CSCE 475/875

Pretest

Assigned: August 29, 2007

Due: 10:30 a.m. September 7, 2007

(Assignment 5 minutes late will not be accepted)

No collaboration is allowed, but you may use any resources you wish, so long as you cite them. Show all work and state all assumptions. Type your work.

1. (5 points)

a. Define the divide and conquer approach to algorithm development.

b. What are the main steps of a divide and conquer algorithm?

c. Give an example of an algorithm that uses divide and conquer. In this algorithm, identify the steps from part (b).

2. (5 points) Consider the bubble sort and HeapSort algorithms. State the best-case, worst-case, and average-case time complexities of each. Under what conditions might one choose one of these algorithms over the other?

3. (5 points) Consider the set of numbers A = {0, 1, 1, 2, 3, 5, 8, 13, 21}. What is its mean? What is its standard deviation?

4. (5 points) Given sets A = {a, b, c} and B = {b, c, d}, what is A Ç B? What is A È B? What is 2^A (called the power set of A)?

5. (10pts) Let a = [a₁, ¼, a_n] be a vector and B = {b₁, ¼, b_m} = {[b₁₁, b₂₁, ¼, b_n1], [b₁₂, ¼, b_n2], ¼, [b_1m, ¼, b_nm]} be a set of vectors. Find the following partial derivative:

,

where c is a constant and a · b_j is the dot product (aka inner product) of a and b_j. Carefully explain each step of your derivation.

6. (20 pts) Write a brief (2–3 pages) essay on any advanced intelligent, or adaptive, or control systems that you have read about (e.g., Deep Blue, CAPTCHA, Google, “Wizard” in MS Word, Washer/Drier automated control system, “smart” traffic lights, “smart” elevators, etc.). Assume that the reader of this essay has a basic computer science and math background, but is unfamiliar with the topic that you are writing about. Thus you want to convey the fundamental ideas and applications of this topic, but do not overwhelm the reader with enormous amounts of detail! Cite all references you use in a style such as that found in any ACM or IEEE journal. Do not simply copy the material from these sources, but instead write this in your own words. Only your presentation and writing style will be graded, so have someone proofread this for you before handing it in.

(Note: Pre-test is based on Dr. Stephen Scott’s)