I have seen two definitions of balanced binary trees, which look different to me.
A binary tree is balanced if for each node it holds that the number of inner nodes in the left subtree and the number of inner nodes in the right subtree differ by at most 1.
A binary tree is balanced if for any two leaves the difference of the depth is at most 1.
Does every tree that satisfies def. 1 also satisfy def. 2? What about the other way round?