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<title data-rh="true">Použití červeno-černých stromů | mf</title><meta data-rh="true" name="viewport" content="width=device-width,initial-scale=1"><meta data-rh="true" name="twitter:card" content="summary_large_image"><meta data-rh="true" property="og:url" content="https://blog.mfocko.xyz/ib002/rb-trees/applications/"><meta data-rh="true" name="docusaurus_locale" content="en"><meta data-rh="true" name="docsearch:language" content="en"><meta data-rh="true" name="docusaurus_version" content="current"><meta data-rh="true" name="docusaurus_tag" content="docs-ib002-current"><meta data-rh="true" name="docsearch:version" content="current"><meta data-rh="true" name="docsearch:docusaurus_tag" content="docs-ib002-current"><meta data-rh="true" property="og:title" content="Použití červeno-černých stromů | mf"><meta data-rh="true" name="description" content="Ukázka použití červeno-černých stromů v standardních knižnicích známých jazyků.
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3.6c-.38-.34-.96-.34-1.34 0l-8.36 7.53c-.34.3-.13.87.33.87H5v7c0 .55.45 1 1 1h3c.55 0 1-.45 1-1z" fill="currentColor"></path></svg></a></li><li itemscope="" itemprop="itemListElement" itemtype="https://schema.org/ListItem" class="breadcrumbs__item"><a class="breadcrumbs__link" itemprop="item" href="/ib002/category/red-black-trees/"><span itemprop="name">Red-Black Trees</span></a><meta itemprop="position" content="1"></li><li itemscope="" itemprop="itemListElement" itemtype="https://schema.org/ListItem" class="breadcrumbs__item breadcrumbs__item--active"><span class="breadcrumbs__link" itemprop="name">Použití červeno-černých stromů</span><meta itemprop="position" content="2"></li></ul></nav><div class="tocCollapsible_ETCw theme-doc-toc-mobile tocMobile_ITEo"><button type="button" class="clean-btn tocCollapsibleButton_TO0P">On this page</button></div><div class="theme-doc-markdown markdown"><header><h1>Použití červeno-černých stromů</h1></header><h2 class="anchor anchorWithStickyNavbar_LWe7" id="použití">Použití<a href="#použití" class="hash-link" aria-label="Direct link to Použití" title="Direct link to Použití"></a></h2><p>Červeno-černé stromy jsou celkem oblíbené pro implementaci ADT množiny nebo slovníku za předpokladu, že nad vkládanými klíči existuje uspořádání. Jazyky níže implementují dané datové struktury v 2 variantách a to:</p><ul><li>seřazené: používají na pozadí právě červeno-černý strom</li><li>neseřazené: používají na pozadí hašovací tabulku</li></ul><p>Pro srovnání, jak jsme si říkali na cvičení, červeno-černý strom má operace hledání, vkládání a mazání v časové složitosti <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="script">O</mi><mo stretchy="false">(</mo><mi>log</mi><mo></mo><mi>n</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">\mathcal{O}(\log n)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em"></span><span class="mord mathcal" style="margin-right:0.02778em">O</span><span class="mopen">(</span><span class="mop">lo<span style="margin-right:0.01389em">g</span></span><span class="mspace" style="margin-right:0.1667em"></span><span class="mord mathnormal">n</span><span class="mclose">)</span></span></span></span></span>. Na druhou stranu hašovací tabulka má ideálně konstantní časovou složitost, ale v nejhorším případě (detaily na posledním cvičení v semestru) je to bohužel <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="script">O</mi><mo stretchy="false">(</mo><mi>n</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">\mathcal{O}(n)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em"></span><span class="mord mathcal" style="margin-right:0.02778em">O</span><span class="mopen">(</span><span class="mord mathnormal">n</span><span class="mclose">)</span></span></span></span></span>.</p><p>Výše jsme si ukázali nějaké předpoklady nutné pro hašovací tabulku i červeno-černý strom. Co je tedy lepší?</p><ul><li>červeno-černý strom nám poskytuje <em>stabilní časovou složitost</em>, ale za cenu požadavku <em>uspořádání</em> nad prvky</li><li>hašovací tabulka nám poskytuje <em>pomyslnou perfektní časovou složitost</em></li></ul><h2 class="anchor anchorWithStickyNavbar_LWe7" id="různé-implementace">Různé implementace<a href="#různé-implementace" class="hash-link" aria-label="Direct link to Různé implementace" title="Direct link to Různé implementace"></a></h2><p>Pro ukázku použití červeno-černých stromů v implementacích standardních knihoven
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jsme vybrali několik jazyků.</p><p>Pokud Vás zajímají různé implementace, tak bychom doporučili „prohrabávat“ se přes ně v následujícím pořadí: <code>C# → Java → C++</code>. Důvod pro zvolené pořadí vychází z toho, že C# implementace je poměrně čitelná a obsahuje množství vysvětlujících komentářů. Implementace v Javě je stejně čitelná, ačkoli již s minimem komentářů, které se maximálně odkazují na CLRS. C++ implementace je „značně poznačená“ podtržítky ;)</p><h3 class="anchor anchorWithStickyNavbar_LWe7" id="c">C++<a href="#c" class="hash-link" aria-label="Direct link to C++" title="Direct link to C++"></a></h3><p>V C++ si můžeme vybrat mezi 2 různými implementacemi (<code>clang</code> nebo <code>gcc</code>).</p><h4 class="anchor anchorWithStickyNavbar_LWe7" id="clang">clang<a href="#clang" class="hash-link" aria-label="Direct link to clang" title="Direct link to clang"></a></h4><p>Hlavičkové soubory, které používáme při práci s množinou nebo slovníkem (zajímavé sekce jsou vytaženy):</p><ul><li><p><a href="https://github.com/llvm/llvm-project/blob/main/libcxx/include/map" target="_blank" rel="noopener noreferrer"><code>map</code></a></p><div class="language-cpp codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#000000;--prism-background-color:#ffffff"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-cpp codeBlock_bY9V thin-scrollbar"><code 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class="token plain"> </span><span class="token operator" style="color:rgb(0, 0, 0)">=</span><span class="token plain"> less</span><span class="token operator" style="color:rgb(0, 0, 0)"><</span><span class="token plain">_Key</span><span class="token operator" style="color:rgb(0, 0, 0)">></span><span class="token punctuation" style="color:rgb(4, 81, 165)">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> </span><span class="token keyword" style="color:rgb(0, 0, 255)">class</span><span class="token plain"> </span><span class="token class-name" style="color:rgb(38, 127, 153)">_Allocator</span><span class="token plain"> </span><span class="token operator" style="color:rgb(0, 0, 0)">=</span><span class="token plain"> allocator</span><span class="token operator" style="color:rgb(0, 0, 0)"><</span><span class="token plain">pair</span><span class="token operator" style="color:rgb(0, 0, 0)"><</span><span class="token keyword" style="color:rgb(0, 0, 255)">const</span><span class="token plain"> _Key</span><span class="token punctuation" style="color:rgb(4, 81, 165)">,</span><span class="token plain"> _Tp</span><span class="token operator" style="color:rgb(0, 0, 0)">></span><span class="token plain"> </span><span class="token operator" style="color:rgb(0, 0, 0)">></span><span class="token plain"> </span><span class="token operator" style="color:rgb(0, 0, 0)">></span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"></span><span class="token keyword" style="color:rgb(0, 0, 255)">class</span><span class="token plain"> </span><span class="token class-name" style="color:rgb(38, 127, 153)">_LIBCPP_TEMPLATE_VIS</span><span class="token plain"> map</span><br></span><span class="token-line" style="color:#000000"><span class="token plain"></span><span class="token punctuation" style="color:rgb(4, 81, 165)">{</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"></span><span class="token keyword" style="color:rgb(0, 0, 255)">public</span><span class="token operator" style="color:rgb(0, 0, 0)">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> </span><span class="token comment" style="color:rgb(0, 128, 0)">// types:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> </span><span class="token keyword" style="color:rgb(0, 0, 255)">typedef</span><span class="token plain"> _Key key_type</span><span class="token punctuation" style="color:rgb(4, 81, 165)">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> </span><span class="token keyword" style="color:rgb(0, 0, 255)">typedef</span><span class="token plain"> _Tp mapped_type</span><span class="token punctuation" style="color:rgb(4, 81, 165)">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> </span><span class="token keyword" style="color:rgb(0, 0, 255)">typedef</span><span class="token plain"> pair</span><span class="token operator" style="color:rgb(0, 0, 0)"><</span><span class="token keyword" style="color:rgb(0, 0, 255)">const</span><span class="token plain"> key_type</span><span class="token punctuation" style="color:rgb(4, 81, 165)">,</span><span class="token plain"> mapped_type</span><span class="token operator" style="color:rgb(0, 0, 0)">></span><span class="token plain"> value_type</span><span class="token punctuation" style="color:rgb(4, 81, 165)">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"></span><span class="token comment" style="color:rgb(0, 128, 0)">// …</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"></span><span class="token keyword" style="color:rgb(0, 0, 255)">private</span><span