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href="#One-dimensional_arrays"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>One-dimensional arrays</span> </div> </a> <ul id="toc-One-dimensional_arrays-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Multidimensional_arrays" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Multidimensional_arrays"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2</span> <span>Multidimensional arrays</span> </div> </a> <ul id="toc-Multidimensional_arrays-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Dope_vectors" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Dope_vectors"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.3</span> <span>Dope vectors</span> </div> </a> <ul id="toc-Dope_vectors-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Compact_layouts" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Compact_layouts"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.4</span> <span>Compact layouts</span> </div> </a> <ul id="toc-Compact_layouts-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Resizing" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Resizing"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.5</span> <span>Resizing</span> </div> </a> <ul id="toc-Resizing-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Non-linear_formulas" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Non-linear_formulas"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.6</span> <span>Non-linear formulas</span> </div> </a> <ul id="toc-Non-linear_formulas-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Efficiency" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Efficiency"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Efficiency</span> </div> </a> <button aria-controls="toc-Efficiency-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Efficiency subsection</span> </button> <ul id="toc-Efficiency-sublist" class="vector-toc-list"> <li id="toc-Comparison_with_other_data_structures" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Comparison_with_other_data_structures"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1</span> <span>Comparison with other data structures</span> </div> </a> <ul id="toc-Comparison_with_other_data_structures-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Dimension" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Dimension"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Dimension</span> </div> </a> <ul id="toc-Dimension-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>External links</span> </div> </a> <ul id="toc-External_links-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Toggle the table of contents</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Array (data structure)</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. Available in 54 languages" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-54" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">54 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%85%D8%B5%D9%81%D9%88%D9%81%D8%A9_(%D8%AD%D9%88%D8%B3%D8%A8%D8%A9)" title="مصفوفة (حوسبة) – Arabic" lang="ar" hreflang="ar" data-title="مصفوفة (حوسبة)" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Massiv" title="Massiv – Azerbaijani" lang="az" hreflang="az" data-title="Massiv" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbaijani" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://zh-min-nan.wikipedia.org/wiki/T%C4%ABn-lia%CC%8Dt" title="Tīn-lia̍t – Minnan" lang="nan" hreflang="nan" data-title="Tīn-lia̍t" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="Minnan" class="interlanguage-link-target"><span>閩南語 / Bân-lâm-gú</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%9C%D0%B0%D1%81%D0%B8%D0%B2_(%D0%BF%D1%80%D0%BE%D0%B3%D1%80%D0%B0%D0%BC%D0%B8%D1%80%D0%B0%D0%BD%D0%B5)" title="Масив (програмиране) – Bulgarian" lang="bg" hreflang="bg" data-title="Масив (програмиране)" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Vector_(programaci%C3%B3)" title="Vector (programació) – Catalan" lang="ca" hreflang="ca" data-title="Vector (programació)" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Pole_(datov%C3%A1_struktura)" title="Pole (datová struktura) – Czech" lang="cs" hreflang="cs" data-title="Pole (datová struktura)" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Tabel_(datastruktur)" title="Tabel (datastruktur) – Danish" lang="da" hreflang="da" data-title="Tabel (datastruktur)" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Array_(Datentyp)" title="Array (Datentyp) – German" lang="de" hreflang="de" data-title="Array (Datentyp)" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Massiiv_(programmeerimine)" title="Massiiv (programmeerimine) – Estonian" lang="et" hreflang="et" data-title="Massiiv (programmeerimine)" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%A0%CE%AF%CE%BD%CE%B1%CE%BA%CE%B1%CF%82_(%CE%B4%CE%BF%CE%BC%CE%AE_%CE%B4%CE%B5%CE%B4%CE%BF%CE%BC%CE%AD%CE%BD%CF%89%CE%BD)" title="Πίνακας (δομή δεδομένων) – Greek" lang="el" hreflang="el" data-title="Πίνακας (δομή δεδομένων)" data-language-autonym="Ελληνικά" data-language-local-name="Greek" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Vector_(inform%C3%A1tica)" title="Vector (informática) – Spanish" lang="es" hreflang="es" data-title="Vector (informática)" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Tabelo_(datumstrukturo)" title="Tabelo (datumstrukturo) – Esperanto" lang="eo" hreflang="eo" data-title="Tabelo (datumstrukturo)" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%A2%D8%B1%D8%A7%DB%8C%D9%87_(%D8%B3%D8%A7%D8%AE%D8%AA%D8%A7%D8%B1_%D8%AF%D8%A7%D8%AF%D9%87)" title="آرایه (ساختار داده) – Persian" lang="fa" hreflang="fa" data-title="آرایه (ساختار داده)" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Tableau_(structure_de_donn%C3%A9es)" title="Tableau (structure de données) – French" lang="fr" hreflang="fr" data-title="Tableau (structure de données)" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EB%B0%B0%EC%97%B4" title="배열 – Korean" lang="ko" hreflang="ko" data-title="배열" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Larik" title="Larik – Indonesian" lang="id" hreflang="id" data-title="Larik" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-ia mw-list-item"><a href="https://ia.wikipedia.org/wiki/Vector_(informatica)" title="Vector (informatica) – Interlingua" lang="ia" hreflang="ia" data-title="Vector (informatica)" data-language-autonym="Interlingua" data-language-local-name="Interlingua" class="interlanguage-link-target"><span>Interlingua</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Fylki_(t%C3%B6lvunarfr%C3%A6%C3%B0i)" title="Fylki (tölvunarfræði) – Icelandic" lang="is" hreflang="is" data-title="Fylki (tölvunarfræði)" data-language-autonym="Íslenska" data-language-local-name="Icelandic" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Array" title="Array – Italian" lang="it" hreflang="it" data-title="Array" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%9E%D7%A2%D7%A8%D7%9A_(%D7%9E%D7%91%D7%A0%D7%94_%D7%A0%D7%AA%D7%95%D7%A0%D7%99%D7%9D)" title="מערך (מבנה נתונים) – Hebrew" lang="he" hreflang="he" data-title="מערך (מבנה נתונים)" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-kn mw-list-item"><a href="https://kn.wikipedia.org/wiki/%E0%B2%85%E0%B2%B0%E0%B3%8D%E0%B2%B0%E0%B3%87_(%E0%B2%A1%E0%B3%87%E0%B2%9F%E0%B2%BE_%E0%B2%B8%E0%B3%8D%E0%B2%9F%E0%B3%8D%E0%B2%B0%E0%B2%95%E0%B3%8D%E0%B2%9A%E0%B2%B0%E0%B3%8D)" title="ಅರ್ರೇ (ಡೇಟಾ ಸ್ಟ್ರಕ್ಚರ್) – Kannada" lang="kn" hreflang="kn" data-title="ಅರ್ರೇ (ಡೇಟಾ ಸ್ಟ್ರಕ್ಚರ್)" data-language-autonym="ಕನ್ನಡ" data-language-local-name="Kannada" class="interlanguage-link-target"><span>ಕನ್ನಡ</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%96%D0%B8%D1%8B%D0%BC" title="Жиым – Kazakh" lang="kk" hreflang="kk" data-title="Жиым" data-language-autonym="Қазақша" data-language-local-name="Kazakh" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Datu_mas%C4%ABvs" title="Datu masīvs – Latvian" lang="lv" hreflang="lv" data-title="Datu masīvs" data-language-autonym="Latviešu" data-language-local-name="Latvian" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Masyvas" title="Masyvas – Lithuanian" lang="lt" hreflang="lt" data-title="Masyvas" data-language-autonym="Lietuvių" data-language-local-name="Lithuanian" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-lmo mw-list-item"><a href="https://lmo.wikipedia.org/wiki/Array" title="Array – Lombard" lang="lmo" hreflang="lmo" data-title="Array" data-language-autonym="Lombard" data-language-local-name="Lombard" class="interlanguage-link-target"><span>Lombard</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/T%C3%B6mb_(adatszerkezet)" title="Tömb (adatszerkezet) – Hungarian" lang="hu" hreflang="hu" data-title="Tömb (adatszerkezet)" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%85%E0%B4%9F%E0%B5%81%E0%B4%95%E0%B5%8D%E0%B4%95%E0%B5%8D_(%E0%B4%A6%E0%B4%A4%E0%B5%8D%E0%B4%A4%E0%B4%B8%E0%B4%99%E0%B5%8D%E0%B4%95%E0%B5%87%E0%B4%A4%E0%B4%82)" title="അടുക്ക് (ദത്തസങ്കേതം) – Malayalam" lang="ml" hreflang="ml" data-title="അടുക്ക് (ദത്തസങ്കേതം)" data-language-autonym="മലയാളം" data-language-local-name="Malayalam" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-mn mw-list-item"><a href="https://mn.wikipedia.org/wiki/%D0%9C%D0%B0%D1%81%D1%81%D0%B8%D0%B2" title="Массив – Mongolian" lang="mn" hreflang="mn" data-title="Массив" data-language-autonym="Монгол" data-language-local-name="Mongolian" class="interlanguage-link-target"><span>Монгол</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Array" title="Array – Dutch" lang="nl" hreflang="nl" data-title="Array" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E9%85%8D%E5%88%97" title="配列 – Japanese" lang="ja" hreflang="ja" data-title="配列" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Tabell_(datastruktur)" title="Tabell (datastruktur) – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Tabell (datastruktur)" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-mhr mw-list-item"><a href="https://mhr.wikipedia.org/wiki/%D0%A7%D1%83%D0%BC%D1%8B%D1%80" title="Чумыр – Eastern Mari" lang="mhr" hreflang="mhr" data-title="Чумыр" data-language-autonym="Олык марий" data-language-local-name="Eastern Mari" class="interlanguage-link-target"><span>Олык марий</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%90%E0%A8%B0%E0%A9%87_(%E0%A8%A1%E0%A8%BE%E0%A8%9F%E0%A8%BE_%E0%A8%AC%E0%A8%A3%E0%A8%A4%E0%A8%B0)" title="ਐਰੇ (ਡਾਟਾ ਬਣਤਰ) – Punjabi" lang="pa" hreflang="pa" data-title="ਐਰੇ (ਡਾਟਾ ਬਣਤਰ)" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="Punjabi" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Tablica_(informatyka)" title="Tablica (informatyka) – Polish" lang="pl" hreflang="pl" data-title="Tablica (informatyka)" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Arranjo_(computa%C3%A7%C3%A3o)" title="Arranjo (computação) – Portuguese" lang="pt" hreflang="pt" data-title="Arranjo (computação)" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%9C%D0%B0%D1%81%D1%81%D0%B8%D0%B2_(%D1%82%D0%B8%D0%BF_%D0%B4%D0%B0%D0%BD%D0%BD%D1%8B%D1%85)" title="Массив (тип данных) – Russian" lang="ru" hreflang="ru" data-title="Массив (тип данных)" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Vektori_(struktura_e_t%C3%AB_dh%C3%ABnave)" title="Vektori (struktura e të dhënave) – Albanian" lang="sq" hreflang="sq" data-title="Vektori (struktura e të dhënave)" data-language-autonym="Shqip" data-language-local-name="Albanian" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Array_data_structure" title="Array data structure – Simple English" lang="en-simple" hreflang="en-simple" data-title="Array data structure" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Pole_(%C3%BAdajov%C3%A1_%C5%A1trukt%C3%BAra)" title="Pole (údajová štruktúra) – Slovak" lang="sk" hreflang="sk" data-title="Pole (údajová štruktúra)" 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class="mw-redirectedfrom">(Redirected from <a href="/w/index.php?title=Array_data_structure&redirect=no" class="mw-redirect" title="Array data structure">Array data structure</a>)</span></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Type of data structure</div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">This article is about the byte-layout-level structure. For the abstract data type, see <a href="/wiki/Array_(data_type)" title="Array (data type)">Array (data type)</a>.</div> <p class="mw-empty-elt"> </p> <style data-mw-deduplicate="TemplateStyles:r1251242444">.mw-parser-output .ambox{border:1px solid #a2a9b1;border-left:10px solid #36c;background-color:#fbfbfb;box-sizing:border-box}.mw-parser-output .ambox+link+.ambox,.mw-parser-output .ambox+link+style+.ambox,.mw-parser-output .ambox+link+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+style+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+link+.ambox{margin-top:-1px}html body.mediawiki .mw-parser-output .ambox.mbox-small-left{margin:4px 1em 4px 0;overflow:hidden;width:238px;border-collapse:collapse;font-size:88%;line-height:1.25em}.mw-parser-output .ambox-speedy{border-left:10px solid #b32424;background-color:#fee7e6}.mw-parser-output .ambox-delete{border-left:10px solid #b32424}.mw-parser-output .ambox-content{border-left:10px solid #f28500}.mw-parser-output .ambox-style{border-left:10px solid #fc3}.mw-parser-output .ambox-move{border-left:10px solid #9932cc}.mw-parser-output .ambox-protection{border-left:10px solid #a2a9b1}.mw-parser-output .ambox .mbox-text{border:none;padding:0.25em 0.5em;width:100%}.mw-parser-output .ambox .mbox-image{border:none;padding:2px 0 2px 0.5em;text-align:center}.mw-parser-output .ambox .mbox-imageright{border:none;padding:2px 0.5em 2px 0;text-align:center}.mw-parser-output .ambox .mbox-empty-cell{border:none;padding:0;width:1px}.mw-parser-output .ambox .mbox-image-div{width:52px}@media(min-width:720px){.mw-parser-output .ambox{margin:0 10%}}@media print{body.ns-0 .mw-parser-output .ambox{display:none!important}}</style><table class="box-More_citations_needed plainlinks metadata ambox ambox-content ambox-Refimprove" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><a href="/wiki/File:Question_book-new.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/50px-Question_book-new.svg.png" decoding="async" width="50" height="39" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/75px-Question_book-new.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/100px-Question_book-new.svg.png 2x" data-file-width="512" data-file-height="399" /></a></span></div></td><td class="mbox-text"><div class="mbox-text-span">This article <b>needs additional citations for <a href="/wiki/Wikipedia:Verifiability" title="Wikipedia:Verifiability">verification</a></b>.<span class="hide-when-compact"> Please help <a href="/wiki/Special:EditPage/Array_(data_structure)" title="Special:EditPage/Array (data structure)">improve this article</a> by <a href="/wiki/Help:Referencing_for_beginners" title="Help:Referencing for beginners">adding citations to reliable sources</a>. Unsourced material may be challenged and removed.<br /><small><span class="plainlinks"><i>Find sources:</i> <a rel="nofollow" class="external text" href="https://www.google.com/search?as_eq=wikipedia&q=%22Array%22+data+structure">"Array" data structure</a> – <a rel="nofollow" class="external text" href="https://www.google.com/search?tbm=nws&q=%22Array%22+data+structure+-wikipedia&tbs=ar:1">news</a> <b>·</b> <a rel="nofollow" class="external text" href="https://www.google.com/search?&q=%22Array%22+data+structure&tbs=bkt:s&tbm=bks">newspapers</a> <b>·</b> <a rel="nofollow" class="external text" href="https://www.google.com/search?tbs=bks:1&q=%22Array%22+data+structure+-wikipedia">books</a> <b>·</b> <a rel="nofollow" class="external text" href="https://scholar.google.com/scholar?q=%22Array%22+data+structure">scholar</a> <b>·</b> <a rel="nofollow" class="external text" href="https://www.jstor.org/action/doBasicSearch?Query=%22Array%22+data+structure&acc=on&wc=on">JSTOR</a></span></small></span> <span class="date-container"><i>(<span class="date">September 2008</span>)</i></span><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> <p>In <a href="/wiki/Computer_science" title="Computer science">computer science</a>, an <b>array</b> is a <a href="/wiki/Data_structure" title="Data structure">data structure</a> consisting of a collection of <i>elements</i> (<a href="/wiki/Value_(computer_science)" title="Value (computer science)">values</a> or <a href="/wiki/Variable_(programming)" class="mw-redirect" title="Variable (programming)">variables</a>), of same memory size, each identified by at least one <i>array index</i> or <i>key</i>. An array is stored such that the position of each element can be computed from its index <a href="/wiki/Tuple" title="Tuple">tuple</a> by a mathematical formula.<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-andres_2-0" class="reference"><a href="#cite_note-andres-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-garcia_3-0" class="reference"><a href="#cite_note-garcia-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> The simplest type of data structure is a linear array, also called a one-dimensional array. </p><p>For example, an array of ten <a href="/wiki/32-bit" class="mw-redirect" title="32-bit">32-bit</a> (4-byte) integer variables, with indices 0 through 9, may be stored as ten <a href="/wiki/Word_(data_type)" class="mw-redirect" title="Word (data type)">words</a> at memory addresses 2000, 2004, 2008, ..., 2036, (in <a href="/wiki/Hexadecimal" title="Hexadecimal">hexadecimal</a>: <code>0x7D0</code>, <code>0x7D4</code>, <code>0x7D8</code>, ..., <code>0x7F4</code>) so that the element with index <i>i</i> has the address 2000 + (<i>i</i> × 4).