# Comparing different asymptotic notations

Suppose we have 3 algorithms complexity times at the worst case:

• A = $$O(nlogn)$$
• B = $$O(n\sqrt{n})$$
• C = $$\Theta(n)$$

In my opinion, it is not possible to define the best solution, since we don't know how Cgrows. I'd like to confirm if that's correct.

• How do you define the best? The asymptotic best is clear one. Maybe you have some constraints or size input in mind, where hidden C does matter? – Evil Apr 27 '19 at 21:25

Well, we know how the algorithm C running time grows - it's linear, and it's two-side (lower and upper) bound.
• We know only upper bounds for algorithms A and B - they might be more efficient than C actually, we just don't know that yet.
• We don't know constants, hidden in the $$\Theta$$ bounds - they might make the algorithm C less practical than A or B for limited problem size.
Using the given information we can say only that for some sufficiently large problem size the algorithm C might win over algorithms A and B.