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85 lines
2.9 KiB
TeX
85 lines
2.9 KiB
TeX
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% Author: Kjell Magne Fauske
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% Source: http://www.texample.net/tikz/examples/prims-algorithm/
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% Declare layers
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\pgfdeclarelayer{background}
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\pgfsetlayers{background,main}
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\subsection{Algorithmus von Prim}
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\begin{frame}{Algorithmus von Prim}{Prim's algorithm}
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$S$ ist Menge aller erreichten Knoten, $E$ ist Menge der ausgewählten Kanten.\pause
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Starte bei einem beliebigen Knoten: füge zu $S$ hinzu.
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\begin{enumerate}
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\item wähle Kante am \emph{Rand} von $S$ mit dem geringsten Gewicht und füge zu $E$ hinzu. \pause
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\item füge zugehörigen Knoten zu $S$ hinzu.
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\item Fehlt ein Knoten in $S$ ? goto 1
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\end{enumerate}
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\end{frame}
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\begin{frame}{Algorithmus von Prim}{Prim's algorithm}
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%% Adjacency matrix of graph
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%% \ a b c d e f g
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%% a x 7 5
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%% b 7 x 8 9 7
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%% c 8 x 5
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%% d 5 9 x 15 6
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%% e 7 5 15 x 8 9
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%% f 6 8 x 11
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%% g 9 11 x
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\begin{figure}
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\begin{tikzpicture}[scale=1.8, auto,swap]
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% Draw a 7,11 network
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% First we draw the vertices
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\foreach \pos/\name in {{(0,2)/a}, {(2,1)/b}, {(4,1)/c},
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{(0,0)/d}, {(3,0)/e}, {(2,-1)/f}, {(4,-1)/g}}
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\node[vertex] (\name) at \pos {$\name$};
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% Connect vertices with edges and draw weights
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\foreach \source/ \dest /\weight in {b/a/7, c/b/8,d/a/5,d/b/9,
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e/b/7, e/c/5,e/d/15,
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f/d/6,f/e/8,
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g/e/9,g/f/11}
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\path[edge] (\source) -- node[weight] {$\weight$} (\dest);
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% Start animating the vertex and edge selection.
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\foreach \vertex / \fr in {d/1,a/2,f/3,b/4,e/5,c/6,g/7}
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\path<\fr-> node[selected vertex] at (\vertex) {$\vertex$};
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% For convenience we use a background layer to highlight edges
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% This way we don't have to worry about the highlighting covering
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% weight labels.
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\begin{pgfonlayer}{background}
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\pause
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\foreach \source / \dest in {d/a,d/f,a/b,b/e,e/c,e/g}
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\path<+->[selected edge] (\source.center) -- (\dest.center);
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\foreach \source / \dest / \fr in {d/b/4,d/e/5,e/f/5,b/c/6,f/g/7}
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\path<\fr->[ignored edge] (\source.center) -- (\dest.center);
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\end{pgfonlayer}
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\end{tikzpicture}
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\end{figure}
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\end{frame}
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%% end of source
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\begin{frame}{Algorithmus von Prim}{Prim's algorithm}
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%source http://inserv.math.muni.cz/biografie/obrazky/jarnik_vojtech.jpg
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%http://www.ams.org/featurecolumn/images/january2006/trees9.jpg
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\textbf{Erfinder}
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\begin{itemize}
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\item 1930: Vojtěch Jarník
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\item 1957: Robert C. Prim
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\item 1959 wiederentdeckt von Edsger Dijkstra
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\end{itemize}
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\begin{figure}
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\centering
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\mbox{\subfigure{\includegraphics[width=0.6in]{Material/jarnik_vojtech.jpg}}\quad
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\subfigure{\includegraphics[width=0.6in]{Material/Prim.jpg} }}
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\caption{Jarnik Vojtech und Prim}
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\end{figure}
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\textbf{Alternative Bezeichnungen}
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\begin{itemize}
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\item DJP algorithm
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\item Jarník algorithm
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\item Prim–Jarník algorithm
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\end{itemize}
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\end{frame}
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