# Big O Estimate

• March 9th 2006, 11:52 AM
hotmail590
Big O Estimate
Can someone please check if the following big O estimate is correct? Thanks!

n^2n + n^(n^2)

Big O Estimate: O(n^n) since n^n must be faster than n^(n^2)?
• March 9th 2006, 12:08 PM
CaptainBlack
Quote:

Originally Posted by hotmail590
Can someone please check if the following big O estimate is correct? Thanks!

n^2n + n^(n^2)

Big O Estimate: O(n^n) since n^n must be faster than n^(n^2)?

This is $O(n^{n^2})$, since $n^{2n}$ is negligable
in comparison to $n^{n^2}$, for large enough $n$

RonL
• March 9th 2006, 10:23 PM
CaptainBlack
Quote:

Originally Posted by hotmail590
Can someone please check if the following big O estimate is correct? Thanks!

n^2n + n^(n^2)

Big O Estimate: O(n^n) since n^n must be faster than n^(n^2)?

To clarify, in case there has been a misunderstanding:

$
n^{2n} + n^{n^2} = O(n^{n^2})
$

and:

$
n^{2n} + n^{n^2} = n^{n^2} + O(n^{2n})
$

RonL