I knew this problem but still fumbled the explanation for like two minutes.
Clarify assumptions (e.g., nodes exist, tree not necessarily BST) and then present a recursive DFS solution that returns the LCA by checking if p and q are found in left and right subtrees. Explain the base cases and how the recursion combines results to identify the lowest common ancestor.
Pro tip: Mention that if the tree is a BST, you can solve it iteratively in O(h) time by comparing node values, but for a general binary tree, the recursive approach is optimal. Also, discuss handling edge cases like when one node is an ancestor of the other.
Ask if the tree is a BST or a general binary tree, and confirm that both nodes exist in the tree. This shows attention to detail and avoids incorrect assumptions.
Explain that you'll traverse the tree recursively, returning the current node if it matches p or q, and otherwise recursing into left and right subtrees.
If the current node is null or matches p or q, return it. If both left and right recursive calls 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 (visiting each node once) and space complexity is O(h) due to recursion stack, where h is the tree height.
Mention handling when p or q is the root, when one is an ancestor of the other, and briefly note that for a BST, an iterative O(h) solution exists.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.