Data structure

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In computer science, a data structure is a data organization and storage format that is usually chosen for efficient access to data.^[1]^[2]^[3] More precisely, a data structure is a collection of data values, the relationships among them, and the functions or operations that can be applied to the data,^[4] i.e., it is an algebraic structure about data.

Usage

Data structures serve as the basis for abstract data types (ADT). The ADT defines the logical form of the data type. The data structure implements the physical form of the data type.^[5]

Different types of data structures are suited to different kinds of applications, and some are highly specialized to specific tasks. For example, relational databases commonly use B-tree indexes for data retrieval,^[6] while compiler implementations usually use hash tables to look up identifiers.^[7]

Data structures provide a means to manage large amounts of data efficiently for uses such as large databases and internet indexing services. Usually, efficient data structures are key to designing efficient algorithms. Some formal design methods and programming languages emphasize data structures, rather than algorithms, as the key organizing factor in software design. Data structures can be used to organize the storage and retrieval of information stored in both main memory and secondary memory.^[8]

Implementation

Data structures can be implemented using a variety of programming languages and techniques, but they all share the common goal of efficiently organizing and storing data.^[9] Data structures are generally based on the ability of a computer to fetch and store data at any place in its memory, specified by a pointer—a bit string, representing a memory address, that can be itself stored in memory and manipulated by the program. Thus, the array and record data structures are based on computing the addresses of data items with arithmetic operations, while the linked data structures are based on storing addresses of data items within the structure itself. This approach to data structuring has profound implications for the efficiency and scalability of algorithms. For instance, the contiguous memory allocation in arrays facilitates rapid access and modification operations, leading to optimized performance in sequential data processing scenarios.^[10]

The implementation of a data structure usually requires writing a set of procedures that create and manipulate instances of that structure. The efficiency of a data structure cannot be analyzed separately from those operations. This observation motivates the theoretical concept of an abstract data type, a data structure that is defined indirectly by the operations that may be performed on it, and the mathematical properties of those operations (including their space and time cost).^[11]

Examples

There are numerous types of data structures, generally built upon simpler primitive data types. Well known examples are:^[12]

An array is a number of elements in a specific order, typically all of the same type (depending on the language, individual elements may either all be forced to be the same type, or may be of almost any type). Elements are accessed using an integer index to specify which element is required. Typical implementations allocate contiguous memory words for the elements of arrays (but this is not always a necessity). Arrays may be fixed-length or resizable.
A linked list (also just called list) is a linear collection of data elements of any type, called nodes, where each node has itself a value, and points to the next node in the linked list. The principal advantage of a linked list over an array is that values can always be efficiently inserted and removed without relocating the rest of the list. Certain other operations, such as random access to a certain element, are however slower on lists than on arrays.
A record (also called tuple or struct) is an aggregate data structure. A record is a value that contains other values, typically in fixed number and sequence and typically indexed by names. The elements of records are usually called fields or members. In the context of object-oriented programming, records are known as plain old data structures to distinguish them from objects.^[13]
Hash tables, also known as hash maps, are data structures that provide fast retrieval of values based on keys. They use a hashing function to map keys to indexes in an array, allowing for constant-time access in the average case. Hash tables are commonly used in dictionaries, caches, and database indexing. However, hash collisions can occur, which can impact their performance. Techniques like chaining and open addressing are employed to handle collisions.
Graphs are collections of nodes connected by edges, representing relationships between entities. Graphs can be used to model social networks, computer networks, and transportation networks, among other things. They consist of vertices (nodes) and edges (connections between nodes). Graphs can be directed or undirected, and they can have cycles or be acyclic. Graph traversal algorithms include breadth-first search and depth-first search.
Stacks and queues are abstract data types that can be implemented using arrays or linked lists. A stack has two primary operations: push (adds an element to the top of the stack) and pop (removes the topmost element from the stack), that follow the Last In, First Out (LIFO) principle. Queues have two main operations: enqueue (adds an element to the rear of the queue) and dequeue (removes an element from the front of the queue) that follow the First In, First Out (FIFO) principle.
Trees represent a hierarchical organization of elements. A tree consists of nodes connected by edges, with one node being the root and all other nodes forming subtrees. Trees are widely used in various algorithms and data storage scenarios. Binary trees (particularly heaps), AVL trees, and B-trees are some popular types of trees. They enable efficient and optimal searching, sorting, and hierarchical representation of data.