class="token operator" style="color:rgb(0, 0, 0)">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> </span><span class="token keyword" style="color:rgb(0, 0, 255)">typedef</span><span class="token plain"> __tree</span><span class="token operator" style="color:rgb(0, 0, 0)"><</span><span class="token plain">__value_type</span><span class="token punctuation" style="color:rgb(4, 81, 165)">,</span><span class="token plain"> __vc</span><span class="token punctuation" style="color:rgb(4, 81, 165)">,</span><span class="token plain"> __allocator_type</span><span class="token operator" style="color:rgb(0, 0, 0)">></span><span class="token plain"> __base</span><span class="token punctuation" style="color:rgb(4, 81, 165)">;</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="Copy code to clipboard" title="Copy" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div></li><li><p><a href="https://github.com/llvm/llvm-project/blob/main/libcxx/include/set" target="_blank" rel="noopener noreferrer"><code>set</code></a></p><div class="language-cpp codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#000000;--prism-background-color:#ffffff"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-cpp codeBlock_bY9V thin-scrollbar"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#000000"><span class="token keyword" style="color:rgb(0, 0, 255)">template</span><span class="token plain"> </span><span class="token operator" style="color:rgb(0, 0, 0)"><</span><span class="token keyword" style="color:rgb(0, 0, 255)">class</span><span class="token plain"> </span><span class="token class-name" style="color:rgb(38, 127, 153)">_Key</span><span class="token punctuation" style="color:rgb(4, 81, 165)">,</span><span class="token plain"> </span><span class="token keyword" style="color:rgb(0, 0, 255)">class</span><span class="token plain"> </span><span class="token class-name" style="color:rgb(38, 127, 153)">_Compare</span><span class="token plain"> </span><span class="token operator" style="color:rgb(0, 0, 0)">=</span><span class="token plain"> less</span><span class="token operator" style="color:rgb(0, 0, 0)"><</span><span class="token plain">_Key</span><span class="token operator" style="color:rgb(0, 0, 0)">></span><span class="token punctuation" style="color:rgb(4, 81, 165)">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> </span><span class="token keyword" style="color:rgb(0, 0, 255)">class</span><span class="token plain"> </span><span class="token class-name" style="color:rgb(38, 127, 153)">_Allocator</span><span class="token plain"> </span><span class="token operator" style="color:rgb(0, 0, 0)">=</span><span class="token plain"> allocator</span><span class="token operator" style="color:rgb(0, 0, 0)"><</span><span class="token plain">_Key</span><span class="token operator" style="color:rgb(0, 0, 0)">></span><span class="token plain"> </span><span class="token operator" style="color:rgb(0, 0, 0)">></span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"></span><span class="token keyword" style="color:rgb(0, 0, 255)">class</span><span class="token plain"> </span><span class="token class-name" style="color:rgb(38, 127, 153)">_LIBCPP_TEMPLATE_VIS</span><span class="token plain"> set</span><br></span><span class="token-line" style="color:#000000"><span class="token plain"></span><span class="token punctuation" style="color:rgb(4, 81, 165)">{</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"></span><span class="token keyword" style="color:rgb(0, 0, 255)">public</span><span class="token operator" style="color:rgb(0, 0, 0)">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> </span><span class="token comment" style="color:rgb(0, 128, 0)">// types:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> </span><span class="token keyword" style="color:rgb(0, 0, 255)">typedef</span><span class="token plain"> _Key key_type</span><span class="token punctuation" style="color:rgb(4, 81, 165)">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> </span><span class="token keyword" style="color:rgb(0, 0, 255)">typedef</span><span class="token plain"> key_type value_type</span><span class="token punctuation" style="color:rgb(4, 81, 165)">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"></span><span class="token comment" style="color:rgb(0, 128, 0)">// …</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"></span><span class="token keyword" style="color:rgb(0, 0, 255)">private</span><span class="token operator" style="color:rgb(0, 0, 0)">:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> </span><span class="token keyword" style="color:rgb(0, 0, 255)">typedef</span><span class="token plain"> __tree</span><span class="token operator" style="color:rgb(0, 0, 0)"><</span><span class="token plain">value_type</span><span class="token punctuation" style="color:rgb(4, 81, 165)">,</span><span class="token plain"> value_compare</span><span class="token punctuation" style="color:rgb(4, 81, 165)">,</span><span class="token plain"> allocator_type</span><span class="token operator" style="color:rgb(0, 0, 0)">></span><span class="token plain"> __base</span><span class="token punctuation" style="color:rgb(4, 81, 165)">;</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="Copy code to clipboard" title="Copy" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div></li></ul><p>U obou hlaviček si můžeme všimnout, že deklarují nějaký soukromý typ <code>__base</code>, který je aliasem pro <code>__tree</code>. Ten nás pak vede k hlavičce <a href="https://github.com/llvm/llvm-project/blob/main/libcxx/include/__tree" target="_blank" rel="noopener noreferrer"><code>__tree</code></a>.</p><p>Výňatek:</p><div class="language-cpp codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#000000;--prism-background-color:#ffffff"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-cpp codeBlock_bY9V thin-scrollbar"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#000000"><span class="token comment" style="color:rgb(0, 128, 0)">/*</span><br></span><span class="token-line" style="color:#000000"><span class="token comment" style="display:inline-block;color:rgb(0, 128, 0)"></span><br></span><span class="token-line" style="color:#000000"><span class="token comment" style="color:rgb(0, 128, 0)">_NodePtr algorithms</span><br></span><span class="token-line" style="color:#000000"><span class="token comment" style="display:inline-block;color:rgb(0, 128, 0)"></span><br></span><span class="token-line" style="color:#000000"><span class="token comment" style="color:rgb(0, 128, 0)">The algorithms taking _NodePtr are red black tree algorithms. Those</span><br></span><span class="token-line" style="color:#000000"><span class="token comment" style="color:rgb(0, 128, 0)">algorithms taking a parameter named __root should assume that __root</span><br></span><span class="token-line" style="color:#000000"><span class="token comment" style="color:rgb(0, 128, 0)">points to a proper red black tree (unless otherwise specified).</span><br></span><span class="token-line" style="color:#000000"><span class="token comment" style="display:inline-block;color:rgb(0, 128, 0)"></span><br></span><span class="token-line" style="color:#000000"><span class="token comment" style="color:rgb(0, 128, 0)">…</span><br></span><span class="token-line" style="color:#000000"><span class="token comment" style="display:inline-block;color:rgb(0, 128, 0)"></span><br></span><span class="token-line" style="color:#000000"><span class="token comment" style="color:rgb(0, 128, 0)">*/</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="Copy code to clipboard" title="Copy" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div><h4 class="anchor anchorWithStickyNavbar_LWe7" id="gcc">gcc<a href="#gcc" class="hash-link" aria-label="Direct link to gcc" title="Direct link to gcc"></a></h4><p>Pro <code>gcc</code> je postup téměř stejný. Pro změnu v hlavičkách <code>map</code> a <code>set</code> nenajdeme nic, deklarace jsou až v hlavičkových souborech:</p><ul><li><a href="https://gcc.gnu.org/git/?p=gcc.git;a=blob;f=libstdc%2B%2B-v3/include/bits/stl_map.h;h=9c2b0745673431b4b396ba27982170478838137e;hb=HEAD" target="_blank" rel="noopener noreferrer"><code>bits/stl_map.h</code></a></li><li><a href="https://gcc.gnu.org/git/?p=gcc.git;a=blob;f=libstdc%2B%2B-v3/include/bits/stl_set.h;h=9c2b0745673431b4b396ba27982170478838137e;hb=HEAD" target="_blank" rel="noopener noreferrer"><code>bits/stl_set.h</code></a></li></ul><p>V obou se zase odkazuje na nějakou hlavičku <a href="https://gcc.gnu.org/git/?p=gcc.git;a=blob;f=libstdc%2B%2B-v3/include/bits/stl_tree.h;h=a4de61417652a288e361a55fcc8bb7a9838c58a5;hb=HEAD" target="_blank" rel="noopener noreferrer"><code>bits/stl_tree.h</code></a>, zase výňatek:</p><div class="language-cpp codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#000000;--prism-background-color:#ffffff"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-cpp codeBlock_bY9V thin-scrollbar"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#000000"><span class="token plain"> </span><span class="token comment" style="color:rgb(0, 128, 0)">// Red-black tree class, designed for use in implementing STL</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> </span><span class="token comment" style="color:rgb(0, 128, 0)">// associative containers (set, multiset, map, and multimap). The</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> </span><span class="token comment" style="color:rgb(0, 128, 0)">// insertion and deletion algorithms are based on those in Cormen,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> </span><span class="token comment" style="color:rgb(0, 128, 0)">// Leiserson, and Rivest, Introduction to Algorithms (MIT Press,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> </span><span class="token comment" style="color:rgb(0, 128, 0)">// 1990), except that</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> </span><span class="token comment" style="color:rgb(0, 128, 0)">//</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> </span><span class="token comment" style="color:rgb(0, 128, 0)">// (1) the header cell is maintained with links not only to the root</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> </span><span class="token comment" style="color:rgb(0, 128, 0)">// but also to the leftmost node of the tree, to enable constant</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> </span><span class="token comment" style="color:rgb(0, 128, 0)">// time begin(), and to the rightmost node of the tree, to enable</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> </span><span class="token comment" style="color:rgb(0, 128, 0)">// linear time performance when used with the generic set algorithms</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> </span><span class="token comment" style="color:rgb(0, 128, 0)">// (set_union, etc.)