MA-351 Homework 3

Due at 9:50 in class, Thursday October 14, 2004

Calculations necessary for these problems may be done either by hand or with Maple. Solutions may be submitted in person in class, or you may email an ASCII text, Maple Worksheet (.mws), html, or postscipt/pdf-formatted document to me.
Note my office hours on my schedule.

1. Consider the formula

   (b2 - 4ac)1/2 - b

   2a

   1. Using the binary operators + (plus), - (minus), * (times), / (divides), and ^ (exponentiation), all of which have exactly 2 operands, please draw the expression tree corresponding to this expression.
   2. Please convert the expression tree into a fully parenthesized linear infix expression string.
   3. Please write the parenthesis string consisting entirely of properly matched left and right parentheses that linearly encodes the structure of the tree given in answer a.
   4. Please write the postfix expression string equivalent to the expression tree.
2. DMM §3.3, Problem 8, page 107. Note: in order to have a unique DFS tree, assume that the order of the neighboring vertices of each vertex is alphabetical and that you start at vertex labeled a.