A trie, or prefix tree, is a special type of tree used to efficiently retrieve strings. In a trie, each node represents a character of a string, and the edges between nodes represent the characters that connect them. This structure is especially useful for tasks like autocomplete, spell-checking, and creating dictionaries. Tries allow for quick searches and operations based on string prefixes.

Language support

Most assembly languages and some low-level languages, such as BCPL (Basic Combined Programming Language), lack built-in support for data structures. On the other hand, many high-level programming languages and some higher-level assembly languages, such as MASM, have special syntax or other built-in support for certain data structures, such as records and arrays. For example, the C (a direct descendant of BCPL) and Pascal languages support structs and records, respectively, in addition to vectors (one-dimensional arrays) and multi-dimensional arrays.^[14]^[15]

Most programming languages feature some sort of library mechanism that allows data structure implementations to be reused by different programs. Modern languages usually come with standard libraries that implement the most common data structures. Examples are the C++ Standard Template Library, the Java Collections Framework, and the Microsoft .NET Framework.

Modern languages also generally support modular programming, the separation between the interface of a library module and its implementation. Some provide opaque data types that allow clients to hide implementation details. Object-oriented programming languages, such as C++, Java, and Smalltalk, typically use classes for this purpose.

Many known data structures have concurrent versions which allow multiple computing threads to access a single concrete instance of a data structure simultaneously.^[16]

References

^ Cormen, Thomas H.; Leiserson, Charles E.; Rivest, Ronald L.; Stein, Clifford (2009). Introduction to Algorithms, Third Edition (3rd ed.). The MIT Press. ISBN 978-0262033848.
^ Black, Paul E. (15 December 2004). "data structure". In Pieterse, Vreda; Black, Paul E. (eds.). Dictionary of Algorithms and Data Structures [online]. National Institute of Standards and Technology. Retrieved 2025-08-05.
^ "Data structure". Encyclopaedia Britannica. 17 April 2017. Retrieved 2025-08-05.
^ Wegner, Peter; Reilly, Edwin D. (2025-08-05). Encyclopedia of Computer Science. Chichester, UK: John Wiley and Sons. pp. 507–512. ISBN 978-0470864128.
^ "Abstract Data Types". Virginia Tech - CS3 Data Structures & Algorithms. Archived from the original on 2025-08-05. Retrieved 2025-08-05.
^ Gavin Powell (2006). "Chapter 8: Building Fast-Performing Database Models". Beginning Database Design. Wrox Publishing. ISBN 978-0-7645-7490-0. Archived from the original on 2025-08-05.
^ "1.5 Applications of a Hash Table". University of Regina - CS210 Lab: Hash Table. Archived from the original on 2025-08-05. Retrieved 2025-08-05.
^ "When data is too big to fit into the main memory". Indiana University Bloomington - Data Structures (C343/A594). 2014. Archived from the original on 2025-08-05.
^ Vaishnavi, Gunjal; Shraddha, Gavane; Yogeshwari, Joshi (2025-08-05). "Survey Paper on Fine-Grained Facial Expression Recognition using Machine Learning" (PDF). International Journal of Computer Applications. 183 (11): 47–49. doi:10.5120/ijca2021921427.
^ Nievergelt, Jürg; Widmayer, Peter (2025-08-05), Sack, J. -R.; Urrutia, J. (eds.), "Chapter 17 - Spatial Data Structures: Concepts and Design Choices", Handbook of Computational Geometry, Amsterdam: North-Holland, pp. 725–764, ISBN 978-0-444-82537-7, retrieved 2025-08-05
^ Dubey, R. C. (2014). Advanced biotechnology : For B Sc and M Sc students of biotechnology and other biological sciences. New Delhi: S Chand. ISBN 978-81-219-4290-4. OCLC 883695533.
^ Seymour, Lipschutz (2014). Data structures (Revised first ed.). New Delhi, India: McGraw Hill Education. ISBN 9781259029967. OCLC 927793728.
^ Walter E. Brown (September 29, 1999). "C++ Language Note: POD Types". Fermi National Accelerator Laboratory. Archived from the original on 2025-08-05. Retrieved 6 December 2016.
^ "The GNU C Manual". Free Software Foundation. Retrieved 2025-08-05.
^ Van Canneyt, Micha?l (September 2017). "Free Pascal: Reference Guide". Free Pascal.
^ Mark Moir and Nir Shavit. "Concurrent Data Structures" (PDF). cs.tau.ac.il. Archived from the original (PDF) on 2025-08-05.

