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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">On the rules of the red-black tree</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>On the rules of the red-black tree</h1></header><h2 class="anchor anchorWithStickyNavbar_LWe7" id="introduction">Introduction<a href="#introduction" class="hash-link" aria-label="Direct link to Introduction" title="Direct link to Introduction"></a></h2><p>Have you ever thought about the red-black tree rules in more depth? Why are they
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formulated the way they are? How come they keep the tree balanced? Let's go through
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each of the red-black tree rules and try to change, break and contemplate about
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them.</p><p>We expect that you are familiar with the following set of the rules<sup id="fnref-1"><a href="#fn-1" class="footnote-ref">1</a></sup>:</p><ol><li>Every node is either red or black.</li><li>The root is black.</li><li>Every leaf (<code>nil</code>) is black.</li><li>If a node is red, then both its children are black.</li><li>For each node, all simple paths from the node to descendant leaves contain the
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same number of black nodes.</li></ol><p>Each section will go into <em>reasonable</em> details of each rule.</p><h2 class="anchor anchorWithStickyNavbar_LWe7" id="1ª-every-node-is-either-red-or-black">1ª Every node is either red or black.<a href="#1ª-every-node-is-either-red-or-black" class="hash-link" aria-label="Direct link to 1ª Every node is either red or black." title="Direct link to 1ª Every node is either red or black."></a></h2><p>OK… This one is very simple. It is just a definition and is used in all other
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rules. Not much to talk about here. Or is there?</p><h3 class="anchor anchorWithStickyNavbar_LWe7" id="do-i-really-need-the-nodes-to-be-explicitly-colored">Do I really need the nodes to be explicitly colored?<a href="#do-i-really-need-the-nodes-to-be-explicitly-colored" class="hash-link" aria-label="Direct link to Do I really need the nodes to be explicitly colored?" title="Direct link to Do I really need the nodes to be explicitly colored?"></a></h3><p>The answer is no. Balancing of the red-black trees is “enforced” by the 4th and
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5th rule in the enumeration above. There are many ways you can avoid using colors.</p><h4 class="anchor anchorWithStickyNavbar_LWe7" id="black-height">Black height<a href="#black-height" class="hash-link" aria-label="Direct link to Black height" title="Direct link to Black height"></a></h4><p>We mentioned the 4th and 5th rule and that it enforces the balancing. What does
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it mean for us?</p><p>Well, we definitely do not have to use the colors, which even as a <em>boolean</em> flag
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would take at least 1 byte of space (and usually even more), cause… well, it is
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easier for the CPU to work with words rather than single bits.</p><p>We could use the black height, couldn't we? It would mean more memory used, cause
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it should be ideally big and unsigned. Can we tell the color of a node from the
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black height? Of course we can, if my child has the same black height as I do,
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it means that there was no black node added on the path between us and therefore
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my child would be colored red.</p><p>Example of a red-black tree that keeps count of black nodes on paths to the
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leaves follows:</p><p><img loading="lazy" alt="Red-black tree with black height" src="/assets/images/rb_height_light-36fa69317ced094d7bb7b0fdf32cb3fe.png#gh-light-mode-only" width="923" height="539" class="img_ev3q">
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<img loading="lazy" alt="Red-black tree with black height" src="/assets/images/rb_height_dark-75a70ddff74e5e1aff7e9986221b5687.png#gh-dark-mode-only" width="923" height="539" class="img_ev3q"></p><p>We mark the <em>black heights</em> in superscript. You can see that all leaves have the
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black height equal to <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1</mn></mrow><annotation encoding="application/x-tex">1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6444em"></span><span class="mord">1</span></span></span></span></span>. Let's take a look at some of the interesting cases:</p><ul><li><p>If we take a look at the node with <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mtext>key</mtext><mo>=</mo><mn>9</mn></mrow><annotation encoding="application/x-tex">\text{key} = 9</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em"></span><span class="mord text"><span class="mord">key</span></span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:0.6444em"></span><span class="mord">9</span></span></span></span></span>, we can see that it is
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coloured red and its black height is 1, because it is a leaf.</p><p>Let's look at its parent (node with <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mtext>key</mtext><mo>=</mo><mn>8</mn></mrow><annotation encoding="application/x-tex">\text{key} = 8</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em"></span><span class="mord text"><span class="mord">key</span></span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:0.6444em"></span><span class="mord">8</span></span></span></span></span>). On its left side it has
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<code>nil</code> and on its right side the <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>9</mn></mrow><annotation encoding="application/x-tex">9</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6444em"></span><span class="mord">9</span></span></span></span></span>. And its black height is still <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1</mn></mrow><annotation encoding="application/x-tex">1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6444em"></span><span class="mord">1</span></span></span></span></span>, cause
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except for the <code>nil</code> leaves, there are no other black nodes.</p><p>We can clearly see that if a node has the same black height as its parent, it
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is a red node.</p></li><li><p>Now let's take a look at the root with <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mtext>key</mtext><mo>=</mo><mn>3</mn></mrow><annotation encoding="application/x-tex">\text{key} = 3</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em"></span><span class="mord text"><span class="mord">key</span></span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:0.6444em"></span><span class="mord">3</span></span></span></span></span>. It has a black height
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of 3. Both of its children are black nodes and have black height of 2.</p><p>We can see that if a node has its height 1 lower than its parent, it is a black
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node.</p><p>The reasoning behind it is rather simple, we count the black nodes all the way
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to the leaves, therefore if my parent has a higher black height, it means that
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on the path from me to my parent there is a black node, but the only node added
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is me, therefore I must be black.</p></li></ul><h4 class="anchor anchorWithStickyNavbar_LWe7" id="isomorphic-trees">Isomorphic trees<a href="#isomorphic-trees" class="hash-link" aria-label="Direct link to Isomorphic trees" title="Direct link to Isomorphic trees"></a></h4><p>One of the other ways to avoid using color is storing the red-black tree in some
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isomorphic tree. The structure of 2-3-4 tree allows us to avoid using the color
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completely. This is a bit different approach, cause we would be basically using
