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@leegao
Last active December 28, 2015 09:09
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\documentclass[11pt,a4paper]{article}
%\usepackage{fullpage}
\usepackage[total={6.5in,8.75in},
top=1.2in, left=0.9in]{geometry}
\usepackage[utf8]{inputenc}
\usepackage[english]{babel}
\usepackage{amsmath, amsthm}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{graphicx}
\usepackage{pifont}
%\usepackage{bussproofs}
\usepackage{enumitem}
\usepackage{centernot}
\usepackage{xspace}
\usepackage{stmaryrd}
\usepackage{mathtools}
\usepackage{cleveref}
\usepackage{listings}
\usepackage{tikz-qtree}
\usepackage{tikz}
\usepackage{algorithm}
\usepackage{algorithmicx}
\usepackage{algpseudocode}
\usepackage[hidelinks]{hyperref}
\usetikzlibrary{automata,trees,fit,backgrounds,shapes,snakes}
\usetikzlibrary{decorations.shapes}
\usepackage{float}
\usepackage{fancyvrb}
\usepackage{framed}
\usepackage{fancyhdr}
\usepackage{lastpage}
\definecolor{light-gray}{gray}{0.95}
\newcommand {\conf} [1] {\ensuremath{\left\langle #1 \right\rangle}}
\newcommand {\bstep} {\ensuremath{\Downarrow}}
\newcommand {\bstepA} {\bstep_{ A}}
\newcommand {\bstepB} {\bstep_{ B}}
\newcommand {\bstepC} {\bstep_{ C}}
%\newcommand {\co} [1] {\ensuremath{\operatorname{\bf #1}}}
\newcommand {\coo} [1] {\ensuremath{\operatorname{\mathsf{#1}}}}
\newcommand {\co} [1] {\coo{#1}}
\newcommand {\pp} {\ensuremath{\mbox{\footnotesize{++}}}}
\newcommand {\Skip} {\co{skip}}
\newcommand {\Not} {\co{not}}
%\newcommand {\If}[3] {\co{if} (#1) \co{then} #2 \co{else} #3}
\newcommand {\Ifp}[3] {\co{ifp} (#1) \co{then} #2 \co{else} #3}
%\newcommand {\While}[2] {\co{while} #1 \co{do} #2}
%\newcommand {\Repeat}[2] {\co{repeat} #1 \co{do} #2}
\newcommand {\Input} {\co{input}}
%\newcommand {\Break} {\co{break}}
%\newcommand {\Continue} {\co{continue}}
\newcommand{\True}{\co{True}}
\newcommand{\False}{\co{False}}
\newcommand{\Or}{\co{or}}
\newcommand{\Let}[1]{\coo{let} #1 \coo{in} }
\newcommand{\Lam}{\ensuremath{{\lambda}}}
\newcommand{\Ref}{\coo{ref}}
\newcommand{\Int}{\coo{int}}
\newcommand{\bool}{\coo{bool}}
\newcommand{\Bool}{\bool}
\newcommand{\Unit}{\coo{unit}}
\newcommand{\Rec}[1]{\left\{#1\right\}}
\newcommand{\pa}[1]{\left(#1\right)}
\newcommand{\dt}[1]{\left|\arr{#1}\right|}
\newcommand{\ba}[1]{\left\langle #1\right\rangle}
\newcommand{\tree}{\coo{tree}}
\newcommand{\fa}{\coo{\forall}}
\newcommand{\more}[1]{\vdots\hspace{-1mm}~^{#1}}
\newcommand{\f}[1]{\textsc{#1}}
\newcommand{\g}[1]{\textsf{#1}}
\newcommand{\finite}{\co{finite}}
\newcommand{\lift}[1]{\left\lfloor #1 \right\rfloor}
\newcommand{\ttwo}{\mbox{\scriptsize\ding{173}}}
\newcommand{\trans}[2]{\ensuremath{\mathcal{#1}\left\llbracket #2\right\rrbracket}}
\newtheorem*{lemma}{Lemma}
\newtheorem*{theorem}{Theorem}
\newtheorem*{definition}{Definition}
\newtheorem*{corollary}{Corollary}
\lstset{ %
language=Matlab, % the language of the code
