CS451/551 Homework 1 - due Friday February 8, 2002
-----------------------------------------------------

You may work in groups of two if you like.

You need to write search algorithms for the following
problems:

1. Maze Problem
2. Tiling Problem
3. Geography Problem
4. PCP Problem

Here is a description of each of the problems:

Maze Problem:  You have a grid.  Some squares in the
grid are considered to be legal spots.  There is a 
designated initial square, and a designated final
square.  The problem is to find a path from the
initial square to the final square, or to say that
one does not exist.  At each point, you may move up,
down, left or right one square, and you may only go
to legal squares.

Tiling Problem:  You have a grid.  You also have a 
set of dominoes.  Each domino has a four numbers on
it: one on top, one on the bottom, one on the left
and one on the right.  The problem is to place dominoes
on all squares of the grid, such that numbers that
touch each other are the same.  You are allowed to 
use each domino as many times as you want.

Geography Problem:  You have a set of words.  A list
of words in legal if the last letter of each word is
the same as the first letter of the following word.
The problem is to find a legal list of words using
all the words exactly once.  (The easiest is to represent
a word as a list of letters)

PCP Problem:  You have a set of dominoes.  Each one
contains a string on the top and a string on the bottom.
The problem is to find a sequence of dominoes of dominoes
such that the concatenation of the strings on the top
gives the same string as the concatenation of all the 
strings on the bottom.  Dominoes may be used as many
times as you want.

I have a generic DFS search algorithm at 
http://www.clarkson.edu/~clynch/cs451/spring02/solve.lsp
The DFS search algorithm is
defined so that it fails when it finds a duplicate state as an
ancestor, but not when it finds a duplicate state elsewhere in
the tree.  You should use my search algorithm,
and then all you need to do is to define each individual problem
as in the template
http://www.clarkson.edu/~clynch/cs451/spring02/mazeprob.lsp

For each problem, please do the following:

A. Print out your problem definition.
B. Print output from some examples.
C. Calculate (approximately) the time complexity,
   space complexity, and completeness of DFS for
   this problem in terms of variables in the general
   problem (not for a specific instance of the problem)
   for the worst case.
D. Repeat step C for BFS instead of DFS.
E. Give an opinion on whether DFS or BFS is better for
   this particular problem.
F. Give a concrete example that illustrates your opinion
   on step E.

Please ask me questions if you have any.  This may
seem vague, but I am willing to explain it better 
if you ask.