Please look at the graph carefully. How can I do this? How do I do mainly Part a$?$

a$)$ For the graph above, trace an execution of Dijkstra$$s algorithm starting at node $1$ by giving the state of the graph just after the call to Line $9.$ Include:

$-$ Which nodes, if any, had their shortest distance from node $1$ updated, and what the new value is

$-$ The edge added to the spanning tree at this iteration

$($b$)$ Suppose we run Dijkstra$$s algorithm using a priority queue which uses an array of length n instead of a min$-$heap.

$($a$)$ Discuss how you would handle Insert, Extract$-$Min, and Change$-$Key.

$($b$)$ Analyze the complexity of your implementations in part $($a$).$

$($c$)$ Analyze the overall runtime of Dijkstra$$s algorithm given part $($b$).$