The recursive framing is what makes this one actually worth thinking about.
Start by clarifying the problem and edge cases, then explain the recursive post-order traversal approach where each node returns whether it has found p and/or q. Emphasize that the first node where both are found in different subtrees (or the node itself is one of them) is the LCA, and analyze time and space complexity.
Pro tip: Mention that this solution assumes p and q are guaranteed to exist in the tree; if not, you'd need to verify their presence first. Also, note that the space complexity is O(H) due to recursion stack, which is O(log N) for balanced trees and O(N) for skewed trees.
Confirm that p and q are distinct and exist in the tree, and that a node can be a descendant of itself. Discuss edge cases like when p or q is the root.
Explain that you'll perform a post-order traversal: recursively search left and right subtrees for p and q. At each node, if the node is p or q, return it; otherwise, combine results from left and right.
Base case: if node is null, return null. If node is p or q, return node. Recursive case: recurse left and right; if both return non-null, current node is LCA; else return the non-null child.
State that time complexity is O(N) since each node is visited once, and space complexity is O(H) due to recursion stack, where H is tree height.
Walk through a simple example (e.g., p and q in different subtrees, or one is ancestor of the other) to validate the logic.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.