3 The Traveling Salesman Distance Calculation

The Traveling Salesman problem is a famous problem in Computer Science. In this question, you will write some code that would be used in solving this problem. (You won't have to write a program to solve the whole problem!) The complete Traveling Salesman Problem can be stated as:

Given: a set of cities that salesman must visit, and the distances between each pair of cities.

Find: the order that the salesman should visit the cities so as to have him travel the least distance.

If there are N cities, the cities are numbered from 1 to N. The distance between cities is stored in a two-dimensional array, D, where is the distance between cities i and j.

You are to write a Turing program that inputs the 2-D distance array, and the order of cities that the salesman visits, from a single file. Your program should prompt the user for the name of the file. The program should simply calculate the distance that the salesman would travel if he visited the cities in that order.

Use the following format for the input file:

N
D11 D21 D31 .. DN1
D12 D22 D32 .. DN2
D13 D23 D33 .. DN3
.
.
D1N D2N D3N .. DNN

C1 C2 C3 C4 .. CN

Here N is the number of cities, the is the distance between city i and city j, and the list C1, C2, .. CN gives the order of the cities visited.

For example, if the distance matrix is given as:

 
 

And the order of cities visited was 4 3 6 1 5 2, then the output would be calculated as: + + + + = 6 + 2 + 66 + 33 + 952 = 1059. The output of your program should simply be:

For the city order 4 3 6 1 5 2 the distance traveled is 1059.

Restrictions and Notes

• You must use a 2-dimensional array to store the distance matrix.
• Your program must use the file format described above. To test your program with above example, (and to be sure that you use the correct format) test your program with the file /usr/copy/aps105/dist.
• Assume that the distance matrix is symmetric, i.e. for all i and j. If you make your own test input files, make sure this is true.
• In the above example, the table includes the city numbers, so as to make it easier to read. However, the input file does not explicitly contain the city numbers.

A solution