This is a famous problem with a variety of solutions of

varying complexity and efficiency. The simplest solution (the

brute force approach) generates all possible routes and

takes the shortest. This becomes impractical as the number of

towns, N, increases since the number of possible routes is

!(N-1). A more intelligent algorithm (similar to iterativedeepening) considers the shortest path to each town which can

be reached in one hop, then two hops, and so on until all

towns have been visited. At each stage the algorithm

maintains a "frontier" of reachable towns along with the

shortest route to each. It then expands this frontier by one

hop each time.