# Find closest point of every point (Nearest Neighbor)

### Tags:

#### points

I am writing a method that takes as input an array of points and finds, for each point in the array, the closest point to it other than itself. I am currently doing this in a brute force way (cheking every point with every other point). My current implimentation doesn't have the array sorted but i can sort it by p.x values with the CompareByX method. I am chekcking the running time of the algorithm, and it gets very time consuming with large values of n. I am not very knowledgable on this subject and know very littel about different types of data structures, any simple help would be great!

My current code is:

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

class My2dPoint {
double x;
double y;

public My2dPoint(double x1, double y1) {
x=x1;
y=y1;
}

}

class CompareByX implements Comparator<My2dPoint> {
public int compare(My2dPoint p1, My2dPoint p2) {
if (p1.x < p2.x) return -1;
if (p1.x == p2.x) return 0;
return 1;
}
}

/* An object of the above comparator class is used by java.util.Arrays.sort() in main to sort an array of points by x-coordinates */

class Auxiliaries {

public static double distSquared(My2dPoint p1, My2dPoint p2) {
double result;
result = (p1.x-p2.x)*(p1.x-p2.x) + (p1.y-p2.y)*(p1.y-p2.y);
return result;
}

}

public class HW3 {
public static void main (String argv []) throws IOException {
int range = 1000000; // Range of x and y coordinates in points

System.out.println("Enter the number of points");

int numpoints = Integer.parseInt(npoints);

// numpoints is now the number of points we wish to generate

My2dPoint inputpoints [] = new My2dPoint [numpoints];

// array to hold points

int closest [] = new int [numpoints];

// array to record soln; closest[i] is index of point closest to i'th

int px, py;
double dx, dy, dist;
int i,j;
double currbest;
int closestPointIndex;
long tStart, tEnd;

for (i = 0; i < numpoints; i++) {

px = (int) ( range * Math.random());
dx = (double) px;
py = (int) (range * Math.random());
dy = (double) py;
inputpoints[i] = new My2dPoint(dx, dy);

}

// array inputpoints has now been filled

tStart = System.currentTimeMillis();

// find closest [0]

closest[0] = 1;
currbest = Auxiliaries.distSquared(inputpoints[0],inputpoints[1]);
for (j = 2; j < numpoints; j++) {
dist = Auxiliaries.distSquared(inputpoints[0],inputpoints[j]);
if (dist < currbest) {
closest[0] = j;
currbest = dist;
}
}

// now find closest[i] for every other i

for (i = 1; i < numpoints; i++) {
closest[i] = 0;
currbest = Auxiliaries.distSquared(inputpoints[i],inputpoints[0]);
for (j = 1; j < i; j++) {
dist = Auxiliaries.distSquared(inputpoints[i],inputpoints[j]);
if (dist < currbest) {
closest[i] = j;
currbest = dist;
}
}

for (j = i+1; j < numpoints; j++) {
dist = Auxiliaries.distSquared(inputpoints[i],inputpoints[j]);
if (dist < currbest) {
closest[i] = j;
currbest = dist;
}
}
}

tEnd = System.currentTimeMillis();
System.out.println("Time taken in Milliseconds: " + (tEnd - tStart));
}
}
``````
630

#### user642012

Brute force for nearest neighbour search is only feasible for a small number of points.

You might want to look into kd-Trees or spatial data structures generally.

Here is a demo for kd-Tree. This is what wikipedia says.

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