This a continuation of the homework from previous week, which requires
further modification of your code (or the one which I provide), which
solves TSP by printing out the shortest tour length and corresponding
tours. Here you will explore how to improve the efficiency of solving
TSP.

1.(3) The code which you are starting with generates all possible solutions
   and prints the total count of them. Modify the code to count the number
   of nodes visited as opposed (to just number of leaf nodes).

   You can think of the permute function as generating different nodes in
   the search tree, in each turn adding an unused symbol to the front of
   partial permutation list, hence creating a child node.  If the recursion
   of permute has bottomed out the, it corresponds to the leaf node.

2.(12) Use partial tour lengths in order to prune the part of the search
   space which cannot contain a minimal tour. This can be accomplished
   by keeping track of the shortest tour length constructed so far and
   comparing each partial tour length to it. If the length of the partial
   tour is already bigger then the length on the current shortest tour it
   cannot possible produce shortest tour. This will result to additional
   saving due to the reduced number of nodes visited and tours produced.

   Suggestion: Using smaller TSP get the incremental length calculation
   working first. This requires changing the permute function to include
   additional argument, the current partial tour length.
   Once its is working, add the prunning code.
 

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Provide answers to the following questions:

1.(5) Problem 2.1 (page 50)
2.(8) Problem 3.9 (page 89)
3.(12) Problem 4.3.(page 118)

Provide consice answers to the questions. Two pages should be enough
to describe the answers.
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Instructions for submission:
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(1) Using script or dribble, you are to capture the output of a Lisp session
    in which you successfully load and execute your code, showing sufficient
    testing of your function(s). On osf1 type script and your session
    will be saved in a file typescript, whose hardcopy you will hand in.
    To exit script simply type 'exit'.
(2) a. In class hand in a hardcopy report consisting of:

       - a cover sheet containing:

         Your name
         CS580 Spring 2001, J. Kosecka
         Homework #4

         (A short summary stating whether you were successful, describing
          any problems, etc.)

       - a print out of the Lisp code.
 

        Hand in the hard copy and include the output from a run on
 cities.dat.  In addition for one of the larger TSP problems (> 7),
 include the efficiency table comparing the node_count and number of
 tours generated by brute force algorithm from the previous homework
 and this version which incorporates prunning. In the following
 form. You can use the version of solve_tsp2 which I provide as a
 solution to hw2.
 

               Node Count              Tour Count

 solve_tsp2
 solve_tsp3

       - answers to the questions should be handed in together with the
         hardcopy
 

    b. Send a SINGLE email to clevcovi@cs.gmu.edu formatted in the
       following way:

       - the subject field of the email should read: CS580 HW#4  Kosecka

       - the content of the email should be a commented version of the
         Lisp code for HW4.  Comments at the top should include:

         Your name
         CS580 Spring 2001, J. Kosecka
         Homework #4
         As a safety precaution, always CC yourself when you submit homework
         this way and keep it around until it has been graded and returned.