Course: Data Structure and Algorithm

$3.($a$)$ Can you calculate the shortest path from vertex A to vertex E in the following graph? If yes, mention the name of the algorithm you will use. If no$,$ write down why.

Figure $2$: A directed grapn $\backslash (\backslash$mathbf$\{$U $($ v $,$ E$\}\backslash ))$ ior Question $\backslash (\backslash$boldsymbol$\{$s $($ a $)\}\backslash )$

$($b$)$ Find out the shortest path from vertex A to vertex G in the following graph using Dijkstra's shortest path algorithm. Show the calculations in detail and write down the vertices in the shortest path along with the path length.

Figure $3$: A directed graph $\backslash ($ G$($V$,$ E$)\backslash )$ for Question $3($b$)$

$($c$)$ Find out a topological ordering of the following directed acyclic graph. You may use Breadth First Search $($BFS$)$ or Depth First Search $($DFS$)$ to find the order.