<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> The memory address of the first element of an array is called first address, foundation address, or base address. </p><p>Because the mathematical concept of a <a href="/wiki/Matrix_(mathematics)" title="Matrix (mathematics)">matrix</a> can be represented as a two-dimensional grid, two-dimensional arrays are also sometimes called "matrices". In some cases the term "vector" is used in computing to refer to an array, although <a href="/wiki/Tuple" title="Tuple">tuples</a> rather than <a href="/wiki/Vector_space" title="Vector space">vectors</a> are the more mathematically correct equivalent. <a href="/wiki/Table_(information)" title="Table (information)">Tables</a> are often implemented in the form of arrays, especially <a href="/wiki/Lookup_table" title="Lookup table">lookup tables</a>; the word "table" is sometimes used as a synonym of array. </p><p>Arrays are among the oldest and most important data structures, and are used by almost every program. They are also used to implement many other data structures, such as <a href="/wiki/List_(computing)" class="mw-redirect" title="List (computing)">lists</a> and <a href="/wiki/String_(computer_science)" title="String (computer science)">strings</a>. They effectively exploit the addressing logic of computers. In most modern computers and many <a href="/wiki/External_storage" title="External storage">external storage</a> devices, the memory is a one-dimensional array of words, whose indices are their addresses. <a href="/wiki/Central_processing_unit" title="Central processing unit">Processors</a>, especially <a href="/wiki/Vector_processor" title="Vector processor">vector processors</a>, are often optimized for array operations. </p><p>Arrays are useful mostly because the element indices can be computed at <a href="/wiki/Run_time_(program_lifecycle_phase)" class="mw-redirect" title="Run time (program lifecycle phase)">run time</a>. Among other things, this feature allows a single iterative <a href="/wiki/Statement_(programming)" class="mw-redirect" title="Statement (programming)">statement</a> to process arbitrarily many elements of an array. For that reason, the elements of an array data structure are required to have the same size and should use the same data representation. The set of valid index tuples and the addresses of the elements (and hence the element addressing formula) are usually,<sup id="cite_ref-garcia_3-1" class="reference"><a href="#cite_note-garcia-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-veldhuizen_5-0" class="reference"><a href="#cite_note-veldhuizen-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> but not always,<sup id="cite_ref-andres_2-1" class="reference"><a href="#cite_note-andres-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> fixed while the array is in use. </p><p>The term "array" may also refer to an <a href="/wiki/Array_data_type" class="mw-redirect" title="Array data type">array data type</a>, a kind of <a href="/wiki/Data_type" title="Data type">data type</a> provided by most <a href="/wiki/High-level_programming_language" title="High-level programming language">high-level programming languages</a> that consists of a collection of values or variables that can be selected by one or more indices computed at run-time. Array types are often implemented by array structures; however, in some languages they may be implemented by <a href="/wiki/Hash_table" title="Hash table">hash tables</a>, <a href="/wiki/Linked_list" title="Linked list">linked lists</a>, <a href="/wiki/Search_tree" title="Search tree">search trees</a>, or other data structures. </p><p>The term is also used, especially in the description of <a href="/wiki/Algorithm" title="Algorithm">algorithms</a>, to mean <a href="/wiki/Associative_array" title="Associative array">associative array</a> or "abstract array", a <a href="/wiki/Theoretical_computer_science" title="Theoretical computer science">theoretical computer science</a> model (an <a href="/wiki/Abstract_data_type" title="Abstract data type">abstract data type</a> or ADT) intended to capture the essential properties of arrays. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="History">History</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Array_(data_structure)&action=edit&section=1" title="Edit section: History"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The first digital computers used machine-language programming to set up and access array structures for data tables, vector and matrix computations, and for many other purposes. <a href="/wiki/John_von_Neumann" title="John von Neumann">John von Neumann</a> wrote the first array-sorting program (<a href="/wiki/Merge_sort" title="Merge sort">merge sort</a>) in 1945, during the building of the <a href="/wiki/EDVAC" title="EDVAC">first stored-program computer</a>.<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> Array indexing was originally done by <a href="/wiki/Self-modifying_code" title="Self-modifying code">self-modifying code</a>, and later using <a href="/wiki/Index_register" title="Index register">index registers</a> and <a href="/wiki/Addressing_mode" title="Addressing mode">indirect addressing</a>. Some mainframes designed in the 1960s, such as the <a href="/wiki/Burroughs_large_systems" class="mw-redirect" title="Burroughs large systems">Burroughs B5000</a> and its successors, used <a href="/wiki/Memory_segmentation" title="Memory segmentation">memory segmentation</a> to perform index-bounds checking in hardware.<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>Assembly languages generally have no special support for arrays, other than what the machine itself provides. The earliest high-level programming languages, including <a href="/wiki/Fortran" title="Fortran">FORTRAN</a> (1957), <a href="/wiki/Lisp_(programming_language)" title="Lisp (programming language)">Lisp</a> (1958), <a href="/wiki/COBOL" title="COBOL">COBOL</a> (1960), and <a href="/wiki/ALGOL" title="ALGOL">ALGOL 60</a> (1960), had support for multi-dimensional arrays, and so has <a href="/wiki/C_(programming_language)" title="C (programming language)">C</a> (1972). In <a href="/wiki/C%2B%2B" title="C++">C++</a> (1983), class templates exist for multi-dimensional arrays whose dimension is fixed at runtime<sup id="cite_ref-garcia_3-2" class="reference"><a href="#cite_note-garcia-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-veldhuizen_5-1" class="reference"><a href="#cite_note-veldhuizen-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> as well as for runtime-flexible arrays.<sup id="cite_ref-andres_2-2" class="reference"><a href="#cite_note-andres-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Applications">Applications</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Array_(data_structure)&action=edit&section=2" title="Edit section: Applications"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Arrays are used to implement mathematical <a href="/wiki/Coordinate_vector" title="Coordinate vector">vectors</a> and <a href="/wiki/Matrix_(mathematics)" title="Matrix (mathematics)">matrices</a>, as well as other kinds of rectangular tables. Many <a href="/wiki/Database" title="Database">databases</a>, small and large, consist of (or include) one-dimensional arrays whose elements are <a href="/wiki/Record_(computer_science)" title="Record (computer science)">records</a>. </p><p>Arrays are used to implement other data structures, such as lists, <a href="/wiki/Heap_(data_structure)" title="Heap (data structure)">heaps</a>, <a href="/wiki/Hash_table" title="Hash table">hash tables</a>, <a href="/wiki/Double-ended_queue" title="Double-ended queue">deques</a>, <a href="/wiki/Queue_(data_structure)" class="mw-redirect" title="Queue (data structure)">queues</a>, <a href="/wiki/Stack_(data_structure)" class="mw-redirect" title="Stack (data structure)">stacks</a>, <a href="/wiki/String_(computer_science)" title="String (computer science)">strings</a>, and VLists. Array-based implementations of other data structures are frequently simple and space-efficient (<a href="/wiki/Implicit_data_structure" title="Implicit data structure">implicit data structures</a>), requiring little space <a href="/wiki/Overhead_(computing)" title="Overhead (computing)">overhead</a>, but may have poor space complexity, particularly when modified, compared to tree-based data structures (compare a <a href="/wiki/Sorted_array" title="Sorted array">sorted array</a> to a <a href="/wiki/Search_tree" title="Search tree">search tree</a>). </p><p>One or more large arrays are sometimes used to emulate in-program <a href="/wiki/Dynamic_memory_allocation" class="mw-redirect" title="Dynamic memory allocation">dynamic memory allocation</a>, particularly <a href="/wiki/Memory_pool" title="Memory pool">memory pool</a> allocation. Historically, this has sometimes been the only way to allocate "dynamic memory" portably. </p><p>Arrays can be used to determine partial or complete <a href="/wiki/Control_flow" title="Control flow">control flow</a> in programs, as a compact alternative to (otherwise repetitive) multiple <code>IF</code> statements. They are known in this context as <a href="/wiki/Control_table" title="Control table">control tables</a> and are used in conjunction with a purpose-built interpreter whose <a href="/wiki/Control_flow" title="Control flow">control flow</a> is altered according to values contained in the array. The array may contain <a href="/wiki/Subroutine" class="mw-redirect" title="Subroutine">subroutine</a> <a href="/wiki/Pointer_(computer_programming)" title="Pointer (computer programming)">pointers</a> (or relative subroutine numbers that can be acted upon by <a href="/wiki/Switch_statement" title="Switch statement">SWITCH</a> statements) that direct the path of the execution. </p> <div class="mw-heading mw-heading2"><h2 id="Element_identifier_and_addressing_formulas">Element identifier and addressing formulas</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Array_(data_structure)&action=edit&section=3" title="Edit section: Element identifier and addressing formulas"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>When data objects are stored in an array, individual objects are selected by an index that is usually a non-negative <a href="/wiki/Scalar_(computing)" class="mw-redirect" title="Scalar (computing)">scalar</a> <a href="/wiki/Integer" title="Integer">integer</a>. Indexes are also called subscripts. An index <i>maps</i> the array value to a stored object. </p><p>There are three ways in which the elements of an array can be indexed: </p> <dl><dt>0 (<i><a href="/wiki/Zero-based_numbering" title="Zero-based numbering">zero-based indexing</a></i>)</dt> <dd>The first element of the array is indexed by subscript of 0.