Why it matters

AVL is foundational balanced tree. Understanding shapes broader BST knowledge.

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The architecture

Balance factor: height(left) - height(right). |bf| ≤ 1 invariant.

Insert/delete may violate; rotations restore.

AVL propertiesBalance factor ≤ 1invariantRotationssingle or doubleHeightO(log n)Slightly stricter balance than red-black; more rotations but faster reads
AVL structure.
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How it works end to end

Rotations: left, right, left-right, right-left. Restore balance after insert/delete.

Height: guaranteed log_φ(n) where φ is golden ratio.

Trade-off: tighter balance means more rotations than red-black; faster search.