1+ // Taken from https://github.com/chemthan/chemthan/blob/master/Computational%20Geometry/ConvexHull.cpp
2+ #include < bits/stdc++.h>
3+ using namespace std ;
4+ 5+ #define RL double
6+ #define EPS 1e-9
7+ struct point_t {
8+ RL x, y;
9+ point_t () : x(0 ), y(0 ) {}
10+ point_t (RL x, RL y) : x(x), y(y) {}
11+ point_t (const point_t & p) : x(p.x), y(p.y) {}
12+ int operator < (const point_t & rhs) const {return make_pair (y, x) < make_pair (rhs.y , rhs.x );}
13+ int operator == (const point_t & rhs) const {return make_pair (y, x) == make_pair (rhs.y , rhs.x );}
14+ point_t operator + (const point_t & p) const {return point_t (x + p.x , y + p.y );}
15+ point_t operator - (const point_t & p) const {return point_t (x - p.x , y - p.y );}
16+ point_t operator * (RL c) const {return point_t (x * c, y * c);}
17+ point_t operator / (RL c) const {return point_t (x / c, y / c);}
18+ };
19+ RL cross (point_t p, point_t q) {return p.x * q.y - p.y * q.x ;}
20+ RL area (point_t a, point_t b, point_t c) {return fabs (cross (a, b) + cross (b, c) + cross (c, a)) / 2 ;}
21+ // ans > 0 => counterclockwise, ans < 0 => clockwise, ans = 0 => collinear
22+ RL area2 (point_t a, point_t b, point_t c) {return cross (a, b) + cross (b, c) + cross (c, a);}
23+ RL dot (point_t p, point_t q) {return p.x * q.x + p.y * q.y ;}
24+ RL dist (point_t p, point_t q) {return sqrt (dot (p - q, p - q));}
25+ RL dist2 (point_t p, point_t q) {return dot (p - q, p - q);}
26+ point_t RotateCCW90 (point_t p) {return point_t (-p.y , p.x );}
27+ point_t RotateCW90 (point_t p) {return point_t (p.y , -p.x );}
28+ point_t RotateCCW (point_t p, RL t) {return point_t (p.x * cos (t) - p.y * sin (t), p.x * sin (t) + p.y * cos (t));}
29+ int sign (RL x) {return x < -EPS ? -1 : x > EPS;}
30+ int sign (RL x, RL y) {return sign (x - y);}
31+ ostream& operator << (ostream& os, const point_t & p) {
32+ os << " (" x << " ," y << " )"
33+ return os;
34+ }
35+ 36+ // Returns points of the convex hull in counterclockwise order in O(nlgn)
37+ void ConvexHull (vector<point_t >& pts) {
38+ sort (pts.begin (), pts.end ());
39+ pts.erase (unique (pts.begin (), pts.end ()), pts.end ());
40+ vector<point_t > up, dn;
41+ for (int i = 0 ; i < pts.size (); i++) {
42+ // If we want to include collinear points in the hull (i.e. points lying on the boundary),
43+ // make the inequality checks strict.
44+ while (up.size () > 1 && area2 (up[up.size () - 2 ], up.back (), pts[i]) >= 0 ) up.pop_back ();
45+ while (dn.size () > 1 && area2 (dn[dn.size () - 2 ], dn.back (), pts[i]) <= 0 ) dn.pop_back ();
46+ up.push_back (pts[i]);
47+ dn.push_back (pts[i]);
48+ }
49+ pts = dn;
50+ for (int i = up.size () - 2 ; i >= 1 ; i--) pts.push_back (up[i]);
51+ }
52+ 53+ int main () {
54+ int n = 10 ;
55+ vector<point_t > pts;
56+ for (int i = 0 ; i < n; i++) {
57+ pts.push_back (point_t (rand () % 100 , rand () % 100 ));
58+ }
59+ cout << " Points:\n "
60+ for (const auto & pt : pts) cout << pt << " "
61+ ConvexHull (pts);
62+ cout << " \n Hull:\n "
63+ for (const auto & pt : pts) cout << pt << " "
64+ return 0 ;
65+ }
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