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


/*****/

#define TRUE true
// #define FALSE false

#include <bits/stdc++.h>

/**/
#pragma GCC target("avx")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
/**/

using namespace std;
using ll = long long;
using ld = long double;
using pint = pair<int, int>;
using pll = pair<long long, long long>;
template <class T> using vec = vector<T>;
template <class T> using vec2 = vector<vector<T>>;
template <class T> using vec3 = vector<vector<vector<T>>>;

constexpr int INF = numeric_limits<int>::max();
constexpr ll INFL = numeric_limits<ll>::max();
constexpr ll MOD = 1000000007; // 10^9+7

#ifdef TRUE

#define rep(i, n) for (ll i = 0, i##_len = (n); i < i##_len; ++i)
#define rep1(i, n) for (ll i = 1, i##_len = (n); i <= i##_len; ++i)
#define rrep(i, n) for (ll i = (n)-1; i >= 0; --i)
#define rrep1(i, n) for (ll i = (n); i > 0; --i)
#define step(i, a, n) for (ll i = (a), i##_len = (a) + (n); i < i##_len; ++i)
#define rstep(i, a, n)                                                         \\
  for (ll i = (a) + (n)-1, i##_len = (a); i >= i##_len; --i)
#define range(i, a, b) for (ll i = (a), i##_len = (b); i < i##_len; ++i)
#define rrange(i, a, b) for (ll i = (b)-1, i##_len = (a); i >= i##_len; --i)

std::string strMulti(const int n, const std::string &t) {
  std::string out = "";
  for (int i = 0; i < n; i++) {
    out += t;
  }
  return out;
}
std::string tab(const int n) { return string(n, '\\t'); }
std::string join(const vector<string> &v, const char *delim = 0) {
  std::string s;
  if (!v.empty()) {
    s += v[0];
    for (decltype(v.size()) i = 1, c = v.size(); i < c; ++i) {
      if (delim)
        s += delim;
      s += v[i];
    }
  }
  return s;
}

string to_string(string &s) { return '"' + s + '"'; }
string to_string(char &c) { return string({'\\'', c, '\\''}); }
template <class T1, class T2> string to_string(pair<T1, T2> p) {
  return "(" + to_string(p.first) + ", " + to_string(p.second) + ")";
}
template <class Tuple, size_t... I>
string _to_string_tuple(Tuple &&t, std::index_sequence<I...>) {
  return "(" + join({to_string(std::get<I>(t))...}, ", ") + ")";
}
template <class... Args> string to_string(tuple<Args...> t) {
  return _to_string_tuple(
      std::forward<tuple<Args...>>(t),
      std::make_index_sequence<
          std::tuple_size<std::decay_t<tuple<Args...>>>::value>{});
}
template <class T> string to_string(vector<T> ar) {
  vector<string> texts(ar.size());
  for (size_t i = 0; i < ar.size(); ++i) {
    texts[i] = to_string(ar[i]);
  }
  return "{" + join(texts, ", ") + "}";
}
template <class T> string to_string(set<T> s) {
  vector<string> texts(s.size());
  int i = 0;
  for (auto e : s) {
    texts[i] = to_string(e);
    i++;
  }
  return "{" + join(texts, ", ") + "}";
}
template <class T1, class T2> string to_string(map<T1, T2> m) {
  vector<string> texts(m.size());
  int i = 0;
  for (auto e : m) {
    texts[i] = to_string(e);
    i++;
  }
  return "{" + join(texts, ", ") + "}";
}
template <class T> string to_string(initializer_list<T> il) {
  vector<string> texts(il.size());
  size_t i = 0;
  for (T v : il) {
    texts[i] = to_string(v);
    i++;
  }
  return "{" + join(texts, ", ") + "}";
}

void debug(string name);
void debugn(string name);
template <class T> void debug(string name, T v);
template <class T> void debugn(string name, T v);
template <class T> void debug(string name, initializer_list<T> il);
template <class T> void debugn(string name, initializer_list<T> il);
template <class... Args> void debug(string name, Args... args);
template <class... Args> void debugn(string name, Args... args);
void debugdo(function<void()> func);

