JavaAlgorithms/divideconquer/SkylineAlgorithm.java

package skylinealgorithm;

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=new ArrayList<>();
        ArrayList<Point> rightSubSkyLine=new ArrayList<>();
        leftSubSkyLine=produceSubSkyLines(leftHalf);
        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);
                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);
                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
            if((this.x<p1.x && this.y<=p1.y) || (this.x<=p1.x && this.y<p1.y)){
                return true;
            }
            return false;
        }
    }
    /**
     * 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 a.x < b.x ? -1 : a.x == b.x ? 0 : 1;
    }
    }
}