diff --git a/chapter09.tex b/chapter09.tex index 73d8795..eb4ebdc 100644 --- a/chapter09.tex +++ b/chapter09.tex @@ -244,10 +244,12 @@ to the position of $X$. Next we will see how we can process range minimum queries in $O(1)$ time -after an $O(n \log n)$ time preprocessing\footnote{There are also -sophisticated techniques \cite{fis06} where the preprocessing time -is only $O(n)$, but such algorithms are not needed in -competitive programming.}. +after an $O(n \log n)$ time preprocessing using \index{sparse table} +a data structure called a \emph{sparse table}\footnote{The +sparse table structure was introduced in \cite{ben00}. +There are also more sophisticated techniques \cite{fis06} where +the preprocessing time of the array is only $O(n)$, but such algorithms +are not needed in competitive programming.}. Note that minimum and maximum queries can always be processed using similar techniques, so it suffices to focus on minimum queries.