Graph Algorithms - GeeksforGeeks

<!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="Graph 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/graph-data-structure-and-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="https://media.geeksforgeeks.org/wp-content/uploads/20240403150314/graph-data-structure.webp" /> <meta property="article:section" content="Graph" /> <meta property="og:type" content="article" /> <meta property="og:locale" content="en_US" /> <meta property="article:published_time" content="2024-01-17 13:44:25+00:00" /> <meta property="article:modified_time" content="2024-11-09 15:14:35+00:00" /> <meta property="og:updated_time" content="2024-11-09 15:14:35+00:00" /> <meta property="og:image:secure_url" content="https://media.geeksforgeeks.org/wp-content/uploads/20240403150314/graph-data-structure.webp" /> <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 src="//cdnjs.cloudflare.com/ajax/libs/require.js/2.1.14/require.min.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>  <title>Graph Algorithms - GeeksforGeeks</title> <link rel="profile" href="http://gmpg.org/xfn/11" /> <link rel="pingback" href="" />   <script> var video_api_response = JSON.parse("{\"id\":8121,\"title\":\"GRAPH Data Structure | What is Graph? | DSA Course\",\"slug\":\"graph-data-structure-what-is-graph-dsa-course\",\"description\":\"<p>In the realm of DSA, graphs play a pivotal role in enhancing user engagement, optimizing resource allocation, and unraveling the complex tapestry of online video sharing.<br>So let's learn about Graphs in Detail!<\/p>\",\"source\":\"https:\/\/videos.geeksforgeeks.org\/hls\/505bcf43ba418f051683f4cb7f95fa9fgfg-GRAPHDataStructureWhatisGraphDSACourseGeeksforGeeks20240401175057.m3u8\",\"category\":[{\"term_id__id\":7,\"term_id__term_name\":\"Data Structures\",\"term_id__term_type\":1,\"term_id__slug\":\"data-structures\"},{\"term_id__id\":321,\"term_id__term_name\":\"graph\",\"term_id__term_type\":2,\"term_id__slug\":\"graph-ghyppy\"},{\"term_id__id\":562,\"term_id__term_name\":\"DSA\",\"term_id__term_type\":1,\"term_id__slug\":\"dsa-lpubwc\"}],\"video_type\":\"geeksforgeeks\",\"meta\":{\"thumbnail\":\"https:\/\/media.geeksforgeeks.org\/geeksforgeeks\/GRAPHDataStructureWhatisGraphDSACourse\/gTsoyORhqkgHD120240401175201-small.png\",\"largeThumbnail\":\"https:\/\/media.geeksforgeeks.org\/geeksforgeeks\/GRAPHDataStructureWhatisGraphDSACourse\/gTsoyORhqkgHD120240401175201.jpg\",\"likes\":0,\"views\":18250,\"isFeatured\":0,\"isPremium\":0,\"isPublic\":0,\"format\":\"video\/mp4\",\"revision\":{}},\"time\":\"01\/04\/2024\",\"seo\":{\"description\":\"<p>In the realm of DSA, graphs play a pivotal role in enhancing user engage\",\"thumbnail\":\"https:\/\/media.geeksforgeeks.org\/geeksforgeeks\/GRAPHDataStructureWhatisGraphDSACourse\/gTsoyORhqkgHD120240401175201-seo.png\"},\"subtitle\":\"https:\/\/videos.geeksforgeeks.org\/subtitles\/GRAPHDataStructureWhatisGraphDSACourseGeeksforGeeks20240401175057.vtt\",\"duration\":891,\"post_list\":[{\"post_id\":1134345,\"post_title\":\"Graph Data Structure And Algorithms\"}],\"course_link\":null,\"views\":\"18250\",\"video_schema\":{\"@context\":\"https:\/\/schema.org\",\"@type\":\"VideoObject\",\"name\":\"GRAPH Data Structure What is Graph? DSA Course\",\"description\":\"In the realm of DSA, graphs play a pivotal role in enhancing user engagement, optimizing resource allocation, and unraveling the complex tapestry of online video sharing.So lets learn about Graphs in Detail\",\"thumbnailUrl\":[\"https:\/\/media.geeksforgeeks.org\/geeksforgeeks\/GRAPHDataStructureWhatisGraphDSACourse\/gTsoyORhqkgHD120240401175201-seo.png\",\"https:\/\/media.geeksforgeeks.org\/geeksforgeeks\/GRAPHDataStructureWhatisGraphDSACourse\/gTsoyORhqkgHD120240401175201-small.png\",\"https:\/\/media.geeksforgeeks.org\/geeksforgeeks\/GRAPHDataStructureWhatisGraphDSACourse\/gTsoyORhqkgHD120240401175201.jpg\"],\"uploadDate\":\"2024-04-01T17:52:52Z\",\"duration\":\"PT0H14M51S\",\"contentUrl\":\"https:\/\/www.geeksforgeeks.org\/videos\/graph-data-structure-what-is-graph-dsa-course\/\"}}"); </script> <script type="application/ld+json">{"@context":"https://schema.org","@type":"VideoObject","name":"GRAPH Data Structure What is Graph? DSA Course","description":"In the realm of DSA, graphs play a pivotal role in enhancing user engagement, optimizing resource allocation, and unraveling the complex tapestry of online video sharing.So lets learn about Graphs in Detail","thumbnailUrl":["https://media.geeksforgeeks.org/geeksforgeeks/GRAPHDataStructureWhatisGraphDSACourse/gTsoyORhqkgHD120240401175201-seo.png","https://media.geeksforgeeks.org/geeksforgeeks/GRAPHDataStructureWhatisGraphDSACourse/gTsoyORhqkgHD120240401175201-small.png","https://media.geeksforgeeks.org/geeksforgeeks/GRAPHDataStructureWhatisGraphDSACourse/gTsoyORhqkgHD120240401175201.jpg"],"uploadDate":"2024-04-01T17:52:52Z","duration":"PT0H14M51S","contentUrl":"https://www.geeksforgeeks.org/videos/graph-data-structure-what-is-graph-dsa-course/"}</script>   <script type="application/ld+json"> { "@context": "https://schema.org", "@type": "Article", "mainEntityOfPage": { "@type": "WebPage", "id": "https://www.geeksforgeeks.org/graph-data-structure-and-algorithms/" }, "headline": "Graph Algorithms", "datePublished": "2024-01-17 01:44:25", "dateModified": "2024-11-09 03:14:35", "image": { "@type": "ImageObject", "url": "https://media.geeksforgeeks.org/wp-content/uploads/20240403150314/graph-data-structure.webp", "width": "1001", "height": "471" }, "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": "Graph algorithms are methods used to manipulate and analyze graphs, solving various range of problems like finding the shortest path, cycles detection. If you are looking for difficulty-wise list of problems, please refer to&nbsp;Graph Data Structure.Basics of Graph:Introduction to GraphsGraph and its representationsTranspose graphBFS and DFS in Graph:Breadth First Traversal", "about": [ { "@type": "Thing", "name": "Graph" }, { "@type": "Thing", "name": "Dsa" } ] }</script> <script type="application/ld+json"> { "@context": "https://schema.org", "@type": "WebSite", "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('2068'); arrPostCat.push('6263'); var tIds = "2068,6263"; var termsNames = "Graph,DSA,DataStructures"; var tIdsInclusiveParents = "2068,6263,2066" var domain = 1; var arrPost = new Array(); var post_id = "1134345"; var post_type = "post"; var post_slug = window.location.href; var ip = "64.252.72.123"; var post_title = `Graph Algorithms`; var post_status = "publish"; var practiceAPIURL="https://practiceapi.geeksforgeeks.org/"; var practiceURL="https://practice.geeksforgeeks.org/"; var post_date = "2024-01-17 13:24:09"; var commentSysUrl = "https://discuss.geeksforgeeks.org/commentEmbedV2.js"; //var postAdApiUrlString = ""; var link_on_code_run = ''; var link_search_modal_top = ''; var country_code_cf = "PK"; var postAdApiUrlString = '2066/2068/6263/'; </script>  <link rel="canonical" href="https://www.geeksforgeeks.org/graph-data-structure-and-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='//www.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=11.75' 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=13.43'></script> <link rel='shortlink' href='https://www.geeksforgeeks.org/?p=1134345' /> <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-1134345 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 Tutorial</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/taking-input-in-python/?ref=outind" target="_self">Taking Input 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/python-operators/?ref=outind" target="_self">Python Operators</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-types/?ref=outind" target="_self">Python Data Types</a></li><li class="mega-dropdown__list-item" data-parent="false" aria-expanded="true" data-expandable="true"><span>Python Loops and Control Flow</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/python3-if-if-else-nested-if-if-elif-statements/?ref=outind" target="_self">Python Conditional Statements</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/loops-in-python/?ref=outind" target="_self">Python Loops</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/python-functions/?ref=outind" target="_self">Python Functions</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/python-oops-concepts/?ref=outind" target="_self">Python OOPS Concept</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><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/python-exception-handling/?ref=outind" target="_self">Python Exception Handling</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/file-handling-python/?ref=outind" target="_self">Python File Handling</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/python-exercises-practice-questions-and-solutions/?ref=outind" target="_self">Python Exercises</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">Learn Java Programming Language</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-parent="false" aria-expanded="true" data-expandable="true"><span>Java Interview Questions</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/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/core-java-interview-questions-for-freshers/?ref=outind" target="_self">Core Java Interview Questions-Freshers</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-java-multithreading-interview-questions-answers/?ref=outind" target="_self">Java Multithreading 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/oops-interview-questions/?ref=outind" target="_self">OOPs Interview Questions and Answers</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/java-exercises/?ref=outind" target="_self">Java Exercises</a></li><li class="mega-dropdown__list-item" data-parent="false" aria-expanded="true" data-expandable="true"><span>Java Quiz</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/quizzes/50-java-language-mcqs-with-answers-2/?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-multiple-choice-questions/?ref=outind" target="_self">Core Java MCQ</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/java-projects/?ref=outind" target="_self">Java Projects</a></li><li class="mega-dropdown__list-item" data-parent="false" aria-expanded="true" data-expandable="true"><span>Advance Java</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/spring/?ref=outind" target="_self">Spring Tutorial</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/spring-boot/?ref=outind" target="_self">Spring Boot Tutorial</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/spring-boot-interview-questions/?ref=outind" target="_self">Spring Boot 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/spring-mvc/?ref=outind" target="_self">Spring MVC Tutorial</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/spring-mvc-interview-questions/?ref=outind" target="_self">Spring MVC 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/hibernate-tutorial/?ref=outind" target="_self">Hibernate Tutorial</a></li><li class="mega-dropdown__list-item" data-child="true" aria-expanded="false" data-expandable="false"><a href="https://www.geeksforgeeks.org/hibernate-interview-questions/?ref=outind" target="_self">Hibernate Interview Questions</a></li></ul></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"><span>System Design</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/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/top-50-graph-coding-problems-for-interviews/?ref=shm">Interview Problems on Graph</a></li><li><a href="https://www.geeksforgeeks.org/explore?page=1&category=Graph&sortBy=submissions&ref=shm">Practice Graph</a></li><li><a href="https://www.geeksforgeeks.org/data-structure-gq/top-mcqs-on-graph-data-strcuture-with-answers/?ref=shm">MCQs