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Why are they\nformulated the way they are? How come they keep the tree balanced? Let's go through\neach of the red-black tree rules and try to change, break and contemplate about\nthem."),(0,s.kt)("p",null,"We expect that you are familiar with the following set of the rules",(0,s.kt)("sup",{parentName:"p",id:"fnref-1"},(0,s.kt)("a",{parentName:"sup",href:"#fn-1",className:"footnote-ref"},"1")),":"),(0,s.kt)("ol",null,(0,s.kt)("li",{parentName:"ol"},"Every node is either red or black."),(0,s.kt)("li",{parentName:"ol"},"The root is black."),(0,s.kt)("li",{parentName:"ol"},"Every leaf (",(0,s.kt)("inlineCode",{parentName:"li"},"nil"),") is black."),(0,s.kt)("li",{parentName:"ol"},"If a node is red, then both its children are black."),(0,s.kt)("li",{parentName:"ol"},"For each node, all simple paths from the node to descendant leaves contain the\nsame number of black nodes.")),(0,s.kt)("p",null,"Each section will go into ",(0,s.kt)("em",{parentName:"p"},"reasonable")," details of each rule."),(0,s.kt)("h2",{id:"1\xaa-every-node-is-either-red-or-black"},"1\xaa Every node is either red or black."),(0,s.kt)("p",null,"OK\u2026 This one is very simple. It is just a definition and is used in all other\nrules. Not much to talk about here. Or is there?"),(0,s.kt)("h3",{id:"do-i-really-need-the-nodes-to-be-explicitly-colored"},"Do I really need the nodes to be explicitly colored?"),(0,s.kt)("p",null,"The answer is no. Balancing of the red-black trees is \u201cenforced\u201d by the 4th and\n5th rule in the enumeration above. There are many ways you can avoid using colors."),(0,s.kt)("h4",{id:"black-height"},"Black height"),(0,s.kt)("p",null,"We mentioned the 4th and 5th rule and that it enforces the balancing. What does\nit mean for us?"),(0,s.kt)("p",null,"Well, we definitely do not have to use the colors, which even as a ",(0,s.kt)("em",{parentName:"p"},"boolean")," flag\nwould take at least 1 byte of space (and usually even more), cause\u2026 well, it is\neasier for the CPU to work with words rather than single bits."),(0,s.kt)("p",null,"We could use the black height, couldn't we? It would mean more memory used, cause\nit should be ideally big and unsigned. Can we tell the color of a node from the\nblack height? Of course we can, if my child has the same black height as I do,\nit means that there was no black node added on the path between us and therefore\nmy child would be colored red."),(0,s.kt)("p",null,"Example of a red-black tree that keeps count of black nodes on paths to the\nleaves follows:"),(0,s.kt)("p",null,(0,s.kt)("img",{alt:"Red-black tree with black height",src:a(5021).Z+"#gh-light-mode-only",width:"923",height:"539"}),"\n",(0,s.kt)("img",{alt:"Red-black tree with black height",src:a(9493).Z+"#gh-dark-mode-only",width:"923",height:"539"})),(0,s.kt)("p",null,"We mark the ",(0,s.kt)("em",{parentName:"p"},"black heights")," in superscript. You can see that all leaves have the\nblack height equal to ",(0,s.kt)("span",{parentName:"p",className:"math math-inline"},(0,s.kt)("span",{parentName:"span",className:"katex"},(0,s.kt)("span",{parentName:"span",className:"katex-mathml"},(0,s.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,s.kt)("semantics",{parentName:"math"},(0,s.kt)("mrow",{parentName:"semantics"},(0,s.kt)("mn",{parentName:"mrow"},"1")),(0,s.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"1")))),(0,s.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,s.kt)("span",{parentName:"span",className:"base"},(0,s.kt)("span",{parentName:"span",className:"strut",style:{height:"0.6444em"}}),(0,s.kt)("span",{parentName:"span",className:"mord"},"1"))))),". Let's take a look at some of the interesting cases:"),(0,s.kt)("ul",null,(0,s.kt)("li",{parentName:"ul"},(0,s.kt)("p",{parentName:"li"},"If we take a look at the node with ",(0,s.kt)("span",{parentName:"p",className:"math math-inline"},(0,s.kt)("span",{parentName:"span",className:"katex"},(0,s.kt)("span",{parentName:"span",className:"katex-mathml"},(0,s.