#ifdef DEBUG_BUILD
#define debugvar(x) debugn(#x, (x))
#define debugvartab(x, t) debugn(tab(t) + #x, (x))
void debug(string name) { std::cerr << name; }
void debugn(string name) { std::cerr << name << '\\n'; }
template <class T> void debug(string name, T v) {
  std::cerr << name << " = " << to_string(v);
}
template <class T> void debugn(string name, T v) {
  std::cerr << name << " = " << to_string(v) << '\\n';
}
template <class T> void debug(string name, initializer_list<T> il) {
  std::cerr << name << " = " << to_string(il);
}
template <class T> void debugn(string name, initializer_list<T> il) {
  std::cerr << name << " = " << to_string(il) << '\\n';
}
template <class... Args> void debug(string name, Args... args) {
  std::cerr << name << " = " << to_string(tuple<Args...>(args...));
}
template <class... Args> void debugn(string name, Args... args) {
  std::cerr << name << " = " << to_string(tuple<Args...>(args...)) << '\\n';
}
void debugdo(function<void()> func) { func(); }
#else
#define debugvar(x)
#define debugvartab(x, t)
void debug(string name) {}
void debugn(string name) {}
template <class T> void debug(string name, T v) {}
template <class T> void debugn(string name, T v) {}
template <class T> void debug(string name, initializer_list<T> il) {}
template <class T> void debugn(string name, initializer_list<T> il) {}
template <class... Args> void debug(string name, Args... args) {}
template <class... Args> void debugn(string name, Args... args) {}
void debugdo(function<void()> func) {}
#endif

#define all(x) (x).begin(), (x).end()
#define pair(a, b) make_pair(a, b)

template <class T> bool chmax(T &a, const T b) {
  if (a < b) {
    a = b;
    return true;
  }
  return false;
}
template <class T> bool chmin(T &a, const T b) {
  if (a > b) {
    a = b;
    return true;
  }
  return false;
}
template <class T> T divup(const T a, const T b) { return (a + (b - 1)) / b; }
template <class T> bool cmp_2nd(pair<T, T> a, pair<T, T> b) {
  if (a.second != b.second) {
    return a.second < b.second;
  }
  return a.first < b.first;
}
ll modpow(ll x, ll n, const ll &p) {
  ll ret = 1;
  while (n > 0) {
    if (n & 1) {
      (ret *= x) %= p;
    }
    (x *= x) %= p;
    n >>= 1;
  }
  return ret;
}
template <class T> T modinv(T a, const T &p) {
  T b = p, u = 1, v = 0;
  while (b) {
    T t = a / b;
    a -= t * b;
    swap(a, b);
    u -= t * v;
    swap(u, v);
  }
  u %= p;
  if (u < 0) {
    u += p;
  }
  return u;
}
template <class T> T math_P(T m, T n) {
  T ret = 1;
  for (T i = m; i > m - n; i--) {
    ret *= i;
  }
  return ret;
}
template <class T> T math_C(T m, T n) {
  T ret = math_P(m, n);
  for (T i = 2; i <= n; i++) {
    ret /= i;
  }
  return ret;
}
ll extended_euclidean(ll u, ll v) {
  ll r0 = u;
  ll r1 = v;
  ll s0 = 1;
  ll s1 = 0;
  ll t0 = 0;
  ll t1 = 1;
  while (r1 != 0) {
    ll q = r0 / r1;
    ll r = r0 - q * r1;
    ll s = s0 - q * s1;
    ll t = t0 - q * t1;
    r0 = r1;
    s0 = s1;
    t0 = t1;
    r1 = r;
    s1 = s;
    t1 = t;
  }
  if (t0 < 0) {
    return t0 + u;
  } else {
    return t0;
  }
}
ll math_C_mod(ll n, ll c, const ll &p) {
  ll upe = 1;
  ll dow = 1;
  for (ll i = 1; i < c + 1; ++i) {
    upe = upe * n % p;
    dow = dow * i % p;
    n -= 1;
  }
  return (upe * extended_euclidean(p, dow)) % p;
}
template <class T> T math_gcd(T a, T b) {
  if (b == 0) {
    return a;
  } else {
    return math_gcd(b, a % b);
  }
}
template <class T> T math_lcm(T a, T b) { return a / math_gcd(a, b) * b; }
template <class T> T SumStep(T a, T n, T d) {
  return n * (2 * a + (n - 1) * d) / 2;
}
template <class T> T SumRange(T a, T b, T d) {
  return SumStep(a, (b - a) / d, d);
}

