73 lines
2.4 KiB
TeX
73 lines
2.4 KiB
TeX
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\documentclass[12pt,a4paper,german]{article}
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\usepackage{url}
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%\usepackage{graphics}
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\usepackage{times}
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\usepackage[T1]{fontenc}
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\usepackage{ngerman}
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\usepackage{float}
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\usepackage{diagbox}
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\usepackage[utf8]{inputenc}
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\usepackage{geometry}
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\usepackage{amsfonts}
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\usepackage{amsmath}
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\usepackage{cancel}
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\usepackage{csquotes}
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\usepackage{graphicx}
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\usepackage{epsfig}
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\usepackage{paralist}
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\usepackage{tikz}
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\geometry{left=2.0cm,textwidth=17cm,top=3.5cm,textheight=23cm}
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%%%%%%%%%% Fill out the the definitions %%%%%%%%%
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\def \name {Valentin Brandl} %
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\def \matrikel {108018274494} %
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\def \pname {Marvin Herrmann} %
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\def \pmatrikel {108018265436} %
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\def \gruppe {2 (Mi 10-12 Andre)}
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\def \qname {Pascal Brackmann}
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\def \qmatrikel {108017113834} %
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\def \uebung {6} %
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% DO NOT MODIFY THIS HEADER
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\newcommand{\hwsol}{
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\vspace*{-2cm}
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\noindent \matrikel \quad \name \hfill \"Ubungsgruppe: \gruppe \\
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\noindent \pmatrikel \quad \pname \\
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\noindent \qmatrikel \quad \qname \\
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\begin{center}{\Large \bf L\"osung f\"ur \"Ubung \# \uebung}\end{center}
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}
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\begin{document}
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%Import header
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\hwsol
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\section*{Aufgabe 6.2}
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\begin{enumerate}[1.]
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\item
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\begin{tabular}{|c|ccccccc|}
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\hline
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Queue & $pred[1]$ & $pred[2]$ & $pred[3]$ & $pred[4]$ & $pred[5]$ & $pred[6]$ & $pred[7]$ \\\hline
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$\emptyset$ & $nil$ & $nil$ & $nil$ & $nil$ & $nil$ & $nil$ & $nil$ \\\hline
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\cancel{1} & $nil$ & $nil$ & $nil$ & $nil$ & $nil$ & $nil$ & $nil$ \\\hline
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\cancel{2}, 5 & $nil$ & $1$ & $nil$ & $nil$ & $1$ & $nil$ & $nil$ \\\hline
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\cancel{5}, 3, 6 & $nil$ & $1$ & $2$ & $nil$ & $1$ & $2$ & $nil$ \\\hline
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\cancel{3}, 6 & $nil$ & $1$ & $2$ & $nil$ & $1$ & $2$ & $nil$ \\\hline
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\cancel{6}, 4 & $nil$ & $1$ & $2$ & $3$ & $1$ & $2$ & $nil$ \\\hline
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\cancel{4}, 7 & $nil$ & $1$ & $2$ & $3$ & $1$ & $2$ & $6$ \\\hline
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\cancel{7} & $nil$ & $1$ & $2$ & $3$ & $1$ & $2$ & $6$ \\\hline
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$\emptyset$ & $nil$ & $1$ & $2$ & $3$ & $1$ & $2$ & $6$ \\\hline
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\end{tabular}
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\item
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Laufzeit Breitensuche mit Adjazenzmatrix: $O(|V|^2)$:
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Jeder Knoten $v$ wird genau einmal besucht und die Bestimmung der Nachbarschaft $\Gamma(v)$ in einer
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Adjazenzmatrix hat eine Laufzeit von $O(|V|)$
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\end{enumerate}
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\end{document}
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