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> </span><span class="token comment" style="color:rgb(0, 128, 0)">//</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> </span><span class="token comment" style="color:rgb(0, 128, 0)">// (2) when a node being deleted has two children its successor node</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> </span><span class="token comment" style="color:rgb(0, 128, 0)">// is relinked into its place, rather than copied, so that the only</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> </span><span class="token comment" style="color:rgb(0, 128, 0)">// iterators invalidated are those referring to the deleted node.</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> </span><span class="token keyword" style="color:rgb(0, 0, 255)">enum</span><span class="token plain"> </span><span class="token class-name" style="color:rgb(38, 127, 153)">_Rb_tree_color</span><span class="token plain"> </span><span class="token punctuation" style="color:rgb(4, 81, 165)">{</span><span class="token plain"> _S_red </span><span class="token operator" style="color:rgb(0, 0, 0)">=</span><span class="token plain"> </span><span class="token boolean">false</span><span class="token punctuation" style="color:rgb(4, 81, 165)">,</span><span class="token plain"> _S_black </span><span class="token operator" style="color:rgb(0, 0, 0)">=</span><span class="token plain"> </span><span class="token boolean">true</span><span class="token plain"> </span><span class="token punctuation" style="color:rgb(4, 81, 165)">}</span><span class="token punctuation" style="color:rgb(4, 81, 165)">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> </span><span class="token keyword" style="color:rgb(0, 0, 255)">struct</span><span class="token plain"> </span><span class="token class-name" style="color:rgb(38, 127, 153)">_Rb_tree_node_base</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> </span><span class="token punctuation" style="color:rgb(4, 81, 165)">{</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> </span><span class="token keyword" style="color:rgb(0, 0, 255)">typedef</span><span class="token plain"> _Rb_tree_node_base</span><span class="token operator" style="color:rgb(0, 0, 0)">*</span><span class="token plain"> _Base_ptr</span><span class="token punctuation" style="color:rgb(4, 81, 165)">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> </span><span class="token keyword" style="color:rgb(0, 0, 255)">typedef</span><span class="token plain"> </span><span class="token keyword" style="color:rgb(0, 0, 255)">const</span><span class="token plain"> _Rb_tree_node_base</span><span class="token operator" style="color:rgb(0, 0, 0)">*</span><span class="token plain"> _Const_Base_ptr</span><span class="token punctuation" style="color:rgb(4, 81, 165)">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> _Rb_tree_color _M_color</span><span class="token punctuation" style="color:rgb(4, 81, 165)">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> _Base_ptr _M_parent</span><span class="token punctuation" style="color:rgb(4, 81, 165)">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> _Base_ptr _M_left</span><span class="token punctuation" style="color:rgb(4, 81, 165)">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> _Base_ptr _M_right</span><span class="token punctuation" style="color:rgb(4, 81, 165)">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> </span><span class="token keyword" style="color:rgb(0, 0, 255)">static</span><span class="token plain"> _Base_ptr</span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> </span><span class="token function" style="color:rgb(0, 0, 255)">_S_minimum</span><span class="token punctuation" style="color:rgb(4, 81, 165)">(</span><span class="token plain">_Base_ptr __x</span><span class="token punctuation" style="color:rgb(4, 81, 165)">)</span><span class="token plain"> _GLIBCXX_NOEXCEPT</span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> </span><span class="token punctuation" style="color:rgb(4, 81, 165)">{</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> </span><span class="token keyword" style="color:rgb(0, 0, 255)">while</span><span class="token plain"> </span><span class="token punctuation" style="color:rgb(4, 81, 165)">(</span><span class="token plain">__x</span><span class="token operator" style="color:rgb(0, 0, 0)">-></span><span class="token plain">_M_left </span><span class="token operator" style="color:rgb(0, 0, 0)">!=</span><span class="token plain"> </span><span class="token number" style="color:rgb(9, 134, 88)">0</span><span class="token punctuation" style="color:rgb(4, 81, 165)">)</span><span class="token plain"> __x </span><span class="token operator" style="color:rgb(0, 0, 0)">=</span><span class="token plain"> __x</span><span class="token operator" style="color:rgb(0, 0, 0)">-></span><span class="token plain">_M_left</span><span class="token punctuation" style="color:rgb(4, 81, 165)">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> </span><span class="token keyword" style="color:rgb(0, 0, 255)">return</span><span class="token plain"> __x</span><span class="token punctuation" style="color:rgb(4, 81, 165)">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> </span><span class="token punctuation" style="color:rgb(4, 81, 165)">}</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> </span><span class="token keyword" style="color:rgb(0, 0, 255)">static</span><span class="token plain"> _Const_Base_ptr</span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> </span><span class="token function" style="color:rgb(0, 0, 255)">_S_minimum</span><span class="token punctuation" style="color:rgb(4, 81, 165)">(</span><span class="token plain">_Const_Base_ptr __x</span><span class="token punctuation" style="color:rgb(4, 81, 165)">)</span><span class="token plain"> _GLIBCXX_NOEXCEPT</span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> </span><span class="token punctuation" style="color:rgb(4, 81, 165)">{</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> </span><span class="token keyword" style="color:rgb(0, 0, 255)">while</span><span class="token plain"> </span><span class="token punctuation" style="color:rgb(4, 81, 165)">(</span><span class="token plain">__x</span><span class="token operator" style="color:rgb(0, 0, 0)">-></span><span class="token plain">_M_left </span><span class="token operator" style="color:rgb(0, 0, 0)">!=</span><span class="token plain"> </span><span class="token number" style="color:rgb(9, 134, 88)">0</span><span class="token punctuation" style="color:rgb(4, 81, 165)">)</span><span class="token plain"> __x </span><span class="token operator" style="color:rgb(0, 0, 0)">=</span><span class="token plain"> __x</span><span class="token operator" style="color:rgb(0, 0, 0)">-></span><span class="token plain">_M_left</span><span class="token punctuation" style="color:rgb(4, 81, 165)">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> </span><span class="token keyword" style="color:rgb(0, 0, 255)">return</span><span class="token plain"> __x</span><span class="token punctuation" style="color:rgb(4, 81, 165)">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> </span><span class="token punctuation" style="color:rgb(4, 81, 165)">}</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> </span><span class="token keyword" style="color:rgb(0, 0, 255)">static</span><span class="token plain"> _Base_ptr</span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> </span><span class="token function" style="color:rgb(0, 0, 255)">_S_maximum</span><span class="token punctuation" style="color:rgb(4, 81, 165)">(</span><span class="token plain">_Base_ptr __x</span><span class="token punctuation" style="color:rgb(4, 81, 165)">)</span><span class="token plain"> _GLIBCXX_NOEXCEPT</span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> </span><span class="token punctuation" style="color:rgb(4, 81, 165)">{</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> </span><span class="token keyword" style="color:rgb(0, 0, 255)">while</span><span class="token plain"> </span><span class="token punctuation" style="color:rgb(4, 81, 165)">(</span><span class="token plain">__x</span><span class="token operator" style="color:rgb(0, 0, 0)">-></span><span class="token plain">_M_right </span><span class="token operator" style="color:rgb(0, 0, 0)">!