Math 3614: Study Guide 6 (10/28-11/4)

Sections 8.1,8.2,8.3 (skip universal address systems)

Objectives:

1. Learn the following terms:
   • tree
   • rooted tree
   • m-ary tree, full m-ary tree
   • parent, child, sibling, ancestor, descendant
   • leaf, internal vertex
   • level, height
   • subtree
   • balanced tree
   • preorder, inorder, and postorder traversal
   • infix, prefix, and postfix notation
2. Become comfortable working the following types of problems:
   1. Given a full m-ary tree, compute the number of leaves and internal vertices from the total number of vertices.
   2. Given the number of vertices in a full, balanced tree, determine the height of the tree.
   3. Given the height of an m-ary tree, determine the maximum number of leaves.
   4. Given a list of words, build a binary search tree for the words.
   5. Given a binary search tree, locate an item in the tree with the fewest number of comparisons.
   6. Given a set of letters, construct a prefix code for those letters.
   7. Given the description of a prefix code, find the word represened by a particular string of 0's and 1's.
   8. Given a tree, determine the order in which the vertices are visited by 1) a preorder traversal, 2) an inorder traversal, 3) a postorder traversal.
   9. Evaluate an expression written using 1) infix notation, 2) prefix notation, 3) postfix notation.
   10. Represent an expression using a binary tree.
3. Problem List:Learn to work the following problems:
   1. Section 8.1: 11, 13, 15
   2. Section 8.2: 1, 3, 11, 14
   3. Section 8.3: 7, 11, 15, 18, 19, 27

   Answers to even numbered problems

   Click here for answers to the even numbered problems.

Evaluation: