<!DOCTYPE html>
<html class="h-100" data-bs-theme="light" data-mantine-color-scheme="light" lang="en" prefix="og: https://ogp.me/ns#">
<head>
<meta content="width=device-width, initial-scale=1.0" name="viewport">
<meta content="IE=Edge" http-equiv="X-UA-Compatible">
<link crossorigin="true" href="https://cdn.hexlet.io" rel="preconnect">
<meta content="aa2vrdtq64dub8knuf83lwywit311w" name="facebook-domain-verification">
<link href="/favicon.ico" rel="icon" sizes="any">
<link href="/favicon.svg" rel="icon" type="image/svg+xml">
<link href="/apple-touch-icon.png" rel="apple-touch-icon">
<link href="/manifest.webmanifest" rel="manifest">
<script>
//<![CDATA[
window.gon={};gon.ym_counter="25559621";gon.is_bot=true;gon.applications={};gon.current_user={"id":null,"last_viewed_notification_id":null,"email":null,"state":null,"first_name":"","last_name":"","current_program":null,"current_team":null,"full_name":"","guest":true,"can_use_paid_features":false,"is_hexlet_employee":false,"sanitized_phone_number":"","can_subscribe":true,"can_renew_education":false};gon.token="pykARnaYmNvQy8HA3UfDw_UODapybbSh5CJxQlnwyEP0721wV_OjO7fBPihv2fQC-aSD8b5zrq1Gp7tRFCwXmA";gon.locale="en";gon.language="en";gon.theme="light";gon.rails_env="production";gon.mobile=false;gon.google={"analytics_key":"UA-1360700-51","optimize_key":"GTM-5QDVFPF"};gon.captcha={"google_v3_site_key":"6LenGbgZAAAAAM7HbrDbn5JlizCSzPcS767c9vaY","yandex_site_key":"ysc1_Vyob5ZPPUdPBsu0ykt8bVFdzsfpoVjQChLGl2b4g19647a89","verification_failed":null};gon.social_signin=false;gon.typoreporter_google_form_id="1FAIpQLScNwxM8rjQRRWqW5G6dn6-0NvLUblFemy7EvA9VsJ7Ov5wXqA";
//]]>
</script>
<meta charset="utf-8">
<title>Definitions | JS: Trees</title>
<meta name="description" content="Definitions / JS: Trees: Grasp the tree terminology">
<link rel="canonical" href="https://hexlet.io/courses/js-trees/lessons/definition/theory_unit">
<meta name="robots" content="noarchive">
<meta property="og:title" content="Definitions">
<meta property="og:title" content="JS: Trees">
<meta property="og:description" content="Definitions / JS: Trees: Grasp the tree terminology">
<meta property="og:url" content="https://hexlet.io/courses/js-trees/lessons/definition/theory_unit">
<meta name="csrf-param" content="authenticity_token" />
<meta name="csrf-token" content="adxuxU7QMB-mlL_anb7rA42Ay5i-N5Xb87uV-IvjOAU6GgPzb7sL_8GeQDIvINzCgSpFw3Ipj9dRPl_rxj_n3g" />
<script src="/vite/assets/inertia-CgrHVkgd.js" crossorigin="anonymous" type="module"></script><link rel="modulepreload" href="/vite/assets/chunk-DsPFFUou.js" as="script" crossorigin="anonymous">
<link rel="modulepreload" href="/vite/assets/preload-helper-C1cfMHAs.js" as="script" crossorigin="anonymous">
<link rel="modulepreload" href="/vite/assets/init-0bhwJkNI.js" as="script" crossorigin="anonymous">
<link rel="modulepreload" href="/vite/assets/ahoy-BXKrsWjp.js" as="script" crossorigin="anonymous">
<link rel="modulepreload" href="/vite/assets/analytics-Du9ljYPK.js" as="script" crossorigin="anonymous">
<link rel="modulepreload" href="/vite/assets/ErrorFallbackBlock-V3hfk_CP.js" as="script" crossorigin="anonymous">
<link rel="modulepreload" href="/vite/assets/RootLayout-CUZzAr0T.js" as="script" crossorigin="anonymous">
<link rel="modulepreload" href="/vite/assets/Surface-DbDKujDz.js" as="script" crossorigin="anonymous">
<link rel="modulepreload" href="/vite/assets/gon-B-jV56Ol.js" as="script" crossorigin="anonymous">
<link rel="modulepreload" href="/vite/assets/mantine-DOJkeu70.js" as="script" crossorigin="anonymous">
<link rel="modulepreload" href="/vite/assets/utils-ClTF9s_T.js" as="script" crossorigin="anonymous">
<link rel="modulepreload" href="/vite/assets/routes-mvvEXZQ8.js" as="script" crossorigin="anonymous">
<link rel="modulepreload" href="/vite/assets/index.esm-DATLpQdV.js" as="script" crossorigin="anonymous">
<link rel="modulepreload" href="/vite/assets/Modal-BhY0AP_c.js" as="script" crossorigin="anonymous">
<link rel="modulepreload" href="/vite/assets/Textarea-P1s4q94S.js" as="script" crossorigin="anonymous">
<link rel="modulepreload" href="/vite/assets/exports-BsSGGK2I.js" as="script" crossorigin="anonymous">
<link rel="modulepreload" href="/vite/assets/dayjs.min-Bfba02I7.js" as="script" crossorigin="anonymous">
<link rel="modulepreload" href="/vite/assets/client-CYyKzrjQ.js" as="script" crossorigin="anonymous">
<link rel="modulepreload" href="/vite/assets/react-dom-SJZekO2j.js" as="script" crossorigin="anonymous">
<link rel="modulepreload" href="/vite/assets/useTranslation-bo78L81P.js" as="script" crossorigin="anonymous">
<link rel="modulepreload" href="/vite/assets/compiler-runtime-BhqaZ6vG.js" as="script" crossorigin="anonymous">
<link rel="modulepreload" href="/vite/assets/jsx-runtime-DlXMvSuQ.js" as="script" crossorigin="anonymous">
<link rel="modulepreload" href="/vite/assets/react-CFtMU8gd.js" as="script" crossorigin="anonymous">
<link rel="stylesheet" href="/vite/assets/application-BhDYOUva.css" />
<script src="/vite/assets/application-ZyVHkzwO.js" crossorigin="anonymous" type="module"></script><link rel="modulepreload" href="/vite/assets/chunk-DsPFFUou.js" as="script" crossorigin="anonymous">
<link rel="modulepreload" href="/vite/assets/autocomplete-BokUl44d.js" as="script" crossorigin="anonymous">
<link rel="modulepreload" href="/vite/assets/routes-mvvEXZQ8.js" as="script" crossorigin="anonymous">
<link rel="modulepreload" href="/vite/assets/createPopper-gQnwoPhY.js" as="script" crossorigin="anonymous">
<link rel="modulepreload" href="/vite/assets/js.cookie-CB1F2-VC.js" as="script" crossorigin="anonymous"><link rel="stylesheet" href="/vite/assets/application-BhDYOUva.css" media="screen" />
<!-- Google Tag Manager - deferred -->
<script>
// dataLayer stub сразу — пуши работают до загрузки скрипта
window.dataLayer = window.dataLayer || [];
// Сам скрипт — отложенно после load
window.addEventListener('load', function() {
setTimeout(function() {
dataLayer.push({'gtm.start': new Date().getTime(), event: 'gtm.js'});
var j = document.createElement('script');
j.async = true;
j.src = 'https://www.googletagmanager.com/gtm.js?id=GTM-WK88TH';
document.head.appendChild(j);
}, 1500);
});
</script>
<!-- End Google Tag Manager -->
</head>
<body>
<!-- Google Tag Manager (noscript) -->
<noscript>
<iframe height="0" src="https://www.googletagmanager.com/ns.html?id=GTM-WK88TH" style="display:none;visibility:hidden" width="0"></iframe>
</noscript>
<!-- End Google Tag Manager (noscript) -->
<header class="sticky-top bg-body">
<nav class="navbar navbar-expand-lg">
<div class="container-xxl">
<a class="navbar-brand" href="/"><img alt="Hexlet logo" height="24" src="https://hexlet.io/vite/assets/logo_en_light-FS-yL6XB.svg" width="96">
</a><button aria-controls="collapsable" aria-expanded="false" aria-label="Menu" class="navbar-toggler border-0 mb-0 mt-1" data-bs-target="#collapsable" data-bs-toggle="collapse">
<span class="navbar-toggler-icon"></span>
</button>
<div class="collapse navbar-collapse" id="collapsable">
<ul class="navbar-nav mb-lg-0 mt-lg-1">
<li class="nav-item dropdown">
<button aria-haspopup class="btn nav-link" data-bs-toggle="dropdown" type="button">
All courses
<span class="bi bi-chevron-down align-middle ms-1"></span>
</button>
<ul class="dropdown-menu">
<li>
<a class="dropdown-item d-flex py-2" href="/courses"><div class="fw-bold me-auto">Everything</div>
<div class="text-muted">8</div>
</a></li>
<li>
<hr class="dropdown-divider">
</li>
<li class="dropdown-item">
<b>Popular categories</b>
</li>
<li>
<a class="dropdown-item py-2" href="/courses_backend-development">Backend Development
</a></li>
<li>
<a class="dropdown-item py-2" href="/courses_devops">DevOps
</a></li>
<li>
<a class="dropdown-item py-2" href="/courses_frontend-development">Frontend Development
</a></li>
<li>
<a class="dropdown-item py-2" href="/courses_testing">Testing
</a></li>
<li>
<hr class="dropdown-divider">
</li>
<li class="dropdown-item">
<b>Popular courses</b>
</li>
<li>
<a class="dropdown-item py-2" href="/programs/frontend">Frontend Developer
</a></li>
</ul>
</li>
<li class="nav-item dropdown">
<button aria-haspopup class="btn nav-link" data-bs-toggle="dropdown" type="button">
About Hexlet
<span class="bi bi-chevron-down align-middle"></span>
</button>
<ul class="dropdown-menu bg-body">
<li>
<a class="dropdown-item py-2" href="/pages/about">About company
</a></li>
<li>
<a class="dropdown-item py-2" href="/blog">Blog
</a></li>
<li>
<span class="dropdown-item py-2 external-link" data-href="https://special.hexlet.io/hse-research" role="button"><span class="translation_missing" title="translation missing: en.layouts.header.results">Results</span>
</span></li>
<li>
<span class="dropdown-item py-2 external-link" data-href="https://career.hexlet.io" role="button"><span class="translation_missing" title="translation missing: en.layouts.header.career">Career</span>
</span></li>
<li>
<a class="dropdown-item py-2" href="/testimonials">Testimonials
</a></li>
<li>
<span class="dropdown-item py-2 external-link" data-href="https://t.me/hexlet_help_bot" role="button"><span class="translation_missing" title="translation missing: en.layouts.header.support">Support</span>
</span></li>
<li>
<span class="dropdown-item py-2 external-link" data-href="https://special.hexlet.io/referal-program/?promo_creative=priglasite-druzei&promo_name=referal-program&promo_position=promo_position&promo_start=010724&promo_type=link" role="button"><span class="translation_missing" title="translation missing: en.layouts.header.referal_program">Referal Program</span>
</span></li>
<li>
<span class="dropdown-item py-2 external-link" data-href="https://special.hexlet.io/certificate" role="button"><span class="translation_missing" title="translation missing: en.layouts.header.certificates">Certificates</span>
