Implement the traveling salesman problem described in the "Intractable Problems" section in this chapter. In spite of its intractability, it will have no trouble solving the problem for small N, say 10 cities or fewer. Try a nondirected graph. Use the brute-force approach of testing every possible sequence of cities. For a way to permute the sequence of cities, see the anagram.java program (Listing 6.2) in Chapter 6, "Recursion." Use infinity to represent nonexistent edges. That way, you won't need to abort the calculation of a sequence when it turns out that an edge from one city to the next does not exist; any total greater than infinity is an impossible route. Also, don't worry about eliminating symmetrical routes. Display both ABCDEA and AEDCBA, for example.