What if the constant were massive? Then the coefficient might not be significant in practise. O(2n) might be worse than O(n+99999999), they both reduce to O(n) though. It is a classification.
Personally I would prefer to use different semantics to express that. It seems big O notation often carries a separate meaning in parlance.
I thought big O notation was about classifying function growth irrespective of the coefficient/constant. Does it not grow at all with respect to n? great you are O(1). Does it grow linearly? cool you are O(n). Logarithmically? Quadratically? In my mind, this kind of analysis aligns with big O notation.
If constant factors are significant in practice and the size of the input is not significant, then big O notation is not the right tool for the analysis, and that's perfectly fine. For instance, we generally don't talk about big O notation when comparing the performance of SSDs and spinning HDs.
Big O notation is for describing how the performance of an algorithm changes as the size of its input changes. If the size of the input is not a significant concern, then it's totally fine to not use big O notation for analyzing the problem.
Personally I would prefer to use different semantics to express that. It seems big O notation often carries a separate meaning in parlance.
I thought big O notation was about classifying function growth irrespective of the coefficient/constant. Does it not grow at all with respect to n? great you are O(1). Does it grow linearly? cool you are O(n). Logarithmically? Quadratically? In my mind, this kind of analysis aligns with big O notation.