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@@ -1,378 +1,338 @@
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package divideconquer;
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/**
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* For a set of points in a coordinates system (10000 maximum),
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* ClosestPair class calculates the two closest points.
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* For a set of points in a coordinates system (10000 maximum), ClosestPair class calculates the two
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* closest points.
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*
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* @author: anonymous
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* @author: Marisa Afuera
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*/
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public final class ClosestPair {
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/** Number of points */
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int numberPoints = 0;
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/** Input data, maximum 10000. */
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private Location[] array;
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/** Minimum point coordinate. */
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Location point1 = null;
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/** Minimum point coordinate. */
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Location point2 = null;
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/** Minimum point length. */
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private static double minNum = Double.MAX_VALUE;
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public static void setMinNum(double minNum) {
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ClosestPair.minNum = minNum;
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}
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public static void setSecondCount(int secondCount) {
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ClosestPair.secondCount = secondCount;
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}
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/** secondCount */
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private static int secondCount = 0;
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/** Constructor. */
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ClosestPair(int points) {
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numberPoints = points;
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array = new Location[numberPoints];
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}
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/** Location class is an auxiliary type to keep points coordinates. */
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public static class Location {
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double x = 0;
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double y = 0;
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/**
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* Number of points
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* @param xpar (IN Parameter) x coordinate <br>
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* @param ypar (IN Parameter) y coordinate <br>
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*/
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int numberPoints = 0;
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/**
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* Input data, maximum 10000.
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*/
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private Location[] array;
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/**
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* Minimum point coordinate.
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*/
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Location point1 = null;
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/**
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* Minimum point coordinate.
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*/
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Location point2 = null;
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/**
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* Minimum point length.
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*/
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private static double minNum = Double.MAX_VALUE;
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public static void setMinNum(double minNum) {
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ClosestPair.minNum = minNum;
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Location(final double xpar, final double ypar) { // Save x, y coordinates
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this.x = xpar;
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this.y = ypar;
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}
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}
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public static void setSecondCount(int secondCount) {
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ClosestPair.secondCount = secondCount;
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}
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public Location[] createLocation(int numberValues) {
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return new Location[numberValues];
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}
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/**
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* secondCount
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*/
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private static int secondCount = 0;
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public Location buildLocation(double x, double y) {
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return new Location(x, y);
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}
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/**
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* Constructor.
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*/
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ClosestPair(int points) {
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numberPoints = points;
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array = new Location[numberPoints];
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}
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/**
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* xPartition function: arrange x-axis.
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*
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* @param a (IN Parameter) array of points <br>
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* @param first (IN Parameter) first point <br>
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* @param last (IN Parameter) last point <br>
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* @return pivot index
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*/
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public int xPartition(final Location[] a, final int first, final int last) {
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/**
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* Location class is an auxiliary type to keep points coordinates.
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*/
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public static class Location {
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double x = 0;
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double y = 0;
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/**
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* @param xpar (IN Parameter) x coordinate <br/>
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* @param ypar (IN Parameter) y coordinate <br/>
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*/
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Location(final double xpar, final double ypar) { //Save x, y coordinates
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this.x = xpar;
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this.y = ypar;
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}
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}
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public Location[] createLocation(int numberValues) {
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return new Location[numberValues];
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}
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public Location buildLocation(double x, double y) {
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return new Location(x, y);
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}
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/**
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* xPartition function: arrange x-axis.
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*
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* @param a (IN Parameter) array of points <br/>
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* @param first (IN Parameter) first point <br/>
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* @param last (IN Parameter) last point <br/>
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* @return pivot index
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*/
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public int xPartition(
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final Location[] a, final int first, final int last) {
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Location pivot = a[last]; // pivot
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int i = first - 1;
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Location temp; // Temporarily store value for position transformation
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for (int j = first; j <= last - 1; j++) {
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if (a[j].x <= pivot.x) { // Less than or less than pivot
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i++;
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temp = a[i]; // array[i] <-> array[j]
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a[i] = a[j];
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a[j] = temp;
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}
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}
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Location pivot = a[last]; // pivot
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int i = first - 1;
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Location temp; // Temporarily store value for position transformation
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for (int j = first; j <= last - 1; j++) {
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if (a[j].x <= pivot.x) { // Less than or less than pivot
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i++;
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temp = a[i]; // array[pivot] <-> array[i]
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a[i] = a[last];
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a[last] = temp;
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return i; // pivot index
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temp = a[i]; // array[i] <-> array[j]
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a[i] = a[j];
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a[j] = temp;
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}
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}
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i++;
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temp = a[i]; // array[pivot] <-> array[i]
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a[i] = a[last];
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a[last] = temp;
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return i; // pivot index
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}
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/**
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* yPartition function: arrange y-axis.
