# Java Program to Implement Graham Scan Algorithm to Find the Convex Hull

This is a Java Program to implement Graham Scan Algorithm. Graham’s scan is a method of computing the convex hull of a finite set of points in the plane with time complexity O(n log n).

Here is the source code of the Java Program to Implement Graham Scan Algorithm to Find the Convex Hull. The Java program is successfully compiled and run on a Windows system. The program output is also shown below.

//This is a java program to implement Graham Scan Algorithm
import java.util.Arrays;
import java.util.Comparator;
import java.util.Scanner;
import java.util.Stack;

class Point2D implements Comparable<Point2D>
{
public static final Comparator<Point2D> X_ORDER = new XOrder();
public static final Comparator<Point2D> Y_ORDER = new YOrder();
public static final Comparator<Point2D> R_ORDER = new ROrder();
public final Comparator<Point2D> POLAR_ORDER = new PolarOrder();
public final Comparator<Point2D> ATAN2_ORDER = new Atan2Order();
public final Comparator<Point2D> DISTANCE_TO_ORDER = new DistanceToOrder();

private final double x; // x coordinate
private final double y; // y coordinate

public Point2D(double x, double y)
{
if (Double.isInfinite(x) || Double.isInfinite(y))
throw new IllegalArgumentException("Coordinates must be finite");
if (Double.isNaN(x) || Double.isNaN(y))
throw new IllegalArgumentException("Coordinates cannot be NaN");
if (x == 0.0)
x = 0.0; // convert -0.0 to +0.0
if (y == 0.0)
y = 0.0; // convert -0.0 to +0.0
this.x = x;
this.y = y;
}

public double x()
{
return x;
}

public double y()
{
return y;
}

public double r()
{
return Math.sqrt(x * x + y * y);
}

public double theta()
{
return Math.atan2(y, x);
}

private double angleTo(Point2D that)
{
double dx = that.x - this.x;
double dy = that.y - this.y;
return Math.atan2(dy, dx);
}

public static int ccw(Point2D a, Point2D b, Point2D c)
{
double area2 = (b.x - a.x) * (c.y - a.y) - (b.y - a.y) * (c.x - a.x);
if (area2 < 0)
return -1;
else if (area2 > 0)
return +1;
else
return 0;
}

public static double area2(Point2D a, Point2D b, Point2D c)
{
return (b.x - a.x) * (c.y - a.y) - (b.y - a.y) * (c.x - a.x);
}

public double distanceTo(Point2D that)
{
double dx = this.x - that.x;
double dy = this.y - that.y;
return Math.sqrt(dx * dx + dy * dy);
}

public double distanceSquaredTo(Point2D that)
{
double dx = this.x - that.x;
double dy = this.y - that.y;
return dx * dx + dy * dy;
}

public int compareTo(Point2D that)
{
if (this.y < that.y)
return -1;
if (this.y > that.y)
return +1;
if (this.x < that.x)
return -1;
if (this.x > that.x)
return +1;
return 0;
}

private static class XOrder implements Comparator<Point2D>
{
public int compare(Point2D p, Point2D q)
{
if (p.x < q.x)
return -1;
if (p.x > q.x)
return +1;
return 0;
}
}

private static class YOrder implements Comparator<Point2D>
{
public int compare(Point2D p, Point2D q)
{
if (p.y < q.y)
return -1;
if (p.y > q.y)
return +1;
return 0;
}
}

private static class ROrder implements Comparator<Point2D>
{
public int compare(Point2D p, Point2D q)
{
double delta = (p.x * p.x + p.y * p.y) - (q.x * q.x + q.y * q.y);
if (delta < 0)
return -1;
if (delta > 0)
return +1;
return 0;
}
}

private class Atan2Order implements Comparator<Point2D>
{
public int compare(Point2D q1, Point2D q2)
{
double angle1 = angleTo(q1);
double angle2 = angleTo(q2);
if (angle1 < angle2)
return -1;
else if (angle1 > angle2)
return +1;
else
return 0;
}
}

private class PolarOrder implements Comparator<Point2D>
{
public int compare(Point2D q1, Point2D q2)
{
double dx1 = q1.x - x;
double dy1 = q1.y - y;
double dx2 = q2.x - x;
double dy2 = q2.y - y;

if (dy1 >= 0 && dy2 < 0)
return -1; // q1 above; q2 below
else if (dy2 >= 0 && dy1 < 0)
return +1; // q1 below; q2 above
else if (dy1 == 0 && dy2 == 0)
{ // 3-collinear and horizontal
if (dx1 >= 0 && dx2 < 0)
return -1;
else if (dx2 >= 0 && dx1 < 0)
return +1;
else
return 0;
} else
return -ccw(Point2D.this, q1, q2); // both above or below
}
}

private class DistanceToOrder implements Comparator<Point2D>
{
public int compare(Point2D p, Point2D q)
{
double dist1 = distanceSquaredTo(p);
double dist2 = distanceSquaredTo(q);
if (dist1 < dist2)
return -1;
else if (dist1 > dist2)
return +1;
else
return 0;
}
}

public boolean equals(Object other)
{
if (other == this)
return true;
if (other == null)
return false;
if (other.getClass() != this.getClass())
return false;
Point2D that = (Point2D) other;
return this.x == that.x && this.y == that.y;
}

public String toString()
{
return "(" + x + ", " + y + ")";
}

public int hashCode()
{
int hashX = ((Double) x).hashCode();
int hashY = ((Double) y).hashCode();
return 31 * hashX + hashY;
}

}

public class GrahamScan
{
private Stack<Point2D> hull = new Stack<Point2D>();

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];
Arrays.sort(points);

Arrays.sort(points, 1, N, points[0].POLAR_ORDER);

hull.push(points[0]); // p[0] is first extreme point
int k1;
for (k1 = 1; k1 < N; k1++)
if (!points[0].equals(points[k1]))
break;
if (k1 == N)
return; // all points equal

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

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();
}

public Iterable<Point2D> hull()
{
Stack<Point2D> s = new Stack<Point2D>();
for (Point2D p : hull)
s.push(p);
return s;
}

private boolean isConvex()
{
int N = hull.size();
if (N <= 2)
return true;

Point2D[] points = new Point2D[N];
int n = 0;
for (Point2D p : hull())
{
points[n++] = 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;
}

// test client
public static void main(String[] args)
{
System.out.println("Graham Scan Test");
Scanner sc = new Scanner(System.in);
System.out.println("Enter the number of points");
int N = sc.nextInt();

Point2D[] points = new Point2D[N];
System.out.println("Enter the coordinates of each points: <x> <y>");
for (int i = 0; i < N; i++)
{
int x = sc.nextInt();
int y = sc.nextInt();
points[i] = new Point2D(x, y);
}
GrahamScan graham = new GrahamScan(points);
System.out.println("The convex hull consists of following points: ");
for (Point2D p : graham.hull())
System.out.println(p);

sc.close();
}

}


Output:

$javac GrahamScan.java$ java GrahamScan

Graham Scan Test
Enter the number of points
5
Enter the coordinates of each points: <x> <y>
1 2
2 3
4 5
20 10
6 4
The convex hull consists of following points:
(1.0, 2.0)
(6.0, 4.0)
(20.0, 10.0)
(4.0, 5.0)

Graham Scan Test
Enter the number of points
5
Enter the coordinates of each points: <x> <y>
1 2
2 3
3 4
4 5
5 6
The convex hull consists of following points:
(1.0, 2.0)
(5.0, 6.0)