</span></li>
<li>
<span class="dropdown-item py-2 external-link" data-href="https://hh.ru/employer/4307094" role="button"><span class="translation_missing" title="translation missing: en.layouts.header.vacancies">Vacancies</span>
</span></li>
<li>
<span class="dropdown-item d-flex external-link" rel="noopener noreferrer nofollow" data-href="https://b2b.hexlet.io" data-target="_blank" role="button"><span class="translation_missing" title="translation missing: en.layouts.header.teams">Teams</span>
</span></li>
<li>
<span class="dropdown-item d-flex external-link" rel="noopener noreferrer nofollow" data-href="https://hexly.ru/" data-target="_blank" role="button"><span class="translation_missing" title="translation missing: en.layouts.header.college">College</span>
</span></li>
<li>
<span class="dropdown-item d-flex external-link" rel="noopener noreferrer nofollow" data-href="https://hexlyschool.ru/" data-target="_blank" role="button"><span class="translation_missing" title="translation missing: en.layouts.header.private_school">Private School</span>
</span></li>
</ul>
</li>
</ul>
<ul class="navbar-nav flex-lg-row align-items-lg-center gap-2 ms-auto">
<li>
<a class="nav-link" aria-label="Switch theme" href="/theme/switch?new_theme=dark"><span aria-hidden="true" class="bi bi-moon"></span>
</a></li>
<li>
<span data-target="_self" class="nav-link external-link" data-href="/u/new" role="button"><span>Sign up</span>
</span></li>
<li>
<span data-target="_self" class="nav-link external-link" data-href="https://hexlet.io/session/new" role="button"><span>Sign in</span>
</span></li>
</ul>
</div>
</div>
</nav>
</header>
<div class="x-container-xxxl">
</div>
<main class="mb-6 min-vh-100 h-100">
<link rel="preload" as="image" href="https://hexlet.io/rails/active_storage/representations/proxy/eyJfcmFpbHMiOnsiZGF0YSI6MTIzNTMsInB1ciI6ImJsb2JfaWQifX0=--f1948fb0c5a45a6d76671a1a32b8cf6f0b53ee57/eyJfcmFpbHMiOnsiZGF0YSI6eyJmb3JtYXQiOiJ3ZWJwIiwicmVzaXplX3RvX2xpbWl0IjpbNDAwLDQwMF0sInNhdmVyIjp7InF1YWxpdHkiOjg1fX0sInB1ciI6InZhcmlhdGlvbiJ9fQ==--5b6f46dacd1af664f27558553a58076185091823/Software%20code%20testing-cuate.png"/><link rel="preload" as="image" href="/vite/assets/development-BVihs_d5.png"/><div id="app" data-page="{"component":"web/courses/lessons/theory_unit","props":{"errors":{},"locale":"en","language":"en","httpsHost":"https://hexlet.io","host":"hexlet.io","colorScheme":"light","auth":{"user":{"id":null,"last_viewed_notification_id":null,"email":null,"state":null,"first_name":"","last_name":"","current_program":null,"current_team":null,"full_name":"","guest":true,"can_use_paid_features":false,"is_hexlet_employee":false,"sanitized_phone_number":"","can_subscribe":true,"can_renew_education":false}},"cloudflareTurnstileSiteKey":"0x4AAAAAAA15KmeFXzd2H0Xo","vkIdClientId":"51586979","yandexIdClientId":null,"formAuthToken":"103lKMeDA6Wa8M3fPE4ijVmmETpZ3NNKJbXRJ02xMoSEi4ge5ug4Rf36MjeO0BVMVQyfYZXCyUaHMBs0AG3tXw","topics":[],"lesson":{"exercise":{"id":2084,"slug":"js_trees_definition_exercise","name":null,"state":"active","kind":"exercise","language":"javascript","locale":"en","has_web_view":false,"has_test_view":false,"reviewable":true,"readme":"In this task, a tree is defined as an array of elements, which, in turn, can also be trees (arrays). Example:\n\n```javascript\n[\n 3, // leaf\n [5, 3], // node\n [[2]] // node\n]\n```\n\nCheck tests for more examples.\n\n## removeFirstLevel.js\n\nImplement and export as default a function that takes a tree, and returns a new one, whose elements are the children of nested nodes (see example).\n\n### Examples\n\n```javascript\nimport removeFirstLevel from '../removeFirstLevel.js';\n\n// Second level here is 5, 3, 4\nconst tree1 = [[5], 1, [3, 4]];\nremoveFirstLevel(tree1); // [5, 3, 4]\n\nconst tree2 = [1, 2, [3, 5], [[4, 3], 2]];\nremoveFirstLevel(tree2);\n// [3, 5, [4, 3], 2]\n```\n\n### Tips\n\n* [Array.prototype.flat()](https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Array/flat) returns a new array where all elements of nested subarrays were recursively \"elevated\" to the upper level\n* [Array.isArray()](https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Array/isArray) checks if a value is an array\n\n","prepared_readme":"In this task, a tree is defined as an array of elements, which, in turn, can also be trees (arrays). Example:\n\n```javascript\n[\n 3, // leaf\n [5, 3], // node\n [[2]] // node\n]\n```\n\nCheck tests for more examples.\n\n## removeFirstLevel.js\n\nImplement and export as default a function that takes a tree, and returns a new one, whose elements are the children of nested nodes (see example).\n\n### Examples\n\n```javascript\nimport removeFirstLevel from '../removeFirstLevel.js';\n\n// Second level here is 5, 3, 4\nconst tree1 = [[5], 1, [3, 4]];\nremoveFirstLevel(tree1); // [5, 3, 4]\n\nconst tree2 = [1, 2, [3, 5], [[4, 3], 2]];\nremoveFirstLevel(tree2);\n// [3, 5, [4, 3], 2]\n```\n\n### Tips\n\n* [Array.prototype.flat()](https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Array/flat) returns a new array where all elements of nested subarrays were recursively \"elevated\" to the upper level\n* [Array.isArray()](https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Array/isArray) checks if a value is an array\n\n","has_solution":true,"entity_name":"Definitions"},"units":[{"id":6919,"name":"theory","url":"/courses/js-trees/lessons/definition/theory_unit"},{"id":6920,"name":"quiz","url":"/courses/js-trees/lessons/definition/quiz_unit"},{"id":6937,"name":"exercise","url":"/courses/js-trees/lessons/definition/exercise_unit"}],"links":[{"id":424599,"name":"Fractal","url":"https://en.wikipedia.org/wiki/Fractal"},{"id":424600,"name":"Abstract syntax JavaScript tree","url":"https://esprima.org/demo/parse.html"}],"ordered_units":[{"id":6919,"name":"theory","url":"/courses/js-trees/lessons/definition/theory_unit"},{"id":6920,"name":"quiz","url":"/courses/js-trees/lessons/definition/quiz_unit"},{"id":6937,"name":"exercise","url":"/courses/js-trees/lessons/definition/exercise_unit"}],"id":3046,"slug":"definition","state":"approved","name":"Definitions","course_order":200,"goal":"Grasp the tree terminology","self_study":null,"theory_video_provider":null,"theory_video_uid":null,"theory":"File structures are an example of a tree that everyone who uses a computer is familiar with. It consists of directories and different kinds of files.\n\n```bash\nnodejs-package # root directory\n├── Makefile # file\n├── README.md # file\n├── __tests__ # directory\n│ └── half.test.js # file\n├── babel.config.js # file\n└── node_modules # directory\n └── @babel # directory\n └── cli # directory\n └── LICENSE # file\n```\n\nIt's called a tree because of its structure. All elements in the file system are arranged in a hierarchy. In it, the top level is the root directory (or disk, if we're talking about Windows), and then there are files and directories, which themselves may contain more files and directories.\n\nA vital feature of the tree structure is that it is **recursive**. In other words, the tree consists of subtrees, which in turn comprised of subtrees, which in turn consist of... This feature is the defining factor of the main ways that developers work with trees, all of which are recursive in one way or another.\n\nTrees consist of **nodes** и **edges** between them. Edges don't actually exist, they only help to visualize the connection and, if necessary, describe it. Nodes are divided into two types: **internal** nodes (those that have child nodes) and **leaf** nodes (that don't). In the case of a file system, leaf nodes are represented by files and internal nodes by directories.\n\n\n\nEach node in the tree has **a parent** (or ancestor). The only exception is the root node – it has no parents, and that's where the tree begins. In general, any number of descendants of any internal node can exist. In addition, working with trees means that you need to understand the concept of depth. Depth determines how many steps through the nodes from the root you need to reach the current one (the one we are looking at). Nodes that are at the same depth and have a common parent are sibling nodes.\n\n## Implementation\n\nThe number of tree implementations is endless. The most basic one is nested arrays:\n\n```javascript\n[['index.html', 'main.js'], 'index.js', ['favicon.ico', 'app.css']];\n// * the root is the array itself\n// / | \\\n// * index.js *\n// / | | \\\n// index.html main.js favicon.ico app.css\n\n// A couple more examples of trees with arbitrary data:\n[]; // empty tree\n[3, 2, [3, 8], [[8], 3]];\n[1, null, [[3]], [5, 'string', [undefined, [3], { key: 'value' }]]];\n```\n\nIn the examples above, the root is the array itself, and all its elements are children. If the child is not an array, it is treated like a leaf node; otherwise, it's treated like an internal node. The inner node, in turn, consists of children.\n\nAny tree consists of two large parts:\n\n1. Data that is stored inside the tree\n1. The tree structure, which is responsible for the relationships between the data\n\n```javascript\n[['index.html', 'main.js'], 'index.js', ['favicon.ico', 'app.css']];\n```\n\nWhat is the structure, and what is the data in this tree? The data here are leaf nodes, and the internal arrays are the structure. They determine where the data (in this case, files) are located but do not contain any data themselves. Organizing a tree in this way is not conducive to a file structure. This tree doesn't even allow you to set a name for the directory.