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class="vector-toc-numb">2.2</span> <span>For sub-structures of a given structure</span> </div> </a> <ul id="toc-For_sub-structures_of_a_given_structure-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Search_for_the_maximum_of_a_function" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Search_for_the_maximum_of_a_function"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.3</span> <span>Search for the maximum of a function</span> </div> </a> <ul id="toc-Search_for_the_maximum_of_a_function-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-For_quantum_computers" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#For_quantum_computers"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.4</span> <span>For quantum computers</span> </div> </a> <ul id="toc-For_quantum_computers-sublist" class="vector-toc-list"> </ul> </li> </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">3</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">4</span> <span>References</span> </div> </a> <button aria-controls="toc-References-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 References subsection</span> </button> <ul id="toc-References-sublist" class="vector-toc-list"> <li id="toc-Citations" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Citations"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1</span> <span>Citations</span> </div> </a> <ul id="toc-Citations-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Bibliography" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Bibliography"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2</span> <span>Bibliography</span> </div> </a> <ul id="toc-Bibliography-sublist" class="vector-toc-list"> <li id="toc-Books" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Books"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2.1</span> <span>Books</span> </div> </a> <ul id="toc-Books-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Articles" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Articles"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2.2</span> <span>Articles</span> </div> </a> <ul id="toc-Articles-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> </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">5</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">Search algorithm</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 31 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-31" 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">31 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/%D8%AE%D9%88%D8%A7%D8%B1%D8%B2%D9%85%D9%8A%D8%A9_%D8%A8%D8%AD%D8%AB" title="خوارزمية بحث – Arabic" lang="ar" hreflang="ar" data-title="خوارزمية بحث" 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/Axtar%C4%B1%C5%9F_alqoritml%C9%99ri" title="Axtarış alqoritmləri – Azerbaijani" lang="az" hreflang="az" data-title="Axtarış alqoritmləri" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbaijani" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%85%E0%A6%A8%E0%A7%81%E0%A6%B8%E0%A6%A8%E0%A7%8D%E0%A6%A7%E0%A6%BE%E0%A6%A8_%E0%A6%85%E0%A7%8D%E0%A6%AF%E0%A6%BE%E0%A6%B2%E0%A6%97%E0%A7%8B%E0%A6%B0%E0%A6%BF%E0%A6%A6%E0%A6%AE" title="অনুসন্ধান অ্যালগোরিদম – Bangla" lang="bn" hreflang="bn" data-title="অনুসন্ধান অ্যালগোরিদম" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%90%D0%BB%D0%B3%D0%BE%D1%80%D0%B8%D1%82%D1%8A%D0%BC_%D0%B7%D0%B0_%D1%82%D1%8A%D1%80%D1%81%D0%B5%D0%BD%D0%B5" title="Алгоритъм за търсене – Bulgarian" lang="bg" hreflang="bg" data-title="Алгоритъм за търсене" 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/Algorisme_de_cerca" title="Algorisme de cerca – Catalan" lang="ca" hreflang="ca" data-title="Algorisme de cerca" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/S%C3%B8gealgoritme" title="Søgealgoritme – Danish" lang="da" hreflang="da" data-title="Søgealgoritme" 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/Suchverfahren" title="Suchverfahren – German" lang="de" hreflang="de" data-title="Suchverfahren" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%91%CE%BB%CE%B3%CF%8C%CF%81%CE%B9%CE%B8%CE%BC%CE%BF%CF%82_%CE%B1%CE%BD%CE%B1%CE%B6%CE%AE%CF%84%CE%B7%CF%83%CE%B7%CF%82" title="Αλγόριθμος αναζήτησης – Greek" lang="el" hreflang="el" data-title="Αλγόριθμος αναζήτησης" 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/Algoritmo_de_b%C3%BAsqueda" title="Algoritmo de búsqueda – Spanish" lang="es" hreflang="es" data-title="Algoritmo de búsqueda" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%A7%D9%84%DA%AF%D9%88%D8%B1%DB%8C%D8%AA%D9%85_%D8%AC%D8%B3%D8%AA%D8%AC%D9%88" title="الگوریتم جستجو – Persian" lang="fa" hreflang="fa" data-title="الگوریتم جستجو" 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/Algorithme_de_recherche" title="Algorithme de recherche – French" lang="fr" hreflang="fr" data-title="Algorithme de recherche" 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/%EA%B2%80%EC%83%89_%EC%95%8C%EA%B3%A0%EB%A6%AC%EC%A6%98" title="검색 알고리즘 – Korean" lang="ko" hreflang="ko" data-title="검색 알고리즘" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D4%BB%D5%B6%D6%86%D5%B8%D6%80%D5%B4%D5%A1%D6%81%D5%AB%D5%B8%D5%B6_%D6%83%D5%B6%D5%BF%D6%80%D5%B8%D6%82%D5%B4" title="Ինֆորմացիոն փնտրում – Armenian" lang="hy" hreflang="hy" data-title="Ինֆորմացիոն