Question

Which of the given options provides the increasing order of asymptotic complexity of functions f1, f2,f3 and f4?

f1(n) = 2ⁿ; f2(n) = n³/²; f3(n) = nlog2 n; f4(n) = nlog2n

(A) f3, f2, f4,f1
(B) f3, f2, f1,f4
(C) f2, f3, f1,f4
(D) f2, f3, f4,f1

Answer 1

The increasing order of asymptotic complexity of the given functions is f3, f2, f4, f1. f3(n) has the lowest growth rate, followed by f2(n), f4(n), and f1(n) which has the highest growth rate.

So, the correct answer is: (A) f3, f2, f4,f1

Step-by-step explanation:

The increasing order of asymptotic complexity of the given functions is f3, f2, f4, f1. Let's compare each function:

1. f3(n) = nlog2 n: This function has a complexity of nlog2 n.
2. f2(n) = n³/²: This function has a complexity of n³/².
3. f4(n) = nlog2 n: This function also has a complexity of nlog2 n.
4. f1(n) = 2ⁿ: This function has an exponential complexity of 2ⁿ.

Based on their complexities, f3(n) has the lowest growth rate, followed by f2(n), f4(n), and f1(n) which has the highest growth rate.