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import java.util.ArrayList;
import java.util.Comparator;
 * @author dimgrichr
 * Space complexity: O(n)
 * Time complexity: O(nlogn), because it is a divide and conquer algorithm
public class SkylineAlgorithm {
    private ArrayList<Point> points;
     * Main constructor of the application.
     * ArrayList points gets created, which represents the sum of all edges.
    public SkylineAlgorithm() {
        points = new ArrayList<>();
     * @return points, the ArrayList that includes all points.
    public ArrayList<Point> getPoints() {
        return points;
     * The main divide and conquer, and also recursive algorithm.
     * It gets an ArrayList full of points as an argument.
     * If the size of that ArrayList is 1 or 2,
     * the ArrayList is returned as it is, or with one less point
     * (if the initial size is 2 and one of it's points, is dominated by the other one).
     * On the other hand, if the ArrayList's size is bigger than 2,
     * the function is called again, twice,
     * with arguments the corresponding half of the initial ArrayList each time.
     * Once the flashback has ended, the function produceFinalSkyLine gets called,
     * in order to produce the final skyline, and return it.
     * @param list, the initial list of points
     * @return leftSkyLine, the combination of first half's and second half's skyline
     * @see Point
     * @see produceFinalSkyLine
    public ArrayList<Point> produceSubSkyLines(ArrayList<Point> list) {
        // part where function exits flashback
        int size = list.size();
        if (size == 1) {
            return list;
        } else if (size == 2) {
            if (list.get(0).dominates(list.get(1))) {
                list.remove(1);
            } else {
                if (list.get(1).dominates(list.get(0))) {
                    list.remove(0);
            return list;
        // recursive part of the function
        ArrayList<Point> leftHalf = new ArrayList<>();
        ArrayList<Point> rightHalf = new ArrayList<>();
        for (int i = 0; i < list.size(); i++) {
            if (i < list.size() / 2) {
                leftHalf.add(list.get(i));
            } else {
                rightHalf.add(list.get(i));
        ArrayList<Point> leftSubSkyLine = produceSubSkyLines(leftHalf);
        ArrayList<Point> rightSubSkyLine= produceSubSkyLines(rightHalf);
        // skyline is produced
        return produceFinalSkyLine(leftSubSkyLine, rightSubSkyLine);
     * The first half's skyline gets cleared
     * from some points that are not part of the final skyline
     * (Points with same x-value and different y=values. The point with the smallest y-value is kept).
     * Then, the minimum y-value of the points of first half's skyline is found.
     * That helps us to clear the second half's skyline, because, the points
     * of second half's skyline that have greater y-value of the minimum y-value that we found before,
     * are dominated, so they are not part of the final skyline.
     * Finally, the "cleaned" first half's and second half's skylines, are combined,
     * producing the final skyline, which is returned.
     * @param left  the skyline of the left part of points
     * @param right the skyline of the right part of points
     * @return left the final skyline
    public ArrayList<Point> produceFinalSkyLine(ArrayList<Point> left, ArrayList<Point> right) {
        // dominated points of ArrayList left are removed
        for (int i = 0; i < left.size() - 1; i++) {
            if (left.get(i).x == left.get(i + 1).x && left.get(i).y > left.get(i + 1).y) {
                left.remove(i);
        // minimum y-value is found
        int min = left.get(0).y;
        for (int i = 1; i < left.size(); i++) {
            if (min > left.get(i).y) {
                min = left.get(i).y;
                if (min == 1) {
                    i = left.size();
        // dominated points of ArrayList right are removed
        for (int i = 0; i < right.size(); i++) {
            if (right.get(i).y >= min) {
                right.remove(i);
        // final skyline found and returned
        left.addAll(right);
        return left;
    public static class Point {
        private int x;
        private int y;
        /**
         * The main constructor of Point Class, used to represent the 2 Dimension points.
         * @param x the point's x-value.
         * @param y the point's y-value.
        public Point(int x, int y) {
            this.x = x;
            this.y = y;
        /**
         * @return x, the x-value
        public int getX() {
            return x;
        /**
         * @return y, the y-value
        public int getY() {
            return y;
        /**
         * Based on the skyline theory,
         * it checks if the point that calls the function dominates the argument point.
         * @param p1 the point that is compared
         * @return true if the point wich calls the function dominates p1
         * false otherwise.
        public boolean dominates(Point p1) {
            // checks if p1 is dominated
            return (this.x < p1.x && this.y <= p1.y) || (this.x <= p1.x && this.y < p1.y);
     * It is used to compare the 2 Dimension points,
     * based on their x-values, in order get sorted later.
    class XComparator implements Comparator<Point> {
        @Override
        public int compare(Point a, Point b) {
            return Integer.compare(a.x, b.x);
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