geometry/convex_hull.hpp

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• Last update: 2024-05-01 23:44:47+09:00
• Include: #include "geometry/convex_hull.hpp"
• Link: http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_4_A

Depends on

• geometry/base.hpp
• geometry/point.hpp
• geometry/polygon.hpp

Verified with

• test/verify/aoj-cgl-4-a.test.cpp

Code

#include "base.hpp"
#include "point.hpp"
#include "polygon.hpp"

namespace geometry {
// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_4_A
Polygon convex_hull(Polygon &p, bool strict = true) {
  int n = (int)p.size(), k = 0;
  if (n <= 2) return p;
  sort(begin(p), end(p), compare_x);
  vector<Point> ch(2 * n);
  auto check = [&](int i) {
    return sign(cross(ch[k - 1] - ch[k - 2], p[i] - ch[k - 1])) <= -1 + strict;
  };
  for (int i = 0; i < n; ch[k++] = p[i++]) {
    while (k >= 2 && check(i)) --k;
  }
  for (int i = n - 2, t = k + 1; i >= 0; ch[k++] = p[i--]) {
    while (k >= t && check(i)) --k;
  }
  ch.resize(k - 1);
  return ch;
}
}  // namespace geometry

#line 2 "geometry/base.hpp"

namespace geometry {
using Real = double;
const Real EPS = 1e-8;
const Real PI = acos(static_cast<Real>(-1));

enum { OUT, ON, IN };

inline int sign(const Real &r) { return r <= -EPS ? -1 : r >= EPS ? 1 : 0; }

inline bool equals(const Real &a, const Real &b) { return sign(a - b) == 0; }
}  // namespace geometry
#line 3 "geometry/point.hpp"

namespace geometry {
using Point = complex<Real>;

istream &operator>>(istream &is, Point &p) {
  Real a, b;
  is >> a >> b;
  p = Point(a, b);
  return is;
}

ostream &operator<<(ostream &os, const Point &p) {
  return os << real(p) << " " << imag(p);
}

Point operator*(const Point &p, const Real &d) {
  return Point(real(p) * d, imag(p) * d);
}

// rotate point p counterclockwise by theta rad
Point rotate(Real theta, const Point &p) {
  return Point(cos(theta) * real(p) - sin(theta) * imag(p),
               sin(theta) * real(p) + cos(theta) * imag(p));
}

Real cross(const Point &a, const Point &b) {
  return real(a) * imag(b) - imag(a) * real(b);
}

Real dot(const Point &a, const Point &b) {
  return real(a) * real(b) + imag(a) * imag(b);
}

bool compare_x(const Point &a, const Point &b) {
  return equals(real(a), real(b)) ? imag(a) < imag(b) : real(a) < real(b);
}

bool compare_y(const Point &a, const Point &b) {
  return equals(imag(a), imag(b)) ? real(a) < real(b) : imag(a) < imag(b);
}

using Points = vector<Point>;
}  // namespace geometry
#line 2 "geometry/polygon.hpp"

#line 4 "geometry/polygon.hpp"

namespace geometry {
using Polygon = vector<Point>;
using Polygons = vector<Polygon>;
}  // namespace geometry
#line 4 "geometry/convex_hull.hpp"

namespace geometry {
// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_4_A
Polygon convex_hull(Polygon &p, bool strict = true) {
  int n = (int)p.size(), k = 0;
  if (n <= 2) return p;
  sort(begin(p), end(p), compare_x);
  vector<Point> ch(2 * n);
  auto check = [&](int i) {
    return sign(cross(ch[k - 1] - ch[k - 2], p[i] - ch[k - 1])) <= -1 + strict;
  };
  for (int i = 0; i < n; ch[k++] = p[i++]) {
    while (k >= 2 && check(i)) --k;
  }
  for (int i = n - 2, t = k + 1; i >= 0; ch[k++] = p[i--]) {
    while (k >= t && check(i)) --k;
  }
  ch.resize(k - 1);
  return ch;
}
}  // namespace geometry

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