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The result of the first, the right, rotation is shown in the middle third of the figure. (With respect to the balance factors, this rotation is not of the same kind as the other AVL single rotations, because the height difference between Y and t 4 is only 1.) The result of the final left rotation is shown in the lower third of the figure.
Since at most 1.5 times lg n nodes are retraced on the journey back to the root, and each AVL rotation takes constant time, the insertion process in total takes O(log n) time. This is correct, but imprecise: After the insert, only one single or double rotation is required. Afterwards, the tree will be balanced, and no more rotations are necessary.
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English: A table showing the 4 cases of AVL tree rebalancing using rotations. Note added regarding double rotations on 2016-05-27 Note added regarding double rotations on 2016-05-27 Date