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

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
#define pb(x) push_back(x)
#define mp(a, b) make_pair(a, b)
#define all(x) x.begin(), x.end()
#define rall(x) x.rbegin(), x.rend()
#define lscan(x) scanf("%I64d", &x)
#define lprint(x) printf("%I64d", x)
#define rep(i, n) for (int i = 0; i < n; i++)
#define rep2(i, n) for (int i = n - 1; i >= 0; i--)
const int mod = 1000000007;
ll gcd(ll a, ll b) {
  ll c = a % b;
  while (c != 0) {
    a = b;
    b = c;
    c = a % b;
  }
  return b;
}
long long extGCD(long long a, long long b, long long &x, long long &y) {
  if (b == 0) {
    x = 1;
    y = 0;
    return a;
  }
  long long d = extGCD(b, a % b, y, x);
  y -= a / b * x;
  return d;
}

struct UnionFind {
  vector<ll> data;

  UnionFind(int sz) { data.assign(sz, -1); }

  bool unite(int x, int y) {
    x = find(x), y = find(y);
    if (x == y)
      return (false);
    if (data[x] > data[y])
      swap(x, y);
    data[x] += data[y];
    data[y] = x;
    return (true);
  }

  int find(int k) {
    if (data[k] < 0)
      return (k);
    return (data[k] = find(data[k]));
  }

  ll size(int k) { return (-data[find(k)]); }
};

ll M = 1000000007;

vector<ll> fac(2000011);  // n!(mod M)
vector<ll> ifac(2000011); // k!^{M-2} (mod M)

ll mpow(ll x, ll n) {
  ll ans = 1;
  while (n != 0) {
    if (n & 1)
      ans = ans * x % M;
    x = x * x % M;
    n = n >> 1;
  }
  return ans;
}
ll mpow2(ll x, ll n, ll mod) {
  ll ans = 1;
  while (n != 0) {
    if (n & 1)
      ans = ans * x % mod;
    x = x * x % mod;
    n = n >> 1;
  }
  return ans;
}
void setcomb() {
  fac[0] = 1;
  ifac[0] = 1;
  for (ll i = 0; i < 2000010; i++) {
    fac[i + 1] = fac[i] * (i + 1) % M; // n!(mod M)
  }
  ifac[2000010] = mpow(fac[2000010], M - 2);
  for (ll i = 2000010; i > 0; i--) {
    ifac[i - 1] = ifac[i] * i % M;
  }
}
ll comb(ll a, ll b) {
  if (a == 0 && b == 0)
    return 1;
  if (a < b || a < 0)
    return 0;
  ll tmp = ifac[a - b] * ifac[b] % M;
  return tmp * fac[a] % M;
}
ll perm(ll a, ll b) {
  if (a == 0 && b == 0)
    return 1;
  if (a < b || a < 0)
    return 0;
  return fac[a] * ifac[a - b] % M;
}
long long modinv(long long a) {
  long long b = M, u = 1, v = 0;
  while (b) {
    long long t = a / b;
    a -= t * b;
    swap(a, b);
    u -= t * v;
    swap(u, v);
  }
  u %= M;
  if (u < 0)
    u += M;
  return u;
}
ll modinv2(ll a, ll mod) {
  ll b = mod, u = 1, v = 0;
  while (b) {
    ll t = a / b;
    a -= t * b;
    swap(a, b);
    u -= t * v;
    swap(u, v);
  }
  u %= mod;
  if (u < 0)
    u += mod;
  return u;
}

template <int mod> struct ModInt {
  int x;

  ModInt() : x(0) {}

  ModInt(int64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}

  ModInt &operator+=(const ModInt &p) {
    if ((x += p.x) >= mod)
      x -= mod;
    return *this;
  }

  ModInt &operator-=(const ModInt &p) {
    if ((x += mod - p.x) >= mod)
      x -= mod;
    return *this;
  }

  ModInt &operator*=(const ModInt &p) {
    x = (int)(1LL * x * p.x % mod);
    return *this;
  }

  ModInt &operator/=(const ModInt &p) {
    *this *= p.inverse();
    return *this;
  }

