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Nearest Neighbor Search Using KdTree





//Input should be in input.txt file
//10(2.1,4.3)(3.3,1.5)(4.7,11.1)(4.9,1.6)(5.0,12.3)(5.1,1.2)(6.7,3.3)(19.2,5.4)(20.5,7.9)(100.3,52)
//The first number is the number of points, n, and following it are the coordinates of the n points in ascending order of the x-coordinate.


import java.util.*;
import java.lang.*;
import java.io.*;
import java.util.StringTokenizer;

class KDNode {
    int axis;
    double[] x;
    int id;
    boolean checked;
    boolean orientation;

    KDNode Parent;
    KDNode Left;
    KDNode Right;

    public KDNode(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 KDNode FindParent(double[] x0) {
        KDNode parent = null;
        KDNode 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 KDNode Insert(double[] p) {
        x = new double[2];
        KDNode parent = FindParent(p);
        if (equal(p, parent.x, 2) == true)
            return null;

        KDNode newNode = new KDNode(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 KDTree {
    KDNode Root;

    int TimeStart, TimeFinish;
    int CounterFreq;

    double d_min;
    KDNode nearest_neighbour;

    int KD_id;

    int nList;

    KDNode CheckedNodes[];
    int checked_nodes;
    KDNode List[];

    double x_min[], x_max[];
    boolean max_boundary[], min_boundary[];
    int n_boundary;

    public KDTree(int i) {
        Root = null;
        KD_id = 1;
        nList = 0;
        List = new KDNode[i];
        CheckedNodes = new KDNode[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 KDNode(x, 0);
            Root.id = KD_id++;
            List[nList++] = Root;
        } else {
            KDNode pNode;
            if ((pNode = Root.Insert(x)) != null) {
                pNode.id = KD_id++;
                List[nList++] = pNode;
            }
        }

        return true;
    }

    public KDNode find_nearest(double[] x) {
        if (Root == null)
            return null;

        checked_nodes = 0;
        KDNode 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(KDNode 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(KDNode 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 KDNode search_parent(KDNode 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;

        double dx;
        KDNode 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 KDTNearest {

    public static void main(String args[]) throws IOException {
        BufferedReader in = new BufferedReader(new FileReader("input.txt"));
        String strLin;
        strLin = in .readLine();

        StringTokenizer strLi = new StringTokenizer(strLin, "(,) ");
        int numpoints = Integer.parseInt(strLi.nextToken());

        KDTree kdt = new KDTree(numpoints);

        while (strLi.hasMoreTokens()) {

            double x[] = new double[2];
            for (int i = 0; i < numpoints; i++) {

                x[0] = Double.parseDouble(strLi.nextToken());
                x[1] = Double.parseDouble(strLi.nextToken());
                kdt.add(x);
            }
        }
        System.out.println("Enter the co-ordinates of the point: (one after the other)");
        InputStreamReader reader = new InputStreamReader(System. in );
        BufferedReader br = new BufferedReader(reader);
        double sx = Double.parseDouble(br.readLine());
        double sy = Double.parseDouble(br.readLine());

        double s[] = {
            sx, sy
        };
        KDNode kdn = kdt.find_nearest(s);
        System.out.println("(" + kdn.x[0] + " , " + kdn.x[1] + ")");
    }
}

Comments

  1. What is the license for this code?
    Would like to use it in a project of mine.

    Greetings.

    ReplyDelete
  2. Thanks for the post.

    ReplyDelete

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