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krahets
2026-03-29 05:07:03 +08:00
parent 9e8c0cb36c
commit 9466700256
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ru/chapter_tree/array_representation_of_tree/index.html
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@@ -35,18 +35,23 @@
<link rel="icon" href="../../assets/images/favicon.png">
<meta name="generator" content="mkdocs-1.6.1, mkdocs-material-9.7.1">
<meta name="generator" content="zensical-0.0.29">
<title>7.3 Представление дерева массивом - Hello Algo</title>
<title>7.3 Представление двоичного дерева массивом - Hello Algo</title>
<link rel="stylesheet" href="../../assets/stylesheets/main.484c7ddc.min.css">
<link rel="stylesheet" href="../../assets/stylesheets/palette.ab4e12ef.min.css">
<link rel="stylesheet" href="../../assets/stylesheets/modern/main.6f2fbb28.min.css">
<link rel="stylesheet" href="../../assets/stylesheets/modern/palette.dfe2e883.min.css">
@@ -60,29 +65,20 @@
<link rel="preconnect" href="https://fonts.gstatic.com" crossorigin>
<link rel="stylesheet" href="https://fonts.googleapis.com/css?family=Noto+Sans:300,300i,400,400i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
<link rel="stylesheet" href="https://fonts.googleapis.com/css?family=Noto+Sans:300,300i,400,400i,500,500i,700,700i%7CJetBrains+Mono:400,400i,700,700i&display=fallback">
<style>:root{--md-text-font:"Noto Sans";--md-code-font:"JetBrains Mono"}</style>
<link rel="stylesheet" href="../../stylesheets/extra.css">
<script>__md_scope=new URL("../..",location),__md_hash=e=>[...e].reduce(((e,_)=>(e<<5)-e+_.charCodeAt(0)),0),__md_get=(e,_=localStorage,t=__md_scope)=>JSON.parse(_.getItem(t.pathname+"."+e)),__md_set=(e,_,t=localStorage,a=__md_scope)=>{try{t.setItem(a.pathname+"."+e,JSON.stringify(_))}catch(e){}}</script>
<script>__md_scope=new URL("../..",location),__md_hash=e=>[...e].reduce(((e,t)=>(e<<5)-e+t.charCodeAt(0)),0),__md_get=(e,t=localStorage,a=__md_scope)=>JSON.parse(t.getItem(("__palette"===e?"/":a.pathname)+"."+e)),__md_set=(e,t,a=localStorage,_=__md_scope)=>{try{a.setItem(("__palette"===e?"/":_.pathname)+"."+e,JSON.stringify(t))}catch(e){}},document.documentElement.setAttribute("data-platform",navigator.platform)</script>
<link href="../../assets/stylesheets/glightbox.min.css" rel="stylesheet"/><style>
html.glightbox-open { overflow: initial; height: 100%; }
.gslide-title { margin-top: 0px; user-select: text; }
.gslide-desc { color: #666; user-select: text; }
.gslide-image img { background: white; }
.gscrollbar-fixer { padding-right: 15px; }
.gdesc-inner { font-size: 0.75rem; }
body[data-md-color-scheme="slate"] .gdesc-inner { background: var(--md-default-bg-color);}
body[data-md-color-scheme="slate"] .gslide-title { color: var(--md-default-fg-color);}
body[data-md-color-scheme="slate"] .gslide-desc { color: var(--md-default-fg-color);}</style> <script src="../../assets/javascripts/glightbox.min.js"></script></head>
</head>
@@ -97,7 +93,7 @@
<input class="md-toggle" data-md-toggle="drawer" type="checkbox" id="__drawer" autocomplete="off">
<input class="md-toggle" data-md-toggle="search" type="checkbox" id="__search" autocomplete="off">
<label class="md-overlay" for="__drawer"></label>
<label class="md-overlay" for="__drawer" aria-label="Навигация"></label>
<div data-md-component="skip">
@@ -137,12 +133,12 @@
<nav class="md-header__inner md-grid" aria-label="Верхний колонтитул">
<a href="../.." title="Hello Algo" class="md-header__button md-logo" aria-label="Hello Algo" data-md-component="logo">
<img src="../../assets/images/logo.svg" alt="logo">
<img src="../../assets/images/logo.svg" alt="Hello Algo">
</a>
<label class="md-header__button md-icon" for="__drawer">
<label class="md-header__button md-icon" for="__drawer" aria-label="Навигация">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 6h18v2H3zm0 5h18v2H3zm0 5h18v2H3z"/></svg>
<svg xmlns="http://www.w3.org/2000/svg" fill="none" stroke="currentColor" stroke-linecap="round" stroke-linejoin="round" stroke-width="2" class="lucide lucide-menu" viewBox="0 0 24 24"><path d="M4 5h16M4 12h16M4 19h16"/></svg>
</label>
<div class="md-header__title" data-md-component="header-title">
<div class="md-header__ellipsis">
@@ -154,7 +150,7 @@
<div class="md-header__topic" data-md-component="header-topic">
<span class="md-ellipsis">
7.3 Представление дерева массивом
7.3 &nbsp; Представление двоичного дерева массивом
</span>
</div>
@@ -167,7 +163,7 @@
<input class="md-option" data-md-color-media="" data-md-color-scheme="default" data-md-color-primary="white" data-md-color-accent="teal" aria-label="Темная тема" type="radio" name="__palette" id="__palette_0">
<input class="md-option" data-md-color-media="none" data-md-color-scheme="default" data-md-color-primary="white" data-md-color-accent="teal" aria-label="Темная тема" type="radio" name="__palette" id="__palette_0">
<label class="md-header__button md-icon" title="Темная тема" for="__palette_1" hidden>
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M7.5 2c-1.79 1.15-3 3.18-3 5.5s1.21 4.35 3.03 5.5C4.46 13 2 10.54 2 7.5A5.5 5.5 0 0 1 7.5 2m11.57 1.5 1.43 1.43L4.93 20.5 3.5 19.07zm-6.18 2.43L11.41 5 9.97 6l.42-1.7L9 3.24l1.75-.12.58-1.65L12 3.1l1.73.03-1.35 1.13zm-3.3 3.61-1.16-.73-1.12.78.34-1.32-1.09-.83 1.36-.09.45-1.29.51 1.27 1.36.03-1.05.87zM19 13.5a5.5 5.5 0 0 1-5.5 5.5c-1.22 0-2.35-.4-3.26-1.07l7.69-7.69c.67.91 1.07 2.04 1.07 3.26m-4.4 6.58 2.77-1.15-.24 3.35zm4.33-2.7 1.15-2.77 2.2 2.54zm1.15-4.96-1.14-2.78 3.34.24zM9.63 18.93l2.77 1.15-2.53 2.19z"/></svg>
@@ -177,7 +173,7 @@
<input class="md-option" data-md-color-media="" data-md-color-scheme="slate" data-md-color-primary="black" data-md-color-accent="teal" aria-label="Светлая тема" type="radio" name="__palette" id="__palette_1">
<input class="md-option" data-md-color-media="none" data-md-color-scheme="slate" data-md-color-primary="black" data-md-color-accent="teal" aria-label="Светлая тема" type="radio" name="__palette" id="__palette_1">