փնտրում" data-language-autonym="Հայերեն" data-language-local-name="Armenian" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Algoritma_pencarian" title="Algoritma pencarian – Indonesian" lang="id" hreflang="id" data-title="Algoritma pencarian" 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/Algorithmo_de_recerca" title="Algorithmo de recerca – Interlingua" lang="ia" hreflang="ia" data-title="Algorithmo de recerca" data-language-autonym="Interlingua" data-language-local-name="Interlingua" class="interlanguage-link-target"><span>Interlingua</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Algoritmo_di_ricerca" title="Algoritmo di ricerca – Italian" lang="it" hreflang="it" data-title="Algoritmo di ricerca" 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%90%D7%9C%D7%92%D7%95%D7%A8%D7%99%D7%AA%D7%9D_%D7%97%D7%99%D7%A4%D7%95%D7%A9" title="אלגוריתם חיפוש – Hebrew" lang="he" hreflang="he" data-title="אלגוריתם חיפוש" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Keres%C5%91algoritmus" title="Keresőalgoritmus – Hungarian" lang="hu" hreflang="hu" data-title="Keresőalgoritmus" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Algoritma_gelintar" title="Algoritma gelintar – Malay" lang="ms" hreflang="ms" data-title="Algoritma gelintar" data-language-autonym="Bahasa Melayu" data-language-local-name="Malay" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Zoekalgoritme" title="Zoekalgoritme – Dutch" lang="nl" hreflang="nl" data-title="Zoekalgoritme" 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/%E6%8E%A2%E7%B4%A2" title="探索 – Japanese" lang="ja" hreflang="ja" data-title="探索" 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-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Algoritmo_de_busca" title="Algoritmo de busca – Portuguese" lang="pt" hreflang="pt" data-title="Algoritmo de busca" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Search_algorithm" title="Search algorithm – Simple English" lang="en-simple" hreflang="en-simple" data-title="Search algorithm" 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-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%90%D0%BB%D0%B3%D0%BE%D1%80%D0%B8%D1%82%D0%BC%D0%B8_%D0%BF%D1%80%D0%B5%D1%82%D1%80%D0%B0%D0%B6%D0%B8%D0%B2%D0%B0%D1%9A%D0%B0" title="Алгоритми претраживања – Serbian" lang="sr" hreflang="sr" data-title="Алгоритми претраживања" data-language-autonym="Српски / srpski" data-language-local-name="Serbian" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Hakualgoritmi" title="Hakualgoritmi – Finnish" lang="fi" hreflang="fi" data-title="Hakualgoritmi" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%82%E0%B8%B1%E0%B9%89%E0%B8%99%E0%B8%95%E0%B8%AD%E0%B8%99%E0%B8%A7%E0%B8%B4%E0%B8%98%E0%B8%B5%E0%B8%81%E0%B8%B2%E0%B8%A3%E0%B8%84%E0%B9%89%E0%B8%99%E0%B8%AB%E0%B8%B2" title="ขั้นตอนวิธีการค้นหา – Thai" lang="th" hreflang="th" data-title="ขั้นตอนวิธีการค้นหา" data-language-autonym="ไทย" data-language-local-name="Thai" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Arama_algoritmas%C4%B1" title="Arama algoritması – Turkish" lang="tr" hreflang="tr" data-title="Arama algoritması" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%90%D0%BB%D0%B3%D0%BE%D1%80%D0%B8%D1%82%D0%BC_%D0%BF%D0%BE%D1%88%D1%83%D0%BA%D1%83" title="Алгоритм пошуку – Ukrainian" lang="uk" hreflang="uk" data-title="Алгоритм пошуку" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/Gi%E1%BA%A3i_thu%E1%BA%ADt_t%C3%ACm_ki%E1%BA%BFm" title="Giải thuật tìm kiếm – Vietnamese" lang="vi" hreflang="vi" data-title="Giải thuật tìm kiếm" data-language-autonym="Tiếng Việt" data-language-local-name="Vietnamese" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E6%90%9C%E5%B0%8B%E6%BC%94%E7%AE%97%E6%B3%95" title="搜尋演算法 – Cantonese" lang="yue" hreflang="yue" data-title="搜尋演算法" data-language-autonym="粵語" data-language-local-name="Cantonese" class="interlanguage-link-target"><span>粵語</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E6%90%9C%E7%B4%A2%E7%AE%97%E6%B3%95" title="搜索算法 – Chinese" lang="zh" hreflang="zh" data-title="搜索算法" data-language-autonym="中文" data-language-local-name="Chinese" class="interlanguage-link-target"><span>中文</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q755673#sitelinks-wikipedia" title="Edit interlanguage links" class="wbc-editpage">Edit links</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Namespaces"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul 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.ambox .mbox-text-span{display:list-item;line-height:1.5em;list-style-type:disc}body.skin-minerva .mw-parser-output .multiple-issues-text>.mw-collapsible-toggle,.mw-parser-output .compact-ambox .ambox .mbox-image,.mw-parser-output .compact-ambox .ambox .mbox-imageright,.mw-parser-output .compact-ambox .ambox .mbox-empty-cell,.mw-parser-output .compact-ambox .hide-when-compact{display:none}</style><table class="box-Multiple_issues plainlinks metadata ambox ambox-content ambox-multiple_issues compact-ambox" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/b/b4/Ambox_important.svg/40px-Ambox_important.svg.png" decoding="async" width="40" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/b/b4/Ambox_important.svg/60px-Ambox_important.svg.png 1.5x, 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typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/f/f2/Edit-clear.svg/40px-Edit-clear.svg.png" decoding="async" width="40" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/f/f2/Edit-clear.svg/60px-Edit-clear.