I'm wondering what's the answer of the following question:
What is the maximal difference between the depths of 2 leaves in an AVL tree?
Intuitively I think that it shouldn't exceed $log n$ but have no idea how to prove that. On the other hand, I saw multiple articles that claim the depth can become larger and larger without any formal proof (I always get a contradiction when trying to draw such trees)
I would really like if someone can explain me why it's correct\incorrect.