Math 176 - Programming Assignment #1
Some Suggestions and Software Aids

   There are two software items that may help you debug your solution to homework #1.

1. A program to help you check that you have declared your classes and methods properly.   This program is called CheckAvlSignature.  Copy CheckAvlSignature.class, CheckClassDefn.class and ThreadedAvlTreeReference.class and ThreadedAvlTreeReference$AvlIterator.class from the ProgHomework1 directory, and place them in the same directory as your own ThreadedAvlTree class.  Run CheckAvlSignature, with the command   "java CheckAvlSignature".  It will either tell you that your implementation of ThreadedAvlTree has the right methods, or print out diagnostics about what is missing or wrong.
          The source code for these three programs is available in the same directory as the class files, if you would like to examine the source code.
          How it works:  CheckAvlSignature uses the java.lang.reflect classes to compare the methods of the ThreadedAvlTreeReference and ThreadedAvlTree classes.  It expects that every method of the first class is exactly signature in the second class.   It also checks which classes are extended and implemented.  Finally, it recursively checks inner classes in the same way.
2. A sample method that you may wish to modify for yourown use: CheckAvlProperties is a method that recursively checks the nodes in an AVL tree to see if all the properties of binary search trees and threaded AVL trees are properly satisfied.  You cannot use this program as-is, but will need to rewrite it for your own classes.  The program checks the binary search tree ordering properties, it checks the AVL height properties and that threads point to nodes that are (or at least appear to be) correct.   It does not check for every possible problem, but will catch most problems. 
           When you look at the code, you will see that I wrote my implementation with a sentinal.  I had hoped this would simplify the threaded AVL tree implementation, but in the end it did not help much at all.  I suggest you do not use a sentinal node.

Some implementation suggestions:

1. Your node class and iterator class should be inner classes of your ThreadedAvlTree class.  There are several advantages of using inner classes.  The first advantage is that by making the inner classes private, you make it impossible for the programmer using your routines to use any methods or objects that they should not have access to  This forces them to use the correct methods from the Collections API.   The second advantage is that objects from the inner class automatically have access to all the fields and methods of the object that created them.  (The first advantage could be achieved through the use of package access, but the second advantage could not, at least not without added more fields to objects of the inner classes.)
2. To implement remove() for your iterator, it is OK to call the remove() method from the TreadedAvlTree class instead of re-writing the remove() method.
3. You can test your threaded AVL tree implementation by comparing what it does with a Java object TreeSet (which implements a Red-Black tree).
4. Check out the figures illustrating how to rebalance after deletion.
5. Your ThreadedAvlTree class should have a field for the root node (private AvlNode root;) and a field for the size (private int numElements;).  It is recommended, but optional, that you also have references to the inorder first and inorder last elements of the tree.
6. Your AvlNode class should have fields for the key (private Comparable key), the children (private AvlNode leftChild, rightChild;) and the height (private int height;)
7. Your AvlIterator class should have fields for the next node and for the previous node.   You will need the previous node to implement remove().  Actually there are several ways to implement the AvlIterator and you may not need both fields.