Worst, Average and Best Case Analysis of Algorithms

<!DOCTYPE html>    <html lang="en-US" prefix="og: http://ogp.me/ns#" >  <head> <meta charset="UTF-8" /> <meta name="viewport" content="width=device-width, initial-scale=1.0, minimum-scale=0.5, maximum-scale=3.0"> <link rel="shortcut icon" href="https://media.geeksforgeeks.org/wp-content/cdn-uploads/gfg_favicon.png" type="image/x-icon" /> <link rel="preconnect" href="https://fonts.googleapis.com"> <link rel="preconnect" href="https://fonts.gstatic.com" crossorigin> <meta name="theme-color" content="#308D46" /> <meta name='robots' content='index, follow, max-image-preview:large, max-snippet:-1' /> <meta name="image" property="og:image" content="https://media.geeksforgeeks.org/wp-content/cdn-uploads/gfg_200x200-min.png"> <meta property="og:image:type" content="image/png"> <meta property="og:image:width" content="200"> <meta property="og:image:height" content="200"> <meta name="facebook-domain-verification" content="xo7t4ve2wn3ywfkjdvwbrk01pvdond" /> <meta property="og:title" content="Worst, Average and Best Case Analysis of Algorithms - GeeksforGeeks" /> <meta name="description" content="A Computer Science portal for geeks. It contains well written, well thought and well explained computer science and programming articles, quizzes and practice/competitive programming/company interview Questions." /> <meta property="og:url" content="https://www.geeksforgeeks.org/worst-average-and-best-case-analysis-of-algorithms/" /> <meta name="keywords" content="Data Structures, Algorithms, Python, Java, C, C++, JavaScript, Android Development, SQL, Data Science, Machine Learning, PHP, Web Development, System Design, Tutorial, Technical Blogs, Interview Experience, Interview Preparation, Programming, Competitive Programming, Jobs, Coding Contests, GATE CSE, HTML, CSS, React, NodeJS, Placement, Aptitude, Quiz, Computer Science, Programming Examples, GeeksforGeeks Courses, Puzzles, SSC, Banking, UPSC, Commerce, Finance, CBSE, School, k12, General Knowledge, News, Mathematics, Exams" /> <meta property="og:site_name" content="GeeksforGeeks" /> <meta property="og:image" content="http://www.geeksforgeeks.org/wp-content/uploads/gfg_200X200-1.png" /> <meta property="article:section" content="Algorithms" /> <meta property="article:tag" content="Complexity-analysis" /> <meta property="og:type" content="article" /> <meta property="og:locale" content="en_US" /> <meta property="article:published_time" content="2012-02-19 09:08:02+00:00" /> <meta property="article:modified_time" content="2024-11-11 12:22:09+00:00" /> <meta property="og:updated_time" content="2024-11-11 12:22:09+00:00" /> <meta property="og:image:secure_url" content="http://www.geeksforgeeks.org/wp-content/uploads/gfg_200X200-1.png" /> <meta property="og:description" content="A Computer Science portal for geeks. It contains well written, well thought and well explained computer science and programming articles, quizzes and practice/competitive programming/company interview Questions." /> <script src="https://cdnads.geeksforgeeks.org/synchronously_gfg_ads.min.js"></script> <script defer src="https://apis.google.com/js/platform.js"></script>        <script> var IHPWT={}; //Initialize Namespace var pbjs = pbjs || {}; pbjs.que = pbjs.que || []; var googletag = googletag || {}; googletag.cmd = googletag.cmd || []; var gptRan = false; </script> <script defer src="https://ads.pubmatic.com/AdServer/js/pwt/162080/12331/pwt.js"></script> <script defer src="https://securepubads.g.doubleclick.net/tag/js/gpt.js"></script> <script defer src="https://cdnads.geeksforgeeks.org/prebid.js?ver=0.1"></script> <script defer src="https://cdnads.geeksforgeeks.org/gfg_ads.min.js?ver=0.1"></script> <script> var video_api_response = JSON.parse("{\"id\":6796,\"title\":\"Analysis of Algorithms | Set 2 (Worst, Average and Best Cases)\",\"slug\":\"analysis-of-algorithms-set-2-worst-average-and-best-cases\",\"description\":\"<p><br>In the previous post, we discussed how Asymptotic analysis overcomes the problems of the naive way of analyzing algorithms. In this post, we will take an example of Linear Search and analyze it using Asymptotic analysis.<br>We can have three cases to analyze an algorithm: <br>1) The Worst Case <br>2) Average Case <br>3) Best Case<\/p><p><br>Analysis of Algorithms _ Set 2 (Worst, Average and Best Cases) : <a href=\\\"https:\/\/www.geeksforgeeks.org\/analysis-of-algorithms-set-2-asymptotic-analysis\/\\\">https:\/\/www.geeksforgeeks.org\/analysis-of-algorithms-set-2-asymptotic-analysis\/<\/a><\/p>\",\"source\":\"https:\/\/videos.geeksforgeeks.org\/hls\/0f0f48e5905d337d33a4fc54ae2fdab4gfg-AnalysisofAlgorithmsSet2WorstAverageandBestCasesGeeksforGeeks20220707182546.m3u8\",\"category\":[{\"term_id__id\":107,\"term_id__term_name\":\"Algorithm\",\"term_id__term_type\":2,\"term_id__slug\":\"algorithm\"},{\"term_id__id\":178,\"term_id__term_name\":\"Algorithms\",\"term_id__term_type\":1,\"term_id__slug\":\"algorithms\"},{\"term_id__id\":466,\"term_id__term_name\":\"complexity-analysis\",\"term_id__term_type\":2,\"term_id__slug\":\"complexity-analysis\"}],\"video_type\":\"geeksforgeeks\",\"meta\":{\"thumbnail\":\"https:\/\/media.geeksforgeeks.org\/geeksforgeeks\/AnalysisofAlgorithmsSet2WorstAverageandBestCases\/AnalysisofAlgorithmsSet220220721183003-small.png\",\"largeThumbnail\":\"https:\/\/media.geeksforgeeks.org\/geeksforgeeks\/AnalysisofAlgorithmsSet2WorstAverageandBestCases\/AnalysisofAlgorithmsSet220220721183003.jpg\",\"likes\":2,\"views\":43940,\"isFeatured\":0,\"isPremium\":0,\"isPublic\":0,\"format\":\"video\/mp4\",\"revision\":{}},\"time\":\"21\/07\/2022\",\"seo\":{\"description\":\"<p><br>In the previous post, we discussed how Asymptotic analysis overcomes\",\"thumbnail\":\"https:\/\/media.geeksforgeeks.org\/geeksforgeeks\/AnalysisofAlgorithmsSet2WorstAverageandBestCases\/AnalysisofAlgorithmsSet220220721183003-seo.png\"},\"subtitle\":\"https:\/\/videos.geeksforgeeks.org\/subtitles\/AnalysisofAlgorithmsSet2WorstAverageandBestCasesGeeksforGeeks20220707182546.vtt\",\"duration\":202,\"post_list\":[{\"post_id\":17020,\"post_title\":\"Analysis of Algorithms | Set 2 (Worst, Average and Best Cases)\"}],\"course_link\":null,\"views\":\"43940\",\"video_schema\":{\"@context\":\"https:\/\/schema.org\",\"@type\":\"VideoObject\",\"name\":\"Analysis of Algorithms Set 2 (Worst, Average and Best Cases)\",\"description\":\"In the previous post, we discussed how Asymptotic analysis overcomes the problems of the naive way of analyzing algorithms. In this post, we will take an example of Linear Search and analyze it using Asymptotic analysis.We can have three cases to analyze an algorithm nbsp1) The Worst Case nbsp2) Average Case nbsp3) Best CaseAnalysis of Algorithms Set 2 (Worst, Average and Best Cases) httpswww.geeksforgeeks.organalysis-of-algorithms-set-2-asymptotic-analysis\",\"thumbnailUrl\":[\"https:\/\/media.geeksforgeeks.org\/geeksforgeeks\/AnalysisofAlgorithmsSet2WorstAverageandBestCases\/AnalysisofAlgorithmsSet220220721183003-small.png\",\"https:\/\/media.geeksforgeeks.org\/geeksforgeeks\/AnalysisofAlgorithmsSet2WorstAverageandBestCases\/AnalysisofAlgorithmsSet220220721183003.jpg\",\"https:\/\/media.geeksforgeeks.org\/geeksforgeeks\/AnalysisofAlgorithmsSet2WorstAverageandBestCases\/AnalysisofAlgorithmsSet220220721183003-seo.png\"],\"uploadDate\":\"2022-07-21T18:30:23Z\",\"duration\":\"PT0H3M22S\",\"contentUrl\":\"https:\/\/www.geeksforgeeks.org\/videos\/analysis-of-algorithms-set-2-worst-average-and-best-cases\/\"}}"); </script>  <script defer src="https://assets.geeksforgeeks.org/codetabs/v3/codetabs.js" environment="production" domain="gfg" no-scroll></script> <title>Worst, Average and Best Case Analysis of Algorithms - GeeksforGeeks</title> <link rel="profile" href="http://gmpg.org/xfn/11" /> <link rel="pingback" href="" />   <script type="application/ld+json">{"@context":"https://schema.org","@type":"VideoObject","name":"Analysis of Algorithms Set 2 (Worst, Average and Best Cases)","description":"In the previous post, we discussed how Asymptotic analysis overcomes the problems of the naive way of analyzing algorithms. In this post, we will take an example of Linear Search and analyze it using Asymptotic analysis.We can have three cases to analyze an algorithm nbsp1) The Worst Case nbsp2) Average Case nbsp3) Best CaseAnalysis of Algorithms Set 2 (Worst, Average and Best Cases) httpswww.geeksforgeeks.organalysis-of-algorithms-set-2-asymptotic-analysis","thumbnailUrl":["https://media.geeksforgeeks.org/geeksforgeeks/AnalysisofAlgorithmsSet2WorstAverageandBestCases/AnalysisofAlgorithmsSet220220721183003-small.png","https://media.geeksforgeeks.org/geeksforgeeks/AnalysisofAlgorithmsSet2WorstAverageandBestCases/AnalysisofAlgorithmsSet220220721183003.jpg","https://media.geeksforgeeks.org/geeksforgeeks/AnalysisofAlgorithmsSet2WorstAverageandBestCases/AnalysisofAlgorithmsSet220220721183003-seo.png"],"uploadDate":"2022-07-21T18:30:23Z","duration":"PT0H3M22S","contentUrl":"https://www.geeksforgeeks.org/videos/analysis-of-algorithms-set-2-worst-average-and-best-cases/"}</script>   <script type="application/ld+json"> { "@context": "https://schema.org", "@type": "Article", "mainEntityOfPage": { "@type": "WebPage", "id": "https://www.geeksforgeeks.org/worst-average-and-best-case-analysis-of-algorithms/" }, "headline": "Worst, Average and Best Case Analysis of Algorithms", "datePublished": "2012-02-19 09:08:02", "dateModified": "2024-11-11 12:22:09", "image": { "@type": "ImageObject", "url": "https://media.geeksforgeeks.org/wp-content/uploads/gfg_200X200-100x100.png", "width": "100", "height": "100" }, "author": { "@type": "Organization", "name": "GeeksforGeeks", "url": "https://www.geeksforgeeks.org/", "logo": { "@type": "ImageObject", "url": "https://media.geeksforgeeks.org/wp-content/cdn-uploads/logo-new-2.svg", "width": "301", "height": "40" } }, "publisher": { "@type": "Organization", "name": "GeeksforGeeks", "url": "https://www.geeksforgeeks.org/", "logo": { "@type": "ImageObject", "url": "https://media.geeksforgeeks.org/wp-content/cdn-uploads/logo-new-2.svg", "width": "301", "height": "40" } }, "description": "In the previous post, we discussed how Asymptotic analysis overcomes the problems of the naive way of analyzing algorithms. Now let us learn about What is Worst, Average, and Best cases of an algorithm:1. Worst Case Analysis (Mostly used)&nbsp;In the worst-case analysis, we calculate the upper bound on the running", "about": [ { "@type": "Thing", "name": "Algorithm" }, { "@type": "Thing", "name": "Analysis" }, { "@type": "Thing", "name": "Dsa" }, { "@type": "Thing", "name": "ComplexityAnalysis" } ] }</script> <script type="application/ld+json"> { "@context": "https://schema.org", "@type": "WebSite", "name": "GeeksforGeeks", "url": "https://www.geeksforgeeks.org/", "potentialAction": { "@type": "SearchAction", "target": "https://www.geeksforgeeks.org/search/{search_term_string}/", "query-input": "required name=search_term_string" } }</script> <script type="application/ld+json"> { "@context": "https://schema.org", "@type": "Organization", "name": "GeeksforGeeks", "url": "https://www.geeksforgeeks.org/", "logo": "https://media.geeksforgeeks.org/wp-content/cdn-uploads/20200817185016/gfg_complete_logo_2x-min.png", "description": "A computer science portal for geeks. It contains well written, well thought and well explained computer science and programming articles, quizzes and practice/competitive programming/company interview Questions.", "founder": [ { "@type": "Person", "name": "Sandeep Jain", "url": "https://in.linkedin.com/in/sandeep-jain-b3940815" } ], "sameAs": [ "https://www.facebook.com/geeksforgeeks.org/", "https://twitter.com/geeksforgeeks", "https://www.linkedin.com/company/1299009", "https://www.youtube.com/geeksforgeeksvideos/" ] }</script> <script> var arrPostCat = new Array(); var arrPostCatName="DSA"; arrPostCat.push('1744'); arrPostCat.push('1745'); arrPostCat.push('6263'); var tIds = "1744,1745,6263,5940"; var termsNames = "Algorithms,DSA,AnalysisofAlgorithms,Complexityanalysis"; var tIdsInclusiveParents = "1744,1745,6263,5940"; var domain = 1; var arrPost = new Array(); var post_id = "17020"; var post_type = "post"; var post_slug = window.location.href; var ip = "64.252.70.56"; var post_title = `Worst, Average and Best Case Analysis of Algorithms`; var post_status = "publish"; var practiceAPIURL="https://practiceapi.geeksforgeeks.org/"; var practiceURL="https://practice.geeksforgeeks.org/"; var post_date = "2012-02-19 09:08:02"; var commentSysUrl = "https://discuss.geeksforgeeks.org/commentEmbedV2.js"; //var postAdApiUrlString = ""; var link_on_code_run = ''; var link_search_modal_top = ''; var country_code_cf = "US"; var postAdApiUrlString = '6263/1744/1744/1745/6263/5940/'; </script>  <link rel="canonical" href="https://www.geeksforgeeks.org/worst-average-and-best-case-analysis-of-algorithms/" /> <script type='application/ld+json'>{"@context":"https:\/\/schema.org","@type":"Organization","url":"https:\/\/www.geeksforgeeks.org\/","sameAs":[],"@id":"https:\/\/www.geeksforgeeks.org\/#organization","name":"GeeksforGeeks","logo":"http:\/\/www.geeksforgeeks.org\/wp-content\/uploads\/gfg_200X200-1.png"}</script>  <link rel='dns-prefetch' href='//cdn.geeksforgeeks.org' /> <link rel='dns-prefetch' href='//s.w.org' /> <script type="text/javascript"> window._wpemojiSettings = {"baseUrl":"https:\/\/s.w.org\/images\/core\/emoji\/11\/72x72\/","ext":".png","svgUrl":"https:\/\/s.w.org\/images\/core\/emoji\/11\/svg\/","svgExt":".svg","source":{"concatemoji":"https:\/\/www.geeksforgeeks.org\/wp-includes\/js\/wp-emoji-release.min.js?ver=4.9.8"}}; !function(a,b,c){function d(a,b){var c=String.fromCharCode;l.clearRect(0,0,k.width,k.height),l.fillText(c.apply(this,a),0,0);var d=k.toDataURL();l.clearRect(0,0,k.width,k.height),l.fillText(c.apply(this,b),0,0);var e=k.toDataURL();return d===e}function e(a){var b;if(!l||!l.fillText)return!1;switch(l.textBaseline="top",l.font="600 32px Arial",a){case"flag":return!(b=d([55356,56826,55356,56819],[55356,56826,8203,55356,56819]))&&(b=d([55356,57332,56128,56423,56128,56418,56128,56421,56128,56430,56128,56423,56128,56447],[55356,57332,8203,56128,56423,8203,56128,56418,8203,56128,56421,8203,56128,56430,8203,56128,56423,8203,56128,56447]),!b);case"emoji":return b=d([55358,56760,9792,65039],[55358,56760,8203,9792,65039]),!b}return!1}function f(a){var c=b.createElement("script");c.src=a,c.defer=c.type="text/javascript",b.getElementsByTagName("head")[0].appendChild(c)}var g,h,i,j,k=b.createElement("canvas"),l=k.getContext&&k.getContext("2d");for(j=Array("flag","emoji"),c.supports={everything:!0,everythingExceptFlag:!0},i=0;i<j.length;i++)c.supports[j[i]]=e(j[i]),c.supports.everything=c.supports.everything&&c.supports[j[i]],"flag"!==j[i]&&(c.supports.everythingExceptFlag=c.supports.everythingExceptFlag&&c.supports[j[i]]);c.supports.everythingExceptFlag=c.supports.everythingExceptFlag&&!c.supports.flag,c.DOMReady=!1,c.readyCallback=function(){c.DOMReady=!0},c.supports.everything||(h=function(){c.readyCallback()},b.addEventListener?(b.addEventListener("DOMContentLoaded",h,!1),a.addEventListener("load",h,!1)):(a.attachEvent("onload",h),b.attachEvent("onreadystatechange",function(){"complete"===b.readyState&&c.readyCallback()})),g=c.source||{},g.concatemoji?f(g.concatemoji):g.wpemoji&&g.twemoji&&(f(g.twemoji),f(g.wpemoji)))}(window,document,window._wpemojiSettings); </script> <style type="text/css"> img.wp-smiley, img.emoji { display: inline !important; border: none !important; box-shadow: none !important; height: 1em !important; width: 1em !important; margin: 0 .07em !important; vertical-align: -0.1em !important; background: none !important; padding: 0 !important; } </style> <link rel='stylesheet' id='custom-style-css' href='https://www.geeksforgeeks.org/wp-content/themes/iconic-one/css/gfg.min.css?ver=11.88' type='text/css' media='all' /> <script type='text/javascript' src='https://code.jquery.com/jquery-3.7.1.min.js?ver=3.7.1'></script> <script type='text/javascript' src='https://code.jquery.com/jquery-migrate-3.5.2.min.js?ver=3.5.2'></script> <script type='text/javascript'> /* <![CDATA[ */ var gfgObject = {"authUrl":"https:\/\/auth.geeksforgeeks.org\/","writeApiUrl":"https:\/\/apiwrite.geeksforgeeks.org\/","writeUrl":"https:\/\/write.geeksforgeeks.org\/","utilUrl":"https:\/\/util.geeksforgeeks.org\/","apiUrl":"https:\/\/api.geeksforgeeks.org\/","cfApiUrl":"https:\/\/gfgapi.geeksforgeeks.org\/","baseCompilerURL":"https:\/\/codejudge.geeksforgeeks.org\/","idePageBaseUrl":"https:\/\/ide.geeksforgeeks.org\/","gfgApiScriptUrl":"https:\/\/apiscript.geeksforgeeks.org\/","gfgSiteUrl":"https:\/\/www.geeksforgeeks.org\/","curatedListId":"1","curatedListTitle":"SDE Sheet Problems","utilDjangoCfUrl":"https:\/\/utilapi.geeksforgeeks.org\/","premiumCheckoutSlug":"premium-plans-payment\/","premiumLandingSlug":"premium-plans\/","premiumCssUrl":"https:\/\/www.geeksforgeeks.org\/wp-content\/themes\/iconic-one\/css\/gfgpremium.min.css?ver=1.6","premiumJsUrl":"https:\/\/www.geeksforgeeks.org\/wp-content\/themes\/iconic-one\/js\/gfgpremium.min.js?ver=1.5","utilGoogleUrl":"https:\/\/ugprod.geeksforgeeks.org\/","communityApiUrl":"https:\/\/communityapi.geeksforgeeks.org\/","utilDjangoUrl":"https:\/\/gfgutil.geeksforgeeks.org\/","gfgPracticeUrl":"https:\/\/practiceapi.geeksforgeeks.org\/","gfgMediaUrl":"https:\/\/media.geeksforgeeks.org\/","authDjangoApiUrl":"https:\/\/authapi.geeksforgeeks.org\/","gfgMlApiUrl":"https:\/\/recommendations.geeksforgeeks.org\/","is_home":"","is_category":"","userlevelPremiumPlus":"2","practiceUrl":"https:\/\/practice.geeksforgeeks.org\/","gfgNotificationsApiUrl":"https:\/\/notificationsapi.geeksforgeeks.org\/"}; /* ]]> */ </script> <script type='text/javascript' async="async" src='https://www.geeksforgeeks.org/wp-content/themes/iconic-one/js/gfg.min.js?ver=13.62'></script> <link rel='shortlink' href='https://www.geeksforgeeks.org/?p=17020' /> <style> #wpadminbar{ background: #ff0000 !important; } </style> <style type="text/css" id="custom-background-css"> body.custom-background { background-color: #ffffff; } </style> <link rel="icon" href="https://www.geeksforgeeks.org/wp-content/uploads/gfg_200X200-100x100.png" sizes="32x32" /> <link rel="icon" href="https://www.geeksforgeeks.org/wp-content/uploads/gfg_200X200.png" sizes="192x192" /> <link rel="apple-touch-icon-precomposed" href="https://www.geeksforgeeks.org/wp-content/uploads/gfg_200X200.png" /> <meta name="msapplication-TileImage" content="https://www.geeksforgeeks.org/wp-content/uploads/gfg_200X200.png" />  <style> #internal-promo-section{ display: none !important; } @media screen and (max-width:1500px) and (min-width:1280px){ body.single .article-page_flex .leftBar { flex-basis: calc(100% - 605px); max-width: calc(100% - 605px); min-width: calc(100% - 605px); } .sidebar_wrapper{ max-width: 300px; min-width: 300px; } div#secondary { min-width: 300px; max-width: 300px; } .widget-area{ padding: 0px; } .article-page_flex .rightBar{ padding: 20px 0px 0px 0px; } .article--viewer_content .a-wrapper .content { padding: 0px 10px 55px 20px; } .oinLeftbar { height: calc(100vh - 350px) !important; } } .autoLeftBar_oin_child{ height: 100% !important; } .autoLeftBar_oin_non_sticky{ height: unset !important; } .sideBar--wrap.newLeftbar > div[id^='GFG_AD_Leftsidebar_']:nth-of-type(1){ padding-top: 20px; } .sideBar--wrap.newLeftbar > div[id^='GFG_AD_Leftsidebar_']{ padding: 5px 0; } @media (max-width:1043px) and (min-width:992px) { .hide-1043992 { display: none!important; } } .mobile-header-list-item{ padding-left:30px; padding-right:10px; margin-top:5px; } .mobile-header-list{ border-bottom: 1px solid rgba(158, 158, 158, 0.3) !important; } .mobile-header-list .dropdown-title{ border-bottom: none !important; font-size: 16px!important; padding: 0px!important; padding-left: 45px!important; font-weight: normal; } .mobile-header-list .upside::after{ transform: rotate(180deg); } </style>    </head> <body class="post-template-default single single-post postid-17020 single-format-standard custom-background custom-background-white"> <script> // Dark mode script const gfgThemeList = Object.freeze({ LIGHT: "gfgThemeLight", DARK: "gfgThemeDark" }) const getThemeFromCookie = () => { let gfg_def_theme = ""; let cookies = document.cookie; let cooks = cookies.split(";"); for (let i = 0; i < cooks.length; i++) { let icook = cooks[i].split("="); if (icook[0].trim() == "gfg_theme") { gfg_def_theme = icook[1].trim(); } } return gfg_def_theme } if(!(post_slug.includes('premium-plans-payment/') || post_slug.includes('premium-plans/'))){ var isDarkMode = getThemeFromCookie() == gfgThemeList.DARK ? true : false; document.querySelector("body").setAttribute("data-dark-mode", isDarkMode); } function setSearchBarFocus() { const myTimeout = setTimeout(searchBarFocus, 0); function searchBarFocus() { document.getElementById("gcse-search-input").focus(); } } </script>  <nav> <div class="header-main__wrapper"> <a class="gfg-stc" style="top:0" href="#main">Skip to content</a> <a href="https://www.geeksforgeeks.org/" aria-label="Logo" class="header-main__logo"> <div class="_logo">  <img class="gfg_logo_img" style="height: 30px; width: 80px; max-width: fit-content;" src="https://media.geeksforgeeks.org/gfg-gg-logo.svg" alt="geeksforgeeks"> </div> </a> <div class="header-main__container">   <ul class="header-main__list"><li class="header-main__list-item Header_1" data-parent="false" aria-expanded="true" data-expandable="true"><span>Courses</span><i class="gfg-icon gfg-icon_arrow-down gfg-icon_header"></i><ul class="mega-dropdown Screen_1"><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/courses/dsa-to-development-coding-guide?itm_source=geeksforgeeks&itm_medium=main_header&itm_campaign=courses" target="_self">DSA to Development</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/courses/data-science-live?itm_source=geeksforgeeks&itm_medium=main_header&itm_campaign=courses" target="_self">Machine Learning & Data Science</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/courses/mastering-generative-ai-and-chat-gpt?itm_source=geeksforgeeks&itm_medium=main_header&itm_campaign=courses" target="_self">Generative AI & ChatGPT</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/courses/search?query=AWS&itm_source=geeksforgeeks&itm_medium=main_header&itm_campaign=courses" target="_self">Become AWS Certified</a></li><li class="mega-dropdown__list-item" data-parent="false" aria-expanded="true" data-expandable="true"><span>DSA Courses</span><i class="gfg-icon gfg-icon_arrow-right"></i><ul class="mega-dropdown Screen_2"><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/courses/dsa-self-paced?itm_source=geeksforgeeks&itm_medium=main_header&itm_campaign=courses" target="_self">Data Structure & Algorithm(C++/JAVA)</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/courses/Data-Structures-With-Python?itm_source=geeksforgeeks&itm_medium=main_header&itm_campaign=courses" target="_self">Data Structure & Algorithm(Python)</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/courses/data-structures-and-algorithms-in-javascript?itm_source=geeksforgeeks&itm_medium=main_header&itm_campaign=courses" target="_self">Data Structure & Algorithm(JavaScript)</a></li></ul></li><li class="mega-dropdown__list-item" data-parent="false" aria-expanded="true" data-expandable="true"><span>Programming Languages</span><i class="gfg-icon gfg-icon_arrow-right"></i><ul class="mega-dropdown Screen_2"><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/courses/cpp-programming-basic-to-advanced?itm_source=geeksforgeeks&itm_medium=main_header&itm_campaign=courses" target="_self">CPP</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/courses/Java-Programming-basic-to-advanced?itm_source=geeksforgeeks&itm_medium=main_header&itm_campaign=courses" target="_self">Java</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/courses/Python-Foundation?itm_source=geeksforgeeks&itm_medium=main_header&itm_campaign=courses" target="_self">Python</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/courses/javascript?itm_source=geeksforgeeks&itm_medium=main_header&itm_campaign=courses" target="_self">JavaScript</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/courses/c-Programming-basic-to-advanced?itm_source=geeksforgeeks&itm_medium=main_header&itm_campaign=courses" target="_self">C</a></li></ul></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/courses?itm_source=geeksforgeeks&itm_medium=main_header&itm_campaign=courses" target="_self">All Courses</a></li></ul></li><li class="header-main__list-item Header_2" data-parent="false" aria-expanded="true" data-expandable="true"><span>Tutorials</span><i class="gfg-icon gfg-icon_arrow-down gfg-icon_header"></i><ul class="mega-dropdown Screen_1"><li class="mega-dropdown__list-item" data-parent="false" aria-expanded="true" data-expandable="true"><span>Python</span><i class="gfg-icon gfg-icon_arrow-right"></i><ul class="mega-dropdown Screen_2"><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/python-programming-language-tutorial/?ref=outind" target="_self">Python Tutorial</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/python-programming-examples/?ref=outind" target="_self">Python Programs</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/python-quizzes/?ref=outind" target="_self">Python Quiz</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/python-projects-beginner-to-advanced/?ref=outind" target="_self">Python Projects</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/python-interview-questions/?ref=outind" target="_self">Python Interview Questions</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/python-data-structures-and-algorithms/?ref=outind" target="_self">Python Data Structures</a></li></ul></li><li class="mega-dropdown__list-item" data-parent="false" aria-expanded="true" data-expandable="true"><span>Java</span><i class="gfg-icon gfg-icon_arrow-right"></i><ul class="mega-dropdown Screen_2"><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/java/?ref=outind" target="_self">Java Tutorial</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/collections-in-java-2/?ref=outind" target="_self">Java Collections</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/java-8-features/?ref=outind" target="_self">Java 8 Tutorial</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/java-programming-examples/?ref=outind" target="_self">Java Programs</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/java-multiple-choice-questions/?ref=outind" target="_self">Java Quiz</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/java-projects/?ref=outind" target="_self">Java Projects</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/java-interview-questions/?ref=outind" target="_self">Java Interview Questions</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/advanced-java/?ref=outind" target="_self">Advanced Java</a></li></ul></li><li class="mega-dropdown__list-item" data-parent="false" aria-expanded="true" data-expandable="true"><span>Programming Languages</span><i class="gfg-icon gfg-icon_arrow-right"></i><ul class="mega-dropdown