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*
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* @param a (IN Parameter) array of points <br/>
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* @param first (IN Parameter) first point <br/>
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* @param last (IN Parameter) last point <br/>
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* @return pivot index
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*/
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/**
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* yPartition function: arrange y-axis.
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*
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* @param a (IN Parameter) array of points <br>
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* @param first (IN Parameter) first point <br>
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* @param last (IN Parameter) last point <br>
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* @return pivot index
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*/
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public int yPartition(final Location[] a, final int first, final int last) {
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public int yPartition(
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final Location[] a, final int first, final int last) {
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Location pivot = a[last]; // pivot
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int i = first - 1;
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Location temp; // Temporarily store value for position transformation
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for (int j = first; j <= last - 1; j++) {
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if (a[j].y <= pivot.y) { // Less than or less than pivot
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i++;
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temp = a[i]; // array[i] <-> array[j]
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a[i] = a[j];
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a[j] = temp;
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}
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}
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Location pivot = a[last]; // pivot
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int i = first - 1;
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Location temp; // Temporarily store value for position transformation
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for (int j = first; j <= last - 1; j++) {
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if (a[j].y <= pivot.y) { // Less than or less than pivot
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i++;
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temp = a[i]; // array[pivot] <-> array[i]
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a[i] = a[last];
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a[last] = temp;
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return i; // pivot index
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temp = a[i]; // array[i] <-> array[j]
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a[i] = a[j];
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a[j] = temp;
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}
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}
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i++;
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temp = a[i]; // array[pivot] <-> array[i]
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a[i] = a[last];
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a[last] = temp;
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return i; // pivot index
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}
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/**
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* xQuickSort function: //x-axis Quick Sorting.
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*
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* @param a (IN Parameter) array of points <br/>
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* @param first (IN Parameter) first point <br/>
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* @param last (IN Parameter) last point <br/>
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*/
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/**
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* xQuickSort function: //x-axis Quick Sorting.
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*
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* @param a (IN Parameter) array of points <br>
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* @param first (IN Parameter) first point <br>
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* @param last (IN Parameter) last point <br>
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*/
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public void xQuickSort(final Location[] a, final int first, final int last) {
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public void xQuickSort(
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final Location[] a, final int first, final int last) {
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if (first < last) {
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int q = xPartition(a, first, last); // pivot
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xQuickSort(a, first, q - 1); // Left
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xQuickSort(a, q + 1, last); // Right
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}
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if (first < last) {
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int q = xPartition(a, first, last); // pivot
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xQuickSort(a, first, q - 1); // Left
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xQuickSort(a, q + 1, last); // Right
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}
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}
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/**
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* yQuickSort function: //y-axis Quick Sorting.
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*
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* @param a (IN Parameter) array of points <br/>
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* @param first (IN Parameter) first point <br/>
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* @param last (IN Parameter) last point <br/>
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*/
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/**
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* yQuickSort function: //y-axis Quick Sorting.
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*
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* @param a (IN Parameter) array of points <br>
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* @param first (IN Parameter) first point <br>
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* @param last (IN Parameter) last point <br>
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*/
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public void yQuickSort(final Location[] a, final int first, final int last) {
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public void yQuickSort(
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final Location[] a, final int first, final int last) {
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if (first < last) {
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int q = yPartition(a, first, last); // pivot
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yQuickSort(a, first, q - 1); // Left
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yQuickSort(a, q + 1, last); // Right
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}
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if (first < last) {
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int q = yPartition(a, first, last); // pivot
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yQuickSort(a, first, q - 1); // Left
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yQuickSort(a, q + 1, last); // Right
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}
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}
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/**
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* closestPair function: find closest pair.
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*
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* @param a (IN Parameter) array stored before divide <br/>
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* @param indexNum (IN Parameter) number coordinates divideArray <br/>
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* @return minimum distance <br/>
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*/
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/**
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* closestPair function: find closest pair.
