did i do the two classes correctly?

$1.$ inexactVC. This algorithm will find non$-$optimal vertex covers, but must run in polynomial time. Your solution cannot be trivial $($e$.$g$.,$ the set of all vertices is a trivial VC$).$

$2.$ inexactIS. This algorithm will find non$-$optimal independent sets, but must run in

polynomial time. Your solution cannot be trivial $($e$.$g$.,$ the set of no vertices is a trivial IS$).$

public class Graph $\{$

$//$ return $($in polynomial time$)$ an array containing the vertex numbers of a VC$.$

public static int$[]$ inexactVC$($Graph inputGraph$)\{$

int$[][]$ graph $=$ inputGraph.getGraph$()$;

boolean$[]$ coveredEdges $=$ new boolean$[$graph$.$length$]$;

List vertexCover $=$ new ArrayList$<>()$;

$//$ Loop over all vertices

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

for $($int neighbor : graph$[$i$])\{$

if $(!$coveredEdges$[$i$]$ && $!$coveredEdges$[$neighbor$])\{$

vertexCover.add$($i$)$;

vertexCover.add$($neighbor$)$;

coveredEdges$[$i$]=$ true;

coveredEdges$[$neighbor$]=$ true;

break; $//$ Move to the next vertex once an edge is covered

$\}$

$\}$

$\}$

$//$ Return the vertex cover as an array

return vertexCover.stream$().$mapToInt$($Integer::intValue$).$toArray$()$;

$\}$

public static int$[]$ inexactIS$($Graph inputGraph$)\{$

int$[][]$ adjacencyList $=$ inputGraph.getGraph$()$;

int n $=$ adjacencyList.length;

$//$ Initialize the independent set array $(1$ means selected, $0$ means not selected$)$

int$[]$ independentSet $=$ new int$[$n$]$;

Arrays.fill$($independentSet$,0)$; $//$ Start with an empty independent set

$//$ To keep track of selected vertices and their neighbors

boolean$[]$ inSet $=$ new boolean$[$n$]$; $//$ Whether a vertex is in the independent set

$//$ Iterate over all vertices and add to the independent set if possible

for $($int vertex $=0$; vertex $<$ n; vertex$++)\{$

if $(!$inSet$[$vertex$])\{//$ If vertex is not already in the independent set

$//$ Add the vertex to the independent set

independentSet$[$vertex$]=1$;

inSet$[$vertex$]=$ true;

$//$ Mark all neighbors of the vertex as excluded

for $($int neighbor : adjacencyList$[$vertex$])\{$

inSet$[$neighbor$]=$ true;

$\}$

$\}$

$\}$

$//$ Collect the vertices that are in the independent set

int setSize $=0$;

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

if $($independentSet$[$i$]==1)\{$

setSize$++$;

$\}$

$\}$

$//$ Create a result array to store the independent set vertices

int$[]$ result $=$ new int$[$setSize$]$;

int index $=0$;

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

if $($independentSet$[$i$]==1)\{$

result$[$index$++]=$ i;

$\}$

$\}$

System.out.println$("$Inexact Independent Set found: $"+$ Arrays.toString$($result$))$;

return result;

$\}$

$\}$