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Start by explaining the classic recursive LCA algorithm for a binary tree, which returns the node if it matches p or q, and otherwise recurses on both subtrees. Then address the follow-up by modifying the recursion to track whether both nodes were actually found, returning a sentinel or null if q is missing.
Pro tip: Explicitly discuss the trade-off between the simpler two-pass approach (first check existence, then find LCA) and the more efficient one-pass method that returns a status flag, showing you understand both correctness and performance.
Ask whether the tree is binary (not BST), whether nodes have parent pointers, and whether p and q are guaranteed to be distinct and non-null. Confirm that the follow-up assumes q may be absent.
Describe the recursive function that returns the current node if it equals p or q, otherwise recurses left and right. If both recursive calls return non-null, the current node is the LCA; otherwise return the non-null result.
State that the algorithm visits each node once, giving O(n) time, and uses O(h) space for the recursion stack, where h is the tree height (O(n) worst case for a skewed tree).
Explain that the classic algorithm can incorrectly return p as the LCA if q is missing. To fix this, modify the recursion to return a pair (node, foundCount) or use a wrapper that tracks whether both p and q were encountered.
Show how to propagate a boolean flag or use a helper that returns null if either node is not found. Walk through edge cases: q missing, p missing, both missing, and one node being an ancestor of the other.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.