=</span><span class="token plain"> </span><span class="token number" style="color:rgb(9, 134, 88)">0</span><span class="token punctuation" style="color:rgb(4, 81, 165)">)</span><span class="token plain"> __x </span><span class="token operator" style="color:rgb(0, 0, 0)">=</span><span class="token plain"> __x</span><span class="token operator" style="color:rgb(0, 0, 0)">-></span><span class="token plain">_M_right</span><span class="token punctuation" style="color:rgb(4, 81, 165)">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> </span><span class="token keyword" style="color:rgb(0, 0, 255)">return</span><span class="token plain"> __x</span><span class="token punctuation" style="color:rgb(4, 81, 165)">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> </span><span class="token punctuation" style="color:rgb(4, 81, 165)">}</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> </span><span class="token keyword" style="color:rgb(0, 0, 255)">static</span><span class="token plain"> _Const_Base_ptr</span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> </span><span class="token function" style="color:rgb(0, 0, 255)">_S_maximum</span><span class="token punctuation" style="color:rgb(4, 81, 165)">(</span><span class="token plain">_Const_Base_ptr __x</span><span class="token punctuation" style="color:rgb(4, 81, 165)">)</span><span class="token plain"> _GLIBCXX_NOEXCEPT</span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> </span><span class="token punctuation" style="color:rgb(4, 81, 165)">{</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> </span><span class="token keyword" style="color:rgb(0, 0, 255)">while</span><span class="token plain"> </span><span class="token punctuation" style="color:rgb(4, 81, 165)">(</span><span class="token plain">__x</span><span class="token operator" style="color:rgb(0, 0, 0)">-></span><span class="token plain">_M_right </span><span class="token operator" style="color:rgb(0, 0, 0)">!=</span><span class="token plain"> </span><span class="token number" style="color:rgb(9, 134, 88)">0</span><span class="token punctuation" style="color:rgb(4, 81, 165)">)</span><span class="token plain"> __x </span><span class="token operator" style="color:rgb(0, 0, 0)">=</span><span class="token plain"> __x</span><span class="token operator" style="color:rgb(0, 0, 0)">-></span><span class="token plain">_M_right</span><span class="token punctuation" style="color:rgb(4, 81, 165)">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> </span><span class="token keyword" style="color:rgb(0, 0, 255)">return</span><span class="token plain"> __x</span><span class="token punctuation" style="color:rgb(4, 81, 165)">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> </span><span class="token punctuation" style="color:rgb(4, 81, 165)">}</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="Copy code to clipboard" title="Copy" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div><p>Tady už taky vidíme nějaký kód pro nalezení minima/maxima ve stromě. Mimo jiné
|
||
ještě existuje <a href="https://gcc.gnu.org/git/?p=gcc.git;a=blob;f=libstdc%2B%2B-v3/src/c%2B%2B98/tree.cc;h=fd14991589a57c6aa847f57105a938cd2bf4df6f;hb=HEAD" target="_blank" rel="noopener noreferrer"><code>tree.cc</code></a>, kde je lze nalézt třeba funkci s následující hlavičkou:</p><div class="language-cpp codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#000000;--prism-background-color:#ffffff"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-cpp codeBlock_bY9V thin-scrollbar"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#000000"><span class="token keyword" style="color:rgb(0, 0, 255)">void</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"></span><span class="token function" style="color:rgb(0, 0, 255)">_Rb_tree_insert_and_rebalance</span><span class="token punctuation" style="color:rgb(4, 81, 165)">(</span><span class="token keyword" style="color:rgb(0, 0, 255)">const</span><span class="token plain"> </span><span class="token keyword" style="color:rgb(0, 0, 255)">bool</span><span class="token plain"> __insert_left</span><span class="token punctuation" style="color:rgb(4, 81, 165)">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> _Rb_tree_node_base</span><span class="token operator" style="color:rgb(0, 0, 0)">*</span><span class="token plain"> __x</span><span class="token punctuation" style="color:rgb(4, 81, 165)">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> _Rb_tree_node_base</span><span class="token operator" style="color:rgb(0, 0, 0)">*</span><span class="token plain"> __p</span><span class="token punctuation" style="color:rgb(4, 81, 165)">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> _Rb_tree_node_base</span><span class="token operator" style="color:rgb(0, 0, 0)">&</span><span class="token plain"> __header</span><span class="token punctuation" style="color:rgb(4, 81, 165)">)</span><span class="token plain"> </span><span class="token keyword" style="color:rgb(0, 0, 255)">throw</span><span class="token plain"> </span><span class="token punctuation" style="color:rgb(4, 81, 165)">(</span><span class="token punctuation" style="color:rgb(4, 81, 165)">)</span><span class="token punctuation" style="color:rgb(4, 81, 165)">;</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="Copy code to clipboard" title="Copy" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div><h3 class="anchor anchorWithStickyNavbar_LWe7" id="java">Java<a href="#java" class="hash-link" aria-label="Direct link to Java" title="Direct link to Java"></a></h3><p>V Javě jsou pro nás klíčové implementace <a href="https://github.com/openjdk/jdk/blob/master/src/java.base/share/classes/java/util/TreeSet.java" target="_blank" rel="noopener noreferrer"><code>TreeSet</code></a> a <a href="https://github.com/openjdk/jdk/blob/master/src/java.base/share/classes/java/util/TreeMap.java" target="_blank" rel="noopener noreferrer"><code>TreeMap</code></a>.</p><p>V implementaci <code>TreeSet</code> si můžete povšimnout:</p><div class="language-java codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#000000;--prism-background-color:#ffffff"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-java codeBlock_bY9V thin-scrollbar"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#000000"><span class="token keyword" style="color:rgb(0, 0, 255)">public</span><span class="token plain"> </span><span class="token keyword" style="color:rgb(0, 0, 255)">class</span><span class="token plain"> </span><span class="token class-name" style="color:rgb(38, 127, 153)">TreeSet</span><span class="token generics punctuation" style="color:rgb(4, 81, 165)"><</span><span class="token generics class-name" style="color:rgb(38, 127, 153)">E</span><span class="token generics punctuation" style="color:rgb(4, 81, 165)">></span><span class="token plain"> </span><span class="token keyword" style="color:rgb(0, 0, 255)">extends</span><span class="token plain"> </span><span class="token class-name" style="color:rgb(38, 127, 153)">AbstractSet</span><span class="token generics punctuation" style="color:rgb(4, 81, 165)"><</span><span class="token generics class-name" style="color:rgb(38, 127, 153)">E</span><span class="token generics punctuation" style="color:rgb(4, 81, 165)">></span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> </span><span class="token keyword" style="color:rgb(0, 0, 255)">implements</span><span class="token plain"> </span><span class="token class-name" style="color:rgb(38, 127, 153)">NavigableSet</span><span class="token generics punctuation" style="color:rgb(4, 81, 165)"><</span><span class="token generics class-name" style="color:rgb(38, 127, 153)">E</span><span class="token generics punctuation" style="color:rgb(4, 81, 165)">></span><span class="token punctuation" style="color:rgb(4, 81, 165)">,</span><span class="token plain"> </span><span class="token class-name" style="color:rgb(38, 127, 153)">Cloneable</span><span class="token punctuation" style="color:rgb(4, 81, 165)">,</span><span class="token plain"> </span><span class="token class-name namespace" style="color:rgb(38, 127, 153)">java</span><span class="token class-name namespace punctuation" style="color:rgb(4, 81, 165)">.</span><span class="token class-name namespace" style="color:rgb(38, 127, 153)">io</span><span class="token class-name namespace punctuation" style="color:rgb(4, 81, 165)">.</span><span class="token class-name" style="color:rgb(38, 127, 153)">Serializable</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"></span><span class="token punctuation" style="color:rgb(4, 81, 165)">{</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> </span><span class="token comment" style="color:rgb(0, 128, 0)">/**</span><br></span><span class="token-line" style="color:#000000"><span class="token comment" style="color:rgb(0, 128, 0)"> * The backing map.