Balanced search trees During a standard AVL insertion, what is the maximum number of separate rebalancing steps needed? Count a single or a double rotation at one unbalanced ancestor as one step.

Question

Balanced search trees During a standard AVL insertion, what is the maximum number of separate  rebalancing steps  needed? Count a single or a double rotation at one unbalanced ancestor as one step.

Accepted Answer

One — rebalancing the lowest unbalanced ancestor restores the balance of every ancestor above it as well.

Answer

Θ(log n) — one for each level on the path from the new leaf back to the root.

Answer

Θ(n) in the worst case, when the tree has degenerated into a chain.

Answer

One for each ancestor that is out of balance, and an insertion can leave several out of balance at once.

Answer

Two — the lowest unbalanced ancestor, and then its parent.

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Balanced search trees During a standard AVL insertion, what is the maximum numbe...

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