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different tree, so we keep this note in just as a “hack”.</p><h2 class="anchor anchorWithStickyNavbar_LWe7" id="2ª-the-root-is-black">2ª The root is black.<a href="#2ª-the-root-is-black" class="hash-link" aria-label="Direct link to 2ª The root is black." title="Direct link to 2ª The root is black."></a></h2><p>This rule might seem like a very important one, but overall is not. You can safely
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omit this rule, but you also need to deal with the consequences.</p><p>Let's refresh our memory with the algorithm of <em>insert fixup</em>:</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">WHILE z.p.color == Red</span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> IF z.p == z.p.p.left</span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> y = z.p.p.right</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"> IF y.color == Red</span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> z.p.color = Black</span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> y.color = Black</span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> z.p.p.color = Red</span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> z = z.p.p</span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> ELSE</span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> IF z == z.p.right</span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> z = z.p</span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> Left-Rotate(T, z)</span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> z.p.color = Black</span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> z.p.p.color = Red</span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> Right-Rotate(T, z.p.p)</span><br></span><span class="token-line" style="color:#000000"><span class="token plain"> ELSE (same as above with “right” and “left” exchanged)</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">T.root.color = Black</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><div class="theme-admonition theme-admonition-tip alert alert--success admonition_LlT9"><div class="admonitionHeading_tbUL"><span class="admonitionIcon_kALy"><svg viewBox="0 0 12 16"><path fill-rule="evenodd" d="M6.5 0C3.48 0 1 2.19 1 5c0 .92.55 2.25 1 3 1.34 2.25 1.78 2.78 2 4v1h5v-1c.22-1.22.66-1.75 2-4 .45-.75 1-2.08 1-3 0-2.81-2.48-5-5.5-5zm3.64 7.48c-.25.44-.47.8-.67 1.11-.86 1.41-1.25 2.06-1.45 3.23-.02.05-.02.11-.02.17H5c0-.06 0-.13-.02-.17-.2-1.17-.59-1.83-1.45-3.23-.2-.31-.42-.67-.67-1.11C2.44 6.78 2 5.65 2 5c0-2.2 2.02-4 4.5-4 1.22 0 2.36.42 3.22 1.19C10.55 2.94 11 3.94 11 5c0 .66-.44 1.78-.86 2.48zM4 14h5c-.23 1.14-1.3 2-2.5 2s-2.27-.86-2.5-2z"></path></svg></span>tip</div><div class="admonitionContent_S0QG"><p>If you have tried to implement any of the more complex data structures, such as
|
||
red-black trees, etc., in a statically typed language that also checks you for
|
||
<code>NULL</code>-correctness (e.g. <em>mypy</em> or even C# with nullable reference types), you
|
||
might have run into numerous issues in the cases where you are 100% sure that you
|
||
cannot obtain <code>NULL</code> because of the invariants, but the static type checking
|
||
doesn't know that.</p><p>The issue we hit with the <em>insert fixup</em> is very similar.</p></div></div><p>You might not realize the issue at the first sight, but the algorithm described
|
||
with the pseudocode above expects that the root of the red-black tree is black by
|
||
both relying on the invariant in the algorithm and afterwards by enforcing the
|
||
black root property.</p><p>If we decide to omit this condition, we need to address it in the pseudocodes
|
||