Screen_2"><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/javascript/?ref=outind" target="_self">JavaScript</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/c-plus-plus/?ref=outind" target="_self">C++</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/r-tutorial/?ref=outind" target="_self">R Tutorial</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/sql-tutorial/?ref=outind" target="_self">SQL</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/php-tutorial/?ref=outind" target="_self">PHP</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/csharp-programming-language/?ref=outind" target="_self">C#</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/c-programming-language/?ref=outind" target="_self">C</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/scala-programming-language/?ref=outind" target="_self">Scala</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/perl-programming-language/?ref=outind" target="_self">Perl</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/golang/?ref=outind" target="_self">Go Language</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/kotlin-programming-language/?ref=outind" target="_self">Kotlin</a></li></ul></li><li class="mega-dropdown__list-item" data-parent="false" aria-expanded="true" data-expandable="true"><a href="https://www.geeksforgeeks.org/data-structures/?ref=ghm" class="remove-anchor__decoration" target="_self" style="display: inline-flex; padding: 0;">System Design</a><i class="gfg-icon gfg-icon_arrow-right"></i><ul class="mega-dropdown Screen_2"><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/system-design-tutorial/?ref=ghm" target="_self">System Design Tutorial</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/software-design-patterns/?ref=outind" target="_self">Software Design Patterns</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/complete-roadmap-to-learn-system-design/?ref=outind" target="_self">System Design Roadmap</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/top-10-system-design-interview-questions-and-answers/?ref=outind" target="_self">Top 10 System Design Interview Questions and Answers</a></li></ul></li><li class="mega-dropdown__list-item" data-parent="false" aria-expanded="true" data-expandable="true"><span>Interview Corner</span><i class="gfg-icon gfg-icon_arrow-right"></i><ul class="mega-dropdown Screen_2"><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/company-preparation/?ref=outind" target="_self">Company Preparation</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/interview-preparation-for-software-developer/?ref=outind" target="_self">Top Topics</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://practice.geeksforgeeks.org/company-tags/?ref=outind" target="_self">Practice Company Questions</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/company-interview-corner/?ref=outind" target="_self">Interview Experiences</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/experienced-interview-experiences-company-wise/?ref=outind" target="_self">Experienced Interviews</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/internship-interview-experiences-company-wise/?ref=outind" target="_self">Internship Interviews</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/competitive-programming-a-complete-guide/?ref=outind" target="_self">Competitive Programming</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/quiz-corner-gq/?ref=outind" target="_self">Multiple Choice Quizzes</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/aptitude-questions-and-answers/?ref=outind" target="_self">Aptitude for Placements</a></li></ul></li><li class="mega-dropdown__list-item" data-parent="false" aria-expanded="true" data-expandable="true"><span>Computer Science Subjects</span><i class="gfg-icon gfg-icon_arrow-right"></i><ul class="mega-dropdown Screen_2"><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/operating-systems/?ref=outind" target="_self">Operating System</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/dbms/?ref=outind" target="_self">DBMS</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/computer-network-tutorials/?ref=outind" target="_self">Computer Networks</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/engineering-mathematics-tutorials/?ref=outind" target="_self">Engineering Mathematics</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/computer-organization-and-architecture-tutorials/?ref=outind" target="_self">Computer Organization and Architecture</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/theory-of-computation-automata-tutorials/?ref=outind" target="_self">Theory of Computation</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/compiler-design-tutorials/?ref=outind" target="_self">Compiler Design</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/digital-electronics-logic-design-tutorials/#blg/?ref=outind" target="_self">Digital Logic</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/software-engineering/?ref=outind" target="_self">Software Engineering</a></li></ul></li><li class="mega-dropdown__list-item" data-parent="false" aria-expanded="true" data-expandable="true"><span>DevOps</span><i class="gfg-icon gfg-icon_arrow-right"></i><ul class="mega-dropdown Screen_2"><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/git-tutorial/?ref=outind" target="_self">GIT</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/aws-tutorial/?ref=outind" target="_self">AWS</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/docker-tutorial/?ref=outind" target="_self">Docker</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/kubernetes-tutorial/?ref=outind" target="_self">Kubernetes</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/microsoft-azure/?ref=outind" target="_self">Microsoft Azure Tutorial</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/google-cloud-platform-tutorial/?ref=outind" target="_self">Google Cloud Platform</a></li></ul></li><li class="mega-dropdown__list-item" data-parent="false" aria-expanded="true" data-expandable="true"><span>Linux</span><i class="gfg-icon gfg-icon_arrow-right"></i><ul class="mega-dropdown Screen_2"><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/linux-tutorial/?ref=outind" target="_self">Linux Tutorial</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/linux-commands/?ref=outind" target="_self">Linux Commands A-Z</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/linux-commands-cheat-sheet/?ref=outind" target="_self">Linux Commands Cheatsheet</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/permissions-in-linux/?ref=outind" target="_self">File Permission Commands</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/beginners-guide-to-linux-system-administration/?ref=outind" target="_self">Linux System Administration</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/linux-file-system/?ref=outind" target="_self">Linux File System</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/introduction-linux-shell-shell-scripting/?ref=outind" target="_self">Linux Shell Scripting</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/network-configuration-trouble-shooting-commands-linux/?ref=outind" target="_self">Linux Networking</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/linux-interview-questions/?ref=outind" target="_self">Linux Interview Questions</a></li></ul></li><li class="mega-dropdown__list-item" data-parent="false" aria-expanded="true" data-expandable="true"><span>Software Testing</span><i class="gfg-icon gfg-icon_arrow-right"></i><ul class="mega-dropdown Screen_2"><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/software-testing-tutorial/?ref=outind" target="_self">Software Testing Tutorial</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/software-engineering/?ref=outind" target="_self">Software Engineering Tutorial</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/software-testing-interview-questions/?ref=outind" target="_self">Testing Interview Questions</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/jira-tutorial/?ref=outind" target="_self">Jira</a></li></ul></li><li class="mega-dropdown__list-item" data-parent="false" aria-expanded="true" data-expandable="true"><span>Databases</span><i class="gfg-icon gfg-icon_arrow-right"></i><ul class="mega-dropdown Screen_2"><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/dbms/?ref=outind" target="_self">DBMS Tutorial</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/sql-tutorial/?ref=outind" target="_self">SQL Tutorial</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/postgresql-tutorial/?ref=outind" target="_self">PostgreSQL Tutorial</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/mongodb-tutorial/?ref=outind" target="_self">MongoDB Tutorial</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/sql-interview-questions/?ref=outind" target="_self">SQL Interview Questions</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/mysql-interview-questions/?ref=outind" target="_self">MySQL Interview Questions</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/pl-sql-interview-questions/?ref=outind" target="_self">PL/SQL Interview Questions</a></li></ul></li><li class="mega-dropdown__list-item" data-parent="false" aria-expanded="true" data-expandable="true"><span>Android</span><i class="gfg-icon gfg-icon_arrow-right"></i><ul class="mega-dropdown Screen_2"><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/android-tutorial/?ref=outind" target="_self">Android Tutorial</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/android-studio-tutorial/?ref=outind" target="_self">Android Studio Tutorial</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/kotlin-android-tutorial/?ref=outind" target="_self">Kotlin For Android</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/android-projects-from-basic-to-advanced-level/?ref=outind" target="_self">Android Projects</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/top-50-android-interview-questions-answers-sde-i-to-sde-iii/?ref=outind" target="_self">Android Interview Questions</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/6-weeks-of-android-app-development-free-project-based-learning/?ref=outind" target="_self">6 Weeks of Android App Development</a></li></ul></li><li class="mega-dropdown__list-item" data-parent="false" aria-expanded="true" data-expandable="true"><span>Excel</span><i class="gfg-icon gfg-icon_arrow-right"></i><ul class="mega-dropdown Screen_2"><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/excel-tutorial/?ref=outind" target="_self">MS Excel Tutorial</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/introduction-to-ms-excel/?ref=outind" target="_self">Introduction to MS Excel</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/data-analysis-in-excel/?ref=outind" target="_self">Data Analysis in Excel</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/basic-excel-formulas-and-functions/?ref=outind" target="_self">Basic Excel Formulas & Functions</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/instant-data-analysis-in-advanced-excel/?ref=outind" target="_self">Data Analysis in Advanced Excel</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/workbooks-in-microsoft-excel/?ref=outind" target="_self">Workbooks</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/statistical-functions-in-excel-with-examples/?ref=outind" target="_self">Statistical Functions</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/data-visualization-in-excel/?ref=outind" target="_self">Data Visualization in Excel</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/pivot-tables-in-excel/?ref=outind" target="_self">Pivot Tables in Excel</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/working-with-excel-spreadsheets-in-python/?ref=outind" target="_self">Excel Spreadsheets in Python</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/basic-excel-shortcuts/?ref=outind" target="_self">Basic Excel Shortcuts</a></li></ul></li><li class="mega-dropdown__list-item" data-parent="false" aria-expanded="true" data-expandable="true"><span>Mathematics</span><i class="gfg-icon gfg-icon_arrow-right"></i><ul class="mega-dropdown Screen_2"><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/number-theory/?ref=outind" target="_self">Number System</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/algebra/?ref=outind" target="_self">Algebra</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/linear-algebra/?ref=outind" target="_self">Linear Algebra</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/math-trigonometry/?ref=outind" target="_self">Trigonometry</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/set-theory/?ref=outind" target="_self">Set Theory</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/statistics/?ref=outind" target="_self">Statistics</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/probability-in-maths/?ref=outind" target="_self">Probability</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/geometry/?ref=outind" target="_self">Geometry</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/mensuration/?ref=outind" target="_self">Mensuration</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/logarithms/?ref=outind" target="_self">Logarithms</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/math-calculus/?ref=outind" target="_self">Calculus</a></li></ul></li></ul></li><li class="header-main__list-item Header_3" data-parent="false" aria-expanded="true" data-expandable="true"><span>DSA</span><i class="gfg-icon gfg-icon_arrow-down gfg-icon_header"></i><ul class="mega-dropdown Screen_1"><li class="mega-dropdown__list-item" data-parent="false" aria-expanded="true" data-expandable="true"><span>Data Structures</span><i class="gfg-icon gfg-icon_arrow-right"></i><ul class="mega-dropdown Screen_2"><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/array-data-structure-guide/?ref=outind" target="_self">Arrays</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/matrix/?ref=outind" target="_self">Matrix</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/string-data-structure/?ref=outind" target="_self">Strings</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/introduction-to-linked-list-data-structure/?ref=ghm" target="_self">Linked List</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/stack-data-structure/?ref=outind" target="_self">Stack</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/queue-data-structure/?ref=outind" target="_self">Queue</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/introduction-to-tree-data-structure-and-algorithm-tutorials/?ref=outind" target="_self">Tree</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/heap-data-structure/?ref=outind" target="_self">Heap</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/hashing-data-structure/?ref=outind" target="_self">Hashing</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/graph-data-structure-and-algorithms/?ref=outind" target="_self">Graph</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/introduction-to-set-data-structure-and-algorithm-tutorials/?ref=outind" target="_self">Set Data Structure</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/introduction-to-map-data-structure-and-algorithm-tutorials/?ref=outind" target="_self">Map Data Structure</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/advanced-data-structures/?ref=outind" target="_self">Advanced Data Structure</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/introduction-to-data-structures/?ref=outind" target="_self">Data Structures Tutorial</a></li></ul></li><li class="mega-dropdown__list-item" data-parent="false" aria-expanded="true" data-expandable="true"><span>Algorithms</span><i class="gfg-icon gfg-icon_arrow-right"></i><ul class="mega-dropdown Screen_2"><li class="mega-dropdown__list-item" data-parent="false" aria-expanded="true" data-expandable="true"><span>Analysis of Algorithms</span><i class="gfg-icon gfg-icon_arrow-right"></i><ul class="mega-dropdown Screen_3"><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/design-and-analysis-of-algorithms/?ref=outind" target="_self">Design and Analysis of Algorithms</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/asymptotic-notation-and-analysis-based-on-input-size-of-algorithms/?ref=outind" target="_self">Asymptotic Analysis</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/types-of-asymptotic-notations-in-complexity-analysis-of-algorithms/?ref=outind" target="_self">Asymptotic Notations</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/worst-average-and-best-case-analysis-of-algorithms/?ref=outind" target="_self">Worst, Average and Best Cases</a></li></ul></li><li class="mega-dropdown__list-item" data-parent="false" aria-expanded="true" data-expandable="true"><span>Searching Algorithms</span><i class="gfg-icon gfg-icon_arrow-right"></i><ul class="mega-dropdown Screen_3"><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/linear-search/?ref=outind" target="_self">Linear Search</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/binary-search/?ref=outind" target="_self">Binary Search</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/searching-algorithms/?ref=outind" target="_self">Searching Algorithms Tutorial</a></li></ul></li><li class="mega-dropdown__list-item" data-parent="false" aria-expanded="true" data-expandable="true"><span>Sorting Algorithms</span><i class="gfg-icon gfg-icon_arrow-right"></i><ul class="mega-dropdown Screen_3"><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/selection-sort/?ref=outind" target="_self">Selection Sort</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/bubble-sort/?ref=outind" target="_self">Bubble Sort</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/insertion-sort/?ref=outind" target="_self">Insertion Sort</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/merge-sort/?ref=outind" target="_self">Merge Sort</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/quick-sort/?ref=outind" target="_self">Quick Sort</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/heap-sort/?ref=outind" target="_self">Heap Sort</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/counting-sort/?ref=outind" target="_self">Counting Sort</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/radix-sort/?ref=outind" target="_self">Radix Sort</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/bucket-sort-2/?ref=outind" target="_self">Bucket Sort</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/introduction-to-sorting-algorithm/?ref=outind" target="_self">Sorting Algorithms Tutorial</a></li></ul></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/introduction-to-greedy-algorithm-data-structures-and-algorithm-tutorials/?ref=outind" target="_self">Greedy Algorithms</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/introduction-to-dynamic-programming-data-structures-and-algorithm-tutorials/?ref=outind" target="_self">Dynamic Programming</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/introduction-to-graphs-data-structure-and-algorithm-tutorials/?ref=outind" target="_self">Graph Algorithms</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/introduction-to-pattern-searching-data-structure-and-algorithm-tutorial/?ref=outind" target="_self">Pattern Searching</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/introduction-to-recursion-data-structure-and-algorithm-tutorials/?ref=outind" target="_self">Recursion</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/introduction-to-backtracking-data-structure-and-algorithm-tutorials/?ref=outind" target="_self">Backtracking</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/introduction-to-divide-and-conquer-algorithm-data-structure-and-algorithm-tutorials/?ref=outind" target="_self">Divide and Conquer</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/mathematical-algorithms/?ref=outind" target="_self">Mathematical Algorithms</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/geometric-algorithms/?ref=outind" target="_self">Geometric Algorithms</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/introduction-to-bitwise-algorithms-data-structures-and-algorithms-tutorial/?ref=outind" target="_self">Bitwise Algorithms</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/randomized-algorithms/?ref=outind" target="_self">Randomized Algorithms</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/introduction-to-branch-and-bound-data-structures-and-algorithms-tutorial/?ref=outind" target="_self">Branch and Bound</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/introduction-to-algorithms/?ref=outind" target="_self">Algorithms Tutorial</a></li></ul></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/learn-data-structures-and-algorithms-dsa-tutorial/?ref=outind" target="_self">DSA Tutorial</a></li><li class="mega-dropdown__list-item" data-parent="false" aria-expanded="true" data-expandable="true"><span>Practice</span><i class="gfg-icon gfg-icon_arrow-right"></i><ul class="mega-dropdown Screen_2"><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/explore?page=1&sortBy=submissions&itm_source=geeksforgeeks&itm_medium=main_header_outIndia&itm_campaign=DSA_Header" target="_self">All DSA Problems</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/problem-of-the-day?itm_source=geeksforgeeksitm_source=geeksforgeeks&itm_medium=main_header_outIndia&itm_campaign=DSA_Header" target="_self">Problem of the Day</a></li><li class="mega-dropdown__list-item" data-parent="false" aria-expanded="true" data-expandable="true"><span>Company Wise Coding Practice</span><i class="gfg-icon gfg-icon_arrow-right"></i><ul class="mega-dropdown Screen_3"><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/explore?page=1&company=Amazon&sortBy=submissions&itm_source=geeksforgeeks&itm_medium=main_header_outIndia&itm_campaign=DSA_Header" target="_self">Amazon</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/explore?page=1&company=Microsoft&sortBy=submissions&itm_source=geeksforgeeks&itm_medium=main_header_outIndia&itm_campaign=DSA_Header" target="_self">Microsoft</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/explore?page=1&company=Flipkart&sortBy=submissions&itm_source=geeksforgeeks&itm_medium=main_header_outIndia&itm_campaign=DSA_Header" target="_self">Flipkart</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/explore?page=1&sortBy=submissions&itm_source=geeksforgeeks&itm_medium=main_header_outIndia&itm_campaign=DSA_Header" target="_self">Explore All</a></li></ul></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/explore?page=1&curated[]=1&sortBy=submissions&curated_names[]=SDE Sheet?itm_source=geeksforgeeks&itm_medium=main_header_outIndia&itm_campaign=DSA_Header" target="_self">GfG SDE Sheet</a></li><li class="mega-dropdown__list-item" data-parent="false" aria-expanded="true" data-expandable="true"><span>Practice Problems Difficulty Wise</span><i class="gfg-icon gfg-icon_arrow-right"></i><ul class="mega-dropdown Screen_3"><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/explore?page=1&difficulty=School&itm_source=geeksforgeeks&itm_medium=main_header_outIndia&itm_campaign=DSA_Header" target="_self">School</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/explore?page=1&difficulty=Basic&itm_source=geeksforgeeks&itm_medium=main_header_outIndia&itm_campaign=DSA_Header" target="_self">Basic</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/explore?page=1&difficulty=Easy&itm_source=geeksforgeeks&itm_medium=main_header_outIndia&itm_campaign=DSA_Header" target="_self">Easy</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/explore?page=1&difficulty=Medium&itm_source=geeksforgeeks&itm_medium=main_header_outIndia&itm_campaign=DSA_Header" target="_self">Medium</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/explore?page=1&difficulty=Hard&itm_source=geeksforgeeks&itm_medium=main_header_outIndia&itm_campaign=DSA_Header" target="_self">Hard</a></li></ul></li><li class="mega-dropdown__list-item" data-parent="false" aria-expanded="true" data-expandable="true"><span>Language Wise Coding Practice</span><i class="gfg-icon gfg-icon_arrow-right"></i><ul class="mega-dropdown Screen_3"><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/explore?page=1&category=CPP&itm_source=geeksforgeeks&itm_medium=main_header_outIndia&itm_campaign=DSA_Header" target="_self">CPP</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/explore?page=1&category=Java&itm_source=geeksforgeeks&itm_medium=main_header_outIndia&itm_campaign=DSA_Header" target="_self">Java</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/explore?category=python&itm_source=geeksforgeeks&itm_medium=main_header_outIndia&itm_campaign=DSA_Header" target="_self">Python</a></li></ul></li><li class="mega-dropdown__list-item" data-parent="false" aria-expanded="true" data-expandable="true"><span>Curated DSA Lists</span><i class="gfg-icon gfg-icon_arrow-right"></i><ul class="mega-dropdown Screen_3"><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/explore?page=1&sprint=ca8ae412173dbd8346c26a0295d098fd&sortBy=submissions&sprint_name=Beginner's DSA Sheet&itm_source=geeksforgeeks&itm_medium=main_header_outIndia&itm_campaign=DSA_Header" target="_self">Beginner's DSA Sheet</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/explore?page=1&sprint=50746f92a895c22a50504ac0c1fb9c84&sortBy=submissions&sprint_name=Top 50 Array Problems&itm_source=geeksforgeeks&itm_medium=main_header_outIndia&itm_campaign=DSA_Header" target="_self">Top 50 Array Problems</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/explore?page=1&sprint=57184072610b884e5df3584cc534115d&sortBy=submissions&sprint_name=Top 50 String Problems&itm_source=geeksforgeeks&itm_medium=main_header_outIndia&itm_campaign=DSA_Header" target="_self">Top 50 String Problems</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/explore?page=1&sprint=93d672753b74440c7427214c8ebf866d&sortBy=submissions&sprint_name=Top 50 DP Problems&itm_source=geeksforgeeks&itm_medium=main_header_outIndia&itm_campaign=DSA_Header" target="_self">Top 50 DP Problems</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/explore?page=1&sprint=405e9db0f353691ad3b2d546b19145e9&sortBy=submissions&sprint_name=Top 50 Graph Problems&itm_source=geeksforgeeks&itm_medium=main_header_outIndia&itm_campaign=DSA_Header" target="_self">Top 50 Graph Problems</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/explore?page=1&sprint=5f24de84b65bf7c4f4399c8111e26b81&sortBy=submissions&sprint_name=Top 50 Tree Problems&itm_source=geeksforgeeks&itm_medium=main_header_outIndia&itm_campaign=DSA_Header" target="_self">Top 50 Tree Problems</a></li></ul></li></ul></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/competitive-programming-a-complete-guide/?ref=outind" target="_self">Competitive Programming</a></li><li class="mega-dropdown__list-item" data-parent="false" aria-expanded="true" data-expandable="true"><span>Company Wise SDE Sheets</span><i class="gfg-icon gfg-icon_arrow-right"></i><ul class="mega-dropdown Screen_2"><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/facebookmeta-sde-sheet-interview-questions-and-answers/?ref=outind" target="_self">Facebook SDE Sheet</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/amazon-sde-sheet-interview-questions-and-answers/?ref=outind" target="_self">Amazon SDE Sheet</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/apple-sde-sheet-interview-questions-and-answers/?ref=outind" target="_self">Apple