Problem $3($Extra Credit $+30$ points$)$

Given a directed graph, determine if it is strongly connected. A graph is Strongly Connected if every node in the graph is reachable from every other node; that is$,$ given any starting node, you can reach every other node in the graph.

Maximum time complexity: O$($n$3)$ Assumptions: None

Example$1$: Graph:

Input: An array of vertices and an array of edges Vertexes: $\{$A$,$ B$,$ C$,$ D$\}$

Edges: $\{($A$,$ B$),($A$,$ C$),($B$,$ D$),($C$,$ A$),($D$,$ A$)\}$ Output: Strongly Connected

Example $2$: Graph:

Input: An array of vertices and an array of edges Vertexes: $\{$A$,$ B$,$ C$,$ D$\}$

Edges: $\{($A$,$ B$),($B$,$ D$),($C$,$ A$),($D$,$ A$)\}$ Output: Not Strongly Connected

Hints:

$-$ You can solve this using an adjacency list or adjacency matrix, it is up to you which to

use

$-$ You cannot assume if the graph is weighted or not, but weights actually do not matter in

this problem $($we only care if a relation$/$edge exists, not what weight it may have$)$