Consider the following algorithm to check connectivity of a graph de$$ned byits adjacency matrix.ALGORITHM Connected$($A$[0..$n $1,0..$n $1])//$Input: Adjacency matrix A$[0..$n $1,0..$n $1])$ of an undirected graph G$//$Output: $1($true$)$ if G is connected and $0($false$)$ if it is notif n $=1$ return $1//$one$-$vertex graph is connected by de$$nitionelseif not Connected$($A$[0..$n $2,0..$n $2])$ return $0$else for j $0$ to n $2$ doif A$[$n $1,$j$]$ return $1$return $0$Does this algorithm work correctly for every undirected graph with n$>0$vertices? If you answer yes, indicate the algorithm$$s ef$$ciency class in theworst case; if you answer no$,$ explain why