Introduction to Data Structures

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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"> <h2><u><b><strong class="GFGEditorTheme__textUnderline">What is Data Structure?</strong></b></u></h2> <blockquote> <p dir="ltr"><span>A </span><a href="https://www.geeksforgeeks.org/data-structures/" rel="noopener"><span>data structure</span></a><span> is a particular way of organising data in a computer so that it can be used effectively. The idea is to reduce the space and time complexities of different tasks.聽</span></p> </blockquote> <p dir="ltr"><span>The choice of a good data structure makes it possible to perform a variety of critical operations effectively. An efficient data structure also uses minimum memory space and execution time to process the structure. A data structure is not only used for organising the data. It is also used for processing, retrieving, and storing data. There are different basic and advanced types of data structures that are used in almost every program or software system that has been developed. So we must have good knowledge of data structures. </span></p><div id="GFG_AD_gfg_mobile_336x280" style="margin: 5px 0;"></div> <h2><u><span class="GFGEditorTheme__textUnderline">Need Of Data Structure:</span></u></h2> <p dir="ltr"><span>The structure of the data and the synthesis of the algorithm are relative to each other. Data presentation must be easy to understand so the developer, as well as the user, can make an efficient implementation of the operation.</span><br /><span>Data structures provide an easy way of organising, retrieving, managing, and storing data.</span></p> <p dir="ltr"><span>Here is a list of the needs for data.</span></p> <ul> <li value="1"><span>Data structure modification is easy.聽</span></li> <li value="2"><span>It requires less time.聽</span></li> <li value="3"><span>Save storage memory space.聽</span></li> <li value="4"><a href="https://www.geeksforgeeks.org/what-are-the-different-ways-of-data-representation/" rel="noopener" target="_self"><span>Data representation</span></a><span> is easy.聽</span></li> <li value="5"><span>Easy access to the large database</span></li> </ul> <h2><a href="https://www.geeksforgeeks.org/what-is-data-structure-types-classifications-and-applications/" rel="noopener"><u><b><strong class="GFGEditorTheme__textUnderline">Classification/Types of Data Structures:</strong></b></u></a></h2> <ol> <li value="1"><span>聽聽 Linear Data Structure</span></li> <li value="2"><span>聽聽 Non-Linear Data Structure.</span></li> </ol> <h3><b><strong>聽 Linear Data Structure:</strong></b></h3> <ul> <li value="1"><span>Elements are arranged in one dimension ,also known as linear dimension.</span></li> <li value="2"><span>Example: lists, stack, queue, etc.</span></li> </ul> <h3><b><strong>聽Non-Linear Data Structure</strong></b></h3> <ul> <li value="1"><span>Elements are arranged in one-many, many-one and many-many dimensions.</span></li> <li value="2"><span>Example: tree, graph, table, etc.</span></li> </ul> <p dir="ltr"><img alt="Classification of Data Structure" height="inherit" src="https://media.geeksforgeeks.org/wp-content/uploads/20220520182504/ClassificationofDataStructure-660x347.jpg" width="inherit"/></p> <div>聽</div> <h2><b><strong>Most Popular Data Structures:聽</strong></b></h2> <h2><b><strong>1. </strong></b><a href="https://www.geeksforgeeks.org/array-data-structure/" rel="noopener"><b><strong>Array</strong></b></a><b><strong>:</strong></b><span> </span></h2> <p dir="ltr"><span>An array is a collection of data items stored at contiguous memory locations. The idea is to store multiple items of the same type together. This makes it easier to calculate the position of each element by simply adding an offset to a base value, i.e., the memory location of the first element of the array (generally denoted by the name of the array).聽</span></p> <div style="width: 810px" class="wp-caption alignnone"><img height="inherit" loading="lazy" src="https://media.geeksforgeeks.org/wp-content/uploads/20230302092653/C-array-initialization.png" width="inherit"/><p class="wp-caption-text">Array Data Structure</p></div> <h2><b><strong>2. </strong></b><a href="https://www.geeksforgeeks.org/data-structures/linked-list/" rel="noopener"><b><strong>Linked Lists</strong></b></a><b><strong>:</strong></b></h2> <p dir="ltr"><span> Like arrays, Linked List is a linear data structure. Unlike arrays, linked list elements are not stored at a contiguous location; the elements are linked using pointers.