Consider the following directed weighted graph given by adjacency lists $($first column

indicates the vertex, the second column shows the outgoing directed edges as a list of

$($vertex$,$ weight$)$ pairs, for example, there are two edges incident to vertex $0,$ the first

joins it to vertex $1$ with weight $-7,$ the second joins it to vertex $3$ with weight $-4)$:

$(4$ pts$.)$ Perform the Bellman$-$Ford Algorithm to find shortest directed paths in this

graph starting from vertex $0.$ Use the improved version so that you either find shortest

paths or a directed cycle with negative total weight. Show the queue while you do

the algorithm. Either find a negative cycle or give shortest paths using the edgeTo

and distTo arrays.