2 . 5 Dynamic Finger Property

In the next two lectures we study the question of dynamic optimality, or whether there exists a binary search tree algorithm that performs ”as well” as all other algorithms on any input string. In this lecture we will define a binary search tree as a formal model of computation, show some analytic bounds that a dynamically optimal binary search tree needs to satisfy, and show two search trees that are conjectured to be dynamically optimal. The first is the splay tree, which we will cover only briefly. The second will require us to build up a geometric view of a sequence of binary search tree queries.