The performance of a binary search tree is proportional to its height. This is because the search and insert operations start from the root and proceed down the tree one node at a time, doing a key comparison at each step. The taller the tree, the more steps are needed to accomplish this. Thus, if we determine the maximum possible height of a binary tree in relation to its input, we can find out the worst runtime complexity.
If we insert keys in a binary tree, by always adding on the right child of the parent node, we end up with a tree similar to the one shown on the left-hand side of Figure 3.12. In this diagram, only the right child pointers on each node are being used. We end up with a tree of height n, where ...