<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></dd> <dt>1 (<i>one-based indexing</i>)</dt> <dd>The first element of the array is indexed by subscript of 1.</dd> <dt>n (<i>n-based indexing</i>)</dt> <dd>The base index of an array can be freely chosen. Usually programming languages allowing <i>n-based indexing</i> also allow negative index values and other <a href="/wiki/Scalar_(computing)" class="mw-redirect" title="Scalar (computing)">scalar</a> data types like <a href="/wiki/Enumerated_type" title="Enumerated type">enumerations</a>, or <a href="/wiki/Character_(computing)" title="Character (computing)">characters</a> may be used as an array index.</dd></dl> <p>Using zero based indexing is the design choice of many influential programming languages, including <a href="/wiki/C_(programming_language)" title="C (programming language)">C</a>, <a href="/wiki/Java_(programming_language)" title="Java (programming language)">Java</a> and <a href="/wiki/Lisp_(programming_language)" title="Lisp (programming language)">Lisp</a>. This leads to simpler implementation where the subscript refers to an offset from the starting position of an array, so the first element has an offset of zero. </p><p>Arrays can have multiple dimensions, thus it is not uncommon to access an array using multiple indices. For example, a two-dimensional array <code>A</code> with three rows and four columns might provide access to the element at the 2nd row and 4th column by the expression <code>A[1][3]</code> in the case of a zero-based indexing system. Thus two indices are used for a two-dimensional array, three for a three-dimensional array, and <i>n</i> for an <i>n</i>-dimensional array. </p><p>The number of indices needed to specify an element is called the dimension, dimensionality, or <a href="/wiki/Rank_(computer_programming)" title="Rank (computer programming)">rank</a> of the array. </p><p>In standard arrays, each index is restricted to a certain range of consecutive integers (or consecutive values of some <a href="/wiki/Enumerated_type" title="Enumerated type">enumerated type</a>), and the address of an element is computed by a "linear" formula on the indices. </p> <div class="mw-heading mw-heading3"><h3 id="One-dimensional_arrays">One-dimensional arrays</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Array_(data_structure)&action=edit&section=4" title="Edit section: One-dimensional arrays"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:1D_array_diagram.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/40/1D_array_diagram.svg/220px-1D_array_diagram.svg.png" decoding="async" width="220" height="170" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/40/1D_array_diagram.svg/330px-1D_array_diagram.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/40/1D_array_diagram.svg/440px-1D_array_diagram.svg.png 2x" data-file-width="590" data-file-height="457" /></a><figcaption>Diagram of a typical 1D array</figcaption></figure> <p>A one-dimensional array (or single dimension array) is a type of linear array. Accessing its elements involves a single subscript which can either represent a row or column index. </p><p>As an example consider the C declaration <code>int anArrayName[10];</code> which declares a one-dimensional array of ten integers. Here, the array can store ten elements of type <code>int</code> . This array has indices starting from zero through nine. For example, the expressions <code>anArrayName[0]</code> and <code>anArrayName[9]</code> are the first and last elements respectively. </p><p>For a vector with linear addressing, the element with index <i>i</i> is located at the address <span class="nowrap"><i>B</i> + <i>c</i> · <i>i</i></span>, where <i>B</i> is a fixed <i>base address</i> and <i>c</i> a fixed constant, sometimes called the <i>address increment</i> or <i>stride</i>. </p><p>If the valid element indices begin at 0, the constant <i>B</i> is simply the address of the first element of the array. For this reason, the <a href="/wiki/C_(programming_language)" title="C (programming language)">C programming language</a> specifies that array indices always begin at 0; and many programmers will call that element "<a href="/wiki/Zero-based_numbering" title="Zero-based numbering">zeroth</a>" rather than "first". </p><p>However, one can choose the index of the first element by an appropriate choice of the base address <i>B</i>. For example, if the array has five elements, indexed 1 through 5, and the base address <i>B</i> is replaced by <span class="nowrap"><i>B</i> + 30<i>c</i></span>, then the indices of those same elements will be 31 to 35. If the numbering does not start at 0, the constant <i>B</i> may not be the address of any element. </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:2D_array_diagram.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f3/2D_array_diagram.svg/220px-2D_array_diagram.svg.png" decoding="async" width="220" height="281" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f3/2D_array_diagram.svg/330px-2D_array_diagram.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f3/2D_array_diagram.svg/440px-2D_array_diagram.svg.png 2x" data-file-width="616" data-file-height="786" /></a><figcaption>Diagram of a typical 2D array</figcaption></figure> <div class="mw-heading mw-heading3"><h3 id="Multidimensional_arrays">Multidimensional arrays</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Array_(data_structure)&action=edit&section=5" title="Edit section: Multidimensional arrays"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:3D_array_diagram.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/97/3D_array_diagram.svg/220px-3D_array_diagram.svg.png" decoding="async" width="220" height="285" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/97/3D_array_diagram.svg/330px-3D_array_diagram.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/97/3D_array_diagram.svg/440px-3D_array_diagram.svg.png 2x" data-file-width="763" data-file-height="990" /></a><figcaption>Diagram of a typical 3D array</figcaption></figure> <p>For a multidimensional array, the element with indices <i>i</i>,<i>j</i> would have address <i>B</i> + <i>c</i> · <i>i</i> + <i>d</i> · <i>j</i>, where the coefficients <i>c</i> and <i>d</i> are the <i>row</i> and <i>column address increments</i>, respectively. </p><p>More generally, in a <i>k</i>-dimensional array, the address of an element with indices <i>i</i><sub>1</sub>, <i>i</i><sub>2</sub>, ..., <i>i</i><sub><i>k</i></sub> is </p> <dl><dd><i>B</i> + <i>c</i><sub>1</sub> · <i>i</i><sub>1</sub> + <i>c</i><sub>2</sub> · <i>i</i><sub>2</sub> + … + <i>c</i><sub><i>k</i></sub> · <i>i</i><sub><i>k</i></sub>.</dd></dl> <p>For example: int a[2][3]; </p><p>This means that array a has 2 rows and 3 columns, and the array is of integer type. Here we can store 6 elements they will be stored linearly but starting from first row linear then continuing with second row. The above array will be stored as a<sub>11</sub>, a<sub>12</sub>, a<sub>13</sub>, a<sub>21</sub>, a<sub>22</sub>, a<sub>23</sub>. </p><p>This formula requires only <i>k</i> multiplications and <i>k</i> additions, for any array that can fit in memory. Moreover, if any coefficient is a fixed power of 2, the multiplication can be replaced by <a href="/wiki/Bitwise_operation" title="Bitwise operation">bit shifting</a>. </p><p>The coefficients <i>c</i><sub><i>k</i></sub> must be chosen so that every valid index tuple maps to the address of a distinct element. </p><p>If the minimum legal value for every index is 0, then <i>B</i> is the address of the element whose indices are all zero. As in the one-dimensional case, the element indices may be changed by changing the base address <i>B</i>. Thus, if a two-dimensional array has rows and columns indexed from 1 to 10 and 1 to 20, respectively, then replacing <i>B</i> by <span class="nowrap"><i>B</i> + <i>c</i><sub>1</sub> − 3<i>c</i><sub>2</sub></span> will cause them to be renumbered from 0 through 9 and 4 through 23, respectively. Taking advantage of this feature, some languages (like FORTRAN 77) specify that array indices begin at 1, as in mathematical tradition while other languages (like Fortran 90, Pascal and Algol) let the user choose the minimum value for each index. </p> <div class="mw-heading mw-heading3"><h3 id="Dope_vectors">Dope vectors</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Array_(data_structure)&action=edit&section=6" title="Edit section: Dope vectors"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Dope_vector" title="Dope vector">Dope vector</a></div> <p>The addressing formula is completely defined by the dimension <i>d</i>, the base address <i>B</i>, and the increments <i>c</i><sub>1</sub>, <i>c</i><sub>2</sub>, ..., <i>c</i><sub><i>k</i></sub>. It is often useful to pack these parameters into a record called the array's descriptor, stride vector, or <a href="/wiki/Dope_vector" title="Dope vector">dope vector</a>.