Add shortcut for optimal query problem times

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}