  ModInt operator-() const { return ModInt(-x); }

  ModInt operator+(const ModInt &p) const { return ModInt(*this) += p; }

  ModInt operator-(const ModInt &p) const { return ModInt(*this) -= p; }

  ModInt operator*(const ModInt &p) const { return ModInt(*this) *= p; }

  ModInt operator/(const ModInt &p) const { return ModInt(*this) /= p; }

  bool operator==(const ModInt &p) const { return x == p.x; }

  bool operator!=(const ModInt &p) const { return x != p.x; }

  ModInt inverse() const {
    int a = x, b = mod, u = 1, v = 0, t;
    while (b > 0) {
      t = a / b;
      swap(a -= t * b, b);
      swap(u -= t * v, v);
    }
    return ModInt(u);
  }

  ModInt pow(int64_t n) const {
    ModInt ret(1), mul(x);
    while (n > 0) {
      if (n & 1)
        ret *= mul;
      mul *= mul;
      n >>= 1;
    }
    return ret;
  }

  friend ostream &operator<<(ostream &os, const ModInt &p) { return os << p.x; }

  friend istream &operator>>(istream &is, ModInt &a) {
    int64_t t;
    is >> t;
    a = ModInt<mod>(t);
    return (is);
  }

  static int get_mod() { return mod; }
};

using mint = ModInt<mod>;

vector<vector<ll>> mul(vector<vector<ll>> a, vector<vector<ll>> b, int n) {
  int i, j, k, t;
  vector<vector<ll>> c(n);
  for (i = 0; i < n; i++) {
    for (j = 0; j < n; j++) {
      t = 0;
      for (k = 0; k < n; k++)
        t = (t + a[i][k] * b[k][j] % M) % M;
      c[i].push_back(t);
    }
  }
  return c;
}

template <typename Monoid> struct SegmentTree {
  using F = function<Monoid(Monoid, Monoid)>;

  int sz;
  vector<Monoid> seg;

  const F f;
  const Monoid M1;

  SegmentTree(int n, const F f, const Monoid &M1) : f(f), M1(M1) {
    sz = 1;
    while (sz < n)
      sz <<= 1;
    seg.assign(2 * sz, M1);
  }

  void set(int k, const Monoid &x) { seg[k + sz] = x; }

  void build() {
    for (int k = sz - 1; k > 0; k--) {
      seg[k] = f(seg[2 * k + 0], seg[2 * k + 1]);
    }
  }

  void update(int k, const Monoid &x) {
    k += sz;
    seg[k] = x;
    while (k >>= 1) {
      seg[k] = f(seg[2 * k + 0], seg[2 * k + 1]);
    }
  }

  Monoid query(int a, int b) {
    Monoid L = M1, R = M1;
    for (a += sz, b += sz; a < b; a >>= 1, b >>= 1) {
      if (a & 1)
        L = f(L, seg[a++]);
      if (b & 1)
        R = f(seg[--b], R);
    }
    return f(L, R);
  }

  Monoid operator[](const int &k) const { return seg[k + sz]; }

  template <typename C>
  int find_subtree(int a, const C &check, Monoid &M, bool type) {
    while (a < sz) {
      Monoid nxt = type ? f(seg[2 * a + type], M) : f(M, seg[2 * a + type]);
      if (check(nxt))
        a = 2 * a + type;
      else
        M = nxt, a = 2 * a + 1 - type;
    }
    return a - sz;
  }

  template <typename C> int find_first(int a, const C &check) {
    Monoid L = M1;
    if (a <= 0) {
      if (check(f(L, seg[1])))
        return find_subtree(1, check, L, false);
      return -1;
    }
    int b = sz;
    for (a += sz, b += sz; a < b; a >>= 1, b >>= 1) {
      if (a & 1) {
        Monoid nxt = f(L, seg[a]);
        if (check(nxt))
          return find_subtree(a, check, L, false);
        L = nxt;
        ++a;
      }
    }
    return -1;
  }