SDE Sheet</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/netflix-sde-sheet-interview-questions-and-answers/?ref=outind" target="_self">Netflix SDE Sheet</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/google-sde-sheet-interview-questions-and-answers/?ref=outind" target="_self">Google SDE Sheet</a></li></ul></li><li class="mega-dropdown__list-item" data-parent="false" aria-expanded="true" data-expandable="true"><span>DSA Cheat Sheets</span><i class="gfg-icon gfg-icon_arrow-right"></i><ul class="mega-dropdown Screen_2"><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/sde-sheet-a-complete-guide-for-sde-preparation/?ref=outind" target="_self">SDE Sheet</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/most-asked-dsa-interview-problems-for-beginners/?ref=outind" target="_self">DSA Sheet for Beginners</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/must-do-coding-questions-for-companies-like-amazon-microsoft-adobe/?ref=outind" target="_self">FAANG Coding Sheet</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/must-do-coding-questions-for-product-based-companies/?ref=outind" target="_self">Product-Based Coding Sheet</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/must-coding-questions-company-wise/?ref=outind" target="_self">Company-Wise Preparation Sheet</a></li></ul></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/top-100-data-structure-and-algorithms-dsa-interview-questions-topic-wise/?ref=outind" target="_self">Top Interview Questions</a></li><li class="mega-dropdown__list-item" data-parent="false" aria-expanded="true" data-expandable="true"><span>Puzzles</span><i class="gfg-icon gfg-icon_arrow-right"></i><ul class="mega-dropdown Screen_2"><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/puzzles/?ref=outind" target="_self">All Puzzles</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/top-100-puzzles-asked-in-interviews/?ref=outind" target="_self">Top 100 Puzzles Asked In Interviews</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/top-20-puzzles-commonly-asked-during-sde-interviews/?ref=outind" target="_self">Top 20 Puzzles Commonly Asked During SDE Interviews</a></li></ul></li></ul></li><li class="header-main__list-item Header_4" data-parent="false" aria-expanded="true" data-expandable="true"><span>Data Science</span><i class="gfg-icon gfg-icon_arrow-down gfg-icon_header"></i><ul class="mega-dropdown Screen_1"><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/python-programming-language/?ref=outind" target="_self">Python Tutorial</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/r-tutorial/?ref=outind" target="_self">R Tutorial</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/machine-learning/?ref=outind" target="_self">Machine Learning</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/data-science-with-python-tutorial/?ref=outind" target="_self">Data Science using Python</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/r-programming-for-data-science/?ref=outind" target="_self">Data Science using R</a></li><li class="mega-dropdown__list-item" data-parent="false" aria-expanded="true" data-expandable="true"><span>Data Science Packages</span><i class="gfg-icon gfg-icon_arrow-right"></i><ul class="mega-dropdown Screen_2"><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/pandas-tutorial/?ref=outind" target="_self">Pandas Tutorial</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/numpy-tutorial/?ref=outind" target="_self">NumPy Tutorial</a></li></ul></li><li class="mega-dropdown__list-item" data-parent="false" aria-expanded="true" data-expandable="true"><span>Data Visualization</span><i class="gfg-icon gfg-icon_arrow-right"></i><ul class="mega-dropdown Screen_2"><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/python-data-visualization-tutorial/?ref=outind" target="_self">Python Data Visualization Tutorial</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/data-visualization-in-r/?ref=outind" target="_self">Data Visualization with R</a></li></ul></li><li class="mega-dropdown__list-item" data-parent="false" aria-expanded="true" data-expandable="true"><span>Data Analysis</span><i class="gfg-icon gfg-icon_arrow-right"></i><ul class="mega-dropdown Screen_2"><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/data-analysis-with-python/?ref=outind" target="_self">Data Analysis with Python</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/data-analysis-using-r/?ref=outind" target="_self">Data Analysis with R</a></li></ul></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/deep-learning-tutorial/?ref=outind" target="_self">Deep Learning</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/natural-language-processing-nlp-tutorial/?ref=outind" target="_self">NLP Tutorial</a></li></ul></li><li class="header-main__list-item Header_5" data-parent="false" aria-expanded="true" data-expandable="true"><span>Web Tech</span><i class="gfg-icon gfg-icon_arrow-down gfg-icon_header"></i><ul class="mega-dropdown Screen_1"><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/html-tutorial/?ref=outind" target="_self">HTML Tutorial</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/css-tutorial/?ref=outind" target="_self">CSS Tutorial</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/javascript/?ref=outind" target="_self">JavaScript Tutorial</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/php-tutorial/?ref=outind" target="_self">PHP Tutorial</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/react-tutorial/?ref=outind" target="_self">ReactJS Tutorial</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/nodejs/?ref=outind" target="_self">NodeJS Tutorial</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/bootstrap/?ref=outind" target="_self">Bootstrap Tutorial</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/typescript/?ref=outind" target="_self">Typescript</a></li><li class="mega-dropdown__list-item" data-parent="false" aria-expanded="true" data-expandable="true"><span>Web Development Using Python</span><i class="gfg-icon gfg-icon_arrow-right"></i><ul class="mega-dropdown Screen_2"><li class="mega-dropdown__list-item" data-parent="false" aria-expanded="true" data-expandable="true"><span>Django</span><i class="gfg-icon gfg-icon_arrow-right"></i><ul class="mega-dropdown Screen_3"><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/django-tutorial/?ref=outind" target="_self">Django Tutorial</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/top-django-projects-for-beginners/?ref=outind" target="_self">Django Projects</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/django-interview-questions/?ref=outind" target="_self">Django Interview Questions</a></li></ul></li><li class="mega-dropdown__list-item" data-parent="false" aria-expanded="true" data-expandable="true"><span>Flask</span><i class="gfg-icon gfg-icon_arrow-right"></i><ul class="mega-dropdown Screen_3"><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/flask-tutorial/?ref=outind" target="_self">Flask Tutorial</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/flask-projects/?ref=outind" target="_self">Flask Projects</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/flask-interview-questions-and-answers/?ref=outind" target="_self">Flask Interview Questions</a></li></ul></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/postman-tutorial/?ref=outind" target="_self">Postman</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/introduction-to-github/?ref=outind" target="_self">Github</a></li></ul></li><li class="mega-dropdown__list-item" data-parent="false" aria-expanded="true" data-expandable="true"><span>Cheat Sheets</span><i class="gfg-icon gfg-icon_arrow-right"></i><ul class="mega-dropdown Screen_2"><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/html-cheat-sheet-a-basic-guide-to-html/?ref=outind" target="_self">HTML Cheat Sheet</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/css-cheat-sheet-a-basic-guide-to-css/?ref=outind" target="_self">CSS Cheat Sheet</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/javascript-cheat-sheet-a-basic-guide-to-javascript/?ref=outind" target="_self">JavaScript Cheat Sheet</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/react-cheat-sheet/?ref=outind" target="_self">React Cheat Sheet</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/angular-cheat-sheet-a-basic-guide-to-angular/?ref=outind" target="_self">Angular Cheat Sheet</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/jquery-cheat-sheet-a-basic-guide-to-jquery/?ref=outind" target="_self">jQuery Cheat Sheet</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/bootstrap-cheatsheet-a-basic-guide-to-bootstrap/?ref=outind" target="_self">Bootstrap Cheat Sheet</a></li></ul></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/web-development/?ref=outind" target="_self">Learn Complete Web Development</a></li></ul></li></ul>  <ul class="header-main__left-list" data-nl="false"> <li class="header-main__left-list-item gcse-search_li p-relative" aria-expanded="false" data-expandable="false"> <div class="gcse-form-search-suggestion_wrapper"> <form id="gcse-form" class="gcse-form_class p-relative closeChatScreen" data-sm="false"> <span class="front-search-icon"><i class="gfg-icon gfg-icon_search gfg-icon_white gcse-search__icon gcse-search-icon_grey"></i> </span> <input class="gcse-search-input__wrapper" id="gcse-search-input" aria-expanded="false" placeholder="Search..." autocomplete="off" /> <i class="gfg-icon gfg-icon_times gfg-icon_white hide-search"></i> <button aria-label="search" type="submit" class="gcse-search__btn not-expanded"> <i class="gfg-icon gfg-icon_search gfg-icon_white gcse-search__icon"></i> </button> </form> <div class="gfg-search-suggestion_wrapper" style="display:none"></div> <div> </li> <li> <div class="darkMode-wrap" data-mode="Switch to Dark Mode"> <button aria-label="toggle theme" data-gfg-action="toggleGFGTheme"> <div id="darkMode-wrap-red-dot" style="height:12px;width:12px;background-color:#EB2222;border-radius:999999px;position:absolute;top:4px;right:0;display:none;"></div> <i class="gfg-icon gfg-icon_dark-mode"></i> </button> <span id="darkModeTooltipText"></span> </div> </li> <li class="header-main__left-list-item google-translate-parent-element" aria-expanded="false" data-expanded="true"> <div class="translate" id="g_translater"> <div id="google_translate_element" data-show="false"></div> </div> <i class ="gfg-icon gfg-icon_translate googleTranslateToggle" data-gfg-action="google_translate_element"></i>   </li> <li id="userProfileId" class="header-main__left-list-item p-relative" aria-expanded="false" data-expandable="false">  </li> </ul> </div>   </div> </nav> <div class="header-main__slider"> <button aria-label="sub header slider previous" class="header-main__slider-arrow previous hideIt"> <i class="gfg-icon gfg-icon_arrow-left gicon-centered"></i> </button>  <ul id="hslider"> <li><a href="https://www.geeksforgeeks.org/learn-data-structures-and-algorithms-dsa-tutorial/?ref=shm">DSA</a></li><li><a href="https://www.geeksforgeeks.org/fundamentals-of-algorithms/?ref=shm">Algorithms</a></li><li><a href="https://www.geeksforgeeks.org/design-and-analysis-of-algorithms/?ref=shm">Analysis of Algorithms</a></li><li><a href="https://www.geeksforgeeks.org/sorting-algorithms/?ref=shm">Sorting</a></li><li><a href="https://www.geeksforgeeks.org/searching-algorithms/?ref=shm">Searching</a></li><li><a href="https://www.geeksforgeeks.org/greedy-algorithms/?ref=shm">Greedy</a></li><li><a href="https://www.geeksforgeeks.org/recursion-algorithms/?ref=shm">Recursion</a></li><li><a href="https://www.geeksforgeeks.org/backtracking-algorithms/?ref=shm">Backtracking</a></li><li><a href="https://www.geeksforgeeks.org/dynamic-programming/?ref=shm">Dynamic Programming</a></li><li><a href="https://www.geeksforgeeks.org/divide-and-conquer/?ref=shm">Divide and Conquer</a></li><li><a href="https://www.geeksforgeeks.org/geometric-algorithms/?ref=shm">Geometric Algorithms</a></li><li><a href="https://www.geeksforgeeks.org/mathematical-algorithms/?ref=shm">Mathematical Algorithms</a></li><li><a href="https://www.geeksforgeeks.org/pattern-searching/?ref=shm">Pattern Searching</a></li><li><a href="https://www.geeksforgeeks.org/bitwise-algorithms/?ref=shm">Bitwise Algorithms</a></li><li><a href="https://www.geeksforgeeks.org/branch-and-bound-algorithm/?ref=shm">Branch & Bound</a></li><li><a href="https://www.geeksforgeeks.org/randomized-algorithms/?ref=shm">Randomized Algorithms</a></li> </ul> <button aria-label="sub header slider next" class="header-main__slider-arrow next hideIt"> <i class="gfg-icon gfg-icon_arrow-right gicon-centered"></i> </button> </div> <button id="scrollTopBtn" title="Scroll to Top" type="button" class="btn btn-success">▲</button>  <div id="main" class="wrapper single-page"> <script> if(post_slug.includes('premium-plans-payment/') || post_slug.includes('premium-plans/')){ $(".header-main__slider").remove(); } //getting tags for the page type data let mobileView = false; let pageTags = JSON.parse('null'); let allTags = JSON.parse('{"0":"Algorithms","1":"DSA","2":"AnalysisofAlgorithms","4":"Complexityanalysis"}'); </script> <script> window.have_dsa_term = false; // var practiceTab = ; </script> <style> .wrapper { flex-direction: column !important; } /* spinner css */ @keyframes spinner { to {transform: rotate(360deg);} } .spinner:before { content: ''; box-sizing: border-box; position: absolute; top: 50%; left: 50%; width: 20px; height: 20px; margin-top: -10px; margin-left: -10px; border-radius: 50%; border: 2px solid #ccc; border-top-color: #000; animation: spinner .6s linear infinite; } .report-loader{ position: relative; } .report-loader.spinner{ margin-left: 16px; } .badges{ display: flex; align-items: center; position: relative; } .badges .gfg-badge-icon.md::after{ transform: scale(0.25); position:relative; top: 2px; left: -2px; } .sep{ margin: 0px 5px; font-size: 20px; color: var(--badge-name-color); } .pub-count{ font-size: 14px; font-family: var(--font-secondary); } .badge-details{ display:none; } .badges{ cursor: pointer; position: relative; /* width: 0px; height: 20px; top: -32px; */ } .badge-icon{ display: flex; align-items: center; } .badge-content{ margin-left: 9px; } .badge-name{ color: var(--badge-nam-color); font-weight: 600; font-size: 16px; text-transform: capitalize; } .badge-data{ color: #A5A4A4; font-size: 10px; } .badges:hover .badge-details{ display: block; background: var(--badge-bg); padding: 10px 18px 10px 18px; position: absolute; width: 175px; top: -10px; z-index: 10; left: 112%; box-shadow: rgb(100 100 111 / 20%) 0px 7px 29px 0px; border-radius: 5px; /* transform-origin: top right; */ } .badge-details::before { content: ""; position: absolute; transform: rotate(90deg); /* transform-origin: right; */ left: -6px; top: 50%; margin-left: -17px; border-width: 12px; border-style: solid; border-color: var(--badge-bg) transparent transparent transparent; margin-top: -12px; } .badge-icon .icon{ border: 1px solid var(--icon-border-color); padding: 4px 3px; border-radius: 4px; width: 22px; height: 24px; position: relative; } .b-icon-pos{ position: relative; top: -34px; left: -34px; } /* article viewer */ .article--viewer .a-wrapper{ margin-top: 0px !important; } .content{ padding-top: 10px !important; } .u-name{ font-size: 14px; } .article--viewer_content .a-wrapper .content{ padding-bottom: 10px !important; } .likeTooltipBottom{ font-size: 14px; } @media (max-width: 434px) { .article-buttons.show-bg{ margin-top: 56px !important; } } @media (max-width: 730px), ((min-width: 992px) and (max-width:1100px)) { .article--viewer .media{ position: relative; } .article--viewer .media{ margin-bottom: 0px !important; } .badges:hover .badge-details{ top: -56px; left: 62px; } .badge-details::before{ transform: rotate(0deg); left: 10%; top: 117%; } .article-buttons.show-bg{ margin-top: 22px; top: 0px !important; } } @media ((min-width:731px) and (max-width:1223px)) { .article-buttons.show-bg{ top: 18px; } } @media ((min-width:993px) and (max-width:1190px)) { .article--viewer .media{ position: relative; } .article--viewer .media{ margin-bottom: 25px !important; } } </style>  <script> function getCookie(name) { function escape(s) { return s.replace(/([.*+?\^$(){}|\[\]\/\\])/g, '\\$1'); } var match = document.cookie.match(RegExp('(?:^|;\\s*)' + escape(name) + '=([^;]*)')); return match ? match[1] : null; } </script>    <div id='openInApp-modal' class='openInApp'> <a href = 'https://geeksforgeeksapp.page.link/?link=https://www.geeksforgeeks.org/worst-average-and-best-case-analysis-of-algorithms/?type%3Darticle%26id%3D17020&apn=free.programming.programming&isi=1641848816&ibi=org.geeksforgeeks.GeeksforGeeksDev&efr=1' class='openInAppLink'> <span style='color: #fff;'>Open In App</span> </a> </div> <script> var consentValue = localStorage.getItem("gfg_cc"); var isIOS = !!navigator.platform && /iPad|iPhone|iPod|MacIntel/.test(navigator.platform) && navigator.maxTouchPoints > 0; const isSafari = navigator.userAgent.indexOf("Safari") > -1; const isMozilla = navigator.userAgent.indexOf("Mozilla") > -1; if(consentValue){ if(window.innerHeight > window.innerWidth && navigator.maxTouchPoints > 1 && (isSafari || isMozilla || navigator.userAgentData.mobile)){ $('.openInApp').css({ display: "block" }); $('#scrollTopBtn').css({ bottom: "44px" }); //adding a new class to check stats for clicks on iOS and Android isIOS ? jQuery('.openInAppLink').addClass("oia-iOS") : $('.openInAppLink').addClass("oia-android"); //for openInApp Link } } </script> <style> .openInApp{ display: none; bottom: 0px; width: 100%; position: fixed; z-index: 1025; opacity: 0.93; } .openInAppLink{ height: 44px; background: var(--color-gfg); font-weight: bold; display: block; text-align: center; padding: 12px; font-size: large; } .openInAppLink, .openInAppLink:hover, .openInAppLink:active, .openInAppLink:visited, .openInAppLink:focus { text-decoration:none; } </style>  <script> companyTagsArray = JSON.parse('[]'); categoryTagsArray = JSON.parse('["Algorithms"]'); </script> <div class="container-fluid bg-light" id="home-page" style="position: relative; max-width:100%;"> <div class="article-page_flex"> <div class="sidebar_wrapper manual_leftbar "> <a href="https://www.geeksforgeeks.org/asymptotic-notation-and-analysis-based-on-input-size-of-algorithms/?ref=next_article_top" class="next_article_leftbar_container"> <div class="next_article_leftbar_content"> <span class="next_article_text">Next Article:</span> <div class="next_article_title">Asymptotic Analysis</div> </div> <img src="https://media.geeksforgeeks.org/auth-dashboard-uploads/ep_right.svg" alt="Next article icon" /> </a> <div class="sideBar " style="height: unset !important">  <div class="sideBar--wrap newLeftbar "> <div id="GFG_AD_Leftsidebar_300x250_chained_1"></div> <div id="GFG_AD_Leftsidebar_300x250_chained_2"></div> <div id="GFG_AD_Leftsidebar_300x250_chained_3"></div> <div id="GFG_AD_Leftsidebar_300x600_chained_1"></div> </div> </div> <div id="GFG_AD_Desktop_LeftSideBar_Docked_160x600" style="max-width:160px; max-height:600px"></div> </div> <div class="leftBar"> <div class="article--viewer"> <div class="article--viewer_content"> <div class="a-wrapper"> <div class="" style="z-index:9999 !important;position:relative;"> </div> <article class="content post-17020 post type-post status-publish format-standard hentry category-algorithm category-analysis category-dsa tag-complexity-analysis" id="post-17020">  <div class="main_wrapper" style="display:flex;"> <div style="width: 100%;"> <div class="article-title"> <h1>Worst, Average and Best Case Analysis of Algorithms</h1> </div> <div class="last_updated_parent"> <div> <span class="strong">Last Updated : </span> <span>11 Nov, 2024</span> </div>  <div class="three_dot_dropdown"> <div style="display: flex;"> <div pid="17020" ptitle="Worst, Average and Best Case Analysis of Algorithms" class="top-summary-icon-div "> <div class="three_dot_dropdown_div tooltip"> <span class="summary_tooltiptext">Summarize</span> <div class="summarize_header"> <i class= "summary_button" style="position: relative;"></i> </div> </div> </div> <div pid="17020" ptitle="Worst, Average and Best Case Analysis of Algorithms" class="article--viewer_comment tooltip top-comment-icon-div"> <span class="comment_tooltiptext">Comments</span> <div class="three_dot_dropdown_div" data-gfg-action='loadComments'> <div class="comment_header"> <i class= "discussion_button" style="position: relative; transform: scale(0.9);"></i> </div> </div> </div> <div pid="17020" ptitle="Worst, Average and Best Case Analysis of Algorithms" class="article--viewer_improve tooltip"> <span class="improve_tooltiptext">Improve</span> <div class="three_dot_dropdown_div three_dot_dropdown_improve" onclick="improveArticleCall()"> <div class="improve_wrapper_top"> <i class="gfg-icon gfg-icon-pencil gfg-icon_edit" style="position: relative; z-index: 3;"></i> </div> </div>  </div>  <ul class="dropbtn icons btn-right showLeft" onclick="showDropdown()"> <li> </li> <li></li> <li></li> </ul> </div> </div> </div> </div> </div>  <div id="myDropdown" class="three_dot_dropdown_content"> <div class="article-buttons drop" onmouseleave="closeKebabMenu()">  <div pid="17020" ptitle="Worst, Average and Best Case Analysis of Algorithms" class="improve_article--viewer tooltip"> <div class="three_dot_dropdown_div three_dot_dropdown_improve" onclick="suggestionArticleCall()" style="margin-top: 1px;"> <div class="three_dot_dropdown_inner_div improve_dot_dropdown_inner_div"> <i class="gfg-icon gfg-icon_suggest_changes gfg-icon_edit"></i> <span>Suggest changes</span> </div> </div> </div> <div pid="17020" class="article--viewer_like tooltip"> <div class="three_dot_dropdown_div three_dot_dropdown_likearticle" onmouseleave='toggleLikeElementVisibility("showLikesContainer", false)' onmouseenter='toggleLikeElementVisibility("showLikesContainer", true)'> <div class="showLikesContainer"> <span class="likeTooltip">Like Article</span> </div> <div class="three_dot_dropdown_inner_div" data-gfg-action="like-article" data-bookmark-value="0"> <i class="gfg-icon gfg-icon_thumbs"></i> <span>Like</span> </div> </div>  </div> <div pid="17020" class="article--viewer_share tooltip"> <div class="three_dot_dropdown_div three_dot_dropdown_share" onmouseleave="closeShareModal()" onmouseenter="openShareModal()"> <div style="display: flex;align-items: center;" class="three_dot_dropdown_inner_div" data-gfg-action="share-article" data-bookmark-value="0"> <i class="gfg-share-icon"></i> <span>Share</span> </div> </div> </div> <div class="article--viewer_report tooltip"> <div class="three_dot_dropdown_div three_dot_dropdown_reportarticle"> <div class="three_dot_dropdown_inner_div" data-gfg-action="report-article" onclick="report_article();"> <i class="gfg-icon gfg-icon_report"></i> <span>Report</span> </div> </div>  </div> <div class="article--viewer_Gnews tooltip"> <a class="three_dot_dropdown_inner_div Gnews_wrapper" href ='https://news.google.com/publications/CAAqBwgKMLTrzwsw44bnAw?hl=en-IN&gl=IN&ceid=IN%3Aen' target="_blank"> <img class="gfg-icon_Gnews no-zoom-in-cursor" src=https://media.geeksforgeeks.org/auth-dashboard-uploads/Google-news.svg loading="lazy" alt="News"></img> <span class='kebab_menu_news_text'>Follow</span> </a> </div> </div> </div> <div class="text"> <p dir="ltr"><span>In the </span><a href="https://www.geeksforgeeks.org/analysis-of-algorithms-set-1-asymptotic-analysis/" rel="noopener"><span>previous post</span></a><span>, we discussed how Asymptotic analysis overcomes the problems of the naive way of analyzing algorithms. Now let us learn about What is Worst, Average, and Best cases of an algorithm:</span></p> <h3><b><strong>1. Worst Case Analysis (Mostly used)</strong></b><span> </span></h3><ul><li value="1"><span>In the worst-case analysis, we calculate the upper bound on the running time of an algorithm. We must know the case that causes a maximum number of operations to be executed. </span></li><li value="2"><span>For </span><a href="https://www.geeksforgeeks.org/linear-search/" target="_blank" rel="noopener"><span>Linear Search</span></a><span>, the worst case happens when the element to be searched (x) is not present in the array. When x is not present, the search()</span><b><strong> </strong></b><span>function compares it with all the elements of arr[] one by one. </span></li><li value="3"><span>This is the most commonly used analysis of algorithms (We will be discussing below why). Most of the time we consider the case that causes maximum operations.</span></li></ul><h3><b><strong>2. Best Case Analysis (Very Rarely used) </strong></b></h3><ul><li value="1"><span>In the best-case analysis, we calculate the lower bound on the running time of an algorithm. We must know the case that causes a minimum number of operations to be executed. </span></li><li value="2"><span>For </span><a href="https://www.geeksforgeeks.org/linear-search/" target="_blank" rel="noopener"><span>linear search</span></a><span>, the best case occurs when x is present at the first location. The number of operations in the best case is constant (not dependent on n). So the order of growth of time taken in terms of input size is constant.</span></li></ul><h3><b><strong>3. Average Case Analysis (Rarely used) </strong></b></h3><ul><li value="1"><span>In average case analysis, we take all possible inputs and calculate the computing time for all of the inputs. Sum all the calculated values and divide the sum by the total number of inputs. </span></li><li value="2"><span>We must know (or predict) the distribution of cases. For the linear search problem, let us assume that all cases are </span><a href="http://en.wikipedia.org/wiki/Uniform_distribution_%28discrete%29" target="_blank" rel="noopener noreferrer nofollow"><span>uniformly distributed</span></a><span> (including the case of x not being present in the array). So we sum all the cases and divide the sum by (n+1). We take (n+1) to consider the case when the element is not present. </span></li></ul><h2><span>Why is Worst Case Analysis Mostly Used?</span></h2><p dir="ltr"><b><strong>Average Case : </strong></b><span>The average case analysis is not easy to do in most practical cases and it is rarely done. In the average case analysis, we need to consider every input, its frequency and time taken by it which may not be possible in many scenarios</span></p> <p dir="ltr"><b><strong>Best Case : </strong></b><span>The Best Case analysis is considered bogus. Guaranteeing a lower bound on an algorithm doesn’t provide any information as in the worst case, an algorithm may take years to run.</span></p> <p dir="ltr"><b><strong>Worst Case: </strong></b><span>This is easier than average case and gives an upper bound which is useful information to analyze software products.</span></p> <h3><span>Interesting information about asymptotic notations:</span></h3><blockquote><p dir="ltr"><span>A) For some algorithms, all the cases (worst, best, average) are asymptotically the same. i.e., there are no worst and best cases. </span></p> <ul><li value="1"><b><strong>Example:  </strong></b><a href="http://en.wikipedia.org/wiki/Merge_sort" target="_blank" rel="noopener noreferrer nofollow"><span>Merge Sort</span></a><span> does order of n log(n) operations in all cases.