Ordering by asymptotic growth ratesa. Rank the following functions by order of growth; tha...

Ordering by asymptotic growth rates

a. Rank the following functions by order of growth; that is, find an arrangement g1, g2,..., g30 of the functions satisfying g1= Ω(g2), g2 =Ω(g3),..., g29 = Ω(g30). Partition your list into equivalence classes such that f(n) and g(n) are in the same class if and only if f(n) = Θ(g(n)).

b. Give an example of a single nonnegative function f(n) such that for all functions gi(n) in part (a), f(n) is neither O(gi (n)) nor Ω(gi(n)).