<sup id="cite_ref-andres_2-3" class="reference"><a href="#cite_note-andres-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-garcia_3-3" class="reference"><a href="#cite_note-garcia-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> The size of each element, and the minimum and maximum values allowed for each index may also be included in the dope vector. The dope vector is a complete <a href="/wiki/Handle_(computing)" title="Handle (computing)">handle</a> for the array, and is a convenient way to pass arrays as arguments to <a href="/wiki/Subroutine" class="mw-redirect" title="Subroutine">procedures</a>. Many useful <a href="/wiki/Array_slicing" title="Array slicing">array slicing</a> operations (such as selecting a sub-array, swapping indices, or reversing the direction of the indices) can be performed very efficiently by manipulating the dope vector.<sup id="cite_ref-andres_2-4" class="reference"><a href="#cite_note-andres-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Compact_layouts">Compact layouts</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Array_(data_structure)&action=edit&section=7" title="Edit section: Compact layouts"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Row-_and_column-major_order" title="Row- and column-major order">Row- and column-major order</a></div> <p>Often the coefficients are chosen so that the elements occupy a contiguous area of memory. However, that is not necessary. Even if arrays are always created with contiguous elements, some array slicing operations may create non-contiguous sub-arrays from them. </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Row_and_column_major_order.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4d/Row_and_column_major_order.svg/170px-Row_and_column_major_order.svg.png" decoding="async" width="170" height="227" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4d/Row_and_column_major_order.svg/255px-Row_and_column_major_order.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4d/Row_and_column_major_order.svg/340px-Row_and_column_major_order.svg.png 2x" data-file-width="512" data-file-height="683" /></a><figcaption>Illustration of row- and column-major order</figcaption></figure> <p>There are two systematic compact layouts for a two-dimensional array. For example, consider the matrix </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A={\begin{bmatrix}1&2&3\\4&5&6\\7&8&9\end{bmatrix}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>[</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>2</mn> </mtd> <mtd> <mn>3</mn> </mtd> </mtr> <mtr> <mtd> <mn>4</mn> </mtd> <mtd> <mn>5</mn> </mtd> <mtd> <mn>6</mn> </mtd> </mtr> <mtr> <mtd> <mn>7</mn> </mtd> <mtd> <mn>8</mn> </mtd> <mtd> <mn>9</mn> </mtd> </mtr> </mtable> <mo>]</mo> </mrow> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A={\begin{bmatrix}1&2&3\\4&5&6\\7&8&9\end{bmatrix}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e5ce1bbaec43174abf6887a29b8f3a3612d0b1f5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.005ex; width:17.473ex; height:9.176ex;" alt="{\displaystyle A={\begin{bmatrix}1&2&3\\4&5&6\\7&8&9\end{bmatrix}}.}"></span></dd></dl> <p>In the row-major order layout (adopted by C for statically declared arrays), the elements in each row are stored in consecutive positions and all of the elements of a row have a lower address than any of the elements of a consecutive row: </p> <dl><dd><table class="wikitable"> <tbody><tr> <td>1</td> <td>2</td> <td>3</td> <td>4</td> <td>5</td> <td>6</td> <td>7</td> <td>8</td> <td>9 </td></tr></tbody></table></dd></dl> <p>In column-major order (traditionally used by Fortran), the elements in each column are consecutive in memory and all of the elements of a column have a lower address than any of the elements of a consecutive column: </p> <dl><dd><table class="wikitable"> <tbody><tr> <td>1</td> <td>4</td> <td>7</td> <td>2</td> <td>5</td> <td>8</td> <td>3</td> <td>6</td> <td>9 </td></tr></tbody></table></dd></dl> <p>For arrays with three or more indices, "row major order" puts in consecutive positions any two elements whose index tuples differ only by one in the <i>last</i> index. "Column major order" is analogous with respect to the <i>first</i> index. </p><p>In systems which use <a href="/wiki/Processor_cache" class="mw-redirect" title="Processor cache">processor cache</a> or <a href="/wiki/Virtual_memory" title="Virtual memory">virtual memory</a>, scanning an array is much faster if successive elements are stored in consecutive positions in memory, rather than sparsely scattered. This is known as spatial locality, which is a type of <a href="/wiki/Locality_of_reference" title="Locality of reference">locality of reference</a>. Many algorithms that use multidimensional arrays will scan them in a predictable order. A programmer (or a sophisticated compiler) may use this information to choose between row- or column-major layout for each array. For example, when computing the product <i>A</i>·<i>B</i> of two matrices, it would be best to have <i>A</i> stored in row-major order, and <i>B</i> in column-major order. </p> <div class="mw-heading mw-heading3"><h3 id="Resizing">Resizing</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Array_(data_structure)&action=edit&section=8" title="Edit section: Resizing"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Dynamic_array" title="Dynamic array">Dynamic array</a></div> <p>Static arrays have a size that is fixed when they are created and consequently do not allow elements to be inserted or removed. However, by allocating a new array and copying the contents of the old array to it, it is possible to effectively implement a <i>dynamic</i> version of an array; see <a href="/wiki/Dynamic_array" title="Dynamic array">dynamic array</a>. If this operation is done infrequently, insertions at the end of the array require only amortized constant time. </p><p>Some array data structures do not reallocate storage, but do store a count of the number of elements of the array in use, called the count or size. This effectively makes the array a <a href="/wiki/Dynamic_array" title="Dynamic array">dynamic array</a> with a fixed maximum size or capacity; <a href="/wiki/Pascal_string" class="mw-redirect" title="Pascal string">Pascal strings</a> are examples of this. </p> <div class="mw-heading mw-heading3"><h3 id="Non-linear_formulas">Non-linear formulas</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Array_(data_structure)&action=edit&section=9" title="Edit section: Non-linear formulas"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>More complicated (non-linear) formulas are occasionally used. For a compact two-dimensional <a href="/wiki/Triangular_array" title="Triangular array">triangular array</a>, for instance, the addressing formula is a polynomial of degree 2. </p> <div class="mw-heading mw-heading2"><h2 id="Efficiency">Efficiency</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Array_(data_structure)&action=edit&section=10" title="Edit section: Efficiency"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Both <i>store</i> and <i>select</i> take (deterministic worst case) <a href="/wiki/Constant_time" class="mw-redirect" title="Constant time">constant time</a>. Arrays take linear (<a href="/wiki/Big-O_notation" class="mw-redirect" title="Big-O notation">O</a>(<i>n</i>)) space in the number of elements <i>n</i> that they hold. </p><p>In an array with element size <i>k</i> and on a machine with a cache line size of B bytes, iterating through an array of <i>n</i> elements requires the minimum of ceiling(<i>nk</i>/B) cache misses, because its elements occupy contiguous memory locations. This is roughly a factor of B/<i>k</i> better than the number of cache misses needed to access <i>n</i> elements at random memory locations. As a consequence, sequential iteration over an array is noticeably faster in practice than iteration over many other data structures, a property called <a href="/wiki/Locality_of_reference" title="Locality of reference">locality of reference</a> (this does <i>not</i> mean however, that using a <a href="/wiki/Perfect_hash_function" title="Perfect hash function">perfect hash</a> or <a href="/wiki/Hash_function#Trivial_hash_function" title="Hash function">trivial hash</a> within the same (local) array, will not be even faster - and achievable in <a href="/wiki/Constant_time" class="mw-redirect" title="Constant time">constant time</a>). Libraries provide low-level optimized facilities for copying ranges of memory (such as <a href="/wiki/String.h" class="mw-redirect" title="String.h">memcpy</a>) which can be used to move <a href="/wiki/Contiguous_data_storage" class="mw-redirect" title="Contiguous data storage">contiguous</a> blocks of array elements significantly faster than can be achieved through individual element access. The speedup of such optimized routines varies by array element size, architecture, and implementation. </p><p>Memory-wise, arrays are compact data structures with no per-element <a href="/wiki/Computational_overhead" class="mw-redirect" title="Computational overhead">overhead</a>. There may be a per-array overhead (e.g., to store index bounds) but this is language-dependent. It can also happen that elements stored in an array require <i>less</i> memory than the same elements stored in individual variables, because several array elements can be stored in a single <a href="/wiki/Word_(data_type)" class="mw-redirect" title="Word (data type)">word</a>; such arrays are often called <i>packed</i> arrays. An extreme (but commonly used) case is the <a href="/wiki/Bit_array" title="Bit array">bit array</a>, where every bit represents a single element. A single <a