Clarify the problem constraints (e.g., whether nodes are guaranteed to exist, if parent pointers are available) and then present a recursive DFS solution that returns the LCA by checking if p and q are found in the left and right subtrees. Explain that if both are found in different subtrees (or one is the current node), the current node is the LCA. Also discuss iterative approaches and complexity trade-offs.
Pro tip: Mention that the recursive solution uses O(h) space due to the call stack, and if the tree is skewed, this could be O(n); an iterative approach with parent pointers can achieve O(1) space if parent pointers are available. This shows awareness of practical constraints.
Ask if p and q are guaranteed to be in the tree, if the tree is binary (not BST), and if parent pointers are available. Confirm the definition of LCA.
Explain that you'll traverse the tree, and at each node, check if the node is p or q. Recursively search left and right subtrees.
Base case: if node is null or equals p or q, return node. Recursive: if both left and right return non-null, current node is LCA; otherwise return the non-null child.
Time complexity O(n) since each node is visited once. Space complexity O(h) for recursion stack, where h is tree height; worst-case O(n).
Mention iterative approaches using parent pointers or path finding, and handle cases where one node is ancestor of the other.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.