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) = n^3/2; f₃(n) = nlog₂ n; f₄(n) = n^log₂n

(A) f₃, f₂, f₄,f₁ 

(B) f₃, f₂, f₁,f₄ 

(C) f₂, f₃, f₁,f₄

(D) f₂, f_3, f₄,f₁

Answer 1

Correct option is (A) f₃, f₂, f₄,f₁ 

Let n = 1024

f₁(n) = 2¹⁰²⁴

f₂(n) = 2¹⁵

f₃(n) = 10 x 2¹⁰

f₄(n) = 1024¹⁰ = 2¹⁰⁰

^∴ f_3, f_2, f_4, f₁ is the required increasing order.