/*This is a Java Program to implement Quick Hull Algorithm to find convex hull. Here we’ll talk about the Quick Hull algorithm, which is one of the easiest to implement and has a reasonable expected running time of O(n log n).*/ import java.util.ArrayList; import java.util.Scanner; public class QuickHull { public ArrayList quickHull(ArrayList points) { ArrayList convexHull = new ArrayList(); if (points.size() < 3) return (ArrayList) points.clone(); int minPoint = -1, maxPoint = -1; int minX = Integer.MAX_VALUE; int maxX = Integer.MIN_VALUE; for (int i = 0; i < points.size(); i++) { if (points.get(i).x < minX) { minX = points.get(i).x; minPoint = i; } if (points.get(i).x > maxX) { maxX = points.get(i).x; maxPoint = i; } } Point A = points.get(minPoint); Point B = points.get(maxPoint); convexHull.add(A); convexHull.add(B); points.remove(A); points.remove(B); ArrayList leftSet = new ArrayList(); ArrayList rightSet = new ArrayList(); for (int i = 0; i < points.size(); i++) { Point p = points.get(i); if (pointLocation(A, B, p) == -1) leftSet.add(p); else if (pointLocation(A, B, p) == 1) rightSet.add(p); } hullSet(A, B, rightSet, convexHull); hullSet(B, A, leftSet, convexHull); return convexHull; } public int distance(Point A, Point B, Point C) { int ABx = B.x - A.x; int ABy = B.y - A.y; int num = ABx * (A.y - C.y) - ABy * (A.x - C.x); if (num < 0) num = -num; return num; } public void hullSet(Point A, Point B, ArrayList set, ArrayList hull) { int insertPosition = hull.indexOf(B); if (set.size() == 0) return; if (set.size() == 1) { Point p = set.get(0); set.remove(p); hull.add(insertPosition, p); return; } int dist = Integer.MIN_VALUE; int furthestPoint = -1; for (int i = 0; i < set.size(); i++) { Point p = set.get(i); int distance = distance(A, B, p); if (distance > dist) { dist = distance; furthestPoint = i; } } Point P = set.get(furthestPoint); set.remove(furthestPoint); hull.add(insertPosition, P); // Determine who's to the left of AP ArrayList leftSetAP = new ArrayList(); for (int i = 0; i < set.size(); i++) { Point M = set.get(i); if (pointLocation(A, P, M) == 1) { leftSetAP.add(M); } } // Determine who's to the left of PB ArrayList leftSetPB = new ArrayList(); for (int i = 0; i < set.size(); i++) { Point M = set.get(i); if (pointLocation(P, B, M) == 1) { leftSetPB.add(M); } } hullSet(A, P, leftSetAP, hull); hullSet(P, B, leftSetPB, hull); } public int pointLocation(Point A, Point B, Point P) { int cp1 = (B.x - A.x) * (P.y - A.y) - (B.y - A.y) * (P.x - A.x); if (cp1 > 0) return 1; else if (cp1 == 0) return 0; else return -1; } public static void main(String args[]) { System.out.println("Quick Hull Test"); Scanner sc = new Scanner(System.in); System.out.println("Enter the number of points"); int N = sc.nextInt(); ArrayList points = new ArrayList(); System.out.println("Enter the coordinates of each points: "); for (int i = 0; i < N; i++) { int x = sc.nextInt(); int y = sc.nextInt(); Point e = new Point(x, y); points.add(i, e); } QuickHull qh = new QuickHull(); ArrayList p = qh.quickHull(points); System.out .println("The points in the Convex hull using Quick Hull are: "); for (int i = 0; i < p.size(); i++) System.out.println("(" + p.get(i).x + ", " + p.get(i).y + ")"); sc.close(); } } /* Quick Hull Test Enter the number of points 4 Enter the coordinates of each points: 12 32 45 98 65 12 10 30 The points in the Convex hull using Quick Hull are: (10, 30) (45, 98) (65, 12)