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)
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