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,s.kt)("semantics",{parentName:"math"},(0,s.kt)("mrow",{parentName:"semantics"},(0,s.kt)("mtext",{parentName:"mrow"},"key"),(0,s.kt)("mo",{parentName:"mrow"},"="),(0,s.kt)("mn",{parentName:"mrow"},"9")),(0,s.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"\\text{key} = 9")))),(0,s.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,s.kt)("span",{parentName:"span",className:"base"},(0,s.kt)("span",{parentName:"span",className:"strut",style:{height:"0.8889em",verticalAlign:"-0.1944em"}}),(0,s.kt)("span",{parentName:"span",className:"mord text"},(0,s.kt)("span",{parentName:"span",className:"mord"},"key")),(0,s.kt)("span",{parentName:"span",className:"mspace",style:{marginRight:"0.2778em"}}),(0,s.kt)("span",{parentName:"span",className:"mrel"},"="),(0,s.kt)("span",{parentName:"span",className:"mspace",style:{marginRight:"0.2778em"}})),(0,s.kt)("span",{parentName:"span",className:"base"},(0,s.kt)("span",{parentName:"span",className:"strut",style:{height:"0.6444em"}}),(0,s.kt)("span",{parentName:"span",className:"mord"},"9"))))),", we can see that it is\ncoloured red and its black height is 1, because it is a leaf."),(0,s.kt)("p",{parentName:"li"},"Let's look at its parent (node with ",(0,s.kt)("span",{parentName:"p",className:"math math-inline"},(0,s.kt)("span",{parentName:"span",className:"katex"},(0,s.kt)("span",{parentName:"span",className:"katex-mathml"},(0,s.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,s.kt)("semantics",{parentName:"math"},(0,s.kt)("mrow",{parentName:"semantics"},(0,s.kt)("mtext",{parentName:"mrow"},"key"),(0,s.kt)("mo",{parentName:"mrow"},"="),(0,s.kt)("mn",{parentName:"mrow"},"8")),(0,s.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"\\text{key} = 8")))),(0,s.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,s.kt)("span",{parentName:"span",className:"base"},(0,s.kt)("span",{parentName:"span",className:"strut",style:{height:"0.8889em",verticalAlign:"-0.1944em"}}),(0,s.kt)("span",{parentName:"span",className:"mord text"},(0,s.kt)("span",{parentName:"span",className:"mord"},"key")),(0,s.kt)("span",{parentName:"span",className:"mspace",style:{marginRight:"0.2778em"}}),(0,s.kt)("span",{parentName:"span",className:"mrel"},"="),(0,s.kt)("span",{parentName:"span",className:"mspace",style:{marginRight:"0.2778em"}})),(0,s.kt)("span",{parentName:"span",className:"base"},(0,s.kt)("span",{parentName:"span",className:"strut",style:{height:"0.6444em"}}),(0,s.kt)("span",{parentName:"span",className:"mord"},"8"))))),"). On its left side it has\n",(0,s.kt)("inlineCode",{parentName:"p"},"nil")," and on its right side the ",(0,s.kt)("span",{parentName:"p",className:"math math-inline"},(0,s.kt)("span",{parentName:"span",className:"katex"},(0,s.kt)("span",{parentName:"span",className:"katex-mathml"},(0,s.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,s.kt)("semantics",{parentName:"math"},(0,s.kt)("mrow",{parentName:"semantics"},(0,s.kt)("mn",{parentName:"mrow"},"9")),(0,s.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"9")))),(0,s.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,s.kt)("span",{parentName:"span",className:"base"},(0,s.kt)("span",{parentName:"span",className:"strut",style:{height:"0.6444em"}}),(0,s.kt)("span",{parentName:"span",className:"mord"},"9"))))),". And its black height is still ",(0,s.kt)("span",{parentName:"p",className:"math math-inline"},(0,s.kt)("span",{parentName:"span",className:"katex"},(0,s.kt)("span",{parentName:"span",className:"katex-mathml"},(0,s.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,s.kt)("semantics",{parentName:"math"},(0,s.kt)("mrow",{parentName:"semantics"},(0,s.kt)("mn",{parentName:"mrow"},"1")),(0,s.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"1")))),(0,s.