on Graph</a></li><li><a href="https://www.geeksforgeeks.org/introduction-to-graphs-data-structure-and-algorithm-tutorials/?ref=shm">Graph Tutorial</a></li><li><a href="https://www.geeksforgeeks.org/graph-and-its-representations/?ref=shm">Graph Representation</a></li><li><a href="https://www.geeksforgeeks.org/basic-properties-of-a-graph/?ref=shm">Graph Properties</a></li><li><a href="https://www.geeksforgeeks.org/graph-types-and-applications/?ref=shm">Types of Graphs</a></li><li><a href="https://www.geeksforgeeks.org/applications-advantages-and-disadvantages-of-graph/?ref=shm">Graph Applications</a></li><li><a href="https://www.geeksforgeeks.org/breadth-first-search-or-bfs-for-a-graph/?ref=shm">BFS on Graph</a></li><li><a href="https://www.geeksforgeeks.org/depth-first-search-or-dfs-for-a-graph/?ref=shm">DFS on Graph</a></li><li><a href="https://www.geeksforgeeks.org/difference-between-graph-and-tree/?ref=shm">Graph VS Tree</a></li><li><a href="https://www.geeksforgeeks.org/transpose-graph/?ref=shm">Transpose Graph</a></li><li><a href="https://www.geeksforgeeks.org/introduction-to-dijkstras-shortest-path-algorithm/?ref=shm">Dijkstra's Algorithm</a></li><li><a href="https://www.geeksforgeeks.org/what-is-minimum-spanning-tree-mst/?ref=shm">Minimum Spanning Tree</a></li><li><a href="https://www.geeksforgeeks.org/prims-minimum-spanning-tree-mst-greedy-algo-5/?ref=shm">Prim’s Algorithm</a></li><li><a href="https://www.geeksforgeeks.org/topological-sorting/?ref=shm">Topological Sorting</a></li><li><a href="https://www.geeksforgeeks.org/floyd-warshall-algorithm-dp-16/?ref=shm">Floyd Warshall Algorithm</a></li><li><a href="https://www.geeksforgeeks.org/strongly-connected-components/?ref=shm">Strongly Connected Components</a></li><li><a href="https://www.geeksforgeeks.org/applications-advantages-and-disadvantages-of-graph/?ref=shm">Advantages & Disadvantages</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('["Graph","DSA","DataStructures"]'); </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/graph-data-structure-and-algorithms/?type%3Darticle%26id%3D1134345&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('["Graph"]'); </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 "> <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-1134345 post type-post status-publish format-standard hentry category-dsa category-graph" id="post-1134345">  <div class="main_wrapper" style="display:flex;"> <div style="width: 100%;"> <div class="article-title"> <h1>Graph Algorithms</h1> </div> <div class="last_updated_parent"> <div> <span class="strong">Last Updated : </span> <span>11 Dec, 2024</span> </div>  <div class="three_dot_dropdown"> <div style="display: flex;"> <div pid="1134345" ptitle="Graph 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="1134345" ptitle="Graph 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="1134345" ptitle="Graph 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="1134345" ptitle="Graph 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="1134345" 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="1134345" class="article--viewer_bookmark tooltip"> <div class="three_dot_dropdown_div three_dot_dropdown_save"> <div class="three_dot_dropdown_inner_div" data-gfg-action="bookmark-article" data-bookmark-value="0"> <i class="gfg-icon gfg-icon_bookmark"></i> <span>Save</span> </div> </div>  </div> <div pid="1134345" 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"><b><strong>Graph algorithms </strong></b><span>are methods used to manipulate and analyze graphs, solving various range of problems like </span><b><strong>finding the shortest path, cycles detection. </strong></b></p><p dir="ltr"><span>If you are looking for difficulty-wise list of problems, please refer to </span><a href="https://www.geeksforgeeks.org/graph-data-structure/" target="_blank" rel="noopener"><span>Graph Data Structure</span></a><span>.</span></p><h2><b><strong>Basics</strong></b></h2><ul><li value="1"><a href="https://www.geeksforgeeks.org/graph-and-its-representations/" rel="noopener"><span>Graph and its representations</span></a></li></ul><h2 id="bfs-and-dfs-in-graph"><b><strong>BFS and DFS </strong></b></h2><ul><li value="1"><a href="https://www.geeksforgeeks.org/breadth-first-traversal-for-a-graph/" rel="noopener"><span>Breadth First Traversal</span></a></li><li value="2"><a href="https://www.geeksforgeeks.org/depth-first-traversal-for-a-graph/" rel="noopener"><span>Depth First Traversal </span></a><span> </span></li><li value="3"><a href="https://www.geeksforgeeks.org/difference-between-bfs-and-dfs/" rel="noopener"><span>Difference between BFS and DFS</span></a></li><li value="4"><a href="https://www.geeksforgeeks.org/minimum-time-required-so-that-all-oranges-become-rotten/" target="_blank" rel="noopener"><span>Rotten Tomatoes</span></a></li><li value="5"><a href="https://www.geeksforgeeks.org/find-the-number-of-islands-using-dfs/" target="_blank" rel="noopener"><span>Islands in a Graph</span></a></li><li value="6"><a href="https://www.geeksforgeeks.org/flood-fill-algorithm/" target="_blank" rel="noopener"><span>Flood Fill</span></a></li><li value="7"><a href="https://www.geeksforgeeks.org/bipartite-graph/" target="_blank" rel="noopener"><span>Check for Bipartite</span></a></li><li value="8"><a href="https://www.geeksforgeeks.org/snake-ladder-problem-2/" target="_blank" rel="noopener"><span>Word Ladder </span></a></li><li value="9"><a href="https://www.geeksforgeeks.org/snake-ladder-problem-2/" target="_blank" rel="noopener"><span>Snakes and Ladder</span></a></li><li value="10"><a href="https://www.geeksforgeeks.org/water-jug-problem-using-bfs/" target="_blank" rel="noopener"><span>Water Jug problem</span></a></li><li value="11"><a href="https://www.geeksforgeeks.org/atlantic-pacific-water-flow/" target="_blank" rel="noopener"><span>Pacific Atlantic Water Flow</span></a></li><li value="12"><a href="https://www.geeksforgeeks.org/shortest-path-in-a-binary-maze/" target="_blank" rel="noopener"><span>Shortest Path in Binary Matrix</span></a></li><li value="13"><a href="https://www.geeksforgeeks.org/clone-an-undirected-graph/" target="_blank" rel="noopener"><span>Clone a Graph</span></a><span> </span></li><li value="14"><a href="https://www.geeksforgeeks.org/transitive-closure-of-a-graph-using-dfs/" rel="noopener"><span>Transitive Closure of a Graph using DFS</span></a></li></ul><h2 id="cycles-in-graph"><b><strong>Cycles </strong></b></h2><ul><li value="1"><a href="https://www.geeksforgeeks.org/detect-cycle-in-a-graph/" rel="noopener"><span>Detect Cycle in a Directed Graph</span></a></li><li value="2"><a href="https://www.geeksforgeeks.org/detect-cycle-undirected-graph/" rel="noopener"><span>Detect cycle in an undirected graph</span></a></li><li value="3"><a href="https://www.geeksforgeeks.org/detect-cycle-direct-graph-using-colors/" rel="noopener"><span>Detect cycle in a direct graph using colors</span></a></li><li value="4"><a href="https://www.geeksforgeeks.org/detect-negative-cycle-graph-bellman-ford/" rel="noopener"><span>Detect a negative cycle in a Graph | (Bellman Ford)</span></a></li><li value="5"><a href="https://www.geeksforgeeks.org/cycles-of-length-n-in-an-undirected-and-connected-graph/" rel="noopener"><span>Cycles of length n in an undirected and connected graph</span></a></li><li value="6"><a href="https://www.geeksforgeeks.org/detecting-negative-cycle-using-floyd-warshall/" rel="noopener"><span>Detecting negative cycle using Floyd Warshall</span></a></li><li value="7"><a href="https://www.geeksforgeeks.org/clone-directed-acyclic-graph/" rel="noopener"><span>Clone a Directed Acyclic Graph</span></a></li><li value="8"><a href="https://www.geeksforgeeks.org/union-by-rank-and-path-compression-in-union-find-algorithm/" rel="noopener"><span>Union By Rank and Path Compression in Union-Find Algorithm</span></a></li><li value="9"><a href="https://www.geeksforgeeks.org/introduction-to-disjoint-set-data-structure-or-union-find-algorithm/" rel="noopener"><span>Introduction to Disjoint Set Data Structure or Union-Find Algorithm</span></a></li></ul><h2 id="shortest-path-in-graph"><b><strong>Shortest Path </strong></b></h2><ul><li value="1"><a href="https://www.geeksforgeeks.org/greedy-algorithms-set-6-dijkstras-shortest-path-algorithm/" rel="noopener"><span>Dijkstra’s shortest path algorithm</span></a></li><li value="2"><a href="https://www.geeksforgeeks.org/dynamic-programming-set-23-bellman-ford-algorithm/" rel="noopener"><span>Bellman–Ford Algorithm</span></a></li><li value="3"><a href="https://www.geeksforgeeks.org/dynamic-programming-set-16-floyd-warshall-algorithm/" rel="noopener"><span>Floyd Warshall Algorithm</span></a></li><li value="4"><a href="https://www.geeksforgeeks.org/johnsons-algorithm/" rel="noopener"><span>Johnson’s algorithm for All-pairs shortest paths</span></a></li><li value="5"><a href="https://www.geeksforgeeks.org/shortest-path-for-directed-acyclic-graphs/" rel="noopener"><span>Shortest Path in Directed Acyclic Graph</span></a></li><li value="6"><a href="https://www.geeksforgeeks.org/dials-algorithm-optimized-dijkstra-for-small-range-weights/" rel="noopener"><span>Dial’s Algorithm</span></a></li><li value="7"><a href="https://www.geeksforgeeks.org/multistage-graph-shortest-path/" rel="noopener"><span>Multistage Graph (Shortest Path)</span></a></li><li value="8"><a href="https://www.geeksforgeeks.org/shortest-path-unweighted-graph/" rel="noopener"><span>Shortest path in an unweighted graph</span></a></li><li value="9"><a href="https://www.geeksforgeeks.org/karps-minimum-mean-average-weight-cycle-algorithm/" rel="noopener"><span>Karp’s minimum mean (or average) weight cycle algorithm</span></a></li><li value="10"><a href="https://www.geeksforgeeks.org/0-1-bfs-shortest-path-binary-graph/" rel="noopener"><span>0-1 BFS (Shortest Path in a Binary Weight Graph)</span></a></li><li value="11"><a href="https://www.geeksforgeeks.org/find-minimum-weight-cycle-undirected-graph/" rel="noopener"><span>Find minimum weight cycle in an undirected graph</span></a></li></ul><h2 id="minimum-spanning-tree"><b><strong>Minimum Spanning Tree</strong></b></h2><ul><li value="1"><a href="https://www.geeksforgeeks.org/greedy-algorithms-set-5-prims-minimum-spanning-tree-mst-2/" rel="noopener"><span>Prim’s Minimum Spanning Tree (MST)</span></a></li><li value="2"><a href="https://www.geeksforgeeks.org/greedy-algorithms-set-2-kruskals-minimum-spanning-tree-mst/" rel="noopener"><span>Kruskal’s Minimum Spanning Tree Algorithm</span></a></li><li value="3"><a href="https://www.geeksforgeeks.org/difference-between-prims-and-kruskals-algorithm-for-mst/" rel="noopener"><span>Difference between Prim’s and Kruskal’s algorithm for MST</span></a></li><li value="4"><a href="https://www.geeksforgeeks.org/applications-of-minimum-spanning-tree/" rel="noopener"><span>Applications of Minimum Spanning Tree Problem</span></a></li><li value="5"><a href="https://www.geeksforgeeks.org/minimum-cost-connect-cities/" rel="noopener"><span>Minimum cost to connect all cities</span></a></li><li value="6"><a href="https://www.geeksforgeeks.org/total-number-spanning-trees-graph/" rel="noopener"><span>Total number of Spanning Trees in a Graph</span></a></li><li value="7"><a href="https://www.geeksforgeeks.org/minimum-product-spanning-tree/" rel="noopener"><span>Minimum Product Spanning Tree</span></a></li><li value="8"><a href="https://www.geeksforgeeks.org/reverse-delete-algorithm-minimum-spanning-tree/" rel="noopener"><span>Reverse Delete Algorithm for Minimum Spanning Tree</span></a></li><li value="9"><a href="https://www.geeksforgeeks.org/greedy-algorithms-set-9-boruvkas-algorithm/" rel="noopener"><span>Boruvka’s algorithm for Minimum Spanning