The base recursive solution came back to me pretty quickly.
Start by clarifying the problem: confirm whether nodes are guaranteed to be in the tree, whether a node can be an ancestor of itself, and whether the tree is binary (not necessarily BST). Then present a recursive post-order traversal solution for the general binary tree, and for the follow-up, describe using parent pointers to find the LCA via a two-pointer technique or by marking ancestors.
Pro tip: Mention that the recursive solution runs in O(n) time and O(h) space, and for the parent-pointer version, you can achieve O(h) time and O(1) space by aligning depths and moving up together. Also, note that if nodes might not be present, you need to handle that case explicitly.
Ask if the nodes are guaranteed to be in the tree, if a node can be its own ancestor, and if the tree is binary (not necessarily a BST). Also consider if the tree is empty or if one node is the root.
Describe a post-order traversal: if the current node is null or matches either target, return it. Recursively search left and right subtrees. If both return non-null, the current node is the LCA; otherwise, return the non-null result.
State that the recursive solution visits each node once, so time complexity is O(n), and space complexity is O(h) due to recursion stack, where h is the tree height.
Explain that with parent pointers, you can find the LCA by first computing the depths of both nodes, then moving the deeper node up until depths match, and finally moving both up simultaneously until they meet. Alternatively, you can mark ancestors of one node and then traverse up from the other.
Highlight that the parent-pointer approach can be more efficient in terms of space (O(1) extra space if depth is computed iteratively) and may be simpler if parent pointers are already available. Mention that the recursive approach is more general and doesn't require extra pointers.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.