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,s.kt)("span",{parentName:"span",className:"base"},(0,s.kt)("span",{parentName:"span",className:"strut",style:{height:"0.6444em"}}),(0,s.kt)("span",{parentName:"span",className:"mord"},"1"))))),", cause\nexcept for the ",(0,s.kt)("inlineCode",{parentName:"p"},"nil")," leaves, there are no other black nodes."),(0,s.kt)("p",{parentName:"li"},"We can clearly see that if a node has the same black height as its parent, it\nis a red node.")),(0,s.kt)("li",{parentName:"ul"},(0,s.kt)("p",{parentName:"li"},"Now let's take a look at the root with ",(0,s.kt)("span",{parentName:"p",className:"math math-inline"},(0,s.kt)("span",{parentName:"span",className:"katex"},(0,s.kt)("span",{parentName:"span",className:"katex-mathml"},(0,s.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,s.kt)("semantics",{parentName:"math"},(0,s.kt)("mrow",{parentName:"semantics"},(0,s.kt)("mtext",{parentName:"mrow"},"key"),(0,s.kt)("mo",{parentName:"mrow"},"="),(0,s.kt)("mn",{parentName:"mrow"},"3")),(0,s.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"\\text{key} = 3")))),(0,s.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,s.kt)("span",{parentName:"span",className:"base"},(0,s.kt)("span",{parentName:"span",className:"strut",style:{height:"0.8889em",verticalAlign:"-0.1944em"}}),(0,s.kt)("span",{parentName:"span",className:"mord text"},(0,s.kt)("span",{parentName:"span",className:"mord"},"key")),(0,s.kt)("span",{parentName:"span",className:"mspace",style:{marginRight:"0.2778em"}}),(0,s.kt)("span",{parentName:"span",className:"mrel"},"="),(0,s.kt)("span",{parentName:"span",className:"mspace",style:{marginRight:"0.2778em"}})),(0,s.kt)("span",{parentName:"span",className:"base"},(0,s.kt)("span",{parentName:"span",className:"strut",style:{height:"0.6444em"}}),(0,s.kt)("span",{parentName:"span",className:"mord"},"3"))))),". It has a black height\nof 3. Both of its children are black nodes and have black height of 2."),(0,s.kt)("p",{parentName:"li"},"We can see that if a node has its height 1 lower than its parent, it is a black\nnode."),(0,s.kt)("p",{parentName:"li"},"The reasoning behind it is rather simple, we count the black nodes all the way\nto the leaves, therefore if my parent has a higher black height, it means that\non the path from me to my parent there is a black node, but the only node added\nis me, therefore I must be black."))),(0,s.kt)("h4",{id:"isomorphic-trees"},"Isomorphic trees"),(0,s.kt)("p",null,"One of the other ways to avoid using color is storing the red-black tree in some\nisomorphic tree. The structure of 2-3-4 tree allows us to avoid using the color\ncompletely. This is a bit different approach, cause we would be basically using\ndifferent tree, so we keep this note in just as a \u201chack\u201d."),(0,s.kt)("h2",{id:"2\xaa-the-root-is-black"},"2\xaa The root is black."),(0,s.kt)("p",null,"This rule might seem like a very important one, but overall is not. You can safely\nomit this rule, but you also need to deal with the consequences."),(0,s.kt)("p",null,"Let's refresh our memory with the algorithm of ",(0,s.kt)("em",{parentName:"p"},"insert fixup"),":"),(0,s.kt)("pre",null,(0,s.kt)("code",{parentName:"pre"},"WHILE z.p.color == Red\n  IF z.p == z.p.p.left\n    y = z.p.p.right\n\n    IF y.color == Red\n      z.p.color = Black\n      y.color = Black\n      z.p.p.color = Red\n      z = z.p.p\n    ELSE\n      IF z == z.p.right\n        z = z.p\n        Left-Rotate(T, z)\n      z.p.color = Black\n      z.p.p.color = Red\n      Right-Rotate(T, z.p.p)\n  ELSE (same as above with \u201cright\u201d and \u201cleft\u201d exchanged)\n\nT.root.color = Black\n")),(0,s.kt)("admonition",{type:"tip"},(0,s.kt)("p",{parentName:"admonition"},"If you have tried to implement any of the more complex data structures, such as\nred-black trees, etc., in a statically typed language that also checks you for\n",(0,s.kt)("inlineCode",{parentName:"p"},"NULL"),"-correctness (e.g. ",(0,s.kt)("em",{parentName:"p"},"mypy")," or even C# with nullable reference types), you\nmight have run into numerous issues in the cases where you are 100% sure that you\ncannot obtain ",(0,s.kt)("inlineCode",{parentName:"p"},"NULL")," because of the invariants, but the static type checking\ndoesn't know that."),(0,s.kt)("p",{parentName:"admonition"},"The issue we hit with the ",(0,s.kt)("em",{parentName:"p"},"insert fixup")," is very