Note: An object of the class java.util.Random has a method nextInt$($int n$)$ that returns a randomly generated number in the range $[0,$n$]$

Note: When a cluster has only one example, that example is centroid!

Provide me with the Clustering.java class given the following:

FeatureVector.java class:

public class FeatureVector $\{$

private String name;

private double$[]$ features;

private boolean verbose;

public FeatureVector$($String name, int size$)\{$

this.name $=$ name;

this.features $=$ new double$[$size$]$;

this.verbose $=$ false;

$\}$

public FeatureVector$($String name, double$[]$ elems$)\{$

this.name $=$ name;

this.features $=$ new double$[$elems$.$length$]$;

System.arraycopy$($elems$,0,$ this.features, $0,$ elems.length$)$;

this.verbose $=$ false;

$\}$

public String getName$()\{$

return name;

$\}$

public int getSize$()\{$

return features.length;

$\}$

public double featureAt$($int index$)\{$

return features$[$index$]$;

$\}$

public void featureSet$($int index, double value$)\{$

features$[$index$]=$ value;

$\}$

public FeatureVector copy$()\{$

return new FeatureVector$($this$.$name, this.features$)$;

$\}$

public double getDistance$($FeatureVector other$)\{$

if $($this$.$getSize$()!=$ other.getSize$())\{$

throw new IllegalArgumentException$("$Vectors must have the same size"$)$;

$\}$

double sumOfSquares $=0\mathrm{.}0$;

for $($int i $=0$; i $$ this.getSize$()$; i$++)\{$

double diff $=$ this.featureAt$($i$)-$ other.featureAt$($i$)$;

sumOfSquares $+=$ diff $*$ diff;

$\}$

return Math.sqrt$($sumOfSquares$)$;

$\}$

public void plus$($FeatureVector other$)\{$

if $($this$.$getSize$()!=$ other.getSize$())\{$

throw new IllegalArgumentException$("$Vectors must have the same size"$)$;

$\}$

for $($int i $=0$; i $$ this.getSize$()$; i$++)\{$

this.features$[$i$]+=$ other.featureAt$($i$)$;

$\}$

$\}$

public void div$($FeatureVector other$)\{$

if $($this$.$getSize$()!=$ other.getSize$())\{$

throw new IllegalArgumentException$("$Vectors must have the same size"$)$;

$\}$

for $($int i $=0$; i $$ this.getSize$()$; i$++)\{$

if $($other$.$featureAt$($i$)==0)\{$

throw new ArithmeticException$("$Division by zero"$)$;

$\}$

this.features$[$i$]/=$ other.featureAt$($i$)$;

$\}$

$\}$

public void div$($double value$)\{$

if $($value $==0)\{$

throw new ArithmeticException$("$Division by zero"$)$;

$\}$

for $($int i $=0$; i $$ this.getSize$()$; i$++)\{$

this.features$[$i$]/=$ value;

$\}$

$\}$

public void setVerbose$($boolean value$)\{$

this.verbose $=$ value;

$\}$

@Override

public String toString$()\{$

StringBuilder sb $=$ new StringBuilder$()$;

if $($verbose$)\{$

sb$.$append$($name$).$append$("$: $")$;

$\}$

sb$.$append$("\{")$;

for $($int i $=0$; i $$ features.length; i$++)\{$

sb$.$append$($features$[$i$])$;

if $($i $$ features.length $-1)\{$

sb$.$append$(",")$;

$\}$

$\}$

sb$.$append$("\}")$;

return sb$.$toString$()$;

$\}$

public boolean equals$($FeatureVector other$)\{$

if $($this$.$getSize$()!=$ other.getSize$())\{$

return false;

$\}$

for $($int i $=0$; i $$ this.getSize$()$; i$++)\{$

if $($this$.$featureAt$($i$)!=$ other.featureAt$($i$))\{$

return false;

$\}$

$\}$

return true;

$\}$

$\}$

Cluster.java class:

public class Cluster $\{$

private FeatureVector$[]$ elements;

private int capacity;

private int size;

public Cluster$($int capacity$)\{$

this.capacity $=$ capacity;

elements $=$ new FeatureVector$[$capacity$]$;

size $=0$;

$\}$

public int getSize$()\{$

return size;

$\}$

public boolean add$($FeatureVector elem$)\{$

if $($size $>=$ capacity$)\{$

return false;

$\}$

elements$[$size$++]=$ elem;

return true;

$\}$

public FeatureVector getElementAt$($int index$)\{$

if $($index $<mtext></mtext><mn>0</mn><mtext></mtext><mi>|</mi><mi>|</mi>$ index $>=$ size$)\{$

return null;

$\}$

return elements$[$index$]$;

$\}$

public FeatureVector getCentroid$()\{$

if $($size $==0)$ return null;

int featureLength $=$ elements$[0].$getSize$()$;

double$[]$ centroidFeatures $=$ new double$[$featureLength$]$;

for $($int i $=0$; i $$ size; i$++)\{$

for $($int j $=0$; j $$ featureLength; j$++)\{$

centroidFeatures$[$j$]+=$ elements$[$i$].$featureAt$($j$)$;

$\}$

$\}$

for $($int j $=0$; j $$ featureLength; j$++)\{$

centroidFeatures$[$j$]/=$ size;

$\}$

return new FeatureVector$("$centroid$",$ centroidFeatures$)$;

$\}$

public double getVariance$()\{$

FeatureVector centroid $=$ getCentroid$()$;

if $($centroid $==$ null$)$ return $0$;

double variance $=0$;

for $($int i $=0$; i $$ size; i$++)\{$

variance $+=$ Math.pow$($elements$[$i$].$getDistance$($centroid$),2)$;

$\}$

return Math.sqrt