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<span id="openzim-page-title" class="mw-page-title-main"><span class="mw-page-title-main">Data structure</span></span>

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</style><div role="note" class="hatnote navigation-not-searchable"><span>Not to be confused with <a href="Data_type" title="Data type">Data type</a> or <a href="Data_model" title="Data model">Data model</a>.</span></div>

<p>In <a href="Computer_science" title="Computer science">computer science</a>, a <b>data structure</b> is a <a href="Data" title="Data">data</a> organization and storage format that is usually chosen for <a href="Efficiency" title="Efficiency">efficient</a> <a href="Data_access" title="Data access">access</a> to data.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> More precisely, a data structure is a collection of data values, the relationships among them, and the <a href="Function_(computer_programming)" title="Function (computer programming)">functions</a> or <a href="Operator_(computer_programming)" title="Operator (computer programming)">operations</a> that can be applied to the data,<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> i.e., it is an <a href="Algebraic_structure" title="Algebraic structure">algebraic structure</a> about <a href="Data" title="Data">data</a>.

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<div class="mw-heading mw-heading2"><h2 id="Usage">Usage</h2></div>

<p>Data structures serve as the basis for <a href="Abstract_data_type" title="Abstract data type">abstract data types</a> (ADT). The ADT defines the logical form of the data type. The data structure implements the physical form of the <a href="Data_type" title="Data type">data type</a>.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup>

</p><p>Different types of data structures are suited to different kinds of applications, and some are highly specialized to specific tasks. For example, <a href="Relational_database" title="Relational database">relational databases</a> commonly use <a href="B-tree" title="B-tree">B-tree</a> indexes for data retrieval,<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> while <a href="Compiler" title="Compiler">compiler</a> <a href="Implementation" title="Implementation">implementations</a> usually use <a href="Hash_table" title="Hash table">hash tables</a> to look up <a href="Identifier_(computer_languages)" title="Identifier (computer languages)">identifiers</a>.<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup>

</p><p>Data structures provide a means to manage large amounts of data efficiently for uses such as large <a href="Database" title="Database">databases</a> and internet indexing services. Usually, efficient data structures are key to designing efficient <a href="Algorithm" title="Algorithm">algorithms</a>. Some formal design methods and <a href="Programming_language" title="Programming language">programming languages</a> 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 <a href="Main_memory" class="mw-redirect" title="Main memory">main memory</a> and <a href="Computer_data_storage" title="Computer data storage">secondary memory</a>.<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup>

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<div class="mw-heading mw-heading2"><h2 id="Implementation">Implementation</h2></div>

<p>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.<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> Data structures are generally based on the ability of a <a href="Computer" title="Computer">computer</a> to fetch and store data at any place in its memory, specified by a <a href="Pointer_(computer_programming)" title="Pointer (computer programming)">pointer</a>—a <a href="Bit" title="Bit">bit</a> <a href="String_(computer_science)" title="String (computer science)">string</a>, representing a <a href="Memory_address" title="Memory address">memory address</a>, that can be itself stored in memory and manipulated by the program. Thus, the <a href="Array_data_structure" class="mw-redirect" title="Array data structure">array</a> and <a href="Record_(computer_science)" title="Record (computer science)">record</a> data structures are based on computing the addresses of data items with <a href="Arithmetic_operations" class="mw-redirect" title="Arithmetic operations">arithmetic operations</a>, while the <a href="Linked_data_structure" title="Linked data structure">linked data structures</a> 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.<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup>

</p><p>The implementation of a data structure usually requires writing a set of <a href="Subroutine" class="mw-redirect" title="Subroutine">procedures</a> 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 <a href="Abstract_data_type" title="Abstract data type">abstract data type</a>, 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).<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup>

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<div class="mw-heading mw-heading2"><h2 id="Examples">Examples</h2></div>

<div role="note" class="hatnote navigation-not-searchable">Main article: <a href="List_of_data_structures" title="List of data structures">List of data structures</a></div>

<p>There are numerous types of data structures, generally built upon simpler <a href="Primitive_data_type" title="Primitive data type">primitive data types</a>. Well known examples are:<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup>

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<ul><li>An <a href="Array_(data_structure)" title="Array (data structure)">array</a> 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.</li>

<li>A <a href="Linked_list" title="Linked list">linked list</a> (also just called <i>list</i>) 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 <a href="Random_access" title="Random access">random access</a> to a certain element, are however slower on lists than on arrays.</li>

<li>A <a href="Record_(computer_science)" title="Record (computer science)">record</a> (also called <i>tuple</i> or <i>struct</i>) is an <a href="Aggregate_data" title="Aggregate data">aggregate data</a> 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 <i>fields</i> or <i>members</i>. In the context of <a href="Object-oriented_programming" title="Object-oriented programming">object-oriented programming</a>, records are known as <a href="Plain_old_data_structure" class="mw-redirect" title="Plain old data structure">plain old data structures</a> to distinguish them from objects.<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup></li>

<li><a href="Hash_table" title="Hash table">Hash tables</a>, 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.</li>

<li><a href="Graph_(abstract_data_type)" title="Graph (abstract data type)">Graphs</a> 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.</li>

<li><a href="Stack_(abstract_data_type)" title="Stack (abstract data type)">Stacks</a> and <a href="Queue_(abstract_data_type)" title="Queue (abstract data type)">queues</a> 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.</li>

<li><a href="Tree_(data_structure)" class="mw-redirect" title="Tree (data structure)">Trees</a> 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. <a href="Binary_tree" title="Binary tree">Binary trees</a> (particularly <a href="Heap_(data_structure)" title="Heap (data structure)">heaps</a>), <a href="AVL_tree" title="AVL tree">AVL trees</a>, and <a href="B-tree" title="B-tree">B-trees</a> are some popular types of trees. They enable efficient and optimal searching, sorting, and hierarchical representation of data.</li></ul>

<p>A <a href="Trie" title="Trie">trie</a>, 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.

