问题
What is the maximum difference between any two leaves in an AVL tree? If I take an example, my tree becomes unbalanced, if the height difference is more than 2(for any two leaves), but the answer is the difference can be any value. I really don't understand, how this is possible.Can anyone explain with examples?
回答1:
The difference in levels of any two leaves can be any value! Definition of AVL describes height difference only on two sub-trees from one node. So you need to fill subtrees with equal height then add new nodes just to create that single node difference. But nobody said that that subtree doesn't contain some subtrees with the exact same definition. Of course tree is selfbalanced but if we'll be that accurate to not touch it's balance then we can create any height difference between some leaves.
Example with leaf 24 on level 3 and leaf 10 on level 6:
回答2:
According to the explanation in this Wikipedia article, the balancing operations in an AVL tree successfully aim at rearranging the tree such that the height of any two leaves differs no more than one. This is the key property of the data structure which makes the retrieval of nodes efficient (namely logarithmic in the number of nodes of the tree, as a path from the root to a leaf is traversed in the worst case).
来源：https://stackoverflow.com/questions/28964971/height-difference-between-leaves-in-an-avl-tree