</span></li></ul><p dir="ltr"><span>B) Where as most of the other sorting algorithms have worst and best cases. </span></p> <ul><li value="1"><b><strong>Example 1: </strong></b><span>In the typical implementation of </span><a href="http://www.geeksforgeeks.org/quick-sort/" rel="noopener"><span>Quick Sort </span></a><span>(where pivot is chosen as a corner element), the worst occurs when the input array is already sorted and the best occurs when the pivot elements always divide the array into two halves.</span></li><li value="2"><b><strong>Example 2: </strong></b><span>For insertion sort, the worst case occurs when the array is reverse sorted and the best case occurs when the array is sorted in the same order as output.</span></li></ul></blockquote><h2><span>Examples with their complexity analysis:</span></h2><h3><b><strong>1. Linear search algorithm:</strong></b></h3><gfg-tabs data-run-ide="true" data-mode="light"> <gfg-tab slot="tab">C++</gfg-tab> <gfg-panel slot="panel" data-code-lang="cpp"> <code class="language-cpp"><div class=highlight><pre><span></span><span class=cp>#include</span><span class=w> </span><span class=cpf><iostream></span> <span class=cp>#include</span><span class=w> </span><span class=cpf><vector></span> <span class=k>using</span><span class=w> </span><span class=k>namespace</span><span class=w> </span><span class=nn>std</span><span class=p>;</span> <span class=c1>// Linearly search target in arr.</span> <span class=c1>// If target is present, return the index;</span> <span class=c1>// otherwise, return -1</span> <span class=kt>int</span><span class=w> </span><span class=nf>search</span><span class=p>(</span><span class=n>vector</span><span class=o><</span><span class=kt>int</span><span class=o>>&</span><span class=w> </span><span class=n>arr</span><span class=p>,</span><span class=w> </span><span class=kt>int</span><span class=w> </span><span class=n>x</span><span class=p>)</span><span class=w> </span><span class=p>{</span> <span class=w> </span><span class=k>for</span><span class=w> </span><span class=p>(</span><span class=kt>int</span><span class=w> </span><span class=n>i</span><span class=w> </span><span class=o>=</span><span class=w> </span><span class=mi>0</span><span class=p>;</span><span class=w> </span><span class=n>i</span><span class=w> </span><span class=o><</span><span class=w> </span><span class=n>arr</span><span class=p>.</span><span class=n>size</span><span class=p>();</span><span class=w> </span><span class=n>i</span><span class=o>++</span><span class=p>)</span><span class=w> </span><span class=p>{</span> <span class=w> </span><span class=k>if</span><span class=w> </span><span class=p>(</span><span class=n>arr</span><span class=p>[</span><span class=n>i</span><span class=p>]</span><span class=w> </span><span class=o>==</span><span class=w> </span><span class=n>x</span><span class=p>)</span> <span class=w> </span><span class=k>return</span><span class=w> </span><span class=n>i</span><span class=p>;</span> <span class=w> </span><span class=p>}</span> <span class=w> </span><span class=k>return</span><span class=w> </span><span class=mi>-1</span><span class=p>;</span> <span class=p>}</span> <span class=kt>int</span><span class=w> </span><span class=nf>main</span><span class=p>()</span><span class=w> </span><span class=p>{</span> <span class=w> </span><span class=n>vector</span><span class=o><</span><span class=kt>int</span><span class=o>></span><span class=w> </span><span class=n>arr</span><span class=w> </span><span class=o>=</span><span class=w> </span><span class=p>{</span><span class=mi>1</span><span class=p>,</span><span class=w> </span><span class=mi>10</span><span class=p>,</span><span class=w> </span><span class=mi>30</span><span class=p>,</span><span class=w> </span><span class=mi>15</span><span class=p>};</span> <span class=w> </span><span class=kt>int</span><span class=w> </span><span class=n>x</span><span class=w> </span><span class=o>=</span><span class=w> </span><span class=mi>30</span><span class=p>;</span> <span class=w> </span><span class=n>cout</span><span class=w> </span><span class=o><<</span><span class=w> </span><span class=n>search</span><span class=p>(</span><span class=n>arr</span><span class=p>,</span><span class=w> </span><span class=n>x</span><span class=p>);</span> <span class=w> </span><span class=k>return</span><span class=w> </span><span class=mi>0</span><span class=p>;</span> <span class=p>}</span> </pre></div></code> </gfg-panel> <gfg-tab slot="tab">C</gfg-tab> <gfg-panel slot="panel" data-code-lang="c"> <code class="language-c"><div class=highlight><pre><span></span><span class=cp>#include</span><span class=w> </span><span class=cpf><stdio.h></span> <span class=cp>#include</span><span class=w> </span><span class=cpf><stdbool.h></span> <span class=c1>// Linearly search target in arr.</span> <span class=c1>// If target is present, return the index;</span> <span class=c1>// otherwise, return -1</span> <span class=kt>int</span><span class=w> </span><span class=nf>search</span><span class=p>(</span><span class=kt>int</span><span class=w> </span><span class=n>arr</span><span class=p>[],</span><span class=w> </span><span class=kt>int</span><span class=w> </span><span class=n>size</span><span class=p>,</span><span class=w> </span><span class=kt>int</span><span class=w> </span><span class=n>x</span><span class=p>)</span><span class=w> </span><span class=p>{</span> <span class=w> </span><span class=k>for</span><span class=w> </span><span class=p>(</span><span class=kt>int</span><span class=w> </span><span class=n>i</span><span class=w> </span><span class=o>=</span><span class=w> </span><span class=mi>0</span><span class=p>;</span><span class=w> </span><span class=n>i</span><span class=w> </span><span class=o><</span><span class=w> </span><span class=n>size</span><span class=p>;</span><span class=w> </span><span class=n>i</span><span class=o>++</span><span class=p>)</span><span class=w> </span><span class=p>{</span> <span class=w> </span><span class=k>if</span><span class=w> </span><span class=p>(</span><span class=n>arr</span><span class=p>[</span><span class=n>i</span><span class=p>]</span><span class=w> </span><span class=o>==</span><span class=w> </span><span class=n>x</span><span class=p>)</span> <span class=w> </span><span class=k>return</span><span class=w> </span><span class=n>i</span><span class=p>;</span> <span class=w> </span><span class=p>}</span> <span class=w> </span><span class=k>return</span><span class=w> </span><span class=mi>-1</span><span class=p>;</span> <span class=p>}</span> <span class=kt>int</span><span class=w> </span><span class=nf>main</span><span class=p>()</span><span class=w> </span><span class=p>{</span> <span class=w> </span><span class=kt>int</span><span class=w> </span><span class=n>arr</span><span class=p>[]</span><span class=w> </span><span class=o>=</span><span class=w> </span><span class=p>{</span><span class=mi>1</span><span class=p>,</span><span class=w> </span><span class=mi>10</span><span class=p>,</span><span class=w> </span><span class=mi>30</span><span class=p>,</span><span class=w> </span><span class=mi>15</span><span class=p>};</span> <span class=w> </span><span class=kt>int</span><span class=w> </span><span class=n>size</span><span class=w> </span><span class=o>=</span><span class=w> </span><span class=k>sizeof</span><span class=p>(</span><span class=n>arr</span><span class=p>)</span><span class=w> </span><span class=o>/</span><span class=w> </span><span class=k>sizeof</span><span class=p>(</span><span class=n>arr</span><span class=p>[</span><span class=mi>0</span><span class=p>]);</span> <span class=w> </span><span class=kt>int</span><span class=w> </span><span class=n>x</span><span class=w> </span><span class=o>=</span><span class=w> </span><span class=mi>30</span><span class=p>;</span> <span class=w> </span><span class=n>printf</span><span class=p>(</span><span class=s>"%d"</span><span class=p>,</span><span class=w> </span><span class=n>search</span><span class=p>(</span><span class=n>arr</span><span class=p>,</span><span class=w> </span><span class=n>size</span><span class=p>,</span><span class=w> </span><span class=n>x</span><span class=p>));</span> <span class=w> </span><span class=k>return</span><span class=w> </span><span class=mi>0</span><span class=p>;</span> <span class=p>}</span> </pre></div></code> </gfg-panel> <gfg-tab slot="tab">Java</gfg-tab> <gfg-panel slot="panel" data-code-lang="java"> <code class="language-java"><div class=highlight><pre><span></span><span class=kn>import</span><span class=w> </span><span class=nn>java.util.Arrays</span><span class=p>;</span> <span class=c1>// Linearly search target in arr.</span> <span class=c1>// If target is present, return the index;</span> <span class=c1>// otherwise, return -1</span> <span class=kd>public</span><span class=w> </span><span class=kd>class</span> <span class=nc>GfG</span><span class=w> </span><span class=p>{</span> <span class=w> </span><span class=kd>public</span><span class=w> </span><span class=kd>static</span><span class=w> </span><span class=kt>int</span><span class=w> </span><span class=nf>search</span><span class=p>(</span><span class=kt>int</span><span class=o>[]</span><span class=w> </span><span class=n>arr</span><span class=p>,</span><span class=w> </span><span class=kt>int</span><span class=w> </span><span class=n>x</span><span class=p>)</span><span class=w> </span><span class=p>{</span> <span class=w> </span><span class=k>for</span><span class=w> </span><span class=p>(</span><span class=kt>int</span><span class=w> </span><span class=n>i</span><span class=w> </span><span class=o>=</span><span class=w> </span><span class=mi>0</span><span class=p>;</span><span class=w> </span><span class=n>i</span><span class=w> </span><span class=o><</span><span class=w> </span><span class=n>arr</span><span class=p>.</span><span class=na>length</span><span class=p>;</span><span class=w> </span><span class=n>i</span><span class=o>++</span><span class=p>)</span><span class=w> </span><span class=p>{</span> <span class=w> </span><span class=k>if</span><span class=w> </span><span class=p>(</span><span class=n>arr</span><span class=o>[</span><span class=n>i</span><span class=o>]</span><span class=w> </span><span class=o>==</span><span class=w> </span><span class=n>x</span><span class=p>)</span> <span class=w> </span><span class=k>return</span><span class=w> </span><span class=n>i</span><span class=p>;</span> <span class=w> </span><span class=p>}</span> <span class=w> </span><span class=k>return</span><span class=w> </span><span class=o>-</span><span class=mi>1</span><span class=p>;</span> <span class=w> </span><span class=p>}</span> <span class=w> </span><span class=kd>public</span><span class=w> </span><span class=kd>static</span><span class=w> </span><span class=kt>void</span><span class=w> </span><span class=nf>main</span><span class=p>(</span><span class=n>String</span><span class=o>[]</span><span class=w> </span><span class=n>args</span><span class=p>)</span><span class=w> </span><span class=p>{</span> <span class=w> </span><span class=kt>int</span><span class=o>[]</span><span class=w> </span><span class=n>arr</span><span class=w> </span><span class=o>=</span><span class=w> </span><span class=p>{</span><span class=mi>1</span><span class=p>,</span><span class=w> </span><span class=mi>10</span><span class=p>,</span><span class=w> </span><span class=mi>30</span><span class=p>,</span><span class=w> </span><span class=mi>15</span><span class=p>};</span> <span class=w> </span><span class=kt>int</span><span class=w> </span><span class=n>x</span><span class=w> </span><span class=o>=</span><span class=w> </span><span class=mi>30</span><span class=p>;</span> <span class=w> </span><span class=n>System</span><span class=p>.</span><span class=na>out</span><span class=p>.</span><span class=na>println</span><span class=p>(</span><span class=n>search</span><span class=p>(</span><span class=n>arr</span><span class=p>,</span><span class=w> </span><span class=n>x</span><span class=p>));</span> <span class=w> </span><span class=p>}</span> <span class=p>}</span> </pre></div></code> </gfg-panel> <gfg-tab slot="tab">Python</gfg-tab> <gfg-panel slot="panel" data-code-lang="python3"> <code class="language-python3"><div class=highlight><pre><span></span><span class=c1># Linearly search target in arr.</span> <span class=c1># If target is present, return the index;</span> <span class=c1># otherwise, return -1</span> <span class=k>def</span> <span class=nf>search</span><span class=p>(</span><span class=n>arr</span><span class=p>,</span> <span class=n>x</span><span class=p>):</span> <span class=k>for</span> <span class=n>i</span> <span class=ow>in</span> <span class=nb>range</span><span class=p>(</span><span class=nb>len</span><span class=p>(</span><span class=n>arr</span><span class=p>)):</span> <span class=k>if</span> <span class=n>arr</span><span class=p>[</span><span class=n>i</span><span class=p>]</span> <span class=o>==</span> <span class=n>x</span><span class=p>:</span> <span class=k>return</span> <span class=n>i</span> <span class=k>return</span> <span class=o>-</span><span class=mi>1</span> <span class=k>if</span> <span class=vm>__name__</span> <span class=o>==</span> <span class=s1>'__main__'</span><span class=p>:</span> <span class=n>arr</span> <span class=o>=</span> <span class=p>[</span><span class=mi>1</span><span class=p>,</span> <span class=mi>10</span><span class=p>,</span> <span class=mi>30</span><span class=p>,</span> <span class=mi>15</span><span class=p>]</span> <span class=n>x</span> <span class=o>=</span> <span class=mi>30</span> <span class=nb>print</span><span class=p>(</span><span class=n>search</span><span class=p>(</span><span class=n>arr</span><span class=p>,</span> <span class=n>x</span><span class=p>))</span> </pre></div></code> </gfg-panel> <gfg-tab slot="tab">C#</gfg-tab> <gfg-panel slot="panel" data-code-lang="csharp"> <code class="language-csharp"><div class=highlight><pre><span></span><span class=k>using</span><span class=w> </span><span class=nn>System</span><span class=p>;</span> <span class=k>public</span><span class=w> </span><span class=k>class</span><span class=w> </span><span class=nc>Program</span><span class=w> </span><span class=p>{</span> <span class=w> </span> <span class=w> </span><span class=c1>// Linearly search target in arr.</span> <span class=w> </span><span class=c1>// If target is present, return the index;</span> <span class=w> </span><span class=c1>// otherwise, return -1</span> <span class=w> </span><span class=k>public</span><span class=w> </span><span class=k>static</span><span class=w> </span><span class=kt>int</span><span class=w> </span><span class=nf>Search</span><span class=p>(</span><span class=kt>int</span><span class=p>[]</span><span class=w> </span><span class=n>arr</span><span class=p>,</span><span class=w> </span><span class=kt>int</span><span class=w> </span><span class=n>target</span><span class=p>)</span><span class=w> </span><span class=p>{</span> <span class=w> </span><span class=k>for</span><span class=w> </span><span class=p>(</span><span class=kt>int</span><span class=w> </span><span class=n>i</span><span class=w> </span><span class=o>=</span><span class=w> </span><span class=m>0</span><span class=p>;</span><span class=w> </span><span class=n>i</span><span class=w> </span><span class=o><</span><span class=w> </span><span class=n>arr</span><span class=p>.</span><span class=n>Length</span><span class=p>;</span><span class=w> </span><span class=n>i</span><span class=o>++</span><span class=p>)</span><span class=w> </span><span class=p>{</span> <span class=w> </span><span class=k>if</span><span class=w> </span><span class=p>(</span><span class=n>arr</span><span class=p>[</span><span class=n>i</span><span class=p>]</span><span class=w> </span><span class=o>==</span><span class=w> </span><span class=n>target</span><span class=p>)</span> <span class=w> </span><span class=k>return</span><span class=w> </span><span class=n>i</span><span class=p>;</span> <span class=w> </span><span class=p>}</span> <span class=w> </span><span class=k>return</span><span class=w> </span><span class=o>-</span><span class=m>1</span><span class=p>;</span> <span class=w> </span><span class=p>}</span> <span class=w> </span><span class=k>public</span><span class=w> </span><span class=k>static</span><span class=w> </span><span class=k>void</span><span class=w> </span><span class=nf>Main</span><span class=p>()</span><span class=w> </span><span class=p>{</span> <span class=w> </span><span class=kt>int</span><span class=p>[]</span><span class=w> </span><span class=n>arr</span><span class=w> </span><span class=o>=</span><span class=w> </span><span class=p>{</span><span class=m>1</span><span class=p>,</span><span class=w> </span><span class=m>10</span><span class=p>,</span><span class=w> </span><span class=m>30</span><span class=p>,</span><span class=w> </span><span class=m>15</span><span class=p>};</span> <span class=w> </span><span class=kt>int</span><span class=w> </span><span class=n>target</span><span class=w> </span><span class=o>=</span><span class=w> </span><span class=m>30</span><span class=p>;</span> <span class=w> </span><span class=n>Console</span><span class=p>.</span><span class=n>WriteLine</span><span class=p>(</span><span class=n>Search</span><span class=p>(</span><span class=n>arr</span><span class=p>,</span><span class=w> </span><span class=n>target</span><span class=p>));</span> <span class=w> </span><span class=p>}</span> <span class=p>}</span> </pre></div></code> </gfg-panel> <gfg-tab slot="tab">JavaScript</gfg-tab> <gfg-panel slot="panel" data-code-lang="javascript"> <code class="language-javascript"><div class=highlight><pre><span></span><span class=c1>// Linearly search target in arr.</span> <span class=c1>// If target is present, return the index;</span> <span class=c1>// otherwise, return -1</span> <span class=kd>function</span><span class=w> </span><span class=nx>search</span><span class=p>(</span><span class=nx>arr</span><span class=p>,</span><span class=w> </span><span class=nx>x</span><span class=p>)</span><span class=w> </span><span class=p>{</span> <span class=w> </span><span class=k>for</span><span class=w> </span><span class=p>(</span><span class=kd>let</span><span class=w> </span><span class=nx>i</span><span class=w> </span><span class=o>=</span><span class=w> </span><span class=mf>0</span><span class=p>;</span><span class=w> </span><span class=nx>i</span><span class=w> </span><span class=o><</span><span class=w> </span><span class=nx>arr</span><span class=p>.</span><span class=nx>length</span><span class=p>;</span><span class=w> </span><span class=nx>i</span><span class=o>++</span><span class=p>)</span><span class=w> </span><span class=p>{</span> <span class=w> </span><span class=k>if</span><span class=w> </span><span class=p>(</span><span class=nx>arr</span><span class=p>[</span><span class=nx>i</span><span class=p>]</span><span class=w> </span><span class=o>===</span><span class=w> </span><span class=nx>x</span><span class=p>)</span> <span class=w> </span><span class=k>return</span><span class=w> </span><span class=nx>i</span><span class=p>;</span> <span class=w> </span><span class=p>}</span> <span class=w> </span><span class=k>return</span><span class=w> </span><span class=o>-</span><span class=mf>1</span><span class=p>;</span> <span class=p>}</span> <span class=kd>const</span><span class=w> </span><span class=nx>arr</span><span class=w> </span><span class=o>=</span><span class=w> </span><span class=p>[</span><span class=mf>1</span><span class=p>,</span><span class=w> </span><span class=mf>10</span><span class=p>,</span><span class=w> </span><span class=mf>30</span><span class=p>,</span><span class=w> </span><span class=mf>15</span><span class=p>];</span> <span class=kd>const</span><span class=w> </span><span class=nx>x</span><span class=w> </span><span class=o>=</span><span class=w> </span><span class=mf>30</span><span class=p>;</span> <span class=nx>console</span><span class=p>.</span><span class=nx>log</span><span class=p>(</span><span class=nx>search</span><span class=p>(</span><span class=nx>arr</span><span class=p>,</span><span class=w> </span><span class=nx>x</span><span class=p>));</span> </pre></div></code> </gfg-panel></gfg-tabs><div class="code-output"><br><strong>Output</strong><pre>2</pre></div><p dir="ltr"><b><strong>Best Case: </strong></b><span> Constant Time irrespective of input size.</span><b><strong> </strong></b><span>This will take place if the element to be searched is on the first index of the given list. So, the number of comparisons, in this case, is 1.</span><br><b><strong>Average Case: </strong></b><span>Linear Time, This will take place if the element to be searched is at the middle index (in an average search) of the given list.</span><br><b><strong>Worst Case:</strong></b><span> The element to be searched is not present in the list</span></p> <p dir="ltr"><b><strong>2. Special Array Sum : </strong></b><span> In this example, we will take an array of length (n) and deals with the following cases :</span></p> <ul><li value="1"><span>If (n) is even then our output will be 0</span></li><li value="2"><span>If (n) is odd then our output will be the sum of the elements of the array.</span></li></ul><p dir="ltr"><span>Below is the implementation of the given problem:</span></p> <gfg-tabs data-run-ide="true" data-mode="light"> <gfg-tab slot="tab">C++</gfg-tab> <gfg-panel slot="panel" data-code-lang="cpp"> <code class="language-cpp"><div class=highlight><pre><span></span><span class=cp>#include</span><span class=w> </span><span class=cpf><iostream></span> <span class=cp>#include</span><span class=w> </span><span class=cpf><vector></span> <span class=k>using</span><span class=w> </span><span class=k>namespace</span><span class=w> </span><span class=nn>std</span><span class=p>;</span> <span class=kt>int</span><span class=w> </span><span class=nf>getSum</span><span class=p>(</span><span class=k>const</span><span class=w> </span><span class=n>vector</span><span class=o><</span><span class=kt>int</span><span class=o>>&</span><span class=w> </span><span class=n>arr1</span><span class=p>)</span><span class=w> </span><span class=p>{</span> <span class=w> </span><span class=kt>int</span><span class=w> </span><span class=n>n</span><span class=w> </span><span class=o>=</span><span class=w> </span><span class=n>arr1</span><span class=p>.</span><span class=n>size</span><span class=p>();</span> <span class=w> </span><span class=k>if</span><span class=w> </span><span class=p>(</span><span class=n>n</span><span class=w> </span><span class=o>%</span><span class=w> </span><span class=mi>2</span><span class=w> </span><span class=o>==</span><span class=w> </span><span class=mi>0</span><span class=p>)</span><span class=w> </span><span class=c1>// (n) is even</span> <span class=w> </span><span class=k>return</span><span class=w> </span><span class=mi>0</span><span class=p>;</span> <span class=w> </span> <span class=w> </span><span class=kt>int</span><span class=w> </span><span class=n>sum</span><span class=w> </span><span class=o>=</span><span class=w> </span><span class=mi>0</span><span class=p>;</span> <span class=w> </span><span class=k>for</span><span class=w> </span><span class=p>(</span><span class=kt>int</span><span class=w> </span><span class=n>i</span><span class=w> </span><span class=o>=</span><span class=w> </span><span class=mi>0</span><span class=p>;</span><span class=w> </span><span class=n>i</span><span class=w> </span><span class=o><</span><span class=w> </span><span class=n>n</span><span class=p>;</span><span class=w> </span><span class=n>i</span><span class=o>++</span><span class=p>)</span><span class=w> </span><span class=p>{</span> <span class=w> </span><span class=n>sum</span><span class=w> </span><span class=o>+=</span><span class=w> </span><span class=n>arr1</span><span class=p>[</span><span class=n>i</span><span class=p>];</span> <span class=w> </span><span class=p>}</span> <span class=w> </span><span class=k>return</span><span class=w> </span><span class=n>sum</span><span class=p>;</span><span class=w> </span><span class=c1>// (n) is odd</span> <span class=p>}</span> <span class=kt>int</span><span class=w> </span><span class=nf>main</span><span class=p>()</span><span class=w> </span><span class=p>{</span> <span class=w> </span> <span class=w> </span><span class=c1>// Declaring two vectors, one with an odd length</span> <span class=w> </span><span class=c1>// and the other with an even length</span> <span class=w> </span><span class=n>vector</span><span class=o><</span><span class=kt>int</span><span class=o>></span><span class=w> </span><span class=n>arr1</span><span class=w> </span><span class=o>=</span><span class=w> </span><span class=p>{</span><span class=mi>1</span><span class=p>,</span><span class=w> </span><span class=mi>2</span><span class=p>,</span><span class=w> </span><span class=mi>3</span><span class=p>,</span><span class=w> </span><span class=mi>4</span><span class=p>};</span> <span class=w> </span><span class=n>vector</span><span class=o><</span><span class=kt>int</span><span class=o>></span><span class=w> </span><span class=n>arr2</span><span class=w> </span><span class=o>=</span><span class=w> </span><span class=p>{</span><span class=mi>1</span><span class=p>,</span><span class=w> </span><span class=mi>2</span><span class=p>,</span><span class=w> </span><span class=mi>3</span><span class=p>,</span><span class=w> </span><span class=mi>4</span><span class=p>,</span><span class=w> </span><span class=mi>5</span><span class=p>};</span> <span class=w> </span><span class=n>cout</span><span class=w> </span><span class=o><<</span><span class=w> </span><span class=n>getSum</span><span class=p>(</span><span class=n>arr1</span><span class=p>)</span><span class=w> </span><span class=o><<</span><span class=w> </span><span class=n>endl</span><span class=p>;</span><span class=w> </span> <span class=w> </span><span class=n>cout</span><span class=w> </span><span class=o><<</span><span class=w> </span><span class=n>getSum</span><span class=p>(</span><span class=n>arr2</span><span class=p>)</span><span class=w> </span><span class=o><<</span><span class=w> </span><span class=n>endl</span><span class=p>;</span> <span class=w> </span><span class=k>return</span><span class=w> </span><span class=mi>0</span><span class=p>;</span> <span class=p>}</span> </pre></div></code> </gfg-panel> <gfg-tab slot="tab">C</gfg-tab> <gfg-panel slot="panel" data-code-lang="c"> <code class="language-c"><div class=highlight><pre><span></span><span class=cp>#include</span><span class=w> </span><span class=cpf><stdio.h></span> <span class=cp>#include</span><span class=w> </span><span class=cpf><stdlib.h></span> <span class=kt>int</span><span class=w> </span><span class=nf>getSum</span><span class=p>(</span><span class=k>const</span><span class=w> </span><span class=kt>int</span><span class=o>*</span><span class=w> </span><span class=n>arr1</span><span class=p>,</span><span class=w> </span><span class=kt>int</span><span class=w> </span><span class=n>n</span><span class=p>)</span><span class=w> </span><span class=p>{</span> <span class=w> </span><span class=k>if</span><span