308 lines
8.6 KiB
Java
308 lines
8.6 KiB
Java
/*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.*/
|
|
|
|
//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();
|
|
}
|
|
}
|
|
|
|
/*
|
|
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) |