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

#include <bits/stdc++.h>
#define rep(i, n) for (ll i = 0; i < (ll)(n); ++i)
#define rep2(i, s, n) for (ll i = s; i < (ll)(n); i++)
#define repr(i, n) for (ll i = n; i >= 0; i--)
#define pb push_back
#define COUT(x) cout << (x) << "\\n"
#define COUTF(x) cout << setprecision(15) << (x) << "\\n"
#define ENDL cout << "\\n"
#define DF(x) x.erase(x.begin())
#define ALL(x) x.begin(), x.end()
#define SORT(x) sort(ALL(x))
#define REVERSE(x) reverse(ALL(x))
#define ANS cout << ans << "\\n"
#define init()                                                                 \\
  cin.tie(0);                                                                  \\
  ios::sync_with_stdio(false)
#define LINE cerr << "[debug] line: " << __LINE__ << "\\n";
#define debug(x) cerr << "[debug] " << #x << ": " << x << "\\n";
#define debugV(v)                                                              \\
  cerr << "[debugV] " << #v << ":";                                            \\
  rep(i, v.size()) cerr << " " << v[i];                                        \\
  cerr << "\\n";
using namespace std;
using ll = long long;
using ld = long double;
using vll = vector<ll>;
using vvll = vector<vector<ll>>;
using mll = map<ll, ll>;
using qll = queue<ll>;
using P = pair<ll, ll>;
using vp = vector<P>;
using vs = vector<string>;

template <typename T> inline istream &operator>>(istream &i, vector<T> &v) {
  rep(j, v.size()) i >> v[j];
  return i;
}

template <typename T1, typename T2>
inline istream &operator>>(istream &i, pair<T1, T2> &v) {
  return i >> v.first >> v.second;
}

constexpr ll INF = 0x3f3f3f3f3f3f3f3f;
constexpr ld PI = 3.141592653589793238462643383279;
ll get_digit(ll x) { return to_string(x).size(); }

ll gcd(ll x, ll y) { return y ? gcd(y, x % y) : x; }

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

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;
}

vector<P> factorize(ll n) {
  vector<P> result;
  for (ll i = 2; i * i <= n; ++i) {
    if (n % i == 0) {
      result.pb({i, 0});
      while (n % i == 0) {
        n /= i;
        result.back().second++;
      }
    }
  }
  if (n != 1) {
    result.pb({n, 1});
  }
  return result;
}

vll divisor(ll n) {
  vll ret;
  for (ll i = 1; i * i <= n; i++) {
    if (n % i == 0) {
      ret.push_back(i);
      if (i * i != n)
        ret.push_back(n / i);
    }
  }
  SORT(ret);
  return (ret);
}

const int mod = 1000000007;
struct mint {
  ll x;
  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 { return mint(*this) += a; }
  mint operator-(const mint a) const { return mint(*this) -= a; }
  mint operator*(const mint a) const { return mint(*this) *= 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 { return mint(*this) /= a; }
};
istream &operator>>(istream &is, const mint &a) { return is >> a.x; }
ostream &operator<<(ostream &os, const mint &a) { return os << a.x; }

struct combination {
  vector<mint> fact, ifact;
  combination(ll n) : fact(n + 1), ifact(n + 1) {
    assert(n < mod);
    fact[0] = 1;
    for (ll i = 1; i <= n; ++i) {
      fact[i] = fact[i - 1] * i;
    }
    ifact[n] = fact[n].inv();
    for (ll i = n; i >= 1; --i) {
      ifact[i - 1] = ifact[i] * i;
    }
  }
  mint operator()(ll n, ll k) {
    if (k < 0 || k > n)
      return 0;
    return fact[n] * ifact[k] * ifact[n - k];
  }
};

ll dp[20][20];

vll calc(vp &a) {
  ll n = a.size();
  SORT(a);
  rep(i, n + 1) rep(j, n + 1) dp[i][j] = INF;
  dp[0][0] = 0;
  rep(l, n) {
    for (ll r = l + 1; r <= n; ++r) {
      {
        ll now = INF;
        for (ll k = l; k < r; ++k) {
          ll s = 0;
          for (ll i = l; i < r; ++i) {
            s += abs(a[i].first - a[k].first) * ll(a[i].second);
          }
          chmin(now, s);
        }
        rep(j, n) chmin(dp[r][j + 1], dp[l][j] + now);
      }
      {
        ll now = 0;
        for (ll i = l; i < r; ++i) {
          now += abs(a[i].first) * ll(a[i].second);
        }
        rep(j, n + 1) chmin(dp[r][j], dp[l][j] + now);
      }
    }
  }
  vll res(n + 1, INF);
  rep(j, n + 1) res[j] = dp[n][j];
  return res;
}

signed main() {
  init();
  ll n;
  cin >> n;
  vll x(n), y(n), p(n);
  rep(i, n) cin >> x[i] >> y[i] >> p[i];

  vll ans(n + 1, INF);
  rep(s, 1 << n) {
    vp ax, ay;
    rep(i, n) {
      if (s >> i & 1)
        ax.emplace_back(x[i], p[i]);
      else
        ay.emplace_back(y[i], p[i]);
    }
    vll dx = calc(ax);
    vll dy = calc(ay);

    rep(i, dx.size()) rep(j, dy.size()) { chmin(ans[i + j], dx[i] + dy[j]); }
  }

  rep(i, n + 1) { COUT(ans[i]); }

  return 0;
}

Error: TLE

Fixed submission:

