Java/src/main/java/com/thealgorithms/geometry/ConvexHull.java

package com.thealgorithms.geometry;

import java.util.ArrayList;
import java.util.Collection;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashSet;
import java.util.List;
import java.util.Set;
import java.util.TreeSet;

/**
 * A class providing algorithms to compute the convex hull of a set of points
 * using brute-force and recursive methods.
 *
 * Convex hull: The smallest convex polygon that contains all the given points.
 *
 * Algorithms provided:
 * 1. Brute-Force Method
 * 2. Recursive (Divide-and-Conquer) Method
 *
 * @author Hardvan
 */
public final class ConvexHull {
    private ConvexHull() {
    }

    private static boolean checkPointOrientation(Point i, Point j, Point k) {
        int detK = Point.orientation(i, j, k);
        if (detK > 0) {
            return true; // pointsLeftOfIJ
        } else if (detK < 0) {
            return false; // pointsRightOfIJ
        } else {
            return k.compareTo(i) >= 0 && k.compareTo(j) <= 0;
        }
    }

    public static List<Point> convexHullBruteForce(List<Point> points) {
        Set<Point> convexSet = new TreeSet<>(Comparator.naturalOrder());

        for (int i = 0; i < points.size() - 1; i++) {
            for (int j = i + 1; j < points.size(); j++) {
                boolean allPointsOnOneSide = true;
                boolean leftSide = checkPointOrientation(points.get(i), points.get(j), points.get((i + 1) % points.size()));

                for (int k = 0; k < points.size(); k++) {
                    if (k != i && k != j && checkPointOrientation(points.get(i), points.get(j), points.get(k)) != leftSide) {
                        allPointsOnOneSide = false;
                        break;
                    }
                }

                if (allPointsOnOneSide) {
                    convexSet.add(points.get(i));
                    convexSet.add(points.get(j));
                }
            }
        }

        return new ArrayList<>(convexSet);
    }

    public static List<Point> convexHullRecursive(List<Point> points) {
        Collections.sort(points);
        Set<Point> convexSet = new HashSet<>();
        Point leftMostPoint = points.get(0);
        Point rightMostPoint = points.get(points.size() - 1);

        convexSet.add(leftMostPoint);
        convexSet.add(rightMostPoint);

        List<Point> upperHull = new ArrayList<>();
        List<Point> lowerHull = new ArrayList<>();

        for (int i = 1; i < points.size() - 1; i++) {
            int det = Point.orientation(leftMostPoint, rightMostPoint, points.get(i));
            if (det > 0) {
                upperHull.add(points.get(i));
            } else if (det < 0) {
                lowerHull.add(points.get(i));
            }
        }

        constructHull(upperHull, leftMostPoint, rightMostPoint, convexSet);
        constructHull(lowerHull, rightMostPoint, leftMostPoint, convexSet);

        List<Point> result = new ArrayList<>(convexSet);
        Collections.sort(result);
        return result;
    }

    private static void constructHull(Collection<Point> points, Point left, Point right, Set<Point> convexSet) {
        if (!points.isEmpty()) {
            Point extremePoint = null;
            int extremePointDistance = Integer.MIN_VALUE;
            List<Point> candidatePoints = new ArrayList<>();

            for (Point p : points) {
                int det = Point.orientation(left, right, p);
                if (det > 0) {
                    candidatePoints.add(p);
                    if (det > extremePointDistance) {
                        extremePointDistance = det;
                        extremePoint = p;
                    }
                }
            }

            if (extremePoint != null) {
                constructHull(candidatePoints, left, extremePoint, convexSet);
                convexSet.add(extremePoint);
                constructHull(candidatePoints, extremePoint, right, convexSet);
            }
        }
    }
}