<label class="md-header__button md-icon" title="Светлая тема" for="__palette_0" hidden>
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M7.5 2c-1.79 1.15-3 3.18-3 5.5s1.21 4.35 3.03 5.5C4.46 13 2 10.54 2 7.5A5.5 5.5 0 0 1 7.5 2m11.57 1.5 1.43 1.43L4.93 20.5 3.5 19.07zm-6.18 2.43L11.41 5 9.97 6l.42-1.7L9 3.24l1.75-.12.58-1.65L12 3.1l1.73.03-1.35 1.13zm-3.3 3.61-1.16-.73-1.12.78.34-1.32-1.09-.83 1.36-.09.45-1.29.51 1.27 1.36.03-1.05.87zM19 13.5a5.5 5.5 0 0 1-5.5 5.5c-1.22 0-2.35-.4-3.26-1.07l7.69-7.69c.67.91 1.07 2.04 1.07 3.26m-4.4 6.58 2.77-1.15-.24 3.35zm4.33-2.7 1.15-2.77 2.2 2.54zm1.15-4.96-1.14-2.78 3.34.24zM9.63 18.93l2.77 1.15-2.53 2.19z"/></svg>
@@ -195,7 +191,7 @@
<div class="md-select">
<button class="md-header__button md-icon" aria-label="Выберите язык">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12.87 15.07-2.54-2.51.03-.03A17.5 17.5 0 0 0 14.07 6H17V4h-7V2H8v2H1v2h11.17C11.5 7.92 10.44 9.75 9 11.35 8.07 10.32 7.3 9.19 6.69 8h-2c.73 1.63 1.73 3.17 2.98 4.56l-5.09 5.02L4 19l5-5 3.11 3.11zM18.5 10h-2L12 22h2l1.12-3h4.75L21 22h2zm-2.62 7 1.62-4.33L19.12 17z"/></svg>
<svg xmlns="http://www.w3.org/2000/svg" fill="none" stroke="currentColor" stroke-linecap="round" stroke-linejoin="round" stroke-width="2" class="lucide lucide-languages" viewBox="0 0 24 24"><path d="m5 8 6 6M4 14l6-6 2-3M2 5h12M7 2h1M22 22l-5-10-5 10M14 18h6"/></svg>
</button>
<div class="md-select__inner">
<ul class="md-select__list">
@@ -238,64 +234,30 @@
<label class="md-header__button md-icon" for="__search">
<label class="md-header__button md-icon" for="__search" aria-label="Поиск">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M9.5 3A6.5 6.5 0 0 1 16 9.5c0 1.61-.59 3.09-1.56 4.23l.27.27h.79l5 5-1.5 1.5-5-5v-.79l-.27-.27A6.52 6.52 0 0 1 9.5 16 6.5 6.5 0 0 1 3 9.5 6.5 6.5 0 0 1 9.5 3m0 2C7 5 5 7 5 9.5S7 14 9.5 14 14 12 14 9.5 12 5 9.5 5"/></svg>
<svg xmlns="http://www.w3.org/2000/svg" fill="none" stroke="currentColor" stroke-linecap="round" stroke-linejoin="round" stroke-width="2" class="lucide lucide-search" viewBox="0 0 24 24"><path d="m21 21-4.34-4.34"/><circle cx="11" cy="11" r="8"/></svg>
</label>
<div class="md-search" data-md-component="search" role="dialog">
<label class="md-search__overlay" for="__search"></label>
<div class="md-search__inner" role="search">
<form class="md-search__form" name="search">
<input type="text" class="md-search__input" name="query" aria-label="Поиск" placeholder="Поиск" autocapitalize="off" autocorrect="off" autocomplete="off" spellcheck="false" data-md-component="search-query" required>
<label class="md-search__icon md-icon" for="__search">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M9.5 3A6.5 6.5 0 0 1 16 9.5c0 1.61-.59 3.09-1.56 4.23l.27.27h.79l5 5-1.5 1.5-5-5v-.79l-.27-.27A6.52 6.52 0 0 1 9.5 16 6.5 6.5 0 0 1 3 9.5 6.5 6.5 0 0 1 9.5 3m0 2C7 5 5 7 5 9.5S7 14 9.5 14 14 12 14 9.5 12 5 9.5 5"/></svg>
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M20 11v2H8l5.5 5.5-1.42 1.42L4.16 12l7.92-7.92L13.5 5.5 8 11z"/></svg>
</label>
<nav class="md-search__options" aria-label="Поиск">
<a href="javascript:void(0)" class="md-search__icon md-icon" title="Поделиться" aria-label="Поделиться" data-clipboard data-clipboard-text="" data-md-component="search-share" tabindex="-1">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 16.08c-.76 0-1.44.3-1.96.77L8.91 12.7c.05-.23.09-.46.09-.7s-.04-.47-.09-.7l7.05-4.11c.54.5 1.25.81 2.04.81a3 3 0 0 0 3-3 3 3 0 0 0-3-3 3 3 0 0 0-3 3c0 .24.04.47.09.7L8.04 9.81C7.5 9.31 6.79 9 6 9a3 3 0 0 0-3 3 3 3 0 0 0 3 3c.79 0 1.5-.31 2.04-.81l7.12 4.15c-.05.21-.08.43-.08.66 0 1.61 1.31 2.91 2.92 2.91s2.92-1.3 2.92-2.91A2.92 2.92 0 0 0 18 16.08"/></svg>
</a>
<button type="reset" class="md-search__icon md-icon" title="Очистить" aria-label="Очистить" tabindex="-1">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 6.41 17.59 5 12 10.59 6.41 5 5 6.41 10.59 12 5 17.59 6.41 19 12 13.41 17.59 19 19 17.59 13.41 12z"/></svg>
</button>
</nav>
<div class="md-search__suggest" data-md-component="search-suggest"></div>
</form>
<div class="md-search__output">
<div class="md-search__scrollwrap" tabindex="0" data-md-scrollfix>
<div class="md-search-result" data-md-component="search-result">
<div class="md-search-result__meta">
Инициализация поиска
</div>
<ol class="md-search-result__list" role="presentation"></ol>
</div>
</div>
</div>
</div>
<div class="md-search" data-md-component="search" role="dialog" aria-label="Поиск">
<button type="button" class="md-search__button">
Поиск
</button>
</div>
<div class="md-header__source">
<div class="md-header__source">
<a href="https://github.com/krahets/hello-algo" title="Перейти к репозиторию" class="md-source" data-md-component="source">
<div class="md-source__icon md-icon">
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</div>
<div class="md-source__repository">
krahets/hello-algo
</div>
</a>
</div>
</div>
</nav>
</header>
@@ -323,7 +285,7 @@
<label class="md-nav__title" for="__drawer">
<a href="../.." title="Hello Algo" class="md-nav__button md-logo" aria-label="Hello Algo" data-md-component="logo">
<img src="../../assets/images/logo.svg" alt="logo">
<img src="../../assets/images/logo.svg" alt="Hello Algo">
</a>
Hello Algo
@@ -333,7 +295,7 @@
<a href="https://github.com/krahets/hello-algo" title="Перейти к репозиторию" class="md-source" data-md-component="source">
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@@ -4416,14 +4380,14 @@
<h2 id="731">7.3.1 &nbsp; Представление идеального двоичного дерева<a class="headerlink" href="#731" title="Permanent link">&para;</a></h2>
<p>Сначала разберем простой случай. Если дана идеальная двоичная структура и все ее узлы хранятся в массиве в порядке обхода по уровням, то каждому узлу будет соответствовать единственный индекс массива.</p>
<p>Из свойств обхода по уровням можно вывести "формулу соответствия" между индексом родителя и индексами дочерних узлов: <strong>если индекс некоторого узла равен <span class="arithmatex">\(i\)</span> , то индекс его левого дочернего узла равен <span class="arithmatex">\(2i + 1\)</span> , а правого - <span class="arithmatex">\(2i + 2\)</span></strong> . На рисунке 7-12 показано соответствие между индексами разных узлов.</p>
