを求めて挿入
  auto calc = [&](VI &V) {
    ll fx = 0; // flag
    ll fy = 0;

    ll line_count = 0;
    rep(i, N) {
      ll v = V[i];
      if (v == 1) {
        fx += (1LL << i);
        line_count++;
      } else if (v == 2) {
        fy += (1LL << i);
        line_count++;
      }
    }

    // スコア計算
    ll sum = 0;
    rep(i, N) {
      ll min_distance = inf;
      // for(ll x : Xs){
      //   ll diff = abs(X[i] - x);
      //   chmin(min_distance, diff);
      // }
      // for(ll y : Ys){
      //   ll diff = abs(Y[i] - y);
      //   chmin(min_distance, diff);
      // }
      chmin(min_distance, dist(i, fx, 'x'));
      chmin(min_distance, dist(i, fy, 'y'));
      sum += min_distance * P[i];
    }
    chmin(Ans[line_count], sum);
  };

  function<void(VI &)> dfs = [&](VI &V) {
    if (SZ(V) == N) {
      calc(V);
      return;
    }
    rep(i, 3) {
      V.push_back(i);
      dfs(V);
      V.pop_back();
    }
  };

  VI V;
  dfs(V);

  rep(i, N + 1) { p(Ans[i]); }

  return 0;
}

Error: TLE

Fixed submission:

#ifdef LOCAL
#define _GLIBCXX_DEBUG
#define __clock__
#else
#pragma GCC optimize("Ofast")
#endif
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ld = long double;
using VI = vector<ll>;
using VV = vector<VI>;
using VS = vector<string>;
using PII = pair<ll, ll>;

// tourist set
template <typename A, typename B> string to_string(pair<A, B> p);

template <typename A, typename B, typename C>
string to_string(tuple<A, B, C> p);

template <typename A, typename B, typename C, typename D>
string to_string(tuple<A, B, C, D> p);

string to_string(const string &s) { return '"' + s + '"'; }

string to_string(const char *s) { return to_string((string)s); }

string to_string(bool b) { return (b ? "true" : "false"); }

string to_string(vector<bool> v) {
  bool first = true;
  string res = "{";
  for (int i = 0; i < static_cast<int>(v.size()); i++) {
    if (!first) {
      res += ", ";
    }
    first = false;
    res += to_string(v[i]);
  }
  res += "}";
  return res;
}

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) + ")";
}

template <typename A, typename B, typename C>
string to_string(tuple<A, B, C> p) {
  return "(" + to_string(get<0>(p)) + ", " + to_string(get<1>(p)) + ", " +
         to_string(get<2>(p)) + ")";
}

template <typename A, typename B, typename C, typename D>
string to_string(tuple<A, B, C, D> p) {
  return "(" + to_string(get<0>(p)) + ", " + to_string(get<1>(p)) + ", " +
         to_string(get<2>(p)) + ", " + to_string(get<3>(p)) + ")";
}

void debug_out() { cerr << '\\n'; }

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
// tourist set end

template <class T> bool chmax(T &a, const T &b) {
  if (a < b) {
    a = b;
    return 1;
  }
  return 0;
}
template <class T> bool chmin(T &a, const T &b) {
  if (b < a) {
    a = b;
    return 1;
  }
  return 0;
}

#define FOR(i, a, b) for (ll i = (a); i < (b); ++i)
#define rep(i, b) FOR(i, 0, b)
#define ALL(v) (v).begin(), (v).end()
#define p(s) cout << (s) << '\\n'
#define p2(s, t) cout << (s) << " " << (t) << '\\n'
#define br() p("")
#define pn(s) cout << (#s) << " " << (s) << '\\n'
#define SZ(x) ((int)(x).size())
#define SORT(A) sort(ALL(A))
#define RSORT(A) sort(ALL(A), greater<ll>())
#define MP make_pair
#define p_yes() p("YES")
#define p_no() p("NO")

ll SUM(VI &V) { return accumulate(ALL(V), 0LL); }

ll MIN(VI &V) { return *min_element(ALL(V)); }
ll MAX(VI &V) { return *max_element(ALL(V)); }

void print_vector(VI &V) {
  ll n = V.size();
  rep(i, n) {
    if (i)
      cout << ' ';
    cout << V[i];
  }
  cout << endl;
}

ll gcd(ll a, ll b) {
  if (b == 0)
    return a;
  return gcd(b, a % b);
}

ll lcm(ll a, ll b) {
  ll g = gcd(a, b);
  return a / g * b;
}

// long double
using ld = long double;
#define EPS (1e-14)
#define equals(a, b) (fabs((a) - (b)) < EPS)

void no() {
  p_no();
  exit(0);
}
void yes() {
  p_yes();
  exit(0);
}

const ll mod = 1e9 + 7;
const ll inf = 1e18;
const double PI = acos(-1);