聽</span></p><div id="GFG_AD_Desktop_InContent_ATF_336x280" style="text-align:center; max-height: 280px;"></div><div id="GFG_AD_gfg_mobile_336x280_1" style="margin: 5px 0;"></div> <div style="width: 810px" class="wp-caption alignnone"><img height="inherit" loading="lazy" src="https://media.geeksforgeeks.org/wp-content/uploads/20220816144425/LLdrawio.png" width="inherit"/><p class="wp-caption-text">Linked Data Structure</p></div> <p dir="ltr"></p><div id="_GFG_ABP_Incontent_728x90" style="text-align:center;"></div> <h2><b><strong>3. </strong></b><a href="https://www.geeksforgeeks.org/stack-data-structure/" rel="noopener"><b><strong>Stack</strong></b></a><b><strong>:</strong></b><span> </span></h2> <p dir="ltr"><span>Stack is a linear data structure which follows a particular order in which the operations are performed. The order may be LIFO(Last In First Out) or FILO(First In Last Out).聽In stack, all insertion and deletion are permitted at only one end of the list.</span></p> <p dir="ltr"><img height="inherit" loading="lazy" src="https://media.geeksforgeeks.org/wp-content/cdn-uploads/20221219100314/stack.drawio2.png" width="inherit"/><b><strong>Stack Operations:</strong></b></p> <ul> <li value="1"><b><strong>push():</strong></b><span> When this operation is performed, an element is inserted into the stack.</span></li> <li value="2"><b><strong>pop(): </strong></b><span>When this operation is performed, an element is removed from the top of the stack and is returned.</span></li> <li value="3"><b><strong>top():</strong></b><span> This operation will return the last inserted element that is at the top without removing it.</span></li> <li value="4"><b><strong>size(): </strong></b><span>This operation will return the size of the stack i.e. the total number of elements present in the stack.</span></li> <li value="5"><b><strong>isEmpty():</strong></b><span> This operation indicates whether the stack is empty or not.</span></li> </ul> <h2><b><strong>4. </strong></b><a href="https://www.geeksforgeeks.org/queue-data-structure/" rel="noopener"><b><strong>Queue</strong></b></a><b><strong>:</strong></b><span> </span></h2> <p dir="ltr"><span>Like Stack, Queue is a linear structure which follows a particular order in which the operations are performed. The order is First In First Out (FIFO). In the queue, items are inserted at one end and deleted from the other end. A good example of the queue is any queue of consumers for a resource where the consumer that came first is served first. The difference between stacks and queues is in removing. In a stack we remove the item the most recently added; in a queue, we remove the item the least recently added.聽</span></p> <div style="width: 810px" class="wp-caption alignnone"><img height="inherit" loading="lazy" src="https://media.geeksforgeeks.org/wp-content/cdn-uploads/20221213113312/Queue-Data-Structures.png" width="inherit"/><p class="wp-caption-text">Queue Data Structure</p></div> <p dir="ltr"><b><strong>Queue Operations:</strong></b></p> <ul> <li value="1"><b><strong>Enqueue():</strong></b><span> Adds (or stores) an element to the end of the queue..</span></li> <li value="2"><b><strong>Dequeue(): </strong></b><span>Removal of elements from the queue.</span></li> <li value="3"><b><strong>Peek() or front(): </strong></b><span>Acquires the data element available at the front node of the queue without deleting it.</span></li> <li value="4"><b><strong>rear(): </strong></b><span>This operation returns the element at the rear end without removing it.</span></li> <li value="5"><b><strong>isFull():</strong></b><span> Validates if the queue is full.</span></li> <li value="6"><b><strong>isNull(): </strong></b><span>Checks if the queue is empty.</span></li> </ul> <h2><b><strong>5. </strong></b><a href="https://www.geeksforgeeks.org/binary-tree-data-structure/" rel="noopener"><b><strong>Binary Tree</strong></b></a><b><strong>:</strong></b><span> </span></h2> <p dir="ltr"><span>Unlike Arrays, Linked Lists, Stack and queues, which are linear data structures, trees are hierarchical data structures. A binary tree is a tree data structure in which each node has at most two children, which are referred to as the left child and the right child. It is implemented mainly using Links.聽</span></p><div style="text-align:center;margin:20px 0; max-height: 280px;" id="GFG_AD_gfg_outstream_incontent"></div> <p><span>A Binary Tree is represented by a pointer to the topmost node in the tree. If the tree is empty, then the value of root is NULL. A Binary Tree node contains the following parts.聽</span></p> <pre><span>1. Data</span><br/><span>2. Pointer to left child</span><br/><span>3. Pointer to the right child</span></pre> <div style="width: 810px" class="wp-caption alignnone"><img height="inherit" loading="lazy" src="https://media.geeksforgeeks.org/wp-content/uploads/20221124174432/binary.png" width="inherit"/><p class="wp-caption-text">Binary Tree Data Structure</p></div> <h2><b><strong>6. </strong></b><a href="https://www.geeksforgeeks.org/binary-search-tree-set-1-search-and-insertion/" rel="noopener"><b><strong>Binary Search Tree</strong></b></a><span>: </span></h2> <p dir="ltr"><span>A Binary Search Tree is a Binary Tree following the additional properties:聽</span></p> <ul> <li value="1"><span>The left part of the root node contains keys less than the root node key.