CS442, Spring 2006, HW #3 Answers

1. a. volume_of_junk(t) = c x 10^t
   b. # photos(t) = c x 10^t
      The fact that the "exponentially" in the sentence could also
      mean "much more" is also a valid answer 
   c. returns(t) = c x 10^t
   d. not a correct use of the term "exponentially"

2. i. O(n x lgn) - each verse is approximately like the verse before,
      but there's counting in the song 
   ii. O(n^2 x lgn) - each verse increases with a constant amount of
       syllables and there is counting in the song 
   iii. O(n) - number of syllables per verse approximately the same

3. Answers depend on the example each one of you took.

4. i. Insertion Sort does 6 comparisons
   ii. Merge Sort does 5 comparisons

5. i. for [1 2 3 4 5 6 7 8], Merge Sort does 12 comparisons
   ii. for [1 5 3 7 2 6 4 8], Merge Sort does 17 comparisons