Apply Dijkstra's algorithm to the following graph to find the shortest path $($and its cost$)$ from $\backslash ($ s $\backslash )$ to $\backslash ($ t $\backslash ).$ Write down all intermediate steps.

Now, instead consider the following graph. The graph is a $($slightly simplified$)$ model of a highway which can be accessed from $\backslash ($ s $\backslash )$ and leads, amongst other destinations, to $\backslash ($ t $\backslash ).$ Think about what happens when you run Dijkstra on this graph and possible ideas how to improve it$,$ given that the nodes represent locations.