This is a Java Program to implement 2D KD Tree and find the nearest neighbor for static input set. 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 Find Nearest Neighbor for Static Data Set. 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 find the nearest neighbor for the static data set import java.io.IOException; import java.util.Scanner; class KDNodes { int axis; double[] x; int id; boolean checked; boolean orientation; KDNodes Parent; KDNodes Left; KDNodes Right; public KDNodes(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 KDNodes FindParent(double[] x0) { KDNodes parent = null; KDNodes 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 KDNodes Insert(double[] p) { x = new double[2]; KDNodes parent = FindParent(p); if (equal(p, parent.x, 2) == true) return null; KDNodes newNode = new KDNodes(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 KDTreeStatic { KDNodes Root; int TimeStart, TimeFinish; int CounterFreq; double d_min; KDNodes nearest_neighbour; int KD_id; int nList; KDNodes CheckedNodes[]; int checked_nodes; KDNodes List[]; double x_min[], x_max[]; boolean max_boundary[], min_boundary[]; int n_boundary; public KDTreeStatic(int i) { Root = null; KD_id = 1; nList = 0; List = new KDNodes[i]; CheckedNodes = new KDNodes[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 KDNodes(x, 0); Root.id = KD_id++; List[nList++] = Root; } else { KDNodes pNode; if ((pNode = Root.Insert(x)) != null) { pNode.id = KD_id++; List[nList++] = pNode; } } return true; } public KDNodes find_nearest(double[] x) { if (Root == null) return null; checked_nodes = 0; KDNodes 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(KDNodes 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(KDNodes 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 KDNodes search_parent(KDNodes 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; KDNodes 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 class Static_Nearest { public static void main(String args[]) throws IOException { int numpoints = 7; Scanner sc = new Scanner(System.in); KDTreeStatic kdt = new KDTreeStatic(numpoints); double x[] = new double[2]; x[0] = 2.1; x[1] = 4.3; 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); x[0] = 12.1; x[1] = 18.2; kdt.add(x); x[0] = 20.5; x[1] = 17.9; kdt.add(x); System.out.println("Enter the co-ordinates of the point: <x> <y>"); double sx = sc.nextDouble(); double sy = sc.nextDouble(); double s[] = { sx, sy }; KDNodes kdn = kdt.find_nearest(s); System.out.println("The nearest neighbor for the static data set is: "); System.out.println("(" + kdn.x[0] + " , " + kdn.x[1] + ")"); sc.close(); } }
Output:
$ javac Static_Nearest.java $ java Static_Nearest Enter the co-ordinates of the point: <x> <y> 9 9 The nearest neighbor for the static data set is: (4.7 , 11.1) Enter the co-ordinates of the point: <x> <y> 5 20 The nearest neighbor for the static data set is: (12.1 , 18.2)
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