Homework #3

Due: Thursday, Sept. 26, 2002

Chapter 1. Exercises 22, plus determine the theta notation for the following sections of code:

Code A:

i := n

while (i >= 1) do

for j := 1 to i do

for k := 1 to n do

some code that takes time

end for k

end for j

i := i / 2

end while

Code B:

for i := 1 to n do

for j := 1 to i do

for k := j to (i + j) do

some code that takes time

end for k

end for j

end for i

Code C:

i := n

while i > 0 do

for k = 1 to n do

j := 1

while j < i do

some code that takes time

j := j * 2

end while

end for

i := i / 2

end while

Ch 2. Exercise 7 give recurrence and solve the recurrence, 15, 39 give recurrence and solve the recurrence

Appendix B. 12b, 12c, 15c, 15d

For all of the exercises we are after the theta notation so you don't need to solve for the ci constants!