CSC 415 Foundations of Computer Science I
Homework #5
Due: Feb 19 (1 week)

• Section 3.4 (p. 137)

  22, 27 

  
  

• Section 3.5 (p. 149-150)

  2, 5, 8, 12, 17, 18, 21, 23

  IMPORTANT NOTES  (for Section 3.5 questions):

  1. For all questions above, prove for big-Oh instead of theta, and supply parameters c and n0, as explained in the class.
  2. Choose the tightest upper bound for big-Oh notation.  For example, 60n² = O(n²) as well as 60n² = O(n³), 60n² = O(2ⁿ) and 60n² = O(n^!).  The tightest upper bound here is n², thus 60n² = O(n²).

  3. For questions 2, 5, 8 and 12, show the proof as shown in the lecture note.
  4. For questions 17, 18, 21, first derive a formula for f(n), the number of times the line x := x+1 is executed, then show the proof of the big-Oh notation of your choice.
  5. For question 23, you do NOT have to derive a precise formula (because it may be challenging, unless you already solved it).  Simply give the tightest big-Oh complexity.