I knew the binary LCA problem cold so I figured this was the same thing.
Clarify the problem constraints (e.g., whether nodes are guaranteed to be in the tree, if parent pointers exist) and then propose a recursive post-order traversal that returns the LCA if found. If parent pointers are available, consider an alternative approach using a hash set to track ancestors of one node and then traverse from the other.
Pro tip: Always discuss trade-offs: the recursive approach uses O(H) stack space (H = height) and O(N) time, while the parent-pointer approach uses O(N) space but can be more intuitive. Mention that handling the 'no common ancestor' case requires checking if both nodes are actually in the tree.
Ask if nodes are guaranteed to be in the tree, if parent pointers are available, and if the tree is static. This determines the approach and edge cases.
If parent pointers exist, use a hash set to store ancestors of p, then traverse from q upward until a common ancestor is found. Otherwise, use a recursive post-order traversal that returns the LCA if both nodes are found in the subtree.
Consider cases where p or q is the root, where one is an ancestor of the other, or where either node is not present in the tree. Ensure the solution returns null if no common ancestor exists.
Write clean code with clear variable names. Walk through a small example to verify correctness, and discuss time and space complexity.
If the tree is very deep, consider an iterative approach to avoid stack overflow. If multiple queries are expected, discuss preprocessing (e.g., binary lifting) for faster LCA queries.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.