diff options
Diffstat (limited to 'vorlesungen/slides/8')
| -rw-r--r-- | vorlesungen/slides/8/Makefile.inc | 11 | ||||
| -rw-r--r-- | vorlesungen/slides/8/chapter.tex | 7 | ||||
| -rw-r--r-- | vorlesungen/slides/8/dgraph.tex | 100 | ||||
| -rw-r--r-- | vorlesungen/slides/8/graph.tex | 117 |
4 files changed, 235 insertions, 0 deletions
diff --git a/vorlesungen/slides/8/Makefile.inc b/vorlesungen/slides/8/Makefile.inc new file mode 100644 index 0000000..e8c7502 --- /dev/null +++ b/vorlesungen/slides/8/Makefile.inc @@ -0,0 +1,11 @@ + +# +# Makefile.inc -- additional depencencies +# +# (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +# +chapter8 = \ + ../slides/8/dgraph.tex \ + ../slides/8/graph.tex \ + ../slides/8/chapter.tex + diff --git a/vorlesungen/slides/8/chapter.tex b/vorlesungen/slides/8/chapter.tex new file mode 100644 index 0000000..761ea63 --- /dev/null +++ b/vorlesungen/slides/8/chapter.tex @@ -0,0 +1,7 @@ +% +% chapter.tex +% +% (c) 2021 Prof Dr Andreas Müller, Hochschule Rapperswi +% +\folie{8/graph.tex} +\folie{8/dgraph.tex} diff --git a/vorlesungen/slides/8/dgraph.tex b/vorlesungen/slides/8/dgraph.tex new file mode 100644 index 0000000..6b5864a --- /dev/null +++ b/vorlesungen/slides/8/dgraph.tex @@ -0,0 +1,100 @@ +% +% dgraph.tex +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\bgroup +\definecolor{darkgreen}{rgb}{0,0.6,0} +\begin{frame} +\frametitle{Gerichteter Graph} +\vspace{-20pt} +\begin{columns}[t,onlytextwidth] +\begin{column}{0.44\textwidth} +\begin{center} +\begin{tikzpicture}[>=latex,thick] +\def\r{2.4} + +\coordinate (A) at ({\r*cos(0*72)},{\r*sin(0*72)}); +\coordinate (B) at ({\r*cos(1*72)},{\r*sin(1*72)}); +\coordinate (C) at ({\r*cos(2*72)},{\r*sin(2*72)}); +\coordinate (D) at ({\r*cos(3*72)},{\r*sin(3*72)}); +\coordinate (E) at ({\r*cos(4*72)},{\r*sin(4*72)}); + +\uncover<3->{ + \draw[->,shorten >= 0.2cm,shorten <= 0.2cm] (A) -- (C); + \draw[color=white,line width=5pt] (B) -- (D); + \draw[->,shorten >= 0.2cm,shorten <= 0.2cm] (B) -- (D); + + \draw[->,shorten >= 0.2cm,shorten <= 0.2cm] (A) -- (B); + \draw[->,shorten >= 0.2cm,shorten <= 0.2cm] (B) -- (C); + \draw[->,shorten >= 0.2cm,shorten <= 0.2cm] (C) -- (D); + \draw[->,shorten >= 0.2cm,shorten <= 0.2cm] (D) -- (E); + \draw[->,shorten >= 0.2cm,shorten <= 0.2cm] (E) -- (A); +} + +\uncover<2->{ + \draw (A) circle[radius=0.2]; + \draw (B) circle[radius=0.2]; + \draw (C) circle[radius=0.2]; + \draw (D) circle[radius=0.2]; + \draw (E) circle[radius=0.2]; + + \node at (A) {$1$}; + \node at (B) {$2$}; + \node at (C) {$3$}; + \node at (D) {$4$}; + \node at (E) {$5$}; +} +\node at (0,0) {$G$}; + +\uncover<3->{ + \node at ($0.5*(A)+0.5*(B)-(0.1,0.1)$) [above right] {$\scriptstyle 1$}; + \node at ($0.5*(B)+0.5*(C)+(0.05,-0.07)$) [above left] {$\scriptstyle 2$}; + \node at ($0.5*(C)+0.5*(D)+(0.05,0)$) [left] {$\scriptstyle 3$}; + \node at ($0.5*(D)+0.5*(E)$) [below] {$\scriptstyle 4$}; + \node at ($0.5*(E)+0.5*(A)+(-0.1,0.1)$) [below right] {$\scriptstyle 5$}; + \node at ($0.6*(A)+0.4*(C)$) [above] {$\scriptstyle 6$}; + \node at ($0.4*(B)+0.6*(D)$) [left] {$\scriptstyle 7$}; +} + +\uncover<7->{ + \draw[->,shorten >= 0.2cm,shorten <= 0.2cm,color=red] + (E) to[out=-18,in=-126,distance=2cm] (E); +} + +\uncover<9->{ + \draw[->,shorten >= 0.2cm,shorten <= 0.2cm,color=darkgreen] + (D) to[out=120,in=-120] (C); +} + +\end{tikzpicture} +\end{center} +\end{column} +\begin{column}{0.52\textwidth} +\begin{block}{Definition} +Ein gerichteter Graph $G=(V,E)$ ist +\begin{enumerate} +\item<2-> Eine Menge $V$ von Knoten (Vertizes) +$V=\{v_1,v_2,\dots\}$ +\item<3-> +Eine Menge $E$ von gerichteten Kanten +(Edges) +\[ +E\subset \{ (v_1,v_2)\;|\; v_i\in V\} +\] +\end{enumerate} +\end{block} +\vspace{-30pt} +\uncover<6->{% +\begin{block}{Achtung} +\begin{itemize} +\item<6-> Kanten sind {\em geordnete} Paare +\uncover<7->{$\Rightarrow$ {\color{red}Schleifen} sind möglich} +\item<8-> Kanten sind immer ``Einbahnstrassen'' +\item<9-> {\color{darkgreen}Gegenrichtung explizit angeben} +\end{itemize} +\end{block}} +\end{column} +\end{columns} +\end{frame} +\egroup diff --git a/vorlesungen/slides/8/graph.tex b/vorlesungen/slides/8/graph.tex new file mode 100644 index 0000000..32150af --- /dev/null +++ b/vorlesungen/slides/8/graph.tex @@ -0,0 +1,117 @@ +% +% graph.tex +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\bgroup +\begin{frame}[t] +\setlength{\abovedisplayskip}{5pt} +\setlength{\belowdisplayskip}{5pt} +\frametitle{Graph} +\vspace{-18pt} +\begin{columns}[t,onlytextwidth] +\begin{column}{0.48\textwidth} +\begin{center} +\begin{tikzpicture}[>=latex,thick] +\def\r{2.4} + +\begin{scope} +\coordinate (A) at ({\r*cos(0*72)},{\r*sin(0*72)}); +\coordinate (B) at ({\r*cos(1*72)},{\r*sin(1*72)}); +\coordinate (C) at ({\r*cos(2*72)},{\r*sin(2*72)}); +\coordinate (D) at ({\r*cos(3*72)},{\r*sin(3*72)}); +\coordinate (E) at ({\r*cos(4*72)},{\r*sin(4*72)}); + +\uncover<3->{ + \draw[shorten >= 0.2cm,shorten <= 0.2cm] (A) -- (C); + \draw[color=white,line width=5pt] (B) -- (D); + \draw[shorten >= 0.2cm,shorten <= 0.2cm] (B) -- (D); + + \draw[shorten >= 0.2cm,shorten <= 0.2cm] (A) -- (B); + \draw[shorten >= 0.2cm,shorten <= 0.2cm] (B) -- (C); + \draw[shorten >= 0.2cm,shorten <= 0.2cm] (C) -- (D); + \draw[shorten >= 0.2cm,shorten <= 0.2cm] (D) -- (E); + \draw[shorten >= 0.2cm,shorten <= 0.2cm] (E) -- (A); +} + +\uncover<2->{ + \draw (A) circle[radius=0.2]; + \draw (B) circle[radius=0.2]; + \draw (C) circle[radius=0.2]; + \draw (D) circle[radius=0.2]; + \draw (E) circle[radius=0.2]; + + \node at (A) {$1$}; + \node at (B) {$2$}; + \node at (C) {$3$}; + \node at (D) {$4$}; + \node at (E) {$5$}; +} +\node at (0,0) {$G$}; + +\uncover<3->{ + \node at ($0.5*(A)+0.5*(B)-(0.1,0.1)$) + [above right] {$\scriptstyle 1$}; + \node at ($0.5*(B)+0.5*(C)+(0.05,-0.07)$) + [above left] {$\scriptstyle 2$}; + \node at ($0.5*(C)+0.5*(D)+(0.05,0)$) + [left] {$\scriptstyle 3$}; + \node at ($0.5*(D)+0.5*(E)$) + [below] {$\scriptstyle 4$}; + \node at ($0.5*(E)+0.5*(A)+(-0.1,0.1)$) + [below right] {$\scriptstyle 5$}; + \node at ($0.6*(A)+0.4*(C)$) + [above] {$\scriptstyle 6$}; + \node at ($0.4*(B)+0.6*(D)$) + [left] {$\scriptstyle 7$}; +} + +\uncover<8->{ + \draw[shorten >= 0.2cm,shorten <= 0.2cm] + (E) to[out=-18,in=-126,distance=2cm] (E); + + \draw[color=red,line width=4pt] ($(E)+(-0.5,-0.5)+(0,-0.5)$) + -- ($(E)+(0.5,0.5)+(0,-0.5)$); + \draw[color=red,line width=4pt] ($(E)+(-0.5,0.5)+(0,-0.5)$) + -- ($(E)+(0.5,-0.5)+(0,-0.5)$); +} + +\end{scope} + +\end{tikzpicture} +\end{center} +\end{column} +\begin{column}{0.48\textwidth} +\begin{block}{Definition} +Ein Graph $G=(V,E)$ ist +\begin{enumerate} +\item<2-> +Eine Menge $V$ von Knoten (Vertizes): +$V=\{v_1,v_2,\dots\}$ +\item<3-> +Eine Menge $E$ von Kanten (Edges): +\[ +E\subset +\left\{ e = \{v_1,v_2\}\;\left|\; \begin{minipage}{1.3cm}\raggedright +$v_i\in V$\\ +$v_1\ne v_2$ +\end{minipage} +\right. +\right\} +\] +\end{enumerate} +\end{block} +\vspace{-20pt} +\uncover<5->{% +\begin{block}{Achtung:} +\begin{itemize} +\item<6-> Kanten sind Mengen +\uncover<7->{$\Rightarrow$ zwei verschiedene Knoten} +\uncover<8->{$\Rightarrow$ Keine Schleifen} +\item<9-> Kanten sind ungerichtet, keine ``Einbahnstrassen'' +\end{itemize} +\end{block}} +\end{column} +\end{columns} +\end{frame} +\egroup |