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/f/f2/Edit-clear.svg/80px-Edit-clear.svg.png 2x" data-file-width="48" data-file-height="48" /></span></span></div></td><td class="mbox-text"><div class="mbox-text-span">This article <b>focuses too much on specific examples</b>.<span class="hide-when-compact"> Please help <a class="external text" href="https://en.wikipedia.org/w/index.php?title=Search_algorithm&action=edit">improve this article</a> by adding <a href="/wiki/Wikipedia:Writing_better_articles#Provide_context_for_the_reader" title="Wikipedia:Writing better articles">sources that evaluate within a broader context</a>.</span> <span class="date-container"><i>(<span class="date">December 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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=%22Search+algorithm%22">"Search algorithm"</a> – <a rel="nofollow" class="external text" href="https://www.google.com/search?tbm=nws&q=%22Search+algorithm%22+-wikipedia&tbs=ar:1">news</a> <b>·</b> <a rel="nofollow" class="external text" href="https://www.google.com/search?&q=%22Search+algorithm%22&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=%22Search+algorithm%22+-wikipedia">books</a> <b>·</b> <a rel="nofollow" class="external text" href="https://scholar.google.com/scholar?q=%22Search+algorithm%22">scholar</a> <b>·</b> <a rel="nofollow" class="external text" href="https://www.jstor.org/action/doBasicSearch?Query=%22Search+algorithm%22&acc=on&wc=on">JSTOR</a></span></small></span> <span class="date-container"><i>(<span class="date">April 2016</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> </div> </div><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> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Hash_table_3_1_1_0_1_0_0_SP.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/7d/Hash_table_3_1_1_0_1_0_0_SP.svg/260px-Hash_table_3_1_1_0_1_0_0_SP.svg.png" decoding="async" width="260" height="190" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/7d/Hash_table_3_1_1_0_1_0_0_SP.svg/390px-Hash_table_3_1_1_0_1_0_0_SP.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/7d/Hash_table_3_1_1_0_1_0_0_SP.svg/520px-Hash_table_3_1_1_0_1_0_0_SP.svg.png 2x" data-file-width="315" data-file-height="230" /></a><figcaption>Visual representation of a <a href="/wiki/Hash_table" title="Hash table">hash table</a>, a <a href="/wiki/Data_structure" title="Data structure">data structure</a> that allows for fast retrieval of information</figcaption></figure> <p>In <a href="/wiki/Computer_science" title="Computer science">computer science</a>, a <b>search algorithm</b> is an <a href="/wiki/Algorithm" title="Algorithm">algorithm</a> designed to solve a <a href="/wiki/Search_problem" title="Search problem">search problem</a>. Search algorithms work to retrieve information stored within particular <a href="/wiki/Data_structure" title="Data structure">data structure</a>, or calculated in the <a href="/wiki/Feasible_region" title="Feasible region">search space</a> of a problem domain, with <a href="/wiki/Continuous_or_discrete_variable" title="Continuous or discrete variable">either discrete or continuous values</a>. </p><p>Although <a href="/wiki/Search_engine_(computing)" title="Search engine (computing)">search engines</a> use search algorithms, they belong to the study of <a href="/wiki/Information_retrieval" title="Information retrieval">information retrieval</a>, not algorithmics. </p><p>The appropriate search algorithm to use often depends on the data structure being searched, and may also include prior knowledge about the data. Search algorithms can be made faster or more efficient by specially constructed database structures, such as <a href="/wiki/Search_tree" title="Search tree">search trees</a>, <a href="/wiki/Hash_map" class="mw-redirect" title="Hash map">hash maps</a>, and <a href="/wiki/Database_index" title="Database index">database indexes</a>.<sup id="cite_ref-FOOTNOTEBeameFich200239_1-0" class="reference"><a href="#cite_note-FOOTNOTEBeameFich200239-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-FOOTNOTEKnuth1998§6.5_("Retrieval_on_Secondary_Keys")_2-0" class="reference"><a href="#cite_note-FOOTNOTEKnuth1998§6.5_("Retrieval_on_Secondary_Keys")-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p><p>Search algorithms can be classified based on their mechanism of searching into three types of algorithms: linear, binary, and hashing. <a href="/wiki/Linear_search" title="Linear search">Linear search</a> algorithms check every record for the one associated with a target key in a linear fashion.<sup id="cite_ref-FOOTNOTEKnuth1998§6.1_("Sequential_Searching")_3-0" class="reference"><a href="#cite_note-FOOTNOTEKnuth1998§6.1_("Sequential_Searching")-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Binary_search_algorithm" class="mw-redirect" title="Binary search algorithm">Binary, or half-interval, searches</a> repeatedly target the center of the search structure and divide the search space in half. Comparison search algorithms improve on linear searching by successively eliminating records based on comparisons of the keys until the target record is found, and can be applied on data structures with a defined order.