  template <typename C> int find_last(int b, const C &check) {
    Monoid R = M1;
    if (b >= sz) {
      if (check(f(seg[1], R)))
        return find_subtree(1, check, R, true);
      return -1;
    }
    int a = sz;
    for (b += sz; a < b; a >>= 1, b >>= 1) {
      if (b & 1) {
        Monoid nxt = f(seg[--b], R);
        if (check(nxt))
          return find_subtree(b, check, R, true);
        R = nxt;
      }
    }
    return -1;
  }
};

template <unsigned mod> struct RollingHash {
  vector<unsigned> hashed, power;

  inline unsigned mul(unsigned a, unsigned b) const {
    unsigned long long x = (unsigned long long)a * b;
    unsigned xh = (unsigned)(x >> 32), xl = (unsigned)x, d, m;
    asm("divl %4; \\n\\t" : "=a"(d), "=d"(m) : "d"(xh), "a"(xl), "r"(mod));
    return m;
  }

  RollingHash(const string &s, unsigned base = 10007) {
    int sz = (int)s.size();
    hashed.assign(sz + 1, 0);
    power.assign(sz + 1, 0);
    power[0] = 1;
    for (int i = 0; i < sz; i++) {
      power[i + 1] = mul(power[i], base);
      hashed[i + 1] = mul(hashed[i], base) + s[i];
      if (hashed[i + 1] >= mod)
        hashed[i + 1] -= mod;
    }
  }

  unsigned get(int l, int r) const {
    unsigned ret = hashed[r] + mod - mul(hashed[l], power[r - l]);
    if (ret >= mod)
      ret -= mod;
    return ret;
  }

  unsigned connect(unsigned h1, int h2, int h2len) const {
    unsigned ret = mul(h1, power[h2len]) + h2;
    if (ret >= mod)
      ret -= mod;
    return ret;
  }

  int LCP(const RollingHash<mod> &b, int l1, int r1, int l2, int r2) {
    int len = min(r1 - l1, r2 - l2);
    int low = -1, high = len + 1;
    while (high - low > 1) {
      int mid = (low + high) / 2;
      if (get(l1, l1 + mid) == b.get(l2, l2 + mid))
        low = mid;
      else
        high = mid;
    }
    return (low);
  }
};

using RH = RollingHash<1000000007>;

template <typename T> struct edge {
  int src, to;
  T cost;

  edge(int to, T cost) : src(-1), to(to), cost(cost) {}

  edge(int src, int to, T cost) : src(src), to(to), cost(cost) {}

  edge &operator=(const int &x) {
    to = x;
    return *this;
  }

  operator int() const { return to; }
};

template <typename T> using Edges = vector<edge<T>>;
template <typename T> using WeightedGraph = vector<Edges<T>>;
using UnWeightedGraph = vector<vector<int>>;
template <typename T> using Matrix = vector<vector<T>>;

template <typename G> struct DoublingLowestCommonAncestor {
  const int LOG;
  vector<int> dep;
  const G &g;
  vector<vector<int>> table;

  DoublingLowestCommonAncestor(const G &g)
      : g(g), dep(g.size()), LOG(32 - __builtin_clz(g.size())) {
    table.assign(LOG, vector<int>(g.size(), -1));
  }

  void dfs(int idx, int par, int d) {
    table[0][idx] = par;
    dep[idx] = d;
    for (auto &to : g[idx]) {
      if (to != par)
        dfs(to, idx, d + 1);
    }
  }

  void build() {
    dfs(0, -1, 0);
    for (int k = 0; k + 1 < LOG; k++) {
      for (int i = 0; i < table[k].size(); i++) {
        if (table[k][i] == -1)
          table[k + 1][i] = -1;
        else
          table[k + 1][i] = table[k][table[k][i]];
      }
    }
  }

  int query(int u, int v) {
    if (dep[u] > dep[v])
      swap(u, v);
    for (int i = LOG - 1; i >= 0; i--) {
      if (((dep[v] - dep[u]) >> i) & 1)
        v = table[i][v];
    }
    if (u == v)
      return u;
    for (int i = LOG - 1; i >= 0; i--) {
      if (table[i][u] != table[i][v]) {
        u = table[i][u];
        v = table[i][v];
      }
    }
    return table[0][u];
  }
};

