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 <ggrubb@sr.hp.com>.

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

Author: PEB

Implementation

Ben Pfaff's explanations and code (C). Maksim Goleta's Collections (C#) implementing singly- and doubly-linked lists, binary search trees, and AVL trees. 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). Herbert Glarner's implementation in (Linoleum).

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.)

Go to the Dictionary of Algorithms and Data Structures home page.

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

Entry modified 18 August 2008.
HTML page formatted Mon Aug 25 09:01:40 2008.

Cite this as:
Paul E. Black, "AVL tree", in Dictionary of Algorithms and Data Structures [online], Paul E. Black, ed., U.S. National Institute of Standards and Technology. 18 August 2008. (accessed TODAY) Available from: http://www.nist.gov/dads/HTML/avltree.html