<sup id="cite_ref-FOOTNOTEKnuth1998§6.2_("Searching_by_Comparison_of_Keys")_4-0" class="reference"><a href="#cite_note-FOOTNOTEKnuth1998§6.2_("Searching_by_Comparison_of_Keys")-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> Digital search algorithms work based on the properties of digits in data structures by using numerical keys.<sup id="cite_ref-FOOTNOTEKnuth1998§6.3_(Digital_Searching)_5-0" class="reference"><a href="#cite_note-FOOTNOTEKnuth1998§6.3_(Digital_Searching)-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> Finally, <a href="/wiki/Hash_table" title="Hash table">hashing</a> directly maps keys to records based on a <a href="/wiki/Hash_function" title="Hash function">hash function</a>.<sup id="cite_ref-FOOTNOTEKnuth1998§6.4,_(Hashing)_6-0" class="reference"><a href="#cite_note-FOOTNOTEKnuth1998§6.4,_(Hashing)-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </p><p>Algorithms are often evaluated by their <a href="/wiki/Computational_complexity" title="Computational complexity">computational complexity</a>, or maximum theoretical run time. Binary search functions, for example, have a maximum complexity of <span class="texhtml"><i>O</i>(log <i>n</i>)</span>, or logarithmic time. In simple terms, the maximum number of operations needed to find the search target is a logarithmic function of the size of the search space. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Applications_of_search_algorithms">Applications of search algorithms</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Search_algorithm&action=edit&section=1" title="Edit section: Applications of search algorithms"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Specific applications of search algorithms include: </p> <ul><li>Problems in <a href="/wiki/Combinatorial_optimization" title="Combinatorial optimization">combinatorial optimization</a>, such as: <ul><li>The <a href="/wiki/Vehicle_routing_problem" title="Vehicle routing problem">vehicle routing problem</a>, a form of <a href="/wiki/Shortest_path_problem" title="Shortest path problem">shortest path problem</a></li> <li>The <a href="/wiki/Knapsack_problem" title="Knapsack problem">knapsack problem</a>: Given a set of items, each with a weight and a value, determine the number of each item to include in a collection so that the total weight is less than or equal to a given limit and the total value is as large as possible.</li> <li>The <a href="/wiki/Nurse_scheduling_problem" title="Nurse scheduling problem">nurse scheduling problem</a></li></ul></li> <li>Problems in <a href="/wiki/Constraint_satisfaction" title="Constraint satisfaction">constraint satisfaction</a>, such as: <ul><li>The <a href="/wiki/Map_coloring_problem" class="mw-redirect" title="Map coloring problem">map coloring problem</a></li> <li>Filling in a <a href="/wiki/Sudoku" title="Sudoku">sudoku</a> or <a href="/wiki/Crossword_puzzle" class="mw-redirect" title="Crossword puzzle">crossword puzzle</a></li></ul></li> <li>In <a href="/wiki/Game_theory" title="Game theory">game theory</a> and especially <a href="/wiki/Combinatorial_game_theory" title="Combinatorial game theory">combinatorial game theory</a>, choosing the best move to make next (such as with the <a href="/wiki/Minmax" class="mw-redirect" title="Minmax">minmax</a> algorithm)</li> <li>Finding a combination or password from the whole set of possibilities</li> <li><a href="/wiki/Factorization" title="Factorization">Factoring</a> an integer (an important problem in <a href="/wiki/Cryptography" title="Cryptography">cryptography</a>)</li> <li>Search engine optimization (SEO) and content optimization for web crawlers</li> <li>Optimizing an industrial process, such as a <a href="/wiki/Chemical_reaction" title="Chemical reaction">chemical reaction</a>, by changing the parameters of the process (like temperature, pressure, and pH)</li> <li>Retrieving a record from a <a href="/wiki/Database" title="Database">database</a></li> <li>Finding the maximum or minimum value in a <a href="/wiki/List_(abstract_data_type)" title="List (abstract data type)">list</a> or <a href="/wiki/Array_data_structure" class="mw-redirect" title="Array data structure">array</a></li> <li>Checking to see if a given value is present in a set of values</li></ul> <div class="mw-heading mw-heading2"><h2 id="Classes">Classes</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Search_algorithm&action=edit&section=2" title="Edit section: Classes"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="For_virtual_search_spaces">For virtual search spaces</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Search_algorithm&action=edit&section=3" title="Edit section: For virtual search spaces"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></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">See also: <a href="/wiki/Solver" title="Solver">Solver</a></div> <p>Algorithms for searching virtual spaces are used in the <a href="/wiki/Constraint_satisfaction_problem" title="Constraint satisfaction problem">constraint satisfaction problem</a>, where the goal is to find a set of value assignments to certain variables that will satisfy specific mathematical <a href="/wiki/Equation" title="Equation">equations</a> and <a href="/wiki/Inequation" title="Inequation">inequations</a> / equalities. They are also used when the goal is to find a variable assignment that will <a href="/wiki/Discrete_optimization" title="Discrete