Below is the syntax highlighted version of GrahamScan.java.
/****************************************************************************** * Compilation: javac GrahamScan.java * Execution: java GrahamScan < input.txt * Dependencies: Point2D.java * Data files: https://algs4.cs.princeton.edu/99hull/rs1423.txt * https://algs4.cs.princeton.edu/99hull/kw1260.txt * * Create points from standard input and compute the convex hull using * Graham scan algorithm. * * May be floating-point issues if x- and y-coordinates are not integers. * * % java GrahamScan < input100.txt * (7486.0, 422.0) * (29413.0, 596.0) * (32011.0, 3140.0) * (30875.0, 28560.0) * (28462.0, 32343.0) * (15731.0, 32661.0) * (822.0, 32301.0) * (823.0, 15895.0) * (1444.0, 10362.0) * (4718.0, 4451.0) * ******************************************************************************/ package edu.princeton.cs.algs4; import java.util.Arrays; /** * The {@code GrahamScan} data type provides methods for computing the * convex hull of a set of <em>n</em> points in the plane. * <p> * The implementation uses the Graham-Scan convex hull algorithm. * It runs in O(<em>n</em> log <em>n</em>) time in the worst case * and uses O(<em>n</em>) extra memory. * <p> * For additional documentation, see <a href="https://algs4.cs.princeton.edu/99scientific">Section 9.9</a> of * <i>Algorithms, 4th Edition</i> by Robert Sedgewick and Kevin Wayne. * * @author Robert Sedgewick * @author Kevin Wayne */ public class GrahamScan { private Stack<Point2D> hull = new Stack<Point2D>(); /** * Computes the convex hull of the specified array of points. * * @param points the array of points * @throws IllegalArgumentException if {@code points} is {@code null} * @throws IllegalArgumentException if any entry in {@code points[]} is {@code null} * @throws IllegalArgumentException if {@code points.length} is {@code 0} */ public GrahamScan(Point2D[] points) { if (points == null) throw new IllegalArgumentException("argument is null"); if (points.length == 0) throw new IllegalArgumentException("array is of length 0"); // defensive copy int n = points.length; Point2D[] a = new Point2D[n]; for (int i = 0; i < n; i++) { if (points[i] == null) throw new IllegalArgumentException("points[" + i + "] is null"); a[i] = points[i]; } // preprocess so that a[0] has lowest y-coordinate; break ties by x-coordinate // a[0] is an extreme point of the convex hull // (alternatively, could do easily in linear time) Arrays.sort(a); // sort by polar angle with respect to base point a[0], // breaking ties by distance to a[0] Arrays.sort(a, 1, n, a[0].polarOrder()); hull.push(a[0]); // a[0] is first extreme point // find index k1 of first point not equal to a[0] int k1; for (k1 = 1; k1 < n; k1++) if (!a[0].equals(a[k1])) break; if (k1 == n) return; // all points equal // find index k2 of first point not collinear with a[0] and a[k1] int k2; for (k2 = k1+1; k2 < n; k2++) if (Point2D.ccw(a[0], a[k1], a[k2]) != 0) break; hull.push(a[k2-1]); // a[k2-1] is second extreme point // Graham scan; note that a[n-1] is extreme point different from a[0] for (int i = k2; i < n; i++) { Point2D top = hull.pop(); while (Point2D.ccw(hull.peek(), top, a[i]) <= 0) { top = hull.pop(); } hull.push(top); hull.push(a[i]); } assert isConvex(); } /** * Returns the extreme points on the convex hull in counterclockwise order. * * @return the extreme points on the convex hull in counterclockwise order */ public Iterable<Point2D> hull() { Stack<Point2D> s = new Stack<Point2D>(); for (Point2D p : hull) s.push(p); return s; } // check that boundary of hull is strictly convex private boolean isConvex() { int n = hull.size(); if (n <= 2) return true; Point2D[] points = new Point2D[n]; int k = 0; for (Point2D p : hull()) { points[k++] = p; } for (int i = 0; i < n; i++) { if (Point2D.ccw(points[i], points[(i+1) % n], points[(i+2) % n]) <= 0) { return false; } } return true; } /** * Unit tests the {@code GrahamScan} 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 their convex hull; and prints out the points on the * convex hull 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); } GrahamScan graham = new GrahamScan(points); for (Point2D p : graham.hull()) StdOut.println(p); } } /****************************************************************************** * Copyright 2002-2022, 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. ******************************************************************************/