int main() {
  ll n, x[22], y[22], p[22], ans[22], i, j, k, t;
  int dx[15][33333], dy[15][33333];
  cin >> n;
  for (i = 0; i < n; i++)
    cin >> x[i] >> y[i] >> p[i];
  for (i = 0; i <= n; i++)
    ans[i] = 1e15;
  for (k = 0; k < (1 << n); k++) {
    set<ll> lx1, lx2, ly1, ly2;
    lx1.insert(1e9);
    lx1.insert(0);
    lx2.insert(1e9);
    lx2.insert(0);
    ly1.insert(1e9);
    ly1.insert(0);
    ly2.insert(1e9);
    ly2.insert(0);
    for (i = 0; i < n; i++) {
      if ((k >> i) & 1) {
        lx1.insert(x[i]);
        lx2.insert(-x[i]);
        ly1.insert(y[i]);
        ly2.insert(-y[i]);
      }
    }
    for (i = 0; i < n; i++) {
      ll bx = 1e9, by = 1e9;
      bx = min(bx, *lx1.lower_bound(x[i]) - x[i]);
      bx = min(bx, *lx2.lower_bound(-x[i]) + x[i]);
      by = min(by, *ly1.lower_bound(y[i]) - y[i]);
      by = min(by, *ly2.lower_bound(-y[i]) + y[i]);
      dx[i][k] = bx;
      dy[i][k] = by;
    }
  }
  t = 1;
  for (i = 0; i < n; i++)
    t *= 3;
  for (k = 0; k < t; k++) {
    ll cnt = 0, sum = 0, ck = k, kx = 0, ky = 0, w = 1;
    for (i = 0; i < n; i++) {
      if (ck % 3 == 0) {
        cnt++;
        kx += w;
      } else if (ck % 3 == 1) {
        cnt++;
        ky += w;
      }
      ck /= 3;
      w *= 2;
    }
    for (i = 0; i < n; i++)
      sum += min(dx[i][kx], dy[i][ky]) * p[i];
    ans[cnt] = min(ans[cnt], sum);
  }
  for (i = 0; i <= n; i++)
    cout << ans[i] << endl;
}

Error: TLE

Fixed submission:

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
#define pb(x) push_back(x)
#define mp(a, b) make_pair(a, b)
#define all(x) x.begin(), x.end()
#define rall(x) x.rbegin(), x.rend()
#define lscan(x) scanf("%I64d", &x)
#define lprint(x) printf("%I64d", x)
#define rep(i, n) for (int i = 0; i < n; i++)
#define rep2(i, n) for (int i = n - 1; i >= 0; i--)
const int mod = 1000000007;
ll gcd(ll a, ll b) {
  ll c = a % b;
  while (c != 0) {
    a = b;
    b = c;
    c = a % b;
  }
  return b;
}
long long extGCD(long long a, long long b, long long &x, long long &y) {
  if (b == 0) {
    x = 1;
    y = 0;
    return a;
  }
  long long d = extGCD(b, a % b, y, x);
  y -= a / b * x;
  return d;
}

struct UnionFind {
  vector<ll> data;

  UnionFind(int sz) { data.assign(sz, -1); }

  bool unite(int x, int y) {
    x = find(x), y = find(y);
    if (x == y)
      return (false);
    if (data[x] > data[y])
      swap(x, y);
    data[x] += data[y];
    data[y] = x;
    return (true);
  }

  int find(int k) {
    if (data[k] < 0)
      return (k);
    return (data[k] = find(data[k]));
  }

  ll size(int k) { return (-data[find(k)]); }
};

ll M = 1000000007;

vector<ll> fac(2000011);  // n!(mod M)
vector<ll> ifac(2000011); // k!^{M-2} (mod M)

