From 7105397e5d51a697cd8ee7190639b6ead7d5d812 Mon Sep 17 00:00:00 2001
From: AYUSH GUPTA <98117063+ayush-1123@users.noreply.github.com>
Date: Sat, 22 Oct 2022 12:15:09 +0530
Subject: [PATCH] Create Convex Hull

C++ Program to Implement Graham Scan Algorithm to find the Convex Hull for a set of points.
---
 Convex Hull | 119 ++++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 119 insertions(+)
 create mode 100644 Convex Hull

diff --git a/Convex Hull b/Convex Hull
new file mode 100644
index 0000000..e2c696e
--- /dev/null
+++ b/Convex Hull	
@@ -0,0 +1,119 @@
+#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
+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;
+}