O（nlogn）+ O（n），O（nlogn）和O（nlogn + n）之间有什么关系？

Question

Intuitively, I thought the three expressions are equivalent.

For example, if an algorithm runs in O(nlogn) + O(n) or O(nlogn + n) (I'm confused), can I say that's an O(nlogn) algorithm?

what's the truth?

Answer 1

Yes, you can say that's an O(nlogn) .

When you are trying to estimate complexity of your algorithm you start with all parts (choose the worst operation which is in each part and ignore the fast ones - hey it's just an estimate). First part is nlogn and the second part is n.

Beacause you don't want/can/need it to be accurate.

O(nlogn + n) - or - O(nlogn) + O(n) -> nlogn grows faster then O(n) and therefore you can ignore O(n) -> O(nlogn)

It's all about how fast is the function growing - think about it like it's huge n then you'll see why you can ignore the slower growing function.

For more exact explanation: http://en.wikipedia.org/wiki/Big_O_notation

Answer 2

O(nlogn)= O(nlogn) + O(n) =O(nlogn+n)

in fact if O(expression1) > O(expression2) then you have:

O(expression1)= O(expression1) + O(expression2) =O(expression1+expression2)

in this case expression1 = nlogn and expression2 = n