Let $\mathbf{CONNECTED}=\{<\mathbf{G}>|\mathbf{G}\mathbf{is}\mathbf{a}\mathbf{connected}\mathbf{undirected}\mathbf{graph}\}.$Analyse the algorithm given on page 185 to show that this language is in .

The technique for finding a solution runs in time$n^k$, where$k$ is a constant, the problem is said to be in $P$.

The very first node is picked but also noted in the very first line.

The nodes are marked in the second and third lines until all of the nodes are marked, which will require a lot of time. If there are n nodes, the nodes are scanned from the list $2,3,4,...,...,...$up to$n-1$.

The order of neighbours for each node will be order of n. Therefore, the following order will be established. $n^3$inspections.

Throughout line$4$, every node being examined to see if they are all marked or not.

This should take an order of n of time.One such method relates to$Psincetheorderis n^3$ .The nodes are marked in all lines differently with marked, which can necessary so much time to scanned from the list of $2,3,4....$