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<div class="mw-heading mw-heading2"><h2 id="Language_support">Language support</h2></div>

<p>Most <a href="Assembly_language" title="Assembly language">assembly languages</a> and some <a href="Low-level_programming_language" title="Low-level programming language">low-level languages</a>, such as <a href="BCPL" title="BCPL">BCPL</a> (Basic Combined Programming Language), lack built-in support for data structures. On the other hand, many <a href="High-level_programming_language" title="High-level programming language">high-level programming languages</a> and some higher-level assembly languages, such as <a href="MASM" class="mw-redirect" title="MASM">MASM</a>, have special syntax or other built-in support for certain data structures, such as records and arrays. For example, the <a href="C_(programming_language)" title="C (programming language)">C</a> (a direct descendant of BCPL) and <a href="Pascal_(programming_language)" title="Pascal (programming language)">Pascal</a> languages support <a href="Record_(computer_science)" title="Record (computer science)">structs</a> and records, respectively, in addition to vectors (one-dimensional <a href="Array_data_type" class="mw-redirect" title="Array data type">arrays</a>) and multi-dimensional arrays.<sup id="cite_ref-gnu-c_14-0" class="reference"><a href="#cite_note-gnu-c-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup>

</p><p>Most programming languages feature some sort of <a href="Library_(computing)" title="Library (computing)">library</a> 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 <a href="C%2B%2B" title="C++">C++</a> <a href="Standard_Template_Library" title="Standard Template Library">Standard Template Library</a>, the <a href="Java_Collections_Framework" class="mw-redirect" title="Java Collections Framework">Java Collections Framework</a>, and the <a href="Microsoft" title="Microsoft">Microsoft</a> <a href=".NET_Framework" title=".NET Framework">.NET Framework</a>.

</p><p>Modern languages also generally support <a href="Modular_programming" title="Modular programming">modular programming</a>, the separation between the <a href="Interface_(computing)" title="Interface (computing)">interface</a> of a library module and its implementation. Some provide <a href="Opaque_data_type" title="Opaque data type">opaque data types</a> that allow clients to hide implementation details. <a href="Object-oriented_programming_language" class="mw-redirect" title="Object-oriented programming language">Object-oriented programming languages</a>, such as <a href="C%2B%2B" title="C++">C++</a>, <a href="Java_(programming_language)" title="Java (programming language)">Java</a>, and <a href="Smalltalk" title="Smalltalk">Smalltalk</a>, typically use <a href="Classes_(computer_science)" class="mw-redirect" title="Classes (computer science)">classes</a> for this purpose.

</p><p>Many known data structures have <a href="Concurrent_data_structure" title="Concurrent data structure">concurrent</a> versions which allow multiple computing threads to access a single concrete instance of a data structure simultaneously.<sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup>

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<ul><li><a href="Abstract_data_type" title="Abstract data type">Abstract data type</a></li>

<li><a href="Concurrent_data_structure" title="Concurrent data structure">Concurrent data structure</a></li>

<li><a href="Data_model" title="Data model">Data model</a></li>

<li><a href="Dynamization" title="Dynamization">Dynamization</a></li>

<li><a href="Linked_data_structure" title="Linked data structure">Linked data structure</a></li>

<li><a href="List_of_data_structures" title="List of data structures">List of data structures</a></li>

<li><a href="Persistent_data_structure" title="Persistent data structure">Persistent data structure</a></li>

<li><a href="Plain_old_data_structure" class="mw-redirect" title="Plain old data structure">Plain old data structure</a></li>

<li><a href="Queap" title="Queap">Queap</a></li>

<li><a href="Succinct_data_structure" title="Succinct data structure">Succinct data structure</a></li>

<li><a href="Tree_(data_structure)" class="mw-redirect" title="Tree (data structure)">Tree (data structure)</a></li></ul>

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<div class="mw-heading mw-heading2"><h2 id="References">References</h2></div>

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</style><cite id="CITEREFCormenLeisersonRivestStein2009" class="citation book cs1">Cormen, Thomas H.; Leiserson, Charles E.; Rivest, Ronald L.; Stein, Clifford (2009). <a rel="nofollow" class="external text" href="https://dl.acm.org/citation.cfm?id=1614191"><i>Introduction to Algorithms, Third Edition</i></a> (3rd ed.). The MIT Press. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-0262033848</bdi>.</cite></span>

</li>

<li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><cite id="CITEREFBlack2004" class="citation book cs1">Black, Paul E. (15 December 2004). <a rel="nofollow" class="external text" href="https://xlinux.nist.gov/dads/HTML/datastructur.html">"data structure"</a>. In Pieterse, Vreda; Black, Paul E. (eds.). <i>Dictionary of Algorithms and Data Structures [online]</i>. <a href="National_Institute_of_Standards_and_Technology" title="National Institute of Standards and Technology">National Institute of Standards and Technology</a><span class="reference-accessdate">. Retrieved <span class="nowrap">2018-11-06</span></span>.</cite></span>

