From 0f1a796934dce669681b0568e3627cc10f736e2f Mon Sep 17 00:00:00 2001 From: CDaut Date: Wed, 17 Jul 2024 14:09:47 +0200 Subject: [PATCH] i really don't know what I changed... --- Culinography/Licking Rocks .pdf | Bin 0 -> 1750203 bytes Culinography/img/ancient_egyptians.png | Bin 1165032 -> 1165032 bytes Socksorting/bibliography.bib | 7 - Socksorting/defs.tex | 286 ------------------------- Socksorting/figs/Sock.jpeg | Bin 305775 -> 0 bytes Socksorting/figs/graph.kra | Bin 175737 -> 0 bytes Socksorting/figs/graph.png | Bin 55467 -> 0 bytes Socksorting/figs/rack.jpeg | Bin 205687 -> 0 bytes Socksorting/main.tex | 36 ---- Socksorting/mydefs.tex | 14 -- Socksorting/project.tex | 201 ----------------- build/Culinography.pdf | Bin 1478020 -> 0 bytes build/Socksorting.pdf | Bin 632295 -> 0 bytes 13 files changed, 544 deletions(-) create mode 100644 Culinography/Licking Rocks .pdf diff --git a/Culinography/Licking Rocks .pdf b/Culinography/Licking Rocks .pdf new file mode 100644 index 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-@article{otherarticle, - title = {A first approach to sock sorting}, - journal = {Journal of laundry science}, - author = {My colleague et al.}, - year = {1969}, - month = {13} -} diff --git a/Socksorting/defs.tex b/Socksorting/defs.tex index e73e66e..e69de29 100644 --- a/Socksorting/defs.tex +++ b/Socksorting/defs.tex @@ -1,286 +0,0 @@ -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -% NEW defs.tex file hack - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -% PACKAGES TO BE USED - -% \usepackage{fontspec} -\usepackage{graphicx} -\usepackage{grffile} -\usepackage{multicol} -\usepackage{amsmath} -\usepackage{amssymb} -\usepackage{bm} -\usepackage{wrapfig} -% \usepackage{url} -\usepackage{pdfpages} - -\usepackage{color} -\usepackage{xcolor} -%\usepackage{floatrow} -\usepackage{hyperref} - -\hypersetup{ - colorlinks=true, - allcolors=blue - } - - - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -% footnote with no marker - -\newcommand\blfootnote[1]{% 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-\def\LCDM{\mbox{$\Lambda$CDM}} -\def\Lsun{\mbox{L$_\odot$}} -\def\Msun{\mbox{M$_\odot$}} -\def\spose#1{\hbox to 0pt{#1\hss}} -\def\simlt{\mathrel{\spose{\lower 3pt\hbox{$\mathchar"218$}} - \raise 2.0pt\hbox{$\mathchar"13C$}}} -\def\simgt{\mathrel{\spose{\lower 3pt\hbox{$\mathchar"218$}} - \raise 2.0pt\hbox{$\mathchar"13E$}}} -\def\eg{{\textit{e.g.}}} -\def\gtsima{$\; \buildrel > \over \sim \;$} -\def\ltsima{$\; \buildrel < \over \sim \;$} -\def\gsim{\lower.5ex\hbox{\gtsima}} -\def\lsim{\lower.5ex\hbox{\ltsima}} -\def\simgt{\lower.5ex\hbox{\gtsima}} -\def\simlt{\lower.5ex\hbox{\ltsima}} -\def\simpr{\lower.5ex\hbox{\prosima}} -\def\la{\lsim} -\def\ga{\gsim} -\def\zcr{Z_{\rm cr}} -\def\ekin{\mbox{\cal E}_{\rm kin}} -\def\ekin{{\cal E}_{\rm kin}} -\def\fgg{f_{\gamma\gamma}} -\def\Lya{Ly$\alpha$~} -\def\sngg{SN$_{\gamma\gamma}$~} -\def\msun{{M_\odot}} - -% Arial doesn't do small caps (so replaced with normal caps) -\newcommand{\spitzer}{\emph{Spitzer}} -\newcommand{\jwst}{\emph{JWST}} 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-\newcommand{\volunit}{\mbox{\,$h^{-3}$\,Mpc$^{3}$}} -\newcommand{\del}{\delta} -\newcommand{\Del}{\Delta} -\newcommand{\nb}{\bar{n}} -\newcommand{\etalb}{et al.} -\def\etal{et~al.~} - - -\def\spose#1{\hbox to 0pt{#1\hss}} - -\def\simgt{\mathrel{\spose{\lower 3pt\hbox{$\mathchar"218$}} - \raise 2.0pt\hbox{$\mathchar"13E$}}} - - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -% highlighting macros - -\newcommand{\red}[1]{{\color{red}{#1}}} -\newcommand{\green}[1]{{\color{green}{#1}}} -\newcommand{\blue}[1]{{\color{blue}{#1}}} -\newcommand{\brown}[1]{{\color{brown}{#1}}} -\newcommand{\white}[1]{{\color{white}{#1}}} - -% Comments, etc -\newcommand{\changed}[2][{}]{\red{\sout{#1}}\blue{#2}} -%\newcommand{\changed}[2][{}]{#2} -\newcommand{\comment}[1]{\brown{#1}} -\newcommand{\todo}[1]{\red{#1}} \ No newline at end of file diff --git a/Socksorting/figs/Sock.jpeg b/Socksorting/figs/Sock.jpeg index f11c23837d281168492a16821d3b2f1b463ca5b1..