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notes-3sum.tex
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notes-3sum.tex
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% ================================================================================
\documentclass{article}
\pagestyle{plain}
\usepackage{fullpage}
% ================================================================================
%\usepackage[left=1in,right=1in, top=1.2in,bottom=1.2in]{geometry}
%\usepackage{times}
\usepackage{amssymb,amsthm,latexsym,amsmath,epsfig,pgf}
\usepackage{graphicx}
\usepackage{comment}
\usepackage{url}
\usepackage{hyperref}
\usepackage{blkarray}
\usepackage{tikzsymbols}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage{blindtext}
% ================================================================================
\usepackage{listings}
\lstset{
%basicstyle=\small\ttfamily,
frame=single,
language=C,
escapechar=|,
numbers=left,
stepnumber=1,
%numbersep=-10pt,
morekeywords={datatype, irrational, string, rule, list, list2D, new, node, node_T, node_Tstring, listnumber, fixedint, map, and, elseif, in, empty, pt}
}
% ================================================================================
\usepackage{algorithmicx}
\usepackage{algpseudocode}
\usepackage{algorithm}
\algnewcommand\algorithmicinput{\textbf{Input:}}
\algnewcommand\Input{\item[\algorithmicinput]}
\algnewcommand\algorithmicoutput{\textbf{Output:}}
\algnewcommand\Output{\item[\algorithmicoutput]}
% ================================================================================
\newtheorem{theorem}{Theorem}[section]
\newtheorem*{theorem A}{Theorem A}
\newtheorem*{theorem B}{N\"olker's Theorem}
\newtheorem{lemma}{Lemma}[section]
\newtheorem{proposition}{Proposition}[section]
\newtheorem{corollary}{Corollary}[section]
\newtheorem{definition}{Definition}
\newtheorem{problem}{Problem}
\newtheorem{example}{Example}
\newtheorem{step}{Step} \setcounter{step}{-1}
\newtheorem*{question}{Question}
\newtheorem {conjecture}{Conjecture}
\theoremstyle{remark}
\newtheorem{remark}{Remark}[section]
\theoremstyle{remark}
\newtheorem{remarks}{Remarks}
% ================================================================================
\begin{document}
% ================================================================================
\title{Notes: A 3SUM algorithm on the binary addition level of atomic generated real numbers}
% ================================================================================
\author{Carolin Z\"obelein\thanks{The author believes in the importance of the independence of research and is funded by the public community. If you also believe in this values, you can find ways for supporting the author's work here: \url{https://research.carolin-zoebelein.de/funding.html}, Email: \href{mailto:contact@carolin-zoebelein.de}{\texttt{contact@carolin-zoebelein.de}}, PGP: D4A7 35E8 D47F 801F 2CF6 2BA7 927A FD3C DE47 E13B, \url{https://research.carolin-zoebelein.de} \LaTeX source availabe at \url{https://github.com/Samdney/notes-3sum}, \texttt{id: notes\_0003}, \Cooley}}
% ================================================================================
\date{September 6, 2020} %\date{\today}
% ================================================================================
\maketitle
% ================================================================================
\begin{center}
DRAFT
\end{center}
% ================================================================================
\input{abstract}
% ================================================================================
\providecommand{\keywords}[1]{\small{\textbf{\textit{Keywords:}} #1}}
\providecommand{\Classification}[1]{\small{\textbf{\textit{ACM Subject Classes:}} #1}}
\begin{flushleft}
\keywords{3SUM Problem, Real Numbers, Irrational Numbers, Data Structures, Binary Representation, Data Storage Representation, Nonnumerical Algorithm, Complexity}\\
\Classification{E1, E2, F1.3, F2.2}
\end{flushleft}
% ================================================================================
%\tableofcontents
% ================================================================================
\input{preamble}
% ================================================================================
\input{introduction}
% ================================================================================
\input{preliminaries}
% ================================================================================
\input{zerosum}
% ================================================================================
%\input{rammodel} % TODO
% ================================================================================
\input{algorithm}
% ================================================================================
\input{complexities}
% ================================================================================
\input{conclusion}
% ================================================================================
\input{acknowledgement}
% ================================================================================
\input{license}
% ================================================================================
%\section*{References}
% --------------------------------------------------------------------------------
%\newpage
%\clearpage
%\markboth{Bibliography}{Bibliography}
%\section*{Bibliography}
%\label{s:bibliography}
% --------------------------------------------------------------------------------
%\bibliographystyle{amsplain}
%\bibliographystyle{unsrtdin}
%\bibliographystyle{plain}
%\nocite{*}
\bibliographystyle{amsplain}
\bibliography{notes-3sum}
% ================================================================================
\end{document}
% ================================================================================