UMBC CMSC441, Design & Analysis of Algorithms, Fall 2003, Section 0201

Homework Assignments

Homework 1, Due Tuesday 09/16

1. Problem 3-3, page 58. Note: You may skip the functions involving lg^* n.
2. Exercise 16.1-4, page 379.
3. Exercise 4.1-2, page 67.

Homework 2, Due Tuesday 09/23

1. Prove using the substitution method that the recurrence relation

   T(n) = 4 T(n/2) + n² log n

   is O( (n log n)²).
   
   
2. Exercise 4.2-3, page 72. Note: Since the question asks for a tight asymptotic bound, you must find an upper and a lower bound on T(n) and you must verify both the upper and lower bounds by substitution.
   
   
3. Problem 4-1, page 85, parts b, d, f & g.

Homework 3, Due Tuesday 09/30

1. Exercise 6.5-7, page 142.
2. Problem 6-3, parts a-e, page 143. Optional: Problem 6-3, part f, page 144.
3. Problem 7-4, page 162.

Homework 4, Due Tuesday 10/07

1. Problem 8-3, page 179.
2. Problem 8-4, page 179.
3. Exercise 9.3-8, page 193.

Homework 5, Due Tuesday 10/14

1. Problem 7-3 parts a-c, page 161-162.
2. Exercise 9.3-9, page 193.
3. Exercise 11.3-1, page .

Homework 6, Due Thursday 11/6

1. Exercise 22.2-6, page 539. Note: you must argue why your algorithm produces a correct result.
2. Exercise 22.3-4, page 548. Note: make sure you prove both directions of the "if and only if".
3. Exercise 22.4-5, page 552. Note: make sure that you can find vertices with indegree zero quickly.

Homework 7, Due Thursday 11/13

1. Exercise 22.5-3, page 557.
2. Exercise 22.5-7, page 557. Hint: First find the component graph of G. What does it look like if the graph is semi-connected? If it isn't semi-connected? Prove your conjecture.
3. Problem 22-3, page 559.

Homework 8, Due Thursday 11/20

1. Problem 23-4, page 577.
2. Exercise 24.3-6, page 600.
3. Problem 24-3, page 615.

Homework 9, Due Tuesday 12/09

1. Problem 15-4, page 367.
2. Exercise 25.2-6, page 635.
3. Problem 25-1, page 641.