</span></li> <li value="2"><span>The right part of the root node contains keys greater than the root node key.</span></li> <li value="3"><span>There is no duplicate key present in the binary tree.</span></li> </ul> <p dir="ltr"><span>A Binary tree having the following properties is known as Binary search tree (BST).</span></p> <div style="width: 810px" class="wp-caption alignnone"><img height="inherit" loading="lazy" src="https://media.geeksforgeeks.org/wp-content/cdn-uploads/20221215114732/bst-21.png" width="inherit"/><p class="wp-caption-text">Binary Search Tree Data Structure</p></div> <h2><b><strong>7. </strong></b><a href="https://www.geeksforgeeks.org/heap-data-structure/" rel="noopener"><b><strong>Heap</strong></b></a><b><strong>:</strong></b><span> </span></h2> <p dir="ltr"><span>A Heap is a special Tree-based data structure in which the tree is a complete binary tree. Generally, Heaps can be of two types:聽</span></p> <ul> <li value="1"><b><strong>Max-Heap:</strong></b><span> In a Max-Heap the key present at the root node must be greatest among the keys present at all of its children. The same property must be recursively true for all sub-trees in that Binary Tree.</span></li> <li value="2"><b><strong>Min-Heap:</strong></b><span> In a Min-Heap the key present at the root node must be minimum among the keys present at all of its children. The same property must be recursively true for all sub-trees in that Binary Tree.</span></li> </ul> <div style="width: 810px" class="wp-caption alignnone"><img height="inherit" loading="lazy" src="https://media.geeksforgeeks.org/wp-content/cdn-uploads/20221220165711/MinHeapAndMaxHeap1.png" width="inherit"/><p class="wp-caption-text">Max and Min Heap</p></div> <h2><b><strong>8. </strong></b><a href="https://www.geeksforgeeks.org/hashing-data-structure/" rel="noopener"><b><strong>Hashing Data Structure</strong></b></a><span>: </span></h2> <p dir="ltr"><span>Hashing is an important Data Structure which is designed to use a special function called the Hash function which is used to map a given value with a particular key for faster access of elements. The efficiency of mapping depends on the efficiency of the hash function used.聽</span></p> <p dir="ltr"><span>Let a hash function H(x) maps the value x at the index x%10 in an Array. For example, if the list of values is [11, 12, 13, 14, 15] it will be stored at positions {1, 2, 3, 4, 5} in the array or Hash table respectively.聽</span></p> <div style="width: 810px" class="wp-caption alignnone"><img height="inherit" loading="lazy" src="https://media.geeksforgeeks.org/wp-content/uploads/20220701080941/ComponentsofHashing-660x342.png" width="inherit"/><p class="wp-caption-text">Hash Data Structure</p></div> <h2><b><strong>9. </strong></b><a href="https://www.geeksforgeeks.org/matrix/" rel="noopener"><b><strong>Matrix</strong></b></a><b><strong>:</strong></b><span> </span></h2> <p dir="ltr"><span>A matrix represents a collection of numbers arranged in an order of rows and columns. It is necessary to enclose the elements of a matrix in parentheses or brackets.聽</span></p> <p dir="ltr"><span>A matrix with 9 elements is shown below.聽</span></p> <div style="width: 810px" class="wp-caption alignnone"><img height="inherit" loading="lazy" src="https://media.geeksforgeeks.org/wp-content/uploads/20221010013158/2Darray.png" width="inherit"/><p class="wp-caption-text">Matrix</p></div> <h2><b><strong>10. </strong></b><a href="https://www.geeksforgeeks.org/trie-insert-and-search/" rel="noopener"><b><strong>Trie</strong></b></a><b><strong>:</strong></b><span> </span></h2> <p dir="ltr"><span>Trie is an efficient information retrieval data structure. Using Trie, search complexities can be brought to an optimal limit (key length). If we store keys in the binary search tree, a well-balanced BST will need time proportional to M * log N, where M is maximum string length and N is the number of keys in the tree. Using Trie, we can search the key in O(M) time. However, the penalty is on Trie storage requirements.聽</span></p> <div style="width: 810px" class="wp-caption alignnone"><img height="inherit" loading="lazy" src="https://media.geeksforgeeks.org/wp-content/uploads/20220828232752/Triedatastructure1.png" width="inherit"/><p class="wp-caption-text">Trie Data Structure</p></div> <h2><span>11. </span><a href="https://www.geeksforgeeks.org/graph-data-structure-and-algorithms/" rel="noopener" target="_blank"><span>Graph</span></a><span>:</span></h2> <p dir="ltr"><span>Graph is a data structure that consists of a collection of nodes (vertices) connected by edges. Graphs are used to represent relationships between objects and are widely used in computer science, mathematics, and other fields. Graphs can be used to model a wide variety of real-world systems, such as social networks, transportation networks, and computer networks.