binary tree

(data structure)

Definition: A tree with at most two children for each node.

Formal Definition: A binary tree either

is empty (no nodes), or
has a root node, a left binary tree, and a right binary tree.

Also known as dyadic tree.

Generalization (I am a kind of ...)
tree, k-ary tree with k=2.

Specialization (... is a kind of me.)
complete binary tree, full binary tree, binary search tree, binary heap, balanced binary tree, threaded tree, Merkle tree, Fibonacci tree, extended binary tree.

Note: Formal definition after [CLR90, page 94].

Author: PEB

Implementation

examples, analysis, and code (C). Bro. David Carlson's tutorial and code (C++). Worst-case behavior of traversal, annotated for real time (WOOP/ADA).

More information

Historical Note
An early use of the term "dyadic tree" is in 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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Entry modified 15 December 2017.
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Cite this as:
Paul E. Black, "binary tree", in Dictionary of Algorithms and Data Structures [online], Paul E. Black, ed. 15 December 2017. (accessed TODAY) Available from: https://www.nist.gov/dads/HTML/binarytree.html