ll mpow(ll x, ll n) {
  ll ans = 1;
  while (n != 0) {
    if (n & 1)
      ans = ans * x % M;
    x = x * x % M;
    n = n >> 1;
  }
  return ans;
}
ll mpow2(ll x, ll n, ll mod) {
  ll ans = 1;
  while (n != 0) {
    if (n & 1)
      ans = ans * x % mod;
    x = x * x % mod;
    n = n >> 1;
  }
  return ans;
}
void setcomb() {
  fac[0] = 1;
  ifac[0] = 1;
  for (ll i = 0; i < 2000010; i++) {
    fac[i + 1] = fac[i] * (i + 1) % M; // n!(mod M)
  }
  ifac[2000010] = mpow(fac[2000010], M - 2);
  for (ll i = 2000010; i > 0; i--) {
    ifac[i - 1] = ifac[i] * i % M;
  }
}
ll comb(ll a, ll b) {
  if (a == 0 && b == 0)
    return 1;
  if (a < b || a < 0)
    return 0;
  ll tmp = ifac[a - b] * ifac[b] % M;
  return tmp * fac[a] % M;
}
ll perm(ll a, ll b) {
  if (a == 0 && b == 0)
    return 1;
  if (a < b || a < 0)
    return 0;
  return fac[a] * ifac[a - b] % M;
}
long long modinv(long long a) {
  long long b = M, u = 1, v = 0;
  while (b) {
    long long t = a / b;
    a -= t * b;
    swap(a, b);
    u -= t * v;
    swap(u, v);
  }
  u %= M;
  if (u < 0)
    u += M;
  return u;
}
ll modinv2(ll a, ll mod) {
  ll b = mod, u = 1, v = 0;
  while (b) {
    ll t = a / b;
    a -= t * b;
    swap(a, b);
    u -= t * v;
    swap(u, v);
  }
  u %= mod;
  if (u < 0)
    u += mod;
  return u;
}

template <int mod> struct ModInt {
  int x;

  ModInt() : x(0) {}

  ModInt(int64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}

  ModInt &operator+=(const ModInt &p) {
    if ((x += p.x) >= mod)
      x -= mod;
    return *this;
  }

  ModInt &operator-=(const ModInt &p) {
    if ((x += mod - p.x) >= mod)
      x -= mod;
    return *this;
  }

  ModInt &operator*=(const ModInt &p) {
    x = (int)(1LL * x * p.x % mod);
    return *this;
  }

  ModInt &operator/=(const ModInt &p) {
    *this *= p.inverse();
    return *this;
  }

  ModInt operator-() const { return ModInt(-x); }

  ModInt operator+(const ModInt &p) const { return ModInt(*this) += p; }

  ModInt operator-(const ModInt &p) const { return ModInt(*this) -= p; }

  ModInt operator*(const ModInt &p) const { return ModInt(*this) *= p; }

  ModInt operator/(const ModInt &p) const { return ModInt(*this) /= p; }

  bool operator==(const ModInt &p) const { return x == p.x; }

  bool operator!=(const ModInt &p) const { return x != p.x; }

  ModInt inverse() const {
    int a = x, b = mod, u = 1, v = 0, t;
    while (b > 0) {
      t = a / b;
      swap(a -= t * b, b);
      swap(u -= t * v, v);
    }
    return ModInt(u);
  }

  ModInt pow(int64_t n) const {
    ModInt ret(1), mul(x);
    while (n > 0) {
      if (n & 1)
        ret *= mul;
      mul *= mul;
      n >>= 1;
    }
    return ret;
  }

  friend ostream &operator<<(ostream &os, const ModInt &p) { return os << p.x; }

  friend istream &operator>>(istream &is, ModInt &a) {
    int64_t t;
    is >> t;
    a = ModInt<mod>(t);
    return (is);
  }

  static int get_mod() { return mod; }
};

using mint = ModInt<mod>;

vector<vector<ll>> mul(vector<vector<ll>> a, vector<vector<ll>> b, int n) {
  int i, j, k, t;
  vector<vector<ll>> c(n);
  for (i = 0; i < n; i++) {
    for (j = 0; j < n; j++) {
      t = 0;
      for (k = 0; k < n; k++)
        t = (t + a[i][k] * b[k][j] % M) % M;
      c[i].push_back(t);
    }
  }
  return c;
}

template <typename Monoid> struct SegmentTree {
  using F = function<Monoid(Monoid, Monoid)>;

  int sz;
  vector<Monoid> seg;

  const F f;
  const Monoid M1;