class=w> </span><span class=p>(</span><span class=n>n</span><span class=w> </span><span class=o>%</span><span class=w> </span><span class=mi>2</span><span class=w> </span><span class=o>==</span><span class=w> </span><span class=mi>0</span><span class=p>)</span><span class=w> </span><span class=c1>// (n) is even</span> <span class=w> </span><span class=k>return</span><span class=w> </span><span class=mi>0</span><span class=p>;</span> <span class=w> </span> <span class=w> </span><span class=kt>int</span><span class=w> </span><span class=n>sum</span><span class=w> </span><span class=o>=</span><span class=w> </span><span class=mi>0</span><span class=p>;</span> <span class=w> </span><span class=k>for</span><span class=w> </span><span class=p>(</span><span class=kt>int</span><span class=w> </span><span class=n>i</span><span class=w> </span><span class=o>=</span><span class=w> </span><span class=mi>0</span><span class=p>;</span><span class=w> </span><span class=n>i</span><span class=w> </span><span class=o><</span><span class=w> </span><span class=n>n</span><span class=p>;</span><span class=w> </span><span class=n>i</span><span class=o>++</span><span class=p>)</span><span class=w> </span><span class=p>{</span> <span class=w> </span><span class=n>sum</span><span class=w> </span><span class=o>+=</span><span class=w> </span><span class=n>arr1</span><span class=p>[</span><span class=n>i</span><span class=p>];</span> <span class=w> </span><span class=p>}</span> <span class=w> </span><span class=k>return</span><span class=w> </span><span class=n>sum</span><span class=p>;</span><span class=w> </span><span class=c1>// (n) is odd</span> <span class=p>}</span> <span class=kt>int</span><span class=w> </span><span class=nf>main</span><span class=p>()</span><span class=w> </span><span class=p>{</span> <span class=w> </span><span class=c1>// Declaring two arrays, one with an odd length</span> <span class=w> </span><span class=c1>// and the other with an even length</span> <span class=w> </span><span class=kt>int</span><span class=w> </span><span class=n>arr1</span><span class=p>[]</span><span class=w> </span><span class=o>=</span><span class=w> </span><span class=p>{</span><span class=mi>1</span><span class=p>,</span><span class=w> </span><span class=mi>2</span><span class=p>,</span><span class=w> </span><span class=mi>3</span><span class=p>,</span><span class=w> </span><span class=mi>4</span><span class=p>};</span> <span class=w> </span><span class=kt>int</span><span class=w> </span><span class=n>arr2</span><span class=p>[]</span><span class=w> </span><span class=o>=</span><span class=w> </span><span class=p>{</span><span class=mi>1</span><span class=p>,</span><span class=w> </span><span class=mi>2</span><span class=p>,</span><span class=w> </span><span class=mi>3</span><span class=p>,</span><span class=w> </span><span class=mi>4</span><span class=p>,</span><span class=w> </span><span class=mi>5</span><span class=p>};</span> <span class=w> </span><span class=n>printf</span><span class=p>(</span><span class=s>"%d</span><span class=se>\n</span><span class=s>"</span><span class=p>,</span><span class=w> </span><span class=n>getSum</span><span class=p>(</span><span class=n>arr1</span><span class=p>,</span><span class=w> </span><span class=mi>4</span><span class=p>));</span> <span class=w> </span><span class=n>printf</span><span class=p>(</span><span class=s>"%d</span><span class=se>\n</span><span class=s>"</span><span class=p>,</span><span class=w> </span><span class=n>getSum</span><span class=p>(</span><span class=n>arr2</span><span class=p>,</span><span class=w> </span><span class=mi>5</span><span class=p>));</span> <span class=w> </span><span class=k>return</span><span class=w> </span><span class=mi>0</span><span class=p>;</span> <span class=p>}</span> </pre></div></code> </gfg-panel> <gfg-tab slot="tab">Java</gfg-tab> <gfg-panel slot="panel" data-code-lang="java"> <code class="language-java"><div class=highlight><pre><span></span><span class=kn>import</span><span class=w> </span><span class=nn>java.util.Arrays</span><span class=p>;</span> <span class=kd>public</span><span class=w> </span><span class=kd>class</span> <span class=nc>Main</span><span class=w> </span><span class=p>{</span> <span class=w> </span><span class=kd>public</span><span class=w> </span><span class=kd>static</span><span class=w> </span><span class=kt>int</span><span class=w> </span><span class=nf>getSum</span><span class=p>(</span><span class=kt>int</span><span class=o>[]</span><span class=w> </span><span class=n>arr1</span><span class=p>)</span><span class=w> </span><span class=p>{</span> <span class=w> </span><span class=kt>int</span><span class=w> </span><span class=n>n</span><span class=w> </span><span class=o>=</span><span class=w> </span><span class=n>arr1</span><span class=p>.</span><span class=na>length</span><span class=p>;</span> <span class=w> </span><span class=k>if</span><span class=w> </span><span class=p>(</span><span class=n>n</span><span class=w> </span><span class=o>%</span><span class=w> </span><span class=mi>2</span><span class=w> </span><span class=o>==</span><span class=w> </span><span class=mi>0</span><span class=p>)</span><span class=w> </span><span class=c1>// (n) is even</span> <span class=w> </span><span class=k>return</span><span class=w> </span><span class=mi>0</span><span class=p>;</span> <span class=w> </span> <span class=w> </span><span class=kt>int</span><span class=w> </span><span class=n>sum</span><span class=w> </span><span class=o>=</span><span class=w> </span><span class=mi>0</span><span class=p>;</span> <span class=w> </span><span class=k>for</span><span class=w> </span><span class=p>(</span><span class=kt>int</span><span class=w> </span><span class=n>i</span><span class=w> </span><span class=o>=</span><span class=w> </span><span class=mi>0</span><span class=p>;</span><span class=w> </span><span class=n>i</span><span class=w> </span><span class=o><</span><span class=w> </span><span class=n>n</span><span class=p>;</span><span class=w> </span><span class=n>i</span><span class=o>++</span><span class=p>)</span><span class=w> </span><span class=p>{</span> <span class=w> </span><span class=n>sum</span><span class=w> </span><span class=o>+=</span><span class=w> </span><span class=n>arr1</span><span class=o>[</span><span class=n>i</span><span class=o>]</span><span class=p>;</span> <span class=w> </span><span class=p>}</span> <span class=w> </span><span class=k>return</span><span class=w> </span><span class=n>sum</span><span class=p>;</span><span class=w> </span><span class=c1>// (n) is odd</span> <span class=w> </span><span class=p>}</span> <span class=w> </span><span class=kd>public</span><span class=w> </span><span class=kd>static</span><span class=w> </span><span class=kt>void</span><span class=w> </span><span class=nf>main</span><span class=p>(</span><span class=n>String</span><span class=o>[]</span><span class=w> </span><span class=n>args</span><span class=p>)</span><span class=w> </span><span class=p>{</span> <span class=w> </span><span class=c1>// Declaring two arrays, one with an odd length</span> <span class=w> </span><span class=c1>// and the other with an even length</span> <span class=w> </span><span class=kt>int</span><span class=o>[]</span><span class=w> </span><span class=n>arr1</span><span class=w> </span><span class=o>=</span><span class=w> </span><span class=p>{</span><span class=mi>1</span><span class=p>,</span><span class=w> </span><span class=mi>2</span><span class=p>,</span><span class=w> </span><span class=mi>3</span><span class=p>,</span><span class=w> </span><span class=mi>4</span><span class=p>};</span> <span class=w> </span><span class=kt>int</span><span class=o>[]</span><span class=w> </span><span class=n>arr2</span><span class=w> </span><span class=o>=</span><span class=w> </span><span class=p>{</span><span class=mi>1</span><span class=p>,</span><span class=w> </span><span class=mi>2</span><span class=p>,</span><span class=w> </span><span class=mi>3</span><span class=p>,</span><span class=w> </span><span class=mi>4</span><span class=p>,</span><span class=w> </span><span class=mi>5</span><span class=p>};</span> <span class=w> </span><span class=n>System</span><span class=p>.</span><span class=na>out</span><span class=p>.</span><span class=na>println</span><span class=p>(</span><span class=n>getSum</span><span class=p>(</span><span class=n>arr1</span><span class=p>));</span> <span class=w> </span><span class=n>System</span><span class=p>.</span><span class=na>out</span><span class=p>.</span><span class=na>println</span><span class=p>(</span><span class=n>getSum</span><span class=p>(</span><span class=n>arr2</span><span class=p>));</span> <span class=w> </span><span class=p>}</span> <span class=p>}</span> </pre></div></code> </gfg-panel> <gfg-tab slot="tab">Python</gfg-tab> <gfg-panel slot="panel" data-code-lang="python3"> <code class="language-python3"><div class=highlight><pre><span></span><span class=k>def</span> <span class=nf>getSum</span><span class=p>(</span><span class=n>arr1</span><span class=p>):</span> <span class=n>n</span> <span class=o>=</span> <span class=nb>len</span><span class=p>(</span><span class=n>arr1</span><span class=p>)</span> <span class=k>if</span> <span class=n>n</span> <span class=o>%</span> <span class=mi>2</span> <span class=o>==</span> <span class=mi>0</span><span class=p>:</span> <span class=c1># (n) is even</span> <span class=k>return</span> <span class=mi>0</span> <span class=nb>sum</span> <span class=o>=</span> <span class=mi>0</span> <span class=k>for</span> <span class=n>i</span> <span class=ow>in</span> <span class=nb>range</span><span class=p>(</span><span class=n>n</span><span class=p>):</span> <span class=nb>sum</span> <span class=o>+=</span> <span class=n>arr1</span><span class=p>[</span><span class=n>i</span><span class=p>]</span> <span class=k>return</span> <span class=nb>sum</span> <span class=c1># (n) is odd</span> <span class=k>if</span> <span class=vm>__name__</span> <span class=o>==</span> <span class=s1>'__main__'</span><span class=p>:</span> <span class=c1># Declaring two lists, one with an odd length</span> <span class=c1># and the other with an even length</span> <span class=n>arr1</span> <span class=o>=</span> <span class=p>[</span><span class=mi>1</span><span class=p>,</span> <span class=mi>2</span><span class=p>,</span> <span class=mi>3</span><span class=p>,</span> <span class=mi>4</span><span class=p>]</span> <span class=n>arr2</span> <span class=o>=</span> <span class=p>[</span><span class=mi>1</span><span class=p>,</span> <span class=mi>2</span><span class=p>,</span> <span class=mi>3</span><span class=p>,</span> <span class=mi>4</span><span class=p>,</span> <span class=mi>5</span><span class=p>]</span> <span class=nb>print</span><span class=p>(</span><span class=n>getSum</span><span class=p>(</span><span class=n>arr1</span><span class=p>))</span> <span class=nb>print</span><span class=p>(</span><span class=n>getSum</span><span class=p>(</span><span class=n>arr2</span><span class=p>))</span> </pre></div></code> </gfg-panel> <gfg-tab slot="tab">C#</gfg-tab> <gfg-panel slot="panel" data-code-lang="csharp"> <code class="language-csharp"><div class=highlight><pre><span></span><span class=k>using</span><span class=w> </span><span class=nn>System</span><span class=p>;</span> <span class=k>class</span><span class=w> </span><span class=nc>Program</span><span class=w> </span><span class=p>{</span> <span class=w> </span><span class=k>static</span><span class=w> </span><span class=kt>int</span><span class=w> </span><span class=nf>getSum</span><span class=p>(</span><span class=kt>int</span><span class=p>[]</span><span class=w> </span><span class=n>arr1</span><span class=p>)</span><span class=w> </span><span class=p>{</span> <span class=w> </span><span class=kt>int</span><span class=w> </span><span class=n>n</span><span class=w> </span><span class=o>=</span><span class=w> </span><span class=n>arr1</span><span class=p>.</span><span class=n>Length</span><span class=p>;</span> <span class=w> </span><span class=k>if</span><span class=w> </span><span class=p>(</span><span class=n>n</span><span class=w> </span><span class=o>%</span><span class=w> </span><span class=m>2</span><span class=w> </span><span class=o>==</span><span class=w> </span><span class=m>0</span><span class=p>)</span><span class=w> </span><span class=c1>// (n) is even</span> <span class=w> </span><span class=k>return</span><span class=w> </span><span class=m>0</span><span class=p>;</span> <span class=w> </span> <span class=w> </span><span class=kt>int</span><span class=w> </span><span class=n>sum</span><span class=w> </span><span class=o>=</span><span class=w> </span><span class=m>0</span><span class=p>;</span> <span class=w> </span><span class=k>for</span><span class=w> </span><span class=p>(</span><span class=kt>int</span><span class=w> </span><span class=n>i</span><span class=w> </span><span class=o>=</span><span class=w> </span><span class=m>0</span><span class=p>;</span><span class=w> </span><span class=n>i</span><span class=w> </span><span class=o><</span><span class=w> </span><span class=n>n</span><span class=p>;</span><span class=w> </span><span class=n>i</span><span class=o>++</span><span class=p>)</span><span class=w> </span><span class=p>{</span> <span class=w> </span><span class=n>sum</span><span class=w> </span><span class=o>+=</span><span class=w> </span><span class=n>arr1</span><span class=p>[</span><span class=n>i</span><span class=p>];</span> <span class=w> </span><span class=p>}</span> <span class=w> </span><span class=k>return</span><span class=w> </span><span class=n>sum</span><span class=p>;</span><span class=w> </span><span class=c1>// (n) is odd</span> <span class=w> </span><span class=p>}</span> <span class=w> </span><span class=k>static</span><span class=w> </span><span class=k>void</span><span class=w> </span><span class=nf>Main</span><span class=p>()</span><span class=w> </span><span class=p>{</span> <span class=w> </span><span class=c1>// Declaring two arrays, one with an odd length</span> <span class=w> </span><span class=c1>// and the other with an even length</span> <span class=w> </span><span class=kt>int</span><span class=p>[]</span><span class=w> </span><span class=n>arr1</span><span class=w> </span><span class=o>=</span><span class=w> </span><span class=p>{</span><span class=m>1</span><span class=p>,</span><span class=w> </span><span class=m>2</span><span class=p>,</span><span class=w> </span><span class=m>3</span><span class=p>,</span><span class=w> </span><span class=m>4</span><span class=p>};</span> <span class=w> </span><span class=kt>int</span><span class=p>[]</span><span class=w> </span><span class=n>arr2</span><span class=w> </span><span class=o>=</span><span class=w> </span><span class=p>{</span><span class=m>1</span><span class=p>,</span><span class=w> </span><span class=m>2</span><span class=p>,</span><span class=w> </span><span class=m>3</span><span class=p>,</span><span class=w> </span><span class=m>4</span><span class=p>,</span><span class=w> </span><span class=m>5</span><span class=p>};</span> <span class=w> </span><span class=n>Console</span><span class=p>.</span><span class=n>WriteLine</span><span class=p>(</span><span class=n>getSum</span><span class=p>(</span><span class=n>arr1</span><span class=p>));</span> <span class=w> </span><span class=n>Console</span><span class=p>.</span><span class=n>WriteLine</span><span class=p>(</span><span class=n>getSum</span><span class=p>(</span><span class=n>arr2</span><span class=p>));</span> <span class=w> </span><span class=p>}</span> <span class=p>}</span> </pre></div></code> </gfg-panel> <gfg-tab slot="tab">JavaScript</gfg-tab> <gfg-panel slot="panel" data-code-lang="javascript"> <code class="language-javascript"><div class=highlight><pre><span></span><span class=kd>function</span><span class=w> </span><span class=nx>getSum</span><span class=p>(</span><span class=nx>arr1</span><span class=p>)</span><span class=w> </span><span class=p>{</span> <span class=w> </span><span class=kd>const</span><span class=w> </span><span class=nx>n</span><span class=w> </span><span class=o>=</span><span class=w> </span><span class=nx>arr1</span><span class=p>.</span><span class=nx>length</span><span class=p>;</span> <span class=w> </span><span class=k>if</span><span class=w> </span><span class=p>(</span><span class=nx>n</span><span class=w> </span><span class=o>%</span><span class=w> </span><span class=mf>2</span><span class=w> </span><span class=o>===</span><span class=w> </span><span class=mf>0</span><span class=p>)</span><span class=w> </span><span class=c1>// (n) is even</span> <span class=w> </span><span class=k>return</span><span class=w> </span><span class=mf>0</span><span class=p>;</span> <span class=w> </span> <span class=w> </span><span class=kd>let</span><span class=w> </span><span class=nx>sum</span><span class=w> </span><span class=o>=</span><span class=w> </span><span class=mf>0</span><span class=p>;</span> <span class=w> </span><span class=k>for</span><span class=w> </span><span class=p>(</span><span class=kd>let</span><span class=w> </span><span class=nx>i</span><span class=w> </span><span class=o>=</span><span class=w> </span><span class=mf>0</span><span class=p>;</span><span class=w> </span><span class=nx>i</span><span class=w> </span><span class=o><</span><span class=w> </span><span class=nx>n</span><span class=p>;</span><span class=w> </span><span class=nx>i</span><span class=o>++</span><span class=p>)</span><span class=w> </span><span class=p>{</span> <span class=w> </span><span class=nx>sum</span><span class=w> </span><span class=o>+=</span><span class=w> </span><span class=nx>arr1</span><span class=p>[</span><span class=nx>i</span><span class=p>];</span> <span class=w> </span><span class=p>}</span> <span class=w> </span><span class=k>return</span><span class=w> </span><span class=nx>sum</span><span class=p>;</span><span class=w> </span><span class=c1>// (n) is odd</span> <span class=p>}</span> <span class=c1>// Declaring two arrays, one with an odd length</span> <span class=c1>// and the other with an even length</span> <span class=kd>const</span><span class=w> </span><span class=nx>arr1</span><span class=w> </span><span class=o>=</span><span class=w> </span><span class=p>[</span><span class=mf>1</span><span class=p>,</span><span class=w> </span><span class=mf>2</span><span class=p>,</span><span class=w> </span><span class=mf>3</span><span class=p>,</span><span class=w> </span><span class=mf>4</span><span class=p>];</span> <span class=kd>const</span><span class=w> </span><span class=nx>arr2</span><span class=w> </span><span class=o>=</span><span class=w> </span><span class=p>[</span><span class=mf>1</span><span class=p>,</span><span class=w> </span><span class=mf>2</span><span class=p>,</span><span class=w> </span><span class=mf>3</span><span class=p>,</span><span class=w> </span><span class=mf>4</span><span class=p>,</span><span class=w> </span><span class=mf>5</span><span class=p>];</span> <span class=nx>console</span><span class=p>.</span><span class=nx>log</span><span class=p>(</span><span class=nx>getSum</span><span class=p>(</span><span class=nx>arr1</span><span class=p>));</span> <span class=nx>console</span><span class=p>.</span><span class=nx>log</span><span class=p>(</span><span class=nx>getSum</span><span class=p>(</span><span class=nx>arr2</span><span class=p>));</span> </pre></div></code> </gfg-panel> <gfg-tab slot="tab">PHP</gfg-tab> <gfg-panel slot="panel" data-code-lang="php"> <code class="language-php"><div class=highlight><pre><span></span><span class=cp><?php</span> <span class=k>function</span> <span class=nf>getSum</span><span class=p>(</span><span class=nv>$arr1</span><span class=p>)</span> <span class=p>{</span> <span class=nv>$n</span> <span class=o>=</span> <span class=nb>count</span><span class=p>(</span><span class=nv>$arr1</span><span class=p>);</span> <span class=k>if</span> <span class=p>(</span><span class=nv>$n</span> <span class=o>%</span> <span class=mi>2</span> <span class=o>==</span> <span class=mi>0</span><span class=p>)</span> <span class=c1>// (n) is even</span> <span class=k>return</span> <span class=mi>0</span><span class=p>;</span> <span class=nv>$sum</span> <span class=o>=</span> <span class=mi>0</span><span class=p>;</span> <span class=k>for</span> <span class=p>(</span><span class=nv>$i</span> <span class=o>=</span> <span class=mi>0</span><span class=p>;</span> <span class=nv>$i</span> <span class=o><</span> <span class=nv>$n</span><span class=p>;</span> <span class=nv>$i</span><span class=o>++</span><span class=p>)</span> <span class=p>{</span> <span class=nv>$sum</span> <span class=o>+=</span> <span class=nv>$arr1</span><span class=p>[</span><span class=nv>$i</span><span class=p>];</span> <span class=p>}</span> <span class=k>return</span> <span class=nv>$sum</span><span class=p>;</span> <span class=c1>// (n) is odd</span> <span class=p>}</span> <span class=c1>// Declaring two arrays, one with an odd length</span> <span class=c1>// and the other with an even length</span> <span class=nv>$arr1</span> <span class=o>=</span> <span class=p>[</span><span class=mi>1</span><span class=p>,</span> <span class=mi>2</span><span class=p>,</span> <span class=mi>3</span><span class=p>,</span> <span class=mi>4</span><span class=p>];</span> <span class=nv>$arr2</span> <span class=o>=</span> <span class=p>[</span><span class=mi>1</span><span class=p>,</span> <span class=mi>2</span><span class=p>,</span> <span class=mi>3</span><span class=p>,</span> <span class=mi>4</span><span class=p>,</span> <span class=mi>5</span><span class=p>];</span> <span class=k>echo</span> <span class=nx>getSum</span><span class=p>(</span><span class=nv>$arr1</span><span class=p>)</span> <span class=o>.</span> <span class=s2>"</span><span class=se>\n</span><span class=s2>"</span><span class=p>;</span> <span class=k>echo</span> <span class=nx>getSum</span><span class=p>(</span><span class=nv>$arr2</span><span class=p>)</span> <span class=o>.</span> <span class=s2>"</span><span class=se>\n</span><span class=s2>"</span><span class=p>;</span> <span class=cp>?></span> </pre></div></code> </gfg-panel></gfg-tabs><div class="code-output"><br><strong>Output</strong><pre>0 15 </pre></div><p dir="ltr"><b><strong>Time Complexity Analysis:</strong></b></p> <ul><li value="1"><b><strong>Best Case: </strong></b><span>The order of growth will be </span><b><strong>constant</strong></b><span> because in the best case we are assuming that (n) is even.</span></li><li value="2"><b><strong>Average Case:</strong></b><span> In this case, we will</span><b><strong> </strong></b><span>assume that even and odd are equally likely, therefore</span><b><strong> </strong></b><span>Order of growth will be </span><b><strong>linear</strong></b></li><li value="3"><b><strong>Worst Case: </strong></b><span>The order of growth will be</span><b><strong> linear</strong></b><span> because in this case, we are assuming that (n) is always odd.</span></li></ul><h3><span>Next Articles to Read</span></h3><ul><li value="1"><a href="https://www.geeksforgeeks.org/how-to-analyse-loops-for-complexity-analysis-of-algorithms/" target="_blank" rel="noopener"><span>Asymptotic Notations</span></a></li><li value="2"><a href="https://www.geeksforgeeks.org/how-to-analyse-complexity-of-recurrence-relation/" target="_blank" rel="noopener"><span>Analysis of Loops</span></a></li><li value="3"><a href="https://www.geeksforgeeks.org/how-to-analyse-complexity-of-recurrence-relation/" target="_blank" rel="noopener"><span>Analysis of Recursive Functions</span></a></li></ul><h3><span>Reference books:</span></h3><ol><li value="1"><span>“Introduction to Algorithms” by Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein is a comprehensive guide to algorithm analysis, including worst, average, and best case analysis.</span></li><li value="2"><span>“Algorithm Design” by Jon Kleinberg and 脡va Tardos provides a modern approach to algorithm design, with a focus on worst case analysis.</span></li><li value="3"><span>“The Art of Computer Programming” by Donald Knuth is a classic text on algorithms and programming, which includes a detailed discussion of worst case analysis.</span></li><li value="4"><span>“Algorithms Unlocked” by Thomas H. Cormen provides a gentle introduction to algorithm analysis, including worst, average, and best case analysis.