accordingly.</p><table><thead><tr><th align="center">Usual algorithm with black root</th><th align="center">Allowing red root</th></tr></thead><tbody><tr><td align="center"><img loading="lazy" alt="1ª insertion" src="data:image/png;base64,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#gh-light-mode-only" width="179" height="155" class="img_ev3q"><img loading="lazy" alt="1ª insertion" src="data:image/png;base64,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#gh-dark-mode-only" width="179" height="155" class="img_ev3q"></td><td align="center"><img loading="lazy" alt="1ª insertion" src="data:image/png;base64,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#gh-light-mode-only" width="179" height="155" class="img_ev3q"><img loading="lazy" alt="1ª insertion" src="data:image/png;base64,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#gh-dark-mode-only" width="179" height="155" class="img_ev3q"></td></tr><tr><td align="center"><img loading="lazy" alt="2ª insertion" src="data:image/png;base64,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#gh-light-mode-only" width="227" height="251" class="img_ev3q"><img loading="lazy" alt="2ª insertion" src="data:image/png;base64,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#gh-dark-mode-only" width="227" height="251" class="img_ev3q"></td><td align="center"><img loading="lazy" alt="2ª insertion" src="data:image/png;base64,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#gh-light-mode-only" width="227" height="251" class="img_ev3q"><img loading="lazy" alt="2ª insertion" src="data:image/png;base64,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#gh-dark-mode-only" width="227" height="251" class="img_ev3q"></td></tr><tr><td align="center"><img loading="lazy" alt="3ª insertion" src="/assets/images/br_2_light-5e6a1d53e559a30e5fb86ee019229bbd.png#gh-light-mode-only" width="371" height="251" class="img_ev3q"><img loading="lazy" alt="3ª insertion" src="/assets/images/br_2_dark-e8c35bc37b250271cf480f71904c15a7.png#gh-dark-mode-only" width="371" height="251" class="img_ev3q"></td><td align="center"><img loading="lazy" alt="3ª insertion" src="/assets/images/rr_2_light-5e6a1d53e559a30e5fb86ee019229bbd.png#gh-light-mode-only" width="371" height="251" class="img_ev3q"><img loading="lazy" alt="3ª insertion" src="/assets/images/rr_2_dark-e8c35bc37b250271cf480f71904c15a7.png#gh-dark-mode-only" width="371" height="251" class="img_ev3q"></td></tr><tr><td align="center"><img loading="lazy" alt="4ª insertion" src="/assets/images/br_3_light-7be3bbcb08f8b7182a1c719693a47615.png#gh-light-mode-only" width="419" height="347" class="img_ev3q"><img loading="lazy" alt="4ª insertion" src="/assets/images/br_3_dark-a2b8248c182059b67c703f75f58f3784.png#gh-dark-mode-only" width="419" height="347" class="img_ev3q"></td><td align="center"><img loading="lazy" alt="4ª insertion" src="/assets/images/rr_3_light-51521ba414ff3a3530ed0109cfab799d.png#gh-light-mode-only" width="419" height="347" class="img_ev3q"><img loading="lazy" alt="4ª insertion" src="/assets/images/rr_3_dark-4e8b2ca938738395e438b7fc2fc5dfe4.png#gh-dark-mode-only" width="419" height="347" class="img_ev3q"></td></tr><tr><td align="center"><img loading="lazy" alt="5ª insertion" src="/assets/images/br_4_light-d72dfa633794ec97eddce8e3a4b02660.png#gh-light-mode-only" width="419" height="347" class="img_ev3q"><img loading="lazy" alt="5ª insertion" src="/assets/images/br_4_dark-eddf4c315becc51f89b0967320f132d8.png#gh-dark-mode-only" width="419" height="347" class="img_ev3q"></td><td align="center"><img loading="lazy" alt="5ª insertion" src="/assets/images/rr_4_light-631a0b3947be21a12b3a489f0cd0c3c4.png#gh-light-mode-only" width="419" height="347" class="img_ev3q"><img loading="lazy" alt="5ª insertion" src="/assets/images/rr_4_dark-3cc1c8d4b39707d2a51b51f4f1b29dc8.png#gh-dark-mode-only" width="419" height="347" class="img_ev3q"></td></tr><tr><td align="center"><img loading="lazy" alt="6ª insertion" src="/assets/images/br_5_light-efb3568bf4aadb19a9dcc57e748f89d8.png#gh-light-mode-only" width="563" height="347" class="img_ev3q"><img loading="lazy" alt="6ª insertion" src="/assets/images/br_5_dark-e24da2d7a3fb2ee63ac8e1ea9c2d45a8.png#gh-dark-mode-only" width="563" height="347" class="img_ev3q"></td><td align="center"><img loading="lazy" alt="6ª insertion" src="/assets/images/rr_5_light-6b8f80047906eb1f58472d231eb9b12a.png#gh-light-mode-only" width="563" height="347" class="img_ev3q"><img loading="lazy" alt="6ª insertion" src="/assets/images/rr_5_dark-9028cc10e78c05cb669d5d438dcbf93f.png#gh-dark-mode-only" width="563" height="347" class="img_ev3q"></td></tr><tr><td align="center"><img loading="lazy" alt="7ª insertion" src="/assets/images/br_6_light-b090675f7b30b574af44d667b083e9b7.png#gh-light-mode-only" width="563" height="443" class="img_ev3q"><img loading="lazy" alt="7ª