</li>

<li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><cite class="citation encyclopaedia cs1"><a rel="nofollow" class="external text" href="https://www.britannica.com/technology/data-structure">"Data structure"</a>. <i>Encyclopaedia Britannica</i>. 17 April 2017<span class="reference-accessdate">. Retrieved <span class="nowrap">2018-11-06</span></span>.</cite></span>

</li>

<li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><cite id="CITEREFWegnerReilly2003" class="citation book cs1">Wegner, Peter; Reilly, Edwin D. (2003-08-29). <a rel="nofollow" class="external text" href="http://dl.acm.org/citation.cfm?id=1074100.1074312"><i>Encyclopedia of Computer Science</i></a>. Chichester, UK: John Wiley and Sons. pp. <span class="nowrap">507–</span>512. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-0470864128</bdi>.</cite></span>

</li>

<li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://opendsa-server.cs.vt.edu/ODSA/Books/CS3/html/ADT.html">"Abstract Data Types"</a>. <i>Virginia Tech - CS3 Data Structures & Algorithms</i>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20230210114105/https://opendsa-server.cs.vt.edu/ODSA/Books/CS3/html/ADT.html">Archived</a> from the original on 2023-02-10<span class="reference-accessdate">. Retrieved <span class="nowrap">2023-02-15</span></span>.</cite></span>

</li>

<li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text"><cite id="CITEREFGavin_Powell2006" class="citation book cs1 cs1-prop-unfit">Gavin Powell (2006). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20070818140343/http://searchsqlserver.techtarget.com/generic/0,295582,sid87_gci1184450,00.html">"Chapter 8: Building Fast-Performing Database Models"</a>. <i>Beginning Database Design</i>. <a href="Wrox_Press" title="Wrox Press">Wrox Publishing</a>. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-0-7645-7490-0</bdi>. Archived from the original on 2007-08-18.</cite></span>

</li>

<li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20210427183057/https://www.cs.uregina.ca/Links/class-info/210/Hash/">"1.5 Applications of a Hash Table"</a>. <i>University of Regina - CS210 Lab: Hash Table</i>. Archived from <a rel="nofollow" class="external text" href="http://www.cs.uregina.ca/Links/class-info/210/Hash/">the original</a> on 2021-04-27<span class="reference-accessdate">. Retrieved <span class="nowrap">2018-06-14</span></span>.</cite></span>

</li>

<li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</a></b></span> <span class="reference-text"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20180410032656/http://homes.sice.indiana.edu/yye/lab/teaching/spring2014-C343/datatoobig.php">"When data is too big to fit into the main memory"</a>. <i>Indiana University Bloomington - Data Structures (C343/A594)</i>. 2014. Archived from <a rel="nofollow" class="external text" href="http://homes.sice.indiana.edu/yye/lab/teaching/spring2014-C343/datatoobig.php">the original</a> on 2018-04-10.</cite></span>

</li>

<li id="cite_note-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-9">^</a></b></span> <span class="reference-text"><cite id="CITEREFVaishnaviShraddhaYogeshwari2021" class="citation journal cs1">Vaishnavi, Gunjal; Shraddha, Gavane; Yogeshwari, Joshi (2021-06-21). <a rel="nofollow" class="external text" href="http://www.ijcaonline.org/archives/volume183/number11/vaishnavi-2021-ijca-921427.pdf">"Survey Paper on Fine-Grained Facial Expression Recognition using Machine Learning"</a> <span class="cs1-format">(PDF)</span>. <i>International Journal of Computer Applications</i>. <b>183</b> (11): <span class="nowrap">47–</span>49. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.5120%2Fijca2021921427">10.5120/ijca2021921427</a>.</cite></span>

</li>

<li id="cite_note-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-10">^</a></b></span> <span class="reference-text"><cite id="CITEREFNievergeltWidmayer2000" class="citation cs2">Nievergelt, Jürg; Widmayer, Peter (2000-01-01), Sack, J. -R.; Urrutia, J. (eds.), <a rel="nofollow" class="external text" href="https://www.sciencedirect.com/science/article/pii/B9780444825377500188">"Chapter 17 - Spatial Data Structures: Concepts and Design Choices"</a>, <i>Handbook of Computational Geometry</i>, Amsterdam: North-Holland, pp. <span class="nowrap">725–</span>764, <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-0-444-82537-7</bdi><span class="reference-accessdate">, retrieved <span class="nowrap">2023-11-12</span></span></cite></span>

</li>

<li id="cite_note-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-11">^</a></b></span> <span class="reference-text"><cite id="CITEREFDubey,_R._C.2014" class="citation book cs1">Dubey, R. C. (2014). <i>Advanced biotechnology : For B Sc and M Sc students of biotechnology and other biological sciences</i>. New Delhi: S Chand. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-81-219-4290-4</bdi>. <a href="OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/883695533">883695533</a>.</cite></span>

</li>

<li id="cite_note-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-12">^</a></b></span> <span class="reference-text"><cite id="CITEREFSeymour2014" class="citation book cs1">Seymour, Lipschutz (2014). <i>Data structures</i> (Revised first ed.). New Delhi, India: McGraw Hill Education. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>9781259029967</bdi>. <a href="OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/927793728">927793728</a>.</cite></span>

