Algorithms | Analysis of Algorithms | Question 15

Consider the following functions
formula
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^(\sqrt{n} \log{n} ) = n^(\sqrt{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^(\sqrt{n}).

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