// snuke's mint
// auto mod int
// https://youtu.be/L8grWxBlIZ4?t=9858
// https://youtu.be/ERZuLAxZffQ?t=4807 : optimize
// https://youtu.be/8uowVvQ_-Mo?t=1329 : division
// const int mod = 1000000007;
struct mint {
  ll x; // typedef long long ll;
  mint(ll x = 0) : x((x % mod + mod) % mod) {}
  mint operator-() const { return mint(-x); }
  mint &operator+=(const mint a) {
    if ((x += a.x) >= mod)
      x -= mod;
    return *this;
  }
  mint &operator-=(const mint a) {
    if ((x += mod - a.x) >= mod)
      x -= mod;
    return *this;
  }
  mint &operator*=(const mint a) {
    (x *= a.x) %= mod;
    return *this;
  }
  mint operator+(const mint a) const {
    mint res(*this);
    return res += a;
  }
  mint operator-(const mint a) const {
    mint res(*this);
    return res -= a;
  }
  mint operator*(const mint a) const {
    mint res(*this);
    return res *= a;
  }
  mint pow(ll t) const {
    if (!t)
      return 1;
    mint a = pow(t >> 1);
    a *= a;
    if (t & 1)
      a *= *this;
    return a;
  }

  // for prime mod
  mint inv() const { return pow(mod - 2); }
  mint &operator/=(const mint a) { return (*this) *= a.inv(); }
  mint operator/(const mint a) const {
    mint res(*this);
    return res /= a;
  }
};

// for codeforces
void solve() {
  ll N;
  cin >> N;
  VI A(N);
  rep(i, N) { cin >> A[i]; }
}

// Xs is sorted
ll f(ll x, VI &Xs) {
  auto it = lower_bound(ALL(Xs), x);
  if (it == Xs.end()) {
    it--;
    return abs(x - *it);
  }
  if (*it == x) {
    return 0;
  } else {
    ll a = *it;
    ll b = a;
    if (it != Xs.begin()) {
      it--;
      b = *it;
    }
    ll dist0 = abs(x - a);
    ll dist1 = abs(x - b);
    return min(dist0, dist1);
  }
}

int main() {
  cin.tie(0);
  ios::sync_with_stdio(false);

  // input
  ll N;
  cin >> N;

  VI X(N);
  VI Y(N);
  VI P(N);
  rep(i, N) { cin >> X[i] >> Y[i] >> P[i]; }

  VI Ans(N + 1, inf);

  // 0:none
  // 1:x line
  // 2:y line

  // スコアを求めて挿入
  auto calc = [&](VI &V) {
    VI Xs = {0};
    VI Ys = {0};
    ll line_count = 0;
    rep(i, N) {
      ll v = V[i];
      if (v == 1) {
        Xs.push_back(X[i]);
        line_count++;
      } else if (v == 2) {
        Ys.push_back(Y[i]);
        line_count++;
      }
    }
    SORT(Xs);
    SORT(Ys);

    // スコア計算
    ll sum = 0;
    rep(i, N) {
      ll min_distance = inf;
      // for(ll x : Xs){
      //   ll diff = abs(X[i] - x);
      //   chmin(min_distance, diff);
      // }
      // for(ll y : Ys){
      //   ll diff = abs(Y[i] - y);
      //   chmin(min_distance, diff);
      // }
      chmin(min_distance, f(X[i], Xs));
      chmin(min_distance, f(Y[i], Ys));
      sum += min_distance * P[i];
    }
    chmin(Ans[line_count], sum);
  };

  function<void(VI &)> dfs = [&](VI &V) {
    if (SZ(V) == N) {
      calc(V);
      return;
    }
    rep(i, 3) {
      V.push_back(i);
      dfs(V);
      V.pop_back();
    }
  };

  VI V;
  dfs(V);

  rep(i, N + 1) { p(Ans[i]); }

  return 0;
}