optimization">maximize or minimize</a> a certain function of those variables. Algorithms for these problems include the basic <a href="/wiki/Brute-force_search" title="Brute-force search">brute-force search</a> (also called "naïve" or "uninformed" search), and a variety of <a href="/wiki/Heuristic_function" class="mw-redirect" title="Heuristic function">heuristics</a> that try to exploit partial knowledge about the structure of this space, such as linear relaxation, constraint generation, and <a href="/wiki/Local_consistency" title="Local consistency">constraint propagation</a>. </p><p>An important subclass are the <a href="/wiki/Local_search_(optimization)" title="Local search (optimization)">local search</a> methods, that view the elements of the search space as the <a href="/wiki/Vertex_(graph_theory)" title="Vertex (graph theory)">vertices</a> of a graph, with edges defined by a set of heuristics applicable to the case; and scan the space by moving from item to item along the edges, for example according to the <a href="/wiki/Gradient_descent" title="Gradient descent">steepest descent</a> or <a href="/wiki/Best-first_search" title="Best-first search">best-first</a> criterion, or in a <a href="/wiki/Stochastic_optimization" title="Stochastic optimization">stochastic search</a>. This category includes a great variety of general <a href="/wiki/Metaheuristic" title="Metaheuristic">metaheuristic</a> methods, such as <a href="/wiki/Simulated_annealing" title="Simulated annealing">simulated annealing</a>, <a href="/wiki/Tabu_search" title="Tabu search">tabu search</a>, A-teams, and <a href="/wiki/Genetic_programming" title="Genetic programming">genetic programming</a>, that combine arbitrary heuristics in specific ways. The opposite of local search would be global search methods. This method is applicable when the search space is not limited and all aspects of the given network are available to the entity running the search algorithm.<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>This class also includes various <a href="/wiki/Tree_traversal" title="Tree traversal">tree search algorithms</a>, that view the elements as vertices of a <a href="/wiki/Tree_(graph_theory)" title="Tree (graph theory)">tree</a>, and traverse that tree in some special order. Examples of the latter include the exhaustive methods such as <a href="/wiki/Depth-first_search" title="Depth-first search">depth-first search</a> and <a href="/wiki/Breadth-first_search" title="Breadth-first search">breadth-first search</a>, as well as various heuristic-based <a href="/wiki/Pruning_(decision_trees)" class="mw-redirect" title="Pruning (decision trees)">search tree pruning</a> methods such as <a href="/wiki/Backtracking" title="Backtracking">backtracking</a> and <a href="/wiki/Branch_and_bound" title="Branch and bound">branch and bound</a>. Unlike general metaheuristics, which at best work only in a probabilistic sense, many of these tree-search methods are guaranteed to find the exact or optimal solution, if given enough time. This is called "<a href="/wiki/Completeness_(logic)" title="Completeness (logic)">completeness</a>". </p><p>Another important sub-class consists of algorithms for exploring the <a href="/wiki/Game_tree" title="Game tree">game tree</a> of multiple-player games, such as <a href="/wiki/Chess" title="Chess">chess</a> or <a href="/wiki/Backgammon" title="Backgammon">backgammon</a>, whose nodes consist of all possible game situations that could result from the current situation. The goal in these problems is to find the move that provides the best chance of a win, taking into account all possible moves of the opponent(s). Similar problems occur when humans or machines have to make successive decisions whose outcomes are not entirely under one's control, such as in <a href="/wiki/Robot" title="Robot">robot</a> guidance or in <a href="/wiki/Marketing" title="Marketing">marketing</a>, <a href="/wiki/Finance" title="Finance">financial</a>, or <a href="/wiki/Military" title="Military">military</a> strategy planning. This kind of problem — <a href="/wiki/Combinatorial_search" title="Combinatorial search">combinatorial search</a> — has been extensively studied in the context of <a href="/wiki/Artificial_intelligence" title="Artificial intelligence">artificial intelligence</a>. Examples of algorithms for this class are the <a href="/wiki/Minimax" title="Minimax">minimax algorithm</a>, <a href="/wiki/Alpha%E2%80%93beta_pruning" title="Alpha–beta pruning">alpha–beta pruning</a>, and the <a href="/wiki/A*_search_algorithm" title="A* search algorithm">A* algorithm</a> and its variants. </p> <div class="mw-heading mw-heading3"><h3 id="For_sub-structures_of_a_given_structure">For sub-structures of a given structure</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Search_algorithm&action=edit&section=4" title="Edit section: For sub-structures of a given structure"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The name "combinatorial search" is generally used for algorithms that look for a specific sub-structure of a given <a href="/wiki/Discrete_mathematics" title="Discrete mathematics">discrete structure</a>, such as a graph, a <a href="/wiki/String_(computer_science)" title="String (computer science)">string</a>, a finite <a href="/wiki/Group_(mathematics)" title="Group (mathematics)">group</a>, and