</span><br></span><span class="token-line" style="color:#000000"><span class="token comment" style="color:rgb(0, 128, 0)"> */</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> </span><span class="token keyword" style="color:rgb(0, 0, 255)">private</span><span class="token plain"> </span><span class="token keyword" style="color:rgb(0, 0, 255)">transient</span><span class="token plain"> </span><span class="token class-name" style="color:rgb(38, 127, 153)">NavigableMap</span><span class="token generics punctuation" style="color:rgb(4, 81, 165)"><</span><span class="token generics class-name" style="color:rgb(38, 127, 153)">E</span><span class="token generics punctuation" style="color:rgb(4, 81, 165)">,</span><span class="token generics class-name" style="color:rgb(38, 127, 153)">Object</span><span class="token generics punctuation" style="color:rgb(4, 81, 165)">></span><span class="token plain"> m</span><span class="token punctuation" style="color:rgb(4, 81, 165)">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> </span><span class="token comment" style="color:rgb(0, 128, 0)">// Dummy value to associate with an Object in the backing Map</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> </span><span class="token keyword" style="color:rgb(0, 0, 255)">private</span><span class="token plain"> </span><span class="token keyword" style="color:rgb(0, 0, 255)">static</span><span class="token plain"> </span><span class="token keyword" style="color:rgb(0, 0, 255)">final</span><span class="token plain"> </span><span class="token class-name" style="color:rgb(38, 127, 153)">Object</span><span class="token plain"> </span><span class="token constant" style="color:rgb(129, 31, 63)">PRESENT</span><span class="token plain"> </span><span class="token operator" style="color:rgb(0, 0, 0)">=</span><span class="token plain"> </span><span class="token keyword" style="color:rgb(0, 0, 255)">new</span><span class="token plain"> </span><span class="token class-name" style="color:rgb(38, 127, 153)">Object</span><span class="token punctuation" style="color:rgb(4, 81, 165)">(</span><span class="token punctuation" style="color:rgb(4, 81, 165)">)</span><span class="token punctuation" style="color:rgb(4, 81, 165)">;</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="Copy code to clipboard" title="Copy" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div><p><code>TreeSet</code> v Javě tedy používá na pozadí <code>TreeMap</code> (což je vidět ve výchozím konstruktoru, kde se volá konstruktor přebírající <code>NavigableMap<E, Object></code>, a je mu předáno <code>new TreeMap<>()</code>).</p><p>Co se týče <code>TreeMap</code>, tak hned ze začátku definice <code>TreeMap</code> je vidět:</p><div class="language-java codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#000000;--prism-background-color:#ffffff"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-java codeBlock_bY9V thin-scrollbar"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#000000"><span class="token keyword" style="color:rgb(0, 0, 255)">public</span><span class="token plain"> </span><span class="token keyword" style="color:rgb(0, 0, 255)">class</span><span class="token plain"> </span><span class="token class-name" style="color:rgb(38, 127, 153)">TreeMap</span><span class="token generics punctuation" style="color:rgb(4, 81, 165)"><</span><span class="token generics class-name" style="color:rgb(38, 127, 153)">K</span><span class="token generics punctuation" style="color:rgb(4, 81, 165)">,</span><span class="token generics class-name" style="color:rgb(38, 127, 153)">V</span><span class="token generics punctuation" style="color:rgb(4, 81, 165)">></span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> </span><span class="token keyword" style="color:rgb(0, 0, 255)">extends</span><span class="token plain"> </span><span class="token class-name" style="color:rgb(38, 127, 153)">AbstractMap</span><span class="token generics punctuation" style="color:rgb(4, 81, 165)"><</span><span class="token generics class-name" style="color:rgb(38, 127, 153)">K</span><span class="token generics punctuation" style="color:rgb(4, 81, 165)">,</span><span class="token generics class-name" style="color:rgb(38, 127, 153)">V</span><span class="token generics punctuation" style="color:rgb(4, 81, 165)">></span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> </span><span class="token keyword" style="color:rgb(0, 0, 255)">implements</span><span class="token plain"> </span><span class="token class-name" style="color:rgb(38, 127, 153)">NavigableMap</span><span class="token generics punctuation" style="color:rgb(4, 81, 165)"><</span><span class="token generics class-name" style="color:rgb(38, 127, 153)">K</span><span class="token generics punctuation" style="color:rgb(4, 81, 165)">,</span><span class="token generics class-name" style="color:rgb(38, 127, 153)">V</span><span class="token generics punctuation" style="color:rgb(4, 81, 165)">></span><span class="token punctuation" style="color:rgb(4, 81, 165)">,</span><span class="token plain"> </span><span class="token class-name" style="color:rgb(38, 127, 153)">Cloneable</span><span class="token punctuation" style="color:rgb(4, 81, 165)">,</span><span class="token plain"> </span><span class="token class-name namespace" style="color:rgb(38, 127, 153)">java</span><span class="token class-name namespace punctuation" style="color:rgb(4, 81, 165)">.</span><span class="token class-name namespace" style="color:rgb(38, 127, 153)">io</span><span class="token class-name namespace punctuation" style="color:rgb(4, 81, 165)">.</span><span class="token class-name" style="color:rgb(38, 127, 153)">Serializable</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"></span><span class="token punctuation" style="color:rgb(4, 81, 165)">{</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> </span><span class="token comment" style="color:rgb(0, 128, 0)">/**</span><br></span><span class="token-line" style="color:#000000"><span class="token comment" style="color:rgb(0, 128, 0)"> * The comparator used to maintain order in this tree map, or</span><br></span><span class="token-line" style="color:#000000"><span class="token comment" style="color:rgb(0, 128, 0)"> * null if it uses the natural ordering of its keys.</span><br></span><span class="token-line" style="color:#000000"><span class="token comment" style="color:rgb(0, 128, 0)"> *</span><br></span><span class="token-line" style="color:#000000"><span class="token comment" style="color:rgb(0, 128, 0)"> * @serial</span><br></span><span class="token-line" style="color:#000000"><span class="token comment" style="color:rgb(0, 128, 0)"> */</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> </span><span class="token annotation punctuation" style="color:rgb(4, 81, 165)">@SuppressWarnings</span><span class="token punctuation" style="color:rgb(4, 81, 165)">(</span><span class="token string" style="color:rgb(163, 21, 21)">"serial"</span><span class="token punctuation" style="color:rgb(4, 81, 165)">)</span><span class="token plain"> </span><span class="token comment" style="color:rgb(0, 128, 0)">// Conditionally serializable</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> </span><span class="token keyword" style="color:rgb(0, 0, 255)">private</span><span class="token plain"> </span><span class="token keyword" style="color:rgb(0, 0, 255)">final</span><span class="token plain"> </span><span class="token class-name" style="color:rgb(38, 127, 153)">Comparator</span><span class="token generics punctuation" style="color:rgb(4, 81, 165)"><</span><span class="token generics operator" style="color:rgb(0, 0, 0)">?</span><span class="token generics"> </span><span class="token generics keyword" style="color:rgb(0, 0, 255)">super</span><span class="token generics"> </span><span class="token generics class-name" style="color:rgb(38, 127, 153)">K</span><span class="token generics punctuation" style="color:rgb(4, 81, 165)">></span><span class="token plain"> comparator</span><span class="token punctuation" style="color:rgb(4, 81, 165)">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> </span><span class="token keyword" style="color:rgb(0, 0, 255)">private</span><span class="token plain"> </span><span class="token keyword" style="color:rgb(0, 0, 255)">transient</span><span class="token plain"> </span><span class="token class-name" style="color:rgb(38, 127, 153)">Entry</span><span class="token generics punctuation" style="color:rgb(4, 81, 165)"><</span><span class="token generics class-name" style="color:rgb(38, 127, 153)">K</span><span class="token generics punctuation" style="color:rgb(4, 81, 165)">,</span><span class="token generics class-name" style="color:rgb(38, 127, 153)">V</span><span class="token generics punctuation" style="color:rgb(4, 81, 165)">></span><span class="token plain"> root</span><span class="token punctuation" style="color:rgb(4, 81, 165)">;</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="Copy code to clipboard" title="Copy" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div><p>Takže máme „nějaký kořen“ typu <code>Entry<K,V></code>. Zkusíme si najít definici daného typu…</p><div class="language-java codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#000000;--prism-background-color:#ffffff"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-java codeBlock_bY9V thin-scrollbar"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#000000"><span class="token plain"> </span><span class="token comment" style="color:rgb(0, 128, 0)">// Red-black mechanics</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> </span><span class="token keyword" style="color:rgb(0, 0, 255)">private</span><span class="token plain"> </span><span