Algorithms Big O notation

Asked Jan 24 '16 at 14:44

Active Jan 24 '16 at 14:44

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I'm currently reading about algorithms and big O notation.

I have come across som examples which for instance says the following:

n is O(n^2)

3n^2 + 7n is O(2n^2 + n)

5n^7 is O(2^n)

3^n is not O(n^4)

(1/n)^2 is not O((1/n)^3)

n^2 is not Ω(n^3)

Can somebody explain to me what is meant with these sentences?

I know what it means when an algorithm has running time O(1), O(N), O(N^2) etc.

But why is n equal to O(n^2) and why is 3^n not equal O(n^4) etc.?

Is there a way to calculate whether a formula containing n (the left side) is equal to another formula containing big O notation (the right side)?

asked Jan 24 '16 at 14:44

James L

1

Keep in mind that using "is" (and "not is") or using the equals sign in these cases is abuse of notation. What is really meant is set membership - $O$ and $\Omega$ define sets of functions bounded from above (resp. from below) by a given function. You should review the definitions of these notations, our reference question might be useful. – Tom van der Zanden Jan 24 '16 at 14:58
2

Hi. Check our reference questions, you'll find all your answers there. – Ran G. Jan 24 '16 at 14:58

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