so on. The term <a href="/wiki/Combinatorial_optimization" title="Combinatorial optimization">combinatorial optimization</a> is typically used when the goal is to find a sub-structure with a maximum (or minimum) value of some parameter. (Since the sub-structure is usually represented in the computer by a set of integer variables with constraints, these problems can be viewed as special cases of constraint satisfaction or discrete optimization; but they are usually formulated and solved in a more abstract setting where the internal representation is not explicitly mentioned.) </p><p>An important and extensively studied subclass are the <a href="/wiki/List_of_algorithms#Graph_algorithms" title="List of algorithms">graph algorithms</a>, in particular <a href="/wiki/Graph_traversal" title="Graph traversal">graph traversal</a> algorithms, for finding specific sub-structures in a given graph — such as <a href="/wiki/Glossary_of_graph_theory#Subgraphs" title="Glossary of graph theory">subgraphs</a>, <a href="/wiki/Path_(graph_theory)" title="Path (graph theory)">paths</a>, circuits, and so on. Examples include <a href="/wiki/Dijkstra%27s_algorithm" title="Dijkstra's algorithm">Dijkstra's algorithm</a>, <a href="/wiki/Kruskal%27s_algorithm" title="Kruskal's algorithm">Kruskal's algorithm</a>, the <a href="/wiki/Nearest_neighbour_algorithm" title="Nearest neighbour algorithm">nearest neighbour algorithm</a>, and <a href="/wiki/Prim%27s_algorithm" title="Prim's algorithm">Prim's algorithm</a>. </p><p>Another important subclass of this category are the <a href="/wiki/String_searching_algorithm" class="mw-redirect" title="String searching algorithm">string searching algorithms</a>, that search for patterns within strings. Two famous examples are the <a href="/wiki/Boyer%E2%80%93Moore_string-search_algorithm" title="Boyer–Moore string-search algorithm">Boyer–Moore</a> and <a href="/wiki/Knuth%E2%80%93Morris%E2%80%93Pratt_algorithm" title="Knuth–Morris–Pratt algorithm">Knuth–Morris–Pratt algorithms</a>, and several algorithms based on the <a href="/wiki/Suffix_tree" title="Suffix tree">suffix tree</a> data structure. </p> <div class="mw-heading mw-heading3"><h3 id="Search_for_the_maximum_of_a_function">Search for the maximum of a function</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Search_algorithm&action=edit&section=5" title="Edit section: Search for the maximum of a function"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In 1953, American <a href="/wiki/Statistics" title="Statistics">statistician</a> <a href="/wiki/Jack_Kiefer_(statistician)" title="Jack Kiefer (statistician)">Jack Kiefer</a> devised <a href="/wiki/Fibonacci_search_technique" title="Fibonacci search technique">Fibonacci search</a> which can be used to find the maximum of a unimodal function and has many other applications in computer science. </p> <div class="mw-heading mw-heading3"><h3 id="For_quantum_computers">For quantum computers</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Search_algorithm&action=edit&section=6" title="Edit section: For quantum computers"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>There are also search methods designed for <a href="/wiki/Quantum_computing" title="Quantum computing">quantum computers</a>, like <a href="/wiki/Grover%27s_algorithm" title="Grover's algorithm">Grover's algorithm</a>, that are theoretically faster than linear or brute-force search even without the help of data structures or heuristics. While the ideas and applications behind quantum computers are still entirely theoretical, studies have been conducted with algorithms like Grover's that accurately replicate the hypothetical physical versions of quantum computing systems.<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> </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=Search_algorithm&action=edit&section=7" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Backward_induction" title="Backward induction">Backward induction</a> – Process of reasoning backwards in sequence</li> <li><a href="/wiki/Content-addressable_memory" title="Content-addressable memory">Content-addressable memory</a> – Special type of computer memory used in certain very-high-speed searching applications hardware</li> <li><a href="/wiki/Dual-phase_evolution" title="Dual-phase evolution">Dual-phase evolution</a> – Process that drives self-organization within complex adaptive systems</li> <li><a href="/wiki/Linear_search_problem" title="Linear search problem">Linear search problem</a> – Computational search problem</li> <li><a href="/wiki/No_free_lunch_in_search_and_optimization" title="No free lunch in search and optimization">No free lunch in search and optimization</a> – Average solution cost is the same with any method</li> <li><a href="/wiki/Recommender_system" title="Recommender system">Recommender system</a> – Information filtering system to predict users' preferences, also use statistical methods to rank results in very large data sets</li> <li><a href="/wiki/Search_engine_(computing)" title="Search engine (computing)">Search engine (computing)</a> – System to help searching for information</li> <li><a href="/wiki/Search_game" title="Search game">Search game</a> – Two-person zero-sum game</li> <li><a href="/wiki/Selection_algorithm" title="Selection algorithm">Selection algorithm</a> – Method