</li>

<li id="cite_note-13"><span class="mw-cite-backlink"><b><a href="#cite_ref-13">^</a></b></span> <span class="reference-text"><cite id="CITEREFWalter_E._Brown1999" class="citation web cs1">Walter E. Brown (September 29, 1999). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20161203130543/http://www.fnal.gov/docs/working-groups/fpcltf/Pkg/ISOcxx/doc/POD.html">"C++ Language Note: POD Types"</a>. <a href="Fermi_National_Accelerator_Laboratory" class="mw-redirect" title="Fermi National Accelerator Laboratory">Fermi National Accelerator Laboratory</a>. Archived from <a rel="nofollow" class="external text" href="http://www.fnal.gov/docs/working-groups/fpcltf/Pkg/ISOcxx/doc/POD.html">the original</a> on 2016-12-03<span class="reference-accessdate">. Retrieved <span class="nowrap">6 December</span> 2016</span>.</cite></span>

</li>

<li id="cite_note-gnu-c-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-gnu-c_14-0">^</a></b></span> <span class="reference-text"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.gnu.org/software/gnu-c-manual/gnu-c-manual.html">"The GNU C Manual"</a>. Free Software Foundation<span class="reference-accessdate">. Retrieved <span class="nowrap">2014-10-15</span></span>.</cite></span>

</li>

<li id="cite_note-15"><span class="mw-cite-backlink"><b><a href="#cite_ref-15">^</a></b></span> <span class="reference-text"><cite id="CITEREFVan_Canneyt2017" class="citation web cs1">Van Canneyt, Michaël (September 2017). <a rel="nofollow" class="external text" href="http://www.freepascal.org/docs-html/ref/ref.html">"Free Pascal: Reference Guide"</a>. Free Pascal.</cite></span>

</li>

<li id="cite_note-16"><span class="mw-cite-backlink"><b><a href="#cite_ref-16">^</a></b></span> <span class="reference-text"><cite id="CITEREFMark_Moir_and_Nir_Shavit" class="citation web cs1">Mark Moir and Nir Shavit. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20110401070433/http://www.cs.tau.ac.il/~shanir/concurrent-data-structures.pdf">"Concurrent Data Structures"</a> <span class="cs1-format">(PDF)</span>. <i>cs.tau.ac.il</i>. Archived from <a rel="nofollow" class="external text" href="https://www.cs.tau.ac.il/~shanir/concurrent-data-structures.pdf">the original</a> <span class="cs1-format">(PDF)</span> on 2011-04-01.</cite></span>

</li>

</ol></div></div>

<div class="mw-heading mw-heading2"><h2 id="Bibliography">Bibliography</h2></div>

<ul><li>Peter Brass, <i>Advanced Data Structures</i>, <a href="Cambridge_University_Press" title="Cambridge University Press">Cambridge University Press</a>, 2008, <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-0521880374</bdi></li>

<li><a href="Donald_Knuth" title="Donald Knuth">Donald Knuth</a>, <i><a href="The_Art_of_Computer_Programming" title="The Art of Computer Programming">The Art of Computer Programming</a></i>, vol. 1. <a href="Addison-Wesley" title="Addison-Wesley">Addison-Wesley</a>, 3rd edition, 1997, <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-0201896831</bdi></li>

<li>Dinesh Mehta and <a href="Sartaj_Sahni" title="Sartaj Sahni">Sartaj Sahni</a>, <i>Handbook of Data Structures and Applications</i>, <a href="Chapman_and_Hall" class="mw-redirect" title="Chapman and Hall">Chapman and Hall</a>/<a href="CRC_Press" title="CRC Press">CRC Press</a>, 2004, <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>1584884355</bdi></li>

<li><a href="Niklaus_Wirth" title="Niklaus Wirth">Niklaus Wirth</a>, <i>Algorithms and Data Structures</i>, <a href="Prentice_Hall" title="Prentice Hall">Prentice Hall</a>, 1985, <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-0130220059</bdi></li></ul>

<div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2></div>

<ul><li><a rel="nofollow" class="external text" href="https://opendatastructures.org">Open Data Structures by Pat Morin</a></li>

<li><a href="Gaston_Gonnet" title="Gaston Gonnet">G. H. Gonnet</a> and <a href="Ricardo_Baeza-Yates" title="Ricardo Baeza-Yates">R. Baeza-Yates</a>, <i><a rel="nofollow" class="external text" href="https://users.dcc.uchile.cl/~rbaeza/handbook/hbook.html">Handbook of Algorithms and Data Structures - in Pascal and C</a></i>, second edition, Addison-Wesley, 1991, <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>0-201-41607-7</bdi></li>

<li><a href="Ellis_Horowitz" title="Ellis Horowitz">Ellis Horowitz</a> and Sartaj Sahni, <i>Fundamentals of Data Structures in Pascal</i>, <a href="Computer_Science_Press" class="mw-redirect" title="Computer Science Press">Computer Science Press</a>, 1984, <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>0-914894-94-3</bdi></li></ul>

<div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2></div>

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<ul><li><a rel="nofollow" class="external text" href="https://xlinux.nist.gov/dads/">Descriptions</a> from the <a href="Dictionary_of_Algorithms_and_Data_Structures" class="mw-redirect" title="Dictionary of Algorithms and Data Structures">Dictionary of Algorithms and Data Structures</a></li>

<li><a rel="nofollow" class="external text" href="https://www.cs.auckland.ac.nz/software/AlgAnim/ds_ToC.html">Data structures course</a></li>