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*
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* @param a (IN Parameter) array stored before divide <br>
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* @param indexNum (IN Parameter) number coordinates divideArray <br>
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* @return minimum distance <br>
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*/
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public double closestPair(final Location[] a, final int indexNum) {
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public double closestPair(final Location[] a, final int indexNum) {
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Location[] divideArray = new Location[indexNum];
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System.arraycopy(a, 0, divideArray, 0, indexNum); // Copy previous array
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int divideX = indexNum / 2; // Intermediate value for divide
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Location[] leftArray = new Location[divideX]; //divide - left array
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//divide-right array
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Location[] rightArray = new Location[indexNum - divideX];
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if (indexNum <= 3) { // If the number of coordinates is 3 or less
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return bruteForce(divideArray);
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}
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//divide-left array
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System.arraycopy(divideArray, 0, leftArray, 0, divideX);
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//divide-right array
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System.arraycopy(
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divideArray, divideX, rightArray, 0, indexNum - divideX);
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double minLeftArea = 0; //Minimum length of left array
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double minRightArea = 0; //Minimum length of right array
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double minValue = 0; //Minimum lengt
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minLeftArea = closestPair(leftArray, divideX); // recursive closestPair
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minRightArea = closestPair(rightArray, indexNum - divideX);
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// window size (= minimum length)
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minValue = Math.min(minLeftArea, minRightArea);
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// Create window. Set the size for creating a window
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// and creating a new array for the coordinates in the window
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for (int i = 0; i < indexNum; i++) {
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double xGap = Math.abs(divideArray[divideX].x - divideArray[i].x);
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if (xGap < minValue) {
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ClosestPair.setSecondCount(secondCount + 1); // size of the array
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} else {
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if (divideArray[i].x > divideArray[divideX].x) {
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break;
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}
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}
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}
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// new array for coordinates in window
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Location[] firstWindow = new Location[secondCount];
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int k = 0;
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for (int i = 0; i < indexNum; i++) {
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double xGap = Math.abs(divideArray[divideX].x - divideArray[i].x);
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if (xGap < minValue) { // if it's inside a window
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firstWindow[k] = divideArray[i]; // put in an array
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k++;
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} else {
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if (divideArray[i].x > divideArray[divideX].x) {
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break;
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}
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}
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}
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yQuickSort(firstWindow, 0, secondCount - 1); // Sort by y coordinates
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/* Coordinates in Window */
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double length = 0;
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// size comparison within window
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for (int i = 0; i < secondCount - 1; i++) {
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for (int j = (i + 1); j < secondCount; j++) {
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double xGap = Math.abs(firstWindow[i].x - firstWindow[j].x);
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double yGap = Math.abs(firstWindow[i].y - firstWindow[j].y);
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if (yGap < minValue) {
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length = Math.sqrt(Math.pow(xGap, 2) + Math.pow(yGap, 2));
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// If measured distance is less than current min distance
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if (length < minValue) {
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// Change minimum distance to current distance
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minValue = length;
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// Conditional for registering final coordinate
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if (length < minNum) {
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ClosestPair.setMinNum(length);
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point1 = firstWindow[i];
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point2 = firstWindow[j];
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}
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}
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} else {
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break;
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}
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}
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}
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ClosestPair.setSecondCount(0);
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return minValue;
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Location[] divideArray = new Location[indexNum];
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System.arraycopy(a, 0, divideArray, 0, indexNum); // Copy previous array
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int divideX = indexNum / 2; // Intermediate value for divide
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Location[] leftArray = new Location[divideX]; // divide - left array
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// divide-right array
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Location[] rightArray = new Location[indexNum - divideX];
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if (indexNum <= 3) { // If the number of coordinates is 3 or less
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return bruteForce(divideArray);
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}
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// divide-left array
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System.arraycopy(divideArray, 0, leftArray, 0, divideX);
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// divide-right array
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System.arraycopy(divideArray, divideX, rightArray, 0, indexNum - divideX);
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/**
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* bruteForce function: When the number of coordinates is less than 3.
