# red-black tree

(data structure)

**Definition:**
A nearly-balanced *tree* that uses an extra bit per *node* to maintain balance. No *leaf* is more than twice as far from the *root* as any other.

**Formal Definition:** A red-black tree with n internal nodes has *height* at most 2log_{2}(n+1).

**Also known as** symmetric binary B-tree.

**Generalization** (I am a kind of ...)

*B-tree*.

**Specialization** (... is a kind of me.)

*AVL tree*.

**Aggregate child** (... is a part of or used in me.)

*left rotation*, *right rotation*.

**See also**
*height-balanced tree*.

*Note:
The extra bit "colors" the node red or black, hence the name. These were called "symmetric binary B-trees" when first invented. The red/black naming and explanation was given by Guibas and Sedgewick. *

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

Author: PEB

## Implementation

analysis, explanation, examples, and code (C). Ben Pfaff's libavl (C) including pointers to other implementations. Glenn Scheper's RBSL (C) which sorts text lines using a red-black tree.
## More information

**Rudolf Bayer**, *Symmetric Binary B-Trees: Data Structures and Maintenance Algorithms*, Acta Informatica, 1:290-306, 1972.

**Leo J. Guibas** and **Robert Sedgewick**, *A Dichromatic Framework for Balanced Trees*, Proceedings of the 19th Annual Symposium on Foundations of Computer Science, pages 8-21. IEEE Computer Society, 1978.

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Entry modified 23 May 2011.

HTML page formatted Mon Feb 2 13:10:40 2015.

Cite this as:

Paul E. Black, "red-black tree", in
*Dictionary of Algorithms and Data Structures* [online], Vreda Pieterse and Paul E. Black, eds. 23 May 2011. (accessed TODAY)
Available from: http://www.nist.gov/dads/HTML/redblack.html