Tree</span></a></li></ul><h2 id="topological-sorting"><b><strong>Topological Sorting</strong></b></h2><ul><li value="1"><a href="https://www.geeksforgeeks.org/topological-sorting/" rel="noopener"><span>Topological Sorting</span></a></li><li value="2"><a href="https://www.geeksforgeeks.org/all-topological-sorts-of-a-directed-acyclic-graph/" rel="noopener"><span>All topological sorts of a Directed Acyclic Graph</span></a></li><li value="3"><a href="https://www.geeksforgeeks.org/topological-sorting-indegree-based-solution/" rel="noopener"><span>Kahn’s Algorithm for Topological Sorting</span></a></li><li value="4"><a href="https://www.geeksforgeeks.org/maximum-edges-can-added-dag-remains-dag/" rel="noopener"><span>Maximum edges that can be added to DAG so that is remains DAG</span></a></li><li value="5"><a href="https://www.geeksforgeeks.org/find-longest-path-directed-acyclic-graph/" rel="noopener"><span>Longest Path in a Directed Acyclic Graph</span></a></li><li value="6"><a href="https://www.geeksforgeeks.org/topological-sorting-using-departure-time-of-vertex/" rel="noopener"><span>Topological Sort of a graph using departure time of vertex</span></a></li><li value="7"><a href="https://www.geeksforgeeks.org/find-itinerary-from-a-given-list-of-tickets/" target="_blank" rel="noopener"><span>Find Itinerary from a given list of tickets</span></a></li></ul><h2 id="connectivity-in-graph"><b><strong>Connectivity in Graph</strong></b></h2><ul><li value="1"><a href="https://www.geeksforgeeks.org/articulation-points-or-cut-vertices-in-a-graph/" rel="noopener"><span>Articulation Points (or Cut Vertices) in a Graph</span></a></li><li value="2"><a href="https://www.geeksforgeeks.org/biconnected-components/" rel="noopener"><span>Biconnected Components</span></a></li><li value="3"><a href="https://www.geeksforgeeks.org/bridge-in-a-graph/" rel="noopener"><span>Bridges in a graph</span></a></li><li value="4"><a href="https://www.geeksforgeeks.org/eulerian-path-and-circuit/" rel="noopener"><span>Eulerian path and circuit</span></a></li><li value="5"><a href="https://www.geeksforgeeks.org/fleurys-algorithm-for-printing-eulerian-path/" rel="noopener"><span>Fleury’s Algorithm for printing Eulerian Path or Circuit</span></a></li><li value="6"><a href="https://www.geeksforgeeks.org/strongly-connected-components/" rel="noopener"><span>Strongly Connected Components</span></a></li><li value="7"><a href="https://www.geeksforgeeks.org/count-possible-paths-source-destination-exactly-k-edges/" rel="noopener"><span>Count all possible walks from a source to a destination with exactly k edges</span></a></li><li value="8"><a href="https://www.geeksforgeeks.org/euler-circuit-directed-graph/" rel="noopener"><span>Euler Circuit in a Directed Graph</span></a></li><li value="9"><a href="https://www.geeksforgeeks.org/length-of-shortest-chain-to-reach-a-target-word/" rel="noopener"><span>Length of shortest chain to reach the target word</span></a></li><li value="10"><a href="https://www.geeksforgeeks.org/given-array-strings-find-strings-can-chained-form-circle/" rel="noopener"><span>Find if an array of strings can be chained to form a circle</span></a></li><li value="11"><a href="https://www.geeksforgeeks.org/tarjan-algorithm-find-strongly-connected-components/" rel="noopener"><span>Tarjan’s Algorithm to find strongly connected Components</span></a></li><li value="12"><a href="https://www.geeksforgeeks.org/paths-travel-nodes-using-edgeseven-bridges-konigsberg/" rel="noopener"><span>Paths to travel each nodes using each edge (Seven Bridges of Königsberg)</span></a></li><li value="13"><a href="https://www.geeksforgeeks.org/dynamic-connectivity-set-1-incremental/" rel="noopener"><span>Dynamic Connectivity | Set 1 (Incremental)</span></a></li></ul><h2 id="maximum-flow-in-graph"><b><strong>Maximum Flow in Graph</strong></b></h2><ul><li value="1"><a href="https://www.geeksforgeeks.org/max-flow-problem-introduction/" rel="noopener"><span>Max Flow Problem Introduction</span></a></li><li value="2"><a href="https://www.geeksforgeeks.org/ford-fulkerson-algorithm-for-maximum-flow-problem/" rel="noopener"><span>Ford-Fulkerson Algorithm for Maximum Flow Problem</span></a></li><li value="3"><a href="https://www.geeksforgeeks.org/find-edge-disjoint-paths-two-vertices/" rel="noopener"><span>Find maximum number of edge disjoint paths between two vertices</span></a></li><li value="4"><a href="https://www.geeksforgeeks.org/minimum-cut-in-a-directed-graph/" rel="noopener"><span>Find minimum s-t cut in a flow network</span></a></li><li value="5"><a href="https://www.geeksforgeeks.org/maximum-bipartite-matching/" rel="noopener"><span>Maximum Bipartite Matching</span></a></li><li value="6"><a href="https://www.geeksforgeeks.org/channel-assignment-problem/" rel="noopener"><span>Channel Assignment Problem</span></a></li><li value="7"><a href="https://www.geeksforgeeks.org/introduction-to-push-relabel-algorithm/" rel="noopener"><span>Introduction to Push Relabel Algorithm</span></a></li><li value="8"><a href="https://www.geeksforgeeks.org/kargers-algorithm-for-minimum-cut-set-1-introduction-and-implementation/" rel="noopener"><span>Karger’s Algorithm- Set 1- Introduction and Implementation</span></a></li><li value="9"><a href="https://www.geeksforgeeks.org/dinics-algorithm-maximum-flow/" rel="noopener"><span>Dinic’s algorithm for Maximum Flow</span></a></li></ul><h2 id="some-must-do-problems-on-graph"><b><strong>Some must do Problems </strong></b></h2><ul><li value="1"><a href="https://www.geeksforgeeks.org/find-length-largest-region-boolean-matrix/" rel="noopener"><span>Find length of the largest region in Boolean Matrix</span></a></li><li value="2"><a href="https://www.geeksforgeeks.org/count-number-trees-forest/" rel="noopener"><span>Count number of trees in a forest</span></a></li><li value="3"><a href="https://www.geeksforgeeks.org/peterson-graph/" rel="noopener"><span>A Peterson Graph Problem</span></a></li><li value="4"><a href="https://www.geeksforgeeks.org/clone-an-undirected-graph/" rel="noopener"><span>Clone an Undirected Graph</span></a></li><li value="5"><a href="https://www.geeksforgeeks.org/graph-coloring-applications/" rel="noopener"><span>Graph Coloring (Introduction and Applications)</span></a></li><li value="6"><a href="https://www.geeksforgeeks.org/traveling-salesman-problem-tsp-implementation/" rel="noopener"><span>Traveling Salesman Problem (TSP) Implementation</span></a></li><li value="7"><a href="https://www.geeksforgeeks.org/vertex-cover-problem-set-1-introduction-approximate-algorithm-2/" rel="noopener"><span>Vertex Cover Problem | Set 1 (Introduction and Approximate Algorithm)</span></a></li><li value="8"><a href="https://www.geeksforgeeks.org/k-centers-problem-set-1-greedy-approximate-algorithm/" rel="noopener"><span>K Centers Problem | Set 1 (Greedy Approximate Algorithm)</span></a></li><li value="9"><a href="https://www.geeksforgeeks.org/erdos-renyl-model-generating-random-graphs/" rel="noopener"><span>Erdos Renyl Model (for generating Random Graphs)</span></a></li><li value="10"><a href="https://www.geeksforgeeks.org/chinese-postman-route-inspection-set-1-introduction/" rel="noopener"><span>Chinese Postman or Route Inspection | Set 1 (introduction)</span></a></li><li value="11"><a href="https://www.geeksforgeeks.org/hierholzers-algorithm-directed-graph/" rel="noopener"><span>Hierholzer’s Algorithm for directed graph</span></a></li><li value="12"><a href="https://www.geeksforgeeks.org/bipartite-graph/" rel="noopener"><span>Check whether a given graph is Bipartite or not</span></a></li><li value="13"><a href="https://www.geeksforgeeks.org/snake-ladder-problem-2/" rel="noopener"><span>Snake and Ladder Problem</span></a></li><li value="14"><a href="https://www.geeksforgeeks.org/boggle-find-possible-words-board-characters/" rel="noopener"><span>Boggle (Find all possible words in a board of characters)</span></a></li><li value="15"><a href="https://www.geeksforgeeks.org/hopcroft-karp-algorithm-for-maximum-matching-set-1-introduction/" rel="noopener"><span>Hopcroft Karp Algorithm for Maximum Matching-Introduction</span></a></li><li value="16"><a href="https://www.geeksforgeeks.org/minimum-time-required-so-that-all-oranges-become-rotten/" rel="noopener"><span>Minimum Time to rot all oranges</span></a></li><li value="17"><a href="https://www.geeksforgeeks.org/construct-graph-given-degrees-vertices/" rel="noopener"><span>Construct a graph from given degrees of all vertices</span></a></li><li value="18"><a href="https://www.geeksforgeeks.org/determine-whether-universal-sink-exists-directed-graph/" rel="noopener"><span>Determine whether a universal sink exists in a directed graph</span></a></li><li value="19"><a href="https://www.geeksforgeeks.org/number-sink-nodes-graph/" rel="noopener"><span>Number of sink nodes in a graph</span></a></li><li value="20"><a href="https://www.geeksforgeeks.org/two-clique-problem-check-graph-can-divided-two-cliques/" rel="noopener"><span>Two Clique Problem (Check if Graph can be divided in two Cliques)</span></a></li></ul><h2 id="some-quizzes"><b><strong>Some Quizzes</strong></b></h2><ul><li value="1"><a href="https://www.geeksforgeeks.org/algorithms-gq/top-mcqs-on-graph-traversals-with-answers/?ref=graph_lp" rel="noopener"><span>Quizzes on Graph Traversal</span></a></li><li value="2"><a href="https://www.geeksforgeeks.org/algorithms-gq/top-mcqs-on-shortest-paths-in-graphs-with-answers/?ref=graph_lp" rel="noopener"><span>Quizzes on Graph Shortest Path</span></a></li><li value="3"><a href="https://www.geeksforgeeks.org/algorithms-gq/top-mcqs-on-minimum-spanning-tree-mst-in-graphs-with-answers/?ref=graph_lp" rel="noopener"><span>Quizzes on Graph Minimum Spanning Tree</span></a></li><li value="4"><a href="https://www.geeksforgeeks.org/data-structure-gq/top-mcqs-on-graph-data-strcuture-with-answers/?ref=graph_lp" rel="noopener"><span>Quizzes on Graphs</span></a></li></ul><p style="text-align: left;" dir="ltr"><b><strong>Quick Links :</strong></b></p><ul><li value="1"><a href="https://www.geeksforgeeks.org/top-10-interview-question-depth-first-search-dfs/" rel="noopener"><span>Top 10 Interview Questions on Depth First Search (DFS)</span></a></li><li value="2"><a href="https://www.geeksforgeeks.org/interesting-shortest-path-questions-set-1/" rel="bookmark noopener"><span>Some interesting shortest path questions</span></a></li><li value="3"><a href="https://www.geeksforgeeks.org/explore?page=1&category=Graph&sortBy=difficulty&itm_source=geeksforgeeks&itm_medium=main_header&itm_campaign=practice_header" target="_blank" rel="noopener"><span>Practice Problems on Graphs</span></a></li><li value="4"><a href="https://www.youtube.com/playlist?list=PLqM7alHXFySEaZgcg7uRYJFBnYMLti-nh" rel="noopener noreferrer"><span>Videos on Graphs</span></a></li></ul><p style="text-align: left;" dir="ltr"><b><strong>Recommended:</strong></b></p><ul><li value="1"><a href="https://www.geeksforgeeks.org/learn-data-structures-and-algorithms-dsa-tutorial?utm_source=Website&utm_medium=Landing+Page+Click&utm_campaign=DSA+Page+Tracker&utm_id=DSA-Page-Tracker&utm_term=DSA+Page+Promo&utm_content=Course+Page" target="_blank" rel="noopener"><b><strong>Learn Data Structure and Algorithms | DSA Tutorial</strong></b></a></li></ul> <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 "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></div> <div class="article-pgnavi_next"> <a href="https://www.geeksforgeeks.org/introduction-to-graphs-data-structure-and-algorithm-tutorials/?