#874612 (C++17) No.2331 Maximum Quadrilateral

• 問題: No.2331 Maximum Quadrilateral
• ユーザー: ei1333333
• 提出日時: 2023-05-28 14:56:17
• 言語: C++17 (gcc 13.3.0 + boost 1.87.0)
• 結果: WA
• 実行時間: -
• コード長: 7,214 bytes
• コンパイル時間: 2,461 ms
• コンパイル使用メモリ: 211,664 KB
• 最終ジャッジ日時: 2025-02-13 12:16:12
• ジャッジサーバーID （参考情報）: judge2 / judge5

ファイルパターン	結果
sample	AC * 2
other	AC * 9 WA * 36

ソースコード

#include<bits/stdc++.h>

using namespace std;

using int64 = long long;
const int mod = 998244353;

const int64 infll = (1LL << 62) - 1;
const int inf = (1 << 30) - 1;

struct IoSetup {
  IoSetup() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(10);
    cerr << fixed << setprecision(10);
  }
} iosetup;

template< typename T1, typename T2 >
ostream &operator<<(ostream &os, const pair< T1, T2 >& p) {
  os << p.first << " " << p.second;
  return os;
}

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

template< typename T >
ostream &operator<<(ostream &os, const vector< T > &v) {
  for(int i = 0; i < (int) v.size(); i++) {
    os << v[i] << (i + 1 != v.size() ? " " : "");
  }
  return os;
}

template< typename T >
istream &operator>>(istream &is, vector< T > &v) {
  for(T &in : v) is >> in;
  return is;
}

template< typename T1, typename T2 >
inline bool chmax(T1 &a, T2 b) { return a < b && (a = b, true); }

template< typename T1, typename T2 >
inline bool chmin(T1 &a, T2 b) { return a > b && (a = b, true); }

template< typename T = int64 >
vector< T > make_v(size_t a) {
  return vector< T >(a);
}

template< typename T, typename... Ts >
auto make_v(size_t a, Ts... ts) {
  return vector< decltype(make_v< T >(ts...)) >(a, make_v< T >(ts...));
}

template< typename T, typename V >
typename enable_if< is_class< T >::value == 0 >::type fill_v(T &t, const V &v) {
  t = v;
}

template< typename T, typename V >
typename enable_if< is_class< T >::value != 0 >::type fill_v(T &t, const V &v) {
  for(auto &e : t) fill_v(e, v);
}

template< typename F >
struct FixPoint : F {
  explicit FixPoint(F &&f) : F(forward< F >(f)) {}

  template< typename... Args >
  decltype(auto) operator()(Args &&... args) const {
    return F::operator()(*this, forward< Args >(args)...);
  }
};

template< typename F >
inline decltype(auto) MFP(F &&f) {
  return FixPoint< F >{forward< F >(f)};
}

/**
 * @brief Rational (有理数型)
 */
template< typename T >
struct Rational {
private:
  T num, den;

  static T gcd(T a, T b) {
    if(a < 0) a = -a;
    if(b < 0) b = -b;
    return std::__gcd(a, b);
  }

  void normalize() {
    if(num == 0) {
      den = 1;
    } else {
      T g = gcd(num, den);
      num /= g;
      den /= g;
      if(den < 0) {
        num = -num;
        den = -den;
      }
    }
  }

public:

  Rational() : num(0), den(1) {}

  explicit Rational(const T &n) : num(n), den(1) {}

  explicit Rational(const T &n, const T &d) : num(n), den(d) {
    normalize();
  }

  Rational &operator=(const T &n) { return assign(n, 1); }

  Rational &assign(const T &n, const T &d) {
    num = n;
    den = d;
    normalize();
    return *this;
  }

  T numerator() const { return num; }

  T denominator() const { return den; }

  Rational &operator+=(const Rational &r) {
    T r_num = r.num, r_den = r.den;
    T g = gcd(den, r_den);
    den /= g;
    num = num * (r_den / g) + r_num * den;
    g = gcd(num, g);
    num /= g;
    den *= r_den / g;
    return *this;
  }

  Rational &operator-=(const Rational &r) {
    T r_num = r.num, r_den = r.den;
    T g = gcd(den, r_den);
    den /= g;
    num = num * (r_den / g) - r_num * den;
    g = gcd(num, g);
    num /= g;
    den *= r_den / g;
    return *this;
  }

  Rational &operator*=(const Rational &r) {
    T r_num = r.num, r_den = r.den;
    T g1 = gcd(num, r_den);
    T g2 = gcd(den, r_num);
    num = (num / g1) * (r_num / g2);
    den = (den / g2) * (r_den / g1);
    return *this;
  }