<li><a rel="nofollow" class="external text" href="http://msdn.microsoft.com/en-us/library/aa289148(VS.71).aspx">An Examination of Data Structures from .NET perspective</a></li>

<li><a rel="nofollow" class="external text" href="http://people.cs.vt.edu/~shaffer/Book/C++3e20110915.pdf">Schaffer, C. <i>Data Structures and Algorithm Analysis</i></a></li></ul>

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</style><div id="Data_structures216" style="font-size:114%;margin:0 4em"></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Types</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Collection_(abstract_data_type)" title="Collection (abstract data type)">Collection</a></li>

<li><a href="Container_(abstract_data_type)" title="Container (abstract data type)">Container</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Abstract_data_type" title="Abstract data type">Abstract</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Associative_array" title="Associative array">Associative array</a>

<ul><li><a href="Multimap" title="Multimap">Multimap</a></li>

<li><a href="Retrieval_Data_Structure" title="Retrieval Data Structure">Retrieval Data Structure</a></li></ul></li>

<li><a href="Stack_(abstract_data_type)" title="Stack (abstract data type)">Stack</a></li>

<li><a href="Queue_(abstract_data_type)" title="Queue (abstract data type)">Queue</a>

<ul><li><a href="Double-ended_queue" title="Double-ended queue">Double-ended queue</a></li></ul></li>

<li><a href="Priority_queue" title="Priority queue">Priority queue</a>

<ul><li><a href="Double-ended_priority_queue" title="Double-ended priority queue">Double-ended priority queue</a></li></ul></li>

<ul><li><a href="Set_(abstract_data_type)#Multiset" title="Set (abstract data type)">Multiset</a></li>

<li><a href="Disjoint-set_data_structure" title="Disjoint-set data structure">Disjoint-set</a></li></ul></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Array_(data_structure)" title="Array (data structure)">Arrays</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Bit_array" title="Bit array">Bit array</a></li>

<li><a href="Circular_buffer" title="Circular buffer">Circular buffer</a></li>

<li><a href="Dynamic_array" title="Dynamic array">Dynamic array</a></li>

<li><a href="Hash_table" title="Hash table">Hash table</a></li>

<li><a href="Hashed_array_tree" title="Hashed array tree">Hashed array tree</a></li>

<li><a href="Sparse_matrix" title="Sparse matrix">Sparse matrix</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Linked_data_structure" title="Linked data structure">Linked</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Association_list" title="Association list">Association list</a></li>

<li><a href="Linked_list" title="Linked list">Linked list</a></li>

<li><a href="Unrolled_linked_list" title="Unrolled linked list">Unrolled linked list</a></li>

<li><a href="XOR_linked_list" title="XOR linked list">XOR linked list</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Tree_(data_structure)" class="mw-redirect" title="Tree (data structure)">Trees</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<li><a href="Binary_search_tree" title="Binary search tree">Binary search tree</a>

<li><a href="Red%E2%80%93black_tree" title="Red–black tree">Red–black tree</a></li>

<li><a href="Self-balancing_binary_search_tree" title="Self-balancing binary search tree">Self-balancing tree</a></li>

<li><a href="Splay_tree" title="Splay tree">Splay tree</a></li></ul></li>

<ul><li><a href="Binary_heap" title="Binary heap">Binary heap</a></li>

<li><a href="Binomial_heap" title="Binomial heap">Binomial heap</a></li>

<li><a href="Fibonacci_heap" title="Fibonacci heap">Fibonacci heap</a></li></ul></li>

<li><a href="Hilbert_R-tree" title="Hilbert R-tree">Hilbert R-tree</a></li></ul></li>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Graph_(abstract_data_type)" title="Graph (abstract data type)">Graphs</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Binary_decision_diagram" title="Binary decision diagram">Binary decision diagram</a></li>

<li><a href="Directed_acyclic_graph" title="Directed acyclic graph">Directed acyclic graph</a></li>

<li><a href="Deterministic_acyclic_finite_state_automaton" title="Deterministic acyclic finite state automaton">Directed acyclic word graph</a></li></ul>

</div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div>

<ul><li><a href="List_of_data_structures" title="List of data structures">List of data structures</a></li></ul>

</div></td></tr></tbody></table></div>

<div class="navbox-styles"></div><div role="navigation" class="navbox" aria-labelledby="Data_types177" style="padding:3px"><table class="nowraplinks hlist mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Data_types177" style="font-size:114%;margin:0 4em"><a href="Data_type" title="Data type">Data types</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Units_of_information" title="Units of information">Uninterpreted</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<li><a href="Ternary_numeral_system#Tryte" title="Ternary numeral system">Tryte</a></li>

<li><a href="Bit_array" title="Bit array">Bit array</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Numeric</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Arbitrary-precision_arithmetic" title="Arbitrary-precision arithmetic">Arbitrary-precision or bignum</a></li>

<li><a href="Complex_data_type" title="Complex data type">Complex</a></li>

<li><a href="Decimal_data_type" title="Decimal data type">Decimal</a></li>

<li><a href="Fixed-point_arithmetic" title="Fixed-point arithmetic">Fixed point</a></li>

<li><a href="Block_floating_point" title="Block floating point">Block floating point</a></li>

<li><a href="Floating-point_arithmetic" title="Floating-point arithmetic">Floating point</a>

<ul><li>Reduced precision

<ul><li><a href="Minifloat" title="Minifloat">Minifloat</a></li>

<li><a href="Half-precision_floating-point_format" title="Half-precision floating-point format">Half precision</a></li>