class="token keyword" style="color:rgb(0, 0, 255)">static</span><span class="token plain"> </span><span class="token keyword" style="color:rgb(0, 0, 255)">final</span><span class="token plain"> </span><span class="token keyword" style="color:rgb(0, 0, 255)">boolean</span><span class="token plain"> </span><span class="token constant" style="color:rgb(129, 31, 63)">RED</span><span class="token plain"> </span><span class="token operator" style="color:rgb(0, 0, 0)">=</span><span class="token plain"> </span><span class="token boolean">false</span><span class="token punctuation" style="color:rgb(4, 81, 165)">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> </span><span class="token keyword" style="color:rgb(0, 0, 255)">private</span><span class="token plain"> </span><span class="token keyword" style="color:rgb(0, 0, 255)">static</span><span class="token plain"> </span><span class="token keyword" style="color:rgb(0, 0, 255)">final</span><span class="token plain"> </span><span class="token keyword" style="color:rgb(0, 0, 255)">boolean</span><span class="token plain"> </span><span class="token constant" style="color:rgb(129, 31, 63)">BLACK</span><span class="token plain"> </span><span class="token operator" style="color:rgb(0, 0, 0)">=</span><span class="token plain"> </span><span class="token boolean">true</span><span class="token punctuation" style="color:rgb(4, 81, 165)">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> </span><span class="token comment" style="color:rgb(0, 128, 0)">/**</span><br></span><span class="token-line" style="color:#000000"><span class="token comment" style="color:rgb(0, 128, 0)"> * Node in the Tree. Doubles as a means to pass key-value pairs back to</span><br></span><span class="token-line" style="color:#000000"><span class="token comment" style="color:rgb(0, 128, 0)"> * user (see Map.Entry).</span><br></span><span class="token-line" style="color:#000000"><span class="token comment" style="color:rgb(0, 128, 0)"> */</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> </span><span class="token keyword" style="color:rgb(0, 0, 255)">static</span><span class="token plain"> </span><span class="token keyword" style="color:rgb(0, 0, 255)">final</span><span class="token plain"> </span><span class="token keyword" style="color:rgb(0, 0, 255)">class</span><span class="token plain"> </span><span class="token class-name" style="color:rgb(38, 127, 153)">Entry</span><span class="token generics punctuation" style="color:rgb(4, 81, 165)"><</span><span class="token generics class-name" style="color:rgb(38, 127, 153)">K</span><span class="token generics punctuation" style="color:rgb(4, 81, 165)">,</span><span class="token generics class-name" style="color:rgb(38, 127, 153)">V</span><span class="token generics punctuation" style="color:rgb(4, 81, 165)">></span><span class="token plain"> </span><span class="token keyword" style="color:rgb(0, 0, 255)">implements</span><span class="token plain"> </span><span class="token class-name" style="color:rgb(38, 127, 153)">Map</span><span class="token class-name punctuation" style="color:rgb(4, 81, 165)">.</span><span class="token class-name" style="color:rgb(38, 127, 153)">Entry</span><span class="token generics punctuation" style="color:rgb(4, 81, 165)"><</span><span class="token generics class-name" style="color:rgb(38, 127, 153)">K</span><span class="token generics punctuation" style="color:rgb(4, 81, 165)">,</span><span class="token generics class-name" style="color:rgb(38, 127, 153)">V</span><span class="token generics punctuation" style="color:rgb(4, 81, 165)">></span><span class="token plain"> </span><span class="token punctuation" style="color:rgb(4, 81, 165)">{</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> </span><span class="token class-name" style="color:rgb(38, 127, 153)">K</span><span class="token plain"> key</span><span class="token punctuation" style="color:rgb(4, 81, 165)">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> </span><span class="token class-name" style="color:rgb(38, 127, 153)">V</span><span class="token plain"> value</span><span class="token punctuation" style="color:rgb(4, 81, 165)">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> </span><span class="token class-name" style="color:rgb(38, 127, 153)">Entry</span><span class="token generics punctuation" style="color:rgb(4, 81, 165)"><</span><span class="token generics class-name" style="color:rgb(38, 127, 153)">K</span><span class="token generics punctuation" style="color:rgb(4, 81, 165)">,</span><span class="token generics class-name" style="color:rgb(38, 127, 153)">V</span><span class="token generics punctuation" style="color:rgb(4, 81, 165)">></span><span class="token plain"> left</span><span class="token punctuation" style="color:rgb(4, 81, 165)">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> </span><span class="token class-name" style="color:rgb(38, 127, 153)">Entry</span><span class="token generics punctuation" style="color:rgb(4, 81, 165)"><</span><span class="token generics class-name" style="color:rgb(38, 127, 153)">K</span><span class="token generics punctuation" style="color:rgb(4, 81, 165)">,</span><span class="token generics class-name" style="color:rgb(38, 127, 153)">V</span><span class="token generics punctuation" style="color:rgb(4, 81, 165)">></span><span class="token plain"> right</span><span class="token punctuation" style="color:rgb(4, 81, 165)">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> </span><span class="token class-name" style="color:rgb(38, 127, 153)">Entry</span><span class="token generics punctuation" style="color:rgb(4, 81, 165)"><</span><span class="token generics class-name" style="color:rgb(38, 127, 153)">K</span><span class="token generics punctuation" style="color:rgb(4, 81, 165)">,</span><span class="token generics class-name" style="color:rgb(38, 127, 153)">V</span><span class="token generics punctuation" style="color:rgb(4, 81, 165)">></span><span class="token plain"> parent</span><span class="token punctuation" style="color:rgb(4, 81, 165)">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> </span><span class="token keyword" style="color:rgb(0, 0, 255)">boolean</span><span class="token plain"> color </span><span class="token operator" style="color:rgb(0, 0, 0)">=</span><span class="token plain"> </span><span class="token constant" style="color:rgb(129, 31, 63)">BLACK</span><span class="token punctuation" style="color:rgb(4, 81, 165)">;</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="Copy code to clipboard" title="Copy" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div><p>A máme RB-tree.</p><p>(Implementace vychází z projektu OpenJDK.)</p><h3 class="anchor anchorWithStickyNavbar_LWe7" id="c-1">C#<a href="#c-1" class="hash-link" aria-label="Direct link to C#" title="Direct link to C#"></a></h3><p>V C# se zaměříme na nejnovější vydání (.NET), které je open-source a podporováno i na operačních systémech založených na Linuxu.</p><p>Nejdříve se podíváme na implementaci slovníku (<a href="https://github.com/dotnet/runtime/blob/main/src/libraries/System.Collections/src/System/Collections/Generic/SortedDictionary.cs" target="_blank" rel="noopener noreferrer"><code>SortedDictionary</code></a>).</p><div class="language-csharp codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#000000;--prism-background-color:#ffffff"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-csharp codeBlock_bY9V thin-scrollbar"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#000000"><span class="token plain"> </span><span class="token keyword" style="color:rgb(0, 0, 255)">public</span><span class="token plain"> </span><span class="token keyword" style="color:rgb(0, 0, 255)">class</span><span class="token plain"> </span><span class="token class-name" style="color:rgb(38, 127, 153)">SortedDictionary</span><span class="token class-name punctuation" style="color:rgb(4, 81, 165)"><</span><span class="token class-name" style="color:rgb(38, 127, 153)">TKey</span><span class="token class-name punctuation" style="color:rgb(4, 81, 165)">,</span><span class="token class-name" style="color:rgb(38, 127, 153)"> TValue</span><span class="token class-name punctuation" style="color:rgb(4, 81, 165)">></span><span class="token plain"> </span><span class="token punctuation" style="color:rgb(4, 81, 165)">:</span><span class="token plain"> </span><span class="token type-list class-name" style="color:rgb(38, 127, 153)">IDictionary</span><span class="token type-list class-name punctuation" style="color:rgb(4, 81, 165)"><</span><span class="token type-list class-name" style="color:rgb(38, 127, 153)">TKey</span><span class="token type-list class-name punctuation" style="color:rgb(4, 81, 165)">,</span><span class="token type-list class-name" style="color:rgb(38, 127, 153)"> TValue</span><span class="token type-list class-name punctuation" style="color:rgb(4, 81, 165)">></span><span class="token type-list punctuation" style="color:rgb(4, 81, 165)">,</span><span class="token type-list"> </span><span class="token type-list class-name" style="color:rgb(38, 127, 153)">IDictionary</span><span class="token type-list punctuation" style="color:rgb(4, 81, 165)">,</span><span class="token type-list"> </span><span class="token type-list class-name" style="color:rgb(38, 127, 153)">IReadOnlyDictionary</span><span class="token type-list class-name punctuation" style="color:rgb(4, 81, 165)"><</span><span class="token type-list class-name" style="color:rgb(38, 