similar.")),(0,s.kt)("p",null,"You might not realize the issue at the first sight, but the algorithm described\nwith the pseudocode above expects that the root of the red-black tree is black by\nboth relying on the invariant in the algorithm and afterwards by enforcing the\nblack root property."),(0,s.kt)("p",null,"If we decide to omit this condition, we need to address it in the pseudocodes\naccordingly."),(0,s.kt)("table",null,(0,s.kt)("thead",{parentName:"table"},(0,s.kt)("tr",{parentName:"thead"},(0,s.kt)("th",{parentName:"tr",align:"center"},"Usual algorithm with black root"),(0,s.kt)("th",{parentName:"tr",align:"center"},"Allowing red root"))),(0,s.kt)("tbody",{parentName:"table"},(0,s.kt)("tr",{parentName:"tbody"},(0,s.kt)("td",{parentName:"tr",align:"center"},(0,s.kt)("img",{alt:"1\xaa insertion",src:a(3416).Z+"#gh-light-mode-only",width:"179",height:"155"}),(0,s.kt)("img",{alt:"1\xaa insertion",src:a(4522).Z+"#gh-dark-mode-only",width:"179",height:"155"})),(0,s.kt)("td",{parentName:"tr",align:"center"},(0,s.kt)("img",{alt:"1\xaa insertion",src:a(477).Z+"#gh-light-mode-only",width:"179",height:"155"}),(0,s.kt)("img",{alt:"1\xaa insertion",src:a(8125).Z+"#gh-dark-mode-only",width:"179",height:"155"}))),(0,s.kt)("tr",{parentName:"tbody"},(0,s.kt)("td",{parentName:"tr",align:"center"},(0,s.kt)("img",{alt:"2\xaa insertion",src:a(6850).Z+"#gh-light-mode-only",width:"227",height:"251"}),(0,s.kt)("img",{alt:"2\xaa insertion",src:a(8983).Z+"#gh-dark-mode-only",width:"227",height:"251"})),(0,s.kt)("td",{parentName:"tr",align:"center"},(0,s.kt)("img",{alt:"2\xaa insertion",src:a(446).Z+"#gh-light-mode-only",width:"227",height:"251"}),(0,s.kt)("img",{alt:"2\xaa insertion",src:a(9905).Z+"#gh-dark-mode-only",width:"227",height:"251"}))),(0,s.kt)("tr",{parentName:"tbody"},(0,s.kt)("td",{parentName:"tr",align:"center"},(0,s.kt)("img",{alt:"3\xaa insertion",src:a(9657).Z+"#gh-light-mode-only",width:"371",height:"251"}),(0,s.kt)("img",{alt:"3\xaa insertion",src:a(9296).Z+"#gh-dark-mode-only",width:"371",height:"251"})),(0,s.kt)("td",{parentName:"tr",align:"center"},(0,s.kt)("img",{alt:"3\xaa insertion",src:a(841).Z+"#gh-light-mode-only",width:"371",height:"251"}),(0,s.kt)("img",{alt:"3\xaa insertion",src:a(7659).Z+"#gh-dark-mode-only",width:"371",height:"251"}))),(0,s.kt)("tr",{parentName:"tbody"},(0,s.kt)("td",{parentName:"tr",align:"center"},(0,s.kt)("img",{alt:"4\xaa insertion",src:a(515).Z+"#gh-light-mode-only",width:"419",height:"347"}),(0,s.kt)("img",{alt:"4\xaa insertion",src:a(9123).Z+"#gh-dark-mode-only",width:"419",height:"347"})),(0,s.kt)("td",{parentName:"tr",align:"center"},(0,s.kt)("img",{alt:"4\xaa insertion",src:a(2658).Z+"#gh-light-mode-only",width:"419",height:"347"}),(0,s.kt)("img",{alt:"4\xaa insertion",src:a(2979).Z+"#gh-dark-mode-only",width:"419",height:"347"}))),(0,s.kt)("tr",{parentName:"tbody"},(0,s.kt)("td",{parentName:"tr",align:"center"},(0,s.kt)("img",{alt:"5\xaa insertion",src:a(8747).Z+"#gh-light-mode-only",width:"419",height:"347"}),(0,s.kt)("img",{alt:"5\xaa insertion",src:a(7518).Z+"#gh-dark-mode-only",width:"419",height:"347"})),(0,s.kt)("td",{parentName:"tr",align:"center"},(0,s.kt)("img",{alt:"5\xaa insertion",src:a(2014).Z+"#gh-light-mode-only",width:"419",height:"347"}),(0,s.kt)("img",{alt:"5\xaa insertion",src:a(5959).Z+"#gh-dark-mode-only",width:"419",height:"347"}))),(0,s.kt)("tr",{parentName:"tbody"},(0,s.kt)("td",{parentName:"tr",align:"center"},(0,s.kt)("img",{alt:"6\xaa insertion",src:a(8317).Z+"#gh-light-mode-only",width:"563",height:"347"}),(0,s.kt)("img",{alt:"6\xaa insertion",src:a(2193).Z+"#gh-dark-mode-only",width:"563",height:"347"})),(0,s.kt)("td",{parentName:"tr",align:"center"},(0,s.kt)("img",{alt:"6\xaa insertion",src:a(162).Z+"#gh-light-mode-only",width:"563",height:"347"}),(0,s.kt)("img",{alt:"6\xaa insertion",src:a(1105).Z+"#gh-dark-mode-only",width:"563",height:"347"}))),(0,s.kt)("tr",{parentName:"tbody"},(0,s.kt)("td",{parentName:"tr",align:"center"},(0,s.kt)("img",{alt:"7\xaa insertion",src:a(8204).Z+"#gh-light-mode-only",width:"563",height:"443"}),(0,s.kt)("img",{alt:"7\xaa