for finding kth smallest value</li> <li><a href="/wiki/Solver" title="Solver">Solver</a> – Software for a class of mathematical problems</li> <li><a href="/wiki/Sorting_algorithm" title="Sorting algorithm">Sorting algorithm</a> – Algorithm that arranges lists in order, necessary for executing certain search algorithms</li> <li><a href="/wiki/Web_search_engine" class="mw-redirect" title="Web search engine">Web search engine</a> – Software system for finding relevant information on the Web<span style="display:none" class="category-annotation-with-redirected-description">Pages displaying short descriptions of redirect targets</span></li></ul> <p>Categories: </p> <ul><li><a href="/wiki/Category:Search_algorithms" title="Category:Search algorithms">Category:Search algorithms</a></li></ul> <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=Search_algorithm&action=edit&section=8" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Citations">Citations</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Search_algorithm&action=edit&section=9" title="Edit section: Citations"><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 reflist-columns references-column-width" style="column-width: 30em;"> <ol class="references"> <li id="cite_note-FOOTNOTEBeameFich200239-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEBeameFich200239_1-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFBeameFich2002">Beame & Fich 2002</a>, p. 39.</span> </li> <li id="cite_note-FOOTNOTEKnuth1998§6.5_("Retrieval_on_Secondary_Keys")-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEKnuth1998§6.5_("Retrieval_on_Secondary_Keys")_2-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFKnuth1998">Knuth 1998</a>, §6.5 ("Retrieval on Secondary Keys").</span> </li> <li id="cite_note-FOOTNOTEKnuth1998§6.1_("Sequential_Searching")-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEKnuth1998§6.1_("Sequential_Searching")_3-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFKnuth1998">Knuth 1998</a>, §6.1 ("Sequential Searching").</span> </li> <li id="cite_note-FOOTNOTEKnuth1998§6.2_("Searching_by_Comparison_of_Keys")-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEKnuth1998§6.2_("Searching_by_Comparison_of_Keys")_4-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFKnuth1998">Knuth 1998</a>, §6.2 ("Searching by Comparison of Keys").</span> </li> <li id="cite_note-FOOTNOTEKnuth1998§6.3_(Digital_Searching)-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEKnuth1998§6.3_(Digital_Searching)_5-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFKnuth1998">Knuth 1998</a>, §6.3 (Digital Searching).</span> </li> <li id="cite_note-FOOTNOTEKnuth1998§6.4,_(Hashing)-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEKnuth1998§6.4,_(Hashing)_6-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFKnuth1998">Knuth 1998</a>, §6.4, (Hashing).</span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text"><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 a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFHunterPippenger2013" class="citation journal cs1">Hunter, A.H.; Pippenger, Nicholas (4 July 2013). "Local versus global search in channel graphs". <i>Networks: An International Journey</i>. <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/1004.2526">1004.2526</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Networks%3A+An+International+Journey&rft.atitle=Local+versus+global+search+in+channel+graphs&rft.date=2013-07-04&rft_id=info%3Aarxiv%2F1004.2526&rft.aulast=Hunter&rft.aufirst=A.H.&rft.au=Pippenger%2C+Nicholas&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASearch+algorithm" class="Z3988"></span></span> </li> <li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLópezGorinLara2008" class="citation journal cs1">López, G V; Gorin, T; Lara, L (26 February 2008). "Simulation of Grover's quantum search algorithm in an Ising-nuclear-spin-chain quantum computer with first- and second-nearest-neighbour couplings". <i>Journal of Physics B: Atomic, Molecular and Optical Physics</i>. <b>41</b> (5): 055504. <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/0710.3196">0710.3196</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2008JPhB...41e5504L">2008JPhB...41e5504L</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1088%2F0953-4075%2F41%2F5%2F055504">10.1088/0953-4075/41/5/055504</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:18796310">18796310</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Physics+B%3A+Atomic%2C+Molecular+and+Optical+Physics&rft.atitle=Simulation+of+Grover%27s+quantum+search+algorithm+in+an+Ising-nuclear-spin-chain+quantum+computer+with+first-+and+second-nearest-neighbour+couplings&rft.volume=41&rft.issue=5&rft.pages=055504&rft.date=2008-02-26&rft_id=info%3Aarxiv%2F0710.3196&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A18796310%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1088%2F0953-4075%2F41%2F5%2F055504&rft_id=info%3Abibcode%2F2008JPhB...41e5504L&rft.aulast=L%C3%B3pez&rft.aufirst=G+V&rft.au=Gorin%2C+T&rft.au=Lara%2C+L&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASearch+algorithm" class="Z3988"></span></span> </li> </ol></div> <div class="mw-heading mw-heading3"><h3 id="Bibliography">Bibliography</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Search_algorithm&action=edit&section=10" title="Edit section: Bibliography"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading4"><h4 id="Books">Books</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Search_algorithm&action=edit&section=11" title="Edit section: Books"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKnuth1998" class="citation book cs1"><a href="/wiki/Donald_Knuth" title="Donald Knuth">Knuth, Donald</a> (1998). <i>Sorting and Searching</i>. <a href="/wiki/The_Art_of_Computer_Programming" title="The Art of Computer Programming">The Art of Computer Programming</a>. Vol. 3 (2nd ed.). Reading, MA: Addison-Wesley Professional.