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*
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* @param arrayParam (IN Parameter) array stored before divide <br/>
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* @return <br/>
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*/
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double minLeftArea = 0; // Minimum length of left array
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double minRightArea = 0; // Minimum length of right array
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double minValue = 0; // Minimum lengt
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public double bruteForce(final Location[] arrayParam) {
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minLeftArea = closestPair(leftArray, divideX); // recursive closestPair
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minRightArea = closestPair(rightArray, indexNum - divideX);
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// window size (= minimum length)
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minValue = Math.min(minLeftArea, minRightArea);
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double minValue = Double.MAX_VALUE; // minimum distance
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double length = 0;
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double xGap = 0; // Difference between x coordinates
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double yGap = 0; // Difference between y coordinates
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double result = 0;
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if (arrayParam.length == 2) {
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// Difference between x coordinates
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xGap = (arrayParam[0].x - arrayParam[1].x);
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// Difference between y coordinates
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yGap = (arrayParam[0].y - arrayParam[1].y);
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// distance between coordinates
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length = Math.sqrt(Math.pow(xGap, 2) + Math.pow(yGap, 2));
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// Conditional statement for registering final coordinate
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// Create window. Set the size for creating a window
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// and creating a new array for the coordinates in the window
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for (int i = 0; i < indexNum; i++) {
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double xGap = Math.abs(divideArray[divideX].x - divideArray[i].x);
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if (xGap < minValue) {
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ClosestPair.setSecondCount(secondCount + 1); // size of the array
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} else {
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if (divideArray[i].x > divideArray[divideX].x) {
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break;
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}
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}
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}
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// new array for coordinates in window
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Location[] firstWindow = new Location[secondCount];
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int k = 0;
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for (int i = 0; i < indexNum; i++) {
|
||||
double xGap = Math.abs(divideArray[divideX].x - divideArray[i].x);
|
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if (xGap < minValue) { // if it's inside a window
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firstWindow[k] = divideArray[i]; // put in an array
|
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k++;
|
||||
} else {
|
||||
if (divideArray[i].x > divideArray[divideX].x) {
|
||||
break;
|
||||
}
|
||||
}
|
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}
|
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yQuickSort(firstWindow, 0, secondCount - 1); // Sort by y coordinates
|
||||
/* Coordinates in Window */
|
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double length = 0;
|
||||
// size comparison within window
|
||||
for (int i = 0; i < secondCount - 1; i++) {
|
||||
for (int j = (i + 1); j < secondCount; j++) {
|
||||
double xGap = Math.abs(firstWindow[i].x - firstWindow[j].x);
|
||||
double yGap = Math.abs(firstWindow[i].y - firstWindow[j].y);
|
||||
if (yGap < minValue) {
|
||||
length = Math.sqrt(Math.pow(xGap, 2) + Math.pow(yGap, 2));
|
||||
// If measured distance is less than current min distance
|
||||
if (length < minValue) {
|
||||
// Change minimum distance to current distance
|
||||
minValue = length;
|
||||
// Conditional for registering final coordinate
|
||||
if (length < minNum) {
|
||||
ClosestPair.setMinNum(length);
|
||||
|
||||
ClosestPair.setMinNum(length);
|
||||
point1 = firstWindow[i];
|
||||
point2 = firstWindow[j];
|
||||
}
|
||||
point1 = arrayParam[0];
|
||||
point2 = arrayParam[1];
|
||||
result = length;
|
||||
}
|
||||
} else {
|
||||
break;
|
||||
}
|
||||
if (arrayParam.length == 3) {
|
||||
for (int i = 0; i < arrayParam.length - 1; i++) {
|
||||
for (int j = (i + 1); j < arrayParam.length; j++) {
|
||||
// Difference between x coordinates
|
||||
xGap = (arrayParam[i].x - arrayParam[j].x);
|
||||
// Difference between y coordinates
|
||||
yGap = (arrayParam[i].y - arrayParam[j].y);
|
||||
// distance between coordinates
|
||||
length =
|
||||
Math.sqrt(Math.pow(xGap, 2) + Math.pow(yGap, 2));
|
||||
// If measured distance is less than current min distance
|
||||
if (length < minValue) {
|
||||
// Change minimum distance to current distance
|
||||
minValue = length;
|
||||
if (length < minNum) {
|
||||
// Registering final coordinate
|
||||
ClosestPair.setMinNum(length);
|
||||
point1 = arrayParam[i];
|
||||
point2 = arrayParam[j];
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
result = minValue;
|
||||
}
|
||||
}
|
||||
ClosestPair.setSecondCount(0);
|
||||
return minValue;
|
||||
}
|
||||
|
||||
/**
|
||||
* bruteForce function: When the number of coordinates is less than 3.
