Code:
import java.util.Arrays;
import java.util.Comparator;
import java.util.Scanner;
import java.util.Stack;
class Point2D implements Comparable
{
public static final Comparator
public static final Comparator
public static final Comparator
public final Comparator
public final Comparator
public final Comparator
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
{
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
{
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
{
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
{
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
{
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
{
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
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
{
Stack
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:
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:
Graham Scan Test
Enter the number of points
5
Enter the coordinates of each points:
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:
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)
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