Notes_CSE105.tex

%%***********************************************
%% 		Setups
%%***********************************************
\documentclass[12pt, letterpaper, titlepage]{article}
%	\setlength{\columnsep}{31pt}		% space b/w columns;

% margins
\usepackage[top=.5in, bottom=1.2in, left=.7in, right=.7in]{geometry}

% title
\title{\Huge CSE 105: \\ Computation
	   \\[-1em] \rule{.8\textwidth}{1pt}
}
\author{\LARGE{\it by} Jy}
\date{}
%\thanks{}

%***********************************************
% 		Graphs
%***********************************************

%% space of caption and the context;
%	\setlength{\abovecaptionskip}{10pt}
%	\setlength{\belowcaptionskip}{15pt}
%\usepackage{subfigure}
\usepackage{graphicx}
	\graphicspath{{pics/}}

%% figures with text wrapped around;
%\usepackage{wrapfig}
%\usepackage{picins}

\usepackage{tikz}
%	\usetikzlibrary{arrows}
%%\usepackage{tkz-euclide}
%\usepackage{pgfplots}
%	\tikzset{
%	myvec/.style={blue, line width = .5pt, -stealth'},
%	every node/.style={black},
%	box/.style={rectangle, rounded corners=5pt,
%			minimum width=30pt, minimum height=15pt,
%			inner sep=5pt,
%			draw=silver, fill=lightpurple},
%	}

% trees
\usepackage{tikz-qtree}
% \usepackage{pst-tree}

%% set wallpaper
%\usepackage{wallpaper}
%	\CenterWallPaper{1}{}

%% Include movies
%\usepackage{media9}

%% use colors
\usepackage{xcolor}
	\definecolor{lightblue}{RGB}{39, 104, 192}
	\definecolor{silver}{RGB}{200,191,231}
	\definecolor{lightpurple}{RGB}{200,200,240}

%%***********************************************
%% 		Tables
%%***********************************************

% linestrech in arrays/tables
\renewcommand{\arraystretch}{1.2}

%% tables w/ wrapped lines;
%\usepackage{tabularx}
%	\newcommand{\ahsize}[1]{ \setlength{\hsize}{#1\hsize} }
%	\newcommand{\bhsize}[1]{ \setlength{\hsize}{#1} }

%% sideways
\usepackage{rotating}

%% makecell
%\usepackage{makecell}
%	\makegapedcells
%	\setcellgapes{6pt}

%% color for tables;
%\usepackage{colortbl}
%% toprule, midrule & bottomrule;
%\usepackage{booktabs}
\usepackage{array} %解决前置命令问题；
	\newcommand{\PreserveBackslash}[1]{\let\temp=\\#1\let\\=\temp}
	\newcolumntype{C}[1]{>{\PreserveBackslash\centering}p{#1}}
	\newcolumntype{R}[1]{>{\PreserveBackslash\raggedleft}p{#1}}
	\newcolumntype{L}[1]{>{\PreserveBackslash\raggedright}p{#1}}
	\newcolumntype{M}[1]{>{$}#1<{$}}

%% multirow;
\usepackage{multirow}

%% long table + tabularx;
%\usepackage{ltxtable, filecontents}

%%***********************************************
%% 		Coding
%%***********************************************

%	\usepackage{listings}
%		\lstset{
%			language=C++,
%			breaklines=true,				%自动换行;
%			extendedchars=false,			%这一条命令可以解决代码跨页时，章节标题，页眉等汉字不显示的问题;
%			numbers=left,
%			numberstyle=\scriptsize,
%			stepnumber=2, 				%行标跳过数;
%			numbersep=1.5em, 				%行标与代码框距离;
%			tabsize=4,
%			basicstyle=\footnotesize\ttfamily,
%			stringstyle=\color{lightblue},
%			keywordstyle=\color{blue!80},
%			commentstyle=\color{red!70!green!70!blue!90},
%			frame=shadowbox,
%%			showspaces=false,
%			showstringspaces=false,
%			showtabs=false,
%			rulesepcolor=\color{red!20!green!20!blue!20},
%			backgroundcolor=\color{red!10!green!3!blue!10},
%			escapeinside=``,
%			xleftmargin=8em,
%			xrightmargin=5em,
%			framexleftmargin=2pt,
%			framexrightmargin=2pt,
%			aboveskip=1em
%		}
%		\renewcommand{\lstlistingname}{CODE}

%***********************************************
% 		Fonts
%***********************************************