\n\nLet's expand the structure to be able to add more data. Let's represent each element in the tree as an array, where the first element is the value stored in the node, and the second element is an array of the node's children. If the second element is missing, then we are dealing with a leaf.\n\n```javascript\n['app', [ // Root\n ['dist', [ // Internal node\n ['index.html'], // Leaf\n ['main.js'] // Leaf\n ]],\n ['index.js'], // Leaf\n ['assets', [ // Internal node\n ['favicon.ico'], // Leaf\n ['app.css'], // Leaf\n ]],\n]];\n\n// app\n// / | \\\n// dist index.js assets\n// / | | \\\n// index.html main.js favicon.ico app.css\n```\n\nThis variant is more verbose, but allows you to store data in any node, even non-leaf. And it doesn't have to be a string, like in the example above. Changing data on objects will allow you to add anything there.\n\nAnd the most flexible and convenient way to represent trees is through objects: each node is an object, and arrays store only the children list.\n\n```javascript\n// Note the separation of structure and data\n// Here it's much more obvious\n{\n value: 5,\n children: [\n { value: 10 },\n { value: 100 },\n { value: 'nested', children: [/* ... */] }\n ]\n}\n```\n\nBy and large, both the array and the object themselves can always represent trees. This is true for any recursive data structure, that is, a structure whose elements can be the structure itself. Any array can contain an array, just as any object can contain an object.\n"},"lessonMember":null,"courseMember":null,"course":{"start_lesson":{"exercise":null,"units":[{"id":6918,"name":"theory","url":"/courses/js-trees/lessons/intro/theory_unit"}],"links":[],"ordered_units":[{"id":6918,"name":"theory","url":"/courses/js-trees/lessons/intro/theory_unit"}],"id":3045,"slug":"intro","state":"approved","name":"Introduction","course_order":100,"goal":"Meet the course and its goals","self_study":null,"theory_video_provider":null,"theory_video_uid":null,"theory":"A tree is one of the most common computer science data structures and a natural way to model certain domains. All people encounter trees (as a data structure) in one way or another, even those who aren't programming or interacting with computers in general. The most obvious example is the family tree, and a file tree when considering computers. HTML (like JSON, XML, and many others) also has a tree structure. Comments and product catalogs on websites are also trees. Any hierarchy is a tree by definition.\n\n\n\nThere is one very intriguing aspect associated with trees. A developer's ability to understand trees and work with them is directly proportional to their overall level. If it is easy for a developer to work with trees, then most likely have a pretty good understanding of coding, including when reading someone else's code. If, on the other hand, they don't know enough about trees, then they'll likely have more difficulty writing and analyzing code.\n\nThere are no new syntax or programming elements in this course that you haven't seen before in Hexlet courses. However, trees are more complicated topic above all because of the recursive nature of the trees themselves. You have to make your brain work properly, and this is probably the hardest part, you can't just read the theory and develop the understanding linearly. The only way is to practice and go through a trial-and-error process.\n\nTo better understand and memorize the learning material, our recommendations are the same as before:\n\n1. Be sure to practice all the code given in the theory yourself, on your local environment\n1. Use the debug print as much as you can. Log all data changes while the code is running\n1. Repeat the lessons from the JS: Functions course on recursion\n\nIn this short course, we'll get to grips with how trees work and how to use them. You won't see algorithms in this course as they're taught at university. This course has very different goals. We'll teach you how to work with recursive data structures through tree recursion.\n"},"id":300,"slug":"js-trees","challenges_count":8,"name":"JS: Trees","allow_indexing":true,"state":"approved","course_state":"finished","pricing_type":"paid","description":"In the realm of computers, a lot of things are structured like trees. Product categories, the file system, source code, comments, HTML, XML, JSON, and other elements are a few examples. These structures all share the property of being recursive. To put it another way, any internal component has the potential to fully transform into an exterior component. Any part of JSON is JSON itself. This fact has a significant impact on organizational methods and working principles with such structures. They extensively employ tree-like recursion, which calls for careful planning.","kind":"basic","updated_at":"2026-01-20T11:47:37.790Z","language":"javascript","duration_cache":38520,"skills":["Understand the principles of the tree structure and construction","Represent in code and process recursive data, for example, a file system, directories or comment trees","Build abstractions on top of tree-like data structures","Use a functional paradigm"],"keywords":[],"lessons_count":9,"cover":"https://hexlet.io/rails/active_storage/representations/proxy/eyJfcmFpbHMiOnsiZGF0YSI6NzkyMywicHVyIjoiYmxvYl9pZCJ9fQ==--3c21fe914cbc9538d98e79c24f6a66dfecee8a6c/eyJfcmFpbHMiOnsiZGF0YSI6eyJmb3JtYXQiOiJqcGciLCJyZXNpemVfdG9fZmlsbCI6WzYwMCw0MDBdfSwicHVyIjoidmFyaWF0aW9uIn19--39ba06fa99226096df9fc6bb31f84e1d29ea98e9/image.png"},"recommendedLandings":[{"stack":{"id":15,"slug":"frontend","title":"Frontend Developer","audience":"for_beginners","start_type":"anytime","pricing_model":"purchase","priority":"low","kind":"profession","state":"published","stack_state":"finished","order":1,"duration_in_months":10},"id":22,"slug":"frontend","title":"Frontend Developer","subtitle":"","subtitle_for_lists":"","locale":"en","current":true,"duration_in_months_text":"10 months","stack_slug":"frontend","price_text":"from $49","duration_text":"10 months","cover_list_variant":"https://hexlet.io/rails/active_storage/representations/proxy/eyJfcmFpbHMiOnsiZGF0YSI6MTIzNTMsInB1ciI6ImJsb2JfaWQifX0=--f1948fb0c5a45a6d76671a1a32b8cf6f0b53ee57/eyJfcmFpbHMiOnsiZGF0YSI6eyJmb3JtYXQiOiJ3ZWJwIiwicmVzaXplX3RvX2xpbWl0IjpbNDAwLDQwMF0sInNhdmVyIjp7InF1YWxpdHkiOjg1fX0sInB1ciI6InZhcmlhdGlvbiJ9fQ==--5b6f46dacd1af664f27558553a58076185091823/Software%20code%20testing-cuate.png"}],"lessonMemberUnit":null,"accessToLearnUnitExists":false,"accessToCourseExists":false},"url":"/courses/js-trees/lessons/definition/theory_unit","version":"1656487db0d1dd5f33634fe1070e57e55135cbeb","encryptHistory":false,"clearHistory":false}"><style data-mantine-styles="true">:root, :host{--mantine-font-family: Arial, sans-serif;--mantine-font-family-headings: Arial, sans-serif;--mantine-heading-font-weight: normal;--mantine-radius-default: 0rem;--mantine-primary-color-filled: var(--mantine-color-indigo-filled);--mantine-primary-color-filled-hover: var(--mantine-color-indigo-filled-hover);--mantine-primary-color-light: var(--mantine-color-indigo-light);--mantine-primary-color-light-hover: var(--mantine-color-indigo-light-hover);--mantine-primary-color-light-color: var(--mantine-color-indigo-light-color);--mantine-spacing-xxl: calc(4rem * var(--mantine-scale));--mantine-font-size-xs: 12px;--mantine-font-size-sm: 14px;--mantine-font-size-md: 16px;--mantine-font-size-lg: clamp(16.0000px, calc(15.2727px + 0.2273vw), 18.0000px);--mantine-font-size-xl: clamp(16.0000px, calc(14.5455px + 0.4545vw), 20.0000px);--mantine-font-size-display-3: clamp(32.0000px, calc(26.1818px + 1.8182vw), 48.0000px);--mantine-font-size-display-2: clamp(36.0000px, calc(25.8182px + 3.1818vw), 64.0000px);--mantine-font-size-display-1: clamp(40.0000px, calc(25.4545px + 4.5455vw), 80.0000px);--mantine-font-size-h1: clamp(28.0000px, calc(23.6364px + 1.3636vw), 40.0000px);--mantine-font-size-h2: clamp(24.0000px, calc(21.0909px + 0.9091vw), 32.0000px);--mantine-font-size-h3: clamp(20.0000px, calc(17.0909px + 0.9091vw), 28.0000px);--mantine-font-size-h4: clamp(16.0000px, calc(13.0909px + 0.9091vw), 24.0000px);--mantine-font-size-h5: clamp(16.0000px, calc(14.5455px + 0.4545vw), 20.0000px);--mantine-font-size-h6: 1rem;--mantine-primary-color-0: var(--mantine-color-indigo-0);--mantine-primary-color-1: var(--mantine-color-indigo-1);--mantine-primary-color-2: var(--mantine-color-indigo-2);--mantine-primary-color-3: var(--mantine-color-indigo-3);--mantine-primary-color-4: var(--mantine-color-indigo-4);--mantine-primary-color-5: var(--mantine-color-indigo-5);--mantine-primary-color-6: var(--mantine-color-indigo-6);--mantine-primary-color-7: var(--mantine-color-indigo-7);--mantine-primary-color-8: var(--mantine-color-indigo-8);--mantine-primary-color-9: var(--mantine-color-indigo-9);--mantine-color-red-0: #ffeaea;--mantine-color-red-1: #fed4d4;--mantine-color-red-2: #f4a7a8;--mantine-color-red-3: #ec7878;--mantine-color-red-4: #e55050;--mantine-color-red-5: #e03131;--mantine-color-red-6: #e02829;--mantine-color-red-7: #c71a1c;--mantine-color-red-8: #b21218;--mantine-color-red-9: #9c0411;--mantine-color-violet-0: #fce9ff;--mantine-color-violet-1: #f1cfff;--mantine-color-violet-2: #e09bff;--mantine-color-violet-3: #d16fff;--mantine-color-violet-4: #be37fe;--mantine-color-violet-5: #b51afe;--mantine-color-violet-6: #b009ff;--mantine-color-violet-7: #9b00e4;--mantine-color-violet-8: #8a00cc;--mantine-color-violet-9: #7800b3;--mantine-color-indigo-0: #edecff;--mantine-color-indigo-1: #d6d5fe;--mantine-color-indigo-2: #aaa9f4;--mantine-color-indigo-3: #7b79eb;--mantine-color-indigo-4: #5451e4;--mantine-color-indigo-5: #3b37e0;--mantine-color-indigo-6: #2d2adf;--mantine-color-indigo-7: #1f1ec7;--mantine-color-indigo-8: #1819b2;--mantine-color-indigo-9: #0c149e;--mantine-color-cyan-0: #dffdff;--mantine-color-cyan-1: #caf5ff;--mantine-color-cyan-2: #99e8ff;--mantine-color-cyan-3: #64daff;--mantine-color-cyan-4: #3ccffe;--mantine-color-cyan-5: #24c8fe;--mantine-color-cyan-6: #00c2ff;--mantine-color-cyan-7: #00ade4;--mantine-color-cyan-8: #009acd;--mantine-color-cyan-9: #0085b5;--mantine-color-green-0: #e9fdec;--mantine-color-green-1: #d7f6dc;--mantine-color-green-2: #b0eab9;--mantine-color-green-3: #86df94;--mantine-color-green-4: #62d574;--mantine-color-green-5: #4ccf5f;--mantine-color-green-6: #3fcc54;--mantine-color-green-7: #2fb344;--mantine-color-green-8: #25a03b;--mantine-color-green-9: #138a2e;--mantine-color-yellow-0: #fff7e2;--mantine-color-yellow-1: #ffeecd;--mantine-color-yellow-2: #ffdc9c;--mantine-color-yellow-3: #ffc966;--mantine-color-yellow-4: #feb93a;--mantine-color-yellow-5: #feae1e;--mantine-color-yellow-6: #ffa90f;--mantine-color-yellow-8: #ca8200;--mantine-color-yellow-9: #af7000;--mantine-h1-font-size: clamp(28.0000px, calc(23.6364px + 1.3636vw), 40.0000px);--mantine-h1-font-weight: normal;--mantine-h2-font-size: clamp(24.0000px, calc(21.0909px + 0.9091vw), 32.0000px);--mantine-h2-font-weight: normal;--mantine-h3-font-size: clamp(20.0000px, calc(17.0909px + 0.9091vw), 28.0000px);--mantine-h3-font-weight: normal;--mantine-h4-font-size: clamp(16.0000px, calc(13.0909px + 0.9091vw), 24.0000px);--mantine-h4-font-weight: normal;--mantine-h5-font-size: clamp(16.0000px, calc(14.5455px + 0.4545vw), 20.0000px);--mantine-h5-font-weight: normal;--mantine-h6-font-size: 1rem;--mantine-h6-font-weight: normal;}
:root[data-mantine-color-scheme="dark"], :host([data-mantine-color-scheme="dark"]){--mantine-color-anchor: var(--mantine-color-text);--mantine-color-dimmed: #495057;--mantine-color-dark-filled: var(--mantine-color-dark-5);--mantine-color-dark-filled-hover: var(--mantine-color-dark-6);--mantine-color-dark-light: rgba(105, 105, 105, 0.15);--mantine-color-dark-light-hover: rgba(105, 105, 105, 0.2);--mantine-color-dark-light-color: var(--mantine-color-dark-0);--mantine-color-dark-outline: var(--mantine-color-dark-1);--mantine-color-dark-outline-hover: rgba(184, 184, 184, 0.05);--mantine-color-gray-filled: var(--mantine-color-gray-5);--mantine-color-gray-filled-hover: var(--mantine-color-gray-6);--mantine-color-gray-light: rgba(222, 226, 230, 0.15);--mantine-color-gray-light-hover: rgba(222, 226, 230, 0.2);--mantine-color-gray-light-color: var(--mantine-color-gray-0);--mantine-color-gray-outline: var(--mantine-color-gray-1);--mantine-color-gray-outline-hover: rgba(241, 243, 245, 0.05);--mantine-color-red-filled: var(--mantine-color-red-5);--mantine-color-red-filled-hover: var(--mantine-color-red-6);--mantine-color-red-light: rgba(236, 120, 120, 0.15);--mantine-color-red-light-hover: rgba(236, 120, 120, 0.2);--mantine-color-red-light-color: var(--mantine-color-red-0);--mantine-color-red-outline: var(--mantine-color-red-1);--mantine-color-red-outline-hover: rgba(254, 212, 212, 0.05);--mantine-color-pink-filled: var(--mantine-color-pink-5);--mantine-color-pink-filled-hover: var(--mantine-color-pink-6);--mantine-color-pink-light: rgba(250, 162, 193, 0.15);--mantine-color-pink-light-hover: rgba(250, 162, 193, 0.2);--mantine-color-pink-light-color: var(--mantine-color-pink-0);--mantine-color-pink-outline: var(--mantine-color-pink-1);--mantine-color-pink-outline-hover: rgba(255, 222, 235, 0.05);--mantine-color-grape-filled: var(--mantine-color-grape-5);--mantine-color-grape-filled-hover: var(--mantine-color-grape-6);--mantine-color-grape-light: rgba(229, 153, 247, 0.15);--mantine-color-grape-light-hover: rgba(229, 153, 247, 0.2);--mantine-color-grape-light-color: var(--mantine-color-grape-0);--mantine-color-grape-outline: var(--mantine-color-grape-1);--mantine-color-grape-outline-hover: rgba(243, 217, 250, 0.05);--mantine-color-violet-filled: var(--mantine-color-violet-5);--mantine-color-violet-filled-hover: var(--mantine-color-violet-6);--mantine-color-violet-light: rgba(209, 111, 255, 0.15);--mantine-color-violet-light-hover: rgba(209, 111, 255, 0.2);--mantine-color-violet-light-color: var(--mantine-color-violet-0);--mantine-color-violet-outline: var(--mantine-color-violet-1);--mantine-color-violet-outline-hover: rgba(241, 207, 255, 0.05);--mantine-color-indigo-filled: var(--mantine-color-indigo-5);--mantine-color-indigo-filled-hover: var(--mantine-color-indigo-6);--mantine-color-indigo-light: rgba(123, 121, 235, 0.15);--mantine-color-indigo-light-hover: rgba(123, 121, 235, 0.2);--mantine-color-indigo-light-color: var(--mantine-color-indigo-0);--mantine-color-indigo-outline: var(--mantine-color-indigo-1);--mantine-color-indigo-outline-hover: rgba(214, 213, 254, 0.05);--mantine-color-blue-filled: var(--mantine-color-blue-5);--mantine-color-blue-filled-hover: var(--mantine-color-blue-6);--mantine-color-blue-light: rgba(116, 192, 252, 0.15);--mantine-color-blue-light-hover: rgba(116, 192, 252, 0.2);--mantine-color-blue-light-color: var(--mantine-color-blue-0);--mantine-color-blue-outline: var(--mantine-color-blue-1);--mantine-color-blue-outline-hover: rgba(208, 235, 255, 0.05);--mantine-color-cyan-filled: var(--mantine-color-cyan-5);--mantine-color-cyan-filled-hover: var(--mantine-color-cyan-6);--mantine-color-cyan-light: rgba(100, 218, 255, 0.15);--mantine-color-cyan-light-hover: rgba(100, 218, 255, 0.2);--mantine-color-cyan-light-color: var(--mantine-color-cyan-0);--mantine-color-cyan-outline: var(--mantine-color-cyan-1);--mantine-color-cyan-outline-hover: rgba(202, 245, 255, 0.05);--mantine-color-teal-filled: var(--mantine-color-teal-5);--mantine-color-teal-filled-hover: var(--mantine-color-teal-6);--mantine-color-teal-light: rgba(99, 230, 190, 0.15);--mantine-color-teal-light-hover: rgba(99, 230, 190, 0.2);--mantine-color-teal-light-color: var(--mantine-color-teal-0);--mantine-color-teal-outline: var(--mantine-color-teal-1);--mantine-color-teal-outline-hover: rgba(195, 250, 232, 0.05);--mantine-color-green-filled: var(--mantine-color-green-5);--mantine-color-green-filled-hover: var(--mantine-color-green-6);--mantine-color-green-light: rgba(134, 223, 148, 0.15);--mantine-color-green-light-hover: rgba(134, 223, 148, 0.2);--mantine-color-green-light-color: var(--mantine-color-green-0);--mantine-color-green-outline: var(--mantine-color-green-1);--mantine-color-green-outline-hover: rgba(215, 246, 220, 0.05);--mantine-color-lime-filled: var(--mantine-color-lime-5);--mantine-color-lime-filled-hover: var(--mantine-color-lime-6);--mantine-color-lime-light: rgba(192, 235, 117, 0.15);--mantine-color-lime-light-hover: rgba(192, 235, 117, 0.2);--mantine-color-lime-light-color: var(--mantine-color-lime-0);--mantine-color-lime-outline: var(--mantine-color-lime-1);--mantine-color-lime-outline-hover: rgba(233, 250, 200, 0.05);--mantine-color-yellow-filled: var(--mantine-color-yellow-5);--mantine-color-yellow-filled-hover: var(--mantine-color-yellow-6);--mantine-color-yellow-light: rgba(255, 201, 102, 0.15);--mantine-color-yellow-light-hover: rgba(255, 201, 102, 0.2);--mantine-color-yellow-light-color: var(--mantine-color-yellow-0);--mantine-color-yellow-outline: var(--mantine-color-yellow-1);--mantine-color-yellow-outline-hover: rgba(255, 238, 205, 0.05);--mantine-color-orange-filled: var(--mantine-color-orange-5);--mantine-color-orange-filled-hover: var(--mantine-color-orange-6);--mantine-color-orange-light: rgba(255, 192, 120, 0.15);--mantine-color-orange-light-hover: rgba(255, 192, 120, 0.2);--mantine-color-orange-light-color: var(--mantine-color-orange-0);--mantine-color-orange-outline: var(--mantine-color-orange-1);--mantine-color-orange-outline-hover: rgba(255, 232, 204, 0.05);--app-cta-gradient: linear-gradient(90deg, var(--mantine-color-blue-9) 0%, var(--mantine-color-cyan-7) 100%);--app-color-surface: #2e2e2e;}
:root[data-mantine-color-scheme="light"], :host([data-mantine-color-scheme="light"]){--mantine-color-anchor: var(--mantine-color-text);--mantine-color-dimmed: #495057;--mantine-color-red-light: rgba(224, 40, 41, 0.1);--mantine-color-red-light-hover: rgba(224, 40, 41, 0.12);--mantine-color-red-outline-hover: rgba(224, 40, 41, 0.05);--mantine-color-violet-light: rgba(176, 9, 255, 0.1);--mantine-color-violet-light-hover: rgba(176, 9, 255, 0.12);--mantine-color-violet-outline-hover: rgba(176, 9, 255, 0.05);--mantine-color-indigo-light: rgba(45, 42, 223, 0.1);--mantine-color-indigo-light-hover: rgba(45, 42, 223, 0.12);--mantine-color-indigo-outline-hover: rgba(45, 42, 223, 0.05);--mantine-color-cyan-light: rgba(0, 194, 255, 0.1);--mantine-color-cyan-light-hover: rgba(0, 194, 255, 0.12);--mantine-color-cyan-outline-hover: rgba(0, 194, 255, 0.05);--mantine-color-green-light: rgba(63, 204, 84, 0.1);--mantine-color-green-light-hover: rgba(63, 204, 84, 0.12);--mantine-color-green-outline-hover: rgba(63, 204, 84, 0.05);--mantine-color-yellow-light: rgba(255, 169, 15, 0.1);--mantine-color-yellow-light-hover: rgba(255, 169, 15, 0.12);--mantine-color-yellow-outline-hover: rgba(255, 169, 15, 0.05);--app-color-surface: #f1f3f5;--app-cta-gradient: linear-gradient(90deg, var(--mantine-color-blue-filled) 0%, var(--mantine-color-cyan-5) 100%);}</style><style data-mantine-styles="classes">@media (max-width: 35.99375em) {.mantine-visible-from-xs {display: none !important;}}@media (min-width: 36em) {.mantine-hidden-from-xs {display: none !important;}}@media (max-width: 47.99375em) {.mantine-visible-from-sm {display: none !important;}}@media (min-width: 48em) {.mantine-hidden-from-sm {display: none !important;}}@media (max-width: 61.99375em) {.mantine-visible-from-md {display: none !important;}}@media (min-width: 62em) {.mantine-hidden-from-md {display: none !important;}}@media (max-width: 74.99375em) {.mantine-visible-from-lg {display: none !important;}}@media (min-width: 75em) {.mantine-hidden-from-lg {display: none !important;}}@media (max-width: 87.99375em) {.mantine-visible-from-xl {display: none !important;}}@media (min-width: 88em) {.mantine-hidden-from-xl {display: none !important;}}</style><div style="position:absolute;top:0rem" class=""></div><div style="max-width:var(--container-size-xl);height:100%;min-height:0rem" class=""><style data-mantine-styles="inline">.