MA-351 Homework 3

Due at 4:59pm in my mailbox in SAS 3151, Tuesday, November 5, 2019

All solutions must be submitted in hardcopy either to me in class or placed in my mailbox. Note my office hours on my schedule.

  1. 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. Please also indicate when the one-way street assignment is impossible and why.
  2. Consider the formula:

     (0–b+(b2 – 4ac)1/2)
    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. Please note that 1/2 is not a constant.
    2. Convert the expression tree into a minimally parenthesized linear infix expression string, using precedence and left-to-right rules whenever possible.
    3. Write the prefix and postfix expression string equivalent to the expression tree.
  3. Problem 1c in the Fall 2018 second exam.
  4. Problem 6 in the Fall 2018 second exam. Additional hint for part b: the x-coordinate of the limit point is the x-coordinate of that vertical side of drawn dash-dotted rectangles that have a vertex of the equilateral triangles on it. For iteration 1 it is x_1 = 2. for iteration 4 it is x_4 = 2–2/27.