#endif

/*****/

int N;
vec2<ll> V;
int solveCnt;
vec<ll> sh;

void solve(int add, int cnt, vec<ll> &D) {
  debugn("add,cnt", add, cnt);

  if (cnt >= N + 1)
    return;

  {
    ll diff = 0;
    rep(i, N) { diff += D[i]; }
    debugvartab(diff, 1);
    chmin(sh[cnt], diff);
  }

  if (add == N)
    return;

  vec<ll> before(N + 1);

  rep(i, N) {
    before[i] = D[i];
    chmin(D[i], abs(V[i][0] - V[add][0]) * V[i][2]);
  }
  solve(add + 1, cnt + 1, D);
  rep(i, N) { D[i] = before[i]; }

  rep(i, N) {
    before[i] = D[i];
    chmin(D[i], abs(V[i][1] - V[add][1]) * V[i][2]);
  }
  solve(add + 1, cnt + 1, D);
  rep(i, N) { D[i] = before[i]; }

  solve(add + 1, cnt, D);
}

void Main() {
  cin >> N;
  V.resize(N, vec<ll>(3));
  rep(i, N) rep(j, 3) cin >> V[i][j];
  sh.resize(N + 1, INFL);
  // before.resize(N + 1);

  // ll ret = INFL;
  // vec<pint> R(iN);
  vec<ll> D(N + 1);
  rep(i, N) {
    ll diff = INFL;
    chmin(diff, abs(V[i][0]) * V[i][2]);
    chmin(diff, abs(V[i][1]) * V[i][2]);
    D[i] = diff;
  }
  solve(0, 0, D);
  rep(i, N + 1) { cout << sh[i] << endl; }
}

/*****/

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

  std::cout << std::fixed << std::setprecision(10);

  Main();
  std::cerr << flush;
  std::cout << flush;

  return 0;
}


Error: TLE

Fixed submission:


/*****/

#define TRUE true
// #define FALSE false

#include <bits/stdc++.h>

/**/
#pragma GCC target("avx")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
/**/

using namespace std;
using ll = long long;
using ld = long double;
using pint = pair<int, int>;
using pll = pair<long long, long long>;
template <class T> using vec = vector<T>;
template <class T> using vec2 = vector<vector<T>>;
template <class T> using vec3 = vector<vector<vector<T>>>;

constexpr int INF = numeric_limits<int>::max();
constexpr ll INFL = numeric_limits<ll>::max();
constexpr ll MOD = 1000000007; // 10^9+7

#ifdef TRUE

#define rep(i, n) for (ll i = 0, i##_len = (n); i < i##_len; ++i)
#define rep1(i, n) for (ll i = 1, i##_len = (n); i <= i##_len; ++i)
#define rrep(i, n) for (ll i = (n)-1; i >= 0; --i)
#define rrep1(i, n) for (ll i = (n); i > 0; --i)
#define step(i, a, n) for (ll i = (a), i##_len = (a) + (n); i < i##_len; ++i)
#define rstep(i, a, n)                                                         \\
  for (ll i = (a) + (n)-1, i##_len = (a); i >= i##_len; --i)
#define range(i, a, b) for (ll i = (a), i##_len = (b); i < i##_len; ++i)
#define rrange(i, a, b) for (ll i = (b)-1, i##_len = (a); i >= i##_len; --i)

std::string strMulti(const int n, const std::string &t) {
  std::string out = "";
  for (int i = 0; i < n; i++) {
    out += t;
  }
  return out;
}
std::string tab(const int n) { return string(n, '\\t'); }
std::string join(const vector<string> &v, const char *delim = 0) {
  std::string s;
  if (!v.empty()) {
    s += v[0];
    for (decltype(v.size()) i = 1, c = v.size(); i < c; ++i) {
      if (delim)
        s += delim;
      s += v[i];
    }
  }
  return s;
}