  SegmentTree(int n, const F f, const Monoid &M1) : f(f), M1(M1) {
    sz = 1;
    while (sz < n)
      sz <<= 1;
    seg.assign(2 * sz, M1);
  }

  void set(int k, const Monoid &x) { seg[k + sz] = x; }

  void build() {
    for (int k = sz - 1; k > 0; k--) {
      seg[k] = f(seg[2 * k + 0], seg[2 * k + 1]);
    }
  }

  void update(int k, const Monoid &x) {
    k += sz;
    seg[k] = x;
    while (k >>= 1) {
      seg[k] = f(seg[2 * k + 0], seg[2 * k + 1]);
    }
  }

  Monoid query(int a, int b) {
    Monoid L = M1, R = M1;
    for (a += sz, b += sz; a < b; a >>= 1, b >>= 1) {
      if (a & 1)
        L = f(L, seg[a++]);
      if (b & 1)
        R = f(seg[--b], R);
    }
    return f(L, R);
  }

  Monoid operator[](const int &k) const { return seg[k + sz]; }

  template <typename C>
  int find_subtree(int a, const C &check, Monoid &M, bool type) {
    while (a < sz) {
      Monoid nxt = type ? f(seg[2 * a + type], M) : f(M, seg[2 * a + type]);
      if (check(nxt))
        a = 2 * a + type;
      else
        M = nxt, a = 2 * a + 1 - type;
    }
    return a - sz;
  }

  template <typename C> int find_first(int a, const C &check) {
    Monoid L = M1;
    if (a <= 0) {
      if (check(f(L, seg[1])))
        return find_subtree(1, check, L, false);
      return -1;
    }
    int b = sz;
    for (a += sz, b += sz; a < b; a >>= 1, b >>= 1) {
      if (a & 1) {
        Monoid nxt = f(L, seg[a]);
        if (check(nxt))
          return find_subtree(a, check, L, false);
        L = nxt;
        ++a;
      }
    }
    return -1;
  }

  template <typename C> int find_last(int b, const C &check) {
    Monoid R = M1;
    if (b >= sz) {
      if (check(f(seg[1], R)))
        return find_subtree(1, check, R, true);
      return -1;
    }
    int a = sz;
    for (b += sz; a < b; a >>= 1, b >>= 1) {
      if (b & 1) {
        Monoid nxt = f(seg[--b], R);
        if (check(nxt))
          return find_subtree(b, check, R, true);
        R = nxt;
      }
    }
    return -1;
  }
};

template <unsigned mod> struct RollingHash {
  vector<unsigned> hashed, power;

  inline unsigned mul(unsigned a, unsigned b) const {
    unsigned long long x = (unsigned long long)a * b;
    unsigned xh = (unsigned)(x >> 32), xl = (unsigned)x, d, m;
    asm("divl %4; \\n\\t" : "=a"(d), "=d"(m) : "d"(xh), "a"(xl), "r"(mod));
    return m;
  }

  RollingHash(const string &s, unsigned base = 10007) {
    int sz = (int)s.size();
    hashed.assign(sz + 1, 0);
    power.assign(sz + 1, 0);
    power[0] = 1;
    for (int i = 0; i < sz; i++) {
      power[i + 1] = mul(power[i], base);
      hashed[i + 1] = mul(hashed[i], base) + s[i];
      if (hashed[i + 1] >= mod)
        hashed[i + 1] -= mod;
    }
  }

  unsigned get(int l, int r) const {
    unsigned ret = hashed[r] + mod - mul(hashed[l], power[r - l]);
    if (ret >= mod)
      ret -= mod;
    return ret;
  }

  unsigned connect(unsigned h1, int h2, int h2len) const {
    unsigned ret = mul(h1, power[h2len]) + h2;
    if (ret >= mod)
      ret -= mod;
    return ret;
  }