Bibliography

Peter Brass, Advanced Data Structures, Cambridge University Press, 2008, ISBN 978-0521880374
Donald Knuth, The Art of Computer Programming, vol. 1. Addison-Wesley, 3rd edition, 1997, ISBN 978-0201896831
Dinesh Mehta and Sartaj Sahni, Handbook of Data Structures and Applications, Chapman and Hall/CRC Press, 2004, ISBN 1584884355
Niklaus Wirth, Algorithms and Data Structures, Prentice Hall, 1985, ISBN 978-0130220059

External links

[1] Cormen, Thomas H.; Leiserson, Charles E.; Rivest, Ronald L.; Stein, Clifford (2009). Introduction to Algorithms, Third Edition (3rd ed.). The MIT Press. ISBN 978-0262033848.

[2] Black, Paul E. (15 December 2004). "data structure". In Pieterse, Vreda; Black, Paul E. (eds.). Dictionary of Algorithms and Data Structures [online]. National Institute of Standards and Technology. Retrieved 2025-08-05.

[3] "Data structure". Encyclopaedia Britannica. 17 April 2017. Retrieved 2025-08-05.

[4] Wegner, Peter; Reilly, Edwin D. (2025-08-05). Encyclopedia of Computer Science. Chichester, UK: John Wiley and Sons. pp. 507–512. ISBN 978-0470864128.

[5] "Abstract Data Types". Virginia Tech - CS3 Data Structures & Algorithms. Archived from the original on 2025-08-05. Retrieved 2025-08-05.

[6] Gavin Powell (2006). "Chapter 8: Building Fast-Performing Database Models". Beginning Database Design. Wrox Publishing. ISBN 978-0-7645-7490-0. Archived from the original on 2025-08-05.

[7] "1.5 Applications of a Hash Table". University of Regina - CS210 Lab: Hash Table. Archived from the original on 2025-08-05. Retrieved 2025-08-05.

[8] "When data is too big to fit into the main memory". Indiana University Bloomington - Data Structures (C343/A594). 2014. Archived from the original on 2025-08-05.

[9] Vaishnavi, Gunjal; Shraddha, Gavane; Yogeshwari, Joshi (2025-08-05). "Survey Paper on Fine-Grained Facial Expression Recognition using Machine Learning" (PDF). International Journal of Computer Applications. 183 (11): 47–49. doi:10.5120/ijca2021921427.

[10] Nievergelt, Jürg; Widmayer, Peter (2025-08-05), Sack, J. -R.; Urrutia, J. (eds.), "Chapter 17 - Spatial Data Structures: Concepts and Design Choices", Handbook of Computational Geometry, Amsterdam: North-Holland, pp. 725–764, ISBN 978-0-444-82537-7, retrieved 2025-08-05

[11] Dubey, R. C. (2014). Advanced biotechnology : For B Sc and M Sc students of biotechnology and other biological sciences. New Delhi: S Chand. ISBN 978-81-219-4290-4. OCLC 883695533.

[12] Seymour, Lipschutz (2014). Data structures (Revised first ed.). New Delhi, India: McGraw Hill Education. ISBN 9781259029967. OCLC 927793728.

