UMBC CMSC441, Design & Analysis of Algorithms, Fall 1999, Section 0201

Fall 1999 Homeworks 1-4

Homework 1, Due Monday September 13

1. For each of the following pairs of functions f(n) and g(n), give the values of , and where is the smallest positive integer such that .

   Hint: you may need to use a calculator. Use the log identity
   
   if your calculator does not take logs in base 2.

   1. f(n) = n and
   2. and
   3. and
2. Prove that the following statements are correct:
   1. 
   2. 
   3. 
3. Show that the following statements are incorrect:
   1. 
   2. 

Homework 2, Due Monday September 20

1. Prove by induction that for and that
   
   
2. Show that .
3. Exercise 4.1-5, page 57.

   Hint: use the fact that for large enough n.

4. Exercise 4.2-1, page 60.

Homework 3, Due Monday September 27

1. Problem 4-1, page 72.

   In the cases where you use the Master Theorem, clearly state which case you are using and the asymptotic bounds on T(n).

2. Exercise 7.5-4, page 151.

3. Exercise 7.5-5, page 151.

4. Problem 7-1, page 152.

Homework 4, Due Monday October 4

1. Problem 8-3, page 169.

2. Problem 8-4, page 169-170.

3. Exercise 9.3-4, page 180.

Last modified: Mon Sep 13 11:44:47 EDT 1999
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