<p><a class="glightbox" href="../array_representation_of_tree.assets/array_representation_binary_tree.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="Представление идеального двоичного дерева массивом" class="animation-figure" src="../array_representation_of_tree.assets/array_representation_binary_tree.png" /></a></p>
<p><img alt="Представление идеального двоичного дерева массивом" class="animation-figure" src="../array_representation_of_tree.assets/array_representation_binary_tree.png" /></p>
<p align="center"> Рисунок 7-12 &nbsp; Представление идеального двоичного дерева массивом </p>
<p><strong>Эта формула соответствия играет ту же роль, что и ссылки на узлы в связной структуре</strong> . Имея любой узел в массиве, мы можем по формуле получить доступ к его левому и правому дочерним узлам.</p>
<h2 id="732">7.3.2 &nbsp; Представление произвольного двоичного дерева<a class="headerlink" href="#732" title="Permanent link">&para;</a></h2>
<p>Идеальное двоичное дерево - лишь частный случай; в обычной двоичной структуре на промежуточных уровнях часто существует множество <code>None</code> . Поскольку последовательность обхода по уровням не содержит этих <code>None</code> , мы не можем по одной лишь этой последовательности определить их количество и расположение. <strong>Это означает, что одному и тому же обходу по уровням может соответствовать сразу несколько различных структур двоичного дерева</strong>.</p>
<p>Как показано на рисунке 7-13, для неполной двоичной структуры описанный выше способ представления массивом уже перестает работать.</p>
<p><a class="glightbox" href="../array_representation_of_tree.assets/array_representation_without_empty.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="Одной последовательности обхода по уровням соответствуют разные двоичные структуры" class="animation-figure" src="../array_representation_of_tree.assets/array_representation_without_empty.png" /></a></p>
<p><img alt="Одной последовательности обхода по уровням соответствуют разные двоичные структуры" class="animation-figure" src="../array_representation_of_tree.assets/array_representation_without_empty.png" /></p>
<p align="center"> Рисунок 7-13 &nbsp; Одной последовательности обхода по уровням соответствуют разные двоичные структуры </p>
<p>Чтобы решить эту проблему, <strong>мы можем явно записывать все <code>None</code> в последовательности обхода по уровням</strong> . Как показано на рисунке 7-14, после такой обработки последовательность обхода по уровням уже сможет однозначно задавать двоичное дерево. Пример кода приведен ниже:</p>
@@ -4509,12 +4473,12 @@
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<p><a class="glightbox" href="../array_representation_of_tree.assets/array_representation_with_empty.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="Представление произвольного двоичного дерева массивом" class="animation-figure" src="../array_representation_of_tree.assets/array_representation_with_empty.png" /></a></p>
<p><img alt="Представление произвольного двоичного дерева массивом" class="animation-figure" src="../array_representation_of_tree.assets/array_representation_with_empty.png" /></p>
<p align="center"> Рисунок 7-14 &nbsp; Представление произвольного двоичного дерева массивом </p>
<p>Стоит отметить, что <strong>полное двоичное дерево очень удобно представлять массивом</strong> . Если вспомнить определение полного двоичного дерева, то <code>None</code> появляются только на самом нижнем уровне и справа, <strong>а значит, все <code>None</code> обязательно находятся в конце последовательности обхода по уровням</strong>.</p>
<p>Это означает, что при представлении полного двоичного дерева массивом можно не хранить все <code>None</code> , что очень удобно. На рисунке 7-15 приведен пример.</p>
<p><a class="glightbox" href="../array_representation_of_tree.assets/array_representation_complete_binary_tree.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="Представление полного двоичного дерева массивом" class="animation-figure" src="../array_representation_of_tree.assets/array_representation_complete_binary_tree.png" /></a></p>
<p><img alt="Представление полного двоичного дерева массивом" class="animation-figure" src="../array_representation_of_tree.assets/array_representation_complete_binary_tree.png" /></p>
<p align="center"> Рисунок 7-15 &nbsp; Представление полного двоичного дерева массивом </p>
<p>Ниже приведен код реализации двоичного дерева, представленного массивом. Он включает следующие операции.</p>
@@ -5590,96 +5554,87 @@
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">array_binary_tree.rb</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="cm">=begin</span>
<a id="__codelineno-25-2" name="__codelineno-25-2" href="#__codelineno-25-2"></a><span class="cm">File: array_binary_tree.rb</span>
<a id="__codelineno-25-3" name="__codelineno-25-3" href="#__codelineno-25-3"></a><span class="cm">Created Time: 2024-04-17</span>
<a id="__codelineno-25-4" name="__codelineno-25-4" href="#__codelineno-25-4"></a><span class="cm">Author: Xuan Khoa Tu Nguyen (ngxktuzkai2000@gmail.com)</span>
<a id="__codelineno-25-5" name="__codelineno-25-5" href="#__codelineno-25-5"></a><span class="cm">=end</span>
<a id="__codelineno-25-6" name="__codelineno-25-6" href="#__codelineno-25-6"></a>
<a id="__codelineno-25-7" name="__codelineno-25-7" href="#__codelineno-25-7"></a><span class="n">require_relative</span><span class="w"> </span><span class="s1">&#39;../utils/tree_node&#39;</span>
<a id="__codelineno-25-8" name="__codelineno-25-8" href="#__codelineno-25-8"></a><span class="n">require_relative</span><span class="w"> </span><span class="s1">&#39;../utils/print_util&#39;</span>
<a id="__codelineno-25-9" name="__codelineno-25-9" href="#__codelineno-25-9"></a>
