Understanding the lowest common ancestor

The lowest common ancestor of two nodes in a binary tree is the lowest node from the root, with both nodes as its descendants. Either of those nodes can also be the lowest common ancestor for itself and the other node. Consider the following examples of the lowest common ancestors for a pair of nodes in a binary tree.

The generic algorithm to find the lowest common ancestor of two nodes in a binary tree uses a slightly modified version of the postorder traversal. However we can use a drastically faster algorithm to find the lowest common ancestor for a binary search tree.