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Graham's convex hull.cpp
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Graham's convex hull.cpp
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// A C++ program to find convex hull of a set of points
// Refer http://www.geeksforgeeks.org/check-if-two-given-line-segments-intersect/
// for explanation of orientation()
#include <iostream>
#include <stack>
#include <stdlib.h>
using namespace std;
struct Point
{
int x;
int y;
};
Point p0;
// A utility function to find next to top in a stack
Point nextToTop(stack<Point> &S)
{
Point p = S.top();
S.pop();
Point res = S.top();
S.push(p);
return res;
}
// A utility function to swap two points
int swap(Point &p1, Point &p2)
{
Point temp = p1;
p1 = p2;
p2 = temp;
}
// A utility function to return square of distance between p1 and p2
int dist(Point p1, Point p2)
{
return (p1.x - p2.x) * (p1.x - p2.x) + (p1.y - p2.y) * (p1.y - p2.y);
}
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; // colinear
return (val > 0) ? 1 : 2; // clock or counterclock wise
}
// A function used by library function qsort() to sort an array of
// points with respect to the first point
int compare(const void *vp1, const void *vp2)
{
Point *p1 = (Point *) vp1;
Point *p2 = (Point *) vp2;
// Find orientation
int o = orientation(p0, *p1, *p2);
if (o == 0)
return (dist(p0, *p2) >= dist(p0, *p1)) ? -1 : 1;
return (o == 2) ? -1 : 1;
}
// Prints convex hull of a set of n points.
void convexHull(Point points[], int n)
{
// Find the bottommost point
int ymin = points[0].y, min = 0;
for (int i = 1; i < n; i++)
{
int y = points[i].y;
// Pick the bottom-most or chose the left most point in case of tie
if ((y < ymin) || (ymin == y && points[i].x < points[min].x))
ymin = points[i].y, min = i;
}
// Place the bottom-most point at first position
swap(points[0], points[min]);
// Sort n-1 points with respect to the first point. A point p1 comes
// before p2 in sorted ouput if p2 has larger polar angle (in
// counterclockwise direction) than p1
p0 = points[0];
qsort(&points[1], n - 1, sizeof(Point), compare);
// Create an empty stack and push first three points to it.
stack<Point> S;
S.push(points[0]);
S.push(points[1]);
S.push(points[2]);
// Process remaining n-3 points
for (int i = 3; i < n; i++)
{
// Keep removing top while the angle formed by points next-to-top,
// top, and points[i] makes a non-left turn
while (orientation(nextToTop(S), S.top(), points[i]) != 2)
S.pop();
S.push(points[i]);
}
// Now stack has the output points, print contents of stack
while (!S.empty())
{
Point p = S.top();
cout << "(" << p.x << ", " << p.y << ")" << endl;
S.pop();
}
}
// Driver program to test above functions
int main()
{
Point points[] = { { 0, 3 }, { 1, 1 }, { 2, 2 }, { 4, 4 }, { 0, 0 },
{ 1, 2 }, { 3, 1 }, { 3, 3 } };
int n = sizeof(points) / sizeof(points[0]);
cout << "The points in the convex hull are: \n";
convexHull(points, n);
return 0;
}