# Question: a Rank the following functions by order of growth that

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)).

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)).

**View Solution:**## Answer to relevant Questions

Give asymptotic upper and lower bounds for T(n) in each of the following recurrences. Assume that T(n) is constant for n ≤ 2. Make your bounds as tight as possible, and justify your answers. The QUICKSORT algorithm of Section 7.1 contains two recursive calls to itself. After the call to PARTITION, the left subarray is recursively sorted and then the right subarray is recursively sorted. The second recursive call ...A hash table of size m is used to store n items, with n ≤ m/2. Open addressing is used for collision resolution. a. Assuming uniform hashing, show that for i = 1, 2, ..., n, the probability that the ith insertion ...Consider the problem of making change for n cents using the fewest number of coins. Assume that each coin's value is an integer.a. Describe a greedy algorithm to make change consisting of quarters, dimes, nickels, and ...Suppose that we have a set of activities to schedule among a large number of lecture halls. We wish to schedule all the activities using as few lecture halls as possible. Give an efficient greedy algorithm to determine which ...Post your question