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Antti H S Laaksonen 2017-02-21 22:19:29 +02:00
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@ -217,9 +217,9 @@ Using such structures, processing each event
takes $O(\log n)$ time, so the total running takes $O(\log n)$ time, so the total running
time of the algorithm is $O(n \log n)$. time of the algorithm is $O(n \log n)$.
\section{Nearest points} \section{Closest pair problem}
\index{nearest points} \index{closest pair}
Given a set of $n$ points, our next problem is Given a set of $n$ points, our next problem is
to find two points whose distance is minimum. to find two points whose distance is minimum.
@ -338,7 +338,7 @@ because we go through $n$ points and
find for each point the nearest point to the left find for each point the nearest point to the left
in $O(\log n)$ time. in $O(\log n)$ time.
\section{Convex hull} \section{Convex hull problem}
A \key{convex hull} is the smallest convex polygon A \key{convex hull} is the smallest convex polygon
that contains all points of a given set. that contains all points of a given set.
@ -391,7 +391,7 @@ the convex hull is as follows:
\index{Andrew's algorithm} \index{Andrew's algorithm}
\key{Andrew's algorithm} provides \key{Andrew's algorithm} \cite{and79} provides
an easy way to an easy way to
construct the convex hull for a set of points construct the convex hull for a set of points
in $O(n \log n)$ time. in $O(n \log n)$ time.