Understanding the lowest common ancestor pattern

The lowest common ancestor of two nodes in a binary tree is the deepest node (farthest from the root) that has both nodes as its descendants. Either of those two nodes can also be the lowest common ancestor for itself and the other node (a node is considered a descendant of itself for this definition). Consider the following examples of the lowest common ancestors for a pair of nodes in a binary tree.

The same idea can be extended to multiple nodes where the lowest common ancestor for all those nodes is the deepest node in the tree such that all those nodes are its descendants. Any of those nodes can itself be the lowest common ancestor of itself and the other nodes.

Let us look at the generic lowest common ancestor problem to understand it better.

The lowest common ancestor problem

Consider we are given a binary tree and a list of n nodes, and we need to find the lowest common ancestor of all these nodes.