Final, CSCI 385, Fall 2006

• Use as much paper as you wish, but please label each question.
• Please write legibly.
• When you are asked to give example algorithms, use only named algorithms we have discussed in class.

1. [10 points] Define/describe the following terms.
   1. Tree
   2. Binary Tree
   3. Binary Search Tree
   4. Height Balance Property
   5. AVL Tree
2. [2 points] Give an example of an AVL tree of height at least 3. Store integer data in the tree, and write the data values inside of the nodes.
3. [3 points] Give an example of a tree of height at least 3 that violates the Height balance property.
4. [10 points] In an AVL-tree,
   1. what is a rotation
   2. What does a rotation accomplish?
   3. How can you tell that a rotation is needed?
   4. Draw a figure illustrating a rotation. Label the data and heights of all nodes in your example both before and after the rotation.
5. [10 points] For each of the following sorts, state the performance expectations for both space and memory. State where it would be advantageous to use the sort.
   • Insertion Sort
   • Bubble Sort
   • Selection Sort
   • Quick sort
   • Bin/Radix Sort
6. [5 points] State the algorithm for merge sort and merge.
7. [5 points] Derive the performance expectations for merge sort.
8. [5 points] Describe the complexity classes P and NP.