33 lines
1.3 KiB
TeX
33 lines
1.3 KiB
TeX
\documentclass{article}
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\usepackage{clrscode3e}
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\begin{document}
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\begin{codebox}
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\Procname{$\proc{Slow-Convex-Hull}(P)$}
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\li \Comment \textit{Input}: A set $P$ of points in the plane.
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\li \Comment \textit{Output}: A list $L$ containing the vertices of $CH(P)$ in clockwise order.
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\li $E \gets 0$
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\li \For $(p, q) \in P \times P$ and $p \neq q$
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\li \Do $valid = true$
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\li \For $r \in P$ and $r \neq p$ and $r \neq q$
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\li \Do \If r lies left of the directed line from $p$ \To $q$
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\li \Then $valid = false$
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\End \End
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\li \If $valid$
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\li \Then $\attrib{E}{append}(\vec{pq})$
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\End \End
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\li From the set $E$ of edges construct a list $L$ of
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vertices of $CH(P)$, sorted in clockwise order.
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\end{codebox}
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\begin{codebox}
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\Procname{$\proc{Convex-Hull}(P)$}
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\li \Comment \textit{Input}: A set $P$ of points in the plane.
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\li \Comment \textit{Output}: A list containing the vertices of $CH(P)$ in clockwise order.
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\li Sort the points by x-coordinate, resulting in a sequence $[p_1,...,p_n]$
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\li $L_{upper} \gets \{p_1, p_2\}$
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\li \For $i \gets 3 \To n$
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\li \Do $\attrib{L_{upper}}{append}(p_i)$
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\li \Do \While $\attrib{L_{upper}}{size}() > 2$ and $\attrib{L_{upper}}{turnRight}() == false$
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\li \Do $\attrib{L_{upper}}{deleteMiddleOfLast3P}()$
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\end{codebox}
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\end{document} |