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Socksorting/mydefs.tex
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\usepackage{algorithmicx} \usepackage{algorithmicx}
\usepackage{algpseudocode} \usepackage{algpseudocode}
\usepackage{emoji} \usepackage{emoji}
\usepackage{soul}
\newcommand{\acronym}{HADES } \newcommand{\acronym}{HADES }

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Socksorting/project.tex
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@ -146,38 +146,56 @@ As evident from the algorithm above, only one loop performing
operations which are all in $\mathscr{O}(1)$ is required thus operations which are all in $\mathscr{O}(1)$ is required thus
putting the algorithm in a $\mathscr{O}(n)$ runtime complexity putting the algorithm in a $\mathscr{O}(n)$ runtime complexity
class. Assuming that $\forall\mathscr{L}\in\Lambda\exists\mathscr{L}^{-1}|\mathscr{L}\cong\mathscr{L}^{-1}$ class. Assuming that $\forall\mathscr{L}\in\Lambda\exists\mathscr{L}^{-1}|\mathscr{L}\cong\mathscr{L}^{-1}$
the algorithm always yields a correct solution for the problem the algorithm always yields a correct solution for the problem
(proof is left as an exercise to the reader). (proof is left as an exercise to the reader).
\section{Discussion and Results} \section{Discussion and Results}
To evaluate the algorithms performance it has been executed To evaluate the algorithms performance it has been executed
on different platforms consisting of diverse hardware:\\ on different platforms consisting of diverse hardware:\\
\begin{tabular}[]{l||l|c} \resizebox*{\linewidth}{!}{
\textbf{Hardware} & \textbf{Algorithm} & \textbf{Runtime [s]}\\ \begin{tabular}[]{l||l|c}
\hline \textbf{Hardware} & \textbf{Algorithm} & \textbf{Runtime [s]} \\
Myself & Conventional (n=20) & 352.7\\ \hline
Myself & \acronym (n=20) & 92.3\\ Myself & Conventional (n=20) & 352.7 \\
Myself & Conventional (n=100) & 42069\\ Myself & \acronym (n=20) & 92.3 \\
Myself & \acronym (n=100) & 420.69\\ Myself & Conventional (n=100) & 42069 \\
\hline Myself & \acronym (n=100) & 420.69 \\
My roommate & Conventional (n=10) & 91.7\\ \hline
My roommate & \acronym (n=10) & -2\\ My roommate & Conventional (n=10) & 91.7 \\
\hline My roommate & \acronym (n=10) & -2 \\
Girlfriend & n.a. & n.a. \hline
\end{tabular}\\ Girlfriend & n.a. & n.a.
\end{tabular}
}\\
\begin{figure}[h] \begin{figure}[h]
\begin{center} \begin{center}
\includegraphics[width=\linewidth]{figs/graph.png} \includegraphics[width=\linewidth]{figs/graph.png}
\bigskip \bigskip
\caption{Comparative statistical time analysis of both algorithms. \acronym in blue, conventional sock sorting in green.} \caption{Comparative statistical time analysis of both algorithms.
The graph depicts algorithm runtime (y-axis) and graphs it against
input size (x-axis). Data for
\acronym in blue, for conventional sock sorting in green.}
\end{center} \end{center}
\end{figure}\\ \end{figure}\\
From the above data it is evident that \acronym bears a clear advantage in comparison From the above data it is evident that \acronym bears a clear advantage in comparison
to the conventional algorithm when it comes to sock sorting. Utilizing advanced statistical modelling we calculated a to the conventional algorithm when it comes to sock sorting. Utilizing advanced statistical modelling we calculated a
speedup factor of about $2.57179072584935274050327\cdot n$. The data also illustrates speedup factor of about $3.1415926535897932384626433\cdot n$. The data also illustrates
the scalability of the algorithm and its adaptability to different hardware. the scalability of the algorithm and its adaptability to different hardware.
\section{Conclusion} \section{Conclusion}
It can be concluded that the algorithm presented in this paper is
greatly superior to the conventional method of sorting socks.
It will probably revolutionize not only the field of laundry science but
also have great impact in the industry.\\
The datastructures outlined above may become abundantly used and be the future
industry standard. Although the field of laundry science is still rather new
there are still a lot of open questions to be answered. However it is unlikely
that a faster sock sorting algorithm than \acronym can be developed.
\section{Acknowledgements} \section{Acknowledgements}
We shall use this historic opportunity to thank the Journal of immaterial science
for publishing great \st{memes} research. We also want to thank our university
for giving us this great opportunity for \st{depression and self loathing}
research and personal advancement.\\
It is also only appropriate to thank the air. Without it no laundry would be
dry and we would not have written this paper.\\
\begingroup \begingroup
\setlength\bibitemsep{0pt} \setlength\bibitemsep{0pt}