Big O equation verification help
- From: KevinZzz <myDublinAddress@xxxxxxxxx>
- Date: 20 Apr 2007 22:58:20 -0700
I'm reading up on Big O notation & am trying to figure out a 'Big O
equation' I came across on Wikipedia, can someone please verify my
primitive working out of the following?
[n + O(n^0.5)] * [n + O(log n)]^2 = n^3 + O(n^2.5)
...given that:
[n + O(n^0.5)] * [n + O(log n)]^2 =
n^3 + 2(n^2) * O(log n) + n * [O(log n)]^2 +
(n^2) * O(n^0.5) + (2n) * O(log n) * (O(n^0.5)) + ((O(log n))^2) *
O(n^0.5)
& 'cancelling' the two (n^3)'s produces a pile of (four)
"logs" (products of "O(log n)") &...
(n^2) * O(n^0.5)
& THAT (the "(n^2)*O(n^0.5)") is equivalent to O(n^2.5)...
Is this right...? I'm not sure if I've made some massive
oversimplification here or not...
Regards,
K
.
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