insertion",src:a(6986).Z+"#gh-dark-mode-only",width:"563",height:"443"})),(0,s.kt)("td",{parentName:"tr",align:"center"},(0,s.kt)("img",{alt:"7\xaa insertion",src:a(355).Z+"#gh-light-mode-only",width:"563",height:"443"}),(0,s.kt)("img",{alt:"7\xaa insertion",src:a(4300).Z+"#gh-dark-mode-only",width:"563",height:"443"}))),(0,s.kt)("tr",{parentName:"tbody"},(0,s.kt)("td",{parentName:"tr",align:"center"},(0,s.kt)("img",{alt:"8\xaa insertion",src:a(345).Z+"#gh-light-mode-only",width:"635",height:"443"}),(0,s.kt)("img",{alt:"8\xaa insertion",src:a(1988).Z+"#gh-dark-mode-only",width:"635",height:"443"})),(0,s.kt)("td",{parentName:"tr",align:"center"},(0,s.kt)("img",{alt:"8\xaa insertion",src:a(2530).Z+"#gh-light-mode-only",width:"635",height:"443"}),(0,s.kt)("img",{alt:"8\xaa insertion",src:a(363).Z+"#gh-dark-mode-only",width:"635",height:"443"}))),(0,s.kt)("tr",{parentName:"tbody"},(0,s.kt)("td",{parentName:"tr",align:"center"},(0,s.kt)("img",{alt:"9\xaa insertion",src:a(6464).Z+"#gh-light-mode-only",width:"755",height:"443"}),(0,s.kt)("img",{alt:"9\xaa insertion",src:a(437).Z+"#gh-dark-mode-only",width:"755",height:"443"})),(0,s.kt)("td",{parentName:"tr",align:"center"},(0,s.kt)("img",{alt:"9\xaa insertion",src:a(6039).Z+"#gh-light-mode-only",width:"755",height:"443"}),(0,s.kt)("img",{alt:"9\xaa insertion",src:a(3122).Z+"#gh-dark-mode-only",width:"755",height:"443"}))))),(0,s.kt)("h2",{id:"3\xaa-every-leaf-nil-is-black"},"3\xaa Every leaf (",(0,s.kt)("inlineCode",{parentName:"h2"},"nil"),") is black."),(0,s.kt)("p",null,"Now, this rule is a funny one. What does this imply and can I interpret this in\nsome other way? Let's go through some of the possible ways I can look at this and\nhow would they affect the other rules and balancing."),(0,s.kt)("p",null,"We will experiment with the following tree:\n",(0,s.kt)("img",{src:a(6769).Z+"#gh-light-mode-only",width:"899",height:"539"}),"\n",(0,s.kt)("img",{src:a(4086).Z+"#gh-dark-mode-only",width:"899",height:"539"})),(0,s.kt)("p",null,"We should start by counting the black nodes from root to the ",(0,s.kt)("inlineCode",{parentName:"p"},"nil")," leaves based\non the rules. We have multiple similar paths, so we will pick only the interesting\nones."),(0,s.kt)("ol",null,(0,s.kt)("li",{parentName:"ol"},"What happens if we do not count the ",(0,s.kt)("inlineCode",{parentName:"li"},"nil")," leaves?"),(0,s.kt)("li",{parentName:"ol"},"What happens if we consider leaves the nodes with ",(0,s.kt)("em",{parentName:"li"},"no descendants"),", i.e. both\nof node's children are ",(0,s.kt)("inlineCode",{parentName:"li"},"nil"),"?"),(0,s.kt)("li",{parentName:"ol"},"What happens if we do not count the ",(0,s.kt)("inlineCode",{parentName:"li"},"nil")," leaves, but consider nodes with at\nleast one ",(0,s.kt)("inlineCode",{parentName:"li"},"nil")," descendant as leaves?")),(0,s.kt)("table",null,(0,s.kt)("thead",{parentName:"table"},(0,s.kt)("tr",{parentName:"thead"},(0,s.kt)("th",{parentName:"tr",align:"right"},"path"),(0,s.kt)("th",{parentName:"tr",align:"right"},"black nodes"),(0,s.kt)("th",{parentName:"tr",align:"right"},"1\xaa idea"),(0,s.kt)("th",{parentName:"tr",align:"right"},"2\xaa idea"),(0,s.kt)("th",{parentName:"tr",align:"right"},"3\xaa idea"))),(0,s.kt)("tbody",{parentName:"table"},(0,s.kt)("tr",{parentName:"tbody"},(0,s.kt)("td",{parentName:"tr",align:"right"},(0,s.kt)("inlineCode",{parentName:"td"},"3 \u2192 1 \u2192 0 \u2192 nil")),(0,s.kt)("td",{parentName:"tr",align:"right"},"4"),(0,s.kt)("td",{parentName:"tr",align:"right"},"3"),(0,s.kt)("td",{parentName:"tr",align:"right"},"4"),(0,s.kt)("td",{parentName:"tr",align:"right"},"3")),(0,s.kt)("tr",{parentName:"tbody"},(0,s.kt)("td",{parentName:"tr",align:"right"},(0,s.kt)("inlineCode",{parentName:"td"},"3 \u2192 5 \u2192 7 \u2192 8 \u2192 nil")),(0,s.kt)("td",{parentName:"tr",align:"right"},"4"),(0,s.kt)("td",{parentName:"tr",align:"right"},"3"),(0,s.kt)("td",{parentName:"tr",align:"right"},"-"),(0,s.kt)("td",{parentName:"tr",align:"right"},"3")),(0,s.kt)("tr",{parentName:"tbody"},(0,s.kt)("td",{parentName:"tr",align:"right"},(0,s.kt)("inlineCode",{parentName:"td"},"3 \u2192 5 \u2192 7 \u2192 8 \u2192 9 \u2192 nil")),(0,s.kt)("td",{parentName:"tr",align:"right"},"4"),(0,s.kt)("td",{parentName:"tr",align:"right"},"3"),(0,s.kt)("td",{parentName:"tr",align:"right"},"4"),(0,s.kt)("td",{parentName:"tr",align:"right"},"3")))),(0,s.kt)("p",null,"First idea is very easy to execute and it is also very easy to argue about its\ncorrectness. It is correct, because we just subtract one from each of the paths.