geometry/MinimumEnclosingCircle.h

• View this file on GitHub
• Last update: 2025-11-21 16:12:02+07:00

Depends on

• geometry/Circumcircle.h
• geometry/Point.h

Verified with

• tests/Minimum_Enclosing_Circle.test.cpp

Code

#include "Circumcircle.h"

pair<P, ld> mec(vector<P> ps) {
  shuffle(all(ps), mt19937(time(0)));
  P o = ps[0];
  ld r = 0, EPS = 1 + 1e-12;
  for (int i = 0; i < sz(ps); ++i) {
    if ((o - ps[i]).dist() > r * EPS) {
      o = ps[i], r = 0;
      for (int j = 0; j < i; ++j) {
        if ((o - ps[j]).dist() > r * EPS) {
          o = (ps[i] + ps[j]) / 2;
          r = (o - ps[i]).dist();
          for (int k = 0; k < j; ++k) {
            if ((o - ps[k]).dist() > r * EPS) {
              o = ccCenter(ps[i], ps[j], ps[k]);
              r = (o - ps[i]).dist();
            }
          }
        }
      }
    }
  }
  return {o, r};
}

#line 2 "geometry/Point.h"

template <class T>
int sgn(T x) { return (x > 0) - (x < 0); }
template <class T>
struct Point {
  typedef Point P;
  T x, y;
  explicit Point(T x = 0, T y = 0) : x(x), y(y) {}
  bool operator<(P p) const { return tie(x, y) < tie(p.x, p.y); }
  bool operator==(P p) const { return tie(x, y) == tie(p.x, p.y); }
  P operator+(P p) const { return P(x + p.x, y + p.y); }
  P operator-(P p) const { return P(x - p.x, y - p.y); }
  P operator*(T d) const { return P(x * d, y * d); }
  P operator/(T d) const { return P(x / d, y / d); }
  T dot(P p) const { return x * p.x + y * p.y; }
  T cross(P p) const { return x * p.y - y * p.x; }
  T cross(P a, P b) const { return (a - *this).cross(b - *this); }
  T dist2() const { return x * x + y * y; }
  T dist() const { return sqrt(dist2()); }
  // angle to x-axis in interval [-pi, pi]
  T angle() const { return atan2l(y, x); }
  P unit() const { return *this / dist(); }  // makes dist()=1
  P perp() const { return P(-y, x); }        // rotates +90 degrees
  P normal() const { return perp().unit(); }
  // returns point rotated 'a' radians ccw around the origin
  P rotate(ld a) const {
    return P(x * cos(a) - y * sin(a), x * sin(a) + y * cos(a));
  }
  friend ostream& operator<<(ostream& os, P p) {
    return os << "(" << p.x << "," << p.y << ")";
  }
};
#line 2 "geometry/Circumcircle.h"

typedef Point<ld> P;
ld ccRadius(const P& A, const P& B, const P& C) {
  return (B - A).dist() * (C - B).dist() * (A - C).dist() /
         abs((B - A).cross(C - A)) / 2;
}
P ccCenter(const P& A, const P& B, const P& C) {
  P b = C - A, c = B - A;
  return A + (b * c.dist2() - c * b.dist2()).perp() / b.cross(c) / 2;
}
#line 2 "geometry/MinimumEnclosingCircle.h"

pair<P, ld> mec(vector<P> ps) {
  shuffle(all(ps), mt19937(time(0)));
  P o = ps[0];
  ld r = 0, EPS = 1 + 1e-12;
  for (int i = 0; i < sz(ps); ++i) {
    if ((o - ps[i]).dist() > r * EPS) {
      o = ps[i], r = 0;
      for (int j = 0; j < i; ++j) {
        if ((o - ps[j]).dist() > r * EPS) {
          o = (ps[i] + ps[j]) / 2;
          r = (o - ps[i]).dist();
          for (int k = 0; k < j; ++k) {
            if ((o - ps[k]).dist() > r * EPS) {
              o = ccCenter(ps[i], ps[j], ps[k]);
              r = (o - ps[i]).dist();
            }
          }
        }
      }
    }
  }
  return {o, r};
}

Back to top page