What is the meaning of O(m+n)?

Question

This is a basic question, but I'm thinking that O(m+n) is the same as O(max(m,n)), since the larger term should dominate as we go to infinity? Also, that would be different from O(min(m,n)). Is that right?

Answer 1

Technically, you are correct, as when 1 goes to infinity it will dominate. However on a smaller scale, the difference would be noticeable. O(m+n) makes it clear that the function scales linearly with m as well as linearly with n, where n & m are 2 distinct datasets/parameters/etc.

Hope this helped!