GrahamScan.java
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/******************************************************************************
* Compilation: javac GrahamaScan.java
* Execution: java GrahamScan < input.txt
* Dependencies: Point2D.java
* Data files: http://algs4.cs.princeton.edu/99hull/rs1423.txt
* http://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="http://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 pts the array of points
* @throws NullPointerException if {@code points} is {@code null} or if any
* entry in {@code points[]} is {@code null}
*/
public GrahamScan(Point2D[] pts) {
// defensive copy
int n = pts.length;
Point2D[] points = new Point2D[n];
for (int i = 0; i < n; i++)
points[i] = pts[i];
// preprocess so that points[0] has lowest y-coordinate; break ties by x-coordinate
// points[0] is an extreme point of the convex hull
// (alternatively, could do easily in linear time)
Arrays.sort(points);
// sort by polar angle with respect to base point points[0],
// breaking ties by distance to points[0]
Arrays.sort(points, 1, n, points[0].polarOrder());
hull.push(points[0]); // p[0] is first extreme point
// find index k1 of first point not equal to points[0]
int k1;
for (k1 = 1; k1 < n; k1++)
if (!points[0].equals(points[k1])) break;
if (k1 == n) return; // all points equal
// find index k2 of first point not collinear with points[0] and points[k1]
int k2;
for (k2 = k1+1; k2 < n; k2++)
if (Point2D.ccw(points[0], points[k1], points[k2]) != 0) break;
hull.push(points[k2-1]); // points[k2-1] is second extreme point
// Graham scan; note that points[n-1] is extreme point different from points[0]
for (int i = k2; i < n; i++) {
Point2D top = hull.pop();
while (Point2D.ccw(hull.peek(), top, points[i]) <= 0) {
top = hull.pop();
}
hull.push(top);
hull.push(points[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 2002-2016, 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.
******************************************************************************/