</span></p> <p dir="ltr"></p> <p dir="ltr"></p> <div style="width: 810px" class="wp-caption alignnone"><img alt="graphp" height="512" loading="lazy" src="https://media.geeksforgeeks.org/wp-content/uploads/20240401130112/graphp.png" srcset="https://media.geeksforgeeks.org/wp-content/uploads/20240401130112/graphp.png 812w,https://media.geeksforgeeks.org/wp-content/uploads/20240401130112/graphp-100.png 100w,https://media.geeksforgeeks.org/wp-content/uploads/20240401130112/graphp-200.png 200w,https://media.geeksforgeeks.org/wp-content/uploads/20240401130112/graphp-300.png 300w,https://media.geeksforgeeks.org/wp-content/uploads/20240401130112/graphp-660.png 660w,https://media.geeksforgeeks.org/wp-content/uploads/20240401130112/graphp-768.png 768w" width="812"/><p class="wp-caption-text">Graph Data Structure</p></div> <p dir="ltr"></p> <p dir="ltr"></p> <h2><u><b><strong class="GFGEditorTheme__textUnderline">Applications of Data Structures:</strong></b></u></h2> <p dir="ltr"><span>Data structures are used in various fields such as:</span></p> <ul> <li value="1"><span>Operating system</span></li> <li value="2"><span>Graphics</span></li> <li value="3"><span>Computer Design</span></li> <li value="4"><span>Blockchain</span></li> <li value="5"><span>Genetics</span></li> <li value="6"><span>Image Processing</span></li> <li value="7"><span>Simulation,</span></li> <li value="8"><span>聽etc.</span></li> </ul> <br/><div id="AP_G4GR_6"></div> <div class='article_bottom_text'></div><br> <div id="video-tab-content" class="video-tab-content"> <div style="text-align: center; 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Queues are commonly used in various algorit</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><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/linked-list-data-structure/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Linked List Data Structure </div> <div class="gfg-similar-read-item-subheading">A linked list is a fundamental data structure in computer science. It mainly allows efficient insertion and deletion operations compared to arrays. Like arrays, it is also used to implement other data structures like stack, queue and deque. Here鈥檚 the comparison of Linked List vs Arrays Linked List:</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/introduction-to-tree-data-structure/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Introduction to Tree Data Structure </div> <div class="gfg-similar-read-item-subheading">Tree data structure is a hierarchical structure that is used to represent and organize data in a way that is easy to navigate and search. It is a collection of nodes that are connected by edges and has a hierarchical relationship between the nodes. The topmost node of the tree is called the root, 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><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/heap-data-structure/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Heap Data Structure </div> <div class="gfg-similar-read-item-subheading">A Heap is a complete binary tree data structure that satisfies the heap property: for every node, the value of its children is greater than or equal to its own value. Heaps are usually used to implement priority queues, where the smallest (or largest) element is always at the root of the tree. Basic</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><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/hashing-data-structure/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Hashing in Data Structure </div> <div class="gfg-similar-read-item-subheading">Hashing is a technique used in data structures that efficiently stores and retrieves data in a way that allows for quick access. Hashing involves mapping data to a specific index in a hash table (an array of items) using a hash function that enables fast retrieval of information based on its key. 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;">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/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><hr style="background:var(--gfg-selected-color); width:70%; margin: 0 auto;"></hr></li><li class="similarReadDropdownItem"><a href="https://www.geeksforgeeks.org/matrix/?ref=lbp"><div class="gfg-similar-read-item-content"> <div class="gfg-similar-read-item-heading">Matrix Data Structure </div> <div class="gfg-similar-read-item-subheading">Matrix Data Structure is a two-dimensional array arranged in rows and columns. It is commonly used to represent mathematical matrices and is fundamental in various fields like mathematics, computer graphics, and data processing. 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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); 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