JAVA BIG O ANALYSIS f(n)=24n+2nlg(n)+280 is of order O(nlog(n)) a.Is it correct say that the expression...

Question

Question

JAVA BIG O ANALYSIS

f(n)=24n+2nlg(n)+280 is of order O(nlog(n))

a.Is it correct say that the expression in Q2 is O(2ⁿ)? Explain

b. Is it useful to say that the expression in Q2 is O(2ⁿ)? Explain.

engineering Computer-Science

Answer 1

Answer #1

--> f(n)=24n+2nlg(n)+280 is of order O(nlog(n))

(a)

If we say that the expression is O(2n), If the n becomes very large then O(2n) will become very less compared

to O(nlog(n)).

ex: n = 2³²

--> 2n = 2 * 2³² = 2³³

--> nlog(n) = 2³² * log(2³²) = 32 * 2³² = 2⁵ * 2³² = 2³⁷

So, clearly we see that O(nlog(n)) overtakes O(2n) for higher values of n. So, It is not correct.

(b)

It is also not useful to say expression is O(2ⁿ) because we will be giving wrong estimation for the time it

will take to run which will be a problem since the difference is very high.

Answer 2

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