PointSET

import edu.princeton.cs.algs4.Point2D;
import edu.princeton.cs.algs4.RectHV;
import edu.princeton.cs.algs4.SET;


public class PointSET {

    private SET<Point2D> pointsBST;

    // Construct an empty set of points
    public PointSET() {
        pointsBST = new SET<>();
    }

    public boolean isEmpty() {
        return pointsBST.isEmpty();
    }

    // number of points in the set
    public int size() {
        return pointsBST.size();
    }

    // Add the point to the set (if it is not already in the set)
    public void insert(Point2D p) {
        if (null == p) throw new IllegalArgumentException();
        if (!pointsBST.contains(p)) {
            pointsBST.add(p);
        }
    }

    //does the set contain point p?
    public boolean contains(Point2D p) {
        if (null == p) throw new IllegalArgumentException();
        return pointsBST.contains(p);
    }

    // draw all points to standard draw
    public void draw() {
        pointsBST.forEach(point2D -> point2D.draw());
    }

    // all points that are inside the rectangle (or on the boundary)
    public Iterable<Point2D> range(RectHV rect) {
        if (null == rect) throw new IllegalArgumentException();
        SET<Point2D> rangePoints = new SET<>();

        for (Point2D point2D : pointsBST) {
            if (rect.contains(point2D)) rangePoints.add(point2D);
        }
        return rangePoints;
    }

    // a nearest neighbor in the set to point p; null if the set is empty
    public Point2D nearest(Point2D p) {
        if (null == p) throw new IllegalArgumentException();

        if (pointsBST.isEmpty()) {
            return null;
        } else {
            // any point in the SET will be a starting point champion
            Point2D championPoint = pointsBST.iterator().next();

            for (Point2D point2D : pointsBST) {
                if (point2D.distanceSquaredTo(p) < championPoint.distanceSquaredTo(p)) {
                    // we have a new champion
                    championPoint = point2D;
                }
            }
            return championPoint;
        }
    }
}