MA-351 Homework 3

Due at 4:59pm, Tuesday October 27, 2009 in my mailbox in SAS 3151


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 Stirling 's formula for approximating n!:


    		n

    		( 2*π*n )1/2 * (
    		)n


    		e
    1. Using the binary operators + (plus), - (minus), * (times), / (divides), and ^ (exponentiation), all of which have exactly 2 operands, 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 and postfix expression string equivalent to the expression tree.
    4. Give the balanced parentheses expression for the expression tree in a., which was discussed in class. Note that there are 7 arithmetic operators, hence 7 pairs of parentheses.
  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.