insertion" src="/assets/images/br_6_dark-160fd071a93e279a5339c7976745f8b1.png#gh-dark-mode-only" width="563" height="443" class="img_ev3q"></td><td align="center"><img loading="lazy" alt="7ª insertion" src="/assets/images/rr_6_light-b090675f7b30b574af44d667b083e9b7.png#gh-light-mode-only" width="563" height="443" class="img_ev3q"><img loading="lazy" alt="7ª insertion" src="/assets/images/rr_6_dark-160fd071a93e279a5339c7976745f8b1.png#gh-dark-mode-only" width="563" height="443" class="img_ev3q"></td></tr><tr><td align="center"><img loading="lazy" alt="8ª insertion" src="/assets/images/br_7_light-018e13c41ce1fc6257c4c65748aaae27.png#gh-light-mode-only" width="635" height="443" class="img_ev3q"><img loading="lazy" alt="8ª insertion" src="/assets/images/br_7_dark-35ede8f297484f4305ea7fd23cbddc49.png#gh-dark-mode-only" width="635" height="443" class="img_ev3q"></td><td align="center"><img loading="lazy" alt="8ª insertion" src="/assets/images/rr_7_light-018e13c41ce1fc6257c4c65748aaae27.png#gh-light-mode-only" width="635" height="443" class="img_ev3q"><img loading="lazy" alt="8ª insertion" src="/assets/images/rr_7_dark-35ede8f297484f4305ea7fd23cbddc49.png#gh-dark-mode-only" width="635" height="443" class="img_ev3q"></td></tr><tr><td align="center"><img loading="lazy" alt="9ª insertion" src="/assets/images/br_8_light-81ac4c8a3988bd43c66f563cd4799d61.png#gh-light-mode-only" width="755" height="443" class="img_ev3q"><img loading="lazy" alt="9ª insertion" src="/assets/images/br_8_dark-b0f871ab182d06edb5c29bb490ad70bc.png#gh-dark-mode-only" width="755" height="443" class="img_ev3q"></td><td align="center"><img loading="lazy" alt="9ª insertion" src="/assets/images/rr_8_light-81ac4c8a3988bd43c66f563cd4799d61.png#gh-light-mode-only" width="755" height="443" class="img_ev3q"><img loading="lazy" alt="9ª insertion" src="/assets/images/rr_8_dark-b0f871ab182d06edb5c29bb490ad70bc.png#gh-dark-mode-only" width="755" height="443" class="img_ev3q"></td></tr></tbody></table><h2 class="anchor anchorWithStickyNavbar_LWe7" id="3ª-every-leaf-nil-is-black">3ª Every leaf (<code>nil</code>) is black.<a href="#3ª-every-leaf-nil-is-black" class="hash-link" aria-label="Direct link to 3ª-every-leaf-nil-is-black" title="Direct link to 3ª-every-leaf-nil-is-black"></a></h2><p>Now, this rule is a funny one. What does this imply and can I interpret this in
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some other way? Let's go through some of the possible ways I can look at this and
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how would they affect the other rules and balancing.</p><p>We will experiment with the following tree:
|
||
<img loading="lazy" src="/assets/images/rb_light-f53bee3b32ddb2e7a4249828bc03b1a4.png#gh-light-mode-only" width="899" height="539" class="img_ev3q">
|
||
<img loading="lazy" src="/assets/images/rb_dark-c025d61dee7913262c86277087751328.png#gh-dark-mode-only" width="899" height="539" class="img_ev3q"></p><p>We should start by counting the black nodes from root to the <code>nil</code> leaves based
|
||
on the rules. We have multiple similar paths, so we will pick only the interesting
|
||
ones.</p><ol><li>What happens if we do not count the <code>nil</code> leaves?</li><li>What happens if we consider leaves the nodes with <em>no descendants</em>, i.e. both
|
||
of node's children are <code>nil</code>?</li><li>What happens if we do not count the <code>nil</code> leaves, but consider nodes with at
|
||
least one <code>nil</code> descendant as leaves?</li></ol><table><thead><tr><th align="right">path</th><th align="right">black nodes</th><th align="right">1ª idea</th><th align="right">2ª idea</th><th align="right">3ª idea</th></tr></thead><tbody><tr><td align="right"><code>3 → 1 → 0 → nil</code></td><td align="right">4</td><td align="right">3</td><td align="right">4</td><td align="right">3</td></tr><tr><td align="right"><code>3 → 5 → 7 → 8 → nil</code></td><td align="right">4</td><td align="right">3</td><td align="right">-</td><td align="right">3</td></tr><tr><td align="right"><code>3 → 5 → 7 → 8 → 9 → nil</code></td><td align="right">4</td><td align="right">3</td><td align="right">4</td><td align="right">3</td></tr></tbody></table><p>First idea is very easy to execute and it is also very easy to argue about its
|
||
correctness. It is correct, because we just subtract one from each of the paths.
