#44086 (C++11（廃止可能性あり）) No.199 星を描こう

• 問題: No.199 星を描こう
• ユーザー: not_522
• 提出日時: 2015-08-17 15:56:46
• 言語: C++11（廃止可能性あり） (gcc 13.3.0)
• 結果: AC
• 実行時間: 2 ms / 2,000 ms
• コード長: 11,184 bytes
• コンパイル時間: 1,692 ms
• コンパイル使用メモリ: 174,016 KB
• 実行使用メモリ: 5,248 KB
• 最終ジャッジ日時: 2024-12-30 03:38:37
• 合計ジャッジ時間: 2,632 ms
• ジャッジサーバーID （参考情報）: judge5 / judge4

ファイルパターン	結果
sample	AC * 3
other	AC * 25

ソースコード

#include <bits/stdc++.h>

using namespace std;

namespace arithmetic {
  template<typename T> class Addition {
  public:
    template<typename V> T operator+(const V& v) const {
      return T(static_cast<const T&>(*this)) += v;
    }
  };

  template<typename T> class Subtraction {
  public:
    template<typename V> T operator-(const V& v) const {
      return T(static_cast<const T&>(*this)) -= v;
    }
  };

  template<typename T> class Multiplication {
  public:
    template<typename V> T operator*(const V& v) const {
      return T(static_cast<const T&>(*this)) *= v;
    }
  };

  template<typename T> class Division {
  public:
    template<typename V> T operator/(const V& v) const {
      return T(static_cast<const T&>(*this)) /= v;
    }
  };

  template<typename T> class Modulus {
  public:
    template<typename V> T operator%(const V& v) const {
      return T(static_cast<const T&>(*this)) %= v;
    }
  };
}

template<typename T> class IndivisibleArithmetic : public arithmetic::Addition<T>, public arithmetic::Subtraction<T>, public arithmetic::Multiplication<T> {};

template<typename T> class Arithmetic : public IndivisibleArithmetic<T>, public arithmetic::Division<T> {};

template<typename T> class Ordered {
public:
  template<typename V> bool operator==(const V& v) const {
    return !(static_cast<T>(v) < static_cast<const T&>(*this) || static_cast<const T&>(*this) < static_cast<T>(v));
  }
  
  template<typename V> bool operator!=(const V& v) const {
    return static_cast<T>(v) < static_cast<const T&>(*this) || static_cast<const T&>(*this) < static_cast<T>(v);
  }

  template<typename V> bool operator>(const V& v) const {
    return static_cast<T>(v) < static_cast<const T&>(*this);
  }

  template<typename V> bool operator<=(const V& v) const {
    return !(static_cast<T>(v) < static_cast<const T&>(*this));
  }

  template<typename V> bool operator>=(const V& v) const {
    return !(static_cast<const T&>(*this) < static_cast<T>(v));
  }
};

template<typename T> inline T gcd(T a, T b) {
  return __gcd(a, b);
}

template<typename T> inline T lcm(T a, T b) {
  return a / gcd(a, b) * b;
}

template<typename T> inline T floor(T a, T b) {
  return floor(a / b) * b <= a ? floor(a / b) : floor(a / b) - 1;
}

template<typename T> inline T ceil(T a, T b) {
  return floor(a + b - 1, b);
}

template<typename T> inline T round(T a, T b) {
  return floor(a + b / 2);
}

template<typename T> inline T mod(T a, T b) {
  return a - floor(a, b) * b;
}

template<typename T> inline T factorial(T n) {
  return n <= 1 ? 1 : factorial(n - 1) * n;
}

class Real : public Arithmetic<Real>, public arithmetic::Modulus<Real>, public Ordered<Real> {
private:
  static long double EPS;
  long double val;

  operator long double() const {
    return val;
  }

public:
  Real() {}

  Real(long double val) : val(val) {}

  Real operator-() const {
    return -val;
  }

  template<typename T> Real operator+=(const T& r) {
    val += static_cast<long double>(r);
    return *this;
  }

  template<typename T> Real operator-=(const T& r) {
    val -= static_cast<long double>(r);
    return *this;
  }

  template<typename T> Real operator*=(const T& r) {
    val *= static_cast<long double>(r);
    return *this;
  }

  template<typename T> Real operator/=(const T& r) {
    val /= static_cast<long double>(r);
    return *this;
  }

  template<typename T> Real operator%=(const T& r) {
    return *this = mod(*this, static_cast<Real>(r));
  }

  template<typename T> Real operator-(const T& v) const {
    return Real(*this) -= v;
  }

  template<typename T> Real operator*(const T& v) const {
    return Real(*this) *= v;
  }

  template<typename T> Real operator/(const T& v) const {
    return Real(*this) /= v;
  }

  template<typename T> bool operator<(const T r) const {
    return val < static_cast<long double>(r) - EPS;
  }

  Real abs() const {
    return std::abs(val);
  }

  Real sqrt() const {
    return std::sqrt(val);
  }

  long double toLongDouble() const {
    return val;
  }
};

long double Real::EPS = 1e-10;

inline ostream& operator<<(ostream& os, const Real& a) {
  os << fixed << setprecision(15) << a.toLongDouble();
  return os;
}

inline istream& operator>>(istream& is, Real& a) {
	long double n;
	is >> n;
	a = n;
	return is;
}

Real floor(const Real& r) {
  return floor(r.toLongDouble());
}

class Point : public Arithmetic<Point>, public Ordered<Point> {
public:
  Real x, y;

  Point() {}

  Point(const Real& x) : x(x), y(0) {}

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

  Point operator+=(const Point& p) {
    x += p.x;
    y += p.y;
    return *this;
  }

  Point operator-=(const Point& p) {
    x -= p.x;
    y -= p.y;
    return *this;
  }

  Point operator*=(const Point& p) {
    Real xx = x * p.x - y * p.y;
    y = x * p.y + y * p.x;
    x = xx;
    return *this;
  }

  Point operator*=(const Real& r) {
    x *= r;
    y *= r;
    return *this;
  }

  Point operator/=(const Point& p) {
    Real nrm = p.norm();
    Real xx = (x * p.x + y * p.y) / nrm;
    y = (y * p.x - x * p.y) / nrm;
    x = xx;
    return *this;
  }

  Point operator/=(const Real& r) {
    x /= r;
    y /= r;
    return *this;
  }

  bool operator<(const Point& p) const {
    return (x == p.x) ? y < p.y : x < p.x;
  }

  Real norm() const {
    return x * x + y * y;
  }

  Real abs() const {
    return norm().sqrt();
  }

  Point conj() const {
    return Point(x, -y);
  }
};

inline Point operator*(const Real& real, const Point& point) {
  return point * real;
}

inline Point operator/(const Real& real, const Point& point) {
  return point / real;
}

inline ostream& operator<<(ostream& os, const Point& point) {
	os << point.x << " " << point.y;
	return os;
}

inline istream& operator>>(istream& is, Point& point) {
  Real x, y;
	is >> x >> y;
	point = Point(x, y);
	return is;
}

class Line {
public:
  Point a, b;

  Line() {}

  Line (const Point& a, const Point& b) : a(a), b(b) {}

  bool operator==(const Line& line) const {
    return ((line.vec() / vec()).y == 0) && (((line.a - a) / vec()).y == 0);
  }

  Point vec() const {
    return b - a;
  }
};

inline ostream& operator<<(ostream& os, const Line& line) {
	os << line.a << " " << line.b;
	return os;
}

inline istream& operator>>(istream& is, Line& line) {
  Point a, b;
  is >> a >> b;
  line = Line(a, b);
  return is;
}

class Segment : public Line, public Ordered<Segment> {
public:
  Segment() {}

  Segment (const Point& a, const Point& b) : Line(a, b) {}

  bool operator<(const Segment& segment) const {
    return a == segment.a ? b < segment.b : a < segment.a;
  }
};

enum CCW{LEFT = 1, RIGHT = 2, BACK = 4, FRONT = 8, ON = 16};

int ccw(const Point& a, const Point& b, const Point& c) {
  Point p = (c - a) / (b - a);
  if (p.y > 0) return LEFT;
  if (p.y < 0) return RIGHT;
  if (p.x < 0) return BACK;
  if (p.x > 1) return FRONT;
  return ON;
}

int ccw(const Segment& segment, const Point& point) {
  return ccw(segment.a, segment.b, point);
}

int ccw(const Line& line, const Point& point) {
  int res = ccw(line.a, line.b, point);
  if (res == BACK || res == FRONT) res = ON;
  return res;
}

class Polygon : public vector<Point> {
public:
  Polygon() {}

  Polygon(int n) : vector<Point>(n) {}

  Polygon(const initializer_list<Point>& p) : vector<Point>(p) {}

  Polygon(const vector<Point>& p) : vector<Point>(p) {}

  vector<Segment> getSides() const {
    if (size() <= 1u) return {};
    vector<Segment> res;
    Point pre = back();
    for (const auto& point : *this) {
      res.emplace_back(pre, point);
      pre = point;
    }
    return res;
  }

  vector<array<Point, 3>> getCorners() const {
    if (size() <= 2u) return {};
    vector<array<Point, 3>> res;
    Point pre1 = *(end() - 2), pre2 = back();
    for (const auto& point : *this) {
      res.emplace_back(array<Point,3>({{pre1, pre2, point}}));
      pre1 = pre2;
      pre2 = point;
    }
    return res;
  }