href="/wiki/Octet_(computing)" title="Octet (computing)">octet</a> can thus hold up to 256 different combinations of up to 8 different conditions, in the most compact form. </p><p>Array accesses with statically predictable access patterns are a major source of <a href="/wiki/Data_parallelism" title="Data parallelism">data parallelism</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Comparison_with_other_data_structures">Comparison with other data structures</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Array_(data_structure)&action=edit&section=11" title="Edit section: Comparison with other data structures"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <table class="wikitable"> <caption>Comparison of list data structures </caption> <tbody><tr> <th rowspan="2"> </th> <th rowspan="2">Peek <br />(index) </th> <th colspan="3">Mutate (insert or delete) at … </th> <th rowspan="2">Excess space, <br />average </th></tr> <tr> <th>Beginning </th> <th>End </th> <th>Middle </th></tr> <tr> <td><a href="/wiki/Linked_list" title="Linked list">Linked list</a> </td> <td style="background:#FFC7C7;color:black;vertical-align:middle;text-align:center;" class="table-no">Θ(<i>n</i>) </td> <td style="background:#9EFF9E;color:black;vertical-align:middle;text-align:center;" class="table-yes">Θ(1) </td> <td style="background:#9EFF9E;color:black;vertical-align:middle;text-align:center;" class="table-yes">Θ(1), known end element;<br />Θ(<i>n</i>), unknown end element </td> <td style="background:#FFC7C7;color:black;vertical-align:middle;text-align:center;" class="table-no">Θ(<i>n</i>) </td> <td style="background:#FFC7C7;color:black;vertical-align:middle;text-align:center;" class="table-no">Θ(<i>n</i>) </td></tr> <tr> <td><a href="/wiki/Array_data_structure" class="mw-redirect" title="Array data structure">Array</a> </td> <td style="background:#9EFF9E;color:black;vertical-align:middle;text-align:center;" class="table-yes">Θ(1) </td> <td data-sort-value="" style="background: var(--background-color-interactive, #ececec); color: var(--color-base, inherit); vertical-align: middle; text-align: center;" class="table-na">— </td> <td data-sort-value="" style="background: var(--background-color-interactive, #ececec); color: var(--color-base, inherit); vertical-align: middle; text-align: center;" class="table-na">— </td> <td data-sort-value="" style="background: var(--background-color-interactive, #ececec); color: var(--color-base, inherit); vertical-align: middle; text-align: center;" class="table-na">— </td> <td style="background:#9EFF9E;color:black;vertical-align:middle;text-align:center;" class="table-yes">0 </td></tr> <tr> <td><a href="/wiki/Dynamic_array" title="Dynamic array">Dynamic array</a> </td> <td style="background:#9EFF9E;color:black;vertical-align:middle;text-align:center;" class="table-yes">Θ(1) </td> <td style="background:#FFC7C7;color:black;vertical-align:middle;text-align:center;" class="table-no">Θ(<i>n</i>) </td> <td style="background:#9EFF9E;color:black;vertical-align:middle;text-align:center;" class="table-yes">Θ(1) <a href="/wiki/Amortized_analysis" title="Amortized analysis">amortized</a> </td> <td style="background:#FFC7C7;color:black;vertical-align:middle;text-align:center;" class="table-no">Θ(<i>n</i>) </td> <td style="background:#FFC7C7;color:black;vertical-align:middle;text-align:center;" class="table-no">Θ(<i>n</i>)<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> </td></tr> <tr> <td><a href="/wiki/Self-balancing_binary_search_tree" title="Self-balancing binary search tree">Balanced tree</a> </td> <td style="background:#FFB; color:black;vertical-align:middle;text-align:center;" class="table-partial">Θ(log n) </td> <td style="background:#FFB; color:black;vertical-align:middle;text-align:center;" class="table-partial">Θ(log n) </td> <td style="background:#FFB; color:black;vertical-align:middle;text-align:center;" class="table-partial">Θ(log <i>n</i>) </td> <td style="background:#FFB; color:black;vertical-align:middle;text-align:center;" class="table-partial">Θ(log <i>n</i>) </td> <td style="background:#FFC7C7;color:black;vertical-align:middle;text-align:center;" class="table-no">Θ(<i>n</i>) </td></tr> <tr> <td>Random-<span class="nowrap">access list</span> </td> <td style="background:#FFB; color:black;vertical-align:middle;text-align:center;" class="table-partial">Θ(log n)<sup id="cite_ref-okasakiComparison_10-0" class="reference"><a href="#cite_note-okasakiComparison-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> </td> <td style="background:#9EFF9E;color:black;vertical-align:middle;text-align:center;" class="table-yes">Θ(1) </td> <td data-sort-value="" style="background: var(--background-color-interactive, #ececec); color: var(--color-base, inherit); vertical-align: middle; text-align: center;" class="table-na">—<sup id="cite_ref-okasakiComparison_10-1" class="reference"><a href="#cite_note-okasakiComparison-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> </td> <td data-sort-value="" style="background: var(--background-color-interactive, #ececec); color: var(--color-base, inherit); vertical-align: middle; text-align: center;" class="table-na">—<sup id="cite_ref-okasakiComparison_10-2" class="reference"><a href="#cite_note-okasakiComparison-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> </td> <td style="background:#FFC7C7;color:black;vertical-align:middle;text-align:center;" class="table-no">Θ(<i>n</i>) </td></tr> <tr> <td><a href="/wiki/Hashed_array_tree" title="Hashed array tree">Hashed array tree</a> </td> <td style="background:#9EFF9E;color:black;vertical-align:middle;text-align:center;" class="table-yes">Θ(1) </td> <td style="background:#FFC7C7;color:black;vertical-align:middle;text-align:center;" class="table-no">Θ(<i>n</i>) </td> <td style="background:#9EFF9E;color:black;vertical-align:middle;text-align:center;" class="table-yes">Θ(1) <a href="/wiki/Amortized_analysis" title="Amortized analysis">amortized</a> </td> <td style="background:#FFC7C7;color:black;vertical-align:middle;text-align:center;" class="table-no">Θ(<i>n</i>) </td> <td style="background:#FFB; color:black;vertical-align:middle;text-align:center;" class="table-partial">Θ(√<i>n</i>) </td></tr></tbody></table> <p><a href="/wiki/Dynamic_array" title="Dynamic array">Dynamic arrays</a> or growable arrays are similar to arrays but add the ability to insert and delete elements; adding and deleting at the end is particularly efficient. However, they reserve linear (<a href="/wiki/Big-O_notation#Family_of_Bachmann–Landau_notations" class="mw-redirect" title="Big-O notation">Θ</a>(<i>n</i>)) additional storage, whereas arrays do not reserve additional storage. </p><p><a href="/wiki/Associative_array" title="Associative array">Associative arrays</a> provide a mechanism for array-like functionality without huge storage overheads when the index values are sparse. For example, an array that contains values only at indexes 1 and 2 billion may benefit from using such a structure. Specialized associative arrays with integer keys include <a href="/wiki/Radix_tree" title="Radix tree">Patricia tries</a>, <a href="/wiki/Judy_array" title="Judy array">Judy arrays</a>, and <a href="/wiki/Van_Emde_Boas_tree" title="Van Emde Boas tree">van Emde Boas trees</a>. </p><p><a href="/wiki/Self-balancing_binary_search_tree" title="Self-balancing binary search tree">Balanced trees</a> require O(log <i>n</i>) time for indexed access, but also permit inserting or deleting elements in O(log <i>n</i>) time,<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> whereas growable arrays require linear (Θ(<i>n</i>)) time to insert or delete elements at an arbitrary position. </p><p><a href="/wiki/Linked_list" title="Linked list">Linked lists</a> allow constant time removal and insertion in the middle but take linear time for indexed access. Their memory use is typically worse than arrays, but is still linear. </p> <figure class="mw-halign-left" typeof="mw:File"><a href="/wiki/File:Array_of_array_storage.svg" class="mw-file-description" title="A two-dimensional array stored as a one-dimensional array of one-dimensional arrays (rows)."><img alt="A two-dimensional array stored as a one-dimensional array of one-dimensional arrays (rows)." src="//upload.wikimedia.org/wikipedia/commons/thumb/0/01/Array_of_array_storage.svg/120px-Array_of_array_storage.svg.png" decoding="async" width="120" height="86" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/01/Array_of_array_storage.svg/180px-Array_of_array_storage.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/01/Array_of_array_storage.svg/240px-Array_of_array_storage.svg.png 2x" data-file-width="206" data-file-height="148" /></a><figcaption>A two-dimensional array stored as a one-dimensional array of one-dimensional arrays (rows).