I've begun learning about AVL trees. It seems that the assertion with this data structure is that with every insertion/deletion, the only nodes whose height changes are nodes on the path towards the root (from the inserted/deleted node). How exactly is this 'proved'? I've gone through many examples and it would appear to hold true, but I haven't seen a convincing proof/explanation from any of the texts I have read.
On an AVL tree insertion/deletion, which nodes have their height changed and why?
data structures