|
||
This affects <strong>all</strong> paths and therefore results in global decrease by one.</p><p>Second idea is a bit more complicated. We count the <code>nil</code>s, so the count is <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>4</mn></mrow><annotation encoding="application/x-tex">4</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6444em"></span><span class="mord">4</span></span></span></span></span>
|
||
as it should be. However, there is one difference. Second path no longer satisfies
|
||
the condition of a <em>leaf</em>. Technically it relaxes the 5th rule, because we leave
|
||
out some of the nodes. We should probably avoid that.</p><div class="theme-admonition theme-admonition-caution alert alert--warning admonition_LlT9"><div class="admonitionHeading_tbUL"><span class="admonitionIcon_kALy"><svg viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>caution</div><div class="admonitionContent_S0QG"><p>With the second idea, you may also feel that we are “bending” the rules a bit,
|
||
especially the definition of the “leaf” nodes.</p><p>Given the definition of the red-black tree, where <code>nil</code> is considered to be an
|
||
external node, we have decided that bending it a bit just to stir a thought about
|
||
it won't hurt anybody. 😉</p></div></div><h2 class="anchor anchorWithStickyNavbar_LWe7" id="4ª-if-a-node-is-red-then-both-its-children-are-black">4ª If a node is red, then both its children are black.<a href="#4ª-if-a-node-is-red-then-both-its-children-are-black" class="hash-link" aria-label="Direct link to 4ª If a node is red, then both its children are black." title="Direct link to 4ª If a node is red, then both its children are black."></a></h2><p>This rule might seem rather silly on the first look, but there are 2 important
|
||
functions:</p><ol><li>it allows the algorithms to <em>“notice”</em> that something went wrong (i.e. the
|
||
tree needs to be rebalanced), and</li><li>it holds the balancing and height of the tree <em>“in check”</em> (with the help of
|
||
the 5th rule).</li></ol><p>When we have a look at the algorithms that are used for fixing up the red-black
|
||
tree after an insertion or deletion, we will notice that all the algorithms need
|
||
is the color of the node. </p><blockquote><p>How come it is the only thing that we need?
|
||
How come such naïve thing can be enough?</p></blockquote><p>Let's say we perform an insertion into the tree… We go with the usual and pretty
|
||
primitive insertion into the binary-search tree and then, if needed, we “fix up”
|
||
broken invariants. <em>How can that be enough?</em> With each insertion and deletion we
|
||
maintain the invariants, therefore if we break them with one operation, there's
|
||
only one path on which the invariants were <em>felled</em>. If we know that rest of the
|
||
tree is correct, it allows us to fix the issues just by propagating it to the
|
||
root and <em>abusing</em> the siblings (which are, of course, correct red-black
|
||
subtrees) to fix or at least partially mitigate the issues and propagate them
|
||
further.</p><p>Let's assume that we do not enforce this rule, you can see how it breaks the
|
||
balancing of the tree below.</p><div class="tabs-container tabList__CuJ"><ul role="tablist" aria-orientation="horizontal" class="tabs"><li role="tab" tabindex="0" aria-selected="true" class="tabs__item tabItem_LNqP tabs__item--active">Enforcing this rule</li><li role="tab" tabindex="-1" aria-selected="false" class="tabs__item tabItem_LNqP">Omitting this rule</li></ul><div class="margin-top--md"><div role="tabpanel" class="tabItem_Ymn6"><p><img loading="lazy" src="/assets/images/correct_light-bc4770146072f748be4a5aa11abf3a0c.png#gh-light-mode-only" width="755" height="347" class="img_ev3q">
|
||