</figcaption></figure> <p>An <a href="/wiki/Iliffe_vector" title="Iliffe vector">Iliffe vector</a> is an alternative to a multidimensional array structure. It uses a one-dimensional array of <a href="/wiki/Reference_(computer_science)" title="Reference (computer science)">references</a> to arrays of one dimension less. For two dimensions, in particular, this alternative structure would be a vector of pointers to vectors, one for each row(pointer on c or c++). Thus an element in row <i>i</i> and column <i>j</i> of an array <i>A</i> would be accessed by double indexing (<i>A</i>[<i>i</i>][<i>j</i>] in typical notation). This alternative structure allows <a href="/wiki/Jagged_array" title="Jagged array">jagged arrays</a>, where each row may have a different size—or, in general, where the valid range of each index depends on the values of all preceding indices. It also saves one multiplication (by the column address increment) replacing it by a bit shift (to index the vector of row pointers) and one extra memory access (fetching the row address), which may be worthwhile in some architectures. </p> <div class="mw-heading mw-heading2"><h2 id="Dimension">Dimension</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Array_(data_structure)&action=edit&section=12" title="Edit section: Dimension"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The <i>dimension</i> of an array is the number of indices needed to select an element. Thus, if the array is seen as a function on a set of possible index combinations, it is the dimension of the space of which its domain is a discrete subset. Thus a one-dimensional array is a list of data, a two-dimensional array is a rectangle of data,<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> a three-dimensional array a block of data, etc. </p><p>This should not be confused with the dimension of the set of all matrices with a given domain, that is, the number of elements in the array. For example, an array with 5 rows and 4 columns is two-dimensional, but such matrices form a 20-dimensional space. Similarly, a three-dimensional vector can be represented by a one-dimensional array of size three. </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Array_(data_structure)&action=edit&section=13" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239009302">.mw-parser-output .portalbox{padding:0;margin:0.5em 0;display:table;box-sizing:border-box;max-width:175px;list-style:none}.mw-parser-output .portalborder{border:1px solid var(--border-color-base,#a2a9b1);padding:0.1em;background:var(--background-color-neutral-subtle,#f8f9fa)}.mw-parser-output .portalbox-entry{display:table-row;font-size:85%;line-height:110%;height:1.9em;font-style:italic;font-weight:bold}.mw-parser-output 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href="/wiki/Variable-length_array" title="Variable-length array">Variable-length array</a></li> <li><a href="/wiki/Bit_array" title="Bit array">Bit array</a></li> <li><a href="/wiki/Array_slicing" title="Array slicing">Array slicing</a></li> <li><a href="/wiki/Offset_(computer_science)" title="Offset (computer science)">Offset (computer science)</a></li> <li><a href="/wiki/Row-_and_column-major_order" title="Row- and column-major order">Row- and column-major order</a></li> <li><a href="/wiki/Stride_of_an_array" title="Stride of an array">Stride of an array</a></li></ul> </div> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Array_(data_structure)&action=edit&section=14" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon 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"Runtime-Flexible Multi-dimensional Arrays and Views for C++98 and C++0x". <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/1008.2909">1008.2909</a></span> [<a rel="nofollow" class="external text" href="https://arxiv.org/archive/cs.DS">cs.DS</a>].</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=preprint&rft.jtitle=arXiv&rft.atitle=Runtime-Flexible+Multi-dimensional+Arrays+and+Views+for+C%2B%2B98+and+C%2B%2B0x&rft.date=2010&rft_id=info%3Aarxiv%2F1008.2909&rft.au=Bjoern+Andres&rft.au=Ullrich+Koethe&rft.au=Thorben+Kroeger&rft.au=Hamprecht&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArray+%28data+structure%29" class="Z3988"></span></span> </li> <li id="cite_note-garcia-3"><span class="mw-cite-backlink">^ <a href="#cite_ref-garcia_3-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-garcia_3-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-garcia_3-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-garcia_3-3"><sup><i><b>d</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGarciaLumsdaine2005" class="citation journal cs1">Garcia, Ronald; Lumsdaine, Andrew (2005). 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0.25em"> <ul><li><a href="/wiki/Associative_array" title="Associative array">Associative array</a> <ul><li><a href="/wiki/Multimap" title="Multimap">Multimap</a></li> <li><a href="/wiki/Retrieval_Data_Structure" title="Retrieval Data Structure">Retrieval Data Structure</a></li></ul></li> <li><a href="/wiki/List_(abstract_data_type)" title="List (abstract data type)">List</a></li> <li><a href="/wiki/Stack_(abstract_data_type)" title="Stack (abstract data type)">Stack</a></li> <li><a href="/wiki/Queue_(abstract_data_type)" title="Queue (abstract data type)">Queue</a> <ul><li><a href="/wiki/Double-ended_queue" title="Double-ended queue">Double-ended queue</a></li></ul></li> <li><a href="/wiki/Priority_queue" title="Priority queue">Priority queue</a> <ul><li><a href="/wiki/Double-ended_priority_queue" title="Double-ended priority queue">Double-ended priority queue</a></li></ul></li> <li><a href="/wiki/Set_(abstract_data_type)" title="Set (abstract data type)">Set</a> <ul><li><a href="/wiki/Set_(abstract_data_type)#Multiset" title="Set (abstract data type)">Multiset</a></li> <li><a href="/wiki/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 class="mw-selflink selflink">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="/wiki/Bit_array" title="Bit array">Bit array</a></li> <li><a href="/wiki/Circular_buffer" title="Circular buffer">Circular buffer</a></li> <li><a href="/wiki/Dynamic_array" title="Dynamic array">Dynamic array</a></li> <li><a href="/wiki/Hash_table" title="Hash table">Hash table</a></li> <li><a href="/wiki/Hashed_array_tree" title="Hashed array tree">Hashed array tree</a></li> <li><a href="/wiki/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="/wiki/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="/wiki/Association_list" title="Association list">Association list</a></li> <li><a href="/wiki/Linked_list" title="Linked list">Linked list</a></li> <li><a href="/wiki/Skip_list" title="Skip list">Skip list</a></li> <li><a href="/wiki/Unrolled_linked_list" title="Unrolled linked list">Unrolled linked list</a></li> <li><a href="/wiki/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="/wiki/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"> <ul><li><a href="/wiki/B-tree" title="B-tree">B-tree</a></li> <li><a href="/wiki/Binary_search_tree" title="Binary search tree">Binary search tree</a> <ul><li><a href="/wiki/AA_tree" title="AA tree">AA tree</a></li> <li><a href="/wiki/AVL_tree" title="AVL tree">AVL tree</a></li> <li><a href="/wiki/Red%E2%80%93black_tree" title="Red–black tree">Red–black tree</a></li> <li><a href="/wiki/Self-balancing_binary_search_tree" title="Self-balancing binary search tree">Self-balancing tree</a></li> <li><a href="/wiki/Splay_tree" title="Splay tree">Splay tree</a></li></ul></li> <li><a href="/wiki/Heap_(data_structure)" title="Heap (data structure)">Heap</a> <ul><li><a href="/wiki/Binary_heap" title="Binary heap">Binary heap</a></li> <li><a href="/wiki/Binomial_heap" title="Binomial heap">Binomial heap</a></li> <li><a href="/wiki/Fibonacci_heap" title="Fibonacci heap">Fibonacci heap</a></li></ul></li> <li><a href="/wiki/R-tree" title="R-tree">R-tree</a> <ul><li><a href="/wiki/R*_tree" class="mw-redirect" title="R* tree">R* tree</a></li> <li><a href="/wiki/R%2B_tree" title="R+ tree">R+ tree</a></li> <li><a href="/wiki/Hilbert_R-tree" title="Hilbert R-tree">Hilbert R-tree</a></li></ul></li> <li><a href="/wiki/Trie" title="Trie">Trie</a> <ul><li><a href="/wiki/Hash_tree_(persistent_data_structure)" title="Hash tree (persistent data structure)">Hash tree</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/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="/wiki/Binary_decision_diagram" title="Binary decision diagram">Binary decision diagram</a></li> <li><a href="/wiki/Directed_acyclic_graph" title="Directed acyclic graph">Directed acyclic graph</a></li> <li><a href="/wiki/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="/wiki/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"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox" aria-labelledby="Parallel_computing" 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"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Parallel_computing" title="Template:Parallel computing"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Parallel_computing" title="Template talk:Parallel computing"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Parallel_computing" title="Special:EditPage/Template:Parallel computing"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Parallel_computing" style="font-size:114%;margin:0 4em"><a href="/wiki/Parallel_computing" title="Parallel computing">Parallel computing</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">General</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="/wiki/Distributed_computing" title="Distributed computing">Distributed computing</a></li> <li><a href="/wiki/Parallel_computing" title="Parallel computing">Parallel computing</a></li> <li><a href="/wiki/Massively_parallel" title="Massively parallel">Massively parallel</a></li> <li><a href="/wiki/Cloud_computing" title="Cloud computing">Cloud computing</a></li> <li><a href="/wiki/High-performance_computing" title="High-performance computing">High-performance computing</a></li> <li><a href="/wiki/Multiprocessing" title="Multiprocessing">Multiprocessing</a></li> <li><a