$5.(10$ pts$)$ In a well$-$planned city, a road network connects intersections. If there is a road between two intersections, then one can go from one intersection to the connected intersection following the road connecting the two intersections. Each road has exactly the same length.

The city planning commission is trying to determine whether electric buses will be a viable option for public transportation in the city. Each bus is routed to travel along the shortest path from a starting intersection to a destination intersection. To reduce the range anxiety of the electric bus drivers, the commission wants to determine the longest such shortest path bus route in the city. Write an algorithm that finds the maximum such shortest path bus route.

Before developing your algorithm, give an outline of the steps in your solution strategy. Also, give the runtime analysis of your algorithm.