<li><a href="Bfloat16_floating-point_format" title="Bfloat16 floating-point format">bfloat16</a></li></ul></li>

<li><a href="Single-precision_floating-point_format" title="Single-precision floating-point format">Single precision</a></li>

<li><a href="Double-precision_floating-point_format" title="Double-precision floating-point format">Double precision</a></li>

<li><a href="Quadruple-precision_floating-point_format" title="Quadruple-precision floating-point format">Quadruple precision</a></li>

<li><a href="Octuple-precision_floating-point_format" title="Octuple-precision floating-point format">Octuple precision</a></li>

<li><a href="Extended_precision" title="Extended precision">Extended precision</a>

<ul><li><a href="Long_double" title="Long double">Long double</a></li></ul></li></ul></li>

<li><a href="Integer_(computer_science)" title="Integer (computer science)">Integer</a>

<ul><li><a href="Signedness" title="Signedness">signedness</a></li></ul></li>

<li><a href="Interval_arithmetic#Implementations" title="Interval arithmetic">Interval</a></li>

<li><a href="Rational_data_type" title="Rational data type">Rational</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Pointer_(computer_programming)" title="Pointer (computer programming)">Pointer</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Memory_address" title="Memory address">Address</a>

<ul><li><a href="Physical_address" title="Physical address">physical</a></li>

<li><a href="Virtual_address_space" title="Virtual address space">virtual</a></li></ul></li>

<li><a href="Reference_(computer_science)" title="Reference (computer science)">Reference</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Plain_text" title="Plain text">Text</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Character_(computing)" title="Character (computing)">Character</a></li>

<li><a href="String_(computer_science)" title="String (computer science)">String</a>

<ul><li><a href="Null-terminated_string" title="Null-terminated string">null-terminated</a></li></ul></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Composite_data_type" title="Composite data type">Composite</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Algebraic_data_type" title="Algebraic data type">Algebraic data type</a>

<ul><li><a href="Generalized_algebraic_data_type" title="Generalized algebraic data type">generalized</a></li></ul></li>

<li><a href="Array_(data_type)" title="Array (data type)">Array</a></li>

<li><a href="Associative_array" title="Associative array">Associative array</a></li>

<li><a href="Class_(computer_programming)" title="Class (computer programming)">Class</a></li>

<li><a href="Dependent_type" title="Dependent type">Dependent</a></li>

<li><a href="Intuitionistic_type_theory#Equality_type" title="Intuitionistic type theory">Equality</a></li>

<li><a href="Inductive_type" title="Inductive type">Inductive</a></li>

<li><a href="Intersection_type" title="Intersection type">Intersection</a></li>

<li><a href="Object_(computer_science)" title="Object (computer science)">Object</a>

<ul><li><a href="Metaobject" title="Metaobject">metaobject</a></li></ul></li>

<li><a href="Option_type" title="Option type">Option type</a></li>

<li><a href="Product_type" title="Product type">Product</a></li>

<li><a href="Record_(computer_science)" title="Record (computer science)">Record or Struct</a></li>

<li><a href="Refinement_type" title="Refinement type">Refinement</a></li>

<li><a href="Union_type" title="Union type">Union</a>

<ul><li><a href="Tagged_union" title="Tagged union">tagged</a></li></ul></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Boolean_data_type" title="Boolean data type">Boolean</a></li>

<li><a href="Bottom_type" title="Bottom type">Bottom type</a></li>

<li><a href="Container_(abstract_data_type)" title="Container (abstract data type)">Collection</a></li>

<li><a href="Enumerated_type" title="Enumerated type">Enumerated type</a></li>

<li><a href="Exception_handling" title="Exception handling">Exception</a></li>

<li><a href="Function_type" title="Function type">Function type</a></li>

<li><a href="Opaque_data_type" title="Opaque data type">Opaque data type</a></li>

<li><a href="Recursive_data_type" title="Recursive data type">Recursive data type</a></li>

<li><a href="Semaphore_(programming)" title="Semaphore (programming)">Semaphore</a></li>

<li><a href="Stream_(computing)" title="Stream (computing)">Stream</a></li>

<li><a href="Strongly_typed_identifier" title="Strongly typed identifier">Strongly typed identifier</a></li>

<li><a href="Type_class" title="Type class">Type class</a></li>

<li><a href="Empty_type" title="Empty type">Empty type</a></li>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Related<br>topics</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Abstract_data_type" title="Abstract data type">Abstract data type</a></li>

<li><a href="Boxing_(computer_programming)" title="Boxing (computer programming)">Boxing</a></li>

<li><a href="Generic_programming" title="Generic programming">Generic</a></li>

<ul><li><a href="Metaclass" title="Metaclass">metaclass</a></li></ul></li>

<li><a href="Parametric_polymorphism" title="Parametric polymorphism">Parametric polymorphism</a></li>

<li><a href="Primitive_data_type" title="Primitive data type">Primitive data type</a></li>

<li><a href="Interface_(object-oriented_programming)" title="Interface (object-oriented programming)">Interface</a></li>

<li><a href="Subtyping" title="Subtyping">Subtyping</a></li>

<li><a href="Type_constructor" title="Type constructor">Type constructor</a></li>

<li><a href="Type_conversion" title="Type conversion">Type conversion</a></li>

<li><a href="Type_system" title="Type system">Type system</a></li>

<li><a href="Type_theory" title="Type theory">Type theory</a></li>

<li><a href="Variable_(computer_science)" title="Variable (computer science)">Variable</a></li></ul>