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391 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inclusion of extra files -\begin{refsection} -\include{project} -\end{refsection} -\end{document} - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - diff --git a/Socksorting/mydefs.tex b/Socksorting/mydefs.tex index 01f1439..e69de29 100644 --- a/Socksorting/mydefs.tex +++ b/Socksorting/mydefs.tex @@ -1,14 +0,0 @@ -\usepackage{lipsum} -\usepackage[T1]{fontenc} -\usepackage[sfdefault]{biolinum} -\biolinum -\usepackage{listings} -\usepackage{mathrsfs} -\usepackage{algorithm} -\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 02cc1d1..e69de29 100644 --- a/Socksorting/project.tex +++ b/Socksorting/project.tex @@ -1,201 +0,0 @@ -\twocolumn[ - \title{\bf \acronym (High end, Advanced, Data driven, Enterprise grade Sock sorting algorithm) - An algorithm for faster sock sorting} - \author{ - CelloClemens$^{1,2}$, - Henri\emoji{duck}$^{1}$, - } - \date{\today} - % List of institutions - \maketitle - $^{1}$Department for theoretical laundry science, Karlsruhe institute of suffering and sorrow (KISS), Karlsruhe, Germany \\ - $^{2}$Institute of laundry sorting, Department for socks, Karlsruhe institute of suffering and sorrow (KISS), Karlsruhe, Germany - \begin{psummary} - Sorting socks can often be a time consuming task. This paper introduces the fastest method known in the scientific community to tackle - this challanging task. To be able to implement this new algorithm - a new datastructure will be introduced and discussed. Abundant application of this novel algorithm may be able to - reduce the time required for sorting socks considerably. - \end{psummary} - \vspace{2mm} -] -\fancypagestyle{firstpage}{% - \lhead{Please help I am stuck in the basement sorting socks} - \rhead{Journal of Immaterial Science} -} -\thispagestyle{firstpage} - -% The introduction -\section{Introduction} -While sorting algorithms are one of the most discussed algorithms in the -computer science community, application of this field to laundry is still quite new. -In fact no research is known to the authors connecting the fields of computer science -and laundry sorting. A few definitions are required in order to establish a baseline -for the algorithm discussed in the following paper. - -\subsection{Definitions} -In this section a few definitions, common in the field of theoretical laundry science shall be -introduced. These are required to understand the algorithm and its advantages. - -\subsubsection{Sock} -Let $\Lambda_a$ be the Set of laundry. The set of socks, $\Sigma\subset\Lambda_a$ -is defined as $\Sigma:=\{s\in\Lambda_a|\chi(s)=1\}$\footnote{Yes, some socks have holes. So what?!}, where $\chi(s)$ is the Euler -characteristic of $s$. For every sock $s$ there is an equal counterpart $s^{-1}$ giving rise -to the identity $s\cong s^{-1}$. The task commonly known as "sock sorting" is in fact the -search for this isomorphism $\eta$ and matching every sock $s$ to its inverse -$s^{-1}$. -\begin{figure}[h] - \centering - \includegraphics[width=\columnwidth]{\projectpath figs/Sock.jpeg} - \vspace{0.1in} - \caption{A pair of blue socks and a single orange sock.} - \label{fig:Sock} - \vspace{0.1in} -\end{figure} -\subsubsection{Laundry basket} -Let $\Lambda\subseteq\Lambda_a$ be a set of laundry items. Then a laundry basket is a -triplet $(\Lambda, +, -)$ representing a datastructure that implements -the following functions: -\begin{itemize} - \item \texttt{get: }$\mathscr{L}\in\Lambda_a$, returns a uniformly random - laundry item from the basket or $\mathscr{L}_0$, the Zero element of laundry, iff - There are no items left. - \item \texttt{put($\mathscr{L}\in\Lambda_a$)}, deposits the given laundry item - into the basket. -\end{itemize} -Note that both operations run in $\mathcal{O}(1)$. Because