<img loading="lazy" src="/assets/images/correct_dark-bbd8d4c1796b145025fed5b6dff03b84.png#gh-dark-mode-only" width="755" height="347" class="img_ev3q"></p></div><div role="tabpanel" class="tabItem_Ymn6" hidden=""><p><img loading="lazy" src="/assets/images/incorrect_light-e787e568e9a1528dcac5bf55ef29fdaa.png#gh-light-mode-only" width="803" height="443" class="img_ev3q">
|
||
<img loading="lazy" src="/assets/images/incorrect_dark-9b8b3be328ffad83233de4536c120016.png#gh-dark-mode-only" width="803" height="443" class="img_ev3q"></p></div></div></div><p>We can create a <strong>big</strong> subtree with only red nodes and <strong>even</strong> when keeping
|
||
the rest of the rules maintained, it will break the time complexity. It stops us
|
||
from “hacking” the black height requirement laid by the 5th rule.</p><h2 class="anchor anchorWithStickyNavbar_LWe7" id="5ª-for-each-node-all-simple-paths-from-the-node-to-descendant-leaves-contain-the-same-number-of-black-nodes">5ª For each node, all simple paths from the node to descendant leaves contain the same number of black nodes.<a href="#5ª-for-each-node-all-simple-paths-from-the-node-to-descendant-leaves-contain-the-same-number-of-black-nodes" class="hash-link" aria-label="Direct link to 5ª For each node, all simple paths from the node to descendant leaves contain the same number of black nodes." title="Direct link to 5ª For each node, all simple paths from the node to descendant leaves contain the same number of black nodes."></a></h2><p>As it was mentioned, with the 4th rule they hold the balancing of the red-black
|
||
tree.</p><div class="theme-admonition theme-admonition-tip alert alert--success admonition_LlT9"><div class="admonitionHeading_tbUL"><span class="admonitionIcon_kALy"><svg viewBox="0 0 12 16"><path fill-rule="evenodd" d="M6.5 0C3.48 0 1 2.19 1 5c0 .92.55 2.25 1 3 1.34 2.25 1.78 2.78 2 4v1h5v-1c.22-1.22.66-1.75 2-4 .45-.75 1-2.08 1-3 0-2.81-2.48-5-5.5-5zm3.64 7.48c-.25.44-.47.8-.67 1.11-.86 1.41-1.25 2.06-1.45 3.23-.02.05-.02.11-.02.17H5c0-.06 0-.13-.02-.17-.2-1.17-.59-1.83-1.45-3.23-.2-.31-.42-.67-.67-1.11C2.44 6.78 2 5.65 2 5c0-2.2 2.02-4 4.5-4 1.22 0 2.36.42 3.22 1.19C10.55 2.94 11 3.94 11 5c0 .66-.44 1.78-.86 2.48zM4 14h5c-.23 1.14-1.3 2-2.5 2s-2.27-.86-2.5-2z"></path></svg></span>tip</div><div class="admonitionContent_S0QG"><p>An important observation here is the fact that the red-black tree is a
|
||
<strong>height</strong>-balanced tree.</p></div></div><p>Enforcing this rule (together with the 4th rule) keeps the tree balanced:</p><ol><li>4th rule makes sure we can't “hack” this requirement.</li><li>This rule ensures that we have “similar”<sup id="fnref-2"><a href="#fn-2" class="footnote-ref">2</a></sup> length to each of the leaves.</li></ol><div class="theme-admonition theme-admonition-tip alert alert--success admonition_LlT9"><div class="admonitionHeading_tbUL"><span class="admonitionIcon_kALy"><svg viewBox="0 0 12 16"><path fill-rule="evenodd" d="M6.5 0C3.48 0 1 2.19 1 5c0 .92.55 2.25 1 3 1.34 2.25 1.78 2.78 2 4v1h5v-1c.22-1.22.66-1.75 2-4 .45-.75 1-2.08 1-3 0-2.81-2.48-5-5.5-5zm3.64 7.48c-.25.44-.47.8-.67 1.11-.86 1.41-1.25 2.06-1.45 3.23-.02.05-.02.11-.02.17H5c0-.06 0-.13-.02-.17-.2-1.17-.59-1.83-1.45-3.23-.2-.31-.42-.67-.67-1.11C2.44 6.78 2 5.65 2 5c0-2.2 2.02-4 4.5-4 1.22 0 2.36.42 3.22 1.19C10.55 2.94 11 3.94 11 5c0 .66-.44 1.78-.86 2.48zM4 14h5c-.23 1.14-1.3 2-2.5 2s-2.27-.86-2.5-2z"></path></svg></span>AVL tree</div><div class="admonitionContent_S0QG"><p>You might have heard about an <em>AVL tree</em> before. It is the first self-balanced
|
||
tree to be ever introduced and works in a very similar nature as the red-black
|
||
tree, the only difference is that it does not deal with the <em>black height</em>, but
|
||
the height in general.</p><p>If you were to compare AVL with the red-black tree, you can say that AVL is much
