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I knew the general LCA problem but had not worked through the version with parent pointers.
Since each node has a parent pointer, you can find the LCA by first computing the depths of both nodes, then moving the deeper node up to the same depth, and finally moving both nodes up in tandem until they meet. This approach runs in O(h) time and O(1) space, where h is the height of the tree.
Pro tip: Mention that this parent-pointer approach is more efficient than the standard recursive method for this specific tree structure, and discuss edge cases like when one node is an ancestor of the other or when nodes are in different trees.
Confirm that the tree is binary, nodes have parent pointers, and both nodes are in the same tree. Ask about handling cases where one node is the ancestor of the other or if nodes could be null.
Traverse from each node up to the root using parent pointers to determine the depth (distance from root) of each node. This can be done by counting steps until the root is reached.
If the depths differ, move the deeper node up by the difference in depths so that both nodes are at the same level.
Move both nodes up simultaneously (using parent pointers) until they point to the same node. That node is the lowest common ancestor.
State that the time complexity is O(h) and space is O(1). Briefly mention alternative approaches like using a hash set to store ancestors of one node, which takes O(h) space.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.