AVL tree

(data structure)

Definition: A balanced binary search tree where the height of the two subtrees (children) of a node differs by at most one. Look-up, insertion, and deletion are O(log n), where n is the number of nodes in the tree.

Generalization (I am a kind of ...)
height-balanced tree, balanced binary tree, binary search tree, red-black tree (when colored).

Aggregate child (... is a part of or used in me.)
left rotation, right rotation.

See also B-tree, threaded tree, Fibonacci tree.

Note: The structure is named for the inventors, Adelson-Velskii and Landis. If necessary, the tree is rebalanced after insertions or deletions using rotations.

After Gary Grubb <>.

An AVL tree is at least as balanced as a red-black tree.

Author: PEB


Ben Pfaff's explanations and code (C). Maksim Goleta's C# Collections uses it to implement sorted set (C#). Bro. David Carlson's tutorial and code (C++). Richard McGraw's Navl-latest.tar.bz2 (C#). Worst-case behavior of traversal, annotated for real time (WOOP/ADA).

More information

explanation and example.

Georgii M. Adelson-Velskii and Evgenii M. Landis, An algorithm for the organization of information, Doklady Akademii Nauk SSSR, 146:263-266, 1962 (Russian). English translation by Myron J. Ricci in Soviet Math. Doklady, 3:1259-1263, 1962.
(Doklady is Russian for "Report". Sometimes transliterated in English as Doclady or Dokladi.)

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If you have suggestions, corrections, or comments, please get in touch with Paul Black.

Entry modified 12 November 2019.
HTML page formatted Mon Nov 2 12:36:42 2020.

Cite this as:
Paul E. Black, "AVL tree", in Dictionary of Algorithms and Data Structures [online], Paul E. Black, ed. 12 November 2019. (accessed TODAY) Available from: