Weekly Problems $->$ Week $10$: Shortest Path

This problem builds on top of our previous problem where we completed Dijkstra's algorithm for the graph below given vertex $A$ as the source.

Recall that the vertexSet represents the graph:public class FHgraph

$\{//$ the graph data is all here $--------------------------$

protected HashSet$$ FHvertex $>$ vertexSet;

$//$ public graph methods $--------------------------------$

public boolean dijkstra$($E x$)\{....\}$

public boolean showDistancesTo$($E x$)\{....\}$

public boolean showShortestPath$($E x$1,$ E x$2)\{....\}$

Below is a reminder of the attributes in the FHvertex class:

After completing Dijkstra's algorithm from source A$,$ the dist and nextInPath attributes of a reachable FHvertex are set.

class FHvertex

$\{$

$//$ omitted class variables

$//$ attributes $--------------------------$

public HashSet$$ Pair $>$ adjList

$=$ new HashSet$$ Pair $>()$;

public E data;

public double dist;

public FHvertex nextInPath; $//$ for client$-$specific info

Problem $1$

What is the output of showDistancesTo$($E x$)$ method?

Note: display your response similar to the previous problem.

Problem $2$

Choose three FHvertex objects.

What is the output of showShortestPath$($A$,$ youVertextChoice$)$ for each?

For problem $1$ show a visual representation of the partiallyProcessedVerts for every iteration of the while loop in dijkstra$()$ method.

The attributes dist and cost for every vertex.