Contents:

• Overview
• Practice Problems
• Problems to be Submitted
• Extra Credit

Topic: Divide and Conquer
Related Reading: Ch. 5
Due:

Please make sure you adhere to the policies on academic integrity.

• See "Solved Exercises" in Chapter 5 of text

1. (10 points)

   Exercise 1 of Chapter 5 (p. 246)

2. (10 points)

   Exercise 3 of Chapter 5 (p. 247)

3. (20 points)

   You are to implement both the O(n²) brute-force and the O(n log n) divide and conquer algorithm for finding the closest pair of points in two dimensions (you may use the programming language of your choice).

   More details to follow soon, as well as some sample data sets, and some required experiments regarding timing. For now, let me just iron out a standard file format. The first line is an integer, which specifies the number of points in the set. Then each additional line specifies a single point, given three fields of form:

         xval yval stringTag
         

   where xval and yval are integers and the remainder of the line (if any) serves as the stringTag. Here is a simple sample file:

   5
   8763 4188 Chicago
   9038 3875 St. Louis
   9458 3912 Kansas City
   8628 3973 Indianapolis
   9365 4153 Des Moines
   

   We have created several random data sets which you can use for testing. Also, please report the running times which your program achieves on each of the data sets, for both the efficient and brute force solutions. (of course when the brute force becomes unreasonably slow, you do not need to wait for it to complete).

4. (4 points)

   In Exercise 3 of the text, you developed an O(n log n) time algorithm for finding an equivalent cluster of cards.

   It is actually possible to solve this problem in O(n) worst case time. Develop and analyze such an algorithm.