__m__-_R_5ub_{--grid-gutter:0rem;}</style><div style="height:100%;min-height:0rem" class="m_410352e9 mantine-Grid-root __m__-_R_5ub_"><div class="m_dee7bd2f mantine-Grid-inner" style="height:100%"><style data-mantine-styles="inline">.__m__-_R_rdub_{--col-flex-grow:auto;--col-flex-basis:91.66666666666667%;--col-max-width:91.66666666666667%;}@media(min-width: 48em){.__m__-_R_rdub_{--col-flex-grow:auto;--col-flex-basis:83.33333333333334%;--col-max-width:83.33333333333334%;}}</style><div style="min-width:0rem;height:100%;min-height:0rem;display:flex" class="m_96bdd299 mantine-Grid-col __m__-_R_rdub_"><style data-mantine-styles="inline">.__m__-_R_6qrdub_{margin-top:0rem;padding-inline:var(--mantine-spacing-xs);width:100%;}@media(min-width: 48em){.__m__-_R_6qrdub_{margin-top:var(--mantine-spacing-xl);width:80%;}}@media(min-width: 62em){.__m__-_R_6qrdub_{padding-inline:var(--mantine-spacing-xl);}}</style><div style="margin-inline:auto;max-width:var(--mantine-breakpoint-xl)" class="__m__-_R_6qrdub_"><div style="color:var(--mantine-color-dimmed)" class="m_4451eb3a mantine-Center-root" data-inline="true"><div style="--ti-size:var(--ti-size-xs);--ti-bg:transparent;--ti-color:var(--mantine-color-indigo-light-color);--ti-bd:calc(0.0625rem * var(--mantine-scale)) solid transparent;margin-inline-end:calc(0.125rem * var(--mantine-scale));color:inherit" class="m_7341320d mantine-ThemeIcon-root" data-variant="transparent" data-size="xs"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="tabler-icon tabler-icon-lock "><path d="M5 13a2 2 0 0 1 2 -2h10a2 2 0 0 1 2 2v6a2 2 0 0 1 -2 2h-10a2 2 0 0 1 -2 -2v-6"></path><path d="M11 16a1 1 0 1 0 2 0a1 1 0 0 0 -2 0"></path><path d="M8 11v-4a4 4 0 1 1 8 0v4"></path></svg></div><p style="font-size:var(--mantine-font-size-sm)" class="mantine-focus-auto m_b6d8b162 mantine-Text-root">JS: Trees</p></div><h1 style="--title-fw:var(--mantine-h1-font-weight);--title-lh:var(--mantine-h1-line-height);--title-fz:var(--mantine-h1-font-size);margin-bottom:var(--mantine-spacing-xl)" class="m_8a5d1357 mantine-Title-root" data-order="1">Theory: Definitions</h1><script type="application/ld+json">{"@context":"https://schema.org","@type":"LearningResource","name":"Definitions","inLanguage":"en","isPartOf":{"@type":"LearningResource","name":"JS: Trees"},"isAccessibleForFree":"False","hasPart":{"@type":"WebPageElement","isAccessibleForFree":"False","cssSelector":".paywalled"}}</script><div class=""><div style="--alert-color:var(--mantine-color-indigo-light-color);margin-bottom:var(--mantine-spacing-lg);font-size:var(--mantine-font-size-lg)" class="m_66836ed3 mantine-Alert-root" id="mantine-_R_remqrdub_" role="alert" aria-describedby="mantine-_R_remqrdub_-body" aria-labelledby="mantine-_R_remqrdub_-title"><div class="m_a5d60502 mantine-Alert-wrapper"><div class="m_667f2a6a mantine-Alert-icon"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="tabler-icon tabler-icon-rocket "><path d="M4 13a8 8 0 0 1 7 7a6 6 0 0 0 3 -5a9 9 0 0 0 6 -8a3 3 0 0 0 -3 -3a9 9 0 0 0 -8 6a6 6 0 0 0 -5 3"></path><path d="M7 14a6 6 0 0 0 -3 6a6 6 0 0 0 6 -3"></path><path d="M14 9a1 1 0 1 0 2 0a1 1 0 1 0 -2 0"></path></svg></div><div class="m_667c2793 mantine-Alert-body"><div class="m_6a03f287 mantine-Alert-title"><span id="mantine-_R_remqrdub_-title" class="m_698f4f23 mantine-Alert-label">Full access to materials</span></div><div id="mantine-_R_remqrdub_-body" class="m_7fa78076 mantine-Alert-message"><div style="--group-gap:var(--mantine-spacing-md);--group-align:center;--group-justify:space-between;--group-wrap:wrap" class="m_4081bf90 mantine-Group-root"><p class="mantine-focus-auto m_b6d8b162 mantine-Text-root">Sign up and get access to this and dozens of other courses</p><a style="--button-height:var(--button-height-xs);--button-padding-x:var(--button-padding-x-xs);--button-fz:var(--mantine-font-size-xs);--button-bg:linear-gradient(45deg, var(--mantine-color-blue-filled) 0%, var(--mantine-color-cyan-filled) 100%);--button-hover:linear-gradient(45deg, var(--mantine-color-blue-filled) 0%, var(--mantine-color-cyan-filled) 100%);--button-color:var(--mantine-color-white);--button-bd:none" class="mantine-focus-auto mantine-active m_77c9d27d mantine-Button-root m_87cf2631 mantine-UnstyledButton-root" data-variant="gradient" data-size="xs" href="/u/new"><span class="m_80f1301b mantine-Button-inner"><span class="m_811560b9 mantine-Button-label">Sign up</span></span></a></div></div></div></div></div><div class="paywalled m_d08caa0 mantine-Typography-root"><p>File structures are an example of a tree that everyone who uses a computer is familiar with. It consists of directories and different kinds of files.</p>
<div style="margin-bottom:var(--mantine-spacing-lg)" class="m_e597c321 mantine-CodeHighlight-codeHighlight" dir="ltr"><div class="m_be7e9c9c mantine-CodeHighlight-controls"><button style="--ai-bg:transparent;--ai-hover:transparent;--ai-color:inherit;--ai-bd:none" class="mantine-focus-auto mantine-active m_d498bab7 mantine-CodeHighlight-control m_8d3f4000 mantine-ActionIcon-root m_87cf2631 mantine-UnstyledButton-root" data-variant="none" type="button" aria-label="Copy code"><span class="m_8d3afb97 mantine-ActionIcon-icon"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" stroke-width="2" stroke="currentColor" fill="none" stroke-linecap="round" stroke-linejoin="round"><path stroke="none" d="M0 0h24v24H0z" fill="none"></path><path d="M8 8m0 2a2 2 0 0 1 2 -2h8a2 2 0 0 1 2 2v8a2 2 0 0 1 -2 2h-8a2 2 0 0 1 -2 -2z"></path><path d="M16 8v-2a2 2 0 0 0 -2 -2h-8a2 2 0 0 0 -2 2v8a2 2 0 0 0 2 2h2"></path></svg></span></button></div><div style="--scrollarea-scrollbar-size:calc(0.25rem * var(--mantine-scale));--sa-corner-width:0px;--sa-corner-height:0px" class="m_f744fd40 mantine-CodeHighlight-scrollarea m_d57069b5 mantine-ScrollArea-root" dir="ltr"><div style="overflow-x:hidden;overflow-y:hidden;overscroll-behavior-inline:none" class="m_c0783ff9 mantine-ScrollArea-viewport" data-scrollbars="xy"><div class="m_b1336c6 mantine-ScrollArea-content"><pre class="m_2c47c4fd mantine-CodeHighlight-pre" style="padding:0"><code class="m_5caae6d3 mantine-CodeHighlight-code">nodejs-package # root directory
├── Makefile # file
├── README.md # file
├── __tests__ # directory
│ └── half.test.js # file
├── babel.config.js # file
└── node_modules # directory
└── @babel # directory
└── cli # directory
└── LICENSE # file</code></pre></div></div></div><button class="mantine-focus-auto m_c9378bc2 mantine-CodeHighlight-showCodeButton m_87cf2631 mantine-UnstyledButton-root" data-hidden="true" type="button">Expand code</button></div>
<p>It's called a tree because of its structure. All elements in the file system are arranged in a hierarchy. In it, the top level is the root directory (or disk, if we're talking about Windows), and then there are files and directories, which themselves may contain more files and directories.</p>
<p>A vital feature of the tree structure is that it is <strong>recursive</strong>. In other words, the tree consists of subtrees, which in turn comprised of subtrees, which in turn consist of... This feature is the defining factor of the main ways that developers work with trees, all of which are recursive in one way or another.</p>
<p>Trees consist of <strong>nodes</strong> и <strong>edges</strong> between them. Edges don't actually exist, they only help to visualize the connection and, if necessary, describe it. Nodes are divided into two types: <strong>internal</strong> nodes (those that have child nodes) and <strong>leaf</strong> nodes (that don't). In the case of a file system, leaf nodes are represented by files and internal nodes by directories.</p>
<p><img style="--image-object-fit:contain;width:auto" class="m_9e117634 mantine-Image-root" src="/rails/active_storage/blobs/proxy/eyJfcmFpbHMiOnsiZGF0YSI6NzkyNSwicHVyIjoiYmxvYl9pZCJ9fQ==--4d51e85f9e99088818d1c43536cbda3ccefff435/tree-terms.png" alt="Trees: nodes and leaves" loading="lazy"/></p>
<p>Each node in the tree has <strong>a parent</strong> (or ancestor). The only exception is the root node – it has no parents, and that's where the tree begins. In general, any number of descendants of any internal node can exist. In addition, working with trees means that you need to understand the concept of depth. Depth determines how many steps through the nodes from the root you need to reach the current one (the one we are looking at). Nodes that are at the same depth and have a common parent are sibling nodes.</p>
<h2 id="heading-2-1">Implementation</h2>
<p>The number of tree implementations is endless. The most basic one is nested arrays:</p>
