Consider the following functions:
f(n) = 2n g(n) = n! h(n) = nlog(n)
Which of the following statements about the asymptotic behavior of f(n), g(n), and h(n) is true?
(A) f(n) = O(g(n)); g(n) = O(h(n))
(B) f(n) = 
(g(n)); g(n) = O(h(n))
(C) g(n) = O(f(n)); h(n) = O(f(n))
(D) h(n) = O(f(n)); g(n) = (f(n))
(A)
A
(B)
B
(C)
C
(D)
D
Answer: (D)
Explanation:
According to the order of growth: h(n) < f(n) < g(n) (g(n) is asymptotically greater than f(n) and f(n) is asymptotically greater than h(n) ) We can easily see above order by taking logs of the given 3 functions
log(n*log(n)) < n < log(n!) (logs of the given f(n), g(n) and h(n)).
Note that log(n!) = (nlogn)
Quiz of this Question
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