CSC297.Java, Class 35: Dictionaries

Admin:
* How did the homework go?
  * Alex tried and couldn't do it
  * Yvonne and three upper-level CS students couldn't do it.
* Weekly Bishop check (No new assignments)
* Thoughts on a final
* Homework:
  * Look up AVL trees and find out how to insert and delete into them.

Overview:
* Review of homework
* Detour: Balanced trees
* The dictionary ADT.
* Implementing dictionaries with sorted lists.
* Implementing dictionaries with search trees.
* Looking ahead: Hash tables

Morals from attempting to implement delete and find
* Think carefully about the strategy you're using.
  * If your strategy involves you doing two things at once (e.g., deleting and finding a value), you're likely to screw up one of the two and it will be hard to figure out which.
  * We don't always have to balance binary trees.  (Of course, if they're not balanced, they won't be efficient.  However, they can't ever be less efficient than sorted lists.)
* Complete trees are almost impossible to maintain.  Instead, we look for "balanced" trees (e.g., not more than a 2:1 ratio of subtree sizes)
  * Balanced subtrees can stil have O(log_2(n)) depth.

Techniques for balancing binary search trees:
* AVL trees
* 2-3 trees
* Red-black trees
* B-trees
* "Splaying"

We'll try AVL trees (named after their designers, Adelson-Velskii and Landis)

Key idea: Allow each node to have different depth subtrees, but allow the subtrees to differ in height by only one.
* How unbalanced can this be?  Probably about a factor of 2 in terms of nodes.

Problem: How do we keep a tree balanced during addition and deletion?
Solution: Keep track of balance and "rotate" key nodes in the tree.

The Dictionary ADT.  (Also called "Keyed Table")
* Dictionaries are collections of values indexed by string.
  * Like vectors (collections of values indexed by number), except that the index is a string rather than a number.
  * Quite similar to binary search trees, when you assume that the key is the name and the comparator is a string.
  * Similar to hash in Perl.
  * Similar to association lists in Scheme.
  
How do we implement dictionaries?  Wait until next week to find out.