Consider the following undirected weighted graph given by adjacency lists $($first col$-$

umn indicates the vertex, the second column shows the incident 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 $9,$ the second joins it to vertex $4$ with weight $26)$:

$($a$)(4$ pts$.)$ Perform Prim's Algorithm to find a minimum weight spanning tree in

this graph starting from vertex $0($you can use either the original or the improved

version$).$ Indicate the edges you are choosing from in each iteration and give the

resulting MWST using the edgeTo array.

$($b$)(4$ pts$.)$ Perform Dijkstra's Algorithm to find shortest paths from vertex $0$ to

every other vertex in the graph. Indicate the content of the queue at each

iteration and give the resulting shortest paths using the edgeTo and distTo

arrays.