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/* 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.distanceTo(n.p);
if (d2 < ncp.d)
{
ncp.d = d2;
ncp.p = n.p;
}
if (vsplit)
{
double nx = n.p.x();
if (p.x() < nx)
{
if (n.left != null)
nearest(n.left, p, ncp, !vsplit);
if (n.right != null && ((nx - p.x()) < ncp.d))
nearest(n.right, p, ncp, !vsplit);
}
else
{
if (n.right != null)
nearest(n.right, p, ncp, !vsplit);
if (n.left != null && ((p.x() - nx) < ncp.d))
nearest(n.left, p, ncp, !vsplit);
}
}
else
{
double ny = n.p.y();
if (p.y() < ny)
{
if (n.left != null)
nearest(n.left, p, ncp, !vsplit);
if (n.right != null && ((ny - p.y()) < ncp.d))
nearest(n.right, p, ncp, !vsplit);
}
else
{
if (n.right != null)
nearest(n.right, p, ncp, !vsplit);
if (n.left != null && ((p.y() - ny) < ncp.d))
nearest(n.left, p, ncp, !vsplit);
}
}
}
}
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