#include <bits/stdc++.h>
#define rep(i, n) for (ll i = 0; i < (ll)(n); ++i)
#define rep2(i, s, n) for (ll i = s; i < (ll)(n); i++)
#define repr(i, n) for (ll i = n; i >= 0; i--)
#define pb push_back
#define COUT(x) cout << (x) << "\\n"
#define COUTF(x) cout << setprecision(15) << (x) << "\\n"
#define ENDL cout << "\\n"
#define DF(x) x.erase(x.begin())
#define ALL(x) x.begin(), x.end()
#define SORT(x) sort(ALL(x))
#define REVERSE(x) reverse(ALL(x))
#define ANS cout << ans << "\\n"
#define init()                                                                 \\
  cin.tie(0);                                                                  \\
  ios::sync_with_stdio(false)
#define LINE cerr << "[debug] line: " << __LINE__ << "\\n";
#define debug(x) cerr << "[debug] " << #x << ": " << x << "\\n";
#define debugV(v)                                                              \\
  cerr << "[debugV] " << #v << ":";                                            \\
  rep(i, v.size()) cerr << " " << v[i];                                        \\
  cerr << "\\n";
using namespace std;
using ll = long long;
using ld = long double;
using vll = vector<ll>;
using vvll = vector<vector<ll>>;
using mll = map<ll, ll>;
using qll = queue<ll>;
using P = pair<ll, ll>;
using vp = vector<P>;
using vs = vector<string>;

template <typename T> inline istream &operator>>(istream &i, vector<T> &v) {
  rep(j, v.size()) i >> v[j];
  return i;
}

template <typename T1, typename T2>
inline istream &operator>>(istream &i, pair<T1, T2> &v) {
  return i >> v.first >> v.second;
}

constexpr ll INF = 0x3f3f3f3f3f3f3f3f;
constexpr ld PI = 3.141592653589793238462643383279;
ll get_digit(ll x) { return to_string(x).size(); }

ll gcd(ll x, ll y) { return y ? gcd(y, x % y) : x; }

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

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;
}

vector<P> factorize(ll n) {
  vector<P> result;
  for (ll i = 2; i * i <= n; ++i) {
    if (n % i == 0) {
      result.pb({i, 0});
      while (n % i == 0) {
        n /= i;
        result.back().second++;
      }
    }
  }
  if (n != 1) {
    result.pb({n, 1});
  }
  return result;
}

vll divisor(ll n) {
  vll ret;
  for (ll i = 1; i * i <= n; i++) {
    if (n % i == 0) {
      ret.push_back(i);
      if (i * i != n)
        ret.push_back(n / i);
    }
  }
  SORT(ret);
  return (ret);
}

const int mod = 1000000007;
struct mint {
  ll x;
  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 { return mint(*this) += a; }
  mint operator-(const mint a) const { return mint(*this) -= a; }
  mint operator*(const mint a) const { return mint(*this) *= 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 { return mint(*this) /= a; }
};
istream &operator>>(istream &is, const mint &a) { return is >> a.x; }
ostream &operator<<(ostream &os, const mint &a) { return os << a.x; }

struct combination {
  vector<mint> fact, ifact;
  combination(ll n) : fact(n + 1), ifact(n + 1) {
    assert(n < mod);
    fact[0] = 1;
    for (ll i = 1; i <= n; ++i) {
      fact[i] = fact[i - 1] * i;
    }
    ifact[n] = fact[n].inv();
    for (ll i = n; i >= 1; --i) {
      ifact[i - 1] = ifact[i] * i;
    }
  }
  mint operator()(ll n, ll k) {
    if (k < 0 || k > n)
      return 0;
    return fact[n] * ifact[k] * ifact[n - k];
  }
};

vll calc(vp a) {
  ll n = a.size();
  SORT(a);
  vll res(n + 1, INF);
  rep(s, 1 << n) {
    vll p(1, 0);
    rep(i, n) if (s >> i & 1) p.pb(a[i].first);
    SORT(p);
    ll now = 0;
    ll pi = 0;
    rep(i, n) {
      ll x = a[i].first;
      while (pi + 1 < p.size() && p[pi + 1] < x)
        i++;
      ll m = abs(x - p[pi]);
      if (pi + 1 < p.size())
        chmin(m, abs(x - p[pi + 1]));
      rep(j, p.size()) chmin(m, abs(p[j] - a[i].first));
      now += m * a[i].second;
    }
    ll b = p.size() - 1;
    chmin(res[b], now);
  }
  return res;
}

signed main() {
  init();
  ll n;
  cin >> n;
  vll x(n), y(n), p(n);
  rep(i, n) cin >> x[i] >> y[i] >> p[i];

  vll ans(n + 1, INF);
  rep(s, 1 << n) {
    vp ax, ay;
    rep(i, n) {
      if (s >> i & 1)
        ax.emplace_back(x[i], p[i]);
      else
        ay.emplace_back(y[i], p[i]);
    }
    vll dx = calc(ax);
    vll dy = calc(ay);

    rep(i, dx.size()) rep(j, dy.size()) { chmin(ans[i + j], dx[i] + dy[j]); }
  }

  rep(i, n + 1) { COUT(ans[i]); }

  return 0;
}