// A C++ program to find convex hull of a set of points. Refer
// https://www.geeksforgeeks.org/orientation-3-ordered-points/
// for explanation of orientation()
#include <bits/stdc++.h>
using namespace std;
struct Point
{
int x, y;
};
// To find orientation of ordered triplet (p, q, r).
// The function returns following values
// 0 --> p, q and r are collinear
// 1 --> Clockwise
// 2 --> Counterclockwise
int orientation(Point p, Point q, Point r)
{
int val = (q.y - p.y) * (r.x - q.x) -
(q.x - p.x) * (r.y - q.y);
if (val == 0) return 0; // collinear
return (val > 0)? 1: 2; // clock or counterclock wise
}
// Prints convex hull of a set of n points.
void convexHull(Point points[], int n)
{
// There must be at least 3 points
if (n < 3) return;
// Initialize Result
vector<Point> hull;
// Find the leftmost point
int l = 0;
for (int i = 1; i < n; i++)
if (points[i].x < points[l].x)
l = i;
// Start from leftmost point, keep moving counterclockwise
// until reach the start point again. This loop runs O(h)
// times where h is number of points in result or output.
int p = l, q;
do
{
// Add current point to result
hull.push_back(points[p]);
// Search for a point 'q' such that orientation(p, q,
// x) is counterclockwise for all points 'x'. The idea
// is to keep track of last visited most counterclock-
// wise point in q. If any point 'i' is more counterclock-
// wise than q, then update q.
q = (p+1)%n;
for (int i = 0; i < n; i++)
{
// If i is more counterclockwise than current q, then
// update q
if (orientation(points[p], points[i], points[q]) == 2)
q = i;
}
// Now q is the most counterclockwise with respect to p
// Set p as q for next iteration, so that q is added to
// result 'hull'
p = q;
} while (p != l); // While we don't come to first point
// Print Result
for (int i = 0; i < hull.size(); i++)
cout << "(" << hull[i].x << ", "
<< hull[i].y << ")\n";
}
// Driver program to test above functions
int main()
{
Point points[] = {{0, 3}, {2, 2}, {1, 1}, {2, 1},
{3, 0}, {0, 0}, {3, 3}};
int n = sizeof(points)/sizeof(points[0]);
convexHull(points, n);
return 0;
}