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Sorting+and+Searching&rft.place=Reading%2C+MA&rft.series=The+Art+of+Computer+Programming&rft.edition=2nd&rft.pub=Addison-Wesley+Professional&rft.date=1998&rft.aulast=Knuth&rft.aufirst=Donald&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASearch+algorithm" class="Z3988"></span></li></ul> <div class="mw-heading mw-heading4"><h4 id="Articles">Articles</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Search_algorithm&action=edit&section=12" title="Edit section: Articles"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBeameFich2002" class="citation journal cs1">Beame, Paul; <a href="/wiki/Faith_Ellen" title="Faith Ellen">Fich, Faith</a> (August 2002). <a rel="nofollow" class="external text" href="https://doi.org/10.1006%2Fjcss.2002.1822">"Optimal Bounds for the Predecessor Problem and Related Problems"</a>. <i><a href="/wiki/Journal_of_Computer_and_System_Sciences" title="Journal of Computer and System Sciences">Journal of Computer and System Sciences</a></i>. <b>65</b> (1): 38–72. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1006%2Fjcss.2002.1822">10.1006/jcss.2002.1822</a></span>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:1991980">1991980</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Computer+and+System+Sciences&rft.atitle=Optimal+Bounds+for+the+Predecessor+Problem+and+Related+Problems&rft.volume=65&rft.issue=1&rft.pages=38-72&rft.date=2002-08&rft_id=info%3Adoi%2F10.1006%2Fjcss.2002.1822&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A1991980%23id-name%3DS2CID&rft.aulast=Beame&rft.aufirst=Paul&rft.au=Fich%2C+Faith&rft_id=https%3A%2F%2Fdoi.org%2F10.1006%252Fjcss.2002.1822&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASearch+algorithm" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation journal cs1">Schmittou, Thomas; Schmittou, Faith E. (2002-08-01). <a rel="nofollow" class="external text" href="https://doi.org/10.1006%2Fjcss.2002.1822">"Optimal Bounds for the Predecessor Problem and Related Problems"</a>. <i>Journal of Computer and System Sciences</i>. <b>65</b> (1): 38–72. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1006%2Fjcss.2002.1822">10.1006/jcss.2002.1822</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Computer+and+System+Sciences&rft.atitle=Optimal+Bounds+for+the+Predecessor+Problem+and+Related+Problems&rft.volume=65&rft.issue=1&rft.pages=38-72&rft.date=2002-08-01&rft_id=info%3Adoi%2F10.1006%2Fjcss.2002.1822&rft.aulast=Schmittou&rft.aufirst=Thomas&rft.au=Schmittou%2C+Faith+E.&rft_id=https%3A%2F%2Fdoi.org%2F10.1006%252Fjcss.2002.1822&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASearch+algorithm" class="Z3988"></span></li></ul> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Search_algorithm&action=edit&section=13" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239549316">.mw-parser-output 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structure">Data structures</a> and <a href="/wiki/Algorithm" title="Algorithm">algorithms</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Data structures</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/Array_(data_structure)" title="Array (data structure)">Array</a></li> <li><a href="/wiki/Associative_array" title="Associative array">Associative array</a></li> <li><a href="/wiki/Binary_search_tree" title="Binary search tree">Binary search tree</a></li> <li><a href="/wiki/Fenwick_tree" title="Fenwick tree">Fenwick tree</a></li> <li><a href="/wiki/Graph_(abstract_data_type)" title="Graph (abstract data type)">Graph</a></li> <li><a href="/wiki/Hash_table" title="Hash table">Hash table</a></li> <li><a href="/wiki/Heap_(data_structure)" title="Heap (data structure)">Heap</a></li> <li><a href="/wiki/Linked_list" title="Linked list">Linked list</a></li> <li><a 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href="/wiki/Randomized_algorithm" title="Randomized algorithm">Randomized</a></li> <li><a href="/wiki/Recursion_(computer_science)" title="Recursion (computer science)">Recursion</a></li> <li><a href="/wiki/Root-finding_algorithms" class="mw-redirect" title="Root-finding algorithms">Root-finding</a></li> <li><a href="/wiki/Sorting_algorithm" title="Sorting algorithm">Sorting</a></li> <li><a href="/wiki/Streaming_algorithm" title="Streaming algorithm">Streaming</a></li> <li><a href="/wiki/Sweep_line_algorithm" title="Sweep line algorithm">Sweep line</a></li> <li><a href="/wiki/String-searching_algorithm" title="String-searching algorithm">String-searching</a></li> <li><a href="/wiki/Topological_sorting" title="Topological sorting">Topological sorting</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> <li><a href="/wiki/List_of_algorithms" 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