I got the core idea pretty quickly since I'd seen LCA before, but this variant with parent pointers trips you up if you default to the recursive tree approach.
Use the parent pointers to find the depth of each node, then align the deeper node by moving up until both nodes are at the same depth. Finally, move both nodes up in tandem until they meet; that meeting point is the LCA. Analyze complexity: O(h) time and O(1) space, where h is the height of the tree.
Pro tip: Mention that you can optimize by using a two-pointer technique without explicitly computing depths: move both pointers up, and when one reaches the root, redirect it to the other node's starting position; they will meet at the LCA after at most two passes. This shows deeper insight and often impresses interviewers.
Confirm that each node has a parent pointer, the tree is not necessarily balanced, and nodes are guaranteed to be in the tree. Ask if the tree can be modified or if extra space is allowed.
Explain that you will compute the depth of each node by traversing up to the root, then align the deeper node by moving up the difference in depths, and finally move both nodes up together until they meet.
Pick a small binary tree and trace the algorithm step by step to demonstrate correctness, showing how the pointers move and where they meet.
State that the time complexity is O(h) where h is the height of the tree (worst-case O(n) for a skewed tree), and space complexity is O(1) since only a constant number of pointers are used.
Mention the two-pointer technique that avoids explicit depth calculation, and compare it to using a hash set to store ancestors (O(h) space). Highlight that the depth-based method is optimal in space.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.