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/introduction-to-graphs-data-structure-and-algorithm-tutorials/?ref=next_article">Introduction to Graph Data Structure</a> </div> </div> </div> <div class="article-meta-author-details hidden-div"> <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/harendrakumar123/contributions/?itm_source=geeksforgeeks&itm_medium=article_author&itm_campaign=auth_user" style="text-decoration: none;"><div class="image-wrap" style="position: relative"><p class="profileCard-profile-picture" style="background-color:#E8F6EF; margin:0px;">H</p> <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/harendrakumar123/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;">harendrakumar123</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="harendrakumar123"> <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="1134345" 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> </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="currentpage similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/graph-data-structure-and-algorithms/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Graph Algorithms </div> <div class="gfg-similar-read-item-subheading">Graph algorithms are methods used to manipulate and analyze graphs, solving various range of problems like finding the shortest path, cycles detection. If you are looking for difficulty-wise list of problems, please refer to Graph Data Structure. Basics of Graph:Introduction to GraphsGraph and its r</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></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/introduction-to-graphs-data-structure-and-algorithm-tutorials/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Introduction to Graph Data Structure </div> <div class="gfg-similar-read-item-subheading">Graph Data Structure is a non-linear data structure consisting of vertices and edges. It is useful in fields such as social network analysis, recommendation systems, and computer networks. In the field of sports data science, graph data structure can be used to analyze and understand the dynamics 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;">15+ min read</span> </div> </a></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/graph-and-its-representations/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Graph and its representations </div> <div class="gfg-similar-read-item-subheading">A Graph is a non-linear data structure consisting of vertices and edges. The vertices are sometimes also referred to as nodes and the edges are lines or arcs that connect any two nodes in the graph. More formally a Graph is composed of a set of vertices( V ) and a set of edges( E ). The graph is den</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;">12 min read</span> </div> </a></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/graph-types-and-applications/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Types of Graphs with Examples </div> <div class="gfg-similar-read-item-subheading">A Graph is a non-linear data structure consisting of nodes and edges. The nodes are sometimes also referred to as vertices and the edges are lines or arcs that connect any two nodes in the graph. More formally a Graph can be defined as, A Graph consisting of a finite set of vertices(or nodes) and a</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="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/basic-properties-of-a-graph/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Basic Properties of a Graph </div> <div class="gfg-similar-read-item-subheading">A Graph is a non-linear data structure consisting of nodes and edges. The nodes are sometimes also referred to as vertices and the edges are lines or arcs that connect any two nodes in the graph. The basic properties of a graph include: Vertices (nodes): The points where edges meet in a graph are kn</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></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/applications-advantages-and-disadvantages-of-graph/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Applications, Advantages and Disadvantages of Graph </div> <div class="gfg-similar-read-item-subheading">Graph is a non-linear data structure that contains nodes (vertices) and edges. A graph is a collection of set of vertices and edges (formed by connecting two vertices). A graph is defined as G = {V, E} where V is the set of vertices and E is the set of edges. Graphs can be used to model a wide varie</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></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/transpose-graph/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Transpose graph </div> <div class="gfg-similar-read-item-subheading">Transpose of a directed graph G is another directed graph on the same set of vertices with all of the edges reversed compared to the orientation of the corresponding edges in G. That is, if G contains an edge (u, v) then the converse/transpose/reverse of G contains an edge (v, u) and vice versa. Giv</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></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/difference-between-graph-and-tree/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Difference Between Graph and Tree </div> <div class="gfg-similar-read-item-subheading">Graphs and trees are two fundamental data structures used in computer science to represent relationships between objects. While they share some similarities, they also have distinct differences that make them suitable for different applications. What is Graph?A graph data structure is a collection 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;">2 min read</span> </div> </a></li><div class="leftbar-dropdown"><h2 class="dropdown-title">BFS and DFS on Graph<span class="gfg-icon gfg-icon_arrow-down-thin"></span></h2><ul style="display: none;"><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/breadth-first-search-or-bfs-for-a-graph/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Breadth First Search or BFS for a Graph </div> <div class="gfg-similar-read-item-subheading">Breadth First Search (BFS) is a fundamental graph traversal algorithm. It begins with a node, then first traverses all its adjacent. Once all adjacent are visited, then their adjacent are traversed. This is different from DFS in a way that closest vertices are visited before others. We mainly traver</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;"></hr></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/depth-first-search-or-dfs-for-a-graph/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Depth First Search or DFS for a Graph </div> <div class="gfg-similar-read-item-subheading">Depth First Search (or DFS) for a graph is similar to Depth First Traversal of a tree. Like trees, we traverse all adjacent vertices one by one. When we traverse an adjacent vertex, we completely finish the traversal of all vertices reachable through that adjacent vertex. After we finish traversing</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;"></hr></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/applications-of-depth-first-search/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Applications, Advantages and Disadvantages of Depth First Search (DFS) </div> <div class="gfg-similar-read-item-subheading">Depth First Search is a widely used algorithm for traversing a graph. Here we have discussed some applications, advantages, and disadvantages of the algorithm. Applications of Depth First Search:1. Detecting cycle in a graph: A graph has a cycle if and only if we see a back edge during DFS. So we ca</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;"></hr></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/applications-of-breadth-first-traversal/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Applications, Advantages and Disadvantages of Breadth First Search (BFS) </div> <div class="gfg-similar-read-item-subheading">We have earlier discussed Breadth First Traversal Algorithm for Graphs. Here in this article, we will see the applications, advantages, and disadvantages of the Breadth First Search. Applications of Breadth First Search: 1. Shortest Path and Minimum Spanning Tree for unweighted graph: In an unweight</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;"></hr></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/iterative-depth-first-traversal/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Iterative Depth First Traversal of Graph </div> <div class="gfg-similar-read-item-subheading">Depth First Traversal (or Search) for a graph is similar to Depth First Traversal (DFS) of a tree. The only catch here is, unlike trees, graphs may contain cycles, so a node might be visited twice. To avoid processing a node more than once, use a boolean visited array. Example: Input: n = 4, e = 6 0</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;"></hr></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/bfs-disconnected-graph/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">BFS for Disconnected Graph </div> <div class="gfg-similar-read-item-subheading">In the previous post, BFS only with a particular vertex is performed i.e. it is assumed that all vertices are reachable from the starting vertex. But in the case of a disconnected graph or any vertex that is unreachable from all vertex, the previous implementation will not give the desired output, s</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;">14 min read</span> </div> </a><hr style="background:var(--gfg-selected-color); width:70%; margin: 0 auto;"></hr></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/transitive-closure-of-a-graph-using-dfs/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Transitive Closure of a Graph using DFS </div> <div class="gfg-similar-read-item-subheading">Given a directed graph, find out if a vertex v is reachable from another vertex u for all vertex pairs (u, v) in the given graph. Here reachable means that there is a path from vertex u to v. The reach-ability matrix is called transitive closure of a graph. For example, consider below graph: Transit</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;"></hr></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/difference-between-bfs-and-dfs/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Difference between BFS and DFS </div> <div class="gfg-similar-read-item-subheading">Breadth-First Search (BFS) and Depth-First Search (DFS) are two fundamental algorithms used for traversing or searching graphs and trees. This article covers the basic difference between Breadth-First Search and Depth-First Search. ParametersBFSDFSStands forBFS stands for Breadth First Search.DFS st</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;"></hr></li></ul></div><div class="leftbar-dropdown"><h2 class="dropdown-title">Cycle in a Graph<span class="gfg-icon gfg-icon_arrow-down-thin"></span></h2><ul style="display: none;"><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/detect-cycle-in-a-graph/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Detect Cycle in a Directed Graph </div> <div class="gfg-similar-read-item-subheading">Given the root of a Directed graph , The task is to check whether the graph contains a cycle or not. Examples: Input: V = 4, E = 6 Output: Yes Explanation: The diagram clearly shows a cycle 0 -> 2 -> 0 Input: V = 4, E = 4 Output: No Explanation: The diagram clearly shows no cycle. Detect Cycle</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;">14 min read</span> </div> </a><hr style="background:var(--gfg-selected-color); width:70%; margin: 0 auto;"></hr></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/detect-cycle-undirected-graph/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Detect cycle in an undirected graph </div> <div class="gfg-similar-read-item-subheading">Given an undirected graph, The task is to check if there is a cycle in the given graph. Examples: Input: V = 4, E = 4 Output: Yes Explanation: The diagram clearly shows a cycle 0 to 2 to 1 to 0 Input: V = 4, E = 3 Output: No Explanation: There is no cycle in the given graph. Find cycle in Undirected</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;"></hr></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/detect-cycle-direct-graph-using-colors/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Detect Cycle in a directed graph using colors </div> <div class="gfg-similar-read-item-subheading">Given a directed graph, check whether the graph contains a cycle or not. Your function should return true if the given graph contains at least one cycle, else return false. Example: Input: n = 4, e = 6 0 -> 1, 0 -> 2, 1 -> 2, 2 -> 0, 2 -> 3, 3 -> 3 Output: Yes Explanation: This dia</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;">11 min read</span> </div> </a><hr style="background:var(--gfg-selected-color); width:70%; margin: 0 auto;"></hr></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/detect-negative-cycle-graph-bellman-ford/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Detect a negative cycle in a Graph | (Bellman Ford) </div> <div class="gfg-similar-read-item-subheading">Given a directed weighted graph, the task is to find whether the given graph contains any negative-weight cycle or not. Note: A negative-weight cycle is a cycle in a graph whose edges sum to a negative value. Example: Input: Output: No Input: Output: Yes Algorithm to Find Negative Cycle in a Directe</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;"></hr></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/cycles-of-length-n-in-an-undirected-and-connected-graph/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Cycles of length n in an undirected and connected graph </div> <div class="gfg-similar-read-item-subheading">Given an undirected and connected graph and a number n, count the total number of simple cycles of length n in the graph. A simple cycle of length n is defined as a cycle that contains exactly n vertices and n edges. Note that for an undirected graph, each cycle should only be counted once, regardle</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;"></hr></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/detecting-negative-cycle-using-floyd-warshall/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Detecting negative cycle using Floyd Warshall </div> <div class="gfg-similar-read-item-subheading">We are given a directed graph. We need compute whether the graph has negative cycle or not. A negative cycle is one in which the overall sum of the cycle comes negative. Negative weights are found in various applications of graphs. For example, instead of paying cost for a path, we may get some adva</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;">12 min read</span> </div> </a><hr style="background:var(--gfg-selected-color); width:70%; margin: 0 auto;"></hr></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/clone-directed-acyclic-graph/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Clone a Directed Acyclic Graph </div> <div class="gfg-similar-read-item-subheading">A directed acyclic graph (DAG) is a graph which doesn't contain a cycle and has directed edges. We are given a DAG, we need to clone it, i.e., create another graph that has copy of its vertices and edges connecting them. Examples: Input : 0 - - - > 1 - - - -> 4 | / \ ^ | / \ | | / \ | | / \ |</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;">12 min read</span> </div> </a><hr style="background:var(--gfg-selected-color); width:70%; margin: 0 auto;"></hr></li></ul></div><div class="leftbar-dropdown"><h2 class="dropdown-title">Shortest Paths in Graph<span class="gfg-icon gfg-icon_arrow-down-thin"></span></h2><ul style="display: none;"><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/dijkstras-shortest-path-algorithm-greedy-algo-7/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">How to find Shortest Paths from Source to all Vertices using Dijkstra's Algorithm </div> <div class="gfg-similar-read-item-subheading">Given a weighted graph and a source vertex in the graph, find the shortest paths from the source to all the other vertices in the given graph. Note: The given graph does not contain any negative edge. Examples: Input: src = 0, the graph is shown below. Output: 0 4 12 19 21 11 9 8 14 Explanation: The</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;"></hr></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/bellman-ford-algorithm-dp-23/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Bellman–Ford Algorithm </div> <div class="gfg-similar-read-item-subheading">Given a weighted graph with V vertices and E edges, and a source vertex src, find the shortest path from the source vertex to all vertices in the given graph. If a vertex cannot be reached from source vertex, mark its distance as 108. Note: If a graph contains negative weight cycle, return -1. Examp</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;"></hr></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/floyd-warshall-algorithm-dp-16/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Floyd Warshall Algorithm </div> <div class="gfg-similar-read-item-subheading">The Floyd-Warshall algorithm, named after its creators Robert Floyd and Stephen Warshall, is a fundamental algorithm in computer science and graph theory. It is used to find the shortest paths between all pairs of nodes in a weighted graph. This algorithm is highly efficient and can handle graphs wi</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;"></hr></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/johnsons-algorithm/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Johnson's algorithm for All-pairs shortest paths </div> <div class="gfg-similar-read-item-subheading">The problem is to find the shortest paths between every pair of vertices in a given weighted directed Graph and weights may be negative. We have discussed Floyd Warshall Algorithm for this problem. The time complexity of the Floyd Warshall Algorithm is Θ(V3). Using Johnson's algorithm, we can find</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;"></hr></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/shortest-path-for-directed-acyclic-graphs/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Shortest Path in Directed Acyclic Graph </div> <div class="gfg-similar-read-item-subheading">Given a Weighted Directed Acyclic Graph and a source vertex in the graph, find the shortest paths from given source to all other vertices. Recommended PracticeShortest path from 1 to nTry It! For a general weighted graph, we can calculate single source shortest distances in O(VE) time using Bellman–</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;"></hr></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/multistage-graph-shortest-path/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Multistage Graph (Shortest Path) </div> <div class="gfg-similar-read-item-subheading">A Multistage graph is a directed, weighted graph in which the nodes can be divided into a set of stages such that all edges are from a stage to next stage only (In other words there is no edge between vertices of same stage and from a vertex of current stage to previous stage). The vertices of a mul</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;"></hr></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/shortest-path-unweighted-graph/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Shortest path in an unweighted graph </div> <div class="gfg-similar-read-item-subheading">Given an unweighted, undirected graph of V nodes and E edges, a source node S, and a destination node D, we need to find the shortest path from node S to node D in the graph. Input: V = 8, E = 10, S = 0, D = 7, edges[][] = {{0, 1}, {1, 2}, {0, 3}, {3, 4}, {4, 7}, {3, 7}, {6, 7}, {4, 5}, {4, 6}, {5,</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;">11 min read</span> </div> </a><hr style="background:var(--gfg-selected-color); width:70%; margin: 0 auto;"></hr></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/karps-minimum-mean-average-weight-cycle-algorithm/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Karp's minimum mean (or average) weight cycle algorithm </div> <div class="gfg-similar-read-item-subheading">Given a directed and strongly connected graph with non-negative edge weights. We define the mean weight of a cycle as the summation of all the edge weights of the cycle divided by the no. of edges. Our task is to find the minimum mean weight among all the directed cycles of the graph. Example: Input</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;">11 min read</span> </div> </a><hr style="background:var(--gfg-selected-color); width:70%; margin: 0 auto;"></hr></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/0-1-bfs-shortest-path-binary-graph/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">0-1 BFS (Shortest Path in a Binary Weight Graph) </div> <div class="gfg-similar-read-item-subheading">Given a graph where every edge has weight as either 0 or 1. A source vertex is also given in the graph. Find the shortest path from the source vertex to every other vertex. For Example: Input : Source Vertex = 0 and below graph Having vertices like(u,v,w): Edges: [[0,1,0], [0, 7, 1], [1,2,1], [1,</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;"></hr></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/find-minimum-weight-cycle-undirected-graph/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Find minimum weight cycle in an undirected graph </div> <div class="gfg-similar-read-item-subheading">Given a positive weighted undirected graph, find the minimum weight cycle in it. Examples: Minimum weighted cycle is : Minimum weighed cycle : 7 + 1 + 6 = 14 or 2 + 6 + 2 + 4 = 14 The idea is to use shortest path algorithm. We one by one remove every edge from the graph, then we find the shortest pa</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;"></hr></li></ul></div><div class="leftbar-dropdown"><h2 class="dropdown-title">Minimum Spanning Tree in Graph<span class="gfg-icon gfg-icon_arrow-down-thin"></span></h2><ul style="display: none;"><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/kruskals-minimum-spanning-tree-algorithm-greedy-algo-2/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Kruskal’s Minimum Spanning Tree (MST) Algorithm </div> <div class="gfg-similar-read-item-subheading">A minimum spanning tree (MST) or minimum weight spanning tree for a weighted, connected, undirected graph is a spanning tree with a weight less than or equal to the weight of every other spanning tree. To learn more about Minimum Spanning Tree, refer to this article. Introduction to Kruskal's Algori</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;"></hr></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/difference-between-prims-and-kruskals-algorithm-for-mst/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Difference between Prim's and Kruskal's algorithm for MST </div> <div class="gfg-similar-read-item-subheading">Minimum Spanning Tree (MST) is a fundamental concept in graph theory and has various applications in network design, clustering, and optimization problems. Two of the most commonly used algorithms to find the MST of a graph are Prim's and Kruskal's algorithms. Although both algorithms achieve the sa</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;"></hr></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/applications-of-minimum-spanning-tree/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Applications of Minimum Spanning Tree </div> <div class="gfg-similar-read-item-subheading">A Minimum Spanning Tree (MST) is a subset of the edges of a connected, undirected graph that connects all the vertices together, without any cycles and with the minimum possible total edge weight. It is a way to connect all the vertices in a graph in a way that minimizes the total weight of the edge</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;"></hr></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/total-number-spanning-trees-graph/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Total number of Spanning Trees in a Graph </div> <div class="gfg-similar-read-item-subheading">If a graph is a complete graph with n vertices, then total number of spanning trees is n(n-2) where n is the number of nodes in the graph. In complete graph, the task is equal to counting different labeled trees with n nodes for which have Cayley's formula. What if graph is not complete? Follow the</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;"></hr></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/minimum-product-spanning-tree/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Minimum Product Spanning Tree </div> <div class="gfg-similar-read-item-subheading">Given a connected and undirected graph, a spanning tree of that graph is a subgraph that is a tree and connects all the vertices together. A single graph can have many different spanning trees. A minimum product spanning tree for a weighted, connected, and undirected graph is a spanning tree with a</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;"></hr></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/reverse-delete-algorithm-minimum-spanning-tree/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Reverse Delete Algorithm for Minimum Spanning Tree </div> <div class="gfg-similar-read-item-subheading">Reverse Delete algorithm is closely related to Kruskal's algorithm. In Kruskal's algorithm what we do is : Sort edges by increasing order of their weights. After sorting, we one by one pick edges in increasing order. We include current picked edge if by including this in spanning tree not form any c</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;">14 min read</span> </div> </a><hr style="background:var(--gfg-selected-color); width:70%; margin: 0 auto;"></hr></li></ul></div><div class="leftbar-dropdown"><h2 class="dropdown-title">Topological Sorting in Graph<span class="gfg-icon gfg-icon_arrow-down-thin"></span></h2><ul style="display: none;"><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/topological-sorting/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Topological Sorting </div> <div class="gfg-similar-read-item-subheading">Topological sorting for Directed Acyclic Graph (DAG) is a linear ordering of vertices such that for every directed edge u-v, vertex u comes before v in the ordering. Note: Topological Sorting for a graph is not possible if the graph is not a DAG. Example: Input: Graph : Output: 5 4 2 3 1 0Explanatio</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;">11 min read</span> </div> </a><hr style="background:var(--gfg-selected-color); width:70%; margin: 0 auto;"></hr></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/all-topological-sorts-of-a-directed-acyclic-graph/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">All Topological Sorts of a Directed Acyclic Graph </div> <div class="gfg-similar-read-item-subheading">Topological sorting for Directed Acyclic Graph (DAG) is a linear ordering of vertices such that for every directed edge uv, vertex u comes before v in the ordering. Topological Sorting for a graph is not possible if the graph is not a DAG. Given a DAG, print all topological sorts of the graph. For e</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;">11 min read</span> </div> </a><hr style="background:var(--gfg-selected-color); width:70%; margin: 0 auto;"></hr></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/topological-sorting-indegree-based-solution/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Kahn's algorithm for Topological Sorting </div> <div class="gfg-similar-read-item-subheading">Given a Directed Acyclic Graph having V vertices and E edges, your task is to find any Topological Sorted order of the graph. Topological Sorted order: It is a linear ordering of vertices such that for every directed edge u -> v, where vertex u comes before v in the ordering. Example: Input: V=6</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;"></hr></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/maximum-edges-can-added-dag-remains-dag/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Maximum edges that can be added to DAG so that it remains DAG </div> <div class="gfg-similar-read-item-subheading">A DAG is given to us, we need to find maximum number of edges that can be added to this DAG, after which new graph still remain a DAG that means the reformed graph should have maximal number of edges, adding even single edge will create a cycle in graph. The Output for above example should be follow</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;">14 min read</span> </div> </a><hr style="background:var(--gfg-selected-color); width:70%; margin: 0 auto;"></hr></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/find-longest-path-directed-acyclic-graph/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Longest Path in a Directed Acyclic Graph </div> <div class="gfg-similar-read-item-subheading">Given a Weighted Directed Acyclic Graph (DAG) and a source vertex s in it, find the longest distances from s to all other vertices in the given graph. The longest path problem for a general graph is not as easy as the shortest path problem because the longest path problem doesn’t have optimal substr</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;"></hr></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/topological-sorting-using-departure-time-of-vertex/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Topological Sort of a graph using departure time of vertex </div> <div class="gfg-similar-read-item-subheading">Given a Directed Acyclic Graph (DAG), find Topological Sort of the graph. Topological sorting for Directed Acyclic Graph (DAG) is a linear ordering of vertices such that for every directed edge uv, vertex u comes before v in the ordering. Topological Sorting for a graph is not possible if the graph</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;"></hr></li></ul></div><div class="leftbar-dropdown"><h2 class="dropdown-title">Connectivity of Graph<span class="gfg-icon gfg-icon_arrow-down-thin"></span></h2><ul style="display: none;"><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/articulation-points-or-cut-vertices-in-a-graph/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Articulation Points (or Cut Vertices) in a Graph </div> <div class="gfg-similar-read-item-subheading">A vertex v is an articulation point (also called cut vertex) if removing v increases the number of connected components. Articulation points represent vulnerabilities in a connected network – single points whose failure would split the network into 2 or more components. They are useful for designing</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;"></hr></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/biconnected-components/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Biconnected Components </div> <div class="gfg-similar-read-item-subheading">A biconnected component is a maximal biconnected subgraph. Biconnected Graph is already discussed here. In this article, we will see how to find biconnected component in a graph using algorithm by John Hopcroft and Robert Tarjan. In above graph, following are the biconnected components: 4--2 3--4 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><hr style="background:var(--gfg-selected-color); width:70%; margin: 0 auto;"></hr></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/bridge-in-a-graph/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Bridges in a graph </div> <div class="gfg-similar-read-item-subheading">Given an undirected Graph, The task is to find the Bridges in this Graph. An edge in an undirected connected graph is a bridge if removing it disconnects the graph. For a disconnected undirected graph, the definition is similar, a bridge is an edge removal that increases the number of disconnected</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;"></hr></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/eulerian-path-and-circuit/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Eulerian path and circuit for undirected graph </div> <div class="gfg-similar-read-item-subheading">Eulerian Path is a path in a graph that visits every edge exactly once. Eulerian Circuit is an Eulerian Path that starts and ends on the same vertex. How to Find Whether a Given Graph is Eulerian or not? The problem is same as following question. "Is it possible to draw a given graph without l</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;"></hr></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/fleurys-algorithm-for-printing-eulerian-path/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Fleury's Algorithm for printing Eulerian Path or Circuit </div> <div class="gfg-similar-read-item-subheading">Eulerian Path is a path in a graph that visits every edge exactly once. Eulerian Circuit is an Eulerian Path that starts and ends on the same vertex. We strongly recommend first reading the following post on Euler Path and Circuit. "https://www.cdn.geeksforgeeks.org/eulerian-path-and-circuit/" In th</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;"></hr></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/strongly-connected-components/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Strongly Connected Components </div> <div class="gfg-similar-read-item-subheading">Strongly Connected Components (SCCs) are a fundamental concept in graph theory and algorithms. In a directed graph, a Strongly Connected Component is a subset of vertices where every vertex in the subset is reachable from every other vertex in the same subset by traversing the directed edges. Findin</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;"></hr></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/count-possible-paths-source-destination-exactly-k-edges/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Count all possible walks from a source to a destination with exactly k edges </div> <div class="gfg-similar-read-item-subheading">Given a directed graph and two vertices 'u' and 'v' in it, count all possible walks from 'u' to 'v' with exactly k edges on the walk. The graph is given adjacency matrix representation where the value of graph[i][j] as 1 indicates that there is an edge from vertex i to vertex j and a value 0 indicat</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;"></hr></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/euler-circuit-directed-graph/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Euler Circuit in a Directed Graph </div> <div class="gfg-similar-read-item-subheading">Eulerian Path is a path in graph that visits every edge exactly once. Eulerian Circuit is an Eulerian Path which starts and ends on the same vertex. A graph is said to be eulerian if it has a eulerian cycle. We have discussed eulerian circuit for an undirected graph. In this post, the same is discus</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;"></hr></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/word-ladder-length-of-shortest-chain-to-reach-a-target-word/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Word Ladder (Length of shortest chain to reach a target word) </div> <div class="gfg-similar-read-item-subheading">Given a dictionary, and two words 