diff --git a/Socksorting/main.pdf b/Socksorting/main.pdf index a5cd99c..320213d 100644 Binary files a/Socksorting/main.pdf and b/Socksorting/main.pdf differ diff --git a/Socksorting/mydefs.tex b/Socksorting/mydefs.tex index 8cc6502..01f1439 100644 --- a/Socksorting/mydefs.tex +++ b/Socksorting/mydefs.tex @@ -8,6 +8,7 @@ \usepackage{algorithmicx} \usepackage{algpseudocode} \usepackage{emoji} +\usepackage{soul} \newcommand{\acronym}{HADES } \ No newline at end of file diff --git a/Socksorting/project.tex b/Socksorting/project.tex index 193d1fa..7952d44 100644 --- a/Socksorting/project.tex +++ b/Socksorting/project.tex @@ -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 putting the algorithm in a $\mathscr{O}(n)$ runtime complexity class. Assuming that $\forall\mathscr{L}\in\Lambda\exists\mathscr{L}^{-1}|\mathscr{L}\cong\mathscr{L}^{-1}$ -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). \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:\\ -\begin{tabular}[]{l||l|c} - \textbf{Hardware} & \textbf{Algorithm} & \textbf{Runtime [s]}\\ - \hline - Myself & Conventional (n=20) & 352.7\\ - Myself & \acronym (n=20) & 92.3\\ - Myself & Conventional (n=100) & 42069\\ - Myself & \acronym (n=100) & 420.69\\ - \hline - My roommate & Conventional (n=10) & 91.7\\ - My roommate & \acronym (n=10) & -2\\ - \hline - Girlfriend & n.a. & n.a. -\end{tabular}\\ +\resizebox*{\linewidth}{!}{ + \begin{tabular}[]{l||l|c} + \textbf{Hardware} & \textbf{Algorithm} & \textbf{Runtime [s]} \\ + \hline + Myself & Conventional (n=20) & 352.7 \\ + Myself & \acronym (n=20) & 92.3 \\ + Myself & Conventional (n=100) & 42069 \\ + Myself & \acronym (n=100) & 420.69 \\ + \hline + My roommate & Conventional (n=10) & 91.7 \\ + My roommate & \acronym (n=10) & -2 \\ + \hline + Girlfriend & n.a. & n.a. + \end{tabular} +}\\ \begin{figure}[h] \begin{center} \includegraphics[width=\linewidth]{figs/graph.png} \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{figure}\\ 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 -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. \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} +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 \setlength\bibitemsep{0pt}