Problem $2.$ Consider the following digraph $G_2$ with a couple of negative$-$weight edges.

a$.$ Perform Dijkstra's algorithm on $G_2$ to find a shortest path from $s$ to every vertex in $G_2.$ Show the updated $d$ and $$ values for each vertex after each iteration of the while loop.

b$.$ Perform Bellman$-$Ford's algorithm on $G_2$ to find a shortest path from $s$ to every vertex in $G_2.$ Show the updated $d$ and $$ values for each vertex after each iteration of the first for loop. Trace the iterations of last for loop to determine whether the algorithm will return TRUE or FALSE.

c$.$ Compare your results obtained in part $b$ with your results obtained in part $a$ to answer the following question: Does Dijkstra's algorithm work on $G_2?$ That is$,$ does the final $d$ value computed for every vertex $v$ is the correct weight of a shortest path from $s$ to $v?$