</span></li></ol><br/><div id="AP_G4GR_6"></div>  <div class='article_bottom_text'></div><br> <div id="video-tab-content" class="video-tab-content"> <div style="text-align: center; margin: 20px 0px;" id="GFG_AD_InContent_Desktop_728x280"></div> </div> <div class="d-row content-bw article-pgnavi v-divider-gfg"style="margin-top: 20px;"> <div class="article-pgnavi_prev"><div class="comment_div" data-title="Comments"><button class="author_footer_btn" data-gfg-action="loadComments"> <div class='discussion_panel'> <i class='discussion_button'> </i> Comment </div></button></div><div class="trigger-div"><button class="author_footer_btn"><div class="more_info">More info<span class="more_info_uparrow gfg-icon gfg-icon_arrow-down-thin"></span></div></button></div> <a href="https://www.geeksforgeeks.org/about/contact-us/?listicles" target="_blank" class="advertise-with-us-div"><button class="advertise-with-us-btn"><span class="advertise-with-us-text">Advertise with us</span></button></a> </div> <div class="article-pgnavi_next"> <a href="https://www.geeksforgeeks.org/asymptotic-notation-and-analysis-based-on-input-size-of-algorithms/?ref=next_article" class="pg-head"> <span>Next Article</span> <span class="gfg-icon gfg-icon_next"></span> </a>  <div class="pg-main"> <a href="https://www.geeksforgeeks.org/asymptotic-notation-and-analysis-based-on-input-size-of-algorithms/?ref=next_article">Asymptotic Analysis</a> </div> </div> </div> <div class="more-info hidden-div"> <div class="article-meta-author-details "> <div class="article-meta-author-details-block"> <div class="article-meta-author-details-profile-display"> <div class="author_info"> <div class="article-meta-author-details-profile-display-icon"> <a href="https://www.geeksforgeeks.org/user/kartik/contributions/?itm_source=geeksforgeeks&itm_medium=article_author&itm_campaign=auth_user" style="text-decoration: none;"><div class="image-wrap" style="position: relative"><img src="https://media.geeksforgeeks.org/auth/profile/sb7ciorr5k5t22woqkes" class="avatarprofile_image restrict-popup-gfg" alt="author"> <div style="position: absolute;top: -35px; left: -13px;"> <i class="gfg-badge-icon md master"></i> </div> </div> </a> </div> <div class="article-meta-author-details-profile-display-name" > <a aria-label="author profile" href="https://www.geeksforgeeks.org/user/kartik/contributions/?itm_source=geeksforgeeks&itm_medium=article_author&itm_campaign=auth_user" style="display: block;overflow: hidden;width: 65px;text-decoration: none;text-overflow: ellipsis;color: var(--gfg-title-color);font-weight: bold;white-space: nowrap;">kartik</a> </div> </div> <div class="author_follow_btn"><div class="article-meta-author-details-follow-button"> <div class="follow-container"> <div class="follow-btn" > <button id="followAuthor" type="button" onclick ="followOrUnfollowAuthor()" value="kartik"> <span role="img" aria-label="plus" class="plus-icon"><svg viewBox="64 64 896 896" focusable="false" data-icon="plus" width="1em" height="1em" fill="currentColor" aria-hidden="true"><defs><style></style></defs><path d="M482 152h60q8 0 8 8v704q0 8-8 8h-60q-8 0-8-8V160q0-8 8-8z"></path><path d="M176 474h672q8 0 8 8v60q0 8-8 8H176q-8 0-8-8v-60q0-8 8-8z"></path></svg></span> <span>Follow</span></button></div></div></div></div> </div> </div> <div class="article_bottom_suggestion_wrapper"> <div class="article_bottom_suggestion" data-title="Follow"> <a href='https://news.google.com/publications/CAAqBwgKMLTrzwsw44bnAw?hl=en-IN&gl=IN&ceid=IN%3Aen' target="_blank"> <img class="gfg-icon_Gnews no-zoom-in-cursor" src=https://media.geeksforgeeks.org/auth-dashboard-uploads/Google-news.svg loading="lazy" alt="News"></img> </a> </div> <div pid="17020" class="article--viewer_like tooltip tooltipBottom" data-title="Like Article">  <button id="likeButton" aria-label="like article" data-gfg-action="like-article" data-bookmark-value="0" data-liked="false" style="color: #5B5A5A !important; display: flex; align-items: center; background-color: unset; margin: 0px !important; padding: 5px 0px;"> <i class="author-badge-like-button"></i> <figure id="likeCount" style="margin-left: 3px; margin-top: 4px; color: var(--like-count-color); font-size: 14px; font-weight: 600;" class="favoriteText"></figure> </button> </div> <div class="article_bottom_suggestion" onclick="improveArticleCall()" data-title="Improve"> <span class="improveTooltipBottom">Improve</span> <i class="author-badge-improvement-button"></i> </div> </div> </div> <div class="bottom-wrap" style="margin-top: 12px; margin-bottom: 25px;"> <div class="improved"> <div class="t-head">Article Tags : </div> <ul> <li style="border-radius: 25px;" class=""> <a href="https://www.geeksforgeeks.org/category/dsa/algorithm/?ref=article_category">Algorithms</a> </li> <li style="border-radius: 25px;" class=""> <a href="https://www.geeksforgeeks.org/category/dsa/algorithm/analysis/?ref=article_category">Analysis of Algorithms</a> </li> <li style="border-radius: 25px;" class=""> <a href="https://www.geeksforgeeks.org/category/dsa/?ref=article_category">DSA</a> </li> <li style="border-radius: 25px;" class=""> <a href="https://www.geeksforgeeks.org/tag/complexity-analysis/?ref=article_tag">Complexity-analysis</a> </li> </ul> </div> <div class="improved"> <div class="t-head">Practice Tags : </div> <ul class="practice-tags"> <li><a href="https://www.geeksforgeeks.org/explore?category=Algorithms&ref=article_practice_tag">Algorithms</a></li> </ul> </div> </div> </div> </article> <div class="article--recommended article--recommended_wrapper" id="similar-reads"> <h3 class="new-top-bar top-bar-title">Similar Reads</h3> <div class="gfg-similar-reads-list"> <ul class="similarReadLeftBarList"><div class="second"><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/analysis-of-algorithms/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Analysis of Algorithms </div> <div class="gfg-similar-read-item-subheading">Analysis of Algorithms is a fundamental aspect of computer science that involves evaluating performance of algorithms and programs. Efficiency is measured in terms of time and space. Basics on Analysis of Algorithms:Why is Analysis Important?Order of GrowthAsymptotic Analysis Worst, Average and Best</div> </div> <div class="reading-time"> <i class="reading-time-icon" data-gfg-action="readingtime"></i> <span style="color: var(--recommendation-card-text-color);font-size: 14px;font-weight: 500;line-height: 17px;">1 min read</span> </div> </a></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/complete-guide-on-complexity-analysis/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Complete Guide On Complexity Analysis - Data Structure and Algorithms Tutorial </div> <div class="gfg-similar-read-item-subheading">Complexity analysis is defined as a technique to characterise the time taken by an algorithm with respect to input size (independent from the machine, language and compiler). It is used for evaluating the variations of execution time on different algorithms. What is the need for Complexity Analysis?</div> </div> <div class="reading-time"> <i class="reading-time-icon" data-gfg-action="readingtime"></i> <span style="color: var(--recommendation-card-text-color);font-size: 14px;font-weight: 500;line-height: 17px;">15+ min read</span> </div> </a></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/what-is-algorithm-and-why-analysis-of-it-is-important/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Why is Analysis of Algorithm important? </div> <div class="gfg-similar-read-item-subheading">Why is Performance of Algorithms Important ? There are many important things that should be taken care of, like user-friendliness, modularity, security, maintainability, etc. Why worry about performance? The answer to this is simple, we can have all the above things only if we have performance. So p</div> </div> <div class="reading-time"> <i class="reading-time-icon" data-gfg-action="readingtime"></i> <span style="color: var(--recommendation-card-text-color);font-size: 14px;font-weight: 500;line-height: 17px;">2 min read</span> </div> </a></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/types-of-asymptotic-notations-in-complexity-analysis-of-algorithms/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Types of Asymptotic Notations in Complexity Analysis of Algorithms </div> <div class="gfg-similar-read-item-subheading">We have discussed Asymptotic Analysis, and Worst, Average, and Best Cases of Algorithms. The main idea of asymptotic analysis is to have a measure of the efficiency of algorithms that don't depend on machine-specific constants and don't require algorithms to be implemented and time taken by programs</div> </div> <div class="reading-time"> <i class="reading-time-icon" data-gfg-action="readingtime"></i> <span style="color: var(--recommendation-card-text-color);font-size: 14px;font-weight: 500;line-height: 17px;">8 min read</span> </div> </a></li><li class="currentpage similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/worst-average-and-best-case-analysis-of-algorithms/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Worst, Average and Best Case Analysis of Algorithms </div> <div class="gfg-similar-read-item-subheading">In the previous post, we discussed how Asymptotic analysis overcomes the problems of the naive way of analyzing algorithms. Now let us learn about What is Worst, Average, and Best cases of an algorithm: 1. Worst Case Analysis (Mostly used) In the worst-case analysis, we calculate the upper bound on</div> </div> <div class="reading-time"> <i class="reading-time-icon" data-gfg-action="readingtime"></i> <span style="color: var(--recommendation-card-text-color);font-size: 14px;font-weight: 500;line-height: 17px;">10 min read</span> </div> </a></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/asymptotic-notation-and-analysis-based-on-input-size-of-algorithms/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Asymptotic Analysis </div> <div class="gfg-similar-read-item-subheading">Given two algorithms for a task, how do we find out which one is better? One naive way of doing this is - to implement both the algorithms and run the two programs on your computer for different inputs and see which one takes less time. There are many problems with this approach for the analysis of</div> </div> <div class="reading-time"> <i class="reading-time-icon" data-gfg-action="readingtime"></i> <span style="color: var(--recommendation-card-text-color);font-size: 14px;font-weight: 500;line-height: 17px;">3 min read</span> </div> </a></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/how-to-analyse-loops-for-complexity-analysis-of-algorithms/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">How to Analyse Loops for Complexity Analysis of Algorithms </div> <div class="gfg-similar-read-item-subheading">We have discussed Asymptotic Analysis, Worst, Average and Best Cases and Asymptotic Notations in previous posts. In this post, an analysis of iterative programs with simple examples is discussed. The analysis of loops for the complexity analysis of algorithms involves finding the number of operation</div> </div> <div class="reading-time"> <i class="reading-time-icon" data-gfg-action="readingtime"></i> <span style="color: var(--recommendation-card-text-color);font-size: 14px;font-weight: 500;line-height: 17px;">15+ min read</span> </div> </a></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/analysis-algorithms-set-5-practice-problems/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Sample Practice Problems on Complexity Analysis of Algorithms </div> <div class="gfg-similar-read-item-subheading">Prerequisite: Asymptotic Analysis, Worst, Average and Best Cases, Asymptotic Notations, Analysis of loops. Problem 1: Find the complexity of the below recurrence: { 3T(n-1), if n>0,T(n) = { 1, otherwise Solution: Let us solve using substitution. T(n) = 3T(n-1) = 3(3T(n-2)) = 32T(n-2) = 33T(n-3) .</div> </div> <div class="reading-time"> <i class="reading-time-icon" data-gfg-action="readingtime"></i> <span style="color: var(--recommendation-card-text-color);font-size: 14px;font-weight: 500;line-height: 17px;">15 min read</span> </div> </a></li><div class="leftbar-dropdown"><h2 class="dropdown-title">Basics on Analysis of Algorithms<span class="gfg-icon gfg-icon_arrow-down-thin"></span></h2><ul style="display: none;"><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/what-is-algorithm-and-why-analysis-of-it-is-important/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Why is Analysis of Algorithm important? </div> <div class="gfg-similar-read-item-subheading">Why is Performance of Algorithms Important ? There are many important things that should be taken care of, like user-friendliness, modularity, security, maintainability, etc. Why worry about performance? The answer to this is simple, we can have all the above things only if we have performance. So p</div> </div> <div class="reading-time"> <i class="reading-time-icon" data-gfg-action="readingtime"></i> <span style="color: var(--recommendation-card-text-color);font-size: 14px;font-weight: 500;line-height: 17px;">2 min read</span> </div> </a><hr style="background:var(--gfg-selected-color); width:70%; margin: 0 auto;"></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/asymptotic-notation-and-analysis-based-on-input-size-of-algorithms/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Asymptotic Analysis </div> <div class="gfg-similar-read-item-subheading">Given two algorithms for a task, how do we find out which one is better? One naive way of doing this is - to implement both the algorithms and run the two programs on your computer for different inputs and see which one takes less time. There are many problems with this approach for the analysis of</div> </div> <div class="reading-time"> <i class="reading-time-icon" data-gfg-action="readingtime"></i> <span style="color: var(--recommendation-card-text-color);font-size: 14px;font-weight: 500;line-height: 17px;">3 min read</span> </div> </a><hr style="background:var(--gfg-selected-color); width:70%; margin: 0 auto;"></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/worst-average-and-best-case-analysis-of-algorithms/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Worst, Average and Best Case Analysis of Algorithms </div> <div class="gfg-similar-read-item-subheading">In the previous post, we discussed how Asymptotic analysis overcomes the problems of the naive way of analyzing algorithms. Now let us learn about What is Worst, Average, and Best cases of an algorithm: 1. Worst Case Analysis (Mostly used) In the worst-case analysis, we calculate the upper bound on</div> </div> <div class="reading-time"> <i class="reading-time-icon" data-gfg-action="readingtime"></i> <span style="color: var(--recommendation-card-text-color);font-size: 14px;font-weight: 500;line-height: 17px;">10 min read</span> </div> </a><hr style="background:var(--gfg-selected-color); width:70%; margin: 0 auto;"></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/types-of-asymptotic-notations-in-complexity-analysis-of-algorithms/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Types of Asymptotic Notations in Complexity Analysis of Algorithms </div> <div class="gfg-similar-read-item-subheading">We have discussed Asymptotic Analysis, and Worst, Average, and Best Cases of Algorithms. The main idea of asymptotic analysis is to have a measure of the efficiency of algorithms that don't depend on machine-specific constants and don't require algorithms to be implemented and time taken by programs</div> </div> <div class="reading-time"> <i class="reading-time-icon" data-gfg-action="readingtime"></i> <span style="color: var(--recommendation-card-text-color);font-size: 14px;font-weight: 500;line-height: 17px;">8 min read</span> </div> </a><hr style="background:var(--gfg-selected-color); width:70%; margin: 0 auto;"></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/how-to-analyse-loops-for-complexity-analysis-of-algorithms/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">How to Analyse Loops for Complexity Analysis of Algorithms </div> <div class="gfg-similar-read-item-subheading">We have discussed Asymptotic Analysis, Worst, Average and Best Cases and Asymptotic Notations in previous posts. In this post, an analysis of iterative programs with simple examples is discussed. The analysis of loops for the complexity analysis of algorithms involves finding the number of operation</div> </div> <div class="reading-time"> <i class="reading-time-icon" data-gfg-action="readingtime"></i> <span style="color: var(--recommendation-card-text-color);font-size: 14px;font-weight: 500;line-height: 17px;">15+ min read</span> </div> </a><hr style="background:var(--gfg-selected-color); width:70%; margin: 0 auto;"></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/how-to-analyse-complexity-of-recurrence-relation/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">How to analyse Complexity of Recurrence Relation </div> <div class="gfg-similar-read-item-subheading">The analysis of the complexity of a recurrence relation involves finding the asymptotic upper bound on the running time of a recursive algorithm. This is usually done by finding a closed-form expression for the number of operations performed by the algorithm as a function of the input size, and then</div> </div> <div class="reading-time"> <i class="reading-time-icon" data-gfg-action="readingtime"></i> <span style="color: var(--recommendation-card-text-color);font-size: 14px;font-weight: 500;line-height: 17px;">7 min read</span> </div> </a><hr style="background:var(--gfg-selected-color); width:70%; margin: 0 auto;"></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/introduction-to-amortized-analysis/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Introduction to Amortized Analysis </div> <div class="gfg-similar-read-item-subheading">Amortized Analysis is used for algorithms where an occasional operation is very slow, but most other operations are faster. In Amortized Analysis, we analyze a sequence of operations and guarantee a worst-case average time that is lower than the worst-case time of a particularly expensive operation.</div> </div> <div class="reading-time"> <i class="reading-time-icon" data-gfg-action="readingtime"></i> <span style="color: var(--recommendation-card-text-color);font-size: 14px;font-weight: 500;line-height: 17px;">10 min read</span> </div> </a><hr style="background:var(--gfg-selected-color); width:70%; margin: 0 auto;"></li></ul></div><div class="leftbar-dropdown"><h2 class="dropdown-title">Asymptotic Notations<span class="gfg-icon gfg-icon_arrow-down-thin"></span></h2><ul style="display: none;"><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/analysis-algorithms-big-o-analysis/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Big O Notation Tutorial - A Guide to Big O Analysis </div> <div class="gfg-similar-read-item-subheading">Big O notation is a powerful tool used in computer science to describe the time complexity or space complexity of algorithms. Big-O is a way to express the upper bound of an algorithmâs time or space complexity. Describes the asymptotic behavior (order of growth of time or space in terms of input si</div> </div> <div class="reading-time"> <i class="reading-time-icon" data-gfg-action="readingtime"></i> <span style="color: var(--recommendation-card-text-color);font-size: 14px;font-weight: 500;line-height: 17px;">10 min read</span> </div> </a><hr style="background:var(--gfg-selected-color); width:70%; margin: 0 auto;"></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/difference-between-big-oh-big-omega-and-big-theta/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Difference between Big O vs Big Theta Î vs Big Omega Î© Notations </div> <div class="gfg-similar-read-item-subheading">Prerequisite - Asymptotic Notations, Properties of Asymptotic Notations, Analysis of Algorithms1. Big O notation (O): It is defined as upper bound and upper bound on an algorithm is the most amount of time required ( the worst case performance).Big O notation is used to describe the asymptotic upper</div> </div> <div class="reading-time"> <i class="reading-time-icon" data-gfg-action="readingtime"></i> <span style="color: var(--recommendation-card-text-color);font-size: 14px;font-weight: 500;line-height: 17px;">4 min read</span> </div> </a><hr style="background:var(--gfg-selected-color); width:70%; margin: 0 auto;"></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/examples-of-big-o-analysis/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Examples of Big-O analysis </div> <div class="gfg-similar-read-item-subheading">Prerequisite: Analysis of Algorithms | Big-O analysis In the previous article, the analysis of the algorithm using Big O asymptotic notation is discussed. In this article, some examples are discussed to illustrate the Big O time complexity notation and also learn how to compute the time complexity o</div> </div> <div class="reading-time"> <i class="reading-time-icon" data-gfg-action="readingtime"></i> <span style="color: var(--recommendation-card-text-color);font-size: 14px;font-weight: 500;line-height: 17px;">13 min read</span> </div> </a><hr style="background:var(--gfg-selected-color); width:70%; margin: 0 auto;"></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/difference-between-big-o-notations-and-tilde/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Difference between big O notations and tilde </div> <div class="gfg-similar-read-item-subheading">In asymptotic analysis of algorithms we often encounter terms like Big-Oh, Omega, Theta and Tilde, which describe the performance of an algorithm. You can refer to the following links to get more insights about asymptotic analysis : Analysis of Algorithms Different NotationsDifference between Big Oh</div> </div> <div class="reading-time"> <i class="reading-time-icon" data-gfg-action="readingtime"></i> <span style="color: var(--recommendation-card-text-color);font-size: 14px;font-weight: 500;line-height: 17px;">4 min read</span> </div> </a><hr style="background:var(--gfg-selected-color); width:70%; margin: 0 auto;"></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/analysis-of-algorithms-big-omega-notation/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Analysis of Algorithms | Big-Omega â¦ Notation </div> <div class="gfg-similar-read-item-subheading">In the analysis of algorithms, asymptotic notations are used to evaluate the performance of an algorithm, in its best cases and worst cases. This article will discuss Big-Omega Notation represented by a Greek letter (â¦). Table of Content What is Big-Omega â¦ Notation?Definition of Big-Omega â¦ Notatio</div> </div> <div class="reading-time"> <i class="reading-time-icon" data-gfg-action="readingtime"></i> <span style="color: var(--recommendation-card-text-color);font-size: 14px;font-weight: 500;line-height: 17px;">9 min read</span> </div> </a><hr style="background:var(--gfg-selected-color); width:70%; margin: 0 auto;"></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/analysis-of-algorithms-big-theta-notation/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Analysis of Algorithms | Î (Theta) Notation </div> <div class="gfg-similar-read-item-subheading">In the analysis of algorithms, asymptotic notations are used to evaluate the performance of an algorithm by providing an exact order of growth. This article will discuss Big - Theta notations represented by a Greek letter (Î). Definition: Let g and f be the function from the set of natural numbers t</div> </div> <div class="reading-time"> <i class="reading-time-icon" data-gfg-action="readingtime"></i> <span style="color: var(--recommendation-card-text-color);font-size: 14px;font-weight: 500;line-height: 17px;">6 min read</span> </div> </a><hr style="background:var(--gfg-selected-color); width:70%; margin: 0 auto;"></li></ul></div></div></ul> </div> </div> <div class="vote-wrap"> <div style="display:none;align-items:center;justify-content:center;width:100%;"> <button aria-label="like" data-type="like" class="vote-this" style="margin-right: 0; margin-left:0 ;"> <i class="gfg-icon gfg-icon_like favoriteIcon"></i> <span class="favoriteLike">Like</span> <figure class="favoriteText"></figure> </button> </div> </div> </div> <div class="article-meta"> <div class="bottom-wrap"> <div id="GFG_AD_InContent_Desktop_BTF_650x250" style="text-align:center;max-height: 300px;"></div> </div>  </div> </div> </div> </div> <div id="report_modal_content" class="report_modal_content" style="display:hidden;"></div> <div class="onopen-discussion-panel"> <div class="discussion-tab"> <div class="discussion_heading"> <div></div> <i class="gfg-icon close-tab-icon"></i> </div> <div class="discussion_content"> <div style="height:100%"> <div style="height:100%" id="comment-system"></div> </div> </div> </div> </div> <div class="rightBar" style="padding-right: 5px;"> <style> .article--container_content{ align-items: unset !important; } .sideBar { position: sticky !important; } .gfg-icon_switch::after { background-position: -40px -281px !important; } .gfg-icon_transaction::after { background-position: -40px -321px !important; } .header-main__profile.selected+.mega-dropdown{ width: 225px !important; } #courses-container .course-price{ display:none; } /* .side--container_wscard .card-content .content .meta:empty, .practiceBannerFromPlugin{ display:none !important; } */ .side--container_wscard .card-content .content .meta{ display:block !important; } .side--container_wscard .card-content .content .meta p{ background-color: rgba(254, 212, 91, 0.6); font-size: 10pt; font-weight: bold; display: inline-block; color: var(--color-black); margin-top: 15px; padding: 0px 5px; } #try-it{ display:initial !important; } #try-it .try-it-div{ line-height: 34px; } .gfg-icon_dark-mode::after { background-position: -40px -680px; } .side--container_wscard .head{ font-size: 14px !important; } .nineDot-menu, .gfg-icon_ndot{ display: none; } #text-15{ flex-direction: column; } .mtq_correct_marker, .mtq_wrong_marker{ display: none; } .sidebar_wrapper > :last-child{ margin: unset !important; margin-left: 5px !important; margin-top: 20px !important; top: 70px !important; } .darkMode-wrap{ bottom:1% !important; } #secondary .textwidget{ margin-left: auto; margin-right: 0; text-align: right; } #secondary .widget_text:last-child{ top: 70px !important; } @media(max-width:768px){ #scrollTopBtn{ display:none !important; } } .rightbar_loggedin_promo_cta{ display:flex; cursor:pointer; margin-bottom:20px; } </style> <div id="secondary" class="widget-area"> <div class='OINTechPromoRightBarBanner' id='rightBarSaleBanner' style='text-align:right; margin-bottom:5px;'><a href=https://www.geeksforgeeks.org/geeksforgeeks-premium-subscription?itm_source=geeksforgeeks&itm_medium=rightbar_oin&itm_campaign=premium><img src=https://media.geeksforgeeks.org/auth-dashboard-uploads/premium_oin_rbar_min.png alt='three90RightbarBannerImg' style='width:300px; height:250px;'></a></div>  <aside id="text-15" class="widget widget_text"> <div class="textwidget"> <div id="_GFG_ABP_Desktop_RightSideBar_ATF_300x600_2"></div> <div id="GFG_AD_Desktop_RightSideBar_ATF_300x250_2" style="min-width: 300px;margin-bottom:10px;"></div> <div id='GFG_AD_Desktop_RightSideBar_ATF_300x600' style='min-width: 300px; min-height: 600px;margin-bottom:10px;'></div> </div> </aside>  <aside id="text-16" class="widget widget_text"> <div class="textwidget"> <div id="_GFG_ABP_Desktop_RightSideBar_MTF_300x600"></div> <div id='GFG_AD_Desktop_RightSideBar_MTF_300x250' style='min-width: 300px;'></div> <div id="_GFG_ABP_Desktop_RightSideBar_BTF_300x600"></div> <div id="_GFG_ABP_Desktop_RightSideBar_BTF_300x600_3"></div> </div> </aside>    <aside id="text-18" class="widget widget_text"> <div class="textwidget"> <div id='GFG_AD_Desktop_RightSideBar_BTF_Sticky_300x250' style='min-width: 300px;margin-bottom:10px'></div> <div id='GFG_AD_Desktop_RightSideBar_Docked_160x600' style='min-width: 160px;'></div><div id='GFG_AD_Desktop_RightSideBar_BTFdocked_300x600' style='min-width: 300px;'></div> </aside>  <aside id="text-20" class="widget widget_text"> <div class="textwidget">  </div> </aside> </div> <div id="user-personal-note" style="display: none;"></div> </div> </div> <section class="disqus-section"> <div class="article-page_flex"> <div class="leftBar"> </div> </div> </section> </div> <div id="video-popup" style="display:none"></div> <link rel="stylesheet" href='https://www.geeksforgeeks.org/wp-content/themes/iconic-one/css/articleList.min.css?ver=1.7'> <script> $(document).ready(function() { var isfollowingApiCall = false; if ($('.follow-btn').length) { var articleRecommendedTop = $(".article--recommended").offset().top; var articleRecommendedBottom = articleRecommendedTop + $(".article--recommended").outerHeight(); $(window).scroll(function() { var top_of_element = $(".article--recommended").offset().top; var bottom_of_element = $(".article--recommended").offset().top + $(".article--recommended").outerHeight(); var bottom_of_screen = $(window).scrollTop() + $(window).innerHeight(); var top_of_screen = $(window).scrollTop(); if ((bottom_of_screen > top_of_element && top_of_screen < bottom_of_element) || (bottom_of_screen > articleRecommendedTop && top_of_screen < articleRecommendedBottom) || (top_of_screen > articleRecommendedBottom)) { if (!isfollowingApiCall) { isfollowingApiCall = true; setTimeout(function(){ if (loginData && loginData.isLoggedIn) { if (loginData.userName !