|
||||
*
|
||||
* @param arrayParam (IN Parameter) array stored before divide <br>
|
||||
* @return <br>
|
||||
*/
|
||||
public double bruteForce(final Location[] arrayParam) {
|
||||
|
||||
double minValue = Double.MAX_VALUE; // minimum distance
|
||||
double length = 0;
|
||||
double xGap = 0; // Difference between x coordinates
|
||||
double yGap = 0; // Difference between y coordinates
|
||||
double result = 0;
|
||||
|
||||
if (arrayParam.length == 2) {
|
||||
// Difference between x coordinates
|
||||
xGap = (arrayParam[0].x - arrayParam[1].x);
|
||||
// Difference between y coordinates
|
||||
yGap = (arrayParam[0].y - arrayParam[1].y);
|
||||
// distance between coordinates
|
||||
length = Math.sqrt(Math.pow(xGap, 2) + Math.pow(yGap, 2));
|
||||
// Conditional statement for registering final coordinate
|
||||
if (length < minNum) {
|
||||
ClosestPair.setMinNum(length);
|
||||
}
|
||||
point1 = arrayParam[0];
|
||||
point2 = arrayParam[1];
|
||||
result = length;
|
||||
}
|
||||
if (arrayParam.length == 3) {
|
||||
for (int i = 0; i < arrayParam.length - 1; i++) {
|
||||
for (int j = (i + 1); j < arrayParam.length; j++) {
|
||||
// Difference between x coordinates
|
||||
xGap = (arrayParam[i].x - arrayParam[j].x);
|
||||
// Difference between y coordinates
|
||||
yGap = (arrayParam[i].y - arrayParam[j].y);
|
||||
// distance between coordinates
|
||||
length = Math.sqrt(Math.pow(xGap, 2) + Math.pow(yGap, 2));
|
||||
// If measured distance is less than current min distance
|
||||
if (length < minValue) {
|
||||
// Change minimum distance to current distance
|
||||
minValue = length;
|
||||
if (length < minNum) {
|
||||
// Registering final coordinate
|
||||
ClosestPair.setMinNum(length);
|
||||
point1 = arrayParam[i];
|
||||
point2 = arrayParam[j];
|
||||
}
|
||||
}
|
||||
}
|
||||
return result; // If only one point returns 0.
|
||||
}
|
||||
result = minValue;
|
||||
}
|
||||
return result; // If only one point returns 0.
|
||||
}
|
||||
|
||||
/**
|
||||
* main function: execute class.
|
||||
*
|
||||
* @param args (IN Parameter) <br>
|
||||
* @throws IOException If an input or output exception occurred
|
||||
*/
|
||||
public static void main(final String[] args) {
|
||||
|
||||
// Input data consists of one x-coordinate and one y-coordinate
|
||||
|
||||
ClosestPair cp = new ClosestPair(12);
|
||||
cp.array[0] = cp.buildLocation(2, 3);
|
||||
cp.array[1] = cp.buildLocation(2, 16);
|
||||
cp.array[2] = cp.buildLocation(3, 9);
|
||||
cp.array[3] = cp.buildLocation(6, 3);
|
||||
cp.array[4] = cp.buildLocation(7, 7);
|
||||
cp.array[5] = cp.buildLocation(19, 4);
|
||||
cp.array[6] = cp.buildLocation(10, 11);
|
||||
cp.array[7] = cp.buildLocation(15, 2);
|
||||
cp.array[8] = cp.buildLocation(15, 19);
|
||||
cp.array[9] = cp.buildLocation(16, 11);
|
||||
cp.array[10] = cp.buildLocation(17, 13);
|
||||
cp.array[11] = cp.buildLocation(9, 12);
|
||||
|
||||
System.out.println("Input data");
|
||||
System.out.println("Number of points: " + cp.array.length);
|
||||
for (int i = 0; i < cp.array.length; i++) {
|
||||
System.out.println("x: " + cp.array[i].x + ", y: " + cp.array[i].y);
|
||||
}
|
||||
|
||||
/**
|
||||
* main function: execute class.
