Algorithms | Analysis of Algorithms | Question 15

Consider the following functions

• f(n) = 3n^{\sqrt{n}}
• g(n) = 2^{\sqrt{n}{\log_{2}n}}
• h(n) = n!

Which of the following is true? (GATE CS 2000)
(A) h(n) is 0(f(n))
(B) h(n) is 0(g(n))
(C) g(n) is not 0(f(n))
(D) f(n) is 0(g(n))

(A)

A

(B)

B

(C)

C

(D)

D

Answer: (D)

Explanation:

g(n) = 2^= n^f(n) and g(n) are of same asymptotic order and following statements are true. f(n) = O(g(n)) g(n) = O(f(n)). (a) and (b) are false because n! is of asymptotically higher order than n^.

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