$3.[7$ pts$]$: Depth$-$first search for finding Strongly Connected Components. Consider the directed graph below. DO a DFS of this graph, when you have a choice of multiple unvisited nodes to visit next, go to the nearest one. If two nodes are equally distance, breakties alphabetically. $(0\mathrm{.}2$ points per box $[$minus the three that l've already filled$])$

Part A: Find the discovery and finish times of the nodes.

Solution:

Part B: Classify the edges as T$($tree$),$ F $($forward$),$ B $($back$),$ or C $($cross$)$ edges

Solution:

Part C: In the table below, show the stack that you generate using Kosaraju's algorithm. Note that the top of the stackis on the left.

Part D: Here's the graph G$\text{'}($G with the edge directions reversed$).$ Show the discoverytimes and finish times of the nodes when you do a heuristic DFS$.$

Part E: List the SCCs$.($Youmay not need all the lines.$)$

Solution:

SCCs: