Balanced Binary Search Trees

In Chap. 6 binary search trees were defined along with a recursive insert algorithm. The discussion of binary search trees pointed out they have problems in some cases. Binary search trees can become unbalanced, actually quite often. When a tree is unbalanced the complexity of insert, delete, and lookup operations can get as bad as \(\Theta (n)\). This problem with unbalanced binary search trees was the motivation for the development of height-balanced AVL trees by G.M. Adelson-Velskii and E.M. Landis, two Soviet computer scientists, in 1962. AVL trees were named for these two inventors. Their paper on AVL trees [AVL62] described the first algorithm for maintaining balanced binary search trees. The chapter goes on to discuss Splay Trees as another example of balanced binary search trees.