%% English;
\usepackage{fontspec}
	\setmainfont[Mapping=tex-text]{Times New Roman}
	\setsansfont[Mapping=tex-text]{Calibri}
	\setmonofont{Courier New}
%	\newfontfamily\rh{Lucida Handwriting}	% rh for Round Handing
%	\newfontfamily\sc{John Handy LET}	% sc for script
%	\newfontfamily\hw{Bradley Hand ITC}	% hw for HandWritting
%% Chinese;
%\usepackage[CJKchecksingle, CJKnumber]{xeCJK}
%	\setCJKmainfont[BoldFont = {STXingkai}, ItalicFont = {STFangsong}]{Microsoft YaHei}
%	\setCJKsansfont{}
%	\setCJKmonofont{KaiTi}
%	\punctstyle{hangmobanjiao}
%\newcommand{\CJKdash}{\rule[3.5pt]{9pt}{.77pt} \hspace{-1.5mm} \rule[3.5pt]{9pt}{.77pt} }

%%***********************************************
%% 		Looking
%%***********************************************

%% links
\usepackage[bookmarksnumbered, pdfencoding=auto, pdfborder=1, breaklinks,
			colorlinks, linkcolor=lightblue, urlcolor=blue]{hyperref}
	\hypersetup{
		unicode=false,			% non-Latin characters in Acrobat’s bookmarks
		pdftoolbar=true,		% show Acrobat toolbar?
		pdfmenubar=true,		% show Acrobat menu?
		pdftitle={},			% title
		pdfauthor={Jinyao Yuan},% author
		pdfsubject={},			% subject of the document
		pdfcreator={Jinyao Yuan},	% creator of the document
		pdfproducer={Jinyao Yuan},	% producter of the document
		citecolor=green,		% color of links to bibliography
		filecolor=magenta,		% color of file links
	}

%% page style
%%---------------------------------------------------------------------------
\usepackage{fancyhdr}
\pagestyle{fancy}
\lhead{}
\chead{}
\rhead{}
\renewcommand{\headrulewidth}{0pt}
\renewcommand{\footrulewidth}{0pt}
\lfoot{}
\cfoot{}
\rfoot{\thepage}

%% paragraphs
%%---------------------------------------------------------------------------
\usepackage{setspace}
	\onehalfspacing
%	\doublespacing
	\setlength{\parindent}{2em}
	\addtolength{\parskip}{3pt}
	\usepackage{indentfirst}

%% floats
%%---------------------------------------------------------------------------
% \renewcommand{\textfraction}{0.15}
% \renewcommand{\topfraction}{0.85}
% \renewcommand{\bottomfraction}{0.65}
\renewcommand{\floatpagefraction}{0.70}

\usepackage[section]{placeins}
% \usepackage[below]{placeins}
\usepackage{caption}

%% underline
%%---------------------------------------------------------------------------
\usepackage{ulem}
%\usepackage{CJKfntef}

%% emphasis
%%---------------------------------------------------------------------------
% \DeclareTextFontCommand{\emshape}{\itshape}
\def\emshape{\itshape}
\makeatletter
\DeclareRobustCommand{\em}{%
    \@nomath\em \if b\expandafter\@car\f@series\@nil \normalfont
    \else \emshape \fi
}
\makeatother
\DeclareTextFontCommand{\emph}{\em}

%% convert terms into Chinese;
%%---------------------------------------------------------------------------
%\renewcommand{\contentsname}{\hfill 目~录 \hfill}
%\renewcommand{\listfigurename}{图目录}
%\renewcommand{\listtablename}{表目录}
%\renewcommand{\thepart}{\CJKnumber{\arabic{part}}}
%\renewcommand{\partname}{第\CJKnumber{\thepart}章}
%\renewcommand{\thesection}{\CJKnumber{\arabic{section}}}
%\newcommand{\sectionname}{\thesection 节}
%\renewcommand{\figurename}{图}
%\renewcommand{\figureautorefname}{图}
%\renewcommand{\tablename}{表}
%\renewcommand{\tableautorefname}{表}
%\renewcommand {\thefootnote}{\arabic{footnote}}
%\renewcommand{\footnoteautorefname}{脚注}
%\renewcommand{\abstractname}{摘 \quad 要}
%\renewcommand{\appendixname}{附录{\thechapter}}
%\renewcommand{\appendixautorefname}{附录}
%\renewcommand{\bibname}{参考文献}
%\renewcommand{\indexname}{索引}

