For this assignment, you are to read an input file that gives the
distances between each possible pair of "cities" for a traveling
sales problem and then compute the cost of a "legal" tour.A legal tour of N cities starts at any one of them
and visits each of the other cities exactly once before returning to
the original destination city.  And the cost of a tour is the sum of
the "distances" between adjacent cities in the tour.

Your program output should print out the cost of the legal tour (or path) and
also list the "cities" (well the integers associated with those cities) in the
order visited.  So, given data for a 4-city (Dallas, New York, Boston) the legal
tours are:

    Dallas, New York, Los Angeles, Boston, Dallas
    Dallas, Boston, New York, Dallas
        New York, Dallas, Boston, New York
        New York, Boston, Dallas, New York
        Boston, New York, Dallas, Boston
        Boston, Dallas, New York, Boston

and if we assume that the "cost" (or distance) or is represented as

    Dallas to New York is 1900 miles
        Boston to Dallas is 1950 miles
        New York to Boston 150 miles
        Los Angeles to Dallas is 1400 miles
        Los Angeles to Boston is 3150 miles
        Los Angeles to New York is 3100 miles

your answer might be something like

   The tour  New York, Dallas, Boston, Los Angeles New York costs 7150.

which would represent the sum of 1900 (New York to Dallas), 1950 (Dallas to Boston),
3150 (Boston to Los Angeles) and 3100 (Los Angeles to New York).  However, we'll
"generalize" both our input and output to use consecutive integers, starting at 1,
to represent the cities of the tour.

NOTE: For the example data given, 7150 would not be the minimal cost tour.  For
      example, the tour Los Angeles, Dallas, Boston, New York, Los Angeles would
      cost only 6600.  However, for THIS program you're not required to come up
      with a minimal cost tour, just a legal tour.  Any legal tour will do.

Requirements:

        Your C program should consist of the single file, X.c (or whatever
        you decide to call your program.)

    Your program will read an input file (from stdin) which includes
        an unspecified number of command lines which describe the problem.
        The input (file) will contain two types of commands,
        and each command will be included on a single line of the file.  The
    commands are:

        c W
        a X Y Z

        for Create a city and Add an edge between two cities. The symbols
        W,X,Y,Z all stand for "arbitrary" integers.  Each "city" will be
    "named" with a distinct integer, specifically the one included in
        the "c" command.  In the "a" command (add an edge) the edge should
        be From X To Y, with Cost Z.  To make the program a bit easier,
        all the "Create" commands will precede any "Add" commands in the input
        file.  If you wish you can assume an upper limit of 20 cities, "named"
        0-19, for this version of the program.  You may also assume that the
        "names" of the nodes will be consecutive integers starting at 1.

        So, here is what the input file might look like for our problem including
        Dallas, Los Angeles, Boston and New York above.

        c 1
        c 2
        c 3
        c 4
        a 1 2 1400
        a 1 3 1950
        a 1 4 1900
        a 2 3 3150
        a 2 4 3100
        a 3 4 150

        Since we assume that the distance between cities X and Y is the same whether
        we go from X to Y or Y to X, we don't need to list the distance for each
        direction of travel between any pair of cities.

Output:
    A single line which lists the nodes in a legal tour and the cost of that
        tour. So, for our the input file provided and the example tour listed above
        (New York, Dallas, Boston, Los Angeles New York) the actual output of your
        program might be:

   The tour  4 1 2 3 4 costs 7150.

 Also, remember that we will (attempt to) compile your program using the command

   gcc *.c