Java Program to Construct K-D Tree for 2 Dimensional Data

This is a Java Program to implement 2D KD Tree and print the various traversals. In computer science, a k-d tree (short for k-dimensional tree) is a space-partitioning data structure for organizing points in a k-dimensional space. k-d trees are a useful data structure for several applications, such as searches involving a multidimensional search key (e.g. range searches and nearest neighbor searches). k-d trees are a special case of binary space partitioning trees.

Here is the source code of the Java Program to Construct K-D Tree for 2 Dimensional Data (assume static data). 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 construct a KD tree for two dimensional static data
import java.io.IOException;
 
class KD2DNode
{
    int axis;
    double[] x;
    int id;
    boolean checked;
    boolean orientation;
 
    KD2DNode Parent;
    KD2DNode Left;
    KD2DNode Right;
 
    public KD2DNode(double[] x0, int axis0)
    {
        x = new double[2];
        axis = axis0;
        for (int k = 0; k < 2; k++)
            x[k] = x0[k];
 
        Left = Right = Parent = null;
        checked = false;
        id = 0;
    }
 
    public KD2DNode FindParent(double[] x0)
    {
        KD2DNode parent = null;
        KD2DNode next = this;
        int split;
        while (next != null)
        {
            split = next.axis;
            parent = next;
            if (x0[split] > next.x[split])
                next = next.Right;
            else
                next = next.Left;
        }
        return parent;
    }
 
    public KD2DNode Insert(double[] p)
    {
        x = new double[2];
        KD2DNode parent = FindParent(p);
        if (equal(p, parent.x, 2) == true)
            return null;
 
        KD2DNode newNode = new KD2DNode(p,
                parent.axis + 1 < 2 ? parent.axis + 1 : 0);
        newNode.Parent = parent;
 
        if (p[parent.axis] > parent.x[parent.axis])
        {
            parent.Right = newNode;
            newNode.orientation = true; //
        } else
        {
            parent.Left = newNode;
            newNode.orientation = false; //
        }
 
        return newNode;
    }
 
    boolean equal(double[] x1, double[] x2, int dim)
    {
        for (int k = 0; k < dim; k++)
        {
            if (x1[k] != x2[k])
                return false;
        }
 
        return true;
    }
 
    double distance2(double[] x1, double[] x2, int dim)
    {
        double S = 0;
        for (int k = 0; k < dim; k++)
            S += (x1[k] - x2[k]) * (x1[k] - x2[k]);
        return S;
    }
}
 
class KD2DTree
{
    KD2DNode Root;
 
    int TimeStart, TimeFinish;
    int CounterFreq;
 
    double d_min;
    KD2DNode nearest_neighbour;
 
    int KD_id;
 
    int nList;
 
    KD2DNode CheckedNodes[];
    int checked_nodes;
    KD2DNode List[];
 
    double x_min[], x_max[];
    boolean max_boundary[], min_boundary[];
    int n_boundary;
 
    public KD2DTree(int i)
    {
        Root = null;
        KD_id = 1;
        nList = 0;
        List = new KD2DNode[i];
        CheckedNodes = new KD2DNode[i];
        max_boundary = new boolean[2];
        min_boundary = new boolean[2];
        x_min = new double[2];
        x_max = new double[2];
    }
 
    public boolean add(double[] x)
    {
        if (nList >= 2000000 - 1)
            return false; // can't add more points
 
        if (Root == null)
        {
            Root = new KD2DNode(x, 0);
            Root.id = KD_id++;
            List[nList++] = Root;
        } else
        {
            KD2DNode pNode;
            if ((pNode = Root.Insert(x)) != null)
            {
                pNode.id = KD_id++;
                List[nList++] = pNode;
            }
        }
 
        return true;
    }
 
    public KD2DNode find_nearest(double[] x)
    {
        if (Root == null)
            return null;
 
        checked_nodes = 0;
        KD2DNode parent = Root.FindParent(x);
        nearest_neighbour = parent;
        d_min = Root.distance2(x, parent.x, 2);
        ;
 
        if (parent.equal(x, parent.x, 2) == true)
            return nearest_neighbour;
 
        search_parent(parent, x);
        uncheck();
 
        return nearest_neighbour;
    }
 
    public void check_subtree(KD2DNode node, double[] x)
    {
        if ((node == null) || node.checked)
            return;
 