<div style="margin-bottom:var(--mantine-spacing-lg)" class="m_e597c321 mantine-CodeHighlight-codeHighlight" dir="ltr"><div class="m_be7e9c9c mantine-CodeHighlight-controls"><button style="--ai-bg:transparent;--ai-hover:transparent;--ai-color:inherit;--ai-bd:none" class="mantine-focus-auto mantine-active m_d498bab7 mantine-CodeHighlight-control m_8d3f4000 mantine-ActionIcon-root m_87cf2631 mantine-UnstyledButton-root" data-variant="none" type="button" aria-label="Copy code"><span class="m_8d3afb97 mantine-ActionIcon-icon"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" stroke-width="2" stroke="currentColor" fill="none" stroke-linecap="round" stroke-linejoin="round"><path stroke="none" d="M0 0h24v24H0z" fill="none"></path><path d="M8 8m0 2a2 2 0 0 1 2 -2h8a2 2 0 0 1 2 2v8a2 2 0 0 1 -2 2h-8a2 2 0 0 1 -2 -2z"></path><path d="M16 8v-2a2 2 0 0 0 -2 -2h-8a2 2 0 0 0 -2 2v8a2 2 0 0 0 2 2h2"></path></svg></span></button></div><div style="--scrollarea-scrollbar-size:calc(0.25rem * var(--mantine-scale));--sa-corner-width:0px;--sa-corner-height:0px" class="m_f744fd40 mantine-CodeHighlight-scrollarea m_d57069b5 mantine-ScrollArea-root" dir="ltr"><div style="overflow-x:hidden;overflow-y:hidden;overscroll-behavior-inline:none" class="m_c0783ff9 mantine-ScrollArea-viewport" data-scrollbars="xy"><div class="m_b1336c6 mantine-ScrollArea-content"><pre class="m_2c47c4fd mantine-CodeHighlight-pre" style="padding:0"><code class="m_5caae6d3 mantine-CodeHighlight-code">[['index.html', 'main.js'], 'index.js', ['favicon.ico', 'app.css']];
// * the root is the array itself
// / | \
// * index.js *
// / | | \
// index.html main.js favicon.ico app.css
// A couple more examples of trees with arbitrary data:
[]; // empty tree
[3, 2, [3, 8], [[8], 3]];
[1, null, [[3]], [5, 'string', [undefined, [3], { key: 'value' }]]];</code></pre></div></div></div><button class="mantine-focus-auto m_c9378bc2 mantine-CodeHighlight-showCodeButton m_87cf2631 mantine-UnstyledButton-root" data-hidden="true" type="button">Expand code</button></div>
<p>In the examples above, the root is the array itself, and all its elements are children. If the child is not an array, it is treated like a leaf node; otherwise, it's treated like an internal node. The inner node, in turn, consists of children.</p>
<p>Any tree consists of two large parts:</p>
<ol>
<li>Data that is stored inside the tree</li>
<li>The tree structure, which is responsible for the relationships between the data</li>
</ol>
<div style="margin-bottom:var(--mantine-spacing-lg)" class="m_e597c321 mantine-CodeHighlight-codeHighlight" dir="ltr"><div class="m_be7e9c9c mantine-CodeHighlight-controls"><button style="--ai-bg:transparent;--ai-hover:transparent;--ai-color:inherit;--ai-bd:none" class="mantine-focus-auto mantine-active m_d498bab7 mantine-CodeHighlight-control m_8d3f4000 mantine-ActionIcon-root m_87cf2631 mantine-UnstyledButton-root" data-variant="none" type="button" aria-label="Copy code"><span class="m_8d3afb97 mantine-ActionIcon-icon"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" stroke-width="2" stroke="currentColor" fill="none" stroke-linecap="round" stroke-linejoin="round"><path stroke="none" d="M0 0h24v24H0z" fill="none"></path><path d="M8 8m0 2a2 2 0 0 1 2 -2h8a2 2 0 0 1 2 2v8a2 2 0 0 1 -2 2h-8a2 2 0 0 1 -2 -2z"></path><path d="M16 8v-2a2 2 0 0 0 -2 -2h-8a2 2 0 0 0 -2 2v8a2 2 0 0 0 2 2h2"></path></svg></span></button></div><div style="--scrollarea-scrollbar-size:calc(0.25rem * var(--mantine-scale));--sa-corner-width:0px;--sa-corner-height:0px" class="m_f744fd40 mantine-CodeHighlight-scrollarea m_d57069b5 mantine-ScrollArea-root" dir="ltr"><div style="overflow-x:hidden;overflow-y:hidden;overscroll-behavior-inline:none" class="m_c0783ff9 mantine-ScrollArea-viewport" data-scrollbars="xy"><div class="m_b1336c6 mantine-ScrollArea-content"><pre class="m_2c47c4fd mantine-CodeHighlight-pre" style="padding:0"><code class="m_5caae6d3 mantine-CodeHighlight-code">[['index.html', 'main.js'], 'index.js', ['favicon.ico', 'app.css']];</code></pre></div></div></div><button class="mantine-focus-auto m_c9378bc2 mantine-CodeHighlight-showCodeButton m_87cf2631 mantine-UnstyledButton-root" data-hidden="true" type="button">Expand code</button></div>
<p>What is the structure, and what is the data in this tree? The data here are leaf nodes, and the internal arrays are the structure. They determine where the data (in this case, files) are located but do not contain any data themselves. Organizing a tree in this way is not conducive to a file structure. This tree doesn't even allow you to set a name for the directory.</p>
<p>Let's expand the structure to be able to add more data. Let's represent each element in the tree as an array, where the first element is the value stored in the node, and the second element is an array of the node's children. If the second element is missing, then we are dealing with a leaf.</p>
<div style="margin-bottom:var(--mantine-spacing-lg)" class="m_e597c321 mantine-CodeHighlight-codeHighlight" dir="ltr"><div class="m_be7e9c9c mantine-CodeHighlight-controls"><button style="--ai-bg:transparent;--ai-hover:transparent;--ai-color:inherit;--ai-bd:none" class="mantine-focus-auto mantine-active m_d498bab7 mantine-CodeHighlight-control m_8d3f4000 mantine-ActionIcon-root m_87cf2631 mantine-UnstyledButton-root" data-variant="none" type="button" aria-label="Copy code"><span class="m_8d3afb97 mantine-ActionIcon-icon"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" stroke-width="2" stroke="currentColor" fill="none" stroke-linecap="round" stroke-linejoin="round"><path stroke="none" d="M0 0h24v24H0z" fill="none"></path><path d="M8 8m0 2a2 2 0 0 1 2 -2h8a2 2 0 0 1 2 2v8a2 2 0 0 1 -2 2h-8a2 2 0 0 1 -2 -2z"></path><path d="M16 8v-2a2 2 0 0 0 -2 -2h-8a2 2 0 0 0 -2 2v8a2 2 0 0 0 2 2h2"></path></svg></span></button></div><div style="--scrollarea-scrollbar-size:calc(0.25rem * var(--mantine-scale));--sa-corner-width:0px;--sa-corner-height:0px" class="m_f744fd40 mantine-CodeHighlight-scrollarea m_d57069b5 mantine-ScrollArea-root" dir="ltr"><div style="overflow-x:hidden;overflow-y:hidden;overscroll-behavior-inline:none" class="m_c0783ff9 mantine-ScrollArea-viewport" data-scrollbars="xy"><div class="m_b1336c6 mantine-ScrollArea-content"><pre class="m_2c47c4fd mantine-CodeHighlight-pre" style="padding:0"><code class="m_5caae6d3 mantine-CodeHighlight-code">['app', [ // Root
['dist', [ // Internal node
['index.html'], // Leaf
['main.js'] // Leaf
]],
['index.js'], // Leaf
['assets', [ // Internal node
['favicon.ico'], // Leaf
['app.css'], // Leaf
]],
]];
// app
// / | \
// dist index.js assets
// / | | \
// index.html main.js favicon.ico app.css</code></pre></div></div></div><button class="mantine-focus-auto m_c9378bc2 mantine-CodeHighlight-showCodeButton m_87cf2631 mantine-UnstyledButton-root" data-hidden="true" type="button">Expand code</button></div>
<p>This variant is more verbose, but allows you to store data in any node, even non-leaf. And it doesn't have to be a string, like in the example above. Changing data on objects will allow you to add anything there.</p>
<p>And the most flexible and convenient way to represent trees is through objects: each node is an object, and arrays store only the children list.</p>
<div style="margin-bottom:var(--mantine-spacing-lg)" class="m_e597c321 mantine-CodeHighlight-codeHighlight" dir="ltr"><div class="m_be7e9c9c mantine-CodeHighlight-controls"><button style="--ai-bg:transparent;--ai-hover:transparent;--ai-color:inherit;--ai-bd:none" class="mantine-focus-auto mantine-active m_d498bab7 mantine-CodeHighlight-control m_8d3f4000 mantine-ActionIcon-root m_87cf2631 mantine-UnstyledButton-root" data-variant="none" type="button" aria-label="Copy code"><span class="m_8d3afb97 mantine-ActionIcon-icon"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" stroke-width="2" stroke="currentColor" fill="none" stroke-linecap="round" stroke-linejoin="round"><path stroke="none" d="M0 0h24v24H0z" fill="none"></path><path d="M8 8m0 2a2 2 0 0 1 2 -2h8a2 2 0 0 1 2 2v8a2 2 0 0 1 -2 2h-8a2 2 0 0 1 -2 -2z"></path><path d="M16 8v-2a2 2 0 0 0 -2 -2h-8a2 2 0 0 0 -2 2v8a2 2 0 0 0 2 2h2"></path></svg></span></button></div><div style="--scrollarea-scrollbar-size:calc(0.25rem * var(--mantine-scale));--sa-corner-width:0px;--sa-corner-height:0px" class="m_f744fd40 mantine-CodeHighlight-scrollarea m_d57069b5 mantine-ScrollArea-root" dir="ltr"><div style="overflow-x:hidden;overflow-y:hidden;overscroll-behavior-inline:none" class="m_c0783ff9 mantine-ScrollArea-viewport" data-scrollbars="xy"><div class="m_b1336c6 mantine-ScrollArea-content"><pre class="m_2c47c4fd mantine-CodeHighlight-pre" style="padding:0"><code class="m_5caae6d3 mantine-CodeHighlight-code">// Note the separation of structure and data
// Here it's much more obvious
{
value: 5,
children: [
{ value: 10 },
{ value: 100 },
{ value: 'nested', children: [/* ... */] }
]
}</code></pre></div></div></div><button class="mantine-focus-auto m_c9378bc2 mantine-CodeHighlight-showCodeButton m_87cf2631 mantine-UnstyledButton-root" data-hidden="true" type="button">Expand code</button></div>
