Classic problem but I still fumbled the edge case where one of the nodes IS the ancestor.
Start by clarifying the problem constraints (e.g., whether parent pointers exist, if nodes are guaranteed present) and then present a recursive solution that traverses the tree, returning the node if it matches p or q, and otherwise combining results from left and right subtrees. Explain that the first node where both subtrees return non-null is the LCA, and analyze time and space complexity.
Pro tip: Mention that this approach assumes both nodes exist; if not, you can add a post-check to verify their presence. Also, relate the problem to real-world ML scenarios like finding common ancestors in decision trees or hierarchical taxonomies.
Ask if the tree is binary, if nodes have parent pointers, if p and q are guaranteed to be in the tree, and if the tree can be empty. This shows thoroughness and avoids incorrect assumptions.
Explain that you'll traverse the tree recursively: if the current node is null or matches p or q, return it; otherwise, recurse left and right. If both return non-null, the current node is the LCA; if only one returns non-null, propagate that up.
Trace the algorithm on a small tree (e.g., root with left and right children) to demonstrate correctness, highlighting how the LCA is identified when both subtrees return non-null.
State that time complexity is O(n) in the worst case (visiting each node once) and space complexity is O(h) for recursion stack, where h is tree height (O(n) worst case for skewed tree).
Cover edge cases: one node is ancestor of the other, p or q is root, tree is skewed. Mention alternative approaches (e.g., using parent pointers to find intersection) and trade-offs.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.