%% make own style of section titles;
%%---------------------------------------------------------------------------
\usepackage{titlesec}
%	\titleformat{\part}{\center\Huge \bf}{\thepart}{1em}{}
%	\titleformat{\section}{\large \bf}{\thesection}{1em}{}
	\titleformat{\part}[frame]{\normalfont}
		{\small \enspace UNIT \thepart \enspace}{6pt}
		{\LARGE\bf\filcenter}
	\titlespacing*{\part}{1pc}{*4}{*3}[1pc]
	\newcommand{\mypart}{\FloatBarrier\part}

%% make own style of table of contents;
%%---------------------------------------------------------------------------
%\usepackage{titletoc}
%\titlecontents{part}[0em]{\addvspace{10pt}\filright\bf\large}
%		{\def\numberline##1{\thecontentslabel\quad\ignorespaces}}
%		{}{\titlerule*[8pt]{.}\contentspage}
%\titlecontents{section}[1em]{\addvspace{10pt}\filright\bf\large}
%		{\def\numberline##1{\thecontentslabel\quad\ignorespaces}}
%		{}{\titlerule*[8pt]{.}\contentspage}
%\titlecontents{subsection}[2em]{\addvspace{5pt}\filright\bf}
%		{\def\numberline##1{\thecontentslabel\quad\ignorespaces}}
%		{}{\titlerule*[8pt]{.} \contentspage}

%***********************************************
% 		Utilities
%***********************************************

%% in-para enum, item, descript;
%%---------------------------------------------------------------------------
\usepackage{paralist}

%% lettrine;
%%---------------------------------------------------------------------------
%\usepackage{lettrine}
%	\newcommand{\mylettrine}[1]{\lettrine[lines=2,lraise=0,nindent=0em]{#1\hspace{1mm}}{}}

%% Math;
%%---------------------------------------------------------------------------
\usepackage{amsmath, amsfonts, amssymb, amsthm}
\usepackage{venndiagram}
%\usepackage{extarrows} 	% special arrows like \xlongequal;
%\input{longdiv.tex}	% divisions;
%\usepackage{dcolumn}	% vertical calculation w/ tabular;
\usepackage{cancel}	% strike out numbers

%% Theorems;
%%---------------------------------------------------------------------------
\newtheoremstyle{mystyle}
	{2em}	% spaceabove
	{2em}	% spacebelow
	{\it}	% bodyfont
	{0em}	% indent
	{\bf}	% headfont
	{}   	% headpunctuation
	{1em}	% headspace
	{%
		\thmname{#1} \thmnumber{#2} \thmnote{#3}.
	}   	% headspecify
\theoremstyle{mystyle}

\newtheorem{definition}{Definition}[section]
\newtheorem{theorem}{Theorem}[section]

%% symbols
%%---------------------------------------------------------------------------
\newcommand{\phteq}{ \phantom{{}={}} }
\renewcommand{\(}{ \left(  }
\renewcommand{\)}{ \right) }
\newcommand{\nth}{\ensuremath{^\text{th}}\xspace}
\newcommand{\st}{\ensuremath{^\text{st}}\xspace}
\newcommand{\nd}{\ensuremath{^\text{nd}}\xspace}
\newcommand{\rd}{\ensuremath{^\text{rd}}\xspace}
\newcommand{\dd}{{ \, \mathrm{d} }}
\newcommand{\abs}[1]{{ \left\lvert #1 \right\rvert }}

\newcommand{\set}[1]{{ \left\{\,#1\,\right\} }}
\newcommand{\lst}[1]{{ \left(\,#1\,\right) }}

%\newcommand{\dne}{ \mathrm{DNE} }	% Does Not Exist;
%\newcommand{\defeq}{ \xlongequal{\mathrm{DEF}} }	% equal by definition;
%\newcommand{\sqr}{ \ensuremath{^2} } % squared;
% \newcommand{\cels}{{ \ensuremath{^\circ \mathrm{C}} }}
%\newcommand{\fahr}{{ \ensuremath{^\circ \mathrm{F}} }}
\newcommand{\Conf}{{ \mathrm{Conf} }}
\newcommand{\true}{{ \text{\upshape True} }}
\newcommand{\false}{{ \text{\upshape False} }}

