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

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