Classic problem but I still fumbled the edge cases a bit.
Clarify whether the question asks for the lowest common ancestor (LCA) or all common ancestors, then present an efficient recursive solution that traverses the tree once. Explain the logic: if the current node is one of the targets or null, return it; otherwise, recurse left and right, and if both return non-null, the current node is the LCA.
Pro tip: Mention that for a binary search tree, you can find the LCA in O(h) time without recursion by iterating from the root, but for a general binary tree, the recursive approach is optimal. Also, note that if parent pointers are available, you can find the LCA by finding the intersection of the two paths to the root.
Ask whether the tree is a binary search tree or a general binary tree, and whether the nodes are guaranteed to be in the tree. Confirm if 'common ancestors' means all ancestors or just the lowest common ancestor (LCA).
For a general binary tree, the optimal approach is a recursive post-order traversal that returns the LCA in O(n) time and O(h) space. Mention alternative approaches like finding paths to both nodes and then finding the last common node, or using parent pointers if available.
Describe the base case: if the current node is null or equals either target, return the current node. 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 height of the tree.
Discuss cases where one or both nodes are not present, or when one node is an ancestor of the other. Also, mention iterative solutions if recursion depth is a concern.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.