'start' and 'target' (both of same length). Find length of the smallest chain from 'start' to 'target' if it exists, such that adjacent words in the chain only differ by one character and each word in the chain is a valid word i.e., it exists in the dictionary. It m</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;"></hr></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/given-array-strings-find-strings-can-chained-form-circle/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Find if an array of strings can be chained to form a circle | Set 1 </div> <div class="gfg-similar-read-item-subheading">Given an array of strings, find if the given strings can be chained to form a circle. A string X can be put before another string Y in circle if the last character of X is same as first character of Y.Examples: Input: arr[] = {"geek", "king"} Output: Yes, the given strings can be chained. Note that</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;"></hr></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/tarjan-algorithm-find-strongly-connected-components/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Tarjan's Algorithm to find Strongly Connected Components </div> <div class="gfg-similar-read-item-subheading">A directed graph is strongly connected if there is a path between all pairs of vertices. A strongly connected component (SCC) of a directed graph is a maximal strongly connected subgraph. For example, there are 3 SCCs in the following graph: We have discussed Kosaraju's algorithm for strongly connec</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;"></hr></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/paths-travel-nodes-using-edgeseven-bridges-konigsberg/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Paths to travel each nodes using each edge (Seven Bridges of Königsberg) </div> <div class="gfg-similar-read-item-subheading">There are n nodes and m bridges in between these nodes. Print the possible path through each node using each edges (if possible), traveling through each edges only once. Examples : Input : [[0, 1, 0, 0, 1], [1, 0, 1, 1, 0], [0, 1, 0, 1, 0], [0, 1, 1, 0, 0], [1, 0, 0, 0, 0]] Output : 5 -> 1 -></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;"></hr></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/dynamic-connectivity-set-1-incremental/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Dynamic Connectivity | Set 1 (Incremental) </div> <div class="gfg-similar-read-item-subheading">Dynamic connectivity is a data structure that dynamically maintains the information about the connected components of graph. In simple words suppose there is a graph G(V, E) in which no. of vertices V is constant but no. of edges E is variable. There are three ways in which we can change the number</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;">11 min read</span> </div> </a><hr style="background:var(--gfg-selected-color); width:70%; margin: 0 auto;"></hr></li></ul></div><div class="leftbar-dropdown"><h2 class="dropdown-title">Maximum flow in a Graph<span class="gfg-icon gfg-icon_arrow-down-thin"></span></h2><ul style="display: none;"><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/max-flow-problem-introduction/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Max Flow Problem Introduction </div> <div class="gfg-similar-read-item-subheading">The max flow problem is a classic optimization problem in graph theory that involves finding the maximum amount of flow that can be sent through a network of pipes, channels, or other pathways, subject to capacity constraints. The problem can be used to model a wide variety of real-world situations,</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;">12 min read</span> </div> </a><hr style="background:var(--gfg-selected-color); width:70%; margin: 0 auto;"></hr></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/ford-fulkerson-algorithm-for-maximum-flow-problem/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Ford-Fulkerson Algorithm for Maximum Flow Problem </div> <div class="gfg-similar-read-item-subheading">The Ford-Fulkerson algorithm is a widely used algorithm to solve the maximum flow problem in a flow network. The maximum flow problem involves determining the maximum amount of flow that can be sent from a source vertex to a sink vertex in a directed weighted graph, subject to capacity constraints 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;">15+ min read</span> </div> </a><hr style="background:var(--gfg-selected-color); width:70%; margin: 0 auto;"></hr></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/find-edge-disjoint-paths-two-vertices/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Find maximum number of edge disjoint paths between two vertices </div> <div class="gfg-similar-read-item-subheading">Given a directed graph and two vertices in it, source 's' and destination 't', find out the maximum number of edge disjoint paths from s to t. Two paths are said edge disjoint if they don't share any edge. There can be maximum two edge disjoint paths from source 0 to destination 7 in the above graph</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;"></hr></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/minimum-cut-in-a-directed-graph/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Find minimum s-t cut in a flow network </div> <div class="gfg-similar-read-item-subheading">In a flow network, an s-t cut is a cut that requires the source 's' and the sink 't' to be in different subsets, and it consists of edges going from the source's side to the sink's side. The capacity of an s-t cut is defined by the sum of the capacity of each edge in the cut-set. (Source: Wiki) The</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;"></hr></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/maximum-bipartite-matching/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Maximum Bipartite Matching </div> <div class="gfg-similar-read-item-subheading">A matching in a Bipartite Graph is a set of the edges chosen in such a way that no two edges share an endpoint. A maximum matching is a matching of maximum size (maximum number of edges). In a maximum matching, if any edge is added to it, it is no longer a matching. There can be more than one maximu</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;"></hr></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/channel-assignment-problem/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Channel Assignment Problem </div> <div class="gfg-similar-read-item-subheading">There are M transmitter and N receiver stations. Given a matrix that keeps track of the number of packets to be transmitted from a given transmitter to a receiver. If the (i; j)-th entry of the matrix is k, it means at that time the station i has k packets for transmission to station j. During a tim</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;">14 min read</span> </div> </a><hr style="background:var(--gfg-selected-color); width:70%; margin: 0 auto;"></hr></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/introduction-to-push-relabel-algorithm/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Introduction to Push Relabel Algorithm </div> <div class="gfg-similar-read-item-subheading">Given a graph which represents a flow network where every edge has a capacity. Also given two vertices source ‘s’ and sink ‘t’ in the graph, find the maximum possible flow from s to t with following constraints: Flow on an edge doesn’t exceed the given capacity of the edge. Incoming flow is equal to</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;"></hr></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/introduction-and-implementation-of-kargers-algorithm-for-minimum-cut/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Introduction and implementation of Karger's algorithm for Minimum Cut </div> <div class="gfg-similar-read-item-subheading">Given an undirected and unweighted graph, find the smallest cut (smallest number of edges that disconnects the graph into two components). The input graph may have parallel edges. For example consider the following example, the smallest cut has 2 edges. A Simple Solution use Max-Flow based s-t cut a</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;"></hr></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/dinics-algorithm-maximum-flow/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Dinic's algorithm for Maximum Flow </div> <div class="gfg-similar-read-item-subheading">Problem Statement : Given a graph that represents a flow network where every edge has a capacity. Also given two vertices source ‘s’ and sink ‘t’ in the graph, find the maximum possible flow from s to t with the following constraints : Flow on an edge doesn’t exceed the given capacity of the edge.An</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;"></hr></li></ul></div><div class="leftbar-dropdown"><h2 class="dropdown-title">Some must do problems on Graph<span class="gfg-icon gfg-icon_arrow-down-thin"></span></h2><ul style="display: none;"><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/find-length-largest-region-boolean-matrix/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Max Area of Island - Largest in Boolean Matrix </div> <div class="gfg-similar-read-item-subheading">Given a binary 2D matrix, find area of the largest region of 1s which are connected horizontally, vertically or diagonally. Examples: Input: M[][]= {{1, 0, 0, 0, 1, 0, 0}, {0, 1, 0, 0, 1, 1, 0}, {1, 1, 0, 0, 0, 0, 0}, {1, 0, 0, 1, 1, 0, 0}, {1, 0, 0, 1, 0, 1, 1}} Output: 6Explanation: The region in</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;"></hr></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/count-number-trees-forest/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Count number of trees in a forest </div> <div class="gfg-similar-read-item-subheading">Given n nodes of a forest (collection of trees), find the number of trees in the forest. Examples : Input : edges[] = {0, 1}, {0, 2}, {3, 4} Output : 2 Explanation : There are 2 trees 0 3 / \ \ 1 2 4 Approach : Apply DFS on every node. Increment count by one if every connected node is visited from 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;">15 min read</span> </div> </a><hr style="background:var(--gfg-selected-color); width:70%; margin: 0 auto;"></hr></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/peterson-graph/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">A Peterson Graph Problem </div> <div class="gfg-similar-read-item-subheading">The following graph G is called a Petersen graph and its vertices have been numbered from 0 to 9. Some letters have also been assigned to vertices of G, as can be seen from the following picture: Let's consider a walk W in graph G, which consists of L vertices W1, W2, ..., WL. A string S of L letter</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;"></hr></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/clone-an-undirected-graph/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Clone an Undirected Graph </div> <div class="gfg-similar-read-item-subheading">Cloning of a LinkedList and a Binary Tree with random pointers has already been discussed. The idea behind cloning a graph is pretty much similar. Recommended ProblemClone an Undirected GraphSolve Problem The idea is to do a BFS traversal of the graph and while visiting a node make a clone node of i</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;"></hr></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/graph-coloring-applications/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Introduction to Graph Coloring </div> <div class="gfg-similar-read-item-subheading">Graph coloring