\nThis affects ",(0,s.kt)("strong",{parentName:"p"},"all")," paths and therefore results in global decrease by one."),(0,s.kt)("p",null,"Second idea is a bit more complicated. We count the ",(0,s.kt)("inlineCode",{parentName:"p"},"nil"),"s, so the count is ",(0,s.kt)("span",{parentName:"p",className:"math math-inline"},(0,s.kt)("span",{parentName:"span",className:"katex"},(0,s.kt)("span",{parentName:"span",className:"katex-mathml"},(0,s.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,s.kt)("semantics",{parentName:"math"},(0,s.kt)("mrow",{parentName:"semantics"},(0,s.kt)("mn",{parentName:"mrow"},"4")),(0,s.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"4")))),(0,s.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,s.kt)("span",{parentName:"span",className:"base"},(0,s.kt)("span",{parentName:"span",className:"strut",style:{height:"0.6444em"}}),(0,s.kt)("span",{parentName:"span",className:"mord"},"4"))))),"\nas it should be. However, there is one difference. Second path no longer satisfies\nthe condition of a ",(0,s.kt)("em",{parentName:"p"},"leaf"),". Technically it relaxes the 5th rule, because we leave\nout some of the nodes. We should probably avoid that."),(0,s.kt)("admonition",{type:"caution"},(0,s.kt)("p",{parentName:"admonition"},"With the second idea, you may also feel that we are \u201cbending\u201d the rules a bit,\nespecially the definition of the \u201cleaf\u201d nodes."),(0,s.kt)("p",{parentName:"admonition"},"Given the definition of the red-black tree, where ",(0,s.kt)("inlineCode",{parentName:"p"},"nil")," is considered to be an\nexternal node, we have decided that bending it a bit just to stir a thought about\nit won't hurt anybody. \ud83d\ude09")),(0,s.kt)("h2",{id:"4\xaa-if-a-node-is-red-then-both-its-children-are-black"},"4\xaa If a node is red, then both its children are black."),(0,s.kt)("p",null,"This rule might seem rather silly on the first look, but there are 2 important\nfunctions:"),(0,s.kt)("ol",null,(0,s.kt)("li",{parentName:"ol"},"it allows the algorithms to ",(0,s.kt)("em",{parentName:"li"},"\u201cnotice\u201d")," that something went wrong (i.e. the\ntree needs to be rebalanced), and"),(0,s.kt)("li",{parentName:"ol"},"it holds the balancing and height of the tree ",(0,s.kt)("em",{parentName:"li"},"\u201cin check\u201d")," (with the help of\nthe 5th rule).")),(0,s.kt)("p",null,"When we have a look at the algorithms that are used for fixing up the red-black\ntree after an insertion or deletion, we will notice that all the algorithms need\nis the color of the node. "),(0,s.kt)("blockquote",null,(0,s.kt)("p",{parentName:"blockquote"},"How come it is the only thing that we need?\nHow come such na\xefve thing can be enough?")),(0,s.kt)("p",null,"Let's say we perform an insertion into the tree\u2026 We go with the usual and pretty\nprimitive insertion into the binary-search tree and then, if needed, we \u201cfix up\u201d\nbroken invariants. ",(0,s.kt)("em",{parentName:"p"},"How can that be enough?")," With each insertion and deletion we\nmaintain the invariants, therefore if we break them with one operation, there's\nonly one path on which the invariants were ",(0,s.kt)("em",{parentName:"p"},"felled"),". If we know that rest of the\ntree is correct, it allows us to fix the issues just by propagating it to the\nroot and ",(0,s.kt)("em",{parentName:"p"},"abusing")," the siblings (which are, of course, correct red-black\nsubtrees) to fix or at least partially mitigate the issues and propagate them\nfurther."),(0,s.kt)("p",null,"Let's assume that we do not enforce this