First, clarify the problem constraints and edge cases. Then, propose an efficient solution by precomputing parent pointers or using a recursive evaluation with memoization to update only affected nodes. Finally, discuss trade-offs and potential optimizations.
Pro tip: Mention that you can preprocess the tree to add parent pointers in O(n) time, which simplifies updates to O(depth) per flip. This shows you think about upfront costs versus per-operation efficiency.
Ask about tree size, number of flips, and whether the tree structure is static. Confirm that only leaf values change and that we need the root value after each flip.
Propose augmenting the tree with parent pointers or storing the path from each leaf to the root. Alternatively, use a recursive function that returns the new value and propagates changes upward.
For each flip, update the leaf's value, then traverse from that leaf up to the root, recomputing each ancestor's value based on its children. Stop early if a node's value doesn't change.
Preprocessing takes O(n) time and space. Each flip takes O(h) time where h is the height of the tree, which is optimal in the worst case. Discuss whether early termination can improve average performance.
Compare with recomputing the whole tree (O(n) per flip). Mention that if the tree is balanced, O(log n) per flip is efficient. Also consider handling NOT nodes with single children.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.