An AVL tree [1] is the original type of balanced binary search tree. An insertion in an n-node
AVL tree takes at most two rotations, but a deletion in an n-node AVL tree can take Θ (log⁡
n). A natural question is whether deletions can take many rotations not only in the worst case
but in the amortized case as well. A sequence of n successive deletions in an n-node tree
takes O (n) rotations [3], but what happens when insertions are intermixed with
deletions?Haeupler, Sen, and Tarjan [2] conjectured that alternating insertions and …