Figure $2$: A weighted graph for shortest paths.

The graph in Figure $2$ is used for questions $6$ to $9.$

$6.(3$ points$)$ Manually run Dijkstra's algorithm from start vertex a on this graph. List the distance label value returned for each of the vertices a to f $.$ Clearly label each distance label value with the vertex letter.

$7.(3$ points$)$ Using the results produced for question $6,$ draw the resulting shortest path tree. Designate vertex $\backslash ($ a $\backslash )$ as the root.

$8.(4$ points$)$ Consider the algorithm specified using pseudocode as "Algorithm $2"$ below. This algorithm aims to find a shortest path from start vertex $\backslash ($ s $\backslash )$ to destination vertex $\backslash ($ t $\backslash )$ in a connected graph. Manually run this algorithm on the graph in Figure $2$ to find a path from vertex $\backslash ($ a $\backslash )$ to vertex $\backslash ($ f $\backslash ).$ List the sequence of vertices visited for the resultant path.

$9.(1$ point$)$ Is the path produced for question $8$ a shortest path between the two vertices? Is it the same as the shortest path indicated by your question $7$ result?