diff --git a/divideconquer/SkylineAlgorithm.java b/divideconquer/SkylineAlgorithm.java new file mode 100644 index 000000000000..51bce90c98d2 --- /dev/null +++ b/divideconquer/SkylineAlgorithm.java @@ -0,0 +1,185 @@ +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 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 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 produceSubSkyLines(ArrayList 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 leftHalf = new ArrayList<>(); + ArrayList 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 leftSubSkyLine = produceSubSkyLines(leftHalf); + ArrayList 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 produceFinalSkyLine(ArrayList left, ArrayList 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 + 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 { + @Override + public int compare(Point a, Point b) { + return Integer.compare(a.x, b.x); + } + } +}