**Math176
Rebalancing an AVL Tree After Deletion**

Below we show the basic schemes for rebalancing an AVL tree after a deletion. The basic algorithm for rebalancing after deletion works similarly to the strategy for rebalancing after insertion. However, unlike the case for insertion, it may be necessary to perform more than one update with a single or double rotation.

We show below **two** diagrams illustrating the rebalancing process. In
both cases, the node with label k_{1} is the lowest node in the AVL tree where the
AVL height properties are violated. In addition to the two cases pictured below,
there are the two dual (i.e., symmetric) cases where the deletion has occurred in the left
subtree below k_{1}.