  int LCP(const RollingHash<mod> &b, int l1, int r1, int l2, int r2) {
    int len = min(r1 - l1, r2 - l2);
    int low = -1, high = len + 1;
    while (high - low > 1) {
      int mid = (low + high) / 2;
      if (get(l1, l1 + mid) == b.get(l2, l2 + mid))
        low = mid;
      else
        high = mid;
    }
    return (low);
  }
};

using RH = RollingHash<1000000007>;

template <typename T> struct edge {
  int src, to;
  T cost;

  edge(int to, T cost) : src(-1), to(to), cost(cost) {}

  edge(int src, int to, T cost) : src(src), to(to), cost(cost) {}

  edge &operator=(const int &x) {
    to = x;
    return *this;
  }

  operator int() const { return to; }
};

template <typename T> using Edges = vector<edge<T>>;
template <typename T> using WeightedGraph = vector<Edges<T>>;
using UnWeightedGraph = vector<vector<int>>;
template <typename T> using Matrix = vector<vector<T>>;

template <typename G> struct DoublingLowestCommonAncestor {
  const int LOG;
  vector<int> dep;
  const G &g;
  vector<vector<int>> table;

  DoublingLowestCommonAncestor(const G &g)
      : g(g), dep(g.size()), LOG(32 - __builtin_clz(g.size())) {
    table.assign(LOG, vector<int>(g.size(), -1));
  }

  void dfs(int idx, int par, int d) {
    table[0][idx] = par;
    dep[idx] = d;
    for (auto &to : g[idx]) {
      if (to != par)
        dfs(to, idx, d + 1);
    }
  }

  void build() {
    dfs(0, -1, 0);
    for (int k = 0; k + 1 < LOG; k++) {
      for (int i = 0; i < table[k].size(); i++) {
        if (table[k][i] == -1)
          table[k + 1][i] = -1;
        else
          table[k + 1][i] = table[k][table[k][i]];
      }
    }
  }

  int query(int u, int v) {
    if (dep[u] > dep[v])
      swap(u, v);
    for (int i = LOG - 1; i >= 0; i--) {
      if (((dep[v] - dep[u]) >> i) & 1)
        v = table[i][v];
    }
    if (u == v)
      return u;
    for (int i = LOG - 1; i >= 0; i--) {
      if (table[i][u] != table[i][v]) {
        u = table[i][u];
        v = table[i][v];
      }
    }
    return table[0][u];
  }
};

int main() {
  ll n, x[22], y[22], p[22], ans[22], i, j, k, t;
  cin >> n;
  for (i = 0; i < n; i++)
    cin >> x[i] >> y[i] >> p[i];
  for (i = 0; i <= n; i++)
    ans[i] = 1e15;
  t = 1;
  for (i = 0; i < n; i++)
    t *= 3;
  for (k = 0; k < t; k++) {
    ll cnt = 0, sum = 0, ck = k;
    for (i = 0; i < n; i++) {
      if (ck % 3 != 2)
        cnt++;
      ck /= 3;
    }
    if (cnt > n)
      continue;
    ck = k;
    set<ll> lx1, lx2, ly1, ly2;
    lx1.insert(1e9);
    lx1.insert(0);
    lx2.insert(1e9);
    lx2.insert(0);
    ly1.insert(1e9);
    ly1.insert(0);
    ly2.insert(1e9);
    ly2.insert(0);
    for (i = 0; i < n; i++) {
      if (ck % 3 == 0) {
        lx1.insert(x[i]);
        lx2.insert(-x[i]);
      } else if (ck % 3 == 1) {
        ly1.insert(y[i]);
        ly2.insert(-y[i]);
      }
      ck /= 3;
    }
    for (i = 0; i < n; i++) {
      ll dx = 1e9, dy = 1e9;
      dx = min(dx, *lx1.lower_bound(x[i]) - x[i]);
      dx = min(dx, *lx2.lower_bound(-x[i]) + x[i]);
      dy = min(dy, *ly1.lower_bound(y[i]) - y[i]);
      dy = min(dy, *ly2.lower_bound(-y[i]) + y[i]);
      sum += min(dx, dy) * p[i];
    }
    ans[cnt] = min(ans[cnt], sum);
  }
  for (i = 0; i <= n; i++)
    cout << ans[i] << endl;
}