  Point& operator[](int i) {
    return vector::operator[](mod(i, (int)size()));
  }

  const Point& operator[](int i) const {
    return vector::operator[](mod(i, (int)size()));
  }

  template<bool strict = false> bool cover(const Point& point) const {
    bool res = false;
    for (auto& side : getSides()) {
      if (ccw(side, point) == ON) return strict ? false : true;
      if (side.a.y > side.b.y) std::swap(side.a, side.b);
      if (side.a.y <= point.y && point.y < side.b.y && ((side.b - point) / (side.a - point)).y > 0) res = !res;
    }
    return res;
  }
};

template<bool strict = false> inline bool intersect(const Line& line1, const Line& line2) {
  if (strict) return (line1.vec() / line2.vec()).y != 0;
  return ((line1.vec() / line2.vec()).y != 0) || (line1 == line2);
}

template<bool strict = false> inline bool intersect(const Line& line, const Segment& segment) {
  Point p1 = (segment.a - line.a) / line.vec(), p2 = (segment.b - line.a) / line.vec();
  if (strict) return p1.y * p2.y < 0;
  return p1.y * p2.y <= 0;
}

template<bool strict = false> inline bool intersect(const Segment& segment, const Line& line) {
  return intersect(line, segment);
}

template<bool strict = false> inline bool intersect(const Segment& segment1, const Segment& segment2) {
  int ccw1 = ccw(segment1, segment2.a) | ccw(segment1, segment2.b);
  int ccw2 = ccw(segment2, segment1.a) | ccw(segment2, segment1.b);
  if (strict) return (ccw1 & ccw2) == (LEFT | RIGHT);
  return ((ccw1 & ccw2) == (LEFT | RIGHT)) || ((ccw1 | ccw2) & ON);
}

inline Point crossPoint(const Line& line1, const Line& line2) {
  return line1.a + line1.vec() * ((line2.a - line1.a) / line2.vec()).y / (line1.vec() / line2.vec()).y;
}

template<bool strict = true> class ConvexPolygon : public Polygon {
public:
  ConvexPolygon() {}

  ConvexPolygon(int n) : Polygon(n) {}

  ConvexPolygon(vector<Point> points) {
    int flag = ~(strict ? LEFT : LEFT | FRONT);
    sort(points.begin(), points.end());
    for (int i = 0; i < (int)points.size(); emplace_back(points[i++])) {
      while (size() > 1u && ccw(*(end() - 2), back(), points[i]) & flag) pop_back();
    }
    for (int i = points.size() - 2, r = size(); i >= 0; emplace_back(points[i--])) {
      while ((int)size() > r && ccw(*(end() - 2), back(), points[i]) & flag) pop_back();
    }
    pop_back();
  }

  Real diameter() {
    auto sides = getSides();
    int i = min_element(sides.begin(), sides.end()) - sides.begin();
    int j = max_element(sides.begin(), sides.end()) - sides.begin();
    sides.insert(sides.end(), sides.begin(), sides.end());
    Real res = 0;
    for (int k = 0; k < 2 * size(); ++k) {
      if ((sides[i].vec() / sides[j].vec()).y >= 0) ++i;
      else ++j;
      res = max(res, (sides[i].a - sides[j].a).abs());
    }
    return res;
  }

  ConvexPolygon cut(const Line& line) {
    ConvexPolygon res;
    auto sides = getSides();
    for (const auto& side : sides) {
      if (ccw(line, side.a) != RIGHT) res.push_back(side.a);
      if (intersect<true>(line, side)) res.push_back(crossPoint(line, side));
    }
    return res;
  }
};

int main() {
  vector<Point> p(5);
  for (auto& i : p) cin >> i;
  cout << (ConvexPolygon<>(p).size() == 5 ? "YES" : "NO") << endl;
}