127, 153)">TKey</span><span class="token type-list class-name punctuation" style="color:rgb(4, 81, 165)">,</span><span class="token type-list class-name" style="color:rgb(38, 127, 153)"> TValue</span><span class="token type-list class-name punctuation" style="color:rgb(4, 81, 165)">></span><span class="token plain"> </span><span class="token keyword" style="color:rgb(0, 0, 255)">where</span><span class="token plain"> </span><span class="token class-name" style="color:rgb(38, 127, 153)">TKey</span><span class="token plain"> </span><span class="token punctuation" style="color:rgb(4, 81, 165)">:</span><span class="token plain"> </span><span class="token type-list keyword" style="color:rgb(0, 0, 255)">notnull</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> </span><span class="token punctuation" style="color:rgb(4, 81, 165)">{</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> </span><span class="token punctuation" style="color:rgb(4, 81, 165)">[</span><span class="token attribute class-name" style="color:rgb(38, 127, 153)">NonSerialized</span><span class="token punctuation" style="color:rgb(4, 81, 165)">]</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> </span><span class="token keyword" style="color:rgb(0, 0, 255)">private</span><span class="token plain"> </span><span class="token class-name" style="color:rgb(38, 127, 153)">KeyCollection</span><span class="token class-name punctuation" style="color:rgb(4, 81, 165)">?</span><span class="token plain"> _keys</span><span class="token punctuation" style="color:rgb(4, 81, 165)">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> </span><span class="token punctuation" style="color:rgb(4, 81, 165)">[</span><span class="token attribute class-name" style="color:rgb(38, 127, 153)">NonSerialized</span><span class="token punctuation" style="color:rgb(4, 81, 165)">]</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> </span><span class="token keyword" style="color:rgb(0, 0, 255)">private</span><span class="token plain"> </span><span class="token class-name" style="color:rgb(38, 127, 153)">ValueCollection</span><span class="token class-name punctuation" style="color:rgb(4, 81, 165)">?</span><span class="token plain"> _values</span><span class="token punctuation" style="color:rgb(4, 81, 165)">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> </span><span class="token keyword" style="color:rgb(0, 0, 255)">private</span><span class="token plain"> </span><span class="token keyword" style="color:rgb(0, 0, 255)">readonly</span><span class="token plain"> </span><span class="token class-name" style="color:rgb(38, 127, 153)">TreeSet</span><span class="token class-name punctuation" style="color:rgb(4, 81, 165)"><</span><span class="token class-name" style="color:rgb(38, 127, 153)">KeyValuePair</span><span class="token class-name punctuation" style="color:rgb(4, 81, 165)"><</span><span class="token class-name" style="color:rgb(38, 127, 153)">TKey</span><span class="token class-name punctuation" style="color:rgb(4, 81, 165)">,</span><span class="token class-name" style="color:rgb(38, 127, 153)"> TValue</span><span class="token class-name punctuation" style="color:rgb(4, 81, 165)">></span><span class="token class-name punctuation" style="color:rgb(4, 81, 165)">></span><span class="token plain"> _set</span><span class="token punctuation" style="color:rgb(4, 81, 165)">;</span><span class="token plain"> </span><span class="token comment" style="color:rgb(0, 128, 0)">// Do not rename (binary serialization)</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="Copy code to clipboard" title="Copy" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div><p>Na první pohled máme problém, protože <code>TreeSet</code> není <code>SortedSet</code>, který by jsme čekali. Když se přesuneme na konec souboru, tak zjistíme, že <code>TreeSet</code> je jenom <em>backward-compatible wrapper</em> pro <code>SortedSet</code>.</p><p>Přesuneme se k <a href="https://github.com/dotnet/runtime/blob/main/src/libraries/System.Collections/src/System/Collections/Generic/SortedSet.cs" target="_blank" rel="noopener noreferrer"><code>SortedSet</code></a>. A hned ze začátku vidíme:</p><div class="language-cs codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#000000;--prism-background-color:#ffffff"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-cs codeBlock_bY9V thin-scrollbar"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#000000"><span class="token plain"> </span><span class="token comment" style="color:rgb(0, 128, 0)">// A binary search tree is a red-black tree if it satisfies the following red-black properties:</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> </span><span class="token comment" style="color:rgb(0, 128, 0)">// 1. Every node is either red or black</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> </span><span class="token comment" style="color:rgb(0, 128, 0)">// 2. Every leaf (nil node) is black</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> </span><span class="token comment" style="color:rgb(0, 128, 0)">// 3. If a node is red, the both its children are black</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> </span><span class="token comment" style="color:rgb(0, 128, 0)">// 4. Every simple path from a node to a descendant leaf contains the same number of black nodes</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> </span><span class="token comment" style="color:rgb(0, 128, 0)">//</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> </span><span class="token comment" style="color:rgb(0, 128, 0)">// The basic idea of a red-black tree is to represent 2-3-4 trees as standard BSTs but to add one extra bit of information</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> </span><span class="token comment" style="color:rgb(0, 128, 0)">// per node to encode 3-nodes and 4-nodes.</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> </span><span class="token comment" style="color:rgb(0, 128, 0)">// 4-nodes will be represented as: B</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> </span><span class="token comment" style="color:rgb(0, 128, 0)">// R R</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> </span><span class="token comment" style="color:rgb(0, 128, 0)">//</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> </span><span class="token comment" style="color:rgb(0, 128, 0)">// 3 -node will be represented as: B or B</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> </span><span class="token comment" style="color:rgb(0, 128, 0)">// R B B R</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> </span><span class="token comment" style="color:rgb(0, 128, 0)">//</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> </span><span class="token comment" style="color:rgb(0, 128, 0)">// For a detailed description of the algorithm, take a look at "Algorithms" by Robert Sedgewick.</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> </span><span class="token keyword" style="color:rgb(0, 0, 255)">internal</span><span class="token plain"> </span><span class="token keyword" style="color:rgb(0, 0, 255)">enum</span><span class="token plain"> </span><span class="token class-name" style="color:rgb(38, 127, 153)">NodeColor</span><span class="token plain"> </span><span class="token punctuation" style="color:rgb(4, 81, 165)">:</span><span class="token plain"> </span><span class="token type-list keyword" style="color:rgb(0, 0, 255)">byte</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> </span><span class="token punctuation" style="color:rgb(4, 81, 165)">{</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> Black</span><span class="token punctuation" style="color:rgb(4, 81, 165)">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> Red</span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> </span><span class="token punctuation" style="color:rgb(4, 81, 165)">}</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> </span><span class="token keyword" style="color:rgb(0, 0, 255)">internal</span><span class="token plain"> </span><span class="token keyword" style="color:rgb(0, 0, 255)">delegate</span><span class="token plain"> </span><span class="token return-type class-name keyword" style="color:rgb(0, 0, 255)">bool</span><span class="token plain"> </span><span class="token generic-method function" style="color:rgb(0, 0, 255)">TreeWalkPredicate</span><span class="token generic-method generic class-name punctuation" style="color:rgb(4, 81, 165)"><</span><span class="token generic-method generic class-name" style="color:rgb(38, 127, 153)">T</span><span class="token generic-method generic class-name punctuation" style="color:rgb(4, 81, 165)">></span><span class="token punctuation" style="color:rgb(4, 81, 165)">(</span><span class="token class-name" style="color:rgb(38, 127, 153)">SortedSet</span><span class="token class-name punctuation" style="color:rgb(4, 81, 165)"><</span><span class="token class-name" style="color:rgb(38, 127, 153)">T</span><span class="token class-name punctuation" style="color:rgb(4, 81, 165)">></span><span class="token class-name punctuation" style="color:rgb(4, 81, 165)">.