Knew this one but still second-guessed myself mid-solution.
Start by clarifying the problem: confirm whether the tree is a binary search tree or a general binary tree, and whether nodes have parent pointers. For a general binary tree, use a recursive post-order traversal that returns the node if it matches either target, otherwise combines results from left and right subtrees to identify the LCA. Discuss time and space complexity, and consider iterative or parent-pointer approaches if applicable.
Pro tip: Demonstrate awareness of edge cases such as when one node is an ancestor of the other, or when a node is not present in the tree, and mention how your solution handles them. Also, briefly discuss how the approach would change if the tree were a BST (using value comparisons) or if parent pointers were available (using a two-pointer technique).
Ask whether the tree is a BST or a general binary tree, whether nodes have parent pointers, and whether both nodes are guaranteed to exist. This determines the optimal approach.
For a general binary tree without parent pointers, use a recursive post-order traversal. For a BST, use value comparisons to navigate. If parent pointers exist, use a two-pointer technique similar to finding the intersection of two linked lists.
For the recursive approach: 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 time complexity is O(n) in the worst case, as each node is visited once. Space complexity is O(h) for the recursion stack, where h is the tree height.
Discuss cases where one node is an ancestor of the other, or when a node is missing. Walk through a simple example to verify correctness.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.