Problem $1(20$ points$)$

Apply STRONGLY$-$CONNECTED$-$COMPONENTS algorithm to the graph below to identify its connected components and the nodes within each component. You need to show the intermediate steps.

STRONGLY$-$CONNECTED$-$COMPONENTS $($G$)$

$1.$ Call DFS $($G$)$ to compute finishing times f$($u$)$ for each vertex $\backslash ($ u $\backslash )$

$2.$ Compute $\backslash ($ G$^\{$T$\}\backslash )$

$3.$ Call DFS $(\backslash ($ G$^\{$T$\}\backslash )),$ but in the main loop of DFS$,$ consider the vertices in order of decreasing $\backslash ($ f$($u$)\backslash )$

$4.$ Output the vertices of each tree in the depth$-$first forest formed in line $3$ as a separate strongly connected component

$-$ Start at node a

$-$ Note: in case there are multiple adjacent nodes, select the one that comes first in the alphabet.