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I knew the standard recursive approach going in, propagate a found-flag or the node itself back up the tree.
Clarify the problem constraints and edge cases first, then propose a recursive solution that traverses the tree once, returning the LCA when found. Discuss time and space complexity, and mention how you would handle the specified edge cases explicitly.
Pro tip: Mention that you would verify the existence of both nodes before or during the traversal to avoid incorrect results when a target is missing, and consider iterative approaches for very deep trees to avoid stack overflow.
Ask about tree properties (binary tree vs BST), whether parent pointers exist, and confirm handling of null nodes, missing targets, single-node tree, and identical targets.
Explain a post-order traversal: if current node is null or matches either target, return current node; otherwise recurse left and right, and if both return non-null, current node is the LCA.
Detail how the algorithm handles null root, missing targets (by tracking found flags or returning null), single-node tree (root is LCA if both targets match), and identical targets (return the node itself).
State time complexity O(n) and space complexity O(h) for recursion, and discuss iterative alternatives (e.g., using parent pointers or path lists) and their trade-offs.
Walk through a few test cases: both nodes in different subtrees, one node ancestor of the other, missing node, and same node, to validate correctness.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.