Algorithm Connected$($A$[0..$n$-1,0..$n$-1])\{$

$//$Input: Adjacency matrix $A$ of an undirected graph $G$

$//$output: $1($true$)$ if $G$ is connected and $($false$)$ if it is not

if $n=1$ return $1$; $////$one$-$vertex graph is connected by definition

else $\{$

if not Connected$(A[dotsn-2,0$dotsn$-2]$ return $$;

else $\{$

for $j=0$ to $n-2$ do $\{$

if $A[n-1,j]$ return $1$ ;

$\}$

return $0$ ;

$\}$

$\}$

$\}$

Does this algorithm work correctly for every undirected graph with $\text{'}n\text{'}$ vertices? If you answer YES, indicate the algorithm's efficiency class in the worst case. If you answer NO$,$ provide a counter example.