of the nature of -a laundry basket finding a unique item requires transferring the content of -the whole basket to a new basket thus requiring $\mathcal{O}(n)$ operations, -$n$ being the number of items currently inside the basket. -\subsection{Ongoing and latest research} -To fully appreciate the gravity of \acronym it has to first be discussed -how most resent research tackles the problem of sock sorting. -The following code describes the most recently developed sock sorting -algorithm from the paper by my colleague which is the current -industry standard. Notice the code has a runtime complexity of $\mathcal{O}(n^2)$. - -\begin{algorithm} - \caption{Conventional sock sorting} - \begin{algorithmic}[1] - \State\Comment initialize a new laundry basket with a given set of laundry - \State $A\gets\Lambda$\Comment WLOG assume $\forall\mathscr{L}\in\Lambda|\mathscr{L}$ is a sock - \State $\text{matches}\gets []$ - \Repeat - \State $\mathscr{L}\gets$ A.get - - \Repeat\Comment find the inverse Sock by checking all other socks - \State $\mathscr{L}^\prime\gets$ A.get - \Until{$\mathscr{L}^\prime =\mathscr{L}^{-1}$} - \State matches.append(($\mathscr{L}, \mathscr{L}^\prime$)) - \Until{$\mathscr{L}\ne\mathscr{L}_0$} - \end{algorithmic} -\end{algorithm} - -\section{Concepts} -The basis for every fast algorithm are simple yet equally fast -datastructures. To enable the low runtime achieved by \acronym, -the introduction of a new datastructure, the "laundry rack" is integral. - -\subsection{Laundry rack} -Let $\Lambda\subseteq\Lambda_a$ be a set of laundry. A laundry rack (See figure \ref{fig:Rack}) is a -triplet $(\Lambda, +, -)$ representing a datastructure that implements the -following methods: -\begin{itemize} - \item \texttt{get($\mathscr{L}\in\Lambda$)}: $\mathscr{L}\in\Lambda$, gets - a specific laundry item from the laundry rack. - \item \texttt{put($\mathscr{L}\in\Lambda$)}, deposits a laundry item onto - the laundry rack. - \item \texttt{match($\mathscr{L}\in\Lambda$)}: $(\mathscr{P}\in\Lambda\times\Lambda)|\mathscr{L}_0$, - returns a tuple $(\mathscr{L}, \mathscr{L}^{-1})$ representing - a pair of socks iff $\mathscr{L}^{-1}$ is already on the laundry rack, - $\mathscr{L}_0$ otherwise. -\end{itemize} -All these operations (especially \texttt{match}) run in $\mathcal{O}(1)$, -making iteration over all $n$ laundry items to find a pair $(\mathscr{L}, \mathscr{L}^{-1})$ -obsolete. -\begin{figure}[h] - \centering - \includegraphics[width=\columnwidth]{\projectpath figs/rack.jpeg} - \vspace{0.1in} - \caption{A blue drying rack, found in many housholds.} - \label{fig:Rack} - \vspace{0.2in} -\end{figure} - -\section{Algorithm} -Making use of the novel advanced features of a "drying rack" we are able to -implement the following algorithm in $\mathscr{O}(n)$:\\ -\begin{algorithm} - \caption{\acronym} - \begin{algorithmic}[1] - \State\Comment initialize a new laundry basket with a given set of laundry - \State $A\gets\Lambda$\Comment WLOG assume $\forall\mathscr{L}\in\Lambda|\mathscr{L}$ is a sock - \State $\text{matches}\gets []$ - \State $\daleth\gets []$ \Comment{Create a new empty drying rack} - \Repeat - \State $\mathscr{L}\gets $ A.get - \State result $\gets$ $\daleth$.match($\mathscr{L}$) - \If{result $\ne\mathscr{L}_0$} - \State matches.append(result) - \Else - \State $\daleth$.put($\mathscr{L}$) - \EndIf - - \Until{$\mathscr{L}\ne\mathscr{L}_0$} - \end{algorithmic} -\end{algorithm} -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 -(proof is left as an exercise to the reader). -\section{Discussion and Results} -To evaluate the algorithms performance it has been executed -on different platforms consisting of diverse hardware:\\ -\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. - 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 $3.1415926535897932384626433\cdot n$. 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. 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