(definition)

**Definition:**
An *algorithm* where the relative order upon input of items with equal *keys* is always preserved in the output. Usually a *sort* algorithm.

*Note:
Many different operations, such as sort, merge, and select the minimum using a priority queue, can be stable. *

Suppose we need to order the following people by age: Max, age 45, Brodsky (19), David (21), Carla (45), and Liang (19). A stable sort would yield Brodsky (19), Liang (19), David (21), Max (45), and Carla (45). Note that Brodsky still precedes Liang, and Max still precedes Carla. A sort that is not stable may put Liang before or after Brodsky and Carla before or after Max. A *radix sort* requires each phase to be stable.

Many algorithms can be turned into a stable variant by appending the original position to the *key*. When otherwise-equal keys are compared, the positions "break the tie" and the original order is maintained.

* From Algorithms and Theory of Computation Handbook, and is Copyright © 1999 by CRC Press LLC. Appearing in the Dictionary of Computer Science, Engineering and Technology, Copyright © 2000 CRC Press LLC.*

Author: CRC-A

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

Entry modified 17 December 2004.

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Cite this as:

Algorithms and Theory of Computation Handbook, CRC Press LLC, 1999, "stable", in
*Dictionary of Algorithms and Data Structures* [online], Vreda Pieterse and Paul E. Black, eds. 17 December 2004. (accessed TODAY)
Available from: http://www.nist.gov/dads/HTML/stable.html