<a id="__codelineno-25-10" name="__codelineno-25-10" href="#__codelineno-25-10"></a><span class="c1"># ## Класс двоичного дерева в массивном представлении ###</span>
<a id="__codelineno-25-11" name="__codelineno-25-11" href="#__codelineno-25-11"></a><span class="k">class</span><span class="w"> </span><span class="nc">ArrayBinaryTree</span>
<a id="__codelineno-25-12" name="__codelineno-25-12" href="#__codelineno-25-12"></a><span class="w"> </span><span class="c1"># ## Конструктор ###</span>
<a id="__codelineno-25-13" name="__codelineno-25-13" href="#__codelineno-25-13"></a><span class="w"> </span><span class="k">def</span><span class="w"> </span><span class="nf">initialize</span><span class="p">(</span><span class="n">arr</span><span class="p">)</span>
<a id="__codelineno-25-14" name="__codelineno-25-14" href="#__codelineno-25-14"></a><span class="w"> </span><span class="vi">@tree</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">arr</span><span class="o">.</span><span class="n">to_a</span>
<a id="__codelineno-25-15" name="__codelineno-25-15" href="#__codelineno-25-15"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-25-16" name="__codelineno-25-16" href="#__codelineno-25-16"></a>
<a id="__codelineno-25-17" name="__codelineno-25-17" href="#__codelineno-25-17"></a><span class="w"> </span><span class="c1"># ## Вместимость списка ###</span>
<a id="__codelineno-25-18" name="__codelineno-25-18" href="#__codelineno-25-18"></a><span class="w"> </span><span class="k">def</span><span class="w"> </span><span class="nf">size</span>
<a id="__codelineno-25-19" name="__codelineno-25-19" href="#__codelineno-25-19"></a><span class="w"> </span><span class="vi">@tree</span><span class="o">.</span><span class="n">length</span>
<a id="__codelineno-25-20" name="__codelineno-25-20" href="#__codelineno-25-20"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-25-21" name="__codelineno-25-21" href="#__codelineno-25-21"></a>
<a id="__codelineno-25-22" name="__codelineno-25-22" href="#__codelineno-25-22"></a><span class="w"> </span><span class="c1"># ## Получить значение узла с индексом i ###</span>
<a id="__codelineno-25-23" name="__codelineno-25-23" href="#__codelineno-25-23"></a><span class="w"> </span><span class="k">def</span><span class="w"> </span><span class="nf">val</span><span class="p">(</span><span class="n">i</span><span class="p">)</span>
<a id="__codelineno-25-24" name="__codelineno-25-24" href="#__codelineno-25-24"></a><span class="w"> </span><span class="c1"># Если индекс выходит за границы, вернуть nil, обозначающий пустую ячейку</span>
<a id="__codelineno-25-25" name="__codelineno-25-25" href="#__codelineno-25-25"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">size</span>
<a id="__codelineno-25-26" name="__codelineno-25-26" href="#__codelineno-25-26"></a>
<a id="__codelineno-25-27" name="__codelineno-25-27" href="#__codelineno-25-27"></a><span class="w"> </span><span class="vi">@tree</span><span class="o">[</span><span class="n">i</span><span class="o">]</span>
<a id="__codelineno-25-28" name="__codelineno-25-28" href="#__codelineno-25-28"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-25-29" name="__codelineno-25-29" href="#__codelineno-25-29"></a>
<a id="__codelineno-25-30" name="__codelineno-25-30" href="#__codelineno-25-30"></a><span class="w"> </span><span class="c1"># ## Получить индекс левого дочернего узла узла с индексом i ###</span>
<a id="__codelineno-25-31" name="__codelineno-25-31" href="#__codelineno-25-31"></a><span class="w"> </span><span class="k">def</span><span class="w"> </span><span class="nf">left</span><span class="p">(</span><span class="n">i</span><span class="p">)</span>
<a id="__codelineno-25-32" name="__codelineno-25-32" href="#__codelineno-25-32"></a><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span>
<a id="__codelineno-25-33" name="__codelineno-25-33" href="#__codelineno-25-33"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-25-34" name="__codelineno-25-34" href="#__codelineno-25-34"></a>
<a id="__codelineno-25-35" name="__codelineno-25-35" href="#__codelineno-25-35"></a><span class="w"> </span><span class="c1"># ## Получить индекс правого дочернего узла узла с индексом i ###</span>
<a id="__codelineno-25-36" name="__codelineno-25-36" href="#__codelineno-25-36"></a><span class="w"> </span><span class="k">def</span><span class="w"> </span><span class="nf">right</span><span class="p">(</span><span class="n">i</span><span class="p">)</span>
<a id="__codelineno-25-37" name="__codelineno-25-37" href="#__codelineno-25-37"></a><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">2</span>
<a id="__codelineno-25-38" name="__codelineno-25-38" href="#__codelineno-25-38"></a><span class="w"> </span><span class="k">end</span>
<div class="highlight"><span class="filename">array_binary_tree.rb</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="c1">### Класс двоичного дерева в массивном представлении ###</span>
<a id="__codelineno-25-2" name="__codelineno-25-2" href="#__codelineno-25-2"></a><span class="k">class</span><span class="w"> </span><span class="nc">ArrayBinaryTree</span>
<a id="__codelineno-25-3" name="__codelineno-25-3" href="#__codelineno-25-3"></a><span class="w"> </span><span class="c1">### Конструктор ###</span>
<a id="__codelineno-25-4" name="__codelineno-25-4" href="#__codelineno-25-4"></a><span class="w"> </span><span class="k">def</span><span class="w"> </span><span class="nf">initialize</span><span class="p">(</span><span class="n">arr</span><span class="p">)</span>
<a id="__codelineno-25-5" name="__codelineno-25-5" href="#__codelineno-25-5"></a><span class="w"> </span><span class="vi">@tree</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">arr</span><span class="o">.</span><span class="n">to_a</span>
<a id="__codelineno-25-6" name="__codelineno-25-6" href="#__codelineno-25-6"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-25-7" name="__codelineno-25-7" href="#__codelineno-25-7"></a>
<a id="__codelineno-25-8" name="__codelineno-25-8" href="#__codelineno-25-8"></a><span class="w"> </span><span class="c1">### Вместимость списка ###</span>
