Clarify the two node models and the special ancestor rule, then present both top-down and bottom-up algorithms with clear pseudocode. Analyze time and space complexity for each, and discuss edge cases such as missing nodes, different trees, and root's manager. Emphasize trade-offs between the approaches and justify choices based on constraints.
Pro tip: Explicitly handle the special rule by checking if one node is an ancestor of the other and returning its parent; this shows attention to detail and avoids a common pitfall. Also, mention that in the parent-pointer model, you can use a hash set to track visited nodes for O(1) lookups, but be mindful of space.
Confirm the two node models, the special ancestor rule, and what to return for edge cases like missing nodes or root's manager. Ask if nodes have unique identifiers or if we can compare references.
Use recursion to find if a node is in the subtree of another. Traverse from root, and for each node, check if both a and b are in its subtree; the lowest such node is the LCA. Then apply the special rule: if one is ancestor of the other, return its parent.
From node a, traverse up to root, storing visited nodes in a hash set. Then from node b, traverse up until a node is found in the set; that's the LCA. Apply the special rule by checking if the LCA is a or b, and if so return its parent.
Top-down: O(N) time, O(H) space for recursion. Bottom-up: O(H) time and space for the hash set, where H is tree height. Discuss when each is preferable based on input and constraints.
Cover missing nodes (return null or error), nodes from different trees (return null), root's manager (return null), and the special rule implementation. Also consider if nodes are the same (return its manager).
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.