edu.princeton.cs.algs4.FarthestPair Maven / Gradle / Ivy
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/******************************************************************************
* Compilation: javac FarthestPair.java
* Execution: java FarthestPair < input.txt
* Dependencies: GrahamScan.java Point2D.java
* Data files: https://algs4.cs.princeton.edu/99hull/rs1423.txt
* https://algs4.cs.princeton.edu/99hull/kw1260.txt
*
* Given a set of n points in the plane, find the farthest pair
* (equivalently, compute the diameter of the set of points).
*
* Computes the convex hull of the set of points and using the
* rotating calipers method to find all antipodal point pairs
* and the farthest pair.
*
* % java FarthestPair < input100.txt
* 42697.98170874122 from (32011.0, 3140.0) to (822.0, 32301.0)
*
******************************************************************************/
package edu.princeton.cs.algs4;
/**
* The {@code FarthestPair} data type computes the farthest pair of points
* in a set of n points in the plane and provides accessor methods
* for getting the farthest pair of points and the distance between them.
* The distance between two points is their Euclidean distance.
*
* This implementation computes the convex hull of the set of points and
* uses the rotating calipers method to find all antipodal point pairs
* and the farthest pair.
* It runs in O(n log n) time in the worst case and uses
* O(N) extra space.
* See also {@link ClosestPair} and {@link GrahamScan}.
*
* For additional documentation, see Section 9.9 of
* Algorithms, 4th Edition by Robert Sedgewick and Kevin Wayne.
*
* @author Robert Sedgewick
* @author Kevin Wayne
*/
public class FarthestPair {
// farthest pair of points and distance
private Point2D best1, best2;
private double bestDistanceSquared = Double.NEGATIVE_INFINITY;
/**
* Computes the farthest 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 FarthestPair(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");
}
GrahamScan graham = new GrahamScan(points);
// single point
if (points.length <= 1) return;
// number of points on the hull
int m = 0;
for (Point2D p : graham.hull())
m++;
// the hull, in counterclockwise order hull[1] to hull[m]
Point2D[] hull = new Point2D[m+1];
m = 1;
for (Point2D p : graham.hull()) {
hull[m++] = p;
}
m--;
// all points are equal
if (m == 1) return;
// points are collinear
if (m == 2) {
best1 = hull[1];
best2 = hull[2];
bestDistanceSquared = best1.distanceSquaredTo(best2);
return;
}
// k = farthest vertex from edge from hull[1] to hull[m]
int k = 2;
while (Point2D.area2(hull[m], hull[1], hull[k+1]) > Point2D.area2(hull[m], hull[1], hull[k])) {
k++;
}
int j = k;
for (int i = 1; i <= k && j <= m; i++) {
// StdOut.println("hull[i] + " and " + hull[j] + " are antipodal");
if (hull[i].distanceSquaredTo(hull[j]) > bestDistanceSquared) {
best1 = hull[i];
best2 = hull[j];
bestDistanceSquared = hull[i].distanceSquaredTo(hull[j]);
}
while ((j < m) && Point2D.area2(hull[i], hull[i+1], hull[j+1]) > Point2D.area2(hull[i], hull[i+1], hull[j])) {
j++;
// StdOut.println(hull[i] + " and " + hull[j] + " are antipodal");
double distanceSquared = hull[i].distanceSquaredTo(hull[j]);
if (distanceSquared > bestDistanceSquared) {
best1 = hull[i];
best2 = hull[j];
bestDistanceSquared = hull[i].distanceSquaredTo(hull[j]);
}
}
}
}
/**
* Returns one of the points in the farthest pair of points.
*
* @return one of the two points in the farthest 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 farthest pair of points.
*
* @return the other point in the farthest 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 farthest pair of points.
* This quantity is also known as the diameter of the set of points.
*
* @return the Euclidean distance between the farthest 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 Math.sqrt(bestDistanceSquared);
}
/**
* Unit tests the {@code FarthestPair} data type.
* Reads in an integer {@code n} and {@code n} points (specified by
* their x- and y-coordinates) from standard input;
* computes a farthest 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++) {
int x = StdIn.readInt();
int y = StdIn.readInt();
points[i] = new Point2D(x, y);
}
FarthestPair farthest = new FarthestPair(points);
StdOut.println(farthest.distance() + " from " + farthest.either() + " to " + farthest.other());
}
}
/******************************************************************************
* Copyright 2002-2018, Robert Sedgewick and Kevin Wayne.
*
* This file is part of algs4.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.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.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.jar. If not, see http://www.gnu.org/licenses.
******************************************************************************/