<a id="__codelineno-25-9" name="__codelineno-25-9" href="#__codelineno-25-9"></a><span class="w"> </span><span class="k">def</span><span class="w"> </span><span class="nf">size</span>
<a id="__codelineno-25-10" name="__codelineno-25-10" href="#__codelineno-25-10"></a><span class="w"> </span><span class="vi">@tree</span><span class="o">.</span><span class="n">length</span>
<a id="__codelineno-25-11" name="__codelineno-25-11" href="#__codelineno-25-11"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-25-12" name="__codelineno-25-12" href="#__codelineno-25-12"></a>
<a id="__codelineno-25-13" name="__codelineno-25-13" href="#__codelineno-25-13"></a><span class="w"> </span><span class="c1">### Получить значение узла с индексом i ###</span>
<a id="__codelineno-25-14" name="__codelineno-25-14" href="#__codelineno-25-14"></a><span class="w"> </span><span class="k">def</span><span class="w"> </span><span class="nf">val</span><span class="p">(</span><span class="n">i</span><span class="p">)</span>
<a id="__codelineno-25-15" name="__codelineno-25-15" href="#__codelineno-25-15"></a><span class="w"> </span><span class="c1"># Если индекс выходит за границы, вернуть nil, обозначающий пустую ячейку</span>
<a id="__codelineno-25-16" name="__codelineno-25-16" href="#__codelineno-25-16"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">size</span>
<a id="__codelineno-25-17" name="__codelineno-25-17" href="#__codelineno-25-17"></a>
<a id="__codelineno-25-18" name="__codelineno-25-18" href="#__codelineno-25-18"></a><span class="w"> </span><span class="vi">@tree</span><span class="o">[</span><span class="n">i</span><span class="o">]</span>
<a id="__codelineno-25-19" name="__codelineno-25-19" href="#__codelineno-25-19"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-25-20" name="__codelineno-25-20" href="#__codelineno-25-20"></a>
<a id="__codelineno-25-21" name="__codelineno-25-21" href="#__codelineno-25-21"></a><span class="w"> </span><span class="c1">### Получить индекс левого дочернего узла узла с индексом i ###</span>
<a id="__codelineno-25-22" name="__codelineno-25-22" href="#__codelineno-25-22"></a><span class="w"> </span><span class="k">def</span><span class="w"> </span><span class="nf">left</span><span class="p">(</span><span class="n">i</span><span class="p">)</span>
<a id="__codelineno-25-23" name="__codelineno-25-23" href="#__codelineno-25-23"></a><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span>
<a id="__codelineno-25-24" name="__codelineno-25-24" href="#__codelineno-25-24"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-25-25" name="__codelineno-25-25" href="#__codelineno-25-25"></a>
<a id="__codelineno-25-26" name="__codelineno-25-26" href="#__codelineno-25-26"></a><span class="w"> </span><span class="c1">### Получить индекс правого дочернего узла узла с индексом i ###</span>
<a id="__codelineno-25-27" name="__codelineno-25-27" href="#__codelineno-25-27"></a><span class="w"> </span><span class="k">def</span><span class="w"> </span><span class="nf">right</span><span class="p">(</span><span class="n">i</span><span class="p">)</span>
<a id="__codelineno-25-28" name="__codelineno-25-28" href="#__codelineno-25-28"></a><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">2</span>
<a id="__codelineno-25-29" name="__codelineno-25-29" href="#__codelineno-25-29"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-25-30" name="__codelineno-25-30" href="#__codelineno-25-30"></a>
<a id="__codelineno-25-31" name="__codelineno-25-31" href="#__codelineno-25-31"></a><span class="w"> </span><span class="c1">### Получить индекс родительского узла узла с индексом i ###</span>
<a id="__codelineno-25-32" name="__codelineno-25-32" href="#__codelineno-25-32"></a><span class="w"> </span><span class="k">def</span><span class="w"> </span><span class="nf">parent</span><span class="p">(</span><span class="n">i</span><span class="p">)</span>
<a id="__codelineno-25-33" name="__codelineno-25-33" href="#__codelineno-25-33"></a><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span>
<a id="__codelineno-25-34" name="__codelineno-25-34" href="#__codelineno-25-34"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-25-35" name="__codelineno-25-35" href="#__codelineno-25-35"></a>
<a id="__codelineno-25-36" name="__codelineno-25-36" href="#__codelineno-25-36"></a><span class="w"> </span><span class="c1">### Обход в ширину ###</span>
<a id="__codelineno-25-37" name="__codelineno-25-37" href="#__codelineno-25-37"></a><span class="w"> </span><span class="k">def</span><span class="w"> </span><span class="nf">level_order</span>
<a id="__codelineno-25-38" name="__codelineno-25-38" href="#__codelineno-25-38"></a><span class="w"> </span><span class="vi">@res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[]</span>
<a id="__codelineno-25-39" name="__codelineno-25-39" href="#__codelineno-25-39"></a>
<a id="__codelineno-25-40" name="__codelineno-25-40" href="#__codelineno-25-40"></a><span class="w"> </span><span class="c1"># ## Получить индекс родительского узла узла с индексом i ###</span>
<a id="__codelineno-25-41" name="__codelineno-25-41" href="#__codelineno-25-41"></a><span class="w"> </span><span class="k">def</span><span class="w"> </span><span class="nf">parent</span><span class="p">(</span><span class="n">i</span><span class="p">)</span>
<a id="__codelineno-25-42" name="__codelineno-25-42" href="#__codelineno-25-42"></a><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span>
<a id="__codelineno-25-43" name="__codelineno-25-43" href="#__codelineno-25-43"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-25-40" name="__codelineno-25-40" href="#__codelineno-25-40"></a><span class="w"> </span><span class="c1"># Непосредственно обходить массив</span>
<a id="__codelineno-25-41" name="__codelineno-25-41" href="#__codelineno-25-41"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">...</span><span class="n">size</span>