|
||
more strict while red-black tree can still maintain the same asymptotic time
|
||
complexity for the operations, but having more relaxed rules.</p></div></div><div class="footnotes"><hr><ol><li id="fn-1">CORMEN, Thomas. Introduction to algorithms. Cambridge, Mass: MIT Press, 2009. isbn 9780262033848.<a href="#fnref-1" class="footnote-backref">↩</a></li><li id="fn-2">red nodes still exist<a href="#fnref-2" class="footnote-backref">↩</a></li></ol></div></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/red-black-trees">red-black trees</a></li><li class="tag_QGVx"><a class="tag_zVej tagRegular_sFm0" href="/ib002/tags/balanced-trees">balanced trees</a></li></ul></div></div><div class="theme-doc-footer-edit-meta-row row"><div class="col"><a href="https://gitlab.com/mfocko/blog/tree/main/ib002/08-rb-trees/2023-06-10-rules.md" target="_blank" rel="noreferrer noopener" class="theme-edit-this-page"><svg fill="currentColor" height="20" width="20" viewBox="0 0 40 40" class="iconEdit_Z9Sw" aria-hidden="true"><g><path d="m34.5 11.7l-3 3.1-6.3-6.3 3.1-3q0.5-0.5 1.2-0.5t1.1 0.5l3.9 3.9q0.5 0.4 0.5 1.1t-0.5 1.2z m-29.5 17.1l18.4-18.5 6.3 6.3-18.4 18.4h-6.3v-6.2z"></path></g></svg>Edit this page</a></div><div class="col lastUpdated_vwxv"><span class="theme-last-updated">Last updated<!-- --> on <b><time datetime="2023-06-10T00:00:00.000Z">Jun 10, 2023</time></b></span></div></div></footer></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="Docs pages"><a class="pagination-nav__link pagination-nav__link--prev" href="/ib002/rb-trees/applications"><div class="pagination-nav__sublabel">Previous</div><div class="pagination-nav__label">Použití červeno-černých stromů</div></a><a class="pagination-nav__link pagination-nav__link--next" href="/ib002/category/graphs"><div class="pagination-nav__sublabel">Next</div><div class="pagination-nav__label">Graphs</div></a></nav></div></div><div class="col col--3"><div class="tableOfContents_bqdL thin-scrollbar theme-doc-toc-desktop"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#introduction" class="table-of-contents__link toc-highlight">Introduction</a></li><li><a href="#1ª-every-node-is-either-red-or-black" class="table-of-contents__link toc-highlight">1ª Every node is either red or black.</a><ul><li><a href="#do-i-really-need-the-nodes-to-be-explicitly-colored" class="table-of-contents__link toc-highlight">Do I really need the nodes to be explicitly colored?</a></li></ul></li><li><a href="#2ª-the-root-is-black" class="table-of-contents__link toc-highlight">2ª The root is black.</a></li><li><a href="#3ª-every-leaf-nil-is-black" class="table-of-contents__link toc-highlight">3ª Every leaf (<code>nil</code>) is black.</a></li><li><a href="#4ª-if-a-node-is-red-then-both-its-children-are-black" class="table-of-contents__link toc-highlight">4ª If a node is red, then both its children are black.</a></li><li><a href="#5ª-for-each-node-all-simple-paths-from-the-node-to-descendant-leaves-contain-the-same-number-of-black-nodes" class="table-of-contents__link toc-highlight">5ª For each node, all simple paths from the node to descendant leaves contain the same number of black nodes.</a></li></ul></div></div></div></div></main></div></div><footer class="footer footer--dark"><div class="container container-fluid"><div class="row footer__links"><div class="col footer__col"><div class="footer__title">Git</div><ul class="footer__items clean-list"><li class="footer__item"><a href="https://github.com/mfocko" target="_blank" rel="noopener noreferrer" class="footer__link-item">GitHub<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_nPIU"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></a></li><li class="footer__item"><a href="https://gitlab.com/mfocko" 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