</div></td></tr></tbody></table></div>

<div class="navbox-styles"></div><div role="navigation" class="navbox" aria-labelledby="Data_model52" style="padding:3px"><table class="nowraplinks mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Data_model52" style="font-size:114%;margin:0 4em"><a href="Data_model" title="Data model">Data model</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Main</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Data_architecture" title="Data architecture">Architecture</a></li>

<li><a href="Data_modeling" title="Data modeling">Modeling</a></li>

</ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Schemas</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Conceptual_schema" title="Conceptual schema">Conceptual </a></li>

<li><a href="Logical_data_model" class="mw-redirect" title="Logical data model">Logical</a></li>

<li><a href="Physical_schema" title="Physical schema">Physical</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Types</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Database_model" title="Database model">Database</a></li>

<li><a href="Data_structure_diagram" title="Data structure diagram">Data structure diagram</a></li>

<li><a href="Entity%E2%80%93relationship_model" title="Entity–relationship model">Entity–relationship model</a> (<a href="Enhanced_entity%E2%80%93relationship_model" title="Enhanced entity–relationship model">enhanced</a>)</li>

<li><a href="Data_model_(GIS)" title="Data model (GIS)">Geographic</a></li>

<li><a href="Generic_data_model" title="Generic data model">Generic</a></li>

<li><a href="Semantic_data_model" title="Semantic data model">Semantic</a></li>

<li><a href="Common_data_model" title="Common data model">Common</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Related models</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Data-flow_diagram" title="Data-flow diagram">Data-flow diagram</a></li>

<li><a href="Information_model" title="Information model">Information model</a></li>

<li><a href="Object_model" title="Object model">Object model</a></li>

<li><a href="Object%E2%80%93role_modeling" title="Object–role modeling">Object–role modeling</a></li>

<li><a href="Unified_Modeling_Language" title="Unified Modeling Language">Unified Modeling Language</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">See also</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Database_design" title="Database design">Database design</a></li>

<li><a href="Business_process_modeling" title="Business process modeling">Business process modeling</a></li>

<li><a href="Core_architecture_data_model" title="Core architecture data model">Core architecture data model</a></li>

<li><a href="Enterprise_modelling" title="Enterprise modelling">Enterprise modelling</a></li>

<li><a href="Function_model" title="Function model">Function model</a></li>

<li><a href="Process_modeling" title="Process modeling">Process modeling</a></li>

<li><a href="XML_schema" title="XML schema">XML schema</a></li>

<li><a href="Data_Format_Description_Language" title="Data Format Description Language">Data Format Description Language</a></li></ul>

</div></td></tr></tbody></table></div>

<div class="navbox-styles"></div><div role="navigation" class="navbox" aria-labelledby="Strings176" style="padding:3px"><table class="nowraplinks mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Strings176" style="font-size:114%;margin:0 4em"><a href="String_(computer_science)" title="String (computer science)">Strings</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="String_metric" title="String metric">String metric</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Approximate_string_matching" title="Approximate string matching">Approximate string matching</a></li>

<li><a href="Bitap_algorithm" title="Bitap algorithm">Bitap algorithm</a></li>

<li><a href="Damerau%E2%80%93Levenshtein_distance" title="Damerau–Levenshtein distance">Damerau–Levenshtein distance</a></li>

<li><a href="Edit_distance" title="Edit distance">Edit distance</a></li>

<li><a href="Gestalt_pattern_matching" title="Gestalt pattern matching">Gestalt pattern matching</a></li>

<li><a href="Hamming_distance" title="Hamming distance">Hamming distance</a></li>

<li><a href="Jaro%E2%80%93Winkler_distance" title="Jaro–Winkler distance">Jaro–Winkler distance</a></li>

<li><a href="Lee_distance" title="Lee distance">Lee distance</a></li>

<li><a href="Levenshtein_automaton" title="Levenshtein automaton">Levenshtein automaton</a></li>

<li><a href="Levenshtein_distance" title="Levenshtein distance">Levenshtein distance</a></li>

<li><a href="Wagner%E2%80%93Fischer_algorithm" title="Wagner–Fischer algorithm">Wagner–Fischer algorithm </a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="String-searching_algorithm" title="String-searching algorithm">String-searching algorithm</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Apostolico%E2%80%93Giancarlo_algorithm" title="Apostolico–Giancarlo algorithm">Apostolico–Giancarlo algorithm</a></li>

<li><a href="Boyer%E2%80%93Moore_string-search_algorithm" title="Boyer–Moore string-search algorithm">Boyer–Moore string-search algorithm</a></li>

<li><a href="Boyer%E2%80%93Moore%E2%80%93Horspool_algorithm" title="Boyer–Moore–Horspool algorithm">Boyer–Moore–Horspool algorithm</a></li>

<li><a href="Knuth%E2%80%93Morris%E2%80%93Pratt_algorithm" title="Knuth–Morris–Pratt algorithm">Knuth–Morris–Pratt algorithm</a></li>

<li><a href="Rabin%E2%80%93Karp_algorithm" title="Rabin–Karp algorithm">Rabin–Karp algorithm</a></li>

<li><a href="Raita_algorithm" title="Raita algorithm">Raita algorithm</a></li>

<li><a href="Trigram_search" title="Trigram search">Trigram search</a></li>

<li><a href="Two-way_string-matching_algorithm" title="Two-way string-matching algorithm">Two-way string-matching algorithm</a></li>

