Discrete Structures Homework #10

Due: Wednesday, Dec. 11 , 2002

Section 4.1 exercises 6, 9

Section 4.4 exercises 6

Determine the best big-oh notation for the algorithms listed in the following problems:

A) 

for i = 1 to n do

    for j = i to n do

        something that takes O(1) time

    end for

end for

B) 

for i = 1 to n/2 do

    for j = 1 to n/2 do

        something that takes O(1) time

    end for

end for

C)

for i = 1 to n do

   j = 1

   while j < n do

      for k = 1 to n do

         something that takes O(1) time

      end for

      j = j * 2

   end while

end for

D) (see exercises on page 105 for a useful identity to help solve this)

for i = 1 to n do

   for j = 1 to n do

      k = 1

      while k <= j do 

         something that takes O(1) time

         k = k * 2

      end while

   end for 

end for