rule, you can see how it breaks the\nbalancing of the tree below."),(0,s.kt)(w,{mdxType:"Tabs"},(0,s.kt)(v,{value:"enforcing",label:"Enforcing this rule",mdxType:"TabItem"},(0,s.kt)("p",null,(0,s.kt)("img",{src:a(772).Z+"#gh-light-mode-only",width:"755",height:"347"}),"\n",(0,s.kt)("img",{src:a(8663).Z+"#gh-dark-mode-only",width:"755",height:"347"}))),(0,s.kt)(v,{value:"omitting",label:"Omitting this rule",mdxType:"TabItem"},(0,s.kt)("p",null,(0,s.kt)("img",{src:a(4130).Z+"#gh-light-mode-only",width:"803",height:"443"}),"\n",(0,s.kt)("img",{src:a(2683).Z+"#gh-dark-mode-only",width:"803",height:"443"})))),(0,s.kt)("p",null,"We can create a ",(0,s.kt)("strong",{parentName:"p"},"big")," subtree with only red nodes and ",(0,s.kt)("strong",{parentName:"p"},"even")," when keeping\nthe rest of the rules maintained, it will break the time complexity. It stops us\nfrom \u201chacking\u201d the black height requirement laid by the 5th rule."),(0,s.kt)("h2",{id:"5\xaa-for-each-node-all-simple-paths-from-the-node-to-descendant-leaves-contain-the-same-number-of-black-nodes"},"5\xaa For each node, all simple paths from the node to descendant leaves contain the same number of black nodes."),(0,s.kt)("p",null,"As it was mentioned, with the 4th rule they hold the balancing of the red-black\ntree."),(0,s.kt)("admonition",{type:"tip"},(0,s.kt)("p",{parentName:"admonition"},"An important observation here is the fact that the red-black tree is a\n",(0,s.kt)("strong",{parentName:"p"},"height"),"-balanced tree.")),(0,s.kt)("p",null,"Enforcing this rule (together with the 4th rule) keeps the tree balanced:"),(0,s.kt)("ol",null,(0,s.kt)("li",{parentName:"ol"},"4th rule makes sure we can't \u201chack\u201d this requirement."),(0,s.kt)("li",{parentName:"ol"},"This rule ensures that we have \u201csimilar\u201d",(0,s.kt)("sup",{parentName:"li",id:"fnref-2"},(0,s.kt)("a",{parentName:"sup",href:"#fn-2",className:"footnote-ref"},"2"))," length to each of the leaves.")),(0,s.kt)("admonition",{title:"AVL tree",type:"tip"},(0,s.kt)("p",{parentName:"admonition"},"You might have heard about an ",(0,s.kt)("em",{parentName:"p"},"AVL tree")," before. It is the first self-balanced\ntree to be ever introduced and works in a very similar nature as the red-black\ntree, the only difference is that it does not deal with the ",(0,s.kt)("em",{parentName:"p"},"black height"),", but\nthe height in general."),(0,s.kt)("p",{parentName:"admonition"},"If you were to compare AVL with the red-black tree, you can say that AVL is much\nmore strict while red-black tree can still maintain the same asymptotic time\ncomplexity for the operations, but having more relaxed rules.")),(0,s.kt)("div",{className:"footnotes"},(0,s.kt)("hr",{parentName:"div"}),(0,s.kt)("ol",{parentName:"div"},(0,s.kt)("li",{parentName:"ol",id:"fn-1"},"CORMEN, Thomas. Introduction to algorithms. 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n="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAALMAAACbCAYAAAAp66qoAAAABmJLR0QA/wD/AP+gvaeTAAASYklEQVR4nO3deVSU1R8G8Ocdhh0FwQVBfyaoECCeLEsMBVMwj1tJLkFJWrnXCcXlZG7Z4QRamNvxmGZFLoBLmkKIiigkirugssqiICAuIOAMzHx/fxQezd2Y9w537ucc/nCcw32AZy6Xd973vhIREQSh+YtVsE4gCE1FlFnghiizwA0l6wA80Wg0KCsrQ1lZGW7dugWNRoPq6mo0NDTAwsICpqamMDc3h42NDdq3bw9bW1vWkbkiyvwC6urqkJ6ejnPnziEjIwOZmZnIy8tDeXk5NBrNM38eMzMzdOjQAS4uLvDw8IC7uzt69uwJNzc3SJKkw6+AT5I4mvF0Wq0Wx44dQ1xcHA4dOoT09HSoVCrY2treK6GLiwvat28PBwcHtGvXDra2tlAoFGjRogWUSiVqa2uhUqlw9+5d3LhxAyUlJSgtLUVxcTEuXLiAzMxMXLx4EWq1Gm3atEHfvn3Rv39/DB8+HP/73/9Yfwuag1hR5idITU3Fpk2bsGvXLpSUlMDZ2Rm+vr7w8fGBj49Pk5esoaEBZ86cweHDh5GcnIzk5GRUVVXh1VdfRUBAAMaNGwcHB4cmHZMjsSDhAdXV1bR69Wrq3r07ASBPT09avHgxnTt3TvYsKpWK4uPjaeLEidS6dWtSKpX07rvv0r59+2TP0gzEiDL/o7q6mpYvX0729vZkZmZGo0aNosTERNax7lGpVBQTE0MDBw4kSZLI09OTYmJiSKvVso6mL0SZNRoNrVmzhuzs7Khly5b01VdfUWVlJetYT3Ty5EkaPnw4SZJEr7/+Oh0/fpx1JH1g2GU+efIk9erVi4yNjSk0NFTvS/xvp06dIl9fX1IoFDR58mS6efMm60gsGWaZtVothYeHk7GxMfXr148yMjJYR3phWq2WoqKiyN7enjp16kSpqamsI7FieGW+ceMG+fv7k7GxMUVERHCz5qyoqKAhQ4aQUqmkiIgI1nFYMKwyFxUVkbu7O3Xs2JHLdaZWq6XvvvuOjIyMaMqUKdTQ0MA6kpxiDOYdwNzcXPTv3x+tWrXC0aNH4ejoyDpSk5MkCTNmzICTkxMCAwNRUVGBLVu2QKk0jB+zQZxoVFpaikGDBsHBwQGHDx/mssj3e+edd5CQkIC4uDhMmjQJZCDvi3Ff5traWgwePBgmJibYu3cvbGxsWEeSRd++fREbG4uoqCgsXryYdRx5sF7o6NrkyZOpVatWVFBQwDoKE2vXriWFQkFJSUmso+ga338A7t69myRJom3btrGOwtR7771HHTp04P04dAy3ywy1Wo2QkBAEBgYiICBAZ+Ncv34dGzZswJAhQ2BqagpJkvDnn38+9LyamhqsX78eb731FhwcHGBqaoquXbti9uzZqKqq0lk+AFi3bh1UKhXCwsJ0Og5zrF9OuhIZGUnm5uZUVFSk03EGDRpEAB74iI+Pf+h5S5Yseeh5jR8vv/wy3bp1S6c5V6xYQWZmZjwvt/icmbVaLSIjIzFlyhR07NhRp2O1adMGEyZMwJ49e/DJJ5889nlWVlYIDg5GQkICiouLcefOHSQkJMDR0REXL17E8uXLdZpz0qRJaNu2LVavXq3TcZhi/XLShYSEBAJAFy9elHXcadOmPXZmfpzffvuNANDQoUN1mOxvCxcupHbt2pFardb5WAzwOTNv3boVXl5ecHV1ZR3lqTp37gwAaN26tc7HGj9+PMrLy5GUlKTzsVjgssxHjhyBn58f6xjPpPGPxaCgIJ2P1alTJ3Tp0gUpKSk6H4sF7sp8/fp15OXlwcvLi3WUpzpz5gyWLl2K999/HwMHDpRlzD59+uDo0aOyjCU37spcWFgIIoKLiwvrKE90+fJlDBs2DJ6enli/fr1s43br1g0FBQWyjScn7sp8/fp1AICdnR3jJI93+fJl+Pr6wsbGBvHx8bCwsJBtbDs7O1RWVso2npy4K3NdXR0AwNzcnHGSR8vLy4OPjw8sLCywf/9+2TeCsbKyQk1NjaxjyoW7Mrdq1QoAcPPmTcZJHpaVlQUfHx+Ym5vj4MGDaNeunewZKisrud1JibsyNy4vKioqGCd5UGZmJnx8fGBpaYmkpCS0b9+eSY6Kigq9XoL9F9yVuWvXrjAzM8Pp06dlGW/RokWQJAmSJN17d23w4MH3Hrt06RIAYOXKlSgrK0N2djYcHR3v/X/jh4eHhyx5T506he7du8sylty4K7OpqSleeeUV/PXXX6yj6B0iQlpaWrM4bPkiuNyea/78+fj5559RUFAAIyMj1nH0RnJyMnx9fXH+/HnZfhPIiM+d88ePH4+rV68iMTGRdRS9smHDBvTq1YvHIgPgcJkBAE5OTujXrx8iIyNZR9EbV65cwbZt2554Zl9zx+UyAwAOHz4MHx8fJCQkwN/fn3Uc5saPH49Dhw7h0qVLMDU1ZR1HF/je0nb48OHIz8/HiRMnYGZmxjoOM2lpafD29savv/6KwMBA1nF0he8yFxcXo0ePHvjggw+wYsUK1nGYuHPnDnr27AknJyfEx8fzvCM/n38ANurYsSPWrFmDVatWITo6mnUc2Wm1WgQHB6O6uhq//PILz0UGYAD3NBk7diyOHTuG4OBgtG7dGgMGDGAdSTbTp09HXFwc9u3bx+Stc9mxusZFThqNhoKCgqhFixZ08OBB1nF0TqvV0syZM8nIyIh27tzJOo5c+N43435qtZrGjh1LpqamtGXLFtZxdEalUlFgYCCZmJjQpk2bWMeRk+GUmejvGXrGjBkkSRLNmTOHuws7CwoKqE+fPtSyZUu9uoWFTAyrzI02bNhAlpaW1Lt3b8rNzWUdp0nExsZSq1atyN3dvVlvnv4fGGaZiYguXLhAPXr0IHNzc/r666/p7t27rCO9kPz8fBo6dCgBoIkTJ1JtbS3rSKwYbpmJ/l5HR0REkJWVFXXp0oWioqKazQbd5eXlNGfOHDI3Nyc3NzdD2BjxaQy7zI2Ki4spODiYlEolubi40MaNG6muro51rEcqKiqiWbNmkZWVFbVt25YiIyO5W/u/IFHm++Xk5NBHH31EJiYmZGtrS1988YVerD/VajX98ccfNGzYMDIyMiJ7e3tatmwZ1dTUsI6mT0SZH+XatWsUFhZGnTt3JgDk6upK8+bNo/T0dNmWIVVVVbRr1y4KDg4mW1tbkiSJBgwYQDExMaRSqWTJ0MzEcH1uxn+l1WqRmpqKHTt2YOfOnSgsLIS1tTW8vb3h7e2Nnj17wsPD4z/fz7qhoQE5OTnIyMhAWloajhw5gtOnT0Or1cLLywsjR47EyJEj8dJLLzXNF8Ynvk80amoZGRlITk7G999/j8rKSty+fRsAYGtri27dusHe3h4dO3ZE27ZtYW1tDVNTU1hYWMDU1BTV1dVoaGhAdXU1qqqqUFxcjLKyMhQVFSE7OxtqtRpKpRLm5ubo168fgoOD0a9fP8N4G7ppiDI/r8zMTHh6emLLli0YMGAAzp8/j8zMTOTm5uLatWu4evUqysrKUFVVBZVKhZqaGqjValhZWcHY2BgtWrRAy5Yt4ejoCHt7e3To0AGurq5wd3eHm5sbgoKCkJWVhbNnz0Kh4Po8sKYmyvy8AgICkJ2drbOy3f9iGT16dJN/fo6JMj+PU6dO4bXXXsPOnTsxYsQInY0TFBSEEydOIDMz02Du4dcERJmfx9ChQ3Ht2jWkp6fr9NzgnJwcuLm5YcOGDRg3bpzOxuGMKPOzSk9PxxtvvIG4uDi8/fbbOh9vwoQJSEpKQlZWFkxMTHQ+HgdEmZ+Vn58f6urqZNuou7CwEN26dcOqVavw6aefyjJmMyfK/CxSUlLQt29fHDx4EP3795dt3KlTp2Lv3r3Izs7m9YrqpiTK/Cx8fX2hVCqxf/9+WcctLS2Fs7MzIiIiMH36dFnHbob4vqC1KSQkJCA5ORkLFy6Ufez27dtj0qRJCAsLQ21trezjNzdiZn6K3r17w87ODnv37mUyfkVFBZydnbFgwQKEhoYyydBMiJn5SXbv3o3jx48zmZUbtWnTBlOnTkV4eDiqq6uZ5WgOxMz8GER0b/OU7du3M81SWVkJJycnzJ49G/PmzWOaRY+Jmflxtm3bhnPnzmHBggWso8DOzg4hISFYtmyZXt7eQl+IMj+CRqPBokWLMGbMGPTo0YN1HABASEgIFAqF2Nn0CUSZH2Hz5s3IysrSi1m5kbW1NWbOnInIyEiUl5ezjqOXxJr5XzQaDdzd3eHl5YWNGzeyjvOAmpoaODs7Izg4GOHh4azj6BuxZv63jRs3Ij8/H/Pnz2cd5SGWlpaYPXs2Vq5ciZKSEtZx9I6Yme+jVqvh6uoKf39/rF27lnWcR7p79y66du2KgIAALF++nHUcfSJm5vv9+OOPKCkp0evDX2ZmZpg7dy7Wrl2L4uJi1nH0ipiZ/9GcZrzm8BuEATEzN1qzZg0qKysxe/Zs1lGeysTEBF9++SV++ukn5Ofns46jN8TMjOZ5lECfj7owImZmAPjhhx9QU1ODmTNnso7yzIyMjDBv3jxERUXdu6WxoTP4mfn27dtwcnLCtGnT8PXXX7OO81w0Gg08PT3Ro0cPbN68mXUc1sTMHBkZCa1Wi5CQENZRnpuRkREWLVqE6OhonD17lnUc5gx6Zr558yacnJwQGhqq14fjnqTx7L7OnTtjx44drOOwZNgzc3h4OJRKJT7//HPWUV6YJElYvHgxfv/9dxw/fpx1HKYMdmbm7QoO1lfE6AHDnZnDwsJgaWmJqVOnso7SJBYvXoy4uDgcOXKEdRRmDHJmbrzqOTw8HJ999hnrOE2G1VXkesIwZ+YlS5agTZs2mDhxIusoTeqbb77BgQMHkJSUxDoKEwY3M/O+U5Cfnx9qa2uRmprKOorcDG8TmI8//hgHDx7kdg83uffE0yOGVWZD2V1Trt1K9Qy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"},6850:(e,t,a)=>{a.d(t,{Z:()=>n});const 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"},446:(e,t,a)=>{a.d(t,{Z:()=>n});const 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