CS 141 Homework Assignment #3
                       Set Feb. 25, 2008
                       Due March 10, 2008, before class


1. [15 pts] [Levitin, p. 203] Question 8.  (The same question is also in 
   the 1st edition of Levitin, Question 8, pp. 198-199.)

   Hint: Some hints are given in the book. For part b, pick any point as
   the radiant and sort the rest of the points by the angles of the rays
   from the radiant to them. Be careful with ordering the points that lie
   on the first and last rays.

2. [15 pts] [Levitin, p. 222] Question 4. (The same question is also in 
   the 1st edition of Levitin, Question 4, p. 217.)

3. [10 pts] [Levitin, p. 292] Question 7 (or page 288 of the 1st edition of 
   Levitin). You should illustrate your answer in a style similar to Figure 8.7 
   on page 291 (or page 287 on the 1st edition of Levitin).

4. [10 pts] Let a, b, c, d, e, f, and g be 7 letters that appear with 
   probabilities 0.2, 0.01, 0.05, 0.04, 0.3, 0.3, and 0.1 respectively.
   Construct an optimal Huffman code (and trie) step by step, and calculate 
   the average code length. 

5. [10 pts] [Levitin, p. 327] Question 2(a) (or page 323 of the 1st edition of 
   Levitin). You should illustrate your answer in a style similar to Figure 9.10 
   on page 325 (or page 321 of the 1st edition of Levitin).

6. [10 pts] Compute the prefix function pi for the pattern abaabab and show
   the comparisons made by the KMP algorithm on the pattern and text
   ababaabaababababaabab, using a diagram similar to the one in 
   http://www.cs.ucr.edu/~jiang/cs141/kmp-example-03.doc

7. [Optional, 10 bonus pts] [Levitin, p. 314] Question 10. (The same question
   is also given in the 1st edition of Levitin, Question 9, p. 311.)