Description
1) Determine T(n) in terms of a Big-O notation for the following cases. Use expansion method:
a. π(π) = π(π β 2) + ππ + π
π(1) = π
where b, c, and d are constants.
b. π(π) = 2π(π β 1) + 1
π(0) = 0
20 points
2) Let π(π) and π(π) be asymptotically nonnegative functions. Using the basic definition of Ξnotation, prove that max(π(π), π(π)) = Ξ(π(π) + π(π)). [CLRS 3.1-1]
20 points
3) Prove that π(π(π)) β© π(π(π)) is the empty set. [CLRS 3.1-7]
10 points