Big O, Theta, and Omega Notation: Comparing Function Growth Rates

Comparing Function Growth Rates: Big O, Theta, and Omega Notation

This exercise focuses on analyzing the growth rates of functions using Big O, Theta, and Omega notation. For each pair of expressions (A, B) below, determine whether A is O, Θ, or Ω of B. Note that zero, one, or more of these relations may hold for a given pair. List all applicable relations.

Instructions:

• No explanation is needed. * If A = O(B) then write A = O(B) which already implies that A = O(B) and A = Θ(B).* If A = Θ(B) and you write A = O(B) or A = Θ(B) only, you will only receive partial credit.* Write out the full relation: A = O(B), A = Θ(B), or A = Ω(B), and not just O(B), Θ(B), or Ω(B).

Function Pairs:

(a) A = n^3 - 100n, B = n^2 + 50n (b) A = log2(n^2), B = log2.7(n^4) (c) A = 1010000, B = n (d) A = 2nlogn, B = n^10 + 8n^2 (e) A = 2^n, B = 2^(n+logn) (f) A = 3^(3n), B = 3^(2n) (g) A = (√2)^logn, B = √logn

Solutions and Analysis:

(a) A = O(B), A = Θ(B) (b) A = O(B), A = Θ(B) (c) A = O(B), A = Θ(B) (d) A = O(B), A = Θ(B) (e) A = O(B), A = Θ(B) (f) A = O(B), A = Θ(B) (g) A = O(B), A = Θ(B)