/* vim: set expandtab tabstop=4 shiftwidth=4 : */

public class KdTree
{
    private static final double XMIN = 0;
    private static final double YMIN = 0;
    private static final double XMAX = 1;
    private static final double YMAX = 1;

    private Node root;
    private int size;

    private class Node {
        private Point2D p;
        private Node left, right;

        public Node(Point2D p)
        {
            this.p = p;
        }
    }

    private class NearestChampion {
        private Point2D p;
        private double d;
        public NearestChampion(Point2D p, double d)
        {
            this.p = p;
            this.d = d;
        }
    }

    // construct an empty tree of points
    public KdTree()
    {
        size = 0;
        root = null;
    }

    // is the tree empty?
    public boolean isEmpty()
    {
        return (size == 0);
    }

    // number of points in the tree
    public int size()
    {
        return size;
    }

    // add the point p to the tree (if it is not already in the tree)
    public void insert(Point2D p)
    {
        if (p == null) return;
        if (root == null)
        {
            root = new Node(p);
            size = 1;
        }
        else if (put(root, p, true))
            size += 1;
    }

    private boolean put(Node n, Point2D p, boolean vsplit) {

        int cmp;
        if (vsplit)
            cmp = Point2D.X_ORDER.compare(p, n.p);
        else
            cmp = Point2D.Y_ORDER.compare(p, n.p);

        if (cmp < 0)
        {
            // add to left subtree
            if (n.left != null)
                return put(n.left, p, !vsplit);
            n.left = new Node(p);
            return true;
        }

        if (cmp == 0)
        {
            if (vsplit)
            {
                if (Point2D.Y_ORDER.compare(p, n.p) == 0)
                    return false;
            }
            else if (Point2D.X_ORDER.compare(p, n.p) == 0)
                return false;
        }

        // add to right subtree
        if (n.right != null)
            return put(n.right, p, !vsplit);
        n.right = new Node(p);
        return true;
    }

    // does the tree contain the point p?
    public boolean contains(Point2D p)
    {
        if ((p == null) || (root == null)) return false;
        return get(root, p, true);
    }

    private boolean get(Node n, Point2D p, boolean vsplit) {
        if (p.compareTo(n.p) == 0) return true;
        int cmp;
        if (vsplit)
            cmp = Point2D.X_ORDER.compare(p, n.p);
        else
            cmp = Point2D.Y_ORDER.compare(p, n.p);

        if (cmp < 0)
        {
            if (n.left == null) return false;
            return get(n.left, p, !vsplit);
        }
        if (n.right == null) return false;
        return get(n.right, p, !vsplit);
    }

    // draw all of the points to standard draw
    public void draw()
    {
        StdDraw.setPenRadius();
        StdDraw.setPenColor(StdDraw.BLACK);
        StdDraw.rectangle(XMAX/2.0, YMAX/2.0, XMAX/2.0, YMAX/2.0);
        draw(root, true, new RectHV(XMIN, YMIN, XMAX, YMAX));
    }

    private void draw(Node n, boolean vsplit, RectHV r)
    {
        if (n == null) return;
        if (vsplit)
        {
            StdDraw.setPenRadius();
            StdDraw.setPenColor(StdDraw.RED);
            StdDraw.line(n.p.x(), r.ymin(), n.p.x(), r.ymax());
            if (n.left != null)
                draw(n.left, !vsplit,
                        new RectHV(r.xmin(), r.ymin(), n.p.x(), r.ymax()));
            if (n.right != null)
                draw(n.right, !vsplit,
                        new RectHV(n.p.x(), r.ymin(), r.xmax(), r.ymax()));
        }
        else
        {
            StdDraw.setPenRadius();
            StdDraw.setPenColor(StdDraw.BLUE);
            StdDraw.line(r.xmin(), n.p.y(), r.xmax(), n.p.y());
            if (n.left != null)
                draw(n.left, !vsplit,
                        new RectHV(r.xmin(), r.ymin(), r.xmax(), n.p.y()));
            if (n.right != null)
                draw(n.right, !vsplit,
                        new RectHV(r.xmin(), n.p.y(), r.xmax(), r.ymax()));
        }
        StdDraw.setPenRadius(.01);
        StdDraw.setPenColor(StdDraw.BLACK);
        n.p.draw();
    }

    // all points in the tree that are inside the rectangle
    public Iterable<Point2D> range(RectHV rect)
    {
        Stack<Point2D> stack = new Stack<Point2D>();

        if ((rect == null) || (root == null)) return stack;

        range(root, rect, stack, true);

        return stack;
    }

    private void range(Node n, RectHV r, Stack<Point2D> s, boolean vsplit)
    {
        if (r.contains(n.p))
            s.push(n.p);
        if (vsplit)
        {
            if (n.left != null && r.xmin() < n.p.x())
                range(n.left, r, s, !vsplit);
            if (n.right != null && r.xmax() >= n.p.x())
                range(n.right, r, s, !vsplit);
        }
        else
        {
            if (n.left != null && r.ymin() < n.p.y())
                range(n.left, r, s, !vsplit);
            if (n.right != null && r.ymax() >= n.p.y())
                range(n.right, r, s, !vsplit);
        }
    }

    // a nearest neighbor in the tree to p; null if tree is empty
    public Point2D nearest(Point2D p)
    {
        if ((p == null) || (root == null)) return null;

        NearestChampion ncp = new NearestChampion(null, Double.MAX_VALUE);
        nearest(root, p, ncp, true);

        return ncp.p;
    }

    private void nearest(Node n, Point2D p, NearestChampion ncp, boolean vsplit)
    {
        double d2 = p.distanceSquaredTo(n.p);
        if (d2 < ncp.d)
        {
            ncp.d = d2;
            ncp.p = n.p;
        }
        if (vsplit)
        {
            double d3 = n.p.x() - p.x();
            if (d3 > 0)
            {
                if (n.left != null)
                    nearest(n.left, p, ncp, !vsplit);
                if (n.right != null && ((d3 * d3) < ncp.d))
                    nearest(n.right, p, ncp, !vsplit);
            }
            else
            {
                if (n.right != null)
                    nearest(n.right, p, ncp, !vsplit);
                if (n.left != null && ((d3 * d3) < ncp.d))
                    nearest(n.left, p, ncp, !vsplit);
            }
        }
        else
        {
            double d3 = n.p.y() - p.y();
            if (d3 > 0)
            {
                if (n.left != null)
                    nearest(n.left, p, ncp, !vsplit);
                if (n.right != null && ((d3 * d3) < ncp.d))
                    nearest(n.right, p, ncp, !vsplit);
            }
            else
            {
                if (n.right != null)
                    nearest(n.right, p, ncp, !vsplit);
                if (n.left != null && ((d3 * d3) < ncp.d))
                    nearest(n.left, p, ncp, !vsplit);
            }
        }
    }

}