COMP 731 - Assignment 2 - Due Thursday, 13 July 2000
- Prove that if f is Theta(n) and
g is O(n) then f+g is Theta(n).
- Find a sequence of 10 integers such that Mergesort takes the maximal
number of possible comparissons to sort your sequence of numbers.
Now do it for 15 numbers.
- We have described two different procedures to build a heap:
repeated insertion, starting from the empty heap; and fixing up each
subtree, processing elements n, n-1, ..., 2, 1.
Do these two methods always result in same heap?
Prove that the do, or provide a counterexample to show that the do not.
- Solve the following recurrence relations to within Theta() accuracy.
Assume T(n) = Theta(1) for sufficiently small n.
- T(n) = 5T(n/5) + n - lg n
- T(n) = 2 T(n/2) + n lg n
- T(n) = n T(n-1)
- T(n) = n + T(n-1)
- T(n) = n^2 + T(n-1)