Merge pull request TheAlgorithms#683 from dimgrichr/master

yanglbme · web-flow · commit 571315df24bf · 2019-01-15T19:55:26.000+08:00
Addition of the Skyline Algorithm
diff --git a/divideconquer/SkylineAlgorithm.java b/divideconquer/SkylineAlgorithm.java
@@ -0,0 +1,185 @@
+import java.util.ArrayList;
+import java.util.Comparator;
+
+/**
+ * @author dimgrichr
+ * <p>
+ * 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);
+                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<Point> {
+        @Override
+        public int compare(Point a, Point b) {
+            return Integer.compare(a.x, b.x);
+        }
+    }
+}