href="/wiki/Manycore_processor" title="Manycore processor">Manycore processor</a></li> <li><a href="/wiki/General-purpose_computing_on_graphics_processing_units" title="General-purpose computing on graphics processing units">GPGPU</a></li> <li><a href="/wiki/Computer_network" title="Computer network">Computer network</a></li> <li><a href="/wiki/Systolic_array" title="Systolic array">Systolic array</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Levels</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="/wiki/Bit-level_parallelism" title="Bit-level parallelism">Bit</a></li> <li><a href="/wiki/Instruction-level_parallelism" title="Instruction-level parallelism">Instruction</a></li> <li><a href="/wiki/Task_parallelism" title="Task parallelism">Thread</a></li> <li><a href="/wiki/Task_parallelism" title="Task parallelism">Task</a></li> <li><a href="/wiki/Data_parallelism" title="Data parallelism">Data</a></li> <li><a href="/wiki/Memory-level_parallelism" title="Memory-level parallelism">Memory</a></li> <li><a href="/wiki/Loop-level_parallelism" title="Loop-level parallelism">Loop</a></li> <li><a href="/wiki/Pipeline_(computing)" title="Pipeline (computing)">Pipeline</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Multithreading_(computer_architecture)" title="Multithreading (computer architecture)">Multithreading</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="/wiki/Temporal_multithreading" title="Temporal multithreading">Temporal</a></li> <li><a href="/wiki/Simultaneous_multithreading" title="Simultaneous multithreading">Simultaneous</a> (SMT)</li> <li><a href="/wiki/Simultaneous_and_heterogeneous_multithreading" title="Simultaneous and heterogeneous multithreading">Simultaneous and heterogenous</a></li> <li><a href="/wiki/Speculative_multithreading" title="Speculative multithreading">Speculative</a> (SpMT)</li> <li><a href="/wiki/Preemption_(computing)" title="Preemption (computing)">Preemptive</a></li> <li><a href="/wiki/Computer_multitasking#Cooperative_multitasking" title="Computer multitasking">Cooperative</a></li> <li><a href="/wiki/Bulldozer_(microarchitecture)#Bulldozer_core" title="Bulldozer (microarchitecture)">Clustered multi-thread</a> (CMT)</li> <li><a href="/wiki/Hardware_scout" title="Hardware scout">Hardware scout</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Theory</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="/wiki/Parallel_RAM" title="Parallel RAM">PRAM model</a></li> <li><a href="/wiki/Parallel_external_memory" title="Parallel external memory">PEM model</a></li> <li><a href="/wiki/Analysis_of_parallel_algorithms" title="Analysis of parallel algorithms">Analysis of parallel algorithms</a></li> <li><a href="/wiki/Amdahl%27s_law" title="Amdahl's law">Amdahl's law</a></li> <li><a href="/wiki/Gustafson%27s_law" title="Gustafson's law">Gustafson's law</a></li> <li><a href="/wiki/Cost_efficiency" title="Cost efficiency">Cost efficiency</a></li> <li><a href="/wiki/Karp%E2%80%93Flatt_metric" title="Karp–Flatt metric">Karp–Flatt metric</a></li> <li><a href="/wiki/Parallel_slowdown" title="Parallel slowdown">Slowdown</a></li> <li><a href="/wiki/Speedup" title="Speedup">Speedup</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Elements</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="/wiki/Process_(computing)" title="Process (computing)">Process</a></li> <li><a href="/wiki/Thread_(computing)" title="Thread (computing)">Thread</a></li> <li><a href="/wiki/Fiber_(computer_science)" title="Fiber (computer science)">Fiber</a></li> <li><a href="/wiki/Instruction_window" title="Instruction window">Instruction window</a></li> <li><a class="mw-selflink selflink">Array</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Coordination</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="/wiki/Multiprocessing" title="Multiprocessing">Multiprocessing</a></li> <li><a href="/wiki/Memory_coherence" title="Memory coherence">Memory coherence</a></li> <li><a href="/wiki/Cache_coherence" title="Cache coherence">Cache coherence</a></li> <li><a href="/wiki/Cache_invalidation" title="Cache invalidation">Cache invalidation</a></li> <li><a href="/wiki/Barrier_(computer_science)" title="Barrier (computer science)">Barrier</a></li> <li><a href="/wiki/Synchronization_(computer_science)" title="Synchronization (computer science)">Synchronization</a></li> <li><a href="/wiki/Application_checkpointing" title="Application checkpointing">Application checkpointing</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Computer_programming" title="Computer programming">Programming</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="/wiki/Stream_processing" title="Stream processing">Stream processing</a></li> <li><a href="/wiki/Dataflow_programming" title="Dataflow programming">Dataflow programming</a></li> <li><a href="/wiki/Parallel_programming_model" title="Parallel programming model">Models</a> <ul><li><a href="/wiki/Implicit_parallelism" title="Implicit parallelism">Implicit parallelism</a></li> <li><a href="/wiki/Explicit_parallelism" title="Explicit parallelism">Explicit parallelism</a></li> <li><a href="/wiki/Concurrency_(computer_science)" title="Concurrency (computer science)">Concurrency</a></li></ul></li> <li><a href="/wiki/Non-blocking_algorithm" title="Non-blocking algorithm">Non-blocking algorithm</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Computer_hardware" title="Computer hardware">Hardware</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="/wiki/Flynn%27s_taxonomy" title="Flynn's taxonomy">Flynn's taxonomy</a> <ul><li><a href="/wiki/Single_instruction,_single_data" title="Single instruction, single data">SISD</a></li> <li><a href="/wiki/Single_instruction,_multiple_data" title="Single instruction, multiple data">SIMD</a> <ul><li><a href="/wiki/Single_instruction,_multiple_threads" title="Single instruction, multiple threads">Array processing</a> (SIMT)</li> <li><a href="/wiki/Flynn%27s_taxonomy#Pipelined_processor" title="Flynn's taxonomy">Pipelined processing</a></li> <li><a href="/wiki/Flynn%27s_taxonomy#Associative_processor" title="Flynn's taxonomy">Associative processing</a></li></ul></li> <li><a href="/wiki/Multiple_instruction,_single_data" title="Multiple instruction, single data">MISD</a></li> <li><a href="/wiki/Multiple_instruction,_multiple_data" title="Multiple instruction, multiple data">MIMD</a></li></ul></li> <li><a href="/wiki/Dataflow_architecture" title="Dataflow architecture">Dataflow architecture</a></li> <li><a href="/wiki/Instruction_pipelining" title="Instruction pipelining">Pipelined processor</a></li> <li><a href="/wiki/Superscalar_processor" title="Superscalar processor">Superscalar processor</a></li> <li><a href="/wiki/Vector_processor" title="Vector processor">Vector processor</a></li> <li><a href="/wiki/Multiprocessing" title="Multiprocessing">Multiprocessor</a> <ul><li><a href="/wiki/Symmetric_multiprocessing" title="Symmetric multiprocessing">symmetric</a></li> <li><a href="/wiki/Asymmetric_multiprocessing" title="Asymmetric multiprocessing">asymmetric</a></li></ul></li> <li><a href="/wiki/Semiconductor_memory" title="Semiconductor memory">Memory</a> <ul><li><a href="/wiki/Shared_memory" title="Shared memory">shared</a></li> <li><a href="/wiki/Distributed_memory" title="Distributed memory">distributed</a></li> <li><a href="/wiki/Distributed_shared_memory" title="Distributed shared memory">distributed shared</a></li> <li><a href="/wiki/Uniform_memory_access" title="Uniform memory access">UMA</a></li> <li><a href="/wiki/Non-uniform_memory_access" title="Non-uniform memory access">NUMA</a></li> <li><a href="/wiki/Cache-only_memory_architecture" title="Cache-only memory architecture">COMA</a></li></ul></li> <li><a href="/wiki/Massively_parallel" title="Massively parallel">Massively parallel</a> computer</li> <li><a href="/wiki/Computer_cluster" title="Computer cluster">Computer cluster</a> <ul><li><a href="/wiki/Beowulf_cluster" title="Beowulf cluster">Beowulf cluster</a></li></ul></li> <li><a href="/wiki/Grid_computing" title="Grid computing">Grid computer</a></li> <li><a href="/wiki/Hardware_acceleration" title="Hardware acceleration">Hardware acceleration</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/API" title="API">APIs</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="/wiki/Ateji_PX" title="Ateji PX">Ateji PX</a></li> <li><a href="/wiki/Boost_(C%2B%2B_libraries)" title="Boost (C++ libraries)">Boost</a></li> <li><a href="/wiki/Chapel_(programming_language)" title="Chapel (programming language)">Chapel</a></li> <li><a href="/wiki/HPX" title="HPX">HPX</a></li> <li><a href="/wiki/Charm%2B%2B" title="Charm++">Charm++</a></li> <li><a href="/wiki/Cilk" title="Cilk">Cilk</a></li> <li><a href="/wiki/Coarray_Fortran" title="Coarray Fortran">Coarray Fortran</a></li> <li><a href="/wiki/CUDA" title="CUDA">CUDA</a></li> <li><a href="/wiki/Dryad_(programming)" title="Dryad (programming)">Dryad</a></li> <li><a href="/wiki/C%2B%2B_AMP" title="C++ AMP">C++ AMP</a></li> <li><a href="/wiki/Global_Arrays" title="Global Arrays">Global Arrays</a></li> <li><a href="/wiki/GPUOpen" title="GPUOpen">GPUOpen</a></li> <li><a href="/wiki/Message_Passing_Interface" title="Message Passing Interface">MPI</a></li> <li><a href="/wiki/OpenMP" title="OpenMP">OpenMP</a></li> <li><a href="/wiki/OpenCL" title="OpenCL">OpenCL</a></li> <li><a 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