Question

f(n)=n+ logn is O(n) and Ω(n) can any one explain me please

Answer 1

Yes. Both are true and hence we can also use theta notation. This basically means f(n) has the same order of growth (asymptotically) as n. So, for very large n, value of f(n) will be growing same like n (log n will become negligible).

Comments

sir can you please explain me why it is Ώ(n)

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Ώ(n) basically means the growth rate (asymptotic) of given function is higher than that of n. Since n is a term in the given function, this is straight forward. 

n, 2n, n², nlogn all are Ώ(n).

It is like saying ≥. Ώ is for ≥, O is for ≤ and when both holds it becomes ϴ or =. All comparisons being done with asymptotic growth and not just value comparison. 

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thanku sir now I got it

Answer 2

The sum of two functions is governed by the dominant one....

O(f(n)) +O(g(n)) → O(max(f(n),g(n))) , similarly

Ω(f(n)) + Ω(g(n))  → Ω(max(f(n),g(n)))