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Never Gude 2026-04-17 18:50:33 +02:00
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übung_1/ads_übung_1.aux
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übung_1/ads_übung_1.fdb_latexmk
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übung_1/ads_übung_1.tex
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@ -3,7 +3,7 @@
\title{1. Übungsblatt} \title{1. Übungsblatt}
\subject{Algorithmische Graphentheorie} \subject{Algorithmische Graphentheorie}
\author{Jasper Gude} \author{Jasper Gude \and Pia Rötgers}
\begin{document} \begin{document}
\maketitle \maketitle
@ -27,6 +27,7 @@ und $s \in V \deg$ ein ausgezeichneter Knoten.
von $G$ ein Breitensuchbaum mit Quelle $s$. von $G$ ein Breitensuchbaum mit Quelle $s$.
\end{quote} \end{quote}
Falsch, siehe \autoref{fig:msb}. Falsch, siehe \autoref{fig:msb}.
\points{2}
\begin{figure}[h] \begin{figure}[h]
\centering \centering
\includegraphics[width=0.2\textwidth]{msb.eps} \includegraphics[width=0.2\textwidth]{msb.eps}
@ -41,9 +42,42 @@ und $s \in V \deg$ ein ausgezeichneter Knoten.
Sei $w(e) = 1$ für Sei $w(e) = 1$ für
alle $e \in E$ so gilt das Gegenbeispiel von oben. Also ist die Aussage alle $e \in E$ so gilt das Gegenbeispiel von oben. Also ist die Aussage
falsch. falsch.
\points{2}
\end{enumerate} \end{enumerate}
\section{Kreissuche} \section{Kreissuche}
\begin{enumerate}
\item
Wähle Startknoten $s$ und füge ihn in eine neue Queue $Q$ ein.
Nimm den vordersten Knoten aus $Q$ und füge seine noch nicht verbrauchten
Nachbarn ein. Markiere diesen Knoten anschließend als verbraucht ($black$).
Wiederhole den Schritt solange bis $Q$ leer ist. Merke dir dabei die zwei
letzten entnommenen Knoten. Sind sie gleich, hat der Graph einen
einfachen Kreis.
\begin{algorithmic}
\alg{EinfacherKreis}(Graph $G$, Vertex $s$) \+ \\
\alg{Initialize}($G$, $s$) \\
$Q \gets$ new \alg{Queue}() \\
$Q.$\alg{Enqueue}($s$) \\
$t_1 \gets nil$ \\
$t_2 \gets s$ \\
while $Q \neq \emptyset$ do \+ \\
$u \gets Q.$\alg{Dequeue}() \\
$t_1 \gets t_2$ \\
$t_2 \gets u$ \\
foreach $v \in Adj[u]$ do \+ \\
if $v.color = white$ then \+ \\
$Q.$\alg{Enqueue}($v$) \-\- \\
$u.color \gets black$ \- \\
if $t_1 = t_2$ then \+ \\
return $true$ \- \\
else \+ \\
return $false$
\end{algorithmic}
\end{enumerate}
\section{Eulerwege} \section{Eulerwege}