<a id="__codelineno-25-42" name="__codelineno-25-42" href="#__codelineno-25-42"></a><span class="w"> </span><span class="vi">@res</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="k">unless</span><span class="w"> </span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">)</span><span class="o">.</span><span class="n">nil?</span>
<a id="__codelineno-25-43" name="__codelineno-25-43" href="#__codelineno-25-43"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-25-44" name="__codelineno-25-44" href="#__codelineno-25-44"></a>
<a id="__codelineno-25-45" name="__codelineno-25-45" href="#__codelineno-25-45"></a><span class="w"> </span><span class="c1"># ## Обход в ширину ###</span>
<a id="__codelineno-25-46" name="__codelineno-25-46" href="#__codelineno-25-46"></a><span class="w"> </span><span class="k">def</span><span class="w"> </span><span class="nf">level_order</span>
<a id="__codelineno-25-47" name="__codelineno-25-47" href="#__codelineno-25-47"></a><span class="w"> </span><span class="vi">@res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[]</span>
<a id="__codelineno-25-48" name="__codelineno-25-48" href="#__codelineno-25-48"></a>
<a id="__codelineno-25-49" name="__codelineno-25-49" href="#__codelineno-25-49"></a><span class="w"> </span><span class="c1"># Непосредственно обходить массив</span>
<a id="__codelineno-25-50" name="__codelineno-25-50" href="#__codelineno-25-50"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">...</span><span class="n">size</span>
<a id="__codelineno-25-51" name="__codelineno-25-51" href="#__codelineno-25-51"></a><span class="w"> </span><span class="vi">@res</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="k">unless</span><span class="w"> </span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">)</span><span class="o">.</span><span class="n">nil?</span>
<a id="__codelineno-25-52" name="__codelineno-25-52" href="#__codelineno-25-52"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-25-53" name="__codelineno-25-53" href="#__codelineno-25-53"></a>
<a id="__codelineno-25-54" name="__codelineno-25-54" href="#__codelineno-25-54"></a><span class="w"> </span><span class="vi">@res</span>
<a id="__codelineno-25-55" name="__codelineno-25-55" href="#__codelineno-25-55"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-25-56" name="__codelineno-25-56" href="#__codelineno-25-56"></a>
<a id="__codelineno-25-57" name="__codelineno-25-57" href="#__codelineno-25-57"></a><span class="w"> </span><span class="c1"># ## Обход в глубину ###</span>
<a id="__codelineno-25-58" name="__codelineno-25-58" href="#__codelineno-25-58"></a><span class="w"> </span><span class="k">def</span><span class="w"> </span><span class="nf">dfs</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">order</span><span class="p">)</span>
<a id="__codelineno-25-59" name="__codelineno-25-59" href="#__codelineno-25-59"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">)</span><span class="o">.</span><span class="n">nil?</span>
<a id="__codelineno-25-60" name="__codelineno-25-60" href="#__codelineno-25-60"></a><span class="w"> </span><span class="c1"># Предварительный обход</span>
<a id="__codelineno-25-61" name="__codelineno-25-61" href="#__codelineno-25-61"></a><span class="w"> </span><span class="vi">@res</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">order</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="ss">:pre</span>
<a id="__codelineno-25-62" name="__codelineno-25-62" href="#__codelineno-25-62"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">left</span><span class="p">(</span><span class="n">i</span><span class="p">),</span><span class="w"> </span><span class="n">order</span><span class="p">)</span>
<a id="__codelineno-25-63" name="__codelineno-25-63" href="#__codelineno-25-63"></a><span class="w"> </span><span class="c1"># Симметричный обход</span>
<a id="__codelineno-25-64" name="__codelineno-25-64" href="#__codelineno-25-64"></a><span class="w"> </span><span class="vi">@res</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">order</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="ss">:in</span>
<a id="__codelineno-25-65" name="__codelineno-25-65" href="#__codelineno-25-65"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">right</span><span class="p">(</span><span class="n">i</span><span class="p">),</span><span class="w"> </span><span class="n">order</span><span class="p">)</span>
<a id="__codelineno-25-66" name="__codelineno-25-66" href="#__codelineno-25-66"></a><span class="w"> </span><span class="c1"># Обратный обход</span>
<a id="__codelineno-25-67" name="__codelineno-25-67" href="#__codelineno-25-67"></a><span class="w"> </span><span class="vi">@res</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">order</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="ss">:post</span>
<a id="__codelineno-25-68" name="__codelineno-25-68" href="#__codelineno-25-68"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-25-69" name="__codelineno-25-69" href="#__codelineno-25-69"></a>
<a id="__codelineno-25-70" name="__codelineno-25-70" href="#__codelineno-25-70"></a><span class="w"> </span><span class="c1"># ## Предварительный обход ###</span>
<a id="__codelineno-25-71" name="__codelineno-25-71" href="#__codelineno-25-71"></a><span class="w"> </span><span class="k">def</span><span class="w"> </span><span class="nf">pre_order</span>
<a id="__codelineno-25-72" name="__codelineno-25-72" href="#__codelineno-25-72"></a><span class="w"> </span><span class="vi">@res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[]</span>
<a id="__codelineno-25-73" name="__codelineno-25-73" href="#__codelineno-25-73"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="ss">:pre</span><span class="p">)</span>
<a id="__codelineno-25-74" name="__codelineno-25-74" href="#__codelineno-25-74"></a><span class="w"> </span><span class="vi">@res</span>
<a id="__codelineno-25-75" name="__codelineno-25-75" href="#__codelineno-25-75"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-25-76" name="__codelineno-25-76" href="#__codelineno-25-76"></a>