</span><span class="token class-name" style="color:rgb(38, 127, 153)">Node</span><span class="token plain"> node</span><span class="token punctuation" style="color:rgb(4, 81, 165)">)</span><span class="token punctuation" style="color:rgb(4, 81, 165)">;</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> </span><span class="token keyword" style="color:rgb(0, 0, 255)">internal</span><span class="token plain"> </span><span class="token keyword" style="color:rgb(0, 0, 255)">enum</span><span class="token plain"> </span><span class="token class-name" style="color:rgb(38, 127, 153)">TreeRotation</span><span class="token plain"> </span><span class="token punctuation" style="color:rgb(4, 81, 165)">:</span><span class="token plain"> </span><span class="token type-list keyword" style="color:rgb(0, 0, 255)">byte</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> </span><span class="token punctuation" style="color:rgb(4, 81, 165)">{</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> Left</span><span class="token punctuation" style="color:rgb(4, 81, 165)">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> LeftRight</span><span class="token punctuation" style="color:rgb(4, 81, 165)">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> Right</span><span class="token punctuation" style="color:rgb(4, 81, 165)">,</span><span class="token plain"></span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> RightLeft</span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> </span><span class="token punctuation" style="color:rgb(4, 81, 165)">}</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="Copy code to clipboard" title="Copy" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div><p>Vysvětlení v komentáři trochu předbíhá náplň cvičení zaměřeného na B-stromy ;)</p><h2 class="anchor anchorWithStickyNavbar_LWe7" id="vztah-mezi-množinou-a-mapou">Vztah mezi množinou a mapou<a href="#vztah-mezi-množinou-a-mapou" class="hash-link" aria-label="Direct link to Vztah mezi množinou a mapou" title="Direct link to Vztah mezi množinou a mapou"></a></h2><p>Při každé implementaci ve standardní knihovně jsme si mohli všimnout, že strom implementuje vždy jenom jeden typ:</p><table><thead><tr><th>Jazyk</th><th>Způsob implementace</th></tr></thead><tbody><tr><td>C++</td><td>mapa ukládá dvojice do množiny</td></tr><tr><td>Java</td><td>množina ukládá prvky s „dummy“ hodnotou do mapy</td></tr><tr><td>C#</td><td>mapa ukládá dvojice do množiny</td></tr></tbody></table><p>Mapa vyžaduje, aby každý klíč měl přiřazenou právě jednu hodnotu, tedy klíče jsou navzájem mezi sebou unikátní. To nám umožňuje organizovat klíče do množiny, zde ale narazíme na nepříjemný problém spočívající v tom, že musíme do množiny vkladat dvojice prvků: <code>(key, value)</code>. Tenhle přístup má ale zásadní problém:</p><div class="language-py codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#000000;--prism-background-color:#ffffff"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-py codeBlock_bY9V thin-scrollbar"><code class="codeBlockLines_e6Vv codeBlockLinesWithNumbering_o6Pm"><span class="token-line codeLine_lJS_" style="color:#000000"><span class="codeLineNumber_Tfdd"></span><span class="codeLineContent_feaV"><span class="token comment" style="color:rgb(0, 128, 0)"># let's represent dictionary/map as a set</span><span class="token plain"></span></span><br></span><span class="token-line codeLine_lJS_" style="color:#000000"><span class="codeLineNumber_Tfdd"></span><span class="codeLineContent_feaV"><span class="token plain">set_of_values </span><span class="token operator" style="color:rgb(0, 0, 0)">=</span><span class="token plain"> </span><span class="token builtin" style="color:rgb(0, 112, 193)">set</span><span class="token punctuation" style="color:rgb(4, 81, 165)">(</span><span class="token punctuation" style="color:rgb(4, 81, 165)">)</span><span class="token plain"></span></span><br></span><span class="token-line codeLine_lJS_" style="color:#000000"><span class="codeLineNumber_Tfdd"></span><span class="codeLineContent_feaV"><span class="token plain" style="display:inline-block"></span></span><br></span><span class="token-line codeLine_lJS_" style="color:#000000"><span class="codeLineNumber_Tfdd"></span><span class="codeLineContent_feaV"><span class="token plain"></span><span class="token comment" style="color:rgb(0, 128, 0)"># let's insert few pairs</span><span class="token plain"></span></span><br></span><span class="token-line codeLine_lJS_" style="color:#000000"><span class="codeLineNumber_Tfdd"></span><span class="codeLineContent_feaV"><span class="token plain">set_of_values</span><span class="token punctuation" style="color:rgb(4, 81, 165)">.</span><span class="token plain">add</span><span class="token punctuation" style="color:rgb(4, 81, 165)">(</span><span class="token punctuation" style="color:rgb(4, 81, 165)">(</span><span class="token number" style="color:rgb(9, 134, 88)">1</span><span class="token punctuation" style="color:rgb(4, 81, 165)">,</span><span class="token plain"> </span><span class="token number" style="color:rgb(9, 134, 88)">2</span><span class="token punctuation" style="color:rgb(4, 81, 165)">)</span><span class="token punctuation" style="color:rgb(4, 81, 165)">)</span><span class="token plain"></span></span><br></span><span class="token-line codeLine_lJS_" style="color:#000000"><span class="codeLineNumber_Tfdd"></span><span class="codeLineContent_feaV"><span class="token plain">set_of_values</span><span class="token punctuation" style="color:rgb(4, 81, 165)">.</span><span class="token plain">add</span><span class="token punctuation" style="color:rgb(4, 81, 165)">(</span><span class="token punctuation" style="color:rgb(4, 81, 165)">(</span><span class="token number" style="color:rgb(9, 134, 88)">0</span><span class="token punctuation" style="color:rgb(4, 81, 165)">,</span><span class="token plain"> </span><span class="token number" style="color:rgb(9, 134, 88)">42</span><span class="token punctuation" style="color:rgb(4, 81, 165)">)</span><span class="token punctuation" style="color:rgb(4, 81, 165)">)</span><span class="token plain"></span></span><br></span><span class="token-line codeLine_lJS_" style="color:#000000"><span class="codeLineNumber_Tfdd"></span><span class="codeLineContent_feaV"><span class="token plain" style="display:inline-block"></span></span><br></span><span class="token-line codeLine_lJS_" style="color:#000000"><span class="codeLineNumber_Tfdd"></span><span class="codeLineContent_feaV"><span class="token plain"></span><span class="token comment" style="color:rgb(0, 128, 0)"># let's set key 1 to value 6</span><span class="token plain"></span></span><br></span><span class="token-line codeLine_lJS_" style="color:#000000"><span class="codeLineNumber_Tfdd"></span><span class="codeLineContent_feaV"><span class="token plain">set_of_values</span><span class="token punctuation" style="color:rgb(4, 81, 165)">.</span><span class="token plain">add</span><span class="token punctuation" style="color:rgb(4, 81, 165)">(</span><span class="token punctuation" style="color:rgb(4, 81, 165)">(</span><span class="token number" style="color:rgb(9, 134, 88)">1</span><span class="token punctuation" style="color:rgb(4, 81, 165)">,</span><span class="token plain"> </span><span class="token number" style="color:rgb(9, 134, 88)">6</span><span class="token punctuation" style="color:rgb(4, 81, 165)">)</span><span class="token punctuation" style="color:rgb(4, 81, 165)">)</span><span class="token plain"></span></span><br></span><span class="token-line codeLine_lJS_" style="color:#000000"><span class="codeLineNumber_Tfdd"></span><span class="codeLineContent_feaV"><span class="token plain" style="display:inline-block"></span></span><br></span><span class="token-line codeLine_lJS_" style="color:#000000"><span class="codeLineNumber_Tfdd"></span><span class="codeLineContent_feaV"><span class="token plain">set_of_values</span></span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="Copy code to clipboard" title="Copy" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div><p>A dostaneme:</p><div class="codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#000000;--prism-background-color:#ffffff"><div class="codeBlockContent_biex"><pre tabindex="0" class="prism-code language-text codeBlock_bY9V thin-scrollbar"><code class="codeBlockLines_e6Vv"><span class="token-line" style="color:#000000"><span class="token plain">{(1, 6), (1, 2), (0, 42)}</span><br></span></code></pre><div class="buttonGroup__atx"><button type="button" aria-label="Copy code to clipboard" title="Copy" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div><p>V jednotlivých implementacích, které jste mohli vidět výše, se využívá nasledující, když:</p><ul><li><em>mapa ukládá dvojice do množiny</em>: Dvojice je obalená v samostatním typu, který porovnává jenom klíče</li><li><em>množina ukládá klíče do mapy</em>: V mapě se ignorují hodnoty přiřazené klíčům</li></ul></div><footer class="theme-doc-footer docusaurus-mt-lg"><div class="theme-doc-footer-tags-row row margin-bottom--sm"><div class="col"><b>Tags:</b><ul class="tags_jXut padding--none margin-left--sm"><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/ib002/tags/balanced-trees/">balanced trees</a></li><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/ib002/tags/red-black-trees/">red-black trees</a></li><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/ib002/tags/applications/">applications</a></li></ul></div></div><div class="theme-doc-footer-edit-meta-row row"><div class="col"><a href="https://github.com/mfocko/blog/tree/main/ib002/08-rb-trees/2022-04-05-applications.md" target="_blank" rel="noreferrer noopener" 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