How do you determine the maximum depth of a binary tree?

Use DFS recursion: the maximum depth of a node is one plus the maximum of the depths of its left and right children. The base case is a null node with depth zero. This naturally computes the answer bottom-up in O of n time and O of h space on the call stack. Alternatively, use BFS and count the number of levels processed, which also gives the maximum depth in O of n time. Maximum depth is equivalent to height for the root node. This simple recursive pattern is the foundation for more complex tree problems like diameter, balanced tree check, and subtree problems.