== $('#followAuthor').val()) { is_following(); } else { $('.profileCard-profile-picture').css('background-color', '#E7E7E7'); } } else { $('.follow-btn').removeClass('hideIt'); } }, 3000); } } }); } $(".accordion-header").click(function() { var arrowIcon = $(this).find('.bottom-arrow-icon'); arrowIcon.toggleClass('rotate180'); }); }); window.isReportArticle = false; function report_article(){ if (!loginData || !loginData.isLoggedIn) { const loginModalButton = $('.login-modal-btn') if (loginModalButton.length) { loginModalButton.click(); } return; } if(!window.isReportArticle){ //to add loader $('.report-loader').addClass('spinner'); jQuery('#report_modal_content').load(gfgSiteUrl+'wp-content/themes/iconic-one/report-modal.php', { PRACTICE_API_URL: practiceAPIURL, PRACTICE_URL:practiceURL },function(responseTxt, statusTxt, xhr){ if(statusTxt == "error"){ alert("Error: " + xhr.status + ": " + xhr.statusText); } }); }else{ window.scrollTo({ top: 0, behavior: 'smooth' }); $("#report_modal_content").show(); } } function closeShareModal() { const shareOption = document.querySelector('[data-gfg-action="share-article"]'); shareOption.classList.remove("hover_share_menu"); let shareModal = document.querySelector(".hover__share-modal-container"); shareModal && shareModal.remove(); } function openShareModal() { closeShareModal(); // Remove existing modal if any let shareModal = document.querySelector(".three_dot_dropdown_share"); shareModal.appendChild(Object.assign(document.createElement("div"), { className: "hover__share-modal-container" })); document.querySelector(".hover__share-modal-container").append( Object.assign(document.createElement('div'), { className: "share__modal" }), ); document.querySelector(".share__modal").append(Object.assign(document.createElement('h1'), { className: "share__modal-heading" }, { textContent: "Share to" })); const socialOptions = ["LinkedIn", "WhatsApp", "Copy Link"]; socialOptions.forEach((socialOption) => { const socialContainer = Object.assign(document.createElement('div'), { className: "social__container" }); const icon = Object.assign(document.createElement("div"), { className: `share__icon share__${socialOption.split(" ").join("")}-icon` }); const socialText = Object.assign(document.createElement("span"), { className: "share__option-text" }, { textContent: `${socialOption}` }); const shareLink = (socialOption === "Copy Link") ? Object.assign(document.createElement('div'), { role: "button", className: "link-container CopyLink" }) : Object.assign(document.createElement('a'), { className: "link-container" }); if (socialOption === "LinkedIn") { shareLink.setAttribute('href', `https://www.linkedin.com/sharing/share-offsite/?url=${window.location.href}`); shareLink.setAttribute('target', '_blank'); } if (socialOption === "WhatsApp") { shareLink.setAttribute('href', `https://api.whatsapp.com/send?text=${window.location.href}`); shareLink.setAttribute('target', "_blank"); } shareLink.append(icon, socialText); socialContainer.append(shareLink); document.querySelector(".share__modal").appendChild(socialContainer); //adding copy url functionality if(socialOption === "Copy Link") { shareLink.addEventListener("click", function() { var tempInput = document.createElement("input"); tempInput.value = window.location.href; document.body.appendChild(tempInput); tempInput.select(); tempInput.setSelectionRange(0, 99999); // For mobile devices document.execCommand('copy'); document.body.removeChild(tempInput); this.querySelector(".share__option-text").textContent = "Copied" }) } }); document.querySelector(".hover__share-modal-container").addEventListener("mouseover", () => document.querySelector('[data-gfg-action="share-article"]').classList.add("hover_share_menu")); } function toggleLikeElementVisibility(selector, show) { document.querySelector(`.${selector}`).style.display = show ? "block" : "none"; } function closeKebabMenu(){ document.getElementById("myDropdown").classList.toggle("show"); } </script>  <script> $(document).ready(function() { $("#showMoreTagsBtn").click(function() { $('.articles-hidden-tags').show(); $(this).hide(); }); $("#showMorePracticeTagsBtn").click(function() { $(".practice-tags li:nth-child(n+5)").show(); $(this).hide(); }); }); </script>  <style> .grecaptcha-badge { visibility: hidden !important; } .thank-you-message { height: 100%; display:flex; flex-direction: column; justify-content: center; align-items: center; } .thank-you-message-content { margin-top: 17px; font: 400 20px var(--font-secondary); color: var(--improve-modal-text); line-height: 180%; text-align: center; } .thank-you-message-content h2{ font-family: var(--font-secondary); } .all-footer-information{ width: 100% !important;; } .footer-wrapper_links-list{ margin-block-start: 0em !important; width: 16% !important; padding-inline-start: 18px !important; } .link-head{ margin-bottom: 0px; } @media only screen and (max-width:1340px) { .footer-wrapper_links-list{ overflow-wrap: break-word; } } @media screen and (min-width: 991px) { .all-footer-information{ padding-left:15px; } } @media only screen and (max-width:980px) { .footer-wrapper_branding-address{ padding-top: 10px; } } @media (max-width: 750px) { .thank-you-message-content{ font-size: 14px; line-height: 170%; } } /* CSS variable meant to handle the dark and light mode icon for three 90 event in header courses dropdown */ :root{ --three90headericon : url('https://media.geeksforgeeks.org/auth-dashboard-uploads/three90daylogocompressed.svg'); --three90headericonposition : 0px -40px; --three90leftbarimggrid : url('https://media.geeksforgeeks.org/auth-dashboard-uploads/three90leftbarspritecompressed.svg'); --three90leftbarimgposition : -5px -55px; --three90leftbarbgcolour : #b3abd0; } body[data-dark-mode="true"]{ --three90leftbarimgposition : -6px 1px; --three90headericonposition : 0px 0px; --three90leftbarbgcolour: #8c82b9; } .three90leftbarimg{ margin-left: -5px; height: 30px; background-image: var(--three90leftbarimggrid); background-repeat: no-repeat; background-position: var(--three90leftbarimgposition); background-size: 212px; } .courseTabShimmer{ position: absolute; height: 110%; width: 0; opacity: .7; -webkit-animation: courseShimmer 2s cubic-bezier(0,0,.07,.61) infinite; animation: courseShimmer 2s cubic-bezier(0,0,.07,.61) infinite; box-shadow: 0 0 25px 5px #dddcdc; -webkit-transform: rotate(90deg); transform: rotate(90deg); padding:0px !important; border:unset !important; } @keyframes courseShimmer{ 0% { left: 0; } 55% { left: 100%; } 99% { left: 110%; } } </style> </div> <div id="displayModal" class="modal fade" role="dialog"> <div class="modal-dialog">  <div class="modal-content"> <div class="error-message"></div>  <div class="modal-body" id="dmBody"> <div id="modal-dm-content"></div> <div class="modal-overlay" aria-hidden=true> <span class="loader__animation"></span> </div>  </div> </div> </div> </div> <div id="displayModalBackdrop" class="backdrop"></div>  <footer class="gfg-footer" id="gfg-footer"> <div class="footer-wrapper"> <div class="footer-wrapper_branding"> <a class="footer-wrapper_branding-anchor" aria-label="GeeksforGeeks Logo" href="https://www.geeksforgeeks.org/"> <img style="height: 32px; width: 230px; max-width: fit-content;" class="footer-wrapper_branding-nlogo" src="https://media.geeksforgeeks.org/auth-dashboard-uploads/gfgFooterLogo.png" alt="geeksforgeeks-footer-logo"/> </a> <div class="footer-wrapper_branding-address"> <div class="address_section"> <div class="address-icon-wrapper"> <i class="gfg-icon gfg-icon_pin"></i> <div class="address_div"> <div class="address_name">Corporate & Communications Address:</div> <div class="footer-address"> A-143, 7th Floor, Sovereign Corporate Tower, Sector- 136, Noida, Uttar Pradesh (201305) </div> </div> </div> <div class="address-icon-wrapper"> <i class="gfg-icon gfg-icon_pin"></i> <div class="address_div"> <div class="address_name">Registered Address:</div> K 061, Tower K, Gulshan Vivante Apartment, Sector 137, Noida, Gautam Buddh Nagar, Uttar Pradesh, 201305 </div> </div> </div> </div> <div class="footer-wrapper_branding-social"> <a href="https://www.facebook.com/geeksforgeeks.org/" rel="noopener noreferrer" aria-label="GeeksforGeeks Facebook" target="_blank"> <div class="facebook"></div> </a> <a href="https://www.instagram.com/geeks_for_geeks/" rel="noopener noreferrer" aria-label="GeeksforGeeks Instagram" target="_blank"> <div class="instagram"></div> </a> <a href="https://in.linkedin.com/company/geeksforgeeks" rel="noopener noreferrer" aria-label="GeeksforGeeks LinkedIn" target="_blank"> <div class="linkedin"></div> </a> <a href="https://twitter.com/geeksforgeeks" rel="noopener noreferrer" aria-label="GeeksforGeeks Twitter" target="_blank"> <div class="twitter"></div> </a> <a href="https://www.youtube.com/geeksforgeeksvideos" rel="noopener noreferrer" aria-label="GeeksforGeeks YouTube" target="_blank"> <div class="youtube"></div> </a> </div> <div class="footer-wrapper_branding-app"> <a aria-label="GeeksforGeeks App Link" href="https://geeksforgeeksapp.page.link/gfg-app" target="_blank" ><img src="https://media.geeksforgeeks.org/auth-dashboard-uploads/googleplay.png" alt="GFG App on Play Store" id="gplay" loading="lazy"></a> <a aria-label="GeeksforGeeks App Link" href="https://geeksforgeeksapp.page.link/gfg-app" target="_blank"><img src="https://media.geeksforgeeks.org/auth-dashboard-uploads/appstore.png" alt="GFG App on App Store" id="appstore" loading="lazy"></a> </div> <div class="footer_advertise_btn_box"> <a href="https://www.geeksforgeeks.org/advertise-with-us/?ref=footer" target="_blank" class="footer_advertise_btn">Advertise with us</a> </div> </div> <div class="all-footer-information"> <div class="footer-wrapper_links" style="justify-content: space-between; text-align: -webkit-left;"><ul class="footer-wrapper_links-list" ><li>Company</li><li><a href=https://www.geeksforgeeks.org/about/?ref=outindfooter>About Us</a></li><li><a href=https://www.geeksforgeeks.org/legal/?ref=outindfooter>Legal</a></li><li><a href=https://www.geeksforgeeks.org/legal/privacy-policy/?ref=outindfooter>Privacy Policy</a></li><li><a href=https://www.geeksforgeeks.org/press-release/?ref=outindfooter>In Media</a></li><li><a href=https://www.geeksforgeeks.org/about/contact-us/?ref=outindfooter>Contact Us</a></li><li><a href=https://www.geeksforgeeks.org/advertise-with-us/?ref=outindfooter>Advertise with us</a></li><li><a href=https://www.geeksforgeeks.org/gfg-corporate-solution/?ref=outindfooter>GFG Corporate Solution</a></li><li><a href=https://www.geeksforgeeks.org/campus-training-program/?ref=outindfooter>Placement Training Program</a></li><li><a href=https://www.geeksforgeeks.org/community/?ref=outindfooter>GeeksforGeeks Community</a></li></ul><ul class="footer-wrapper_links-list" ><li><a class="link-head" href=https://www.geeksforgeeks.org/introduction-to-programming-languages/?ref=outindfooter>Languages</a></li><li><a href=https://www.geeksforgeeks.org/python-programming-language/?ref=outindfooter>Python</a></li><li><a href=https://www.geeksforgeeks.org/java/?ref=outindfooter>Java</a></li><li><a href=https://www.geeksforgeeks.org/c-plus-plus/?ref=outindfooter>C++</a></li><li><a href=https://www.geeksforgeeks.org/php-tutorials/?ref=outindfooter>PHP</a></li><li><a href=https://www.geeksforgeeks.org/golang/?ref=outindfooter>GoLang</a></li><li><a href=https://www.geeksforgeeks.org/sql-tutorial/?ref=outindfooter>SQL</a></li><li><a href=https://www.geeksforgeeks.org/r-tutorial/?ref=outindfooter>R Language</a></li><li><a href=https://www.geeksforgeeks.org/android-tutorial/?ref=outindfooter>Android Tutorial</a></li><li><a href=https://www.geeksforgeeks.org/geeksforgeeks-online-tutorials-free/?ref=outindfooter>Tutorials Archive</a></li></ul><ul class="footer-wrapper_links-list" ><li><a class="link-head" href=https://www.geeksforgeeks.org/learn-data-structures-and-algorithms-dsa-tutorial/?ref=outindfooter>DSA</a></li><li><a href=https://www.geeksforgeeks.org/data-structures/?ref=outindfooter>Data Structures</a></li><li><a href=https://www.geeksforgeeks.org/fundamentals-of-algorithms/?ref=outindfooter>Algorithms</a></li><li><a href=https://www.geeksforgeeks.org/complete-guide-to-dsa-for-beginners/?ref=outindfooter>DSA for Beginners</a></li><li><a href=https://www.geeksforgeeks.org/basic-coding-problems-in-dsa-for-beginners/?ref=outindfooter>Basic DSA Problems</a></li><li><a href=https://www.geeksforgeeks.org/complete-roadmap-to-learn-dsa-from-scratch/?ref=outindfooter>DSA Roadmap</a></li><li><a href=https://www.geeksforgeeks.org/top-100-data-structure-and-algorithms-dsa-interview-questions-topic-wise/?ref=outindfooter>Top 100 DSA Interview Problems</a></li><li><a href=https://www.geeksforgeeks.org/dsa-roadmap-for-beginner-to-advanced-by-sandeep-jain/?ref=outindfooter>DSA Roadmap by Sandeep Jain</a></li><li><a href=https://www.geeksforgeeks.org/geeksforgeeks-master-sheet-list-of-all-cheat-sheets/?ref=outindfooter>All Cheat Sheets</a></li></ul><ul class="footer-wrapper_links-list" ><li><a class="link-head" href=https://www.geeksforgeeks.org/ai-ml-ds/?ref=outindfooter>Data Science & ML</a></li><li><a href=https://www.geeksforgeeks.org/data-science-tutorial/?ref=outindfooter>Data Science With Python</a></li><li><a href=https://www.geeksforgeeks.org/data-science-for-beginners/?ref=outindfooter>Data Science For Beginner</a></li><li><a href=https://www.geeksforgeeks.org/machine-learning/?ref=outindfooter>Machine Learning</a></li><li><a href=https://www.geeksforgeeks.org/machine-learning-mathematics/?ref=outindfooter>ML Maths</a></li><li><a href=https://www.geeksforgeeks.org/python-data-visualization-tutorial/?ref=outindfooter>Data Visualisation</a></li><li><a href=https://www.geeksforgeeks.org/pandas-tutorial/?ref=outindfooter>Pandas</a></li><li><a href=https://www.geeksforgeeks.org/numpy-tutorial/?ref=outindfooter>NumPy</a></li><li><a href=https://www.geeksforgeeks.org/natural-language-processing-nlp-tutorial/?ref=outindfooter>NLP</a></li><li><a href=https://www.geeksforgeeks.org/deep-learning-tutorial/?ref=outindfooter>Deep Learning</a></li></ul><ul class="footer-wrapper_links-list" ><li><a class="link-head" href=https://www.geeksforgeeks.org/web-technology/?ref=outindfooter>Web Technologies</a></li><li><a href=https://www.geeksforgeeks.org/html/?ref=outindfooter>HTML</a></li><li><a href=https://www.geeksforgeeks.org/css/?ref=outindfooter>CSS</a></li><li><a href=https://www.geeksforgeeks.org/javascript/?ref=outindfooter>JavaScript</a></li><li><a href=https://www.geeksforgeeks.org/typescript/?ref=outindfooter>TypeScript</a></li><li><a href=https://www.geeksforgeeks.org/learn-reactjs/?ref=outindfooter>ReactJS</a></li><li><a href=https://www.geeksforgeeks.org/nextjs/?ref=outindfooter>NextJS</a></li><li><a href=https://www.geeksforgeeks.org/bootstrap/?ref=outindfooter>Bootstrap</a></li><li><a href=https://www.geeksforgeeks.org/web-design/?ref=outindfooter>Web Design</a></li></ul><ul class="footer-wrapper_links-list" ><li><a class="link-head" href=https://www.geeksforgeeks.org/python-programming-language/?ref=outindfooter>Python Tutorial</a></li><li><a href=https://www.geeksforgeeks.org/python-programming-examples/?ref=outindfooter>Python Programming Examples</a></li><li><a href=https://www.geeksforgeeks.org/python-projects-beginner-to-advanced/?ref=outindfooter>Python Projects</a></li><li><a href=https://www.geeksforgeeks.org/python-tkinter-tutorial/?ref=outindfooter>Python Tkinter</a></li><li><a href=https://www.geeksforgeeks.org/python-web-scraping-tutorial/?ref=outindfooter>Web Scraping</a></li><li><a href=https://www.geeksforgeeks.org/opencv-python-tutorial/?ref=outindfooter>OpenCV Tutorial</a></li><li><a href=https://www.geeksforgeeks.org/python-interview-questions/?ref=outindfooter>Python Interview Question</a></li><li><a href=https://www.geeksforgeeks.org/django-tutorial/?ref=outindfooter>Django</a></li></ul></div><div class="footer-wrapper_links" style="justify-content: space-between; text-align: -webkit-left;"><ul class="footer-wrapper_links-list" style="margin-block-start: 0em; width:16%; padding-inline-start: 18px;"><li>Computer Science</li><li><a href=https://www.geeksforgeeks.org/operating-systems/?ref=outindfooter>Operating Systems</a></li><li><a href=https://www.geeksforgeeks.org/computer-network-tutorials/?ref=outindfooter>Computer Network</a></li><li><a href=https://www.geeksforgeeks.org/dbms/?ref=outindfooter>Database Management System</a></li><li><a href=https://www.geeksforgeeks.org/software-engineering/?ref=outindfooter>Software Engineering</a></li><li><a href=https://www.geeksforgeeks.org/digital-electronics-logic-design-tutorials/?ref=outindfooter>Digital Logic Design</a></li><li><a href=https://www.geeksforgeeks.org/engineering-mathematics-tutorials/?ref=outindfooter>Engineering Maths</a></li><li><a href=https://www.geeksforgeeks.org/software-development/?ref=outindfooter>Software Development</a></li><li><a href=https://www.geeksforgeeks.org/software-testing-tutorial/?ref=outindfooter>Software Testing</a></li></ul><ul class="footer-wrapper_links-list" ><li><a class="link-head" href=https://www.geeksforgeeks.org/devops-tutorial/?ref=outindfooter>DevOps</a></li><li><a href=https://www.geeksforgeeks.org/git-tutorial/?ref=outindfooter>Git</a></li><li><a href=https://www.geeksforgeeks.org/linux-tutorial/?ref=outindfooter>Linux</a></li><li><a href=https://www.geeksforgeeks.org/aws-tutorial/?ref=outindfooter>AWS</a></li><li><a href=https://www.geeksforgeeks.org/docker-tutorial/?ref=outindfooter>Docker</a></li><li><a href=https://www.geeksforgeeks.org/kubernetes-tutorial/?ref=outindfooter>Kubernetes</a></li><li><a href=https://www.geeksforgeeks.org/microsoft-azure/?ref=outindfooter>Azure</a></li><li><a href=https://www.geeksforgeeks.org/google-cloud-platform-tutorial/?ref=outindfooter>GCP</a></li><li><a href=https://www.geeksforgeeks.org/devops-roadmap/?ref=outindfooter>DevOps Roadmap</a></li></ul><ul class="footer-wrapper_links-list" ><li><a class="link-head" href=https://www.geeksforgeeks.org/system-design-tutorial/?ref=outindfooter>System Design</a></li><li><a href=https://www.geeksforgeeks.org/what-is-high-level-design-learn-system-design/?ref=outindfooter>High Level Design</a></li><li><a href=https://www.geeksforgeeks.org/what-is-low-level-design-or-lld-learn-system-design/?ref=outindfooter>Low Level Design</a></li><li><a href=https://www.geeksforgeeks.org/unified-modeling-language-uml-introduction/?ref=outindfooter>UML Diagrams</a></li><li><a href=https://www.geeksforgeeks.org/system-design-interview-guide/?ref=outindfooter>Interview Guide</a></li><li><a href=https://www.geeksforgeeks.org/software-design-patterns/?ref=outindfooter>Design Patterns</a></li><li><a href=https://www.geeksforgeeks.org/object-oriented-analysis-and-design/?ref=outindfooter>OOAD</a></li><li><a href=https://www.geeksforgeeks.org/system-design-interview-bootcamp-guide/?ref=outindfooter>System Design Bootcamp</a></li><li><a href=https://www.geeksforgeeks.org/most-commonly-asked-system-design-interview-problems-questions/?ref=outindfooter>Interview Questions</a></li></ul><ul class="footer-wrapper_links-list" ><li><a class="link-head" href=https://www.geeksforgeeks.org/technical-interview-preparation/?ref=outindfooter>Inteview Preparation</a></li><li><a href=https://www.geeksforgeeks.org/competitive-programming-a-complete-guide/?ref=outindfooter>Competitive Programming</a></li><li><a href=https://www.geeksforgeeks.org/top-algorithms-and-data-structures-for-competitive-programming/?ref=outindfooter>Top DS or Algo for CP</a></li><li><a href=https://www.geeksforgeeks.org/company-wise-recruitment-process/?ref=outindfooter>Company-Wise Recruitment Process</a></li><li><a href=https://www.geeksforgeeks.org/company-preparation/?ref=outindfooter>Company-Wise Preparation</a></li><li><a href=https://www.geeksforgeeks.org/aptitude-questions-and-answers/?ref=outindfooter>Aptitude Preparation</a></li><li><a href=https://www.geeksforgeeks.org/puzzles/?ref=outindfooter>Puzzles</a></li></ul><ul class="footer-wrapper_links-list" ><li>School Subjects</li><li><a href=https://www.geeksforgeeks.org/maths/?ref=outindfooter>Mathematics</a></li><li><a href=https://www.geeksforgeeks.org/physics/?ref=outindfooter>Physics</a></li><li><a href=https://www.geeksforgeeks.org/chemistry/?ref=outindfooter>Chemistry</a></li><li><a href=https://www.geeksforgeeks.org/biology/?ref=outindfooter>Biology</a></li><li><a href=https://www.geeksforgeeks.org/social-science/?ref=outindfooter>Social Science</a></li><li><a href=https://www.geeksforgeeks.org/english-grammar/?ref=outindfooter>English Grammar</a></li><li><a href=https://www.geeksforgeeks.org/commerce/?ref=outindfooter>Commerce</a></li><li><a href=https://www.geeksforgeeks.org/tag/world-general-knowledge/?ref=outindfooter>World GK</a></li></ul><ul class="footer-wrapper_links-list" ><li><a class="link-head" href=https://www.geeksforgeeks.org/videos/?ref=outindfooter>GeeksforGeeks Videos</a></li><li><a href=https://www.geeksforgeeks.org/videos/category/sde-sheet/?ref=outindfooter>DSA</a></li><li><a href=https://www.geeksforgeeks.org/videos/category/python/?ref=outindfooter>Python</a></li><li><a href=https://www.geeksforgeeks.org/videos/category/java-w6y5f4/?ref=outindfooter>Java</a></li><li><a href=https://www.geeksforgeeks.org/videos/category/c/?ref=outindfooter>C++</a></li><li><a href=https://www.geeksforgeeks.org/videos/category/web-development/?ref=outindfooter>Web Development</a></li><li><a href=https://www.geeksforgeeks.org/videos/category/data-science/?ref=outindfooter>Data Science</a></li><li><a href=https://www.geeksforgeeks.org/videos/category/cs-subjects/?ref=outindfooter>CS Subjects</a></li></ul></div> </div> </div>  <style> :root{ --home-jobs-section-jf-logo: url('https://media.geeksforgeeks.org/auth-dashboard-uploads/JobFair2024Logo.svg'); } body[data-dark-mode="true"] { --home-jobs-section-jf-logo: url('https://media.geeksforgeeks.org/auth-dashboard-uploads/JobFair2024LogoDark.svg'); } .hp_job_section_jf_logo, .job-a-thon-jf-sticky-header-logo{ background: var(--home-jobs-section-jf-logo); height: 50px; background-repeat: no-repeat; width: 105px; background-size: 100px; } @keyframes challenge { 0%{ transform: scale(1); } 50%{ transform: scale(1.03); } 100%{ transform: scale(1); } } .job-a-thon-jf-sticky-header-logo{ height: 45px; } </style>  <div class="footer-strip" > <div class="copyright"> <a href="https://www.geeksforgeeks.org/" rel="noopener noreferrer" target="_blank">@GeeksforGeeks, Sanchhaya Education Private Limited</a><span>, <a href="https://www.geeksforgeeks.org/copyright-information/">All rights reserved</a></span> </div> <div class="social-links"> </div> </div> </footer> </div> <script type='text/javascript' src='https://www.geeksforgeeks.org/wp-includes/js/wp-embed.min.js?ver=4.9.8'></script>  <div class="cookie-consent hide-consent"> <span class="cookie-text"> We use cookies to ensure you have the best browsing experience on our website. By using our site, you acknowledge that you have read and understood our <a href="https://www.geeksforgeeks.org/cookie-policy/" target="_blank"><u>Cookie Policy</u></a> & <a href="https://www.geeksforgeeks.org/privacy-policy/" target="_blank"><u>Privacy Policy</u></a> </span> <button class="consent-btn"> Got It ! </button> </div>   <div class="lightbox-target"> <img id="lightbox-image" src="" alt="Lightbox"/> <span class="lightbox-close"></span> </div>   <link href="https://fonts.googleapis.com/css2?family=Nunito:wght@400;700&family=Source+Sans+3:wght@400;600&display=swap" rel="stylesheet"> <script> if(post_slug.includes('premium-plans-payment/') || post_slug.includes('premium-plans/')){ $('.darkMode-wrap').remove(); $('.toggle-darkMode').remove(); } function setGoogleRecaptcha() { var captchaSiteKey = '6LdMFNUZAAAAAIuRtzg0piOT-qXCbDF-iQiUi9KY'; grecaptcha.ready(function() { grecaptcha.execute(captchaSiteKey).then(function(token) { document.getElementById('g-recaptcha-response-suggestion-form').value = token; suggestionCall(); }); }); } </script> <div class="improve-modal--overlay" style="display: none;"> <div class="improve-modal--improvement" status="locked"> <div class="improve-modal--improve-header"> <div class="improve-header-fst-child">Improvement</div> <div class="improve-header-sec-child"> <i class="gfg-icon improve-cross-icon"></i> </div> </div> <div class="locked-status--impove-modal"> <div class="improve-modal--improve-content error-message"></div> <div class="improve-modal--improve-bottom"> <button class="improve-bottom-btn" type="button">Suggest changes</button> </div> </div> <div class="unlocked-status--improve-modal-content"> <div class="suggest-change_wrapper"> <div class="suggest-change-content_wrapper"> <div class="suggest-change">Suggest Changes</div> <div class="suggest-changes-about">Help us improve. Share your suggestions to enhance the article. Contribute your expertise and make a difference in the GeeksforGeeks portal.</div> </div> <div class="suggest-change-icon_wrapper"> <img class="suggest-change-icon" src="https://media.geeksforgeeks.org/auth-dashboard-uploads/suggestChangeIcon.png" alt="geeksforgeeks-suggest-icon"/> </div> </div> <div class="create-improvement_wrapper"> <div class="create-improvement-content_wrapper"> <div class="create-improvement">Create Improvement</div> <div class="create-improvements-about">Enhance the article with your expertise. Contribute to the GeeksforGeeks community and help create better learning resources for all.</div> </div> <div class="create-improvement-icon_wrapper"> <img class="create-improvement-icon" src="https://media.geeksforgeeks.org/auth-dashboard-uploads/createImprovementIcon.png" alt="geeksforgeeks-improvement-icon"/> </div> </div> <div class="error-status"></div> </div> </div> <div class="improve-modal--suggestion" style="display: none;">  <div class="improve-modal--improve-header"> <div class="left-arrow-icon_suggest_wrapper"> <div class="left-arrow-icon_wrapper"> <i class="gfg-icon improve-left-arrow-icon"></i> </div> <div class="improve-header-fst-child">Suggest Changes</div> </div> <div class="improve-header-sec-child"> <i class="gfg-icon improve-cross-icon"></i> </div> </div> <div class="suggestion-modal-section"> <form> <label for="suggestion-section">min 4 words, max CharLimit:2000</label> <textarea id="suggestion-section-textarea" name="suggestion-section" placeholder="Write your suggestions here"></textarea> <input type="hidden" name="g-recaptcha-suggestion-response" id="g-recaptcha-response-suggestion-form"> </form> </div>  <div class="improve-modal--improve-bottom suggestion-btn"> <p><span id="suggestion-modal-alert" style="display: none;"></span></p> <button class="suggest-bottom-btn" type="button"></button> </div> </div> <a href="#" style="visibility:hidden" class="create-improvement-redirection-to-write" target="_blank"></a> </div> <script> var lockedCasesHtml = `<span class="improve-modal--improve-content-modified"></span><span>You can suggest the changes for now and it will be under 'My Suggestions' Tab on Write.</span><br><br><span>You will be notified via email once the article is available for improvement. Thank you for your valuable feedback!</span>`; var badgesRequiredHtml = `<span>It seems that you do not meet the eligibility criteria to create improvements for this article, as only users who have earned specific badges are permitted to do so.</span><br><br><span>However, you can still create improvements through the <a href="https://write.geeksforgeeks.org/pick-improvements/pick" target='_blank'>Pick for Improvement</a> section.