Question 1 (a) Run the strongly connected component detection algorithm discussed in class on the following graph. Show the start and finish time during execution of depth first search, the parenthesis string and then process the string to get the strongly connected components.

(b) Someone claims that you can compute the strongly connected components using the following algorithm: 1) Run depth first on the graph 2) Run depth first again but processing the vertices in order of finish time In other words, instead of transposing the graph and then running depth first search in reverse order of finish time, the algorithm processes the vertices in order of finish time without transpose. Construct an example that shows that the algorithm described above is incorrect (doesnt compute the correct strongly connected components).