<a id="__codelineno-25-77" name="__codelineno-25-77" href="#__codelineno-25-77"></a><span class="w"> </span><span class="c1"># ## Симметричный обход ###</span>
<a id="__codelineno-25-78" name="__codelineno-25-78" href="#__codelineno-25-78"></a><span class="w"> </span><span class="k">def</span><span class="w"> </span><span class="nf">in_order</span>
<a id="__codelineno-25-79" name="__codelineno-25-79" href="#__codelineno-25-79"></a><span class="w"> </span><span class="vi">@res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[]</span>
<a id="__codelineno-25-80" name="__codelineno-25-80" href="#__codelineno-25-80"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="ss">:in</span><span class="p">)</span>
<a id="__codelineno-25-81" name="__codelineno-25-81" href="#__codelineno-25-81"></a><span class="w"> </span><span class="vi">@res</span>
<a id="__codelineno-25-82" name="__codelineno-25-82" href="#__codelineno-25-82"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-25-83" name="__codelineno-25-83" href="#__codelineno-25-83"></a>
<a id="__codelineno-25-84" name="__codelineno-25-84" href="#__codelineno-25-84"></a><span class="w"> </span><span class="c1"># ## Обратный обход ###</span>
<a id="__codelineno-25-85" name="__codelineno-25-85" href="#__codelineno-25-85"></a><span class="w"> </span><span class="k">def</span><span class="w"> </span><span class="nf">post_order</span>
<a id="__codelineno-25-86" name="__codelineno-25-86" href="#__codelineno-25-86"></a><span class="w"> </span><span class="vi">@res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[]</span>
<a id="__codelineno-25-87" name="__codelineno-25-87" href="#__codelineno-25-87"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="ss">:post</span><span class="p">)</span>
<a id="__codelineno-25-88" name="__codelineno-25-88" href="#__codelineno-25-88"></a><span class="w"> </span><span class="vi">@res</span>
<a id="__codelineno-25-89" name="__codelineno-25-89" href="#__codelineno-25-89"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-25-90" name="__codelineno-25-90" href="#__codelineno-25-90"></a><span class="k">end</span>
<a id="__codelineno-25-45" name="__codelineno-25-45" href="#__codelineno-25-45"></a><span class="w"> </span><span class="vi">@res</span>
<a id="__codelineno-25-46" name="__codelineno-25-46" href="#__codelineno-25-46"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-25-47" name="__codelineno-25-47" href="#__codelineno-25-47"></a>
<a id="__codelineno-25-48" name="__codelineno-25-48" href="#__codelineno-25-48"></a><span class="w"> </span><span class="c1">### Обход в глубину ###</span>
<a id="__codelineno-25-49" name="__codelineno-25-49" href="#__codelineno-25-49"></a><span class="w"> </span><span class="k">def</span><span class="w"> </span><span class="nf">dfs</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">order</span><span class="p">)</span>
<a id="__codelineno-25-50" name="__codelineno-25-50" href="#__codelineno-25-50"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">)</span><span class="o">.</span><span class="n">nil?</span>
<a id="__codelineno-25-51" name="__codelineno-25-51" href="#__codelineno-25-51"></a><span class="w"> </span><span class="c1"># Предварительный обход</span>
<a id="__codelineno-25-52" name="__codelineno-25-52" href="#__codelineno-25-52"></a><span class="w"> </span><span class="vi">@res</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">order</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="ss">:pre</span>
<a id="__codelineno-25-53" name="__codelineno-25-53" href="#__codelineno-25-53"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">left</span><span class="p">(</span><span class="n">i</span><span class="p">),</span><span class="w"> </span><span class="n">order</span><span class="p">)</span>
<a id="__codelineno-25-54" name="__codelineno-25-54" href="#__codelineno-25-54"></a><span class="w"> </span><span class="c1"># Симметричный обход</span>
<a id="__codelineno-25-55" name="__codelineno-25-55" href="#__codelineno-25-55"></a><span class="w"> </span><span class="vi">@res</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">order</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="ss">:in</span>
<a id="__codelineno-25-56" name="__codelineno-25-56" href="#__codelineno-25-56"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">right</span><span class="p">(</span><span class="n">i</span><span class="p">),</span><span class="w"> </span><span class="n">order</span><span class="p">)</span>
<a id="__codelineno-25-57" name="__codelineno-25-57" href="#__codelineno-25-57"></a><span class="w"> </span><span class="c1"># Обратный обход</span>
<a id="__codelineno-25-58" name="__codelineno-25-58" href="#__codelineno-25-58"></a><span class="w"> </span><span class="vi">@res</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">order</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="ss">:post</span>
<a id="__codelineno-25-59" name="__codelineno-25-59" href="#__codelineno-25-59"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-25-60" name="__codelineno-25-60" href="#__codelineno-25-60"></a>
<a id="__codelineno-25-61" name="__codelineno-25-61" href="#__codelineno-25-61"></a><span class="w"> </span><span class="c1">### Предварительный обход ###</span>
<a id="__codelineno-25-62" name="__codelineno-25-62" href="#__codelineno-25-62"></a><span class="w"> </span><span class="k">def</span><span class="w"> </span><span class="nf">pre_order</span>
<a id="__codelineno-25-63" name="__codelineno-25-63" href="#__codelineno-25-63"></a><span class="w"> </span><span class="vi">@res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[]</span>
<a id="__codelineno-25-64" name="__codelineno-25-64" href="#__codelineno-25-64"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="ss">:pre</span><span class="p">)</span>
<a id="__codelineno-25-65" name="__codelineno-25-65" href="#__codelineno-25-65"></a><span class="w"> </span><span class="vi">@res</span>