basicstyle=\footnotesize, % the size of the fonts that are used for the code
numbers=left, % where to put the line-numbers
numberstyle=\tiny\color{gray}, % the style that is used for the line-numbers
stepnumber=1, % the step between two line-numbers. If it's 1, each line
% will be numbered
numbersep=10pt, % how far the line-numbers are from the code
backgroundcolor=\color{white}, % choose the background color. You must add \usepackage{color}
showspaces=false, % show spaces adding particular underscores
showstringspaces=false, % underline spaces within strings
showtabs=false, % show tabs within strings adding particular underscores
mathescape=true,
frame=leftline, % adds a frame around the code
rulecolor=\color{gray}, % if not set, the frame-color may be changed on line-breaks within not-black text (e.g. comments (green here))
tabsize=2, % sets default tabsize to 2 spaces
captionpos=t, % sets the caption-position to bottom
breaklines=true, % sets automatic line breaking
breakatwhitespace=false, % sets if automatic breaks should only happen at whitespace
title=\lstname, % show the filename of files included with \lstinputlisting;
% also try caption instead of title
escapeinside={\%*}{*)}, % if you want to add LaTeX within your code
morekeywords={*,...}, % if you want to add more keywords to the set
deletekeywords={...} % if you want to delete keywords from the given language
}
\newcommand\tmark[2]{%
\ensuremath{\tikz[baseline] \node[anchor=base] (#1) {#2};}}
\tikzstyle{every picture}+=[remember picture]
\newcommand{\tm}[2]{\tmark{#1}{\ensuremath{#2}}}
\newcommand{\tr}[2]{\tmark{#1}{\color{red}{\ensuremath{#2}}}}
\newcommand{\arr}[1]{\begin{array}{cccccccccc} #1\end{array}}
\newcommand{\mat}[1]{\left(\arr{#1}\right)}
\newcommand{\Malloc}{\co{malloc}}
\newcommand{\Null}{\co{null}}
\newcommand{\SN}{\ensuremath{\mathcal{SN}}}
\newcommand{\Inl}{\co{inl}}
\newcommand{\Inr}{\co{inr}}
\newcommand{\Case}[3]{\co{case}~#1~\co{of} #2 \mid #3}
\newcommand{\R}{\co{rec}}
\newcommand{\Fold}{\co{fold}}
\newcommand{\Unfold}{\co{unfold}}
\newcommand{\coerce}[1]{\ensuremath{\Theta\left\llbracket #1\right\rrbracket}}
\allowdisplaybreaks
\setlength{\headheight}{15pt}
\pagestyle{fancyplain}
%\renewcommand{\chaptermark}[1]{\markboth{#1}{}}
\lhead{\fancyplain{}{\footnotesize\leftmark}}
\chead{}
\rhead{\fancyplain{}{\textsc{Lee Gao}}}
\lfoot{}
\cfoot{\thepage\ of \pageref{LastPage}}
\rfoot{}
\author{Lee Gao (lg342)}
\title{CS 6210 Homework 4}
\date{\today}
\begin{document}
\tikzset{every tree node/.style={minimum width=2em,draw,circle},
blank/.style={draw=none},
edge from parent/.style=
{draw, edge from parent path={(\tikzparentnode) -- (\tikzchildnode)}},
level distance=1.5cm}
\maketitle
\setlength{\parindent}{0pt}
\begin{enumerate}[label=\textbf{Exercise \arabic*\ },leftmargin=1cm,rightmargin=0cm]
\setcounter{enumi}{0}
\item \textbf{Problem Title}
\end{enumerate}
\end{document}
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