string to_string(string &s) { return '"' + s + '"'; }
string to_string(char &c) { return string({'\\'', c, '\\''}); }
template <class T1, class T2> string to_string(pair<T1, T2> p) {
  return "(" + to_string(p.first) + ", " + to_string(p.second) + ")";
}
template <class Tuple, size_t... I>
string _to_string_tuple(Tuple &&t, std::index_sequence<I...>) {
  return "(" + join({to_string(std::get<I>(t))...}, ", ") + ")";
}
template <class... Args> string to_string(tuple<Args...> t) {
  return _to_string_tuple(
      std::forward<tuple<Args...>>(t),
      std::make_index_sequence<
          std::tuple_size<std::decay_t<tuple<Args...>>>::value>{});
}
template <class T> string to_string(vector<T> ar) {
  vector<string> texts(ar.size());
  for (size_t i = 0; i < ar.size(); ++i) {
    texts[i] = to_string(ar[i]);
  }
  return "{" + join(texts, ", ") + "}";
}
template <class T> string to_string(set<T> s) {
  vector<string> texts(s.size());
  int i = 0;
  for (auto e : s) {
    texts[i] = to_string(e);
    i++;
  }
  return "{" + join(texts, ", ") + "}";
}
template <class T1, class T2> string to_string(map<T1, T2> m) {
  vector<string> texts(m.size());
  int i = 0;
  for (auto e : m) {
    texts[i] = to_string(e);
    i++;
  }
  return "{" + join(texts, ", ") + "}";
}
template <class T> string to_string(initializer_list<T> il) {
  vector<string> texts(il.size());
  size_t i = 0;
  for (T v : il) {
    texts[i] = to_string(v);
    i++;
  }
  return "{" + join(texts, ", ") + "}";
}

void debug(string name);
void debugn(string name);
template <class T> void debug(string name, T v);
template <class T> void debugn(string name, T v);
template <class T> void debug(string name, initializer_list<T> il);
template <class T> void debugn(string name, initializer_list<T> il);
template <class... Args> void debug(string name, Args... args);
template <class... Args> void debugn(string name, Args... args);
void debugdo(function<void()> func);

#ifdef DEBUG_BUILD
#define debugvar(x) debugn(#x, (x))
#define debugvartab(x, t) debugn(tab(t) + #x, (x))
void debug(string name) { std::cerr << name; }
void debugn(string name) { std::cerr << name << '\\n'; }
template <class T> void debug(string name, T v) {
  std::cerr << name << " = " << to_string(v);
}
template <class T> void debugn(string name, T v) {
  std::cerr << name << " = " << to_string(v) << '\\n';
}
template <class T> void debug(string name, initializer_list<T> il) {
  std::cerr << name << " = " << to_string(il);
}
template <class T> void debugn(string name, initializer_list<T> il) {
  std::cerr << name << " = " << to_string(il) << '\\n';
}
template <class... Args> void debug(string name, Args... args) {
  std::cerr << name << " = " << to_string(tuple<Args...>(args...));
}
template <class... Args> void debugn(string name, Args... args) {
  std::cerr << name << " = " << to_string(tuple<Args...>(args...)) << '\\n';
}
void debugdo(function<void()> func) { func(); }
#else
#define debugvar(x)
#define debugvartab(x, t)
void debug(string name) {}
void debugn(string name) {}
template <class T> void debug(string name, T v) {}
template <class T> void debugn(string name, T v) {}
template <class T> void debug(string name, initializer_list<T> il) {}
template <class T> void debugn(string name, initializer_list<T> il) {}
template <class... Args> void debug(string name, Args... args) {}
template <class... Args> void debugn(string name, Args... args) {}
void debugdo(function<void()> func) {}
#endif

