In computer science theory, a deque (short for "double-ended queue"—"Deque" is usually pronounced "deck.") is an abstract list type data structure, also called a head-tail linked list, for which elements can be added to or removed from the front (head) or back (tail).

;Naming conventions"Deque" is sometimes written "dequeue", but this use is generally deprecated (not preferred) in technical literature or technical writing because "dequeue" is also a verb meaning "to remove from a queue". Nevertheless, several libraries and some writers, such as Aho, Hopcroft, and Ullman in their textbook "Data Structures and Algorithms", spell it "dequeue". DEQ and DQ are also used.

;Distinctions and sub-typesThis differs from the queue abstract data type or First-In-First-Out List (FIFO), where elements can only be added to one end and removed from the other. This general data class has some possible sub-types:

*An input-restricted deque is one where deletion can be made from both ends, but input can only be made at one end.

*An output-restricted deque is one where input can be made at both ends, but output can be made from one end only.

Both the basic and most common list types in computing, the queues and stacks can be considered specializations of deques, and can be implemented using deques.


The following operations are possible on a deque:


There are at least two common ways to efficiently implement a deque: with a modified dynamic array or with a doubly-linked list. For information about doubly-linked lists, see the linked list article.

Dynamic array implementation

Deque are often implemented using a variant of a dynamic array that can grow from both ends, sometimes called array deques. These array deques have all the properties of a dynamic array, such as constant time random access, good locality of reference, and inefficient insertion/removal in the middle, with the addition of amortized constant time insertion/removal at both ends, instead of just one end. Two common implementations include:
* Storing deque contents in a circular buffer, and only resizing when the buffer becomes completely full. This decreases the frequency of resizings, but requires an expensive branch instruction for indexing.
* Allocating deque contents from the center of the underlying array, and resizing the underlying array when either end is reached. This approach may require more frequent resizings and waste more space, particularly when elements are only inserted at one end.

Language support

C++'s Standard Template Library provides the templated classes std::deque and std::list, for the dynamic array and linked list implementations, respectively.

As of Java 6, Java's Collections Framework provides a new Javadoc:SE|java/util|Deque interface that provides the functionality of insertion and removal at both ends. It is implemented by classes such as Javadoc:SE|java/util|ArrayDeque (also new in Java 6) and Javadoc:SE|java/util|LinkedList, providing the dynamic array and linked list implementations, respectively.

Python 2.4 introduced the "collections" module with support for deque objects.


* In a doubly-linked list implementation, the time complexity of all operations is O(1), except for accessing an element in the middle using only its index, which is O(n).
* In a growing array, the amortized time complexity of all operations is O(1), except for removals and inserts into the middle of the array, which are O(n).

See also

*Data structure
**Linear data structures
***Linked list


* Donald Knuth. "The Art of Computer Programming", Volume 1: "Fundamental Algorithms", Third Edition. Addison-Wesley, 1997. ISBN 0-201-89683-4. Section 2.2.1: Stacks, Queues, and Deques, pp. 238–243.

External links

* [ SGI STL Documentation: deque]
* [ Code Project: An In-Depth Study of the STL Deque Container]
* [ Diagram of a typical STL deque implementation]

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