# ClosestPair.java

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
*
******************************************************************************/

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>
*  <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)
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;
}

/**
* 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 Eucliden 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) {
Point2D[] points = new Point2D[n];
for (int i = 0; i < n; i++) {