        CheckedNodes[checked_nodes++] = node;
        node.checked = true;
        set_bounding_cube(node, x);
 
        int dim = node.axis;
        double d = node.x[dim] - x[dim];
 
        if (d * d > d_min)
        {
            if (node.x[dim] > x[dim])
                check_subtree(node.Left, x);
            else
                check_subtree(node.Right, x);
        } else
        {
            check_subtree(node.Left, x);
            check_subtree(node.Right, x);
        }
    }
 
    public void set_bounding_cube(KD2DNode node, double[] x)
    {
        if (node == null)
            return;
        int d = 0;
        double dx;
        for (int k = 0; k < 2; k++)
        {
            dx = node.x[k] - x[k];
            if (dx > 0)
            {
                dx *= dx;
                if (!max_boundary[k])
                {
                    if (dx > x_max[k])
                        x_max[k] = dx;
                    if (x_max[k] > d_min)
                    {
                        max_boundary[k] = true;
                        n_boundary++;
                    }
                }
            } else
            {
                dx *= dx;
                if (!min_boundary[k])
                {
                    if (dx > x_min[k])
                        x_min[k] = dx;
                    if (x_min[k] > d_min)
                    {
                        min_boundary[k] = true;
                        n_boundary++;
                    }
                }
            }
            d += dx;
            if (d > d_min)
                return;
 
        }
 
        if (d < d_min)
        {
            d_min = d;
            nearest_neighbour = node;
        }
    }
 
    public KD2DNode search_parent(KD2DNode parent, double[] x)
    {
        for (int k = 0; k < 2; k++)
        {
            x_min[k] = x_max[k] = 0;
            max_boundary[k] = min_boundary[k] = false; //
        }
        n_boundary = 0;
 
        KD2DNode search_root = parent;
        while (parent != null && (n_boundary != 2 * 2))
        {
            check_subtree(parent, x);
            search_root = parent;
            parent = parent.Parent;
        }
 
        return search_root;
    }
 
    public void uncheck()
    {
        for (int n = 0; n < checked_nodes; n++)
            CheckedNodes[n].checked = false;
    }
 
    public void inorder()
    {
        inorder(Root);
    }
 
    private void inorder(KD2DNode root)
    {
        if (root != null)
        {
            inorder(root.Left);
            System.out.print("(" + root.x[0] + ", " + root.x[1] + ")  ");
            inorder(root.Right);
        }
    }
 
    public void preorder()
    {
        preorder(Root);
    }
 
    private void preorder(KD2DNode root)
    {
        if (root != null)
        {
            System.out.print("(" + root.x[0] + ", " + root.x[1] + ")  ");
            inorder(root.Left);
            inorder(root.Right);
        }
    }
 
    public void postorder()
    {
        postorder(Root);
    }
 
    private void postorder(KD2DNode root)
    {
        if (root != null)
        {
            inorder(root.Left);
            inorder(root.Right);
            System.out.print("(" + root.x[0] + ", " + root.x[1] + ")  ");
        }
    }
}
 
public class KDTree_TwoD_Data
{
    public static void main(String args[]) throws IOException
    {
        int numpoints = 5;
 
        KD2DTree kdt = new KD2DTree(numpoints);
        double x[] = new double[2];
 
        x[0] = 0.0;
        x[1] = 0.0;
        kdt.add(x);
 
        x[0] = 3.3;
        x[1] = 1.5;
        kdt.add(x);
 
        x[0] = 4.7;
        x[1] = 11.1;
        kdt.add(x);
 
        x[0] = 5.0;
        x[1] = 12.3;
        kdt.add(x);
 
        x[0] = 5.1;
        x[1] = 1.2;
        kdt.add(x);
 
        System.out.println("Inorder of 2D Kd tree: ");
        kdt.inorder();
 
        System.out.println("\nPreorder of 2D Kd tree: ");
        kdt.preorder();
 
        System.out.println("\nPostorder of 2D Kd tree: ");
        kdt.postorder();
    }
}

Output:

$ javac KDTree_TwoD_Data.java
$ java KDTree_TwoD_Data
 
Inorder of 2D Kd tree: 
(0.0, 0.0)  (5.1, 1.2)  (3.3, 1.5)  (4.7, 11.1)  (5.0, 12.3)  
Preorder of 2D Kd tree: 
(0.0, 0.0)  (5.1, 1.2)  (3.3, 1.5)  (4.7, 11.1)  (5.0, 12.3)  
Postorder of 2D Kd tree: 
(5.1, 1.2)  (3.3, 1.5)  (4.7, 11.1)  (5.0, 12.3)  (0.0, 0.0)