CS 336: Design and Analysis of Algorithms
Department of Electrical Engineering and Computer Science
Northwestern University

Spring 2006

Problem Set #1



Due Time:

At the start of class on Thursday, 4/13/2006.

Required Problems:

  1. (15 points) Exercise 4.2-1.
  2. (15 points) Exercise 4.2-2.
  3. (10 points) Exercise 4.2-4.
  4. (20 points) Problem 4-4: b, d, f, h, and j.
  5. (40 points) Give asymptotic upper and lower bounds for T(n) in each of the following recurrences. Assume that T(n) equals a positive constant for n less than or equal to a sufficiently large positive integer. Make your bounds as tight as possible, and justify your answers.
    1. T(n) = T(7n/10) + n.
    2. T(n) = 9∙T(n/4) + n2.
    3. T(n) = 3∙T(n/9) + n1/2.
    4. T(n) = T(n1/3) + 10.

Extra-Credit Problems:

  1. (15 points) Problem 4-6.