<li><a href="Zhu%E2%80%93Takaoka_string_matching_algorithm" title="Zhu–Takaoka string matching algorithm">Zhu–Takaoka string matching algorithm</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Multiple string searching</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Aho%E2%80%93Corasick_algorithm" title="Aho–Corasick algorithm">Aho–Corasick</a></li>

<li><a href="Commentz-Walter_algorithm" title="Commentz-Walter algorithm">Commentz-Walter algorithm</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Regular_expression" title="Regular expression">Regular expression</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Comparison_of_regular-expression_engines" class="mw-redirect" title="Comparison of regular-expression engines">Comparison of regular-expression engines</a></li>

<li><a href="Regular_grammar" title="Regular grammar">Regular grammar</a></li>

<li><a href="Thompson's_construction" title="Thompson's construction">Thompson's construction</a></li>

<li><a href="Nondeterministic_finite_automaton" title="Nondeterministic finite automaton">Nondeterministic finite automaton</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Sequence_alignment" title="Sequence alignment">Sequence alignment</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="BLAST_(biotechnology)" title="BLAST (biotechnology)">BLAST</a></li>

<li><a href="Hirschberg's_algorithm" title="Hirschberg's algorithm">Hirschberg's algorithm</a></li>

<li><a href="Needleman%E2%80%93Wunsch_algorithm" title="Needleman–Wunsch algorithm">Needleman–Wunsch algorithm</a></li>

<li><a href="Smith%E2%80%93Waterman_algorithm" title="Smith–Waterman algorithm">Smith–Waterman algorithm</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Deterministic_acyclic_finite_state_automaton" title="Deterministic acyclic finite state automaton">DAFSA</a></li>

<li><a href="Substring_index" title="Substring index">Substring index</a>

<ul><li><a href="Suffix_array" title="Suffix array">Suffix array</a></li>

<li><a href="Suffix_automaton" title="Suffix automaton">Suffix automaton</a></li>

<li><a href="Suffix_tree" title="Suffix tree">Suffix tree</a></li>

<li><a href="Compressed_suffix_array" title="Compressed suffix array">Compressed suffix array</a></li>

<li><a href="LCP_array" title="LCP array">LCP array</a></li>

<li><a href="FM-index" title="FM-index">FM-index</a></li></ul></li>

<li><a href="Generalized_suffix_tree" title="Generalized suffix tree">Generalized suffix tree</a></li>

<li><a href="Ternary_search_tree" title="Ternary search tree">Ternary search tree</a></li>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Parsing" title="Parsing">Parsing</a></li>

<li><a href="Pattern_matching" title="Pattern matching">Pattern matching</a></li>

<li><a href="Compressed_pattern_matching" title="Compressed pattern matching">Compressed pattern matching</a></li>

<li><a href="Longest_common_subsequence" title="Longest common subsequence">Longest common subsequence</a></li>

<li><a href="Longest_common_substring" title="Longest common substring">Longest common substring</a></li>

<li><a href="Sequential_pattern_mining" title="Sequential pattern mining">Sequential pattern mining</a></li>

<li>Sorting</li>

<li><a href="Semi-Thue_system" title="Semi-Thue system">String rewriting systems</a></li>

<li><a href="String_operations" title="String operations">String operations</a></li></ul>

</div></td></tr></tbody></table></div>

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</style></div><div role="navigation" class="navbox authority-control" aria-labelledby="Authority_control_databases_frameless&#124;text-top&#124;10px&#124;alt=Edit_this_at_Wikidata&#124;link=https&#58;//www.wikidata.org/wiki/Q175263#identifiers&#124;class=noprint&#124;Edit_this_at_Wikidata1560" style="padding:3px"><table class="nowraplinks hlist mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Authority_control_databases_frameless&#124;text-top&#124;10px&#124;alt=Edit_this_at_Wikidata&#124;link=https&#58;//www.wikidata.org/wiki/Q175263#identifiers&#124;class=noprint&#124;Edit_this_at_Wikidata1560" style="font-size:114%;margin:0 4em">Authority control databases </div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">National</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://d-nb.info/gnd/4011146-5">Germany</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://id.loc.gov/authorities/sh85035862">United States</a></span></li><li><span class="uid"><span class="rt-commentedText tooltip tooltip-dotted" title="Structures de données (informatique)"><a rel="nofollow" class="external text" href="https://catalogue.bnf.fr/ark:/12148/cb119313298">France</a></span></span></li><li><span class="uid"><span class="rt-commentedText tooltip tooltip-dotted" title="Structures de données (informatique)"><a rel="nofollow" class="external text" href="https://data.bnf.fr/ark:/12148/cb119313298">BnF data</a></span></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://id.ndl.go.jp/auth/ndlna/01167757">Japan</a></span></li><li><span class="uid"><span class="rt-commentedText tooltip tooltip-dotted" title="datové struktury"><a rel="nofollow" class="external text" href="https://aleph.nkp.cz/F/?func=find-c&local_base=aut&ccl_term=ica=ph119336&CON_LNG=ENG">Czech Republic</a></span></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://www.nli.org.il/en/authorities/987007543369805171">Israel</a></span></li></ul></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://lux.collections.yale.edu/view/concept/d3c8ea88-4745-46a1-98e1-c792754d5ea0">Yale LUX</a></span></li></ul></div></td></tr></tbody></table></div></div><div><div class="zim-footer">

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