Question

The big-O notation for f(n) = 2log(n!) + (n^2 + 1)logn is?

(a) n

(b) n^2

(c) nlogn

(d) n^2logn

I have been asked this question during an online interview.

I want to ask this question from The Growth of Functions in section Basic Structures: Sets, Functions, Sequences, Sums and Matrices of Discrete Mathematics

Answer 1

Correct answer is (d) n^2logn

Easy explanation: log(n!) < n^2logn, it follows that 2log(n!) + (n^2 + 1)logn is less than or equal n^2logn.