[13] Walter E. Brown (September 29, 1999). "C++ Language Note: POD Types". Fermi National Accelerator Laboratory. Archived from the original on 2025-08-05. Retrieved 6 December 2016.

[gnu-c-14] "The GNU C Manual". Free Software Foundation. Retrieved 2025-08-05.

[15] Van Canneyt, Micha?l (September 2017). "Free Pascal: Reference Guide". Free Pascal.

[16] Mark Moir and Nir Shavit. "Concurrent Data Structures" (PDF). cs.tau.ac.il. Archived from the original (PDF) on 2025-08-05.

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v t e Data structures
Types	Collection Container
Abstract	Associative array Multimap Retrieval Data Structure List Stack Queue Double-ended queue Priority queue Double-ended priority queue Set Multiset Disjoint-set
Arrays	Bit array Circular buffer Dynamic array Hash table Hashed array tree Sparse matrix
Linked	Association list Linked list Skip list Unrolled linked list XOR linked list
Trees	B-tree Binary search tree AA tree AVL tree Red–black tree Self-balancing tree Splay tree Heap Binary heap Binomial heap Fibonacci heap R-tree R* tree R+ tree Hilbert R-tree Trie Hash tree
Graphs	Binary decision diagram Directed acyclic graph Directed acyclic word graph
List of data structures

v t e Data types
Uninterpreted	Bit Byte Trit Tryte Word Bit array
Numeric	Arbitrary-precision or bignum Complex Decimal Fixed point Block floating point Floating point Reduced precision Minifloat Half precision bfloat16 Single precision Double precision Quadruple precision Octuple precision Extended precision Long double Integer signedness Interval Rational
Pointer	Address physical virtual Reference
Text	Character String null-terminated
Composite	Algebraic data type generalized Array Associative array Class Dependent Equality Inductive Intersection List Object metaobject Option type Product Record or Struct Refinement Set Union tagged
Other	Boolean Bottom type Collection Enumerated type Exception Function type Opaque data type Recursive data type Semaphore Stream Strongly typed identifier Top type Type class Empty type Unit type Void
Related topics	Abstract data type Boxing Data structure Generic Kind metaclass Parametric polymorphism Primitive data type Interface Subtyping Type constructor Type conversion Type system Type theory Variable

v t e Data model
Main	Architecture Modeling Structure
Schemas	Conceptual Logical Physical
Types	Database Data structure diagram Entity–relationship model (enhanced) Geographic Generic Semantic Common
Related models	Data-flow diagram Information model Object model Object–role modeling Unified Modeling Language
See also	Database design Business process modeling Core architecture data model Enterprise modelling Function model Process modeling XML schema Data Format Description Language

v t e Strings
String metric	Approximate string matching Bitap algorithm Damerau–Levenshtein distance Edit distance Gestalt pattern matching Hamming distance Jaro–Winkler distance Lee distance Levenshtein automaton Levenshtein distance Wagner–Fischer algorithm
String-searching algorithm	Apostolico–Giancarlo algorithm Boyer–Moore string-search algorithm Boyer–Moore–Horspool algorithm Knuth–Morris–Pratt algorithm Rabin–Karp algorithm Raita algorithm Trigram search Two-way string-matching algorithm Zhu–Takaoka string matching algorithm
Multiple string searching	Aho–Corasick Commentz-Walter algorithm
Regular expression	Comparison of regular-expression engines Regular grammar Thompson's construction Nondeterministic finite automaton
Sequence alignment	BLAST Hirschberg's algorithm Needleman–Wunsch algorithm Smith–Waterman algorithm
Data structure	DAFSA Substring index Suffix array Suffix automaton Suffix tree Compressed suffix array LCP array FM-index Generalized suffix tree Rope Ternary search tree Trie
Other	Parsing Pattern matching Compressed pattern matching Longest common subsequence Longest common substring Sequential pattern mining Sorting String rewriting systems String operations

Authority control databases
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Other	Yale LUX

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