refers to the problem of coloring vertices of a graph in such a way that no two adjacent vertices have the same color. This is also called the vertex coloring problem. If coloring is done using at most m colors, it is called m-coloring. Chromatic Number:The minimum number of colors ne</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;">11 min read</span> </div> </a><hr style="background:var(--gfg-selected-color); width:70%; margin: 0 auto;"></hr></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/traveling-salesman-problem-tsp-implementation/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Traveling Salesman Problem (TSP) Implementation </div> <div class="gfg-similar-read-item-subheading">Given a 2d matrix cost[][] of size n where cost[i][j] denotes the cost of moving from city i to city j. The task is to complete a tour from city 0 (0-based index) to all other cities such that we visit each city exactly once and then at the end come back to city 0 at minimum cost. Note the differenc</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;"></hr></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/introduction-and-approximate-solution-for-vertex-cover-problem/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Introduction and Approximate Solution for Vertex Cover Problem </div> <div class="gfg-similar-read-item-subheading">A vertex cover of an undirected graph is a subset of its vertices such that for every edge (u, v) of the graph, either 'u' or 'v' is in the vertex cover. Although the name is Vertex Cover, the set covers all edges of the given graph. Given an undirected graph, the vertex cover problem is to find min</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;"></hr></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/erdos-renyl-model-generating-random-graphs/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Erdos Renyl Model (for generating Random Graphs) </div> <div class="gfg-similar-read-item-subheading">In graph theory, the Erdos–Rényi model is either of two closely related models for generating random graphs. There are two closely related variants of the Erdos–Rényi (ER) random graph model. In the G(n, M) model, a graph is chosen uniformly at random from the collection of all graphs which have n n</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;">5 min read</span> </div> </a><hr style="background:var(--gfg-selected-color); width:70%; margin: 0 auto;"></hr></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/chinese-postman-route-inspection-set-1-introduction/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Chinese Postman or Route Inspection | Set 1 (introduction) </div> <div class="gfg-similar-read-item-subheading">Chinese Postman Problem is a variation of Eulerian circuit problem for undirected graphs. An Euler Circuit is a closed walk that covers every edge once starting and ending position is same. Chinese Postman problem is defined for connected and undirected graph. The problem is to find shortest path or</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;"></hr></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/hierholzers-algorithm-directed-graph/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Hierholzer's Algorithm for directed graph </div> <div class="gfg-similar-read-item-subheading">Given a directed Eulerian graph, print an Euler circuit. Euler circuit is a path that traverses every edge of a graph, and the path ends on the starting vertex. Examples: Input : Adjacency list for the below graph Output : 0 -> 1 -> 2 -> 0 Input : Adjacency list for the below graph Output :</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;"></hr></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/boggle-find-possible-words-board-characters/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Boggle (Find all possible words in a board of characters) | Set 1 </div> <div class="gfg-similar-read-item-subheading">Given a dictionary, a method to do lookup in dictionary and a M x N board where every cell has one character. Find all possible words that can be formed by a sequence of adjacent characters. Note that we can move to any of 8 adjacent characters, but a word should not have multiple instances of same</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;"></hr></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/hopcroft-karp-algorithm-for-maximum-matching-set-1-introduction/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Hopcroft–Karp Algorithm for Maximum Matching | Set 1 (Introduction) </div> <div class="gfg-similar-read-item-subheading">A matching in a Bipartite Graph is a set of the edges chosen in such a way that no two edges share an endpoint. A maximum matching is a matching of maximum size (maximum number of edges). In a maximum matching, if any edge is added to it, it is no longer a matching. There can be more than one maximu</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;"></hr></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/construct-graph-given-degrees-vertices/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Construct a graph from given degrees of all vertices </div> <div class="gfg-similar-read-item-subheading">This is a C++ program to generate a graph for a given fixed degree sequence. This algorithm generates a undirected graph for the given degree sequence.It does not include self-edge and multiple edges. Examples: Input : degrees[] = {2, 2, 1, 1} Output : (0) (1) (2) (3) (0) 0 1 1 0 (1) 1 0 0 1 (2) 1 0</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;"></hr></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/determine-whether-universal-sink-exists-directed-graph/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Determine whether a universal sink exists in a directed graph </div> <div class="gfg-similar-read-item-subheading">Determine whether a universal sink exists in a directed graph. A universal sink is a vertex which has no edge emanating from it, and all other vertices have an edge towards the sink. Input : v1 -> v2 (implies vertex 1 is connected to vertex 2) v3 -> v2 v4 -> v2 v5 -> v2 v6 -> v2 Outpu</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;"></hr></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/number-sink-nodes-graph/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Number of sink nodes in a graph </div> <div class="gfg-similar-read-item-subheading">Given a Directed Acyclic Graph of n nodes (numbered from 1 to n) and m edges. The task is to find the number of sink nodes. A sink node is a node such that no edge emerges out of it. Examples: Input : n = 4, m = 2 Edges[] = {{2, 3}, {4, 3}} Output : 2 Only node 1 and node 3 are sink nodes. Input : n</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;">5 min read</span> </div> </a><hr style="background:var(--gfg-selected-color); width:70%; margin: 0 auto;"></hr></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/two-clique-problem-check-graph-can-divided-two-cliques/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Two Clique Problem (Check if Graph can be divided in two Cliques) </div> <div class="gfg-similar-read-item-subheading">A Clique is a subgraph of graph such that all vertices in subgraph are completely connected with each other. Given a Graph, find if it can be divided into two Cliques. Examples: Input : G[][] = {{0, 1, 1, 0, 0}, {1, 0, 1, 1, 0}, {1, 1, 0, 0, 0}, {0, 1, 0, 0, 1}, {0, 0, 0, 1, 0}}; Output : Yes This 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;">13 min read</span> </div> </a><hr style="background:var(--gfg-selected-color); width:70%; margin: 0 auto;"></hr></li></ul></div></div></ul> </div> </div> <div class="bottom-wrap" style="padding: 0px 20px;margin-bottom: 10px;"> <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/data-structures/graph/?ref=article_category">Graph</a> </li> <li style="border-radius: 25px;" class=""> <a href="https://www.geeksforgeeks.org/category/dsa/?ref=article_category">DSA</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=Graph&ref=article_practice_tag">Graph</a></li> </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>  <style>.right-bar-explore-more{ visibility: hidden; min-height: 230px;text-align:left;min-width:300px;max-width:300px; padding-left: 19px; padding-right: 25px; margin-top: 20px;} .right-bar-explore-more .title{text-align:left;font-size:20px; font-weight: 600; line-height: 22px; color:var(--em-heading);padding:14px 0;font-family:var(--font-primary)} .right-bar-explore-more .rightbar-sticky-ul {list-style: disc outside; padding-left: 17px;} .right-bar-explore-more li{font-size: 14px !important;font-weight: 400;line-height: 18px !important;color: var(--em-text);margin: 14px 0;font-family:var(--font-primary);} .right-bar-explore-more li::marker{color: var(--em-text) !important;} .right-bar-explore-more .rightbar-sticky-ul a{text-align:left !important; color: var(--em-text); display: block !important;} .right-bar-explore-more .rightbar-sticky-ul a:hover{text-decoration:underline;color:var(--em-link)!important;} .right-bar-explore-more hr {margin: 0;background-color: var(--tn-hr);} @media (max-width: 991px){ .right-bar-explore-more{ width: 85%; margin: auto; margin-top: 20px; max-width: unset; display: none !important; } #text-18 .textwidget{ width: 100%; } }</style> <script> var rightBarExploreMoreList = `<li style="color:var(--color-black)"><a href="https://www.geeksforgeeks.org/quick-sort-algorithm/?ref=rightbar_explore" target="_blank" style="font-family:var(--font-primary)">Quick Sort</a></li><li style="color:var(--color-black)"><a href="https://www.geeksforgeeks.org/merge-sort/?ref=rightbar_explore" target="_blank" style="font-family:var(--font-primary)">Merge Sort - Data Structure and Algorithms Tutorials</a></li><li style="color:var(--color-black)"><a href="https://www.geeksforgeeks.org/dsa-tutorial-learn-data-structures-and-algorithms/?ref=rightbar_explore" target="_blank" style="font-family:var(--font-primary)">DSA Tutorial - Learn Data Structures and Algorithms</a></li><li style="color:var(--color-black)"><a href="https://www.geeksforgeeks.org/breadth-first-search-or-bfs-for-a-graph/?ref=rightbar_explore" target="_blank" style="font-family:var(--font-primary)">Breadth First Search or BFS for a Graph</a></li><li style="color:var(--color-black)"><a href="https://www.geeksforgeeks.org/bubble-sort-algorithm/?ref=rightbar_explore" target="_blank" style="font-family:var(--font-primary)">Bubble Sort Algorithm</a></li>` </script>  <aside id="text-18" class="widget widget_text"> <div class="textwidget"> <div class="right-bar-explore-more" style="display:none;visibility: unset;"> <div class="title">Explore More</div> <ul class="rightbar-sticky-ul"></ul> </div> <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="footer-address"> Corporate & Communications Address:- A-143, 7th Floor, Sovereign Corporate Tower, Sector- 136, Noida, Uttar Pradesh (201305) | Registered Address:- K 061, Tower K, Gulshan Vivante Apartment, Sector 137, Noida, Gautam Buddh Nagar, Uttar Pradesh, 201305 </div> </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> <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/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"}]}}`); 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>(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><script type="text/javascript"> $(window).on('load', function() { (function(c,l,a,r,i,t,y){ c[a]=c[a]||function(){(c[a].q=c[a].q||[]).push(arguments)}; t=l.createElement(r);t.async=1;t.src="https://www.clarity.ms/tag/"+i; y=l.getElementsByTagName(r)[0];y.parentNode.insertBefore(t,y); })(window, document, "clarity", "script", "ayc7ypwwuk"); }); </script>  </body> </html>

CINXE.COM

Graph Algorithms - GeeksforGeeks