$(15$ points$)$ A company named Wise Telephone & Telegraph $($WT&T$)$ has a network of $n$

switching stations connected by $m$ high$-$speed communication links. Each customer's

phone is directly connected to one station in his or her area. The engineers of WT&T have

developed a prototype video$-$phone system that allows two customers to see each other

during a phone call. In order to have acceptable image quality, however, the number of

links used to transmit video signals between the two parties cannot exceed four. Suppose

that WT&T$\text{'}$s network is represented by a graph. Design an efficient algorithm that

computes, for each station, the set of stations reachable using no more than four links.