8000 Update redblack.tex (Issue #84) by LautaroLobo12 · Pull Request #86 · patmorin/ods · GitHub
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Update redblack.tex (Issue #84) #86

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Update redblack.tex (Issue #84) #86

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4 changes: 2 additions & 2 deletions latex/redblack.tex
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Expand Up @@ -236,8 +236,8 @@ \subsection{Red-Black Trees and 2-4 Trees}
at most $\log (#n#+1)$. Now, every root to leaf path in the 2-4 tree corresponds
to a path from the root of the red-black tree $T$ to an external node.
The first and last node in this path are black and at most one out of
every two internal nodes is red, so this path has at most $\log(#n#+1)$
black nodes and at most $\log(#n#+1)-1$ red nodes. Therefore, the longest path from the root to any \emph{internal} node in $T$ is at most
every two internal nodes is red, so this path has at most $\log(#n#+1)+1$
black nodes and at most $\log(#n#+1)$ red nodes. Therefore, the longest path from the root to any \emph{internal} node in $T$ is at most
\[
2\log(#n#+1) -2 \le 2\log #n# \enspace ,
\]
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