Given the following adjacency matrix for a directed weighted graph:

ABCDE

A $04001$

B $20004$

C $02020$

D $00600$

E $30030$

a$.$ Draw the directed graph

b$.$ Show the depth$-$first search of that graph

c$.$ Show the shortest path from A to D

d$.$ Is there an Euler path?

e$.$ Is there a Hamiltonian circuit?