76 lines
2.4 KiB
TeX
76 lines
2.4 KiB
TeX
\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{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{csquotes}
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\usepackage{graphicx}
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\usepackage{epsfig}
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\usepackage{paralist}
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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 \qname {Pascal Brackmann}
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\def \qmatrikel {108017113834} %
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\def \gruppe {2 (Mi 10-12 Andre)}
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\def \uebung {3} %
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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 3.4}
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% \begin{itemize}
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% \item $o$ impliziert $O$
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% \item $\omega$ impliziert $\Omega$
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% \item $f = \Theta(g) \Rightarrow f = \Omega(g) \text{ und } f = O(g)$
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% \item $f = O(g) \Rightarrow g = \Omega(f)$
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% \item $f = o(g) \Rightarrow g = \omega(f)$
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% \end{itemize}
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\begin{tabular}{|l||l|l|l|l|l|l|l|l|}
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\hline
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\backslashbox{f}{g} & $4^n$ & $e^{2n}$ & $\sum\limits_{k=1}^n k$ & $n \ln n$ & $2^{(2^{n+1})}$ & $51^{\ln n}$ & $2^{(2^n)}$ &
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$2^{\sqrt{\ln n}}$ \\\hline
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$4^n$ & $\Theta$ & $o$ & $o$ & $\omega$ & $O$ & $\omega$ & $O$ & $\omega$ \\\hline
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$e^{2n}$ & $\omega$ & $\Theta$ & $o$ & $\omega$ & $\omega$ & $\omega$ & $\omega$ & $\omega$ \\\hline
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$\sum\limits_{k=1}^n k$ & $\omega$ & $\omega$ & $\Theta$ & $\omega$ & $\omega$ & $\omega$ & $\omega$ & $\omega$ \\\hline
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$n \ln n$ & $o$ & $o$ & $o$ & $\Theta$ & $o$ & $o$ & $o$ & $\omega$ \\\hline
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$2^{(2^n)}$ & $\Omega$ & $o$ & $o$ & $\omega$ & $\Theta$ & $\Omega$ & $\Omega$ & $\omega$ \\\hline
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$51^{\ln n}$ & $o$ & $o$ & $o$ & $\omega$ & $O$ & $\Theta$ & $O$ & $\omega$ \\\hline
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$2^{(2n)}$ & $\Omega$ & $o$ & $o$ & $\omega$ & $O$ & $\Omega$ & $\Theta$ & $\omega$ \\\hline
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$2^{\sqrt{\ln n}}$ & $o$ & $o$ & $o$ & $o$ & $o$ & $o$ & $o$ & $\Theta$ \\\hline
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\end{tabular}
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\end{document}
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