#define all(x) (x).begin(), (x).end()
#define pair(a, b) make_pair(a, b)

template <class T> bool chmax(T &a, const T b) {
  if (a < b) {
    a = b;
    return true;
  }
  return false;
}
template <class T> bool chmin(T &a, const T b) {
  if (a > b) {
    a = b;
    return true;
  }
  return false;
}
template <class T> T divup(const T a, const T b) { return (a + (b - 1)) / b; }
template <class T> bool cmp_2nd(pair<T, T> a, pair<T, T> b) {
  if (a.second != b.second) {
    return a.second < b.second;
  }
  return a.first < b.first;
}
ll modpow(ll x, ll n, const ll &p) {
  ll ret = 1;
  while (n > 0) {
    if (n & 1) {
      (ret *= x) %= p;
    }
    (x *= x) %= p;
    n >>= 1;
  }
  return ret;
}
template <class T> T modinv(T a, const T &p) {
  T b = p, u = 1, v = 0;
  while (b) {
    T t = a / b;
    a -= t * b;
    swap(a, b);
    u -= t * v;
    swap(u, v);
  }
  u %= p;
  if (u < 0) {
    u += p;
  }
  return u;
}
template <class T> T math_P(T m, T n) {
  T ret = 1;
  for (T i = m; i > m - n; i--) {
    ret *= i;
  }
  return ret;
}
template <class T> T math_C(T m, T n) {
  T ret = math_P(m, n);
  for (T i = 2; i <= n; i++) {
    ret /= i;
  }
  return ret;
}
ll extended_euclidean(ll u, ll v) {
  ll r0 = u;
  ll r1 = v;
  ll s0 = 1;
  ll s1 = 0;
  ll t0 = 0;
  ll t1 = 1;
  while (r1 != 0) {
    ll q = r0 / r1;
    ll r = r0 - q * r1;
    ll s = s0 - q * s1;
    ll t = t0 - q * t1;
    r0 = r1;
    s0 = s1;
    t0 = t1;
    r1 = r;
    s1 = s;
    t1 = t;
  }
  if (t0 < 0) {
    return t0 + u;
  } else {
    return t0;
  }
}
ll math_C_mod(ll n, ll c, const ll &p) {
  ll upe = 1;
  ll dow = 1;
  for (ll i = 1; i < c + 1; ++i) {
    upe = upe * n % p;
    dow = dow * i % p;
    n -= 1;
  }
  return (upe * extended_euclidean(p, dow)) % p;
}
template <class T> T math_gcd(T a, T b) {
  if (b == 0) {
    return a;
  } else {
    return math_gcd(b, a % b);
  }
}
template <class T> T math_lcm(T a, T b) { return a / math_gcd(a, b) * b; }
template <class T> T SumStep(T a, T n, T d) {
  return n * (2 * a + (n - 1) * d) / 2;
}
template <class T> T SumRange(T a, T b, T d) {
  return SumStep(a, (b - a) / d, d);
}

#endif

/*****/

int N;
vec2<ll> V;
int solveCnt;
vec<ll> sh;

ll solve(int addmode, int add, int cnt, vec<ll> &D) {
  if (add == N) {
    addmode++;
    add = 0;
  }

  if (cnt >= N + 1)
    return INFL;

  debugn("\\tadd, cnt", add, cnt);
  // debugvartab(R, 2);

  {
    ll diff = 0;
    rep(i, N) { diff += D[i]; }
    debugvartab(diff, 2);
    chmin(sh[cnt], diff);
  }

  if (addmode == 2)
    return INFL;

  ll ret = INFL;

  // R[cnt] = pair(addmode, add);
  vec<ll> before(D);
  rep(i, N) { chmin(D[i], abs(V[i][addmode] - V[add][addmode]) * V[i][2]); }
  chmin(ret, solve(addmode, add + 1, cnt + 1, D));
  rep(i, N) { D[i] = before[i]; }

  if (ret == 0)
    return ret;

  chmin(ret, solve(addmode, add + 1, cnt, D));

  return ret;
}

void Main() {
  cin >> N;
  V.resize(N, vec<ll>(3));
  rep(i, N) rep(j, 3) cin >> V[i][j];
  sh.resize(N + 1, INFL);

  // ll ret = INFL;
  // vec<pint> R(iN);
  vec<ll> D(N);
  rep(i, N) {
    ll diff = INFL;
    chmin(diff, abs(V[i][0]) * V[i][2]);
    chmin(diff, abs(V[i][1]) * V[i][2]);
    D[i] = diff;
  }
  solve(0, 0, 0, D);
  rep(i, N + 1) { cout << sh[i] << endl; }
}

/*****/

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

  std::cout << std::fixed << std::setprecision(10);

  Main();
  std::cerr << flush;
  std::cout << flush;

  return 0;
}