<a id="__codelineno-25-66" name="__codelineno-25-66" href="#__codelineno-25-66"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-25-67" name="__codelineno-25-67" href="#__codelineno-25-67"></a>
<a id="__codelineno-25-68" name="__codelineno-25-68" href="#__codelineno-25-68"></a><span class="w"> </span><span class="c1">### Симметричный обход ###</span>
<a id="__codelineno-25-69" name="__codelineno-25-69" href="#__codelineno-25-69"></a><span class="w"> </span><span class="k">def</span><span class="w"> </span><span class="nf">in_order</span>
<a id="__codelineno-25-70" name="__codelineno-25-70" href="#__codelineno-25-70"></a><span class="w"> </span><span class="vi">@res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[]</span>
<a id="__codelineno-25-71" name="__codelineno-25-71" href="#__codelineno-25-71"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="ss">:in</span><span class="p">)</span>
<a id="__codelineno-25-72" name="__codelineno-25-72" href="#__codelineno-25-72"></a><span class="w"> </span><span class="vi">@res</span>
<a id="__codelineno-25-73" name="__codelineno-25-73" href="#__codelineno-25-73"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-25-74" name="__codelineno-25-74" href="#__codelineno-25-74"></a>
<a id="__codelineno-25-75" name="__codelineno-25-75" href="#__codelineno-25-75"></a><span class="w"> </span><span class="c1">### Обратный обход ###</span>
<a id="__codelineno-25-76" name="__codelineno-25-76" href="#__codelineno-25-76"></a><span class="w"> </span><span class="k">def</span><span class="w"> </span><span class="nf">post_order</span>
<a id="__codelineno-25-77" name="__codelineno-25-77" href="#__codelineno-25-77"></a><span class="w"> </span><span class="vi">@res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[]</span>
<a id="__codelineno-25-78" name="__codelineno-25-78" href="#__codelineno-25-78"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="ss">:post</span><span class="p">)</span>
<a id="__codelineno-25-79" name="__codelineno-25-79" href="#__codelineno-25-79"></a><span class="w"> </span><span class="vi">@res</span>
<a id="__codelineno-25-80" name="__codelineno-25-80" href="#__codelineno-25-80"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-25-81" name="__codelineno-25-81" href="#__codelineno-25-81"></a><span class="k">end</span>
</code></pre></div>
</div>
</div>
@@ -5729,7 +5684,7 @@ aria-label="Нижний колонтитул"
>
<div class="md-footer__button md-icon">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M20 11v2H8l5.5 5.5-1.42 1.42L4.16 12l7.92-7.92L13.5 5.5 8 11z"/></svg>
<svg xmlns="http://www.w3.org/2000/svg" fill="none" stroke="currentColor" stroke-linecap="round" stroke-linejoin="round" stroke-width="2" class="lucide lucide-arrow-left" viewBox="0 0 24 24"><path d="m12 19-7-7 7-7M19 12H5"/></svg>
</div>
<div class="md-footer__title">
<span class="md-footer__direction">
@@ -5761,7 +5716,7 @@ aria-label="Нижний колонтитул"
</div>
<div class="md-footer__button md-icon">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M4 11v2h12l-5.5 5.5 1.42 1.42L19.84 12l-7.92-7.92L10.5 5.5 16 11z"/></svg>
<svg xmlns="http://www.w3.org/2000/svg" fill="none" stroke="currentColor" stroke-linecap="round" stroke-linejoin="round" stroke-width="2" class="lucide lucide-arrow-right" viewBox="0 0 24 24"><path d="M5 12h14M12 5l7 7-7 7"/></svg>
</div>
</a>
@@ -5839,7 +5794,7 @@ aria-label="Нижний колонтитул"
<button type="button" class="md-top md-icon" data-md-component="top" hidden>
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M13 20h-2V8l-5.5 5.5-1.42-1.42L12 4.16l7.92 7.92-1.42 1.42L13 8z"/></svg>
<svg xmlns="http://www.w3.org/2000/svg" fill="none" stroke="currentColor" stroke-linecap="round" stroke-linejoin="round" stroke-width="2" class="lucide lucide-circle-arrow-up" viewBox="0 0 24 24"><circle cx="12" cy="12" r="10"/><path d="m16 12-4-4-4 4M12 16V8"/></svg>
К началу
</button>
@@ -5847,46 +5802,6 @@ aria-label="Нижний колонтитул"
<footer class="md-footer">
<nav class="md-footer__inner md-grid" aria-label="Нижний колонтитул" >
<a href="../binary_tree_traversal/" class="md-footer__link md-footer__link--prev" aria-label="Назад: 7.2 Обход двоичного дерева">
<div class="md-footer__button md-icon">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M20 11v2H8l5.5 5.5-1.42 1.42L4.16 12l7.92-7.92L13.5 5.5 8 11z"/></svg>
</div>
<div class="md-footer__title">
<span class="md-footer__direction">
Назад
</span>
<div class="md-ellipsis">
7.2 Обход двоичного дерева
</div>
</div>
</a>
<a href="../binary_search_tree/" class="md-footer__link md-footer__link--next" aria-label="Вперед: 7.4 Двоичное дерево поиска">
<div class="md-footer__title">
<span class="md-footer__direction">
Вперед
</span>
<div class="md-ellipsis">
7.4 Двоичное дерево поиска
</div>
</div>
<div class="md-footer__button md-icon">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M4 11v2h12l-5.5 5.5 1.42 1.42L19.84 12l-7.92-7.92L10.5 5.5 16 11z"/></svg>
</div>
</a>
</nav>
<div class="md-footer-meta md-typeset">
<div class="md-footer-meta__inner md-grid">
<div class="md-copyright">
@@ -5909,7 +5824,7 @@ aria-label="Нижний колонтитул"
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@@ -5920,7 +5835,7 @@ aria-label="Нижний колонтитул"
<a href="https://twitter.com/krahets" target="_blank" rel="noopener" title="twitter.com" class="md-social__link">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 448 512"><!--! Font Awesome Free 7.1.0 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2025 Fonticons, Inc.--><path d="M357.2 48h70.6L273.6 224.2 455 464H313L201.7 318.6 74.5 464H3.8l164.9-188.5L-5.2 48h145.6l100.5 132.9zm-24.8 373.8h39.1L119.1 88h-42z"/></svg>
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@@ -5931,7 +5846,7 @@ aria-label="Нижний колонтитул"
<a href="https://leetcode.cn/u/jyd/" target="_blank" rel="noopener" title="leetcode.cn" class="md-social__link">
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