<p>By and large, both the array and the object themselves can always represent trees. This is true for any recursive data structure, that is, a structure whose elements can be the structure itself. Any array can contain an array, just as any object can contain an object.</p></div><div style="margin-block:var(--mantine-spacing-xl)" class=""><h2 style="--title-fw:var(--mantine-h2-font-weight);--title-lh:var(--mantine-h2-line-height);--title-fz:var(--mantine-h2-font-size);margin-bottom:var(--mantine-spacing-md)" class="m_8a5d1357 mantine-Title-root" data-order="2">Recommended programs</h2><style data-mantine-styles="inline">.__m__-_R_2mremqrdub_{--carousel-slide-gap:var(--mantine-spacing-xs);--carousel-slide-size:70%;}@media(min-width: 36em){.__m__-_R_2mremqrdub_{--carousel-slide-gap:var(--mantine-spacing-xl);--carousel-slide-size:50%;}}</style><div style="--carousel-control-size:calc(2.5rem * var(--mantine-scale));--carousel-controls-offset:var(--mantine-spacing-sm);margin-bottom:var(--mantine-spacing-lg);padding-block:var(--mantine-spacing-sm);background:var(--app-color-surface)" class="m_17884d0f mantine-Carousel-root responsiveClassName" data-orientation="horizontal" data-include-gap-in-size="true"><div class="m_39bc3463 mantine-Carousel-controls" data-orientation="horizontal"><button class="mantine-focus-auto m_64f58e10 mantine-Carousel-control m_87cf2631 mantine-UnstyledButton-root" type="button" data-inactive="true" data-type="previous" tabindex="-1"><svg viewBox="0 0 15 15" fill="none" xmlns="http://www.w3.org/2000/svg" style="transform:rotate(90deg);width:calc(1rem * var(--mantine-scale));height:calc(1rem * var(--mantine-scale));display:block"><path d="M3.13523 6.15803C3.3241 5.95657 3.64052 5.94637 3.84197 6.13523L7.5 9.56464L11.158 6.13523C11.3595 5.94637 11.6759 5.95657 11.8648 6.15803C12.0536 6.35949 12.0434 6.67591 11.842 6.86477L7.84197 10.6148C7.64964 10.7951 7.35036 10.7951 7.15803 10.6148L3.15803 6.86477C2.95657 6.67591 2.94637 6.35949 3.13523 6.15803Z" fill="currentColor" fill-rule="evenodd" clip-rule="evenodd"></path></svg></button><button class="mantine-focus-auto m_64f58e10 mantine-Carousel-control m_87cf2631 mantine-UnstyledButton-root" type="button" data-inactive="true" data-type="next" tabindex="-1"><svg viewBox="0 0 15 15" fill="none" xmlns="http://www.w3.org/2000/svg" style="transform:rotate(-90deg);width:calc(1rem * var(--mantine-scale));height:calc(1rem * var(--mantine-scale));display:block"><path d="M3.13523 6.15803C3.3241 5.95657 3.64052 5.94637 3.84197 6.13523L7.5 9.56464L11.158 6.13523C11.3595 5.94637 11.6759 5.95657 11.8648 6.15803C12.0536 6.35949 12.0434 6.67591 11.842 6.86477L7.84197 10.6148C7.64964 10.7951 7.35036 10.7951 7.15803 10.6148L3.15803 6.86477C2.95657 6.67591 2.94637 6.35949 3.13523 6.15803Z" fill="currentColor" fill-rule="evenodd" clip-rule="evenodd"></path></svg></button></div><div class="m_a2dae653 mantine-Carousel-viewport" data-type="media"><div class="m_fcd81474 mantine-Carousel-container __m__-_R_2mremqrdub_" data-orientation="horizontal"><div class="m_d98df724 mantine-Carousel-slide" data-orientation="horizontal"><div tabindex="0" style="cursor:pointer;height:100%"><a style="text-decoration:none" class="mantine-focus-auto m_849cf0da m_b6d8b162 mantine-Text-root mantine-Anchor-root" data-underline="hover" href="/programs/frontend?promo_name=programs_list&promo_position=course&promo_creative=catalog_card&promo_type=card" target="_blank"><div style="height:100%" class="m_e615b15f mantine-Card-root m_1b7284a3 mantine-Paper-root" data-with-border="true"><div style="--group-gap:calc(0.25rem * var(--mantine-scale));--group-align:center;--group-justify:flex-start;--group-wrap:nowrap" class="m_4081bf90 mantine-Group-root"><span style="font-size:var(--mantine-font-size-sm)" class="mantine-focus-auto m_b6d8b162 mantine-Text-root">10 months</span><span class="mantine-focus-auto m_b6d8b162 mantine-Text-root">·</span><span style="font-size:var(--mantine-font-size-sm)" class="mantine-focus-auto m_b6d8b162 mantine-Text-root">For beginners</span></div><p style="margin-bottom:var(--mantine-spacing-sm);font-size:var(--mantine-font-size-h5);font-weight:bold" class="mantine-focus-auto m_b6d8b162 mantine-Text-root">Frontend Developer</p><p class="mantine-focus-auto m_b6d8b162 mantine-Text-root"></p><div style="margin-top:auto" class=""><div class="m_4451eb3a mantine-Center-root"><img style="opacity:0.8;width:70%" class="m_9e117634 mantine-Image-root mantine-visible-from-xs" src="https://hexlet.io/rails/active_storage/representations/proxy/eyJfcmFpbHMiOnsiZGF0YSI6MTIzNTMsInB1ciI6ImJsb2JfaWQifX0=--f1948fb0c5a45a6d76671a1a32b8cf6f0b53ee57/eyJfcmFpbHMiOnsiZGF0YSI6eyJmb3JtYXQiOiJ3ZWJwIiwicmVzaXplX3RvX2xpbWl0IjpbNDAwLDQwMF0sInNhdmVyIjp7InF1YWxpdHkiOjg1fX0sInB1ciI6InZhcmlhdGlvbiJ9fQ==--5b6f46dacd1af664f27558553a58076185091823/Software%20code%20testing-cuate.png" alt="Frontend Developer" loading="eager"/></div><div style="--group-gap:var(--mantine-spacing-md);--group-align:end;--group-justify:space-between;--group-wrap:wrap;margin-top:var(--mantine-spacing-xs)" class="m_4081bf90 mantine-Group-root"><p style="font-size:var(--mantine-font-size-xl)" class="mantine-focus-auto m_b6d8b162 mantine-Text-root">from $49</p><p style="font-size:var(--mantine-font-size-sm)" class="mantine-focus-auto m_b6d8b162 mantine-Text-root">Explore →</p></div></div></div></a></div></div><div class="m_d98df724 mantine-Carousel-slide" data-orientation="horizontal"><div tabindex="0" style="cursor:pointer;height:100%"><a style="text-decoration:none" class="mantine-focus-auto m_849cf0da m_b6d8b162 mantine-Text-root mantine-Anchor-root" data-underline="hover" href="/courses?promo_name=programs_list&promo_position=course&promo_creative=catalog_card&promo_type=card"><div style="height:100%" class="m_e615b15f mantine-Card-root m_1b7284a3 mantine-Paper-root" data-with-border="true"><h2 style="--title-fw:var(--mantine-h2-font-weight);--title-lh:var(--mantine-h2-line-height);--title-fz:var(--mantine-h2-font-size);margin-bottom:var(--mantine-spacing-md);font-size:var(--mantine-font-size-h3)" class="m_8a5d1357 mantine-Title-root" data-order="2" data-responsive="true">Catalog</h2><p style="margin-bottom:auto" class="mantine-focus-auto m_b6d8b162 mantine-Text-root">A complete list of available courses by direction</p><div style="margin-top:auto" class=""><div class="m_4451eb3a mantine-Center-root"><img style="opacity:0.8;width:70%" class="m_9e117634 mantine-Image-root mantine-visible-from-xs" src="/vite/assets/development-BVihs_d5.png" alt="Orientation"/></div></div></div></a></div></div></div></div></div></div></div></div></div><style data-mantine-styles="inline">.__m__-_R_1bdub_{--col-flex-grow:auto;--col-flex-basis:8.333333333333334%;--col-max-width:8.333333333333334%;}@media(min-width: 48em){.__m__-_R_1bdub_{--col-flex-grow:auto;--col-flex-basis:16.666666666666668%;--col-max-width:16.666666666666668%;}}</style><div style="min-width:0rem;height:100%;min-height:0rem" class="m_96bdd299 mantine-Grid-col __m__-_R_1bdub_"><div style="margin-inline:var(--mantine-spacing-xs)" class="mantine-visible-from-sm"><button style="--button-color:var(--mantine-color-white);margin-bottom:var(--mantine-spacing-lg);text-decoration:none" class="mantine-focus-auto m_849cf0da mantine-focus-auto m_77c9d27d mantine-Button-root m_87cf2631 mantine-UnstyledButton-root m_b6d8b162 mantine-Text-root mantine-Anchor-root" data-underline="hover" data-disabled="true" data-block="true" disabled="" type="button"><span class="m_80f1301b mantine-Button-inner"><span class="m_811560b9 mantine-Button-label"><span style="margin-inline-end:var(--mantine-spacing-xs)" class="mantine-focus-auto m_b6d8b162 mantine-Text-root">Next</span>→</span></span></button><a style="padding-inline:0rem" class="mantine-focus-auto m_f0824112 mantine-NavLink-root m_87cf2631 mantine-UnstyledButton-root"><span class="m_690090b5 mantine-NavLink-section" data-position="left"><div style="--ti-size:var(--ti-size-sm);--ti-bg:transparent;--ti-color:var(--mantine-color-indigo-light-color);--ti-bd:calc(0.0625rem * var(--mantine-scale)) solid transparent;color:inherit" class="m_7341320d mantine-ThemeIcon-root" data-variant="transparent" data-size="sm"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="1.2" stroke-linecap="round" stroke-linejoin="round" class="tabler-icon tabler-icon-list-numbers "><path d="M11 6h9"></path><path d="M11 12h9"></path><path d="M12 18h8"></path><path d="M4 16a2 2 0 1 1 4 0c0 .591 -.5 1 -1 1.5l-3 2.5h4"></path><path d="M6 10v-6l-2 2"></path></svg></div></span><div class="m_f07af9d2 mantine-NavLink-body"><span class="m_1f6ac4c4 mantine-NavLink-label">Navigation</span><span class="m_57492dcc mantine-NavLink-description">Theory</span></div><span class="m_690090b5 mantine-NavLink-section" data-position="right"></span></a><div style="margin-block:var(--mantine-spacing-lg)" class="m_3eebeb36 mantine-Divider-root" data-orientation="horizontal" role="separator"></div><div style="margin-block:var(--mantine-spacing-lg)" class=""><div style="justify-content:space-between;margin-bottom:calc(0.1875rem * var(--mantine-scale));color:var(--mantine-color-dimmed);font-size:var(--mantine-font-size-xs)" class="m_8bffd616 mantine-Flex-root __m__-_R_qimrbdub_"><p style="font-size:var(--mantine-font-size-xs)" class="mantine-focus-auto m_b6d8b162 mantine-Text-root">Completed</p><p style="font-size:var(--mantine-font-size-xs)" class="mantine-focus-auto m_b6d8b162 mantine-Text-root">0 / 9</p></div><div style="--progress-size:var(--progress-size-sm)" class="m_db6d6462 mantine-Progress-root" data-size="sm"><div style="--progress-section-size:0%;--progress-section-color:var(--mantine-color-gray-filled)" class="m_2242eb65 mantine-Progress-section" role="progressbar" aria-valuemax="100" aria-valuemin="0" aria-valuenow="0" aria-valuetext="0%"></div></div></div><div style="--toc-bg:var(--mantine-color-blue-light);--toc-color:var(--mantine-color-blue-light-color);--toc-size:var(--mantine-font-size-sm);--toc-radius:var(--mantine-radius-sm);margin-top:var(--mantine-spacing-xl)" class="m_bcaa9990 mantine-TableOfContents-root" data-variant="light" data-size="sm"></div></div><div class="mantine-hidden-from-sm"><div style="--stack-gap:0rem;--stack-align:stretch;--stack-justify:flex-start" class="m_6d731127 mantine-Stack-root"><button style="--button-color:var(--mantine-color-white);margin-bottom:var(--mantine-spacing-xs);padding:0rem;text-decoration:none" class="mantine-focus-auto m_849cf0da mantine-focus-auto m_77c9d27d mantine-Button-root m_87cf2631 mantine-UnstyledButton-root m_b6d8b162 mantine-Text-root mantine-Anchor-root" data-underline="hover" data-disabled="true" data-block="true" disabled="" type="button"><span class="m_80f1301b mantine-Button-inner"><span class="m_811560b9 mantine-Button-label">→</span></span></button><button style="--ai-size:var(--ai-size-sm);--ai-bg:transparent;--ai-hover:var(--mantine-color-indigo-light-hover);--ai-color:var(--mantine-color-indigo-light-color);--ai-bd:calc(0.0625rem * var(--mantine-scale)) solid transparent;padding-block:var(--mantine-spacing-lg);color:inherit;width:100%" class="mantine-focus-auto m_8d3f4000 mantine-ActionIcon-root m_87cf2631 mantine-UnstyledButton-root" data-variant="subtle" data-size="sm" data-disabled="true" type="button" disabled=""><span class="m_8d3afb97 mantine-ActionIcon-icon"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="1.2" stroke-linecap="round" stroke-linejoin="round" class="tabler-icon tabler-icon-list-numbers "><path d="M11 6h9"></path><path d="M11 12h9"></path><path d="M12 18h8"></path><path d="M4 16a2 2 0 1 1 4 0c0 .591 -.5 1 -1 1.5l-3 2.5h4"></path><path d="M6 10v-6l-2 2"></path></svg></span></button></div></div></div></div></div></div></div>
