CS 253  Homework # 3

Problem 1.

You have a choice beween the following two versions of the 
assignment. 

"Arithmentic" version:

Write a program that converts infix arithmetic expressions 
into a postfix form and then evaluates the resulting postfix
expression (as described in the lecture notes). Use
linked lists for the data structures.You must create your 
own  Stack and Queue class (you may want to use my code to 
start with).

"Logic" version:

Same as above, but you will be converting and evaluating
logical expressions. Here is some extra help, if you decide to
take this challenge.

In propositional logic, elementary propositions can be combined
by five logical connectives:

P <--> Q   : P if and only if Q
P --> Q    : If P then Q   (or P implies Q)
P & Q      : P and Q
P v Q      : P or Q
~ P        : not P

The truth tables for these logical connectives are:

P      Q  |  P <--> Q  |  P --> Q  |  P & Q  | P v Q | ~ P
          |            |           |         |       |
T      T  |      T     |     T     |    T    |   T   |   F 
T      F  |      F     |     F     |    F    |   T   |   F 
F      T  |      F     |     T     |    F    |   T   |   T 
F      F  |      T     |     T     |    F    |   F   |   T 

Logical expressions involving these connectives may combine 
many connectives applied according to the following operation
hierarchy:

all ~ are applied first
next all & are applied
next all v are applied
next all --> are applied
finally all <--> are applied

Parentheses may be used to override this hierarchy.
A Logical expression which always evaluates to true is called
a tautology. Example:  (P --> Q) <--> (~P v Q) is a tautology,
because it is true for all possible combinations of true/false 
values of P and Q.

Write a program that tells you if the expression entered is a
tautology or not. Assume that you have no more than three 
propositional symbols in your expressions -- call them P, Q, R. 
Again, you must use the linked list implementation of the data
structures needed.

For both versions, submit the code and example runs to prove 
that your program works as intended. Use the examples from the
lecture notes as one of the test cases. Explain the data structures 
used.

Problem 2.

Given the following postorder and inorder traversals of a binary 
tree, draw the tree:
   
   Postorder:  A   B   C   D   E   F   I   K   J   G   H

   Inorder:    C   B   A   E   D   F   H   I   G   K   J

Explain your answer in a systematic and recursive fashion.