Below is the syntax highlighted version of ClosestPair.java
from §9.9 Convex Hull.
/****************************************************************************** * Compilation: javac ClosestPair.java * Execution: java ClosestPair < input.txt * Dependencies: Point2D.java * Data files: https://algs4.cs.princeton.edu/99hull/rs1423.txt * https://algs4.cs.princeton.edu/99hull/kw1260.txt * * Given n points in the plane, find the closest pair in n log n time. * * Note: could speed it up by comparing square of Euclidean distances * instead of Euclidean distances. * ******************************************************************************/ import java.util.Arrays; /** * The {@code ClosestPair} data type computes a closest pair of points * in a set of <em>n</em> points in the plane and provides accessor methods * for getting the closest pair of points and the distance between them. * The distance between two points is their Euclidean distance. * <p> * This implementation uses a divide-and-conquer algorithm. * It runs in O(<em>n</em> log <em>n</em>) time in the worst case and uses * O(<em>n</em>) extra space. * <p> * See also {@link FarthestPair}. * <p> * For additional documentation, see <a href="https://algs4.cs.princeton.edu/99hull">Section 9.9</a> of * <i>Algorithms, 4th Edition</i> by Robert Sedgewick and Kevin Wayne. * * @author Robert Sedgewick * @author Kevin Wayne */ public class ClosestPair { // closest pair of points and their Euclidean distance private Point2D best1, best2; private double bestDistance = Double.POSITIVE_INFINITY; /** * Computes the closest pair of points in the specified array of points. * * @param points the array of points * @throws IllegalArgumentException if {@code points} is {@code null} or if any * entry in {@code points[]} is {@code null} */ public ClosestPair(Point2D[] points) { if (points == null) throw new IllegalArgumentException("constructor argument is null"); for (int i = 0; i < points.length; i++) { if (points[i] == null) throw new IllegalArgumentException("array element " + i + " is null"); } int n = points.length; if (n <= 1) return; // sort by x-coordinate (breaking ties by y-coordinate via stability) Point2D[] pointsByX = new Point2D[n]; for (int i = 0; i < n; i++) pointsByX[i] = points[i]; Arrays.sort(pointsByX, Point2D.Y_ORDER); Arrays.sort(pointsByX, Point2D.X_ORDER); // check for coincident points for (int i = 0; i < n-1; i++) { if (pointsByX[i].equals(pointsByX[i+1])) { bestDistance = 0.0; best1 = pointsByX[i]; best2 = pointsByX[i+1]; return; } } // sort by y-coordinate (but not yet sorted) Point2D[] pointsByY = new Point2D[n]; for (int i = 0; i < n; i++) pointsByY[i] = pointsByX[i]; // auxiliary array Point2D[] aux = new Point2D[n]; closest(pointsByX, pointsByY, aux, 0, n-1); } // find closest pair of points in pointsByX[lo..hi] // precondition: pointsByX[lo..hi] and pointsByY[lo..hi] are the same sequence of points // precondition: pointsByX[lo..hi] sorted by x-coordinate // postcondition: pointsByY[lo..hi] sorted by y-coordinate private double closest(Point2D[] pointsByX, Point2D[] pointsByY, Point2D[] aux, int lo, int hi) { if (hi <= lo) return Double.POSITIVE_INFINITY; int mid = lo + (hi - lo) / 2; Point2D median = pointsByX[mid]; // compute closest pair with both endpoints in left subarray or both in right subarray double delta1 = closest(pointsByX, pointsByY, aux, lo, mid); double delta2 = closest(pointsByX, pointsByY, aux, mid+1, hi); double delta = Math.min(delta1, delta2); // merge back so that pointsByY[lo..hi] are sorted by y-coordinate merge(pointsByY, aux, lo, mid, hi); // aux[0..m-1] = sequence of points closer than delta, sorted by y-coordinate int m = 0; for (int i = lo; i <= hi; i++) { if (Math.abs(pointsByY[i].x() - median.x()) < delta) aux[m++] = pointsByY[i]; } // compare each point to its neighbors with y-coordinate closer than delta for (int i = 0; i < m; i++) { // a geometric packing argument shows that this loop iterates at most 7 times for (int j = i+1; (j < m) && (aux[j].y() - aux[i].y() < delta); j++) { double distance = aux[i].distanceTo(aux[j]); if (distance < delta) { delta = distance; if (distance < bestDistance) { bestDistance = delta; best1 = aux[i]; best2 = aux[j]; // StdOut.println("better distance = " + delta + " from " + best1 + " to " + best2); } } } } return delta; } /** * Returns one of the points in the closest pair of points. * * @return one of the two points in the closest pair of points; * {@code null} if no such point (because there are fewer than 2 points) */ public Point2D either() { return best1; } /** * Returns the other point in the closest pair of points. * * @return the other point in the closest pair of points * {@code null} if no such point (because there are fewer than 2 points) */ public Point2D other() { return best2; } /** * Returns the Euclidean distance between the closest pair of points. * * @return the Euclidean distance between the closest pair of points * {@code Double.POSITIVE_INFINITY} if no such pair of points * exist (because there are fewer than 2 points) */ public double distance() { return bestDistance; } // is v < w ? private static boolean less(Comparable v, Comparable w) { return v.compareTo(w) < 0; } // stably merge a[lo .. mid] with a[mid+1 ..hi] using aux[lo .. hi] // precondition: a[lo .. mid] and a[mid+1 .. hi] are sorted subarrays private static void merge(Comparable[] a, Comparable[] aux, int lo, int mid, int hi) { // copy to aux[] for (int k = lo; k <= hi; k++) { aux[k] = a[k]; } // merge back to a[] int i = lo, j = mid+1; for (int k = lo; k <= hi; k++) { if (i > mid) a[k] = aux[j++]; else if (j > hi) a[k] = aux[i++]; else if (less(aux[j], aux[i])) a[k] = aux[j++]; else a[k] = aux[i++]; } } /** * Unit tests the {@code ClosestPair} data type. * Reads in an integer {@code n} and {@code n} points (specified by * their <em>x</em>- and <em>y</em>-coordinates) from standard input; * computes a closest pair of points; and prints the pair to standard * output. * * @param args the command-line arguments */ public static void main(String[] args) { int n = StdIn.readInt(); Point2D[] points = new Point2D[n]; for (int i = 0; i < n; i++) { double x = StdIn.readDouble(); double y = StdIn.readDouble(); points[i] = new Point2D(x, y); } ClosestPair closest = new ClosestPair(points); StdOut.println(closest.distance() + " from " + closest.either() + " to " + closest.other()); } }