Binary search trees

This is a solution to our problem: We will consider how to store our data using a binary tree such that searching for a particular item takes a minimal effort. The underlying idea is simple: At each node, we want the value of this node to tell us whether we should search in the corresponding left or right subtree. Hence we define:

Definition.A binary search tree is a binary tree that is either empty or satisfies the following conditions:

• All values occurring in the left subtree are smaller than that of the root.
• All values occurring in the right subtree are larger than that of the root.
• The left and the right subtree are themselves binary search trees.

An example is given in Figure 2.1.