</main>
<footer class="bg-dark fw-light text-light px-3 py-5">
<div class="row small">
<div class="col-12 col-sm-6 col-md-3">
<div class="h5 mb-3">About Hexlet</div>
<ul class="list-unstyled">
<li>
<a class="nav-link link-light py-1 ps-0" href="/pages/about">About us</a>
</li>
<li>
<span class="nav-link link-light py-1 ps-0 external-link" data-href="https://help.hexlet.io/category/4316" data-target="_blank" role="button">Help</span>
</li>
<li>
<a class="nav-link link-light py-1 ps-0" target="_blank" rel="noopener noreferrer" href="/map">Site Map</a>
</li>
</ul>
</div>
<div class="col-12 col-sm-6 col-md-3">
<div class="h5 fw-normal mb-3">Learn</div>
<ul class="list-unstyled">
<li>
<a class="nav-link link-light py-1 ps-0" href="/courses_backend-development">Backend
</a></li>
<li>
<a class="nav-link link-light py-1 ps-0" href="/courses_devops">DevOps
</a></li>
<li>
<a class="nav-link link-light py-1 ps-0" href="/courses_frontend-development">Frontend
</a></li>
<li>
<a class="nav-link link-light py-1 ps-0" href="/courses_python">Python
</a></li>
<li>
<a class="nav-link link-light py-1 ps-0" href="/courses_testing">Testing
</a></li>
</ul>
</div>
<div class="col-12 col-sm-6 col-md-3">
<div class="h5"><span class="translation_missing" title="translation missing: en.layouts.footer_content.popular_courses_for_beginners">Popular Courses For Beginners</span></div>
<ul class="list-unstyled">
<li>
<a class="nav-link link-light py-1 ps-0" href="/programs/frontend">Frontend Developer</a>
</li>
</ul>
</div>
<div class="col-12 col-sm-6 col-md-3">
<div class="h5"><span class="translation_missing" title="translation missing: en.layouts.footer_content.popular_courses_for_advanced">Popular Courses For Advanced</span></div>
<ul class="list-unstyled">
<li>
<a class="nav-link link-light py-1 ps-0" href="/programs/web-development-free">Fundamentals of Web Development</a>
</li>
<li>
<a class="nav-link link-light py-1 ps-0" href="/programs/js-react-development">React</a>
</li>
<li>
<a class="nav-link link-light py-1 ps-0" href="/programs/css-animation">CSS Animation</a>
</li>
<li>
<a class="nav-link link-light py-1 ps-0" href="/programs/http-api">HTTP API</a>
</li>
<li>
<a class="nav-link link-light py-1 ps-0" href="/programs/layout-designer-positioning">Position CSS</a>
</li>
<li>
<a class="nav-link link-light py-1 ps-0" href="/programs/cli-basics">Command line basics</a>
</li>
<li>
<a class="nav-link link-light py-1 ps-0" href="/programs/git-basics-free">Git fundamentals</a>
</li>
</ul>
</div>
</div>
<hr>
<div class="row">
<div class="col-12 col-sm-4 col-md-2">
<div class="fs-4">
<ul class="list-unstyled d-flex">
<li class="me-3">
<a aria-label="Facebook" target="_blank" class="link-light" rel="noopener noreferrer nofollow" href="https://www.facebook.com/hexlethq"><span class="bi bi-facebook"></span>
</a></li>
<li class="me-3">
<a aria-label="Instagram" target="_blank" class="link-light" rel="noopener noreferrer nofollow" href="https://www.instagram.com/hello_hexlet/"><span class="bi bi-instagram"></span>
</a></li>
<li>
<a aria-label="Twitter" target="_blank" class="link-light" rel="noopener noreferrer nofollow" href="https://twitter.com/Hexlet_IO"><span class="bi bi-twitter-x"></span>
</a></li>
</ul>
</div>
<div class="mb-2 d-flex flex-column">
<a class="link-light text-decoration-none" rel="nofollow" href="mailto:support@hexlet.io">support@hexlet.io</a>
<a class="link-light text-decoration-none py-2" target="_blank" href="https://t.me/hexlet_help_bot">t.me/hexlet_help_bot</a>
</div>
<ul class="list-unstyled d-flex">
<li class="me-3">
<span class="link-light text-decoration-none opacity-50 x-font-size-18 opacity-100 external-link" rel="nofollow" data-href="https://hexlet.io/locale/switch?new_locale=en" data-target="_self" role="button"><span class="my-auto">EN</span>
</span></li>
<li class="me-3">
<span class="link-light text-decoration-none opacity-50 x-font-size-18 external-link" rel="nofollow" data-href="https://ru.hexlet.io/locale/switch?new_locale=ru" data-target="_self" role="button"><span class="my-auto">RU</span>
</span></li>
<li class="me-3">
<span class="link-light text-decoration-none opacity-50 x-font-size-18 external-link" rel="nofollow" data-href="https://kz.hexlet.io/locale/switch?new_locale=kz" data-target="_self" role="button"><span class="my-auto">KZ</span>
</span></li>
</ul>
</div>
<div class="col-12 col-sm-4 col-md-3">
<ul class="list-unstyled fs-4">
<li class="mb-3">
<a class="link-light text-decoration-none" href="tel:%2B7%20717%20272%2076%2070">+7 717 272 76 70</a>
<span class="d-block opacity-50 small">free call</span>
</li>
</ul>
</div>
<div class="col-12 col-sm-4 col-md-3">
<ul class="list-unstyled small">
<li>
<a class="nav-link link-light py-1 ps-0" href="/pages/legal">Legal</a>
</li>
<li>
<a class="nav-link link-light py-1 ps-0" href="/pages/offer"><span class="translation_missing" title="translation missing: en.layouts.footer_content.offer">Offer</span></a>
</li>
<li>
<a class="nav-link link-light py-1 ps-0" href="/pages/contacts"><span class="translation_missing" title="translation missing: en.layouts.footer_content.contacts">Contacts</span></a>
</li>
</ul>
</div>
<div class="col-12 col-sm-12 col-md-4 small">
<div class="mb-2">
<div>TOO "Hexlet"</div>
<div>The Republic of Kazakhstan, Almaty</div>
<div>Auezova St., 14A</div>
<div>BIN 230340043714
</div>
</div>
</div>
</div>
</footer>
<div id="root-assistant-offcanvas"></div>
<script src="/vite/assets/assistant-CIOaBlj-.js" crossorigin="anonymous" type="module"></script><link rel="modulepreload" href="/vite/assets/chunk-DsPFFUou.js" as="script" crossorigin="anonymous">
<link rel="modulepreload" href="/vite/assets/init-0bhwJkNI.js" as="script" crossorigin="anonymous">
<link rel="modulepreload" href="/vite/assets/ErrorFallbackBlock-V3hfk_CP.js" as="script" crossorigin="anonymous">
<link rel="modulepreload" href="/vite/assets/MarkdownBlock-DejNWqwz.js" as="script" crossorigin="anonymous">
<link rel="modulepreload" href="/vite/assets/gon-B-jV56Ol.js" as="script" crossorigin="anonymous">
<link rel="modulepreload" href="/vite/assets/mantine-DOJkeu70.js" as="script" crossorigin="anonymous">
<link rel="modulepreload" href="/vite/assets/shiki-DZwEN4Zo.js" as="script" crossorigin="anonymous">
<link rel="modulepreload" href="/vite/assets/utils-ClTF9s_T.js" as="script" crossorigin="anonymous">
<link rel="modulepreload" href="/vite/assets/routes-mvvEXZQ8.js" as="script" crossorigin="anonymous">
<link rel="modulepreload" href="/vite/assets/lib-CJocDKTE.js" as="script" crossorigin="anonymous">
<link rel="modulepreload" href="/vite/assets/Box-DH3_MBnL.js" as="script" crossorigin="anonymous">
<link rel="modulepreload" href="/vite/assets/notifications.store-Cj65YiRw.js" as="script" crossorigin="anonymous">
<link rel="modulepreload" href="/vite/assets/useIsomorphicEffect-Csl7vw8x.js" as="script" crossorigin="anonymous">
<link rel="modulepreload" href="/vite/assets/lib-DeAQqnBE.js" as="script" crossorigin="anonymous">
<link rel="modulepreload" href="/vite/assets/axios-CN66HKVH.js" as="script" crossorigin="anonymous">
<link rel="modulepreload" href="/vite/assets/classnames-DQgTDFJJ.js" as="script" crossorigin="anonymous">
<link rel="modulepreload" href="/vite/assets/dayjs.min-Bfba02I7.js" as="script" crossorigin="anonymous">
<link rel="modulepreload" href="/vite/assets/debounce-BcxwEZ7X.js" as="script" crossorigin="anonymous">
<link rel="modulepreload" href="/vite/assets/prop-types-DGBR76ns.js" as="script" crossorigin="anonymous">
<link rel="modulepreload" href="/vite/assets/client-CYyKzrjQ.js" as="script" crossorigin="anonymous">
<link rel="modulepreload" href="/vite/assets/react-dom-SJZekO2j.js" as="script" crossorigin="anonymous">
<link rel="modulepreload" href="/vite/assets/useTranslation-bo78L81P.js" as="script" crossorigin="anonymous">
<link rel="modulepreload" href="/vite/assets/compiler-runtime-BhqaZ6vG.js" as="script" crossorigin="anonymous">
<link rel="modulepreload" href="/vite/assets/jsx-runtime-DlXMvSuQ.js" as="script" crossorigin="anonymous">
<link rel="modulepreload" href="/vite/assets/react-CFtMU8gd.js" as="script" crossorigin="anonymous">
<script defer src="https://static.cloudflareinsights.com/beacon.min.js/vcd15cbe7772f49c399c6a5babf22c1241717689176015" integrity="sha512-ZpsOmlRQV6y907TI0dKBHq9Md29nnaEIPlkf84rnaERnq6zvWvPUqr2ft8M1aS28oN72PdrCzSjY4U6VaAw1EQ==" data-cf-beacon='{"version":"2024.11.0","token":"d11015b65d11429ea6b4a2ef37dd7e0b","server_timing":{"name":{"cfCacheStatus":true,"cfEdge":true,"cfExtPri":true,"cfL4":true,"cfOrigin":true,"cfSpeedBrain":true},"location_startswith":null}}' crossorigin="anonymous"></script>
</body>
</html>