Let G $=($V$,$ E$,$ w$)$ be a weighted graph.

$($a$)$ Give an example to show that if the weight of the edges can be

negative, then Dijkstra$$s algorithm will not be able to compute

correct distances.

$($b$)$ Can we first add a constant value to the weight of each edge to

make all weights non$-$negative, then run the Dijkstra$$s algorithm

to compute shortest paths? Justify your answer.