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^.
Quiz of this Question
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