\newcommand{\DFA}{{ M = \lst{Q, \Sigma, \delta, s, F} }}
\newcommand{\NFA}{{ N = \lst{Q, \Sigma, \delta, s, F} }}
\newcommand{\reducable}{{ \,\le_{\text{\upshape FST}}\, }}
\newcommand{\reducableN}{{ \,\le_{\text{\upshape NFST}}\, }}
\newcommand{\reverse}{{ \mathrm{rev} }}
\newcommand{\combination}{{ \mathrm{C} }}
\newcommand{\permutation}{{ \mathrm{P} }}
\newcommand{\variance}[1]{{ \mathrm{Var}(#1) }}
\newcommand{\stirling}{{ \mathrm{S} }}
\newcommand{\powerset}{{ \mathcal{P} }}
\newcommand{\Degree}{{ \mathbb{Deg} }}
\newcommand{\degree}{{ \mathbb{deg} }}

%% visiblespace
\renewcommand\textvisiblespace[1][.5em]{%
	\makebox[#1]{%
		\kern.07em
		\vrule height.3ex
		\hrulefill
		\vrule height.3ex
		\kern.07em
	}
}

%% fillable forms
%%---------------------------------------------------------------------------
%\newcommand{\fform}[2]{
%#1 \vbox{\hbox{\TextField[name=#1,width=#2,borderwidth=0]{\null}}\kern0pt\hrule}
%}

%% Margin notes;
%%---------------------------------------------------------------------------
\usepackage{marginnote}
\marginparsep 2em
\marginparwidth 2.5in

% fancy boxes like \fbox,\shadowbox,\doublebox,\ovalbox, \Ovalbox。
\usepackage{fancybox}

%%***********************************************
%%	Self-defined environments
%%***********************************************

\usepackage{float} % used to define float environments

%% list point
%%---------------------------------------------------------------------------
%\newcommand{\lspnt}[1]{&\textrm{#1}}
%\newenvironment{pntlist} {
%	$
%	\left\{
%	\begin{aligned}
%}{
%	\end{aligned}
%	\right.
%	$
%}

%% centered graph
%%---------------------------------------------------------------------------
\newcommand{\centgraph}[2][.7\linewidth]{
	\begin{center}
		\includegraphics[width=#1]{#2}
	\end{center}
}

%% questions & solutions
%%---------------------------------------------------------------------------
%\input{environment.question/quest.tex}

% shadowpage
%---------------------------------------------------------------------------
\newenvironment{shadowpage}%
{
	\begin{Sbox} \begin{minipage}
	}{
	\end{minipage} \end{Sbox}
	\setlength{\fboxsep}{10pt}
	\shadowbox{\TheSbox}
}%

% examples
%---------------------------------------------------------------------------

%\floatstyle{plaintop}
%\newfloat{exp}{htb}{log}[subsection]
%\floatname{exp}{Example}
\DeclareCaptionType[%
	placement=htbp,
	within=section,
	fileext=loe
]{myExample}[Example][List of Examples]
\newenvironment{example}[1][~]%
{%
	\begin{myExample}
		\hfill
		\begin{Sbox}
			\begin{minipage}{.8\linewidth}
				\footnotesize
				\vspace{-.5em} \caption{#1} ~ \\[-2em]
				\rule{\linewidth}{.3pt}
				\par
				\setlength{\parindent}{2em}
				\addtolength{\parskip}{3pt}
			}{%
			\end{minipage}
		\end{Sbox}
		\setlength{\fboxsep}{10pt}
		\shadowbox{\TheSbox}
	\end{myExample}
}%

%\newenvironment{example}%
%{
%	\par\noindent
%	\hfill
%	\begin{Sbox}
%	\begin{minipage}{.8\linewidth}
%	\footnotesize
%	{\bf Example} \\[-1em]
%	\rule{\linewidth}{.5pt}
%	\par
%	\setlength{\parindent}{2em}
%}{
%	\end{minipage}
%	\end{Sbox}
%	\setlength{\fboxsep}{10pt}
%	\fbox{\TheSbox}
%	\par
%}%



%***********************************************
% 		START
%***********************************************
\begin{document}

\maketitle
\pagenumbering{roman}
\tableofcontents\clearpage
\pagenumbering{arabic}

\input{lec1}
\input{lec2}
\input{lec3}
\input{lec4}
\input{lec5}
\input{lec6}
\input{lec7}
% \input{lec8}
\input{lec9}
\input{lec10}
\input{lec11}
\input{lec12}
% \input{lec13}
% \input{lec14}
\input{lec15}

\end{document}