</span>`; jQuery('.improve-header-sec-child').on('click', function(){ jQuery('.improve-modal--overlay').hide(); $('.improve-modal--suggestion').hide(); }); $('.suggest-change_wrapper, .locked-status--impove-modal .improve-bottom-btn').on('click',function(){ // when suggest changes option is clicked $('#suggestion-section-textarea').val(""); $('.suggest-bottom-btn').html("Suggest changes"); $('.improve-modal--improvement').hide(); $('.improve-modal--suggestion').show(); }); $('.create-improvement_wrapper').on('click',function(){ // when create improvement option clicked then improvement reason will be shown if(loginData && loginData.isLoggedIn) { $('body').append('<div class="spinner-loading-overlay"></div>'); $('.spinner-loading-overlay').show(); jQuery.ajax({ url: writeApiUrl + 'create-improvement-post/?v=1', type: "POST", contentType: 'application/json; charset=utf-8', dataType: 'json', xhrFields: { withCredentials: true }, data: JSON.stringify({ gfg_id: post_id }), success:function(result) { $('.spinner-loading-overlay:eq(0)').remove(); $('.improve-modal--overlay').hide(); $('.unlocked-status--improve-modal-content').css("display","none"); $('.create-improvement-redirection-to-write').attr('href',writeUrl + 'improve-post/' + `${result.id}` + '/', '_blank'); $('.create-improvement-redirection-to-write')[0].click(); }, error:function(e) { showErrorMessage(e.responseJSON,e.status) }, }); } else { if(loginData && !loginData.isLoggedIn) { $('.improve-modal--overlay').hide(); if ($('.header-main__wrapper').find('.header-main__signup.login-modal-btn').length) { $('.header-main__wrapper').find('.header-main__signup.login-modal-btn').click(); } return; } } }); $('.left-arrow-icon_wrapper').on('click',function(){ if($('.improve-modal--suggestion').is(":visible")) $('.improve-modal--suggestion').hide(); else{ } $('.improve-modal--improvement').show(); }); const showErrorMessage = (result,statusCode) => { if(!result) return; $('.spinner-loading-overlay:eq(0)').remove(); if(statusCode == 403) { $('.improve-modal--improve-content.error-message').html(result.message); jQuery('.improve-modal--overlay').show(); jQuery('.improve-modal--improvement').show(); $('.locked-status--impove-modal').css("display","block"); $('.unlocked-status--improve-modal-content').css("display","none"); $('.improve-modal--improvement').attr("status","locked"); return; } } function loadScript(src, callback) { var script = document.createElement('script'); script.src = src; script.onload = callback; document.head.appendChild(script); } function suggestionCall() { var suggest_val = $.trim($("#suggestion-section-textarea").val()); var array_String= suggest_val.split(" ") var gCaptchaToken = $("#g-recaptcha-response-suggestion-form").val(); var error_msg = false; if(suggest_val != "" && array_String.length >=4){ if(suggest_val.length <= 2000){ var payload = { "gfg_post_id" : `${post_id}`, "suggestion" : `<p>${suggest_val}</p>`, } if(!loginData || !loginData.isLoggedIn) // User is not logged in payload["g-recaptcha-token"] = gCaptchaToken jQuery.ajax({ type:'post', url: "https://apiwrite.geeksforgeeks.org/suggestions/auth/create/", xhrFields: { withCredentials: true }, crossDomain: true, contentType:'application/json', data: JSON.stringify(payload), success:function(data) { jQuery('.spinner-loading-overlay:eq(0)').remove(); jQuery('#suggestion-section-textarea').val(""); jQuery('.suggest-bottom-btn').css("display","none"); // Update the modal content const modalSection = document.querySelector('.suggestion-modal-section'); modalSection.innerHTML = ` <div class="thank-you-message" style="text-align: center;"> <h2>Thank You!</h2> <div class="thank-you-message-content">Your suggestions are valuable to us.</div> </div> `; }, error:function(data) { jQuery('.spinner-loading-overlay:eq(0)').remove(); jQuery('#suggestion-modal-alert').html("Something went wrong."); jQuery('#suggestion-modal-alert').show(); error_msg = true; } }); } else{ jQuery('.spinner-loading-overlay:eq(0)').remove(); jQuery('#suggestion-modal-alert').html("Minimum 5 Words and Maximum Character limit is 2000."); jQuery('#suggestion-modal-alert').show(); jQuery('#suggestion-section-textarea').focus(); error_msg = true; } } else{ jQuery('.spinner-loading-overlay:eq(0)').remove(); jQuery('#suggestion-modal-alert').html("Enter atleast four words !"); jQuery('#suggestion-modal-alert').show(); jQuery('#suggestion-section-textarea').focus(); error_msg = true; } if(error_msg){ setTimeout(() => { jQuery('#suggestion-section-textarea').focus(); jQuery('#suggestion-modal-alert').hide(); }, 3000); } } document.querySelector('.suggest-bottom-btn').addEventListener('click', function(){ jQuery('body').append('<div class="spinner-loading-overlay"></div>'); jQuery('.spinner-loading-overlay').show(); if(loginData && loginData.isLoggedIn) { suggestionCall(); return; } // load the captcha script and set the token loadScript('https://www.google.com/recaptcha/api.js?render=6LdMFNUZAAAAAIuRtzg0piOT-qXCbDF-iQiUi9KY',[], function() { setGoogleRecaptcha(); }); }); $('.improvement-bottom-btn.create-improvement-btn').click(function() { //create improvement button is clicked $('body').append('<div class="spinner-loading-overlay"></div>'); $('.spinner-loading-overlay').show(); // send this option via create-improvement-post api jQuery.ajax({ url: writeApiUrl + 'create-improvement-post/?v=1', type: "POST", contentType: 'application/json; charset=utf-8', dataType: 'json', xhrFields: { withCredentials: true }, data: JSON.stringify({ gfg_id: post_id }), success:function(result) { $('.spinner-loading-overlay:eq(0)').remove(); $('.improve-modal--overlay').hide(); $('.create-improvement-redirection-to-write').attr('href',writeUrl + 'improve-post/' + `${result.id}` + '/', '_blank'); $('.create-improvement-redirection-to-write')[0].click(); }, error:function(e) { showErrorMessage(e.responseJSON,e.status); }, }); }); </script> <script> var AdblockPlus = new function() { this.detect = function(px, callback) { var detected = false; var checksRemain = 2; var error1 = false; var error2 = false; if (typeof callback != "function") return; px += "?ch=*&rn=*"; function beforeCheck(callback, timeout) { if (checksRemain == 0 || timeout > 1E3) callback(checksRemain == 0 && detected); else setTimeout(function() { beforeCheck(callback, timeout * 2) }, timeout * 2) } function checkImages() { if (--checksRemain) return; detected = !error1 && error2 } var random = Math.random() * 11; var img1 = new Image; img1.onload = checkImages; img1.onerror = function() { error1 = true; checkImages() }; img1.src = px.replace(/\*/, 1).replace(/\*/, random); var img2 = new Image; img2.onload = checkImages; img2.onerror = function() { error2 = true; checkImages() }; img2.src = px.replace(/\*/, 2).replace(/\*/, random); beforeCheck(callback, 250) } }; /* AdblockPlus.detect("https://cdnads.geeksforgeeks.org/res/px.gif", function(abp){ window.googletag = window.googletag || {cmd: []}; window.abp=abp; var elms = [...document.querySelectorAll('div[id^=_GFG_ABP_]')]; const units=elms.map(elem=>elem.id) if(abp) { for(let curr_unit of units) { const iframe = document.createElement('iframe'); iframe.setAttribute('src',"https://aa.geeksforgeeks.org/iframe.html?code="+curr_unit.substr(1)) const elem = document.getElementById(curr_unit) const div = document.createElement('div'); div.setAttribute('id',curr_unit.substr(1)) let sizes = curr_unit.split("_"); sizes = sizes.filter(val => val.includes('x')); let [width, height] = sizes[0].split("x"); iframe.style.width = `${+width+20}px` iframe.style.height = `${+height+20}px` if(elem) { elem.appendChild(iframe); } } var gfgAdDivs = [...document.querySelectorAll('div[id^=GFG_AD_]')]; gfgAdDivs.forEach(gfgDiv => document.getElementById(gfgDiv.id).removeAttribute("style")); jQuery('#secondary .widget_text:last-child').css({"position": "unset"}); } });*/ AdblockPlus.detect("https://cdnads.geeksforgeeks.org/res/px.gif", function(abp){ window.googletag = window.googletag || {cmd: []}; window.abp=abp; var elms = [...document.querySelectorAll('div[id^=_GFG_ABP_]')]; //const units=elms.map(elem=>elem.id) const units = elms .filter(elem => !(window.innerWidth < 1500 && elem.id === "_GFG_ABP_Incontent_728x90")) .map(elem => elem.id); if(abp) { isAdBlockerPresent = true; for(let curr_unit of units) { const iframe = document.createElement('iframe'); iframe.addEventListener("load", () => { iframe.contentWindow.postMessage(JSON.stringify({host: window.location.host,category: window.arrPostCatName,parentWidth: window.innerWidth}),'https://aa.geeksforgeeks.org'); }); iframe.setAttribute('src',"https://aa.geeksforgeeks.org/iframe.html?code="+curr_unit.substr(1)) const elem = document.getElementById(curr_unit) const div = document.createElement('div'); div.setAttribute('id',curr_unit.substr(1)) let sizes = curr_unit.split("_"); sizes = sizes.filter(val => val.includes('x')); let [width, height] = sizes[0].split("x"); iframe.style.width = `${+width+20}px` iframe.style.height = `${+height+20}px` if(elem) { elem.appendChild(iframe); } } var gfgAdDivs = [...document.querySelectorAll('div[id^=GFG_AD_]')]; gfgAdDivs.forEach(gfgDiv => document.getElementById(gfgDiv.id).removeAttribute("style")); jQuery('#secondary .widget_text:last-child').css({"position": "unset"}); } else{ try { var isAdblockEnabled = t => fetch( new Request('https://pagead2.googlesyndication.com/pagead/js/adsbygoogle.js', { method: 'HEAD', mode: 'no-cors' }) ).catch(t); isAdblockEnabled(() => { // here goes modal pop-up code isAdBlockerPresent = true; }); } catch (err) {console.log(err);} } }); function closeAdBlockPopupModal(){ const modal = document.getElementById("adBlockerModal"); $('body').removeClass('body-for-ad-blocker'); $('#adBlockerModal').remove() localStorage.setItem('gfgAdBlockPopup',new Date()) } function showAdblockerModal(){ let randomNumberForButtonText = Math.round(Math.random()); let currTime = new Date(); let lastTime = new Date(localStorage.getItem('gfgAdBlockPopup')); if(((currTime-lastTime)/(1000*60*60))<1) { return; } const adBlockerModal = `<div id="adBlockerModal" class="ad-blocker-modal"> <div id="ad-blocker-modal-overlay"> <div id="ad-blocker-outer-div"> <div id="ad-blocker-div"> <p id="ad-blocker-div-warning" style="margin-bottom: 30px;">It seems that you are using an ad blocker.<br><span style="font-size: 22px;font-weight: normal;">Please disable it to support us!</span></p> <div id="ad-blocker-div-btns"> <button id="ad-blocker-div-button1" onclick="handleAdBlockerClick('disabled')"> I disabled my ad blocker </button> <a href="https://www.geeksforgeeks.org/geeksforgeeks-premium-subscription${randomNumberForButtonText === 1 ? "/?itm_source=geeksforgeeks&itm_medium=adblocker&itm_campaign=premium1" : "/?itm_source=geeksforgeeks&itm_medium=adblocker&itm_campaign=premium2"}" target="_blank"> <button id="ad-blocker-div-button2" style=" background: linear-gradient(45deg, #f0bd36, #bf873f); border: 1px solid transparent; color: white; " > ${randomNumberForButtonText === 1 ? "Go Ad-Free with Premium" : "Upgrade for No Ads"} </button> </a> </div> <div id="ad-blocker-div-continue-premium-promo-text"> "For an ad-free experience and exclusive features, subscribe to our Premium Plan!"<br> </div> <div id="ad-blocker-div-continue-btn-div"> <a id="ad-blocker-div-continue-btn" href="#" onclick="closeAdBlockPopupModal()">Continue without supporting</a> </div> </div> </div> </div> </div>`; $('body').append(adBlockerModal); $('body').addClass('body-for-ad-blocker'); const modal = document.getElementById("adBlockerModal"); modal.style.display = "block"; } function handleAdBlockerClick(type){ if(type == 'disabled'){ window.location.reload(); } else if(type == 'info'){ document.getElementById("ad-blocker-div").style.display = "none"; document.getElementById("ad-blocker-info-div").style.display = "flex"; handleAdBlockerIconClick(0); } } var lastSelected= null; //Mapping of name and video URL with the index. const adBlockerVideoMap = [ ['Ad Block Plus','https://media.geeksforgeeks.org/auth-dashboard-uploads/abp-blocker-min.mp4'], ['Ad Block','https://media.geeksforgeeks.org/auth-dashboard-uploads/Ad-block-min.mp4'], ['uBlock Origin','https://media.geeksforgeeks.org/auth-dashboard-uploads/ub-blocke-min.mp4'], ['uBlock','https://media.geeksforgeeks.org/auth-dashboard-uploads/U-blocker-min.mp4'], ] function handleAdBlockerIconClick(currSelected){ const videocontainer = document.getElementById('ad-blocker-info-div-gif'); const videosource = document.getElementById('ad-blocker-info-div-gif-src'); if(lastSelected != null){ document.getElementById("ad-blocker-info-div-icons-"+lastSelected).style.backgroundColor = "white"; document.getElementById("ad-blocker-info-div-icons-"+lastSelected).style.borderColor = "#D6D6D6"; } document.getElementById("ad-blocker-info-div-icons-"+currSelected).style.backgroundColor = "#D9D9D9"; document.getElementById("ad-blocker-info-div-icons-"+currSelected).style.borderColor = "#848484"; document.getElementById('ad-blocker-info-div-name-span').innerHTML = adBlockerVideoMap[currSelected][0] videocontainer.pause(); videosource.setAttribute('src', adBlockerVideoMap[currSelected][1]); videocontainer.load(); videocontainer.play(); lastSelected = currSelected; } </script>  <style> /* Temporary CSS for Three90 pop up modal (START)*/ .three90popup__container { width: 100vw; height: 100vh; position: fixed; top:0px; background: var(--job-tab-faded-background); z-index: 1024; display: flex; align-items: center; justify-content: center; } .three90modal__wrapper{ background-color: white; max-width: 350px; display: flex; flex-direction: column; border-radius: 10px; overflow: hidden; } .three90modal__message-container { display: flex; flex-direction: column; align-items: center; font-family: var(--font-primary); } .three90modal__subheading { margin-top: 20px; font-size: 22px; font-weight: 600; } .three90modal__text-message { margin-top: 20px; font-size: 15px; font-weight: 400; text-align: center; padding: 0 5px; } .three90__modal__button-wrapper { width: 100%; padding: 20px 0px; display: flex; justify-content: space-evenly; } .three90__modal__button-wrapper > button { width: 105px; height: 35px; border-radius: 13px; border:none; font-weight: 600; cursor: pointer; } #three90__modal-close-btn:hover { background-color: #cacbcd; } #three90__modal-explore-btn { background-color: #0a0727; color: white } @media screen and (max-width: 441px) { .three90modal__wrapper { max-width: 300px; } } /* Temporary CSS for Three90 pop up modal (END)*/ </style> <script type="text/javascript" > const coursePromotionCities = JSON.parse(`{"NCR":{"LOCATIONS":["Noida","Greater Noida","Ghaziabad","Faridabad","Delhi","New Delhi"],"COURSES":[{"name":"GATE CS 2025 Classroom Program","url":"https:\/\/www.geeksforgeeks.org\/courses\/gate-cs-self-paced"},{"name":"MERN Full Stack Development","url":"https:\/\/www.geeksforgeeks.org\/courses\/mern-full-stack-development-classroom"},{"name":"DSA For Interview Preparation","url":" https:\/\/www.geeksforgeeks.org\/courses\/dsa-interview-preparation-classroom"},{"name":"JAVA Backend Development","url":"https:\/\/www.geeksforgeeks.org\/courses\/complete-java-backend-development-program"},{"name":"Data Analytics Programme","url":"https:\/\/www.geeksforgeeks.org\/courses\/complete-data-analytics-program"},{"name":"AWS Solutions Architect Certification","url":"https:\/\/www.geeksforgeeks.org\/courses\/aws-solutions-architect-certification-classroom-training"},{"name":"Explore All","url":"https:\/\/www.geeksforgeeks.org\/courses\/offline-courses"}]},"NON_NCR":{"Bengaluru":[{"name":"Data Science Classroom Program","url":"https:\/\/www.geeksforgeeks.org\/courses\/data-science-classroom-program"},{"name":"System Design Classroom Program","url":"https:\/\/www.geeksforgeeks.org\/courses\/system-design-classroom-program"},{"name":"MERN Full Stack Development","url":"https:\/\/www.geeksforgeeks.org\/courses\/mern-full-stack-development-classroom"},{"name":"DSA For Interview Preparation","url":"https:\/\/www.geeksforgeeks.org\/courses\/dsa-interview-preparation-classroom"},{"name":"JAVA Backend Development","url":"https:\/\/www.geeksforgeeks.org\/courses\/complete-java-backend-development-program"},{"name":"Data Analytics Programme","url":"https:\/\/www.geeksforgeeks.org\/courses\/complete-data-analytics-program"},{"name":"AWS Solutions Architect Certification","url":"https:\/\/www.geeksforgeeks.org\/courses\/aws-solutions-architect-certification-classroom-training"},{"name":"Explore All","url":"https:\/\/www.geeksforgeeks.org\/courses\/offline-courses"}],"Pune":[{"name":"MERN Full Stack Development","url":"https:\/\/www.geeksforgeeks.org\/courses\/mern-full-stack-development-classroom"},{"name":"DSA For Interview Preparation","url":"https:\/\/www.geeksforgeeks.org\/courses\/dsa-interview-preparation-classroom"},{"name":"Complete Data Analytics Program","url":"https:\/\/www.geeksforgeeks.org\/courses\/complete-data-analytics-program"},{"name":"Explore All","url":"https:\/\/www.geeksforgeeks.org\/courses\/offline-courses"}],"Hyderabad":[{"name":"Complete Data Analytics Program","url":"https:\/\/www.geeksforgeeks.org\/courses\/complete-data-analytics-program"},{"name":"Complete Backend Development Program","url":"https:\/\/www.geeksforgeeks.org\/courses\/complete-java-backend-development-program"},{"name":"DSA for Interview Preparation","url":"https:\/\/www.geeksforgeeks.org\/courses\/dsa-interview-preparation-classroom"},{"name":"MERN Full Stack Web Development","url":"https:\/\/www.geeksforgeeks.org\/courses\/mern-full-stack-development-classroom"}]}}`); const offlineCourseTermMapper = JSON.parse(`{"ALL_TERMIDS":["2058","6263","2628","1745","1789","2601","2057","5037","2971","2023","2162","2795"],"COURSE_TERMID_MAP":{"JAVA":["2058"],"DATA_ANALYTICS":["1745","1789","2601","2057","5037","2971","2023","2162","2795"],"DSA":["6263"],"MERN":["2628"]}}`); </script> <script async src="https://www.geeksforgeeks.org/wp-content/themes/iconic-one/js/event-promotion.min.js?ver=4.5"></script>   <script>(function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start': new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0], j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src= 'https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f); })(window,document,'script','dataLayer','GTM-KDVRCT5');</script>  <script async src="https://www.googletagmanager.com/gtag/js?id=G-DWCCJLKX3X"></script> <script> window.dataLayer = window.dataLayer || []; function gtag(){dataLayer.push(arguments);} gtag('js', new Date()); // gtag('config', 'AW-474915276'); gtag('config', 'G-DWCCJLKX3X'); gtag('config', 'AW-796001856'); </script>  <div id="GFG_AD_Desktop_Stickyunit_1x1"></div>   <style> :root { --com-extra-icons-mobile-image: url(https://media.geeksforgeeks.org/auth-dashboard-uploads/Com-Extra-Icons13.svg); --write-experience-card-1: #ECF5F5; --write-experience-card-icon-1: #21898C; --write-experience-card-2: #EAF2F7; --write-experience-card-icon-2: #3079AC; --write-experience-card-3: #FDEFE6; --write-experience-card-icon-3: #F5A572; --write-experience-card-4: #F1F8F5; --write-experience-card-icon-4: #91C4AD; --write-experience-card-5: #EEE7FF; --write-experience-card-icon-5: #8B72C9; --write-experience-card-6: #F2F8E6; --write-experience-card-icon-6: #78C57F; --editor-button-text-color: #6E6E73; --write-modal-background: #fefefe; --experience-sidebar: #000; --left-bar-background: #FFFFFF; --write-redirect-container:#EAF2F7; --write-redirect-container-hover:#d6e7f2; } /* Dark Mode */ body[data-dark-mode="true"] { --write-modal-background: #161c23; --experience-sidebar: #000; --left-bar-background: #F0F3F5; } .popup-main { padding: 20px 18px 20px 18px; border-radius: 8px; } .popup-main .popup-heading { display: flex; align-items: center; color: #E9E9EA; margin-bottom: 10px; justify-content: space-between; } .popup-main .close-icon { background-image: var(--com-extra-icons-mobile-image);background-position: -15px -1651px;height: 22px;width: 22px;transform: scale(1); margin-bottom: 12px; cursor: pointer; } .popup-main .experience-card { color: #000; display: grid; grid-template-columns: repeat(2, 1fr); gap: 16px; /* margin-bottom:10px; */ } .popup-main a:hover, .popup-main a:active, .popup-main a:visited { color: inherit; text-decoration: none; } .popup-main .exp-card1, .popup-main .exp-card2, .popup-main .exp-card3, .popup-main .exp-card4, .popup-main .exp-card5, .popup-main .exp-card6 { display: flex; align-items: center; border-radius: 10px; cursor: pointer; } .popup-main .exp-card1 .icon1, .popup-main .exp-card2 .icon2, .popup-main .exp-card3 .icon3, .popup-main .exp-card4 .icon4, .popup-main .exp-card5 .icon5, .popup-main .exp-card6 .icon6 { width: 80px; height: 80px; border-radius: 10px 0px 0px 10px; display: flex; align-items: center; justify-content: center; background: var(--write-experience-card-icon-1); } .popup-main .exp-card1 .icon1, .popup-main .exp-card2 .icon2, .popup-main .exp-card3 .icon3, .popup-main .exp-card4 .icon4, .popup-main .exp-card5 .icon5, .popup-main .exp-card6 .icon6 { width: 80px; height: 80px; border-radius: 10px 0px 0px 10px; display: flex; align-items: center; justify-content: center; } .popup-main .exp-card1 .icon1 { background: var(--write-experience-card-icon-1); } .popup-main .exp-card2 .icon2 { background: var(--write-experience-card-icon-2); } .popup-main .exp-card3 .icon3 { background: var(--write-experience-card-icon-3); } .popup-main .exp-card4 .icon4 { background: var(--write-experience-card-icon-4); } .popup-main .exp-card5 .icon5 { background: var(--write-experience-card-icon-5); } .popup-main .exp-card6 .icon6 { background: var(--write-experience-card-icon-6); } .popup-main .exp-card6 .icon6-image { background-image: url(https://media.geeksforgeeks.org/auth-dashboard-uploads/compass.svg); width: 46px; height: 30px; background-size: 30px; background-repeat: no-repeat; background-position: center; } .popup-main .exp-card1 .icon1-image { background-image: var(--com-extra-icons-mobile-image); width: 46px; height: 28px; background-position: -4px -812px; } .popup-main .exp-card2 .icon2-image { background-image: var(--com-extra-icons-mobile-image); width: 46px; height: 28px; background-position: -4px -888px; } .popup-main .exp-card3 .icon3-image { background-image: var(--com-extra-icons-mobile-image); width: 46px; height: 28px; background-position: -4px -848px; } .popup-main .exp-card4 .icon4-image { background-image: url(https://media.geeksforgeeks.org/auth-dashboard-uploads/competitive.svg); width: 46px; height: 30px; background-size: 30px; background-repeat: no-repeat; background-position: center; } .popup-main .exp-card5 .icon5-image { background-image: var(--com-extra-icons-mobile-image); width: 46px; height: 33px; background-position: -4px -1217px; } .popup-main .exp-card1 .exp-card1-text, .popup-main .exp-card2 .exp-card2-text, .popup-main .exp-card3 .exp-card3-text, .popup-main .exp-card4 .exp-card4-text, .popup-main .exp-card5 .exp-card5-text, .popup-main .exp-card6 .exp-card6-text { display: flex; align-items: center; border-radius: 0px 10px 10px 0px; height: 80px; width: calc(100% - 80px); } .popup-main .exp-card1 { justify-content: flex-start; background: var(--write-experience-card-1); } .popup-main .exp-card2 { justify-content: flex-start; background: var(--write-experience-card-2); } .popup-main .exp-card3 { justify-content: flex-start; background: var(--write-experience-card-3); } .popup-main .exp-card4 { justify-content: flex-start; background: var(--write-experience-card-4); } .popup-main .exp-card5 { justify-content: flex-start; background: var(--write-experience-card-5); } .popup-main .exp-card6 { justify-content: flex-start; background: var(--write-experience-card-6); } .popup-main span { font-family: var(--font-primary); font-size: 14px; font-style: normal; font-weight: 500; line-height: normal; padding-left: 5px; padding-right: 5px; } #popup { display: none; background-color: var(--write-modal-background); padding: 20px; text-align: center; position: fixed; top: 50%; left: 50%; transform: translate(-50%, -50%); z-index: 1026; width: min(650px, calc(100% - 20px)); } .link-container-write{ display:flex; flex-direction:column; } .link-container-write > a { margin:7px 0px; } .phrase__container{ color:var(--color-gfg); border-radius: 6px; width: 100%; background-color:var(--write-redirect-container); padding: 15px; text-align: justify; font-size:14px; } .phrase__container:hover { color:var(--color-gfg) !important; background-color:var(--write-redirect-container-hover); } </style> <div class="popup-container"> <div id="popup" accesskey="" class="popup-main"> <div class="popup-heading"> <h2>What kind of Experience do you want to share?</h2> <div class="close-icon share-experience-modal-close"></div> </div>  <div class="experience-card"> <a class="exp-card5" href= "https://write.geeksforgeeks.org/posts-new?cid=e8fc46fe-75e7-4a4b-be3c-0c862d655ed0" target="_blank"> <div class="icon5"> <div class="icon5-image"></div> </div> <div class="exp-card5-text"> <span style="color: #000;">Interview Experiences</span> </div> </a> <a class="exp-card1" href="https://write.geeksforgeeks.org/posts-new?cid=82536bdb-84e6-4661-87c3-e77c3ac04ede" target="_blank"> <div class="icon1"> <div class="icon1-image"></div> </div> <div class="exp-card1-text"> <span style="color: #000;">Admission Experiences</span> </div> </a> <a class="exp-card6" href= "https://write.geeksforgeeks.org/posts-new?cid=5219b0b2-7671-40a0-9bda-503e28a61c31" target="_blank"> <div class="icon6"> <div class="icon6-image"></div> </div> <div class="exp-card6-text"> <span style="color: #000;">Career Journeys</span> </div> </a> <a class="exp-card2" href="https://write.geeksforgeeks.org/posts-new?cid=22ae3354-15b6-4dd4-a5b4-5c7a105b8a8f" target="_blank"> <div class="icon2"> <div class="icon2-image"></div> </div> <div class="exp-card2-text"> <span style="color: #000;">Work Experiences</span> </div> </a> <a class="exp-card3" href= "https://write.geeksforgeeks.org/posts-new?cid=c5e1ac90-9490-440a-a5fa-6180c87ab8ae" target="_blank"> <div class="icon3"> <div class="icon3-image"></div> </div> <div class="exp-card3-text"> <span style="color: #000;">Campus Experiences</span> </div> </a> <a class="exp-card4" href= "https://write.geeksforgeeks.org/posts-new?cid=5ebb8fe9-b980-4891-af07-f2d62a9735f2" target="_blank"> <div class="icon4"> <div class="icon4-image"></div> </div> <div class="exp-card4-text"> <span style="color: #000;">Competitive Exam Experiences</span> </div> </a> </div>  </div> <div id="overlay" onclick="toggleExperiencePopup()" style="display: block;min-height: 100vh;min-width: 100vw;position: fixed;top: 0;bottom: 0;right: 0;left: 0;display: none;justify-content: center;align-items: center;background: rgba(0,0,0,.702);z-index: 1025 !important;backdrop-filter: blur(4px); -webkit-backdrop-filter: blur(4px);word-break: keep-all;"></div> </div> <script> $('.share-experience-modal').click(function(e){ e.preventDefault(); var link = $(this).attr('href'); toggleExperiencePopup(link); }); function toggleExperiencePopup(link) { var popup = document.getElementById("popup"); var overlay = document.getElementById("overlay"); if (window.innerWidth < 992) { window.location.href = link; } else { popup.style.display = (popup.style.display === "block") ? "none" : "block"; overlay.style.display = (overlay.style.display === "block") ? "none" : "block"; } } $('.share-experience-modal-close').click(function(e){ var popup = document.getElementById("popup"); popup.style.display = 'none'; var overlay = document.getElementById("overlay"); overlay.style.display = 'none'; }); </script> </div> </body> </html>

CINXE.COM

Worst, Average and Best Case Analysis of Algorithms - GeeksforGeeks