$(25$ points$)$ The city planning commission are also trying to implement a new network of

electric buses to enhance the public transportation. Each bus is routed to travel along the

shortest path from the starting intersection to its destination intersection. To ensure the elec$-$

tric buses are used efficiently and to alleviate range anxiety among drivers, the city planning

commission wants to determine the longest bus route within the city. Write an algorithm to

output the length of the longest shortest path.