|
||||
*
|
||||
* @param args (IN Parameter) <br/>
|
||||
* @throws IOException If an input or output
|
||||
* exception occurred
|
||||
*/
|
||||
cp.xQuickSort(cp.array, 0, cp.array.length - 1); // Sorting by x value
|
||||
|
||||
public static void main(final String[] args) {
|
||||
double result; // minimum distance
|
||||
|
||||
//Input data consists of one x-coordinate and one y-coordinate
|
||||
|
||||
ClosestPair cp = new ClosestPair(12);
|
||||
cp.array[0] = cp.buildLocation(2, 3);
|
||||
cp.array[1] = cp.buildLocation(2, 16);
|
||||
cp.array[2] = cp.buildLocation(3, 9);
|
||||
cp.array[3] = cp.buildLocation(6, 3);
|
||||
cp.array[4] = cp.buildLocation(7, 7);
|
||||
cp.array[5] = cp.buildLocation(19, 4);
|
||||
cp.array[6] = cp.buildLocation(10, 11);
|
||||
cp.array[7] = cp.buildLocation(15, 2);
|
||||
cp.array[8] = cp.buildLocation(15, 19);
|
||||
cp.array[9] = cp.buildLocation(16, 11);
|
||||
cp.array[10] = cp.buildLocation(17, 13);
|
||||
cp.array[11] = cp.buildLocation(9, 12);
|
||||
|
||||
System.out.println("Input data");
|
||||
System.out.println("Number of points: " + cp.array.length);
|
||||
for (int i = 0; i < cp.array.length; i++) {
|
||||
System.out.println("x: " + cp.array[i].x + ", y: " + cp.array[i].y);
|
||||
}
|
||||
|
||||
cp.xQuickSort(cp.array, 0, cp.array.length - 1); // Sorting by x value
|
||||
|
||||
double result; // minimum distance
|
||||
|
||||
result = cp.closestPair(cp.array, cp.array.length);
|
||||
// ClosestPair start
|
||||
// minimum distance coordinates and distance output
|
||||
System.out.println("Output Data");
|
||||
System.out.println("(" + cp.point1.x + ", " + cp.point1.y + ")");
|
||||
System.out.println("(" + cp.point2.x + ", " + cp.point2.y + ")");
|
||||
System.out.println("Minimum Distance : " + result);
|
||||
|
||||
}
|
||||
result = cp.closestPair(cp.array, cp.array.length);
|
||||
// ClosestPair start
|
||||
// minimum distance coordinates and distance output
|
||||
System.out.println("Output Data");
|
||||
System.out.println("(" + cp.point1.x + ", " + cp.point1.y + ")");
|
||||
System.out.println("(" + cp.point2.x + ", " + cp.point2.y + ")");
|
||||
System.out.println("Minimum Distance : " + result);
|
||||
}
|
||||
}
|
||||
|
||||
@@ -5,182 +5,165 @@ import java.util.Comparator;
|
||||
|
||||
/**
|
||||
* @author dimgrichr
|
||||
* <p>
|
||||
* Space complexity: O(n)
|
||||
* Time complexity: O(nlogn), because it is a divide and conquer algorithm
|
||||
* <p>Space complexity: O(n) Time complexity: O(nlogn), because it is a divide and conquer
|
||||
* algorithm
|
||||
*/
|
||||
public class SkylineAlgorithm {
|
||||
private ArrayList<Point> points;
|
||||
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<>();
|
||||
/**
|
||||
* 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
|
||||
*/
|
||||
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);
|
||||
|
||||
/**
|
||||
* @return points, the ArrayList that includes all points.
|
||||
*/
|
||||
public ArrayList<Point> getPoints() {
|
||||
return points;
|
||||
// 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 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.
|
||||
* The main constructor of Point Class, used to represent the 2 Dimension points.
|
||||
*
|
||||
* @param list, the initial list of points
|
||||
* @return leftSkyLine, the combination of first half's and second half's skyline
|
||||
* @see Point
|
||||
* @param x the point's x-value.
|
||||
* @param y the point's y-value.
|
||||
*/
|
||||
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);
|
||||
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;
|
||||
}
|
||||
|
||||
/**
|
||||
* 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.
|
||||
* Based on the skyline theory, it checks if the point that calls the function dominates the
|
||||
* argument point.
|
||||
*
|
||||
* @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
|
||||
* @param p1 the point that is compared
|
||||
* @return true if the point wich calls the function dominates p1 false otherwise.
|
||||
*/
|
||||
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 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);
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
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);
|
||||
}
|
||||
/**
|
||||
* 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);
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
Reference in New Issue
Block a user