You are developing a GPS navigation system and need to compute the shortest path between various locations. The graph is given below.

$($a$).$ Apply Dijkstra's algorithm to the given graph, starting from vertex $"$ s $",$ and compute the shortest path to all other vertices in the set $\backslash ($ V$=\backslash \{$a$,$ b$,$ c$,$ d$,$ e$,$ f$,$ g$,$ h$,$ s$\backslash \}\backslash ).$

$($b$).$ List the vertices in the order they are removed from the priority queue.

$($c$).$ Discuss how the algorithm would handle dynamic changes, such as road closures or the addition of new routes.