  Rational &operator/=(const Rational &r) {
    T r_num = r.num, r_den = r.den;
    T g1 = gcd(num, r_num);
    T g2 = gcd(den, r_den);
    num = (num / g1) * (r_den / g2);
    den = (den / g2) * (r_num / g1);
    if(den < 0) {
      num = -num;
      den = -den;
    }
    return *this;
  }

  Rational &operator+=(const T &i) { return (*this) += Rational{i}; }

  Rational &operator-=(const T &i) { return (*this) -= Rational{i}; }

  Rational &operator*=(const T &i) { return (*this) *= Rational{i}; }

  Rational &operator/=(const T &i) { return (*this) /= Rational{i}; }

  Rational operator+(const Rational &r) const { return Rational(*this) += r; }

  Rational operator-(const Rational &r) const { return Rational(*this) -= r; }

  Rational operator*(const Rational &r) const { return Rational(*this) *= r; }

  Rational operator/(const Rational &r) const { return Rational(*this) /= r; }

  Rational operator+(const T &i) const { return Rational(*this) += i; }

  Rational operator-(const T &i) const { return Rational(*this) -= i; }

  Rational operator*(const T &i) const { return Rational(*this) *= i; }

  Rational operator/(const T &i) const { return Rational(*this) /= i; }

  Rational operator-() const { return Rational{-num, den}; }

  Rational &operator++() {
    num += den;
    return *this;
  }

  Rational &operator--() {
    num -= den;
    return *this;
  }

#define define_cmp(op) \
  bool operator op (const Rational& r) const { return num * r.den op r.num * den; } \
  bool operator op (const T& i) const { return num op i * den; }

  define_cmp(==)

  define_cmp(!=)

  define_cmp(<)

  define_cmp(>)

  define_cmp(<=)

  define_cmp(>=)

#undef define_cmp


  template< typename Real = double >
  Real to_double() const {
    return static_cast < Real >(numerator()) / denominator();
  }

  Rational abs() const {
    return Rational{num < 0 ? -num : num, den};
  }

  friend ostream &operator<<(ostream &os, const Rational &r) {
    return os << r.numerator() << "/" << r.denominator();
  }
};

template< typename T >
struct Point {
  T x, y;

  Point() : x(0), y(0) {}

  Point(const T& x, const T& y) : x(x), y(y) {}

  int dir() const {
    if(y < 0) return -1;
    if(y == 0 and x >= 0) return 0;
    return 1;
  }
};

template< typename T >
T cross(const Point< T >& a, const Point< T >& b) {
  return a.x * b.y - a.y * b.x;
}


template< typename T >
vector< int > arg_sort(const vector< Point< T > >& ps) {
  vector< int > ord(ps.size());
  iota(begin(ord), end(ord), 0);
  sort(begin(ord), end(ord), [&](int a, int b) {
    if(ps[a].dir() != ps[b].dir()) return ps[a].dir() < ps[b].dir();
    return cross(ps[a], ps[b]) > 0;
  });
  return ord;
}

int main() {
  int N;
  cin >> N;
  using T = Rational< int64_t >;
  using P = Point< T >;
  vector< P > ps;
  ps.reserve(N);
  vector< int64 > xx(N), yy(N);
  for(int i = 0; i < N; i++) {
    int64_t x, y;
    cin >> x >> y;
    ps.emplace_back(T(x), T(y));
    xx[i] = x;
    yy[i] = y;
  }
  auto ord = arg_sort(ps);
  vector< int64 > X(N), Y(N);
  for(int i = 0; i < N; i++) {
    X[i] = xx[ord[i]];
    Y[i] = yy[ord[i]];
  }
  int64 ret = 0;
  for(int i = 0; i < N; i++) {
    auto dp = make_v< int64 >(N, 4);
    fill_v(dp, -infll);
    dp[0][0] = 0;
    for(int j = 0; j < N; j++) {
      for(int k = j + 1; k < N; k++) {
        for(int l = 0; l < 3; l++) {
          chmax(dp[k][l + 1], dp[j][l] + X[j] * Y[k] - Y[j] * X[k]);
        }
      }
      chmax(ret,dp[j][3] + X[j] * Y[i] - Y[j] * X[i]);
    }
    rotate(X.begin(), X.begin() + 1, X.end());
    rotate(Y.begin(), Y.begin() + 1, Y.end());
  }
  cout << ret << endl;
}