/************************************************************************* * Compilation: javac ClosestPair.java * Execution: java ClosestPair < input.txt * Dependencies: Point2D.java * * 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; import edu.princeton.cs.introcs.StdIn; import edu.princeton.cs.introcs.StdOut; public class ClosestPair { // closest pair of points and their Euclidean distance private Point2D best1, best2; private double bestDistance = Double.POSITIVE_INFINITY; public ClosestPair(Point2D[] points) { int N = points.length; if (N <= 1) return; // sort by x-coordinate (breaking ties by y-coordinate) Point2D[] pointsByX = new Point2D[N]; for (int i = 0; i < N; i++) pointsByX[i] = points[i]; 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; } public Point2D either() { return best1; } public Point2D other() { return best2; } 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++]; } } 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()); } }