MA-351 Homework 3

Due at 9:50 in class, Thursday October 11, 2001


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 (kaltofen@math.ncsu.edu).
Note my office hours on my schedule.

  1. Consider Stirling's formula for approximating n!:


    		n
    		( 2*pi*n )1/2 * (
    		)n


    		e
    1. Using the binary operators + (plus), - (minus), * (times), / (divides), and ** (exponentiation), all of which have exactly 2 operands, and assuming left-to-right grouping of operators of equal precedence, draw the expression tree corresponding to this expression.
    2. Convert the expression tree into a fully parenthesized linear infix expression string.
    3. Write the prefix 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 always start at the vertex labelled a.
  3. Consider the formula a+b+c/d*(e*f). Please give the parse tree for this expression according to the context free grammar for expressions given in class.