Maybe the title is bad format but, I want to ask if is possible proof the Segment Tree complexity with the recursion tree.
In other words I'm making a simple report on segment tree and I want to try to prove with a simple image that the complexity time on each query is O(log N), so to do that I make a simple assertion that if the merge sort complexity is O(N log N) so sort the array, I can say that to traverse only one part of the tree I need only O(log N) time.
And the image that I choose to prove that is the recursion, like the tree below.
I will post also what I'm trying to explain inside the report and maybe there is some different idea to prove that.
p.s: Sorry for the error inside the report image but it is without spell check and I'm a person with a dyslexia problem