Question: We augment a red-black tree T by adding a field f to each node v storing some additional information. Which of the following augmentations could
We augment a red-black tree T by adding a field f to each node v storing some additional information. Which of the following augmentations could be maintained under insertions and deletions without affecting the O(logn) running time?
1) f stores the sum of all keys smaller than v
2) f stores the order-statistic of v
3) f stores the maximum of all keys in the subtree rooted at v
4) f stores the number of nodes that are descendants of v
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