package edu.princeton.cs.algs4.ch12;
import edu.princeton.cs.introcs.*;
/*************************************************************************
* 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;
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());
}
}
/*************************************************************************
* Copyright 2002-2012, Robert Sedgewick and Kevin Wayne.
*
* This file is part of algs4-package.jar, which accompanies the textbook
*
* Algorithms, 4th edition by Robert Sedgewick and Kevin Wayne,
* Addison-Wesley Professional, 2011, ISBN 0-321-57351-X.
* http://algs4.cs.princeton.edu
*
*
* algs4-package.jar is free software: you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* algs4-package.jar is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
* You should have received a copy of the GNU General Public License
* along with algs4-package.jar. If not, see http://www.gnu.org/licenses.
*************************************************************************/