Simplifying Big-o notation

Question

I know we can eliminate the lower function in our Big-O notation if it is in addition.

Something like O(4^n + n^2) will be simplified to O(4^n)

However, if it is something like O(4^n * n^2) or O(n * 3^n), how do they get simplified, now that the functions are in multiplication?

Please do help me understand

This can't be simplified , because they are order of `n` and multiply to each other , and also this question has nothing to do with python! — ᴀʀᴍᴀɴ, Sep 07 '18 at 07:52
https://en.wikipedia.org/wiki/Big_O_notation#Infinite_asymptotics — Patrick Artner, Sep 07 '18 at 08:00

score 1 · Answer 1 · answered Sep 07 '18 at 07:54

1

You don't simplify the products.

Simplification in the sums occurs because

f(x) + g(x) = f(x) (1 + g(x) / f(x))

and for large x, g / f becomes insignificant in front of 1.

For the products f(x).g(x), there is no similar rule.

answered Sep 07 '18 at 07:54

Thank you so much. I understand it now. – Valli Pichappan Sep 07 '18 at 08:00
Also, could you help me with this? Is O(1^n) bigger or O(n^2) huger – Valli Pichappan Sep 07 '18 at 08:09
@ValliPichappan= come on, 1^n=1. – Sep 07 '18 at 08:18
Yes i did realise that. I got slightly confused because, as per the order of big-O notations, n in the exponent is higher than n^2. – Valli Pichappan Sep 07 '18 at 08:21

1 Answers1