From 930494e488c830bf43205bf6740bf7070183e51a Mon Sep 17 00:00:00 2001 From: Marcin Chrzanowski Date: Tue, 10 Aug 2021 11:36:09 -0400 Subject: Add shortcut for optimal query problem times --- definitions.sty | 1 + mgr.tex | 4 ++-- 2 files changed, 3 insertions(+), 2 deletions(-) diff --git a/definitions.sty b/definitions.sty index 21ba74c..cbe36f2 100644 --- a/definitions.sty +++ b/definitions.sty @@ -15,5 +15,6 @@ } \newcommand{\qptime}[2]{$\langle$#1, #2$\rangle$} +\newcommand{\qpoptimal}{\qptime{$O(n)$}{$O(1)$}} \newcommand{\definedterm}[1]{\emph{#1}} diff --git a/mgr.tex b/mgr.tex index 8929626..c13ccc1 100644 --- a/mgr.tex +++ b/mgr.tex @@ -206,7 +206,7 @@ serve as examples and because we will be using them in our algorithm. ancestor. } -\textcite{tarjan1984} were the first to show an optimal \qptime{$O(n)$}{$O(1)$} +\textcite{tarjan1984} were the first to show an optimal \qpoptimal{} algorithm for LCA. \textcite{schieber1988} used a similar approach but simplified the indexing structure, keeping the same time complexities. \textcite{berkman1993} showed a completely new approach to the problem, which @@ -224,7 +224,7 @@ problems. element in the subarray $A[i, j]$. } -As mentioned above, \textcite{bender2000} show an \qptime{$O(n)$}{$O(1)$} +As mentioned above, \textcite{bender2000} show an \qpoptimal{} algorithm for the RMQ problem. \subsection{Word infix regular queries} -- cgit v1.2.3