programming-examples/c++/Computational_Geometry/C++ Program to Implement Graham Scan Algorithm to Find the Convex Hull.cpp

/*This is a C++ Program to implement Graham Scan algorithm. Graham’s scan is a method of computing the convex hull of a finite set of points in the plane with time complexity O(n log n).*/

// 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;
}

/*

The points in the convex hull are:
(0, 3)
(4, 4)
(3, 1)
(0, 0)