Problem $3.$ Consider the undirected weighted graph $G(V,E,w)$ pictured below. Work through Dijkstra's al$-$

gorithm on the following graph, using the source vertex $a.$ Note: In order to get full credits consider the

following:

Clearly include the contents of the priority queue, the distance from a and the parent of each vertex at each

iteration.

If you use a table to store the distances, clearly label the keys according to the vertex names rather than

numeric indices $($i$.$e$.,$ dist $[\text{'}$B$\text{'}]$ is more descriptive than dist $[\text{'}1\text{'}]).$

You do not need to draw the graph at each iteration, though you are welcome to do so$.[$This may be helpful

scratch work, which you do not need to include.$]$

Finally represent the shortest path graph.