``` 001 002 003 004 005 006 007 008 009 010 011 012 013 014 015 016 017 018 019 020 021 022 023 024 025 026 027 028 029 030 031 032 033 034 035 036 037 038 039 040 041 042 043 044 045 046 047 048 049 050 051 052 053 054 055 056 057 058 059 060 061 062 063 064 065 066 067 068 069 070 071 072 073 074 075 076 077 078 079 080 081 082 083 084 085 086 087 088 089 090 091 092 093 094 095 096 097 098 099 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 ``` ```package algs9; // section 9.8 import stdlib.*; import java.util.Arrays; import algs12.Point2D; import algs22.Merge; /* *********************************************************************** * 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. * * % java ClosestPair < rs1423.txt * 15.0 from (11364.0, 12693.0) to (11373.0, 12705.0) * *************************************************************************/ 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.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; } public static void main(String[] args) { StdIn.fromFile ("data/rs1423.txt"); 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()); } } ```